LMFDB - Embedded newform 2100.2.bi.k.101.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(101,2100)]

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, 0, 1]))

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

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

chi := DirichletCharacter("2100.101");

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.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.29471584693248.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 13x^{6} - 36x^{5} + 39x^{4} - 36x^{3} + 54x^{2} - 162x + 243 $ x^10 - 2x^9 + 2x^8 - 4x^7 + 13x^6 - 36x^5 + 39x^4 - 36x^3 + 54x^2 - 162*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.5
Root			$0.527154 - 1.64988i$ of defining polynomial
Character	$\chi$	$=$	2100.101
Dual form			2100.2.bi.k.1601.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.69242 + 0.368412i) q^{3} +(1.80025 - 1.93884i) q^{7} +(2.72854 + 1.24701i) q^{9} +O(q^{10})$	\(q+(1.69242 + 0.368412i) q^{3} +(1.80025 - 1.93884i) q^{7} +(2.72854 + 1.24701i) q^{9} +(4.05595 + 2.34170i) q^{11} +2.18938i q^{13} +(-3.74984 + 6.49492i) q^{17} +(-0.638109 + 0.368412i) q^{19} +(3.76107 - 2.61808i) q^{21} +(-6.99627 + 4.03930i) q^{23} +(4.15842 + 3.11570i) q^{27} -1.15414i q^{29} +(8.95201 + 5.16845i) q^{31} +(6.00164 + 5.45740i) q^{33} +(-2.30923 - 3.99970i) q^{37} +(-0.806595 + 3.70534i) q^{39} -1.43758 q^{41} +9.24142 q^{43} +(-4.34224 - 7.52098i) q^{47} +(-0.518179 - 6.98079i) q^{49} +(-8.73910 + 9.61061i) q^{51} +(-7.03514 - 4.06174i) q^{53} +(-1.21567 + 0.388420i) q^{57} +(3.48730 - 6.04018i) q^{59} +(5.13811 - 2.96649i) q^{61} +(7.32983 - 3.04526i) q^{63} +(-0.691639 + 1.19795i) q^{67} +(-13.3287 + 4.25866i) q^{69} +7.26258i q^{71} +(0.211355 + 0.122026i) q^{73} +(11.8419 - 3.64817i) q^{77} +(-5.79653 - 10.0399i) q^{79} +(5.88991 + 6.80507i) q^{81} +16.4610 q^{83} +(0.425199 - 1.95328i) q^{87} +(0.658248 + 1.14012i) q^{89} +(4.24485 + 3.94144i) q^{91} +(13.2464 + 12.0452i) q^{93} -4.84232i q^{97} +(8.14670 + 11.4473i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} + 5 q^{7} - 3 q^{9}+O(q^{10}) $ 10 * q + q^3 + 5 * q^7 - 3 * q^9	$ 10 q + q^{3} + 5 q^{7} - 3 q^{9} - 6 q^{11} - 6 q^{17} + 3 q^{19} + 10 q^{21} - 24 q^{23} - 8 q^{27} + 15 q^{31} + 20 q^{33} + q^{37} + 15 q^{39} - 8 q^{41} + 26 q^{43} - 14 q^{47} - 13 q^{49} - 44 q^{51} + 24 q^{53} - 18 q^{57} + 42 q^{61} + q^{63} - 7 q^{67} - 14 q^{69} + 3 q^{73} + 26 q^{77} + q^{79} + 41 q^{81} + 8 q^{83} + 26 q^{87} + 28 q^{89} - 11 q^{91} + 47 q^{93} + 36 q^{99}+O(q^{100}) $ 10 * q + q^3 + 5 * q^7 - 3 * q^9 - 6 * q^11 - 6 * q^17 + 3 * q^19 + 10 * q^21 - 24 * q^23 - 8 * q^27 + 15 * q^31 + 20 * q^33 + q^37 + 15 * q^39 - 8 * q^41 + 26 * q^43 - 14 * q^47 - 13 * q^49 - 44 * q^51 + 24 * q^53 - 18 * q^57 + 42 * q^61 + q^63 - 7 * q^67 - 14 * q^69 + 3 * q^73 + 26 * q^77 + q^79 + 41 * q^81 + 8 * q^83 + 26 * q^87 + 28 * q^89 - 11 * q^91 + 47 * q^93 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.69242	+	0.368412i	0.977117	+	0.212703i
$3$	1.69242	+	0.368412i	0.977117	+	0.212703i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.80025	−	1.93884i	0.680432	−	0.732812i
$7$	1.80025	−	1.93884i	0.680432	−	0.732812i
$8$		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
$13$			2.18938i			0.607225i	0.952796	+	0.303612i	$0.0981928\pi$
$13$			2.18938i			0.607225i	−0.952796	+	0.303612i	$0.901807\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.74984	+	6.49492i	−0.909470	+	1.57525i	−0.0946686	+	0.995509i	$0.530179\pi$
$17$	−3.74984	+	6.49492i	−0.909470	+	1.57525i	−0.814802	+	0.579740i	$0.803154\pi$
$18$		0			0
$19$	−0.638109	+	0.368412i	−0.146392	+	0.0845196i	−0.571407	−	0.820667i	$-0.693602\pi$
$19$	−0.638109	+	0.368412i	−0.146392	+	0.0845196i	0.425015	+	0.905186i	$0.360269\pi$
$20$		0			0
$21$	3.76107	−	2.61808i	0.820732	−	0.571313i
$22$		0			0
$23$	−6.99627	+	4.03930i	−1.45882	+	0.842252i	−0.998954	−	0.0457338i	$-0.985437\pi$
$23$	−6.99627	+	4.03930i	−1.45882	+	0.842252i	−0.459870	+	0.887986i	$0.652104\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	4.15842	+	3.11570i	0.800288	+	0.599616i
$28$		0			0
$29$		−	1.15414i		−	0.214318i	−0.994242	−	0.107159i	$-0.965825\pi$
$29$		−	1.15414i		−	0.214318i	0.994242	−	0.107159i	$-0.0341754\pi$
$30$		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
$33$	6.00164	+	5.45740i	1.04475	+	0.950012i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.30923	−	3.99970i	−0.379635	−	0.657547i	0.611374	−	0.791342i	$-0.290617\pi$
$37$	−2.30923	−	3.99970i	−0.379635	−	0.657547i	−0.991009	+	0.133795i	$0.957284\pi$
$38$		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
$43$	9.24142			1.40930			0.704651	−	0.709554i	$-0.251103\pi$
$43$	9.24142			1.40930			0.704651	+	0.709554i	$0.251103\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.34224	−	7.52098i	−0.633380	−	1.09705i	−0.986856	−	0.161603i	$-0.948333\pi$
$47$	−4.34224	−	7.52098i	−0.633380	−	1.09705i	0.353475	−	0.935444i	$-0.385000\pi$
$48$		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
$53$	−7.03514	−	4.06174i	−0.966351	−	0.557923i	−0.0682291	−	0.997670i	$-0.521735\pi$
$53$	−7.03514	−	4.06174i	−0.966351	−	0.557923i	−0.898122	+	0.439747i	$0.855068\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.21567	+	0.388420i	−0.161020	+	0.0514475i
$58$		0			0
$59$	3.48730	−	6.04018i	0.454008	−	0.786364i	−0.544623	−	0.838681i	$-0.683327\pi$
