LMFDB - Embedded newform 1680.2.bg.t.1201.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1680,2,Mod(961,1680)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1680, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))

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

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

chi := DirichletCharacter("1680.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.bg (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1201.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1680.1201
Dual form			1680.2.bg.t.961.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.62132 - 0.358719i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.62132 - 0.358719i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(2.12132 - 3.67423i) q^{11} -5.24264 q^{13} +1.00000 q^{15} +(2.12132 - 3.67423i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(1.00000 - 2.44949i) q^{21} +(2.12132 + 3.67423i) q^{23} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{27} -10.2426 q^{29} +(3.74264 - 6.48244i) q^{31} +(-2.12132 - 3.67423i) q^{33} +(1.62132 + 2.09077i) q^{35} +(2.62132 + 4.54026i) q^{37} +(-2.62132 + 4.54026i) q^{39} +4.24264 q^{41} +5.24264 q^{43} +(0.500000 - 0.866025i) q^{45} +(-3.00000 - 5.19615i) q^{47} +(6.74264 - 1.88064i) q^{49} +(-2.12132 - 3.67423i) q^{51} +(4.24264 - 7.34847i) q^{53} +4.24264 q^{55} -7.00000 q^{57} +(-0.878680 + 1.52192i) q^{59} +(6.24264 + 10.8126i) q^{61} +(-1.62132 - 2.09077i) q^{63} +(-2.62132 - 4.54026i) q^{65} +(1.62132 - 2.80821i) q^{67} +4.24264 q^{69} -12.7279 q^{71} +(-0.378680 + 0.655892i) q^{73} +(0.500000 + 0.866025i) q^{75} +(4.24264 - 10.3923i) q^{77} +(5.50000 + 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{81} +1.75736 q^{83} +4.24264 q^{85} +(-5.12132 + 8.87039i) q^{87} +(0.878680 + 1.52192i) q^{89} +(-13.7426 + 1.88064i) q^{91} +(-3.74264 - 6.48244i) q^{93} +(3.50000 - 6.06218i) q^{95} +16.4853 q^{97} -4.24264 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 2 * q^9	$ 4 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 2 q^{9} - 4 q^{13} + 4 q^{15} - 14 q^{19} + 4 q^{21} - 2 q^{25} - 4 q^{27} - 24 q^{29} - 2 q^{31} - 2 q^{35} + 2 q^{37} - 2 q^{39} + 4 q^{43} + 2 q^{45} - 12 q^{47} + 10 q^{49} - 28 q^{57} - 12 q^{59} + 8 q^{61} + 2 q^{63} - 2 q^{65} - 2 q^{67} - 10 q^{73} + 2 q^{75} + 22 q^{79} - 2 q^{81} + 24 q^{83} - 12 q^{87} + 12 q^{89} - 38 q^{91} + 2 q^{93} + 14 q^{95} + 32 q^{97}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 2 * q^9 - 4 * q^13 + 4 * q^15 - 14 * q^19 + 4 * q^21 - 2 * q^25 - 4 * q^27 - 24 * q^29 - 2 * q^31 - 2 * q^35 + 2 * q^37 - 2 * q^39 + 4 * q^43 + 2 * q^45 - 12 * q^47 + 10 * q^49 - 28 * q^57 - 12 * q^59 + 8 * q^61 + 2 * q^63 - 2 * q^65 - 2 * q^67 - 10 * q^73 + 2 * q^75 + 22 * q^79 - 2 * q^81 + 24 * q^83 - 12 * q^87 + 12 * q^89 - 38 * q^91 + 2 * q^93 + 14 * q^95 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$	$1$

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
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	2.62132	−	0.358719i	0.990766	−	0.135583i
$7$	2.62132	−	0.358719i	0.990766	−	0.135583i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	2.12132	−	3.67423i	0.639602	−	1.10782i	−0.345918	−	0.938265i	$-0.612432\pi$
$11$	2.12132	−	3.67423i	0.639602	−	1.10782i	0.985520	−	0.169559i	$-0.0542342\pi$
$12$		0			0
$13$	−5.24264			−1.45405			−0.727023	−	0.686613i	$-0.759097\pi$
$13$	−5.24264			−1.45405			−0.727023	+	0.686613i	$0.759097\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	2.12132	−	3.67423i	0.514496	−	0.891133i	−0.485363	−	0.874313i	$-0.661312\pi$
$17$	2.12132	−	3.67423i	0.514496	−	0.891133i	0.999859	−	0.0168199i	$-0.00535420\pi$
$18$		0			0
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	0.114708	−	0.993399i	$-0.463407\pi$
$20$		0			0
$21$	1.00000	−	2.44949i	0.218218	−	0.534522i
$22$		0			0
$23$	2.12132	+	3.67423i	0.442326	+	0.766131i	0.997862	−	0.0653618i	$-0.0208201\pi$
$23$	2.12132	+	3.67423i	0.442326	+	0.766131i	−0.555536	+	0.831493i	$0.687487\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−10.2426			−1.90201			−0.951005	−	0.309175i	$-0.899947\pi$
$29$	−10.2426			−1.90201			−0.951005	+	0.309175i	$0.899947\pi$
$30$		0			0
$31$	3.74264	−	6.48244i	0.672198	−	1.16428i	−0.305081	−	0.952326i	$-0.598684\pi$
$31$	3.74264	−	6.48244i	0.672198	−	1.16428i	0.977279	−	0.211955i	$-0.0679830\pi$
$32$		0			0
$33$	−2.12132	−	3.67423i	−0.369274	−	0.639602i
$34$		0			0
$35$	1.62132	+	2.09077i	0.274053	+	0.353405i
$36$		0			0
$37$	2.62132	+	4.54026i	0.430942	+	0.746414i	0.996955	−	0.0779826i	$-0.0248479\pi$
$37$	2.62132	+	4.54026i	0.430942	+	0.746414i	−0.566012	+	0.824397i	$0.691515\pi$
$38$		0			0
$39$	−2.62132	+	4.54026i	−0.419747	+	0.727023i
$40$		0			0
$41$	4.24264			0.662589			0.331295	−	0.943527i	$-0.392515\pi$
$41$	4.24264			0.662589			0.331295	+	0.943527i	$0.392515\pi$
$42$		0			0
$43$	5.24264			0.799495			0.399748	−	0.916625i	$-0.369098\pi$
$43$	5.24264			0.799495			0.399748	+	0.916625i	$0.369098\pi$
$44$		0			0
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$		0			0
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$		0			0
$49$	6.74264	−	1.88064i	0.963234	−	0.268662i
$50$		0			0
$51$	−2.12132	−	3.67423i	−0.297044	−	0.514496i
$52$		0			0
$53$	4.24264	−	7.34847i	0.582772	−	1.00939i	−0.412378	−	0.911013i	$-0.635302\pi$
$53$	4.24264	−	7.34847i	0.582772	−	1.00939i	0.995149	−	0.0983769i	$-0.0313651\pi$
$54$		0			0
$55$	4.24264			0.572078
$56$		0			0
$57$	−7.00000			−0.927173
$58$		0			0
$59$	−0.878680	+	1.52192i	−0.114394	+	0.198137i	−0.917537	−	0.397649i	$-0.869826\pi$
$59$	−0.878680	+	1.52192i	−0.114394	+	0.198137i	0.803143	+	0.595786i	$0.203159\pi$
$60$		0			0
$61$	6.24264	+	10.8126i	0.799288	+	1.38441i	0.920080	+	0.391730i	$0.128123\pi$
$61$	6.24264	+	10.8126i	0.799288	+	1.38441i	−0.120792	+	0.992678i	$0.538543\pi$
$62$		0			0
$63$	−1.62132	−	2.09077i	−0.204267	−	0.263412i
$64$		0			0
$65$	−2.62132	−	4.54026i	−0.325135	−	0.563150i
$66$		0			0
$67$	1.62132	−	2.80821i	0.198076	−	0.343077i	−0.749829	−	0.661632i	$-0.769864\pi$
$67$	1.62132	−	2.80821i	0.198076	−	0.343077i	0.947904	+	0.318555i	$0.103197\pi$
$68$		0			0
$69$	4.24264			0.510754
$70$		0			0
$71$	−12.7279			−1.51053			−0.755263	−	0.655422i	$-0.772491\pi$
$71$	−12.7279			−1.51053			−0.755263	+	0.655422i	$0.772491\pi$
$72$		0			0
$73$	−0.378680	+	0.655892i	−0.0443211	+	0.0767664i	−0.887335	−	0.461125i	$-0.847446\pi$
$73$	−0.378680	+	0.655892i	−0.0443211	+	0.0767664i	0.843014	+	0.537892i	$0.180779\pi$
