LMFDB - Embedded newform 2100.2.bo.h.1349.8

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:	$\Z[a_1, \ldots, a_{7}]$
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			1349.8
Root			$-1.56233 + 0.747749i$ of defining polynomial
Character	$\chi$	$=$	2100.1349
Dual form			2100.2.bo.h.1949.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.56233 - 0.747749i) q^{3} +(2.60608 + 0.456468i) q^{7} +(1.88174 - 2.33646i) q^{9} +O(q^{10})$	\(q+(1.56233 - 0.747749i) q^{3} +(2.60608 + 0.456468i) q^{7} +(1.88174 - 2.33646i) q^{9} +(-0.698384 + 0.403212i) q^{11} -3.86649 q^{13} +(1.83578 - 1.05989i) q^{17} +(-2.70603 - 1.56233i) q^{19} +(4.41287 - 1.23554i) q^{21} +(2.43635 - 4.21989i) q^{23} +(1.19282 - 5.05739i) q^{27} -6.67701i q^{29} +(5.65010 - 3.26209i) q^{31} +(-0.789604 + 1.15217i) q^{33} +(6.75485 + 3.89991i) q^{37} +(-6.04074 + 2.89117i) q^{39} +8.44841 q^{41} -0.819076i q^{43} +(2.40368 + 1.38776i) q^{47} +(6.58327 + 2.37918i) q^{49} +(2.07556 - 3.02860i) q^{51} +(-6.67216 - 11.5565i) q^{53} +(-5.39594 - 0.417438i) q^{57} +(2.86351 + 4.95974i) q^{59} +(1.79397 + 1.03575i) q^{61} +(5.97049 - 5.23004i) q^{63} +(-9.44157 + 5.45110i) q^{67} +(0.650969 - 8.41464i) q^{69} +10.3850i q^{71} +(1.54270 + 2.67203i) q^{73} +(-2.00410 + 0.732012i) q^{77} +(-6.76342 + 11.7146i) q^{79} +(-1.91809 - 8.79323i) q^{81} -12.8948i q^{83} +(-4.99273 - 10.4317i) q^{87} +(-1.60530 + 2.78046i) q^{89} +(-10.0764 - 1.76493i) q^{91} +(6.38809 - 9.32131i) q^{93} -1.01388 q^{97} +(-0.372090 + 2.39049i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{9}+O(q^{10}) $ 20 * q + 6 * q^9	$ 20 q + 6 q^{9} - 12 q^{11} - 6 q^{19} + 20 q^{21} + 30 q^{31} - 30 q^{39} - 16 q^{41} + 26 q^{49} - 88 q^{51} + 84 q^{61} + 28 q^{69} - 2 q^{79} + 82 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 + 20 * q^21 + 30 * q^31 - 30 * q^39 - 16 * q^41 + 26 * q^49 - 88 * q^51 + 84 * q^61 + 28 * q^69 - 2 * q^79 + 82 * 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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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
$3$	1.56233	−	0.747749i	0.902011	−	0.431713i
$3$	1.56233	−	0.747749i	0.902011	−	0.431713i
$4$		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
$9$	1.88174	−	2.33646i	0.627248	−	0.778820i
$10$		0			0
$11$	−0.698384	+	0.403212i	−0.210571	+	0.121573i	−0.601577	−	0.798815i	$-0.705461\pi$
$11$	−0.698384	+	0.403212i	−0.210571	+	0.121573i	0.391006	+	0.920388i	$0.372127\pi$
$12$		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	$-0.583913\pi$
$17$	1.83578	−	1.05989i	0.445242	−	0.257061i	0.705819	+	0.708393i	$0.250579\pi$
$18$		0			0
$19$	−2.70603	−	1.56233i	−0.620807	−	0.358423i	0.156376	−	0.987698i	$-0.450019\pi$
$19$	−2.70603	−	1.56233i	−0.620807	−	0.358423i	−0.777183	+	0.629275i	$0.783352\pi$
$20$		0			0
$21$	4.41287	−	1.23554i	0.962968	−	0.269617i
$22$		0			0
$23$	2.43635	−	4.21989i	0.508015	−	0.879908i	−0.491942	−	0.870628i	$-0.663713\pi$
$23$	2.43635	−	4.21989i	0.508015	−	0.879908i	0.999957	−	0.00927994i	$-0.00295394\pi$
$24$		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	0.102198	−	0.994764i	$-0.467413\pi$
$31$	5.65010	−	3.26209i	1.01479	−	0.585888i	0.912590	+	0.408876i	$0.134079\pi$
$32$		0			0
$33$	−0.789604	+	1.15217i	−0.137452	+	0.200566i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.75485	+	3.89991i	1.11049	+	0.641142i	0.938956	−	0.344036i	$-0.111794\pi$
$37$	6.75485	+	3.89991i	1.11049	+	0.641142i	0.171534	+	0.985178i	$0.445128\pi$
$38$		0			0
$39$	−6.04074	+	2.89117i	−0.967292	+	0.462957i
$40$		0			0
$41$	8.44841			1.31942			0.659710	−	0.751520i	$-0.270679\pi$
$41$	8.44841			1.31942			0.659710	+	0.751520i	$0.270679\pi$
$42$		0			0
$43$		−	0.819076i		−	0.124908i	−0.998048	−	0.0624540i	$-0.980107\pi$
$43$		−	0.819076i		−	0.124908i	0.998048	−	0.0624540i	$-0.0198927\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.40368	+	1.38776i	0.350612	+	0.202426i	0.664955	−	0.746883i	$-0.268451\pi$
$47$	2.40368	+	1.38776i	0.350612	+	0.202426i	−0.314343	+	0.949310i	$0.601784\pi$
$48$		0			0
$49$	6.58327	+	2.37918i	0.940468	+	0.339883i
$50$		0			0
$51$	2.07556	−	3.02860i	0.290637	−	0.424088i
$52$		0			0
$53$	−6.67216	−	11.5565i	−0.916492	−	1.58741i	−0.804703	−	0.593678i	$-0.797675\pi$
$53$	−6.67216	−	11.5565i	−0.916492	−	1.58741i	−0.111789	−	0.993732i	$-0.535658\pi$
$54$		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	$-0.0450655\pi$
$59$	2.86351	+	4.95974i	0.372797	+	0.645703i	−0.617198	+	0.786808i	$0.711732\pi$
$60$		0			0
$61$	1.79397	+	1.03575i	0.229694	+	0.132614i	0.610431	−	0.792070i	$-0.290996\pi$
$61$	1.79397	+	1.03575i	0.229694	+	0.132614i	−0.380737	+	0.924683i	$0.624330\pi$
$62$		0			0
$63$	5.97049	−	5.23004i	0.752211	−	0.658923i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−9.44157	+	5.45110i	−1.15347	+	0.665957i	−0.949731	−	0.313067i	$-0.898643\pi$
