LMFDB - Embedded newform 1472.2.j.c.369.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1472,2,Mod(369,1472)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1472, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1472.369");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1472 = 2^{6} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1472.j (of order $4$, 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:	$11.7539791775$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.221124989353984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 2 x^{10} + 2 x^{9} + 12 x^{8} - 8 x^{7} - 14 x^{6} - 16 x^{5} + 48 x^{4} + 16 x^{3} + \cdots + 64 $ x^12 - 2x^11 - 2x^10 + 2x^9 + 12x^8 - 8x^7 - 14x^6 - 16x^5 + 48x^4 + 16x^3 - 32x^2 - 64*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 368)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			369.3
Root			$-1.18970 + 0.764606i$ of defining polynomial
Character	$\chi$	$=$	1472.369
Dual form			1472.2.j.c.1105.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.631541 + 0.631541i) q^{3} +(-2.74053 - 2.74053i) q^{5} -1.52921i q^{7} +2.20231i q^{9} +(2.02278 + 2.02278i) q^{11} +(2.71814 - 2.71814i) q^{13} +3.46152 q^{15} +3.66304 q^{17} +(-1.20231 + 1.20231i) q^{19} +(0.965760 + 0.965760i) q^{21} -1.00000i q^{23} +10.0210i q^{25} +(-3.28547 - 3.28547i) q^{27} +(2.52960 - 2.52960i) q^{29} -2.74954 q^{31} -2.55494 q^{33} +(-4.19086 + 4.19086i) q^{35} +(-4.37038 - 4.37038i) q^{37} +3.43323i q^{39} -7.70478i q^{41} +(-8.96110 - 8.96110i) q^{43} +(6.03551 - 6.03551i) q^{45} -4.24239 q^{47} +4.66151 q^{49} +(-2.31336 + 2.31336i) q^{51} +(-7.11480 - 7.11480i) q^{53} -11.0870i q^{55} -1.51862i q^{57} +(-5.81873 - 5.81873i) q^{59} +(-6.37705 + 6.37705i) q^{61} +3.36780 q^{63} -14.8983 q^{65} +(0.0827674 - 0.0827674i) q^{67} +(0.631541 + 0.631541i) q^{69} +6.62784i q^{71} +7.91866i q^{73} +(-6.32869 - 6.32869i) q^{75} +(3.09326 - 3.09326i) q^{77} -6.42623 q^{79} -2.45712 q^{81} +(11.6430 - 11.6430i) q^{83} +(-10.0387 - 10.0387i) q^{85} +3.19510i q^{87} +2.76733i q^{89} +(-4.15662 - 4.15662i) q^{91} +(1.73645 - 1.73645i) q^{93} +6.58995 q^{95} -6.61383 q^{97} +(-4.45480 + 4.45480i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} - 4 q^{5} + 4 q^{11} + 18 q^{13} - 8 q^{17} + 8 q^{19} + 8 q^{21} - 14 q^{27} + 2 q^{29} - 20 q^{31} - 36 q^{33} - 4 q^{35} - 4 q^{37} - 20 q^{43} - 20 q^{45} + 16 q^{47} + 52 q^{49} + 4 q^{51}+ \cdots - 36 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 - 4 * q^5 + 4 * q^11 + 18 * q^13 - 8 * q^17 + 8 * q^19 + 8 * q^21 - 14 * q^27 + 2 * q^29 - 20 * q^31 - 36 * q^33 - 4 * q^35 - 4 * q^37 - 20 * q^43 - 20 * q^45 + 16 * q^47 + 52 * q^49 + 4 * q^51 - 16 * q^53 - 8 * q^59 + 12 * q^61 + 4 * q^63 - 52 * q^65 + 4 * q^67 + 2 * q^69 + 46 * q^75 - 12 * q^77 + 4 * q^79 + 48 * q^81 - 28 * q^83 - 8 * q^85 - 14 * q^93 - 48 * q^95 + 36 * q^97 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1472\mathbb{Z}\right)^\times$.

$n$	$645$	$833$	$1151$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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
$3$	−0.631541	+	0.631541i	−0.364620	+	0.364620i	−0.865511	−	0.500890i	$-0.833006\pi$
$3$	−0.631541	+	0.631541i	−0.364620	+	0.364620i	0.500890	+	0.865511i	$0.333006\pi$
$4$		0			0
$5$	−2.74053	−	2.74053i	−1.22560	−	1.22560i	−0.965611	−	0.259993i	$-0.916280\pi$
$5$	−2.74053	−	2.74053i	−1.22560	−	1.22560i	−0.259993	−	0.965611i	$-0.583720\pi$
$6$		0			0
$7$		−	1.52921i		−	0.577988i	−0.957331	−	0.288994i	$-0.906679\pi$
$7$		−	1.52921i		−	0.577988i	0.957331	−	0.288994i	$-0.0933207\pi$
$8$		0			0
$9$			2.20231i			0.734104i
$10$		0			0
$11$	2.02278	+	2.02278i	0.609892	+	0.609892i	0.942918	−	0.333026i	$-0.108070\pi$
$11$	2.02278	+	2.02278i	0.609892	+	0.609892i	−0.333026	+	0.942918i	$0.608070\pi$
$12$		0			0
$13$	2.71814	−	2.71814i	0.753877	−	0.753877i	−0.221324	−	0.975200i	$-0.571038\pi$
$13$	2.71814	−	2.71814i	0.753877	−	0.753877i	0.975200	+	0.221324i	$0.0710377\pi$
$14$		0			0
$15$	3.46152			0.893760
$16$		0			0
$17$	3.66304			0.888419			0.444209	−	0.895923i	$-0.353485\pi$
$17$	3.66304			0.888419			0.444209	+	0.895923i	$0.353485\pi$
$18$		0			0
$19$	−1.20231	+	1.20231i	−0.275829	+	0.275829i	−0.831442	−	0.555612i	$-0.812484\pi$
$19$	−1.20231	+	1.20231i	−0.275829	+	0.275829i	0.555612	+	0.831442i	$0.312484\pi$
$20$		0			0
$21$	0.965760	+	0.965760i	0.210746	+	0.210746i
$22$		0			0
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$		0			0
$25$			10.0210i			2.00421i
$26$		0			0
$27$	−3.28547	−	3.28547i	−0.632289	−	0.632289i
$28$		0			0
$29$	2.52960	−	2.52960i	0.469736	−	0.469736i	−0.432093	−	0.901829i	$-0.642225\pi$
$29$	2.52960	−	2.52960i	0.469736	−	0.469736i	0.901829	+	0.432093i	$0.142225\pi$
$30$		0			0
$31$	−2.74954			−0.493832			−0.246916	−	0.969037i	$-0.579417\pi$
$31$	−2.74954			−0.493832			−0.246916	+	0.969037i	$0.579417\pi$
$32$		0			0
$33$	−2.55494			−0.444758
$34$		0			0
$35$	−4.19086	+	4.19086i	−0.708384	+	0.708384i
$36$		0			0
$37$	−4.37038	−	4.37038i	−0.718487	−	0.718487i	0.249808	−	0.968295i	$-0.419632\pi$
$37$	−4.37038	−	4.37038i	−0.718487	−	0.718487i	−0.968295	+	0.249808i	$0.919632\pi$
$38$		0			0
$39$			3.43323i			0.549757i
$40$		0			0
$41$		−	7.70478i		−	1.20328i	−0.798766	−	0.601642i	$-0.794513\pi$
$41$		−	7.70478i		−	1.20328i	0.798766	−	0.601642i	$-0.205487\pi$
$42$		0			0
$43$	−8.96110	−	8.96110i	−1.36655	−	1.36655i	−0.865299	−	0.501255i	$-0.832872\pi$
$43$	−8.96110	−	8.96110i	−1.36655	−	1.36655i	−0.501255	−	0.865299i	$-0.667128\pi$
$44$		0			0
$45$	6.03551	−	6.03551i	0.899721	−	0.899721i
$46$		0			0
$47$	−4.24239			−0.618816			−0.309408	−	0.950929i	$-0.600131\pi$
$47$	−4.24239			−0.618816			−0.309408	+	0.950929i	$0.600131\pi$
$48$		0			0
$49$	4.66151			0.665930
$50$		0			0
$51$	−2.31336	+	2.31336i	−0.323935	+	0.323935i
$52$		0			0
$53$	−7.11480	−	7.11480i	−0.977292	−	0.977292i	0.0224555	−	0.999748i	$-0.492852\pi$
$53$	−7.11480	−	7.11480i	−0.977292	−	0.977292i	−0.999748	+	0.0224555i	$0.992852\pi$
$54$		0			0
$55$		−	11.0870i		−	1.49497i
$56$		0			0
$57$		−	1.51862i		−	0.201146i
$58$		0			0
$59$	−5.81873	−	5.81873i	−0.757534	−	0.757534i	0.218339	−	0.975873i	$-0.429936\pi$
