LMFDB - Embedded newform 2100.2.bo.g.1949.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1349,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

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

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

chi := DirichletCharacter("2100.1349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.bo (of order $6$, degree $2$, not 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:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{18} - 16 x^{16} + 87 x^{14} + 91 x^{12} - 1104 x^{10} + 819 x^{8} + 7047 x^{6} + \cdots + 59049 $ x^20 - 3x^18 - 16x^16 + 87x^14 + 91x^12 - 1104x^10 + 819x^8 + 7047x^6 - 11664x^4 - 19683*x^2 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1949.2
Root			$1.56233 + 0.747749i$ of defining polynomial
Character	$\chi$	$=$	2100.1949
Dual form			2100.2.bo.g.1349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.42873 - 0.979142i) q^{3} +(2.60608 - 0.456468i) q^{7} +(1.08256 + 2.79787i) q^{9} +O(q^{10})$	\(q+(-1.42873 - 0.979142i) q^{3} +(2.60608 - 0.456468i) q^{7} +(1.08256 + 2.79787i) q^{9} +(0.698384 + 0.403212i) q^{11} -3.86649 q^{13} +(-1.83578 - 1.05989i) q^{17} +(-2.70603 + 1.56233i) q^{19} +(-4.17034 - 1.89955i) q^{21} +(-2.43635 - 4.21989i) q^{23} +(1.19282 - 5.05739i) q^{27} -6.67701i q^{29} +(5.65010 + 3.26209i) q^{31} +(-0.603003 - 1.25990i) q^{33} +(6.75485 - 3.89991i) q^{37} +(5.52419 + 3.78585i) q^{39} -8.44841 q^{41} +0.819076i q^{43} +(-2.40368 + 1.38776i) q^{47} +(6.58327 - 2.37918i) q^{49} +(1.58506 + 3.31179i) q^{51} +(6.67216 - 11.5565i) q^{53} +(5.39594 + 0.417438i) q^{57} +(-2.86351 + 4.95974i) q^{59} +(1.79397 - 1.03575i) q^{61} +(4.09838 + 6.79730i) q^{63} +(-9.44157 - 5.45110i) q^{67} +(-0.650969 + 8.41464i) q^{69} +10.3850i q^{71} +(1.54270 - 2.67203i) q^{73} +(2.00410 + 0.732012i) q^{77} +(-6.76342 - 11.7146i) q^{79} +(-6.65612 + 6.05773i) q^{81} -12.8948i q^{83} +(-6.53775 + 9.53968i) q^{87} +(1.60530 + 2.78046i) q^{89} +(-10.0764 + 1.76493i) q^{91} +(-4.87844 - 10.1929i) q^{93} -1.01388 q^{97} +(-0.372090 + 2.39049i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{9}+O(q^{10}) $ 20 * q - 6 * q^9	$ 20 q - 6 q^{9} + 12 q^{11} - 6 q^{19} + 24 q^{21} + 30 q^{31} + 42 q^{39} + 16 q^{41} + 26 q^{49} + 80 q^{51} + 84 q^{61} - 28 q^{69} - 2 q^{79} - 26 q^{81} + 56 q^{89} - 22 q^{91} - 72 q^{99}+O(q^{100}) $ 20 * q - 6 * q^9 + 12 * q^11 - 6 * q^19 + 24 * q^21 + 30 * q^31 + 42 * q^39 + 16 * q^41 + 26 * q^49 + 80 * q^51 + 84 * q^61 - 28 * q^69 - 2 * q^79 - 26 * q^81 + 56 * q^89 - 22 * q^91 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.42873	−	0.979142i	−0.824880	−	0.565308i
$3$	−1.42873	−	0.979142i	−0.824880	−	0.565308i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.60608	−	0.456468i	0.985004	−	0.172529i
$7$	2.60608	−	0.456468i	0.985004	−	0.172529i
$8$		0			0
$9$	1.08256	+	2.79787i	0.360854	+	0.932622i
$10$		0			0
$11$	0.698384	+	0.403212i	0.210571	+	0.121573i	0.601577	−	0.798815i	$-0.294539\pi$
$11$	0.698384	+	0.403212i	0.210571	+	0.121573i	−0.391006	+	0.920388i	$0.627873\pi$
$12$		0			0
$13$	−3.86649			−1.07237			−0.536186	−	0.844100i	$-0.680136\pi$
$13$	−3.86649			−1.07237			−0.536186	+	0.844100i	$0.680136\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.83578	−	1.05989i	−0.445242	−	0.257061i	0.260577	−	0.965453i	$-0.416087\pi$
$17$	−1.83578	−	1.05989i	−0.445242	−	0.257061i	−0.705819	+	0.708393i	$0.749421\pi$
$18$		0			0
$19$	−2.70603	+	1.56233i	−0.620807	+	0.358423i	−0.777183	−	0.629275i	$-0.783352\pi$
$19$	−2.70603	+	1.56233i	−0.620807	+	0.358423i	0.156376	+	0.987698i	$0.450019\pi$
$20$		0			0
$21$	−4.17034	−	1.89955i	−0.910042	−	0.414515i
$22$		0			0
$23$	−2.43635	−	4.21989i	−0.508015	−	0.879908i	−0.999957	−	0.00927994i	$-0.997046\pi$
$23$	−2.43635	−	4.21989i	−0.508015	−	0.879908i	0.491942	−	0.870628i	$-0.336287\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	1.19282	−	5.05739i	0.229558	−	0.973295i
$28$		0			0
$29$		−	6.67701i		−	1.23989i	−0.784645	−	0.619945i	$-0.787155\pi$
$29$		−	6.67701i		−	1.23989i	0.784645	−	0.619945i	$-0.212845\pi$
$30$		0			0
$31$	5.65010	+	3.26209i	1.01479	+	0.585888i	0.912590	−	0.408876i	$-0.134079\pi$
$31$	5.65010	+	3.26209i	1.01479	+	0.585888i	0.102198	+	0.994764i	$0.467413\pi$
$32$		0			0
$33$	−0.603003	−	1.25990i	−0.104969	−	0.219320i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.75485	−	3.89991i	1.11049	−	0.641142i	0.171534	−	0.985178i	$-0.445128\pi$
$37$	6.75485	−	3.89991i	1.11049	−	0.641142i	0.938956	+	0.344036i	$0.111794\pi$
$38$		0			0
$39$	5.52419	+	3.78585i	0.884579	+	0.606221i
$40$		0			0
$41$	−8.44841			−1.31942			−0.659710	−	0.751520i	$-0.729321\pi$
$41$	−8.44841			−1.31942			−0.659710	+	0.751520i	$0.729321\pi$
$42$		0			0
$43$			0.819076i			0.124908i	0.998048	+	0.0624540i	$0.0198927\pi$
$43$			0.819076i			0.124908i	−0.998048	+	0.0624540i	$0.980107\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.40368	+	1.38776i	−0.350612	+	0.202426i	−0.664955	−	0.746883i	$-0.731549\pi$
$47$	−2.40368	+	1.38776i	−0.350612	+	0.202426i	0.314343	+	0.949310i	$0.398216\pi$
$48$		0			0
$49$	6.58327	−	2.37918i	0.940468	−	0.339883i
$50$		0			0
$51$	1.58506	+	3.31179i	0.221953	+	0.463743i
$52$		0			0
$53$	6.67216	−	11.5565i	0.916492	−	1.58741i	0.111789	−	0.993732i	$-0.464342\pi$
$53$	6.67216	−	11.5565i	0.916492	−	1.58741i	0.804703	−	0.593678i	$-0.202325\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	5.39594	+	0.417438i	0.714710	+	0.0552910i
$58$		0			0
$59$	−2.86351	+	4.95974i	−0.372797	+	0.645703i	−0.989995	−	0.141105i	$-0.954935\pi$
$59$	−2.86351	+	4.95974i	−0.372797	+	0.645703i	0.617198	+	0.786808i	$0.288268\pi$
$60$		0			0
$61$	1.79397	−	1.03575i	0.229694	−	0.132614i	−0.380737	−	0.924683i	$-0.624330\pi$
$61$	1.79397	−	1.03575i	0.229694	−	0.132614i	0.610431	+	0.792070i	$0.290996\pi$
$62$		0			0
$63$	4.09838	+	6.79730i	0.516347	+	0.856380i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−9.44157	−	5.45110i	−1.15347	−	0.665957i	−0.203741	−	0.979025i	$-0.565310\pi$
$67$	−9.44157	−	5.45110i	−1.15347	−	0.665957i	−0.949731	+	0.313067i	$0.898643\pi$
$68$		0			0
$69$	−0.650969	+	8.41464i	−0.0783674	+	1.01300i
$70$		0			0
$71$			10.3850i			1.23248i	0.787559	+	0.616239i	$0.211344\pi$
$71$			10.3850i			1.23248i	−0.787559	+	0.616239i	$0.788656\pi$
$72$		0			0
$73$	1.54270	−	2.67203i	0.180559	−	0.312737i	−0.761512	−	0.648151i	$-0.775543\pi$
