LMFDB - Embedded newform 420.2.q.d.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(121,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("420.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.35371688489$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	420.121
Dual form			420.2.q.d.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-2.12132 - 3.67423i) q^{11} -5.24264 q^{13} -1.00000 q^{15} +(2.12132 + 3.67423i) q^{17} +(3.50000 - 6.06218i) q^{19} +(1.00000 + 2.44949i) q^{21} +(-2.12132 + 3.67423i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} -10.2426 q^{29} +(-3.74264 - 6.48244i) q^{31} +(-2.12132 + 3.67423i) q^{33} +(-1.62132 + 2.09077i) q^{35} +(2.62132 - 4.54026i) q^{37} +(2.62132 + 4.54026i) q^{39} +4.24264 q^{41} -5.24264 q^{43} +(0.500000 + 0.866025i) q^{45} +(3.00000 - 5.19615i) q^{47} +(6.74264 + 1.88064i) q^{49} +(2.12132 - 3.67423i) q^{51} +(4.24264 + 7.34847i) q^{53} -4.24264 q^{55} -7.00000 q^{57} +(0.878680 + 1.52192i) q^{59} +(6.24264 - 10.8126i) q^{61} +(1.62132 - 2.09077i) q^{63} +(-2.62132 + 4.54026i) q^{65} +(-1.62132 - 2.80821i) q^{67} +4.24264 q^{69} +12.7279 q^{71} +(-0.378680 - 0.655892i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(4.24264 + 10.3923i) q^{77} +(-5.50000 + 9.52628i) q^{79} +(-0.500000 - 0.866025i) q^{81} -1.75736 q^{83} +4.24264 q^{85} +(5.12132 + 8.87039i) q^{87} +(0.878680 - 1.52192i) q^{89} +(13.7426 + 1.88064i) q^{91} +(-3.74264 + 6.48244i) q^{93} +(-3.50000 - 6.06218i) q^{95} +16.4853 q^{97} +4.24264 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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	−0.985520	−	0.169559i	$-0.945766\pi$
$11$	−2.12132	−	3.67423i	−0.639602	−	1.10782i	0.345918	−	0.938265i	$-0.387568\pi$
$12$		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	0.999859	+	0.0168199i	$0.00535420\pi$
$17$	2.12132	+	3.67423i	0.514496	+	0.891133i	−0.485363	+	0.874313i	$0.661312\pi$
$18$		0			0
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	0.917663	−	0.397360i	$-0.130073\pi$
$20$		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	$-0.979180\pi$
$23$	−2.12132	+	3.67423i	−0.442326	+	0.766131i	0.555536	+	0.831493i	$0.312513\pi$
$24$		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	−0.977279	−	0.211955i	$-0.932017\pi$
$31$	−3.74264	−	6.48244i	−0.672198	−	1.16428i	0.305081	−	0.952326i	$-0.401316\pi$
$32$		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	−0.566012	−	0.824397i	$-0.691515\pi$
$37$	2.62132	−	4.54026i	0.430942	−	0.746414i	0.996955	+	0.0779826i	$0.0248479\pi$
$38$		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	$-0.630902\pi$
$43$	−5.24264			−0.799495			−0.399748	+	0.916625i	$0.630902\pi$
$44$		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	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$		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	0.995149	+	0.0983769i	$0.0313651\pi$
$53$	4.24264	+	7.34847i	0.582772	+	1.00939i	−0.412378	+	0.911013i	$0.635302\pi$
$54$		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	$-0.130174\pi$
$59$	0.878680	+	1.52192i	0.114394	+	0.198137i	−0.803143	+	0.595786i	$0.796841\pi$
$60$		0			0
$61$	6.24264	−	10.8126i	0.799288	−	1.38441i	−0.120792	−	0.992678i	$-0.538543\pi$
$61$	6.24264	−	10.8126i	0.799288	−	1.38441i	0.920080	−	0.391730i	$-0.128123\pi$
$62$		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	$-0.230136\pi$
