LMFDB - Embedded newform 2100.2.bi.n.1601.2

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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1601.2
Character	$\chi$	$=$	2100.1601
Dual form			2100.2.bi.n.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64956 + 0.528155i) q^{3} +(-1.63251 + 2.08204i) q^{7} +(2.44211 - 1.74245i) q^{9} +O(q^{10})$	\(q+(-1.64956 + 0.528155i) q^{3} +(-1.63251 + 2.08204i) q^{7} +(2.44211 - 1.74245i) q^{9} +(-5.09034 + 2.93891i) q^{11} +3.54004i q^{13} +(1.55406 + 2.69171i) q^{17} +(-3.58419 - 2.06933i) q^{19} +(1.59329 - 4.29667i) q^{21} +(6.19358 + 3.57587i) q^{23} +(-3.10812 + 4.16408i) q^{27} -6.84761i q^{29} +(-3.90384 + 2.25388i) q^{31} +(6.84463 - 7.53639i) q^{33} +(0.986843 - 1.70926i) q^{37} +(-1.86969 - 5.83952i) q^{39} +6.33142 q^{41} -3.88979 q^{43} +(0.916997 - 1.58829i) q^{47} +(-1.66979 - 6.79793i) q^{49} +(-3.98516 - 3.61936i) q^{51} +(-11.9579 + 6.90391i) q^{53} +(7.00526 + 1.52048i) q^{57} +(2.32584 + 4.02848i) q^{59} +(0.702144 + 0.405383i) q^{61} +(-0.358927 + 7.92913i) q^{63} +(-5.10469 - 8.84158i) q^{67} +(-12.1053 - 2.62744i) q^{69} +1.18684i q^{71} +(1.87966 - 1.08522i) q^{73} +(2.19112 - 15.3961i) q^{77} +(5.05228 - 8.75081i) q^{79} +(2.92776 - 8.51048i) q^{81} +5.31243 q^{83} +(3.61660 + 11.2956i) q^{87} +(-6.28986 + 10.8944i) q^{89} +(-7.37052 - 5.77917i) q^{91} +(5.24922 - 5.77975i) q^{93} -4.50686i q^{97} +(-7.31025 + 16.0468i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 12 q^{19} - 8 q^{21} - 12 q^{31} - 24 q^{39} + 44 q^{49} - 10 q^{51} - 24 q^{61} + 28 q^{79} - 20 q^{81} + 16 q^{91} + 28 q^{99}+O(q^{100}) $ 32 * q - 12 * q^19 - 8 * q^21 - 12 * q^31 - 24 * q^39 + 44 * q^49 - 10 * q^51 - 24 * q^61 + 28 * q^79 - 20 * q^81 + 16 * q^91 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.64956	+	0.528155i	−0.952375	+	0.304930i
$3$	−1.64956	+	0.528155i	−0.952375	+	0.304930i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.63251	+	2.08204i	−0.617033	+	0.786938i
$7$	−1.63251	+	2.08204i	−0.617033	+	0.786938i
$8$		0			0
$9$	2.44211	−	1.74245i	0.814035	−	0.580816i
$10$		0			0
$11$	−5.09034	+	2.93891i	−1.53479	+	0.886114i	−0.535663	+	0.844432i	$0.679938\pi$
$11$	−5.09034	+	2.93891i	−1.53479	+	0.886114i	−0.999131	+	0.0416823i	$0.986728\pi$
$12$		0			0
$13$			3.54004i			0.981831i	0.871207	+	0.490916i	$0.163338\pi$
$13$			3.54004i			0.981831i	−0.871207	+	0.490916i	$0.836662\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.55406	+	2.69171i	0.376915	+	0.652836i	0.990612	−	0.136706i	$-0.0436515\pi$
$17$	1.55406	+	2.69171i	0.376915	+	0.652836i	−0.613697	+	0.789542i	$0.710318\pi$
$18$		0			0
$19$	−3.58419	−	2.06933i	−0.822269	−	0.474737i	0.0289296	−	0.999581i	$-0.490790\pi$
$19$	−3.58419	−	2.06933i	−0.822269	−	0.474737i	−0.851198	+	0.524844i	$0.824123\pi$
$20$		0			0
$21$	1.59329	−	4.29667i	0.347685	−	0.937611i
$22$		0			0
$23$	6.19358	+	3.57587i	1.29145	+	0.745620i	0.978911	−	0.204285i	$-0.0654870\pi$
$23$	6.19358	+	3.57587i	1.29145	+	0.745620i	0.312539	+	0.949905i	$0.398820\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.10812	+	4.16408i	−0.598158	+	0.801378i
$28$		0			0
$29$		−	6.84761i		−	1.27157i	−0.771867	−	0.635785i	$-0.780677\pi$
$29$		−	6.84761i		−	1.27157i	0.771867	−	0.635785i	$-0.219323\pi$
$30$		0			0
$31$	−3.90384	+	2.25388i	−0.701150	+	0.404809i	−0.807776	−	0.589490i	$-0.799329\pi$
$31$	−3.90384	+	2.25388i	−0.701150	+	0.404809i	0.106626	+	0.994299i	$0.465995\pi$
$32$		0			0
$33$	6.84463	−	7.53639i	1.19150	−	1.31192i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.986843	−	1.70926i	0.162236	−	0.281001i	−0.773434	−	0.633876i	$-0.781463\pi$
$37$	0.986843	−	1.70926i	0.162236	−	0.281001i	0.935670	+	0.352875i	$0.114796\pi$
$38$		0			0
$39$	−1.86969	−	5.83952i	−0.299390	−	0.935071i
$40$		0			0
$41$	6.33142			0.988801			0.494401	−	0.869234i	$-0.335388\pi$
$41$	6.33142			0.988801			0.494401	+	0.869234i	$0.335388\pi$
$42$		0			0
$43$	−3.88979			−0.593187			−0.296594	−	0.955004i	$-0.595851\pi$
$43$	−3.88979			−0.593187			−0.296594	+	0.955004i	$0.595851\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.916997	−	1.58829i	0.133758	−	0.231675i	−0.791364	−	0.611345i	$-0.790629\pi$
$47$	0.916997	−	1.58829i	0.133758	−	0.231675i	0.925122	+	0.379669i	$0.123962\pi$
$48$		0			0
$49$	−1.66979	−	6.79793i	−0.238541	−	0.971132i
$50$		0			0
$51$	−3.98516	−	3.61936i	−0.558034	−	0.506812i
$52$		0			0
$53$	−11.9579	+	6.90391i	−1.64255	+	0.948325i	−0.662622	+	0.748954i	$0.730557\pi$
$53$	−11.9579	+	6.90391i	−1.64255	+	0.948325i	−0.979924	+	0.199371i	$0.936110\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	7.00526	+	1.52048i	0.927869	+	0.201393i
$58$		0			0
$59$	2.32584	+	4.02848i	0.302799	+	0.524463i	0.976769	−	0.214296i	$-0.0687456\pi$
$59$	2.32584	+	4.02848i	0.302799	+	0.524463i	−0.673970	+	0.738759i	$0.735412\pi$
$60$		0			0
$61$	0.702144	+	0.405383i	0.0899003	+	0.0519040i	0.544276	−	0.838906i	$-0.316804\pi$
$61$	0.702144	+	0.405383i	0.0899003	+	0.0519040i	−0.454376	+	0.890810i	$0.650138\pi$
$62$		0			0
$63$	−0.358927	+	7.92913i	−0.0452206	+	0.998977i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−5.10469	−	8.84158i	−0.623637	−	1.08017i	−0.988803	−	0.149228i	$-0.952321\pi$
$67$	−5.10469	−	8.84158i	−0.623637	−	1.08017i	0.365166	−	0.930942i	$-0.381012\pi$
$68$		0			0
$69$	−12.1053	−	2.62744i	−1.45731	−	0.316307i
$70$		0			0
$71$			1.18684i			0.140852i	0.997517	+	0.0704262i	$0.0224359\pi$
$71$			1.18684i			0.140852i	−0.997517	+	0.0704262i	$0.977564\pi$
$72$		0			0
$73$	1.87966	−	1.08522i	0.219998	−	0.127016i	−0.385951	−	0.922519i	$-0.626127\pi$
$73$	1.87966	−	1.08522i	0.219998	−	0.127016i	0.605949	+	0.795503i	$0.292793\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.19112	−	15.3961i	0.249702	−	1.75455i
$78$		0			0
$79$	5.05228	−	8.75081i	0.568426	−	0.984543i	−0.428296	−	0.903639i	$-0.640886\pi$
$79$	5.05228	−	8.75081i	0.568426	−	0.984543i	0.996722	−	0.0809043i	$-0.0257808\pi$
$80$		0			0
$81$	2.92776	−	8.51048i	0.325306	−	0.945609i
$82$		0			0
$83$	5.31243			0.583115			0.291558	−	0.956553i	$-0.405826\pi$
$83$	5.31243			0.583115			0.291558	+	0.956553i	$0.405826\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.61660	+	11.2956i	0.387740	+	1.21101i
$88$		0			0
$89$	−6.28986	+	10.8944i	−0.666724	+	1.15480i	0.312091	+	0.950052i	$0.398971\pi$