$67$	−9.44157	+	5.45110i	−1.15347	+	0.665957i	−0.203741	+	0.979025i	$0.565310\pi$
$68$		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	0.942071	−	0.335413i	$-0.108876\pi$
$73$	1.54270	+	2.67203i	0.180559	+	0.312737i	−0.761512	+	0.648151i	$0.775543\pi$
$74$		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	0.181420	+	0.983406i	$0.441931\pi$
$79$	−6.76342	+	11.7146i	−0.760944	+	1.31799i	−0.942364	+	0.334589i	$0.891403\pi$
$80$		0			0
$81$	−1.91809	−	8.79323i	−0.213121	−	0.977026i
$82$		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
$87$	−4.99273	−	10.4317i	−0.535277	−	1.11839i
$88$		0			0
$89$	−1.60530	+	2.78046i	−0.170161	+	0.294728i	−0.938476	−	0.345344i	$-0.887762\pi$
$89$	−1.60530	+	2.78046i	−0.170161	+	0.294728i	0.768315	+	0.640072i	$0.221096\pi$
$90$		0			0
$91$	−10.0764	−	1.76493i	−1.05629	−	0.185015i
$92$		0			0
$93$	6.38809	−	9.32131i	0.662414	−	0.966574i
$94$		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	$-0.0267040\pi$
$101$	4.27796	+	7.40965i	0.425673	+	0.737288i	−0.570810	+	0.821082i	$0.693371\pi$
$102$		0			0
$103$	−4.88921	+	8.46835i	−0.481748	+	0.834411i	−0.999781	−	0.0209492i	$-0.993331\pi$
$103$	−4.88921	+	8.46835i	−0.481748	+	0.834411i	0.518033	+	0.855361i	$0.326664\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.14150	−	15.8336i	0.883743	−	1.53069i	0.0365946	−	0.999330i	$-0.488349\pi$
$107$	9.14150	−	15.8336i	0.883743	−	1.53069i	0.847148	−	0.531357i	$-0.178318\pi$
$108$		0			0
$109$	8.74840	+	15.1527i	0.837945	+	1.45136i	0.891610	+	0.452804i	$0.149576\pi$
$109$	8.74840	+	15.1527i	0.837945	+	1.45136i	−0.0536658	+	0.998559i	$0.517091\pi$
$110$		0			0
$111$	13.4695	+	1.04202i	1.27846	+	0.0989039i
$112$		0			0
$113$	6.96021			0.654761			0.327381	−	0.944893i	$-0.393834\pi$
$113$	6.96021			0.654761			0.327381	+	0.944893i	$0.393834\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−7.27575	+	9.03391i	−0.672643	+	0.835185i
$118$		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
$123$	13.1992	−	6.31729i	1.19013	−	0.569611i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	7.77139i		−	0.689600i	−0.938676	−	0.344800i	$-0.887947\pi$
$127$		−	7.77139i		−	0.689600i	0.938676	−	0.344800i	$-0.112053\pi$
$128$		0			0
$129$	−0.612463	−	1.27967i	−0.0539244	−	0.112668i
$130$		0			0
$131$	5.93761	−	10.2842i	0.518772	−	0.898539i	−0.480990	−	0.876726i	$-0.659723\pi$
$131$	5.93761	−	10.2842i	0.518772	−	0.898539i	0.999762	−	0.0218131i	$-0.00694387\pi$
$132$		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	$-0.200155\pi$
$137$	−1.22915	−	2.12894i	−0.105013	−	0.181888i	−0.913744	+	0.406291i	$0.866822\pi$
$138$		0			0
$139$		−	2.81335i		−	0.238625i	−0.992857	−	0.119313i	$-0.961931\pi$
$139$		−	2.81335i		−	0.238625i	0.992857	−	0.119313i	$-0.0380691\pi$
$140$		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
$147$	12.0643	−	1.20557i	0.995044	−	0.0994339i
$148$		0			0
$149$	−12.8234	−	7.40357i	−1.05053	−	0.606524i	−0.127733	−	0.991809i	$-0.540770\pi$
$149$	−12.8234	−	7.40357i	−1.05053	−	0.606524i	−0.922798	+	0.385285i	$0.874103\pi$
$150$		0			0
$151$	0.427898	+	0.741141i	0.0348218	+	0.0603132i	0.882911	−	0.469540i	$-0.155580\pi$
$151$	0.427898	+	0.741141i	0.0348218	+	0.0603132i	−0.848089	+	0.529853i	$0.822247\pi$
$152$		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	−0.688173	−	0.725547i	$-0.741587\pi$
$157$	−12.1845	−	21.1042i	−0.972428	−	1.68430i	−0.284256	−	0.958748i	$-0.591746\pi$
$158$		0			0
$159$	−19.0655	−	13.0660i	−1.51199	−	1.03620i
$160$		0			0
$161$	8.27557	−	9.88524i	0.652207	−	0.779066i
$162$		0			0
$163$	−1.36728	−	0.789402i	−0.107094	−	0.0618307i	0.445496	−	0.895284i	$-0.353027\pi$
$163$	−1.36728	−	0.789402i	−0.107094	−	0.0618307i	−0.552590	+	0.833453i	$0.686361\pi$
$164$		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
$171$	−8.74238	+	3.38264i	−0.668546	+	0.258677i
$172$		0			0
$173$	4.03633	+	2.33037i	0.306876	+	0.177175i	0.645528	−	0.763737i	$-0.276637\pi$
$173$	4.03633	+	2.33037i	0.306876	+	0.177175i	−0.338652	+	0.940912i	$0.609971\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	8.18238	+	5.60756i	0.615025	+	0.421490i
$178$		0			0
$179$	3.11674	−	1.79945i	0.232956	−	0.134497i	−0.378979	−	0.925405i	$-0.623725\pi$
$179$	3.11674	−	1.79945i	0.232956	−	0.134497i	0.611935	+	0.790908i	$0.290391\pi$
$180$		0			0
$181$			22.5821i			1.67851i	0.543737	+	0.839256i	$0.317009\pi$
$181$			22.5821i			1.67851i	−0.543737	+	0.839256i	$0.682991\pi$
$182$		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
$189$	5.41711	−	12.6355i	0.394037	−	0.919095i
$190$		0			0
$191$	2.92355	+	1.68791i	0.211541	+	0.122133i	0.602027	−	0.798475i	$-0.294360\pi$
$191$	2.92355	+	1.68791i	0.211541	+	0.122133i	−0.390486	+	0.920609i	$0.627693\pi$
$192$		0			0
