LMFDB - Embedded newform 2100.2.bi.k.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 1]))

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

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

chi := DirichletCharacter("2100.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			101.1
Root			$-1.08831 + 1.34743i$ of defining polynomial
Character	$\chi$	$=$	2100.101
Dual form			2100.2.bi.k.1601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71107 + 0.268793i) q^{3} +(-2.57325 + 0.615143i) q^{7} +(2.85550 - 0.919845i) q^{9} +O(q^{10})$	\(q+(-1.71107 + 0.268793i) q^{3} +(-2.57325 + 0.615143i) q^{7} +(2.85550 - 0.919845i) q^{9} +(-1.80606 - 1.04273i) q^{11} -0.245770i q^{13} +(0.471640 - 0.816904i) q^{17} +(-0.465563 + 0.268793i) q^{19} +(4.23765 - 1.74422i) q^{21} +(-2.40010 + 1.38570i) q^{23} +(-4.63871 + 2.34145i) q^{27} -0.267475i q^{29} +(0.981097 + 0.566436i) q^{31} +(3.37057 + 1.29872i) q^{33} +(-3.08164 - 5.33755i) q^{37} +(0.0660611 + 0.420528i) q^{39} -2.38340 q^{41} +11.4354 q^{43} +(-6.23215 - 10.7944i) q^{47} +(6.24320 - 3.16583i) q^{49} +(-0.587429 + 1.52455i) q^{51} +(10.8541 + 6.26660i) q^{53} +(0.724359 - 0.585062i) q^{57} +(-6.25478 + 10.8336i) q^{59} +(4.96556 - 2.86687i) q^{61} +(-6.78207 + 4.12353i) q^{63} +(-2.78001 + 4.81512i) q^{67} +(3.73427 - 3.01616i) q^{69} +10.1375i q^{71} +(11.3758 + 6.56784i) q^{73} +(5.28887 + 1.57221i) q^{77} +(3.17314 + 5.49605i) q^{79} +(7.30777 - 5.25324i) q^{81} -1.06674 q^{83} +(0.0718953 + 0.457667i) q^{87} +(-0.463787 - 0.803302i) q^{89} +(0.151184 + 0.632426i) q^{91} +(-1.83098 - 0.705499i) q^{93} +3.01245i q^{97} +(-6.11636 - 1.31622i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} + 5 q^{7} - 3 q^{9}+O(q^{10}) $ 10 * q + q^3 + 5 * q^7 - 3 * q^9	$ 10 q + q^{3} + 5 q^{7} - 3 q^{9} - 6 q^{11} - 6 q^{17} + 3 q^{19} + 10 q^{21} - 24 q^{23} - 8 q^{27} + 15 q^{31} + 20 q^{33} + q^{37} + 15 q^{39} - 8 q^{41} + 26 q^{43} - 14 q^{47} - 13 q^{49} - 44 q^{51} + 24 q^{53} - 18 q^{57} + 42 q^{61} + q^{63} - 7 q^{67} - 14 q^{69} + 3 q^{73} + 26 q^{77} + q^{79} + 41 q^{81} + 8 q^{83} + 26 q^{87} + 28 q^{89} - 11 q^{91} + 47 q^{93} + 36 q^{99}+O(q^{100}) $ 10 * q + q^3 + 5 * q^7 - 3 * q^9 - 6 * q^11 - 6 * q^17 + 3 * q^19 + 10 * q^21 - 24 * q^23 - 8 * q^27 + 15 * q^31 + 20 * q^33 + q^37 + 15 * q^39 - 8 * q^41 + 26 * q^43 - 14 * q^47 - 13 * q^49 - 44 * q^51 + 24 * q^53 - 18 * q^57 + 42 * q^61 + q^63 - 7 * q^67 - 14 * q^69 + 3 * q^73 + 26 * q^77 + q^79 + 41 * q^81 + 8 * q^83 + 26 * q^87 + 28 * q^89 - 11 * q^91 + 47 * q^93 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.71107	+	0.268793i	−0.987885	+	0.155188i
$3$	−1.71107	+	0.268793i	−0.987885	+	0.155188i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.57325	+	0.615143i	−0.972596	+	0.232502i
$7$	−2.57325	+	0.615143i	−0.972596	+	0.232502i
$8$		0			0
$9$	2.85550	−	0.919845i	0.951834	−	0.306615i
$10$		0			0
$11$	−1.80606	−	1.04273i	−0.544548	−	0.314395i	0.202372	−	0.979309i	$-0.435135\pi$
$11$	−1.80606	−	1.04273i	−0.544548	−	0.314395i	−0.746920	+	0.664914i	$0.768468\pi$
$12$		0			0
$13$		−	0.245770i		−	0.0681643i	−0.999419	−	0.0340821i	$-0.989149\pi$
$13$		−	0.245770i		−	0.0681643i	0.999419	−	0.0340821i	$-0.0108508\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.471640	−	0.816904i	0.114389	−	0.198128i	−0.803146	−	0.595782i	$-0.796842\pi$
$17$	0.471640	−	0.816904i	0.114389	−	0.198128i	0.917536	+	0.397654i	$0.130176\pi$
$18$		0			0
$19$	−0.465563	+	0.268793i	−0.106807	+	0.0616653i	−0.552452	−	0.833545i	$-0.686308\pi$
$19$	−0.465563	+	0.268793i	−0.106807	+	0.0616653i	0.445645	+	0.895210i	$0.352974\pi$
$20$		0			0
$21$	4.23765	−	1.74422i	0.924731	−	0.380620i
$22$		0			0
$23$	−2.40010	+	1.38570i	−0.500456	+	0.288938i	−0.728902	−	0.684618i	$-0.759969\pi$
$23$	−2.40010	+	1.38570i	−0.500456	+	0.288938i	0.228446	+	0.973557i	$0.426636\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−4.63871	+	2.34145i	−0.892719	+	0.450613i
$28$		0			0
$29$		−	0.267475i		−	0.0496688i	−0.999692	−	0.0248344i	$-0.992094\pi$
$29$		−	0.267475i		−	0.0496688i	0.999692	−	0.0248344i	$-0.00790585\pi$
$30$		0			0
$31$	0.981097	+	0.566436i	0.176210	+	0.101735i	0.585511	−	0.810665i	$-0.300894\pi$
$31$	0.981097	+	0.566436i	0.176210	+	0.101735i	−0.409301	+	0.912400i	$0.634227\pi$
$32$		0			0
$33$	3.37057	+	1.29872i	0.586741	+	0.226079i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.08164	−	5.33755i	−0.506618	−	0.877488i	−0.999971	−	0.00765857i	$-0.997562\pi$
$37$	−3.08164	−	5.33755i	−0.506618	−	0.877488i	0.493353	−	0.869829i	$-0.335771\pi$
$38$		0			0
$39$	0.0660611	+	0.420528i	0.0105782	+	0.0673384i
$40$		0			0
$41$	−2.38340			−0.372224			−0.186112	−	0.982529i	$-0.559589\pi$
$41$	−2.38340			−0.372224			−0.186112	+	0.982529i	$0.559589\pi$
$42$		0			0
$43$	11.4354			1.74388			0.871938	−	0.489616i	$-0.162863\pi$
$43$	11.4354			1.74388			0.871938	+	0.489616i	$0.162863\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.23215	−	10.7944i	−0.909052	−	1.57452i	−0.815384	−	0.578921i	$-0.803474\pi$
$47$	−6.23215	−	10.7944i	−0.909052	−	1.57452i	−0.0936683	−	0.995603i	$-0.529859\pi$
$48$		0			0
$49$	6.24320	−	3.16583i	0.891885	−	0.452261i
$50$		0			0
$51$	−0.587429	+	1.52455i	−0.0822565	+	0.213480i
$52$		0			0
$53$	10.8541	+	6.26660i	1.49092	+	0.860784i	0.999946	−	0.0103892i	$-0.00330704\pi$
$53$	10.8541	+	6.26660i	1.49092	+	0.860784i	0.490976	+	0.871173i	$0.336640\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.724359	−	0.585062i	0.0959437	−	0.0774934i
$58$		0			0
$59$	−6.25478	+	10.8336i	−0.814303	+	1.41041i	0.0955244	+	0.995427i	$0.469547\pi$
$59$	−6.25478	+	10.8336i	−0.814303	+	1.41041i	−0.909827	+	0.414987i	$0.863786\pi$
$60$		0			0
$61$	4.96556	−	2.86687i	0.635775	−	0.367065i	−0.147210	−	0.989105i	$-0.547029\pi$
$61$	4.96556	−	2.86687i	0.635775	−	0.367065i	0.782985	+	0.622040i	$0.213696\pi$
$62$		0			0
$63$	−6.78207	+	4.12353i	−0.854461	+	0.519516i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.78001	+	4.81512i	−0.339633	+	0.588261i	−0.984364	−	0.176149i	$-0.943636\pi$
$67$	−2.78001	+	4.81512i	−0.339633	+	0.588261i	0.644731	+	0.764410i	$0.276969\pi$
$68$		0			0
$69$	3.73427	−	3.01616i	0.449553	−	0.363103i
$70$		0			0
$71$			10.1375i			1.20310i	0.798835	+	0.601551i	$0.205450\pi$
$71$			10.1375i			1.20310i	−0.798835	+	0.601551i	$0.794550\pi$
$72$		0			0
$73$	11.3758	+	6.56784i	1.33144	+	0.768707i	0.985520	−	0.169557i	$-0.0542337\pi$