$89$	−6.28986	+	10.8944i	−0.666724	+	1.15480i	−0.978815	+	0.204747i	$0.934363\pi$
$90$		0			0
$91$	−7.37052	−	5.77917i	−0.772640	−	0.605822i
$92$		0			0
$93$	5.24922	−	5.77975i	0.544319	−	0.599332i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	4.50686i		−	0.457602i	−0.973473	−	0.228801i	$-0.926519\pi$
$97$		−	4.50686i		−	0.457602i	0.973473	−	0.228801i	$-0.0734805\pi$
$98$		0			0
$99$	−7.31025	+	16.0468i	−0.734708	+	1.61276i
$100$		0			0
$101$	−0.896791	−	1.55329i	−0.0892340	−	0.154558i	0.817954	−	0.575284i	$-0.195109\pi$
$101$	−0.896791	−	1.55329i	−0.0892340	−	0.154558i	−0.907188	+	0.420726i	$0.861775\pi$
$102$		0			0
$103$	−10.9238	−	6.30688i	−1.07636	−	0.621436i	−0.146446	−	0.989219i	$-0.546784\pi$
$103$	−10.9238	−	6.30688i	−1.07636	−	0.621436i	−0.929912	+	0.367783i	$0.880117\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.01335	−	1.73976i	−0.291311	−	0.168189i	0.347222	−	0.937783i	$-0.387125\pi$
$107$	−3.01335	−	1.73976i	−0.291311	−	0.168189i	−0.638533	+	0.769594i	$0.720458\pi$
$108$		0			0
$109$	−4.98802	−	8.63951i	−0.477766	−	0.827515i	0.521909	−	0.853001i	$-0.325220\pi$
$109$	−4.98802	−	8.63951i	−0.477766	−	0.827515i	−0.999675	+	0.0254860i	$0.991887\pi$
$110$		0			0
$111$	−0.725103	+	3.34074i	−0.0688238	+	0.317089i
$112$		0			0
$113$			2.54532i			0.239444i	0.992807	+	0.119722i	$0.0382003\pi$
$113$			2.54532i			0.239444i	−0.992807	+	0.119722i	$0.961800\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	6.16834	+	8.64516i	0.570263	+	0.799245i
$118$		0			0
$119$	−8.14128	−	1.15864i	−0.746310	−	0.106213i
$120$		0			0
$121$	11.7744	−	20.3938i	1.07040	−	1.85398i
$122$		0			0
$123$	−10.4441	+	3.34397i	−0.941709	+	0.301515i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−12.6616			−1.12353			−0.561767	−	0.827295i	$-0.689878\pi$
$127$	−12.6616			−1.12353			−0.561767	+	0.827295i	$0.689878\pi$
$128$		0			0
$129$	6.41644	−	2.05441i	0.564936	−	0.180881i
$130$		0			0
$131$	6.34770	−	10.9945i	0.554601	−	0.960597i	−0.443333	−	0.896357i	$-0.646204\pi$
$131$	6.34770	−	10.9945i	0.554601	−	0.960597i	0.997934	−	0.0642406i	$-0.0204625\pi$
$132$		0			0
$133$	10.1597	−	4.08421i	0.880955	−	0.354146i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.54475	−	2.62391i	0.388284	−	0.224176i	−0.293132	−	0.956072i	$-0.594698\pi$
$137$	4.54475	−	2.62391i	0.388284	−	0.224176i	0.681416	+	0.731896i	$0.261364\pi$
$138$		0			0
$139$		−	14.2842i		−	1.21157i	−0.795627	−	0.605787i	$-0.792858\pi$
$139$		−	14.2842i		−	1.21157i	0.795627	−	0.605787i	$-0.207142\pi$
$140$		0			0
$141$	−0.673782	+	3.10429i	−0.0567427	+	0.261428i
$142$		0			0
$143$	−10.4039	−	18.0200i	−0.870014	−	1.50691i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	6.34478	+	10.3317i	0.523308	+	0.852143i
$148$		0			0
$149$	−13.0762	−	7.54956i	−1.07125	−	0.618484i	−0.142724	−	0.989763i	$-0.545586\pi$
$149$	−13.0762	−	7.54956i	−1.07125	−	0.618484i	−0.928521	+	0.371279i	$0.878919\pi$
$150$		0			0
$151$	4.16979	+	7.22229i	0.339333	+	0.587742i	0.984307	−	0.176462i	$-0.0564654\pi$
$151$	4.16979	+	7.22229i	0.339333	+	0.587742i	−0.644975	+	0.764204i	$0.723132\pi$
$152$		0			0
$153$	8.48535	+	3.86558i	0.686000	+	0.312513i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.831900	−	0.480298i	0.0663929	−	0.0383319i	−0.466436	−	0.884555i	$-0.654462\pi$
$157$	0.831900	−	0.480298i	0.0663929	−	0.0383319i	0.532829	+	0.846223i	$0.321129\pi$
$158$		0			0
$159$	16.0790	−	17.7040i	1.27515	−	1.40402i
$160$		0			0
$161$	−17.5562	+	7.05764i	−1.38362	+	0.556220i
$162$		0			0
$163$	9.33565	−	16.1698i	0.731224	−	1.26652i	−0.225136	−	0.974327i	$-0.572283\pi$
$163$	9.33565	−	16.1698i	0.731224	−	1.26652i	0.956360	−	0.292190i	$-0.0943840\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−14.2212			−1.10047			−0.550233	−	0.835011i	$-0.685461\pi$
$167$	−14.2212			−1.10047			−0.550233	+	0.835011i	$0.685461\pi$
$168$		0			0
$169$	0.468096			0.0360074
$170$		0			0
$171$	−12.3587	+	1.19173i	−0.945090	+	0.0911338i
$172$		0			0
$173$	0.357131	−	0.618569i	0.0271522	−	0.0470289i	−0.852130	−	0.523330i	$-0.824689\pi$
$173$	0.357131	−	0.618569i	0.0271522	−	0.0470289i	0.879282	+	0.476301i	$0.158023\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−5.96428	−	5.41682i	−0.448303	−	0.407153i
$178$		0			0
$179$	9.68510	−	5.59169i	0.723898	−	0.417943i	−0.0922876	−	0.995732i	$-0.529418\pi$
$179$	9.68510	−	5.59169i	0.723898	−	0.417943i	0.816186	+	0.577790i	$0.196085\pi$
$180$		0			0
$181$		−	3.69700i		−	0.274796i	−0.990516	−	0.137398i	$-0.956126\pi$
$181$		−	3.69700i		−	0.274796i	0.990516	−	0.137398i	$-0.0438739\pi$
$182$		0			0
$183$	−1.37233	−	0.297864i	−0.101446	−	0.0220187i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−15.8214	−	9.13448i	−1.15697	−	0.667979i
$188$		0			0
$189$	−3.59574	−	13.2692i	−0.261551	−	0.965190i
$190$		0			0
$191$	8.99652	+	5.19414i	0.650965	+	0.375835i	0.788826	−	0.614617i	$-0.210689\pi$
$191$	8.99652	+	5.19414i	0.650965	+	0.375835i	−0.137861	+	0.990452i	$0.544023\pi$
$192$		0			0
$193$	−2.96053	−	5.12779i	−0.213104	−	0.369106i	0.739581	−	0.673068i	$-0.235024\pi$
$193$	−2.96053	−	5.12779i	−0.213104	−	0.369106i	−0.952684	+	0.303962i	$0.901691\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			11.1053i			0.791221i	0.918418	+	0.395610i	$0.129467\pi$
$197$			11.1053i			0.791221i	−0.918418	+	0.395610i	$0.870533\pi$
$198$		0			0
$199$	−11.4667	+	6.62029i	−0.812851	+	0.469300i	−0.847945	−	0.530084i	$-0.822160\pi$
$199$	−11.4667	+	6.62029i	−0.812851	+	0.469300i	0.0350939	+	0.999384i	$0.488827\pi$
$200$		0			0
$201$	13.0902	+	11.8887i	0.923312	+	0.838561i
$202$		0			0
$203$	14.2570	+	11.1788i	1.00065	+	0.784600i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	21.3561	−	2.05934i	1.48435	−	0.143134i
$208$		0			0
$209$	24.3263			1.68268
$210$		0			0
$211$	−19.9122			−1.37082			−0.685408	−	0.728160i	$-0.740376\pi$
$211$	−19.9122			−1.37082			−0.685408	+	0.728160i	$0.740376\pi$
$212$		0			0
$213$	−0.626837	−	1.95777i	−0.0429502	−	0.134144i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	1.68040	−	11.8074i	0.114073	−	0.801542i
$218$		0			0
$219$	−2.52745	+	2.78289i	−0.170789	+	0.188051i
$220$		0			0
$221$	−9.52878	+	5.50144i	−0.640975	+	0.370067i
$222$		0			0
$223$			10.4924i			0.702623i	0.936259	+	0.351311i	$0.114264\pi$