$193$	−9.60463	+	5.54524i	−0.691357	+	0.399155i	−0.804120	−	0.594467i	$-0.797363\pi$
$193$	−9.60463	+	5.54524i	−0.691357	+	0.399155i	0.112763	+	0.993622i	$0.464030\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−16.2585			−1.15837			−0.579184	−	0.815197i	$-0.696629\pi$
$197$	−16.2585			−1.15837			−0.579184	+	0.815197i	$0.696629\pi$
$198$		0			0
$199$	1.07964	−	0.623332i	0.0765338	−	0.0441868i	−0.461245	−	0.887273i	$-0.652597\pi$
$199$	1.07964	−	0.623332i	0.0765338	−	0.0441868i	0.537779	+	0.843086i	$0.319264\pi$
$200$		0			0
$201$	−10.6748	+	15.5763i	−0.752942	+	1.09867i
$202$		0			0
$203$	3.04784	−	17.4008i	0.213917	−	1.22130i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−5.27501	−	13.6332i	−0.366639	−	0.947573i
$208$		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
$213$	7.76541	+	16.2249i	0.532077	+	1.11171i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	16.2136	−	5.92216i	1.10065	−	0.402022i
$218$		0			0
$219$	4.40821	+	3.02104i	0.297879	+	0.204143i
$220$		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	$-0.618076\pi$
$227$	3.96818	−	2.29103i	0.263377	−	0.152061i	0.625874	+	0.779924i	$0.284742\pi$
$228$		0			0
$229$	−0.845272	−	0.488018i	−0.0558572	−	0.0322492i	0.471811	−	0.881700i	$-0.343600\pi$
$229$	−0.845272	−	0.488018i	−0.0558572	−	0.0322492i	−0.527669	+	0.849450i	$0.676934\pi$
$230$		0			0
$231$	−2.58370	+	2.64220i	−0.169995	+	0.173844i
$232$		0			0
$233$	−9.95247	+	17.2382i	−0.652008	+	1.12931i	0.330627	+	0.943762i	$0.392740\pi$
$233$	−9.95247	+	17.2382i	−0.652008	+	1.12931i	−0.982635	+	0.185550i	$0.940593\pi$
$234$		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	−0.0981065	−	0.995176i	$-0.531279\pi$
$241$	11.0949	−	6.40567i	0.714688	−	0.412625i	0.812794	+	0.582551i	$0.197945\pi$
$242$		0			0
$243$	−9.57181	−	12.3037i	−0.614032	−	0.789281i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	10.4629	+	6.04074i	0.665736	+	0.384363i
$248$		0			0
$249$	−9.64207	−	20.1459i	−0.611042	−	1.27670i
$250$		0			0
$251$	10.3349			0.652335			0.326167	−	0.945312i	$-0.394243\pi$
$251$	10.3349			0.652335			0.326167	+	0.945312i	$0.394243\pi$
$252$		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	−0.977889	−	0.209124i	$-0.932939\pi$
$257$	−26.4185	−	15.2527i	−1.64794	−	0.951439i	−0.670052	−	0.742315i	$-0.733728\pi$
$258$		0			0
$259$	15.8235	+	13.2469i	0.983223	+	0.823119i
$260$		0			0
$261$	−15.6006	−	12.5644i	−0.965651	−	0.777718i
$262$		0			0
$263$	10.3377	+	17.9054i	0.637447	+	1.10409i	0.985991	+	0.166799i	$0.0533430\pi$
$263$	10.3377	+	17.9054i	0.637447	+	1.10409i	−0.348543	+	0.937293i	$0.613324\pi$
$264$		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	−0.944566	−	0.328322i	$-0.893517\pi$
$269$	−12.4095	−	21.4938i	−0.756618	−	1.31050i	0.187948	−	0.982179i	$-0.439816\pi$
$270$		0			0
$271$	18.8571	+	10.8871i	1.14548	+	0.661346i	0.947783	−	0.318916i	$-0.103319\pi$
$271$	18.8571	+	10.8871i	1.14548	+	0.661346i	0.197702	+	0.980262i	$0.436652\pi$
$272$		0			0
$273$	−17.0623	+	4.77720i	−1.03266	+	0.289129i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−13.1831	+	7.61126i	−0.792095	+	0.457316i	−0.840699	−	0.541502i	$-0.817856\pi$
$277$	−13.1831	+	7.61126i	−0.792095	+	0.457316i	0.0486048	+	0.998818i	$0.484523\pi$
$278$		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	−0.918192	−	0.396135i	$-0.870351\pi$
$283$	−13.4944	−	23.3730i	−0.802159	−	1.38938i	0.116033	−	0.993245i	$-0.462982\pi$
$284$		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
$291$	−1.58402	+	0.758129i	−0.0928567	+	0.0444423i
$292$		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
$297$	1.20616	+	4.01296i	0.0699884	+	0.232855i
$298$		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
$303$	12.2241	+	8.37747i	0.702259	+	0.481273i
$304$		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	−0.896726	−	0.442586i	$-0.854061\pi$
$311$	−14.6664	−	25.4029i	−0.831654	−	1.44047i	0.0650722	−	0.997881i	$-0.479272\pi$
$312$		0			0
$313$	−5.51790	+	9.55728i	−0.311890	+	0.540209i	−0.978772	−	0.204954i	$-0.934295\pi$
$313$	−5.51790	+	9.55728i	−0.311890	+	0.540209i	0.666881	+	0.745164i	$0.267629\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.48631	−	14.6987i	0.476639	−	0.825563i	−0.523003	−	0.852331i	$-0.675188\pi$
$317$	8.48631	−	14.6987i	0.476639	−	0.825563i	0.999642	+	0.0267682i	$0.00852159\pi$
$318$		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
$327$	24.9983	+	17.1318i	1.38241	+	0.947393i
$328$		0			0
$329$	5.63070	+	4.71382i	0.310430	+	0.259881i
$330$		0			0
$331$	5.82739	−	10.0933i	0.320302	−	0.554780i	−0.660248	−	0.751048i	$-0.729549\pi$
$331$	5.82739	−	10.0933i	0.320302	−	0.554780i	0.980550	+	0.196268i	$0.0628822\pi$
$332$		0			0
$333$	21.8229	−	8.44380i	1.19589	−	0.462717i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	10.1753i		−	0.554286i	−0.960829	−	0.277143i	$-0.910612\pi$
