LMFDB - Embedded newform 1152.2.i.j.385.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(385,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1152.385");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.i (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:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} + \cdots + 729 $ x^12 - 2x^11 + 3x^10 - 8x^9 + 22x^8 - 42x^7 + 51x^6 - 126x^5 + 198x^4 - 216x^3 + 243x^2 - 486*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			385.4
Root			$-1.28252 + 1.16410i$ of defining polynomial
Character	$\chi$	$=$	1152.385
Dual form			1152.2.i.j.769.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366879 + 1.69275i) q^{3} +(1.05471 + 1.82681i) q^{5} +(-1.43914 + 2.49267i) q^{7} +(-2.73080 - 1.24207i) q^{9} +O(q^{10})$	\(q+(-0.366879 + 1.69275i) q^{3} +(1.05471 + 1.82681i) q^{5} +(-1.43914 + 2.49267i) q^{7} +(-2.73080 - 1.24207i) q^{9} +(1.21325 - 2.10141i) q^{11} +(-3.30008 - 5.71590i) q^{13} +(-3.47929 + 1.11514i) q^{15} -7.56848 q^{17} -6.25779 q^{19} +(-3.69147 - 3.35061i) q^{21} +(2.63611 + 4.56587i) q^{23} +(0.275172 - 0.476612i) q^{25} +(3.10438 - 4.16687i) q^{27} +(1.57821 - 2.73353i) q^{29} +(1.79039 + 3.10104i) q^{31} +(3.11204 + 2.82469i) q^{33} -6.07151 q^{35} +6.70957 q^{37} +(10.8863 - 3.48916i) q^{39} +(-1.74537 - 3.02306i) q^{41} +(-3.12570 + 5.41388i) q^{43} +(-0.611180 - 6.29868i) q^{45} +(-1.32972 + 2.30314i) q^{47} +(-0.642255 - 1.11242i) q^{49} +(2.77671 - 12.8115i) q^{51} -0.953009 q^{53} +5.11850 q^{55} +(2.29585 - 10.5929i) q^{57} +(-4.84757 - 8.39624i) q^{59} +(-2.57821 + 4.46558i) q^{61} +(7.02607 - 5.01946i) q^{63} +(6.96125 - 12.0572i) q^{65} +(-0.949546 - 1.64466i) q^{67} +(-8.69601 + 2.78715i) q^{69} -5.82491 q^{71} -5.01222 q^{73} +(0.705829 + 0.640656i) q^{75} +(3.49207 + 6.04844i) q^{77} +(-6.49996 + 11.2583i) q^{79} +(5.91454 + 6.78368i) q^{81} +(-1.54502 + 2.67606i) q^{83} +(-7.98256 - 13.8262i) q^{85} +(4.04818 + 3.67438i) q^{87} -2.95301 q^{89} +18.9971 q^{91} +(-5.90614 + 1.89297i) q^{93} +(-6.60015 - 11.4318i) q^{95} +(-5.51242 + 9.54779i) q^{97} +(-5.92323 + 4.23159i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} + 2 q^{5} + 6 q^{7} - 2 q^{9}+O(q^{10}) $ 12 * q - 4 * q^3 + 2 * q^5 + 6 * q^7 - 2 * q^9	$ 12 q - 4 q^{3} + 2 q^{5} + 6 q^{7} - 2 q^{9} - 4 q^{11} - 10 q^{13} + 4 q^{15} + 4 q^{17} - 4 q^{19} - 2 q^{21} + 8 q^{23} - 14 q^{25} + 14 q^{27} + 2 q^{29} + 8 q^{31} - 10 q^{33} - 8 q^{35} + 22 q^{39} - 2 q^{41} + 2 q^{43} - 10 q^{45} - 14 q^{47} - 18 q^{49} + 38 q^{51} - 24 q^{53} - 16 q^{55} - 38 q^{57} - 6 q^{59} - 14 q^{61} - 16 q^{63} - 8 q^{65} - 4 q^{67} + 50 q^{69} - 28 q^{71} + 60 q^{73} - 50 q^{75} - 2 q^{77} + 16 q^{79} + 22 q^{81} - 24 q^{83} - 16 q^{85} - 36 q^{87} - 48 q^{89} + 52 q^{91} - 42 q^{93} - 20 q^{95} - 14 q^{97} - 68 q^{99}+O(q^{100}) $ 12 * q - 4 * q^3 + 2 * q^5 + 6 * q^7 - 2 * q^9 - 4 * q^11 - 10 * q^13 + 4 * q^15 + 4 * q^17 - 4 * q^19 - 2 * q^21 + 8 * q^23 - 14 * q^25 + 14 * q^27 + 2 * q^29 + 8 * q^31 - 10 * q^33 - 8 * q^35 + 22 * q^39 - 2 * q^41 + 2 * q^43 - 10 * q^45 - 14 * q^47 - 18 * q^49 + 38 * q^51 - 24 * q^53 - 16 * q^55 - 38 * q^57 - 6 * q^59 - 14 * q^61 - 16 * q^63 - 8 * q^65 - 4 * q^67 + 50 * q^69 - 28 * q^71 + 60 * q^73 - 50 * q^75 - 2 * q^77 + 16 * q^79 + 22 * q^81 - 24 * q^83 - 16 * q^85 - 36 * q^87 - 48 * q^89 + 52 * q^91 - 42 * q^93 - 20 * q^95 - 14 * q^97 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−0.366879	+	1.69275i	−0.211818	+	0.977309i
$3$	−0.366879	+	1.69275i	−0.211818	+	0.977309i
$4$		0			0
$5$	1.05471	+	1.82681i	0.471681	+	0.816975i	0.999475	−	0.0323971i	$-0.0103141\pi$
$5$	1.05471	+	1.82681i	0.471681	+	0.816975i	−0.527794	+	0.849372i	$0.676981\pi$
$6$		0			0
$7$	−1.43914	+	2.49267i	−0.543944	+	0.942139i	0.454728	+	0.890630i	$0.349736\pi$
$7$	−1.43914	+	2.49267i	−0.543944	+	0.942139i	−0.998673	+	0.0515089i	$0.983597\pi$
$8$		0			0
$9$	−2.73080	−	1.24207i	−0.910267	−	0.414022i
$10$		0			0
$11$	1.21325	−	2.10141i	0.365808	−	0.633598i	−0.623097	−	0.782144i	$-0.714126\pi$
$11$	1.21325	−	2.10141i	0.365808	−	0.633598i	0.988905	+	0.148546i	$0.0474594\pi$
$12$		0			0