$67$	−1.62132	−	2.80821i	−0.198076	−	0.343077i	−0.947904	+	0.318555i	$0.896803\pi$
$68$		0			0
$69$	4.24264			0.510754
$70$		0			0
$71$	12.7279			1.51053			0.755263	−	0.655422i	$-0.227509\pi$
$71$	12.7279			1.51053			0.755263	+	0.655422i	$0.227509\pi$
$72$		0			0
$73$	−0.378680	−	0.655892i	−0.0443211	−	0.0767664i	0.843014	−	0.537892i	$-0.180779\pi$
$73$	−0.378680	−	0.655892i	−0.0443211	−	0.0767664i	−0.887335	+	0.461125i	$0.847446\pi$
$74$		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	0.370907	+	0.928670i	$0.379047\pi$
$79$	−5.50000	+	9.52628i	−0.618798	+	1.07179i	−0.989705	+	0.143120i	$0.954286\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−1.75736			−0.192895			−0.0964476	−	0.995338i	$-0.530748\pi$
$83$	−1.75736			−0.192895			−0.0964476	+	0.995338i	$0.530748\pi$
$84$		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	−0.815691	−	0.578488i	$-0.803643\pi$
$89$	0.878680	−	1.52192i	0.0931399	−	0.161323i	0.908831	+	0.417165i	$0.136976\pi$
$90$		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	0.914177	+	0.405315i	$0.132838\pi$
$101$	8.12132	+	14.0665i	0.808102	+	1.39967i	−0.106076	+	0.994358i	$0.533829\pi$
$102$		0			0
$103$	4.37868	−	7.58410i	0.431444	−	0.747283i	−0.565554	−	0.824711i	$-0.691338\pi$
$103$	4.37868	−	7.58410i	0.431444	−	0.747283i	0.996998	+	0.0774283i	$0.0246709\pi$
$104$		0			0
$105$	2.62132	+	0.358719i	0.255815	+	0.0350074i
$106$		0			0
$107$	6.36396	−	11.0227i	0.615227	−	1.06561i	−0.375117	−	0.926977i	$-0.622398\pi$
$107$	6.36396	−	11.0227i	0.615227	−	1.06561i	0.990345	−	0.138628i	$-0.0442691\pi$
$108$		0			0
$109$	−3.74264	−	6.48244i	−0.358480	−	0.620906i	0.629227	−	0.777221i	$-0.283372\pi$
$109$	−3.74264	−	6.48244i	−0.358480	−	0.620906i	−0.987707	+	0.156316i	$0.950038\pi$
$110$		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	$-0.666230\pi$
$127$	−11.2426			−0.997623			−0.498812	+	0.866710i	$0.666230\pi$
$128$		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	$-0.798706\pi$
$131$	1.24264	−	2.15232i	0.108570	−	0.188049i	0.915191	+	0.403020i	$0.132039\pi$
$132$		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	0.942302	−	0.334764i	$-0.108657\pi$
$137$	2.12132	+	3.67423i	0.181237	+	0.313911i	−0.761065	+	0.648675i	$0.775323\pi$
$138$		0			0
$139$	1.48528			0.125980			0.0629900	−	0.998014i	$-0.479936\pi$
$139$	1.48528			0.125980			0.0629900	+	0.998014i	$0.479936\pi$
$140$		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	−0.508413	−	0.861113i	$-0.669768\pi$
$149$	6.00000	−	10.3923i	0.491539	−	0.851371i	0.999953	+	0.00974235i	$0.00310113\pi$
$150$		0			0
$151$	−2.75736	−	4.77589i	−0.224391	−	0.388656i	0.731746	−	0.681578i	$-0.238706\pi$
$151$	−2.75736	−	4.77589i	−0.224391	−	0.388656i	−0.956136	+	0.292922i	$0.905373\pi$
$152$		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	0.577371	−	0.816482i	$-0.304079\pi$
$157$	−5.24264	−	9.08052i	−0.418408	−	0.724704i	−0.995780	+	0.0917773i	$0.970745\pi$
$158$		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	$-0.934769\pi$
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	0.665771	+	0.746156i	$0.268103\pi$
$164$		0			0
$165$	2.12132	+	3.67423i	0.165145	+	0.286039i
$166$		0			0
$167$	−6.72792			−0.520622			−0.260311	−	0.965525i	$-0.583825\pi$
$167$	−6.72792			−0.520622			−0.260311	+	0.965525i	$0.583825\pi$
$168$		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	−0.791456	−	0.611226i	$-0.790677\pi$
