LMFDB - Embedded newform 2100.2.q.l.1201.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1201,2100)]

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, 0, 0, 4]))

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

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

chi := DirichletCharacter("2100.1201");

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.q (of order $3$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.17819046144.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 10x^{6} + 8x^{5} + 38x^{4} - 4x^{3} + 16x^{2} + 4x + 4 $ x^8 - 2x^7 + 10x^6 + 8x^5 + 38x^4 - 4x^3 + 16x^2 + 4*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1201.3
Root			$1.75161 - 3.03388i$ of defining polynomial
Character	$\chi$	$=$	2100.1201
Dual form			2100.2.q.l.1801.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(-0.618546 + 2.57243i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.618546 + 2.57243i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.46616 + 2.53947i) q^{11} -5.76936 q^{13} +(-0.118546 + 0.205328i) q^{17} +(-2.37016 - 4.10523i) q^{19} +(-1.91852 - 1.82189i) q^{21} +(-3.38468 - 5.86244i) q^{23} +1.00000 q^{27} +6.03549 q^{29} +(5.26936 - 9.12679i) q^{31} +(-1.46616 - 2.53947i) q^{33} +(1.53706 + 2.66227i) q^{37} +(2.88468 - 4.99641i) q^{39} +1.06768 q^{41} +9.79697 q^{43} +(-1.85635 - 3.21530i) q^{47} +(-6.23480 - 3.18233i) q^{49} +(-0.118546 - 0.205328i) q^{51} +(-5.50322 + 9.53186i) q^{53} +4.74032 q^{57} +(4.65633 - 8.06499i) q^{59} +(4.06861 + 7.04704i) q^{61} +(2.53706 - 0.750539i) q^{63} +(1.12177 - 1.94296i) q^{67} +6.76936 q^{69} -11.8421 q^{71} +(-1.89848 + 3.28827i) q^{73} +(-5.62571 - 5.34237i) q^{77} +(-0.00873900 - 0.0151364i) q^{79} +(-0.500000 + 0.866025i) q^{81} +7.30162 q^{83} +(-3.01774 + 5.22689i) q^{87} +(-8.97583 - 15.5466i) q^{89} +(3.56861 - 14.8413i) q^{91} +(5.26936 + 9.12679i) q^{93} +2.31122 q^{97} +2.93232 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 - 2 * q^7 - 4 * q^9	$ 8 q - 4 q^{3} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{13} + 2 q^{17} - 4 q^{19} - 2 q^{21} - 6 q^{23} + 8 q^{27} - 12 q^{29} - 4 q^{33} - 4 q^{37} + 2 q^{39} + 24 q^{41} + 32 q^{43} - 2 q^{47} - 4 q^{49} + 2 q^{51} - 20 q^{53} + 8 q^{57} + 14 q^{59} - 16 q^{61} + 4 q^{63} - 18 q^{67} + 12 q^{69} - 28 q^{71} + 8 q^{73} + 10 q^{77} + 8 q^{79} - 4 q^{81} - 20 q^{83} + 6 q^{87} + 8 q^{89} - 20 q^{91} - 20 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^13 + 2 * q^17 - 4 * q^19 - 2 * q^21 - 6 * q^23 + 8 * q^27 - 12 * q^29 - 4 * q^33 - 4 * q^37 + 2 * q^39 + 24 * q^41 + 32 * q^43 - 2 * q^47 - 4 * q^49 + 2 * q^51 - 20 * q^53 + 8 * q^57 + 14 * q^59 - 16 * q^61 + 4 * q^63 - 18 * q^67 + 12 * q^69 - 28 * q^71 + 8 * q^73 + 10 * q^77 + 8 * q^79 - 4 * q^81 - 20 * q^83 + 6 * q^87 + 8 * q^89 - 20 * q^91 - 20 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.618546	+	2.57243i	−0.233788	+	0.972288i
$7$	−0.618546	+	2.57243i	−0.233788	+	0.972288i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.46616	+	2.53947i	−0.442064	+	0.765678i	−0.997843	−	0.0656529i	$-0.979087\pi$
$11$	−1.46616	+	2.53947i	−0.442064	+	0.765678i	0.555778	+	0.831330i	$0.312420\pi$
$12$		0			0
$13$	−5.76936			−1.60013			−0.800066	−	0.599912i	$-0.795202\pi$
$13$	−5.76936			−1.60013			−0.800066	+	0.599912i	$0.795202\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.118546	+	0.205328i	−0.0287516	+	0.0497993i	−0.880043	−	0.474894i	$-0.842487\pi$
$17$	−0.118546	+	0.205328i	−0.0287516	+	0.0497993i	0.851292	+	0.524693i	$0.175820\pi$
$18$		0			0
$19$	−2.37016	−	4.10523i	−0.543752	−	0.941805i	−0.998684	−	0.0512796i	$-0.983670\pi$
$19$	−2.37016	−	4.10523i	−0.543752	−	0.941805i	0.454933	−	0.890526i	$-0.349663\pi$
$20$		0			0
$21$	−1.91852	−	1.82189i	−0.418655	−	0.397569i
$22$		0			0
$23$	−3.38468	−	5.86244i	−0.705754	−	1.22240i	−0.966419	−	0.256973i	$-0.917275\pi$
$23$	−3.38468	−	5.86244i	−0.705754	−	1.22240i	0.260664	−	0.965429i	$-0.416058\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	6.03549			1.12076			0.560381	−	0.828235i	$-0.310655\pi$
$29$	6.03549			1.12076			0.560381	+	0.828235i	$0.310655\pi$
$30$		0			0
$31$	5.26936	−	9.12679i	0.946404	−	1.63922i	0.193490	−	0.981102i	$-0.438019\pi$
$31$	5.26936	−	9.12679i	0.946404	−	1.63922i	0.752915	−	0.658118i	$-0.228647\pi$
$32$		0			0
$33$	−1.46616	−	2.53947i	−0.255226	−	0.442064i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.53706	+	2.66227i	0.252692	+	0.437675i	0.964266	−	0.264936i	$-0.0853508\pi$
$37$	1.53706	+	2.66227i	0.252692	+	0.437675i	−0.711574	+	0.702611i	$0.752018\pi$
$38$		0			0
$39$	2.88468	−	4.99641i	0.461918	−	0.800066i
$40$		0			0
$41$	1.06768			0.166743			0.0833717	−	0.996519i	$-0.473431\pi$
$41$	1.06768			0.166743			0.0833717	+	0.996519i	$0.473431\pi$
$42$		0			0
$43$	9.79697			1.49402			0.747012	−	0.664811i	$-0.231488\pi$
$43$	9.79697			1.49402			0.747012	+	0.664811i	$0.231488\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.85635	−	3.21530i	−0.270777	−	0.469000i	0.698284	−	0.715821i	$-0.253947\pi$
$47$	−1.85635	−	3.21530i	−0.270777	−	0.469000i	−0.969061	+	0.246821i	$0.920614\pi$
$48$		0			0
$49$	−6.23480	−	3.18233i	−0.890686	−	0.454619i
$50$		0			0
$51$	−0.118546	−	0.205328i	−0.0165998	−	0.0287516i
$52$		0			0
$53$	−5.50322	+	9.53186i	−0.755926	+	1.30930i	0.188987	+	0.981980i	$0.439480\pi$
$53$	−5.50322	+	9.53186i	−0.755926	+	1.30930i	−0.944913	+	0.327323i	$0.893854\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	4.74032			0.627870
$58$		0			0
$59$	4.65633	−	8.06499i	0.606202	−	1.04997i	−0.385658	−	0.922642i	$-0.626026\pi$
$59$	4.65633	−	8.06499i	0.606202	−	1.04997i	0.991860	−	0.127331i	$-0.0406410\pi$
$60$		0			0
$61$	4.06861	+	7.04704i	0.520932	+	0.902281i	0.999704	+	0.0243418i	$0.00774899\pi$
$61$	4.06861	+	7.04704i	0.520932	+	0.902281i	−0.478771	+	0.877940i	$0.658918\pi$
$62$		0			0
$63$	2.53706	−	0.750539i	0.319640	−	0.0945590i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.12177	−	1.94296i	0.137046	−	0.237371i	−0.789331	−	0.613968i	$-0.789572\pi$
$67$	1.12177	−	1.94296i	0.137046	−	0.237371i	0.926377	+	0.376597i	$0.122906\pi$
$68$		0			0
$69$	6.76936			0.814935
$70$		0			0
$71$	−11.8421			−1.40539			−0.702696	−	0.711490i	$-0.748021\pi$
$71$	−11.8421			−1.40539			−0.702696	+	0.711490i	$0.748021\pi$