$73$	1.54270	−	2.67203i	0.180559	−	0.312737i	0.942071	+	0.335413i	$0.108876\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.00410	+	0.732012i	0.228388	+	0.0834205i
$78$		0			0
$79$	−6.76342	−	11.7146i	−0.760944	−	1.31799i	−0.942364	−	0.334589i	$-0.891403\pi$
$79$	−6.76342	−	11.7146i	−0.760944	−	1.31799i	0.181420	−	0.983406i	$-0.441931\pi$
$80$		0			0
$81$	−6.65612	+	6.05773i	−0.739569	+	0.673081i
$82$		0			0
$83$		−	12.8948i		−	1.41539i	−0.706519	−	0.707694i	$-0.749735\pi$
$83$		−	12.8948i		−	1.41539i	0.706519	−	0.707694i	$-0.250265\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−6.53775	+	9.53968i	−0.700920	+	1.02276i
$88$		0			0
$89$	1.60530	+	2.78046i	0.170161	+	0.294728i	0.938476	−	0.345344i	$-0.112238\pi$
$89$	1.60530	+	2.78046i	0.170161	+	0.294728i	−0.768315	+	0.640072i	$0.778904\pi$
$90$		0			0
$91$	−10.0764	+	1.76493i	−1.05629	+	0.185015i
$92$		0			0
$93$	−4.87844	−	10.1929i	−0.505871	−	1.05695i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.01388			−0.102944			−0.0514721	−	0.998674i	$-0.516391\pi$
$97$	−1.01388			−0.102944			−0.0514721	+	0.998674i	$0.516391\pi$
$98$		0			0
$99$	−0.372090	+	2.39049i	−0.0373965	+	0.240253i
$100$		0			0
$101$	−4.27796	+	7.40965i	−0.425673	+	0.737288i	−0.996483	−	0.0837947i	$-0.973296\pi$
$101$	−4.27796	+	7.40965i	−0.425673	+	0.737288i	0.570810	+	0.821082i	$0.306629\pi$
$102$		0			0
$103$	−4.88921	−	8.46835i	−0.481748	−	0.834411i	0.518033	−	0.855361i	$-0.326664\pi$
$103$	−4.88921	−	8.46835i	−0.481748	−	0.834411i	−0.999781	+	0.0209492i	$0.993331\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.14150	−	15.8336i	−0.883743	−	1.53069i	−0.847148	−	0.531357i	$-0.821682\pi$
$107$	−9.14150	−	15.8336i	−0.883743	−	1.53069i	−0.0365946	−	0.999330i	$-0.511651\pi$
$108$		0			0
$109$	8.74840	−	15.1527i	0.837945	−	1.45136i	−0.0536658	−	0.998559i	$-0.517091\pi$
$109$	8.74840	−	15.1527i	0.837945	−	1.45136i	0.891610	−	0.452804i	$-0.149576\pi$
$110$		0			0
$111$	−13.4695	−	1.04202i	−1.27846	−	0.0989039i
$112$		0			0
$113$	−6.96021			−0.654761			−0.327381	−	0.944893i	$-0.606166\pi$
$113$	−6.96021			−0.654761			−0.327381	+	0.944893i	$0.606166\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−4.18572	−	10.8179i	−0.386970	−	1.00012i
$118$		0			0
$119$	−5.26799	−	1.92417i	−0.482916	−	0.176389i
$120$		0			0
$121$	−5.17484	−	8.96309i	−0.470440	−	0.814826i
$122$		0			0
$123$	12.0705	+	8.27219i	1.08836	+	0.745879i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			7.77139i			0.689600i	0.938676	+	0.344800i	$0.112053\pi$
$127$			7.77139i			0.689600i	−0.938676	+	0.344800i	$0.887947\pi$
$128$		0			0
$129$	0.801992	−	1.17024i	0.0706114	−	0.103034i
$130$		0			0
$131$	−5.93761	−	10.2842i	−0.518772	−	0.898539i	−0.999762	−	0.0218131i	$-0.993056\pi$
$131$	−5.93761	−	10.2842i	−0.518772	−	0.898539i	0.480990	−	0.876726i	$-0.340277\pi$
$132$		0			0
$133$	−6.33898	+	5.30677i	−0.549659	+	0.460155i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.22915	−	2.12894i	0.105013	−	0.181888i	−0.808730	−	0.588179i	$-0.799845\pi$
$137$	1.22915	−	2.12894i	0.105013	−	0.181888i	0.913744	+	0.406291i	$0.133178\pi$
$138$		0			0
$139$			2.81335i			0.238625i	0.992857	+	0.119313i	$0.0380691\pi$
$139$			2.81335i			0.238625i	−0.992857	+	0.119313i	$0.961931\pi$
$140$		0			0
$141$	4.79303	+	0.370796i	0.403646	+	0.0312267i
$142$		0			0
$143$	−2.70030	−	1.55902i	−0.225810	−	0.130372i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−11.7353	−	3.04674i	−0.967912	−	0.251291i
$148$		0			0
$149$	12.8234	−	7.40357i	1.05053	−	0.606524i	0.127733	−	0.991809i	$-0.459230\pi$
$149$	12.8234	−	7.40357i	1.05053	−	0.606524i	0.922798	+	0.385285i	$0.125897\pi$
$150$		0			0
$151$	0.427898	−	0.741141i	0.0348218	−	0.0603132i	−0.848089	−	0.529853i	$-0.822247\pi$
$151$	0.427898	−	0.741141i	0.0348218	−	0.0603132i	0.882911	+	0.469540i	$0.155580\pi$
$152$		0			0
$153$	0.978080	−	6.28366i	0.0790731	−	0.508004i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−12.1845	+	21.1042i	−0.972428	+	1.68430i	−0.284256	+	0.958748i	$0.591746\pi$
$157$	−12.1845	+	21.1042i	−0.972428	+	1.68430i	−0.688173	+	0.725547i	$0.741587\pi$
$158$		0			0
$159$	−20.8482	+	9.97820i	−1.65337	+	0.791323i
$160$		0			0
$161$	−8.27557	−	9.88524i	−0.652207	−	0.779066i
$162$		0			0
$163$	−1.36728	+	0.789402i	−0.107094	+	0.0618307i	−0.552590	−	0.833453i	$-0.686361\pi$
$163$	−1.36728	+	0.789402i	−0.107094	+	0.0618307i	0.445496	+	0.895284i	$0.353027\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			16.9264i			1.30980i	0.755714	+	0.654902i	$0.227290\pi$
$167$			16.9264i			1.30980i	−0.755714	+	0.654902i	$0.772710\pi$
$168$		0			0
$169$	1.94978			0.149983
$170$		0			0
$171$	−7.30064	−	5.87980i	−0.558294	−	0.449640i
$172$		0			0
$173$	−4.03633	+	2.33037i	−0.306876	+	0.177175i	−0.645528	−	0.763737i	$-0.723363\pi$
$173$	−4.03633	+	2.33037i	−0.306876	+	0.177175i	0.338652	+	0.940912i	$0.390029\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	8.94748	−	4.28237i	0.672534	−	0.321883i
$178$		0			0
$179$	−3.11674	−	1.79945i	−0.232956	−	0.134497i	0.378979	−	0.925405i	$-0.376275\pi$
$179$	−3.11674	−	1.79945i	−0.232956	−	0.134497i	−0.611935	+	0.790908i	$0.709609\pi$
$180$		0			0
$181$		−	22.5821i		−	1.67851i	−0.543737	−	0.839256i	$-0.682991\pi$
$181$		−	22.5821i		−	1.67851i	0.543737	−	0.839256i	$-0.317009\pi$
$182$		0			0
$183$	−3.57725	−	0.276741i	−0.264438	−	0.0204573i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.854719	−	1.48042i	−0.0625033	−	0.108259i
$188$		0			0
$189$	0.800034	−	13.7244i	0.0581939	−	0.998305i
$190$		0			0
$191$	−2.92355	+	1.68791i	−0.211541	+	0.122133i	−0.602027	−	0.798475i	$-0.705640\pi$
$191$	−2.92355	+	1.68791i	−0.211541	+	0.122133i	0.390486	+	0.920609i	$0.372307\pi$
$192$		0			0
$193$	−9.60463	−	5.54524i	−0.691357	−	0.399155i	0.112763	−	0.993622i	$-0.464030\pi$
$193$	−9.60463	−	5.54524i	−0.691357	−	0.399155i	−0.804120	+	0.594467i	$0.797363\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	16.2585			1.15837			0.579184	−	0.815197i	$-0.303371\pi$
$197$	16.2585			1.15837			0.579184	+	0.815197i	$0.303371\pi$
$198$		0			0
$199$	1.07964	+	0.623332i	0.0765338	+	0.0441868i	0.537779	−	0.843086i	$-0.319264\pi$
$199$	1.07964	+	0.623332i	0.0765338	+	0.0441868i	−0.461245	+	0.887273i	$0.652597\pi$
$200$		0			0
$201$	8.15210	+	17.0328i	0.575005	+	1.20140i
$202$		0			0