$59$	3.48730	−	6.04018i	0.454008	−	0.786364i	0.998631	+	0.0523168i	$0.0166606\pi$
$60$		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
$63$	7.32983	−	3.04526i	0.923472	−	0.383667i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−0.691639	+	1.19795i	−0.0844971	+	0.146353i	−0.905177	−	0.425035i	$-0.860262\pi$
$67$	−0.691639	+	1.19795i	−0.0844971	+	0.146353i	0.820680	+	0.571389i	$0.193595\pi$
$68$		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
$73$	0.211355	+	0.122026i	0.0247372	+	0.0142820i	0.512318	−	0.858796i	$-0.328787\pi$
$73$	0.211355	+	0.122026i	0.0247372	+	0.0142820i	−0.487580	+	0.873078i	$0.662120\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	11.8419	−	3.64817i	1.34951	−	0.415747i
$78$		0			0
$79$	−5.79653	−	10.0399i	−0.652160	−	1.12957i	−0.982598	−	0.185747i	$-0.940530\pi$
$79$	−5.79653	−	10.0399i	−0.652160	−	1.12957i	0.330438	−	0.943828i	$-0.392804\pi$
$80$		0			0
$81$	5.88991	+	6.80507i	0.654435	+	0.756119i
$82$		0			0
$83$	16.4610			1.80683			0.903413	−	0.428772i	$-0.141054\pi$
$83$	16.4610			1.80683			0.903413	+	0.428772i	$0.141054\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.425199	−	1.95328i	0.0455862	−	0.209414i
$88$		0			0
$89$	0.658248	+	1.14012i	0.0697741	+	0.120852i	0.898802	−	0.438355i	$-0.144439\pi$
$89$	0.658248	+	1.14012i	0.0697741	+	0.120852i	−0.829028	+	0.559208i	$0.811105\pi$
$90$		0			0
$91$	4.24485	+	3.94144i	0.444981	+	0.413175i
$92$		0			0
$93$	13.2464	+	12.0452i	1.37359	+	1.24903i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	4.84232i		−	0.491663i	−0.969313	−	0.245832i	$-0.920939\pi$
$97$		−	4.84232i		−	0.491663i	0.969313	−	0.245832i	$-0.0790611\pi$
$98$		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
$103$	7.07000	−	4.08187i	0.696628	−	0.402199i	−0.109462	−	0.993991i	$-0.534913\pi$
$103$	7.07000	−	4.08187i	0.696628	−	0.402199i	0.806090	+	0.591792i	$0.201579\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.186331	−	0.107578i	0.0180133	−	0.0104000i	−0.490966	−	0.871179i	$-0.663356\pi$
$107$	0.186331	−	0.107578i	0.0180133	−	0.0104000i	0.508980	+	0.860779i	$0.330023\pi$
$108$		0			0
$109$	−1.08683	+	1.88245i	−0.104100	+	0.180306i	−0.913370	−	0.407131i	$-0.866529\pi$
$109$	−1.08683	+	1.88245i	−0.104100	+	0.180306i	0.809270	+	0.587436i	$0.199863\pi$
$110$		0			0
$111$	−2.43464	−	7.61990i	−0.231085	−	0.723249i
$112$		0			0
$113$			11.2195i			1.05544i	0.849419	+	0.527719i	$0.176952\pi$
$113$			11.2195i			1.05544i	−0.849419	+	0.527719i	$0.823048\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.73019	+	5.97382i	−0.252406	+	0.552280i
$118$		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
$123$	−2.43299	−	0.529624i	−0.219375	−	0.0477546i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−17.2228			−1.52828			−0.764140	−	0.645051i	$-0.776836\pi$
$127$	−17.2228			−1.52828			−0.764140	+	0.645051i	$0.776836\pi$
$128$		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
$133$	−0.434466	+	1.90042i	−0.0376730	+	0.164788i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.68866	−	5.59375i	−0.827758	−	0.477907i	0.0253261	−	0.999679i	$-0.491938\pi$
$137$	−9.68866	−	5.59375i	−0.827758	−	0.477907i	−0.853085	+	0.521773i	$0.825271\pi$
$138$		0			0
$139$			2.16017i			0.183223i	0.995795	+	0.0916116i	$0.0292018\pi$
$139$			2.16017i			0.183223i	−0.995795	+	0.0916116i	$0.970798\pi$
$140$		0			0
$141$	−4.57805	−	14.3284i	−0.385542	−	1.20667i
$142$		0			0
$143$	−5.12688	+	8.88002i	−0.428731	+	0.742585i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	1.69484	−	12.0053i	0.139788	−	0.990181i
$148$		0			0
$149$	1.37427	−	0.793438i	0.112585	−	0.0650010i	−0.442650	−	0.896694i	$-0.645962\pi$
$149$	1.37427	−	0.793438i	0.112585	−	0.0650010i	0.555235	+	0.831693i	$0.312628\pi$
$150$		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
$153$	−18.3309	+	13.0456i	−1.48196	+	1.05467i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	5.62174	+	3.24572i	0.448664	+	0.259036i	0.707266	−	0.706948i	$-0.249928\pi$
$157$	5.62174	+	3.24572i	0.448664	+	0.259036i	−0.258602	+	0.965984i	$0.583262\pi$
$158$		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
$163$	2.68350	+	4.64797i	0.210188	+	0.364057i	0.951773	−	0.306802i	$-0.0992590\pi$
$163$	2.68350	+	4.64797i	0.210188	+	0.364057i	−0.741585	+	0.670859i	$0.765926\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.84082			0.529359			0.264679	−	0.964336i	$-0.414734\pi$
$167$	6.84082			0.529359			0.264679	+	0.964336i	$0.414734\pi$
$168$		0			0
$169$	8.20661			0.631278
$170$		0			0
$171$	−2.20052	+	0.209499i	−0.168278	+	0.0160208i
$172$		0			0
$173$	−5.81618	−	10.0739i	−0.442196	−	0.765906i	0.555656	−	0.831412i	$-0.312467\pi$
$173$	−5.81618	−	10.0739i	−0.442196	−	0.765906i	−0.997852	+	0.0655063i	$0.979134\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	8.12724	−	8.93773i	0.610881	−	0.671801i
$178$		0			0
$179$	−6.95741	−	4.01686i	−0.520021	−	0.300234i	0.216922	−	0.976189i	$-0.430398\pi$
$179$	−6.95741	−	4.01686i	−0.520021	−	0.300234i	−0.736943	+	0.675955i	$0.763732\pi$
$180$		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
$183$	9.78871	−	3.12759i	0.723602	−	0.231198i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−30.4184	+	17.5620i	−2.22441	+	1.28426i
$188$		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
$193$	3.19143	−	5.52771i	0.229724	−	0.397894i	−0.728002	−	0.685575i	$-0.759551\pi$