$72$		0			0
$73$	−1.89848	+	3.28827i	−0.222201	+	0.384863i	−0.955476	−	0.295069i	$-0.904657\pi$
$73$	−1.89848	+	3.28827i	−0.222201	+	0.384863i	0.733275	+	0.679932i	$0.237991\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.62571	−	5.34237i	−0.641109	−	0.608820i
$78$		0			0
$79$	−0.00873900	−	0.0151364i	−0.000983215	−	0.00170298i	0.865533	−	0.500851i	$-0.166980\pi$
$79$	−0.00873900	−	0.0151364i	−0.000983215	−	0.00170298i	−0.866517	+	0.499148i	$0.833646\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	7.30162			0.801457			0.400729	−	0.916197i	$-0.368757\pi$
$83$	7.30162			0.801457			0.400729	+	0.916197i	$0.368757\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−3.01774	+	5.22689i	−0.323536	+	0.560381i
$88$		0			0
$89$	−8.97583	−	15.5466i	−0.951437	−	1.64794i	−0.742320	−	0.670046i	$-0.766274\pi$
$89$	−8.97583	−	15.5466i	−0.951437	−	1.64794i	−0.209117	−	0.977891i	$-0.567059\pi$
$90$		0			0
$91$	3.56861	−	14.8413i	0.374092	−	1.55579i
$92$		0			0
$93$	5.26936	+	9.12679i	0.546407	+	0.946404i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	2.31122			0.234669			0.117334	−	0.993092i	$-0.462565\pi$
$97$	2.31122			0.234669			0.117334	+	0.993092i	$0.462565\pi$
$98$		0			0
$99$	2.93232			0.294709
$100$		0			0
$101$	3.92103	−	6.79142i	0.390157	−	0.675771i	−0.602313	−	0.798260i	$-0.705754\pi$
$101$	3.92103	−	6.79142i	0.390157	−	0.675771i	0.992470	+	0.122489i	$0.0390875\pi$
$102$		0			0
$103$	2.04029	+	3.53388i	0.201036	+	0.348204i	0.948862	−	0.315690i	$-0.102236\pi$
$103$	2.04029	+	3.53388i	0.201036	+	0.348204i	−0.747827	+	0.663894i	$0.768903\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.17335	−	15.8887i	−0.886822	−	1.53602i	−0.843611	−	0.536954i	$-0.819575\pi$
$107$	−9.17335	−	15.8887i	−0.886822	−	1.53602i	−0.0432102	−	0.999066i	$-0.513759\pi$
$108$		0			0
$109$	5.20719	−	9.01912i	0.498759	−	0.863875i	−0.501240	−	0.865308i	$-0.667123\pi$
$109$	5.20719	−	9.01912i	0.498759	−	0.863875i	0.999999	+	0.00143278i	$0.000456070\pi$
$110$		0			0
$111$	−3.07413			−0.291783
$112$		0			0
$113$	−2.14825			−0.202091			−0.101045	−	0.994882i	$-0.532219\pi$
$113$	−2.14825			−0.202091			−0.101045	+	0.994882i	$0.532219\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.88468	+	4.99641i	0.266689	+	0.461918i
$118$		0			0
$119$	−0.454865	−	0.431956i	−0.0416974	−	0.0395973i
$120$		0			0
$121$	1.20074	+	2.07975i	0.109159	+	0.189068i
$122$		0			0
$123$	−0.533839	+	0.924636i	−0.0481347	+	0.0833717i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−1.82457			−0.161905			−0.0809524	−	0.996718i	$-0.525796\pi$
$127$	−1.82457			−0.161905			−0.0809524	+	0.996718i	$0.525796\pi$
$128$		0			0
$129$	−4.89848	+	8.48442i	−0.431287	+	0.747012i
$130$		0			0
$131$	−1.35313	−	2.34369i	−0.118223	−	0.204769i	0.800840	−	0.598878i	$-0.204387\pi$
$131$	−1.35313	−	2.34369i	−0.118223	−	0.204769i	−0.919064	+	0.394109i	$0.871053\pi$
$132$		0			0
$133$	12.0265	−	3.55779i	1.04283	−	0.308500i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.00251	+	8.66460i	−0.427393	+	0.740267i	−0.996641	−	0.0818996i	$-0.973901\pi$
$137$	−5.00251	+	8.66460i	−0.427393	+	0.740267i	0.569247	+	0.822166i	$0.307235\pi$
$138$		0			0
$139$	−2.07269			−0.175804			−0.0879018	−	0.996129i	$-0.528016\pi$
$139$	−2.07269			−0.175804			−0.0879018	+	0.996129i	$0.528016\pi$
$140$		0			0
$141$	3.71271			0.312666
$142$		0			0
$143$	8.45881	−	14.6511i	0.707361	−	1.22518i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	5.87338	−	3.80833i	0.484428	−	0.314106i
$148$		0			0
$149$	0.551584	+	0.955371i	0.0451875	+	0.0782671i	0.887735	−	0.460356i	$-0.152278\pi$
$149$	0.551584	+	0.955371i	0.0451875	+	0.0782671i	−0.842547	+	0.538623i	$0.818945\pi$
$150$		0			0
$151$	−5.23158	+	9.06136i	−0.425740	+	0.737403i	−0.996489	−	0.0837214i	$-0.973319\pi$
$151$	−5.23158	+	9.06136i	−0.425740	+	0.737403i	0.570749	+	0.821124i	$0.306653\pi$
$152$		0			0
$153$	0.237092			0.0191677
$154$		0			0
$155$		0			0
$156$		0			0
$157$	4.53083	−	7.84763i	0.361600	−	0.626309i	−0.626624	−	0.779321i	$-0.715564\pi$
$157$	4.53083	−	7.84763i	0.361600	−	0.626309i	0.988224	+	0.153012i	$0.0488973\pi$
$158$		0			0
$159$	−5.50322	−	9.53186i	−0.436434	−	0.755926i
$160$		0			0
$161$	17.1743	−	5.08067i	1.35352	−	0.400413i
$162$		0			0
$163$	−4.16941	−	7.22164i	−0.326574	−	0.565642i	0.655256	−	0.755407i	$-0.272561\pi$
$163$	−4.16941	−	7.22164i	−0.326574	−	0.565642i	−0.981830	+	0.189765i	$0.939227\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−10.2886			−0.796158			−0.398079	−	0.917351i	$-0.630323\pi$
$167$	−10.2886			−0.796158			−0.398079	+	0.917351i	$0.630323\pi$
$168$		0			0
$169$	20.2855			1.56042
$170$		0			0
$171$	−2.37016	+	4.10523i	−0.181251	+	0.313935i
$172$		0			0
$173$	−8.64687	−	14.9768i	−0.657409	−	1.13867i	−0.981284	−	0.192566i	$-0.938319\pi$
$173$	−8.64687	−	14.9768i	−0.657409	−	1.13867i	0.323875	−	0.946100i	$-0.395014\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.65633	+	8.06499i	0.349991	+	0.606202i
$178$		0			0
$179$	5.50967	−	9.54303i	0.411812	−	0.713280i	−0.583276	−	0.812274i	$-0.698229\pi$
$179$	5.50967	−	9.54303i	0.411812	−	0.713280i	0.995088	+	0.0989944i	$0.0315626\pi$
$180$		0			0
$181$	4.53685			0.337221			0.168611	−	0.985683i	$-0.446072\pi$
$181$	4.53685			0.337221			0.168611	+	0.985683i	$0.446072\pi$
$182$		0			0
$183$	−8.13722			−0.601521
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.347615	−	0.602087i	−0.0254201	−	0.0440289i
$188$		0			0
$189$	−0.618546	+	2.57243i	−0.0449926	+	0.187117i
$190$		0			0
$191$	−4.34026	−	7.51755i	−0.314050	−	0.543951i	0.665185	−	0.746679i	$-0.268353\pi$
$191$	−4.34026	−	7.51755i	−0.314050	−	0.543951i	−0.979235	+	0.202728i	$0.935019\pi$
$192$		0			0
$193$	−3.53061	+	6.11520i	−0.254139	+	0.440182i	−0.964661	−	0.263493i	$-0.915125\pi$
$193$	−3.53061	+	6.11520i	−0.254139	+	0.440182i	0.710522	+	0.703675i	$0.248459\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3.58891			0.255700			0.127850	−	0.991794i	$-0.459192\pi$
$197$	3.58891			0.255700			0.127850	+	0.991794i	$0.459192\pi$
$198$		0			0
$199$	1.49126	−	2.58294i	0.105713	−	0.183100i	−0.808316	−	0.588748i	$-0.799621\pi$
$199$	1.49126	−	2.58294i	0.105713	−	0.183100i	0.914029	+	0.405648i	$0.132954\pi$
$200$		0			0
$201$	1.12177	+	1.94296i	0.0791236	+	0.137046i
$202$		0			0