$13$	−3.30008	−	5.71590i	−0.915277	−	1.58531i	−0.806496	−	0.591240i	$-0.798639\pi$
$13$	−3.30008	−	5.71590i	−0.915277	−	1.58531i	−0.108781	−	0.994066i	$-0.534695\pi$
$14$		0			0
$15$	−3.47929	+	1.11514i	−0.898348	+	0.287928i
$16$		0			0
$17$	−7.56848			−1.83563			−0.917813	−	0.397013i	$-0.870047\pi$
$17$	−7.56848			−1.83563			−0.917813	+	0.397013i	$0.870047\pi$
$18$		0			0
$19$	−6.25779			−1.43563			−0.717817	−	0.696231i	$-0.754859\pi$
$19$	−6.25779			−1.43563			−0.717817	+	0.696231i	$0.754859\pi$
$20$		0			0
$21$	−3.69147	−	3.35061i	−0.805544	−	0.731163i
$22$		0			0
$23$	2.63611	+	4.56587i	0.549666	+	0.952050i	0.998297	+	0.0583329i	$0.0185785\pi$
$23$	2.63611	+	4.56587i	0.549666	+	0.952050i	−0.448631	+	0.893717i	$0.648088\pi$
$24$		0			0
$25$	0.275172	−	0.476612i	0.0550344	−	0.0953223i
$26$		0			0
$27$	3.10438	−	4.16687i	0.597438	−	0.801915i
$28$		0			0
$29$	1.57821	−	2.73353i	0.293065	−	0.507604i	−0.681468	−	0.731848i	$-0.738658\pi$
$29$	1.57821	−	2.73353i	0.293065	−	0.507604i	0.974533	+	0.224244i	$0.0719913\pi$
$30$		0			0
$31$	1.79039	+	3.10104i	0.321563	+	0.556964i	0.980811	−	0.194962i	$-0.0624584\pi$
$31$	1.79039	+	3.10104i	0.321563	+	0.556964i	−0.659248	+	0.751926i	$0.729125\pi$
$32$		0			0
$33$	3.11204	+	2.82469i	0.541737	+	0.491715i
$34$		0			0
$35$	−6.07151			−1.02627
$36$		0			0
$37$	6.70957			1.10305			0.551524	−	0.834159i	$-0.314047\pi$
$37$	6.70957			1.10305			0.551524	+	0.834159i	$0.314047\pi$
$38$		0			0
$39$	10.8863	−	3.48916i	1.74321	−	0.558713i
$40$		0			0
$41$	−1.74537	−	3.02306i	−0.272580	−	0.472123i	0.696941	−	0.717128i	$-0.254544\pi$
$41$	−1.74537	−	3.02306i	−0.272580	−	0.472123i	−0.969522	+	0.245005i	$0.921210\pi$
$42$		0			0
$43$	−3.12570	+	5.41388i	−0.476665	+	0.825608i	−0.999642	−	0.0267383i	$-0.991488\pi$
$43$	−3.12570	+	5.41388i	−0.476665	+	0.825608i	0.522977	+	0.852347i	$0.324821\pi$
$44$		0			0
$45$	−0.611180	−	6.29868i	−0.0911093	−	0.938952i
$46$		0			0
$47$	−1.32972	+	2.30314i	−0.193960	+	0.335948i	−0.946559	−	0.322531i	$-0.895466\pi$
$47$	−1.32972	+	2.30314i	−0.193960	+	0.335948i	0.752599	+	0.658479i	$0.228800\pi$
$48$		0			0
$49$	−0.642255	−	1.11242i	−0.0917508	−	0.158917i
$50$		0			0
$51$	2.77671	−	12.8115i	0.388818	−	1.79397i
$52$		0			0
$53$	−0.953009			−0.130906			−0.0654529	−	0.997856i	$-0.520849\pi$
$53$	−0.953009			−0.130906			−0.0654529	+	0.997856i	$0.520849\pi$
$54$		0			0
$55$	5.11850			0.690178
$56$		0			0
$57$	2.29585	−	10.5929i	0.304093	−	1.40306i
$58$		0			0
$59$	−4.84757	−	8.39624i	−0.631100	−	1.09310i	−0.987327	−	0.158698i	$-0.949270\pi$
$59$	−4.84757	−	8.39624i	−0.631100	−	1.09310i	0.356227	−	0.934400i	$-0.384063\pi$
$60$		0			0
$61$	−2.57821	+	4.46558i	−0.330105	+	0.571759i	−0.982532	−	0.186092i	$-0.940418\pi$
$61$	−2.57821	+	4.46558i	−0.330105	+	0.571759i	0.652427	+	0.757852i	$0.273751\pi$
$62$		0			0
$63$	7.02607	−	5.01946i	0.885201	−	0.632393i
$64$		0			0
$65$	6.96125	−	12.0572i	0.863437	−	1.49552i
$66$		0			0
$67$	−0.949546	−	1.64466i	−0.116005	−	0.200927i	0.802176	−	0.597088i	$-0.203676\pi$
$67$	−0.949546	−	1.64466i	−0.116005	−	0.200927i	−0.918181	+	0.396161i	$0.870342\pi$
$68$		0			0
$69$	−8.69601	+	2.78715i	−1.04688	+	0.335533i
$70$		0			0
$71$	−5.82491			−0.691290			−0.345645	−	0.938365i	$-0.612340\pi$
$71$	−5.82491			−0.691290			−0.345645	+	0.938365i	$0.612340\pi$
$72$		0			0
$73$	−5.01222			−0.586636			−0.293318	−	0.956015i	$-0.594760\pi$
$73$	−5.01222			−0.586636			−0.293318	+	0.956015i	$0.594760\pi$
$74$		0			0
$75$	0.705829	+	0.640656i	0.0815021	+	0.0739765i
$76$		0			0
$77$	3.49207	+	6.04844i	0.397958	+	0.689284i
$78$		0			0
$79$	−6.49996	+	11.2583i	−0.731303	+	1.26665i	0.225024	+	0.974353i	$0.427754\pi$
$79$	−6.49996	+	11.2583i	−0.731303	+	1.26665i	−0.956327	+	0.292301i	$0.905579\pi$
$80$		0			0
$81$	5.91454	+	6.78368i	0.657171	+	0.753742i
$82$		0			0
$83$	−1.54502	+	2.67606i	−0.169588	+	0.293735i	−0.938275	−	0.345890i	$-0.887577\pi$
$83$	−1.54502	+	2.67606i	−0.169588	+	0.293735i	0.768687	+	0.639625i	$0.220910\pi$
$84$		0			0
$85$	−7.98256	−	13.8262i	−0.865830	−	1.49966i
$86$		0			0
$87$	4.04818	+	3.67438i	0.434010	+	0.393935i
$88$		0			0
$89$	−2.95301			−0.313018			−0.156509	−	0.987677i	$-0.550024\pi$