$223$			10.4924i			0.702623i	−0.936259	+	0.351311i	$0.885736\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.21273	+	14.2249i	0.545098	+	0.944138i	0.998601	+	0.0528829i	$0.0168410\pi$
$227$	8.21273	+	14.2249i	0.545098	+	0.944138i	−0.453502	+	0.891255i	$0.649826\pi$
$228$		0			0
$229$	0.903838	+	0.521831i	0.0597273	+	0.0344836i	0.529566	−	0.848269i	$-0.322355\pi$
$229$	0.903838	+	0.521831i	0.0597273	+	0.0344836i	−0.469839	+	0.882752i	$0.655688\pi$
$230$		0			0
$231$	4.51713	+	26.5541i	0.297205	+	1.74713i
$232$		0			0
$233$	−25.0488	−	14.4619i	−1.64100	−	0.947431i	−0.980479	−	0.196622i	$-0.937003\pi$
$233$	−25.0488	−	14.4619i	−1.64100	−	0.947431i	−0.660519	−	0.750809i	$-0.729664\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−3.71227	+	17.1034i	−0.241138	+	1.11098i
$238$		0			0
$239$		−	5.69731i		−	0.368528i	−0.982877	−	0.184264i	$-0.941010\pi$
$239$		−	5.69731i		−	0.368528i	0.982877	−	0.184264i	$-0.0589902\pi$
$240$		0			0
$241$	−6.10598	+	3.52529i	−0.393321	+	0.227084i	−0.683598	−	0.729859i	$-0.739586\pi$
$241$	−6.10598	+	3.52529i	−0.393321	+	0.227084i	0.290277	+	0.956943i	$0.406253\pi$
$242$		0			0
$243$	−0.334668	+	15.5849i	−0.0214690	+	0.999770i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	7.32552	−	12.6882i	0.466112	−	0.807329i
$248$		0			0
$249$	−8.76319	+	2.80579i	−0.555344	+	0.177809i
$250$		0			0
$251$	−3.93237			−0.248209			−0.124105	−	0.992269i	$-0.539606\pi$
$251$	−3.93237			−0.248209			−0.124105	+	0.992269i	$0.539606\pi$
$252$		0			0
$253$	−42.0366			−2.64282
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.65287	+	13.2552i	−0.477373	+	0.826834i	−0.999664	−	0.0259335i	$-0.991744\pi$
$257$	−7.65287	+	13.2552i	−0.477373	+	0.826834i	0.522291	+	0.852767i	$0.325078\pi$
$258$		0			0
$259$	1.94772	+	4.84504i	0.121025	+	0.301056i
$260$		0			0
$261$	−11.9316	−	16.7226i	−0.738547	−	1.03510i
$262$		0			0
$263$	16.9044	−	9.75977i	1.04237	−	0.601813i	0.121867	−	0.992546i	$-0.461112\pi$
$263$	16.9044	−	9.75977i	1.04237	−	0.601813i	0.920504	+	0.390733i	$0.127778\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	4.62161	−	21.2929i	0.282838	−	1.30311i
$268$		0			0
$269$	4.91865	+	8.51935i	0.299895	+	0.519434i	0.976112	−	0.217269i	$-0.0697149\pi$
$269$	4.91865	+	8.51935i	0.299895	+	0.519434i	−0.676216	+	0.736703i	$0.736382\pi$
$270$		0			0
$271$	18.0820	+	10.4397i	1.09841	+	0.634164i	0.935802	−	0.352527i	$-0.114678\pi$
$271$	18.0820	+	10.4397i	1.09841	+	0.634164i	0.162603	+	0.986691i	$0.448011\pi$
$272$		0			0
$273$	15.2104	+	5.64033i	0.920576	+	0.341368i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−4.25187	−	7.36446i	−0.255470	−	0.442487i	0.709553	−	0.704652i	$-0.248897\pi$
$277$	−4.25187	−	7.36446i	−0.255470	−	0.442487i	−0.965023	+	0.262165i	$0.915564\pi$
$278$		0			0
$279$	−5.60632	+	12.3064i	−0.335641	+	0.736768i
$280$		0			0
$281$		−	7.63690i		−	0.455579i	−0.973710	−	0.227790i	$-0.926850\pi$
$281$		−	7.63690i		−	0.455579i	0.973710	−	0.227790i	$-0.0731499\pi$
$282$		0			0
$283$	7.80072	−	4.50375i	0.463705	−	0.267720i	−0.249896	−	0.968273i	$-0.580396\pi$
$283$	7.80072	−	4.50375i	0.463705	−	0.267720i	0.713601	+	0.700553i	$0.247063\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−10.3361	+	13.1823i	−0.610123	+	0.778125i
$288$		0			0
$289$	3.66979	−	6.35626i	0.215870	−	0.373898i
$290$		0			0
$291$	2.38032	+	7.43434i	0.139537	+	0.435809i
$292$		0			0
$293$	27.6102			1.61301			0.806503	−	0.591231i	$-0.201358\pi$
$293$	27.6102			1.61301			0.806503	+	0.591231i	$0.201358\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	3.58353	−	30.3311i	0.207938	−	1.75999i
$298$		0			0
$299$	−12.6587	+	21.9255i	−0.732073	+	1.26799i
$300$		0			0
$301$	6.35014	−	8.09870i	0.366016	−	0.466801i
$302$		0			0
$303$	2.29969	+	2.08860i	0.132114	+	0.119987i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			9.99609i			0.570507i	0.958452	+	0.285253i	$0.0920778\pi$
$307$			9.99609i			0.570507i	−0.958452	+	0.285253i	$0.907922\pi$
$308$		0			0
$309$	21.3506	+	4.63411i	1.21459	+	0.263625i
$310$		0			0
$311$	11.9336	+	20.6696i	0.676693	+	1.17207i	0.975971	+	0.217901i	$0.0699210\pi$
$311$	11.9336	+	20.6696i	0.676693	+	1.17207i	−0.299278	+	0.954166i	$0.596746\pi$
$312$		0			0
$313$	4.84558	+	2.79759i	0.273888	+	0.158129i	0.630653	−	0.776065i	$-0.282787\pi$
$313$	4.84558	+	2.79759i	0.273888	+	0.158129i	−0.356765	+	0.934194i	$0.616120\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.1642	+	5.86828i	0.570876	+	0.329596i	0.757499	−	0.652836i	$-0.226421\pi$
$317$	10.1642	+	5.86828i	0.570876	+	0.329596i	−0.186623	+	0.982432i	$0.559754\pi$
$318$		0			0
$319$	20.1245	+	34.8566i	1.12676	+	1.95160i
$320$		0			0
$321$	5.88956	+	1.27832i	0.328723	+	0.0713490i
$322$		0			0
$323$		−	12.8635i		−	0.715742i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	12.7910	+	11.6170i	0.707347	+	0.642419i
$328$		0			0
$329$	1.80986	+	4.50212i	0.0997810	+	0.248210i
$330$		0			0
$331$	−1.26453	+	2.19023i	−0.0695050	+	0.120386i	−0.898684	−	0.438598i	$-0.855475\pi$
$331$	−1.26453	+	2.19023i	−0.0695050	+	0.120386i	0.829179	+	0.558984i	$0.188809\pi$
$332$		0			0
$333$	−0.568324	−	5.89372i	−0.0311440	−	0.322974i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−34.3299			−1.87007			−0.935033	−	0.354560i	$-0.884631\pi$
$337$	−34.3299			−1.87007			−0.935033	+	0.354560i	$0.884631\pi$
$338$		0			0
$339$	−1.34432	−	4.19866i	−0.0730136	−	0.228040i
$340$		0			0
$341$	13.2479	−	22.9460i	0.717414	−	1.24260i
$342$		0			0
$343$	16.8795	+	7.62114i	0.911408	+	0.411503i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.515915	−	0.297864i	0.0276958	−	0.0159902i	−0.486088	−	0.873910i	$-0.661577\pi$
$347$	0.515915	−	0.297864i	0.0276958	−	0.0159902i	0.513784	+	0.857920i	$0.328243\pi$
$348$		0			0
$349$			23.0392i			1.23326i	0.787253	+	0.616630i	$0.211503\pi$
$349$			23.0392i			1.23326i	−0.787253	+	0.616630i	$0.788497\pi$
$350$		0			0
$351$	−14.7410	−	11.0029i	−0.786818	−	0.587290i
$352$		0			0
$353$	5.44856	+	9.43718i	0.289997	+	0.502290i	0.973809	−	0.227369i	$-0.0730122\pi$
$353$	5.44856	+	9.43718i	0.289997	+	0.502290i	−0.683811	+	0.729659i	$0.739679\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	14.0415	−	2.38861i	0.743154	−	0.126418i
$358$		0			0
$359$	−9.03320	−	5.21532i	−0.476754	−	0.275254i	0.242309	−	0.970199i	$-0.422095\pi$