$203$	−3.04784	−	17.4008i	−0.213917	−	1.22130i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	9.16919	−	11.3849i	0.637303	−	0.791305i
$208$		0			0
$209$	−2.51980			−0.174298
$210$		0			0
$211$	−7.65466			−0.526968			−0.263484	−	0.964664i	$-0.584872\pi$
$211$	−7.65466			−0.526968			−0.263484	+	0.964664i	$0.584872\pi$
$212$		0			0
$213$	10.1684	−	14.8375i	0.696730	−	1.01665i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	16.2136	+	5.92216i	1.10065	+	0.402022i
$218$		0			0
$219$	−4.82040	+	2.30710i	−0.325732	+	0.155899i
$220$		0			0
$221$	7.09803	+	4.09805i	0.477465	+	0.275665i
$222$		0			0
$223$	−20.9369			−1.40204			−0.701019	−	0.713143i	$-0.747271\pi$
$223$	−20.9369			−1.40204			−0.701019	+	0.713143i	$0.747271\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.96818	−	2.29103i	−0.263377	−	0.152061i	0.362497	−	0.931985i	$-0.381924\pi$
$227$	−3.96818	−	2.29103i	−0.263377	−	0.152061i	−0.625874	+	0.779924i	$0.715258\pi$
$228$		0			0
$229$	−0.845272	+	0.488018i	−0.0558572	+	0.0322492i	−0.527669	−	0.849450i	$-0.676934\pi$
$229$	−0.845272	+	0.488018i	−0.0558572	+	0.0322492i	0.471811	+	0.881700i	$0.343600\pi$
$230$		0			0
$231$	−2.14658	−	3.00814i	−0.141234	−	0.197921i
$232$		0			0
$233$	9.95247	+	17.2382i	0.652008	+	1.12931i	0.982635	+	0.185550i	$0.0594065\pi$
$233$	9.95247	+	17.2382i	0.652008	+	1.12931i	−0.330627	+	0.943762i	$0.607260\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.80712	+	23.3594i	−0.117385	+	1.51736i
$238$		0			0
$239$			28.2703i			1.82865i	0.404977	+	0.914327i	$0.367279\pi$
$239$			28.2703i			1.82865i	−0.404977	+	0.914327i	$0.632721\pi$
$240$		0			0
$241$	11.0949	+	6.40567i	0.714688	+	0.412625i	0.812794	−	0.582551i	$-0.197945\pi$
$241$	11.0949	+	6.40567i	0.714688	+	0.412625i	−0.0981065	+	0.995176i	$0.531279\pi$
$242$		0			0
$243$	15.4412	−	2.13760i	0.990553	−	0.137127i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	10.4629	−	6.04074i	0.665736	−	0.384363i
$248$		0			0
$249$	−12.6258	+	18.4232i	−0.800130	+	1.16753i
$250$		0			0
$251$	−10.3349			−0.652335			−0.326167	−	0.945312i	$-0.605757\pi$
$251$	−10.3349			−0.652335			−0.326167	+	0.945312i	$0.605757\pi$
$252$		0			0
$253$		−	3.92947i		−	0.247044i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	26.4185	−	15.2527i	1.64794	−	0.951439i	0.670052	−	0.742315i	$-0.266272\pi$
$257$	26.4185	−	15.2527i	1.64794	−	0.951439i	0.977889	−	0.209124i	$-0.0670614\pi$
$258$		0			0
$259$	15.8235	−	13.2469i	0.983223	−	0.823119i
$260$		0			0
$261$	18.6814	−	7.22828i	1.15635	−	0.447419i
$262$		0			0
$263$	−10.3377	+	17.9054i	−0.637447	+	1.10409i	0.348543	+	0.937293i	$0.386676\pi$
$263$	−10.3377	+	17.9054i	−0.637447	+	1.10409i	−0.985991	+	0.166799i	$0.946657\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.428919	−	5.54435i	0.0262494	−	0.339309i
$268$		0			0
$269$	12.4095	−	21.4938i	0.756618	−	1.31050i	−0.187948	−	0.982179i	$-0.560184\pi$
$269$	12.4095	−	21.4938i	0.756618	−	1.31050i	0.944566	−	0.328322i	$-0.106483\pi$
$270$		0			0
$271$	18.8571	−	10.8871i	1.14548	−	0.661346i	0.197702	−	0.980262i	$-0.436652\pi$
$271$	18.8571	−	10.8871i	1.14548	−	0.661346i	0.947783	+	0.318916i	$0.103319\pi$
$272$		0			0
$273$	16.1246	+	7.34459i	0.975905	+	0.444515i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−13.1831	−	7.61126i	−0.792095	−	0.457316i	0.0486048	−	0.998818i	$-0.484523\pi$
$277$	−13.1831	−	7.61126i	−0.792095	−	0.457316i	−0.840699	+	0.541502i	$0.817856\pi$
$278$		0			0
$279$	−3.01030	+	19.3396i	−0.180222	+	1.15783i
$280$		0			0
$281$			17.9488i			1.07073i	0.844619	+	0.535367i	$0.179827\pi$
$281$			17.9488i			1.07073i	−0.844619	+	0.535367i	$0.820173\pi$
$282$		0			0
$283$	−13.4944	+	23.3730i	−0.802159	+	1.38938i	0.116033	+	0.993245i	$0.462982\pi$
$283$	−13.4944	+	23.3730i	−0.802159	+	1.38938i	−0.918192	+	0.396135i	$0.870351\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−22.0172	+	3.85643i	−1.29963	+	0.227638i
$288$		0			0
$289$	−6.25328	−	10.8310i	−0.367840	−	0.637117i
$290$		0			0
$291$	1.44857	+	0.992735i	0.0849166	+	0.0581951i
$292$		0			0
$293$			14.4450i			0.843887i	0.906622	+	0.421944i	$0.138652\pi$
$293$			14.4450i			0.843887i	−0.906622	+	0.421944i	$0.861348\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	2.87224	−	3.05104i	0.166665	−	0.177039i
$298$		0			0
$299$	9.42015	+	16.3162i	0.544782	+	0.943589i
$300$		0			0
$301$	0.373882	+	2.13457i	0.0215502	+	0.123035i
$302$		0			0
$303$	13.3672	−	6.39768i	0.767924	−	0.367537i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	9.34543			0.533372			0.266686	−	0.963783i	$-0.414071\pi$
$307$	9.34543			0.533372			0.266686	+	0.963783i	$0.414071\pi$
$308$		0			0
$309$	−1.30635	+	16.8862i	−0.0743154	+	0.960625i
$310$		0			0
$311$	14.6664	−	25.4029i	0.831654	−	1.44047i	−0.0650722	−	0.997881i	$-0.520728\pi$
$311$	14.6664	−	25.4029i	0.831654	−	1.44047i	0.896726	−	0.442586i	$-0.145939\pi$
$312$		0			0
$313$	−5.51790	−	9.55728i	−0.311890	−	0.540209i	0.666881	−	0.745164i	$-0.267629\pi$
$313$	−5.51790	−	9.55728i	−0.311890	−	0.540209i	−0.978772	+	0.204954i	$0.934295\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.48631	−	14.6987i	−0.476639	−	0.825563i	0.523003	−	0.852331i	$-0.324812\pi$
$317$	−8.48631	−	14.6987i	−0.476639	−	0.825563i	−0.999642	+	0.0267682i	$0.991478\pi$
$318$		0			0
$319$	2.69225	−	4.66312i	0.150737	−	0.261085i
$320$		0			0
$321$	−2.44252	+	31.5728i	−0.136328	+	1.76222i
$322$		0			0
$323$	6.62357			0.368546
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−27.3357	+	13.0832i	−1.51167	+	0.723503i
$328$		0			0
$329$	−5.63070	+	4.71382i	−0.310430	+	0.259881i
$330$		0			0
$331$	5.82739	+	10.0933i	0.320302	+	0.554780i	0.980550	−	0.196268i	$-0.0628822\pi$
$331$	5.82739	+	10.0933i	0.320302	+	0.554780i	−0.660248	+	0.751048i	$0.729549\pi$
$332$		0			0
$333$	18.2240	+	14.6773i	0.998668	+	0.804310i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			10.1753i			0.554286i	0.960829	+	0.277143i	$0.0893875\pi$
$337$			10.1753i			0.554286i	−0.960829	+	0.277143i	$0.910612\pi$
$338$		0			0
$339$	9.94428	+	6.81503i	0.540099	+	0.370142i
$340$		0			0
$341$	2.63063	+	4.55638i	0.142456	+	0.246742i
$342$		0			0
$343$	16.0705	−	9.20538i	0.867725	−	0.497044i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−0.796887	+	1.38025i	−0.0427791	+	0.0740956i	−0.886622	−	0.462494i	$-0.846955\pi$
$347$	−0.796887	+	1.38025i	−0.0427791	+	0.0740956i	0.843843	+	0.536590i	$0.180288\pi$