$203$	−3.73323	+	15.5259i	−0.262021	+	1.08970i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−3.38468	+	5.86244i	−0.235251	+	0.407467i
$208$		0			0
$209$	13.9001			0.961492
$210$		0			0
$211$	−21.4273			−1.47512			−0.737558	−	0.675284i	$-0.764021\pi$
$211$	−21.4273			−1.47512			−0.737558	+	0.675284i	$0.764021\pi$
$212$		0			0
$213$	5.92103	−	10.2555i	0.405702	−	0.702696i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	20.2187	+	19.2004i	1.37254	+	1.30341i
$218$		0			0
$219$	−1.89848	−	3.28827i	−0.128288	−	0.222201i
$220$		0			0
$221$	0.683934	−	1.18461i	0.0460064	−	0.0796854i
$222$		0			0
$223$	−16.3969			−1.09802			−0.549009	−	0.835816i	$-0.684995\pi$
$223$	−16.3969			−1.09802			−0.549009	+	0.835816i	$0.684995\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.76685	−	8.25642i	0.316387	−	0.547998i	−0.663344	−	0.748314i	$-0.730864\pi$
$227$	4.76685	−	8.25642i	0.316387	−	0.547998i	0.979731	+	0.200316i	$0.0641969\pi$
$228$		0			0
$229$	−9.05987	−	15.6922i	−0.598693	−	1.03697i	−0.993014	−	0.117994i	$-0.962354\pi$
$229$	−9.05987	−	15.6922i	−0.598693	−	1.03697i	0.394321	−	0.918973i	$-0.370980\pi$
$230$		0			0
$231$	7.43949	−	2.20082i	0.489482	−	0.144803i
$232$		0			0
$233$	−6.02720	−	10.4394i	−0.394855	−	0.683909i	0.598228	−	0.801326i	$-0.295872\pi$
$233$	−6.02720	−	10.4394i	−0.394855	−	0.683909i	−0.993083	+	0.117417i	$0.962538\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.0174780			0.00113532
$238$		0			0
$239$	−21.3868			−1.38340			−0.691698	−	0.722187i	$-0.743137\pi$
$239$	−21.3868			−1.38340			−0.691698	+	0.722187i	$0.743137\pi$
$240$		0			0
$241$	−8.59443	+	14.8860i	−0.553616	+	0.958891i	0.444394	+	0.895831i	$0.353419\pi$
$241$	−8.59443	+	14.8860i	−0.553616	+	0.958891i	−0.998010	+	0.0630593i	$0.979914\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	13.6743	+	23.6846i	0.870074	+	1.50701i
$248$		0			0
$249$	−3.65081	+	6.32339i	−0.231361	+	0.400729i
$250$		0			0
$251$	23.1939			1.46398			0.731992	−	0.681313i	$-0.238591\pi$
$251$	23.1939			1.46398			0.731992	+	0.681313i	$0.238591\pi$
$252$		0			0
$253$	19.8499			1.24795
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−13.0781	−	22.6519i	−0.815787	−	1.41299i	−0.908761	−	0.417317i	$-0.862971\pi$
$257$	−13.0781	−	22.6519i	−0.815787	−	1.41299i	0.0929737	−	0.995669i	$-0.470363\pi$
$258$		0			0
$259$	−7.79926	+	2.30725i	−0.484622	+	0.143366i
$260$		0			0
$261$	−3.01774	−	5.22689i	−0.186794	−	0.323536i
$262$		0			0
$263$	−3.84991	+	6.66823i	−0.237395	+	0.411181i	−0.959966	−	0.280116i	$-0.909627\pi$
$263$	−3.84991	+	6.66823i	−0.237395	+	0.411181i	0.722571	+	0.691297i	$0.242960\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	17.9517			1.09862
$268$		0			0
$269$	−12.5194	+	21.6842i	−0.763321	+	1.32211i	0.177809	+	0.984065i	$0.443099\pi$
$269$	−12.5194	+	21.6842i	−0.763321	+	1.32211i	−0.941130	+	0.338046i	$0.890234\pi$
$270$		0			0
$271$	−9.54423	−	16.5311i	−0.579771	−	1.00419i	−0.995505	−	0.0947062i	$-0.969809\pi$
$271$	−9.54423	−	16.5311i	−0.579771	−	1.00419i	0.415735	−	0.909486i	$-0.363524\pi$
$272$		0			0
$273$	11.0686	+	10.5111i	0.669903	+	0.636163i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−6.06933	+	10.5124i	−0.364671	+	0.631628i	−0.988723	−	0.149754i	$-0.952152\pi$
$277$	−6.06933	+	10.5124i	−0.364671	+	0.631628i	0.624053	+	0.781382i	$0.285485\pi$
$278$		0			0
$279$	−10.5387			−0.630936
$280$		0			0
$281$	−6.34537			−0.378533			−0.189267	−	0.981926i	$-0.560611\pi$
$281$	−6.34537			−0.378533			−0.189267	+	0.981926i	$0.560611\pi$
$282$		0			0
$283$	−6.80964	+	11.7947i	−0.404791	+	0.701119i	−0.994297	−	0.106645i	$-0.965989\pi$
$283$	−6.80964	+	11.7947i	−0.404791	+	0.701119i	0.589506	+	0.807764i	$0.299323\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.660408	+	2.74653i	−0.0389827	+	0.162122i
$288$		0			0
$289$	8.47189	+	14.6738i	0.498347	+	0.863162i
$290$		0			0
$291$	−1.15561	+	2.00157i	−0.0677430	+	0.117334i
$292$		0			0
$293$	−15.5221			−0.906813			−0.453406	−	0.891304i	$-0.649791\pi$
$293$	−15.5221			−0.906813			−0.453406	+	0.891304i	$0.649791\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.46616	+	2.53947i	−0.0850753	+	0.147355i
$298$		0			0
$299$	19.5274	+	33.8225i	1.12930	+	1.95600i
$300$		0			0
$301$	−6.05987	+	25.2020i	−0.349285	+	1.45262i
$302$		0			0
$303$	3.92103	+	6.79142i	0.225257	+	0.390157i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	13.4406			0.767093			0.383547	−	0.923521i	$-0.374703\pi$
$307$	13.4406			0.767093			0.383547	+	0.923521i	$0.374703\pi$
$308$		0			0
$309$	−4.08058			−0.232136
$310$		0			0
$311$	−1.22580	+	2.12314i	−0.0695085	+	0.120392i	−0.898685	−	0.438595i	$-0.855476\pi$
$311$	−1.22580	+	2.12314i	−0.0695085	+	0.120392i	0.829177	+	0.558987i	$0.188810\pi$
$312$		0			0
$313$	−4.95971	−	8.59047i	−0.280340	−	0.485562i	0.691129	−	0.722732i	$-0.257114\pi$
$313$	−4.95971	−	8.59047i	−0.280340	−	0.485562i	−0.971468	+	0.237169i	$0.923780\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−12.9975	−	22.5124i	−0.730013	−	1.26442i	−0.956877	−	0.290494i	$-0.906180\pi$
$317$	−12.9975	−	22.5124i	−0.730013	−	1.26442i	0.226863	−	0.973927i	$-0.427153\pi$
$318$		0			0
$319$	−8.84900	+	15.3269i	−0.495449	+	0.858142i
$320$		0			0
$321$	18.3467			1.02401
$322$		0			0
$323$	1.12389			0.0625350
$324$		0			0
$325$		0			0
$326$		0			0
$327$	5.20719	+	9.01912i	0.287958	+	0.498759i
$328$		0			0
$329$	9.41938	−	2.78653i	0.519307	−	0.153626i
$330$		0			0
$331$	−3.76613	−	6.52313i	−0.207005	−	0.358544i	0.743764	−	0.668442i	$-0.233038\pi$
$331$	−3.76613	−	6.52313i	−0.207005	−	0.358544i	−0.950770	+	0.309898i	$0.899705\pi$
$332$		0			0
$333$	1.53706	−	2.66227i	0.0842306	−	0.145892i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−15.7050			−0.855505			−0.427752	−	0.903896i	$-0.640694\pi$
$337$	−15.7050			−0.855505			−0.427752	+	0.903896i	$0.640694\pi$
$338$		0			0
$339$	1.07413	−	1.86044i	0.0583386	−	0.101045i
$340$		0			0
$341$	15.4515	+	26.7627i	0.836743	+	1.44928i
$342$		0			0
$343$	12.0428	−	14.0702i	0.650252	−	0.759718i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.60639	−	7.97850i	0.247284	−	0.428309i	−0.715487	−	0.698626i	$-0.753795\pi$
$347$	4.60639	−	7.97850i	0.247284	−	0.428309i	0.962771	+	0.270317i	$0.0871286\pi$
$348$		0			0
$349$	21.1518			1.13223			0.566116	−	0.824326i	$-0.308445\pi$