$359$	−9.03320	−	5.21532i	−0.476754	−	0.275254i	−0.719063	+	0.694945i	$0.755429\pi$
$360$		0			0
$361$	−0.935743	−	1.62075i	−0.0492496	−	0.0853028i
$362$		0			0
$363$	−8.65145	+	39.8595i	−0.454083	+	2.09208i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	7.40402	−	4.27471i	0.386486	−	0.223138i	−0.294150	−	0.955759i	$-0.595037\pi$
$367$	7.40402	−	4.27471i	0.386486	−	0.223138i	0.680637	+	0.732621i	$0.261703\pi$
$368$		0			0
$369$	15.4620	−	11.0322i	0.804919	−	0.574311i
$370$		0			0
$371$	5.14726	−	36.1676i	0.267232	−	1.87773i
$372$		0			0
$373$	−3.31473	+	5.74129i	−0.171630	+	0.297273i	−0.938990	−	0.343944i	$-0.888237\pi$
$373$	−3.31473	+	5.74129i	−0.171630	+	0.297273i	0.767360	+	0.641217i	$0.221570\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	24.2408			1.24847
$378$		0			0
$379$	−22.3165			−1.14632			−0.573162	−	0.819442i	$-0.694283\pi$
$379$	−22.3165			−1.14632			−0.573162	+	0.819442i	$0.694283\pi$
$380$		0			0
$381$	20.8861	−	6.68728i	1.07003	−	0.342600i
$382$		0			0
$383$	−14.0945	+	24.4124i	−0.720196	+	1.24742i	0.240725	+	0.970593i	$0.422615\pi$
$383$	−14.0945	+	24.4124i	−0.720196	+	1.24742i	−0.960921	+	0.276822i	$0.910719\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−9.49927	+	6.77775i	−0.482875	+	0.344532i
$388$		0			0
$389$	3.57909	−	2.06639i	0.181467	−	0.104770i	−0.406515	−	0.913644i	$-0.633256\pi$
$389$	3.57909	−	2.06639i	0.181467	−	0.104770i	0.587982	+	0.808874i	$0.299923\pi$
$390$		0			0
$391$			22.2284i			1.12414i
$392$		0			0
$393$	−4.66411	+	21.4887i	−0.235273	+	1.08396i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−11.4643	−	6.61890i	−0.575375	−	0.332193i	0.183918	−	0.982942i	$-0.441122\pi$
$397$	−11.4643	−	6.61890i	−0.575375	−	0.332193i	−0.759293	+	0.650748i	$0.774455\pi$
$398$		0			0
$399$	−14.6019	+	12.1030i	−0.731009	+	0.605909i
$400$		0			0
$401$	−0.671383	−	0.387623i	−0.0335273	−	0.0193570i	0.483143	−	0.875542i	$-0.339495\pi$
$401$	−0.671383	−	0.387623i	−0.0335273	−	0.0193570i	−0.516670	+	0.856185i	$0.672829\pi$
$402$		0			0
$403$	−7.97884	−	13.8198i	−0.397454	−	0.688411i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			11.6010i			0.575038i
$408$		0			0
$409$	−3.97093	+	2.29262i	−0.196350	+	0.113363i	−0.594952	−	0.803761i	$-0.702829\pi$
$409$	−3.97093	+	2.29262i	−0.196350	+	0.113363i	0.398602	+	0.917124i	$0.369496\pi$
$410$		0			0
$411$	−6.11101	+	6.72863i	−0.301434	+	0.331899i
$412$		0			0
$413$	−12.1844	−	1.73405i	−0.599556	−	0.0853270i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	7.54429	+	23.5627i	0.369445	+	1.15387i
$418$		0			0
$419$	−11.9761			−0.585070			−0.292535	−	0.956255i	$-0.594499\pi$
$419$	−11.9761			−0.585070			−0.292535	+	0.956255i	$0.594499\pi$
$420$		0			0
$421$	25.5487			1.24517			0.622584	−	0.782553i	$-0.286083\pi$
$421$	25.5487			1.24517			0.622584	+	0.782553i	$0.286083\pi$
$422$		0			0
$423$	−0.528099	−	5.47658i	−0.0256771	−	0.266280i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.99028	+	0.800099i	−0.0963166	+	0.0387195i
$428$		0			0
$429$	26.6792	+	24.2303i	1.28808	+	1.16985i
$430$		0			0
$431$	12.5634	−	7.25351i	0.605160	−	0.349389i	−0.165909	−	0.986141i	$-0.553056\pi$
$431$	12.5634	−	7.25351i	0.605160	−	0.349389i	0.771069	+	0.636752i	$0.219722\pi$
$432$		0			0
$433$			40.0655i			1.92543i	0.270524	+	0.962713i	$0.412803\pi$
$433$			40.0655i			1.92543i	−0.270524	+	0.962713i	$0.587197\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−14.7993	−	25.6331i	−0.707946	−	1.22620i
$438$		0			0
$439$	27.1838	+	15.6945i	1.29741	+	0.749060i	0.979956	−	0.199214i	$-0.0638388\pi$
$439$	27.1838	+	15.6945i	1.29741	+	0.749060i	0.317454	+	0.948274i	$0.397172\pi$
$440$		0			0
$441$	−15.9228	−	13.6917i	−0.758230	−	0.651987i
$442$		0			0
$443$	−8.69101	−	5.01776i	−0.412923	−	0.238401i	0.279122	−	0.960256i	$-0.409957\pi$
$443$	−8.69101	−	5.01776i	−0.412923	−	0.238401i	−0.692045	+	0.721855i	$0.743290\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	25.5574	+	5.54719i	1.20882	+	0.262373i
$448$		0			0
$449$		−	16.7060i		−	0.788405i	−0.919024	−	0.394203i	$-0.871021\pi$
$449$		−	16.7060i		−	0.788405i	0.919024	−	0.394203i	$-0.128979\pi$
$450$		0			0
$451$	−32.2291	+	18.6075i	−1.51761	+	0.876191i
$452$		0			0
$453$	−10.6928	−	9.71131i	−0.502392	−	0.456277i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−7.07406	+	12.2526i	−0.330910	+	0.573154i	−0.982691	−	0.185254i	$-0.940689\pi$
$457$	−7.07406	+	12.2526i	−0.330910	+	0.573154i	0.651780	+	0.758408i	$0.274022\pi$
$458$		0			0
$459$	−16.0387	−	1.89493i	−0.748623	−	0.0884478i
$460$		0			0
$461$	−4.22519			−0.196787			−0.0983935	−	0.995148i	$-0.531370\pi$
$461$	−4.22519			−0.196787			−0.0983935	+	0.995148i	$0.531370\pi$
$462$		0			0
$463$	−33.2490			−1.54521			−0.772606	−	0.634886i	$-0.781047\pi$
$463$	−33.2490			−1.54521			−0.772606	+	0.634886i	$0.781047\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	18.4314	−	31.9242i	0.852905	−	1.47727i	−0.0256700	−	0.999670i	$-0.508172\pi$
$467$	18.4314	−	31.9242i	0.852905	−	1.47727i	0.878575	−	0.477604i	$-0.158495\pi$
$468$		0			0
$469$	26.7420	+	3.80584i	1.23483	+	0.175737i
$470$		0			0
$471$	−1.11860	+	1.23165i	−0.0515423	+	0.0567516i
$472$		0			0
$473$	19.8003	−	11.4317i	0.910420	−	0.525631i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−17.1728	+	37.6961i	−0.786289	+	1.72599i
$478$		0			0
$479$	−4.66797	−	8.08516i	−0.213285	−	0.369420i	0.739456	−	0.673205i	$-0.235083\pi$
$479$	−4.66797	−	8.08516i	−0.213285	−	0.369420i	−0.952741	+	0.303785i	$0.901750\pi$
$480$		0			0
$481$	6.05086	+	3.49347i	0.275896	+	0.159288i
$482$		0			0
$483$	25.2325	−	20.9144i	1.14812	−	0.951638i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−12.6695	−	21.9442i	−0.574109	−	0.994385i	−0.996138	−	0.0878031i	$-0.972015\pi$
$487$	−12.6695	−	21.9442i	−0.574109	−	0.994385i	0.422029	−	0.906582i	$-0.361318\pi$
$488$		0			0
$489$	−6.85956	+	31.6038i	−0.310200	+	1.42917i
$490$		0			0
$491$			35.4614i			1.60035i	0.599765	+	0.800176i	$0.295261\pi$
$491$			35.4614i			1.60035i	−0.599765	+	0.800176i	$0.704739\pi$
$492$		0			0
$493$	18.4318	−	10.6416i	0.830126	−	0.479274i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.47106	−	1.93754i	−0.110842	−	0.0869106i
$498$		0			0
$499$	−14.7087	+	25.4762i	−0.658451	+	1.14047i	0.322566	+	0.946547i	$0.395455\pi$