$337$		−	10.1753i		−	0.554286i	0.960829	−	0.277143i	$-0.0893875\pi$
$338$		0			0
$339$	10.8741	−	5.20449i	0.590602	−	0.282669i
$340$		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	$-0.153045\pi$
$347$	0.796887	+	1.38025i	0.0427791	+	0.0740956i	−0.843843	+	0.536590i	$0.819712\pi$
$348$		0			0
$349$			15.4812i			0.828690i	0.910120	+	0.414345i	$0.135989\pi$
$349$			15.4812i			0.828690i	−0.910120	+	0.414345i	$0.864011\pi$
$350$		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	$-0.777320\pi$
$353$	−11.0861	+	6.40056i	−0.590054	+	0.340668i	0.175065	+	0.984557i	$0.443986\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	6.79153	−	6.94533i	0.359446	−	0.367586i
$358$		0			0
$359$	5.66697	+	3.27183i	0.299091	+	0.172680i	0.642035	−	0.766676i	$-0.278091\pi$
$359$	5.66697	+	3.27183i	0.299091	+	0.172680i	−0.342943	+	0.939356i	$0.611424\pi$
$360$		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	0.998515	−	0.0544847i	$-0.0173516\pi$
$367$	8.66046	+	15.0004i	0.452072	+	0.783012i	−0.546442	+	0.837497i	$0.684018\pi$
$368$		0			0
$369$	15.8977	−	19.7394i	0.827603	−	1.02759i
$370$		0			0
$371$	−12.1130	−	33.1628i	−0.628875	−	1.72173i
$372$		0			0
$373$	0.862445	+	0.497933i	0.0446557	+	0.0257820i	0.522162	−	0.852847i	$-0.325126\pi$
$373$	0.862445	+	0.497933i	0.0446557	+	0.0257820i	−0.477506	+	0.878629i	$0.658459\pi$
$374$		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
$381$	−5.81105	−	12.1415i	−0.297709	−	0.622026i
$382$		0			0
$383$	17.2120	+	9.93736i	0.879493	+	0.507776i	0.870491	−	0.492184i	$-0.163801\pi$
$383$	17.2120	+	9.93736i	0.879493	+	0.507776i	0.00900178	+	0.999959i	$0.497135\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.91374	−	1.54129i	−0.0972808	−	0.0783482i
$388$		0			0
$389$	−1.56923	+	0.905994i	−0.0795630	+	0.0459357i	−0.539254	−	0.842143i	$-0.681294\pi$
$389$	−1.56923	+	0.905994i	−0.0795630	+	0.0459357i	0.459691	+	0.888079i	$0.347960\pi$
$390$		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	−0.0143590	+	0.999897i	$0.504571\pi$
$397$	−17.3967	+	30.1320i	−0.873116	+	1.51228i	−0.858757	+	0.512384i	$0.828763\pi$
$398$		0			0
$399$	−13.8717	−	3.55095i	−0.694453	−	0.177770i
$400$		0			0
$401$	−32.5121	−	18.7709i	−1.62358	−	0.937374i	−0.985952	−	0.167029i	$-0.946583\pi$
$401$	−32.5121	−	18.7709i	−1.62358	−	0.937374i	−0.637627	−	0.770345i	$-0.720084\pi$
$402$		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	−0.578140	−	0.815937i	$-0.696221\pi$
$409$	−3.24769	+	1.87505i	−0.160588	+	0.0927154i	0.417552	+	0.908653i	$0.362888\pi$
$410$		0			0
$411$	−3.51225	−	2.40702i	−0.173246	−	0.118729i
$412$		0			0
$413$	5.19856	+	14.2326i	0.255804	+	0.700339i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−2.10368	−	4.39538i	−0.103018	−	0.215242i
$418$		0			0
$419$	30.0547			1.46827			0.734134	−	0.679005i	$-0.237589\pi$
$419$	30.0547			1.46827			0.734134	+	0.679005i	$0.237589\pi$
$420$		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
$423$	7.76556	−	3.00468i	0.377574	−	0.146093i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	4.20243	+	3.51813i	0.203370	+	0.170254i
$428$		0			0
$429$	3.05300	−	4.45484i	0.147400	−	0.215082i
$430$		0			0
$431$	−31.7400	+	18.3251i	−1.52886	+	0.882688i	−0.529451	+	0.848340i	$0.677602\pi$
$431$	−31.7400	+	18.3251i	−1.52886	+	0.882688i	−0.999410	+	0.0343478i	$0.989065\pi$
$432$		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	0.677807	−	0.735240i	$-0.262930\pi$
$439$	7.96135	+	4.59649i	0.379975	+	0.219378i	−0.297833	+	0.954618i	$0.596264\pi$
$440$		0			0
$441$	17.9469	−	10.9045i	0.854614	−	0.519264i
$442$		0			0
$443$	−11.9703	+	20.7332i	−0.568727	+	0.985063i	0.427966	+	0.903795i	$0.359230\pi$
$443$	−11.9703	+	20.7332i	−0.568727	+	0.985063i	−0.996692	+	0.0812683i	$0.974103\pi$
$444$		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
$453$	1.22270	+	0.837945i	0.0574476	+	0.0393701i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	5.77786	+	3.33585i	0.270277	+	0.156044i	0.629013	−	0.777394i	$-0.283459\pi$
$457$	5.77786	+	3.33585i	0.270277	+	0.156044i	−0.358737	+	0.933439i	$0.616792\pi$
$458$		0			0
$459$	−3.17052	−	10.5485i	−0.147987	−	0.492362i
$460$		0			0
$461$	26.6895			1.24305			0.621527	−	0.783393i	$-0.286513\pi$
$461$	26.6895			1.24305			0.621527	+	0.783393i	$0.286513\pi$
$462$		0			0
$463$			10.9550i			0.509123i	0.967057	+	0.254562i	$0.0819312\pi$
$463$			10.9550i			0.509123i	−0.967057	+	0.254562i	$0.918069\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−0.952153	−	0.549726i	−0.0440604	−	0.0254383i	0.477808	−	0.878464i	$-0.341431\pi$
$467$	−0.952153	−	0.549726i	−0.0440604	−	0.0254383i	−0.521868	+	0.853026i	$0.674765\pi$
$468$		0			0
$469$	−27.0937	+	9.89620i	−1.25107	+	0.456964i
$470$		0			0
$471$	−34.8168	−	23.8607i	−1.60427	−	1.09944i