$193$	3.19143	−	5.52771i	0.229724	−	0.397894i	0.957726	+	0.287681i	$0.0928843\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			2.54995i			0.181677i	0.995866	+	0.0908384i	$0.0289547\pi$
$197$			2.54995i			0.181677i	−0.995866	+	0.0908384i	$0.971045\pi$
$198$		0			0
$199$	−6.27973	−	3.62561i	−0.445159	−	0.257012i	0.260625	−	0.965440i	$-0.416071\pi$
$199$	−6.27973	−	3.62561i	−0.445159	−	0.257012i	−0.705783	+	0.708428i	$0.749405\pi$
$200$		0			0
$201$	−1.61188	+	1.77263i	−0.113693	+	0.125031i
$202$		0			0
$203$	−2.23769	−	2.07774i	−0.157055	−	0.145829i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−24.1267	+	2.29696i	−1.67692	+	0.159650i
$208$		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
$213$	−2.67562	+	12.2913i	−0.183331	+	0.842186i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	26.1367	−	8.05198i	1.77427	−	0.546604i
$218$		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
$223$		−	28.1032i		−	1.88193i	−0.338506	−	0.940964i	$-0.609922\pi$
$223$		−	28.1032i		−	1.88193i	0.338506	−	0.940964i	$-0.390078\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.71504	+	11.6308i	−0.445693	+	0.771963i	−0.998100	−	0.0616117i	$-0.980376\pi$
$227$	−6.71504	+	11.6308i	−0.445693	+	0.771963i	0.552407	+	0.833574i	$0.313709\pi$
$228$		0			0
$229$	−7.24605	+	4.18351i	−0.478833	+	0.276454i	−0.719930	−	0.694047i	$-0.755826\pi$
$229$	−7.24605	+	4.18351i	−0.478833	+	0.276454i	0.241097	+	0.970501i	$0.422493\pi$
$230$		0			0
$231$	21.3855	−	1.81151i	1.40706	−	0.119188i
$232$		0			0
$233$	7.07871	−	4.08689i	0.463742	−	0.267741i	−0.249875	−	0.968278i	$-0.580389\pi$
$233$	7.07871	−	4.08689i	0.463742	−	0.267741i	0.713616	+	0.700537i	$0.247056\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−6.11132	−	19.1272i	−0.396973	−	1.24244i
$238$		0			0
$239$		−	12.5553i		−	0.812134i	−0.913843	−	0.406067i	$-0.866900\pi$
$239$		−	12.5553i		−	0.812134i	0.913843	−	0.406067i	$-0.133100\pi$
$240$		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
$243$	7.46111	+	13.6869i	0.478630	+	0.878016i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.806595	−	1.39706i	−0.0513224	−	0.0888930i
$248$		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
$253$	−37.8354			−2.37869
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.602166	−	1.04298i	−0.0375621	−	0.0650594i	0.846633	−	0.532177i	$-0.178626\pi$
$257$	−0.602166	−	1.04298i	−0.0375621	−	0.0650594i	−0.884195	+	0.467117i	$0.845293\pi$
$258$		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
$263$	4.34275	+	2.50729i	0.267785	+	0.154606i	0.627881	−	0.778310i	$-0.283923\pi$
$263$	4.34275	+	2.50729i	0.267785	+	0.154606i	−0.360095	+	0.932915i	$0.617256\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.693995	+	2.17206i	0.0424718	+	0.132928i
$268$		0			0
$269$	−7.94487	+	13.7609i	−0.484407	+	0.839018i	−0.999840	−	0.0179121i	$-0.994298\pi$
$269$	−7.94487	+	13.7609i	−0.484407	+	0.839018i	0.515432	+	0.856930i	$0.327631\pi$
$270$		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
$273$	5.73198	+	8.23441i	0.346915	+	0.498369i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	2.20512	−	3.81938i	0.132493	−	0.229484i	−0.792144	−	0.610334i	$-0.791035\pi$
$277$	2.20512	−	3.81938i	0.132493	−	0.229484i	0.924637	+	0.380850i	$0.124369\pi$
$278$		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
$283$	−10.0054	−	5.77663i	−0.594760	−	0.343385i	0.172217	−	0.985059i	$-0.444907\pi$
$283$	−10.0054	−	5.77663i	−0.594760	−	0.343385i	−0.766978	+	0.641674i	$0.778240\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.58802	+	2.78724i	−0.152766	+	0.164526i
$288$		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
$293$	7.17953			0.419433			0.209716	−	0.977762i	$-0.432746\pi$
$293$	7.17953			0.419433			0.209716	+	0.977762i	$0.432746\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	9.57030	+	22.3749i	0.555325	+	1.29832i
$298$		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
$303$	3.22625	−	3.54799i	0.185343	−	0.203827i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	2.44348i		−	0.139457i	−0.997566	−	0.0697284i	$-0.977787\pi$
$307$		−	2.44348i		−	0.139457i	0.997566	−	0.0697284i	$-0.0222133\pi$
$308$		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
$313$	1.41881	−	0.819152i	0.0801961	−	0.0463012i	−0.459366	−	0.888247i	$-0.651923\pi$
$313$	1.41881	−	0.819152i	0.0801961	−	0.0463012i	0.539562	+	0.841946i	$0.318590\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	14.3446	−	8.28184i	0.805672	−	0.465155i	−0.0397789	−	0.999209i	$-0.512665\pi$
$317$	14.3446	−	8.28184i	0.805672	−	0.465155i	0.845451	+	0.534054i	$0.179332\pi$
$318$		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
$323$		−	5.52595i		−	0.307472i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−2.53289	+	2.78548i	−0.140069	+	0.154037i
$328$		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
$333$	−1.31315	−	13.7930i	−0.0719601	−	0.755852i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	9.25410			0.504103			0.252051	−	0.967714i	$-0.418895\pi$
$337$	9.25410			0.504103			0.252051	+	0.967714i	$0.418895\pi$
$338$		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
$343$	−14.4675	−	11.5625i	−0.781170	−	0.624318i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	23.0038	+	13.2812i	1.23491	+	0.712973i	0.968049	−	0.250763i	$-0.0806814\pi$
$347$	23.0038	+	13.2812i	1.23491	+	0.712973i	0.266857	+	0.963736i	$0.414015\pi$
$348$		0			0
$349$		−	14.8893i		−	0.797004i	−0.917167	−	0.398502i	$-0.869530\pi$