$73$	11.3758	+	6.56784i	1.33144	+	0.768707i	0.345919	+	0.938264i	$0.387567\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.28887	+	1.57221i	0.602722	+	0.179170i
$78$		0			0
$79$	3.17314	+	5.49605i	0.357007	+	0.618353i	0.987459	−	0.157874i	$-0.0504641\pi$
$79$	3.17314	+	5.49605i	0.357007	+	0.618353i	−0.630453	+	0.776228i	$0.717131\pi$
$80$		0			0
$81$	7.30777	−	5.25324i	0.811975	−	0.583693i
$82$		0			0
$83$	−1.06674			−0.117090			−0.0585449	−	0.998285i	$-0.518646\pi$
$83$	−1.06674			−0.117090			−0.0585449	+	0.998285i	$0.518646\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.0718953	+	0.457667i	0.00770798	+	0.0490671i
$88$		0			0
$89$	−0.463787	−	0.803302i	−0.0491613	−	0.0851499i	0.840398	−	0.541970i	$-0.182322\pi$
$89$	−0.463787	−	0.803302i	−0.0491613	−	0.0851499i	−0.889559	+	0.456820i	$0.848988\pi$
$90$		0			0
$91$	0.151184	+	0.632426i	0.0158483	+	0.0662963i
$92$		0			0
$93$	−1.83098	−	0.705499i	−0.189863	−	0.0731568i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			3.01245i			0.305868i	0.988236	+	0.152934i	$0.0488722\pi$
$97$			3.01245i			0.305868i	−0.988236	+	0.152934i	$0.951128\pi$
$98$		0			0
$99$	−6.11636	−	1.31622i	−0.614717	−	0.132285i
$100$		0			0
$101$	−6.19049	+	10.7223i	−0.615977	+	1.06690i	0.374235	+	0.927334i	$0.377905\pi$
$101$	−6.19049	+	10.7223i	−0.615977	+	1.06690i	−0.990212	+	0.139570i	$0.955428\pi$
$102$		0			0
$103$	14.5787	−	8.41703i	1.43648	−	0.829355i	0.438881	−	0.898545i	$-0.355375\pi$
$103$	14.5787	−	8.41703i	1.43648	−	0.829355i	0.997603	+	0.0691903i	$0.0220416\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	11.1031	−	6.41036i	1.07337	−	0.619713i	0.144273	−	0.989538i	$-0.453916\pi$
$107$	11.1031	−	6.41036i	1.07337	−	0.619713i	0.929101	+	0.369825i	$0.120582\pi$
$108$		0			0
$109$	1.79448	−	3.10813i	0.171880	−	0.297705i	−0.767197	−	0.641411i	$-0.778349\pi$
$109$	1.79448	−	3.10813i	0.171880	−	0.297705i	0.939077	+	0.343707i	$0.111683\pi$
$110$		0			0
$111$	6.70758	+	8.30459i	0.636655	+	0.788236i
$112$		0			0
$113$			1.00353i			0.0944041i	0.998885	+	0.0472020i	$0.0150305\pi$
$113$			1.00353i			0.0944041i	−0.998885	+	0.0472020i	$0.984970\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.226070	−	0.701796i	−0.0209002	−	0.0648810i
$118$		0			0
$119$	−0.711132	+	2.39222i	−0.0651894	+	0.219295i
$120$		0			0
$121$	−3.32543	−	5.75981i	−0.302312	−	0.523619i
$122$		0			0
$123$	4.07815	−	0.640639i	0.367714	−	0.0577645i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	7.76096			0.688674			0.344337	−	0.938846i	$-0.388104\pi$
$127$	7.76096			0.688674			0.344337	+	0.938846i	$0.388104\pi$
$128$		0			0
$129$	−19.5667	+	3.07374i	−1.72275	+	0.270628i
$130$		0			0
$131$	8.58199	+	14.8644i	0.749812	+	1.29871i	0.947913	+	0.318530i	$0.103189\pi$
$131$	8.58199	+	14.8644i	0.749812	+	1.29871i	−0.198101	+	0.980182i	$0.563477\pi$
$132$		0			0
$133$	1.03266	−	0.978058i	0.0895431	−	0.0848084i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.0137	+	7.51345i	1.11183	+	0.641918i	0.939304	−	0.343087i	$-0.111472\pi$
$137$	13.0137	+	7.51345i	1.11183	+	0.641918i	0.172530	+	0.985004i	$0.444806\pi$
$138$		0			0
$139$			9.83141i			0.833889i	0.908932	+	0.416945i	$0.136899\pi$
$139$			9.83141i			0.833889i	−0.908932	+	0.416945i	$0.863101\pi$
$140$		0			0
$141$	13.5651	+	16.7948i	1.14239	+	1.41438i
$142$		0			0
$143$	−0.256271	+	0.443875i	−0.0214305	+	0.0371187i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−9.83158	+	7.09507i	−0.810895	+	0.585192i
$148$		0			0
$149$	19.9895	−	11.5409i	1.63760	−	0.945469i	0.655943	−	0.754810i	$-0.272271\pi$
$149$	19.9895	−	11.5409i	1.63760	−	0.945469i	0.981656	−	0.190658i	$-0.0610623\pi$
$150$		0			0
$151$	7.20527	−	12.4799i	0.586357	−	1.01560i	−0.408348	−	0.912826i	$-0.633895\pi$
$151$	7.20527	−	12.4799i	0.586357	−	1.01560i	0.994705	−	0.102774i	$-0.0327717\pi$
$152$		0			0
$153$	0.595343	−	2.76650i	0.0481306	−	0.223659i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	1.90441	+	1.09951i	0.151988	+	0.0877506i	0.574065	−	0.818809i	$-0.305365\pi$
$157$	1.90441	+	1.09951i	0.151988	+	0.0877506i	−0.422077	+	0.906560i	$0.638699\pi$
$158$		0			0
$159$	−20.2565	−	7.80508i	−1.60644	−	0.618983i
$160$		0			0
$161$	5.32365	−	5.04216i	0.419563	−	0.397378i
$162$		0			0
$163$	4.92757	+	8.53481i	0.385957	+	0.668498i	0.991902	−	0.127009i	$-0.0405378\pi$
$163$	4.92757	+	8.53481i	0.385957	+	0.668498i	−0.605944	+	0.795507i	$0.707205\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−22.8349			−1.76702			−0.883509	−	0.468415i	$-0.844825\pi$
$167$	−22.8349			−1.76702			−0.883509	+	0.468415i	$0.844825\pi$
$168$		0			0
$169$	12.9396			0.995354
$170$		0			0
$171$	−1.08217	+	1.19578i	−0.0827554	+	0.0914438i
$172$		0			0
$173$	4.87085	+	8.43656i	0.370324	+	0.641420i	0.989615	−	0.143741i	$-0.0459133\pi$
$173$	4.87085	+	8.43656i	0.370324	+	0.641420i	−0.619291	+	0.785161i	$0.712580\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	7.79036	−	20.2182i	0.585559	−	1.51970i
$178$		0			0
$179$	−15.6543	−	9.03800i	−1.17006	−	0.675532i	−0.216363	−	0.976313i	$-0.569419\pi$
$179$	−15.6543	−	9.03800i	−1.17006	−	0.675532i	−0.953693	+	0.300781i	$0.902753\pi$
$180$		0			0
$181$			17.7230i			1.31734i	0.752433	+	0.658669i	$0.228880\pi$
$181$			17.7230i			1.31734i	−0.752433	+	0.658669i	$0.771120\pi$
$182$		0			0
$183$	−7.72582	+	6.24011i	−0.571109	+	0.461282i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.70362	+	0.983585i	−0.124581	+	0.0719269i
$188$		0			0
$189$	10.4962	−	8.87861i	0.763487	−	0.645824i
$190$		0			0
$191$	19.0353	−	10.9901i	1.37735	−	0.795212i	0.385508	−	0.922704i	$-0.374026\pi$
$191$	19.0353	−	10.9901i	1.37735	−	0.795212i	0.991840	+	0.127492i	$0.0406927\pi$
$192$		0			0
$193$	−4.48820	+	7.77378i	−0.323067	+	0.559569i	−0.981119	−	0.193403i	$-0.938047\pi$
$193$	−4.48820	+	7.77378i	−0.323067	+	0.559569i	0.658052	+	0.752973i	$0.271381\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			22.3002i			1.58882i	0.607382	+	0.794410i	$0.292220\pi$
$197$			22.3002i			1.58882i	−0.607382	+	0.794410i	$0.707780\pi$
$198$		0			0
$199$	16.3807	+	9.45740i	1.16120	+	0.670417i	0.951591	−	0.307368i	$-0.0994484\pi$
$199$	16.3807	+	9.45740i	1.16120	+	0.670417i	0.209606	+	0.977786i	$0.432782\pi$
$200$		0			0
$201$	3.46252	−	8.98625i	0.244227	−	0.633841i
$202$		0			0
$203$	0.164535	+	0.688279i	0.0115481	+	0.0483077i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−5.57887	+	6.16459i	−0.387758	+	0.428469i