$173$	1.75736	−	3.04384i	0.133610	−	0.231419i	0.925065	+	0.379808i	$0.124010\pi$
$174$		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	$-0.0946798\pi$
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	−0.731858	+	0.681457i	$0.761346\pi$
$180$		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	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$		0			0
$193$	−7.62132	−	13.2005i	−0.548595	−	0.950194i	−0.998371	−	0.0570527i	$-0.981830\pi$
$193$	−7.62132	−	13.2005i	−0.548595	−	0.950194i	0.449777	−	0.893141i	$-0.351504\pi$
$194$		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	$-0.0928383\pi$
$199$	3.24264	+	5.61642i	0.229865	+	0.398137i	−0.727903	+	0.685680i	$0.759505\pi$
$200$		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	$-0.439208\pi$
$211$	5.51472			0.379649			0.189824	+	0.981818i	$0.439208\pi$
$212$		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	$-0.805931\pi$
$223$	−24.4853			−1.63966			−0.819828	+	0.572610i	$0.805931\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−13.6066	−	23.5673i	−0.903102	−	1.56422i	−0.823445	−	0.567396i	$-0.807951\pi$
$227$	−13.6066	−	23.5673i	−0.903102	−	1.56422i	−0.0796568	−	0.996822i	$-0.525382\pi$
$228$		0			0
$229$	3.50000	−	6.06218i	0.231287	−	0.400600i	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	3.50000	−	6.06218i	0.231287	−	0.400600i	0.958187	+	0.286143i	$0.0923732\pi$
$230$		0			0
$231$	6.87868	−	8.87039i	0.452584	−	0.583629i
$232$		0			0
$233$	1.24264	−	2.15232i	0.0814081	−	0.141003i	−0.822447	−	0.568842i	$-0.807392\pi$
$233$	1.24264	−	2.15232i	0.0814081	−	0.141003i	0.903855	+	0.427839i	$0.140725\pi$
$234$		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	$-0.766560\pi$
$239$	−22.9706			−1.48584			−0.742921	+	0.669379i	$0.766560\pi$
$240$		0			0
$241$	2.00000	+	3.46410i	0.128831	+	0.223142i	0.923224	−	0.384262i	$-0.125544\pi$
$241$	2.00000	+	3.46410i	0.128831	+	0.223142i	−0.794393	+	0.607404i	$0.792211\pi$
$242$		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	$-0.431894\pi$
$251$	6.72792			0.424663			0.212331	+	0.977198i	$0.431894\pi$
$252$		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	−0.892129	−	0.451781i	$-0.850789\pi$
$257$	−0.878680	+	1.52192i	−0.0548105	+	0.0949346i	0.837318	+	0.546716i	$0.184122\pi$
$258$		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	$-0.250921\pi$
$263$	−4.24264	−	7.34847i	−0.261612	−	0.453126i	−0.966671	+	0.256023i	$0.917588\pi$
$264$		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	0.556216	−	0.831038i	$-0.312253\pi$
$269$	−7.24264	−	12.5446i	−0.441592	−	0.764859i	−0.997808	+	0.0661785i	$0.978919\pi$
$270$		0			0
$271$	−13.7279	+	23.7775i	−0.833912	+	1.44438i	0.0610014	+	0.998138i	$0.480571\pi$
$271$	−13.7279	+	23.7775i	−0.833912	+	1.44438i	−0.894913	+	0.446240i	$0.852763\pi$
$272$		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	0.958444	−	0.285279i	$-0.0920864\pi$
$277$	3.86396	+	6.69258i	0.232163	+	0.402118i	−0.726281	+	0.687397i	$0.758753\pi$
$278$		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	$-0.150312\pi$
$283$	0.863961	+	1.49642i	0.0513572	+	0.0889532i	−0.839204	+	0.543817i	$0.816979\pi$
$284$		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	$-0.547801\pi$
$307$	−5.24264			−0.299213			−0.149607	+	0.988746i	$0.547801\pi$
$308$		0			0
$309$	−8.75736			−0.498189
$310$		0			0