$89$	−2.95301			−0.313018			−0.156509	+	0.987677i	$0.550024\pi$
$90$		0			0
$91$	18.9971			1.99144
$92$		0			0
$93$	−5.90614	+	1.89297i	−0.612439	+	0.196292i
$94$		0			0
$95$	−6.60015	−	11.4318i	−0.677161	−	1.17288i
$96$		0			0
$97$	−5.51242	+	9.54779i	−0.559702	+	0.969432i	0.437820	+	0.899063i	$0.355751\pi$
$97$	−5.51242	+	9.54779i	−0.559702	+	0.969432i	−0.997521	+	0.0703686i	$0.977582\pi$
$98$		0			0
$99$	−5.92323	+	4.23159i	−0.595307	+	0.425290i
$100$		0			0
$101$	−1.82357	+	3.15852i	−0.181452	+	0.314284i	−0.942375	−	0.334558i	$-0.891413\pi$
$101$	−1.82357	+	3.15852i	−0.181452	+	0.314284i	0.760923	+	0.648842i	$0.224746\pi$
$102$		0			0
$103$	5.43914	+	9.42087i	0.535935	+	0.928266i	0.999117	+	0.0420031i	$0.0133739\pi$
$103$	5.43914	+	9.42087i	0.535935	+	0.928266i	−0.463183	+	0.886263i	$0.653293\pi$
$104$		0			0
$105$	2.22751	−	10.2775i	0.217382	−	1.00299i
$106$		0			0
$107$	5.94922			0.575133			0.287567	−	0.957761i	$-0.407154\pi$
$107$	5.94922			0.575133			0.287567	+	0.957761i	$0.407154\pi$
$108$		0			0
$109$	−9.87113			−0.945483			−0.472741	−	0.881201i	$-0.656735\pi$
$109$	−9.87113			−0.945483			−0.472741	+	0.881201i	$0.656735\pi$
$110$		0			0
$111$	−2.46160	+	11.3576i	−0.233645	+	1.07802i
$112$		0			0
$113$	−7.51518	−	13.0167i	−0.706969	−	1.22451i	−0.965976	−	0.258630i	$-0.916729\pi$
$113$	−7.51518	−	13.0167i	−0.706969	−	1.22451i	0.259008	−	0.965875i	$-0.416604\pi$
$114$		0			0
$115$	−5.56066	+	9.63134i	−0.518534	+	0.898128i
$116$		0			0
$117$	1.91232	+	19.7079i	0.176794	+	1.82200i
$118$		0			0
$119$	10.8921	−	18.8657i	0.998478	−	1.72942i
$120$		0			0
$121$	2.55606	+	4.42722i	0.232369	+	0.402475i
$122$		0			0
$123$	5.75763	−	1.84537i	0.519148	−	0.166391i
$124$		0			0
$125$	11.7080			1.04720
$126$		0			0
$127$	−8.07789			−0.716797			−0.358398	−	0.933569i	$-0.616677\pi$
$127$	−8.07789			−0.716797			−0.358398	+	0.933569i	$0.616677\pi$
$128$		0			0
$129$	−8.01758	−	7.27727i	−0.705909	−	0.640728i
$130$		0			0
$131$	−11.1329	−	19.2827i	−0.972684	−	1.68474i	−0.687375	−	0.726303i	$-0.741237\pi$
$131$	−11.1329	−	19.2827i	−0.972684	−	1.68474i	−0.285309	−	0.958435i	$-0.592096\pi$
$132$		0			0
$133$	9.00584	−	15.5986i	0.780905	−	1.35257i
$134$		0			0
$135$	10.8863	+	1.27628i	0.936945	+	0.109844i
$136$		0			0
$137$	−4.62365	+	8.00839i	−0.395025	+	0.684203i	−0.993104	−	0.117234i	$-0.962597\pi$
$137$	−4.62365	+	8.00839i	−0.395025	+	0.684203i	0.598079	+	0.801437i	$0.295931\pi$
$138$		0			0
$139$	−4.20256	−	7.27905i	−0.356456	−	0.617401i	0.630910	−	0.775856i	$-0.282682\pi$
$139$	−4.20256	−	7.27905i	−0.356456	−	0.617401i	−0.987366	+	0.158456i	$0.949349\pi$
$140$		0			0
$141$	−3.41080	−	3.09586i	−0.287241	−	0.260718i
$142$		0			0
$143$	−16.0152			−1.33926
$144$		0			0
$145$	6.65820			0.552934
$146$		0			0
$147$	2.11868	−	0.679055i	0.174745	−	0.0560075i
$148$		0			0
$149$	−6.17836	−	10.7012i	−0.506151	−	0.876679i	−0.999975	−	0.00711709i	$-0.997735\pi$
$149$	−6.17836	−	10.7012i	−0.506151	−	0.876679i	0.493824	−	0.869562i	$-0.335599\pi$
$150$		0			0
$151$	4.91424	−	8.51171i	0.399915	−	0.692673i	−0.593800	−	0.804613i	$-0.702373\pi$
$151$	4.91424	−	8.51171i	0.399915	−	0.692673i	0.993715	+	0.111940i	$0.0357063\pi$
$152$		0			0
$153$	20.6680	+	9.40056i	1.67091	+	0.759990i
$154$		0			0
$155$	−3.77668	+	6.54141i	−0.303350	+	0.525418i
$156$		0			0
$157$	0.108083	+	0.187206i	0.00862598	+	0.0149406i	0.870306	−	0.492511i	$-0.163921\pi$
$157$	0.108083	+	0.187206i	0.00862598	+	0.0149406i	−0.861680	+	0.507452i	$0.830588\pi$
$158$		0			0
$159$	0.349639	−	1.61321i	0.0277282	−	0.127935i
$160$		0			0
$161$	−15.1749			−1.19595
$162$		0			0
$163$	5.78116			0.452815			0.226408	−	0.974033i	$-0.427302\pi$
$163$	5.78116			0.452815			0.226408	+	0.974033i	$0.427302\pi$
$164$		0			0
$165$	−1.87787	+	8.66434i	−0.146192	+	0.674518i
$166$		0			0
$167$	−0.818646	−	1.41794i	−0.0633487	−	0.109723i	0.832612	−	0.553857i	$-0.186845\pi$
$167$	−0.818646	−	1.41794i	−0.0633487	−	0.109723i	−0.895960	+	0.444134i	$0.853511\pi$
$168$		0			0
$169$	−15.2810	+	26.4675i	−1.17546	+	2.03596i
$170$		0			0
$171$	17.0888	+	7.77259i	1.30681	+	0.594385i
$172$		0			0