$208$		0			0
$209$	1.12111			0.0775490
$210$		0			0
$211$	20.4152			1.40544			0.702722	−	0.711465i	$-0.251968\pi$
$211$	20.4152			1.40544			0.702722	+	0.711465i	$0.251968\pi$
$212$		0			0
$213$	−2.72489	−	17.3460i	−0.186706	−	1.18853i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−2.87304	−	0.854066i	−0.195035	−	0.0579778i
$218$		0			0
$219$	−21.2302	−	8.18027i	−1.43460	−	0.552771i
$220$		0			0
$221$	−0.200770	−	0.115915i	−0.0135053	−	0.00779727i
$222$		0			0
$223$		−	13.5949i		−	0.910379i	−0.890395	−	0.455189i	$-0.849572\pi$
$223$		−	13.5949i		−	0.910379i	0.890395	−	0.455189i	$-0.150428\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.03260	+	8.71671i	−0.334025	+	0.578549i	−0.983297	−	0.182008i	$-0.941740\pi$
$227$	−5.03260	+	8.71671i	−0.334025	+	0.578549i	0.649272	+	0.760556i	$0.275074\pi$
$228$		0			0
$229$	12.3651	−	7.13897i	0.817106	−	0.471756i	−0.0323114	−	0.999478i	$-0.510287\pi$
$229$	12.3651	−	7.13897i	0.817106	−	0.471756i	0.849418	+	0.527721i	$0.176953\pi$
$230$		0			0
$231$	−9.47221	−	1.26856i	−0.623225	−	0.0834648i
$232$		0			0
$233$	−17.9716	+	10.3759i	−1.17736	+	0.679750i	−0.955403	−	0.295306i	$-0.904578\pi$
$233$	−17.9716	+	10.3759i	−1.17736	+	0.679750i	−0.221958	+	0.975056i	$0.571245\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−6.90676	−	8.55118i	−0.448642	−	0.555459i
$238$		0			0
$239$		−	4.86422i		−	0.314640i	−0.987548	−	0.157320i	$-0.949715\pi$
$239$		−	4.86422i		−	0.314640i	0.987548	−	0.157320i	$-0.0502854\pi$
$240$		0			0
$241$	−14.9239	−	8.61634i	−0.961336	−	0.555028i	−0.0647520	−	0.997901i	$-0.520626\pi$
$241$	−14.9239	−	8.61634i	−0.961336	−	0.555028i	−0.896584	+	0.442874i	$0.853959\pi$
$242$		0			0
$243$	−11.0921	+	10.9529i	−0.711556	+	0.702630i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.0660611	+	0.114421i	0.00420337	+	0.00728045i
$248$		0			0
$249$	1.82526	−	0.286732i	0.115671	−	0.0181709i
$250$		0			0
$251$	−15.8276			−0.999031			−0.499516	−	0.866305i	$-0.666489\pi$
$251$	−15.8276			−0.999031			−0.499516	+	0.866305i	$0.666489\pi$
$252$		0			0
$253$	5.77964			0.363363
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.10800	−	15.7755i	−0.568141	−	0.984050i	−0.996750	−	0.0805593i	$-0.974329\pi$
$257$	−9.10800	−	15.7755i	−0.568141	−	0.984050i	0.428609	−	0.903490i	$-0.359004\pi$
$258$		0			0
$259$	11.2132	+	11.8392i	0.696752	+	0.735651i
$260$		0			0
$261$	−0.246035	−	0.763775i	−0.0152292	−	0.0472765i
$262$		0			0
$263$	4.55971	+	2.63255i	0.281164	+	0.162330i	0.633950	−	0.773374i	$-0.281432\pi$
$263$	4.55971	+	2.63255i	0.281164	+	0.162330i	−0.352786	+	0.935704i	$0.614766\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.00949	+	1.24984i	0.0617799	+	0.0764891i
$268$		0			0
$269$	0.775418	−	1.34306i	0.0472780	−	0.0818880i	−0.841418	−	0.540385i	$-0.818279\pi$
$269$	0.775418	−	1.34306i	0.0472780	−	0.0818880i	0.888696	+	0.458497i	$0.151612\pi$
$270$		0			0
$271$	−9.77676	+	5.64461i	−0.593896	+	0.342886i	−0.766636	−	0.642082i	$-0.778071\pi$
$271$	−9.77676	+	5.64461i	−0.593896	+	0.342886i	0.172741	+	0.984967i	$0.444738\pi$
$272$		0			0
$273$	−0.428677	−	1.04149i	−0.0259447	−	0.0630336i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	8.54371	−	14.7981i	0.513342	−	0.889134i	−0.486538	−	0.873659i	$-0.661741\pi$
$277$	8.54371	−	14.7981i	0.513342	−	0.889134i	0.999880	−	0.0154751i	$-0.00492606\pi$
$278$		0			0
$279$	3.32256	+	0.715003i	0.198916	+	0.0428061i
$280$		0			0
$281$		−	15.2188i		−	0.907880i	−0.891032	−	0.453940i	$-0.850018\pi$
$281$		−	15.2188i		−	0.907880i	0.891032	−	0.453940i	$-0.149982\pi$
$282$		0			0
$283$	14.2634	+	8.23500i	0.847874	+	0.489520i	0.859933	−	0.510407i	$-0.170505\pi$
$283$	14.2634	+	8.23500i	0.847874	+	0.489520i	−0.0120590	+	0.999927i	$0.503839\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.13307	−	1.46613i	0.362023	−	0.0865429i
$288$		0			0
$289$	8.05511	+	13.9519i	0.473830	+	0.820698i
$290$		0			0
$291$	−0.809725	−	5.15450i	−0.0474669	−	0.302162i
$292$		0			0
$293$	−18.1748			−1.06179			−0.530893	−	0.847439i	$-0.678143\pi$
$293$	−18.1748			−1.06179			−0.530893	+	0.847439i	$0.678143\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	10.8193	+	0.608108i	0.627799	+	0.0352860i
$298$		0			0
$299$	0.340563	+	0.589873i	0.0196953	+	0.0341132i
$300$		0			0
$301$	−29.4260	+	7.03438i	−1.69609	+	0.405455i
$302$		0			0
$303$	7.71029	−	20.0104i	0.442944	−	1.14957i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			24.6960i			1.40948i	0.709468	+	0.704738i	$0.248935\pi$
$307$			24.6960i			1.40948i	−0.709468	+	0.704738i	$0.751065\pi$
$308$		0			0
$309$	−22.6827	+	18.3208i	−1.29038	+	1.04223i
$310$		0			0
$311$	11.5061	−	19.9291i	0.652448	−	1.13007i	−0.330079	−	0.943953i	$-0.607075\pi$
$311$	11.5061	−	19.9291i	0.652448	−	1.13007i	0.982527	−	0.186120i	$-0.0595914\pi$
$312$		0			0
$313$	−2.73490	+	1.57900i	−0.154586	+	0.0892502i	−0.575298	−	0.817944i	$-0.695114\pi$
$313$	−2.73490	+	1.57900i	−0.154586	+	0.0892502i	0.420712	+	0.907194i	$0.361780\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.78696	−	1.60905i	0.156531	−	0.0903734i	−0.419688	−	0.907668i	$-0.637861\pi$
$317$	2.78696	−	1.60905i	0.156531	−	0.0903734i	0.576220	+	0.817295i	$0.304527\pi$
$318$		0			0
$319$	−0.278904	+	0.483076i	−0.0156156	+	0.0270471i
$320$		0			0
$321$	−17.2750	+	13.9530i	−0.964199	+	0.778780i
$322$		0			0
$323$			0.507093i			0.0282154i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−2.23503	+	5.80056i	−0.123598	+	0.320772i
$328$		0			0
$329$	22.6770	+	23.9430i	1.25022	+	1.32002i
$330$		0			0
$331$	−14.0918	−	24.4077i	−0.774554	−	1.34157i	−0.935045	−	0.354529i	$-0.884641\pi$
$331$	−14.0918	−	24.4077i	−0.774554	−	1.34157i	0.160491	−	0.987037i	$-0.448692\pi$
$332$		0			0
$333$	−13.7093	−	12.4068i	−0.751267	−	0.679886i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	18.4497			1.00502			0.502510	−	0.864571i	$-0.332410\pi$
$337$	18.4497			1.00502			0.502510	+	0.864571i	$0.332410\pi$
$338$		0			0
$339$	−0.269741	−	1.71711i	−0.0146503	−	0.0932604i
$340$		0			0
$341$	−1.18128	−	2.04604i	−0.0639699	−	0.110799i
$342$		0			0
$343$	−14.1178	+	11.9869i	−0.762292	+	0.647233i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.3367	−	7.69997i	−0.715953	−	0.413356i	0.0973081	−	0.995254i	$-0.468977\pi$
$347$	−13.3367	−	7.69997i	−0.715953	−	0.413356i	−0.813261	+	0.581898i	$0.802310\pi$
$348$		0			0
$349$		−	21.9727i		−	1.17617i	−0.808799	−	0.588086i	$-0.799882\pi$