$311$	10.6066	+	18.3712i	0.601445	+	1.04173i	0.992602	+	0.121410i	$0.0387415\pi$
$311$	10.6066	+	18.3712i	0.601445	+	1.04173i	−0.391157	+	0.920324i	$0.627925\pi$
$312$		0			0
$313$	0.863961	−	1.49642i	0.0488340	−	0.0845829i	−0.840575	−	0.541695i	$-0.817783\pi$
$313$	0.863961	−	1.49642i	0.0488340	−	0.0845829i	0.889409	+	0.457112i	$0.151116\pi$
$314$		0			0
$315$	−1.00000	−	2.44949i	−0.0563436	−	0.138013i
$316$		0			0
$317$	−0.363961	+	0.630399i	−0.0204421	+	0.0354067i	−0.876065	−	0.482192i	$-0.839841\pi$
$317$	−0.363961	+	0.630399i	−0.0204421	+	0.0354067i	0.855623	+	0.517599i	$0.173174\pi$
$318$		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	$-0.988071\pi$
$331$	−8.50000	+	14.7224i	−0.467202	+	0.809218i	0.532096	+	0.846684i	$0.321405\pi$
$332$		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	0.984487	+	0.175457i	$0.0561403\pi$
$347$	12.0000	+	20.7846i	0.644194	+	1.11578i	−0.340293	+	0.940319i	$0.610526\pi$
$348$		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	0.888462	−	0.458951i	$-0.151775\pi$
$353$	0.878680	+	1.52192i	0.0467674	+	0.0810035i	−0.841694	+	0.539955i	$0.818441\pi$
$354$		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	$-0.920454\pi$
$359$	−5.12132	+	8.87039i	−0.270293	+	0.468161i	0.698644	+	0.715470i	$0.253787\pi$
$360$		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	$-0.253062\pi$
$367$	−5.13604	−	8.89588i	−0.268099	−	0.464361i	−0.968371	+	0.249515i	$0.919729\pi$
$368$		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	−0.748482	−	0.663155i	$-0.769217\pi$
$373$	3.86396	−	6.69258i	0.200068	−	0.346528i	0.948550	+	0.316627i	$0.102550\pi$
$374$		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	$-0.214095\pi$
$379$	30.4558			1.56441			0.782206	+	0.623020i	$0.214095\pi$
$380$		0			0
$381$	5.62132	+	9.73641i	0.287989	+	0.498812i
$382$		0			0
$383$	12.7279	−	22.0454i	0.650366	−	1.12647i	−0.332668	−	0.943044i	$-0.607949\pi$
$383$	12.7279	−	22.0454i	0.650366	−	1.12647i	0.983034	−	0.183424i	$-0.0587180\pi$
$384$		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	−0.999023	−	0.0441839i	$-0.985931\pi$
$389$	−10.6066	−	18.3712i	−0.537776	−	0.931455i	0.461247	−	0.887272i	$-0.347402\pi$
$390$		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	−0.564412	−	0.825493i	$-0.690897\pi$
$397$	8.62132	−	14.9326i	0.432692	−	0.749444i	0.997104	+	0.0760490i	$0.0242305\pi$
$398$		0			0
$399$	18.3492	+	2.51104i	0.918611	+	0.125709i
$400$		0			0
$401$	10.2426	−	17.7408i	0.511493	−	0.885932i	−0.488418	−	0.872610i	$-0.662426\pi$
$401$	10.2426	−	17.7408i	0.511493	−	0.885932i	0.999911	−	0.0133223i	$-0.00424074\pi$
$402$		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	0.575670	−	0.817682i	$-0.304741\pi$
$409$	−8.50000	−	14.7224i	−0.420298	−	0.727977i	−0.995968	+	0.0897044i	$0.971408\pi$
$410$		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	$-0.480664\pi$
$419$	2.48528			0.121414			0.0607070	+	0.998156i	$0.480664\pi$
$420$		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	0.944078	+	0.329723i	$0.106955\pi$
$431$	15.7279	+	27.2416i	0.757587	+	1.31218i	−0.186490	+	0.982457i	$0.559711\pi$
$432$		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	$-0.756633\pi$
$439$	5.00000	−	8.66025i	0.238637	−	0.413331i	0.960323	+	0.278889i	$0.0899661\pi$
$440$		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	$-0.859941\pi$