$59$	−5.81873	−	5.81873i	−0.757534	−	0.757534i	−0.975873	+	0.218339i	$0.929936\pi$
$60$		0			0
$61$	−6.37705	+	6.37705i	−0.816497	+	0.816497i	−0.985599	−	0.169101i	$-0.945913\pi$
$61$	−6.37705	+	6.37705i	−0.816497	+	0.816497i	0.169101	+	0.985599i	$0.445913\pi$
$62$		0			0
$63$	3.36780			0.424303
$64$		0			0
$65$	−14.8983			−1.84791
$66$		0			0
$67$	0.0827674	−	0.0827674i	0.0101116	−	0.0101116i	−0.702033	−	0.712145i	$-0.747724\pi$
$67$	0.0827674	−	0.0827674i	0.0101116	−	0.0101116i	0.712145	+	0.702033i	$0.247724\pi$
$68$		0			0
$69$	0.631541	+	0.631541i	0.0760286	+	0.0760286i
$70$		0			0
$71$			6.62784i			0.786579i	0.919415	+	0.393290i	$0.128663\pi$
$71$			6.62784i			0.786579i	−0.919415	+	0.393290i	$0.871337\pi$
$72$		0			0
$73$			7.91866i			0.926809i	0.886147	+	0.463405i	$0.153372\pi$
$73$			7.91866i			0.926809i	−0.886147	+	0.463405i	$0.846628\pi$
$74$		0			0
$75$	−6.32869	−	6.32869i	−0.730775	−	0.730775i
$76$		0			0
$77$	3.09326	−	3.09326i	0.352510	−	0.352510i
$78$		0			0
$79$	−6.42623			−0.723007			−0.361504	−	0.932371i	$-0.617736\pi$
$79$	−6.42623			−0.723007			−0.361504	+	0.932371i	$0.617736\pi$
$80$		0			0
$81$	−2.45712			−0.273013
$82$		0			0
$83$	11.6430	−	11.6430i	1.27799	−	1.27799i	0.336200	−	0.941791i	$-0.390858\pi$
$83$	11.6430	−	11.6430i	1.27799	−	1.27799i	0.941791	−	0.336200i	$-0.109142\pi$
$84$		0			0
$85$	−10.0387	−	10.0387i	−1.08885	−	1.08885i
$86$		0			0
$87$			3.19510i			0.342550i
$88$		0			0
$89$			2.76733i			0.293336i	0.989186	+	0.146668i	$0.0468549\pi$
$89$			2.76733i			0.293336i	−0.989186	+	0.146668i	$0.953145\pi$
$90$		0			0
$91$	−4.15662	−	4.15662i	−0.435732	−	0.435732i
$92$		0			0
$93$	1.73645	−	1.73645i	0.180061	−	0.180061i
$94$		0			0
$95$	6.58995			0.676115
$96$		0			0
$97$	−6.61383			−0.671533			−0.335766	−	0.941945i	$-0.608995\pi$
$97$	−6.61383			−0.671533			−0.335766	+	0.941945i	$0.608995\pi$
$98$		0			0
$99$	−4.45480	+	4.45480i	−0.447724	+	0.447724i
$100$		0			0
$101$	11.5250	+	11.5250i	1.14678	+	1.14678i	0.987182	+	0.159596i	$0.0510193\pi$
$101$	11.5250	+	11.5250i	1.14678	+	1.14678i	0.159596	+	0.987182i	$0.448981\pi$
$102$		0			0
$103$			0.605918i			0.0597028i	0.999554	+	0.0298514i	$0.00950341\pi$
$103$			0.605918i			0.0597028i	−0.999554	+	0.0298514i	$0.990497\pi$
$104$		0			0
$105$		−	5.29339i		−	0.516582i
$106$		0			0
$107$	−6.39585	−	6.39585i	−0.618310	−	0.618310i	0.326788	−	0.945098i	$-0.394034\pi$
$107$	−6.39585	−	6.39585i	−0.618310	−	0.618310i	−0.945098	+	0.326788i	$0.894034\pi$
$108$		0			0
$109$	−4.79918	+	4.79918i	−0.459678	+	0.459678i	−0.898550	−	0.438872i	$-0.855378\pi$
$109$	−4.79918	+	4.79918i	−0.459678	+	0.459678i	0.438872	+	0.898550i	$0.355378\pi$
$110$		0			0
$111$	5.52015			0.523950
$112$		0			0
$113$	4.58640			0.431452			0.215726	−	0.976454i	$-0.430788\pi$
$113$	4.58640			0.431452			0.215726	+	0.976454i	$0.430788\pi$
$114$		0			0
$115$	−2.74053	+	2.74053i	−0.255556	+	0.255556i
$116$		0			0
$117$	5.98620	+	5.98620i	0.553424	+	0.553424i
$118$		0			0
$119$		−	5.60157i		−	0.513495i
$120$		0			0
$121$		−	2.81670i		−	0.256063i
$122$		0			0
$123$	4.86588	+	4.86588i	0.438742	+	0.438742i
$124$		0			0
$125$	13.7603	−	13.7603i	1.23076	−	1.23076i
$126$		0			0
$127$	−8.38407			−0.743966			−0.371983	−	0.928240i	$-0.621322\pi$
$127$	−8.38407			−0.743966			−0.371983	+	0.928240i	$0.621322\pi$
$128$		0			0
$129$	11.3186			0.996547
$130$		0			0
$131$	15.3109	−	15.3109i	1.33772	−	1.33772i	0.439459	−	0.898263i	$-0.355170\pi$
$131$	15.3109	−	15.3109i	1.33772	−	1.33772i	0.898263	−	0.439459i	$-0.144830\pi$
$132$		0			0
$133$	1.83859	+	1.83859i	0.159426	+	0.159426i
$134$		0			0
$135$			18.0079i			1.54987i
$136$		0			0
$137$		−	20.1453i		−	1.72113i	−0.509339	−	0.860566i	$-0.670110\pi$
$137$		−	20.1453i		−	1.72113i	0.509339	−	0.860566i	$-0.329890\pi$
$138$		0			0
$139$	11.0916	+	11.0916i	0.940775	+	0.940775i	0.998342	−	0.0575665i	$-0.0183341\pi$
$139$	11.0916	+	11.0916i	0.940775	+	0.940775i	−0.0575665	+	0.998342i	$0.518334\pi$
$140$		0			0
$141$	2.67924	−	2.67924i	0.225633	−	0.225633i
$142$		0			0
$143$	10.9964			0.919567
$144$		0			0
$145$	−13.8649			−1.15142
$146$		0			0
$147$	−2.94393	+	2.94393i	−0.242812	+	0.242812i
$148$		0			0
$149$	−15.6772	−	15.6772i	−1.28432	−	1.28432i	−0.938183	−	0.346140i	$-0.887492\pi$
$149$	−15.6772	−	15.6772i	−1.28432	−	1.28432i	−0.346140	−	0.938183i	$-0.612508\pi$
$150$		0			0
$151$		−	15.1976i		−	1.23677i	−0.785876	−	0.618384i	$-0.787788\pi$
$151$		−	15.1976i		−	1.23677i	0.785876	−	0.618384i	$-0.212212\pi$
$152$		0			0
$153$			8.06717i			0.652192i
$154$		0			0
$155$	7.53521	+	7.53521i	0.605242	+	0.605242i
$156$		0			0
$157$	3.41307	−	3.41307i	0.272393	−	0.272393i	−0.557670	−	0.830063i	$-0.688305\pi$
$157$	3.41307	−	3.41307i	0.272393	−	0.272393i	0.830063	+	0.557670i	$0.188305\pi$
$158$		0			0
$159$	8.98657			0.712681
$160$		0			0
$161$	−1.52921			−0.120519
$162$		0			0
$163$	−2.00990	+	2.00990i	−0.157428	+	0.157428i	−0.781426	−	0.623998i	$-0.785507\pi$
$163$	−2.00990	+	2.00990i	−0.157428	+	0.157428i	0.623998	+	0.781426i	$0.285507\pi$
$164$		0			0
$165$	7.00190	+	7.00190i	0.545097	+	0.545097i
$166$		0			0
$167$		−	13.4952i		−	1.04429i	−0.852857	−	0.522144i	$-0.825132\pi$
$167$		−	13.4952i		−	1.04429i	0.852857	−	0.522144i	$-0.174868\pi$
$168$		0			0
$169$		−	1.77659i		−	0.136661i
$170$		0			0
$171$	−2.64787	−	2.64787i	−0.202488	−	0.202488i
$172$		0			0
$173$	−0.604284	+	0.604284i	−0.0459429	+	0.0459429i	−0.729705	−	0.683762i	$-0.760343\pi$
$173$	−0.604284	+	0.604284i	−0.0459429	+	0.0459429i	0.683762	+	0.729705i	$0.260343\pi$
$174$		0			0
$175$	15.3243			1.15841
$176$		0			0
$177$	7.34952			0.552424
$178$		0			0
$179$	−12.6718	+	12.6718i	−0.947132	+	0.947132i	−0.998671	−	0.0515388i	$-0.983587\pi$
$179$	−12.6718	+	12.6718i	−0.947132	+	0.947132i	0.0515388	+	0.998671i	$0.483587\pi$
$180$		0			0
$181$	6.30067	+	6.30067i	0.468325	+	0.468325i	0.901372	−	0.433046i	$-0.142561\pi$
$181$	6.30067	+	6.30067i	0.468325	+	0.468325i	−0.433046	+	0.901372i	$0.642561\pi$
$182$		0			0
$183$		−	8.05473i		−	0.595423i
$184$		0			0
$185$			23.9544i			1.76116i
$186$		0			0
$187$	7.40954	+	7.40954i	0.541839	+	0.541839i
$188$		0			0
$189$	−5.02418	+	5.02418i	−0.365456	+	0.365456i
$190$		0			0