$74$		0			0
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$		0			0
$77$	4.24264	−	10.3923i	0.483494	−	1.18431i
$78$		0			0
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	0.989705	+	0.143120i	$0.0457135\pi$
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	−0.370907	+	0.928670i	$0.620953\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	1.75736			0.192895			0.0964476	−	0.995338i	$-0.469252\pi$
$83$	1.75736			0.192895			0.0964476	+	0.995338i	$0.469252\pi$
$84$		0			0
$85$	4.24264			0.460179
$86$		0			0
$87$	−5.12132	+	8.87039i	−0.549063	+	0.951005i
$88$		0			0
$89$	0.878680	+	1.52192i	0.0931399	+	0.161323i	0.908831	−	0.417165i	$-0.136976\pi$
$89$	0.878680	+	1.52192i	0.0931399	+	0.161323i	−0.815691	+	0.578488i	$0.803643\pi$
$90$		0			0
$91$	−13.7426	+	1.88064i	−1.44062	+	0.197144i
$92$		0			0
$93$	−3.74264	−	6.48244i	−0.388094	−	0.672198i
$94$		0			0
$95$	3.50000	−	6.06218i	0.359092	−	0.621966i
$96$		0			0
$97$	16.4853			1.67383			0.836913	−	0.547335i	$-0.184358\pi$
$97$	16.4853			1.67383			0.836913	+	0.547335i	$0.184358\pi$
$98$		0			0
$99$	−4.24264			−0.426401
$100$		0			0
$101$	8.12132	−	14.0665i	0.808102	−	1.39967i	−0.106076	−	0.994358i	$-0.533829\pi$
$101$	8.12132	−	14.0665i	0.808102	−	1.39967i	0.914177	−	0.405315i	$-0.132838\pi$
$102$		0			0
$103$	−4.37868	−	7.58410i	−0.431444	−	0.747283i	0.565554	−	0.824711i	$-0.308662\pi$
$103$	−4.37868	−	7.58410i	−0.431444	−	0.747283i	−0.996998	+	0.0774283i	$0.975329\pi$
$104$		0			0
$105$	2.62132	−	0.358719i	0.255815	−	0.0350074i
$106$		0			0
$107$	−6.36396	−	11.0227i	−0.615227	−	1.06561i	−0.990345	−	0.138628i	$-0.955731\pi$
$107$	−6.36396	−	11.0227i	−0.615227	−	1.06561i	0.375117	−	0.926977i	$-0.377602\pi$
$108$		0			0
$109$	−3.74264	+	6.48244i	−0.358480	+	0.620906i	−0.987707	−	0.156316i	$-0.950038\pi$
$109$	−3.74264	+	6.48244i	−0.358480	+	0.620906i	0.629227	+	0.777221i	$0.283372\pi$
$110$		0			0
$111$	5.24264			0.497609
$112$		0			0
$113$	−18.0000			−1.69330			−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000			−1.69330			−0.846649	+	0.532152i	$0.821383\pi$
$114$		0			0
$115$	−2.12132	+	3.67423i	−0.197814	+	0.342624i
$116$		0			0
$117$	2.62132	+	4.54026i	0.242341	+	0.419747i
$118$		0			0
$119$	4.24264	−	10.3923i	0.388922	−	0.952661i
$120$		0			0
$121$	−3.50000	−	6.06218i	−0.318182	−	0.551107i
$122$		0			0
$123$	2.12132	−	3.67423i	0.191273	−	0.331295i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	11.2426			0.997623			0.498812	−	0.866710i	$-0.333770\pi$
$127$	11.2426			0.997623			0.498812	+	0.866710i	$0.333770\pi$
$128$		0			0
$129$	2.62132	−	4.54026i	0.230794	−	0.399748i
$130$		0			0
$131$	−1.24264	−	2.15232i	−0.108570	−	0.188049i	0.806621	−	0.591069i	$-0.201294\pi$
$131$	−1.24264	−	2.15232i	−0.108570	−	0.188049i	−0.915191	+	0.403020i	$0.867961\pi$
$132$		0			0
$133$	−11.3492	−	14.6354i	−0.984104	−	1.26905i
$134$		0			0
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$		0			0
$137$	2.12132	−	3.67423i	0.181237	−	0.313911i	−0.761065	−	0.648675i	$-0.775323\pi$
$137$	2.12132	−	3.67423i	0.181237	−	0.313911i	0.942302	+	0.334764i	$0.108657\pi$
$138$		0			0
$139$	−1.48528			−0.125980			−0.0629900	−	0.998014i	$-0.520064\pi$
$139$	−1.48528			−0.125980			−0.0629900	+	0.998014i	$0.520064\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$		0			0
$143$	−11.1213	+	19.2627i	−0.930012	+	1.61083i
$144$		0			0
$145$	−5.12132	−	8.87039i	−0.425303	−	0.736646i
$146$		0			0
$147$	1.74264	−	6.77962i	0.143731	−	0.559173i
$148$		0			0
$149$	6.00000	+	10.3923i	0.491539	+	0.851371i	0.999953	−	0.00974235i	$-0.00310113\pi$
$149$	6.00000	+	10.3923i	0.491539	+	0.851371i	−0.508413	+	0.861113i	$0.669768\pi$
$150$		0			0
$151$	2.75736	−	4.77589i	0.224391	−	0.388656i	−0.731746	−	0.681578i	$-0.761294\pi$
$151$	2.75736	−	4.77589i	0.224391	−	0.388656i	0.956136	+	0.292922i	$0.0946275\pi$
$152$		0			0
$153$	−4.24264			−0.342997
$154$		0			0
$155$	7.48528			0.601232
$156$		0			0
$157$	−5.24264	+	9.08052i	−0.418408	+	0.724704i	−0.995780	−	0.0917773i	$-0.970745\pi$
$157$	−5.24264	+	9.08052i	−0.418408	+	0.724704i	0.577371	+	0.816482i	$0.304079\pi$
$158$		0			0
$159$	−4.24264	−	7.34847i	−0.336463	−	0.582772i
$160$		0			0
$161$	6.87868	+	8.87039i	0.542116	+	0.699084i
$162$		0			0
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	0.979076	−	0.203497i	$-0.0652307\pi$
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	−0.665771	+	0.746156i	$0.731897\pi$
$164$		0			0
$165$	2.12132	−	3.67423i	0.165145	−	0.286039i
$166$		0			0
$167$	6.72792			0.520622			0.260311	−	0.965525i	$-0.416175\pi$
$167$	6.72792			0.520622			0.260311	+	0.965525i	$0.416175\pi$
$168$		0			0
$169$	14.4853			1.11425
$170$		0			0
$171$	−3.50000	+	6.06218i	−0.267652	+	0.463586i
$172$		0			0
$173$	1.75736	+	3.04384i	0.133610	+	0.231419i	0.925065	−	0.379808i	$-0.124010\pi$
$173$	1.75736	+	3.04384i	0.133610	+	0.231419i	−0.791456	+	0.611226i	$0.790677\pi$
$174$		0			0
$175$	−1.00000	+	2.44949i	−0.0755929	+	0.185164i
$176$		0			0
$177$	0.878680	+	1.52192i	0.0660456	+	0.114394i
$178$		0			0
$179$	−3.00000	+	5.19615i	−0.224231	+	0.388379i	−0.956088	−	0.293079i	$-0.905320\pi$
$179$	−3.00000	+	5.19615i	−0.224231	+	0.388379i	0.731858	+	0.681457i	$0.238654\pi$
$180$		0			0
$181$	−13.0000			−0.966282			−0.483141	−	0.875542i	$-0.660504\pi$
$181$	−13.0000			−0.966282			−0.483141	+	0.875542i	$0.660504\pi$
$182$		0			0
$183$	12.4853			0.922939
$184$		0			0
$185$	−2.62132	+	4.54026i	−0.192723	+	0.333807i
$186$		0			0
$187$	−9.00000	−	15.5885i	−0.658145	−	1.13994i
$188$		0			0
$189$	−2.62132	+	0.358719i	−0.190673	+	0.0260930i
$190$		0			0
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	0.953912	−	0.300088i	$-0.0970159\pi$
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	−0.736839	+	0.676068i	$0.763683\pi$
$192$		0			0
$193$	−7.62132	+	13.2005i	−0.548595	+	0.950194i	0.449777	+	0.893141i	$0.351504\pi$
$193$	−7.62132	+	13.2005i	−0.548595	+	0.950194i	−0.998371	+	0.0570527i	$0.981830\pi$
$194$		0			0
$195$	−5.24264			−0.375433
$196$		0			0
$197$	−7.75736			−0.552689			−0.276344	−	0.961059i	$-0.589123\pi$
$197$	−7.75736			−0.552689			−0.276344	+	0.961059i	$0.589123\pi$
$198$		0			0
$199$	−3.24264	+	5.61642i	−0.229865	+	0.398137i	−0.957768	−	0.287543i	$-0.907162\pi$
$199$	−3.24264	+	5.61642i	−0.229865	+	0.398137i	0.727903	+	0.685680i	$0.240495\pi$
$200$		0			0
$201$	−1.62132	−	2.80821i	−0.114359	−	0.198076i
$202$		0			0
$203$	−26.8492	+	3.67423i	−1.88445	+	0.257881i
$204$		0			0
$205$	2.12132	+	3.67423i	0.148159	+	0.256620i
$206$		0			0