$349$	21.1518			1.13223			0.566116	+	0.824326i	$0.308445\pi$
$350$		0			0
$351$	−5.76936			−0.307945
$352$		0			0
$353$	7.48969	−	12.9725i	0.398636	−	0.690457i	−0.594922	−	0.803783i	$-0.702817\pi$
$353$	7.48969	−	12.9725i	0.398636	−	0.690457i	0.993558	+	0.113326i	$0.0361504\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	0.601517	−	0.177947i	0.0318357	−	0.00941794i
$358$		0			0
$359$	−10.4823	−	18.1559i	−0.553236	−	0.958233i	−0.998038	−	0.0626045i	$-0.980059\pi$
$359$	−10.4823	−	18.1559i	−0.553236	−	0.958233i	0.444802	−	0.895629i	$-0.353274\pi$
$360$		0			0
$361$	−1.73530	+	3.00563i	−0.0913316	+	0.158191i
$362$		0			0
$363$	−2.40149			−0.126045
$364$		0			0
$365$		0			0
$366$		0			0
$367$	9.55732	−	16.5538i	0.498888	−	0.864099i	−0.501111	−	0.865383i	$-0.667075\pi$
$367$	9.55732	−	16.5538i	0.498888	−	0.864099i	0.999999	+	0.00128371i	$0.000408617\pi$
$368$		0			0
$369$	−0.533839	−	0.924636i	−0.0277906	−	0.0481347i
$370$		0			0
$371$	−21.1161	−	20.0526i	−1.09629	−	1.04108i
$372$		0			0
$373$	3.25713	+	5.64151i	0.168648	+	0.292106i	0.937945	−	0.346785i	$-0.112727\pi$
$373$	3.25713	+	5.64151i	0.168648	+	0.292106i	−0.769297	+	0.638891i	$0.779393\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−34.8209			−1.79337
$378$		0			0
$379$	14.4254			0.740984			0.370492	−	0.928836i	$-0.379189\pi$
$379$	14.4254			0.740984			0.370492	+	0.928836i	$0.379189\pi$
$380$		0			0
$381$	0.912287	−	1.58013i	0.0467379	−	0.0809524i
$382$		0			0
$383$	−12.6450	−	21.9018i	−0.646131	−	1.11913i	−0.984039	−	0.177952i	$-0.943053\pi$
$383$	−12.6450	−	21.9018i	−0.646131	−	1.11913i	0.337908	−	0.941179i	$-0.390281\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−4.89848	−	8.48442i	−0.249004	−	0.431287i
$388$		0			0
$389$	−13.4984	+	23.3799i	−0.684395	+	1.18541i	0.289232	+	0.957259i	$0.406600\pi$
$389$	−13.4984	+	23.3799i	−0.684395	+	1.18541i	−0.973627	+	0.228148i	$0.926733\pi$
$390$		0			0
$391$	1.60496			0.0811663
$392$		0			0
$393$	2.70626			0.136513
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−15.8082	−	27.3806i	−0.793391	−	1.37419i	−0.923856	−	0.382741i	$-0.874980\pi$
$397$	−15.8082	−	27.3806i	−0.793391	−	1.37419i	0.130464	−	0.991453i	$-0.458353\pi$
$398$		0			0
$399$	−2.93210	+	12.1941i	−0.146789	+	0.610470i
$400$		0			0
$401$	6.24497	+	10.8166i	0.311859	+	0.540156i	0.978765	−	0.204986i	$-0.0657150\pi$
$401$	6.24497	+	10.8166i	0.311859	+	0.540156i	−0.666906	+	0.745142i	$0.732382\pi$
$402$		0			0
$403$	−30.4008	+	52.6557i	−1.51437	+	2.62297i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−9.01433			−0.446824
$408$		0			0
$409$	−6.28039	+	10.8779i	−0.310545	+	0.537880i	−0.978480	−	0.206339i	$-0.933845\pi$
$409$	−6.28039	+	10.8779i	−0.310545	+	0.537880i	0.667935	+	0.744219i	$0.267178\pi$
$410$		0			0
$411$	−5.00251	−	8.66460i	−0.246756	−	0.427393i
$412$		0			0
$413$	17.8665	+	16.9666i	0.879152	+	0.834874i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.03635	−	1.79501i	0.0507502	−	0.0879018i
$418$		0			0
$419$	−17.6520			−0.862357			−0.431179	−	0.902267i	$-0.641902\pi$
$419$	−17.6520			−0.862357			−0.431179	+	0.902267i	$0.641902\pi$
$420$		0			0
$421$	29.2634			1.42621			0.713106	−	0.701056i	$-0.247288\pi$
$421$	29.2634			1.42621			0.713106	+	0.701056i	$0.247288\pi$
$422$		0			0
$423$	−1.85635	+	3.21530i	−0.0902590	+	0.156333i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−20.6447	+	6.10730i	−0.999065	+	0.295553i
$428$		0			0
$429$	8.45881	+	14.6511i	0.408395	+	0.707361i
$430$		0			0
$431$	−14.4613	+	25.0477i	−0.696577	+	1.20651i	0.273069	+	0.961994i	$0.411961\pi$
$431$	−14.4613	+	25.0477i	−0.696577	+	1.20651i	−0.969646	+	0.244512i	$0.921372\pi$
$432$		0			0
$433$	10.0338			0.482192			0.241096	−	0.970501i	$-0.422493\pi$
$433$	10.0338			0.482192			0.241096	+	0.970501i	$0.422493\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−16.0444	+	27.7898i	−0.767510	+	1.32937i
$438$		0			0
$439$	8.40744	+	14.5621i	0.401265	+	0.695012i	0.993879	−	0.110475i	$-0.0352372\pi$
$439$	8.40744	+	14.5621i	0.401265	+	0.695012i	−0.592614	+	0.805487i	$0.701904\pi$
$440$		0			0
$441$	0.361419	+	6.99066i	0.0172104	+	0.332889i
$442$		0			0
$443$	5.09030	+	8.81665i	0.241847	+	0.418892i	0.961241	−	0.275711i	$-0.0889133\pi$
$443$	5.09030	+	8.81665i	0.241847	+	0.418892i	−0.719393	+	0.694603i	$0.755580\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−1.10317			−0.0521780
$448$		0			0
$449$	−33.9937			−1.60426			−0.802131	−	0.597148i	$-0.796300\pi$
$449$	−33.9937			−1.60426			−0.802131	+	0.597148i	$0.796300\pi$
$450$		0			0
$451$	−1.56539	+	2.71133i	−0.0737112	+	0.127672i
$452$		0			0
$453$	−5.23158	−	9.06136i	−0.245801	−	0.425740i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	11.8911	+	20.5960i	0.556243	+	0.963442i	0.997806	+	0.0662113i	$0.0210911\pi$
$457$	11.8911	+	20.5960i	0.556243	+	0.963442i	−0.441562	+	0.897231i	$0.645576\pi$
$458$		0			0
$459$	−0.118546	+	0.205328i	−0.00553325	+	0.00958387i
$460$		0			0
$461$	−35.2649			−1.64245			−0.821224	−	0.570606i	$-0.806708\pi$
$461$	−35.2649			−1.64245			−0.821224	+	0.570606i	$0.806708\pi$
$462$		0			0
$463$	38.6505			1.79624			0.898120	−	0.439750i	$-0.144933\pi$
$463$	38.6505			1.79624			0.898120	+	0.439750i	$0.144933\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.42910	−	7.67142i	−0.204954	−	0.354991i	0.745164	−	0.666881i	$-0.232371\pi$
$467$	−4.42910	−	7.67142i	−0.204954	−	0.354991i	−0.950118	+	0.311890i	$0.899038\pi$
$468$		0			0
$469$	4.30427	+	4.08749i	0.198753	+	0.188743i
$470$		0			0
$471$	4.53083	+	7.84763i	0.208770	+	0.361600i
$472$		0			0
$473$	−14.3639	+	24.8791i	−0.660454	+	1.14394i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	11.0064			0.503951
$478$		0			0
$479$	4.26797	−	7.39235i	0.195009	−	0.337765i	−0.751895	−	0.659283i	$-0.770860\pi$
$479$	4.26797	−	7.39235i	0.195009	−	0.337765i	0.946903	+	0.321518i	$0.104193\pi$
$480$		0			0
$481$	−8.86787	−	15.3596i	−0.404340	−	0.700337i
$482$		0			0
$483$	−4.18716	+	17.4137i	−0.190522	+	0.792351i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−0.984545	+	1.70528i	−0.0446140	+	0.0772737i	−0.887470	−	0.460865i	$-0.847539\pi$
$487$	−0.984545	+	1.70528i	−0.0446140	+	0.0772737i	0.842856	+	0.538139i	$0.180872\pi$
$488$		0			0
$489$	8.33883			0.377095
$490$		0			0
$491$	21.4549			0.968246			0.484123	−	0.875000i	$-0.339139\pi$