$349$		−	14.8893i		−	0.797004i	0.917167	−	0.398502i	$-0.130470\pi$
$350$		0			0
$351$	−6.82145	+	9.10436i	−0.364102	+	0.485955i
$352$		0			0
$353$	8.41481	−	14.5749i	0.447875	−	0.775743i	−0.550372	−	0.834919i	$-0.685514\pi$
$353$	8.41481	−	14.5749i	0.447875	−	0.775743i	0.998248	+	0.0591766i	$0.0188475\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	2.90082	+	34.2452i	0.153528	+	1.81245i
$358$		0			0
$359$	24.3673	−	14.0685i	1.28606	−	0.742506i	0.308109	−	0.951351i	$-0.400304\pi$
$359$	24.3673	−	14.0685i	1.28606	−	0.742506i	0.977949	+	0.208846i	$0.0669706\pi$
$360$		0			0
$361$	−9.22854	+	15.9843i	−0.485713	+	0.841279i
$362$		0			0
$363$	5.76407	+	18.0403i	0.302535	+	0.946872i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	12.7963	+	7.38797i	0.667963	+	0.385649i	0.795304	−	0.606210i	$-0.207311\pi$
$367$	12.7963	+	7.38797i	0.667963	+	0.385649i	−0.127341	+	0.991859i	$0.540644\pi$
$368$		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
$373$	−10.9537	−	18.9723i	−0.567159	−	0.982348i	−0.996845	−	0.0793696i	$-0.974709\pi$
$373$	−10.9537	−	18.9723i	−0.567159	−	0.982348i	0.429687	−	0.902978i	$-0.358624\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.52685			0.130139
$378$		0			0
$379$	−8.15057			−0.418667			−0.209333	−	0.977844i	$-0.567129\pi$
$379$	−8.15057			−0.418667			−0.209333	+	0.977844i	$0.567129\pi$
$380$		0			0
$381$	−29.1482	−	6.34511i	−1.49331	−	0.325070i
$382$		0			0
$383$	−0.164775	−	0.285399i	−0.00841962	−	0.0145832i	0.861785	−	0.507274i	$-0.169347\pi$
$383$	−0.164775	−	0.285399i	−0.00841962	−	0.0145832i	−0.870205	+	0.492691i	$0.836013\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	25.2156	+	11.5242i	1.28178	+	0.585807i
$388$		0			0
$389$	11.5387	+	6.66185i	0.585033	+	0.337769i	0.763131	−	0.646244i	$-0.223661\pi$
$389$	11.5387	+	6.66185i	0.585033	+	0.337769i	−0.178098	+	0.984013i	$0.556994\pi$
$390$		0			0
$391$		−	60.5869i		−	3.06401i
$392$		0			0
$393$	−9.12830	−	28.5697i	−0.460462	−	1.44115i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	24.7694	−	14.3006i	1.24314	−	0.717728i	0.273409	−	0.961898i	$-0.411849\pi$
$397$	24.7694	−	14.3006i	1.24314	−	0.717728i	0.969733	+	0.244169i	$0.0785153\pi$
$398$		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
$403$	−11.3157	+	19.5994i	−0.563675	+	0.976314i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	21.6301i		−	1.07217i
$408$		0			0
$409$	0.852979	+	0.492468i	0.0421771	+	0.0243510i	0.520940	−	0.853593i	$-0.325581\pi$
$409$	0.852979	+	0.492468i	0.0421771	+	0.0243510i	−0.478763	+	0.877944i	$0.658915\pi$
$410$		0			0
$411$	−14.3364	−	13.0364i	−0.707165	−	0.643037i
$412$		0			0
$413$	−5.43290	−	17.6352i	−0.267336	−	0.867769i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.795833	+	3.65590i	−0.0389721	+	0.179030i
$418$		0			0
$419$	−31.2166			−1.52503			−0.762515	−	0.646970i	$-0.776036\pi$
$419$	−31.2166			−1.52503			−0.762515	+	0.646970i	$0.776036\pi$
$420$		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
$423$	−2.46922	−	25.9362i	−0.120058	−	1.26106i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	3.49836	−	15.3024i	0.169297	−	0.740534i
$428$		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
$433$		−	24.6833i		−	1.18621i	−0.805127	−	0.593103i	$-0.797903\pi$
$433$		−	24.6833i		−	1.18621i	0.805127	−	0.593103i	$-0.202097\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.97626	−	5.15503i	0.142374	−	0.246598i
$438$		0			0
$439$	−13.1758	+	7.60702i	−0.628844	+	0.363063i	−0.780304	−	0.625400i	$-0.784936\pi$
$439$	−13.1758	+	7.60702i	−0.628844	+	0.363063i	0.151460	+	0.988463i	$0.451602\pi$
$440$		0			0
$441$	7.29128	−	19.6936i	0.347204	−	0.937790i
$442$		0			0
$443$	−26.1325	+	15.0876i	−1.24159	+	0.716834i	−0.969418	−	0.245414i	$-0.921076\pi$
$443$	−26.1325	+	15.0876i	−1.24159	+	0.716834i	−0.272174	+	0.962248i	$0.587743\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	2.61816	−	0.836527i	0.123835	−	0.0395664i
$448$		0			0
$449$			27.7596i			1.31006i	0.755603	+	0.655029i	$0.227344\pi$
$449$			27.7596i			1.31006i	−0.755603	+	0.655029i	$0.772656\pi$
$450$		0			0
$451$	−5.83077	−	3.36640i	−0.274560	−	0.158518i
$452$		0			0
$453$	−11.9376	+	13.1281i	−0.560878	+	0.616812i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	16.9273	+	29.3189i	0.791825	+	1.37148i	0.924836	+	0.380366i	$0.124202\pi$
$457$	16.9273	+	29.3189i	0.791825	+	1.37148i	−0.133011	+	0.991115i	$0.542465\pi$
$458$		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
$463$	−1.60640			−0.0746559			−0.0373280	−	0.999303i	$-0.511885\pi$
$463$	−1.60640			−0.0746559			−0.0373280	+	0.999303i	$0.511885\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.18589	−	5.51812i	−0.147425	−	0.255348i	0.782850	−	0.622211i	$-0.213765\pi$
$467$	−3.18589	−	5.51812i	−0.147425	−	0.255348i	−0.930275	+	0.366863i	$0.880432\pi$
$468$		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
$473$	37.4827	+	21.6407i	1.72346	+	0.995039i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−14.1306	−	19.8556i	−0.646998	−	0.909124i
$478$		0			0
$479$	−1.66105	+	2.87702i	−0.0758953	+	0.131455i	−0.901475	−	0.432831i	$-0.857515\pi$
$479$	−1.66105	+	2.87702i	−0.0758953	+	0.131455i	0.825580	+	0.564285i	$0.190848\pi$
$480$		0			0
$481$	8.75687	−	5.05578i	0.399279	−	0.230524i
$482$		0			0
$483$	−15.7382	+	33.5089i	−0.716115	+	1.52471i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−10.3313	+	17.8943i	−0.468155	+	0.810868i	−0.999338	−	0.0363892i	$-0.988414\pi$
