LMFDB - Embedded newform 819.2.o.i.568.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [819,2,Mod(568,819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("819.568"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(819, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [12,0,0,-8,0,0,-6,0,0,22,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 8x^{10} + 51x^{8} - 98x^{6} + 145x^{4} - 39x^{2} + 9 $ x^12 - 8x^10 + 51x^8 - 98x^6 + 145x^4 - 39*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			568.6
Root			$1.17800 - 0.680121i$ of defining polynomial
Character	$\chi$	$=$	819.568
Dual form			819.2.o.i.757.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.38547 - 2.39970i) q^{2} +(-2.83905 - 4.91737i) q^{4} +3.18587 q^{5} +(-0.500000 - 0.866025i) q^{7} -10.1918 q^{8} +(4.41392 - 7.64513i) q^{10} +(-1.17800 + 2.04036i) q^{11} +(-1.91392 - 3.05564i) q^{13} -2.77094 q^{14} +(-8.44226 + 14.6224i) q^{16} +(-1.38547 - 2.39970i) q^{17} +(-0.649743 - 1.12539i) q^{19} +(-9.04482 - 15.6661i) q^{20} +(3.26417 + 5.65371i) q^{22} +(1.14694 - 1.98655i) q^{23} +5.14974 q^{25} +(-9.98429 + 0.359340i) q^{26} +(-2.83905 + 4.91737i) q^{28} +(4.68095 - 8.10764i) q^{29} +8.52835 q^{31} +(13.2012 + 22.8652i) q^{32} -7.67809 q^{34} +(-1.59293 - 2.75904i) q^{35} +(-1.61443 + 2.79627i) q^{37} -3.60080 q^{38} -32.4696 q^{40} +(-2.77094 + 4.79940i) q^{41} +(0.189302 + 0.327880i) q^{43} +13.3776 q^{44} +(-3.17809 - 5.50461i) q^{46} +0.477062 q^{47} +(-0.500000 + 0.866025i) q^{49} +(7.13481 - 12.3578i) q^{50} +(-9.59201 + 18.0865i) q^{52} +12.9627 q^{53} +(-3.75296 + 6.50032i) q^{55} +(5.09588 + 8.82632i) q^{56} +(-12.9706 - 22.4658i) q^{58} +(0.317078 + 0.549195i) q^{59} +(6.32783 + 10.9601i) q^{61} +(11.8158 - 20.4655i) q^{62} +39.3905 q^{64} +(-6.09748 - 9.73485i) q^{65} +(-6.95347 + 12.0438i) q^{67} +(-7.86681 + 13.6257i) q^{68} -8.82783 q^{70} +(3.39333 + 5.87742i) q^{71} +10.7348 q^{73} +(4.47348 + 7.74830i) q^{74} +(-3.68930 + 6.39006i) q^{76} +2.35601 q^{77} +13.2856 q^{79} +(-26.8959 + 46.5851i) q^{80} +(7.67809 + 13.2988i) q^{82} -7.06802 q^{83} +(-4.41392 - 7.64513i) q^{85} +1.04909 q^{86} +(12.0059 - 20.7949i) q^{88} +(4.18747 - 7.25291i) q^{89} +(-1.68930 + 3.18532i) q^{91} -13.0248 q^{92} +(0.660955 - 1.14481i) q^{94} +(-2.07000 - 3.58534i) q^{95} +(-3.73583 - 6.47064i) q^{97} +(1.38547 + 2.39970i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{4} - 6 q^{7} + 22 q^{10} + 8 q^{13} - 28 q^{16} + 2 q^{19} + 18 q^{22} + 52 q^{25} - 8 q^{28} + 60 q^{31} - 40 q^{34} - 8 q^{37} - 116 q^{40} - 14 q^{43} + 14 q^{46} - 6 q^{49} - 32 q^{52} + 12 q^{55}+ \cdots - 66 q^{97}+O(q^{100}) $ 12 * q - 8 * q^4 - 6 * q^7 + 22 * q^10 + 8 * q^13 - 28 * q^16 + 2 * q^19 + 18 * q^22 + 52 * q^25 - 8 * q^28 + 60 * q^31 - 40 * q^34 - 8 * q^37 - 116 * q^40 - 14 * q^43 + 14 * q^46 - 6 * q^49 - 32 * q^52 + 12 * q^55 - 40 * q^58 + 14 * q^61 + 212 * q^64 - 46 * q^67 - 44 * q^70 - 8 * q^73 - 28 * q^76 + 52 * q^79 + 40 * q^82 - 22 * q^85 + 30 * q^88 - 4 * q^91 + 34 * q^94 - 66 * q^97

Character values

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

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

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 $

$2$	1.38547	−	2.39970i	0.979674	−	1.69685i	0.316116	−	0.948721i	$-0.397621\pi$
$2$	1.38547	−	2.39970i	0.979674	−	1.69685i	0.663558	−	0.748125i	$-0.269045\pi$
$3$		0			0
$3$		0			0
$4$	−2.83905	−	4.91737i	−1.41952	−	2.45869i
$5$	3.18587			1.42476			0.712381	−	0.701793i	$-0.247617\pi$
$5$	3.18587			1.42476			0.712381	+	0.701793i	$0.247617\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	−10.1918			−3.60333
$9$		0			0
$10$	4.41392	−	7.64513i	1.39580	−	2.41760i
$11$	−1.17800	+	2.04036i	−0.355181	+	0.615192i	−0.987149	−	0.159803i	$-0.948914\pi$
$11$	−1.17800	+	2.04036i	−0.355181	+	0.615192i	0.631968	+	0.774995i	$0.282248\pi$
$12$		0			0
$13$	−1.91392	−	3.05564i	−0.530825	−	0.847481i
$13$	−1.91392	−	3.05564i	−0.530825	−	0.847481i
$14$	−2.77094			−0.740564
$15$		0			0
$16$	−8.44226	+	14.6224i	−2.11057	+	3.65561i
$17$	−1.38547	−	2.39970i	−0.336025	−	0.582013i	0.647656	−	0.761933i	$-0.275749\pi$
$17$	−1.38547	−	2.39970i	−0.336025	−	0.582013i	−0.983681	+	0.179920i	$0.942416\pi$
$18$		0			0
$19$	−0.649743	−	1.12539i	−0.149061	−	0.258182i	0.781819	−	0.623505i	$-0.214292\pi$
$19$	−0.649743	−	1.12539i	−0.149061	−	0.258182i	−0.930881	+	0.365323i	$0.880959\pi$
$20$	−9.04482	−	15.6661i	−2.02248	−	3.50304i
$21$		0			0
$22$	3.26417	+	5.65371i	0.695924	+	1.20538i
$23$	1.14694	−	1.98655i	0.239153	−	0.414225i	−0.721319	−	0.692603i	$-0.756464\pi$
$23$	1.14694	−	1.98655i	0.239153	−	0.414225i	0.960471	+	0.278378i	$0.0897969\pi$
$24$		0			0
$25$	5.14974			1.02995
$26$	−9.98429	+	0.359340i	−1.95808	+	0.0704723i
$27$		0			0
$28$	−2.83905	+	4.91737i	−0.536529	+	0.929296i
$29$	4.68095	−	8.10764i	0.869230	−	1.50555i	0.00644556	−	0.999979i	$-0.497948\pi$
$29$	4.68095	−	8.10764i	0.869230	−	1.50555i	0.862785	−	0.505572i	$-0.168718\pi$
$30$		0			0
$31$	8.52835			1.53174			0.765868	−	0.642998i	$-0.222310\pi$
$31$	8.52835			1.53174			0.765868	+	0.642998i	$0.222310\pi$
$32$	13.2012	+	22.8652i	2.33367	+	4.04203i
$33$		0			0
$34$	−7.67809			−1.31678
$35$	−1.59293	−	2.75904i	−0.269255	−	0.466363i
$36$		0			0
$37$	−1.61443	+	2.79627i	−0.265411	+	0.459705i	−0.967671	−	0.252215i	$-0.918841\pi$
$37$	−1.61443	+	2.79627i	−0.265411	+	0.459705i	0.702260	+	0.711920i	$0.252174\pi$
$38$	−3.60080			−0.584126
$39$		0			0
$40$	−32.4696			−5.13389
$41$	−2.77094	+	4.79940i	−0.432748	+	0.749541i	−0.997109	−	0.0759871i	$-0.975789\pi$
$41$	−2.77094	+	4.79940i	−0.432748	+	0.749541i	0.564361	+	0.825528i	$0.309123\pi$
$42$		0			0
$43$	0.189302	+	0.327880i	0.0288682	+	0.0500012i	0.880099	−	0.474791i	$-0.157476\pi$
$43$	0.189302	+	0.327880i	0.0288682	+	0.0500012i	−0.851230	+	0.524792i	$0.824143\pi$
$44$	13.3776			2.01675
$45$		0			0
$46$	−3.17809	−	5.50461i	−0.468584	−	0.811611i
$47$	0.477062			0.0695867			0.0347934	−	0.999395i	$-0.488923\pi$
$47$	0.477062			0.0695867			0.0347934	+	0.999395i	$0.488923\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	7.13481	−	12.3578i	1.00901	−	1.74766i
$51$		0			0
$52$	−9.59201	+	18.0865i	−1.33017	+	2.50815i
$53$	12.9627			1.78056			0.890281	−	0.455411i	$-0.150508\pi$
$53$	12.9627			1.78056			0.890281	+	0.455411i	$0.150508\pi$
$54$		0			0
$55$	−3.75296	+	6.50032i	−0.506049	+	0.876503i
$56$	5.09588	+	8.82632i	0.680965	+	1.17947i
$57$		0			0
$58$	−12.9706	−	22.4658i	−1.70312	−	2.94990i
$59$	0.317078	+	0.549195i	0.0412800	+	0.0714991i	0.885927	−	0.463824i	$-0.153523\pi$
$59$	0.317078	+	0.549195i	0.0412800	+	0.0714991i	−0.844647	+	0.535323i	$0.820190\pi$
$60$		0			0
$61$	6.32783	+	10.9601i	0.810196	+	1.40330i	0.912727	+	0.408571i	$0.133973\pi$
$61$	6.32783	+	10.9601i	0.810196	+	1.40330i	−0.102531	+	0.994730i	$0.532694\pi$
$62$	11.8158	−	20.4655i	1.50060	−	2.59912i
$63$		0			0
$64$	39.3905			4.92381
$65$	−6.09748	−	9.73485i	−0.756300	−	1.20746i
$66$		0			0
$67$	−6.95347	+	12.0438i	−0.849502	+	1.47138i	0.0321510	+	0.999483i	$0.489764\pi$