$191$	15.8762			1.14876			0.574382	−	0.818588i	$-0.305243\pi$
$191$	15.8762			1.14876			0.574382	+	0.818588i	$0.305243\pi$
$192$		0			0
$193$	−15.8800			−1.14307			−0.571535	−	0.820578i	$-0.693652\pi$
$193$	−15.8800			−1.14307			−0.571535	+	0.820578i	$0.693652\pi$
$194$		0			0
$195$	9.40889	−	9.40889i	0.673785	−	0.673785i
$196$		0			0
$197$	−4.36304	−	4.36304i	−0.310854	−	0.310854i	0.534387	−	0.845240i	$-0.320543\pi$
$197$	−4.36304	−	4.36304i	−0.310854	−	0.310854i	−0.845240	+	0.534387i	$0.820543\pi$
$198$		0			0
$199$			1.83276i			0.129921i	0.997888	+	0.0649604i	$0.0206921\pi$
$199$			1.83276i			0.129921i	−0.997888	+	0.0649604i	$0.979308\pi$
$200$		0			0
$201$			0.104542i			0.00737382i
$202$		0			0
$203$	−3.86830	−	3.86830i	−0.271502	−	0.271502i
$204$		0			0
$205$	−21.1152	+	21.1152i	−1.47475	+	1.47475i
$206$		0			0
$207$	2.20231			0.153071
$208$		0			0
$209$	−4.86404			−0.336452
$210$		0			0
$211$	0.176084	−	0.176084i	0.0121221	−	0.0121221i	−0.701020	−	0.713142i	$-0.747272\pi$
$211$	0.176084	−	0.176084i	0.0121221	−	0.0121221i	0.713142	+	0.701020i	$0.247272\pi$
$212$		0			0
$213$	−4.18575	−	4.18575i	−0.286803	−	0.286803i
$214$		0			0
$215$			49.1164i			3.34971i
$216$		0			0
$217$			4.20463i			0.285429i
$218$		0			0
$219$	−5.00096	−	5.00096i	−0.337933	−	0.337933i
$220$		0			0
$221$	9.95667	−	9.95667i	0.669758	−	0.669758i
$222$		0			0
$223$	−7.23146			−0.484254			−0.242127	−	0.970245i	$-0.577845\pi$
$223$	−7.23146			−0.484254			−0.242127	+	0.970245i	$0.577845\pi$
$224$		0			0
$225$	−22.0695			−1.47130
$226$		0			0
$227$	−15.8466	+	15.8466i	−1.05177	+	1.05177i	−0.0531903	+	0.998584i	$0.516939\pi$
$227$	−15.8466	+	15.8466i	−1.05177	+	1.05177i	−0.998584	+	0.0531903i	$0.983061\pi$
$228$		0			0
$229$	7.41129	+	7.41129i	0.489752	+	0.489752i	0.908228	−	0.418476i	$-0.137436\pi$
$229$	7.41129	+	7.41129i	0.489752	+	0.489752i	−0.418476	+	0.908228i	$0.637436\pi$
$230$		0			0
$231$			3.90704i			0.257065i
$232$		0			0
$233$			0.641549i			0.0420293i	0.999779	+	0.0210146i	$0.00668966\pi$
$233$			0.641549i			0.0420293i	−0.999779	+	0.0210146i	$0.993310\pi$
$234$		0			0
$235$	11.6264	+	11.6264i	0.758423	+	0.758423i
$236$		0			0
$237$	4.05842	−	4.05842i	0.263623	−	0.263623i
$238$		0			0
$239$	7.78652			0.503668			0.251834	−	0.967770i	$-0.418966\pi$
$239$	7.78652			0.503668			0.251834	+	0.967770i	$0.418966\pi$
$240$		0			0
$241$	5.29100			0.340824			0.170412	−	0.985373i	$-0.445490\pi$
$241$	5.29100			0.340824			0.170412	+	0.985373i	$0.445490\pi$
$242$		0			0
$243$	11.4082	−	11.4082i	0.731836	−	0.731836i
$244$		0			0
$245$	−12.7750	−	12.7750i	−0.816166	−	0.816166i
$246$		0			0
$247$			6.53611i			0.415883i
$248$		0			0
$249$			14.7061i			0.931962i
$250$		0			0
$251$	−20.1654	−	20.1654i	−1.27283	−	1.27283i	−0.944599	−	0.328227i	$-0.893549\pi$
$251$	−20.1654	−	20.1654i	−1.27283	−	1.27283i	−0.328227	−	0.944599i	$-0.606451\pi$
$252$		0			0
$253$	2.02278	−	2.02278i	0.127171	−	0.127171i
$254$		0			0
$255$	12.6797			0.794033
$256$		0			0
$257$	−2.15836			−0.134635			−0.0673174	−	0.997732i	$-0.521444\pi$
$257$	−2.15836			−0.134635			−0.0673174	+	0.997732i	$0.521444\pi$
$258$		0			0
$259$	−6.68325	+	6.68325i	−0.415277	+	0.415277i
$260$		0			0
$261$	5.57098	+	5.57098i	0.344835	+	0.344835i
$262$		0			0
$263$		−	13.7070i		−	0.845209i	−0.906314	−	0.422604i	$-0.861116\pi$
$263$		−	13.7070i		−	0.845209i	0.906314	−	0.422604i	$-0.138884\pi$
$264$		0			0
$265$			38.9967i			2.39555i
$266$		0			0
$267$	−1.74768	−	1.74768i	−0.106956	−	0.106956i
$268$		0			0
$269$	18.5467	−	18.5467i	1.13081	−	1.13081i	0.140767	−	0.990043i	$-0.455043\pi$
$269$	18.5467	−	18.5467i	1.13081	−	1.13081i	0.990043	−	0.140767i	$-0.0449569\pi$
$270$		0			0
$271$	6.66642			0.404956			0.202478	−	0.979287i	$-0.435100\pi$
$271$	6.66642			0.404956			0.202478	+	0.979287i	$0.435100\pi$
$272$		0			0
$273$	5.25014			0.317753
$274$		0			0
$275$	−20.2704	+	20.2704i	−1.22235	+	1.22235i
$276$		0			0
$277$	−12.6524	−	12.6524i	−0.760208	−	0.760208i	0.216152	−	0.976360i	$-0.430649\pi$
$277$	−12.6524	−	12.6524i	−0.760208	−	0.760208i	−0.976360	+	0.216152i	$0.930649\pi$
$278$		0			0
$279$		−	6.05535i		−	0.362524i
$280$		0			0
$281$		−	5.57139i		−	0.332361i	−0.986095	−	0.166181i	$-0.946856\pi$
$281$		−	5.57139i		−	0.332361i	0.986095	−	0.166181i	$-0.0531435\pi$
$282$		0			0
$283$	11.5638	+	11.5638i	0.687397	+	0.687397i	0.961656	−	0.274259i	$-0.0884325\pi$
$283$	11.5638	+	11.5638i	0.687397	+	0.687397i	−0.274259	+	0.961656i	$0.588433\pi$
$284$		0			0
$285$	−4.16182	+	4.16182i	−0.246525	+	0.246525i
$286$		0			0
$287$	−11.7822			−0.695483
$288$		0			0
$289$	−3.58211			−0.210712
$290$		0			0
$291$	4.17690	−	4.17690i	0.244854	−	0.244854i
$292$		0			0
$293$	−0.585664	−	0.585664i	−0.0342149	−	0.0342149i	0.689792	−	0.724007i	$-0.257702\pi$
$293$	−0.585664	−	0.585664i	−0.0342149	−	0.0342149i	−0.724007	+	0.689792i	$0.757702\pi$
$294$		0			0
$295$			31.8928i			1.85687i
$296$		0			0
$297$		−	13.2916i		−	0.771257i
$298$		0			0
$299$	−2.71814	−	2.71814i	−0.157194	−	0.157194i
$300$		0			0
$301$	−13.7034	+	13.7034i	−0.789852	+	0.789852i
$302$		0			0
$303$	−14.5570			−0.836277
$304$		0			0
$305$	34.9530			2.00140
$306$		0			0
$307$	−20.2702	+	20.2702i	−1.15688	+	1.15688i	−0.171738	+	0.985143i	$0.554938\pi$
$307$	−20.2702	+	20.2702i	−1.15688	+	1.15688i	−0.985143	+	0.171738i	$0.945062\pi$
$308$		0			0
$309$	−0.382662	−	0.382662i	−0.0217689	−	0.0217689i
$310$		0			0
$311$		−	10.5264i		−	0.596899i	−0.954425	−	0.298449i	$-0.903531\pi$
$311$		−	10.5264i		−	0.596899i	0.954425	−	0.298449i	$-0.0964694\pi$
$312$		0			0
$313$		−	17.6161i		−	0.995722i	−0.867257	−	0.497861i	$-0.834119\pi$
$313$		−	17.6161i		−	0.995722i	0.867257	−	0.497861i	$-0.165881\pi$
$314$		0			0
$315$	−9.22957	−	9.22957i	−0.520028	−	0.520028i
$316$		0			0
$317$	−7.47881	+	7.47881i	−0.420052	+	0.420052i	−0.885222	−	0.465170i	$-0.845993\pi$
$317$	−7.47881	+	7.47881i	−0.420052	+	0.420052i	0.465170	+	0.885222i	$0.345993\pi$
$318$		0			0
$319$	10.2337			0.572976
$320$		0			0
$321$	8.07848			0.450897
$322$		0			0
$323$	−4.40412	+	4.40412i	−0.245052	+	0.245052i
$324$		0			0
$325$	27.2386	+	27.2386i	1.51093	+	1.51093i
$326$		0			0
$327$		−	6.06175i		−	0.335216i
$328$		0			0
$329$			6.48751i			0.357668i