$487$	−10.3313	+	17.8943i	−0.468155	+	0.810868i	0.531183	+	0.847257i	$0.321748\pi$
$488$		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
$493$	7.49604	+	4.32784i	0.337605	+	0.194916i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	14.0810	+	13.0745i	0.631617	+	0.586470i
$498$		0			0
$499$	−3.10558	−	5.37903i	−0.139025	−	0.240798i	0.788103	−	0.615544i	$-0.211064\pi$
$499$	−3.10558	−	5.37903i	−0.139025	−	0.240798i	−0.927128	+	0.374745i	$0.877730\pi$
$500$		0			0
$501$	11.5775	+	2.52024i	0.517245	+	0.112596i
$502$		0			0
$503$	5.52940			0.246544			0.123272	−	0.992373i	$-0.460661\pi$
$503$	5.52940			0.246544			0.123272	+	0.992373i	$0.460661\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	13.8890	+	3.02342i	0.616832	+	0.134275i
$508$		0			0
$509$	14.8857	+	25.7827i	0.659796	+	1.14280i	0.980668	+	0.195678i	$0.0626906\pi$
$509$	14.8857	+	25.7827i	0.659796	+	1.14280i	−0.320872	+	0.947122i	$0.603976\pi$
$510$		0			0
$511$	0.617080	−	0.190105i	0.0272980	−	0.00840977i
$512$		0			0
$513$	−3.80138	−	0.456142i	−0.167835	−	0.0201391i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	40.6729i		−	1.78879i
$518$		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
$523$	−20.3535	+	11.7511i	−0.889996	+	0.513839i	−0.873941	−	0.486032i	$-0.838444\pi$
$523$	−20.3535	+	11.7511i	−0.889996	+	0.513839i	−0.0160547	+	0.999871i	$0.505111\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−67.1372	+	38.7617i	−2.92454	+	1.68849i
$528$		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
$533$		−	3.14742i		−	0.136330i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−10.2950	−	9.36139i	−0.444260	−	0.403974i
$538$		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
$543$	3.61703	−	16.6160i	0.155222	−	0.713059i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−41.2183			−1.76237			−0.881184	−	0.472774i	$-0.843253\pi$
$547$	−41.2183			−1.76237			−0.881184	+	0.472774i	$0.843253\pi$
$548$		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
$553$	−29.9009	−	6.83580i	−1.27152	−	0.290688i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−5.03375	−	2.90624i	−0.213287	−	0.123141i	0.389551	−	0.921005i	$-0.372630\pi$
$557$	−5.03375	−	2.90624i	−0.213287	−	0.123141i	−0.602838	+	0.797864i	$0.705963\pi$
$558$		0			0
$559$			20.2330i			0.855764i
$560$		0			0
$561$	−57.9506	+	18.5158i	−2.44668	+	0.781737i
$562$		0			0
$563$	10.5187	−	18.2190i	0.443312	−	0.767838i	−0.554621	−	0.832103i	$-0.687137\pi$
$563$	10.5187	−	18.2190i	0.443312	−	0.767838i	0.997933	+	0.0642647i	$0.0204702\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	23.7972	+	0.831265i	0.999390	+	0.0349098i
$568$		0			0
$569$	30.2091	−	17.4412i	1.26643	−	0.731173i	0.292119	−	0.956382i	$-0.405640\pi$
$569$	30.2091	−	17.4412i	1.26643	−	0.731173i	0.974311	+	0.225209i	$0.0723064\pi$
$570$		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
$573$	26.4915	−	8.46429i	1.10670	−	0.353601i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	4.69855	+	2.71271i	0.195603	+	0.112932i	0.594603	−	0.804019i	$-0.297309\pi$
$577$	4.69855	+	2.71271i	0.195603	+	0.112932i	−0.399000	+	0.916951i	$0.630643\pi$
$578$		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
$583$	−19.0228	−	32.9484i	−0.787844	−	1.36459i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−8.71317			−0.359631			−0.179816	−	0.983700i	$-0.557550\pi$
$587$	−8.71317			−0.359631			−0.179816	+	0.983700i	$0.557550\pi$
$588$		0			0
$589$	−7.61648			−0.313832
$590$		0			0
$591$	−0.939435	+	4.31558i	−0.0386432	+	0.177519i
$592$		0			0
$593$	−9.79341	−	16.9627i	−0.402167	−	0.696574i	0.591820	−	0.806070i	$-0.298410\pi$
$593$	−9.79341	−	16.9627i	−0.402167	−	0.696574i	−0.993987	+	0.109496i	$0.965076\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−9.29221	−	8.44957i	−0.380305	−	0.345818i
$598$		0			0
$599$	−14.2397	−	8.22129i	−0.581818	−	0.335913i	0.180038	−	0.983660i	$-0.442378\pi$
$599$	−14.2397	−	8.22129i	−0.581818	−	0.335913i	−0.761855	+	0.647747i	$0.775711\pi$
$600$		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
$603$	−3.38103	+	2.40619i	−0.137686	+	0.0979875i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−10.5191	+	6.07323i	−0.426959	+	0.246505i	−0.698050	−	0.716049i	$-0.745949\pi$
$607$	−10.5191	+	6.07323i	−0.426959	+	0.246505i	0.271091	+	0.962554i	$0.412615\pi$
$608$		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
$613$	−8.26802	+	14.3206i	−0.333942	+	0.578405i	−0.983281	−	0.182094i	$-0.941712\pi$
$613$	−8.26802	+	14.3206i	−0.333942	+	0.578405i	0.649339	+	0.760499i	$0.275046\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			34.8433i			1.40274i	0.712799	+	0.701368i	$0.247427\pi$
$617$			34.8433i			1.40274i	−0.712799	+	0.701368i	$0.752573\pi$
$618$		0			0
$619$	−21.3120	−	12.3045i	−0.856603	−	0.494560i	0.00627057	−	0.999980i	$-0.498004\pi$
$619$	−21.3120	−	12.3045i	−0.856603	−	0.494560i	−0.862873	+	0.505421i	$0.831337\pi$
$620$		0			0
$621$	−41.6787	−	5.00117i	−1.67251	−	0.200690i
$622$		0			0
$623$	3.39552	+	0.776267i	0.136039	+	0.0311005i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−5.84028	−	1.27134i	−0.233238	−	0.0507723i
$628$		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
$633$	−22.4506	−	4.88715i	−0.892332	−	0.194247i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	15.2836	−	1.13449i	0.605559	−	0.0449501i
