LMFDB - Embedded newform 2100.2.bo.h.1949.7

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			1949.7
Root			$-0.368412 + 1.69242i$ of defining polynomial
Character	$\chi$	$=$	2100.1949
Dual form			2100.2.bo.h.1349.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.368412 - 1.69242i) q^{3} +(1.93884 + 1.80025i) q^{7} +(-2.72854 - 1.24701i) q^{9} +O(q^{10})$	\(q+(0.368412 - 1.69242i) q^{3} +(1.93884 + 1.80025i) q^{7} +(-2.72854 - 1.24701i) q^{9} +(4.05595 + 2.34170i) q^{11} +2.18938 q^{13} +(-6.49492 - 3.74984i) q^{17} +(0.638109 - 0.368412i) q^{19} +(3.76107 - 2.61808i) q^{21} +(4.03930 + 6.99627i) q^{23} +(-3.11570 + 4.15842i) q^{27} +1.15414i q^{29} +(8.95201 + 5.16845i) q^{31} +(5.45740 - 6.00164i) q^{33} +(3.99970 - 2.30923i) q^{37} +(0.806595 - 3.70534i) q^{39} -1.43758 q^{41} -9.24142i q^{43} +(7.52098 - 4.34224i) q^{47} +(0.518179 + 6.98079i) q^{49} +(-8.73910 + 9.61061i) q^{51} +(-4.06174 + 7.03514i) q^{53} +(-0.388420 - 1.21567i) q^{57} +(-3.48730 + 6.04018i) q^{59} +(5.13811 - 2.96649i) q^{61} +(-3.04526 - 7.32983i) q^{63} +(-1.19795 - 0.691639i) q^{67} +(13.3287 - 4.25866i) q^{69} +7.26258i q^{71} +(0.122026 - 0.211355i) q^{73} +(3.64817 + 11.8419i) q^{77} +(5.79653 + 10.0399i) q^{79} +(5.88991 + 6.80507i) q^{81} -16.4610i q^{83} +(1.95328 + 0.425199i) q^{87} +(-0.658248 - 1.14012i) q^{89} +(4.24485 + 3.94144i) q^{91} +(12.0452 - 13.2464i) q^{93} +4.84232 q^{97} +(-8.14670 - 11.4473i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

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

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
$3$	0.368412	−	1.69242i	0.212703	−	0.977117i
$3$	0.368412	−	1.69242i	0.212703	−	0.977117i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.93884	+	1.80025i	0.732812	+	0.680432i
$7$	1.93884	+	1.80025i	0.732812	+	0.680432i
$8$		0			0
$9$	−2.72854	−	1.24701i	−0.909515	−	0.415671i
$10$		0			0
$11$	4.05595	+	2.34170i	1.22292	+	0.706050i	0.965538	−	0.260261i	$-0.0838085\pi$
$11$	4.05595	+	2.34170i	1.22292	+	0.706050i	0.257377	+	0.966311i	$0.417142\pi$
$12$		0			0
$13$	2.18938			0.607225			0.303612	−	0.952796i	$-0.401807\pi$
$13$	2.18938			0.607225			0.303612	+	0.952796i	$0.401807\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.49492	−	3.74984i	−1.57525	−	0.909470i	−0.995509	−	0.0946686i	$-0.969821\pi$
$17$	−6.49492	−	3.74984i	−1.57525	−	0.909470i	−0.579740	−	0.814802i	$-0.696846\pi$
$18$		0			0
$19$	0.638109	−	0.368412i	0.146392	−	0.0845196i	−0.425015	−	0.905186i	$-0.639731\pi$
$19$	0.638109	−	0.368412i	0.146392	−	0.0845196i	0.571407	+	0.820667i	$0.306398\pi$
$20$		0			0
$21$	3.76107	−	2.61808i	0.820732	−	0.571313i
$22$		0			0
$23$	4.03930	+	6.99627i	0.842252	+	1.45882i	0.887986	+	0.459870i	$0.152104\pi$
$23$	4.03930	+	6.99627i	0.842252	+	1.45882i	−0.0457338	+	0.998954i	$0.514563\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.11570	+	4.15842i	−0.599616	+	0.800288i
$28$		0			0
$29$			1.15414i			0.214318i	0.994242	+	0.107159i	$0.0341754\pi$
$29$			1.15414i			0.214318i	−0.994242	+	0.107159i	$0.965825\pi$
$30$		0			0
$31$	8.95201	+	5.16845i	1.60783	+	0.928280i	0.989855	+	0.142081i	$0.0453794\pi$
$31$	8.95201	+	5.16845i	1.60783	+	0.928280i	0.617974	+	0.786199i	$0.287954\pi$
$32$		0			0
$33$	5.45740	−	6.00164i	0.950012	−	1.04475i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.99970	−	2.30923i	0.657547	−	0.379635i	−0.133795	−	0.991009i	$-0.542716\pi$
$37$	3.99970	−	2.30923i	0.657547	−	0.379635i	0.791342	+	0.611374i	$0.209383\pi$
$38$		0			0
$39$	0.806595	−	3.70534i	0.129159	−	0.593330i
$40$		0			0
$41$	−1.43758			−0.224513			−0.112256	−	0.993679i	$-0.535808\pi$
$41$	−1.43758			−0.224513			−0.112256	+	0.993679i	$0.535808\pi$
$42$		0			0
$43$		−	9.24142i		−	1.40930i	−0.709554	−	0.704651i	$-0.751103\pi$
$43$		−	9.24142i		−	1.40930i	0.709554	−	0.704651i	$-0.248897\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	7.52098	−	4.34224i	1.09705	−	0.633380i	0.161603	−	0.986856i	$-0.448333\pi$
$47$	7.52098	−	4.34224i	1.09705	−	0.633380i	0.935444	+	0.353475i	$0.115000\pi$
$48$		0			0
$49$	0.518179	+	6.98079i	0.0740255	+	0.997256i
$50$		0			0
$51$	−8.73910	+	9.61061i	−1.22372	+	1.34576i
$52$		0			0
$53$	−4.06174	+	7.03514i	−0.557923	+	0.966351i	0.439747	+	0.898122i	$0.355068\pi$
$53$	−4.06174	+	7.03514i	−0.557923	+	0.966351i	−0.997670	+	0.0682291i	$0.978265\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.388420	−	1.21567i	−0.0514475	−	0.161020i
$58$		0			0
$59$	−3.48730	+	6.04018i	−0.454008	+	0.786364i	−0.998631	−	0.0523168i	$-0.983339\pi$
$59$	−3.48730	+	6.04018i	−0.454008	+	0.786364i	0.544623	+	0.838681i	$0.316673\pi$
$60$		0			0
$61$	5.13811	−	2.96649i	0.657867	−	0.379820i	−0.133596	−	0.991036i	$-0.542653\pi$
$61$	5.13811	−	2.96649i	0.657867	−	0.379820i	0.791464	+	0.611216i	$0.209319\pi$
$62$		0			0
$63$	−3.04526	−	7.32983i	−0.383667	−	0.923472i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.19795	−	0.691639i	−0.146353	−	0.0844971i	0.425035	−	0.905177i	$-0.360262\pi$
$67$	−1.19795	−	0.691639i	−0.146353	−	0.0844971i	−0.571389	+	0.820680i	$0.693595\pi$
$68$		0			0
$69$	13.3287	−	4.25866i	1.60459	−	0.512683i
$70$		0			0
$71$			7.26258i			0.861909i	0.902374	+	0.430955i	$0.141823\pi$
$71$			7.26258i			0.861909i	−0.902374	+	0.430955i	$0.858177\pi$
$72$		0			0
$73$	0.122026	−	0.211355i	0.0142820	−	0.0247372i	−0.858796	−	0.512318i	$-0.828787\pi$
$73$	0.122026	−	0.211355i	0.0142820	−	0.0247372i	0.873078	+	0.487580i	$0.162120\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.64817	+	11.8419i	0.415747	+	1.34951i
$78$		0			0
$79$	5.79653	+	10.0399i	0.652160	+	1.12957i	0.982598	+	0.185747i	$0.0594704\pi$
$79$	5.79653	+	10.0399i	0.652160	+	1.12957i	−0.330438	+	0.943828i	$0.607196\pi$
$80$		0			0
$81$	5.88991	+	6.80507i	0.654435	+	0.756119i
$82$		0			0
$83$		−	16.4610i		−	1.80683i	−0.428772	−	0.903413i	$-0.641054\pi$
$83$		−	16.4610i		−	1.80683i	0.428772	−	0.903413i	$-0.358946\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.95328	+	0.425199i	0.209414	+	0.0455862i
$88$		0			0
$89$	−0.658248	−	1.14012i	−0.0697741	−	0.120852i	0.829028	−	0.559208i	$-0.188895\pi$
$89$	−0.658248	−	1.14012i	−0.0697741	−	0.120852i	−0.898802	+	0.438355i	$0.855561\pi$