$67$	−6.95347	+	12.0438i	−0.849502	+	1.47138i	−0.881653	+	0.471898i	$0.843569\pi$
$68$	−7.86681	+	13.6257i	−0.953991	+	1.65236i
$69$		0			0
$70$	−8.82783			−1.05513
$71$	3.39333	+	5.87742i	0.402714	+	0.697522i	0.994052	−	0.108902i	$-0.0347335\pi$
$71$	3.39333	+	5.87742i	0.402714	+	0.697522i	−0.591338	+	0.806424i	$0.701400\pi$
$72$		0			0
$73$	10.7348			1.25641			0.628206	−	0.778047i	$-0.283790\pi$
$73$	10.7348			1.25641			0.628206	+	0.778047i	$0.283790\pi$
$74$	4.47348	+	7.74830i	0.520032	+	0.900722i
$75$		0			0
$76$	−3.68930	+	6.39006i	−0.423192	+	0.732990i
$77$	2.35601			0.268492
$78$		0			0
$79$	13.2856			1.49474			0.747371	−	0.664407i	$-0.231316\pi$
$79$	13.2856			1.49474			0.747371	+	0.664407i	$0.231316\pi$
$80$	−26.8959	+	46.5851i	−3.00706	+	5.20837i
$81$		0			0
$82$	7.67809	+	13.2988i	0.847903	+	1.46861i
$83$	−7.06802			−0.775816			−0.387908	−	0.921698i	$-0.626802\pi$
$83$	−7.06802			−0.775816			−0.387908	+	0.921698i	$0.626802\pi$
$84$		0			0
$85$	−4.41392	−	7.64513i	−0.478756	−	0.829231i
$86$	1.04909			0.113126
$87$		0			0
$88$	12.0059	−	20.7949i	1.27984	−	2.21674i
$89$	4.18747	−	7.25291i	0.443871	−	0.768807i	−0.554102	−	0.832449i	$-0.686938\pi$
$89$	4.18747	−	7.25291i	0.443871	−	0.768807i	0.997973	+	0.0636417i	$0.0202715\pi$
$90$		0			0
$91$	−1.68930	+	3.18532i	−0.177087	+	0.333912i
$92$	−13.0248			−1.35793
$93$		0			0
$94$	0.660955	−	1.14481i	0.0681723	−	0.118078i
$95$	−2.07000	−	3.58534i	−0.212377	−	0.367848i
$96$		0			0
$97$	−3.73583	−	6.47064i	−0.379316	−	0.656994i	0.611647	−	0.791131i	$-0.290507\pi$
$97$	−3.73583	−	6.47064i	−0.379316	−	0.656994i	−0.990963	+	0.134137i	$0.957174\pi$
$98$	1.38547	+	2.39970i	0.139953	+	0.242406i
$99$		0			0
$100$	−14.6204	−	25.3232i	−1.46204	−	2.53232i
$101$	3.08801	−	5.34860i	0.307269	−	0.532205i	−0.670495	−	0.741914i	$-0.733918\pi$
$101$	3.08801	−	5.34860i	0.307269	−	0.532205i	0.977764	+	0.209709i	$0.0672515\pi$
$102$		0			0
$103$	−10.3562			−1.02042			−0.510212	−	0.860048i	$-0.670433\pi$
$103$	−10.3562			−1.02042			−0.510212	+	0.860048i	$0.670433\pi$
$104$	19.5062	+	31.1423i	1.91274	+	3.05375i
$105$		0			0
$106$	17.9594	−	31.1066i	1.74437	−	3.02134i
$107$	4.91948	−	8.52079i	0.475584	−	0.823736i	−0.524025	−	0.851703i	$-0.675570\pi$
$107$	4.91948	−	8.52079i	0.475584	−	0.823736i	0.999609	+	0.0279673i	$0.00890344\pi$
$108$		0			0
$109$	−3.90695			−0.374218			−0.187109	−	0.982339i	$-0.559912\pi$
$109$	−3.90695			−0.374218			−0.187109	+	0.982339i	$0.559912\pi$
$110$	10.3992	+	18.0120i	0.991527	+	1.71737i
$111$		0			0
$112$	16.8845			1.59544
$113$	−5.30334	−	9.18566i	−0.498896	−	0.864114i	0.501103	−	0.865388i	$-0.332928\pi$
$113$	−5.30334	−	9.18566i	−0.498896	−	0.864114i	−0.999999	+	0.00127379i	$0.999595\pi$
$114$		0			0
$115$	3.65399	−	6.32889i	0.340736	−	0.590172i
$116$	−53.1577			−4.93557
$117$		0			0
$118$	1.75721			0.161764
$119$	−1.38547	+	2.39970i	−0.127006	+	0.219980i
$120$		0			0
$121$	2.72462	+	4.71917i	0.247692	+	0.429016i
$122$	35.0681			3.17491
$123$		0			0
$124$	−24.2124	−	41.9370i	−2.17433	−	3.76606i
$125$	0.477062			0.0426698
$126$		0			0
$127$	−6.21340	+	10.7619i	−0.551350	+	0.954967i	0.446827	+	0.894620i	$0.352554\pi$
$127$	−6.21340	+	10.7619i	−0.551350	+	0.954967i	−0.998177	+	0.0603466i	$0.980779\pi$
$128$	28.1718	−	48.7949i	2.49006	−	4.31290i
$129$		0			0
$130$	−31.8086	+	1.14481i	−2.78980	+	0.100406i
$131$	−19.8115			−1.73094			−0.865469	−	0.500963i	$-0.832979\pi$
$131$	−19.8115			−1.73094			−0.865469	+	0.500963i	$0.832979\pi$
$132$		0			0
$133$	−0.649743	+	1.12539i	−0.0563399	+	0.0975836i
$134$	19.2676	+	33.3725i	1.66447	+	2.88295i
$135$		0			0
$136$	14.1204	+	24.4572i	1.21081	+	2.09718i
$137$	−6.89628	−	11.9447i	−0.589189	−	1.02050i	−0.994339	−	0.106254i	$-0.966114\pi$
$137$	−6.89628	−	11.9447i	−0.589189	−	1.02050i	0.405150	−	0.914250i	$-0.367219\pi$
$138$		0			0
$139$	4.78131	+	8.28147i	0.405545	+	0.702425i	0.994385	−	0.105825i	$-0.0337483\pi$
$139$	4.78131	+	8.28147i	0.405545	+	0.702425i	−0.588839	+	0.808250i	$0.700415\pi$
$140$	−9.04482	+	15.6661i	−0.764427	+	1.32403i
$141$		0			0
$142$	18.8054			1.57811
$143$	8.48921	−	0.305531i	0.709903	−	0.0255498i
$144$		0			0
$145$	14.9129	−	25.8299i	1.23845	−	2.14505i
$146$	14.8727	−	25.7603i	1.23087	−	2.13194i
$147$		0			0
$148$	18.3338			1.50703
$149$	−0.286012	−	0.495387i	−0.0234310	−	0.0405837i	0.854072	−	0.520155i	$-0.174126\pi$
$149$	−0.286012	−	0.495387i	−0.0234310	−	0.0405837i	−0.877503	+	0.479571i	$0.840792\pi$
$150$		0			0
$151$	13.6557			1.11128			0.555641	−	0.831422i	$-0.312473\pi$
$151$	13.6557			1.11128			0.555641	+	0.831422i	$0.312473\pi$
$152$	6.62203	+	11.4697i	0.537117	+	0.930314i
$153$		0			0
$154$	3.26417	−	5.65371i	0.263035	−	0.455589i
$155$	27.1702			2.18236
$156$		0			0
$157$	8.18401			0.653155			0.326578	−	0.945170i	$-0.394105\pi$
$157$	8.18401			0.653155			0.326578	+	0.945170i	$0.394105\pi$
$158$	18.4067	−	31.8814i	1.46436	−	2.53635i
$159$		0			0
$160$	42.0573	+	72.8454i	3.32492	+	5.75894i
$161$	−2.29387			−0.180783
$162$		0			0
$163$	3.32783	+	5.76398i	0.260656	+	0.451469i	0.966416	−	0.256981i	$-0.0827278\pi$
$163$	3.32783	+	5.76398i	0.260656	+	0.451469i	−0.705760	+	0.708451i	$0.749394\pi$
$164$	31.4673			2.45718
$165$		0			0
$166$	−9.79252	+	16.9611i	−0.760047	+	1.31644i
$167$	−8.00749	+	13.8694i	−0.619638	+	1.07325i	0.369913	+	0.929066i	$0.379387\pi$
$167$	−8.00749	+	13.8694i	−0.619638	+	1.07325i	−0.989552	+	0.144179i	$0.953946\pi$
$168$		0			0
$169$	−5.67385	+	11.6965i	−0.436450	+	0.899729i
$170$	−24.4614			−1.87610
$171$		0			0
$172$	1.07487	−	1.86173i	0.0819582	−	0.141956i
$173$	−5.79682	−	10.0404i	−0.440724	−	0.763356i	0.557019	−	0.830499i	$-0.311945\pi$
$173$	−5.79682	−	10.0404i	−0.440724	−	0.763356i	−0.997743	+	0.0671432i	$0.978612\pi$
$174$		0			0
$175$	−2.57487	−	4.45981i	−0.194642	−	0.337130i
$176$	−19.8900	−	34.4505i	−1.49927	−	2.59681i
$177$		0			0
$178$	−11.6032	−	20.0974i	−0.869698	−	1.50636i
$179$	−3.15480	+	5.46427i	−0.235801	+	0.408419i	−0.959505	−	0.281691i	$-0.909105\pi$
$179$	−3.15480	+	5.46427i	−0.235801	+	0.408419i	0.723704	+	0.690110i	$0.242438\pi$
$180$		0			0
$181$	−15.5766			−1.15780			−0.578898	−	0.815400i	$-0.696517\pi$
$181$	−15.5766			−1.15780			−0.578898	+	0.815400i	$0.696517\pi$
$182$	5.30334	+	8.46698i	0.393110	+	0.627614i
$183$		0			0
$184$	−11.6893	+	20.2465i	−0.861747	+	1.49259i
$185$	−5.14336	+	8.90856i	−0.378147	+	0.654970i
$186$		0			0
$187$	6.52835			0.477400
$188$	−1.35440	−	2.34589i	−0.0987799	−	0.171092i
$189$		0			0
$190$	−11.4717			−0.832241
$191$	3.28372	+	5.68757i	0.237601	+	0.411538i	0.960026	−	0.279912i	$-0.0903054\pi$
$191$	3.28372	+	5.68757i	0.237601	+	0.411538i	−0.722424	+	0.691450i	$0.756972\pi$
$192$		0			0
$193$	−1.13261	+	1.96174i	−0.0815269	+	0.141209i	−0.903906	−	0.427731i	$-0.859313\pi$
$193$	−1.13261	+	1.96174i	−0.0815269	+	0.141209i	0.822379	+	0.568940i	$0.192646\pi$
$194$	−20.7035			−1.48642
$195$		0			0
$196$	5.67809			0.405578
$197$	9.09230	−	15.7483i	0.647799	−	1.12202i	−0.335848	−	0.941916i	$-0.609023\pi$