$173$	2.99228	−	5.18278i	0.227499	−	0.394040i	−0.729567	−	0.683909i	$-0.760279\pi$
$173$	2.99228	−	5.18278i	0.227499	−	0.394040i	0.957066	+	0.289869i	$0.0936119\pi$
$174$		0			0
$175$	0.792022	+	1.37182i	0.0598713	+	0.103700i
$176$		0			0
$177$	15.9912	−	5.12532i	1.20197	−	0.385243i
$178$		0			0
$179$	−9.51313			−0.711045			−0.355522	−	0.934668i	$-0.615697\pi$
$179$	−9.51313			−0.711045			−0.355522	+	0.934668i	$0.615697\pi$
$180$		0			0
$181$	23.7526			1.76551			0.882757	−	0.469830i	$-0.155685\pi$
$181$	23.7526			1.76551			0.882757	+	0.469830i	$0.155685\pi$
$182$		0			0
$183$	−6.61322	−	6.00258i	−0.488864	−	0.443724i
$184$		0			0
$185$	7.07666	+	12.2571i	0.520286	+	0.901162i
$186$		0			0
$187$	−9.18244	+	15.9045i	−0.671487	+	1.16305i
$188$		0			0
$189$	5.91898	+	13.7349i	0.430542	+	0.999067i
$190$		0			0
$191$	−4.14164	+	7.17352i	−0.299678	+	0.519058i	−0.976062	−	0.217491i	$-0.930213\pi$
$191$	−4.14164	+	7.17352i	−0.299678	+	0.519058i	0.676384	+	0.736549i	$0.263546\pi$
$192$		0			0
$193$	5.00315	+	8.66572i	0.360135	+	0.623772i	0.987983	−	0.154564i	$-0.0493973\pi$
$193$	5.00315	+	8.66572i	0.360135	+	0.623772i	−0.627848	+	0.778336i	$0.716064\pi$
$194$		0			0
$195$	17.8559	+	16.2072i	1.27869	+	1.16062i
$196$		0			0
$197$	−0.556259			−0.0396318			−0.0198159	−	0.999804i	$-0.506308\pi$
$197$	−0.556259			−0.0396318			−0.0198159	+	0.999804i	$0.506308\pi$
$198$		0			0
$199$	−21.5526			−1.52782			−0.763912	−	0.645320i	$-0.776724\pi$
$199$	−21.5526			−1.52782			−0.763912	+	0.645320i	$0.776724\pi$
$200$		0			0
$201$	3.13237	−	1.00395i	0.220940	−	0.0708133i
$202$		0			0
$203$	4.54252	+	7.86788i	0.318823	+	0.552217i
$204$		0			0
$205$	3.68171	−	6.37691i	0.257142	−	0.445383i
$206$		0			0
$207$	−1.52756	−	15.7427i	−0.106173	−	1.09419i
$208$		0			0
$209$	−7.59225	+	13.1502i	−0.525167	+	0.909615i
$210$		0			0
$211$	8.32984	+	14.4277i	0.573450	+	0.993245i	0.996208	+	0.0870022i	$0.0277287\pi$
$211$	8.32984	+	14.4277i	0.573450	+	0.993245i	−0.422758	+	0.906243i	$0.638938\pi$
$212$		0			0
$213$	2.13704	−	9.86011i	0.146427	−	0.675604i
$214$		0			0
$215$	−13.1868			−0.899335
$216$		0			0
$217$	−10.3065			−0.699650
$218$		0			0
$219$	1.83888	−	8.48443i	0.124260	−	0.573325i
$220$		0			0
$221$	24.9766	+	43.2607i	1.68011	+	2.91003i
$222$		0			0
$223$	4.49251	−	7.78126i	0.300841	−	0.521072i	−0.675486	−	0.737373i	$-0.736066\pi$
$223$	4.49251	−	7.78126i	0.300841	−	0.521072i	0.976327	+	0.216301i	$0.0693993\pi$
$224$		0			0
$225$	−1.34342	+	0.959749i	−0.0895615	+	0.0639833i
$226$		0			0
$227$	−5.32448	+	9.22226i	−0.353398	+	0.612103i	−0.986842	−	0.161685i	$-0.948307\pi$
$227$	−5.32448	+	9.22226i	−0.353398	+	0.612103i	0.633445	+	0.773788i	$0.281640\pi$
$228$		0			0
$229$	5.50786	+	9.53988i	0.363969	+	0.630413i	0.988610	−	0.150499i	$-0.0480880\pi$
$229$	5.50786	+	9.53988i	0.363969	+	0.630413i	−0.624641	+	0.780912i	$0.714755\pi$
$230$		0			0
$231$	−11.5197	+	3.69215i	−0.757938	+	0.242926i
$232$		0			0
$233$	27.2595			1.78583			0.892915	−	0.450225i	$-0.148656\pi$
$233$	27.2595			1.78583			0.892915	+	0.450225i	$0.148656\pi$
$234$		0			0
$235$	−5.60988			−0.365948
$236$		0			0
$237$	−16.6727	−	15.1332i	−1.08301	−	0.983009i
$238$		0			0
$239$	−5.82295	−	10.0856i	−0.376655	−	0.652386i	0.613918	−	0.789370i	$-0.289593\pi$
$239$	−5.82295	−	10.0856i	−0.376655	−	0.652386i	−0.990573	+	0.136984i	$0.956259\pi$
$240$		0			0
$241$	9.83554	−	17.0356i	0.633563	−	1.09736i	−0.353255	−	0.935527i	$-0.614925\pi$
$241$	9.83554	−	17.0356i	0.633563	−	1.09736i	0.986818	−	0.161835i	$-0.0517414\pi$
$242$		0			0
$243$	−13.6530	+	7.52304i	−0.875839	+	0.482603i
$244$		0			0
$245$	1.35479	−	2.34656i	0.0865542	−	0.149916i
$246$		0			0
$247$	20.6512	+	35.7689i	1.31400	+	2.27592i
$248$		0			0
$249$	−3.96306	−	3.59712i	−0.251149	−	0.227958i
$250$		0			0
$251$	−23.3802			−1.47575			−0.737873	−	0.674940i	$-0.764170\pi$
$251$	−23.3802			−1.47575			−0.737873	+	0.674940i	$0.764170\pi$
$252$		0			0
$253$	12.7930			0.804289
$254$		0			0
$255$	26.3329	−	8.43993i	1.64903	−	0.528529i
$256$		0			0
$257$	−1.89037	−	3.27421i	−0.117918	−	0.204240i	0.801024	−	0.598632i	$-0.204289\pi$
$257$	−1.89037	−	3.27421i	−0.117918	−	0.204240i	−0.918942	+	0.394392i	$0.870955\pi$