$207$	2.12132	−	3.67423i	0.147442	−	0.255377i
$208$		0			0
$209$	−29.6985			−2.05429
$210$		0			0
$211$	−5.51472			−0.379649			−0.189824	−	0.981818i	$-0.560792\pi$
$211$	−5.51472			−0.379649			−0.189824	+	0.981818i	$0.560792\pi$
$212$		0			0
$213$	−6.36396	+	11.0227i	−0.436051	+	0.755263i
$214$		0			0
$215$	2.62132	+	4.54026i	0.178773	+	0.309643i
$216$		0			0
$217$	7.48528	−	18.3351i	0.508134	−	1.24467i
$218$		0			0
$219$	0.378680	+	0.655892i	0.0255888	+	0.0443211i
$220$		0			0
$221$	−11.1213	+	19.2627i	−0.748101	+	1.29575i
$222$		0			0
$223$	24.4853			1.63966			0.819828	−	0.572610i	$-0.194069\pi$
$223$	24.4853			1.63966			0.819828	+	0.572610i	$0.194069\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	13.6066	−	23.5673i	0.903102	−	1.56422i	0.0796568	−	0.996822i	$-0.474618\pi$
$227$	13.6066	−	23.5673i	0.903102	−	1.56422i	0.823445	−	0.567396i	$-0.192049\pi$
$228$		0			0
$229$	3.50000	+	6.06218i	0.231287	+	0.400600i	0.958187	−	0.286143i	$-0.0923732\pi$
$229$	3.50000	+	6.06218i	0.231287	+	0.400600i	−0.726900	+	0.686743i	$0.759040\pi$
$230$		0			0
$231$	−6.87868	−	8.87039i	−0.452584	−	0.583629i
$232$		0			0
$233$	1.24264	+	2.15232i	0.0814081	+	0.141003i	0.903855	−	0.427839i	$-0.140725\pi$
$233$	1.24264	+	2.15232i	0.0814081	+	0.141003i	−0.822447	+	0.568842i	$0.807392\pi$
$234$		0			0
$235$	3.00000	−	5.19615i	0.195698	−	0.338960i
$236$		0			0
$237$	11.0000			0.714527
$238$		0			0
$239$	22.9706			1.48584			0.742921	−	0.669379i	$-0.233440\pi$
$239$	22.9706			1.48584			0.742921	+	0.669379i	$0.233440\pi$
$240$		0			0
$241$	2.00000	−	3.46410i	0.128831	−	0.223142i	−0.794393	−	0.607404i	$-0.792211\pi$
$241$	2.00000	−	3.46410i	0.128831	−	0.223142i	0.923224	+	0.384262i	$0.125544\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	5.00000	+	4.89898i	0.319438	+	0.312984i
$246$		0			0
$247$	18.3492	+	31.7818i	1.16753	+	2.02223i
$248$		0			0
$249$	0.878680	−	1.52192i	0.0556841	−	0.0964476i
$250$		0			0
$251$	−6.72792			−0.424663			−0.212331	−	0.977198i	$-0.568106\pi$
$251$	−6.72792			−0.424663			−0.212331	+	0.977198i	$0.568106\pi$
$252$		0			0
$253$	18.0000			1.13165
$254$		0			0
$255$	2.12132	−	3.67423i	0.132842	−	0.230089i
$256$		0			0
$257$	−0.878680	−	1.52192i	−0.0548105	−	0.0949346i	0.837318	−	0.546716i	$-0.184122\pi$
$257$	−0.878680	−	1.52192i	−0.0548105	−	0.0949346i	−0.892129	+	0.451781i	$0.850789\pi$
$258$		0			0
$259$	8.50000	+	10.9612i	0.528164	+	0.681093i
$260$		0			0
$261$	5.12132	+	8.87039i	0.317002	+	0.549063i
$262$		0			0
$263$	4.24264	−	7.34847i	0.261612	−	0.453126i	−0.705058	−	0.709150i	$-0.749079\pi$
$263$	4.24264	−	7.34847i	0.261612	−	0.453126i	0.966671	+	0.256023i	$0.0824124\pi$
$264$		0			0
$265$	8.48528			0.521247
$266$		0			0
$267$	1.75736			0.107549
$268$		0			0
$269$	−7.24264	+	12.5446i	−0.441592	+	0.764859i	−0.997808	−	0.0661785i	$-0.978919\pi$
$269$	−7.24264	+	12.5446i	−0.441592	+	0.764859i	0.556216	+	0.831038i	$0.312253\pi$
$270$		0			0
$271$	13.7279	+	23.7775i	0.833912	+	1.44438i	0.894913	+	0.446240i	$0.147237\pi$
$271$	13.7279	+	23.7775i	0.833912	+	1.44438i	−0.0610014	+	0.998138i	$0.519429\pi$
$272$		0			0
$273$	−5.24264	+	12.8418i	−0.317299	+	0.777221i
$274$		0			0
$275$	2.12132	+	3.67423i	0.127920	+	0.221565i
$276$		0			0
$277$	3.86396	−	6.69258i	0.232163	−	0.402118i	−0.726281	−	0.687397i	$-0.758753\pi$
$277$	3.86396	−	6.69258i	0.232163	−	0.402118i	0.958444	+	0.285279i	$0.0920864\pi$
$278$		0			0
$279$	−7.48528			−0.448132
$280$		0			0
$281$	−4.97056			−0.296519			−0.148259	−	0.988948i	$-0.547367\pi$
$281$	−4.97056			−0.296519			−0.148259	+	0.988948i	$0.547367\pi$
$282$		0			0
$283$	−0.863961	+	1.49642i	−0.0513572	+	0.0889532i	−0.890561	−	0.454864i	$-0.849688\pi$
$283$	−0.863961	+	1.49642i	−0.0513572	+	0.0889532i	0.839204	+	0.543817i	$0.183021\pi$
$284$		0			0
$285$	−3.50000	−	6.06218i	−0.207322	−	0.359092i
$286$		0			0
$287$	11.1213	−	1.52192i	0.656471	−	0.0898360i
$288$		0			0
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$		0			0
$291$	8.24264	−	14.2767i	0.483192	−	0.836913i
$292$		0			0
$293$	28.9706			1.69248			0.846239	−	0.532803i	$-0.178861\pi$
$293$	28.9706			1.69248			0.846239	+	0.532803i	$0.178861\pi$
$294$		0			0
$295$	−1.75736			−0.102317
$296$		0			0
$297$	−2.12132	+	3.67423i	−0.123091	+	0.213201i
$298$		0			0
$299$	−11.1213	−	19.2627i	−0.643163	−	1.11399i
$300$		0			0
$301$	13.7426	−	1.88064i	0.792113	−	0.108398i
$302$		0			0
$303$	−8.12132	−	14.0665i	−0.466558	−	0.808102i
$304$		0			0
$305$	−6.24264	+	10.8126i	−0.357453	+	0.619126i
$306$		0			0
$307$	5.24264			0.299213			0.149607	−	0.988746i	$-0.452199\pi$
$307$	5.24264			0.299213			0.149607	+	0.988746i	$0.452199\pi$
$308$		0			0
$309$	−8.75736			−0.498189
$310$		0			0
$311$	−10.6066	+	18.3712i	−0.601445	+	1.04173i	0.391157	+	0.920324i	$0.372075\pi$
$311$	−10.6066	+	18.3712i	−0.601445	+	1.04173i	−0.992602	+	0.121410i	$0.961258\pi$
$312$		0			0
$313$	0.863961	+	1.49642i	0.0488340	+	0.0845829i	0.889409	−	0.457112i	$-0.151116\pi$
$313$	0.863961	+	1.49642i	0.0488340	+	0.0845829i	−0.840575	+	0.541695i	$0.817783\pi$
$314$		0			0
$315$	1.00000	−	2.44949i	0.0563436	−	0.138013i
$316$		0			0
$317$	−0.363961	−	0.630399i	−0.0204421	−	0.0354067i	0.855623	−	0.517599i	$-0.173174\pi$
$317$	−0.363961	−	0.630399i	−0.0204421	−	0.0354067i	−0.876065	+	0.482192i	$0.839841\pi$
$318$		0			0
$319$	−21.7279	+	37.6339i	−1.21653	+	2.10709i
$320$		0			0
$321$	−12.7279			−0.710403
$322$		0			0
$323$	−29.6985			−1.65247
$324$		0			0
$325$	2.62132	−	4.54026i	0.145405	−	0.251848i
$326$		0			0
$327$	3.74264	+	6.48244i	0.206969	+	0.358480i
$328$		0			0
$329$	−9.72792	−	12.5446i	−0.536318	−	0.691607i
$330$		0			0
$331$	8.50000	+	14.7224i	0.467202	+	0.809218i	0.999298	−	0.0374662i	$-0.0119287\pi$
$331$	8.50000	+	14.7224i	0.467202	+	0.809218i	−0.532096	+	0.846684i	$0.678595\pi$
$332$		0			0
$333$	2.62132	−	4.54026i	0.143647	−	0.248805i
$334$		0			0
$335$	3.24264			0.177164
$336$		0			0
$337$	11.7279			0.638861			0.319430	−	0.947610i	$-0.396508\pi$
$337$	11.7279			0.638861			0.319430	+	0.947610i	$0.396508\pi$
$338$		0			0
$339$	−9.00000	+	15.5885i	−0.488813	+	0.846649i
$340$		0			0
$341$	−15.8787	−	27.5027i	−0.859879	−	1.48935i
$342$		0			0
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$		0			0
$345$	2.12132	+	3.67423i	0.114208	+	0.197814i
$346$		0			0
$347$	−12.0000	+	20.7846i	−0.644194	+	1.11578i	0.340293	+	0.940319i	$0.389474\pi$
$347$	−12.0000	+	20.7846i	−0.644194	+	1.11578i	−0.984487	+	0.175457i	$0.943860\pi$
$348$		0			0
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$		0			0