$197$	9.09230	−	15.7483i	0.647799	−	1.12202i	0.983647	−	0.180105i	$-0.0576438\pi$
$198$		0			0
$199$	−1.31070	−	2.27020i	−0.0929129	−	0.160930i	0.815823	−	0.578302i	$-0.196284\pi$
$199$	−1.31070	−	2.27020i	−0.0929129	−	0.160930i	−0.908736	+	0.417372i	$0.862951\pi$
$200$	−52.4849			−3.71124
$201$		0			0
$202$	−8.55669	−	14.8206i	−0.602047	−	1.04278i
$203$	−9.36190			−0.657076
$204$		0			0
$205$	−8.82783	+	15.2903i	−0.616563	+	1.06792i
$206$	−14.3482	+	24.8517i	−0.999684	+	1.73150i
$207$		0			0
$208$	60.8386	−	2.18961i	4.21840	−	0.151822i
$209$	3.06160			0.211775
$210$		0			0
$211$	2.66095	−	4.60891i	0.183188	−	0.317290i	−0.759777	−	0.650184i	$-0.774692\pi$
$211$	2.66095	−	4.60891i	0.183188	−	0.317290i	0.942964	+	0.332894i	$0.108025\pi$
$212$	−36.8017	−	63.7424i	−2.52755	−	4.37784i
$213$		0			0
$214$	−13.6316	−	23.6106i	−0.931835	−	1.61398i
$215$	0.603090	+	1.04458i	0.0411304	+	0.0712399i
$216$		0			0
$217$	−4.26417	−	7.38576i	−0.289471	−	0.501378i
$218$	−5.41296	+	9.37551i	−0.366612	+	0.634990i
$219$		0			0
$220$	42.6193			2.87339
$221$	−4.68095	+	8.82632i	−0.314875	+	0.593722i
$222$		0			0
$223$	−9.47758	+	16.4156i	−0.634665	+	1.09927i	0.351920	+	0.936030i	$0.385529\pi$
$223$	−9.47758	+	16.4156i	−0.634665	+	1.09927i	−0.986586	+	0.163243i	$0.947805\pi$
$224$	13.2012	−	22.8652i	0.882044	−	1.52774i
$225$		0			0
$226$	−29.3905			−1.95502
$227$	1.54545	+	2.67680i	0.102575	+	0.177666i	0.912745	−	0.408530i	$-0.133958\pi$
$227$	1.54545	+	2.67680i	0.102575	+	0.177666i	−0.810170	+	0.586195i	$0.800625\pi$
$228$		0			0
$229$	6.51986			0.430844			0.215422	−	0.976521i	$-0.430887\pi$
$229$	6.51986			0.430844			0.215422	+	0.976521i	$0.430887\pi$
$230$	−10.1250	−	17.5370i	−0.667621	−	1.15635i
$231$		0			0
$232$	−47.7071	+	82.6311i	−3.13212	+	5.42500i
$233$	−4.10138			−0.268690			−0.134345	−	0.990935i	$-0.542893\pi$
$233$	−4.10138			−0.268690			−0.134345	+	0.990935i	$0.542893\pi$
$234$		0			0
$235$	1.51986			0.0991446
$236$	1.80040	−	3.11838i	0.117196	−	0.202989i
$237$		0			0
$238$	3.83905	+	6.64942i	0.248848	+	0.431018i
$239$	−5.41761			−0.350436			−0.175218	−	0.984530i	$-0.556063\pi$
$239$	−5.41761			−0.350436			−0.175218	+	0.984530i	$0.556063\pi$
$240$		0			0
$241$	−12.5637	−	21.7609i	−0.809296	−	1.40174i	−0.913352	−	0.407171i	$-0.866515\pi$
$241$	−12.5637	−	21.7609i	−0.809296	−	1.40174i	0.104055	−	0.994572i	$-0.466818\pi$
$242$	15.0995			0.970631
$243$		0			0
$244$	35.9300	−	62.2326i	2.30018	−	3.98403i
$245$	−1.59293	+	2.75904i	−0.101769	+	0.176269i
$246$		0			0
$247$	−2.19523	+	4.13928i	−0.139679	+	0.263376i
$248$	−86.9188			−5.51935
$249$		0			0
$250$	0.660955	−	1.14481i	0.0418025	−	0.0724040i
$251$	−3.83933	−	6.64991i	−0.242336	−	0.419739i	0.719043	−	0.694965i	$-0.244580\pi$
$251$	−3.83933	−	6.64991i	−0.242336	−	0.419739i	−0.961379	+	0.275227i	$0.911247\pi$
$252$		0			0
$253$	2.70219	+	4.68033i	0.169885	+	0.294250i
$254$	17.2169	+	29.8206i	1.08029	+	1.87111i
$255$		0			0
$256$	−38.6718	−	66.9815i	−2.41698	−	4.18634i
$257$	−13.1702	+	22.8114i	−0.821532	+	1.42293i	0.0830095	+	0.996549i	$0.473547\pi$
$257$	−13.1702	+	22.8114i	−0.821532	+	1.42293i	−0.904541	+	0.426386i	$0.859787\pi$
$258$		0			0
$259$	3.22886			0.200632
$260$	−30.5589	+	57.6213i	−1.89518	+	3.57352i
$261$		0			0
$262$	−27.4482	+	47.5417i	−1.69575	+	2.93713i
$263$	1.51439	−	2.62299i	0.0933811	−	0.161741i	−0.815551	−	0.578686i	$-0.803566\pi$
$263$	1.51439	−	2.62299i	0.0933811	−	0.161741i	0.908932	+	0.416945i	$0.136899\pi$
$264$		0			0
$265$	41.2974			2.53688
$266$	1.80040	+	3.11838i	0.110389	+	0.191200i
$267$		0			0
$268$	78.9649			4.82355
$269$	0.810554	+	1.40392i	0.0494204	+	0.0855986i	0.889677	−	0.456590i	$-0.150929\pi$
$269$	0.810554	+	1.40392i	0.0494204	+	0.0855986i	−0.840257	+	0.542188i	$0.817596\pi$
$270$		0			0
$271$	−7.83208	+	13.5656i	−0.475765	+	0.824049i	−0.999615	−	0.0277618i	$-0.991162\pi$
$271$	−7.83208	+	13.5656i	−0.475765	+	0.824049i	0.523850	+	0.851811i	$0.324495\pi$
$272$	46.7860			2.83682
$273$		0			0
$274$	−38.2183			−2.30885
$275$	−6.06642	+	10.5073i	−0.365819	+	0.633617i
$276$		0			0
$277$	−1.35618	−	2.34897i	−0.0814850	−	0.141136i	0.822403	−	0.568905i	$-0.192633\pi$
$277$	−1.35618	−	2.34897i	−0.0814850	−	0.141136i	−0.903888	+	0.427769i	$0.859300\pi$
$278$	26.4974			1.58921
$279$		0			0
$280$	16.2348	+	28.1195i	0.970214	+	1.68046i
$281$	20.0307			1.19493			0.597466	−	0.801894i	$-0.296174\pi$
$281$	20.0307			1.19493			0.597466	+	0.801894i	$0.296174\pi$
$282$		0			0
$283$	−10.4027	+	18.0180i	−0.618377	+	1.07106i	0.371405	+	0.928471i	$0.378876\pi$
$283$	−10.4027	+	18.0180i	−0.618377	+	1.07106i	−0.989782	+	0.142589i	$0.954457\pi$
$284$	19.2676	−	33.3725i	1.14332	−	1.98030i
$285$		0			0
$286$	11.0283	−	20.7949i	0.652120	−	1.22963i
$287$	5.54187			0.327126
$288$		0			0
$289$	4.66095	−	8.07301i	0.274174	−	0.474883i
$290$	−41.3226	−	71.5729i	−2.42655	−	4.20290i
$291$		0			0
$292$	−30.4765	−	52.7869i	−1.78350	−	3.08912i
$293$	−2.00786	−	3.47772i	−0.117301	−	0.203171i	0.801396	−	0.598134i	$-0.204091\pi$
$293$	−2.00786	−	3.47772i	−0.117301	−	0.203171i	−0.918697	+	0.394963i	$0.870757\pi$
$294$		0			0
$295$	1.01017	+	1.74966i	0.0588143	+	0.101869i
$296$	16.4539	−	28.4989i	0.956362	−	1.65647i
$297$		0			0
$298$	−1.58504			−0.0918189
$299$	−8.26533	+	0.297473i	−0.477996	+	0.0172033i
$300$		0			0
$301$	0.189302	−	0.327880i	0.0109112	−	0.0188987i
$302$	18.9195	−	32.7695i	1.08869	−	1.88567i
$303$		0			0
$304$	21.9412			1.25842
$305$	20.1596	+	34.9175i	1.15434	+	1.99937i
$306$		0			0
$307$	−13.1049			−0.747936			−0.373968	−	0.927442i	$-0.622003\pi$
$307$	−13.1049			−0.747936			−0.373968	+	0.927442i	$0.622003\pi$
$308$	−6.68881	−	11.5854i	−0.381130	−	0.660137i
$309$		0			0
$310$	37.6434	−	65.2003i	2.13800	−	3.70313i
$311$	21.4947			1.21885			0.609427	−	0.792842i	$-0.291399\pi$
$311$	21.4947			1.21885			0.609427	+	0.792842i	$0.291399\pi$
$312$		0			0
$313$	−6.47165			−0.365799			−0.182900	−	0.983132i	$-0.558548\pi$
$313$	−6.47165			−0.365799			−0.182900	+	0.983132i	$0.558548\pi$
$314$	11.3387	−	19.6392i	0.639879	−	1.10830i
$315$		0			0
$316$	−37.7183	−	65.3300i	−2.12182	−	3.67510i
$317$	−6.92023			−0.388679			−0.194339	−	0.980934i	$-0.562256\pi$
$317$	−6.92023			−0.388679			−0.194339	+	0.980934i	$0.562256\pi$
$318$		0			0
$319$	11.0283	+	19.1017i	0.617469	+	1.06949i
$320$	125.493			7.01526
$321$		0			0
$322$	−3.17809	+	5.50461i	−0.177108	+	0.306760i
$323$	−1.80040	+	3.11838i	−0.100177	+	0.173511i
$324$		0			0
$325$	−9.85618	−	15.7358i	−0.546723	−	0.872862i
$326$	18.4424			1.02143
$327$		0			0
$328$	28.2407	−	48.9143i	1.55933	−	2.70084i
$329$	−0.238531	−	0.413148i	−0.0131507	−	0.0227776i
$330$		0			0
$331$	9.71068	+	16.8194i	0.533747	+	0.924477i	0.999223	+	0.0394167i	$0.0125500\pi$
$331$	9.71068	+	16.8194i	0.533747	+	0.924477i	−0.465476	+	0.885061i	$0.654117\pi$
$332$	20.0664	+	34.7561i	1.10129	+	1.90749i
$333$		0			0
$334$	22.1883	+	38.4312i	1.21409	+	2.10286i
$335$	−22.1528	+	38.3698i	−1.21034	+	2.09637i
$336$		0			0
$337$	−10.3422			−0.563378			−0.281689	−	0.959506i	$-0.590895\pi$
$337$	−10.3422			−0.563378			−0.281689	+	0.959506i	$0.590895\pi$