$349$		−	21.9727i		−	1.17617i	0.808799	−	0.588086i	$-0.200118\pi$
$350$		0			0
$351$	0.575458	+	1.14005i	0.0307157	+	0.0608516i
$352$		0			0
$353$	8.66505	−	15.0083i	0.461194	−	0.798811i	−0.537827	−	0.843055i	$-0.680755\pi$
$353$	8.66505	−	15.0083i	0.461194	−	0.798811i	0.999021	+	0.0442440i	$0.0140879\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	0.573783	−	4.28440i	0.0303678	−	0.226754i
$358$		0			0
$359$	0.270990	−	0.156456i	0.0143023	−	0.00825745i	−0.492832	−	0.870125i	$-0.664038\pi$
$359$	0.270990	−	0.156456i	0.0143023	−	0.00825745i	0.507134	+	0.861867i	$0.330705\pi$
$360$		0			0
$361$	−9.35550	+	16.2042i	−0.492395	+	0.852853i
$362$		0			0
$363$	7.23823	+	8.96158i	0.379909	+	0.470361i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−3.20094	−	1.84807i	−0.167088	−	0.0964682i	0.414124	−	0.910220i	$-0.364088\pi$
$367$	−3.20094	−	1.84807i	−0.167088	−	0.0964682i	−0.581212	+	0.813752i	$0.697421\pi$
$368$		0			0
$369$	−6.80579	+	2.19235i	−0.354295	+	0.114129i
$370$		0			0
$371$	−31.7851	−	9.44871i	−1.65020	−	0.490552i
$372$		0			0
$373$	−0.351666	−	0.609103i	−0.0182086	−	0.0315381i	0.856778	−	0.515686i	$-0.172463\pi$
$373$	−0.351666	−	0.609103i	−0.0182086	−	0.0315381i	−0.874986	+	0.484148i	$0.839130\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.0657372			−0.00338564
$378$		0			0
$379$	−10.3929			−0.533849			−0.266924	−	0.963717i	$-0.586007\pi$
$379$	−10.3929			−0.533849			−0.266924	+	0.963717i	$0.586007\pi$
$380$		0			0
$381$	−13.2795	+	2.08609i	−0.680331	+	0.106874i
$382$		0			0
$383$	−14.7524	−	25.5519i	−0.753813	−	1.30564i	−0.945963	−	0.324276i	$-0.894879\pi$
$383$	−14.7524	−	25.5519i	−0.753813	−	1.30564i	0.192150	−	0.981366i	$-0.438454\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	32.6537	−	10.5188i	1.65988	−	0.534698i
$388$		0			0
$389$	−11.5224	−	6.65245i	−0.584208	−	0.337293i	0.178596	−	0.983923i	$-0.442845\pi$
$389$	−11.5224	−	6.65245i	−0.584208	−	0.337293i	−0.762804	+	0.646630i	$0.776178\pi$
$390$		0			0
$391$			2.61420i			0.132206i
$392$		0			0
$393$	−18.6798	−	23.1273i	−0.942271	−	1.16662i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	3.82832	−	2.21028i	0.192138	−	0.110931i	−0.400845	−	0.916146i	$-0.631283\pi$
$397$	3.82832	−	2.21028i	0.192138	−	0.110931i	0.592983	+	0.805215i	$0.297950\pi$
$398$		0			0
$399$	−1.50406	+	1.95109i	−0.0752971	+	0.0976769i
$400$		0			0
$401$	25.4507	−	14.6940i	1.27095	−	0.733781i	0.295780	−	0.955256i	$-0.404420\pi$
$401$	25.4507	−	14.6940i	1.27095	−	0.733781i	0.975166	+	0.221475i	$0.0710871\pi$
$402$		0			0
$403$	0.139213	−	0.241124i	0.00693469	−	0.0120112i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			12.8533i			0.637112i
$408$		0			0
$409$	6.67308	+	3.85270i	0.329962	+	0.190504i	0.655824	−	0.754913i	$-0.272321\pi$
$409$	6.67308	+	3.85270i	0.329962	+	0.190504i	−0.325862	+	0.945417i	$0.605654\pi$
$410$		0			0
$411$	−24.2868	−	9.35804i	−1.19798	−	0.461598i
$412$		0			0
$413$	9.43088	−	31.7251i	0.464063	−	1.56109i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−2.64261	−	16.8222i	−0.129409	−	0.823787i
$418$		0			0
$419$	−1.40692			−0.0687327			−0.0343663	−	0.999409i	$-0.510941\pi$
$419$	−1.40692			−0.0687327			−0.0343663	+	0.999409i	$0.510941\pi$
$420$		0			0
$421$	−7.23785			−0.352751			−0.176375	−	0.984323i	$-0.556437\pi$
$421$	−7.23785			−0.352751			−0.176375	+	0.984323i	$0.556437\pi$
$422$		0			0
$423$	−27.7251	−	25.0908i	−1.34804	−	1.21996i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−11.0141	+	10.4317i	−0.533009	+	0.504825i
$428$		0			0
$429$	0.319187	−	0.828384i	0.0154105	−	0.0399947i
$430$		0			0
$431$	−9.16199	−	5.28968i	−0.441317	−	0.254795i	0.262839	−	0.964840i	$-0.415341\pi$
$431$	−9.16199	−	5.28968i	−0.441317	−	0.254795i	−0.704156	+	0.710045i	$0.748675\pi$
$432$		0			0
$433$			23.7164i			1.13974i	0.821735	+	0.569869i	$0.193006\pi$
$433$			23.7164i			1.13974i	−0.821735	+	0.569869i	$0.806994\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.744932	−	1.29026i	0.0356349	−	0.0617215i
$438$		0			0
$439$	−17.6684	+	10.2009i	−0.843268	+	0.486861i	−0.858374	−	0.513025i	$-0.828525\pi$
$439$	−17.6684	+	10.2009i	−0.843268	+	0.486861i	0.0151058	+	0.999886i	$0.495191\pi$
$440$		0			0
$441$	14.9154	−	14.7828i	0.710256	−	0.703943i
$442$		0			0
$443$	0.475830	−	0.274720i	0.0226074	−	0.0130524i	−0.488654	−	0.872478i	$-0.662512\pi$
$443$	0.475830	−	0.274720i	0.0226074	−	0.0130524i	0.511261	+	0.859425i	$0.329179\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−31.1012	+	25.1203i	−1.47104	+	1.18815i
$448$		0			0
$449$		−	1.12469i		−	0.0530772i	−0.999648	−	0.0265386i	$-0.991552\pi$
$449$		−	1.12469i		−	0.0530772i	0.999648	−	0.0265386i	$-0.00844850\pi$
$450$		0			0
$451$	4.30456	+	2.48524i	0.202694	+	0.117025i
$452$		0			0
$453$	−8.97420	+	23.2907i	−0.421645	+	1.09429i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−14.6946	−	25.4518i	−0.687385	−	1.19059i	−0.972681	−	0.232146i	$-0.925425\pi$
$457$	−14.6946	−	25.4518i	−0.687385	−	1.19059i	0.285296	−	0.958439i	$-0.407908\pi$
$458$		0			0
$459$	−0.275055	+	4.89370i	−0.0128385	+	0.228418i
$460$		0			0
$461$	−29.9734			−1.39600			−0.697999	−	0.716098i	$-0.745926\pi$
$461$	−29.9734			−1.39600			−0.697999	+	0.716098i	$0.745926\pi$
$462$		0			0
$463$	−13.0355			−0.605809			−0.302905	−	0.953021i	$-0.597956\pi$
$463$	−13.0355			−0.605809			−0.302905	+	0.953021i	$0.597956\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.21626	−	2.10662i	−0.0562817	−	0.0974828i	0.836512	−	0.547949i	$-0.184591\pi$
$467$	−1.21626	−	2.10662i	−0.0562817	−	0.0974828i	−0.892794	+	0.450466i	$0.851258\pi$
$468$		0			0
$469$	4.19167	−	14.1006i	0.193553	−	0.651105i
$470$		0			0
$471$	−3.55411	−	1.36945i	−0.163765	−	0.0631008i
$472$		0			0
$473$	−20.6530	−	11.9240i	−0.949624	−	0.548266i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	36.7581	+	7.91023i	1.68304	+	0.362184i
$478$		0			0
$479$	5.49101	−	9.51071i	0.250891	−	0.434555i	−0.712881	−	0.701285i	$-0.752610\pi$
$479$	5.49101	−	9.51071i	0.250891	−	0.434555i	0.963771	+	0.266730i	$0.0859432\pi$
$480$		0			0
$481$	−1.31181	+	0.757373i	−0.0598133	+	0.0345332i
$482$		0			0
$483$	−7.75383	+	10.0584i	−0.352812	+	0.457674i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	13.4393	−	23.2776i	0.608993	−	1.05481i	−0.382414	−	0.923991i	$-0.624907\pi$
$487$	13.4393	−	23.2776i	0.608993	−	1.05481i	0.991407	−	0.130816i	$-0.0417596\pi$
$488$		0			0
$489$	−10.7255	−	13.2791i	−0.485024	−	0.600503i
$490$		0			0