$443$	−1.75736	+	3.04384i	−0.0834947	+	0.144617i	0.821254	+	0.570563i	$0.193275\pi$
$444$		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	−0.721516	−	0.692398i	$-0.756554\pi$
$457$	5.10660	−	8.84489i	0.238877	−	0.413747i	0.960392	+	0.278652i	$0.0898875\pi$
$458$		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	$-0.188221\pi$
$463$	35.7279			1.66042			0.830209	+	0.557453i	$0.188221\pi$
$464$		0			0
$465$	3.74264	+	6.48244i	0.173561	+	0.300616i
$466$		0			0
$467$	−11.4853	+	19.8931i	−0.531475	+	0.920542i	0.467850	+	0.883808i	$0.345029\pi$
$467$	−11.4853	+	19.8931i	−0.531475	+	0.920542i	−0.999325	+	0.0367344i	$0.988304\pi$
$468$		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	$-0.255062\pi$
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	−0.969920	+	0.243426i	$0.921729\pi$
$480$		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	$-0.0769784\pi$
$487$	6.13604	+	10.6279i	0.278050	+	0.481598i	−0.692850	+	0.721082i	$0.743645\pi$
$488$		0			0
$489$	8.00000			0.361773
$490$		0			0
$491$	32.4853			1.46604			0.733020	−	0.680207i	$-0.238110\pi$
$491$	32.4853			1.46604			0.733020	+	0.680207i	$0.238110\pi$
$492$		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	$-0.851260\pi$
$499$	−1.25736	+	2.17781i	−0.0562871	+	0.0974922i	0.836509	+	0.547953i	$0.184593\pi$
$500$		0			0
$501$	3.36396	+	5.82655i	0.150291	+	0.260311i
$502$		0			0
$503$	−9.51472			−0.424240			−0.212120	−	0.977244i	$-0.568037\pi$
$503$	−9.51472			−0.424240			−0.212120	+	0.977244i	$0.568037\pi$
$504$		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	0.272330	+	0.962204i	$0.412206\pi$
$509$	−15.7279	+	27.2416i	−0.697128	+	1.20746i	−0.969458	+	0.245257i	$0.921128\pi$
$510$		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	−0.905321	−	0.424727i	$-0.860370\pi$
$521$	−18.7279	−	32.4377i	−0.820485	−	1.42112i	0.0848363	−	0.996395i	$-0.472963\pi$
$522$		0			0
$523$	−1.62132	+	2.80821i	−0.0708954	+	0.122794i	−0.899294	−	0.437345i	$-0.855919\pi$
$523$	−1.62132	+	2.80821i	−0.0708954	+	0.122794i	0.828399	+	0.560139i	$0.189252\pi$
$524$		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	0.416433	+	0.909166i	$0.363280\pi$
$541$	−13.4706	+	23.3317i	−0.579145	+	1.00311i	−0.995578	+	0.0939417i	$0.970053\pi$
$542$		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	$-0.621732\pi$
$547$	−17.4558			−0.746358			−0.373179	+	0.927759i	$0.621732\pi$
$548$		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	0.986394	+	0.164399i	$0.0525683\pi$
$557$	15.0000	+	25.9808i	0.635570	+	1.10084i	−0.350824	+	0.936442i	$0.614098\pi$
$558$		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	$-0.126313\pi$
$563$	3.00000	+	5.19615i	0.126435	+	0.218992i	−0.795858	+	0.605483i	$0.792980\pi$
$564$		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	−0.989717	−	0.143043i	$-0.954311\pi$
$569$	−8.84924	+	15.3273i	−0.370980	+	0.642555i	0.618737	+	0.785598i	$0.287645\pi$
$570$		0			0
$571$	−19.4706	−	33.7240i	−0.814818	−	1.41131i	−0.909459	−	0.415794i	$-0.863504\pi$
$571$	−19.4706	−	33.7240i	−0.814818	−	1.41131i	0.0946410	−	0.995511i	$-0.469830\pi$
$572$		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	0.555679	−	0.831397i	$-0.312458\pi$
$577$	−10.6213	−	18.3967i	−0.442171	−	0.765863i	−0.997850	+	0.0655337i	$0.979125\pi$
$578$		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	$-0.481683\pi$
$587$	2.78680			0.115023			0.0575117	+	0.998345i	$0.481683\pi$