$338$	20.2071	+	29.8206i	1.09912	+	1.62203i
$339$		0			0
$340$	−25.0626	+	43.4097i	−1.35921	+	2.35422i
$341$	−10.0464	+	17.4009i	−0.544044	+	0.942312i
$342$		0			0
$343$	1.00000			0.0539949
$344$	−1.92932	−	3.34167i	−0.104022	−	0.180171i
$345$		0			0
$346$	−32.1252			−1.72706
$347$	3.63186	+	6.29057i	0.194969	+	0.337695i	0.946890	−	0.321557i	$-0.104206\pi$
$347$	3.63186	+	6.29057i	0.194969	+	0.337695i	−0.751922	+	0.659252i	$0.770873\pi$
$348$		0			0
$349$	10.2530	−	17.7587i	0.548828	−	0.950599i	−0.449527	−	0.893267i	$-0.648407\pi$
$349$	10.2530	−	17.7587i	0.548828	−	0.950599i	0.998355	−	0.0573319i	$-0.0182593\pi$
$350$	−14.2696			−0.762743
$351$		0			0
$352$	−62.2044			−3.31550
$353$	−13.5540	+	23.4762i	−0.721408	+	1.24951i	0.239028	+	0.971013i	$0.423171\pi$
$353$	−13.5540	+	23.4762i	−0.721408	+	1.24951i	−0.960436	+	0.278502i	$0.910162\pi$
$354$		0			0
$355$	10.8107	+	18.7247i	0.573772	+	0.993803i
$356$	−47.5537			−2.52034
$357$		0			0
$358$	8.74175	+	15.1412i	0.462016	+	0.800235i
$359$	10.6923			0.564320			0.282160	−	0.959367i	$-0.408949\pi$
$359$	10.6923			0.564320			0.282160	+	0.959367i	$0.408949\pi$
$360$		0			0
$361$	8.65567	−	14.9921i	0.455561	−	0.789056i
$362$	−21.5808	+	37.3791i	−1.13426	+	1.96460i
$363$		0			0
$364$	20.4594	−	0.736344i	1.07236	−	0.0385949i
$365$	34.1996			1.79009
$366$		0			0
$367$	−10.2236	+	17.7077i	−0.533666	+	0.924337i	0.465561	+	0.885016i	$0.345853\pi$
$367$	−10.2236	+	17.7077i	−0.533666	+	0.924337i	−0.999227	+	0.0393208i	$0.987481\pi$
$368$	19.3655	+	33.5420i	1.00950	+	1.74850i
$369$		0			0
$370$	14.2519	+	24.6850i	0.740922	+	1.28331i
$371$	−6.48135	−	11.2260i	−0.336495	−	0.582826i
$372$		0			0
$373$	1.33905	+	2.31929i	0.0693331	+	0.120088i	0.898608	−	0.438753i	$-0.144580\pi$
$373$	1.33905	+	2.31929i	0.0693331	+	0.120088i	−0.829275	+	0.558841i	$0.811246\pi$
$374$	9.04482	−	15.6661i	0.467696	−	0.810074i
$375$		0			0
$376$	−4.86210			−0.250744
$377$	−33.7330	+	1.21407i	−1.73734	+	0.0625276i
$378$		0			0
$379$	4.65567	−	8.06385i	0.239146	−	0.414212i	−0.721324	−	0.692598i	$-0.756466\pi$
$379$	4.65567	−	8.06385i	0.239146	−	0.414212i	0.960469	+	0.278386i	$0.0897994\pi$
$380$	−11.7536	+	20.3579i	−0.602948	+	1.04434i
$381$		0			0
$382$	18.1979			0.931088
$383$	−3.82002	−	6.61647i	−0.195194	−	0.338086i	0.751770	−	0.659425i	$-0.229200\pi$
$383$	−3.82002	−	6.61647i	−0.195194	−	0.338086i	−0.946964	+	0.321339i	$0.895867\pi$
$384$		0			0
$385$	7.50592			0.382537
$386$	3.13839	+	5.43584i	0.159740	+	0.276677i
$387$		0			0
$388$	−21.2124	+	36.7409i	−1.07689	+	1.86524i
$389$	9.29976			0.471517			0.235758	−	0.971812i	$-0.424243\pi$
$389$	9.29976			0.471517			0.235758	+	0.971812i	$0.424243\pi$
$390$		0			0
$391$	−6.35618			−0.321446
$392$	5.09588	−	8.82632i	0.257381	−	0.445796i
$393$		0			0
$394$	−25.1942	−	43.6376i	−1.26926	−	2.19843i
$395$	42.3260			2.12965
$396$		0			0
$397$	6.06366	+	10.5026i	0.304326	+	0.527109i	0.977111	−	0.212730i	$-0.0682353\pi$
$397$	6.06366	+	10.5026i	0.304326	+	0.527109i	−0.672785	+	0.739838i	$0.734902\pi$
$398$	−7.26372			−0.364098
$399$		0			0
$400$	−43.4755	+	75.3018i	−2.17377	+	3.76509i
$401$	−18.2778	+	31.6581i	−0.912750	+	1.58093i	−0.102586	+	0.994724i	$0.532712\pi$
$401$	−18.2778	+	31.6581i	−0.912750	+	1.58093i	−0.810163	+	0.586204i	$0.800622\pi$
$402$		0			0
$403$	−16.3225	−	26.0595i	−0.813084	−	1.29812i
$404$	−35.0681			−1.74470
$405$		0			0
$406$	−12.9706	+	22.4658i	−0.643721	+	1.11496i
$407$	−3.80361	−	6.58804i	−0.188538	−	0.326557i
$408$		0			0
$409$	−2.80373	−	4.85621i	−0.138636	−	0.240124i	0.788345	−	0.615234i	$-0.210938\pi$
$409$	−2.80373	−	4.85621i	−0.138636	−	0.240124i	−0.926980	+	0.375110i	$0.877605\pi$
$410$	24.4614	+	42.3683i	1.20806	+	2.09242i
$411$		0			0
$412$	29.4017	+	50.9252i	1.44852	+	2.50890i
$413$	0.317078	−	0.549195i	0.0156024	−	0.0270241i
$414$		0			0
$415$	−22.5178			−1.10535
$416$	44.6017	−	84.1002i	2.18678	−	4.12335i
$417$		0			0
$418$	4.24175	−	7.34693i	0.207471	−	0.359350i
$419$	−7.76896	+	13.4562i	−0.379539	+	0.657380i	−0.990995	−	0.133898i	$-0.957251\pi$
$419$	−7.76896	+	13.4562i	−0.379539	+	0.657380i	0.611456	+	0.791278i	$0.290584\pi$
$420$		0			0
$421$	1.81599			0.0885058			0.0442529	−	0.999020i	$-0.485909\pi$
$421$	1.81599			0.0885058			0.0442529	+	0.999020i	$0.485909\pi$
$422$	−7.37334	−	12.7710i	−0.358928	−	0.621682i
$423$		0			0
$424$	−132.113			−6.41595
$425$	−7.13481	−	12.3578i	−0.346089	−	0.599444i
$426$		0			0
$427$	6.32783	−	10.9601i	0.306225	−	0.530398i
$428$	−55.8665			−2.70041
$429$		0			0
$430$	3.34225			0.161177
$431$	8.01215	−	13.8774i	0.385931	−	0.668453i	−0.605966	−	0.795490i	$-0.707213\pi$
$431$	8.01215	−	13.8774i	0.385931	−	0.668453i	0.991898	+	0.127037i	$0.0405468\pi$
$432$		0			0
$433$	1.64974	+	2.85744i	0.0792816	+	0.137320i	0.902940	−	0.429766i	$-0.141404\pi$
$433$	1.64974	+	2.85744i	0.0792816	+	0.137320i	−0.823659	+	0.567086i	$0.808071\pi$
$434$	−23.6315			−1.13435
$435$		0			0
$436$	11.0920	+	19.2119i	0.531211	+	0.920084i
$437$	−2.98086			−0.142594
$438$		0			0
$439$	4.87436	−	8.44264i	0.232640	−	0.402945i	−0.725944	−	0.687754i	$-0.758597\pi$
$439$	4.87436	−	8.44264i	0.232640	−	0.402945i	0.958584	+	0.284809i	$0.0919301\pi$
$440$	38.2493	−	66.2497i	1.82346	−	3.15833i
$441$		0			0
$442$	14.6952	+	23.4615i	0.698981	+	1.11595i
$443$	−12.0086			−0.570544			−0.285272	−	0.958447i	$-0.592084\pi$
$443$	−12.0086			−0.570544			−0.285272	+	0.958447i	$0.592084\pi$
$444$		0			0
$445$	13.3407	−	23.1068i	0.632411	−	1.09537i
$446$	26.2618	+	45.4867i	1.24353	+	2.15386i
$447$		0			0
$448$	−19.6952	−	34.1131i	−0.930512	−	1.61169i
$449$	1.94573	+	3.37010i	0.0918247	+	0.159045i	0.908279	−	0.418365i	$-0.137397\pi$
$449$	1.94573	+	3.37010i	0.0918247	+	0.159045i	−0.816454	+	0.577410i	$0.804063\pi$
$450$		0			0
$451$	−6.52835	−	11.3074i	−0.307408	−	0.532446i
$452$	−30.1129	+	52.1570i	−1.41639	+	2.45326i
$453$		0			0
$454$	8.56470			0.401961
$455$	−5.38189	+	10.1480i	−0.252307	+	0.475746i
$456$		0			0
$457$	−4.03956	+	6.99672i	−0.188963	+	0.327293i	−0.944905	−	0.327346i	$-0.893846\pi$
$457$	−4.03956	+	6.99672i	−0.188963	+	0.327293i	0.755942	+	0.654639i	$0.227179\pi$
$458$	9.03306	−	15.6457i	0.422087	−	0.731076i
$459$		0			0
$460$	−41.4953			−1.93473
$461$	11.5415	+	19.9905i	0.537541	+	0.931049i	0.999036	+	0.0439059i	$0.0139802\pi$
$461$	11.5415	+	19.9905i	0.537541	+	0.931049i	−0.461494	+	0.887143i	$0.652686\pi$
$462$		0			0
$463$	4.53684			0.210845			0.105422	−	0.994428i	$-0.466381\pi$
$463$	4.53684			0.210845			0.105422	+	0.994428i	$0.466381\pi$
$464$	79.0356	+	136.894i	3.66914	+	6.35513i
$465$		0			0
$466$	−5.68233	+	9.84209i	−0.263229	+	0.455926i
$467$	29.5555			1.36766			0.683832	−	0.729639i	$-0.260312\pi$
$467$	29.5555			1.36766			0.683832	+	0.729639i	$0.260312\pi$
$468$		0			0
$469$	13.9069			0.642163
$470$	2.10571	−	3.64720i	0.0971293	−	0.168233i
$471$		0			0
$472$	−3.23158	−	5.59726i	−0.148746	−	0.257635i
$473$	−0.891992			−0.0410138
$474$		0			0
$475$	−3.34601	−	5.79546i	−0.153526	−	0.265914i
$476$	15.7336			0.721150
$477$		0			0