$90$		0			0
$91$	4.24485	+	3.94144i	0.444981	+	0.413175i
$92$		0			0
$93$	12.0452	−	13.2464i	1.24903	−	1.37359i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	4.84232			0.491663			0.245832	−	0.969313i	$-0.420939\pi$
$97$	4.84232			0.491663			0.245832	+	0.969313i	$0.420939\pi$
$98$		0			0
$99$	−8.14670	−	11.4473i	−0.818775	−	1.15049i
$100$		0			0
$101$	1.38435	−	2.39776i	0.137748	−	0.238586i	−0.788896	−	0.614527i	$-0.789347\pi$
$101$	1.38435	−	2.39776i	0.137748	−	0.238586i	0.926644	+	0.375941i	$0.122680\pi$
$102$		0			0
$103$	−4.08187	−	7.07000i	−0.402199	−	0.696628i	0.591792	−	0.806090i	$-0.298421\pi$
$103$	−4.08187	−	7.07000i	−0.402199	−	0.696628i	−0.993991	+	0.109462i	$0.965087\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.107578	+	0.186331i	0.0104000	+	0.0180133i	0.871179	−	0.490966i	$-0.163356\pi$
$107$	0.107578	+	0.186331i	0.0104000	+	0.0180133i	−0.860779	+	0.508980i	$0.830023\pi$
$108$		0			0
$109$	1.08683	−	1.88245i	0.104100	−	0.180306i	−0.809270	−	0.587436i	$-0.800137\pi$
$109$	1.08683	−	1.88245i	0.104100	−	0.180306i	0.913370	+	0.407131i	$0.133471\pi$
$110$		0			0
$111$	−2.43464	−	7.61990i	−0.231085	−	0.723249i
$112$		0			0
$113$	11.2195			1.05544			0.527719	−	0.849419i	$-0.323048\pi$
$113$	11.2195			1.05544			0.527719	+	0.849419i	$0.323048\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−5.97382	−	2.73019i	−0.552280	−	0.252406i
$118$		0			0
$119$	−5.84192	−	18.9628i	−0.535528	−	1.73832i
$120$		0			0
$121$	5.46716	+	9.46940i	0.497015	+	0.860854i
$122$		0			0
$123$	−0.529624	+	2.43299i	−0.0477546	+	0.219375i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	17.2228i		−	1.52828i	−0.645051	−	0.764140i	$-0.723164\pi$
$127$		−	17.2228i		−	1.52828i	0.645051	−	0.764140i	$-0.276836\pi$
$128$		0			0
$129$	−15.6403	−	3.40465i	−1.37705	−	0.299763i
$130$		0			0
$131$	−8.65810	−	14.9963i	−0.756462	−	1.31023i	−0.944644	−	0.328096i	$-0.893593\pi$
$131$	−8.65810	−	14.9963i	−0.756462	−	1.31023i	0.188183	−	0.982134i	$-0.439740\pi$
$132$		0			0
$133$	1.90042	+	0.434466i	0.164788	+	0.0376730i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.59375	−	9.68866i	0.477907	−	0.827758i	−0.521773	−	0.853085i	$-0.674729\pi$
$137$	5.59375	−	9.68866i	0.477907	−	0.827758i	0.999679	+	0.0253261i	$0.00806240\pi$
$138$		0			0
$139$		−	2.16017i		−	0.183223i	−0.995795	−	0.0916116i	$-0.970798\pi$
$139$		−	2.16017i		−	0.183223i	0.995795	−	0.0916116i	$-0.0292018\pi$
$140$		0			0
$141$	−4.57805	−	14.3284i	−0.385542	−	1.20667i
$142$		0			0
$143$	8.88002	+	5.12688i	0.742585	+	0.428731i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	12.0053	+	1.69484i	0.990181	+	0.139788i
$148$		0			0
$149$	−1.37427	+	0.793438i	−0.112585	+	0.0650010i	−0.555235	−	0.831693i	$-0.687372\pi$
$149$	−1.37427	+	0.793438i	−0.112585	+	0.0650010i	0.442650	+	0.896694i	$0.354038\pi$
$150$		0			0
$151$	−5.12229	+	8.87206i	−0.416846	+	0.721998i	−0.995620	−	0.0934894i	$-0.970198\pi$
$151$	−5.12229	+	8.87206i	−0.416846	+	0.721998i	0.578774	+	0.815488i	$0.303531\pi$
$152$		0			0
$153$	13.0456	+	18.3309i	1.05467	+	1.48196i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−3.24572	+	5.62174i	−0.259036	+	0.448664i	−0.965984	−	0.258602i	$-0.916738\pi$
$157$	−3.24572	+	5.62174i	−0.259036	+	0.448664i	0.706948	+	0.707266i	$0.250072\pi$
$158$		0			0
$159$	10.4100	+	9.46599i	0.825566	+	0.750702i
$160$		0			0
$161$	−4.76352	+	20.8364i	−0.375418	+	1.64214i
$162$		0			0
$163$	4.64797	−	2.68350i	0.364057	−	0.210188i	−0.306802	−	0.951773i	$-0.599259\pi$
$163$	4.64797	−	2.68350i	0.364057	−	0.210188i	0.670859	+	0.741585i	$0.265926\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			6.84082i			0.529359i	0.964336	+	0.264679i	$0.0852661\pi$
$167$			6.84082i			0.529359i	−0.964336	+	0.264679i	$0.914734\pi$
$168$		0			0
$169$	−8.20661			−0.631278
$170$		0			0
$171$	−2.20052	+	0.209499i	−0.168278	+	0.0160208i
$172$		0			0
$173$	−10.0739	+	5.81618i	−0.765906	+	0.442196i	−0.831412	−	0.555656i	$-0.812467\pi$
$173$	−10.0739	+	5.81618i	−0.765906	+	0.442196i	0.0655063	+	0.997852i	$0.479134\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	8.93773	+	8.12724i	0.671801	+	0.610881i
$178$		0			0
$179$	6.95741	+	4.01686i	0.520021	+	0.300234i	0.736943	−	0.675955i	$-0.236268\pi$
$179$	6.95741	+	4.01686i	0.520021	+	0.300234i	−0.216922	+	0.976189i	$0.569602\pi$
$180$		0			0
$181$		−	9.81789i		−	0.729758i	−0.931055	−	0.364879i	$-0.881110\pi$
$181$		−	9.81789i		−	0.729758i	0.931055	−	0.364879i	$-0.118890\pi$
$182$		0			0
$183$	−3.12759	−	9.78871i	−0.231198	−	0.723602i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−17.5620	−	30.4184i	−1.28426	−	2.22441i
$188$		0			0
$189$	−13.5270	+	2.45345i	−0.983947	+	0.178462i
$190$		0			0
$191$	13.9054	−	8.02830i	1.00616	−	0.580907i	0.0960953	−	0.995372i	$-0.469365\pi$
$191$	13.9054	−	8.02830i	1.00616	−	0.580907i	0.910065	+	0.414465i	$0.136031\pi$
$192$		0			0
$193$	−5.52771	−	3.19143i	−0.397894	−	0.229724i	0.287681	−	0.957726i	$-0.407116\pi$
$193$	−5.52771	−	3.19143i	−0.397894	−	0.229724i	−0.685575	+	0.728002i	$0.740449\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.54995			−0.181677			−0.0908384	−	0.995866i	$-0.528955\pi$
$197$	−2.54995			−0.181677			−0.0908384	+	0.995866i	$0.528955\pi$
$198$		0			0
$199$	6.27973	+	3.62561i	0.445159	+	0.257012i	0.705783	−	0.708428i	$-0.250595\pi$
$199$	6.27973	+	3.62561i	0.445159	+	0.257012i	−0.260625	+	0.965440i	$0.583929\pi$
$200$		0			0
$201$	−1.61188	+	1.77263i	−0.113693	+	0.125031i
$202$		0			0
$203$	−2.07774	+	2.23769i	−0.145829	+	0.157055i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−2.29696	−	24.1267i	−0.159650	−	1.67692i
$208$		0			0
$209$	3.45085			0.238700
$210$		0			0
$211$	−13.2654			−0.913230			−0.456615	−	0.889664i	$-0.650938\pi$
$211$	−13.2654			−0.913230			−0.456615	+	0.889664i	$0.650938\pi$
$212$		0			0
$213$	12.2913	+	2.67562i	0.842186	+	0.183331i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	8.05198	+	26.1367i	0.546604	+	1.77427i
$218$		0			0
$219$	−0.312745	−	0.284384i	−0.0211333	−	0.0192169i
$220$		0			0
$221$	−14.2198	−	8.20983i	−0.956530	−	0.552253i
$222$		0			0
$223$	−28.1032			−1.88193			−0.940964	−	0.338506i	$-0.890078\pi$