$258$		0			0
$259$	−9.65603	+	16.7247i	−0.599996	+	1.03922i
$260$		0			0
$261$	−7.70500	+	5.50449i	−0.476927	+	0.340720i
$262$		0			0
$263$	−10.3638	+	17.9507i	−0.639060	+	1.10689i	0.346579	+	0.938021i	$0.387343\pi$
$263$	−10.3638	+	17.9507i	−0.639060	+	1.10689i	−0.985639	+	0.168864i	$0.945990\pi$
$264$		0			0
$265$	−1.00515	−	1.74097i	−0.0617458	−	0.106947i
$266$		0			0
$267$	1.08340	−	4.99870i	0.0663028	−	0.305916i
$268$		0			0
$269$	−0.965772			−0.0588842			−0.0294421	−	0.999566i	$-0.509373\pi$
$269$	−0.965772			−0.0588842			−0.0294421	+	0.999566i	$0.509373\pi$
$270$		0			0
$271$	−4.28219			−0.260124			−0.130062	−	0.991506i	$-0.541518\pi$
$271$	−4.28219			−0.260124			−0.130062	+	0.991506i	$0.541518\pi$
$272$		0			0
$273$	−6.96963	+	32.1573i	−0.421821	+	1.94625i
$274$		0			0
$275$	−0.667703	−	1.15650i	−0.0402640	−	0.0697393i
$276$		0			0
$277$	−4.83619	+	8.37653i	−0.290579	+	0.503297i	−0.973947	−	0.226777i	$-0.927181\pi$
$277$	−4.83619	+	8.37653i	−0.290579	+	0.503297i	0.683368	+	0.730074i	$0.260514\pi$
$278$		0			0
$279$	−1.03749	−	10.6921i	−0.0621128	−	0.640120i
$280$		0			0
$281$	7.34848	−	12.7279i	0.438373	−	0.759285i	−0.559191	−	0.829039i	$-0.688888\pi$
$281$	7.34848	−	12.7279i	0.438373	−	0.759285i	0.997564	+	0.0697540i	$0.0222214\pi$
$282$		0			0
$283$	7.90174	+	13.6862i	0.469710	+	0.813561i	0.999400	−	0.0346299i	$-0.0110252\pi$
$283$	7.90174	+	13.6862i	0.469710	+	0.813561i	−0.529690	+	0.848191i	$0.677692\pi$
$284$		0			0
$285$	21.7726	−	6.97832i	1.28970	−	0.413360i
$286$		0			0
$287$	10.0473			0.593074
$288$		0			0
$289$	40.2819			2.36952
$290$		0			0
$291$	−14.1396	−	12.8340i	−0.828880	−	0.752344i
$292$		0			0
$293$	2.99866	+	5.19384i	0.175184	+	0.303427i	0.940225	−	0.340554i	$-0.110615\pi$
$293$	2.99866	+	5.19384i	0.175184	+	0.303427i	−0.765041	+	0.643981i	$0.777281\pi$
$294$		0			0
$295$	10.2256	−	17.7112i	0.595356	−	1.03119i
$296$		0			0
$297$	−4.98991	−	11.5790i	−0.289544	−	0.671883i
$298$		0			0
$299$	17.3987	−	30.1355i	1.00619	−	1.74278i
$300$		0			0
$301$	−8.99666	−	15.5827i	−0.518559	−	0.898170i
$302$		0			0
$303$	−4.67755	−	4.24564i	−0.268718	−	0.243906i
$304$		0			0
$305$	−10.8770			−0.622818
$306$		0			0
$307$	11.7568			0.670994			0.335497	−	0.942041i	$-0.391096\pi$
$307$	11.7568			0.670994			0.335497	+	0.942041i	$0.391096\pi$
$308$		0			0
$309$	−17.9427	+	5.75079i	−1.02072	+	0.327151i
$310$		0			0
$311$	−16.1797	−	28.0240i	−0.917465	−	1.58910i	−0.803252	−	0.595640i	$-0.796899\pi$
$311$	−16.1797	−	28.0240i	−0.917465	−	1.58910i	−0.114213	−	0.993456i	$-0.536435\pi$
$312$		0			0
$313$	−14.6062	+	25.2987i	−0.825591	+	1.42997i	0.0758750	+	0.997117i	$0.475825\pi$
$313$	−14.6062	+	25.2987i	−0.825591	+	1.42997i	−0.901466	+	0.432849i	$0.857508\pi$
$314$		0			0
$315$	16.5801	+	7.54122i	0.934182	+	0.424900i
$316$		0			0
$317$	−13.7011	+	23.7310i	−0.769530	+	1.33286i	0.168288	+	0.985738i	$0.446176\pi$
$317$	−13.7011	+	23.7310i	−0.769530	+	1.33286i	−0.937818	+	0.347127i	$0.887157\pi$
$318$		0			0
$319$	−3.82951	−	6.63291i	−0.214411	−	0.371371i
$320$		0			0
$321$	−2.18264	+	10.0705i	−0.121823	+	0.562083i
$322$		0			0
$323$	47.3619			2.63529
$324$		0			0
$325$	−3.63235			−0.201487
$326$		0			0
$327$	3.62151	−	16.7093i	0.200270	−	0.924029i
$328$		0			0
$329$	−3.82731	−	6.62910i	−0.211007	−	0.365474i
$330$		0			0
$331$	1.08930	−	1.88673i	0.0598735	−	0.103704i	−0.834535	−	0.550955i	$-0.814264\pi$
$331$	1.08930	−	1.88673i	0.0598735	−	0.103704i	0.894408	+	0.447251i	$0.147597\pi$
$332$		0			0
$333$	−18.3225	−	8.33374i	−1.00407	−	0.456686i
$334$		0			0
$335$	2.00299	−	3.46928i	0.109435	−	0.189547i
$336$		0			0
$337$	−0.715700	−	1.23963i	−0.0389866	−	0.0675268i	0.845874	−	0.533383i	$-0.179080\pi$
$337$	−0.715700	−	1.23963i	−0.0389866	−	0.0675268i	−0.884860	+	0.465856i	$0.845746\pi$
$338$		0			0
$339$	24.7911	−	7.94577i	1.34647	−	0.431555i
$340$		0			0
$341$	8.68874			0.470522
$342$		0			0
$343$	−16.4508			−0.888259
$344$		0			0
$345$	−14.2634	−	12.9463i	−0.767914	−	0.697007i
$346$		0			0
$347$	13.1223	+	22.7285i	0.704441	+	1.22013i	0.966893	+	0.255183i	$0.0821357\pi$
$347$	13.1223	+	22.7285i	0.704441	+	1.22013i	−0.262452	+	0.964945i	$0.584531\pi$