$478$	−7.50592	+	13.0006i	−0.343313	+	0.594635i
$479$	10.2656	−	17.7806i	0.469050	−	0.812418i	−0.530325	−	0.847795i	$-0.677930\pi$
$479$	10.2656	−	17.7806i	0.469050	−	0.812418i	0.999374	+	0.0353772i	$0.0112632\pi$
$480$		0			0
$481$	11.6343	−	0.418724i	0.530478	−	0.0190922i
$482$	−69.6262			−3.17139
$483$		0			0
$484$	15.4706	−	26.7959i	0.703210	−	1.21799i
$485$	−11.9018	−	20.6146i	−0.540435	−	0.936061i
$486$		0			0
$487$	10.7813	+	18.6738i	0.488548	+	0.846189i	0.999913	−	0.0131739i	$-0.00419349\pi$
$487$	10.7813	+	18.6738i	0.488548	+	0.846189i	−0.511366	+	0.859363i	$0.670860\pi$
$488$	−64.4917	−	111.703i	−2.91940	−	5.05655i
$489$		0			0
$490$	4.41392	+	7.64513i	0.199400	+	0.345372i
$491$	4.46172	−	7.72793i	0.201355	−	0.348757i	−0.747610	−	0.664137i	$-0.768799\pi$
$491$	4.46172	−	7.72793i	0.201355	−	0.348757i	0.948965	+	0.315381i	$0.102132\pi$
$492$		0			0
$493$	−25.9412			−1.16833
$494$	6.89162	+	11.0027i	0.310069	+	0.495036i
$495$		0			0
$496$	−71.9985	+	124.705i	−3.23283	+	5.59943i
$497$	3.39333	−	5.87742i	0.152212	−	0.263638i
$498$		0			0
$499$	−34.9755			−1.56572			−0.782859	−	0.622199i	$-0.786239\pi$
$499$	−34.9755			−1.56572			−0.782859	+	0.622199i	$0.786239\pi$
$500$	−1.35440	−	2.34589i	−0.0605707	−	0.104912i
$501$		0			0
$502$	−21.2771			−0.949642
$503$	−0.743769	−	1.28825i	−0.0331630	−	0.0574401i	0.848968	−	0.528445i	$-0.177225\pi$
$503$	−0.743769	−	1.28825i	−0.0331630	−	0.0574401i	−0.882131	+	0.471005i	$0.843891\pi$
$504$		0			0
$505$	9.83800	−	17.0399i	0.437785	−	0.758266i
$506$	14.9752			0.665729
$507$		0			0
$508$	70.5605			3.13062
$509$	−3.53866	+	6.12914i	−0.156848	+	0.271670i	−0.933731	−	0.357977i	$-0.883467\pi$
$509$	−3.53866	+	6.12914i	−0.156848	+	0.271670i	0.776882	+	0.629646i	$0.216800\pi$
$510$		0			0
$511$	−5.36739	−	9.29660i	−0.237439	−	0.411257i
$512$	−101.627			−4.49132
$513$		0			0
$514$	36.4937	+	63.2089i	1.60967	+	2.78802i
$515$	−32.9934			−1.45386
$516$		0			0
$517$	−0.561981	+	0.973380i	−0.0247159	+	0.0428092i
$518$	4.47348	−	7.74830i	0.196554	−	0.340441i
$519$		0			0
$520$	62.1440	+	99.2152i	2.72520	+	4.35088i
$521$	−5.08833			−0.222924			−0.111462	−	0.993769i	$-0.535553\pi$
$521$	−5.08833			−0.222924			−0.111462	+	0.993769i	$0.535553\pi$
$522$		0			0
$523$	8.26417	−	14.3140i	0.361367	−	0.625906i	−0.626819	−	0.779165i	$-0.715643\pi$
$523$	8.26417	−	14.3140i	0.361367	−	0.625906i	0.988186	+	0.153259i	$0.0489768\pi$
$524$	56.2457	+	97.4204i	2.45710	+	4.25583i
$525$		0			0
$526$	−4.19627	−	7.26815i	−0.182966	−	0.316906i
$527$	−11.8158	−	20.4655i	−0.514702	−	0.891491i
$528$		0			0
$529$	8.86907	+	15.3617i	0.385612	+	0.667899i
$530$	57.2162	−	99.1014i	2.48531	−	4.30469i
$531$		0			0
$532$	7.37860			0.319903
$533$	19.9686	−	0.718679i	0.864935	−	0.0311294i
$534$		0			0
$535$	15.6728	−	27.1461i	0.677594	−	1.17363i
$536$	70.8681	−	122.747i	3.06104	−	5.30187i
$537$		0			0
$538$	4.49199			0.193663
$539$	−1.17800	−	2.04036i	−0.0507402	−	0.0878846i
$540$		0			0
$541$	4.55077			0.195653			0.0978264	−	0.995203i	$-0.468811\pi$
$541$	4.55077			0.195653			0.0978264	+	0.995203i	$0.468811\pi$
$542$	21.7022	+	37.5893i	0.932189	+	1.61460i
$543$		0			0
$544$	36.5798	−	63.3580i	1.56834	−	2.71645i
$545$	−12.4470			−0.533172
$546$		0			0
$547$	23.8054			1.01785			0.508923	−	0.860812i	$-0.330044\pi$
$547$	23.8054			1.01785			0.508923	+	0.860812i	$0.330044\pi$
$548$	−39.1577	+	67.8231i	−1.67273	+	2.89726i
$549$		0			0
$550$	16.8097	+	29.1152i	0.716766	+	1.24148i
$551$	−12.1657			−0.518275
$552$		0			0
$553$	−6.64278	−	11.5056i	−0.282480	−	0.489269i
$554$	−7.51578			−0.319315
$555$		0			0
$556$	27.1487	−	47.0229i	1.15136	−	1.99422i
$557$	−1.69078	+	2.92852i	−0.0716408	+	0.124086i	−0.899621	−	0.436672i	$-0.856157\pi$
$557$	−1.69078	+	2.92852i	−0.0716408	+	0.124086i	0.827980	+	0.560758i	$0.189490\pi$
$558$		0			0
$559$	0.639575	−	1.20597i	0.0270511	−	0.0510072i
$560$	53.7918			2.27312
$561$		0			0
$562$	27.7519	−	48.0677i	1.17064	−	2.02761i
$563$	−13.8711	−	24.0254i	−0.584597	−	1.01255i	−0.994926	−	0.100614i	$-0.967919\pi$
$563$	−13.8711	−	24.0254i	−0.584597	−	1.01255i	0.410328	−	0.911938i	$-0.365414\pi$
$564$		0			0
$565$	−16.8957	−	29.2643i	−0.710809	−	1.23116i
$566$	28.8252	+	49.9268i	1.21162	+	2.09858i
$567$		0			0
$568$	−34.5840	−	59.9012i	−1.45111	−	2.51340i
$569$	−7.38510	+	12.7914i	−0.309599	+	0.536242i	−0.978275	−	0.207313i	$-0.933528\pi$
$569$	−7.38510	+	12.7914i	−0.309599	+	0.536242i	0.668675	+	0.743555i	$0.266862\pi$
$570$		0			0
$571$	32.4492			1.35796			0.678979	−	0.734158i	$-0.262423\pi$
$571$	32.4492			1.35796			0.678979	+	0.734158i	$0.262423\pi$
$572$	−25.6037	−	40.8772i	−1.07054	−	1.70916i
$573$		0			0
$574$	7.67809	−	13.2988i	0.320477	−	0.555083i
$575$	5.90643	−	10.2302i	0.246315	−	0.426630i
$576$		0			0
$577$	18.5199			0.770992			0.385496	−	0.922710i	$-0.374030\pi$
$577$	18.5199			0.770992			0.385496	+	0.922710i	$0.374030\pi$
$578$	−12.9152	−	22.3698i	−0.537202	−	0.930461i
$579$		0			0
$580$	−169.353			−7.03201
$581$	3.53401	+	6.12109i	0.146615	+	0.253945i
$582$		0			0
$583$	−15.2701	+	26.4486i	−0.632423	+	1.09539i
$584$	−109.406			−4.52726
$585$		0			0
$586$	−11.1273			−0.459665
$587$	19.2202	−	33.2903i	0.793301	−	1.37404i	−0.130612	−	0.991434i	$-0.541694\pi$
$587$	19.2202	−	33.2903i	0.793301	−	1.37404i	0.923913	−	0.382604i	$-0.124973\pi$
$588$		0			0
$589$	−5.54124	−	9.59770i	−0.228323	−	0.395467i
$590$	5.59822			0.230475
$591$		0			0
$592$	−27.2589	−	47.2138i	−1.12033	−	1.94047i
$593$	−24.6420			−1.01193			−0.505963	−	0.862555i	$-0.668863\pi$
$593$	−24.6420			−1.01193			−0.505963	+	0.862555i	$0.668863\pi$
$594$		0			0
$595$	−4.41392	+	7.64513i	−0.180953	+	0.313420i
$596$	−1.62400	+	2.81285i	−0.0665216	+	0.115219i
$597$		0			0
$598$	−10.7375	+	20.2465i	−0.439089	+	0.827939i
$599$	−7.10663			−0.290369			−0.145185	−	0.989405i	$-0.546378\pi$
$599$	−7.10663			−0.290369			−0.145185	+	0.989405i	$0.546378\pi$
$600$		0			0
$601$	0.314943	−	0.545497i	0.0128468	−	0.0222513i	−0.859531	−	0.511084i	$-0.829244\pi$
$601$	0.314943	−	0.545497i	0.0128468	−	0.0222513i	0.872377	+	0.488833i	$0.162577\pi$
$602$	−0.524543	−	0.908535i	−0.0213788	−	0.0370291i
$603$		0			0
$604$	−38.7691	−	67.1500i	−1.57749	−	2.73229i
$605$	8.68026	+	15.0346i	0.352903	+	0.611245i
$606$		0			0
$607$	−23.1883	−	40.1632i	−0.941182	−	1.63018i	−0.763220	−	0.646138i	$-0.776383\pi$
$607$	−23.1883	−	40.1632i	−0.941182	−	1.63018i	−0.177962	−	0.984037i	$-0.556950\pi$
$608$	17.1548	−	29.7130i	0.695720	−	1.20502i
$609$		0			0
$610$	111.722			4.52350
$611$	−0.913058	−	1.45773i	−0.0369384	−	0.0589734i
$612$		0			0
$613$	15.3268	−	26.5468i	0.619043	−	1.07221i	−0.370617	−	0.928786i	$-0.620854\pi$
$613$	15.3268	−	26.5468i	0.619043	−	1.07221i	0.989661	−	0.143429i	$-0.0458128\pi$
$614$	−18.1564	+	31.4478i	−0.732733	+	1.26913i
$615$		0			0
$616$	−24.0118			−0.967465
$617$	13.9215	+	24.1127i	0.560457	+	0.970740i	0.997456	+	0.0712785i	$0.0227079\pi$
$617$	13.9215	+	24.1127i	0.560457	+	0.970740i	−0.436999	+	0.899462i	$0.643959\pi$
$618$		0			0
$619$	−40.0237			−1.60869			−0.804344	−	0.594164i	$-0.797483\pi$