$348$		0			0
$349$		−	15.4812i		−	0.828690i	−0.910120	−	0.414345i	$-0.864011\pi$
$349$		−	15.4812i		−	0.828690i	0.910120	−	0.414345i	$-0.135989\pi$
$350$		0			0
$351$	−4.61202	+	19.5544i	−0.246171	+	1.04374i
$352$		0			0
$353$	11.0861	+	6.40056i	0.590054	+	0.340668i	0.765119	−	0.643889i	$-0.222680\pi$
$353$	11.0861	+	6.40056i	0.590054	+	0.340668i	−0.175065	+	0.984557i	$0.556014\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	5.64251	+	7.90724i	0.298633	+	0.418496i
$358$		0			0
$359$	−5.66697	+	3.27183i	−0.299091	+	0.172680i	−0.642035	−	0.766676i	$-0.721909\pi$
$359$	−5.66697	+	3.27183i	−0.299091	+	0.172680i	0.342943	+	0.939356i	$0.388576\pi$
$360$		0			0
$361$	−4.61826	+	7.99906i	−0.243066	+	0.421003i
$362$		0			0
$363$	−1.38266	+	17.8728i	−0.0725710	+	0.938077i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	8.66046	−	15.0004i	0.452072	−	0.783012i	−0.546442	−	0.837497i	$-0.684018\pi$
$367$	8.66046	−	15.0004i	0.452072	−	0.783012i	0.998515	+	0.0544847i	$0.0173516\pi$
$368$		0			0
$369$	−9.14593	−	23.6375i	−0.476118	−	1.23052i
$370$		0			0
$371$	12.1130	−	33.1628i	0.628875	−	1.72173i
$372$		0			0
$373$	0.862445	−	0.497933i	0.0446557	−	0.0257820i	−0.477506	−	0.878629i	$-0.658459\pi$
$373$	0.862445	−	0.497933i	0.0446557	−	0.0257820i	0.522162	+	0.852847i	$0.325126\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			25.8166i			1.32962i
$378$		0			0
$379$	20.2985			1.04266			0.521331	−	0.853355i	$-0.325436\pi$
$379$	20.2985			1.04266			0.521331	+	0.853355i	$0.325436\pi$
$380$		0			0
$381$	7.60930	−	11.1033i	0.389836	−	0.568837i
$382$		0			0
$383$	−17.2120	+	9.93736i	−0.879493	+	0.507776i	−0.870491	−	0.492184i	$-0.836199\pi$
$383$	−17.2120	+	9.93736i	−0.879493	+	0.507776i	−0.00900178	+	0.999959i	$0.502865\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.29167	+	0.886700i	−0.116492	+	0.0450735i
$388$		0			0
$389$	1.56923	+	0.905994i	0.0795630	+	0.0459357i	0.539254	−	0.842143i	$-0.318706\pi$
$389$	1.56923	+	0.905994i	0.0795630	+	0.0459357i	−0.459691	+	0.888079i	$0.652040\pi$
$390$		0			0
$391$			10.3291i			0.522363i
$392$		0			0
$393$	−1.58647	+	20.5072i	−0.0800268	+	1.03445i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−17.3967	−	30.1320i	−0.873116	−	1.51228i	−0.858757	−	0.512384i	$-0.828763\pi$
$397$	−17.3967	−	30.1320i	−0.873116	−	1.51228i	−0.0143590	−	0.999897i	$-0.504571\pi$
$398$		0			0
$399$	14.2528	−	1.37520i	0.713532	−	0.0688461i
$400$		0			0
$401$	32.5121	−	18.7709i	1.62358	−	0.937374i	0.637627	−	0.770345i	$-0.279916\pi$
$401$	32.5121	−	18.7709i	1.62358	−	0.937374i	0.985952	−	0.167029i	$-0.0534173\pi$
$402$		0			0
$403$	−21.8461	−	12.6128i	−1.08823	−	0.628290i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6.28997			0.311782
$408$		0			0
$409$	−3.24769	−	1.87505i	−0.160588	−	0.0927154i	0.417552	−	0.908653i	$-0.362888\pi$
$409$	−3.24769	−	1.87505i	−0.160588	−	0.0927154i	−0.578140	+	0.815937i	$0.696221\pi$
$410$		0			0
$411$	−3.84066	+	1.83819i	−0.189446	+	0.0906710i
$412$		0			0
$413$	−5.19856	+	14.2326i	−0.255804	+	0.700339i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	2.75467	−	4.01953i	0.134897	−	0.196837i
$418$		0			0
$419$	−30.0547			−1.46827			−0.734134	−	0.679005i	$-0.762411\pi$
$419$	−30.0547			−1.46827			−0.734134	+	0.679005i	$0.762411\pi$
$420$		0			0
$421$	20.5447			1.00129			0.500643	−	0.865654i	$-0.333097\pi$
$421$	20.5447			1.00129			0.500643	+	0.865654i	$0.333097\pi$
$422$		0			0
$423$	−6.48491	−	5.22283i	−0.315307	−	0.253943i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	4.20243	−	3.51813i	0.203370	−	0.170254i
$428$		0			0
$429$	2.33151	+	4.87140i	0.112566	+	0.235193i
$430$		0			0
$431$	31.7400	+	18.3251i	1.52886	+	0.882688i	0.999410	+	0.0343478i	$0.0109354\pi$
$431$	31.7400	+	18.3251i	1.52886	+	0.882688i	0.529451	+	0.848340i	$0.322398\pi$
$432$		0			0
$433$	36.4397			1.75118			0.875589	−	0.483057i	$-0.160474\pi$
$433$	36.4397			1.75118			0.875589	+	0.483057i	$0.160474\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	13.1857	+	7.61278i	0.630758	+	0.364168i
$438$		0			0
$439$	7.96135	−	4.59649i	0.379975	−	0.219378i	−0.297833	−	0.954618i	$-0.596264\pi$
$439$	7.96135	−	4.59649i	0.379975	−	0.219378i	0.677807	+	0.735240i	$0.262930\pi$
$440$		0			0
$441$	13.7834	+	15.8435i	0.656354	+	0.754453i
$442$		0			0
$443$	11.9703	+	20.7332i	0.568727	+	0.985063i	0.996692	+	0.0812683i	$0.0258971\pi$
$443$	11.9703	+	20.7332i	0.568727	+	0.985063i	−0.427966	+	0.903795i	$0.640770\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−25.5703	−	1.97816i	−1.20943	−	0.0935636i
$448$		0			0
$449$		−	24.0126i		−	1.13322i	−0.823985	−	0.566611i	$-0.808254\pi$
$449$		−	24.0126i		−	1.13322i	0.823985	−	0.566611i	$-0.191746\pi$
$450$		0			0
$451$	−5.90023	−	3.40650i	−0.277831	−	0.160406i
$452$		0			0
$453$	−1.33703	+	0.639920i	−0.0628193	+	0.0300661i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	5.77786	−	3.33585i	0.270277	−	0.156044i	−0.358737	−	0.933439i	$-0.616792\pi$
$457$	5.77786	−	3.33585i	0.270277	−	0.156044i	0.629013	+	0.777394i	$0.283459\pi$
$458$		0			0
$459$	−7.55001	+	8.02000i	−0.352404	+	0.374342i
$460$		0			0
$461$	−26.6895			−1.24305			−0.621527	−	0.783393i	$-0.713487\pi$
$461$	−26.6895			−1.24305			−0.621527	+	0.783393i	$0.713487\pi$
$462$		0			0
$463$		−	10.9550i		−	0.509123i	−0.967057	−	0.254562i	$-0.918069\pi$
$463$		−	10.9550i		−	0.509123i	0.967057	−	0.254562i	$-0.0819312\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.952153	−	0.549726i	0.0440604	−	0.0254383i	−0.477808	−	0.878464i	$-0.658569\pi$
$467$	0.952153	−	0.549726i	0.0440604	−	0.0254383i	0.521868	+	0.853026i	$0.325235\pi$
$468$		0			0
$469$	−27.0937	−	9.89620i	−1.25107	−	0.456964i
$470$		0			0
$471$	38.0724	−	18.2219i	1.75428	−	0.839620i
$472$		0			0
$473$	−0.330261	+	0.572029i	−0.0151854	+	0.0263019i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	39.5566	+	6.15717i	1.81117	+	0.281917i
$478$		0			0
$479$	6.91657	−	11.9798i	0.316026	−	0.547373i	−0.663629	−	0.748062i	$-0.730985\pi$
$479$	6.91657	−	11.9798i	0.316026	−	0.547373i	0.979655	+	0.200689i	$0.0643180\pi$
$480$		0			0
$481$	−26.1176	+	15.0790i	−1.19086	+	0.687543i
$482$		0			0
$483$	2.14454	+	22.2263i	0.0975799	+	1.01133i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	27.4385	+	15.8416i	1.24336	+	0.717854i	0.969776	−	0.243995i	$-0.0784581\pi$