$491$			25.1295i			1.13408i	0.823692	+	0.567038i	$0.191911\pi$
$491$			25.1295i			1.13408i	−0.823692	+	0.567038i	$0.808089\pi$
$492$		0			0
$493$	−0.218501	−	0.126152i	−0.00984080	−	0.00568159i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.23602	−	26.0863i	−0.279724	−	1.17013i
$498$		0			0
$499$	−2.58341	−	4.47460i	−0.115649	−	0.200311i	0.802390	−	0.596800i	$-0.203562\pi$
$499$	−2.58341	−	4.47460i	−0.115649	−	0.200311i	−0.918039	+	0.396490i	$0.870228\pi$
$500$		0			0
$501$	39.0720	−	6.13785i	1.74561	−	0.274219i
$502$		0			0
$503$	42.2496			1.88382			0.941908	−	0.335872i	$-0.109031\pi$
$503$	42.2496			1.88382			0.941908	+	0.335872i	$0.109031\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−22.1405	+	3.47807i	−0.983295	+	0.154466i
$508$		0			0
$509$	−3.76320	−	6.51806i	−0.166801	−	0.288908i	0.770492	−	0.637449i	$-0.220010\pi$
$509$	−3.76320	−	6.51806i	−0.166801	−	0.288908i	−0.937293	+	0.348541i	$0.886677\pi$
$510$		0			0
$511$	−33.3130	−	9.90290i	−1.47368	−	0.438079i
$512$		0			0
$513$	1.53024	−	2.33694i	0.0675619	−	0.103179i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			25.9938i			1.14320i
$518$		0			0
$519$	−10.6020	−	13.1263i	−0.465378	−	0.576180i
$520$		0			0
$521$	10.1668	−	17.6095i	0.445417	−	0.771484i	−0.552665	−	0.833404i	$-0.686389\pi$
$521$	10.1668	−	17.6095i	0.445417	−	0.771484i	0.998081	+	0.0619196i	$0.0197222\pi$
$522$		0			0
$523$	−3.14832	+	1.81768i	−0.137666	+	0.0794818i	−0.567251	−	0.823545i	$-0.691993\pi$
$523$	−3.14832	+	1.81768i	−0.137666	+	0.0794818i	0.429585	+	0.903026i	$0.358660\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.925448	−	0.534308i	0.0403131	−	0.0232748i
$528$		0			0
$529$	−7.65967	+	13.2669i	−0.333029	+	0.576823i
$530$		0			0
$531$	−7.89530	+	36.6888i	−0.342627	+	1.59216i
$532$		0			0
$533$			0.585766i			0.0253724i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	29.2149	+	11.2569i	1.26071	+	0.485770i
$538$		0			0
$539$	−14.5767	−	0.792285i	−0.627863	−	0.0341261i
$540$		0			0
$541$	−9.20758	−	15.9480i	−0.395865	−	0.685658i	0.597346	−	0.801983i	$-0.296222\pi$
$541$	−9.20758	−	15.9480i	−0.395865	−	0.685658i	−0.993211	+	0.116325i	$0.962888\pi$
$542$		0			0
$543$	−4.76381	−	30.3252i	−0.204434	−	1.30138i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	22.6376			0.967915			0.483957	−	0.875092i	$-0.339199\pi$
$547$	22.6376			0.967915			0.483957	+	0.875092i	$0.339199\pi$
$548$		0			0
$549$	11.5421	−	12.7539i	0.492605	−	0.544323i
$550$		0			0
$551$	0.0718953	+	0.124526i	0.00306284	+	0.00530500i
$552$		0			0
$553$	−11.5461	−	12.1907i	−0.490992	−	0.518403i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	33.9272	+	19.5879i	1.43754	+	0.829965i	0.997679	−	0.0680994i	$-0.0216935\pi$
$557$	33.9272	+	19.5879i	1.43754	+	0.829965i	0.439863	+	0.898065i	$0.355027\pi$
$558$		0			0
$559$		−	2.81047i		−	0.118870i
$560$		0			0
$561$	2.65063	−	2.14090i	0.111910	−	0.0903889i
$562$		0			0
$563$	−1.82483	+	3.16069i	−0.0769073	+	0.133207i	−0.901914	−	0.431915i	$-0.857838\pi$
$563$	−1.82483	+	3.16069i	−0.0769073	+	0.133207i	0.825007	+	0.565123i	$0.191171\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−15.5732	+	18.0132i	−0.654013	+	0.756483i
$568$		0			0
$569$	−17.1456	+	9.89902i	−0.718781	+	0.414988i	−0.814304	−	0.580439i	$-0.802881\pi$
$569$	−17.1456	+	9.89902i	−0.718781	+	0.414988i	0.0955229	+	0.995427i	$0.469548\pi$
$570$		0			0
$571$	−18.7342	+	32.4487i	−0.784004	+	1.35793i	0.145589	+	0.989345i	$0.453492\pi$
$571$	−18.7342	+	32.4487i	−0.784004	+	1.35793i	−0.929592	+	0.368589i	$0.879841\pi$
$572$		0			0
$573$	−29.6167	+	23.9213i	−1.23725	+	0.999326i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−22.1156	−	12.7684i	−0.920685	−	0.531558i	−0.0368312	−	0.999322i	$-0.511726\pi$
$577$	−22.1156	−	12.7684i	−0.920685	−	0.531558i	−0.883853	+	0.467764i	$0.845060\pi$
$578$		0			0
$579$	5.59007	−	14.5079i	0.232315	−	0.602926i
$580$		0			0
$581$	2.74498	−	0.656198i	0.113881	−	0.0272237i
$582$		0			0
$583$	−13.0687	−	22.6357i	−0.541252	−	0.937476i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	7.57204			0.312531			0.156266	−	0.987715i	$-0.450054\pi$
$587$	7.57204			0.312531			0.156266	+	0.987715i	$0.450054\pi$
$588$		0			0
$589$	−0.609016			−0.0250941
$590$		0			0
$591$	−5.99412	−	38.1571i	−0.246565	−	1.56957i
$592$		0			0
$593$	1.58920	+	2.75258i	0.0652606	+	0.113035i	0.896810	−	0.442417i	$-0.145879\pi$
$593$	1.58920	+	2.75258i	0.0652606	+	0.113035i	−0.831549	+	0.555452i	$0.812545\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−30.5706	−	11.7792i	−1.25117	−	0.482092i
$598$		0			0
$599$	23.5750	+	13.6110i	0.963247	+	0.556131i	0.897171	−	0.441684i	$-0.145619\pi$
$599$	23.5750	+	13.6110i	0.963247	+	0.556131i	0.0660761	+	0.997815i	$0.478952\pi$
$600$		0			0
$601$		−	13.1953i		−	0.538247i	−0.963106	−	0.269123i	$-0.913266\pi$
$601$		−	13.1953i		−	0.538247i	0.963106	−	0.269123i	$-0.0867340\pi$
$602$		0			0
$603$	−3.50916	+	16.3068i	−0.142904	+	0.664063i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	6.66879	−	3.85023i	0.270678	−	0.156276i	−0.358518	−	0.933523i	$-0.616718\pi$
$607$	6.66879	−	3.85023i	0.270678	−	0.156276i	0.629196	+	0.777247i	$0.283384\pi$
$608$		0			0
$609$	−0.466535	−	1.13347i	−0.0189050	−	0.0459303i
$610$		0			0
$611$	−2.65294	+	1.53167i	−0.107326	+	0.0619649i
$612$		0			0
$613$	−14.4287	+	24.9912i	−0.582769	+	1.00939i	0.412381	+	0.911012i	$0.364697\pi$
$613$	−14.4287	+	24.9912i	−0.582769	+	1.00939i	−0.995150	+	0.0983735i	$0.968636\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			31.5272i			1.26924i	0.772825	+	0.634619i	$0.218843\pi$
$617$			31.5272i			1.26924i	−0.772825	+	0.634619i	$0.781157\pi$
$618$		0			0
$619$	25.4695	+	14.7048i	1.02370	+	0.591036i	0.915175	−	0.403057i	$-0.132052\pi$
$619$	25.4695	+	14.7048i	1.02370	+	0.591036i	0.108530	+	0.994093i	$0.465386\pi$
$620$		0			0
$621$	7.88882	−	12.0476i	0.316567	−	0.483453i
$622$		0			0
$623$	1.68758	+	1.78180i	0.0676116	+	0.0713863i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−1.91830	+	0.301347i	−0.0766095	+	0.0120346i
$628$		0			0
$629$	−5.81369			−0.231807
$630$		0			0
$631$	29.9987			1.19423			0.597115	−	0.802155i	$-0.296313\pi$
$631$	29.9987			1.19423			0.597115	+	0.802155i	$0.296313\pi$
$632$		0			0
$633$	−34.9319	+	5.48747i	−1.38842	+	0.218107i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−0.778065	−	1.53439i	−0.0308281	−	0.0607947i
$638$		0			0
$639$	9.32494	+	28.9477i	0.368889	+	1.14515i