$491$	21.4549			0.968246			0.484123	+	0.875000i	$0.339139\pi$
$492$		0			0
$493$	−0.715483	+	1.23925i	−0.0322237	+	0.0558131i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	7.32485	−	30.4629i	0.328565	−	1.36645i
$498$		0			0
$499$	7.47239	+	12.9426i	0.334510	+	0.579389i	0.983391	−	0.181502i	$-0.0580958\pi$
$499$	7.47239	+	12.9426i	0.334510	+	0.579389i	−0.648880	+	0.760890i	$0.724762\pi$
$500$		0			0
$501$	5.14431	−	8.91021i	0.229831	−	0.398079i
$502$		0			0
$503$	−10.9715			−0.489195			−0.244597	−	0.969625i	$-0.578656\pi$
$503$	−10.9715			−0.489195			−0.244597	+	0.969625i	$0.578656\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−10.1427	+	17.5677i	−0.450455	+	0.780211i
$508$		0			0
$509$	18.6050	+	32.2247i	0.824650	+	1.42834i	0.902186	+	0.431347i	$0.141961\pi$
$509$	18.6050	+	32.2247i	0.824650	+	1.42834i	−0.0775359	+	0.996990i	$0.524705\pi$
$510$		0			0
$511$	−7.28454	−	6.91766i	−0.322249	−	0.306019i
$512$		0			0
$513$	−2.37016	−	4.10523i	−0.104645	−	0.181251i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	10.8869			0.478803
$518$		0			0
$519$	17.2937			0.759111
$520$		0			0
$521$	−8.24999	+	14.2894i	−0.361439	+	0.626030i	−0.988198	−	0.153183i	$-0.951048\pi$
$521$	−8.24999	+	14.2894i	−0.361439	+	0.626030i	0.626759	+	0.779213i	$0.284381\pi$
$522$		0			0
$523$	−21.1747	−	36.6757i	−0.925907	−	1.60372i	−0.790097	−	0.612982i	$-0.789970\pi$
$523$	−21.1747	−	36.6757i	−0.925907	−	1.60372i	−0.135810	−	0.990735i	$-0.543364\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.24932	+	2.16389i	0.0544213	+	0.0942605i
$528$		0			0
$529$	−11.4121	+	19.7663i	−0.496178	+	0.859406i
$530$		0			0
$531$	−9.31265			−0.404135
$532$		0			0
$533$	−6.15982			−0.266811
$534$		0			0
$535$		0			0
$536$		0			0
$537$	5.50967	+	9.54303i	0.237760	+	0.411812i
$538$		0			0
$539$	17.2226	−	11.1672i	0.741832	−	0.481007i
$540$		0			0
$541$	21.1579	+	36.6466i	0.909650	+	1.57556i	0.814550	+	0.580093i	$0.196984\pi$
$541$	21.1579	+	36.6466i	0.909650	+	1.57556i	0.0951000	+	0.995468i	$0.469683\pi$
$542$		0			0
$543$	−2.26842	+	3.92902i	−0.0973473	+	0.168611i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.34528			−0.0575199			−0.0287599	−	0.999586i	$-0.509156\pi$
$547$	−1.34528			−0.0575199			−0.0287599	+	0.999586i	$0.509156\pi$
$548$		0			0
$549$	4.06861	−	7.04704i	0.173644	−	0.300760i
$550$		0			0
$551$	−14.3051	−	24.7771i	−0.609416	−	1.05554i
$552$		0			0
$553$	0.0443428	−	0.0131179i	0.00188565	−	0.000557831i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.49493	+	2.58930i	−0.0633424	+	0.109712i	−0.895958	−	0.444140i	$-0.853509\pi$
$557$	−1.49493	+	2.58930i	−0.0633424	+	0.109712i	0.832615	+	0.553852i	$0.186843\pi$
$558$		0			0
$559$	−56.5222			−2.39063
$560$		0			0
$561$	0.695230			0.0293526
$562$		0			0
$563$	9.10174	−	15.7647i	0.383592	−	0.664402i	−0.607980	−	0.793952i	$-0.708020\pi$
$563$	9.10174	−	15.7647i	0.383592	−	0.664402i	0.991573	+	0.129550i	$0.0413534\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.91852	−	1.82189i	−0.0805702	−	0.0765123i
$568$		0			0
$569$	9.88700	+	17.1248i	0.414484	+	0.717908i	0.995374	−	0.0960741i	$-0.0306286\pi$
$569$	9.88700	+	17.1248i	0.414484	+	0.717908i	−0.580890	+	0.813982i	$0.697295\pi$
$570$		0			0
$571$	9.87481	−	17.1037i	0.413248	−	0.715767i	−0.581995	−	0.813193i	$-0.697728\pi$
$571$	9.87481	−	17.1037i	0.413248	−	0.715767i	0.995243	+	0.0974259i	$0.0310609\pi$
$572$		0			0
$573$	8.68052			0.362634
$574$		0			0
$575$		0			0
$576$		0			0
$577$	8.53616	−	14.7851i	0.355365	−	0.615510i	−0.631815	−	0.775119i	$-0.717690\pi$
$577$	8.53616	−	14.7851i	0.355365	−	0.615510i	0.987180	+	0.159609i	$0.0510233\pi$
$578$		0			0
$579$	−3.53061	−	6.11520i	−0.146727	−	0.254139i
$580$		0			0
$581$	−4.51639	+	18.7829i	−0.187371	+	0.779247i
$582$		0			0
$583$	−16.1372	−	27.9505i	−0.668336	−	1.15759i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	17.5308			0.723575			0.361787	−	0.932261i	$-0.382167\pi$
$587$	17.5308			0.723575			0.361787	+	0.932261i	$0.382167\pi$
$588$		0			0
$589$	−49.9568			−2.05844
$590$		0			0
$591$	−1.79446	+	3.10809i	−0.0738141	+	0.127850i
$592$		0			0
$593$	−13.0781	−	22.6519i	−0.537052	−	0.930201i	−0.999061	−	0.0433259i	$-0.986205\pi$
$593$	−13.0781	−	22.6519i	−0.537052	−	0.930201i	0.462009	−	0.886875i	$-0.347129\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.49126	+	2.58294i	0.0610332	+	0.105713i
$598$		0			0
$599$	−14.9595	+	25.9107i	−0.611229	+	1.05868i	0.379804	+	0.925067i	$0.375991\pi$
$599$	−14.9595	+	25.9107i	−0.611229	+	1.05868i	−0.991034	+	0.133614i	$0.957342\pi$
$600$		0			0
$601$	15.6887			0.639955			0.319977	−	0.947425i	$-0.396325\pi$
$601$	15.6887			0.639955			0.319977	+	0.947425i	$0.396325\pi$
$602$		0			0
$603$	−2.24354			−0.0913640
$604$		0			0
$605$		0			0
$606$		0			0
$607$	17.3732	+	30.0913i	0.705156	+	1.22137i	0.966635	+	0.256157i	$0.0824564\pi$
$607$	17.3732	+	30.0913i	0.705156	+	1.22137i	−0.261479	+	0.965209i	$0.584210\pi$
$608$		0			0
$609$	−11.5792	−	10.9960i	−0.469213	−	0.445581i
$610$		0			0
$611$	10.7100	+	18.5502i	0.433279	+	0.750461i
$612$		0			0
$613$	3.17954	−	5.50712i	0.128420	−	0.222430i	−0.794644	−	0.607075i	$-0.792343\pi$
$613$	3.17954	−	5.50712i	0.128420	−	0.222430i	0.923065	+	0.384645i	$0.125676\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	25.1778			1.01362			0.506811	−	0.862057i	$-0.330824\pi$
$617$	25.1778			1.01362			0.506811	+	0.862057i	$0.330824\pi$
$618$		0			0
$619$	−3.35963	+	5.81904i	−0.135035	+	0.233887i	−0.925611	−	0.378477i	$-0.876448\pi$
$619$	−3.35963	+	5.81904i	−0.135035	+	0.233887i	0.790576	+	0.612364i	$0.209781\pi$
$620$		0			0
$621$	−3.38468	−	5.86244i	−0.135822	−	0.235251i
$622$		0			0
$623$	45.5445	−	13.4734i	1.82470	−	0.539801i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−6.95007	+	12.0379i	−0.277559	+	0.480746i
$628$		0			0
$629$	−0.728851			−0.0290612
$630$		0			0
$631$	0.439228			0.0174854			0.00874269	−	0.999962i	$-0.497217\pi$
$631$	0.439228			0.0174854			0.00874269	+	0.999962i	$0.497217\pi$
$632$		0			0
$633$	10.7136	−	18.5566i	0.425829	−	0.737558i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	35.9708	+	18.3600i	1.42521	+	0.727450i
$638$		0			0
$639$	5.92103	+	10.2555i	0.234232	+	0.405702i
$640$		0			0
$641$	5.53886	−	9.59358i	0.218772	−	0.378924i	−0.735661	−	0.677350i	$-0.763128\pi$