$619$	−40.0237			−1.60869			−0.804344	+	0.594164i	$0.797483\pi$
$620$	−77.1373	−	133.606i	−3.09791	−	5.36574i
$621$		0			0
$622$	29.7803	−	51.5809i	1.19408	−	2.06821i
$623$	−8.37494			−0.335535
$624$		0			0
$625$	−24.2289			−0.969154
$626$	−8.96627	+	15.5300i	−0.358364	+	0.620705i
$627$		0			0
$628$	−23.2348	−	40.2438i	−0.927169	−	1.60590i
$629$	8.94697			0.356739
$630$		0			0
$631$	8.75296	+	15.1606i	0.348450	+	0.603533i	0.985974	−	0.166897i	$-0.0533748\pi$
$631$	8.75296	+	15.1606i	0.348450	+	0.603533i	−0.637524	+	0.770430i	$0.720041\pi$
$632$	−135.403			−5.38605
$633$		0			0
$634$	−9.58776	+	16.6065i	−0.380779	+	0.659528i
$635$	−19.7951	+	34.2861i	−0.785543	+	1.36060i
$636$		0			0
$637$	3.60322	−	0.129682i	0.142765	−	0.00513817i
$638$	61.1177			2.41967
$639$		0			0
$640$	89.7515	−	155.454i	3.54774	−	6.14487i
$641$	−5.28693	−	9.15723i	−0.208821	−	0.361689i	0.742522	−	0.669821i	$-0.233629\pi$
$641$	−5.28693	−	9.15723i	−0.208821	−	0.361689i	−0.951343	+	0.308133i	$0.900296\pi$
$642$		0			0
$643$	25.0402	+	43.3709i	0.987489	+	1.71038i	0.630307	+	0.776346i	$0.282929\pi$
$643$	25.0402	+	43.3709i	0.987489	+	1.71038i	0.357182	+	0.934035i	$0.383738\pi$
$644$	6.51241	+	11.2798i	0.256625	+	0.444488i
$645$		0			0
$646$	4.98879	+	8.64084i	0.196281	+	0.339969i
$647$	8.37670	−	14.5089i	0.329322	−	0.570403i	−0.653055	−	0.757310i	$-0.726513\pi$
$647$	8.37670	−	14.5089i	0.329322	−	0.570403i	0.982378	+	0.186907i	$0.0598464\pi$
$648$		0			0
$649$	−1.49408			−0.0586476
$650$	−51.4165	+	1.85051i	−2.01672	+	0.0725828i
$651$		0			0
$652$	18.8957	−	32.7284i	0.740014	−	1.28174i
$653$	2.72346	−	4.71716i	0.106577	−	0.184597i	−0.807804	−	0.589451i	$-0.799344\pi$
$653$	2.72346	−	4.71716i	0.106577	−	0.184597i	0.914381	+	0.404854i	$0.132678\pi$
$654$		0			0
$655$	−63.1167			−2.46618
$656$	−46.7860	−	81.0357i	−1.82668	−	3.16391i
$657$		0			0
$658$	−1.32191			−0.0515334
$659$	0.591328	+	1.02421i	0.0230349	+	0.0398975i	0.877313	−	0.479919i	$-0.159334\pi$
$659$	0.591328	+	1.02421i	0.0230349	+	0.0398975i	−0.854278	+	0.519816i	$0.826000\pi$
$660$		0			0
$661$	−4.51546	+	7.82100i	−0.175631	+	0.304202i	−0.940379	−	0.340127i	$-0.889530\pi$
$661$	−4.51546	+	7.82100i	−0.175631	+	0.304202i	0.764749	+	0.644329i	$0.222863\pi$
$662$	53.8154			2.09159
$663$		0			0
$664$	72.0355			2.79552
$665$	−2.07000	+	3.58534i	−0.0802710	+	0.139033i
$666$		0			0
$667$	−10.7375	−	18.5979i	−0.415758	−	0.720114i
$668$	90.9345			3.51836
$669$		0			0
$670$	61.3841	+	106.320i	2.37148	+	4.10752i
$671$	−29.8168			−1.15107
$672$		0			0
$673$	−6.33905	+	10.9795i	−0.244352	+	0.423230i	−0.961949	−	0.273228i	$-0.911909\pi$
$673$	−6.33905	+	10.9795i	−0.244352	+	0.423230i	0.717597	+	0.696459i	$0.245242\pi$
$674$	−14.3289	+	24.8183i	−0.551927	+	0.955965i
$675$		0			0
$676$	73.6242	−	5.30642i	2.83170	−	0.204093i
$677$	4.21143			0.161858			0.0809292	−	0.996720i	$-0.474211\pi$
$677$	4.21143			0.161858			0.0809292	+	0.996720i	$0.474211\pi$
$678$		0			0
$679$	−3.73583	+	6.47064i	−0.143368	+	0.248320i
$680$	44.9856	+	77.9173i	1.72512	+	2.98799i
$681$		0			0
$682$	27.8380	+	48.2168i	1.06597	+	1.84632i
$683$	−5.31976	−	9.21409i	−0.203555	−	0.352567i	0.746117	−	0.665815i	$-0.231916\pi$
$683$	−5.31976	−	9.21409i	−0.203555	−	0.352567i	−0.949671	+	0.313248i	$0.898583\pi$
$684$		0			0
$685$	−21.9706	−	38.0542i	−0.839454	−	1.45398i
$686$	1.38547	−	2.39970i	0.0528974	−	0.0916210i
$687$		0			0
$688$	−6.39254			−0.243713
$689$	−24.8095	−	39.6093i	−0.945167	−	1.50899i
$690$		0			0
$691$	−14.0171	+	24.2784i	−0.533237	+	0.923593i	0.466010	+	0.884780i	$0.345691\pi$
$691$	−14.0171	+	24.2784i	−0.533237	+	0.923593i	−0.999246	+	0.0388138i	$0.987642\pi$
$692$	−32.9149	+	57.0102i	−1.25124	+	2.16720i
$693$		0			0
$694$	20.1273			0.764023
$695$	15.2326	+	26.3837i	0.577806	+	1.00079i
$696$		0			0
$697$	15.3562			0.581657
$698$	−28.4103	−	49.2081i	−1.07535	−	1.86255i
$699$		0			0
$700$	−14.6204	+	25.3232i	−0.552597	+	0.957127i
$701$	47.7166			1.80223			0.901115	−	0.433581i	$-0.142750\pi$
$701$	47.7166			1.80223			0.901115	+	0.433581i	$0.142750\pi$
$702$		0			0
$703$	4.19586			0.158250
$704$	−46.4021	+	80.3708i	−1.74884	+	3.02909i
$705$		0			0
$706$	37.5573	+	65.0512i	1.41349	+	2.44823i
$707$	−6.17603			−0.232273
$708$		0			0
$709$	12.8957	+	22.3361i	0.484310	+	0.838849i	0.999838	−	0.0180239i	$-0.00573750\pi$
$709$	12.8957	+	22.3361i	0.484310	+	0.838849i	−0.515528	+	0.856873i	$0.672404\pi$
$710$	59.9115			2.24844
$711$		0			0
$712$	−42.6777	+	73.9199i	−1.59941	+	2.77027i
$713$	9.78148	−	16.9420i	0.366319	−	0.634483i
$714$		0			0
$715$	27.0455	−	0.973380i	1.01144	−	0.0364024i
$716$	35.8265			1.33890
$717$		0			0
$718$	14.8139	−	25.6584i	0.552850	−	0.957564i
$719$	−20.0425	−	34.7146i	−0.747458	−	1.29464i	−0.949037	−	0.315163i	$-0.897941\pi$
$719$	−20.0425	−	34.7146i	−0.747458	−	1.29464i	0.201579	−	0.979472i	$-0.435393\pi$
$720$		0			0
$721$	5.17809	+	8.96872i	0.192842	+	0.334012i
$722$	−23.9843	−	41.5420i	−0.892603	−	1.54603i
$723$		0			0
$724$	44.2225	+	76.5957i	1.64352	+	2.84666i
$725$	24.1057	−	41.7523i	0.895262	−	1.55064i
$726$		0			0
$727$	−43.2868			−1.60542			−0.802710	−	0.596370i	$-0.796609\pi$
$727$	−43.2868			−1.60542			−0.802710	+	0.596370i	$0.796609\pi$
$728$	17.2169	−	32.4640i	0.638103	−	1.20320i
$729$		0			0
$730$	47.3824	−	82.0688i	1.75370	−	3.03750i
$731$	0.524543	−	0.908535i	0.0194009	−	0.0336034i
$732$		0			0
$733$	−31.9636			−1.18060			−0.590302	−	0.807182i	$-0.700991\pi$
$733$	−31.9636			−1.18060			−0.590302	+	0.807182i	$0.700991\pi$
$734$	28.3289	+	49.0670i	1.04564	+	1.81110i
$735$		0			0
$736$	60.5639			2.23241
$737$	−16.3824	−	28.3752i	−0.603455	−	1.04521i
$738$		0			0
$739$	−14.1102	+	24.4396i	−0.519052	+	0.899024i	0.480703	+	0.876883i	$0.340381\pi$
$739$	−14.1102	+	24.4396i	−0.519052	+	0.899024i	−0.999755	+	0.0221404i	$0.992952\pi$
$740$	58.4089			2.14715
$741$		0			0
$742$	−35.9188			−1.31862
$743$	15.1927	−	26.3145i	0.557365	−	0.965385i	−0.440350	−	0.897826i	$-0.645146\pi$
$743$	15.1927	−	26.3145i	0.557365	−	0.965385i	0.997715	−	0.0675585i	$-0.0215209\pi$
$744$		0			0
$745$	−0.911195	−	1.57824i	−0.0333836	−	0.0578221i
$746$	7.42082			0.271695
$747$		0			0
$748$	−18.5343	−	32.1023i	−0.677680	−	1.17378i
$749$	−9.83896			−0.359508
$750$		0			0
$751$	−16.2166	+	28.0880i	−0.591752	+	1.02495i	0.402244	+	0.915532i	$0.368230\pi$
$751$	−16.2166	+	28.0880i	−0.591752	+	1.02495i	−0.993996	+	0.109413i	$0.965103\pi$
$752$	−4.02749	+	6.97581i	−0.146867	+	0.254382i
$753$		0			0
$754$	−43.8225	+	82.6311i	−1.59592	+	3.00925i
$755$	43.5051			1.58331
$756$		0			0
$757$	−15.4182	+	26.7050i	−0.560383	+	0.970611i	0.437080	+	0.899423i	$0.356013\pi$
$757$	−15.4182	+	26.7050i	−0.560383	+	0.970611i	−0.997463	+	0.0711886i	$0.977321\pi$
$758$	−12.9006	−	22.3444i	−0.468569	−	0.811586i
$759$		0			0
$760$	21.0969	+	36.5409i	0.765265	+	1.32548i
$761$	−11.1652	−	19.3387i	−0.404738	−	0.701026i	0.589553	−	0.807729i	$-0.299304\pi$
$761$	−11.1652	−	19.3387i	−0.404738	−	0.701026i	−0.994291	+	0.106703i	$0.965970\pi$
$762$		0			0