$351$	5.24264			0.279831
$352$		0			0
$353$	0.878680	−	1.52192i	0.0467674	−	0.0810035i	−0.841694	−	0.539955i	$-0.818441\pi$
$353$	0.878680	−	1.52192i	0.0467674	−	0.0810035i	0.888462	+	0.458951i	$0.151775\pi$
$354$		0			0
$355$	−6.36396	−	11.0227i	−0.337764	−	0.585024i
$356$		0			0
$357$	−6.87868	−	8.87039i	−0.364058	−	0.469471i
$358$		0			0
$359$	5.12132	+	8.87039i	0.270293	+	0.468161i	0.968937	−	0.247309i	$-0.0795461\pi$
$359$	5.12132	+	8.87039i	0.270293	+	0.468161i	−0.698644	+	0.715470i	$0.746213\pi$
$360$		0			0
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$		0			0
$363$	−7.00000			−0.367405
$364$		0			0
$365$	−0.757359			−0.0396420
$366$		0			0
$367$	5.13604	−	8.89588i	0.268099	−	0.464361i	−0.700272	−	0.713876i	$-0.746938\pi$
$367$	5.13604	−	8.89588i	0.268099	−	0.464361i	0.968371	+	0.249515i	$0.0802712\pi$
$368$		0			0
$369$	−2.12132	−	3.67423i	−0.110432	−	0.191273i
$370$		0			0
$371$	8.48528	−	20.7846i	0.440534	−	1.07908i
$372$		0			0
$373$	3.86396	+	6.69258i	0.200068	+	0.346528i	0.948550	−	0.316627i	$-0.102550\pi$
$373$	3.86396	+	6.69258i	0.200068	+	0.346528i	−0.748482	+	0.663155i	$0.769217\pi$
$374$		0			0
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$		0			0
$377$	53.6985			2.76561
$378$		0			0
$379$	−30.4558			−1.56441			−0.782206	−	0.623020i	$-0.785905\pi$
$379$	−30.4558			−1.56441			−0.782206	+	0.623020i	$0.785905\pi$
$380$		0			0
$381$	5.62132	−	9.73641i	0.287989	−	0.498812i
$382$		0			0
$383$	−12.7279	−	22.0454i	−0.650366	−	1.12647i	−0.983034	−	0.183424i	$-0.941282\pi$
$383$	−12.7279	−	22.0454i	−0.650366	−	1.12647i	0.332668	−	0.943044i	$-0.392051\pi$
$384$		0			0
$385$	11.1213	−	1.52192i	0.566795	−	0.0775641i
$386$		0			0
$387$	−2.62132	−	4.54026i	−0.133249	−	0.230794i
$388$		0			0
$389$	−10.6066	+	18.3712i	−0.537776	+	0.931455i	0.461247	+	0.887272i	$0.347402\pi$
$389$	−10.6066	+	18.3712i	−0.537776	+	0.931455i	−0.999023	+	0.0441839i	$0.985931\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$		0			0
$393$	−2.48528			−0.125366
$394$		0			0
$395$	−5.50000	+	9.52628i	−0.276735	+	0.479319i
$396$		0			0
$397$	8.62132	+	14.9326i	0.432692	+	0.749444i	0.997104	−	0.0760490i	$-0.0242305\pi$
$397$	8.62132	+	14.9326i	0.432692	+	0.749444i	−0.564412	+	0.825493i	$0.690897\pi$
$398$		0			0
$399$	−18.3492	+	2.51104i	−0.918611	+	0.125709i
$400$		0			0
$401$	10.2426	+	17.7408i	0.511493	+	0.885932i	0.999911	+	0.0133223i	$0.00424074\pi$
$401$	10.2426	+	17.7408i	0.511493	+	0.885932i	−0.488418	+	0.872610i	$0.662426\pi$
$402$		0			0
$403$	−19.6213	+	33.9851i	−0.977408	+	1.69292i
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	22.2426			1.10253
$408$		0			0
$409$	−8.50000	+	14.7224i	−0.420298	+	0.727977i	−0.995968	−	0.0897044i	$-0.971408\pi$
$409$	−8.50000	+	14.7224i	−0.420298	+	0.727977i	0.575670	+	0.817682i	$0.304741\pi$
$410$		0			0
$411$	−2.12132	−	3.67423i	−0.104637	−	0.181237i
$412$		0			0
$413$	−1.75736	+	4.30463i	−0.0864740	+	0.211817i
$414$		0			0
$415$	0.878680	+	1.52192i	0.0431327	+	0.0747080i
$416$		0			0
$417$	−0.742641	+	1.28629i	−0.0363673	+	0.0629900i
$418$		0			0
$419$	−2.48528			−0.121414			−0.0607070	−	0.998156i	$-0.519336\pi$
$419$	−2.48528			−0.121414			−0.0607070	+	0.998156i	$0.519336\pi$
$420$		0			0
$421$	14.5147			0.707404			0.353702	−	0.935358i	$-0.384923\pi$
$421$	14.5147			0.707404			0.353702	+	0.935358i	$0.384923\pi$
$422$		0			0
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$		0			0
$425$	2.12132	+	3.67423i	0.102899	+	0.178227i
$426$		0			0
$427$	20.2426	+	26.1039i	0.979610	+	1.26325i
$428$		0			0
$429$	11.1213	+	19.2627i	0.536942	+	0.930012i
$430$		0			0
$431$	−15.7279	+	27.2416i	−0.757587	+	1.31218i	0.186490	+	0.982457i	$0.440289\pi$
$431$	−15.7279	+	27.2416i	−0.757587	+	1.31218i	−0.944078	+	0.329723i	$0.893045\pi$
$432$		0			0
$433$	24.7574			1.18976			0.594881	−	0.803814i	$-0.297199\pi$
$433$	24.7574			1.18976			0.594881	+	0.803814i	$0.297199\pi$
$434$		0			0
$435$	−10.2426			−0.491097
$436$		0			0
$437$	14.8492	−	25.7196i	0.710336	−	1.23034i
$438$		0			0
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	0.721686	−	0.692220i	$-0.243367\pi$
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	−0.960323	+	0.278889i	$0.910034\pi$
$440$		0			0
$441$	−5.00000	−	4.89898i	−0.238095	−	0.233285i
$442$		0			0
$443$	1.75736	+	3.04384i	0.0834947	+	0.144617i	0.904749	−	0.425946i	$-0.140059\pi$
$443$	1.75736	+	3.04384i	0.0834947	+	0.144617i	−0.821254	+	0.570563i	$0.806725\pi$
$444$		0			0
$445$	−0.878680	+	1.52192i	−0.0416534	+	0.0721458i
$446$		0			0
$447$	12.0000			0.567581
$448$		0			0
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$		0			0
$451$	9.00000	−	15.5885i	0.423793	−	0.734032i
$452$		0			0
$453$	−2.75736	−	4.77589i	−0.129552	−	0.224391i
$454$		0			0
$455$	−8.50000	−	10.9612i	−0.398486	−	0.513867i
$456$		0			0
$457$	5.10660	+	8.84489i	0.238877	+	0.413747i	0.960392	−	0.278652i	$-0.0898875\pi$
$457$	5.10660	+	8.84489i	0.238877	+	0.413747i	−0.721516	+	0.692398i	$0.756554\pi$
$458$		0			0
$459$	−2.12132	+	3.67423i	−0.0990148	+	0.171499i
$460$		0			0
$461$	−6.72792			−0.313351			−0.156675	−	0.987650i	$-0.550078\pi$
$461$	−6.72792			−0.313351			−0.156675	+	0.987650i	$0.550078\pi$
$462$		0			0
$463$	−35.7279			−1.66042			−0.830209	−	0.557453i	$-0.811779\pi$
$463$	−35.7279			−1.66042			−0.830209	+	0.557453i	$0.811779\pi$
$464$		0			0
$465$	3.74264	−	6.48244i	0.173561	−	0.300616i
$466$		0			0
$467$	11.4853	+	19.8931i	0.531475	+	0.920542i	0.999325	+	0.0367344i	$0.0116955\pi$
$467$	11.4853	+	19.8931i	0.531475	+	0.920542i	−0.467850	+	0.883808i	$0.654971\pi$
$468$		0			0
$469$	3.24264	−	7.94282i	0.149731	−	0.366765i
$470$		0			0
$471$	5.24264	+	9.08052i	0.241568	+	0.418408i
$472$		0			0
$473$	11.1213	−	19.2627i	0.511359	−	0.885700i
$474$		0			0
$475$	7.00000			0.321182
$476$		0			0
$477$	−8.48528			−0.388514
$478$		0			0
$479$	6.00000	−	10.3923i	0.274147	−	0.474837i	−0.695773	−	0.718262i	$-0.744938\pi$
$479$	6.00000	−	10.3923i	0.274147	−	0.474837i	0.969920	+	0.243426i	$0.0782712\pi$
$480$		0			0
$481$	−13.7426	−	23.8030i	−0.626610	−	1.08532i
$482$		0			0
$483$	11.1213	−	1.52192i	0.506038	−	0.0692497i
$484$		0			0
$485$	8.24264	+	14.2767i	0.374279	+	0.648270i
$486$		0			0
$487$	−6.13604	+	10.6279i	−0.278050	+	0.481598i	−0.970900	−	0.239484i	$-0.923022\pi$
$487$	−6.13604	+	10.6279i	−0.278050	+	0.481598i	0.692850	+	0.721082i	$0.256355\pi$
$488$		0			0
$489$	8.00000			0.361773
$490$		0			0
$491$	−32.4853			−1.46604			−0.733020	−	0.680207i	$-0.761890\pi$
$491$	−32.4853			−1.46604			−0.733020	+	0.680207i	$0.761890\pi$