$588$		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	−0.111045	−	0.993815i	$-0.535420\pi$
$593$	19.6066	−	33.9596i	0.805147	−	1.39455i	0.916192	−	0.400740i	$-0.131247\pi$
$594$		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	$-0.0640055\pi$
$599$	7.75736	+	13.4361i	0.316957	+	0.548986i	−0.662894	+	0.748713i	$0.730672\pi$
$600$		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	$-0.694922\pi$
$607$	10.3787	−	17.9764i	0.421258	−	0.729640i	0.996063	+	0.0886507i	$0.0282555\pi$
$608$		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	−0.802491	−	0.596665i	$-0.796492\pi$
$613$	−22.7279	−	39.3659i	−0.917972	−	1.58997i	−0.115482	−	0.993310i	$-0.536841\pi$
$614$		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	$-0.312233\pi$
$619$	−10.9853	−	19.0271i	−0.441536	−	0.764762i	−0.997804	+	0.0662407i	$0.978899\pi$
$620$		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	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$		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	−0.999950	−	0.0100488i	$-0.996801\pi$
$641$	−12.8787	−	22.3065i	−0.508677	−	0.881055i	0.491272	−	0.871006i	$-0.336532\pi$
$642$		0			0
$643$	5.72792			0.225887			0.112944	−	0.993601i	$-0.463972\pi$
$643$	5.72792			0.225887			0.112944	+	0.993601i	$0.463972\pi$
$644$		0			0
$645$	5.24264			0.206429
$646$		0			0
$647$	−0.878680	−	1.52192i	−0.0345445	−	0.0598328i	0.848236	−	0.529618i	$-0.177665\pi$
$647$	−0.878680	−	1.52192i	−0.0345445	−	0.0598328i	−0.882781	+	0.469785i	$0.844331\pi$
$648$		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	−0.882706	−	0.469926i	$-0.844281\pi$
$653$	−0.878680	+	1.52192i	−0.0343854	+	0.0595572i	0.848321	+	0.529483i	$0.177614\pi$
$654$		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	$-0.456282\pi$
$659$	7.02944			0.273828			0.136914	+	0.990583i	$0.456282\pi$
$660$		0			0
$661$	17.9853	+	31.1514i	0.699546	+	1.21165i	0.968624	+	0.248531i	$0.0799479\pi$
$661$	17.9853	+	31.1514i	0.699546	+	1.21165i	−0.269077	+	0.963119i	$0.586719\pi$
$662$		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	−0.717428	−	0.696632i	$-0.754681\pi$
$677$	6.36396	−	11.0227i	0.244587	−	0.423637i	0.962015	+	0.272995i	$0.0880143\pi$
$678$		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	$-0.110265\pi$
$683$	4.60660	+	7.97887i	0.176267	+	0.305303i	−0.764332	+	0.644823i	$0.776931\pi$
$684$		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	−0.153933	−	0.988081i	$-0.549194\pi$
$691$	20.4706	−	35.4561i	0.778737	−	1.34881i	0.932670	−	0.360731i	$-0.117473\pi$
$692$		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	−0.622562	−	0.782571i	$-0.713908\pi$
$709$	9.75736	−	16.9002i	0.366445	−	0.634702i	0.989007	+	0.147869i	$0.0472413\pi$
$710$		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	$-0.890108\pi$
$719$	−4.75736	+	8.23999i	−0.177420	+	0.307300i	0.763576	+	0.645718i	$0.223442\pi$
$720$		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	$-0.445172\pi$
$727$	9.24264			0.342791			0.171395	+	0.985202i	$0.445172\pi$
$728$		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	0.0917010	+	0.995787i	$0.470770\pi$
$733$	−22.1066	+	38.2898i	−0.816526	+	1.41426i	−0.908227	+	0.418478i	$0.862564\pi$
$734$		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	$-0.175363\pi$
$739$	−0.742641	−	1.28629i	−0.0273185	−	0.0473170i	−0.879361	+	0.476155i	$0.842030\pi$