$763$	1.95347	+	3.38352i	0.0707205	+	0.122492i
$764$	18.6452	−	32.2945i	0.674561	−	1.16837i
$765$		0			0
$766$	−21.1701			−0.764906
$767$	1.07128	−	2.01999i	0.0386817	−	0.0729376i
$768$		0			0
$769$	−9.22037	+	15.9701i	−0.332495	+	0.575898i	−0.983000	−	0.183603i	$-0.941224\pi$
$769$	−9.22037	+	15.9701i	−0.332495	+	0.575898i	0.650505	+	0.759502i	$0.274557\pi$
$770$	10.3992	−	18.0120i	0.374762	−	0.649107i
$771$		0			0
$772$	12.8621			0.462917
$773$	12.3449	+	21.3821i	0.444017	+	0.769060i	0.997983	−	0.0634792i	$-0.0202197\pi$
$773$	12.3449	+	21.3821i	0.444017	+	0.769060i	−0.553966	+	0.832539i	$0.686886\pi$
$774$		0			0
$775$	43.9188			1.57761
$776$	38.0746	+	65.9472i	1.36680	+	2.36737i
$777$		0			0
$778$	12.8845	−	22.3167i	0.461933	−	0.800091i
$779$	7.20159			0.258024
$780$		0			0
$781$	−15.9894			−0.572147
$782$	−8.80629	+	15.2529i	−0.314912	+	0.545444i
$783$		0			0
$784$	−8.44226	−	14.6224i	−0.301509	−	0.522230i
$785$	26.0732			0.930591
$786$		0			0
$787$	−13.6540	−	23.6494i	−0.486712	−	0.843010i	0.513171	−	0.858286i	$-0.328471\pi$
$787$	−13.6540	−	23.6494i	−0.486712	−	0.843010i	−0.999883	+	0.0152762i	$0.995137\pi$
$788$	−103.254			−3.67826
$789$		0			0
$790$	58.6413	−	101.570i	2.08636	−	3.61369i
$791$	−5.30334	+	9.18566i	−0.188565	+	0.326604i
$792$		0			0
$793$	21.3792	−	40.3123i	0.759199	−	1.43153i
$794$	33.6040			1.19256
$795$		0			0
$796$	−7.44226	+	12.8904i	−0.263784	+	0.456887i
$797$	−15.9411	−	27.6108i	−0.564662	−	0.978024i	−0.997081	−	0.0763511i	$-0.975673\pi$
$797$	−15.9411	−	27.6108i	−0.564662	−	0.978024i	0.432419	−	0.901673i	$-0.357660\pi$
$798$		0			0
$799$	−0.660955	−	1.14481i	−0.0233829	−	0.0405004i
$800$	67.9829	+	117.750i	2.40356	+	4.16309i
$801$		0			0
$802$	50.6466	+	87.7225i	1.78839	+	3.09759i
$803$	−12.6456	+	21.9028i	−0.446254	+	0.772935i
$804$		0			0
$805$	−7.30798			−0.257572
$806$	−85.1495	+	3.06457i	−2.99926	+	0.107945i
$807$		0			0
$808$	−31.4723	+	54.5116i	−1.10719	+	1.91771i
$809$	23.3573	−	40.4560i	0.821197	−	1.42236i	−0.0835935	−	0.996500i	$-0.526640\pi$
$809$	23.3573	−	40.4560i	0.821197	−	1.42236i	0.904791	−	0.425856i	$-0.140027\pi$
$810$		0			0
$811$	−7.79148			−0.273596			−0.136798	−	0.990599i	$-0.543681\pi$
$811$	−7.79148			−0.273596			−0.136798	+	0.990599i	$0.543681\pi$
$812$	26.5788	+	46.0359i	0.932735	+	1.61554i
$813$		0			0
$814$	−21.0791			−0.738823
$815$	10.6020	+	18.3633i	0.371373	+	0.643237i
$816$		0			0
$817$	0.245995	−	0.426076i	0.00860627	−	0.0149065i
$818$	−15.5379			−0.543271
$819$		0			0
$820$	100.250			3.50090
$821$	−15.2566	+	26.4251i	−0.532458	+	0.922244i	0.466824	+	0.884350i	$0.345398\pi$
$821$	−15.2566	+	26.4251i	−0.532458	+	0.922244i	−0.999282	+	0.0378937i	$0.987935\pi$
$822$		0			0
$823$	5.45515	+	9.44860i	0.190155	+	0.329358i	0.945301	−	0.326198i	$-0.105768\pi$
$823$	5.45515	+	9.44860i	0.190155	+	0.329358i	−0.755147	+	0.655556i	$0.772434\pi$
$824$	105.548			3.67693
$825$		0			0
$826$	−0.878603	−	1.52179i	−0.0305705	−	0.0529497i
$827$	−7.87436			−0.273818			−0.136909	−	0.990584i	$-0.543717\pi$
$827$	−7.87436			−0.273818			−0.136909	+	0.990584i	$0.543717\pi$
$828$		0			0
$829$	10.0343	−	17.3799i	0.348505	−	0.603628i	−0.637479	−	0.770467i	$-0.720023\pi$
$829$	10.0343	−	17.3799i	0.348505	−	0.603628i	0.985984	+	0.166840i	$0.0533562\pi$
$830$	−31.1977	+	54.0359i	−1.08289	+	1.87561i
$831$		0			0
$832$	−75.3900	−	120.363i	−2.61368	−	4.17283i
$833$	2.77094			0.0960073
$834$		0			0
$835$	−25.5108	+	44.1860i	−0.882838	+	1.52912i
$836$	−8.69202	−	15.0550i	−0.300620	−	0.520689i
$837$		0			0
$838$	21.5273	+	37.2864i	0.743648	+	1.28804i
$839$	−14.2385	−	24.6619i	−0.491569	−	0.851423i	0.508384	−	0.861131i	$-0.330243\pi$
$839$	−14.2385	−	24.6619i	−0.491569	−	0.851423i	−0.999953	+	0.00970783i	$0.996910\pi$
$840$		0			0
$841$	−29.3225	−	50.7881i	−1.01112	−	1.75132i
$842$	2.51599	−	4.35783i	0.0867068	−	0.150181i
$843$		0			0
$844$	−30.2183			−1.04016
$845$	−18.0761	+	37.2634i	−0.621837	+	1.28190i
$846$		0			0
$847$	2.72462	−	4.71917i	0.0936189	−	0.162153i
$848$	−109.434	+	189.546i	−3.75799	+	6.50904i
$849$		0			0
$850$	−39.5402			−1.35622
$851$	3.70330	+	6.41430i	0.126947	+	0.219879i
$852$		0			0
$853$	−18.8930			−0.646885			−0.323442	−	0.946248i	$-0.604840\pi$
$853$	−18.8930			−0.646885			−0.323442	+	0.946248i	$0.604840\pi$
$854$	−17.5340	−	30.3698i	−0.600002	−	1.03923i
$855$		0			0
$856$	−50.1381	+	86.8418i	−1.71369	+	2.96819i
$857$	36.9470			1.26209			0.631043	−	0.775748i	$-0.282627\pi$
$857$	36.9470			1.26209			0.631043	+	0.775748i	$0.282627\pi$
$858$		0			0
$859$	−35.4268			−1.20875			−0.604374	−	0.796701i	$-0.706577\pi$
$859$	−35.4268			−1.20875			−0.604374	+	0.796701i	$0.706577\pi$
$860$	3.42440	−	5.93123i	0.116771	−	0.202253i
$861$		0			0
$862$	−22.2011	−	38.4535i	−0.756174	−	1.30973i
$863$	52.8763			1.79993			0.899966	−	0.435961i	$-0.143591\pi$
$863$	52.8763			1.79993			0.899966	+	0.435961i	$0.143591\pi$
$864$		0			0
$865$	−18.4679	−	31.9873i	−0.627927	−	1.08760i
$866$	9.14267			0.310681
$867$		0			0
$868$	−24.2124	+	41.9370i	−0.821821	+	1.42344i
$869$	−15.6504	+	27.1073i	−0.530904	+	0.919553i
$870$		0			0
$871$	50.1098	−	1.80348i	1.69791	−	0.0611084i
$872$	39.8187			1.34843
$873$		0			0
$874$	−4.12989	+	7.15317i	−0.139695	+	0.241960i
$875$	−0.238531	−	0.413148i	−0.00806383	−	0.0139670i
$876$		0			0
$877$	−2.01017	−	3.48171i	−0.0678786	−	0.117569i	0.830089	−	0.557631i	$-0.188290\pi$
$877$	−2.01017	−	3.48171i	−0.0678786	−	0.117569i	−0.897967	+	0.440062i	$0.854956\pi$
$878$	−13.5065	−	23.3940i	−0.455824	−	0.789510i
$879$		0			0
$880$	−63.3670	−	109.755i	−2.13610	−	3.69983i
$881$	3.21693	−	5.57189i	0.108381	−	0.187722i	−0.806733	−	0.590916i	$-0.798767\pi$
$881$	3.21693	−	5.57189i	0.108381	−	0.187722i	0.915115	+	0.403194i	$0.132100\pi$
$882$		0			0
$883$	−36.4835			−1.22777			−0.613884	−	0.789396i	$-0.710394\pi$
$883$	−36.4835			−1.22777			−0.613884	+	0.789396i	$0.710394\pi$
$884$	56.6917	−	2.04036i	1.90675	−	0.0686248i
$885$		0			0
$886$	−16.6375	+	28.8170i	−0.558947	+	0.968125i
$887$	25.3862	−	43.9702i	0.852385	−	1.47637i	−0.0266654	−	0.999644i	$-0.508489\pi$
$887$	25.3862	−	43.9702i	0.852385	−	1.47637i	0.879050	−	0.476729i	$-0.158178\pi$
$888$		0			0
$889$	12.4268			0.416782
$890$	−36.9663	−	64.0275i	−1.23911	−	2.14621i
$891$		0			0
$892$	107.629			3.60369
$893$	−0.309968	−	0.536881i	−0.0103727	−	0.0179660i
$894$		0			0
$895$	−10.0508	+	17.4084i	−0.335960	+	0.581900i
$896$	−56.3436			−1.88231
$897$		0			0
$898$	10.7830			0.359833
$899$	39.9207	−	69.1448i	1.33143	−	2.30611i
$900$		0			0
$901$	−17.9594	−	31.1066i	−0.598314	−	1.03631i
$902$	−36.1793			−1.20464
$903$		0			0
$904$	54.0504	+	93.6180i	1.79769	+	3.11369i
$905$	−49.6248			−1.64958
$906$		0			0
$907$	23.6263	−	40.9219i	0.784498	−	1.35879i	−0.144801	−	0.989461i	$-0.546254\pi$
$907$	23.6263	−	40.9219i	0.784498	−	1.35879i	0.929299	−	0.369329i	$-0.120412\pi$
$908$	8.77522	−	15.1991i	0.291216	−	0.504401i
$909$		0			0
$910$	16.8957	+	26.9747i	0.560088	+	0.894201i
$911$	−33.4705			−1.10893			−0.554463	−	0.832208i	$-0.687076\pi$
$911$	−33.4705			−1.10893			−0.554463	+	0.832208i	$0.687076\pi$