$492$		0			0
$493$	−21.7279	+	37.6339i	−0.978576	+	1.69494i
$494$		0			0
$495$	−2.12132	−	3.67423i	−0.0953463	−	0.165145i
$496$		0			0
$497$	−33.3640	+	4.56575i	−1.49658	+	0.204802i
$498$		0			0
$499$	1.25736	+	2.17781i	0.0562871	+	0.0974922i	0.892796	−	0.450461i	$-0.148740\pi$
$499$	1.25736	+	2.17781i	0.0562871	+	0.0974922i	−0.836509	+	0.547953i	$0.815407\pi$
$500$		0			0
$501$	3.36396	−	5.82655i	0.150291	−	0.260311i
$502$		0			0
$503$	9.51472			0.424240			0.212120	−	0.977244i	$-0.431963\pi$
$503$	9.51472			0.424240			0.212120	+	0.977244i	$0.431963\pi$
$504$		0			0
$505$	16.2426			0.722788
$506$		0			0
$507$	7.24264	−	12.5446i	0.321657	−	0.557126i
$508$		0			0
$509$	−15.7279	−	27.2416i	−0.697128	−	1.20746i	−0.969458	−	0.245257i	$-0.921128\pi$
$509$	−15.7279	−	27.2416i	−0.697128	−	1.20746i	0.272330	−	0.962204i	$-0.412206\pi$
$510$		0			0
$511$	−0.757359	+	1.85514i	−0.0335036	+	0.0820667i
$512$		0			0
$513$	3.50000	+	6.06218i	0.154529	+	0.267652i
$514$		0			0
$515$	4.37868	−	7.58410i	0.192948	−	0.334195i
$516$		0			0
$517$	−25.4558			−1.11955
$518$		0			0
$519$	3.51472			0.154279
$520$		0			0
$521$	−18.7279	+	32.4377i	−0.820485	+	1.42112i	0.0848363	+	0.996395i	$0.472963\pi$
$521$	−18.7279	+	32.4377i	−0.820485	+	1.42112i	−0.905321	+	0.424727i	$0.860370\pi$
$522$		0			0
$523$	1.62132	+	2.80821i	0.0708954	+	0.122794i	0.899294	−	0.437345i	$-0.144081\pi$
$523$	1.62132	+	2.80821i	0.0708954	+	0.122794i	−0.828399	+	0.560139i	$0.810748\pi$
$524$		0			0
$525$	1.62132	+	2.09077i	0.0707602	+	0.0912487i
$526$		0			0
$527$	−15.8787	−	27.5027i	−0.691686	−	1.19804i
$528$		0			0
$529$	2.50000	−	4.33013i	0.108696	−	0.188266i
$530$		0			0
$531$	1.75736			0.0762629
$532$		0			0
$533$	−22.2426			−0.963436
$534$		0			0
$535$	6.36396	−	11.0227i	0.275138	−	0.476553i
$536$		0			0
$537$	3.00000	+	5.19615i	0.129460	+	0.224231i
$538$		0			0
$539$	7.39340	−	28.7635i	0.318456	−	1.23893i
$540$		0			0
$541$	−13.4706	−	23.3317i	−0.579145	−	1.00311i	−0.995578	−	0.0939417i	$-0.970053\pi$
$541$	−13.4706	−	23.3317i	−0.579145	−	1.00311i	0.416433	−	0.909166i	$-0.363280\pi$
$542$		0			0
$543$	−6.50000	+	11.2583i	−0.278942	+	0.483141i
$544$		0			0
$545$	−7.48528			−0.320634
$546$		0			0
$547$	17.4558			0.746358			0.373179	−	0.927759i	$-0.378268\pi$
$547$	17.4558			0.746358			0.373179	+	0.927759i	$0.378268\pi$
$548$		0			0
$549$	6.24264	−	10.8126i	0.266429	−	0.461469i
$550$		0			0
$551$	35.8492	+	62.0927i	1.52723	+	2.64524i
$552$		0			0
$553$	17.8345	+	22.9985i	0.758401	+	0.977995i
$554$		0			0
$555$	2.62132	+	4.54026i	0.111269	+	0.192723i
$556$		0			0
$557$	15.0000	−	25.9808i	0.635570	−	1.10084i	−0.350824	−	0.936442i	$-0.614098\pi$
$557$	15.0000	−	25.9808i	0.635570	−	1.10084i	0.986394	−	0.164399i	$-0.0525683\pi$
$558$		0			0
$559$	−27.4853			−1.16250
$560$		0			0
$561$	−18.0000			−0.759961
$562$		0			0
$563$	−3.00000	+	5.19615i	−0.126435	+	0.218992i	−0.922293	−	0.386492i	$-0.873687\pi$
$563$	−3.00000	+	5.19615i	−0.126435	+	0.218992i	0.795858	+	0.605483i	$0.207020\pi$
$564$		0			0
$565$	−9.00000	−	15.5885i	−0.378633	−	0.655811i
$566$		0			0
$567$	−1.00000	+	2.44949i	−0.0419961	+	0.102869i
$568$		0			0
$569$	−8.84924	−	15.3273i	−0.370980	−	0.642555i	0.618737	−	0.785598i	$-0.287645\pi$
$569$	−8.84924	−	15.3273i	−0.370980	−	0.642555i	−0.989717	+	0.143043i	$0.954311\pi$
$570$		0			0
$571$	19.4706	−	33.7240i	0.814818	−	1.41131i	−0.0946410	−	0.995511i	$-0.530170\pi$
$571$	19.4706	−	33.7240i	0.814818	−	1.41131i	0.909459	−	0.415794i	$-0.136496\pi$
$572$		0			0
$573$	6.00000			0.250654
$574$		0			0
$575$	−4.24264			−0.176930
$576$		0			0
$577$	−10.6213	+	18.3967i	−0.442171	+	0.765863i	−0.997850	−	0.0655337i	$-0.979125\pi$
$577$	−10.6213	+	18.3967i	−0.442171	+	0.765863i	0.555679	+	0.831397i	$0.312458\pi$
$578$		0			0
$579$	7.62132	+	13.2005i	0.316731	+	0.548595i
$580$		0			0
$581$	4.60660	−	0.630399i	0.191114	−	0.0261534i
$582$		0			0
$583$	−18.0000	−	31.1769i	−0.745484	−	1.29122i
$584$		0			0
$585$	−2.62132	+	4.54026i	−0.108378	+	0.187717i
$586$		0			0
$587$	−2.78680			−0.115023			−0.0575117	−	0.998345i	$-0.518317\pi$
$587$	−2.78680			−0.115023			−0.0575117	+	0.998345i	$0.518317\pi$
$588$		0			0
$589$	−52.3970			−2.15898
$590$		0			0
$591$	−3.87868	+	6.71807i	−0.159548	+	0.276344i
$592$		0			0
$593$	19.6066	+	33.9596i	0.805147	+	1.39455i	0.916192	+	0.400740i	$0.131247\pi$
$593$	19.6066	+	33.9596i	0.805147	+	1.39455i	−0.111045	+	0.993815i	$0.535420\pi$
$594$		0			0
$595$	11.1213	−	1.52192i	0.455930	−	0.0623925i
$596$		0			0
$597$	3.24264	+	5.61642i	0.132712	+	0.229865i
$598$		0			0
$599$	−7.75736	+	13.4361i	−0.316957	+	0.548986i	−0.979852	−	0.199727i	$-0.935994\pi$
$599$	−7.75736	+	13.4361i	−0.316957	+	0.548986i	0.662894	+	0.748713i	$0.269328\pi$
$600$		0			0
$601$	13.4853			0.550076			0.275038	−	0.961433i	$-0.411310\pi$
$601$	13.4853			0.550076			0.275038	+	0.961433i	$0.411310\pi$
$602$		0			0
$603$	−3.24264			−0.132051
$604$		0			0
$605$	3.50000	−	6.06218i	0.142295	−	0.246463i
$606$		0			0
$607$	−10.3787	−	17.9764i	−0.421258	−	0.729640i	0.574805	−	0.818290i	$-0.305078\pi$
$607$	−10.3787	−	17.9764i	−0.421258	−	0.729640i	−0.996063	+	0.0886507i	$0.971745\pi$
$608$		0			0
$609$	−10.2426	+	25.0892i	−0.415053	+	1.01667i
$610$		0			0
$611$	15.7279	+	27.2416i	0.636284	+	1.10208i
$612$		0			0
$613$	−22.7279	+	39.3659i	−0.917972	+	1.58997i	−0.115482	+	0.993310i	$0.536841\pi$
$613$	−22.7279	+	39.3659i	−0.917972	+	1.58997i	−0.802491	+	0.596665i	$0.796492\pi$
$614$		0			0
$615$	4.24264			0.171080
$616$		0			0
$617$	−9.51472			−0.383048			−0.191524	−	0.981488i	$-0.561343\pi$
$617$	−9.51472			−0.383048			−0.191524	+	0.981488i	$0.561343\pi$
$618$		0			0
$619$	10.9853	−	19.0271i	0.441536	−	0.764762i	−0.556268	−	0.831003i	$-0.687767\pi$
$619$	10.9853	−	19.0271i	0.441536	−	0.764762i	0.997804	+	0.0662407i	$0.0211005\pi$
$620$		0			0
$621$	−2.12132	−	3.67423i	−0.0851257	−	0.147442i
$622$		0			0
$623$	2.84924	+	3.67423i	0.114152	+	0.147205i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−14.8492	+	25.7196i	−0.593022	+	1.02714i
$628$		0			0
$629$	22.2426			0.886872
$630$		0			0
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$		0			0
$633$	−2.75736	+	4.77589i	−0.109595	+	0.189824i
$634$		0			0
$635$	5.62132	+	9.73641i	0.223075	+	0.386378i
$636$		0			0
$637$	−35.3492	+	9.85951i	−1.40059	+	0.390648i
$638$		0			0
$639$	6.36396	+	11.0227i	0.251754	+	0.436051i
$640$		0			0
$641$	−12.8787	+	22.3065i	−0.508677	+	0.881055i	0.491272	+	0.871006i	$0.336532\pi$