$499$	−14.7087	+	25.4762i	−0.658451	+	1.14047i	−0.981017	+	0.193923i	$0.937879\pi$
$500$		0			0
$501$	23.4587	−	7.51097i	1.04806	−	0.335565i
$502$		0			0
$503$	−20.9709			−0.935046			−0.467523	−	0.883981i	$-0.654853\pi$
$503$	−20.9709			−0.935046			−0.467523	+	0.883981i	$0.654853\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.772153	+	0.247227i	−0.0342925	+	0.0109797i
$508$		0			0
$509$	3.71821	−	6.44013i	0.164807	−	0.285454i	−0.771780	−	0.635890i	$-0.780633\pi$
$509$	3.71821	−	6.44013i	0.164807	−	0.285454i	0.936587	+	0.350436i	$0.113967\pi$
$510$		0			0
$511$	−0.809096	+	5.68518i	−0.0357923	+	0.251497i
$512$		0			0
$513$	19.7569	−	8.49311i	0.872290	−	0.374980i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			10.7799i			0.474098i
$518$		0			0
$519$	−0.262409	+	1.20899i	−0.0115185	+	0.0530687i
$520$		0			0
$521$	−2.55125	−	4.41889i	−0.111772	−	0.193595i	0.804713	−	0.593665i	$-0.202319\pi$
$521$	−2.55125	−	4.41889i	−0.111772	−	0.193595i	−0.916485	+	0.400069i	$0.868986\pi$
$522$		0			0
$523$	−14.2865	−	8.24829i	−0.624703	−	0.360673i	0.153995	−	0.988072i	$-0.450786\pi$
$523$	−14.2865	−	8.24829i	−0.624703	−	0.360673i	−0.778698	+	0.627399i	$0.784119\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−12.1336	−	7.00534i	−0.528548	−	0.305157i
$528$		0			0
$529$	14.0736	+	24.3762i	0.611897	+	1.05984i
$530$		0			0
$531$	12.6994	+	5.78531i	0.551105	+	0.251061i
$532$		0			0
$533$			22.4135i			0.970836i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−13.0229	+	14.3391i	−0.561979	+	0.618777i
$538$		0			0
$539$	28.4783	+	29.6964i	1.22665	+	1.27911i
$540$		0			0
$541$	−10.3077	+	17.8534i	−0.443162	+	0.767578i	−0.997922	−	0.0644316i	$-0.979477\pi$
$541$	−10.3077	+	17.8534i	−0.443162	+	0.767578i	0.554760	+	0.832010i	$0.312810\pi$
$542$		0			0
$543$	1.95259	+	6.09843i	0.0837935	+	0.261709i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	25.6070			1.09488			0.547438	−	0.836846i	$-0.315603\pi$
$547$	25.6070			1.09488			0.547438	+	0.836846i	$0.315603\pi$
$548$		0			0
$549$	2.42107	−	0.233460i	0.103329	−	0.00996385i
$550$		0			0
$551$	−14.1700	+	24.5431i	−0.603661	+	1.04557i
$552$		0			0
$553$	9.97162	+	24.8049i	0.424036	+	1.05481i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−31.3477	+	18.0986i	−1.32824	+	0.766862i	−0.985028	−	0.172394i	$-0.944850\pi$
$557$	−31.3477	+	18.0986i	−1.32824	+	0.766862i	−0.343216	+	0.939256i	$0.611516\pi$
$558$		0			0
$559$		−	13.7700i		−	0.582410i
$560$		0			0
$561$	30.9228	+	6.71175i	1.30556	+	0.283370i
$562$		0			0
$563$	15.3233	+	26.5408i	0.645801	+	1.11856i	0.984116	+	0.177527i	$0.0568096\pi$
$563$	15.3233	+	26.5408i	0.645801	+	1.11856i	−0.338315	+	0.941033i	$0.609857\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	12.9396	+	19.9892i	0.543410	+	0.839467i
$568$		0			0
$569$	13.2153	+	7.62988i	0.554016	+	0.319861i	0.750740	−	0.660598i	$-0.229697\pi$
$569$	13.2153	+	7.62988i	0.554016	+	0.319861i	−0.196724	+	0.980459i	$0.563030\pi$
$570$		0			0
$571$	9.05228	+	15.6790i	0.378826	+	0.656146i	0.990892	−	0.134661i	$-0.0429945\pi$
$571$	9.05228	+	15.6790i	0.378826	+	0.656146i	−0.612066	+	0.790807i	$0.709661\pi$
$572$		0			0
$573$	−17.5836	−	3.81650i	−0.734566	−	0.159437i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−5.68695	+	3.28336i	−0.236751	+	0.136688i	−0.613682	−	0.789553i	$-0.710312\pi$
$577$	−5.68695	+	3.28336i	−0.236751	+	0.136688i	0.376932	+	0.926241i	$0.376979\pi$
$578$		0			0
$579$	7.59184	+	6.89498i	0.315506	+	0.286546i
$580$		0			0
$581$	−8.67263	+	11.0607i	−0.359801	+	0.458875i
$582$		0			0
$583$	40.5799	−	70.2864i	1.68065	−	2.91097i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.35074			0.385946			0.192973	−	0.981204i	$-0.438187\pi$
$587$	9.35074			0.385946			0.192973	+	0.981204i	$0.438187\pi$
$588$		0			0
$589$	18.6561			0.768712
$590$		0			0
$591$	−5.86532	−	18.3189i	−0.241267	−	0.753539i
$592$		0			0
$593$	13.4988	−	23.3806i	0.554329	−	0.960126i	−0.443626	−	0.896212i	$-0.646308\pi$
$593$	13.4988	−	23.3806i	0.554329	−	0.960126i	0.997955	−	0.0639141i	$-0.0203584\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	15.4185	−	16.9768i	0.631035	−	0.694812i
$598$		0			0
$599$	19.7216	−	11.3863i	0.805803	−	0.465231i	−0.0396931	−	0.999212i	$-0.512638\pi$
$599$	19.7216	−	11.3863i	0.805803	−	0.465231i	0.845496	+	0.533981i	$0.179305\pi$
$600$		0			0
$601$		−	5.26871i		−	0.214915i	−0.994210	−	0.107458i	$-0.965729\pi$
$601$		−	5.26871i		−	0.214915i	0.994210	−	0.107458i	$-0.0342710\pi$
$602$		0			0
$603$	−27.8722	−	12.6974i	−1.13504	−	0.517079i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−8.10166	−	4.67749i	−0.328836	−	0.189854i	0.326488	−	0.945201i	$-0.394135\pi$
$607$	−8.10166	−	4.67749i	−0.328836	−	0.189854i	−0.655324	+	0.755348i	$0.727468\pi$
$608$		0			0
$609$	−29.4220	−	10.9103i	−1.19224	−	0.442106i
$610$		0			0
$611$	5.62260	+	3.24621i	0.227466	+	0.131328i
$612$		0			0
$613$	−15.7796	−	27.3310i	−0.637330	−	1.10389i	−0.986016	−	0.166649i	$-0.946705\pi$
$613$	−15.7796	−	27.3310i	−0.637330	−	1.10389i	0.348686	−	0.937240i	$-0.386628\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	39.6450i		−	1.59605i	−0.602626	−	0.798023i	$-0.705879\pi$
$617$		−	39.6450i		−	1.59605i	0.602626	−	0.798023i	$-0.294121\pi$
$618$		0			0
$619$	−33.2406	+	19.1915i	−1.33605	+	0.771370i	−0.986219	−	0.165443i	$-0.947095\pi$
$619$	−33.2406	+	19.1915i	−1.33605	+	0.771370i	−0.349832	+	0.936812i	$0.613761\pi$
$620$		0			0
$621$	−34.1406	+	14.6764i	−1.37002	+	0.588942i
$622$		0			0
$623$	−12.4142	−	30.8810i	−0.497365	−	1.23722i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−40.1277	+	12.8480i	−1.60255	+	0.513101i
$628$		0			0
$629$	6.13446			0.244597
$630$		0			0
$631$	1.06381			0.0423495			0.0211748	−	0.999776i	$-0.493259\pi$
$631$	1.06381			0.0423495			0.0211748	+	0.999776i	$0.493259\pi$
$632$		0			0
$633$	32.8465	−	10.5167i	1.30553	−	0.418003i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	24.0650	−	5.91113i	0.953488	−	0.234207i
$638$		0			0
$639$	2.06801	+	2.89840i	0.0818093	+	0.114659i
$640$		0			0
$641$	−25.9645	+	14.9906i	−1.02553	+	0.592093i	−0.915702	−	0.401858i	$-0.868365\pi$
$641$	−25.9645	+	14.9906i	−1.02553	+	0.592093i	−0.109832	+	0.993950i	$0.535031\pi$
$642$		0			0
$643$			16.0861i			0.634373i	0.948363	+	0.317187i	$0.102738\pi$