$641$	5.53886	−	9.59358i	0.218772	−	0.378924i	0.954433	+	0.298426i	$0.0964617\pi$
$642$		0			0
$643$	−16.2243			−0.639826			−0.319913	−	0.947447i	$-0.603654\pi$
$643$	−16.2243			−0.639826			−0.319913	+	0.947447i	$0.603654\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	12.9813	−	22.4844i	0.510349	−	0.883951i	−0.489579	−	0.871959i	$-0.662849\pi$
$647$	12.9813	−	22.4844i	0.510349	−	0.883951i	0.999928	−	0.0119921i	$-0.00381728\pi$
$648$		0			0
$649$	13.6538	+	23.6492i	0.535960	+	0.928310i
$650$		0			0
$651$	−26.7374	+	7.90972i	−1.04792	+	0.310006i
$652$		0			0
$653$	3.66184	+	6.34249i	0.143299	+	0.248201i	0.928737	−	0.370739i	$-0.120896\pi$
$653$	3.66184	+	6.34249i	0.143299	+	0.248201i	−0.785438	+	0.618940i	$0.787562\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	3.79697			0.148134
$658$		0			0
$659$	2.45499			0.0956328			0.0478164	−	0.998856i	$-0.484774\pi$
$659$	2.45499			0.0956328			0.0478164	+	0.998856i	$0.484774\pi$
$660$		0			0
$661$	7.64417	−	13.2401i	0.297324	−	0.514980i	−0.678199	−	0.734878i	$-0.737239\pi$
$661$	7.64417	−	13.2401i	0.297324	−	0.514980i	0.975523	+	0.219898i	$0.0705726\pi$
$662$		0			0
$663$	0.683934	+	1.18461i	0.0265618	+	0.0460064i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−20.4282	−	35.3827i	−0.790983	−	1.37002i
$668$		0			0
$669$	8.19845	−	14.2001i	0.316971	−	0.549009i
$670$		0			0
$671$	−23.8610			−0.921142
$672$		0			0
$673$	39.7823			1.53349			0.766747	−	0.641950i	$-0.221874\pi$
$673$	39.7823			1.53349			0.766747	+	0.641950i	$0.221874\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	16.2332	+	28.1167i	0.623892	+	1.08061i	0.988754	+	0.149551i	$0.0477827\pi$
$677$	16.2332	+	28.1167i	0.623892	+	1.08061i	−0.364862	+	0.931061i	$0.618884\pi$
$678$		0			0
$679$	−1.42960	+	5.94545i	−0.0548628	+	0.228165i
$680$		0			0
$681$	4.76685	+	8.25642i	0.182666	+	0.316387i
$682$		0			0
$683$	5.18625	−	8.98285i	0.198446	−	0.343719i	−0.749578	−	0.661916i	$-0.769744\pi$
$683$	5.18625	−	8.98285i	0.198446	−	0.343719i	0.948025	+	0.318196i	$0.103077\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	18.1197			0.691311
$688$		0			0
$689$	31.7501	−	54.9927i	1.20958	−	2.09506i
$690$		0			0
$691$	2.73852	+	4.74326i	0.104178	+	0.180442i	0.913402	−	0.407058i	$-0.133445\pi$
$691$	2.73852	+	4.74326i	0.104178	+	0.180442i	−0.809224	+	0.587500i	$0.800112\pi$
$692$		0			0
$693$	−1.81378	+	7.54320i	−0.0688996	+	0.286542i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−0.126569	+	0.219224i	−0.00479414	+	0.00830370i
$698$		0			0
$699$	12.0544			0.455939
$700$		0			0
$701$	29.8292			1.12663			0.563317	−	0.826241i	$-0.309525\pi$
$701$	29.8292			1.12663			0.563317	+	0.826241i	$0.309525\pi$
$702$		0			0
$703$	7.28617	−	12.6200i	0.274803	−	0.475973i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	15.0451	+	14.2874i	0.565830	+	0.537332i
$708$		0			0
$709$	−20.0525	−	34.7319i	−0.753086	−	1.30438i	−0.946320	−	0.323231i	$-0.895231\pi$
$709$	−20.0525	−	34.7319i	−0.753086	−	1.30438i	0.193234	−	0.981153i	$-0.438102\pi$
$710$		0			0
$711$	−0.00873900	+	0.0151364i	−0.000327738	+	0.000567659i
$712$		0			0
$713$	−71.3403			−2.67172
$714$		0			0
$715$		0			0
$716$		0			0
$717$	10.6934	−	18.5215i	0.399352	−	0.691698i
$718$		0			0
$719$	10.5888	+	18.3403i	0.394895	+	0.683979i	0.993088	−	0.117374i	$-0.0374476\pi$
$719$	10.5888	+	18.3403i	0.394895	+	0.683979i	−0.598193	+	0.801352i	$0.704114\pi$
$720$		0			0
$721$	−10.3527	+	3.06263i	−0.385554	+	0.114058i
$722$		0			0
$723$	−8.59443	−	14.8860i	−0.319630	−	0.553616i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−12.3642			−0.458562			−0.229281	−	0.973360i	$-0.573638\pi$
$727$	−12.3642			−0.458562			−0.229281	+	0.973360i	$0.573638\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−1.16139	+	2.01159i	−0.0429556	+	0.0744013i
$732$		0			0
$733$	18.2268	+	31.5698i	0.673222	+	1.16606i	0.976985	+	0.213308i	$0.0684237\pi$
$733$	18.2268	+	31.5698i	0.673222	+	1.16606i	−0.303763	+	0.952748i	$0.598243\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.28939	+	5.69739i	0.121166	+	0.209866i
$738$		0			0
$739$	19.2136	−	33.2790i	0.706785	−	1.22419i	−0.259258	−	0.965808i	$-0.583478\pi$
$739$	19.2136	−	33.2790i	0.706785	−	1.22419i	0.966043	−	0.258380i	$-0.0831886\pi$
$740$		0			0
$741$	−27.3486			−1.00468
$742$		0			0
$743$	38.1561			1.39981			0.699906	−	0.714235i	$-0.253225\pi$
$743$	38.1561			1.39981			0.699906	+	0.714235i	$0.253225\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−3.65081	−	6.32339i	−0.133576	−	0.231361i
$748$		0			0
$749$	46.5468	−	13.7699i	1.70078	−	0.503142i
$750$		0			0
$751$	6.58058	+	11.3979i	0.240129	+	0.415915i	0.960751	−	0.277413i	$-0.0894770\pi$
$751$	6.58058	+	11.3979i	0.240129	+	0.415915i	−0.720622	+	0.693328i	$0.756144\pi$
$752$		0			0
$753$	−11.5969	+	20.0865i	−0.422616	+	0.731992i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.92272			0.0698826			0.0349413	−	0.999389i	$-0.488876\pi$
$757$	1.92272			0.0698826			0.0349413	+	0.999389i	$0.488876\pi$
$758$		0			0
$759$	−9.92497	+	17.1905i	−0.360253	+	0.623977i
$760$		0			0
$761$	9.10658	+	15.7731i	0.330113	+	0.571773i	0.982534	−	0.186084i	$-0.0595797\pi$
$761$	9.10658	+	15.7731i	0.330113	+	0.571773i	−0.652420	+	0.757857i	$0.726246\pi$
$762$		0			0
$763$	19.9802	+	18.9739i	0.723331	+	0.686901i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−26.8640	+	46.5298i	−0.970003	+	1.68009i
$768$		0			0
$769$	32.1465			1.15923			0.579617	−	0.814889i	$-0.303202\pi$
$769$	32.1465			1.15923			0.579617	+	0.814889i	$0.303202\pi$
$770$		0			0
$771$	26.1561			0.941990
$772$		0			0
$773$	−14.6186	+	25.3202i	−0.525795	+	0.910704i	0.473753	+	0.880658i	$0.342899\pi$
$773$	−14.6186	+	25.3202i	−0.525795	+	0.910704i	−0.999549	+	0.0300465i	$0.990434\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	1.90149	−	7.90798i	0.0682155	−	0.283697i
$778$		0			0
$779$	−2.53057	−	4.38307i	−0.0906669	−	0.157040i
$780$		0			0
$781$	17.3624	−	30.0725i	0.621274	−	1.07608i
$782$		0			0
$783$	6.03549			0.215691
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−3.60639	+	6.24645i	−0.128554	+	0.222662i	−0.923117	−	0.384520i	$-0.874367\pi$
$787$	−3.60639	+	6.24645i	−0.128554	+	0.222662i	0.794563	+	0.607182i	$0.207700\pi$
$788$		0			0
$789$	−3.84991	−	6.66823i	−0.137060	−	0.237395i
$790$		0			0