$640$		0			0
$641$	27.8245	+	16.0645i	1.09900	+	0.634510i	0.935959	−	0.352109i	$-0.114535\pi$
$641$	27.8245	+	16.0645i	1.09900	+	0.634510i	0.163044	+	0.986619i	$0.447869\pi$
$642$		0			0
$643$		−	5.88352i		−	0.232024i	−0.993248	−	0.116012i	$-0.962989\pi$
$643$		−	5.88352i		−	0.232024i	0.993248	−	0.116012i	$-0.0370110\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−9.99202	+	17.3067i	−0.392827	+	0.680396i	−0.992821	−	0.119608i	$-0.961836\pi$
$647$	−9.99202	+	17.3067i	−0.392827	+	0.680396i	0.599994	+	0.800004i	$0.295170\pi$
$648$		0			0
$649$	22.5930	−	13.0441i	0.886854	−	0.512025i
$650$		0			0
$651$	5.14554	+	0.689111i	0.201669	+	0.0270084i
$652$		0			0
$653$	2.19720	−	1.26856i	0.0859832	−	0.0496424i	−0.456392	−	0.889779i	$-0.650858\pi$
$653$	2.19720	−	1.26856i	0.0859832	−	0.0496424i	0.542375	+	0.840136i	$0.317525\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	38.5251	+	8.29047i	1.50301	+	0.323442i
$658$		0			0
$659$		−	28.5964i		−	1.11396i	−0.830526	−	0.556979i	$-0.811960\pi$
$659$		−	28.5964i		−	1.11396i	0.830526	−	0.556979i	$-0.188040\pi$
$660$		0			0
$661$	25.4569	+	14.6975i	0.990158	+	0.571668i	0.905321	−	0.424727i	$-0.139630\pi$
$661$	25.4569	+	14.6975i	0.990158	+	0.571668i	0.0848363	+	0.996395i	$0.472963\pi$
$662$		0			0
$663$	0.374688	+	0.144372i	0.0145517	+	0.00560696i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.370640	+	0.641967i	0.0143512	+	0.0248571i
$668$		0			0
$669$	3.65420	+	23.2617i	0.141279	+	0.899350i
$670$		0			0
$671$	−11.9575			−0.461613
$672$		0			0
$673$	18.1428			0.699354			0.349677	−	0.936870i	$-0.386291\pi$
$673$	18.1428			0.699354			0.349677	+	0.936870i	$0.386291\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	19.2622	+	33.3630i	0.740305	+	1.28225i	0.952356	+	0.304987i	$0.0986523\pi$
$677$	19.2622	+	33.3630i	0.740305	+	1.28225i	−0.212051	+	0.977259i	$0.568014\pi$
$678$		0			0
$679$	−1.85309	−	7.75178i	−0.0711150	−	0.297486i
$680$		0			0
$681$	6.26812	−	16.2676i	0.240195	−	0.623376i
$682$		0			0
$683$	8.24278	+	4.75897i	0.315401	+	0.182097i	0.649341	−	0.760497i	$-0.275045\pi$
$683$	8.24278	+	4.75897i	0.315401	+	0.182097i	−0.333940	+	0.942594i	$0.608378\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−19.2385	+	15.5389i	−0.733996	+	0.592846i
$688$		0			0
$689$	1.54014	−	2.66760i	0.0586747	−	0.101628i
$690$		0			0
$691$	36.4810	−	21.0623i	1.38780	−	0.801248i	0.394734	−	0.918795i	$-0.370837\pi$
$691$	36.4810	−	21.0623i	1.38780	−	0.801248i	0.993067	+	0.117548i	$0.0375033\pi$
$692$		0			0
$693$	16.5486	−	0.375477i	0.628628	−	0.0142632i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.12410	+	1.94700i	−0.0425785	+	0.0737481i
$698$		0			0
$699$	27.9617	−	22.5846i	1.05761	−	0.854226i
$700$		0			0
$701$			20.1103i			0.759555i	0.925078	+	0.379778i	$0.123999\pi$
$701$			20.1103i			0.759555i	−0.925078	+	0.379778i	$0.876001\pi$
$702$		0			0
$703$	2.86939	+	1.65664i	0.108221	+	0.0624815i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	9.33395	−	31.3990i	0.351039	−	1.18088i
$708$		0			0
$709$	12.6523	+	21.9145i	0.475168	+	0.823015i	0.999596	−	0.0284398i	$-0.00905390\pi$
$709$	12.6523	+	21.9145i	0.475168	+	0.823015i	−0.524427	+	0.851455i	$0.675721\pi$
$710$		0			0
$711$	14.1164	+	12.7752i	0.529407	+	0.479106i
$712$		0			0
$713$	−3.13964			−0.117581
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.30747	+	8.32300i	0.0488282	+	0.310828i
$718$		0			0
$719$	7.70568	+	13.3466i	0.287373	+	0.497745i	0.973182	−	0.230037i	$-0.0738846\pi$
$719$	7.70568	+	13.3466i	0.287373	+	0.497745i	−0.685809	+	0.727782i	$0.740551\pi$
$720$		0			0
$721$	−32.3370	+	30.6271i	−1.20429	+	1.14061i
$722$		0			0
$723$	27.8519	+	10.7317i	1.03582	+	0.399116i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			17.2053i			0.638109i	0.947736	+	0.319054i	$0.103365\pi$
$727$			17.2053i			0.638109i	−0.947736	+	0.319054i	$0.896635\pi$
$728$		0			0
$729$	16.0352	−	21.7226i	0.593896	−	0.804542i
$730$		0			0
$731$	5.39337	−	9.34159i	0.199481	−	0.345511i
$732$		0			0
$733$	4.21946	−	2.43611i	0.155849	−	0.0899797i	−0.420047	−	0.907502i	$-0.637986\pi$
$733$	4.21946	−	2.43611i	0.155849	−	0.0899797i	0.575896	+	0.817523i	$0.304653\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	10.0417	−	5.79760i	0.369892	−	0.213557i
$738$		0			0
$739$	−11.2489	+	19.4836i	−0.413796	+	0.716716i	−0.995301	−	0.0968269i	$-0.969131\pi$
$739$	−11.2489	+	19.4836i	−0.413796	+	0.716716i	0.581505	+	0.813543i	$0.302464\pi$
$740$		0			0
$741$	−0.143791	−	0.178026i	−0.00528228	−	0.00653993i
$742$		0			0
$743$			5.74923i			0.210919i	0.994424	+	0.105459i	$0.0336313\pi$
$743$			5.74923i			0.210919i	−0.994424	+	0.105459i	$0.966369\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−3.04608	+	0.981235i	−0.111450	+	0.0359015i
$748$		0			0
$749$	−24.6277	+	23.3254i	−0.899875	+	0.852292i
$750$		0			0
$751$	−13.4867	−	23.3597i	−0.492138	−	0.852409i	0.507821	−	0.861463i	$-0.330451\pi$
$751$	−13.4867	−	23.3597i	−0.492138	−	0.852409i	−0.999959	+	0.00905407i	$0.997118\pi$
$752$		0			0
$753$	27.0821	−	4.25435i	0.986928	−	0.155037i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	3.74640			0.136165			0.0680826	−	0.997680i	$-0.478312\pi$
$757$	3.74640			0.136165			0.0680826	+	0.997680i	$0.478312\pi$
$758$		0			0
$759$	−9.88936	+	1.55353i	−0.358961	+	0.0563894i
$760$		0			0
$761$	9.03998	+	15.6577i	0.327699	+	0.567591i	0.982055	−	0.188595i	$-0.0603935\pi$
$761$	9.03998	+	15.6577i	0.327699	+	0.567591i	−0.654356	+	0.756187i	$0.727060\pi$
$762$		0			0
$763$	−2.70569	+	9.10184i	−0.0979527	+	0.329509i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.66257	+	1.53724i	0.0961398	+	0.0555064i
$768$		0			0
$769$		−	25.1297i		−	0.906199i	−0.891460	−	0.453100i	$-0.850318\pi$
$769$		−	25.1297i		−	0.906199i	0.891460	−	0.453100i	$-0.149682\pi$
$770$		0			0
$771$	19.8247	+	24.5448i	0.713971	+	0.883959i
$772$		0			0
$773$	−16.3082	+	28.2467i	−0.586567	+	1.01596i	0.408112	+	0.912932i	$0.366187\pi$
$773$	−16.3082	+	28.2467i	−0.586567	+	1.01596i	−0.994678	+	0.103031i	$0.967146\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−22.3688	−	17.2436i	−0.802475	−	0.618612i
$778$		0			0
$779$	1.10962	−	0.640639i	0.0397563	−	0.0229533i
$780$		0			0
$781$	10.5707	−	18.3090i	0.378249	−	0.655146i
$782$		0			0
$783$	0.626280	+	1.24074i	0.0223814	+	0.0443403i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−3.98518	−	2.30085i	−0.142056	−	0.0820164i	0.427287	−	0.904116i	$-0.359469\pi$