$330$		0			0
$331$	1.01083	+	1.01083i	0.0555603	+	0.0555603i	0.734341	−	0.678781i	$-0.237491\pi$
$331$	1.01083	+	1.01083i	0.0555603	+	0.0555603i	−0.678781	+	0.734341i	$0.737491\pi$
$332$		0			0
$333$	9.62495	−	9.62495i	0.527444	−	0.527444i
$334$		0			0
$335$	−0.453653			−0.0247857
$336$		0			0
$337$	27.4738			1.49659			0.748296	−	0.663366i	$-0.230873\pi$
$337$	27.4738			1.49659			0.748296	+	0.663366i	$0.230873\pi$
$338$		0			0
$339$	−2.89650	+	2.89650i	−0.157316	+	0.157316i
$340$		0			0
$341$	−5.56172	−	5.56172i	−0.301184	−	0.301184i
$342$		0			0
$343$		−	17.8329i		−	0.962887i
$344$		0			0
$345$		−	3.46152i		−	0.186362i
$346$		0			0
$347$	5.81298	+	5.81298i	0.312057	+	0.312057i	0.845706	−	0.533649i	$-0.179180\pi$
$347$	5.81298	+	5.81298i	0.312057	+	0.312057i	−0.533649	+	0.845706i	$0.679180\pi$
$348$		0			0
$349$	−16.7479	+	16.7479i	−0.896495	+	0.896495i	−0.995124	−	0.0986290i	$-0.968554\pi$
$349$	−16.7479	+	16.7479i	−0.896495	+	0.896495i	0.0986290	+	0.995124i	$0.468554\pi$
$350$		0			0
$351$	−17.8608			−0.953337
$352$		0			0
$353$	33.2587			1.77018			0.885091	−	0.465418i	$-0.154096\pi$
$353$	33.2587			1.77018			0.885091	+	0.465418i	$0.154096\pi$
$354$		0			0
$355$	18.1638	−	18.1638i	0.964034	−	0.964034i
$356$		0			0
$357$	3.53762	+	3.53762i	0.187231	+	0.187231i
$358$		0			0
$359$		−	18.6590i		−	0.984786i	−0.870373	−	0.492393i	$-0.836122\pi$
$359$		−	18.6590i		−	0.984786i	0.870373	−	0.492393i	$-0.163878\pi$
$360$		0			0
$361$			16.1089i			0.847836i
$362$		0			0
$363$	1.77886	+	1.77886i	0.0933659	+	0.0933659i
$364$		0			0
$365$	21.7014	−	21.7014i	1.13590	−	1.13590i
$366$		0			0
$367$	8.93581			0.466446			0.233223	−	0.972423i	$-0.425073\pi$
$367$	8.93581			0.466446			0.233223	+	0.972423i	$0.425073\pi$
$368$		0			0
$369$	16.9683			0.883336
$370$		0			0
$371$	−10.8800	+	10.8800i	−0.564863	+	0.564863i
$372$		0			0
$373$	9.78549	+	9.78549i	0.506673	+	0.506673i	0.913504	−	0.406830i	$-0.133366\pi$
$373$	9.78549	+	9.78549i	0.506673	+	0.506673i	−0.406830	+	0.913504i	$0.633366\pi$
$374$		0			0
$375$			17.3804i			0.897520i
$376$		0			0
$377$		−	13.7516i		−	0.708246i
$378$		0			0
$379$	−23.5423	−	23.5423i	−1.20928	−	1.20928i	−0.971259	−	0.238026i	$-0.923500\pi$
$379$	−23.5423	−	23.5423i	−1.20928	−	1.20928i	−0.238026	−	0.971259i	$-0.576500\pi$
$380$		0			0
$381$	5.29488	−	5.29488i	0.271265	−	0.271265i
$382$		0			0
$383$	33.3581			1.70452			0.852260	−	0.523119i	$-0.175232\pi$
$383$	33.3581			1.70452			0.852260	+	0.523119i	$0.175232\pi$
$384$		0			0
$385$	−16.9544			−0.864075
$386$		0			0
$387$	19.7351	−	19.7351i	1.00319	−	1.00319i
$388$		0			0
$389$	22.4106	+	22.4106i	1.13626	+	1.13626i	0.989115	+	0.147146i	$0.0470087\pi$
$389$	22.4106	+	22.4106i	1.13626	+	1.13626i	0.147146	+	0.989115i	$0.452991\pi$
$390$		0			0
$391$		−	3.66304i		−	0.185248i
$392$		0			0
$393$			19.3389i			0.975521i
$394$		0			0
$395$	17.6113	+	17.6113i	0.886120	+	0.886120i
$396$		0			0
$397$	1.72193	−	1.72193i	0.0864212	−	0.0864212i	−0.662575	−	0.748996i	$-0.730536\pi$
$397$	1.72193	−	1.72193i	0.0864212	−	0.0864212i	0.748996	+	0.662575i	$0.230536\pi$
$398$		0			0
$399$	−2.32229			−0.116260
$400$		0			0
$401$	−4.68163			−0.233790			−0.116895	−	0.993144i	$-0.537294\pi$
$401$	−4.68163			−0.233790			−0.116895	+	0.993144i	$0.537294\pi$
$402$		0			0
$403$	−7.47364	+	7.47364i	−0.372289	+	0.372289i
$404$		0			0
$405$	6.73381	+	6.73381i	0.334606	+	0.334606i
$406$		0			0
$407$		−	17.6807i		−	0.876399i
$408$		0			0
$409$			4.60355i			0.227631i	0.993502	+	0.113815i	$0.0363073\pi$
$409$			4.60355i			0.227631i	−0.993502	+	0.113815i	$0.963693\pi$
$410$		0			0
$411$	12.7226	+	12.7226i	0.627559	+	0.627559i
$412$		0			0
$413$	−8.89807	+	8.89807i	−0.437845	+	0.437845i
$414$		0			0
$415$	−63.8163			−3.13262
$416$		0			0
$417$	−14.0096			−0.686051
$418$		0			0
$419$	−13.2797	+	13.2797i	−0.648758	+	0.648758i	−0.952693	−	0.303935i	$-0.901699\pi$
$419$	−13.2797	+	13.2797i	−0.648758	+	0.648758i	0.303935	+	0.952693i	$0.401699\pi$
$420$		0			0
$421$	−8.04601	−	8.04601i	−0.392138	−	0.392138i	0.483311	−	0.875449i	$-0.339434\pi$
$421$	−8.04601	−	8.04601i	−0.392138	−	0.392138i	−0.875449	+	0.483311i	$0.839434\pi$
$422$		0			0
$423$		−	9.34306i		−	0.454275i
$424$		0			0
$425$			36.7075i			1.78058i
$426$		0			0
$427$	9.75186	+	9.75186i	0.471926	+	0.471926i
$428$		0			0
$429$	−6.94469	+	6.94469i	−0.335293	+	0.335293i
$430$		0			0
$431$	−23.9168			−1.15203			−0.576016	−	0.817439i	$-0.695393\pi$
$431$	−23.9168			−1.15203			−0.576016	+	0.817439i	$0.695393\pi$
$432$		0			0
$433$	13.5472			0.651039			0.325519	−	0.945535i	$-0.394461\pi$
$433$	13.5472			0.651039			0.325519	+	0.945535i	$0.394461\pi$
$434$		0			0
$435$	8.75627	−	8.75627i	0.419831	−	0.419831i
$436$		0			0
$437$	1.20231	+	1.20231i	0.0575144	+	0.0575144i
$438$		0			0
$439$		−	11.2376i		−	0.536343i	−0.963371	−	0.268172i	$-0.913581\pi$
$439$		−	11.2376i		−	0.536343i	0.963371	−	0.268172i	$-0.0864194\pi$
$440$		0			0
$441$			10.2661i			0.488862i
$442$		0			0
$443$	25.7097	+	25.7097i	1.22150	+	1.22150i	0.967098	+	0.254406i	$0.0818799\pi$
$443$	25.7097	+	25.7097i	1.22150	+	1.22150i	0.254406	+	0.967098i	$0.418120\pi$
$444$		0			0
$445$	7.58395	−	7.58395i	0.359514	−	0.359514i
$446$		0			0
$447$	19.8015			0.936580
$448$		0			0
$449$	−5.13588			−0.242377			−0.121188	−	0.992630i	$-0.538671\pi$
$449$	−5.13588			−0.242377			−0.121188	+	0.992630i	$0.538671\pi$
$450$		0			0
$451$	15.5851	−	15.5851i	0.733873	−	0.733873i
$452$		0			0
$453$	9.59793	+	9.59793i	0.450950	+	0.450950i
$454$		0			0
$455$			22.7827i			1.06807i
$456$		0			0
$457$		−	27.2294i		−	1.27374i	−0.770972	−	0.636870i	$-0.780229\pi$
$457$		−	27.2294i		−	1.27374i	0.770972	−	0.636870i	$-0.219771\pi$
$458$		0			0
$459$	−12.0348	−	12.0348i	−0.561738	−	0.561738i
$460$		0			0
$461$	−21.9976	+	21.9976i	−1.02453	+	1.02453i	−0.0248390	+	0.999691i	$0.507907\pi$
$461$	−21.9976	+	21.9976i	−1.02453	+	1.02453i	−0.999691	+	0.0248390i	$0.992093\pi$
$462$		0			0
$463$	21.8570			1.01578			0.507890	−	0.861422i	$-0.330425\pi$
$463$	21.8570			1.01578			0.507890	+	0.861422i	$0.330425\pi$
$464$		0			0
$465$	−9.51758			−0.441367
$466$		0			0
$467$	8.55730	−	8.55730i	0.395985	−	0.395985i	−0.480829	−	0.876814i	$-0.659664\pi$