$740$		0			0
$741$	36.6985			1.34815
$742$		0			0
$743$	−27.2132			−0.998356			−0.499178	−	0.866500i	$-0.666365\pi$
$743$	−27.2132			−0.998356			−0.499178	+	0.866500i	$0.666365\pi$
$744$		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	$-0.695866\pi$
$751$	11.4706	−	19.8676i	0.418567	−	0.724979i	0.995796	+	0.0916035i	$0.0291992\pi$
$752$		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	0.289288	+	0.957242i	$0.406581\pi$
$761$	−18.8787	+	32.6988i	−0.684352	+	1.18533i	−0.973640	+	0.228090i	$0.926752\pi$
$762$		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	0.874025	+	0.485881i	$0.161501\pi$
$773$	23.8492	+	41.3081i	0.857798	+	1.48575i	−0.0162275	+	0.999868i	$0.505166\pi$
$774$		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	$-0.232460\pi$
$787$	−5.75736	−	9.97204i	−0.205228	−	0.355465i	−0.950205	+	0.311625i	$0.899127\pi$
$788$		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	0.967718	+	0.252035i	$0.0810997\pi$
$809$	19.9706	+	34.5900i	0.702128	+	1.21612i	−0.265591	+	0.964086i	$0.585567\pi$
$810$		0			0
$811$	−55.9411			−1.96436			−0.982179	−	0.187946i	$-0.939817\pi$
$811$	−55.9411			−1.96436			−0.982179	+	0.187946i	$0.939817\pi$
$812$		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	0.166099	−	0.986109i	$-0.446883\pi$
$821$	26.8492	−	46.5043i	0.937045	−	1.62301i	0.770946	−	0.636901i	$-0.219784\pi$
$822$		0			0
$823$	2.51472	+	4.35562i	0.0876576	+	0.151827i	0.906521	−	0.422162i	$-0.138729\pi$
$823$	2.51472	+	4.35562i	0.0876576	+	0.151827i	−0.818863	+	0.573989i	$0.805395\pi$
$824$		0			0
$825$	4.24264			0.147710
$826$		0			0
$827$	−7.45584			−0.259265			−0.129633	−	0.991562i	$-0.541380\pi$
$827$	−7.45584			−0.259265			−0.129633	+	0.991562i	$0.541380\pi$
$828$		0			0
$829$	−5.50000	−	9.52628i	−0.191023	−	0.330861i	0.754567	−	0.656223i	$-0.227847\pi$
$829$	−5.50000	−	9.52628i	−0.191023	−	0.330861i	−0.945589	+	0.325362i	$0.894514\pi$
$830$		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	$-0.298696\pi$
$839$	34.2426			1.18219			0.591094	+	0.806603i	$0.298696\pi$
$840$		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	0.899980	−	0.435931i	$-0.143581\pi$
$857$	2.12132	+	3.67423i	0.0724629	+	0.125509i	−0.827517	+	0.561440i	$0.810247\pi$
$858$		0			0
$859$	11.0000	−	19.0526i	0.375315	−	0.650065i	−0.615059	−	0.788481i	$-0.710868\pi$
$859$	11.0000	−	19.0526i	0.375315	−	0.650065i	0.990374	+	0.138416i	$0.0442012\pi$
$860$		0			0
$861$	4.24264	+	10.3923i	0.144589	+	0.354169i
$862$		0			0
$863$	19.2426	−	33.3292i	0.655027	−	1.13454i	−0.326860	−	0.945073i	$-0.605991\pi$
$863$	19.2426	−	33.3292i	0.655027	−	1.13454i	0.981887	−	0.189467i	$-0.0606761\pi$
$864$		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	−0.769174	−	0.639040i	$-0.779332\pi$
$877$	5.00000	−	8.66025i	0.168838	−	0.292436i	0.938012	+	0.346604i	$0.112665\pi$
$878$		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	$-0.607706\pi$
$883$	−19.7279			−0.663897			−0.331949	+	0.943297i	$0.607706\pi$
$884$		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	$-0.682306\pi$
$887$	13.6066	−	23.5673i	0.456865	−	0.791313i	0.998793	+	0.0491114i	$0.0156389\pi$
$888$		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	0.791227	+	0.611523i	$0.209443\pi$
$907$	27.8640	+	48.2618i	0.925208	+	1.60251i	0.133981	+	0.990984i	$0.457224\pi$
$908$		0			0
$909$	−16.2426			−0.538734
$910$		0			0