$472$		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	$-0.269015\pi$
$479$	−6.91657	−	11.9798i	−0.316026	−	0.547373i	−0.979655	+	0.200689i	$0.935682\pi$
$480$		0			0
$481$	−26.1176	−	15.0790i	−1.19086	−	0.687543i
$482$		0			0
$483$	5.53749	−	21.6320i	0.251964	−	0.984292i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	27.4385	−	15.8416i	1.24336	−	0.717854i	0.273582	−	0.961849i	$-0.411791\pi$
$487$	27.4385	−	15.8416i	1.24336	−	0.717854i	0.969776	+	0.243995i	$0.0784581\pi$
$488$		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	−0.962480	−	0.271352i	$-0.912529\pi$
$499$	−5.50065	+	9.52740i	−0.246243	+	0.426505i	0.716237	+	0.697857i	$0.245863\pi$
$500$		0			0
$501$	12.6567	+	26.4446i	0.565460	+	1.18146i
$502$		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
$507$	3.04620	−	1.45795i	0.135287	−	0.0647497i
$508$		0			0
$509$	−5.24557	+	9.08560i	−0.232506	+	0.402712i	−0.958545	−	0.284941i	$-0.908026\pi$
$509$	−5.24557	+	9.08560i	−0.232506	+	0.402712i	0.726039	+	0.687654i	$0.241359\pi$
$510$		0			0
$511$	2.80069	+	7.66771i	0.123895	+	0.339199i
$512$		0			0
$513$	−11.1291	+	11.8219i	−0.491362	+	0.521949i
$514$		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	$-0.251353\pi$
$521$	−6.00130	−	10.3946i	−0.262922	−	0.455394i	−0.967017	+	0.254712i	$0.918019\pi$
$522$		0			0
$523$	4.46891	−	7.74038i	0.195412	−	0.338463i	−0.751624	−	0.659592i	$-0.770729\pi$
$523$	4.46891	−	7.74038i	0.195412	−	0.338463i	0.947035	+	0.321129i	$0.104062\pi$
$524$		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
$537$	3.52383	−	5.14187i	0.152065	−	0.221888i
$538$		0			0
$539$	−5.55697	+	0.992874i	−0.239356	+	0.0427661i
$540$		0			0
$541$	−15.9695	+	27.6599i	−0.686581	+	1.18919i	0.286357	+	0.958123i	$0.407556\pi$
$541$	−15.9695	+	27.6599i	−0.686581	+	1.18919i	−0.972937	+	0.231069i	$0.925778\pi$
$542$		0			0
$543$	16.8857	+	35.2806i	0.724635	+	1.51404i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			33.6313i			1.43797i	0.695026	+	0.718984i	$0.255393\pi$
$547$			33.6313i			1.43797i	−0.695026	+	0.718984i	$0.744607\pi$
$548$		0			0
$549$	5.79577	−	2.24252i	0.247357	−	0.0957085i
$550$		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	$-0.0945695\pi$
$557$	5.30000	+	9.17988i	0.224568	+	0.388964i	−0.731621	+	0.681711i	$0.761236\pi$
$558$		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	$-0.682073\pi$
$563$	−1.98833	+	1.14796i	−0.0837980	+	0.0483808i	0.457515	+	0.889202i	$0.348739\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.984852	−	23.7914i	−0.0413599	−	0.999144i
$568$		0			0
$569$	−24.1648	−	13.9515i	−1.01304	−	0.584878i	−0.100959	−	0.994891i	$-0.532191\pi$
$569$	−24.1648	−	13.9515i	−1.01304	−	0.584878i	−0.912080	+	0.410012i	$0.865524\pi$
$570$		0			0
$571$	3.11649	+	5.39791i	0.130421	+	0.225896i	0.923839	−	0.382782i	$-0.125034\pi$
$571$	3.11649	+	5.39791i	0.130421	+	0.225896i	−0.793418	+	0.608677i	$0.791700\pi$
$572$		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	0.694484	−	0.719508i	$-0.255632\pi$
$577$	−6.62662	−	11.4776i	−0.275870	−	0.477820i	−0.970354	+	0.241687i	$0.922299\pi$
$578$		0			0
$579$	−10.8592	+	15.8453i	−0.451291	+	0.658510i
$580$		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
$591$	−25.4011	+	12.1572i	−1.04486	+	0.500082i
$592$		0			0
$593$	2.38715	+	1.37822i	0.0980284	+	0.0565967i	0.548213	−	0.836339i	$-0.315308\pi$
$593$	2.38715	+	1.37822i	0.0980284	+	0.0565967i	−0.450184	+	0.892936i	$0.648642\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.22066	−	1.78115i	0.0499583	−	0.0728976i
$598$		0			0
$599$	16.2530	−	9.38368i	0.664080	−	0.383407i	−0.129750	−	0.991547i	$-0.541417\pi$
$599$	16.2530	−	9.38368i	0.664080	−	0.383407i	0.793830	+	0.608140i	$0.208084\pi$
$600$		0			0
$601$			16.5669i			0.675779i	0.941186	+	0.337890i	$0.109713\pi$
$601$			16.5669i			0.675779i	−0.941186	+	0.337890i	$0.890287\pi$
$602$		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	−0.296213	−	0.955122i	$-0.595724\pi$
$607$	16.7301	−	28.9773i	0.679053	−	1.17615i	0.975266	−	0.221032i	$-0.0709427\pi$
$608$		0			0
$609$	−8.24971	−	29.4648i	−0.334295	−	1.19397i
$610$		0			0
$611$	−9.29381	−	5.36578i	−0.375987	−	0.217076i
$612$		0			0
$613$	−32.5231	+	18.7772i	−1.31359	+	0.758404i	−0.982690	−	0.185260i	$-0.940687\pi$
$613$	−32.5231	+	18.7772i	−1.31359	+	0.758404i	−0.330905	+	0.943664i	$0.607354\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−22.5088			−0.906172			−0.453086	−	0.891467i	$-0.649677\pi$
$617$	−22.5088			−0.906172			−0.453086	+	0.891467i	$0.649677\pi$
$618$		0			0
$619$	23.3812	−	13.4991i	0.939770	−	0.542576i	0.0498816	−	0.998755i	$-0.484116\pi$
$619$	23.3812	−	13.4991i	0.939770	−	0.542576i	0.889888	+	0.456179i	$0.150782\pi$
$620$		0			0
$621$	−18.4355	−	17.3551i	−0.739791	−	0.696438i
$622$		0			0