$223$	−28.1032			−1.88193			−0.940964	+	0.338506i	$0.890078\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−11.6308	−	6.71504i	−0.771963	−	0.445693i	0.0616117	−	0.998100i	$-0.480376\pi$
$227$	−11.6308	−	6.71504i	−0.771963	−	0.445693i	−0.833574	+	0.552407i	$0.813709\pi$
$228$		0			0
$229$	7.24605	−	4.18351i	0.478833	−	0.276454i	−0.241097	−	0.970501i	$-0.577507\pi$
$229$	7.24605	−	4.18351i	0.478833	−	0.276454i	0.719930	+	0.694047i	$0.244174\pi$
$230$		0			0
$231$	21.3855	−	1.81151i	1.40706	−	0.119188i
$232$		0			0
$233$	−4.08689	−	7.07871i	−0.267741	−	0.463742i	0.700537	−	0.713616i	$-0.252944\pi$
$233$	−4.08689	−	7.07871i	−0.267741	−	0.463742i	−0.968278	+	0.249875i	$0.919611\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	19.1272	−	6.11132i	1.24244	−	0.396973i
$238$		0			0
$239$			12.5553i			0.812134i	0.913843	+	0.406067i	$0.133100\pi$
$239$			12.5553i			0.812134i	−0.913843	+	0.406067i	$0.866900\pi$
$240$		0			0
$241$	19.1154	+	11.0363i	1.23133	+	0.710910i	0.967308	−	0.253606i	$-0.0816166\pi$
$241$	19.1154	+	11.0363i	1.23133	+	0.710910i	0.264025	+	0.964516i	$0.414950\pi$
$242$		0			0
$243$	13.6869	−	7.46111i	0.878016	−	0.478630i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.39706	−	0.806595i	0.0888930	−	0.0513224i
$248$		0			0
$249$	−27.8588	−	6.06442i	−1.76548	−	0.384317i
$250$		0			0
$251$	1.66808			0.105288			0.0526441	−	0.998613i	$-0.483235\pi$
$251$	1.66808			0.105288			0.0526441	+	0.998613i	$0.483235\pi$
$252$		0			0
$253$			37.8354i			2.37869i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.04298	−	0.602166i	0.0650594	−	0.0375621i	−0.467117	−	0.884195i	$-0.654707\pi$
$257$	1.04298	−	0.602166i	0.0650594	−	0.0375621i	0.532177	+	0.846633i	$0.321374\pi$
$258$		0			0
$259$	11.9120	+	2.72326i	0.740173	+	0.169215i
$260$		0			0
$261$	1.43923	−	3.14912i	0.0890860	−	0.194926i
$262$		0			0
$263$	2.50729	−	4.34275i	0.154606	−	0.267785i	−0.778310	−	0.627881i	$-0.783923\pi$
$263$	2.50729	−	4.34275i	0.154606	−	0.267785i	0.932915	+	0.360095i	$0.117256\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−2.17206	+	0.693995i	−0.132928	+	0.0424718i
$268$		0			0
$269$	7.94487	−	13.7609i	0.484407	−	0.839018i	−0.515432	−	0.856930i	$-0.672369\pi$
$269$	7.94487	−	13.7609i	0.484407	−	0.839018i	0.999840	+	0.0179121i	$0.00570189\pi$
$270$		0			0
$271$	−17.4197	+	10.0573i	−1.05817	+	0.610937i	−0.924927	−	0.380146i	$-0.875874\pi$
$271$	−17.4197	+	10.0573i	−1.05817	+	0.610937i	−0.133248	+	0.991083i	$0.542541\pi$
$272$		0			0
$273$	8.23441	−	5.73198i	0.498369	−	0.346915i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	3.81938	+	2.20512i	0.229484	+	0.132493i	0.610334	−	0.792144i	$-0.291035\pi$
$277$	3.81938	+	2.20512i	0.229484	+	0.132493i	−0.380850	+	0.924637i	$0.624369\pi$
$278$		0			0
$279$	−17.9808	−	25.2656i	−1.07648	−	1.51261i
$280$		0			0
$281$		−	17.9173i		−	1.06886i	−0.845213	−	0.534429i	$-0.820527\pi$
$281$		−	17.9173i		−	1.06886i	0.845213	−	0.534429i	$-0.179473\pi$
$282$		0			0
$283$	−5.77663	+	10.0054i	−0.343385	+	0.594760i	−0.985059	−	0.172217i	$-0.944907\pi$
$283$	−5.77663	+	10.0054i	−0.343385	+	0.594760i	0.641674	+	0.766978i	$0.278240\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.78724	−	2.58802i	−0.164526	−	0.152766i
$288$		0			0
$289$	19.6226	+	33.9874i	1.15427	+	1.99926i
$290$		0			0
$291$	1.78397	−	8.19522i	0.104578	−	0.480413i
$292$		0			0
$293$		−	7.17953i		−	0.419433i	−0.977762	−	0.209716i	$-0.932746\pi$
$293$		−	7.17953i		−	0.419433i	0.977762	−	0.209716i	$-0.0672540\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−22.3749	+	9.57030i	−1.29832	+	0.555325i
$298$		0			0
$299$	8.84357	+	15.3175i	0.511437	+	0.885834i
$300$		0			0
$301$	16.6369	−	17.9176i	0.958934	−	1.03275i
$302$		0			0
$303$	−3.54799	−	3.22625i	−0.203827	−	0.185343i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	2.44348			0.139457			0.0697284	−	0.997566i	$-0.477787\pi$
$307$	2.44348			0.139457			0.0697284	+	0.997566i	$0.477787\pi$
$308$		0			0
$309$	−13.4692	+	4.30354i	−0.766236	+	0.244820i
$310$		0			0
$311$	2.56348	−	4.44007i	0.145361	−	0.251773i	−0.784146	−	0.620576i	$-0.786899\pi$
$311$	2.56348	−	4.44007i	0.145361	−	0.251773i	0.929508	+	0.368803i	$0.120232\pi$
$312$		0			0
$313$	−0.819152	−	1.41881i	−0.0463012	−	0.0801961i	0.841946	−	0.539562i	$-0.181410\pi$
$313$	−0.819152	−	1.41881i	−0.0463012	−	0.0801961i	−0.888247	+	0.459366i	$0.848077\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.28184	+	14.3446i	0.465155	+	0.805672i	0.999209	−	0.0397789i	$-0.0126654\pi$
$317$	8.28184	+	14.3446i	0.465155	+	0.805672i	−0.534054	+	0.845451i	$0.679332\pi$
$318$		0			0
$319$	−2.70265	+	4.68113i	−0.151320	+	0.262093i
$320$		0			0
$321$	0.354983	−	0.113421i	0.0198132	−	0.00633052i
$322$		0			0
$323$	−5.52595			−0.307472
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−2.78548	−	2.53289i	−0.154037	−	0.140069i
$328$		0			0
$329$	22.3991	+	5.12077i	1.23490	+	0.282317i
$330$		0			0
$331$	11.9722	+	20.7364i	0.658049	+	1.13977i	0.981120	+	0.193400i	$0.0619513\pi$
$331$	11.9722	+	20.7364i	0.658049	+	1.13977i	−0.323071	+	0.946375i	$0.604715\pi$
$332$		0			0
$333$	−13.7930	+	1.31315i	−0.755852	+	0.0719601i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			9.25410i			0.504103i	0.967714	+	0.252051i	$0.0811052\pi$
$337$			9.25410i			0.504103i	−0.967714	+	0.252051i	$0.918895\pi$
$338$		0			0
$339$	4.13338	−	18.9880i	0.224495	−	1.03129i
$340$		0			0
$341$	24.2059	+	41.9259i	1.31083	+	2.27042i
$342$		0			0
$343$	−11.5625	+	14.4675i	−0.624318	+	0.781170i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.2812	+	23.0038i	−0.712973	+	1.23491i	0.250763	+	0.968049i	$0.419319\pi$
$347$	−13.2812	+	23.0038i	−0.712973	+	1.23491i	−0.963736	+	0.266857i	$0.914015\pi$
$348$		0			0
$349$			14.8893i			0.797004i	0.917167	+	0.398502i	$0.130470\pi$
$349$			14.8893i			0.797004i	−0.917167	+	0.398502i	$0.869530\pi$
$350$		0			0
$351$	−6.82145	+	9.10436i	−0.364102	+	0.485955i
$352$		0			0
$353$	−14.5749	−	8.41481i	−0.775743	−	0.447875i	0.0591766	−	0.998248i	$-0.481152\pi$
$353$	−14.5749	−	8.41481i	−0.775743	−	0.447875i	−0.834919	+	0.550372i	$0.814486\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−34.2452	+	2.90082i	−1.81245	+	0.153528i
$358$		0			0