$912$		0			0
$913$	8.32615	−	14.4213i	0.275556	−	0.477276i
$914$	11.1934	+	19.3875i	0.370243	+	0.641280i
$915$		0			0
$916$	−18.5102	−	32.0606i	−0.611593	−	1.05931i
$917$	9.90574	+	17.1573i	0.327116	+	0.566582i
$918$		0			0
$919$	19.2054	+	33.2647i	0.633527	+	1.09730i	0.986825	+	0.161791i	$0.0517270\pi$
$919$	19.2054	+	33.2647i	0.633527	+	1.09730i	−0.353298	+	0.935511i	$0.614940\pi$
$920$	−37.2406	+	64.5025i	−1.22778	+	2.12659i
$921$		0			0
$922$	63.9616			2.10646
$923$	11.4647	−	21.6177i	0.377366	−	0.711555i
$924$		0			0
$925$	−8.31390	+	14.4001i	−0.273359	+	0.473472i
$926$	6.28564	−	10.8871i	0.206559	−	0.357771i
$927$		0			0
$928$	247.177			8.11398
$929$	−13.0131	−	22.5393i	−0.426945	−	0.739490i	0.569655	−	0.821884i	$-0.307077\pi$
$929$	−13.0131	−	22.5393i	−0.426945	−	0.739490i	−0.996600	+	0.0823939i	$0.973743\pi$
$930$		0			0
$931$	1.29949			0.0425890
$932$	11.6440	+	20.1680i	0.381412	+	0.660625i
$933$		0			0
$934$	40.9482	−	70.9243i	1.33987	−	2.32072i
$935$	20.7984			0.680182
$936$		0			0
$937$	51.4247			1.67997			0.839986	−	0.542608i	$-0.182563\pi$
$937$	51.4247			1.67997			0.839986	+	0.542608i	$0.182563\pi$
$938$	19.2676	−	33.3725i	0.629111	−	1.08965i
$939$		0			0
$940$	−4.31494	−	7.47370i	−0.140738	−	0.243765i
$941$	−24.7134			−0.805635			−0.402817	−	0.915280i	$-0.631969\pi$
$941$	−24.7134			−0.805635			−0.402817	+	0.915280i	$0.631969\pi$
$942$		0			0
$943$	6.35618	+	11.0092i	0.206986	+	0.358510i
$944$	−10.7074			−0.348497
$945$		0			0
$946$	−1.23583	+	2.14051i	−0.0401802	+	0.0695941i
$947$	2.37531	−	4.11416i	0.0771873	−	0.133692i	−0.824848	−	0.565354i	$-0.808739\pi$
$947$	2.37531	−	4.11416i	0.0771873	−	0.133692i	0.902035	+	0.431662i	$0.142073\pi$
$948$		0			0
$949$	−20.5455	−	32.8016i	−0.666935	−	1.06479i
$950$	−18.5432			−0.601620
$951$		0			0
$952$	14.1204	−	24.4572i	0.457643	−	0.792661i
$953$	5.68255	+	9.84247i	0.184076	+	0.318829i	0.943265	−	0.332042i	$-0.107737\pi$
$953$	5.68255	+	9.84247i	0.184076	+	0.318829i	−0.759189	+	0.650870i	$0.774404\pi$
$954$		0			0
$955$	10.4615	+	18.1198i	0.338526	+	0.586344i
$956$	15.3808	+	26.6404i	0.497452	+	0.861612i
$957$		0			0
$958$	−28.4455	−	49.2690i	−0.919031	−	1.59181i
$959$	−6.89628	+	11.9447i	−0.222692	+	0.385714i
$960$		0			0
$961$	41.7327			1.34622
$962$	15.1141	−	28.4989i	0.487299	−	0.918843i
$963$		0			0
$964$	−71.3376	+	123.560i	−2.29763	+	3.97961i
$965$	−3.60834	+	6.24983i	−0.116157	+	0.201189i
$966$		0			0
$967$	27.5711			0.886627			0.443314	−	0.896367i	$-0.353803\pi$
$967$	27.5711			0.886627			0.443314	+	0.896367i	$0.353803\pi$
$968$	−27.7686	−	48.0966i	−0.892517	−	1.54588i
$969$		0			0
$970$	−65.9585			−2.11780
$971$	27.0841	+	46.9110i	0.869170	+	1.50545i	0.862847	+	0.505466i	$0.168679\pi$
$971$	27.0841	+	46.9110i	0.869170	+	1.50545i	0.00632291	+	0.999980i	$0.497987\pi$
$972$		0			0
$973$	4.78131	−	8.28147i	0.153282	−	0.265492i
$974$	59.7486			1.91447
$975$		0			0
$976$	−213.685			−6.83989
$977$	−3.28372	+	5.68757i	−0.105055	+	0.181961i	−0.913761	−	0.406253i	$-0.866835\pi$
$977$	−3.28372	+	5.68757i	−0.105055	+	0.181961i	0.808705	+	0.588214i	$0.200169\pi$
$978$		0			0
$979$	9.86571	+	17.0879i	0.315310	+	0.546132i
$980$	18.0896			0.577852
$981$		0			0
$982$	−12.3631	−	21.4136i	−0.394524	−	0.683335i
$983$	−23.7323			−0.756941			−0.378471	−	0.925613i	$-0.623550\pi$
$983$	−23.7323			−0.756941			−0.378471	+	0.925613i	$0.623550\pi$
$984$		0			0
$985$	28.9668	−	50.1720i	0.922960	−	1.59861i
$986$	−35.9407	+	62.2512i	−1.14459	+	1.98248i
$987$		0			0
$988$	26.5867	−	0.956869i	0.845836	−	0.0304421i
$989$	0.868468			0.0276157
$990$		0			0
$991$	22.6883	−	39.2972i	0.720716	−	1.24832i	−0.239997	−	0.970774i	$-0.577146\pi$
$991$	22.6883	−	39.2972i	0.720716	−	1.24832i	0.960713	−	0.277544i	$-0.0895203\pi$
$992$	112.585	+	195.002i	3.57456	+	6.19133i
$993$		0			0
$994$	−9.40271	−	16.2860i	−0.298236	−	0.516559i
$995$	−4.17571	−	7.23254i	−0.132379	−	0.229287i
$996$		0			0
$997$	−17.7830	−	30.8010i	−0.563193	−	0.975479i	−0.997215	−	0.0745766i	$-0.976239\pi$
$997$	−17.7830	−	30.8010i	−0.563193	−	0.975479i	0.434022	−	0.900902i	$-0.357094\pi$
$998$	−48.4574	+	83.9307i	−1.53389	+	2.65678i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.o.i.568.6	yes	12
3.2	odd	2	inner	819.2.o.i.568.1	✓	12
13.3	even	3	inner	819.2.o.i.757.6	yes	12
39.29	odd	6	inner	819.2.o.i.757.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.o.i.568.1	✓	12	3.2	odd	2	inner
819.2.o.i.568.6	yes	12	1.1	even	1	trivial
819.2.o.i.757.1	yes	12	39.29	odd	6	inner
819.2.o.i.757.6	yes	12	13.3	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.38547 - 2.39970i) q^{2} +(-2.83905 - 4.91737i) q^{4} +3.18587 q^{5} +(-0.500000 - 0.866025i) q^{7} -10.1918 q^{8} +(4.41392 - 7.64513i) q^{10} +(-1.17800 + 2.04036i) q^{11} +(-1.91392 - 3.05564i) q^{13} -2.77094 q^{14} +(-8.44226 + 14.6224i) q^{16} +(-1.38547 - 2.39970i) q^{17} +(-0.649743 - 1.12539i) q^{19} +(-9.04482 - 15.6661i) q^{20} +(3.26417 + 5.65371i) q^{22} +(1.14694 - 1.98655i) q^{23} +5.14974 q^{25} +(-9.98429 + 0.359340i) q^{26} +(-2.83905 + 4.91737i) q^{28} +(4.68095 - 8.10764i) q^{29} +8.52835 q^{31} +(13.2012 + 22.8652i) q^{32} -7.67809 q^{34} +(-1.59293 - 2.75904i) q^{35} +(-1.61443 + 2.79627i) q^{37} -3.60080 q^{38} -32.4696 q^{40} +(-2.77094 + 4.79940i) q^{41} +(0.189302 + 0.327880i) q^{43} +13.3776 q^{44} +(-3.17809 - 5.50461i) q^{46} +0.477062 q^{47} +(-0.500000 + 0.866025i) q^{49} +(7.13481 - 12.3578i) q^{50} +(-9.59201 + 18.0865i) q^{52} +12.9627 q^{53} +(-3.75296 + 6.50032i) q^{55} +(5.09588 + 8.82632i) q^{56} +(-12.9706 - 22.4658i) q^{58} +(0.317078 + 0.549195i) q^{59} +(6.32783 + 10.9601i) q^{61} +(11.8158 - 20.4655i) q^{62} +39.3905 q^{64} +(-6.09748 - 9.73485i) q^{65} +(-6.95347 + 12.0438i) q^{67} +(-7.86681 + 13.6257i) q^{68} -8.82783 q^{70} +(3.39333 + 5.87742i) q^{71} +10.7348 q^{73} +(4.47348 + 7.74830i) q^{74} +(-3.68930 + 6.39006i) q^{76} +2.35601 q^{77} +13.2856 q^{79} +(-26.8959 + 46.5851i) q^{80} +(7.67809 + 13.2988i) q^{82} -7.06802 q^{83} +(-4.41392 - 7.64513i) q^{85} +1.04909 q^{86} +(12.0059 - 20.7949i) q^{88} +(4.18747 - 7.25291i) q^{89} +(-1.68930 + 3.18532i) q^{91} -13.0248 q^{92} +(0.660955 - 1.14481i) q^{94} +(-2.07000 - 3.58534i) q^{95} +(-3.73583 - 6.47064i) q^{97} +(1.38547 + 2.39970i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4} - 6 q^{7} + 22 q^{10} + 8 q^{13} - 28 q^{16} + 2 q^{19} + 18 q^{22} + 52 q^{25} - 8 q^{28} + 60 q^{31} - 40 q^{34} - 8 q^{37} - 116 q^{40} - 14 q^{43} + 14 q^{46} - 6 q^{49} - 32 q^{52} + 12 q^{55}+ \cdots - 66 q^{97}+O(q^{100}) \) 12 * q - 8 * q^4 - 6 * q^7 + 22 * q^10 + 8 * q^13 - 28 * q^16 + 2 * q^19 + 18 * q^22 + 52 * q^25 - 8 * q^28 + 60 * q^31 - 40 * q^34 - 8 * q^37 - 116 * q^40 - 14 * q^43 + 14 * q^46 - 6 * q^49 - 32 * q^52 + 12 * q^55 - 40 * q^58 + 14 * q^61 + 212 * q^64 - 46 * q^67 - 44 * q^70 - 8 * q^73 - 28 * q^76 + 52 * q^79 + 40 * q^82 - 22 * q^85 + 30 * q^88 - 4 * q^91 + 34 * q^94 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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