$467$	8.55730	−	8.55730i	0.395985	−	0.395985i	0.876814	+	0.480829i	$0.159664\pi$
$468$		0			0
$469$	−0.126569	−	0.126569i	−0.00584441	−	0.00584441i
$470$		0			0
$471$			4.31098i			0.198640i
$472$		0			0
$473$		−	36.2527i		−	1.66690i
$474$		0			0
$475$	−12.0484	−	12.0484i	−0.552819	−	0.552819i
$476$		0			0
$477$	15.6690	−	15.6690i	0.717434	−	0.717434i
$478$		0			0
$479$	−40.7842			−1.86348			−0.931739	−	0.363129i	$-0.881708\pi$
$479$	−40.7842			−1.86348			−0.931739	+	0.363129i	$0.881708\pi$
$480$		0			0
$481$	−23.7587			−1.08330
$482$		0			0
$483$	0.965760	−	0.965760i	0.0439436	−	0.0439436i
$484$		0			0
$485$	18.1254	+	18.1254i	0.823033	+	0.823033i
$486$		0			0
$487$			31.6590i			1.43460i	0.696762	+	0.717302i	$0.254623\pi$
$487$			31.6590i			1.43460i	−0.696762	+	0.717302i	$0.745377\pi$
$488$		0			0
$489$		−	2.53867i		−	0.114803i
$490$		0			0
$491$	16.7060	+	16.7060i	0.753931	+	0.753931i	0.975210	−	0.221279i	$-0.0710233\pi$
$491$	16.7060	+	16.7060i	0.753931	+	0.753931i	−0.221279	+	0.975210i	$0.571023\pi$
$492$		0			0
$493$	9.26605	−	9.26605i	0.417322	−	0.417322i
$494$		0			0
$495$	24.4171			1.09746
$496$		0			0
$497$	10.1354			0.454633
$498$		0			0
$499$	21.7208	−	21.7208i	0.972357	−	0.972357i	−0.0272707	−	0.999628i	$-0.508682\pi$
$499$	21.7208	−	21.7208i	0.972357	−	0.972357i	0.999628	+	0.0272707i	$0.00868160\pi$
$500$		0			0
$501$	8.52276	+	8.52276i	0.380769	+	0.380769i
$502$		0			0
$503$		−	12.3248i		−	0.549534i	−0.961511	−	0.274767i	$-0.911399\pi$
$503$		−	12.3248i		−	0.549534i	0.961511	−	0.274767i	$-0.0886008\pi$
$504$		0			0
$505$		−	63.1692i		−	2.81099i
$506$		0			0
$507$	1.12199	+	1.12199i	0.0498293	+	0.0498293i
$508$		0			0
$509$	−19.2068	+	19.2068i	−0.851326	+	0.851326i	−0.990296	−	0.138971i	$-0.955621\pi$
$509$	−19.2068	+	19.2068i	−0.851326	+	0.851326i	0.138971	+	0.990296i	$0.455621\pi$
$510$		0			0
$511$	12.1093			0.535684
$512$		0			0
$513$	7.90033			0.348808
$514$		0			0
$515$	1.66054	−	1.66054i	0.0731720	−	0.0731720i
$516$		0			0
$517$	−8.58143	−	8.58143i	−0.377411	−	0.377411i
$518$		0			0
$519$		−	0.763260i		−	0.0335034i
$520$		0			0
$521$		−	0.515650i		−	0.0225910i	−0.999936	−	0.0112955i	$-0.996404\pi$
$521$		−	0.515650i		−	0.0225910i	0.999936	−	0.0112955i	$-0.00359555\pi$
$522$		0			0
$523$	6.17927	+	6.17927i	0.270201	+	0.270201i	0.829181	−	0.558980i	$-0.188807\pi$
$523$	6.17927	+	6.17927i	0.270201	+	0.270201i	−0.558980	+	0.829181i	$0.688807\pi$
$524$		0			0
$525$	−9.67791	+	9.67791i	−0.422379	+	0.422379i
$526$		0			0
$527$	−10.0717			−0.438730
$528$		0			0
$529$	−1.00000			−0.0434783
$530$		0			0
$531$	12.8147	−	12.8147i	0.556109	−	0.556109i
$532$		0			0
$533$	−20.9427	−	20.9427i	−0.907128	−	0.907128i
$534$		0			0
$535$			35.0561i			1.51561i
$536$		0			0
$537$		−	16.0055i		−	0.690687i
$538$		0			0
$539$	9.42923	+	9.42923i	0.406145	+	0.406145i
$540$		0			0
$541$	−5.80628	+	5.80628i	−0.249632	+	0.249632i	−0.820819	−	0.571188i	$-0.806483\pi$
$541$	−5.80628	+	5.80628i	−0.249632	+	0.249632i	0.571188	+	0.820819i	$0.306483\pi$
$542$		0			0
$543$	−7.95826			−0.341522
$544$		0			0
$545$	26.3046			1.12677
$546$		0			0
$547$	−16.8634	+	16.8634i	−0.721029	+	0.721029i	−0.968815	−	0.247786i	$-0.920297\pi$
$547$	−16.8634	+	16.8634i	−0.721029	+	0.721029i	0.247786	+	0.968815i	$0.420297\pi$
$548$		0			0
$549$	−14.0443	−	14.0443i	−0.599394	−	0.599394i
$550$		0			0
$551$			6.08275i			0.259134i
$552$		0			0
$553$			9.82706i			0.417889i
$554$		0			0
$555$	−15.1282	−	15.1282i	−0.642155	−	0.642155i
$556$		0			0
$557$	12.6709	−	12.6709i	0.536885	−	0.536885i	−0.385728	−	0.922613i	$-0.626050\pi$
$557$	12.6709	−	12.6709i	0.536885	−	0.536885i	0.922613	+	0.385728i	$0.126050\pi$
$558$		0			0
$559$	−48.7151			−2.06043
$560$		0			0
$561$	−9.35886			−0.395131
$562$		0			0
$563$	30.8676	−	30.8676i	1.30091	−	1.30091i	0.373136	−	0.927777i	$-0.378282\pi$
$563$	30.8676	−	30.8676i	1.30091	−	1.30091i	0.927777	−	0.373136i	$-0.121718\pi$
$564$		0			0
$565$	−12.5692	−	12.5692i	−0.528789	−	0.528789i
$566$		0			0
$567$			3.75746i			0.157798i
$568$		0			0
$569$			26.9844i			1.13125i	0.824664	+	0.565623i	$0.191364\pi$
$569$			26.9844i			1.13125i	−0.824664	+	0.565623i	$0.808636\pi$
$570$		0			0
$571$	1.83019	+	1.83019i	0.0765912	+	0.0765912i	0.744365	−	0.667773i	$-0.232752\pi$
$571$	1.83019	+	1.83019i	0.0765912	+	0.0765912i	−0.667773	+	0.744365i	$0.732752\pi$
$572$		0			0
$573$	−10.0265	+	10.0265i	−0.418862	+	0.418862i
$574$		0			0
$575$	10.0210			0.417906
$576$		0			0
$577$	−18.1595			−0.755991			−0.377995	−	0.925807i	$-0.623386\pi$
$577$	−18.1595			−0.755991			−0.377995	+	0.925807i	$0.623386\pi$
$578$		0			0
$579$	10.0289	−	10.0289i	0.416787	−	0.416787i
$580$		0			0
$581$	−17.8047	−	17.8047i	−0.738663	−	0.738663i
$582$		0			0
$583$		−	28.7834i		−	1.19209i
$584$		0			0
$585$		−	32.8107i		−	1.35656i
$586$		0			0
$587$	14.8262	+	14.8262i	0.611941	+	0.611941i	0.943452	−	0.331510i	$-0.107558\pi$
$587$	14.8262	+	14.8262i	0.611941	+	0.611941i	−0.331510	+	0.943452i	$0.607558\pi$
$588$		0			0
$589$	3.30581	−	3.30581i	0.136213	−	0.136213i
$590$		0			0
$591$	5.51087			0.226687
$592$		0			0
$593$	31.8803			1.30917			0.654583	−	0.755990i	$-0.272844\pi$
$593$	31.8803			1.30917			0.654583	+	0.755990i	$0.272844\pi$
$594$		0			0
$595$	−15.3513	+	15.3513i	−0.629341	+	0.629341i
$596$		0			0
$597$	−1.15746	−	1.15746i	−0.0473717	−	0.0473717i
$598$		0			0
$599$			39.1635i			1.60018i	0.599882	+	0.800088i	$0.295214\pi$
$599$			39.1635i			1.60018i	−0.599882	+	0.800088i	$0.704786\pi$
$600$		0			0
$601$		−	44.0527i		−	1.79695i	−0.439026	−	0.898474i	$-0.644676\pi$
$601$		−	44.0527i		−	1.79695i	0.439026	−	0.898474i	$-0.355324\pi$
$602$		0			0
$603$	0.182280	+	0.182280i	0.00742300	+	0.00742300i
$604$		0			0
$605$	−7.71925	+	7.71925i	−0.313832	+	0.313832i
$606$		0			0
$607$	−21.5920			−0.876393			−0.438196	−	0.898879i	$-0.644383\pi$
$607$	−21.5920			−0.876393			−0.438196	+	0.898879i	$0.644383\pi$
$608$		0			0
$609$	4.88598			0.197990
$610$		0			0
$611$	−11.5314	+	11.5314i	−0.466511	+	0.466511i
$612$		0			0
$613$	20.9053	+	20.9053i	0.844357	+	0.844357i	0.989422	−	0.145065i	$-0.0463392\pi$
$613$	20.9053	+	20.9053i	0.844357	+	0.844357i	−0.145065	+	0.989422i	$0.546339\pi$
$614$		0			0