$787$	−3.98518	−	2.30085i	−0.142056	−	0.0820164i	−0.569344	+	0.822100i	$0.692803\pi$
$788$		0			0
$789$	−8.50958	−	3.27885i	−0.302949	−	0.116730i
$790$		0			0
$791$	−0.617314	−	2.58233i	−0.0219492	−	0.0918170i
$792$		0			0
$793$	−0.704590	−	1.22038i	−0.0250207	−	0.0433371i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−13.3722			−0.473666			−0.236833	−	0.971550i	$-0.576109\pi$
$797$	−13.3722			−0.473666			−0.236833	+	0.971550i	$0.576109\pi$
$798$		0			0
$799$	−11.7573			−0.415944
$800$		0			0
$801$	−2.06326	−	1.86722i	−0.0729016	−	0.0659749i
$802$		0			0
$803$	−13.6970	−	23.7238i	−0.483355	−	0.837196i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.965786	+	2.50650i	−0.0339973	+	0.0882329i
$808$		0			0
$809$	−20.3694	−	11.7603i	−0.716152	−	0.413470i	0.0971830	−	0.995267i	$-0.469017\pi$
$809$	−20.3694	−	11.7603i	−0.716152	−	0.413470i	−0.813335	+	0.581796i	$0.802350\pi$
$810$		0			0
$811$			25.5058i			0.895628i	0.894127	+	0.447814i	$0.147797\pi$
$811$			25.5058i			0.895628i	−0.894127	+	0.447814i	$0.852203\pi$
$812$		0			0
$813$	15.2115	−	12.2862i	0.533489	−	0.430897i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−5.32388	+	3.07374i	−0.186259	+	0.107537i
$818$		0			0
$819$	1.01344	+	1.66683i	0.0354124	+	0.0582437i
$820$		0			0
$821$	−1.50477	+	0.868778i	−0.0525167	+	0.0303205i	−0.526028	−	0.850467i	$-0.676319\pi$
$821$	−1.50477	+	0.868778i	−0.0525167	+	0.0303205i	0.473512	+	0.880788i	$0.342986\pi$
$822$		0			0
$823$	0.100180	−	0.173518i	0.00349207	−	0.00604844i	−0.864274	−	0.503021i	$-0.832222\pi$
$823$	0.100180	−	0.173518i	0.00349207	−	0.00604844i	0.867766	+	0.496973i	$0.165555\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	21.7179i		−	0.755207i	−0.925967	−	0.377603i	$-0.876748\pi$
$827$		−	21.7179i		−	0.755207i	0.925967	−	0.377603i	$-0.123252\pi$
$828$		0			0
$829$	−22.5419	−	13.0146i	−0.782913	−	0.452015i	0.0545485	−	0.998511i	$-0.482628\pi$
$829$	−22.5419	−	13.0146i	−0.782913	−	0.452015i	−0.837462	+	0.546496i	$0.815961\pi$
$830$		0			0
$831$	−10.6412	+	27.6171i	−0.369140	+	0.958027i
$832$		0			0
$833$	0.358360	−	6.59322i	0.0124165	−	0.228442i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−5.87730	−	0.330339i	−0.203149	−	0.0114182i
$838$		0			0
$839$	2.46944			0.0852546			0.0426273	−	0.999091i	$-0.486427\pi$
$839$	2.46944			0.0852546			0.0426273	+	0.999091i	$0.486427\pi$
$840$		0			0
$841$	28.9285			0.997533
$842$		0			0
$843$	4.09072	+	26.0405i	0.140892	+	0.896881i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	12.1003	+	12.7758i	0.415770	+	0.438982i
$848$		0			0
$849$	−26.6192	−	10.2567i	−0.913569	−	0.352010i
$850$		0			0
$851$	14.7925	+	8.54045i	0.507080	+	0.292763i
$852$		0			0
$853$		−	30.3776i		−	1.04011i	−0.854133	−	0.520055i	$-0.825912\pi$
$853$		−	30.3776i		−	1.04011i	0.854133	−	0.520055i	$-0.174088\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	25.8422	−	44.7601i	0.882754	−	1.52898i	0.0344882	−	0.999405i	$-0.489020\pi$
$857$	25.8422	−	44.7601i	0.882754	−	1.52898i	0.848266	−	0.529570i	$-0.177647\pi$
$858$		0			0
$859$	−21.0239	+	12.1381i	−0.717326	+	0.414148i	−0.813768	−	0.581190i	$-0.802587\pi$
$859$	−21.0239	+	12.1381i	−0.717326	+	0.414148i	0.0964418	+	0.995339i	$0.469254\pi$
$860$		0			0
$861$	−10.1000	+	4.15717i	−0.344207	+	0.141676i
$862$		0			0
$863$	39.3631	−	22.7263i	1.33993	−	0.773611i	0.353137	−	0.935572i	$-0.385115\pi$
$863$	39.3631	−	22.7263i	1.33993	−	0.773611i	0.986797	+	0.161960i	$0.0517817\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−17.5330	−	21.7074i	−0.595452	−	0.737223i
$868$		0			0
$869$		−	13.2349i		−	0.448964i
$870$		0			0
$871$	1.18341	+	0.683243i	0.0400984	+	0.0231508i
$872$		0			0
$873$	2.77099	+	8.60205i	0.0937837	+	0.291135i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	12.6911	+	21.9817i	0.428549	+	0.742268i	0.996744	−	0.0806254i	$-0.0256917\pi$
$877$	12.6911	+	21.9817i	0.428549	+	0.742268i	−0.568196	+	0.822893i	$0.692358\pi$
$878$		0			0
$879$	31.0984	−	4.88527i	1.04892	−	0.164776i
$880$		0			0
$881$	−42.5616			−1.43394			−0.716969	−	0.697105i	$-0.754471\pi$
$881$	−42.5616			−1.43394			−0.716969	+	0.697105i	$0.754471\pi$
$882$		0			0
$883$	6.16214			0.207372			0.103686	−	0.994610i	$-0.466936\pi$
$883$	6.16214			0.207372			0.103686	+	0.994610i	$0.466936\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.87420	+	6.71032i	0.130083	+	0.225310i	0.923708	−	0.383096i	$-0.125142\pi$
$887$	3.87420	+	6.71032i	0.130083	+	0.225310i	−0.793625	+	0.608407i	$0.791809\pi$
$888$		0			0
$889$	−19.9709	+	4.77410i	−0.669802	+	0.160118i
$890$		0			0
$891$	−18.6760	+	1.86763i	−0.625669	+	0.0625680i
$892$		0			0
$893$	5.80291	+	3.35031i	0.194187	+	0.112114i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.741280	−	0.917771i	−0.0247506	−	0.0306435i
$898$		0			0
$899$	0.151507	−	0.262419i	0.00505306	−	0.00875215i
$900$		0			0
$901$	10.2384	−	5.91116i	0.341091	−	0.196929i
$902$		0			0
$903$	48.4591	−	19.9458i	1.61262	−	0.663755i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	22.7236	−	39.3584i	0.754524	−	1.30687i	−0.191087	−	0.981573i	$-0.561201\pi$
$907$	22.7236	−	39.3584i	0.754524	−	1.30687i	0.945611	−	0.325300i	$-0.105465\pi$
$908$		0			0
$909$	−7.81416	+	36.3117i	−0.259179	+	1.20438i
$910$		0			0
$911$			35.7765i			1.18533i	0.805449	+	0.592665i	$0.201924\pi$
$911$			35.7765i			1.18533i	−0.805449	+	0.592665i	$0.798076\pi$
$912$		0			0
$913$	1.92660	+	1.11232i	0.0637610	+	0.0368124i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−31.2273	−	32.9707i	−1.03122	−	1.08879i
$918$		0			0
$919$	−14.4006	−	24.9427i	−0.475034	−	0.822782i	0.524558	−	0.851375i	$-0.324231\pi$
$919$	−14.4006	−	24.9427i	−0.475034	−	0.822782i	−0.999591	+	0.0285927i	$0.990897\pi$
$920$		0			0
$921$	−6.63811	−	42.2565i	−0.218733	−	1.39240i
$922$		0			0
$923$	2.49149			0.0820085
$924$		0			0
$925$		0			0
$926$		0			0
$927$	33.8872	−	37.4450i	1.11300	−	1.22986i
$928$		0			0
$929$	15.9490	+	27.6244i	0.523269	+	0.906329i	0.999633	+	0.0270805i	$0.00862104\pi$
$929$	15.9490	+	27.6244i	0.523269	+	0.906329i	−0.476364	+	0.879248i	$0.658046\pi$
$930$		0			0
$931$	−2.05565	+	3.15202i	−0.0673711	+	0.103303i
$932$		0			0
$933$	−14.3308	+	37.1927i	−0.469171	+	1.21763i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			36.5715i			1.19474i	0.801966	+	0.597370i	$0.203787\pi$
$937$			36.5715i			1.19474i	−0.801966	+	0.597370i	$0.796213\pi$
$938$		0			0