$487$	27.4385	+	15.8416i	1.24336	+	0.717854i	0.273582	+	0.961849i	$0.411791\pi$
$488$		0			0
$489$	2.72642	+	0.210920i	0.123293	+	0.00953813i
$490$		0			0
$491$			37.3388i			1.68508i	0.538636	+	0.842538i	$0.318940\pi$
$491$			37.3388i			1.68508i	−0.538636	+	0.842538i	$0.681060\pi$
$492$		0			0
$493$	−7.07689	+	12.2575i	−0.318727	+	0.552051i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.74044	+	27.0642i	0.212638	+	1.21400i
$498$		0			0
$499$	−5.50065	−	9.52740i	−0.246243	−	0.426505i	0.716237	−	0.697857i	$-0.245863\pi$
$499$	−5.50065	−	9.52740i	−0.246243	−	0.426505i	−0.962480	+	0.271352i	$0.912529\pi$
$500$		0			0
$501$	16.5734	−	24.1833i	0.740443	−	1.08043i
$502$		0			0
$503$			20.2246i			0.901772i	0.892582	+	0.450886i	$0.148892\pi$
$503$			20.2246i			0.901772i	−0.892582	+	0.450886i	$0.851108\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−2.78572	−	1.90911i	−0.123718	−	0.0847867i
$508$		0			0
$509$	5.24557	+	9.08560i	0.232506	+	0.402712i	0.958545	−	0.284941i	$-0.0919742\pi$
$509$	5.24557	+	9.08560i	0.232506	+	0.402712i	−0.726039	+	0.687654i	$0.758641\pi$
$510$		0			0
$511$	2.80069	−	7.66771i	0.123895	−	0.339199i
$512$		0			0
$513$	4.67351	+	15.5490i	0.206340	+	0.686507i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−2.23825			−0.0984383
$518$		0			0
$519$	8.04860	+	0.622652i	0.353295	+	0.0273314i
$520$		0			0
$521$	6.00130	−	10.3946i	0.262922	−	0.455394i	−0.704095	−	0.710105i	$-0.748647\pi$
$521$	6.00130	−	10.3946i	0.262922	−	0.455394i	0.967017	+	0.254712i	$0.0819806\pi$
$522$		0			0
$523$	4.46891	+	7.74038i	0.195412	+	0.338463i	0.947035	−	0.321129i	$-0.104062\pi$
$523$	4.46891	+	7.74038i	0.195412	+	0.338463i	−0.751624	+	0.659592i	$0.770729\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.91489	−	11.9769i	−0.301217	−	0.521724i
$528$		0			0
$529$	−0.371651	+	0.643719i	−0.0161587	+	0.0279878i
$530$		0			0
$531$	−16.9766	−	2.64249i	−0.736723	−	0.114674i
$532$		0			0
$533$	32.6657			1.41491
$534$		0			0
$535$		0			0
$536$		0			0
$537$	2.69107	+	5.62266i	0.116128	+	0.242636i
$538$		0			0
$539$	5.55697	+	0.992874i	0.239356	+	0.0427661i
$540$		0			0
$541$	−15.9695	−	27.6599i	−0.686581	−	1.18919i	−0.972937	−	0.231069i	$-0.925778\pi$
$541$	−15.9695	−	27.6599i	−0.686581	−	1.18919i	0.286357	−	0.958123i	$-0.407556\pi$
$542$		0			0
$543$	−22.1110	+	32.2638i	−0.948876	+	1.38457i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	33.6313i		−	1.43797i	−0.695026	−	0.718984i	$-0.744607\pi$
$547$		−	33.6313i		−	1.43797i	0.695026	−	0.718984i	$-0.255393\pi$
$548$		0			0
$549$	4.83996	+	3.89802i	0.206565	+	0.166363i
$550$		0			0
$551$	10.4317	+	18.0682i	0.444405	+	0.769732i
$552$		0			0
$553$	−22.9733	−	27.4418i	−0.976926	−	1.16695i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−5.30000	+	9.17988i	−0.224568	+	0.388964i	−0.956190	−	0.292747i	$-0.905431\pi$
$557$	−5.30000	+	9.17988i	−0.224568	+	0.388964i	0.731621	+	0.681711i	$0.238764\pi$
$558$		0			0
$559$		−	3.16695i		−	0.133948i
$560$		0			0
$561$	−0.228372	+	2.95201i	−0.00964188	+	0.124634i
$562$		0			0
$563$	1.98833	+	1.14796i	0.0837980	+	0.0483808i	0.541313	−	0.840821i	$-0.317927\pi$
$563$	1.98833	+	1.14796i	0.0837980	+	0.0483808i	−0.457515	+	0.889202i	$0.651261\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−14.5812	+	18.8252i	−0.612353	+	0.790585i
$568$		0			0
$569$	24.1648	−	13.9515i	1.01304	−	0.584878i	0.100959	−	0.994891i	$-0.467809\pi$
$569$	24.1648	−	13.9515i	1.01304	−	0.584878i	0.912080	+	0.410012i	$0.134476\pi$
$570$		0			0
$571$	3.11649	−	5.39791i	0.130421	−	0.225896i	−0.793418	−	0.608677i	$-0.791700\pi$
$571$	3.11649	−	5.39791i	0.130421	−	0.225896i	0.923839	+	0.382782i	$0.125034\pi$
$572$		0			0
$573$	5.82969	+	0.450993i	0.243539	+	0.0188405i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−6.62662	+	11.4776i	−0.275870	+	0.477820i	−0.970354	−	0.241687i	$-0.922299\pi$
$577$	−6.62662	+	11.4776i	−0.275870	+	0.477820i	0.694484	+	0.719508i	$0.255632\pi$
$578$		0			0
$579$	8.29289	+	17.3270i	0.344641	+	0.720084i
$580$		0			0
$581$	−5.88606	−	33.6048i	−0.244195	−	1.39416i
$582$		0			0
$583$	9.31946	−	5.38059i	0.385973	−	0.222841i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			18.6209i			0.768568i	0.923215	+	0.384284i	$0.125552\pi$
$587$			18.6209i			0.768568i	−0.923215	+	0.384284i	$0.874448\pi$
$588$		0			0
$589$	−20.3858			−0.839982
$590$		0			0
$591$	−23.2290	−	15.9193i	−0.955514	−	0.654834i
$592$		0			0
$593$	−2.38715	+	1.37822i	−0.0980284	+	0.0565967i	−0.548213	−	0.836339i	$-0.684692\pi$
$593$	−2.38715	+	1.37822i	−0.0980284	+	0.0565967i	0.450184	+	0.892936i	$0.351358\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.932191	−	1.94770i	−0.0381520	−	0.0797140i
$598$		0			0
$599$	−16.2530	−	9.38368i	−0.664080	−	0.383407i	0.129750	−	0.991547i	$-0.458583\pi$
$599$	−16.2530	−	9.38368i	−0.664080	−	0.383407i	−0.793830	+	0.608140i	$0.791916\pi$
$600$		0			0
$601$		−	16.5669i		−	0.675779i	−0.941186	−	0.337890i	$-0.890287\pi$
$601$		−	16.5669i		−	0.675779i	0.941186	−	0.337890i	$-0.109713\pi$
$602$		0			0
$603$	5.03035	−	32.3174i	0.204852	−	1.31607i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	16.7301	+	28.9773i	0.679053	+	1.17615i	0.975266	+	0.221032i	$0.0709427\pi$
$607$	16.7301	+	28.9773i	0.679053	+	1.17615i	−0.296213	+	0.955122i	$0.595724\pi$
$608$		0			0
$609$	−12.6833	+	27.8454i	−0.513954	+	1.12835i
$610$		0			0
$611$	9.29381	−	5.36578i	0.375987	−	0.217076i
$612$		0			0
$613$	−32.5231	−	18.7772i	−1.31359	−	0.758404i	−0.330905	−	0.943664i	$-0.607354\pi$
$613$	−32.5231	−	18.7772i	−1.31359	−	0.758404i	−0.982690	+	0.185260i	$0.940687\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	22.5088			0.906172			0.453086	−	0.891467i	$-0.350323\pi$
$617$	22.5088			0.906172			0.453086	+	0.891467i	$0.350323\pi$
$618$		0			0
$619$	23.3812	+	13.4991i	0.939770	+	0.542576i	0.889888	−	0.456179i	$-0.150782\pi$
$619$	23.3812	+	13.4991i	0.939770	+	0.542576i	0.0498816	+	0.998755i	$0.484116\pi$
$620$		0			0
$621$	−24.2478	+	7.28804i	−0.973029	+	0.292459i
$622$		0			0
$623$	5.45272	+	6.51332i	0.218459	+	0.260951i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	3.60012	+	2.46724i	0.143775	+	0.0985322i
$628$		0			0
$629$	−16.5339			−0.659249
$630$		0			0
$631$	9.17965			0.365436			0.182718	−	0.983165i	$-0.441510\pi$
$631$	9.17965			0.365436			0.182718	+	0.983165i	$0.441510\pi$
$632$		0			0