$359$	−24.3673	+	14.0685i	−1.28606	+	0.742506i	−0.977949	−	0.208846i	$-0.933029\pi$
$359$	−24.3673	+	14.0685i	−1.28606	+	0.742506i	−0.308109	+	0.951351i	$0.599696\pi$
$360$		0			0
$361$	−9.22854	+	15.9843i	−0.485713	+	0.841279i
$362$		0			0
$363$	18.0403	−	5.76407i	0.946872	−	0.302535i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−7.38797	+	12.7963i	−0.385649	+	0.667963i	−0.991859	−	0.127341i	$-0.959356\pi$
$367$	−7.38797	+	12.7963i	−0.385649	+	0.667963i	0.606210	+	0.795304i	$0.292689\pi$
$368$		0			0
$369$	3.92251	+	1.79269i	0.204198	+	0.0933236i
$370$		0			0
$371$	−20.5401	+	6.32783i	−1.06639	+	0.328525i
$372$		0			0
$373$	−18.9723	+	10.9537i	−0.982348	+	0.567159i	−0.902978	−	0.429687i	$-0.858624\pi$
$373$	−18.9723	+	10.9537i	−0.982348	+	0.567159i	−0.0793696	+	0.996845i	$0.525291\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			2.52685i			0.130139i
$378$		0			0
$379$	8.15057			0.418667			0.209333	−	0.977844i	$-0.432871\pi$
$379$	8.15057			0.418667			0.209333	+	0.977844i	$0.432871\pi$
$380$		0			0
$381$	−29.1482	−	6.34511i	−1.49331	−	0.325070i
$382$		0			0
$383$	−0.285399	+	0.164775i	−0.0145832	+	0.00841962i	−0.507274	−	0.861785i	$-0.669347\pi$
$383$	−0.285399	+	0.164775i	−0.0145832	+	0.00841962i	0.492691	+	0.870205i	$0.336013\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−11.5242	+	25.2156i	−0.585807	+	1.28178i
$388$		0			0
$389$	−11.5387	−	6.66185i	−0.585033	−	0.337769i	0.178098	−	0.984013i	$-0.443006\pi$
$389$	−11.5387	−	6.66185i	−0.585033	−	0.337769i	−0.763131	+	0.646244i	$0.776339\pi$
$390$		0			0
$391$		−	60.5869i		−	3.06401i
$392$		0			0
$393$	−28.5697	+	9.12830i	−1.44115	+	0.460462i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	14.3006	+	24.7694i	0.717728	+	1.24314i	0.961898	+	0.273409i	$0.0881513\pi$
$397$	14.3006	+	24.7694i	0.717728	+	1.24314i	−0.244169	+	0.969733i	$0.578515\pi$
$398$		0			0
$399$	1.43544	−	3.05625i	0.0718618	−	0.153004i
$400$		0			0
$401$	−24.2076	+	13.9763i	−1.20887	+	0.697941i	−0.962512	−	0.271238i	$-0.912567\pi$
$401$	−24.2076	+	13.9763i	−1.20887	+	0.697941i	−0.246357	+	0.969179i	$0.579234\pi$
$402$		0			0
$403$	19.5994	+	11.3157i	0.976314	+	0.563675i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	21.6301			1.07217
$408$		0			0
$409$	−0.852979	−	0.492468i	−0.0421771	−	0.0243510i	0.478763	−	0.877944i	$-0.341085\pi$
$409$	−0.852979	−	0.492468i	−0.0421771	−	0.0243510i	−0.520940	+	0.853593i	$0.674419\pi$
$410$		0			0
$411$	−14.3364	−	13.0364i	−0.707165	−	0.643037i
$412$		0			0
$413$	−17.6352	+	5.43290i	−0.867769	+	0.267336i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−3.65590	−	0.795833i	−0.179030	−	0.0389721i
$418$		0			0
$419$	31.2166			1.52503			0.762515	−	0.646970i	$-0.223964\pi$
$419$	31.2166			1.52503			0.762515	+	0.646970i	$0.223964\pi$
$420$		0			0
$421$	−34.7393			−1.69309			−0.846544	−	0.532319i	$-0.821321\pi$
$421$	−34.7393			−1.69309			−0.846544	+	0.532319i	$0.821321\pi$
$422$		0			0
$423$	−25.9362	+	2.46922i	−1.26106	+	0.120058i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	15.3024	+	3.49836i	0.740534	+	0.169297i
$428$		0			0
$429$	11.9483	−	13.1399i	0.576871	−	0.634400i
$430$		0			0
$431$	−15.9115	−	9.18649i	−0.766429	−	0.442498i	0.0651704	−	0.997874i	$-0.479241\pi$
$431$	−15.9115	−	9.18649i	−0.766429	−	0.442498i	−0.831599	+	0.555376i	$0.812574\pi$
$432$		0			0
$433$	−24.6833			−1.18621			−0.593103	−	0.805127i	$-0.702097\pi$
$433$	−24.6833			−1.18621			−0.593103	+	0.805127i	$0.702097\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.15503	+	2.97626i	0.246598	+	0.142374i
$438$		0			0
$439$	13.1758	−	7.60702i	0.628844	−	0.363063i	−0.151460	−	0.988463i	$-0.548398\pi$
$439$	13.1758	−	7.60702i	0.628844	−	0.363063i	0.780304	+	0.625400i	$0.215064\pi$
$440$		0			0
$441$	7.29128	−	19.6936i	0.347204	−	0.937790i
$442$		0			0
$443$	15.0876	+	26.1325i	0.716834	+	1.24159i	0.962248	+	0.272174i	$0.0877427\pi$
$443$	15.0876	+	26.1325i	0.716834	+	1.24159i	−0.245414	+	0.969418i	$0.578924\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.836527	+	2.61816i	0.0395664	+	0.123835i
$448$		0			0
$449$		−	27.7596i		−	1.31006i	−0.755603	−	0.655029i	$-0.772656\pi$
$449$		−	27.7596i		−	1.31006i	0.755603	−	0.655029i	$-0.227344\pi$
$450$		0			0
$451$	−5.83077	−	3.36640i	−0.274560	−	0.158518i
$452$		0			0
$453$	13.1281	+	11.9376i	0.616812	+	0.560878i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−29.3189	+	16.9273i	−1.37148	+	0.791825i	−0.991115	−	0.133011i	$-0.957535\pi$
$457$	−29.3189	+	16.9273i	−1.37148	+	0.791825i	−0.380366	+	0.924836i	$0.624202\pi$
$458$		0			0
$459$	35.8296	−	15.3252i	1.67238	−	0.715319i
$460$		0			0
$461$	23.7084			1.10421			0.552104	−	0.833775i	$-0.313825\pi$
$461$	23.7084			1.10421			0.552104	+	0.833775i	$0.313825\pi$
$462$		0			0
$463$			1.60640i			0.0746559i	0.999303	+	0.0373280i	$0.0118846\pi$
$463$			1.60640i			0.0746559i	−0.999303	+	0.0373280i	$0.988115\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.51812	−	3.18589i	0.255348	−	0.147425i	−0.366863	−	0.930275i	$-0.619568\pi$
$467$	5.51812	−	3.18589i	0.255348	−	0.147425i	0.622211	+	0.782850i	$0.286235\pi$
$468$		0			0
$469$	−1.07751	−	3.49759i	−0.0497549	−	0.161504i
$470$		0			0
$471$	8.31857	+	7.56422i	0.383299	+	0.348541i
$472$		0			0
$473$	21.6407	−	37.4827i	0.995039	−	1.72346i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	19.8556	−	14.1306i	0.909124	−	0.646998i
$478$		0			0
$479$	1.66105	−	2.87702i	0.0758953	−	0.131455i	−0.825580	−	0.564285i	$-0.809152\pi$
$479$	1.66105	−	2.87702i	0.0758953	−	0.131455i	0.901475	+	0.432831i	$0.142485\pi$
$480$		0			0
$481$	8.75687	−	5.05578i	0.399279	−	0.230524i
$482$		0			0
$483$	33.5089	+	15.7382i	1.52471	+	0.716115i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−17.8943	−	10.3313i	−0.810868	−	0.468155i	0.0363892	−	0.999338i	$-0.488414\pi$
$487$	−17.8943	−	10.3313i	−0.810868	−	0.468155i	−0.847257	+	0.531183i	$0.821748\pi$
$488$		0			0
$489$	−2.82924	−	8.85493i	−0.127943	−	0.400434i
$490$		0			0
$491$		−	15.1679i		−	0.684518i	−0.939606	−	0.342259i	$-0.888808\pi$
$491$		−	15.1679i		−	0.684518i	0.939606	−	0.342259i	$-0.111192\pi$
$492$		0			0
$493$	4.32784	−	7.49604i	0.194916	−	0.337605i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−13.0745	+	14.0810i	−0.586470	+	0.631617i