$939$	4.25518	−	3.43689i	0.138863	−	0.112159i
$940$		0			0
$941$	−11.5675	+	20.0355i	−0.377091	+	0.653140i	−0.990638	−	0.136518i	$-0.956409\pi$
$941$	−11.5675	+	20.0355i	−0.377091	+	0.653140i	0.613547	+	0.789658i	$0.289742\pi$
$942$		0			0
$943$	5.72040	−	3.30267i	0.186282	−	0.107550i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−29.4876	+	17.0247i	−0.958220	+	0.553228i	−0.895625	−	0.444811i	$-0.853271\pi$
$947$	−29.4876	+	17.0247i	−0.958220	+	0.553228i	−0.0625952	+	0.998039i	$0.519938\pi$
$948$		0			0
$949$	1.61418	−	2.79583i	0.0523984	−	0.0907566i
$950$		0			0
$951$	−4.33618	+	3.50231i	−0.140610	+	0.113570i
$952$		0			0
$953$			4.08410i			0.132297i	0.997810	+	0.0661485i	$0.0210711\pi$
$953$			4.08410i			0.132297i	−0.997810	+	0.0661485i	$0.978929\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	0.347376	−	0.901542i	0.0112291	−	0.0291427i
$958$		0			0
$959$	−38.1093	−	11.3287i	−1.23061	−	0.365822i
$960$		0			0
$961$	−14.8583	−	25.7353i	−0.479300	−	0.830172i
$962$		0			0
$963$	25.8083	−	28.5179i	0.831661	−	0.918976i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	8.66642			0.278693			0.139347	−	0.990244i	$-0.455500\pi$
$967$	8.66642			0.278693			0.139347	+	0.990244i	$0.455500\pi$
$968$		0			0
$969$	−0.136303	−	0.867670i	−0.00437868	−	0.0278736i
$970$		0			0
$971$	−9.79452	−	16.9646i	−0.314321	−	0.544420i	0.664972	−	0.746868i	$-0.268444\pi$
$971$	−9.79452	−	16.9646i	−0.314321	−	0.544420i	−0.979293	+	0.202448i	$0.935110\pi$
$972$		0			0
$973$	−6.04772	−	25.2986i	−0.193881	−	0.811037i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−26.5041	−	15.3022i	−0.847942	−	0.489559i	0.0120141	−	0.999928i	$-0.496176\pi$
$977$	−26.5041	−	15.3022i	−0.847942	−	0.489559i	−0.859956	+	0.510368i	$0.829509\pi$
$978$		0			0
$979$			1.93442i			0.0618242i
$980$		0			0
$981$	2.26514	−	10.5259i	0.0723204	−	0.336066i
$982$		0			0
$983$	−14.1107	+	24.4405i	−0.450063	+	0.779532i	−0.998389	−	0.0567327i	$-0.981932\pi$
$983$	−14.1107	+	24.4405i	−0.450063	+	0.779532i	0.548327	+	0.836264i	$0.315265\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−45.2375	−	34.8726i	−1.43992	−	1.11001i
$988$		0			0
$989$	−27.4460	+	15.8460i	−0.872734	+	0.503873i
$990$		0			0
$991$	12.2999	−	21.3040i	0.390719	−	0.676745i	−0.601826	−	0.798628i	$-0.705560\pi$
$991$	12.2999	−	21.3040i	0.390719	−	0.676745i	0.992545	+	0.121882i	$0.0388931\pi$
$992$		0			0
$993$	30.6726	+	37.9754i	0.973364	+	1.20511i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−48.3054	−	27.8892i	−1.52985	−	0.883258i	−0.999367	−	0.0355613i	$-0.988678\pi$
$997$	−48.3054	−	27.8892i	−1.52985	−	0.883258i	−0.530481	−	0.847697i	$-0.677989\pi$
$998$		0			0
$999$	26.7924	+	17.5438i	0.847675	+	0.555062i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bi.k.101.1		10
3.2	odd	2		2100.2.bi.j.101.3		10
5.2	odd	4		2100.2.bo.h.1949.6		20
5.3	odd	4		2100.2.bo.h.1949.5		20
5.4	even	2		420.2.bh.a.101.5	✓	10
7.5	odd	6		2100.2.bi.j.1601.3		10
15.2	even	4		2100.2.bo.g.1949.1		20
15.8	even	4		2100.2.bo.g.1949.10		20
15.14	odd	2		420.2.bh.b.101.3	yes	10
21.5	even	6	inner	2100.2.bi.k.1601.1		10
35.4	even	6		2940.2.d.b.881.3		10
35.12	even	12		2100.2.bo.g.1349.10		20
35.19	odd	6		420.2.bh.b.341.3	yes	10
35.24	odd	6		2940.2.d.a.881.8		10
35.33	even	12		2100.2.bo.g.1349.1		20
105.47	odd	12		2100.2.bo.h.1349.5		20
105.59	even	6		2940.2.d.b.881.4		10
105.68	odd	12		2100.2.bo.h.1349.6		20
105.74	odd	6		2940.2.d.a.881.7		10
105.89	even	6		420.2.bh.a.341.5	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bh.a.101.5	✓	10	5.4	even	2
420.2.bh.a.341.5	yes	10	105.89	even	6
420.2.bh.b.101.3	yes	10	15.14	odd	2
420.2.bh.b.341.3	yes	10	35.19	odd	6
2100.2.bi.j.101.3		10	3.2	odd	2
2100.2.bi.j.1601.3		10	7.5	odd	6
2100.2.bi.k.101.1		10	1.1	even	1	trivial
2100.2.bi.k.1601.1		10	21.5	even	6	inner
2100.2.bo.g.1349.1		20	35.33	even	12
2100.2.bo.g.1349.10		20	35.12	even	12
2100.2.bo.g.1949.1		20	15.2	even	4
2100.2.bo.g.1949.10		20	15.8	even	4
2100.2.bo.h.1349.5		20	105.47	odd	12
2100.2.bo.h.1349.6		20	105.68	odd	12
2100.2.bo.h.1949.5		20	5.3	odd	4
2100.2.bo.h.1949.6		20	5.2	odd	4
2940.2.d.a.881.7		10	105.74	odd	6
2940.2.d.a.881.8		10	35.24	odd	6
2940.2.d.b.881.3		10	35.4	even	6
2940.2.d.b.881.4		10	105.59	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.71107 + 0.268793i) q^{3} +(-2.57325 + 0.615143i) q^{7} +(2.85550 - 0.919845i) q^{9} +O(q^{10})\)	\(q+(-1.71107 + 0.268793i) q^{3} +(-2.57325 + 0.615143i) q^{7} +(2.85550 - 0.919845i) q^{9} +(-1.80606 - 1.04273i) q^{11} -0.245770i q^{13} +(0.471640 - 0.816904i) q^{17} +(-0.465563 + 0.268793i) q^{19} +(4.23765 - 1.74422i) q^{21} +(-2.40010 + 1.38570i) q^{23} +(-4.63871 + 2.34145i) q^{27} -0.267475i q^{29} +(0.981097 + 0.566436i) q^{31} +(3.37057 + 1.29872i) q^{33} +(-3.08164 - 5.33755i) q^{37} +(0.0660611 + 0.420528i) q^{39} -2.38340 q^{41} +11.4354 q^{43} +(-6.23215 - 10.7944i) q^{47} +(6.24320 - 3.16583i) q^{49} +(-0.587429 + 1.52455i) q^{51} +(10.8541 + 6.26660i) q^{53} +(0.724359 - 0.585062i) q^{57} +(-6.25478 + 10.8336i) q^{59} +(4.96556 - 2.86687i) q^{61} +(-6.78207 + 4.12353i) q^{63} +(-2.78001 + 4.81512i) q^{67} +(3.73427 - 3.01616i) q^{69} +10.1375i q^{71} +(11.3758 + 6.56784i) q^{73} +(5.28887 + 1.57221i) q^{77} +(3.17314 + 5.49605i) q^{79} +(7.30777 - 5.25324i) q^{81} -1.06674 q^{83} +(0.0718953 + 0.457667i) q^{87} +(-0.463787 - 0.803302i) q^{89} +(0.151184 + 0.632426i) q^{91} +(-1.83098 - 0.705499i) q^{93} +3.01245i q^{97} +(-6.11636 - 1.31622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} + 5 q^{7} - 3 q^{9}+O(q^{10}) \) 10 * q + q^3 + 5 * q^7 - 3 * q^9	\( 10 q + q^{3} + 5 q^{7} - 3 q^{9} - 6 q^{11} - 6 q^{17} + 3 q^{19} + 10 q^{21} - 24 q^{23} - 8 q^{27} + 15 q^{31} + 20 q^{33} + q^{37} + 15 q^{39} - 8 q^{41} + 26 q^{43} - 14 q^{47} - 13 q^{49} - 44 q^{51} + 24 q^{53} - 18 q^{57} + 42 q^{61} + q^{63} - 7 q^{67} - 14 q^{69} + 3 q^{73} + 26 q^{77} + q^{79} + 41 q^{81} + 8 q^{83} + 26 q^{87} + 28 q^{89} - 11 q^{91} + 47 q^{93} + 36 q^{99}+O(q^{100}) \) 10 * q + q^3 + 5 * q^7 - 3 * q^9 - 6 * q^11 - 6 * q^17 + 3 * q^19 + 10 * q^21 - 24 * q^23 - 8 * q^27 + 15 * q^31 + 20 * q^33 + q^37 + 15 * q^39 - 8 * q^41 + 26 * q^43 - 14 * q^47 - 13 * q^49 - 44 * q^51 + 24 * q^53 - 18 * q^57 + 42 * q^61 + q^63 - 7 * q^67 - 14 * q^69 + 3 * q^73 + 26 * q^77 + q^79 + 41 * q^81 + 8 * q^83 + 26 * q^87 + 28 * q^89 - 11 * q^91 + 47 * q^93 + 36 * q^99

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