$791$	1.32879	−	5.52624i	0.0472465	−	0.196490i
$792$		0			0
$793$	−23.4733	−	40.6569i	−0.833561	−	1.44377i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−32.3827			−1.14706			−0.573528	−	0.819186i	$-0.694425\pi$
$797$	−32.3827			−1.14706			−0.573528	+	0.819186i	$0.694425\pi$
$798$		0			0
$799$	0.880253			0.0311411
$800$		0			0
$801$	−8.97583	+	15.5466i	−0.317146	+	0.549312i
$802$		0			0
$803$	−5.56696	−	9.64226i	−0.196454	−	0.340268i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−12.5194	−	21.6842i	−0.440704	−	0.763321i
$808$		0			0
$809$	−16.2132	+	28.0821i	−0.570026	+	0.987313i	0.426537	+	0.904470i	$0.359733\pi$
$809$	−16.2132	+	28.0821i	−0.570026	+	0.987313i	−0.996563	+	0.0828431i	$0.973600\pi$
$810$		0			0
$811$	5.01118			0.175966			0.0879832	−	0.996122i	$-0.471958\pi$
$811$	5.01118			0.175966			0.0879832	+	0.996122i	$0.471958\pi$
$812$		0			0
$813$	19.0885			0.669461
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−23.2204	−	40.2188i	−0.812377	−	1.40708i
$818$		0			0
$819$	−14.6372	+	4.33013i	−0.511466	+	0.151307i
$820$		0			0
$821$	−25.5256	−	44.2116i	−0.890849	−	1.54300i	−0.838860	−	0.544348i	$-0.816777\pi$
$821$	−25.5256	−	44.2116i	−0.890849	−	1.54300i	−0.0519891	−	0.998648i	$-0.516556\pi$
$822$		0			0
$823$	−25.7104	+	44.5317i	−0.896207	+	1.55228i	−0.0639036	+	0.997956i	$0.520355\pi$
$823$	−25.7104	+	44.5317i	−0.896207	+	1.55228i	−0.832303	+	0.554320i	$0.812978\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	11.7679			0.409211			0.204605	−	0.978845i	$-0.434409\pi$
$827$	11.7679			0.409211			0.204605	+	0.978845i	$0.434409\pi$
$828$		0			0
$829$	−21.0994	+	36.5453i	−0.732814	+	1.26927i	0.222862	+	0.974850i	$0.428460\pi$
$829$	−21.0994	+	36.5453i	−0.732814	+	1.26927i	−0.955676	+	0.294421i	$0.904873\pi$
$830$		0			0
$831$	−6.06933	−	10.5124i	−0.210543	−	0.364671i
$832$		0			0
$833$	1.39253	−	0.902924i	0.0482484	−	0.0312845i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	5.26936	−	9.12679i	0.182136	−	0.315468i
$838$		0			0
$839$	−34.6127			−1.19496			−0.597482	−	0.801882i	$-0.703832\pi$
$839$	−34.6127			−1.19496			−0.597482	+	0.801882i	$0.703832\pi$
$840$		0			0
$841$	7.42713			0.256108
$842$		0			0
$843$	3.17269	−	5.49525i	0.109273	−	0.189267i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−6.09273	+	1.80241i	−0.209349	+	0.0619316i
$848$		0			0
$849$	−6.80964	−	11.7947i	−0.233706	−	0.404791i
$850$		0			0
$851$	10.4049	−	18.0219i	0.356676	−	0.617782i
$852$		0			0
$853$	−7.87710			−0.269707			−0.134853	−	0.990866i	$-0.543056\pi$
$853$	−7.87710			−0.269707			−0.134853	+	0.990866i	$0.543056\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	2.24103	−	3.88158i	0.0765522	−	0.132592i	−0.825208	−	0.564829i	$-0.808942\pi$
$857$	2.24103	−	3.88158i	0.0765522	−	0.132592i	0.901760	+	0.432237i	$0.142275\pi$
$858$		0			0
$859$	−13.2214	−	22.9002i	−0.451110	−	0.781345i	0.547345	−	0.836907i	$-0.315638\pi$
$859$	−13.2214	−	22.9002i	−0.451110	−	0.781345i	−0.998455	+	0.0555615i	$0.982305\pi$
$860$		0			0
$861$	−2.04836	−	1.94519i	−0.0698079	−	0.0662920i
$862$		0			0
$863$	19.0000	+	32.9090i	0.646768	+	1.12024i	0.983890	+	0.178775i	$0.0572133\pi$
$863$	19.0000	+	32.9090i	0.646768	+	1.12024i	−0.337122	+	0.941461i	$0.609453\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−16.9438			−0.575441
$868$		0			0
$869$	0.0512511			0.00173858
$870$		0			0
$871$	−6.47189	+	11.2096i	−0.219292	+	0.379824i
$872$		0			0
$873$	−1.15561	−	2.00157i	−0.0391115	−	0.0677430i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	6.42910	+	11.1355i	0.217095	+	0.376020i	0.953919	−	0.300065i	$-0.0970085\pi$
$877$	6.42910	+	11.1355i	0.217095	+	0.376020i	−0.736823	+	0.676085i	$0.763675\pi$
$878$		0			0
$879$	7.76107	−	13.4426i	0.261774	−	0.453406i
$880$		0			0
$881$	32.9744			1.11094			0.555468	−	0.831538i	$-0.312539\pi$
$881$	32.9744			1.11094			0.555468	+	0.831538i	$0.312539\pi$
$882$		0			0
$883$	20.3321			0.684229			0.342115	−	0.939658i	$-0.388857\pi$
$883$	20.3321			0.684229			0.342115	+	0.939658i	$0.388857\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−20.1287	−	34.8639i	−0.675856	−	1.17062i	−0.976218	−	0.216791i	$-0.930441\pi$
$887$	−20.1287	−	34.8639i	−0.675856	−	1.17062i	0.300362	−	0.953825i	$-0.402892\pi$
$888$		0			0
$889$	1.12858	−	4.69359i	0.0378515	−	0.157418i
$890$		0			0
$891$	−1.46616	−	2.53947i	−0.0491182	−	0.0850753i
$892$		0			0
$893$	−8.79970	+	15.2415i	−0.294471	+	0.510039i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−39.0548			−1.30400
$898$		0			0
$899$	31.8031	−	55.0847i	1.06069	−	1.83718i
$900$		0			0
$901$	−1.30477	−	2.25993i	−0.0434682	−	0.0752891i
$902$		0			0
$903$	−18.7957	−	17.8490i	−0.625480	−	0.593978i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−24.0758	+	41.7005i	−0.799423	+	1.38464i	0.120569	+	0.992705i	$0.461528\pi$
$907$	−24.0758	+	41.7005i	−0.799423	+	1.38464i	−0.919992	+	0.391936i	$0.871805\pi$
$908$		0			0
$909$	−7.84205			−0.260104
$910$		0			0
$911$	−30.2224			−1.00131			−0.500656	−	0.865646i	$-0.666908\pi$
$911$	−30.2224			−1.00131			−0.500656	+	0.865646i	$0.666908\pi$
$912$		0			0
$913$	−10.7054	+	18.5422i	−0.354295	+	0.613658i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	6.86595	−	2.03115i	0.226734	−	0.0670746i
$918$		0			0
$919$	−12.6387	−	21.8908i	−0.416911	−	0.722111i	0.578716	−	0.815529i	$-0.303554\pi$
$919$	−12.6387	−	21.8908i	−0.416911	−	0.722111i	−0.995627	+	0.0934183i	$0.970221\pi$
$920$		0			0
$921$	−6.72028	+	11.6399i	−0.221441	+	0.383547i
$922$		0			0
$923$	68.3210			2.24881
$924$		0			0
$925$		0			0
$926$		0			0
$927$	2.04029	−	3.53388i	0.0670118	−	0.116068i
$928$		0			0
$929$	13.8502	+	23.9892i	0.454409	+	0.787060i	0.998654	−	0.0518664i	$-0.0165170\pi$
$929$	13.8502	+	23.9892i	0.454409	+	0.787060i	−0.544245	+	0.838927i	$0.683184\pi$
$930$		0			0
$931$	1.71324	+	33.1380i	0.0561492	+	1.08605i
$932$		0			0
$933$	−1.22580	−	2.12314i	−0.0401308	−	0.0695085i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−30.8163			−1.00673			−0.503363	−	0.864075i	$-0.667904\pi$
$937$	−30.8163			−1.00673			−0.503363	+	0.864075i	$0.667904\pi$
$938$		0			0
$939$	9.91942			0.323708
$940$		0			0
$941$	14.1180	−	24.4532i	0.460235	−	0.797151i	−0.538737	−	0.842474i	$-0.681098\pi$
$941$	14.1180	−	24.4532i	0.460235	−	0.797151i	0.998972	+	0.0453231i	$0.0144317\pi$