$498$		0			0
$499$	3.10558	+	5.37903i	0.139025	+	0.240798i	0.927128	−	0.374745i	$-0.122270\pi$
$499$	3.10558	+	5.37903i	0.139025	+	0.240798i	−0.788103	+	0.615544i	$0.788936\pi$
$500$		0			0
$501$	11.5775	+	2.52024i	0.517245	+	0.112596i
$502$		0			0
$503$		−	5.52940i		−	0.246544i	−0.992373	−	0.123272i	$-0.960661\pi$
$503$		−	5.52940i		−	0.246544i	0.992373	−	0.123272i	$-0.0393387\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−3.02342	+	13.8890i	−0.134275	+	0.616832i
$508$		0			0
$509$	−14.8857	−	25.7827i	−0.659796	−	1.14280i	−0.980668	−	0.195678i	$-0.937309\pi$
$509$	−14.8857	−	25.7827i	−0.659796	−	1.14280i	0.320872	−	0.947122i	$-0.396024\pi$
$510$		0			0
$511$	0.617080	−	0.190105i	0.0272980	−	0.00840977i
$512$		0			0
$513$	−0.456142	+	3.80138i	−0.0201391	+	0.167835i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	40.6729			1.78879
$518$		0			0
$519$	6.13204	+	19.1920i	0.269167	+	0.842436i
$520$		0			0
$521$	11.2112	−	19.4183i	0.491170	−	0.850732i	−0.508778	−	0.860898i	$-0.669903\pi$
$521$	11.2112	−	19.4183i	0.491170	−	0.850732i	0.999948	+	0.0101659i	$0.00323595\pi$
$522$		0			0
$523$	11.7511	+	20.3535i	0.513839	+	0.889996i	0.999871	+	0.0160547i	$0.00511059\pi$
$523$	11.7511	+	20.3535i	0.513839	+	0.889996i	−0.486032	+	0.873941i	$0.661556\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−38.7617	−	67.1372i	−1.68849	−	2.92454i
$528$		0			0
$529$	−21.1319	+	36.6015i	−0.918778	+	1.59137i
$530$		0			0
$531$	17.0474	−	12.1322i	0.739796	−	0.526492i
$532$		0			0
$533$	−3.14742			−0.136330
$534$		0			0
$535$		0			0
$536$		0			0
$537$	9.36139	−	10.2950i	0.403974	−	0.444260i
$538$		0			0
$539$	−14.2453	+	29.5272i	−0.613586	+	1.27183i
$540$		0			0
$541$	−0.0653647	−	0.113215i	−0.00281025	−	0.00486749i	0.864617	−	0.502432i	$-0.167561\pi$
$541$	−0.0653647	−	0.113215i	−0.00281025	−	0.00486749i	−0.867427	+	0.497564i	$0.834228\pi$
$542$		0			0
$543$	−16.6160	−	3.61703i	−0.713059	−	0.155222i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	41.2183i		−	1.76237i	−0.472774	−	0.881184i	$-0.656747\pi$
$547$		−	41.2183i		−	1.76237i	0.472774	−	0.881184i	$-0.343253\pi$
$548$		0			0
$549$	−17.7188	+	1.68690i	−0.756221	+	0.0719952i
$550$		0			0
$551$	0.425199	+	0.736467i	0.0181141	+	0.0313745i
$552$		0			0
$553$	−6.83580	+	29.9009i	−0.290688	+	1.27152i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.90624	−	5.03375i	0.123141	−	0.213287i	−0.797864	−	0.602838i	$-0.794037\pi$
$557$	2.90624	−	5.03375i	0.123141	−	0.213287i	0.921005	+	0.389551i	$0.127370\pi$
$558$		0			0
$559$		−	20.2330i		−	0.855764i
$560$		0			0
$561$	−57.9506	+	18.5158i	−2.44668	+	0.781737i
$562$		0			0
$563$	−18.2190	−	10.5187i	−0.767838	−	0.443312i	0.0642647	−	0.997933i	$-0.479530\pi$
$563$	−18.2190	−	10.5187i	−0.767838	−	0.443312i	−0.832103	+	0.554621i	$0.812863\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.831265	+	23.7972i	−0.0349098	+	0.999390i
$568$		0			0
$569$	−30.2091	+	17.4412i	−1.26643	+	0.731173i	−0.974311	−	0.225209i	$-0.927694\pi$
$569$	−30.2091	+	17.4412i	−1.26643	+	0.731173i	−0.292119	+	0.956382i	$0.594360\pi$
$570$		0			0
$571$	−18.9889	+	32.8897i	−0.794661	+	1.37639i	0.128394	+	0.991723i	$0.459018\pi$
$571$	−18.9889	+	32.8897i	−0.794661	+	1.37639i	−0.923054	+	0.384670i	$0.874315\pi$
$572$		0			0
$573$	−8.46429	−	26.4915i	−0.353601	−	1.10670i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−2.71271	+	4.69855i	−0.112932	+	0.195603i	−0.916951	−	0.399000i	$-0.869357\pi$
$577$	−2.71271	+	4.69855i	−0.112932	+	0.195603i	0.804019	+	0.594603i	$0.202691\pi$
$578$		0			0
$579$	−7.43770	+	8.17943i	−0.309100	+	0.339926i
$580$		0			0
$581$	29.6339	−	31.9151i	1.22942	−	1.32406i
$582$		0			0
$583$	−32.9484	+	19.0228i	−1.36459	+	0.787844i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	8.71317i		−	0.359631i	−0.983700	−	0.179816i	$-0.942450\pi$
$587$		−	8.71317i		−	0.359631i	0.983700	−	0.179816i	$-0.0575501\pi$
$588$		0			0
$589$	7.61648			0.313832
$590$		0			0
$591$	−0.939435	+	4.31558i	−0.0386432	+	0.177519i
$592$		0			0
$593$	−16.9627	+	9.79341i	−0.696574	+	0.402167i	−0.806070	−	0.591820i	$-0.798410\pi$
$593$	−16.9627	+	9.79341i	−0.696574	+	0.402167i	0.109496	+	0.993987i	$0.465076\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	8.44957	−	9.29221i	0.345818	−	0.380305i
$598$		0			0
$599$	14.2397	+	8.22129i	0.581818	+	0.335913i	0.761855	−	0.647747i	$-0.224289\pi$
$599$	14.2397	+	8.22129i	0.581818	+	0.335913i	−0.180038	+	0.983660i	$0.557622\pi$
$600$		0			0
$601$		−	11.0177i		−	0.449420i	−0.974426	−	0.224710i	$-0.927857\pi$
$601$		−	11.0177i		−	0.449420i	0.974426	−	0.224710i	$-0.0721435\pi$
$602$		0			0
$603$	2.40619	+	3.38103i	0.0979875	+	0.137686i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−6.07323	−	10.5191i	−0.246505	−	0.426959i	0.716049	−	0.698050i	$-0.245949\pi$
$607$	−6.07323	−	10.5191i	−0.246505	−	0.426959i	−0.962554	+	0.271091i	$0.912615\pi$
$608$		0			0
$609$	3.02163	+	4.34080i	0.122443	+	0.175898i
$610$		0			0
$611$	16.4663	−	9.50681i	0.666154	−	0.384604i
$612$		0			0
$613$	14.3206	+	8.26802i	0.578405	+	0.333942i	0.760499	−	0.649339i	$-0.224954\pi$
$613$	14.3206	+	8.26802i	0.578405	+	0.333942i	−0.182094	+	0.983281i	$0.558288\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−34.8433			−1.40274			−0.701368	−	0.712799i	$-0.747427\pi$
$617$	−34.8433			−1.40274			−0.701368	+	0.712799i	$0.747427\pi$
$618$		0			0
$619$	21.3120	+	12.3045i	0.856603	+	0.494560i	0.862873	−	0.505421i	$-0.168663\pi$
$619$	21.3120	+	12.3045i	0.856603	+	0.494560i	−0.00627057	+	0.999980i	$0.501996\pi$
$620$		0			0
$621$	−41.6787	−	5.00117i	−1.67251	−	0.200690i
$622$		0			0
$623$	0.776267	−	3.39552i	0.0311005	−	0.136039i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1.27134	−	5.84028i	0.0507723	−	0.233238i
$628$		0			0
$629$	−34.6370			−1.38107
$630$		0			0
$631$	−37.4776			−1.49196			−0.745979	−	0.665969i	$-0.768018\pi$
$631$	−37.4776			−1.49196			−0.745979	+	0.665969i	$0.768018\pi$
$632$		0			0
$633$	−4.88715	+	22.4506i	−0.194247	+	0.892332i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	1.13449	+	15.2836i	0.0449501	+	0.605559i
$638$		0			0
$639$	9.05653	−	19.8163i	0.358271	−	0.783919i