$638$		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
$643$		−	11.7173i		−	0.462086i	−0.972943	−	0.231043i	$-0.925786\pi$
$643$		−	11.7173i		−	0.462086i	0.972943	−	0.231043i	$-0.0742139\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	13.2263	−	22.9086i	0.519980	−	0.900632i	−0.479750	−	0.877405i	$-0.659273\pi$
$647$	13.2263	−	22.9086i	0.519980	−	0.900632i	0.999730	−	0.0232268i	$-0.00739398\pi$
$648$		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
$653$	3.13762	−	1.81151i	0.122785	−	0.0708898i	−0.437350	−	0.899292i	$-0.644083\pi$
$653$	3.13762	−	1.81151i	0.122785	−	0.0708898i	0.560134	+	0.828402i	$0.310749\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	0.424523	+	0.596515i	0.0165622	+	0.0232723i
$658$		0			0
$659$			24.1855i			0.942132i	0.882098	+	0.471066i	$0.156131\pi$
$659$			24.1855i			0.942132i	−0.882098	+	0.471066i	$0.843869\pi$
$660$		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
$663$	−21.0413	−	19.1332i	−0.817176	−	0.743073i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4.66192	+	8.07468i	0.180510	+	0.312653i
$668$		0			0
$669$	10.3536	−	47.5623i	0.400292	−	1.83886i
$670$		0			0
$671$	27.7866			1.07269
$672$		0			0
$673$	3.48623			0.134384			0.0671922	−	0.997740i	$-0.478596\pi$
$673$	3.48623			0.134384			0.0671922	+	0.997740i	$0.478596\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−19.4486	−	33.6859i	−0.747469	−	1.29465i	−0.949032	−	0.315179i	$-0.897936\pi$
$677$	−19.4486	−	33.6859i	−0.747469	−	1.29465i	0.201564	−	0.979475i	$-0.435398\pi$
$678$		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
$683$	−10.4809	−	6.05116i	−0.401041	−	0.231541i	0.285892	−	0.958262i	$-0.407710\pi$
$683$	−10.4809	−	6.05116i	−0.401041	−	0.231541i	−0.686933	+	0.726721i	$0.741044\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−13.8046	+	4.41070i	−0.526678	+	0.168279i
$688$		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
$693$	36.8605	+	4.81285i	1.40022	+	0.182825i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	5.39071	−	9.33699i	0.204188	−	0.353664i
$698$		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
$703$	2.94708	+	1.70150i	0.111151	+	0.0641732i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.15669	−	7.00059i	−0.0811106	−	0.263284i
$708$		0			0
$709$	5.13129	+	8.88765i	0.192710	+	0.333783i	0.946147	−	0.323737i	$-0.104939\pi$
$709$	5.13129	+	8.88765i	0.192710	+	0.333783i	−0.753438	+	0.657519i	$0.771606\pi$
$710$		0			0
$711$	−3.29621	−	34.6226i	−0.123618	−	1.29845i
$712$		0			0
$713$	−83.5076			−3.12738
$714$		0			0
$715$		0			0
$716$		0			0
$717$	4.62552	−	21.2488i	0.172743	−	0.793549i
$718$		0			0
$719$	24.3969	+	42.2566i	0.909850	+	1.57591i	0.814271	+	0.580485i	$0.197137\pi$
$719$	24.3969	+	42.2566i	0.909850	+	1.57591i	0.0955793	+	0.995422i	$0.469530\pi$
$720$		0			0
$721$	4.81372	−	21.0560i	0.179272	−	0.784166i
$722$		0			0
$723$	28.2853	+	25.7204i	1.05194	+	0.956550i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			9.98665i			0.370384i	0.982702	+	0.185192i	$0.0592907\pi$
$727$			9.98665i			0.370384i	−0.982702	+	0.185192i	$0.940709\pi$
$728$		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
$733$	31.9630	−	18.4538i	1.18058	−	0.681608i	0.224432	−	0.974490i	$-0.427947\pi$
$733$	31.9630	−	18.4538i	1.18058	−	0.681608i	0.956149	+	0.292881i	$0.0946141\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.61051	+	3.23923i	−0.206666	+	0.119318i
$738$		0			0
$739$	−19.7107	+	34.1399i	−0.725070	+	1.25586i	0.233875	+	0.972267i	$0.424859\pi$
$739$	−19.7107	+	34.1399i	−0.725070	+	1.25586i	−0.958945	+	0.283591i	$0.908474\pi$
$740$		0			0
$741$	−0.850399	−	2.66157i	−0.0312402	−	0.0977753i
$742$		0			0
$743$			12.7786i			0.468800i	0.972140	+	0.234400i	$0.0753125\pi$
$743$			12.7786i			0.468800i	−0.972140	+	0.234400i	$0.924688\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	44.9145	+	20.5271i	1.64333	+	0.751046i
$748$		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
$753$	2.82309	+	0.614541i	0.102879	+	0.0223951i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−26.6532			−0.968727			−0.484364	−	0.874867i	$-0.660949\pi$
$757$	−26.6532			−0.968727			−0.484364	+	0.874867i	$0.660949\pi$
$758$		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
$763$	1.69319	+	5.49607i	0.0612975	+	0.198971i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	13.2242	+	7.63502i	0.477500	+	0.275685i
$768$		0			0
$769$			26.0781i			0.940400i	0.882560	+	0.470200i	$0.155818\pi$
$769$			26.0781i			0.940400i	−0.882560	+	0.470200i	$0.844182\pi$
$770$		0			0
$771$	−0.634868	−	1.98700i	−0.0228642	−	0.0715602i
$772$		0			0
$773$	−19.9307	+	34.5210i	−0.716858	+	1.24163i	0.245381	+	0.969427i	$0.421087\pi$
$773$	−19.9307	+	34.5210i	−0.716858	+	1.24163i	−0.962239	+	0.272208i	$0.912246\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−19.1567	−	8.99740i	−0.687243	−	0.322780i
$778$		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
$783$	3.59595	−	4.79939i	0.128509	−	0.171516i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−21.2458	−	12.2663i	−0.757331	−	0.437245i	0.0710057	−	0.997476i	$-0.477379\pi$
$787$	−21.2458	−	12.2663i	−0.757331	−	0.437245i	−0.828337	+	0.560231i	$0.810712\pi$
$788$		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
$793$	6.49477	+	11.2493i	0.230636	+	0.399473i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	33.4163			1.18367			0.591834	−	0.806060i	$-0.298404\pi$