$348$		0			0
$349$	−17.1673	+	29.7346i	−0.918944	+	1.59166i	−0.117923	+	0.993023i	$0.537623\pi$
$349$	−17.1673	+	29.7346i	−0.918944	+	1.59166i	−0.801022	+	0.598635i	$0.795710\pi$
$350$		0			0
$351$	−34.0621	−	3.99334i	−1.81810	−	0.213149i
$352$		0			0
$353$	−2.28933	+	3.96523i	−0.121849	+	0.211048i	−0.920497	−	0.390750i	$-0.872216\pi$
$353$	−2.28933	+	3.96523i	−0.121849	+	0.211048i	0.798648	+	0.601798i	$0.205549\pi$
$354$		0			0
$355$	−6.14359	−	10.6410i	−0.326068	−	0.564766i
$356$		0			0
$357$	27.9388	+	25.3590i	1.47868	+	1.34214i
$358$		0			0
$359$	13.0591			0.689231			0.344616	−	0.938744i	$-0.388009\pi$
$359$	13.0591			0.689231			0.344616	+	0.938744i	$0.388009\pi$
$360$		0			0
$361$	20.1599			1.06105
$362$		0			0
$363$	−8.43195	+	2.70251i	−0.442562	+	0.141845i
$364$		0			0
$365$	−5.28644	−	9.15639i	−0.276705	−	0.479267i
$366$		0			0
$367$	1.70626	−	2.95533i	0.0890660	−	0.154267i	−0.818051	−	0.575146i	$-0.804945\pi$
$367$	1.70626	−	2.95533i	0.0890660	−	0.154267i	0.907117	+	0.420879i	$0.138278\pi$
$368$		0			0
$369$	1.01140	+	10.4232i	0.0526513	+	0.542612i
$370$		0			0
$371$	1.37151	−	2.37553i	0.0712055	−	0.123332i
$372$		0			0
$373$	−6.42179	−	11.1229i	−0.332508	−	0.575921i	0.650495	−	0.759511i	$-0.274561\pi$
$373$	−6.42179	−	11.1229i	−0.332508	−	0.575921i	−0.983003	+	0.183590i	$0.941228\pi$
$374$		0			0
$375$	−4.29542	+	19.8187i	−0.221815	+	1.02343i
$376$		0			0
$377$	−20.8328			−1.07294
$378$		0			0
$379$	−12.1642			−0.624833			−0.312417	−	0.949945i	$-0.601138\pi$
$379$	−12.1642			−0.624833			−0.312417	+	0.949945i	$0.601138\pi$
$380$		0			0
$381$	2.96361	−	13.6738i	0.151830	−	0.700532i
$382$		0			0
$383$	8.84072	+	15.3126i	0.451740	+	0.782436i	0.998494	−	0.0548568i	$-0.0174702\pi$
$383$	8.84072	+	15.3126i	0.451740	+	0.782436i	−0.546755	+	0.837293i	$0.684137\pi$
$384$		0			0
$385$	−7.36625	+	12.7587i	−0.375419	+	0.650244i
$386$		0			0
$387$	15.2601	−	10.9019i	0.775713	−	0.554174i
$388$		0			0
$389$	3.77658	−	6.54123i	0.191480	−	0.331654i	−0.754261	−	0.656575i	$-0.772005\pi$
$389$	3.77658	−	6.54123i	0.191480	−	0.331654i	0.945741	+	0.324921i	$0.105338\pi$
$390$		0			0
$391$	−19.9513	−	34.5567i	−1.00898	−	1.74761i
$392$		0			0
$393$	36.7252	−	11.7708i	1.85254	−	0.593756i
$394$		0			0
$395$	−27.4223			−1.37977
$396$		0			0
$397$	−7.97075			−0.400040			−0.200020	−	0.979792i	$-0.564101\pi$
$397$	−7.97075			−0.400040			−0.200020	+	0.979792i	$0.564101\pi$
$398$		0			0
$399$	23.1004	+	20.9674i	1.15647	+	1.04968i
$400$		0			0
$401$	−3.53771	−	6.12750i	−0.176665	−	0.305993i	0.764071	−	0.645132i	$-0.223198\pi$
$401$	−3.53771	−	6.12750i	−0.176665	−	0.305993i	−0.940736	+	0.339139i	$0.889864\pi$
$402$		0			0
$403$	11.8168	−	20.4674i	0.588639	−	1.01955i
$404$		0			0
$405$	−6.15438	+	17.9596i	−0.305813	+	0.892418i
$406$		0			0
$407$	8.14038	−	14.0995i	0.403503	−	0.698889i
$408$		0			0
$409$	−16.0499	−	27.7993i	−0.793619	−	1.37459i	−0.923713	−	0.383086i	$-0.874861\pi$
$409$	−16.0499	−	27.7993i	−0.793619	−	1.37459i	0.130094	−	0.991502i	$-0.458472\pi$
$410$		0			0
$411$	−11.8599	−	10.7648i	−0.585005	−	0.530988i
$412$		0			0
$413$	27.9054			1.37313
$414$		0			0
$415$	−6.51820			−0.319966
$416$		0			0
$417$	13.8634	−	4.44335i	0.678895	−	0.217592i
$418$		0			0
$419$	5.63571	+	9.76133i	0.275322	+	0.476872i	0.970216	−	0.242240i	$-0.0778821\pi$
$419$	5.63571	+	9.76133i	0.275322	+	0.476872i	−0.694894	+	0.719112i	$0.744549\pi$
$420$		0			0
$421$	−4.82872	+	8.36359i	−0.235337	+	0.407616i	−0.959371	−	0.282149i	$-0.908953\pi$
$421$	−4.82872	+	8.36359i	−0.235337	+	0.407616i	0.724033	+	0.689765i	$0.242286\pi$
$422$		0			0
$423$	6.49186	−	4.63782i	0.315645	−	0.225499i
$424$		0			0
$425$	−2.08263	+	3.60723i	−0.101023	+	0.174976i
$426$		0			0
$427$	−7.42081	−	12.8532i	−0.359118	−	0.622011i
$428$		0			0
$429$	5.87565	−	27.1098i	0.283679	−	1.30887i
$430$		0			0
$431$	40.1842			1.93560			0.967802	−	0.251711i	$-0.0809933\pi$
$431$	40.1842			1.93560			0.967802	+	0.251711i	$0.0809933\pi$
$432$		0			0
$433$	16.1510			0.776168			0.388084	−	0.921624i	$-0.373137\pi$
$433$	16.1510			0.776168			0.388084	+	0.921624i	$0.373137\pi$
$434$		0			0