$640$		0			0
$641$	−13.6348	−	7.87204i	−0.538541	−	0.310927i	0.205946	−	0.978563i	$-0.433973\pi$
$641$	−13.6348	−	7.87204i	−0.538541	−	0.310927i	−0.744488	+	0.667636i	$0.767306\pi$
$642$		0			0
$643$	−11.7173			−0.462086			−0.231043	−	0.972943i	$-0.574214\pi$
$643$	−11.7173			−0.462086			−0.231043	+	0.972943i	$0.574214\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	22.9086	+	13.2263i	0.900632	+	0.519980i	0.877405	−	0.479750i	$-0.159273\pi$
$647$	22.9086	+	13.2263i	0.900632	+	0.519980i	0.0232268	+	0.999730i	$0.492606\pi$
$648$		0			0
$649$	−28.2886	+	16.3324i	−1.11043	+	0.641105i
$650$		0			0
$651$	47.2005	−	3.99823i	1.84994	−	0.156703i
$652$		0			0
$653$	−1.81151	−	3.13762i	−0.0708898	−	0.122785i	0.828402	−	0.560134i	$-0.189251\pi$
$653$	−1.81151	−	3.13762i	−0.0708898	−	0.122785i	−0.899292	+	0.437350i	$0.855917\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−0.596515	+	0.424523i	−0.0232723	+	0.0165622i
$658$		0			0
$659$		−	24.1855i		−	0.942132i	−0.882098	−	0.471066i	$-0.843869\pi$
$659$		−	24.1855i		−	0.942132i	0.882098	−	0.471066i	$-0.156131\pi$
$660$		0			0
$661$	13.7414	+	7.93363i	0.534480	+	0.308582i	0.742839	−	0.669470i	$-0.233479\pi$
$661$	13.7414	+	7.93363i	0.534480	+	0.308582i	−0.208359	+	0.978053i	$0.566812\pi$
$662$		0			0
$663$	−19.1332	+	21.0413i	−0.743073	+	0.817176i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−8.07468	+	4.66192i	−0.312653	+	0.180510i
$668$		0			0
$669$	−10.3536	+	47.5623i	−0.400292	+	1.83886i
$670$		0			0
$671$	27.7866			1.07269
$672$		0			0
$673$		−	3.48623i		−	0.134384i	−0.997740	−	0.0671922i	$-0.978596\pi$
$673$		−	3.48623i		−	0.134384i	0.997740	−	0.0671922i	$-0.0214041\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	33.6859	−	19.4486i	1.29465	−	0.747469i	0.315179	−	0.949032i	$-0.397936\pi$
$677$	33.6859	−	19.4486i	1.29465	−	0.747469i	0.979475	+	0.201564i	$0.0646022\pi$
$678$		0			0
$679$	9.38847	+	8.71741i	0.360297	+	0.334543i
$680$		0			0
$681$	−15.6496	+	17.2102i	−0.599693	+	0.659497i
$682$		0			0
$683$	−6.05116	+	10.4809i	−0.231541	+	0.401041i	−0.958262	−	0.285892i	$-0.907710\pi$
$683$	−6.05116	+	10.4809i	−0.231541	+	0.401041i	0.726721	+	0.686933i	$0.241044\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−4.41070	−	13.8046i	−0.168279	−	0.526678i
$688$		0			0
$689$	−8.89270	+	15.4026i	−0.338785	+	0.586792i
$690$		0			0
$691$	−18.7139	+	10.8044i	−0.711908	+	0.411021i	−0.811767	−	0.583981i	$-0.801494\pi$
$691$	−18.7139	+	10.8044i	−0.711908	+	0.411021i	0.0998588	+	0.995002i	$0.468161\pi$
$692$		0			0
$693$	4.81285	−	36.8605i	0.182825	−	1.40022i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	9.33699	+	5.39071i	0.353664	+	0.204188i
$698$		0			0
$699$	−13.4858	+	4.30884i	−0.510079	+	0.162975i
$700$		0			0
$701$		−	25.2893i		−	0.955163i	−0.878587	−	0.477582i	$-0.841513\pi$
$701$		−	25.2893i		−	0.955163i	0.878587	−	0.477582i	$-0.158487\pi$
$702$		0			0
$703$	1.70150	−	2.94708i	0.0641732	−	0.111151i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	7.00059	−	2.15669i	0.263284	−	0.0811106i
$708$		0			0
$709$	−5.13129	−	8.88765i	−0.192710	−	0.333783i	0.753438	−	0.657519i	$-0.228394\pi$
$709$	−5.13129	−	8.88765i	−0.192710	−	0.333783i	−0.946147	+	0.323737i	$0.895061\pi$
$710$		0			0
$711$	−3.29621	−	34.6226i	−0.123618	−	1.29845i
$712$		0			0
$713$			83.5076i			3.12738i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	21.2488	+	4.62552i	0.793549	+	0.172743i
$718$		0			0
$719$	−24.3969	−	42.2566i	−0.909850	−	1.57591i	−0.814271	−	0.580485i	$-0.802863\pi$
$719$	−24.3969	−	42.2566i	−0.909850	−	1.57591i	−0.0955793	−	0.995422i	$-0.530470\pi$
$720$		0			0
$721$	4.81372	−	21.0560i	0.179272	−	0.784166i
$722$		0			0
$723$	25.7204	−	28.2853i	0.956550	−	1.05194i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−9.98665			−0.370384			−0.185192	−	0.982702i	$-0.559291\pi$
$727$	−9.98665			−0.370384			−0.185192	+	0.982702i	$0.559291\pi$
$728$		0			0
$729$	−7.58487	−	25.9127i	−0.280921	−	0.959731i
$730$		0			0
$731$	−34.6538	+	60.0222i	−1.28172	+	2.22000i
$732$		0			0
$733$	−18.4538	−	31.9630i	−0.681608	−	1.18058i	−0.974490	−	0.224432i	$-0.927947\pi$
$733$	−18.4538	−	31.9630i	−0.681608	−	1.18058i	0.292881	−	0.956149i	$-0.405386\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.23923	−	5.61051i	−0.119318	−	0.206666i
$738$		0			0
$739$	19.7107	−	34.1399i	0.725070	−	1.25586i	−0.233875	−	0.972267i	$-0.575141\pi$
$739$	19.7107	−	34.1399i	0.725070	−	1.25586i	0.958945	−	0.283591i	$-0.0915259\pi$
$740$		0			0
$741$	−0.850399	−	2.66157i	−0.0312402	−	0.0977753i
$742$		0			0
$743$	12.7786			0.468800			0.234400	−	0.972140i	$-0.424688\pi$
$743$	12.7786			0.468800			0.234400	+	0.972140i	$0.424688\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−20.5271	+	44.9145i	−0.751046	+	1.64333i
$748$		0			0
$749$	−0.126866	+	0.554934i	−0.00463559	+	0.0202768i
$750$		0			0
$751$	−4.32518	−	7.49143i	−0.157828	−	0.273366i	0.776257	−	0.630416i	$-0.217116\pi$
$751$	−4.32518	−	7.49143i	−0.157828	−	0.273366i	−0.934085	+	0.357050i	$0.883782\pi$
$752$		0			0
$753$	0.614541	−	2.82309i	0.0223951	−	0.102879i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	26.6532i		−	0.968727i	−0.874867	−	0.484364i	$-0.839051\pi$
$757$		−	26.6532i		−	0.968727i	0.874867	−	0.484364i	$-0.160949\pi$
$758$		0			0
$759$	64.0332	+	13.9390i	2.32426	+	0.505955i
$760$		0			0
$761$	−18.2462	−	31.6034i	−0.661425	−	1.14562i	−0.980241	−	0.197805i	$-0.936619\pi$
$761$	−18.2462	−	31.6034i	−0.661425	−	1.14562i	0.318816	−	0.947817i	$-0.396715\pi$
$762$		0			0
$763$	5.49607	−	1.69319i	0.198971	−	0.0612975i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−7.63502	+	13.2242i	−0.275685	+	0.477500i
$768$		0			0
$769$		−	26.0781i		−	0.940400i	−0.882560	−	0.470200i	$-0.844182\pi$
$769$		−	26.0781i		−	0.940400i	0.882560	−	0.470200i	$-0.155818\pi$
$770$		0			0
$771$	−0.634868	−	1.98700i	−0.0228642	−	0.0715602i
$772$		0			0
$773$	34.5210	+	19.9307i	1.24163	+	0.716858i	0.969427	−	0.245381i	$-0.0789129\pi$
$773$	34.5210	+	19.9307i	1.24163	+	0.716858i	0.272208	+	0.962239i	$0.412246\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	8.99740	−	19.1567i	0.322780	−	0.687243i
$778$		0			0