$633$	10.9365	+	7.49499i	0.434686	+	0.297899i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−25.4542	+	9.19909i	−1.00853	+	0.364481i
$638$		0			0
$639$	−29.0560	+	11.2425i	−1.14944	+	0.444745i
$640$		0			0
$641$	26.6664	+	15.3959i	1.05326	+	0.608100i	0.923560	−	0.383453i	$-0.125265\pi$
$641$	26.6664	+	15.3959i	1.05326	+	0.608100i	0.129700	+	0.991553i	$0.458599\pi$
$642$		0			0
$643$	3.42929			0.135238			0.0676189	−	0.997711i	$-0.478460\pi$
$643$	3.42929			0.135238			0.0676189	+	0.997711i	$0.478460\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−43.8152	−	25.2967i	−1.72255	−	0.994516i	−0.913567	−	0.406689i	$-0.866683\pi$
$647$	−43.8152	−	25.2967i	−1.72255	−	0.994516i	−0.808986	−	0.587828i	$-0.799983\pi$
$648$		0			0
$649$	−3.99966	+	2.30920i	−0.157000	+	0.0906441i
$650$		0			0
$651$	−17.3663	−	24.3366i	−0.680640	−	0.953828i
$652$		0			0
$653$	−2.64220	−	4.57643i	−0.103397	−	0.179090i	0.809685	−	0.586865i	$-0.199638\pi$
$653$	−2.64220	−	4.57643i	−0.103397	−	0.179090i	−0.913082	+	0.407775i	$0.866305\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	9.14605	+	1.42362i	0.356821	+	0.0555408i
$658$		0			0
$659$			26.0502i			1.01477i	0.861719	+	0.507385i	$0.169388\pi$
$659$			26.0502i			1.01477i	−0.861719	+	0.507385i	$0.830612\pi$
$660$		0			0
$661$	−28.3751	−	16.3823i	−1.10366	−	0.637199i	−0.166481	−	0.986045i	$-0.553241\pi$
$661$	−28.3751	−	16.3823i	−1.10366	−	0.637199i	−0.937180	+	0.348845i	$0.886574\pi$
$662$		0			0
$663$	−6.12863	−	12.8050i	−0.238016	−	0.497305i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−28.1763	+	16.2676i	−1.09099	+	0.629883i
$668$		0			0
$669$	29.9132	+	20.5002i	1.15651	+	0.792583i
$670$		0			0
$671$	1.67050			0.0644891
$672$		0			0
$673$			38.5194i			1.48481i	0.669950	+	0.742406i	$0.266315\pi$
$673$			38.5194i			1.48481i	−0.669950	+	0.742406i	$0.733685\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16.5938	+	9.58044i	−0.637752	+	0.368206i	−0.783748	−	0.621079i	$-0.786695\pi$
$677$	−16.5938	+	9.58044i	−0.637752	+	0.368206i	0.145996	+	0.989285i	$0.453361\pi$
$678$		0			0
$679$	−2.64225	+	0.462805i	−0.101400	+	0.0177608i
$680$		0			0
$681$	3.42623	+	7.15868i	0.131293	+	0.274321i
$682$		0			0
$683$	14.4812	−	25.0821i	0.554107	−	0.959741i	−0.443866	−	0.896093i	$-0.646393\pi$
$683$	14.4812	−	25.0821i	0.554107	−	0.959741i	0.997972	−	0.0636479i	$-0.0202735\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	1.68551	+	0.130393i	0.0643062	+	0.00497482i
$688$		0			0
$689$	−25.7979	+	44.6832i	−0.982821	+	1.70230i
$690$		0			0
$691$	39.4572	−	22.7806i	1.50102	−	0.866616i	0.501024	−	0.865433i	$-0.332957\pi$
$691$	39.4572	−	22.7806i	1.50102	−	0.866616i	0.999999	−	0.00118303i	$-0.000376571\pi$
$692$		0			0
$693$	0.121486	+	6.39964i	0.00461485	+	0.243102i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	15.5094	+	8.95437i	0.587461	+	0.339171i
$698$		0			0
$699$	2.65920	−	34.3737i	0.100580	−	1.30013i
$700$		0			0
$701$			39.2878i			1.48388i	0.670466	+	0.741940i	$0.266094\pi$
$701$			39.2878i			1.48388i	−0.670466	+	0.741940i	$0.733906\pi$
$702$		0			0
$703$	−12.1859	+	21.1066i	−0.459600	+	0.796050i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−7.76643	+	21.2629i	−0.292087	+	0.799672i
$708$		0			0
$709$	9.88537	+	17.1220i	0.371253	+	0.643029i	0.989759	−	0.142752i	$-0.0455950\pi$
$709$	9.88537	+	17.1220i	0.371253	+	0.643029i	−0.618506	+	0.785780i	$0.712262\pi$
$710$		0			0
$711$	25.4540	−	31.6049i	0.954601	−	1.18528i
$712$		0			0
$713$		−	31.7904i		−	1.19056i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	27.6806	−	40.3907i	1.03375	−	1.50842i
$718$		0			0
$719$	0.740641	+	1.28283i	0.0276212	+	0.0478414i	0.879506	−	0.475889i	$-0.157873\pi$
$719$	0.740641	+	1.28283i	0.0276212	+	0.0478414i	−0.851884	+	0.523730i	$0.824540\pi$
$720$		0			0
$721$	−16.6072	−	19.8374i	−0.618484	−	0.738784i
$722$		0			0
$723$	−9.57966	−	20.0155i	−0.356271	−	0.744385i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−6.35193			−0.235580			−0.117790	−	0.993039i	$-0.537581\pi$
$727$	−6.35193			−0.235580			−0.117790	+	0.993039i	$0.537581\pi$
$728$		0			0
$729$	−24.1544	−	12.0651i	−0.894607	−	0.446855i
$730$		0			0
$731$	0.868129	−	1.50364i	0.0321089	−	0.0556142i
$732$		0			0
$733$	19.6357	+	34.0100i	0.725261	+	1.25619i	0.958866	+	0.283857i	$0.0916143\pi$
$733$	19.6357	+	34.0100i	0.725261	+	1.25619i	−0.233605	+	0.972331i	$0.575052\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.39590	−	7.61392i	−0.161925	−	0.280462i
$738$		0			0
$739$	−11.2904	+	19.5555i	−0.415324	+	0.719362i	−0.995462	−	0.0951558i	$-0.969665\pi$
$739$	−11.2904	+	19.5555i	−0.415324	+	0.719362i	0.580139	+	0.814518i	$0.302998\pi$
$740$		0			0
$741$	−20.8634	−	1.61402i	−0.766436	−	0.0592926i
$742$		0			0
$743$	−26.6330			−0.977070			−0.488535	−	0.872544i	$-0.662468\pi$
$743$	−26.6330			−0.977070			−0.488535	+	0.872544i	$0.662468\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	36.0779	−	13.9594i	1.32002	−	0.510748i
$748$		0			0
$749$	−31.0510	−	37.0906i	−1.13458	−	1.35526i
$750$		0			0
$751$	8.62709	+	14.9426i	0.314807	+	0.545262i	0.979396	−	0.201947i	$-0.0647268\pi$
$751$	8.62709	+	14.9426i	0.314807	+	0.545262i	−0.664589	+	0.747209i	$0.731393\pi$
$752$		0			0
$753$	14.7659	+	10.1194i	0.538098	+	0.368770i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			25.1712i			0.914863i	0.889245	+	0.457431i	$0.151230\pi$
$757$			25.1712i			0.914863i	−0.889245	+	0.457431i	$0.848770\pi$
$758$		0			0
$759$	−3.84751	+	5.61417i	−0.139656	+	0.203781i
$760$		0			0
$761$	−0.00796126	−	0.0137893i	−0.000288596	−	0.000499862i	0.865881	−	0.500250i	$-0.166759\pi$
$761$	−0.00796126	−	0.0137893i	−0.000288596	−	0.000499862i	−0.866170	+	0.499750i	$0.833425\pi$
$762$		0			0
$763$	15.8823	−	43.4824i	0.574977	−	1.57417i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	11.0717	−	19.1768i	0.399777	−	0.692435i
$768$		0			0
$769$		−	13.0356i		−	0.470075i	−0.971986	−	0.235037i	$-0.924479\pi$
$769$		−	13.0356i		−	0.470075i	0.971986	−	0.235037i	$-0.0755213\pi$
$770$		0			0
$771$	−52.6796	−	4.07537i	−1.89721	−	0.146771i
$772$		0			0
$773$	25.4758	+	14.7085i	0.916301	+	0.529027i	0.882453	−	0.470400i	$-0.155890\pi$
$773$	25.4758	+	14.7085i	0.916301	+	0.529027i	0.0338481	+	0.999427i	$0.489224\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−35.5781	+	3.43280i	−1.27636	+	0.123151i
$778$		0			0
$779$	22.8617	−	13.1992i	0.819105	−	0.472910i
$780$		0			0