$623$	−5.45272	+	6.51332i	−0.218459	+	0.260951i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	3.93676	−	1.88418i	0.157219	−	0.0752468i
$628$		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
$633$	−11.9591	+	5.72376i	−0.475331	+	0.227499i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−25.4542	−	9.19909i	−1.00853	−	0.364481i
$638$		0			0
$639$	24.2642	+	19.5420i	0.959878	+	0.773069i
$640$		0			0
$641$	−26.6664	+	15.3959i	−1.05326	+	0.608100i	−0.923560	−	0.383453i	$-0.874735\pi$
$641$	−26.6664	+	15.3959i	−1.05326	+	0.608100i	−0.129700	+	0.991553i	$0.541401\pi$
$642$		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	0.808986	−	0.587828i	$-0.200017\pi$
$647$	43.8152	−	25.2967i	1.72255	−	0.994516i	0.913567	−	0.406689i	$-0.133317\pi$
$648$		0			0
$649$	−3.99966	−	2.30920i	−0.157000	−	0.0906441i
$650$		0			0
$651$	20.9027	−	21.3761i	0.819243	−	0.837795i
$652$		0			0
$653$	2.64220	−	4.57643i	0.103397	−	0.179090i	−0.809685	−	0.586865i	$-0.800362\pi$
$653$	2.64220	−	4.57643i	0.103397	−	0.179090i	0.913082	+	0.407775i	$0.133695\pi$
$654$		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	−0.937180	−	0.348845i	$-0.886574\pi$
$661$	−28.3751	+	16.3823i	−1.10366	+	0.637199i	−0.166481	+	0.986045i	$0.553241\pi$
$662$		0			0
$663$	−8.02515	+	11.7101i	−0.311671	+	0.454781i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−28.1763	−	16.2676i	−1.09099	−	0.629883i
$668$		0			0
$669$	−32.7103	+	15.6555i	−1.26465	+	0.605278i
$670$		0			0
$671$	−1.67050			−0.0644891
$672$		0			0
$673$		−	38.5194i		−	1.48481i	−0.669950	−	0.742406i	$-0.733685\pi$
$673$		−	38.5194i		−	1.48481i	0.669950	−	0.742406i	$-0.266315\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	16.5938	+	9.58044i	0.637752	+	0.368206i	0.783748	−	0.621079i	$-0.213305\pi$
$677$	16.5938	+	9.58044i	0.637752	+	0.368206i	−0.145996	+	0.989285i	$0.546639\pi$
$678$		0			0
$679$	−2.64225	−	0.462805i	−0.101400	−	0.0177608i
$680$		0			0
$681$	4.48649	−	6.54654i	0.171923	−	0.250864i
$682$		0			0
$683$	−14.4812	−	25.0821i	−0.554107	−	0.959741i	−0.997972	−	0.0636479i	$-0.979727\pi$
$683$	−14.4812	−	25.0821i	−0.554107	−	0.959741i	0.443866	−	0.896093i	$-0.353607\pi$
$684$		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	0.999999	+	0.00118303i	$0.000376571\pi$
$691$	39.4572	+	22.7806i	1.50102	+	0.866616i	0.501024	+	0.865433i	$0.332957\pi$
$692$		0			0
$693$	−2.06088	+	6.05995i	−0.0782862	+	0.230198i
$694$		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	−0.618506	−	0.785780i	$-0.712262\pi$
$709$	9.88537	−	17.1220i	0.371253	−	0.643029i	0.989759	+	0.142752i	$0.0455950\pi$
$710$		0			0
$711$	14.6436	+	37.8463i	0.549180	+	1.41935i
$712$		0			0
$713$		−	31.7904i		−	1.19056i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	21.1391	+	44.1675i	0.789454	+	1.64947i
$718$		0			0
$719$	−0.740641	+	1.28283i	−0.0276212	+	0.0478414i	−0.879506	−	0.475889i	$-0.842127\pi$
$719$	−0.740641	+	1.28283i	−0.0276212	+	0.0478414i	0.851884	+	0.523730i	$0.175460\pi$
$720$		0			0
$721$	−16.6072	+	19.8374i	−0.618484	+	0.738784i
$722$		0			0
$723$	12.5441	−	18.3040i	0.466521	−	0.680733i
$724$		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	−0.233605	−	0.972331i	$-0.575052\pi$
$733$	19.6357	−	34.0100i	0.725261	−	1.25619i	0.958866	−	0.283857i	$-0.0916143\pi$
$734$		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	0.580139	−	0.814518i	$-0.302998\pi$
$739$	−11.2904	−	19.5555i	−0.415324	−	0.719362i	−0.995462	+	0.0951558i	$0.969665\pi$
$740$		0			0
$741$	20.8634	+	1.61402i	0.766436	+	0.0592926i
$742$		0			0
$743$	26.6330			0.977070			0.488535	−	0.872544i	$-0.337532\pi$
$743$	26.6330			0.977070			0.488535	+	0.872544i	$0.337532\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−30.1282	−	24.2647i	−1.10233	−	0.887799i
$748$		0			0
$749$	31.0510	−	37.0906i	1.13458	−	1.35526i
$750$		0			0
$751$	8.62709	−	14.9426i	0.314807	−	0.545262i	−0.664589	−	0.747209i	$-0.731393\pi$
$751$	8.62709	−	14.9426i	0.314807	−	0.545262i	0.979396	+	0.201947i	$0.0647268\pi$
$752$		0			0
$753$	16.1466	−	7.72793i	0.588413	−	0.281621i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	25.1712i		−	0.914863i	−0.889245	−	0.457431i	$-0.848770\pi$
$757$		−	25.1712i		−	0.914863i	0.889245	−	0.457431i	$-0.151230\pi$
$758$		0			0
$759$	2.93826	+	6.13913i	0.106652	+	0.222836i
$760$		0			0
$761$	0.00796126	−	0.0137893i	0.000288596	−	0.000499862i	−0.865881	−	0.500250i	$-0.833241\pi$
$761$	0.00796126	−	0.0137893i	0.000288596	−	0.000499862i	0.866170	+	0.499750i	$0.166575\pi$
$762$		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	$0.0755213\pi$
$769$			13.0356i			0.470075i	−0.971986	+	0.235037i	$0.924479\pi$
$770$		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	$-0.844110\pi$