$643$			16.0861i			0.634373i	−0.948363	+	0.317187i	$0.897262\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12.4819	−	21.6193i	−0.490716	−	0.849944i	0.509227	−	0.860632i	$-0.329931\pi$
$647$	−12.4819	−	21.6193i	−0.490716	−	0.849944i	−0.999943	+	0.0106878i	$0.996598\pi$
$648$		0			0
$649$	−23.6786	−	13.6709i	−0.929468	−	0.536629i
$650$		0			0
$651$	3.46424	+	20.3646i	0.135774	+	0.798152i
$652$		0			0
$653$	−3.80370	−	2.19607i	−0.148850	−	0.0859387i	0.423725	−	0.905791i	$-0.360722\pi$
$653$	−3.80370	−	2.19607i	−0.148850	−	0.0859387i	−0.572575	+	0.819852i	$0.694056\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.69939	−	5.92544i	0.105313	−	0.231173i
$658$		0			0
$659$		−	1.93959i		−	0.0755557i	−0.999286	−	0.0377778i	$-0.987972\pi$
$659$		−	1.93959i		−	0.0755557i	0.999286	−	0.0377778i	$-0.0120279\pi$
$660$		0			0
$661$	21.6034	−	12.4727i	0.840274	−	0.485132i	−0.0170833	−	0.999854i	$-0.505438\pi$
$661$	21.6034	−	12.4727i	0.840274	−	0.485132i	0.857357	+	0.514722i	$0.172105\pi$
$662$		0			0
$663$	12.8127	−	14.1076i	0.497604	−	0.547895i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	24.4861	−	42.4112i	0.948107	−	1.64217i
$668$		0			0
$669$	−5.54161	−	17.3078i	−0.214251	−	0.669160i
$670$		0			0
$671$	−4.76553			−0.183971
$672$		0			0
$673$	6.21519			0.239578			0.119789	−	0.992799i	$-0.461778\pi$
$673$	6.21519			0.239578			0.119789	+	0.992799i	$0.461778\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	8.33017	−	14.4283i	0.320154	−	0.554524i	−0.660365	−	0.750945i	$-0.729599\pi$
$677$	8.33017	−	14.4283i	0.320154	−	0.554524i	0.980520	+	0.196421i	$0.0629319\pi$
$678$		0			0
$679$	9.38346	+	7.35751i	0.360104	+	0.282355i
$680$		0			0
$681$	−21.0603	−	19.1272i	−0.807034	−	0.732956i
$682$		0			0
$683$	−19.2844	+	11.1339i	−0.737898	+	0.426025i	−0.821304	−	0.570490i	$-0.806753\pi$
$683$	−19.2844	+	11.1339i	−0.737898	+	0.426025i	0.0834067	+	0.996516i	$0.473420\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−1.76654	−	0.383426i	−0.0673979	−	0.0146286i
$688$		0			0
$689$	−24.4401	−	42.3315i	−0.931095	−	1.61270i
$690$		0			0
$691$	−24.0492	−	13.8848i	−0.914873	−	0.528202i	−0.0328772	−	0.999459i	$-0.510467\pi$
$691$	−24.0492	−	13.8848i	−0.914873	−	0.528202i	−0.881996	+	0.471257i	$0.843800\pi$
$692$		0			0
$693$	−21.4759	−	41.4168i	−0.815803	−	1.57329i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	9.83941	+	17.0424i	0.372694	+	0.645525i
$698$		0			0
$699$	48.9576	+	10.6262i	1.85175	+	0.401919i
$700$		0			0
$701$			0.789291i			0.0298111i	0.999889	+	0.0149056i	$0.00474476\pi$
$701$			0.789291i			0.0298111i	−0.999889	+	0.0149056i	$0.995255\pi$
$702$		0			0
$703$	−7.07406	+	4.08421i	−0.266803	+	0.154039i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.69803	+	0.668609i	0.176688	+	0.0251456i
$708$		0			0
$709$	7.93432	−	13.7427i	0.297980	−	0.516116i	−0.677694	−	0.735344i	$-0.737021\pi$
$709$	7.93432	−	13.7427i	0.297980	−	0.516116i	0.975674	+	0.219228i	$0.0703539\pi$
$710$		0			0
$711$	−2.90961	−	30.1737i	−0.109119	−	1.13160i
$712$		0			0
$713$	−32.2383			−1.20733
$714$		0			0
$715$		0			0
$716$		0			0
$717$	3.00906	+	9.39806i	0.112375	+	0.350977i
$718$		0			0
$719$	22.6303	−	39.1968i	0.843967	−	1.46179i	−0.0425492	−	0.999094i	$-0.513548\pi$
$719$	22.6303	−	39.1968i	0.843967	−	1.46179i	0.886516	−	0.462699i	$-0.153119\pi$
$720$		0			0
$721$	30.9645	−	12.4478i	1.15318	−	0.463581i
$722$		0			0
$723$	8.21029	−	9.04009i	0.305344	−	0.336204i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	21.4724i		−	0.796369i	−0.917305	−	0.398185i	$-0.869640\pi$
$727$		−	21.4724i		−	0.796369i	0.917305	−	0.398185i	$-0.130360\pi$
$728$		0			0
$729$	−7.67916	−	25.8849i	−0.284413	−	0.958702i
$730$		0			0
$731$	−6.04497	−	10.4702i	−0.223581	−	0.387254i
$732$		0			0
$733$	−12.7846	−	7.38122i	−0.472211	−	0.272631i	0.244954	−	0.969535i	$-0.421227\pi$
$733$	−12.7846	−	7.38122i	−0.472211	−	0.272631i	−0.717165	+	0.696903i	$0.754561\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	51.9691	+	30.0044i	1.91431	+	1.10523i
$738$		0			0
$739$	−1.22065	−	2.11423i	−0.0449024	−	0.0777733i	0.842701	−	0.538382i	$-0.180964\pi$
$739$	−1.22065	−	2.11423i	−0.0449024	−	0.0777733i	−0.887603	+	0.460609i	$0.847631\pi$
$740$		0			0
$741$	−5.38258	+	24.7989i	−0.197734	+	0.911011i
$742$		0			0
$743$			32.2677i			1.18379i	0.806016	+	0.591894i	$0.201620\pi$
$743$			32.2677i			1.18379i	−0.806016	+	0.591894i	$0.798380\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	12.9735	−	9.25663i	0.474676	−	0.338683i
$748$		0			0
$749$	8.54158	−	3.43373i	0.312103	−	0.125466i
$750$		0			0
$751$	−7.00840	+	12.1389i	−0.255740	+	0.442955i	−0.965096	−	0.261895i	$-0.915652\pi$
$751$	−7.00840	+	12.1389i	−0.255740	+	0.442955i	0.709356	+	0.704850i	$0.248986\pi$
$752$		0			0
$753$	6.48669	−	2.07690i	0.236388	−	0.0756864i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−41.4500			−1.50653			−0.753263	−	0.657720i	$-0.771521\pi$
$757$	−41.4500			−1.50653			−0.753263	+	0.657720i	$0.771521\pi$
$758$		0			0
$759$	69.3419	−	22.2018i	2.51695	−	0.805874i
$760$		0			0
$761$	20.0586	−	34.7425i	0.727124	−	1.25942i	−0.230969	−	0.972961i	$-0.574190\pi$
$761$	20.0586	−	34.7425i	0.727124	−	1.25942i	0.958094	−	0.286455i	$-0.0924769\pi$
$762$		0			0
$763$	26.1308	+	3.71886i	0.946000	+	0.134632i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−14.2610	+	8.23358i	−0.514934	+	0.297297i
$768$		0			0
$769$		−	22.4441i		−	0.809355i	−0.914459	−	0.404677i	$-0.867384\pi$
$769$		−	22.4441i		−	0.809355i	0.914459	−	0.404677i	$-0.132616\pi$
$770$		0			0
$771$	5.62310	−	25.9071i	0.202511	−	0.933021i
$772$		0			0
$773$	14.5464	+	25.1951i	0.523198	+	0.906206i	0.999636	+	0.0269973i	$0.00859455\pi$
$773$	14.5464	+	25.1951i	0.523198	+	0.906206i	−0.476437	+	0.879208i	$0.658072\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−5.77181	−	6.96350i	−0.207063	−	0.249814i
$778$		0			0
$779$	−22.6930	−	13.1018i	−0.813060	−	0.469421i
$780$		0			0
$781$	−3.48802	−	6.04143i	−0.124811	−	0.216180i
$782$		0			0
$783$	28.5140	+	21.2832i	1.01901	+	0.760600i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−29.3516	+	16.9461i	−1.04627	+	0.604064i	−0.921603	−	0.388134i	$-0.873120\pi$
$787$	−29.3516	+	16.9461i	−1.04627	+	0.604064i	−0.124667	+	0.992199i	$0.539786\pi$
$788$		0			0