$435$	−2.44275	+	11.2707i	−0.117121	+	0.540387i
$436$		0			0
$437$	−16.4962	−	28.5723i	−0.789120	−	1.36680i
$438$		0			0
$439$	−9.25383	+	16.0281i	−0.441661	+	0.764980i	−0.997813	−	0.0661011i	$-0.978944\pi$
$439$	−9.25383	+	16.0281i	−0.441661	+	0.764980i	0.556152	+	0.831081i	$0.312277\pi$
$440$		0			0
$441$	0.372172	+	3.83552i	0.0177225	+	0.182644i
$442$		0			0
$443$	−1.72586	+	2.98927i	−0.0819979	+	0.142025i	−0.904108	−	0.427304i	$-0.859463\pi$
$443$	−1.72586	+	2.98927i	−0.0819979	+	0.142025i	0.822110	+	0.569329i	$0.192797\pi$
$444$		0			0
$445$	−3.11457	−	5.39459i	−0.147645	−	0.255728i
$446$		0			0
$447$	20.3812	−	6.53236i	0.963998	−	0.308970i
$448$		0			0
$449$	9.83790			0.464279			0.232140	−	0.972682i	$-0.425427\pi$
$449$	9.83790			0.464279			0.232140	+	0.972682i	$0.425427\pi$
$450$		0			0
$451$	−8.47025			−0.398848
$452$		0			0
$453$	12.6053	+	11.4413i	0.592247	+	0.537561i
$454$		0			0
$455$	20.0364	+	34.7041i	0.939323	+	1.62696i
$456$		0			0
$457$	0.0111990	−	0.0193973i	0.000523869	−	0.000907367i	−0.865763	−	0.500454i	$-0.833167\pi$
$457$	0.0111990	−	0.0193973i	0.000523869	−	0.000907367i	0.866287	+	0.499546i	$0.166500\pi$
$458$		0			0
$459$	−23.4954	+	31.5369i	−1.09667	+	1.47202i
$460$		0			0
$461$	7.50986	−	13.0075i	0.349769	−	0.605818i	−0.636439	−	0.771327i	$-0.719593\pi$
$461$	7.50986	−	13.0075i	0.349769	−	0.605818i	0.986208	+	0.165509i	$0.0529267\pi$
$462$		0			0
$463$	16.2691	+	28.1790i	0.756091	+	1.30959i	0.944830	+	0.327561i	$0.106227\pi$
$463$	16.2691	+	28.1790i	0.756091	+	1.30959i	−0.188738	+	0.982027i	$0.560440\pi$
$464$		0			0
$465$	−9.68738	−	8.79288i	−0.449241	−	0.407760i
$466$		0			0
$467$	−10.2983			−0.476550			−0.238275	−	0.971198i	$-0.576582\pi$
$467$	−10.2983			−0.476550			−0.238275	+	0.971198i	$0.576582\pi$
$468$		0			0
$469$	5.46612			0.252402
$470$		0			0
$471$	−0.356545	+	0.114276i	−0.0164287	+	0.00526556i
$472$		0			0
$473$	7.58450	+	13.1367i	0.348736	+	0.604028i
$474$		0			0
$475$	−1.72197	+	2.98253i	−0.0790093	+	0.136848i
$476$		0			0
$477$	2.60248	+	1.18370i	0.119159	+	0.0541980i
$478$		0			0
$479$	−3.79020	+	6.56481i	−0.173178	+	0.299954i	−0.939529	−	0.342468i	$-0.888737\pi$
$479$	−3.79020	+	6.56481i	−0.173178	+	0.299954i	0.766351	+	0.642422i	$0.222070\pi$
$480$		0			0
$481$	−22.1421	−	38.3513i	−1.00959	−	1.74867i
$482$		0			0
$483$	5.56736	−	25.6873i	0.253323	−	1.16881i
$484$		0			0
$485$	−23.2560			−1.05600
$486$		0			0
$487$	−20.6214			−0.934444			−0.467222	−	0.884140i	$-0.654745\pi$
$487$	−20.6214			−0.934444			−0.467222	+	0.884140i	$0.654745\pi$
$488$		0			0
$489$	−2.12098	+	9.78605i	−0.0959142	+	0.442541i
$490$		0			0
$491$	3.98229	+	6.89752i	0.179718	+	0.311281i	0.941784	−	0.336219i	$-0.109148\pi$
$491$	3.98229	+	6.89752i	0.179718	+	0.311281i	−0.762066	+	0.647499i	$0.775815\pi$
$492$		0			0
$493$	−11.9446	+	20.6887i	−0.537959	+	0.931772i
$494$		0			0
$495$	−13.9776	−	6.35752i	−0.628246	−	0.285749i
$496$		0			0
$497$	8.38287	−	14.5196i	0.376023	−	0.651291i
$498$		0			0
$499$	−10.5911	−	18.3444i	−0.474125	−	0.821208i	0.525436	−	0.850833i	$-0.323902\pi$
$499$	−10.5911	−	18.3444i	−0.474125	−	0.821208i	−0.999561	+	0.0296248i	$0.990569\pi$
$500$		0			0
$501$	2.70055	−	0.865552i	0.120652	−	0.0386700i
$502$		0			0
$503$	−19.0876			−0.851073			−0.425536	−	0.904941i	$-0.639915\pi$
$503$	−19.0876			−0.851073			−0.425536	+	0.904941i	$0.639915\pi$
$504$		0			0
$505$	−7.69336			−0.342350
$506$		0			0
$507$	−39.1965	−	35.5773i	−1.74078	−	1.58004i
$508$		0			0
$509$	−18.3596	−	31.7998i	−0.813776	−	1.40950i	−0.910204	−	0.414161i	$-0.864075\pi$
$509$	−18.3596	−	31.7998i	−0.813776	−	1.40950i	0.0964283	−	0.995340i	$-0.469258\pi$
$510$		0			0
$511$	7.21330	−	12.4938i	0.319097	−	0.552693i
$512$		0			0
$513$	−19.4266	+	26.0754i	−0.857703	+	1.15126i
$514$		0			0
$515$	−11.4734	+	19.8726i	−0.505580	+	0.875690i
$516$		0			0
$517$	3.22656	+	5.58857i	0.141904	+	0.245785i
$518$		0			0
$519$	7.67535	+	6.96663i	0.336910	+	0.305801i
$520$		0			0
$521$	20.5620			0.900839			0.450419	−	0.892817i	$-0.351275\pi$
$521$	20.5620			0.900839			0.450419	+	0.892817i	$0.351275\pi$
$522$		0			0
$523$	16.2754			0.711672			0.355836	−	0.934548i	$-0.384196\pi$