$797$	33.4163			1.18367			0.591834	+	0.806060i	$0.298404\pi$
$798$		0			0
$799$	65.1308			2.30416
$800$		0			0
$801$	0.374314	+	3.93171i	0.0132258	+	0.138920i
$802$		0			0
$803$	0.571497	+	0.989861i	0.0201677	+	0.0349315i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−18.5157	+	20.3622i	−0.651784	+	0.716784i
$808$		0			0
$809$	−43.1974	−	24.9400i	−1.51874	−	0.876845i	−0.999757	−	0.0220612i	$-0.992977\pi$
$809$	−43.1974	−	24.9400i	−1.51874	−	0.876845i	−0.518984	−	0.854784i	$-0.673690\pi$
$810$		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
$813$	−33.1867	+	10.6035i	−1.16391	+	0.371880i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−5.89703	+	3.40465i	−0.206311	+	0.119114i
$818$		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
$823$	−17.8141	+	30.8549i	−0.620960	+	1.07553i	0.368347	+	0.929688i	$0.379924\pi$
$823$	−17.8141	+	30.8549i	−0.620960	+	1.07553i	−0.989307	+	0.145846i	$0.953409\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	48.8191i		−	1.69761i	−0.528709	−	0.848803i	$-0.677324\pi$
$827$		−	48.8191i		−	1.69761i	0.528709	−	0.848803i	$-0.322676\pi$
$828$		0			0
$829$	11.5060	+	6.64300i	0.399621	+	0.230721i	0.686320	−	0.727299i	$-0.259225\pi$
$829$	11.5060	+	6.64300i	0.399621	+	0.230721i	−0.286700	+	0.958021i	$0.592558\pi$
$830$		0			0
$831$	5.13908	−	5.65158i	0.178273	−	0.196051i
$832$		0			0
$833$	47.2828	+	22.8113i	1.63825	+	0.790366i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	21.1229	+	49.3843i	0.730114	+	1.70697i
$838$		0			0
$839$	−42.5549			−1.46916			−0.734579	−	0.678523i	$-0.762620\pi$
$839$	−42.5549			−1.46916			−0.734579	+	0.678523i	$0.762620\pi$
$840$		0			0
$841$	27.6680			0.954068
$842$		0			0
$843$	6.60097	−	30.3236i	0.227349	−	1.04440i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	28.2019	+	6.44738i	0.969028	+	0.221535i
$848$		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
$853$			27.4196i			0.938830i	0.882978	+	0.469415i	$0.155535\pi$
$853$			27.4196i			0.938830i	−0.882978	+	0.469415i	$0.844465\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−4.27514	+	7.40476i	−0.146036	+	0.252942i	−0.929759	−	0.368169i	$-0.879985\pi$
$857$	−4.27514	+	7.40476i	−0.146036	+	0.252942i	0.783723	+	0.621111i	$0.213318\pi$
$858$		0			0
$859$	−2.23617	+	1.29105i	−0.0762970	+	0.0440501i	−0.537663	−	0.843160i	$-0.680693\pi$
$859$	−2.23617	+	1.29105i	−0.0762970	+	0.0440501i	0.461366	+	0.887210i	$0.347359\pi$
$860$		0			0
$861$	−5.40685	+	3.76372i	−0.184265	+	0.128267i
$862$		0			0
$863$	18.5478	−	10.7086i	0.631373	−	0.364523i	−0.149911	−	0.988700i	$-0.547899\pi$
$863$	18.5478	−	10.7086i	0.631373	−	0.364523i	0.781284	+	0.624176i	$0.214565\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−20.6883	−	64.7500i	−0.702611	−	2.19903i
$868$		0			0
$869$		−	54.2950i		−	1.84183i
$870$		0			0
$871$	−2.62278	−	1.51426i	−0.0888694	−	0.0513088i
$872$		0			0
$873$	6.03845	−	13.2125i	0.204370	−	0.447175i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	23.9665	+	41.5112i	0.809291	+	1.40173i	0.913355	+	0.407163i	$0.133482\pi$
$877$	23.9665	+	41.5112i	0.809291	+	1.40173i	−0.104064	+	0.994571i	$0.533185\pi$
$878$		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
$883$	57.8898			1.94815			0.974073	−	0.226236i	$-0.0726419\pi$
$883$	57.8898			1.94815			0.974073	+	0.226236i	$0.0726419\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.415272	+	0.719272i	0.0139435	+	0.0241508i	0.872913	−	0.487876i	$-0.162228\pi$
$887$	0.415272	+	0.719272i	0.0139435	+	0.0241508i	−0.858969	+	0.512027i	$0.828895\pi$
$888$		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
$893$	5.54164	+	3.19947i	0.185444	+	0.107066i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−9.32383	−	29.1817i	−0.311314	−	0.974348i
$898$		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
$903$	34.7576	−	24.1948i	1.15666	−	0.805152i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−21.9547	+	38.0267i	−0.728995	+	1.26266i	0.228313	+	0.973588i	$0.426679\pi$
$907$	−21.9547	+	38.0267i	−0.728995	+	1.26266i	−0.957308	+	0.289069i	$0.906654\pi$
$908$		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
$913$	66.7649	+	38.5467i	2.20959	+	1.27571i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−44.6621	−	10.2104i	−1.47487	−	0.337178i
$918$		0			0
$919$	22.9387	+	39.7309i	0.756677	+	1.31060i	0.944537	+	0.328406i	$0.106512\pi$
$919$	22.9387	+	39.7309i	0.756677	+	1.31060i	−0.187860	+	0.982196i	$0.560155\pi$
$920$		0			0
$921$	0.900209	−	4.13539i	0.0296629	−	0.136266i
$922$		0			0
$923$	−15.9005			−0.523373
$924$		0			0
$925$		0			0
$926$		0			0
$927$	24.3810	−	2.32117i	0.800776	−	0.0762371i
$928$		0			0
$929$	−5.79774	−	10.0420i	−0.190218	−	0.329467i	0.755105	−	0.655604i	$-0.227586\pi$
$929$	−5.79774	−	10.0420i	−0.190218	−	0.329467i	−0.945322	+	0.326137i	$0.894253\pi$
$930$		0			0
$931$	2.90247	+	4.26360i	0.0951245	+	0.139734i
$932$		0			0
$933$	5.97425	−	6.57003i	0.195588	−	0.215093i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	39.7618i		−	1.29896i	−0.760378	−	0.649481i	$-0.774986\pi$
$937$		−	39.7618i		−	1.29896i	0.760378	−	0.649481i	$-0.225014\pi$
$938$		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
$943$	10.0577	−	5.80684i	0.327525	−	0.189097i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	26.5502	−	15.3288i	0.862767	−	0.498119i	−0.00217116	−	0.999998i	$-0.500691\pi$
$947$	26.5502	−	15.3288i	0.862767	−	0.498119i	0.864938	+	0.501879i	$0.167358\pi$