$779$	−0.917336	+	0.529624i	−0.0328670	+	0.0189757i
$780$		0			0
$781$	−17.0068	+	29.4566i	−0.608551	+	1.05404i
$782$		0			0
$783$	−4.79939	−	3.59595i	−0.171516	−	0.128509i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	12.2663	−	21.2458i	0.437245	−	0.757331i	−0.560231	−	0.828337i	$-0.689288\pi$
$787$	12.2663	−	21.2458i	0.437245	−	0.757331i	0.997476	+	0.0710057i	$0.0226208\pi$
$788$		0			0
$789$	−6.42602	−	5.84330i	−0.228773	−	0.208027i
$790$		0			0
$791$	21.7527	+	20.1978i	0.773436	+	0.718153i
$792$		0			0
$793$	11.2493	−	6.49477i	0.399473	−	0.230636i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			33.4163i			1.18367i	0.806060	+	0.591834i	$0.201596\pi$
$797$			33.4163i			1.18367i	−0.806060	+	0.591834i	$0.798404\pi$
$798$		0			0
$799$	−65.1308			−2.30416
$800$		0			0
$801$	0.374314	+	3.93171i	0.0132258	+	0.138920i
$802$		0			0
$803$	0.989861	−	0.571497i	0.0349315	−	0.0201677i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−20.3622	−	18.5157i	−0.716784	−	0.651784i
$808$		0			0
$809$	43.1974	+	24.9400i	1.51874	+	0.876845i	0.999757	+	0.0220612i	$0.00702286\pi$
$809$	43.1974	+	24.9400i	1.51874	+	0.876845i	0.518984	+	0.854784i	$0.326310\pi$
$810$		0			0
$811$		−	16.9220i		−	0.594210i	−0.954845	−	0.297105i	$-0.903979\pi$
$811$		−	16.9220i		−	0.594210i	0.954845	−	0.297105i	$-0.0960212\pi$
$812$		0			0
$813$	10.6035	+	33.1867i	0.371880	+	1.16391i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−3.40465	−	5.89703i	−0.119114	−	0.206311i
$818$		0			0
$819$	−6.66724	−	16.0478i	−0.232972	−	0.560755i
$820$		0			0
$821$	−0.856494	+	0.494497i	−0.0298918	+	0.0172581i	−0.514871	−	0.857267i	$-0.672160\pi$
$821$	−0.856494	+	0.494497i	−0.0298918	+	0.0172581i	0.484980	+	0.874525i	$0.338827\pi$
$822$		0			0
$823$	30.8549	+	17.8141i	1.07553	+	0.620960i	0.929688	−	0.368347i	$-0.120076\pi$
$823$	30.8549	+	17.8141i	1.07553	+	0.620960i	0.145846	+	0.989307i	$0.453409\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	48.8191			1.69761			0.848803	−	0.528709i	$-0.177324\pi$
$827$	48.8191			1.69761			0.848803	+	0.528709i	$0.177324\pi$
$828$		0			0
$829$	−11.5060	−	6.64300i	−0.399621	−	0.230721i	0.286700	−	0.958021i	$-0.407442\pi$
$829$	−11.5060	−	6.64300i	−0.399621	−	0.230721i	−0.686320	+	0.727299i	$0.740775\pi$
$830$		0			0
$831$	5.13908	−	5.65158i	0.178273	−	0.196051i
$832$		0			0
$833$	22.8113	−	47.2828i	0.790366	−	1.63825i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−49.3843	+	21.1229i	−1.70697	+	0.730114i
$838$		0			0
$839$	42.5549			1.46916			0.734579	−	0.678523i	$-0.237380\pi$
$839$	42.5549			1.46916			0.734579	+	0.678523i	$0.237380\pi$
$840$		0			0
$841$	27.6680			0.954068
$842$		0			0
$843$	−30.3236	−	6.60097i	−1.04440	−	0.227349i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−6.44738	+	28.2019i	−0.221535	+	0.969028i
$848$		0			0
$849$	14.8052	+	13.4626i	0.508111	+	0.462035i
$850$		0			0
$851$	32.3120	+	18.6553i	1.10764	+	0.639496i
$852$		0			0
$853$	27.4196			0.938830			0.469415	−	0.882978i	$-0.344465\pi$
$853$	27.4196			0.938830			0.469415	+	0.882978i	$0.344465\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−7.40476	−	4.27514i	−0.252942	−	0.146036i	0.368169	−	0.929759i	$-0.379985\pi$
$857$	−7.40476	−	4.27514i	−0.252942	−	0.146036i	−0.621111	+	0.783723i	$0.713318\pi$
$858$		0			0
$859$	2.23617	−	1.29105i	0.0762970	−	0.0440501i	−0.461366	−	0.887210i	$-0.652641\pi$
$859$	2.23617	−	1.29105i	0.0762970	−	0.0440501i	0.537663	+	0.843160i	$0.319307\pi$
$860$		0			0
$861$	−5.40685	+	3.76372i	−0.184265	+	0.128267i
$862$		0			0
$863$	−10.7086	−	18.5478i	−0.364523	−	0.631373i	0.624176	−	0.781284i	$-0.285435\pi$
$863$	−10.7086	−	18.5478i	−0.364523	−	0.631373i	−0.988700	+	0.149911i	$0.952101\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	64.7500	−	20.6883i	2.19903	−	0.702611i
$868$		0			0
$869$			54.2950i			1.84183i
$870$		0			0
$871$	−2.62278	−	1.51426i	−0.0888694	−	0.0513088i
$872$		0			0
$873$	−13.2125	−	6.03845i	−0.447175	−	0.204370i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−41.5112	+	23.9665i	−1.40173	+	0.809291i	−0.994571	−	0.104064i	$-0.966815\pi$
$877$	−41.5112	+	23.9665i	−1.40173	+	0.809291i	−0.407163	+	0.913355i	$0.633482\pi$
$878$		0			0
$879$	−12.1508	−	2.64503i	−0.409835	−	0.0892146i
$880$		0			0
$881$	−16.0526			−0.540827			−0.270413	−	0.962744i	$-0.587160\pi$
$881$	−16.0526			−0.540827			−0.270413	+	0.962744i	$0.587160\pi$
$882$		0			0
$883$		−	57.8898i		−	1.94815i	−0.226236	−	0.974073i	$-0.572642\pi$
$883$		−	57.8898i		−	1.94815i	0.226236	−	0.974073i	$-0.427358\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−0.719272	+	0.415272i	−0.0241508	+	0.0139435i	−0.512027	−	0.858969i	$-0.671105\pi$
$887$	−0.719272	+	0.415272i	−0.0241508	+	0.0139435i	0.487876	+	0.872913i	$0.337772\pi$
$888$		0			0
$889$	31.0055	−	33.3923i	1.03989	−	1.11994i
$890$		0			0
$891$	7.95373	+	41.3935i	0.266460	+	1.38673i
$892$		0			0
$893$	3.19947	−	5.54164i	0.107066	−	0.185444i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	29.1817	−	9.32383i	0.974348	−	0.311314i
$898$		0			0
$899$	−5.96511	+	10.3319i	−0.198947	+	0.344587i
$900$		0			0
$901$	52.7613	−	30.4618i	1.75773	−	1.01483i
$902$		0			0
$903$	−24.1948	−	34.7576i	−0.805152	−	1.15666i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−38.0267	−	21.9547i	−1.26266	−	0.728995i	−0.289069	−	0.957308i	$-0.593346\pi$
$907$	−38.0267	−	21.9547i	−1.26266	−	0.728995i	−0.973588	+	0.228313i	$0.926679\pi$
$908$		0			0
$909$	−6.76729	+	4.81609i	−0.224457	+	0.159740i
$910$		0			0
$911$		−	1.64586i		−	0.0545299i	−0.999628	−	0.0272649i	$-0.991320\pi$
$911$		−	1.64586i		−	0.0545299i	0.999628	−	0.0272649i	$-0.00867978\pi$
$912$		0			0
$913$	38.5467	−	66.7649i	1.27571	−	2.20959i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	10.2104	−	44.6621i	0.337178	−	1.47487i
$918$		0			0
$919$	−22.9387	−	39.7309i	−0.756677	−	1.31060i	−0.944537	−	0.328406i	$-0.893488\pi$
$919$	−22.9387	−	39.7309i	−0.756677	−	1.31060i	0.187860	−	0.982196i	$-0.439845\pi$
$920$		0			0
$921$	0.900209	−	4.13539i	0.0296629	−	0.136266i
$922$		0			0
$923$			15.9005i			0.523373i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	2.32117	+	24.3810i	0.0762371	+	0.800776i
$928$		0			0