$641$	−12.8787	+	22.3065i	−0.508677	+	0.881055i	−0.999950	+	0.0100488i	$0.996801\pi$
$642$		0			0
$643$	−5.72792			−0.225887			−0.112944	−	0.993601i	$-0.536028\pi$
$643$	−5.72792			−0.225887			−0.112944	+	0.993601i	$0.536028\pi$
$644$		0			0
$645$	5.24264			0.206429
$646$		0			0
$647$	0.878680	−	1.52192i	0.0345445	−	0.0598328i	−0.848236	−	0.529618i	$-0.822335\pi$
$647$	0.878680	−	1.52192i	0.0345445	−	0.0598328i	0.882781	+	0.469785i	$0.155669\pi$
$648$		0			0
$649$	3.72792	+	6.45695i	0.146334	+	0.253457i
$650$		0			0
$651$	−12.1360	−	15.6500i	−0.475649	−	0.613372i
$652$		0			0
$653$	−0.878680	−	1.52192i	−0.0343854	−	0.0595572i	0.848321	−	0.529483i	$-0.177614\pi$
$653$	−0.878680	−	1.52192i	−0.0343854	−	0.0595572i	−0.882706	+	0.469926i	$0.844281\pi$
$654$		0			0
$655$	1.24264	−	2.15232i	0.0485540	−	0.0840980i
$656$		0			0
$657$	0.757359			0.0295474
$658$		0			0
$659$	−7.02944			−0.273828			−0.136914	−	0.990583i	$-0.543718\pi$
$659$	−7.02944			−0.273828			−0.136914	+	0.990583i	$0.543718\pi$
$660$		0			0
$661$	17.9853	−	31.1514i	0.699546	−	1.21165i	−0.269077	−	0.963119i	$-0.586719\pi$
$661$	17.9853	−	31.1514i	0.699546	−	1.21165i	0.968624	−	0.248531i	$-0.0799479\pi$
$662$		0			0
$663$	11.1213	+	19.2627i	0.431916	+	0.748101i
$664$		0			0
$665$	7.00000	−	17.1464i	0.271448	−	0.664910i
$666$		0			0
$667$	−21.7279	−	37.6339i	−0.841309	−	1.45719i
$668$		0			0
$669$	12.2426	−	21.2049i	0.473328	−	0.819828i
$670$		0			0
$671$	52.9706			2.04491
$672$		0			0
$673$	4.27208			0.164677			0.0823383	−	0.996604i	$-0.473761\pi$
$673$	4.27208			0.164677			0.0823383	+	0.996604i	$0.473761\pi$
$674$		0			0
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$		0			0
$677$	6.36396	+	11.0227i	0.244587	+	0.423637i	0.962015	−	0.272995i	$-0.0880143\pi$
$677$	6.36396	+	11.0227i	0.244587	+	0.423637i	−0.717428	+	0.696632i	$0.754681\pi$
$678$		0			0
$679$	43.2132	−	5.91359i	1.65837	−	0.226943i
$680$		0			0
$681$	−13.6066	−	23.5673i	−0.521406	−	0.903102i
$682$		0			0
$683$	−4.60660	+	7.97887i	−0.176267	+	0.305303i	−0.940599	−	0.339520i	$-0.889735\pi$
$683$	−4.60660	+	7.97887i	−0.176267	+	0.305303i	0.764332	+	0.644823i	$0.223069\pi$
$684$		0			0
$685$	4.24264			0.162103
$686$		0			0
$687$	7.00000			0.267067
$688$		0			0
$689$	−22.2426	+	38.5254i	−0.847377	+	1.46770i
$690$		0			0
$691$	−20.4706	−	35.4561i	−0.778737	−	1.34881i	−0.932670	−	0.360731i	$-0.882527\pi$
$691$	−20.4706	−	35.4561i	−0.778737	−	1.34881i	0.153933	−	0.988081i	$-0.450806\pi$
$692$		0			0
$693$	−11.1213	+	1.52192i	−0.422464	+	0.0578129i
$694$		0			0
$695$	−0.742641	−	1.28629i	−0.0281700	−	0.0487918i
$696$		0			0
$697$	9.00000	−	15.5885i	0.340899	−	0.590455i
$698$		0			0
$699$	2.48528			0.0940020
$700$		0			0
$701$	51.2132			1.93430			0.967148	−	0.254214i	$-0.0818167\pi$
$701$	51.2132			1.93430			0.967148	+	0.254214i	$0.0818167\pi$
$702$		0			0
$703$	18.3492	−	31.7818i	0.692055	−	1.19867i
$704$		0			0
$705$	−3.00000	−	5.19615i	−0.112987	−	0.195698i
$706$		0			0
$707$	16.2426	−	39.7862i	0.610867	−	1.49631i
$708$		0			0
$709$	9.75736	+	16.9002i	0.366445	+	0.634702i	0.989007	−	0.147869i	$-0.0472413\pi$
$709$	9.75736	+	16.9002i	0.366445	+	0.634702i	−0.622562	+	0.782571i	$0.713908\pi$
$710$		0			0
$711$	5.50000	−	9.52628i	0.206266	−	0.357263i
$712$		0			0
$713$	31.7574			1.18932
$714$		0			0
$715$	−22.2426			−0.831828
$716$		0			0
$717$	11.4853	−	19.8931i	0.428926	−	0.742921i
$718$		0			0
$719$	4.75736	+	8.23999i	0.177420	+	0.307300i	0.940996	−	0.338418i	$-0.109892\pi$
$719$	4.75736	+	8.23999i	0.177420	+	0.307300i	−0.763576	+	0.645718i	$0.776558\pi$
$720$		0			0
$721$	−14.1985	−	18.3096i	−0.528779	−	0.681886i
$722$		0			0
$723$	−2.00000	−	3.46410i	−0.0743808	−	0.128831i
$724$		0			0
$725$	5.12132	−	8.87039i	0.190201	−	0.329438i
$726$		0			0
$727$	−9.24264			−0.342791			−0.171395	−	0.985202i	$-0.554828\pi$
$727$	−9.24264			−0.342791			−0.171395	+	0.985202i	$0.554828\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	11.1213	−	19.2627i	0.411337	−	0.712456i
$732$		0			0
$733$	−22.1066	−	38.2898i	−0.816526	−	1.41426i	−0.908227	−	0.418478i	$-0.862564\pi$
$733$	−22.1066	−	38.2898i	−0.816526	−	1.41426i	0.0917010	−	0.995787i	$-0.470770\pi$
$734$		0			0
$735$	6.74264	−	1.88064i	0.248706	−	0.0693684i
$736$		0			0
$737$	−6.87868	−	11.9142i	−0.253379	−	0.438866i
$738$		0			0
$739$	0.742641	−	1.28629i	0.0273185	−	0.0473170i	−0.852043	−	0.523472i	$-0.824637\pi$
$739$	0.742641	−	1.28629i	0.0273185	−	0.0473170i	0.879361	+	0.476155i	$0.157970\pi$
$740$		0			0
$741$	36.6985			1.34815
$742$		0			0
$743$	27.2132			0.998356			0.499178	−	0.866500i	$-0.333635\pi$
$743$	27.2132			0.998356			0.499178	+	0.866500i	$0.333635\pi$
$744$		0			0
$745$	−6.00000	+	10.3923i	−0.219823	+	0.380745i
$746$		0			0
$747$	−0.878680	−	1.52192i	−0.0321492	−	0.0556841i
$748$		0			0
$749$	−20.6360	−	26.6112i	−0.754024	−	0.972351i
$750$		0			0
$751$	−11.4706	−	19.8676i	−0.418567	−	0.724979i	0.577229	−	0.816582i	$-0.304134\pi$
$751$	−11.4706	−	19.8676i	−0.418567	−	0.724979i	−0.995796	+	0.0916035i	$0.970801\pi$
$752$		0			0
$753$	−3.36396	+	5.82655i	−0.122590	+	0.212331i
$754$		0			0
$755$	5.51472			0.200701
$756$		0			0
$757$	42.9706			1.56179			0.780896	−	0.624661i	$-0.214763\pi$
$757$	42.9706			1.56179			0.780896	+	0.624661i	$0.214763\pi$
$758$		0			0
$759$	9.00000	−	15.5885i	0.326679	−	0.565825i
$760$		0			0
$761$	−18.8787	−	32.6988i	−0.684352	−	1.18533i	−0.973640	−	0.228090i	$-0.926752\pi$
$761$	−18.8787	−	32.6988i	−0.684352	−	1.18533i	0.289288	−	0.957242i	$-0.406581\pi$
$762$		0			0
$763$	−7.48528	+	18.3351i	−0.270985	+	0.663776i
$764$		0			0
$765$	−2.12132	−	3.67423i	−0.0766965	−	0.132842i
$766$		0			0
$767$	4.60660	−	7.97887i	0.166335	−	0.288100i
$768$		0			0
$769$	5.00000			0.180305			0.0901523	−	0.995928i	$-0.471265\pi$
$769$	5.00000			0.180305			0.0901523	+	0.995928i	$0.471265\pi$
$770$		0			0
$771$	−1.75736			−0.0632897
$772$		0			0
$773$	23.8492	−	41.3081i	0.857798	−	1.48575i	−0.0162275	−	0.999868i	$-0.505166\pi$
$773$	23.8492	−	41.3081i	0.857798	−	1.48575i	0.874025	−	0.485881i	$-0.161501\pi$
$774$		0			0
$775$	3.74264	+	6.48244i	0.134440	+	0.232856i
$776$		0			0
$777$	13.7426	−	1.88064i	0.493014	−	0.0674675i
$778$		0			0
$779$	−14.8492	−	25.7196i	−0.532029	−	0.921502i
$780$		0			0
$781$	−27.0000	+	46.7654i	−0.966136	+	1.67340i
$782$		0			0
$783$	10.2426			0.366042
$784$		0			0
$785$	−10.4853			−0.374236
$786$		0			0
$787$	5.75736	−	9.97204i	0.205228	−	0.355465i	−0.744978	−	0.667090i	$-0.767540\pi$
$787$	5.75736	−	9.97204i	0.205228	−	0.355465i	0.950205	+	0.311625i	$0.100873\pi$