$789$	−22.7302	+	25.0275i	−0.809217	+	0.891002i
$790$		0			0
$791$	−5.29946	−	4.15527i	−0.188427	−	0.147745i
$792$		0			0
$793$	−1.43507	+	2.48562i	−0.0509609	+	0.0882669i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−30.8362			−1.09227			−0.546137	−	0.837696i	$-0.683902\pi$
$797$	−30.8362			−1.09227			−0.546137	+	0.837696i	$0.683902\pi$
$798$		0			0
$799$	5.70028			0.201661
$800$		0			0
$801$	3.62234	+	37.5649i	0.127989	+	1.32729i
$802$		0			0
$803$	−6.37874	+	11.0483i	−0.225101	+	0.389886i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−12.6131	−	11.4554i	−0.444004	−	0.403249i
$808$		0			0
$809$	−32.1338	+	18.5524i	−1.12976	+	0.652269i	−0.943875	−	0.330302i	$-0.892849\pi$
$809$	−32.1338	+	18.5524i	−1.12976	+	0.652269i	−0.185888	+	0.982571i	$0.559516\pi$
$810$		0			0
$811$		−	33.9956i		−	1.19375i	−0.802336	−	0.596873i	$-0.796410\pi$
$811$		−	33.9956i		−	1.19375i	0.802336	−	0.596873i	$-0.203590\pi$
$812$		0			0
$813$	−35.3412	−	7.67076i	−1.23947	−	0.269025i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	13.9417	+	8.04926i	0.487759	+	0.281608i
$818$		0			0
$819$	−28.0695	−	1.27062i	−0.980827	−	0.0443990i
$820$		0			0
$821$	40.0563	+	23.1265i	1.39798	+	0.807122i	0.994180	−	0.107727i	$-0.0343573\pi$
$821$	40.0563	+	23.1265i	1.39798	+	0.807122i	0.403796	+	0.914849i	$0.367691\pi$
$822$		0			0
$823$	−23.5324	−	40.7593i	−0.820288	−	1.42078i	−0.905468	−	0.424414i	$-0.860480\pi$
$823$	−23.5324	−	40.7593i	−0.820288	−	1.42078i	0.0851803	−	0.996366i	$-0.472853\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			14.6102i			0.508046i	0.967198	+	0.254023i	$0.0817539\pi$
$827$			14.6102i			0.508046i	−0.967198	+	0.254023i	$0.918246\pi$
$828$		0			0
$829$	−27.9876	+	16.1586i	−0.972049	+	0.561213i	−0.899860	−	0.436178i	$-0.856332\pi$
$829$	−27.9876	+	16.1586i	−0.972049	+	0.561213i	−0.0721885	+	0.997391i	$0.522998\pi$
$830$		0			0
$831$	10.9033	+	9.90248i	0.378231	+	0.343513i
$832$		0			0
$833$	15.7031	−	15.0590i	0.544080	−	0.521763i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	2.74825	−	23.2612i	0.0949935	−	0.804026i
$838$		0			0
$839$	−15.0113			−0.518249			−0.259124	−	0.965844i	$-0.583434\pi$
$839$	−15.0113			−0.518249			−0.259124	+	0.965844i	$0.583434\pi$
$840$		0			0
$841$	−17.8898			−0.616888
$842$		0			0
$843$	4.03346	+	12.5975i	0.138920	+	0.433882i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	23.2389	+	57.8078i	0.798497	+	1.98630i
$848$		0			0
$849$	−10.4891	+	11.5492i	−0.359985	+	0.396367i
$850$		0			0
$851$	12.2242	−	7.05764i	0.419040	−	0.241933i
$852$		0			0
$853$			43.2807i			1.48190i	0.671558	+	0.740952i	$0.265626\pi$
$853$			43.2807i			1.48190i	−0.671558	+	0.740952i	$0.734374\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	10.5802	+	18.3255i	0.361413	+	0.625986i	0.988194	−	0.153210i	$-0.0489610\pi$
$857$	10.5802	+	18.3255i	0.361413	+	0.625986i	−0.626780	+	0.779196i	$0.715628\pi$
$858$		0			0
$859$	−36.5871	−	21.1236i	−1.24834	−	0.720728i	−0.277560	−	0.960708i	$-0.589526\pi$
$859$	−36.5871	−	21.1236i	−1.24834	−	0.720728i	−0.970778	+	0.239981i	$0.922859\pi$
$860$		0			0
$861$	10.0878	−	27.2040i	0.343792	−	0.927111i
$862$		0			0
$863$	30.9097	+	17.8457i	1.05218	+	0.607475i	0.923258	−	0.384181i	$-0.125516\pi$
$863$	30.9097	+	17.8457i	1.05218	+	0.607475i	0.128919	+	0.991655i	$0.458849\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−2.69645	+	12.4233i	−0.0915764	+	0.421916i
$868$		0			0
$869$			59.3927i			2.01476i
$870$		0			0
$871$	31.2996	−	18.0708i	1.06055	−	0.612306i
$872$		0			0
$873$	−7.85296	−	11.0062i	−0.265782	−	0.372504i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.09996	+	1.90519i	−0.0371430	+	0.0643336i	−0.883999	−	0.467488i	$-0.845159\pi$
$877$	−1.09996	+	1.90519i	−0.0371430	+	0.0643336i	0.846856	+	0.531822i	$0.178492\pi$
$878$		0			0
$879$	−45.5447	+	14.5825i	−1.53619	+	0.491854i
$880$		0			0
$881$	−29.2075			−0.984025			−0.492013	−	0.870588i	$-0.663739\pi$
$881$	−29.2075			−0.984025			−0.492013	+	0.870588i	$0.663739\pi$
$882$		0			0
$883$	2.21069			0.0743956			0.0371978	−	0.999308i	$-0.488157\pi$
$883$	2.21069			0.0743956			0.0371978	+	0.999308i	$0.488157\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	6.68134	−	11.5724i	0.224337	−	0.388564i	−0.731783	−	0.681538i	$-0.761312\pi$
$887$	6.68134	−	11.5724i	0.224337	−	0.388564i	0.956120	+	0.292974i	$0.0946449\pi$
$888$		0			0
$889$	20.6702	−	26.3620i	0.693258	−	0.884152i
$890$		0			0
$891$	10.1082	+	51.9256i	0.338639	+	1.73957i
$892$		0			0
$893$	−6.57337	+	3.79514i	−0.219970	+	0.126999i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	9.30126	−	42.8533i	0.310560	−	1.43083i
$898$		0			0
$899$	15.4337	+	26.7320i	0.514743	+	0.891561i
$900$		0			0
$901$	−37.1667	−	21.4582i	−1.23820	−	0.714876i
$902$		0			0
$903$	−6.19758	+	16.7132i	−0.206242	+	0.556179i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−2.09445	−	3.62770i	−0.0695451	−	0.120456i	0.829156	−	0.559017i	$-0.188821\pi$
$907$	−2.09445	−	3.62770i	−0.0695451	−	0.120456i	−0.898701	+	0.438562i	$0.855488\pi$
$908$		0			0
$909$	−4.89658	−	2.23068i	−0.162409	−	0.0739870i
$910$		0			0
$911$		−	22.5190i		−	0.746087i	−0.927814	−	0.373043i	$-0.878314\pi$
$911$		−	22.5190i		−	0.746087i	0.927814	−	0.373043i	$-0.121686\pi$
$912$		0			0
$913$	−27.0421	+	15.6128i	−0.894962	+	0.516707i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	12.5284	+	31.1649i	0.413723	+	1.02916i
$918$		0			0
$919$	7.26453	−	12.5825i	0.239635	−	0.415060i	−0.720975	−	0.692961i	$-0.756306\pi$
$919$	7.26453	−	12.5825i	0.239635	−	0.415060i	0.960610	+	0.277902i	$0.0896390\pi$
$920$		0			0
$921$	−5.27948	−	16.4892i	−0.173965	−	0.543336i
$922$		0			0
$923$	−4.20148			−0.138293
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−37.6666	+	3.63214i	−1.23713	+	0.119295i
$928$		0			0
$929$	−20.7788	+	35.9900i	−0.681732	+	1.18079i	0.292720	+	0.956198i	$0.405440\pi$
$929$	−20.7788	+	35.9900i	−0.681732	+	1.18079i	−0.974452	+	0.224596i	$0.927894\pi$
$930$		0			0
$931$	−8.08232	+	27.8204i	−0.264887	+	0.911776i
$932$		0			0
$933$	−30.6020	−	27.7930i	−1.00186	−	0.909903i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			45.5010i			1.48645i	0.669040	+	0.743226i	$0.266705\pi$
$937$			45.5010i			1.48645i	−0.669040	+	0.743226i	$0.733295\pi$
$938$		0			0
$939$	−9.47064	−	2.05559i	−0.309063	−	0.0670817i