$942$		0			0
$943$	−3.61375	−	6.25919i	−0.117680	−	0.203827i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.49785	−	2.59436i	−0.0486736	−	0.0843052i	0.840662	−	0.541560i	$-0.182166\pi$
$947$	−1.49785	−	2.59436i	−0.0486736	−	0.0843052i	−0.889336	+	0.457255i	$0.848833\pi$
$948$		0			0
$949$	10.9530	−	18.9712i	0.355550	−	0.615831i
$950$		0			0
$951$	25.9950			0.842947
$952$		0			0
$953$	10.0423			0.325303			0.162651	−	0.986684i	$-0.447995\pi$
$953$	10.0423			0.325303			0.162651	+	0.986684i	$0.447995\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−8.84900	−	15.3269i	−0.286047	−	0.495449i
$958$		0			0
$959$	−19.1948	−	18.2281i	−0.619832	−	0.588615i
$960$		0			0
$961$	−40.0322	−	69.3379i	−1.29136	−	2.23671i
$962$		0			0
$963$	−9.17335	+	15.8887i	−0.295607	+	0.512007i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−21.3514			−0.686616			−0.343308	−	0.939223i	$-0.611547\pi$
$967$	−21.3514			−0.686616			−0.343308	+	0.939223i	$0.611547\pi$
$968$		0			0
$969$	−0.561945	+	0.973318i	−0.0180523	+	0.0312675i
$970$		0			0
$971$	−19.0000	−	32.9090i	−0.609740	−	1.05610i	−0.991283	−	0.131749i	$-0.957941\pi$
$971$	−19.0000	−	32.9090i	−0.609740	−	1.05610i	0.381543	−	0.924351i	$-0.375393\pi$
$972$		0			0
$973$	1.28206	−	5.33186i	0.0411009	−	0.170932i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	21.3851	−	37.0401i	0.684170	−	1.18502i	−0.289526	−	0.957170i	$-0.593498\pi$
$977$	21.3851	−	37.0401i	0.684170	−	1.18502i	0.973697	−	0.227848i	$-0.0731689\pi$
$978$		0			0
$979$	52.6401			1.68238
$980$		0			0
$981$	−10.4144			−0.332506
$982$		0			0
$983$	−6.73968	+	11.6735i	−0.214962	+	0.372326i	−0.953261	−	0.302148i	$-0.902296\pi$
$983$	−6.73968	+	11.6735i	−0.214962	+	0.372326i	0.738299	+	0.674474i	$0.235630\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−2.29648	+	9.55068i	−0.0730978	+	0.304002i
$988$		0			0
$989$	−33.1596	−	57.4341i	−1.05441	−	1.82630i
$990$		0			0
$991$	−13.2993	+	23.0351i	−0.422467	+	0.731735i	−0.996180	−	0.0873218i	$-0.972169\pi$
$991$	−13.2993	+	23.0351i	−0.422467	+	0.731735i	0.573713	+	0.819056i	$0.305503\pi$
$992$		0			0
$993$	7.53226			0.239029
$994$		0			0
$995$		0			0
$996$		0			0
$997$	7.19366	−	12.4598i	0.227825	−	0.394605i	−0.729338	−	0.684154i	$-0.760172\pi$
$997$	7.19366	−	12.4598i	0.227825	−	0.394605i	0.957163	+	0.289548i	$0.0935051\pi$
$998$		0			0
$999$	1.53706	+	2.66227i	0.0486305	+	0.0842306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.q.l.1201.3		8
5.2	odd	4		420.2.bb.a.109.5	yes	16
5.3	odd	4		420.2.bb.a.109.4	✓	16
5.4	even	2		2100.2.q.m.1201.2		8
7.2	even	3	inner	2100.2.q.l.1801.3		8
15.2	even	4		1260.2.bm.c.109.7		16
15.8	even	4		1260.2.bm.c.109.2		16
20.3	even	4		1680.2.di.e.529.8		16
20.7	even	4		1680.2.di.e.529.1		16
35.2	odd	12		420.2.bb.a.289.4	yes	16
35.3	even	12		2940.2.k.g.589.2		8
35.9	even	6		2100.2.q.m.1801.2		8
35.12	even	12		2940.2.bb.i.1549.5		16
35.13	even	4		2940.2.bb.i.949.5		16
35.17	even	12		2940.2.k.g.589.6		8
35.18	odd	12		2940.2.k.f.589.7		8
35.23	odd	12		420.2.bb.a.289.5	yes	16
35.27	even	4		2940.2.bb.i.949.4		16
35.32	odd	12		2940.2.k.f.589.3		8
35.33	even	12		2940.2.bb.i.1549.4		16
105.2	even	12		1260.2.bm.c.289.2		16
105.23	even	12		1260.2.bm.c.289.7		16
140.23	even	12		1680.2.di.e.289.1		16
140.107	even	12		1680.2.di.e.289.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bb.a.109.4	✓	16	5.3	odd	4
420.2.bb.a.109.5	yes	16	5.2	odd	4
420.2.bb.a.289.4	yes	16	35.2	odd	12
420.2.bb.a.289.5	yes	16	35.23	odd	12
1260.2.bm.c.109.2		16	15.8	even	4
1260.2.bm.c.109.7		16	15.2	even	4
1260.2.bm.c.289.2		16	105.2	even	12
1260.2.bm.c.289.7		16	105.23	even	12
1680.2.di.e.289.1		16	140.23	even	12
1680.2.di.e.289.8		16	140.107	even	12
1680.2.di.e.529.1		16	20.7	even	4
1680.2.di.e.529.8		16	20.3	even	4
2100.2.q.l.1201.3		8	1.1	even	1	trivial
2100.2.q.l.1801.3		8	7.2	even	3	inner
2100.2.q.m.1201.2		8	5.4	even	2
2100.2.q.m.1801.2		8	35.9	even	6
2940.2.k.f.589.3		8	35.32	odd	12
2940.2.k.f.589.7		8	35.18	odd	12
2940.2.k.g.589.2		8	35.3	even	12
2940.2.k.g.589.6		8	35.17	even	12
2940.2.bb.i.949.4		16	35.27	even	4
2940.2.bb.i.949.5		16	35.13	even	4
2940.2.bb.i.1549.4		16	35.33	even	12
2940.2.bb.i.1549.5		16	35.12	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.618546 + 2.57243i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.618546 + 2.57243i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.46616 + 2.53947i) q^{11} -5.76936 q^{13} +(-0.118546 + 0.205328i) q^{17} +(-2.37016 - 4.10523i) q^{19} +(-1.91852 - 1.82189i) q^{21} +(-3.38468 - 5.86244i) q^{23} +1.00000 q^{27} +6.03549 q^{29} +(5.26936 - 9.12679i) q^{31} +(-1.46616 - 2.53947i) q^{33} +(1.53706 + 2.66227i) q^{37} +(2.88468 - 4.99641i) q^{39} +1.06768 q^{41} +9.79697 q^{43} +(-1.85635 - 3.21530i) q^{47} +(-6.23480 - 3.18233i) q^{49} +(-0.118546 - 0.205328i) q^{51} +(-5.50322 + 9.53186i) q^{53} +4.74032 q^{57} +(4.65633 - 8.06499i) q^{59} +(4.06861 + 7.04704i) q^{61} +(2.53706 - 0.750539i) q^{63} +(1.12177 - 1.94296i) q^{67} +6.76936 q^{69} -11.8421 q^{71} +(-1.89848 + 3.28827i) q^{73} +(-5.62571 - 5.34237i) q^{77} +(-0.00873900 - 0.0151364i) q^{79} +(-0.500000 + 0.866025i) q^{81} +7.30162 q^{83} +(-3.01774 + 5.22689i) q^{87} +(-8.97583 - 15.5466i) q^{89} +(3.56861 - 14.8413i) q^{91} +(5.26936 + 9.12679i) q^{93} +2.31122 q^{97} +2.93232 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 - 2 * q^7 - 4 * q^9	\( 8 q - 4 q^{3} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{13} + 2 q^{17} - 4 q^{19} - 2 q^{21} - 6 q^{23} + 8 q^{27} - 12 q^{29} - 4 q^{33} - 4 q^{37} + 2 q^{39} + 24 q^{41} + 32 q^{43} - 2 q^{47} - 4 q^{49} + 2 q^{51} - 20 q^{53} + 8 q^{57} + 14 q^{59} - 16 q^{61} + 4 q^{63} - 18 q^{67} + 12 q^{69} - 28 q^{71} + 8 q^{73} + 10 q^{77} + 8 q^{79} - 4 q^{81} - 20 q^{83} + 6 q^{87} + 8 q^{89} - 20 q^{91} - 20 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^13 + 2 * q^17 - 4 * q^19 - 2 * q^21 - 6 * q^23 + 8 * q^27 - 12 * q^29 - 4 * q^33 - 4 * q^37 + 2 * q^39 + 24 * q^41 + 32 * q^43 - 2 * q^47 - 4 * q^49 + 2 * q^51 - 20 * q^53 + 8 * q^57 + 14 * q^59 - 16 * q^61 + 4 * q^63 - 18 * q^67 + 12 * q^69 - 28 * q^71 + 8 * q^73 + 10 * q^77 + 8 * q^79 - 4 * q^81 - 20 * q^83 + 6 * q^87 + 8 * q^89 - 20 * q^91 - 20 * q^97 + 8 * q^99

Introduction

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