$788$		0			0
$789$	−4.24264	−	7.34847i	−0.151042	−	0.261612i
$790$		0			0
$791$	−47.1838	+	6.45695i	−1.67766	+	0.229583i
$792$		0			0
$793$	−32.7279	−	56.6864i	−1.16220	−	2.01299i
$794$		0			0
$795$	4.24264	−	7.34847i	0.150471	−	0.260623i
$796$		0			0
$797$	−40.2426			−1.42547			−0.712734	−	0.701435i	$-0.752543\pi$
$797$	−40.2426			−1.42547			−0.712734	+	0.701435i	$0.752543\pi$
$798$		0			0
$799$	−25.4558			−0.900563
$800$		0			0
$801$	0.878680	−	1.52192i	0.0310466	−	0.0537743i
$802$		0			0
$803$	1.60660	+	2.78272i	0.0566957	+	0.0981999i
$804$		0			0
$805$	−4.24264	+	10.3923i	−0.149533	+	0.366281i
$806$		0			0
$807$	7.24264	+	12.5446i	0.254953	+	0.441592i
$808$		0			0
$809$	19.9706	−	34.5900i	0.702128	−	1.21612i	−0.265591	−	0.964086i	$-0.585567\pi$
$809$	19.9706	−	34.5900i	0.702128	−	1.21612i	0.967718	−	0.252035i	$-0.0810997\pi$
$810$		0			0
$811$	55.9411			1.96436			0.982179	−	0.187946i	$-0.0601831\pi$
$811$	55.9411			1.96436			0.982179	+	0.187946i	$0.0601831\pi$
$812$		0			0
$813$	27.4558			0.962918
$814$		0			0
$815$	−4.00000	+	6.92820i	−0.140114	+	0.242684i
$816$		0			0
$817$	−18.3492	−	31.7818i	−0.641959	−	1.11191i
$818$		0			0
$819$	8.50000	+	10.9612i	0.297014	+	0.383014i
$820$		0			0
$821$	26.8492	+	46.5043i	0.937045	+	1.62301i	0.770946	+	0.636901i	$0.219784\pi$
$821$	26.8492	+	46.5043i	0.937045	+	1.62301i	0.166099	+	0.986109i	$0.446883\pi$
$822$		0			0
$823$	−2.51472	+	4.35562i	−0.0876576	+	0.151827i	−0.906521	−	0.422162i	$-0.861271\pi$
$823$	−2.51472	+	4.35562i	−0.0876576	+	0.151827i	0.818863	+	0.573989i	$0.194605\pi$
$824$		0			0
$825$	4.24264			0.147710
$826$		0			0
$827$	7.45584			0.259265			0.129633	−	0.991562i	$-0.458620\pi$
$827$	7.45584			0.259265			0.129633	+	0.991562i	$0.458620\pi$
$828$		0			0
$829$	−5.50000	+	9.52628i	−0.191023	+	0.330861i	−0.945589	−	0.325362i	$-0.894514\pi$
$829$	−5.50000	+	9.52628i	−0.191023	+	0.330861i	0.754567	+	0.656223i	$0.227847\pi$
$830$		0			0
$831$	−3.86396	−	6.69258i	−0.134039	−	0.232163i
$832$		0			0
$833$	7.39340	−	28.7635i	0.256166	−	0.996595i
$834$		0			0
$835$	3.36396	+	5.82655i	0.116415	+	0.201636i
$836$		0			0
$837$	−3.74264	+	6.48244i	−0.129365	+	0.224066i
$838$		0			0
$839$	−34.2426			−1.18219			−0.591094	−	0.806603i	$-0.701304\pi$
$839$	−34.2426			−1.18219			−0.591094	+	0.806603i	$0.701304\pi$
$840$		0			0
$841$	75.9117			2.61764
$842$		0			0
$843$	−2.48528	+	4.30463i	−0.0855976	+	0.148259i
$844$		0			0
$845$	7.24264	+	12.5446i	0.249154	+	0.431548i
$846$		0			0
$847$	−11.3492	−	14.6354i	−0.389965	−	0.502878i
$848$		0			0
$849$	0.863961	+	1.49642i	0.0296511	+	0.0513572i
$850$		0			0
$851$	−11.1213	+	19.2627i	−0.381234	+	0.660317i
$852$		0			0
$853$	−0.272078			−0.00931577			−0.00465789	−	0.999989i	$-0.501483\pi$
$853$	−0.272078			−0.00931577			−0.00465789	+	0.999989i	$0.501483\pi$
$854$		0			0
$855$	−7.00000			−0.239395
$856$		0			0
$857$	2.12132	−	3.67423i	0.0724629	−	0.125509i	−0.827517	−	0.561440i	$-0.810247\pi$
$857$	2.12132	−	3.67423i	0.0724629	−	0.125509i	0.899980	+	0.435931i	$0.143581\pi$
$858$		0			0
$859$	−11.0000	−	19.0526i	−0.375315	−	0.650065i	0.615059	−	0.788481i	$-0.289132\pi$
$859$	−11.0000	−	19.0526i	−0.375315	−	0.650065i	−0.990374	+	0.138416i	$0.955799\pi$
$860$		0			0
$861$	4.24264	−	10.3923i	0.144589	−	0.354169i
$862$		0			0
$863$	−19.2426	−	33.3292i	−0.655027	−	1.13454i	−0.981887	−	0.189467i	$-0.939324\pi$
$863$	−19.2426	−	33.3292i	−0.655027	−	1.13454i	0.326860	−	0.945073i	$-0.394009\pi$
$864$		0			0
$865$	−1.75736	+	3.04384i	−0.0597520	+	0.103494i
$866$		0			0
$867$	−1.00000			−0.0339618
$868$		0			0
$869$	46.6690			1.58314
$870$		0			0
$871$	−8.50000	+	14.7224i	−0.288012	+	0.498851i
$872$		0			0
$873$	−8.24264	−	14.2767i	−0.278971	−	0.483192i
$874$		0			0
$875$	−2.62132	+	0.358719i	−0.0886168	+	0.0121269i
$876$		0			0
$877$	5.00000	+	8.66025i	0.168838	+	0.292436i	0.938012	−	0.346604i	$-0.112665\pi$
$877$	5.00000	+	8.66025i	0.168838	+	0.292436i	−0.769174	+	0.639040i	$0.779332\pi$
$878$		0			0
$879$	14.4853	−	25.0892i	0.488576	−	0.846239i
$880$		0			0
$881$	7.02944			0.236828			0.118414	−	0.992964i	$-0.462219\pi$
$881$	7.02944			0.236828			0.118414	+	0.992964i	$0.462219\pi$
$882$		0			0
$883$	19.7279			0.663897			0.331949	−	0.943297i	$-0.392294\pi$
$883$	19.7279			0.663897			0.331949	+	0.943297i	$0.392294\pi$
$884$		0			0
$885$	−0.878680	+	1.52192i	−0.0295365	+	0.0511587i
$886$		0			0
$887$	−13.6066	−	23.5673i	−0.456865	−	0.791313i	0.541928	−	0.840425i	$-0.317694\pi$
$887$	−13.6066	−	23.5673i	−0.456865	−	0.791313i	−0.998793	+	0.0491114i	$0.984361\pi$
$888$		0			0
$889$	29.4706	−	4.03295i	0.988411	−	0.135261i
$890$		0			0
$891$	2.12132	+	3.67423i	0.0710669	+	0.123091i
$892$		0			0
$893$	−21.0000	+	36.3731i	−0.702738	+	1.21718i
$894$		0			0
$895$	−6.00000			−0.200558
$896$		0			0
$897$	−22.2426			−0.742660
$898$		0			0
$899$	−38.3345	+	66.3973i	−1.27853	+	2.21448i
$900$		0			0
$901$	−18.0000	−	31.1769i	−0.599667	−	1.03865i
$902$		0			0
$903$	5.24264	−	12.8418i	0.174464	−	0.427348i
$904$		0			0
$905$	−6.50000	−	11.2583i	−0.216067	−	0.374240i
$906$		0			0
$907$	−27.8640	+	48.2618i	−0.925208	+	1.60251i	−0.133981	+	0.990984i	$0.542776\pi$
$907$	−27.8640	+	48.2618i	−0.925208	+	1.60251i	−0.791227	+	0.611523i	$0.790557\pi$
$908$		0			0
$909$	−16.2426			−0.538734
$910$		0			0
$911$	−8.78680			−0.291120			−0.145560	−	0.989349i	$-0.546498\pi$
$911$	−8.78680			−0.291120			−0.145560	+	0.989349i	$0.546498\pi$
$912$		0			0
$913$	3.72792	−	6.45695i	0.123376	−	0.213694i
$914$		0			0
$915$	6.24264	+	10.8126i	0.206375	+	0.357453i
$916$		0			0
$917$	−4.02944	−	5.19615i	−0.133064	−	0.171592i
$918$		0			0
$919$	0.0147186	+	0.0254934i	0.000485523	+	0.000840950i	0.866268	−	0.499579i	$-0.166512\pi$
$919$	0.0147186	+	0.0254934i	0.000485523	+	0.000840950i	−0.865783	+	0.500420i	$0.833179\pi$
$920$		0			0
$921$	2.62132	−	4.54026i	0.0863754	−	0.149607i
$922$		0			0
$923$	66.7279			2.19638
$924$		0			0
$925$	−5.24264			−0.172377
$926$		0			0
$927$	−4.37868	+	7.58410i	−0.143815	+	0.249094i
$928$		0			0
$929$	−5.63604	−	9.76191i	−0.184912	−	0.320278i	0.758635	−	0.651516i	$-0.225867\pi$
$929$	−5.63604	−	9.76191i	−0.184912	−	0.320278i	−0.943547	+	0.331239i	$0.892533\pi$
$930$		0			0
$931$	−35.0000	−	34.2929i	−1.14708	−	1.12390i
$932$		0			0
$933$	10.6066	+	18.3712i	0.347245	+	0.601445i
$934$		0			0
$935$	9.00000	−	15.5885i	0.294331	−	0.509797i
$936$		0			0
$937$	40.6985			1.32956			0.664781	−	0.747039i	$-0.268525\pi$
$937$	40.6985			1.32956			0.664781	+	0.747039i	$0.268525\pi$
$938$		0			0