$948$		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
$953$		−	22.7409i		−	0.736650i	−0.929697	−	0.368325i	$-0.879931\pi$
$953$		−	22.7409i		−	0.736650i	0.929697	−	0.368325i	$-0.120069\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	6.29860	−	6.92674i	0.203605	−	0.223910i
$958$		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
$963$	0.642564	−	0.0611747i	0.0207063	−	0.00197133i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−18.4381			−0.592928			−0.296464	−	0.955044i	$-0.595807\pi$
$967$	−18.4381			−0.592928			−0.296464	+	0.955044i	$0.595807\pi$
$968$		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
$973$	4.18822	+	3.88885i	0.134268	+	0.124671i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	18.3718	+	10.6070i	0.587766	+	0.339347i	0.764214	−	0.644963i	$-0.223127\pi$
$977$	18.3718	+	10.6070i	0.587766	+	0.339347i	−0.176448	+	0.984310i	$0.556461\pi$
$978$		0			0
$979$			6.16569i			0.197056i
$980$		0			0
$981$	−5.31291	+	3.78105i	−0.169628	+	0.120720i
$982$		0			0
$983$	18.2639	−	31.6340i	0.582528	−	1.00897i	−0.412651	−	0.910889i	$-0.635397\pi$
$983$	18.2639	−	31.6340i	0.582528	−	1.00897i	0.995179	−	0.0980782i	$-0.0312695\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−36.0220	−	16.9186i	−1.14659	−	0.538524i
$988$		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
$993$	12.6223	+	39.5053i	0.400557	+	1.25366i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−24.2658	−	14.0098i	−0.768504	−	0.443696i	0.0638366	−	0.997960i	$-0.479666\pi$
$997$	−24.2658	−	14.0098i	−0.768504	−	0.443696i	−0.832341	+	0.554264i	$0.813000\pi$
$998$		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.bi.k.101.5		10
3.2	odd	2		2100.2.bi.j.101.4		10
5.2	odd	4		2100.2.bo.h.1949.7		20
5.3	odd	4		2100.2.bo.h.1949.4		20
5.4	even	2		420.2.bh.a.101.1	✓	10
7.5	odd	6		2100.2.bi.j.1601.4		10
15.2	even	4		2100.2.bo.g.1949.8		20
15.8	even	4		2100.2.bo.g.1949.3		20
15.14	odd	2		420.2.bh.b.101.2	yes	10
21.5	even	6	inner	2100.2.bi.k.1601.5		10
35.4	even	6		2940.2.d.b.881.6		10
35.12	even	12		2100.2.bo.g.1349.3		20
35.19	odd	6		420.2.bh.b.341.2	yes	10
35.24	odd	6		2940.2.d.a.881.5		10
35.33	even	12		2100.2.bo.g.1349.8		20
105.47	odd	12		2100.2.bo.h.1349.4		20
105.59	even	6		2940.2.d.b.881.5		10
105.68	odd	12		2100.2.bo.h.1349.7		20
105.74	odd	6		2940.2.d.a.881.6		10
105.89	even	6		420.2.bh.a.341.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bh.a.101.1	✓	10	5.4	even	2
420.2.bh.a.341.1	yes	10	105.89	even	6
420.2.bh.b.101.2	yes	10	15.14	odd	2
420.2.bh.b.341.2	yes	10	35.19	odd	6
2100.2.bi.j.101.4		10	3.2	odd	2
2100.2.bi.j.1601.4		10	7.5	odd	6
2100.2.bi.k.101.5		10	1.1	even	1	trivial
2100.2.bi.k.1601.5		10	21.5	even	6	inner
2100.2.bo.g.1349.3		20	35.12	even	12
2100.2.bo.g.1349.8		20	35.33	even	12
2100.2.bo.g.1949.3		20	15.8	even	4
2100.2.bo.g.1949.8		20	15.2	even	4
2100.2.bo.h.1349.4		20	105.47	odd	12
2100.2.bo.h.1349.7		20	105.68	odd	12
2100.2.bo.h.1949.4		20	5.3	odd	4
2100.2.bo.h.1949.7		20	5.2	odd	4
2940.2.d.a.881.5		10	35.24	odd	6
2940.2.d.a.881.6		10	105.74	odd	6
2940.2.d.b.881.5		10	105.59	even	6
2940.2.d.b.881.6		10	35.4	even	6

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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.69242 + 0.368412i) q^{3} +(1.80025 - 1.93884i) q^{7} +(2.72854 + 1.24701i) q^{9} +O(q^{10})\)	\(q+(1.69242 + 0.368412i) q^{3} +(1.80025 - 1.93884i) q^{7} +(2.72854 + 1.24701i) q^{9} +(4.05595 + 2.34170i) q^{11} +2.18938i q^{13} +(-3.74984 + 6.49492i) q^{17} +(-0.638109 + 0.368412i) q^{19} +(3.76107 - 2.61808i) q^{21} +(-6.99627 + 4.03930i) q^{23} +(4.15842 + 3.11570i) q^{27} -1.15414i q^{29} +(8.95201 + 5.16845i) q^{31} +(6.00164 + 5.45740i) q^{33} +(-2.30923 - 3.99970i) q^{37} +(-0.806595 + 3.70534i) q^{39} -1.43758 q^{41} +9.24142 q^{43} +(-4.34224 - 7.52098i) q^{47} +(-0.518179 - 6.98079i) q^{49} +(-8.73910 + 9.61061i) q^{51} +(-7.03514 - 4.06174i) q^{53} +(-1.21567 + 0.388420i) q^{57} +(3.48730 - 6.04018i) q^{59} +(5.13811 - 2.96649i) q^{61} +(7.32983 - 3.04526i) q^{63} +(-0.691639 + 1.19795i) q^{67} +(-13.3287 + 4.25866i) q^{69} +7.26258i q^{71} +(0.211355 + 0.122026i) q^{73} +(11.8419 - 3.64817i) q^{77} +(-5.79653 - 10.0399i) q^{79} +(5.88991 + 6.80507i) q^{81} +16.4610 q^{83} +(0.425199 - 1.95328i) q^{87} +(0.658248 + 1.14012i) q^{89} +(4.24485 + 3.94144i) q^{91} +(13.2464 + 12.0452i) q^{93} -4.84232i q^{97} +(8.14670 + 11.4473i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} + 5 q^{7} - 3 q^{9}+O(q^{10}) \) 10 * q + q^3 + 5 * q^7 - 3 * q^9	\( 10 q + q^{3} + 5 q^{7} - 3 q^{9} - 6 q^{11} - 6 q^{17} + 3 q^{19} + 10 q^{21} - 24 q^{23} - 8 q^{27} + 15 q^{31} + 20 q^{33} + q^{37} + 15 q^{39} - 8 q^{41} + 26 q^{43} - 14 q^{47} - 13 q^{49} - 44 q^{51} + 24 q^{53} - 18 q^{57} + 42 q^{61} + q^{63} - 7 q^{67} - 14 q^{69} + 3 q^{73} + 26 q^{77} + q^{79} + 41 q^{81} + 8 q^{83} + 26 q^{87} + 28 q^{89} - 11 q^{91} + 47 q^{93} + 36 q^{99}+O(q^{100}) \) 10 * q + q^3 + 5 * q^7 - 3 * q^9 - 6 * q^11 - 6 * q^17 + 3 * q^19 + 10 * q^21 - 24 * q^23 - 8 * q^27 + 15 * q^31 + 20 * q^33 + q^37 + 15 * q^39 - 8 * q^41 + 26 * q^43 - 14 * q^47 - 13 * q^49 - 44 * q^51 + 24 * q^53 - 18 * q^57 + 42 * q^61 + q^63 - 7 * q^67 - 14 * q^69 + 3 * q^73 + 26 * q^77 + q^79 + 41 * q^81 + 8 * q^83 + 26 * q^87 + 28 * q^89 - 11 * q^91 + 47 * q^93 + 36 * q^99

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