$940$		0			0
$941$	10.0244	+	17.3627i	0.326785	+	0.566007i	0.981872	−	0.189546i	$-0.0607015\pi$
$941$	10.0244	+	17.3627i	0.326785	+	0.566007i	−0.655087	+	0.755553i	$0.727368\pi$
$942$		0			0
$943$	39.2142	+	22.6403i	1.27699	+	0.737270i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−25.5460	−	14.7490i	−0.830133	−	0.479278i	0.0237652	−	0.999718i	$-0.492435\pi$
$947$	−25.5460	−	14.7490i	−0.830133	−	0.479278i	−0.853898	+	0.520440i	$0.825768\pi$
$948$		0			0
$949$	3.84174	+	6.65408i	0.124708	+	0.216001i
$950$		0			0
$951$	−19.8658	−	4.31184i	−0.644192	−	0.139821i
$952$		0			0
$953$		−	1.26250i		−	0.0408964i	−0.999791	−	0.0204482i	$-0.993491\pi$
$953$		−	1.26250i		−	0.0408964i	0.999791	−	0.0204482i	$-0.00650931\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−51.6063	−	46.8693i	−1.66819	−	1.51507i
$958$		0			0
$959$	−1.95628	+	13.7459i	−0.0631715	+	0.443879i
$960$		0			0
$961$	−5.34003	+	9.24920i	−0.172259	+	0.298361i
$962$		0			0
$963$	−10.3903	+	1.00193i	−0.334824	+	0.0322867i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	26.0942			0.839132			0.419566	−	0.907725i	$-0.362182\pi$
$967$	26.0942			0.839132			0.419566	+	0.907725i	$0.362182\pi$
$968$		0			0
$969$	6.79390	+	21.2191i	0.218251	+	0.681655i
$970$		0			0
$971$	−6.95317	+	12.0432i	−0.223138	+	0.386486i	−0.955759	−	0.294150i	$-0.904963\pi$
$971$	−6.95317	+	12.0432i	−0.223138	+	0.386486i	0.732621	+	0.680636i	$0.238297\pi$
$972$		0			0
$973$	29.7404	+	23.3192i	0.953433	+	0.747580i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.45787	+	1.41905i	−0.0786342	+	0.0453995i	−0.538802	−	0.842433i	$-0.681123\pi$
$977$	−2.45787	+	1.41905i	−0.0786342	+	0.0453995i	0.460167	+	0.887832i	$0.347789\pi$
$978$		0			0
$979$		−	73.9413i		−	2.36317i
$980$		0			0
$981$	−27.2352	−	12.4072i	−0.869552	−	0.396132i
$982$		0			0
$983$	−24.5705	−	42.5573i	−0.783677	−	1.35737i	−0.929787	−	0.368099i	$-0.880009\pi$
$983$	−24.5705	−	42.5573i	−0.783677	−	1.35737i	0.146110	−	0.989268i	$-0.453325\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−5.36330	−	6.47064i	−0.170716	−	0.205963i
$988$		0			0
$989$	−24.0917	−	13.9094i	−0.766072	−	0.442292i
$990$		0			0
$991$	−10.3281	−	17.8887i	−0.328081	−	0.568254i	0.654050	−	0.756452i	$-0.273069\pi$
$991$	−10.3281	−	17.8887i	−0.328081	−	0.568254i	−0.982131	+	0.188198i	$0.939735\pi$
$992$		0			0
$993$	0.929142	−	4.28080i	0.0294854	−	0.135847i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	36.1051	−	20.8453i	1.14346	−	0.660177i	0.196175	−	0.980569i	$-0.437148\pi$
$997$	36.1051	−	20.8453i	1.14346	−	0.660177i	0.947285	+	0.320392i	$0.103814\pi$
$998$		0			0
$999$	4.05028	+	9.42189i	0.128145	+	0.298095i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bi.n.1601.2		32
3.2	odd	2	inner	2100.2.bi.n.1601.4		32
5.2	odd	4		420.2.bn.a.89.10	yes	32
5.3	odd	4		420.2.bn.a.89.7	yes	32
5.4	even	2	inner	2100.2.bi.n.1601.15		32
7.3	odd	6	inner	2100.2.bi.n.101.4		32
15.2	even	4		420.2.bn.a.89.12	yes	32
15.8	even	4		420.2.bn.a.89.5	✓	32
15.14	odd	2	inner	2100.2.bi.n.1601.13		32
21.17	even	6	inner	2100.2.bi.n.101.2		32
35.2	odd	12		2940.2.f.a.1469.2		32
35.3	even	12		420.2.bn.a.269.12	yes	32
35.12	even	12		2940.2.f.a.1469.31		32
35.17	even	12		420.2.bn.a.269.5	yes	32
35.23	odd	12		2940.2.f.a.1469.32		32
35.24	odd	6	inner	2100.2.bi.n.101.13		32
35.33	even	12		2940.2.f.a.1469.1		32
105.2	even	12		2940.2.f.a.1469.3		32
105.17	odd	12		420.2.bn.a.269.7	yes	32
105.23	even	12		2940.2.f.a.1469.29		32
105.38	odd	12		420.2.bn.a.269.10	yes	32
105.47	odd	12		2940.2.f.a.1469.30		32
105.59	even	6	inner	2100.2.bi.n.101.15		32
105.68	odd	12		2940.2.f.a.1469.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bn.a.89.5	✓	32	15.8	even	4
420.2.bn.a.89.7	yes	32	5.3	odd	4
420.2.bn.a.89.10	yes	32	5.2	odd	4
420.2.bn.a.89.12	yes	32	15.2	even	4
420.2.bn.a.269.5	yes	32	35.17	even	12
420.2.bn.a.269.7	yes	32	105.17	odd	12
420.2.bn.a.269.10	yes	32	105.38	odd	12
420.2.bn.a.269.12	yes	32	35.3	even	12
2100.2.bi.n.101.2		32	21.17	even	6	inner
2100.2.bi.n.101.4		32	7.3	odd	6	inner
2100.2.bi.n.101.13		32	35.24	odd	6	inner
2100.2.bi.n.101.15		32	105.59	even	6	inner
2100.2.bi.n.1601.2		32	1.1	even	1	trivial
2100.2.bi.n.1601.4		32	3.2	odd	2	inner
2100.2.bi.n.1601.13		32	15.14	odd	2	inner
2100.2.bi.n.1601.15		32	5.4	even	2	inner
2940.2.f.a.1469.1		32	35.33	even	12
2940.2.f.a.1469.2		32	35.2	odd	12
2940.2.f.a.1469.3		32	105.2	even	12
2940.2.f.a.1469.4		32	105.68	odd	12
2940.2.f.a.1469.29		32	105.23	even	12
2940.2.f.a.1469.30		32	105.47	odd	12
2940.2.f.a.1469.31		32	35.12	even	12
2940.2.f.a.1469.32		32	35.23	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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.64956 + 0.528155i) q^{3} +(-1.63251 + 2.08204i) q^{7} +(2.44211 - 1.74245i) q^{9} +O(q^{10})\)	\(q+(-1.64956 + 0.528155i) q^{3} +(-1.63251 + 2.08204i) q^{7} +(2.44211 - 1.74245i) q^{9} +(-5.09034 + 2.93891i) q^{11} +3.54004i q^{13} +(1.55406 + 2.69171i) q^{17} +(-3.58419 - 2.06933i) q^{19} +(1.59329 - 4.29667i) q^{21} +(6.19358 + 3.57587i) q^{23} +(-3.10812 + 4.16408i) q^{27} -6.84761i q^{29} +(-3.90384 + 2.25388i) q^{31} +(6.84463 - 7.53639i) q^{33} +(0.986843 - 1.70926i) q^{37} +(-1.86969 - 5.83952i) q^{39} +6.33142 q^{41} -3.88979 q^{43} +(0.916997 - 1.58829i) q^{47} +(-1.66979 - 6.79793i) q^{49} +(-3.98516 - 3.61936i) q^{51} +(-11.9579 + 6.90391i) q^{53} +(7.00526 + 1.52048i) q^{57} +(2.32584 + 4.02848i) q^{59} +(0.702144 + 0.405383i) q^{61} +(-0.358927 + 7.92913i) q^{63} +(-5.10469 - 8.84158i) q^{67} +(-12.1053 - 2.62744i) q^{69} +1.18684i q^{71} +(1.87966 - 1.08522i) q^{73} +(2.19112 - 15.3961i) q^{77} +(5.05228 - 8.75081i) q^{79} +(2.92776 - 8.51048i) q^{81} +5.31243 q^{83} +(3.61660 + 11.2956i) q^{87} +(-6.28986 + 10.8944i) q^{89} +(-7.37052 - 5.77917i) q^{91} +(5.24922 - 5.77975i) q^{93} -4.50686i q^{97} +(-7.31025 + 16.0468i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 12 q^{19} - 8 q^{21} - 12 q^{31} - 24 q^{39} + 44 q^{49} - 10 q^{51} - 24 q^{61} + 28 q^{79} - 20 q^{81} + 16 q^{91} + 28 q^{99}+O(q^{100}) \) 32 * q - 12 * q^19 - 8 * q^21 - 12 * q^31 - 24 * q^39 + 44 * q^49 - 10 * q^51 - 24 * q^61 + 28 * q^79 - 20 * q^81 + 16 * q^91 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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