$911$	8.78680			0.291120			0.145560	−	0.989349i	$-0.453502\pi$
$911$	8.78680			0.291120			0.145560	+	0.989349i	$0.453502\pi$
$912$		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	$-0.833488\pi$
$919$	−0.0147186	+	0.0254934i	−0.000485523	+	0.000840950i	0.865783	+	0.500420i	$0.166821\pi$
$920$		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	−0.943547	−	0.331239i	$-0.892533\pi$
$929$	−5.63604	+	9.76191i	−0.184912	+	0.320278i	0.758635	+	0.651516i	$0.225867\pi$
$930$		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	0.754796	−	0.655960i	$-0.227736\pi$
$941$	−5.84924	−	10.1312i	−0.190680	−	0.330267i	−0.945476	+	0.325693i	$0.894403\pi$
$942$		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	0.348931	+	0.937148i	$0.386545\pi$
$947$	−19.6066	+	33.9596i	−0.637129	+	1.10354i	−0.986060	+	0.166391i	$0.946789\pi$
$948$		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	$-0.641567\pi$
$967$	−26.7574			−0.860459			−0.430229	+	0.902720i	$0.641567\pi$
$968$		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	$-0.932104\pi$
$971$	−9.51472	+	16.4800i	−0.305342	+	0.528868i	0.671996	+	0.740555i	$0.265437\pi$
$972$		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	0.906252	+	0.422738i	$0.138931\pi$
$977$	25.6066	+	44.3519i	0.819228	+	1.41894i	−0.0870242	+	0.996206i	$0.527736\pi$
$978$		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	$-0.257746\pi$
$983$	−8.84924	−	15.3273i	−0.282247	−	0.488866i	−0.971938	+	0.235238i	$0.924413\pi$
$984$		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	0.889164	+	0.457588i	$0.151287\pi$
$991$	26.4706	+	45.8484i	0.840865	+	1.45642i	−0.0482991	+	0.998833i	$0.515380\pi$
$992$		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	0.868172	−	0.496264i	$-0.165295\pi$
$997$	0.136039	+	0.235626i	0.00430840	+	0.00746236i	−0.863863	+	0.503727i	$0.831962\pi$
$998$		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	420.2.q.d.121.1	✓	4
3.2	odd	2		1260.2.s.e.541.1		4
4.3	odd	2		1680.2.bg.t.961.2		4
5.2	odd	4		2100.2.bc.f.1549.2		8
5.3	odd	4		2100.2.bc.f.1549.3		8
5.4	even	2		2100.2.q.k.1801.2		4
7.2	even	3		2940.2.a.r.1.2		2
7.3	odd	6		2940.2.q.q.361.1		4
7.4	even	3	inner	420.2.q.d.361.1	yes	4
7.5	odd	6		2940.2.a.p.1.2		2
7.6	odd	2		2940.2.q.q.961.1		4
21.2	odd	6		8820.2.a.bk.1.1		2
21.5	even	6		8820.2.a.bf.1.1		2
21.11	odd	6		1260.2.s.e.361.1		4
28.11	odd	6		1680.2.bg.t.1201.2		4
35.4	even	6		2100.2.q.k.1201.2		4
35.18	odd	12		2100.2.bc.f.949.2		8
35.32	odd	12		2100.2.bc.f.949.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.q.d.121.1	✓	4	1.1	even	1	trivial
420.2.q.d.361.1	yes	4	7.4	even	3	inner
1260.2.s.e.361.1		4	21.11	odd	6
1260.2.s.e.541.1		4	3.2	odd	2
1680.2.bg.t.961.2		4	4.3	odd	2
1680.2.bg.t.1201.2		4	28.11	odd	6
2100.2.q.k.1201.2		4	35.4	even	6
2100.2.q.k.1801.2		4	5.4	even	2
2100.2.bc.f.949.2		8	35.18	odd	12
2100.2.bc.f.949.3		8	35.32	odd	12
2100.2.bc.f.1549.2		8	5.2	odd	4
2100.2.bc.f.1549.3		8	5.3	odd	4
2940.2.a.p.1.2		2	7.5	odd	6
2940.2.a.r.1.2		2	7.2	even	3
2940.2.q.q.361.1		4	7.3	odd	6
2940.2.q.q.961.1		4	7.6	odd	2
8820.2.a.bf.1.1		2	21.5	even	6
8820.2.a.bk.1.1		2	21.2	odd	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:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.q (of order \(3\), degree \(2\), 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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