$773$	−25.4758	+	14.7085i	−0.916301	+	0.529027i	−0.0338481	+	0.999427i	$0.510776\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	34.6268	+	8.86395i	1.24223	+	0.317993i
$778$		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	0.845154	−	0.534522i	$-0.179508\pi$
$787$	−1.13148	−	1.95977i	−0.0403327	−	0.0698584i	−0.885487	+	0.464664i	$0.846175\pi$
$788$		0			0
$789$	29.5395	+	20.2441i	1.05164	+	0.720708i
$790$		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
$801$	3.47567	+	8.98283i	0.122807	+	0.317393i
$802$		0			0
$803$	−2.15479	−	1.24407i	−0.0760409	−	0.0439022i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−35.4596	−	24.3012i	−1.24824	−	0.855444i
$808$		0			0
$809$	−21.2506	+	12.2690i	−0.747130	+	0.431356i	−0.824656	−	0.565635i	$-0.808631\pi$
$809$	−21.2506	+	12.2690i	−0.747130	+	0.431356i	0.0775260	+	0.996990i	$0.475298\pi$
$810$		0			0
$811$		−	38.7927i		−	1.36220i	−0.732192	−	0.681098i	$-0.761503\pi$
$811$		−	38.7927i		−	1.36220i	0.732192	−	0.681098i	$-0.238497\pi$
$812$		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
$819$	−23.0849	+	20.2219i	−0.806650	+	0.706611i
$820$		0			0
$821$	−11.8734	−	6.85513i	−0.414386	−	0.239246i	0.278287	−	0.960498i	$-0.410233\pi$
$821$	−11.8734	−	6.85513i	−0.414386	−	0.239246i	−0.692672	+	0.721252i	$0.743567\pi$
$822$		0			0
$823$	7.00040	−	4.04168i	0.244019	−	0.140884i	−0.373004	−	0.927830i	$-0.621672\pi$
$823$	7.00040	−	4.04168i	0.244019	−	0.140884i	0.617022	+	0.786946i	$0.288339\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−37.6581			−1.30950			−0.654751	−	0.755845i	$-0.727226\pi$
$827$	−37.6581			−1.30950			−0.654751	+	0.755845i	$0.727226\pi$
$828$		0			0
$829$	−15.4475	+	8.91864i	−0.536515	+	0.309757i	−0.743665	−	0.668552i	$-0.766914\pi$
$829$	−15.4475	+	8.91864i	−0.536515	+	0.309757i	0.207150	+	0.978309i	$0.433581\pi$
$830$		0			0
$831$	−14.9050	+	21.7489i	−0.517049	+	0.754462i
$832$		0			0
$833$	14.6071	−	2.60988i	0.506106	−	0.0904269i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−9.75811	−	32.4658i	−0.337290	−	1.12218i
$838$		0			0
$839$	4.49497			0.155183			0.0775917	−	0.996985i	$-0.475277\pi$
$839$	4.49497			0.155183			0.0775917	+	0.996985i	$0.475277\pi$
$840$		0			0
$841$	−15.5825			−0.537329
$842$		0			0
$843$	13.4212	+	28.0419i	0.462250	+	0.965814i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−17.5774	+	20.9963i	−0.603966	+	0.721443i
$848$		0			0
$849$	−38.5598	−	26.4259i	−1.32337	−	0.906934i
$850$		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	$-0.664375\pi$
$857$	0.365051	−	0.210762i	0.0124699	−	0.00719949i	0.506222	+	0.862403i	$0.331042\pi$
$858$		0			0
$859$	17.0294	+	9.83192i	0.581035	+	0.335461i	0.761545	−	0.648112i	$-0.224441\pi$
$859$	17.0294	+	9.83192i	0.581035	+	0.335461i	−0.180509	+	0.983573i	$0.557775\pi$
$860$		0			0
$861$	37.2818	−	10.4383i	1.27056	−	0.355737i
$862$		0			0
$863$	−0.451820	+	0.782575i	−0.0153801	+	0.0266392i	−0.873613	−	0.486621i	$-0.838229\pi$
$863$	−0.451820	+	0.782575i	−0.0153801	+	0.0266392i	0.858233	+	0.513260i	$0.171563\pi$
$864$		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
$873$	−1.90787	+	2.36889i	−0.0645715	+	0.0801749i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−13.2661	−	7.65916i	−0.447963	−	0.258632i	0.259006	−	0.965876i	$-0.416605\pi$
$877$	−13.2661	−	7.65916i	−0.447963	−	0.258632i	−0.706970	+	0.707244i	$0.749938\pi$
$878$		0			0
$879$	10.8013	+	22.5679i	0.364317	+	0.761196i
$880$		0			0
$881$	43.8614			1.47773			0.738863	−	0.673855i	$-0.235363\pi$
$881$	43.8614			1.47773			0.738863	+	0.673855i	$0.235363\pi$
$882$		0			0
$883$		−	2.91300i		−	0.0980304i	−0.998798	−	0.0490152i	$-0.984392\pi$
$883$		−	2.91300i		−	0.0980304i	0.998798	−	0.0490152i	$-0.0156083\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.9001	−	7.44790i	−0.433145	−	0.250076i	0.267541	−	0.963547i	$-0.413789\pi$
$887$	−12.9001	−	7.44790i	−0.433145	−	0.250076i	−0.700685	+	0.713470i	$0.747122\pi$
$888$		0			0
$889$	3.54739	−	20.2528i	0.118976	−	0.679259i
$890$		0			0
$891$	4.88510	+	5.36766i	0.163657	+	0.179823i
$892$		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
$903$	−1.01200	−	3.61448i	−0.0336772	−	0.120282i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−16.5393	+	9.54899i	−0.549180	+	0.317069i	−0.748791	−	0.662806i	$-0.769365\pi$
$907$	−16.5393	+	9.54899i	−0.549180	+	0.317069i	0.199611	+	0.979875i	$0.436032\pi$
$908$		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	−0.510668	−	0.859778i	$-0.670602\pi$
$919$	14.8318	−	25.6894i	0.489255	−	0.847415i	0.999924	+	0.0123630i	$0.00393538\pi$
$920$		0			0
$921$	14.6006	−	6.98804i	0.481107	−	0.230264i
$922$		0			0
$923$		−	40.1537i		−	1.32168i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	10.5857	+	27.3587i	0.347681	+	0.898577i
$928$		0			0
$929$	16.8256	−	29.1428i	0.552030	−	0.956144i	−0.446098	−	0.894984i	$-0.647187\pi$