$929$	5.79774	+	10.0420i	0.190218	+	0.329467i	0.945322	−	0.326137i	$-0.105747\pi$
$929$	5.79774	+	10.0420i	0.190218	+	0.329467i	−0.755105	+	0.655604i	$0.772414\pi$
$930$		0			0
$931$	2.90247	+	4.26360i	0.0951245	+	0.139734i
$932$		0			0
$933$	−6.57003	−	5.97425i	−0.215093	−	0.195588i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	39.7618			1.29896			0.649481	−	0.760378i	$-0.274986\pi$
$937$	39.7618			1.29896			0.649481	+	0.760378i	$0.274986\pi$
$938$		0			0
$939$	−2.70301	+	0.863638i	−0.0882094	+	0.0281838i
$940$		0			0
$941$	−20.7590	+	35.9557i	−0.676724	+	1.17212i	0.299237	+	0.954179i	$0.403268\pi$
$941$	−20.7590	+	35.9557i	−0.676724	+	1.17212i	−0.975962	+	0.217942i	$0.930066\pi$
$942$		0			0
$943$	−5.80684	−	10.0577i	−0.189097	−	0.327525i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	15.3288	+	26.5502i	0.498119	+	0.862767i	0.999998	−	0.00217116i	$-0.000691101\pi$
$947$	15.3288	+	26.5502i	0.498119	+	0.862767i	−0.501879	+	0.864938i	$0.667358\pi$
$948$		0			0
$949$	0.267161	−	0.462736i	0.00867241	−	0.0150211i
$950$		0			0
$951$	27.3281	−	8.73161i	0.886175	−	0.283142i
$952$		0			0
$953$	−22.7409			−0.736650			−0.368325	−	0.929697i	$-0.620069\pi$
$953$	−22.7409			−0.736650			−0.368325	+	0.929697i	$0.620069\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	6.92674	+	6.29860i	0.223910	+	0.203605i
$958$		0			0
$959$	28.2874	−	8.71457i	0.913449	−	0.281408i
$960$		0			0
$961$	37.9257	+	65.6892i	1.22341	+	2.11901i
$962$		0			0
$963$	−0.0611747	−	0.642564i	−0.00197133	−	0.0207063i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	18.4381i		−	0.592928i	−0.955044	−	0.296464i	$-0.904193\pi$
$967$		−	18.4381i		−	0.592928i	0.955044	−	0.296464i	$-0.0958074\pi$
$968$		0			0
$969$	−2.03583	+	9.35221i	−0.0654003	+	0.300436i
$970$		0			0
$971$	0.784910	+	1.35950i	0.0251889	+	0.0436285i	0.878345	−	0.478027i	$-0.158648\pi$
$971$	0.784910	+	1.35950i	0.0251889	+	0.0436285i	−0.853156	+	0.521656i	$0.825315\pi$
$972$		0			0
$973$	3.88885	−	4.18822i	0.124671	−	0.134268i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.6070	+	18.3718i	−0.339347	+	0.587766i	−0.984310	−	0.176448i	$-0.943539\pi$
$977$	−10.6070	+	18.3718i	−0.339347	+	0.587766i	0.644963	+	0.764214i	$0.276873\pi$
$978$		0			0
$979$		−	6.16569i		−	0.197056i
$980$		0			0
$981$	−5.31291	+	3.78105i	−0.169628	+	0.120720i
$982$		0			0
$983$	−31.6340	−	18.2639i	−1.00897	−	0.582528i	−0.0980782	−	0.995179i	$-0.531270\pi$
$983$	−31.6340	−	18.2639i	−1.00897	−	0.582528i	−0.910889	+	0.412651i	$0.864603\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	16.9186	−	36.0220i	0.538524	−	1.14659i
$988$		0			0
$989$	64.6555	−	37.3289i	2.05592	−	1.18699i
$990$		0			0
$991$	9.43293	−	16.3383i	0.299647	−	0.519004i	−0.676408	−	0.736527i	$-0.736464\pi$
$991$	9.43293	−	16.3383i	0.299647	−	0.519004i	0.976055	+	0.217523i	$0.0697978\pi$
$992$		0			0
$993$	39.5053	−	12.6223i	1.25366	−	0.400557i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	14.0098	−	24.2658i	0.443696	−	0.768504i	−0.554264	−	0.832341i	$-0.687000\pi$
$997$	14.0098	−	24.2658i	0.443696	−	0.768504i	0.997960	+	0.0638366i	$0.0203337\pi$
$998$		0			0
$999$	−2.85912	+	23.8273i	−0.0904585	+	0.753862i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bo.h.1949.7		20
3.2	odd	2		2100.2.bo.g.1949.8		20
5.2	odd	4		420.2.bh.a.101.1	✓	10
5.3	odd	4		2100.2.bi.k.101.5		10
5.4	even	2	inner	2100.2.bo.h.1949.4		20
7.5	odd	6		2100.2.bo.g.1349.3		20
15.2	even	4		420.2.bh.b.101.2	yes	10
15.8	even	4		2100.2.bi.j.101.4		10
15.14	odd	2		2100.2.bo.g.1949.3		20
21.5	even	6	inner	2100.2.bo.h.1349.4		20
35.12	even	12		420.2.bh.b.341.2	yes	10
35.17	even	12		2940.2.d.a.881.5		10
35.19	odd	6		2100.2.bo.g.1349.8		20
35.32	odd	12		2940.2.d.b.881.6		10
35.33	even	12		2100.2.bi.j.1601.4		10
105.17	odd	12		2940.2.d.b.881.5		10
105.32	even	12		2940.2.d.a.881.6		10
105.47	odd	12		420.2.bh.a.341.1	yes	10
105.68	odd	12		2100.2.bi.k.1601.5		10
105.89	even	6	inner	2100.2.bo.h.1349.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bh.a.101.1	✓	10	5.2	odd	4
420.2.bh.a.341.1	yes	10	105.47	odd	12
420.2.bh.b.101.2	yes	10	15.2	even	4
420.2.bh.b.341.2	yes	10	35.12	even	12
2100.2.bi.j.101.4		10	15.8	even	4
2100.2.bi.j.1601.4		10	35.33	even	12
2100.2.bi.k.101.5		10	5.3	odd	4
2100.2.bi.k.1601.5		10	105.68	odd	12
2100.2.bo.g.1349.3		20	7.5	odd	6
2100.2.bo.g.1349.8		20	35.19	odd	6
2100.2.bo.g.1949.3		20	15.14	odd	2
2100.2.bo.g.1949.8		20	3.2	odd	2
2100.2.bo.h.1349.4		20	21.5	even	6	inner
2100.2.bo.h.1349.7		20	105.89	even	6	inner
2100.2.bo.h.1949.4		20	5.4	even	2	inner
2100.2.bo.h.1949.7		20	1.1	even	1	trivial
2940.2.d.a.881.5		10	35.17	even	12
2940.2.d.a.881.6		10	105.32	even	12
2940.2.d.b.881.5		10	105.17	odd	12
2940.2.d.b.881.6		10	35.32	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)

\(f(q)\)	\(=\)	\(q+(0.368412 - 1.69242i) q^{3} +(1.93884 + 1.80025i) q^{7} +(-2.72854 - 1.24701i) q^{9} +O(q^{10})\)	\(q+(0.368412 - 1.69242i) q^{3} +(1.93884 + 1.80025i) q^{7} +(-2.72854 - 1.24701i) q^{9} +(4.05595 + 2.34170i) q^{11} +2.18938 q^{13} +(-6.49492 - 3.74984i) q^{17} +(0.638109 - 0.368412i) q^{19} +(3.76107 - 2.61808i) q^{21} +(4.03930 + 6.99627i) q^{23} +(-3.11570 + 4.15842i) q^{27} +1.15414i q^{29} +(8.95201 + 5.16845i) q^{31} +(5.45740 - 6.00164i) q^{33} +(3.99970 - 2.30923i) q^{37} +(0.806595 - 3.70534i) q^{39} -1.43758 q^{41} -9.24142i q^{43} +(7.52098 - 4.34224i) q^{47} +(0.518179 + 6.98079i) q^{49} +(-8.73910 + 9.61061i) q^{51} +(-4.06174 + 7.03514i) q^{53} +(-0.388420 - 1.21567i) q^{57} +(-3.48730 + 6.04018i) q^{59} +(5.13811 - 2.96649i) q^{61} +(-3.04526 - 7.32983i) q^{63} +(-1.19795 - 0.691639i) q^{67} +(13.3287 - 4.25866i) q^{69} +7.26258i q^{71} +(0.122026 - 0.211355i) q^{73} +(3.64817 + 11.8419i) q^{77} +(5.79653 + 10.0399i) q^{79} +(5.88991 + 6.80507i) q^{81} -16.4610i q^{83} +(1.95328 + 0.425199i) q^{87} +(-0.658248 - 1.14012i) q^{89} +(4.24485 + 3.94144i) q^{91} +(12.0452 - 13.2464i) q^{93} +4.84232 q^{97} +(-8.14670 - 11.4473i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{9}+O(q^{10}) \) 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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Database

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