$615$		−	26.6702i		−	1.07545i
$616$		0			0
$617$			4.01122i			0.161486i	0.996735	+	0.0807429i	$0.0257293\pi$
$617$			4.01122i			0.161486i	−0.996735	+	0.0807429i	$0.974271\pi$
$618$		0			0
$619$	8.52811	+	8.52811i	0.342774	+	0.342774i	0.857409	−	0.514635i	$-0.172073\pi$
$619$	8.52811	+	8.52811i	0.342774	+	0.342774i	−0.514635	+	0.857409i	$0.672073\pi$
$620$		0			0
$621$	−3.28547	+	3.28547i	−0.131841	+	0.131841i
$622$		0			0
$623$	4.23183			0.169545
$624$		0			0
$625$	−25.3160			−1.01264
$626$		0			0
$627$	3.07184	−	3.07184i	0.122677	−	0.122677i
$628$		0			0
$629$	−16.0089	−	16.0089i	−0.638317	−	0.638317i
$630$		0			0
$631$		−	14.7297i		−	0.586379i	−0.956054	−	0.293189i	$-0.905283\pi$
$631$		−	14.7297i		−	0.586379i	0.956054	−	0.293189i	$-0.0947166\pi$
$632$		0			0
$633$			0.222408i			0.00883992i
$634$		0			0
$635$	22.9768	+	22.9768i	0.911808	+	0.911808i
$636$		0			0
$637$	12.6706	−	12.6706i	0.502029	−	0.502029i
$638$		0			0
$639$	−14.5966			−0.577431
$640$		0			0
$641$	−25.1609			−0.993796			−0.496898	−	0.867809i	$-0.665528\pi$
$641$	−25.1609			−0.993796			−0.496898	+	0.867809i	$0.665528\pi$
$642$		0			0
$643$	−16.7541	+	16.7541i	−0.660718	+	0.660718i	−0.955549	−	0.294831i	$-0.904737\pi$
$643$	−16.7541	+	16.7541i	−0.660718	+	0.660718i	0.294831	+	0.955549i	$0.404737\pi$
$644$		0			0
$645$	−31.0190	−	31.0190i	−1.22137	−	1.22137i
$646$		0			0
$647$		−	17.2641i		−	0.678721i	−0.940656	−	0.339360i	$-0.889789\pi$
$647$		−	17.2641i		−	0.678721i	0.940656	−	0.339360i	$-0.110211\pi$
$648$		0			0
$649$		−	23.5400i		−	0.924027i
$650$		0			0
$651$	−2.65540	−	2.65540i	−0.104073	−	0.104073i
$652$		0			0
$653$	−29.8896	+	29.8896i	−1.16967	+	1.16967i	−0.187384	+	0.982287i	$0.560001\pi$
$653$	−29.8896	+	29.8896i	−1.16967	+	1.16967i	−0.982287	+	0.187384i	$0.939999\pi$
$654$		0			0
$655$	−83.9202			−3.27903
$656$		0			0
$657$	−17.4394			−0.680375
$658$		0			0
$659$	18.7646	−	18.7646i	0.730967	−	0.730967i	−0.239845	−	0.970811i	$-0.577097\pi$
$659$	18.7646	−	18.7646i	0.730967	−	0.730967i	0.970811	+	0.239845i	$0.0770965\pi$
$660$		0			0
$661$	30.7092	+	30.7092i	1.19445	+	1.19445i	0.975805	+	0.218644i	$0.0701635\pi$
$661$	30.7092	+	30.7092i	1.19445	+	1.19445i	0.218644	+	0.975805i	$0.429837\pi$
$662$		0			0
$663$			12.5761i			0.488415i
$664$		0			0
$665$		−	10.0774i		−	0.390786i
$666$		0			0
$667$	−2.52960	−	2.52960i	−0.0979467	−	0.0979467i
$668$		0			0
$669$	4.56696	−	4.56696i	0.176569	−	0.176569i
$670$		0			0
$671$	−25.7988			−0.995950
$672$		0			0
$673$	−18.7694			−0.723506			−0.361753	−	0.932274i	$-0.617822\pi$
$673$	−18.7694			−0.723506			−0.361753	+	0.932274i	$0.617822\pi$
$674$		0			0
$675$	32.9238	−	32.9238i	1.26724	−	1.26724i
$676$		0			0
$677$	−7.27989	−	7.27989i	−0.279789	−	0.279789i	0.553236	−	0.833025i	$-0.313393\pi$
$677$	−7.27989	−	7.27989i	−0.279789	−	0.279789i	−0.833025	+	0.553236i	$0.813393\pi$
$678$		0			0
$679$			10.1140i			0.388138i
$680$		0			0
$681$		−	20.0155i		−	0.766997i
$682$		0			0
$683$	12.4210	+	12.4210i	0.475277	+	0.475277i	0.903618	−	0.428340i	$-0.140901\pi$
$683$	12.4210	+	12.4210i	0.475277	+	0.475277i	−0.428340	+	0.903618i	$0.640901\pi$
$684$		0			0
$685$	−55.2089	+	55.2089i	−2.10943	+	2.10943i
$686$		0			0
$687$	−9.36106			−0.357147
$688$		0			0
$689$	−38.6780			−1.47352
$690$		0			0
$691$	33.8504	−	33.8504i	1.28773	−	1.28773i	0.351565	−	0.936163i	$-0.385650\pi$
$691$	33.8504	−	33.8504i	1.28773	−	1.28773i	0.936163	−	0.351565i	$-0.114350\pi$
$692$		0			0
$693$	6.81233	+	6.81233i	0.258779	+	0.258779i
$694$		0			0
$695$		−	60.7937i		−	2.30603i
$696$		0			0
$697$		−	28.2229i		−	1.06902i
$698$		0			0
$699$	−0.405164	−	0.405164i	−0.0153247	−	0.0153247i
$700$		0			0
$701$	−11.9805	+	11.9805i	−0.452498	+	0.452498i	−0.896183	−	0.443685i	$-0.853671\pi$
$701$	−11.9805	+	11.9805i	−0.452498	+	0.452498i	0.443685	+	0.896183i	$0.353671\pi$
$702$		0			0
$703$	10.5091			0.396360
$704$		0			0
$705$	−14.6851			−0.553073
$706$		0			0
$707$	17.6241	−	17.6241i	0.662824	−	0.662824i
$708$		0			0
$709$	−8.81693	−	8.81693i	−0.331127	−	0.331127i	0.521887	−	0.853014i	$-0.325228\pi$
$709$	−8.81693	−	8.81693i	−0.331127	−	0.331127i	−0.853014	+	0.521887i	$0.825228\pi$
$710$		0			0
$711$		−	14.1526i		−	0.530762i
$712$		0			0
$713$			2.74954i			0.102971i
$714$		0			0
$715$	−30.1361	−	30.1361i	−1.12702	−	1.12702i
$716$		0			0
$717$	−4.91751	+	4.91751i	−0.183648	+	0.183648i
$718$		0			0
$719$	41.8588			1.56107			0.780534	−	0.625113i	$-0.214947\pi$
$719$	41.8588			1.56107			0.780534	+	0.625113i	$0.214947\pi$
$720$		0			0
$721$	0.926576			0.0345075
$722$		0			0
$723$	−3.34148	+	3.34148i	−0.124271	+	0.124271i
$724$		0			0
$725$	25.3493	+	25.3493i	0.941448	+	0.941448i
$726$		0			0
$727$		−	2.66804i		−	0.0989520i	−0.998775	−	0.0494760i	$-0.984245\pi$
$727$		−	2.66804i		−	0.0989520i	0.998775	−	0.0494760i	$-0.0157551\pi$
$728$		0			0
$729$			7.03811i			0.260671i
$730$		0			0
$731$	−32.8249	−	32.8249i	−1.21407	−	1.21407i
$732$		0			0
$733$	16.3265	−	16.3265i	0.603033	−	0.603033i	−0.338083	−	0.941116i	$-0.609778\pi$
$733$	16.3265	−	16.3265i	0.603033	−	0.603033i	0.941116	+	0.338083i	$0.109778\pi$
$734$		0			0
$735$	16.1359			0.595181
$736$		0			0
$737$	0.334841			0.0123340
$738$		0			0
$739$	13.4540	−	13.4540i	0.494913	−	0.494913i	−0.414937	−	0.909850i	$-0.636196\pi$
$739$	13.4540	−	13.4540i	0.494913	−	0.494913i	0.909850	+	0.414937i	$0.136196\pi$
$740$		0			0
$741$	−4.12782	−	4.12782i	−0.151639	−	0.151639i
$742$		0			0
$743$		−	6.92795i		−	0.254162i	−0.991892	−	0.127081i	$-0.959439\pi$
$743$		−	6.92795i		−	0.254162i	0.991892	−	0.127081i	$-0.0405608\pi$
$744$		0			0
$745$			85.9275i			3.14814i
$746$		0			0
$747$	25.6416	+	25.6416i	0.938178	+	0.938178i
$748$		0			0
$749$	−9.78061	+	9.78061i	−0.357376	+	0.357376i
$750$		0			0
$751$	18.5653			0.677457			0.338729	−	0.940884i	$-0.390003\pi$
$751$	18.5653			0.677457			0.338729	+	0.940884i	$0.390003\pi$
$752$		0			0
$753$	25.4705			0.928196
$754$		0			0
$755$	−41.6497	+	41.6497i	−1.51579	+	1.51579i
$756$		0			0
$757$	18.6823	+	18.6823i	0.679020	+	0.679020i	0.959778	−	0.280759i	$-0.0905860\pi$
$757$	18.6823	+	18.6823i	0.679020	+	0.679020i	−0.280759	+	0.959778i	$0.590586\pi$
$758$		0			0
$759$			2.55494i			0.0927384i
$760$		0			0