$781$	−4.18738	+	7.25275i	−0.149836	+	0.259524i
$782$		0			0
$783$	−33.7683	−	7.96445i	−1.20678	−	0.284626i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−1.13148	+	1.95977i	−0.0403327	+	0.0698584i	−0.885487	−	0.464664i	$-0.846175\pi$
$787$	−1.13148	+	1.95977i	−0.0403327	+	0.0698584i	0.845154	+	0.534522i	$0.179508\pi$
$788$		0			0
$789$	32.3017	−	15.4600i	1.14997	−	0.550389i
$790$		0			0
$791$	−18.1388	+	3.17711i	−0.644943	+	0.112965i
$792$		0			0
$793$	−6.93636	+	4.00471i	−0.246318	+	0.142211i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			19.6277i			0.695250i	0.937634	+	0.347625i	$0.113012\pi$
$797$			19.6277i			0.695250i	−0.937634	+	0.347625i	$0.886988\pi$
$798$		0			0
$799$	5.88350			0.208143
$800$		0			0
$801$	−6.04152	+	7.50143i	−0.213467	+	0.265050i
$802$		0			0
$803$	2.15479	−	1.24407i	0.0760409	−	0.0439022i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−38.7753	+	18.5583i	−1.36496	+	0.653284i
$808$		0			0
$809$	21.2506	+	12.2690i	0.747130	+	0.431356i	0.824656	−	0.565635i	$-0.191369\pi$
$809$	21.2506	+	12.2690i	0.747130	+	0.431356i	−0.0775260	+	0.996990i	$0.524702\pi$
$810$		0			0
$811$			38.7927i			1.36220i	0.732192	+	0.681098i	$0.238497\pi$
$811$			38.7927i			1.36220i	−0.732192	+	0.681098i	$0.761503\pi$
$812$		0			0
$813$	−37.6018	−	2.90893i	−1.31875	−	0.102021i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−1.27967	−	2.21645i	−0.0447698	−	0.0775436i
$818$		0			0
$819$	−15.8464	−	26.2817i	−0.553716	−	0.918358i
$820$		0			0
$821$	11.8734	−	6.85513i	0.414386	−	0.239246i	−0.278287	−	0.960498i	$-0.589767\pi$
$821$	11.8734	−	6.85513i	0.414386	−	0.239246i	0.692672	+	0.721252i	$0.256433\pi$
$822$		0			0
$823$	7.00040	+	4.04168i	0.244019	+	0.140884i	0.617022	−	0.786946i	$-0.288339\pi$
$823$	7.00040	+	4.04168i	0.244019	+	0.140884i	−0.373004	+	0.927830i	$0.621672\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	37.6581			1.30950			0.654751	−	0.755845i	$-0.272774\pi$
$827$	37.6581			1.30950			0.654751	+	0.755845i	$0.272774\pi$
$828$		0			0
$829$	−15.4475	−	8.91864i	−0.536515	−	0.309757i	0.207150	−	0.978309i	$-0.433581\pi$
$829$	−15.4475	−	8.91864i	−0.536515	−	0.309757i	−0.743665	+	0.668552i	$0.766914\pi$
$830$		0			0
$831$	11.3826	+	23.7826i	0.394859	+	0.825008i
$832$		0			0
$833$	−14.6071	−	2.60988i	−0.506106	−	0.0904269i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	23.2372	−	24.6837i	0.803194	−	0.853193i
$838$		0			0
$839$	−4.49497			−0.155183			−0.0775917	−	0.996985i	$-0.524723\pi$
$839$	−4.49497			−0.155183			−0.0775917	+	0.996985i	$0.524723\pi$
$840$		0			0
$841$	−15.5825			−0.537329
$842$		0			0
$843$	17.5744	−	25.6440i	0.605295	−	0.883228i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−17.5774	−	20.9963i	−0.603966	−	0.721443i
$848$		0			0
$849$	42.1654	−	20.1809i	1.44711	−	0.692605i
$850$		0			0
$851$	−32.9144	−	19.0032i	−1.12829	−	0.651420i
$852$		0			0
$853$	33.0503			1.13162			0.565811	−	0.824535i	$-0.308563\pi$
$853$	33.0503			1.13162			0.565811	+	0.824535i	$0.308563\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.365051	−	0.210762i	−0.0124699	−	0.00719949i	0.493752	−	0.869603i	$-0.335625\pi$
$857$	−0.365051	−	0.210762i	−0.0124699	−	0.00719949i	−0.506222	+	0.862403i	$0.668958\pi$
$858$		0			0
$859$	17.0294	−	9.83192i	0.581035	−	0.335461i	−0.180509	−	0.983573i	$-0.557775\pi$
$859$	17.0294	−	9.83192i	0.581035	−	0.335461i	0.761545	+	0.648112i	$0.224441\pi$
$860$		0			0
$861$	35.2327	+	16.0482i	1.20073	+	0.546920i
$862$		0			0
$863$	0.451820	+	0.782575i	0.0153801	+	0.0266392i	0.873613	−	0.486621i	$-0.161771\pi$
$863$	0.451820	+	0.782575i	0.0153801	+	0.0266392i	−0.858233	+	0.513260i	$0.828437\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1.67081	+	21.5974i	−0.0567437	+	0.733488i
$868$		0			0
$869$		−	10.9084i		−	0.370041i
$870$		0			0
$871$	36.5058	+	21.0766i	1.23695	+	0.714154i
$872$		0			0
$873$	−1.09759	−	2.83671i	−0.0371478	−	0.0960080i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−13.2661	+	7.65916i	−0.447963	+	0.258632i	−0.706970	−	0.707244i	$-0.749938\pi$
$877$	−13.2661	+	7.65916i	−0.447963	+	0.258632i	0.259006	+	0.965876i	$0.416605\pi$
$878$		0			0
$879$	14.1437	−	20.6381i	0.477056	−	0.696106i
$880$		0			0
$881$	−43.8614			−1.47773			−0.738863	−	0.673855i	$-0.764637\pi$
$881$	−43.8614			−1.47773			−0.738863	+	0.673855i	$0.764637\pi$
$882$		0			0
$883$			2.91300i			0.0980304i	0.998798	+	0.0490152i	$0.0156083\pi$
$883$			2.91300i			0.0980304i	−0.998798	+	0.0490152i	$0.984392\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.9001	−	7.44790i	0.433145	−	0.250076i	−0.267541	−	0.963547i	$-0.586211\pi$
$887$	12.9001	−	7.44790i	0.433145	−	0.250076i	0.700685	+	0.713470i	$0.252878\pi$
$888$		0			0
$889$	3.54739	+	20.2528i	0.118976	+	0.679259i
$890$		0			0
$891$	−7.09108	+	1.54679i	−0.237560	+	0.0518195i
$892$		0			0
$893$	4.33629	−	7.51067i	0.145108	−	0.251335i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	2.51697	−	32.5352i	0.0840391	−	1.08632i
$898$		0			0
$899$	21.7810	−	37.7258i	0.726437	−	1.25823i
$900$		0			0
$901$	−24.4972	+	14.1435i	−0.816121	+	0.471188i
$902$		0			0
$903$	1.55587	−	3.41582i	0.0517762	−	0.113671i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−16.5393	−	9.54899i	−0.549180	−	0.317069i	0.199611	−	0.979875i	$-0.436032\pi$
$907$	−16.5393	−	9.54899i	−0.549180	−	0.317069i	−0.748791	+	0.662806i	$0.769365\pi$
$908$		0			0
$909$	−25.3624	−	3.94777i	−0.841217	−	0.130939i
$910$		0			0
$911$			6.16915i			0.204393i	0.994764	+	0.102197i	$0.0325871\pi$
$911$			6.16915i			0.204393i	−0.994764	+	0.102197i	$0.967413\pi$
$912$		0			0
$913$	5.19934	−	9.00552i	0.172073	−	0.298039i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−20.1683	−	24.0912i	−0.666016	−	0.795562i
$918$		0			0
$919$	14.8318	+	25.6894i	0.489255	+	0.847415i	0.999924	−	0.0123630i	$-0.00393538\pi$
$919$	14.8318	+	25.6894i	0.489255	+	0.847415i	−0.510668	+	0.859778i	$0.670602\pi$
$920$		0			0
$921$	−13.3521	−	9.15051i	−0.439968	−	0.301519i
$922$		0			0
$923$		−	40.1537i		−	1.32168i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	18.4005	−	22.8469i	0.604350	−	0.750389i
$928$		0			0
$929$	−16.8256	−	29.1428i	−0.552030	−	0.956144i	−0.998128	−	0.0611601i	$-0.980520\pi$
$929$	−16.8256	−	29.1428i	−0.552030	−	0.956144i	0.446098	−	0.894984i	$-0.352813\pi$
$930$		0			0
$931$	−14.0975	+	16.7234i	−0.462027	+	0.548087i