$929$	16.8256	−	29.1428i	0.552030	−	0.956144i	0.998128	−	0.0611601i	$-0.0194800\pi$
$930$		0			0
$931$	−14.0975	−	16.7234i	−0.462027	−	0.548087i
$932$		0			0
$933$	−41.9087	−	28.7209i	−1.37203	−	0.940281i
$934$		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	$-0.0751955\pi$
$941$	8.69431	+	15.0590i	0.283426	+	0.490909i	−0.688800	+	0.724951i	$0.741862\pi$
$942$		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	−0.285496	−	0.958380i	$-0.592158\pi$
$947$	21.1485	−	36.6302i	0.687233	−	1.19032i	0.972729	−	0.231943i	$-0.0745083\pi$
$948$		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	$-0.271845\pi$
$953$	40.5612			1.31391			0.656953	+	0.753932i	$0.271845\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	7.69303	+	5.27220i	0.248680	+	0.170426i
$958$		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
$963$	−19.7925	−	51.1534i	−0.637804	−	1.64840i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			37.6713i			1.21143i	0.795682	+	0.605714i	$0.207112\pi$
$967$			37.6713i			1.21143i	−0.795682	+	0.605714i	$0.792888\pi$
$968$		0			0
$969$	−10.3482	+	4.95277i	−0.332432	+	0.159106i
$970$		0			0
$971$	21.5452	−	37.3173i	0.691418	−	1.19757i	−0.279956	−	0.960013i	$-0.590320\pi$
$971$	21.5452	−	37.3173i	0.691418	−	1.19757i	0.971373	−	0.237558i	$-0.0763469\pi$
$972$		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	$-0.285469\pi$
$977$	−11.3970	−	19.7402i	−0.364622	−	0.631545i	−0.988716	+	0.149805i	$0.952135\pi$
$978$		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	$-0.410532\pi$
$983$	39.1321	−	22.5929i	1.24812	−	0.720602i	0.970734	+	0.240157i	$0.0771990\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	12.3218	+	3.15419i	0.392206	+	0.100399i
$988$		0			0
$989$	−3.45641	−	1.99556i	−0.109907	−	0.0634551i
$990$		0			0
$991$	−25.2760	−	43.7793i	−0.802919	−	1.39070i	−0.917687	−	0.397304i	$-0.869946\pi$
$991$	−25.2760	−	43.7793i	−0.802919	−	1.39070i	0.114768	−	0.993392i	$-0.463388\pi$
$992$		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	0.995170	−	0.0981654i	$-0.0312974\pi$
$997$	13.0271	+	22.5635i	0.412571	+	0.714595i	−0.582599	+	0.812760i	$0.697964\pi$
$998$		0			0
$999$	27.7807	−	29.5100i	0.878942	−	0.933656i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bh.a.101.2	✓	10	105.17	odd	12
420.2.bh.a.341.2	yes	10	5.2	odd	4
420.2.bh.b.101.4	yes	10	35.17	even	12
420.2.bh.b.341.4	yes	10	15.2	even	4
2100.2.bi.j.101.2		10	35.3	even	12
2100.2.bi.j.1601.2		10	15.8	even	4
2100.2.bi.k.101.4		10	105.38	odd	12
2100.2.bi.k.1601.4		10	5.3	odd	4
2100.2.bo.g.1349.2		20	3.2	odd	2
2100.2.bo.g.1349.9		20	15.14	odd	2
2100.2.bo.g.1949.2		20	35.24	odd	6
2100.2.bo.g.1949.9		20	7.3	odd	6
2100.2.bo.h.1349.3		20	5.4	even	2	inner
2100.2.bo.h.1349.8		20	1.1	even	1	trivial
2100.2.bo.h.1949.3		20	21.17	even	6	inner
2100.2.bo.h.1949.8		20	105.59	even	6	inner
2940.2.d.a.881.1		10	35.12	even	12
2940.2.d.a.881.2		10	105.2	even	12
2940.2.d.b.881.9		10	105.47	odd	12
2940.2.d.b.881.10		10	35.2	odd	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)

\(f(q)\)	\(=\)	\(q+(1.56233 - 0.747749i) q^{3} +(2.60608 + 0.456468i) q^{7} +(1.88174 - 2.33646i) q^{9} +O(q^{10})\)	\(q+(1.56233 - 0.747749i) q^{3} +(2.60608 + 0.456468i) q^{7} +(1.88174 - 2.33646i) q^{9} +(-0.698384 + 0.403212i) q^{11} -3.86649 q^{13} +(1.83578 - 1.05989i) q^{17} +(-2.70603 - 1.56233i) q^{19} +(4.41287 - 1.23554i) q^{21} +(2.43635 - 4.21989i) q^{23} +(1.19282 - 5.05739i) q^{27} -6.67701i q^{29} +(5.65010 - 3.26209i) q^{31} +(-0.789604 + 1.15217i) q^{33} +(6.75485 + 3.89991i) q^{37} +(-6.04074 + 2.89117i) q^{39} +8.44841 q^{41} -0.819076i q^{43} +(2.40368 + 1.38776i) q^{47} +(6.58327 + 2.37918i) q^{49} +(2.07556 - 3.02860i) q^{51} +(-6.67216 - 11.5565i) q^{53} +(-5.39594 - 0.417438i) q^{57} +(2.86351 + 4.95974i) q^{59} +(1.79397 + 1.03575i) q^{61} +(5.97049 - 5.23004i) q^{63} +(-9.44157 + 5.45110i) q^{67} +(0.650969 - 8.41464i) q^{69} +10.3850i q^{71} +(1.54270 + 2.67203i) q^{73} +(-2.00410 + 0.732012i) q^{77} +(-6.76342 + 11.7146i) q^{79} +(-1.91809 - 8.79323i) q^{81} -12.8948i q^{83} +(-4.99273 - 10.4317i) q^{87} +(-1.60530 + 2.78046i) q^{89} +(-10.0764 - 1.76493i) q^{91} +(6.38809 - 9.32131i) q^{93} -1.01388 q^{97} +(-0.372090 + 2.39049i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{9}+O(q^{10}) \) 20 * q + 6 * q^9	\( 20 q + 6 q^{9} - 12 q^{11} - 6 q^{19} + 20 q^{21} + 30 q^{31} - 30 q^{39} - 16 q^{41} + 26 q^{49} - 88 q^{51} + 84 q^{61} + 28 q^{69} - 2 q^{79} + 82 q^{81} - 56 q^{89} - 22 q^{91} - 72 q^{99}+O(q^{100}) \) 20 * q + 6 * q^9 - 12 * q^11 - 6 * q^19 + 20 * q^21 + 30 * q^31 - 30 * q^39 - 16 * q^41 + 26 * q^49 - 88 * q^51 + 84 * q^61 + 28 * q^69 - 2 * q^79 + 82 * q^81 - 56 * q^89 - 22 * q^91 - 72 * q^99

Introduction

L-functions

Modular forms

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