$761$		−	43.1942i		−	1.56579i	−0.622154	−	0.782895i	$-0.713742\pi$
$761$		−	43.1942i		−	1.56579i	0.622154	−	0.782895i	$-0.286258\pi$
$762$		0			0
$763$	7.33896	+	7.33896i	0.265688	+	0.265688i
$764$		0			0
$765$	22.1083	−	22.1083i	0.799329	−	0.799329i
$766$		0			0
$767$	−31.6322			−1.14217
$768$		0			0
$769$	0.777724			0.0280454			0.0140227	−	0.999902i	$-0.495536\pi$
$769$	0.777724			0.0280454			0.0140227	+	0.999902i	$0.495536\pi$
$770$		0			0
$771$	1.36309	−	1.36309i	0.0490906	−	0.0490906i
$772$		0			0
$773$	5.97402	+	5.97402i	0.214870	+	0.214870i	0.806333	−	0.591462i	$-0.201449\pi$
$773$	5.97402	+	5.97402i	0.214870	+	0.214870i	−0.591462	+	0.806333i	$0.701449\pi$
$774$		0			0
$775$		−	27.5533i		−	0.989742i
$776$		0			0
$777$		−	8.44148i		−	0.302837i
$778$		0			0
$779$	9.26355	+	9.26355i	0.331901	+	0.331901i
$780$		0			0
$781$	−13.4067	+	13.4067i	−0.479728	+	0.479728i
$782$		0			0
$783$	−16.6219			−0.594018
$784$		0			0
$785$	−18.7072			−0.667690
$786$		0			0
$787$	−25.2892	+	25.2892i	−0.901463	+	0.901463i	−0.995563	−	0.0940993i	$-0.970003\pi$
$787$	−25.2892	+	25.2892i	−0.901463	+	0.901463i	0.0940993	+	0.995563i	$0.470003\pi$
$788$		0			0
$789$	8.65652	+	8.65652i	0.308180	+	0.308180i
$790$		0			0
$791$		−	7.01357i		−	0.249374i
$792$		0			0
$793$			34.6674i			1.23108i
$794$		0			0
$795$	−24.6280	−	24.6280i	−0.873464	−	0.873464i
$796$		0			0
$797$	11.1069	−	11.1069i	0.393428	−	0.393428i	−0.482479	−	0.875907i	$-0.660264\pi$
$797$	11.1069	−	11.1069i	0.393428	−	0.393428i	0.875907	+	0.482479i	$0.160264\pi$
$798$		0			0
$799$	−15.5401			−0.549767
$800$		0			0
$801$	−6.09452			−0.215339
$802$		0			0
$803$	−16.0177	+	16.0177i	−0.565254	+	0.565254i
$804$		0			0
$805$	4.19086	+	4.19086i	0.147708	+	0.147708i
$806$		0			0
$807$			23.4259i			0.824632i
$808$		0			0
$809$			20.5338i			0.721930i	0.932579	+	0.360965i	$0.117553\pi$
$809$			20.5338i			0.721930i	−0.932579	+	0.360965i	$0.882447\pi$
$810$		0			0
$811$	−7.79332	−	7.79332i	−0.273660	−	0.273660i	0.556911	−	0.830572i	$-0.311986\pi$
$811$	−7.79332	−	7.79332i	−0.273660	−	0.273660i	−0.830572	+	0.556911i	$0.811986\pi$
$812$		0			0
$813$	−4.21012	+	4.21012i	−0.147655	+	0.147655i
$814$		0			0
$815$	11.0164			0.385888
$816$		0			0
$817$	21.5481			0.753872
$818$		0			0
$819$	9.15417	−	9.15417i	0.319872	−	0.319872i
$820$		0			0
$821$	−14.2693	−	14.2693i	−0.498003	−	0.498003i	0.412813	−	0.910816i	$-0.364546\pi$
$821$	−14.2693	−	14.2693i	−0.498003	−	0.498003i	−0.910816	+	0.412813i	$0.864546\pi$
$822$		0			0
$823$		−	17.0118i		−	0.592995i	−0.955034	−	0.296497i	$-0.904181\pi$
$823$		−	17.0118i		−	0.592995i	0.955034	−	0.296497i	$-0.0958186\pi$
$824$		0			0
$825$		−	25.6032i		−	0.891387i
$826$		0			0
$827$	11.1872	+	11.1872i	0.389017	+	0.389017i	0.874337	−	0.485320i	$-0.161297\pi$
$827$	11.1872	+	11.1872i	0.389017	+	0.389017i	−0.485320	+	0.874337i	$0.661297\pi$
$828$		0			0
$829$	23.8978	−	23.8978i	0.830006	−	0.830006i	−0.157511	−	0.987517i	$-0.550347\pi$
$829$	23.8978	−	23.8978i	0.830006	−	0.830006i	0.987517	+	0.157511i	$0.0503470\pi$
$830$		0			0
$831$	15.9810			0.554374
$832$		0			0
$833$	17.0753			0.591625
$834$		0			0
$835$	−36.9840	+	36.9840i	−1.27988	+	1.27988i
$836$		0			0
$837$	9.03354	+	9.03354i	0.312245	+	0.312245i
$838$		0			0
$839$		−	18.4135i		−	0.635703i	−0.948140	−	0.317852i	$-0.897039\pi$
$839$		−	18.4135i		−	0.635703i	0.948140	−	0.317852i	$-0.102961\pi$
$840$		0			0
$841$			16.2022i			0.558697i
$842$		0			0
$843$	3.51856	+	3.51856i	0.121186	+	0.121186i
$844$		0			0
$845$	−4.86880	+	4.86880i	−0.167492	+	0.167492i
$846$		0			0
$847$	−4.30733			−0.148001
$848$		0			0
$849$	−14.6060			−0.501278
$850$		0			0
$851$	−4.37038	+	4.37038i	−0.149815	+	0.149815i
$852$		0			0
$853$	−29.8210	−	29.8210i	−1.02105	−	1.02105i	−0.999774	−	0.0212793i	$-0.993226\pi$
$853$	−29.8210	−	29.8210i	−1.02105	−	1.02105i	−0.0212793	−	0.999774i	$-0.506774\pi$
$854$		0			0
$855$			14.5131i			0.496339i
$856$		0			0
$857$			10.5633i			0.360836i	0.983590	+	0.180418i	$0.0577451\pi$
$857$			10.5633i			0.360836i	−0.983590	+	0.180418i	$0.942255\pi$
$858$		0			0
$859$	−7.21536	−	7.21536i	−0.246185	−	0.246185i	0.573218	−	0.819403i	$-0.305695\pi$
$859$	−7.21536	−	7.21536i	−0.246185	−	0.246185i	−0.819403	+	0.573218i	$0.805695\pi$
$860$		0			0
$861$	7.44096	−	7.44096i	0.253587	−	0.253587i
$862$		0			0
$863$	56.9903			1.93997			0.969986	−	0.243161i	$-0.0781844\pi$
$863$	56.9903			1.93997			0.969986	+	0.243161i	$0.0781844\pi$
$864$		0			0
$865$	3.31212			0.112615
$866$		0			0
$867$	2.26225	−	2.26225i	0.0768300	−	0.0768300i
$868$		0			0
$869$	−12.9989	−	12.9989i	−0.440956	−	0.440956i
$870$		0			0
$871$		−	0.449947i		−	0.0152459i
$872$		0			0
$873$		−	14.5657i		−	0.492975i
$874$		0			0
$875$	−21.0424	−	21.0424i	−0.711364	−	0.711364i
$876$		0			0
$877$	12.2367	−	12.2367i	0.413205	−	0.413205i	−0.469649	−	0.882853i	$-0.655619\pi$
$877$	12.2367	−	12.2367i	0.413205	−	0.413205i	0.882853	+	0.469649i	$0.155619\pi$
$878$		0			0
$879$	0.739741			0.0249509
$880$		0			0
$881$	38.5162			1.29764			0.648822	−	0.760940i	$-0.275262\pi$
$881$	38.5162			1.29764			0.648822	+	0.760940i	$0.275262\pi$
$882$		0			0
$883$	4.60476	−	4.60476i	0.154962	−	0.154962i	−0.625368	−	0.780330i	$-0.715051\pi$
$883$	4.60476	−	4.60476i	0.154962	−	0.154962i	0.780330	+	0.625368i	$0.215051\pi$
$884$		0			0
$885$	−20.1416	−	20.1416i	−0.677053	−	0.677053i
$886$		0			0
$887$			6.69978i			0.224957i	0.993654	+	0.112478i	$0.0358789\pi$
$887$			6.69978i			0.224957i	−0.993654	+	0.112478i	$0.964121\pi$
$888$		0			0
$889$			12.8210i			0.430003i
$890$		0			0
$891$	−4.97022	−	4.97022i	−0.166509	−	0.166509i
$892$		0			0
$893$	5.10068	−	5.10068i	0.170688	−	0.170688i
$894$		0			0
$895$	69.4548			2.32162
$896$		0			0
$897$	3.43323			0.114632
$898$		0			0
$899$	−6.95525	+	6.95525i	−0.231971	+	0.231971i
$900$		0			0
$901$	−26.0618	−	26.0618i	−0.868245	−	0.868245i
$902$		0			0
$903$		−	17.3085i		−	0.575992i
$904$		0			0
$905$		−	34.5344i		−	1.14796i
$906$		0			0
$907$	27.1221	+	27.1221i	0.900573	+	0.900573i	0.995486	−	0.0949124i	$-0.0302571\pi$
$907$	27.1221	+	27.1221i	0.900573	+	0.900573i	−0.0949124	+	0.995486i	$0.530257\pi$
$908$		0			0
$909$	−25.3816	+	25.3816i	−0.841855	+	0.841855i