$932$		0			0
$933$	−45.8274	+	21.9335i	−1.50032	+	0.718072i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	7.99276			0.261112			0.130556	−	0.991441i	$-0.458324\pi$
$937$	7.99276			0.261112			0.130556	+	0.991441i	$0.458324\pi$
$938$		0			0
$939$	−1.47433	+	19.0576i	−0.0481128	+	0.621922i
$940$		0			0
$941$	−8.69431	+	15.0590i	−0.283426	+	0.490909i	−0.972226	−	0.234043i	$-0.924804\pi$
$941$	−8.69431	+	15.0590i	−0.283426	+	0.490909i	0.688800	+	0.724951i	$0.258138\pi$
$942$		0			0
$943$	20.5833	+	35.6514i	0.670285	+	1.16097i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−21.1485	−	36.6302i	−0.687233	−	1.19032i	−0.972729	−	0.231943i	$-0.925492\pi$
$947$	−21.1485	−	36.6302i	−0.687233	−	1.19032i	0.285496	−	0.958380i	$-0.407842\pi$
$948$		0			0
$949$	−5.96483	+	10.3314i	−0.193627	+	0.335371i
$950$		0			0
$951$	−2.26746	+	29.3099i	−0.0735273	+	0.950438i
$952$		0			0
$953$	−40.5612			−1.31391			−0.656953	−	0.753932i	$-0.728155\pi$
$953$	−40.5612			−1.31391			−0.656953	+	0.753932i	$0.728155\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−8.41237	+	4.02626i	−0.271933	+	0.130150i
$958$		0			0
$959$	2.23145	−	6.10926i	0.0720574	−	0.197278i
$960$		0			0
$961$	5.78241	+	10.0154i	0.186529	+	0.323078i
$962$		0			0
$963$	34.4039	−	42.7175i	1.10865	−	1.37655i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	37.6713i		−	1.21143i	−0.795682	−	0.605714i	$-0.792888\pi$
$967$		−	37.6713i		−	1.21143i	0.795682	−	0.605714i	$-0.207112\pi$
$968$		0			0
$969$	−9.46333	−	6.48542i	−0.304006	−	0.208342i
$970$		0			0
$971$	−21.5452	−	37.3173i	−0.691418	−	1.19757i	−0.971373	−	0.237558i	$-0.923653\pi$
$971$	−21.5452	−	37.3173i	−0.691418	−	1.19757i	0.279956	−	0.960013i	$-0.409680\pi$
$972$		0			0
$973$	1.28420	+	7.33180i	0.0411697	+	0.235047i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	11.3970	−	19.7402i	0.364622	−	0.631545i	−0.624093	−	0.781350i	$-0.714531\pi$
$977$	11.3970	−	19.7402i	0.364622	−	0.631545i	0.988716	+	0.149805i	$0.0478647\pi$
$978$		0			0
$979$			2.58910i			0.0827481i
$980$		0			0
$981$	51.8658	+	8.07315i	1.65595	+	0.257756i
$982$		0			0
$983$	−39.1321	−	22.5929i	−1.24812	−	0.720602i	−0.277385	−	0.960759i	$-0.589468\pi$
$983$	−39.1321	−	22.5929i	−1.24812	−	0.720602i	−0.970734	+	0.240157i	$0.922801\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	12.6603	−	1.22154i	0.402981	−	0.0388822i
$988$		0			0
$989$	3.45641	−	1.99556i	0.109907	−	0.0634551i
$990$		0			0
$991$	−25.2760	+	43.7793i	−0.802919	+	1.39070i	0.114768	+	0.993392i	$0.463388\pi$
$991$	−25.2760	+	43.7793i	−0.802919	+	1.39070i	−0.917687	+	0.397304i	$0.869946\pi$
$992$		0			0
$993$	1.55702	−	20.1265i	0.0494105	−	0.638696i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	13.0271	−	22.5635i	0.412571	−	0.714595i	−0.582599	−	0.812760i	$-0.697964\pi$
$997$	13.0271	−	22.5635i	0.412571	−	0.714595i	0.995170	+	0.0981654i	$0.0312974\pi$
$998$		0			0
$999$	−11.6661	−	38.8138i	−0.369099	−	1.22801i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bo.g.1949.2		20
3.2	odd	2		2100.2.bo.h.1949.8		20
5.2	odd	4		2100.2.bi.j.101.2		10
5.3	odd	4		420.2.bh.b.101.4	yes	10
5.4	even	2	inner	2100.2.bo.g.1949.9		20
7.5	odd	6		2100.2.bo.h.1349.3		20
15.2	even	4		2100.2.bi.k.101.4		10
15.8	even	4		420.2.bh.a.101.2	✓	10
15.14	odd	2		2100.2.bo.h.1949.3		20
21.5	even	6	inner	2100.2.bo.g.1349.9		20
35.3	even	12		2940.2.d.b.881.10		10
35.12	even	12		2100.2.bi.k.1601.4		10
35.18	odd	12		2940.2.d.a.881.1		10
35.19	odd	6		2100.2.bo.h.1349.8		20
35.33	even	12		420.2.bh.a.341.2	yes	10
105.38	odd	12		2940.2.d.a.881.2		10
105.47	odd	12		2100.2.bi.j.1601.2		10
105.53	even	12		2940.2.d.b.881.9		10
105.68	odd	12		420.2.bh.b.341.4	yes	10
105.89	even	6	inner	2100.2.bo.g.1349.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bh.a.101.2	✓	10	15.8	even	4
420.2.bh.a.341.2	yes	10	35.33	even	12
420.2.bh.b.101.4	yes	10	5.3	odd	4
420.2.bh.b.341.4	yes	10	105.68	odd	12
2100.2.bi.j.101.2		10	5.2	odd	4
2100.2.bi.j.1601.2		10	105.47	odd	12
2100.2.bi.k.101.4		10	15.2	even	4
2100.2.bi.k.1601.4		10	35.12	even	12
2100.2.bo.g.1349.2		20	105.89	even	6	inner
2100.2.bo.g.1349.9		20	21.5	even	6	inner
2100.2.bo.g.1949.2		20	1.1	even	1	trivial
2100.2.bo.g.1949.9		20	5.4	even	2	inner
2100.2.bo.h.1349.3		20	7.5	odd	6
2100.2.bo.h.1349.8		20	35.19	odd	6
2100.2.bo.h.1949.3		20	15.14	odd	2
2100.2.bo.h.1949.8		20	3.2	odd	2
2940.2.d.a.881.1		10	35.18	odd	12
2940.2.d.a.881.2		10	105.38	odd	12
2940.2.d.b.881.9		10	105.53	even	12
2940.2.d.b.881.10		10	35.3	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.bo (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.42873 - 0.979142i) q^{3} +(2.60608 - 0.456468i) q^{7} +(1.08256 + 2.79787i) q^{9} +O(q^{10})\)	\(q+(-1.42873 - 0.979142i) q^{3} +(2.60608 - 0.456468i) q^{7} +(1.08256 + 2.79787i) q^{9} +(0.698384 + 0.403212i) q^{11} -3.86649 q^{13} +(-1.83578 - 1.05989i) q^{17} +(-2.70603 + 1.56233i) q^{19} +(-4.17034 - 1.89955i) q^{21} +(-2.43635 - 4.21989i) q^{23} +(1.19282 - 5.05739i) q^{27} -6.67701i q^{29} +(5.65010 + 3.26209i) q^{31} +(-0.603003 - 1.25990i) q^{33} +(6.75485 - 3.89991i) q^{37} +(5.52419 + 3.78585i) q^{39} -8.44841 q^{41} +0.819076i q^{43} +(-2.40368 + 1.38776i) q^{47} +(6.58327 - 2.37918i) q^{49} +(1.58506 + 3.31179i) q^{51} +(6.67216 - 11.5565i) q^{53} +(5.39594 + 0.417438i) q^{57} +(-2.86351 + 4.95974i) q^{59} +(1.79397 - 1.03575i) q^{61} +(4.09838 + 6.79730i) q^{63} +(-9.44157 - 5.45110i) q^{67} +(-0.650969 + 8.41464i) q^{69} +10.3850i q^{71} +(1.54270 - 2.67203i) q^{73} +(2.00410 + 0.732012i) q^{77} +(-6.76342 - 11.7146i) q^{79} +(-6.65612 + 6.05773i) q^{81} -12.8948i q^{83} +(-6.53775 + 9.53968i) q^{87} +(1.60530 + 2.78046i) q^{89} +(-10.0764 + 1.76493i) q^{91} +(-4.87844 - 10.1929i) q^{93} -1.01388 q^{97} +(-0.372090 + 2.39049i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{9}+O(q^{10}) \) 20 * q - 6 * q^9	\( 20 q - 6 q^{9} + 12 q^{11} - 6 q^{19} + 24 q^{21} + 30 q^{31} + 42 q^{39} + 16 q^{41} + 26 q^{49} + 80 q^{51} + 84 q^{61} - 28 q^{69} - 2 q^{79} - 26 q^{81} + 56 q^{89} - 22 q^{91} - 72 q^{99}+O(q^{100}) \) 20 * q - 6 * q^9 + 12 * q^11 - 6 * q^19 + 24 * q^21 + 30 * q^31 + 42 * q^39 + 16 * q^41 + 26 * q^49 + 80 * q^51 + 84 * q^61 - 28 * q^69 - 2 * q^79 - 26 * q^81 + 56 * q^89 - 22 * q^91 - 72 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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