$939$	1.72792			0.0563886
$940$		0			0
$941$	−5.84924	+	10.1312i	−0.190680	+	0.330267i	−0.945476	−	0.325693i	$-0.894403\pi$
$941$	−5.84924	+	10.1312i	−0.190680	+	0.330267i	0.754796	+	0.655960i	$0.227736\pi$
$942$		0			0
$943$	9.00000	+	15.5885i	0.293080	+	0.507630i
$944$		0			0
$945$	−1.62132	−	2.09077i	−0.0527416	−	0.0680128i
$946$		0			0
$947$	19.6066	+	33.9596i	0.637129	+	1.10354i	0.986060	+	0.166391i	$0.0532115\pi$
$947$	19.6066	+	33.9596i	0.637129	+	1.10354i	−0.348931	+	0.937148i	$0.613455\pi$
$948$		0			0
$949$	1.98528	−	3.43861i	0.0644450	−	0.111622i
$950$		0			0
$951$	−0.727922			−0.0236045
$952$		0			0
$953$	−44.4853			−1.44102			−0.720510	−	0.693445i	$-0.756092\pi$
$953$	−44.4853			−1.44102			−0.720510	+	0.693445i	$0.756092\pi$
$954$		0			0
$955$	−3.00000	+	5.19615i	−0.0970777	+	0.168144i
$956$		0			0
$957$	21.7279	+	37.6339i	0.702364	+	1.21653i
$958$		0			0
$959$	4.24264	−	10.3923i	0.137002	−	0.335585i
$960$		0			0
$961$	−12.5147	−	21.6761i	−0.403701	−	0.699230i
$962$		0			0
$963$	−6.36396	+	11.0227i	−0.205076	+	0.355202i
$964$		0			0
$965$	−15.2426			−0.490678
$966$		0			0
$967$	26.7574			0.860459			0.430229	−	0.902720i	$-0.358433\pi$
$967$	26.7574			0.860459			0.430229	+	0.902720i	$0.358433\pi$
$968$		0			0
$969$	−14.8492	+	25.7196i	−0.477026	+	0.826234i
$970$		0			0
$971$	9.51472	+	16.4800i	0.305342	+	0.528868i	0.977337	−	0.211688i	$-0.0678959\pi$
$971$	9.51472	+	16.4800i	0.305342	+	0.528868i	−0.671996	+	0.740555i	$0.734563\pi$
$972$		0			0
$973$	−3.89340	+	0.532799i	−0.124817	+	0.0170808i
$974$		0			0
$975$	−2.62132	−	4.54026i	−0.0839494	−	0.145405i
$976$		0			0
$977$	25.6066	−	44.3519i	0.819228	−	1.41894i	−0.0870242	−	0.996206i	$-0.527736\pi$
$977$	25.6066	−	44.3519i	0.819228	−	1.41894i	0.906252	−	0.422738i	$-0.138931\pi$
$978$		0			0
$979$	7.45584			0.238290
$980$		0			0
$981$	7.48528			0.238987
$982$		0			0
$983$	8.84924	−	15.3273i	0.282247	−	0.488866i	−0.689691	−	0.724104i	$-0.742254\pi$
$983$	8.84924	−	15.3273i	0.282247	−	0.488866i	0.971938	+	0.235238i	$0.0755869\pi$
$984$		0			0
$985$	−3.87868	−	6.71807i	−0.123585	−	0.214056i
$986$		0			0
$987$	−15.7279	+	2.15232i	−0.500625	+	0.0685090i
$988$		0			0
$989$	11.1213	+	19.2627i	0.353637	+	0.612518i
$990$		0			0
$991$	−26.4706	+	45.8484i	−0.840865	+	1.45642i	0.0482991	+	0.998833i	$0.484620\pi$
$991$	−26.4706	+	45.8484i	−0.840865	+	1.45642i	−0.889164	+	0.457588i	$0.848713\pi$
$992$		0			0
$993$	17.0000			0.539479
$994$		0			0
$995$	−6.48528			−0.205597
$996$		0			0
$997$	0.136039	−	0.235626i	0.00430840	−	0.00746236i	−0.863863	−	0.503727i	$-0.831962\pi$
$997$	0.136039	−	0.235626i	0.00430840	−	0.00746236i	0.868172	+	0.496264i	$0.165295\pi$
$998$		0			0
$999$	−2.62132	−	4.54026i	−0.0829349	−	0.143647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.bg.t.1201.2		4
4.3	odd	2		420.2.q.d.361.1	yes	4
7.2	even	3	inner	1680.2.bg.t.961.2		4
12.11	even	2		1260.2.s.e.361.1		4
20.3	even	4		2100.2.bc.f.949.2		8
20.7	even	4		2100.2.bc.f.949.3		8
20.19	odd	2		2100.2.q.k.1201.2		4
28.3	even	6		2940.2.a.p.1.2		2
28.11	odd	6		2940.2.a.r.1.2		2
28.19	even	6		2940.2.q.q.961.1		4
28.23	odd	6		420.2.q.d.121.1	✓	4
28.27	even	2		2940.2.q.q.361.1		4
84.11	even	6		8820.2.a.bk.1.1		2
84.23	even	6		1260.2.s.e.541.1		4
84.59	odd	6		8820.2.a.bf.1.1		2
140.23	even	12		2100.2.bc.f.1549.3		8
140.79	odd	6		2100.2.q.k.1801.2		4
140.107	even	12		2100.2.bc.f.1549.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.q.d.121.1	✓	4	28.23	odd	6
420.2.q.d.361.1	yes	4	4.3	odd	2
1260.2.s.e.361.1		4	12.11	even	2
1260.2.s.e.541.1		4	84.23	even	6
1680.2.bg.t.961.2		4	7.2	even	3	inner
1680.2.bg.t.1201.2		4	1.1	even	1	trivial
2100.2.q.k.1201.2		4	20.19	odd	2
2100.2.q.k.1801.2		4	140.79	odd	6
2100.2.bc.f.949.2		8	20.3	even	4
2100.2.bc.f.949.3		8	20.7	even	4
2100.2.bc.f.1549.2		8	140.107	even	12
2100.2.bc.f.1549.3		8	140.23	even	12
2940.2.a.p.1.2		2	28.3	even	6
2940.2.a.r.1.2		2	28.11	odd	6
2940.2.q.q.361.1		4	28.27	even	2
2940.2.q.q.961.1		4	28.19	even	6
8820.2.a.bf.1.1		2	84.59	odd	6
8820.2.a.bk.1.1		2	84.11	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:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.bg (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.62132 - 0.358719i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.62132 - 0.358719i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(2.12132 - 3.67423i) q^{11} -5.24264 q^{13} +1.00000 q^{15} +(2.12132 - 3.67423i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(1.00000 - 2.44949i) q^{21} +(2.12132 + 3.67423i) q^{23} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{27} -10.2426 q^{29} +(3.74264 - 6.48244i) q^{31} +(-2.12132 - 3.67423i) q^{33} +(1.62132 + 2.09077i) q^{35} +(2.62132 + 4.54026i) q^{37} +(-2.62132 + 4.54026i) q^{39} +4.24264 q^{41} +5.24264 q^{43} +(0.500000 - 0.866025i) q^{45} +(-3.00000 - 5.19615i) q^{47} +(6.74264 - 1.88064i) q^{49} +(-2.12132 - 3.67423i) q^{51} +(4.24264 - 7.34847i) q^{53} +4.24264 q^{55} -7.00000 q^{57} +(-0.878680 + 1.52192i) q^{59} +(6.24264 + 10.8126i) q^{61} +(-1.62132 - 2.09077i) q^{63} +(-2.62132 - 4.54026i) q^{65} +(1.62132 - 2.80821i) q^{67} +4.24264 q^{69} -12.7279 q^{71} +(-0.378680 + 0.655892i) q^{73} +(0.500000 + 0.866025i) q^{75} +(4.24264 - 10.3923i) q^{77} +(5.50000 + 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{81} +1.75736 q^{83} +4.24264 q^{85} +(-5.12132 + 8.87039i) q^{87} +(0.878680 + 1.52192i) q^{89} +(-13.7426 + 1.88064i) q^{91} +(-3.74264 - 6.48244i) q^{93} +(3.50000 - 6.06218i) q^{95} +16.4853 q^{97} -4.24264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 2 * q^9	\( 4 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 2 q^{9} - 4 q^{13} + 4 q^{15} - 14 q^{19} + 4 q^{21} - 2 q^{25} - 4 q^{27} - 24 q^{29} - 2 q^{31} - 2 q^{35} + 2 q^{37} - 2 q^{39} + 4 q^{43} + 2 q^{45} - 12 q^{47} + 10 q^{49} - 28 q^{57} - 12 q^{59} + 8 q^{61} + 2 q^{63} - 2 q^{65} - 2 q^{67} - 10 q^{73} + 2 q^{75} + 22 q^{79} - 2 q^{81} + 24 q^{83} - 12 q^{87} + 12 q^{89} - 38 q^{91} + 2 q^{93} + 14 q^{95} + 32 q^{97}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 2 * q^9 - 4 * q^13 + 4 * q^15 - 14 * q^19 + 4 * q^21 - 2 * q^25 - 4 * q^27 - 24 * q^29 - 2 * q^31 - 2 * q^35 + 2 * q^37 - 2 * q^39 + 4 * q^43 + 2 * q^45 - 12 * q^47 + 10 * q^49 - 28 * q^57 - 12 * q^59 + 8 * q^61 + 2 * q^63 - 2 * q^65 - 2 * q^67 - 10 * q^73 + 2 * q^75 + 22 * q^79 - 2 * q^81 + 24 * q^83 - 12 * q^87 + 12 * q^89 - 38 * q^91 + 2 * q^93 + 14 * q^95 + 32 * q^97

Introduction

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