$910$		0			0
$911$	40.4261			1.33938			0.669688	−	0.742643i	$-0.266428\pi$
$911$	40.4261			1.33938			0.669688	+	0.742643i	$0.266428\pi$
$912$		0			0
$913$	47.1027			1.55887
$914$		0			0
$915$	−22.0743	+	22.0743i	−0.729752	+	0.729752i
$916$		0			0
$917$	−23.4137	−	23.4137i	−0.773187	−	0.773187i
$918$		0			0
$919$			28.9812i			0.956002i	0.878359	+	0.478001i	$0.158639\pi$
$919$			28.9812i			0.956002i	−0.878359	+	0.478001i	$0.841361\pi$
$920$		0			0
$921$		−	25.6029i		−	0.843644i
$922$		0			0
$923$	18.0154	+	18.0154i	0.592984	+	0.592984i
$924$		0			0
$925$	43.7958	−	43.7958i	1.44000	−	1.44000i
$926$		0			0
$927$	−1.33442			−0.0438281
$928$		0			0
$929$	−1.76699			−0.0579730			−0.0289865	−	0.999580i	$-0.509228\pi$
$929$	−1.76699			−0.0579730			−0.0289865	+	0.999580i	$0.509228\pi$
$930$		0			0
$931$	−5.60459	+	5.60459i	−0.183683	+	0.183683i
$932$		0			0
$933$	6.64787	+	6.64787i	0.217641	+	0.217641i
$934$		0			0
$935$		−	40.6122i		−	1.32816i
$936$		0			0
$937$			2.15821i			0.0705055i	0.999378	+	0.0352528i	$0.0112236\pi$
$937$			2.15821i			0.0705055i	−0.999378	+	0.0352528i	$0.988776\pi$
$938$		0			0
$939$	11.1253	+	11.1253i	0.363060	+	0.363060i
$940$		0			0
$941$	−6.70952	+	6.70952i	−0.218724	+	0.218724i	−0.807961	−	0.589237i	$-0.799429\pi$
$941$	−6.70952	+	6.70952i	−0.218724	+	0.218724i	0.589237	+	0.807961i	$0.299429\pi$
$942$		0			0
$943$	−7.70478			−0.250902
$944$		0			0
$945$	27.5379			0.895807
$946$		0			0
$947$	11.6213	−	11.6213i	0.377642	−	0.377642i	−0.492609	−	0.870251i	$-0.663957\pi$
$947$	11.6213	−	11.6213i	0.377642	−	0.377642i	0.870251	+	0.492609i	$0.163957\pi$
$948$		0			0
$949$	21.5240	+	21.5240i	0.698700	+	0.698700i
$950$		0			0
$951$		−	9.44634i		−	0.306319i
$952$		0			0
$953$		−	20.7869i		−	0.673354i	−0.941620	−	0.336677i	$-0.890697\pi$
$953$		−	20.7869i		−	0.673354i	0.941620	−	0.336677i	$-0.109303\pi$
$954$		0			0
$955$	−43.5093	−	43.5093i	−1.40793	−	1.40793i
$956$		0			0
$957$	−6.46299	+	6.46299i	−0.208919	+	0.208919i
$958$		0			0
$959$	−30.8065			−0.994793
$960$		0			0
$961$	−23.4400			−0.756130
$962$		0			0
$963$	14.0857	−	14.0857i	0.453904	−	0.453904i
$964$		0			0
$965$	43.5198	+	43.5198i	1.40095	+	1.40095i
$966$		0			0
$967$			34.3551i			1.10479i	0.833584	+	0.552393i	$0.186285\pi$
$967$			34.3551i			1.10479i	−0.833584	+	0.552393i	$0.813715\pi$
$968$		0			0
$969$		−	5.56277i		−	0.178702i
$970$		0			0
$971$	5.58481	+	5.58481i	0.179225	+	0.179225i	0.791018	−	0.611793i	$-0.209551\pi$
$971$	5.58481	+	5.58481i	0.179225	+	0.179225i	−0.611793	+	0.791018i	$0.709551\pi$
$972$		0			0
$973$	16.9614	−	16.9614i	0.543757	−	0.543757i
$974$		0			0
$975$	−34.4046			−1.10183
$976$		0			0
$977$	−28.9353			−0.925723			−0.462861	−	0.886431i	$-0.653177\pi$
$977$	−28.9353			−0.925723			−0.462861	+	0.886431i	$0.653177\pi$
$978$		0			0
$979$	−5.59770	+	5.59770i	−0.178903	+	0.178903i
$980$		0			0
$981$	−10.5693	−	10.5693i	−0.337451	−	0.337451i
$982$		0			0
$983$		−	37.8206i		−	1.20629i	−0.797631	−	0.603145i	$-0.793914\pi$
$983$		−	37.8206i		−	1.20629i	0.797631	−	0.603145i	$-0.206086\pi$
$984$		0			0
$985$			23.9141i			0.761966i
$986$		0			0
$987$	−4.09713	−	4.09713i	−0.130413	−	0.130413i
$988$		0			0
$989$	−8.96110	+	8.96110i	−0.284946	+	0.284946i
$990$		0			0
$991$	−26.7617			−0.850114			−0.425057	−	0.905166i	$-0.639746\pi$
$991$	−26.7617			−0.850114			−0.425057	+	0.905166i	$0.639746\pi$
$992$		0			0
$993$	−1.27676			−0.0405168
$994$		0			0
$995$	5.02273	−	5.02273i	0.159231	−	0.159231i
$996$		0			0
$997$	−5.50519	−	5.50519i	−0.174351	−	0.174351i	0.614537	−	0.788888i	$-0.289343\pi$
$997$	−5.50519	−	5.50519i	−0.174351	−	0.174351i	−0.788888	+	0.614537i	$0.789343\pi$
$998$		0			0
$999$			28.7176i			0.908583i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1472.2.j.c.369.3		12
4.3	odd	2		368.2.j.c.277.5	yes	12
16.3	odd	4		368.2.j.c.93.5	✓	12
16.13	even	4	inner	1472.2.j.c.1105.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
368.2.j.c.93.5	✓	12	16.3	odd	4
368.2.j.c.277.5	yes	12	4.3	odd	2
1472.2.j.c.369.3		12	1.1	even	1	trivial
1472.2.j.c.1105.3		12	16.13	even	4	inner

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:	\( N \)	\(=\)	\( 1472 = 2^{6} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1472.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.631541 + 0.631541i) q^{3} +(-2.74053 - 2.74053i) q^{5} -1.52921i q^{7} +2.20231i q^{9} +(2.02278 + 2.02278i) q^{11} +(2.71814 - 2.71814i) q^{13} +3.46152 q^{15} +3.66304 q^{17} +(-1.20231 + 1.20231i) q^{19} +(0.965760 + 0.965760i) q^{21} -1.00000i q^{23} +10.0210i q^{25} +(-3.28547 - 3.28547i) q^{27} +(2.52960 - 2.52960i) q^{29} -2.74954 q^{31} -2.55494 q^{33} +(-4.19086 + 4.19086i) q^{35} +(-4.37038 - 4.37038i) q^{37} +3.43323i q^{39} -7.70478i q^{41} +(-8.96110 - 8.96110i) q^{43} +(6.03551 - 6.03551i) q^{45} -4.24239 q^{47} +4.66151 q^{49} +(-2.31336 + 2.31336i) q^{51} +(-7.11480 - 7.11480i) q^{53} -11.0870i q^{55} -1.51862i q^{57} +(-5.81873 - 5.81873i) q^{59} +(-6.37705 + 6.37705i) q^{61} +3.36780 q^{63} -14.8983 q^{65} +(0.0827674 - 0.0827674i) q^{67} +(0.631541 + 0.631541i) q^{69} +6.62784i q^{71} +7.91866i q^{73} +(-6.32869 - 6.32869i) q^{75} +(3.09326 - 3.09326i) q^{77} -6.42623 q^{79} -2.45712 q^{81} +(11.6430 - 11.6430i) q^{83} +(-10.0387 - 10.0387i) q^{85} +3.19510i q^{87} +2.76733i q^{89} +(-4.15662 - 4.15662i) q^{91} +(1.73645 - 1.73645i) q^{93} +6.58995 q^{95} -6.61383 q^{97} +(-4.45480 + 4.45480i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} - 4 q^{5} + 4 q^{11} + 18 q^{13} - 8 q^{17} + 8 q^{19} + 8 q^{21} - 14 q^{27} + 2 q^{29} - 20 q^{31} - 36 q^{33} - 4 q^{35} - 4 q^{37} - 20 q^{43} - 20 q^{45} + 16 q^{47} + 52 q^{49} + 4 q^{51}+ \cdots - 36 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 - 4 * q^5 + 4 * q^11 + 18 * q^13 - 8 * q^17 + 8 * q^19 + 8 * q^21 - 14 * q^27 + 2 * q^29 - 20 * q^31 - 36 * q^33 - 4 * q^35 - 4 * q^37 - 20 * q^43 - 20 * q^45 + 16 * q^47 + 52 * q^49 + 4 * q^51 - 16 * q^53 - 8 * q^59 + 12 * q^61 + 4 * q^63 - 52 * q^65 + 4 * q^67 + 2 * q^69 + 46 * q^75 - 12 * q^77 + 4 * q^79 + 48 * q^81 - 28 * q^83 - 8 * q^85 - 14 * q^93 - 48 * q^95 + 36 * q^97 - 36 * q^99

Introduction

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