$523$	16.2754			0.711672			0.355836	+	0.934548i	$0.384196\pi$
$524$		0			0
$525$	−2.61273	+	0.837403i	−0.114029	+	0.0365472i
$526$		0			0
$527$	−13.5505	−	23.4702i	−0.590270	−	1.02238i
$528$		0			0
$529$	−2.39812	+	4.15367i	−0.104266	+	0.180594i
$530$		0			0
$531$	2.80905	+	28.9495i	0.121903	+	1.25630i
$532$		0			0
$533$	−11.5197	+	19.9527i	−0.498973	+	0.864246i
$534$		0			0
$535$	6.27471	+	10.8681i	0.271279	+	0.469870i
$536$		0			0
$537$	3.49017	−	16.1033i	0.150612	−	0.694911i
$538$		0			0
$539$	−3.11686			−0.134253
$540$		0			0
$541$	3.19402			0.137322			0.0686609	−	0.997640i	$-0.478127\pi$
$541$	3.19402			0.137322			0.0686609	+	0.997640i	$0.478127\pi$
$542$		0			0
$543$	−8.71431	+	40.2071i	−0.373967	+	1.72545i
$544$		0			0
$545$	−10.4112	−	18.0327i	−0.445966	−	0.772436i
$546$		0			0
$547$	7.43936	−	12.8854i	0.318084	−	0.550938i	−0.662004	−	0.749500i	$-0.730294\pi$
$547$	7.43936	−	12.8854i	0.318084	−	0.550938i	0.980088	+	0.198562i	$0.0636272\pi$
$548$		0			0
$549$	12.5871	−	8.99231i	0.537205	−	0.383782i
$550$		0			0
$551$	−9.87608	+	17.1059i	−0.420735	+	0.728734i
$552$		0			0
$553$	−18.7087	−	32.4045i	−0.795576	−	1.37798i
$554$		0			0
$555$	−23.3445	+	7.48213i	−0.990920	+	0.317599i
$556$		0			0
$557$	5.76686			0.244350			0.122175	−	0.992509i	$-0.461013\pi$
$557$	5.76686			0.244350			0.122175	+	0.992509i	$0.461013\pi$
$558$		0			0
$559$	41.2602			1.74512
$560$		0			0
$561$	−23.5534	−	21.3786i	−0.994426	−	0.902604i
$562$		0			0
$563$	−4.76738	−	8.25734i	−0.200921	−	0.348005i	0.747904	−	0.663806i	$-0.231060\pi$
$563$	−4.76738	−	8.25734i	−0.200921	−	0.348005i	−0.948825	+	0.315801i	$0.897727\pi$
$564$		0			0
$565$	15.8527	−	27.4576i	0.666927	−	1.15515i
$566$		0			0
$567$	−25.4213	+	4.98030i	−1.06759	+	0.209153i
$568$		0			0
$569$	−4.27200	+	7.39933i	−0.179092	+	0.310196i	−0.941570	−	0.336818i	$-0.890649\pi$
$569$	−4.27200	+	7.39933i	−0.179092	+	0.310196i	0.762478	+	0.647014i	$0.223983\pi$
$570$		0			0
$571$	−18.1444	−	31.4270i	−0.759318	−	1.31518i	−0.943199	−	0.332229i	$-0.892199\pi$
$571$	−18.1444	−	31.4270i	−0.759318	−	1.31518i	0.183881	−	0.982949i	$-0.441134\pi$
$572$		0			0
$573$	−10.6235	−	9.64256i	−0.443803	−	0.402824i
$574$		0			0
$575$	2.90153			0.121002
$576$		0			0
$577$	−6.11652			−0.254634			−0.127317	−	0.991862i	$-0.540637\pi$
$577$	−6.11652			−0.254634			−0.127317	+	0.991862i	$0.540637\pi$
$578$		0			0
$579$	−16.5044	+	5.28982i	−0.685901	+	0.219837i
$580$		0			0
$581$	−4.44701	−	7.70245i	−0.184493	−	0.319551i
$582$		0			0
$583$	−1.15624	+	2.00266i	−0.0478864	+	0.0829417i
$584$		0			0
$585$	−33.9857	+	24.2796i	−1.40514	+	1.00384i
$586$		0			0
$587$	−1.92500	+	3.33419i	−0.0794532	+	0.137617i	−0.903014	−	0.429611i	$-0.858651\pi$
$587$	−1.92500	+	3.33419i	−0.0794532	+	0.137617i	0.823561	+	0.567228i	$0.191984\pi$
$588$		0			0
$589$	−11.2039	−	19.4057i	−0.461647	−	0.799597i
$590$		0			0
$591$	0.204079	−	0.941606i	0.00839471	−	0.0387325i
$592$		0			0
$593$	16.6462			0.683579			0.341789	−	0.939777i	$-0.388967\pi$
$593$	16.6462			0.683579			0.341789	+	0.939777i	$0.388967\pi$
$594$		0			0
$595$	45.9521			1.88385
$596$		0			0
$597$	7.90720	−	36.4832i	0.323620	−	1.49316i
$598$		0			0
$599$	17.8791	+	30.9675i	0.730520	+	1.26530i	0.956661	+	0.291203i	$0.0940557\pi$
$599$	17.8791	+	30.9675i	0.730520	+	1.26530i	−0.226141	+	0.974095i	$0.572611\pi$
$600$		0			0
$601$	6.77202	−	11.7295i	0.276236	−	0.478455i	−0.694210	−	0.719773i	$-0.744246\pi$
$601$	6.77202	−	11.7295i	0.276236	−	0.478455i	0.970446	+	0.241317i	$0.0775794\pi$
$602$		0			0
$603$	0.550239	+	5.67064i	0.0224075	+	0.230926i
$604$		0			0
$605$	−5.39181	+	9.33888i	−0.219208	+	0.379679i
$606$		0			0
$607$	14.0131	+	24.2714i	0.568775	+	0.985147i	0.996688	+	0.0813266i	$0.0259157\pi$
$607$	14.0131	+	24.2714i	0.568775	+	0.985147i	−0.427913	+	0.903820i	$0.640751\pi$
$608$		0			0
$609$	−14.9849	+	4.80279i	−0.607219	+	0.194619i
$610$		0			0
$611$	17.5527			0.710107
$612$		0			0
$613$	37.6283			1.51979			0.759897	−	0.650043i	$-0.225249\pi$
$613$	37.6283			1.51979			0.759897	+	0.650043i	$0.225249\pi$
$614$		0			0
$615$	9.44377	+	8.57177i	0.380810	+	0.345647i
$616$		0			0
$617$	5.57241	+	9.65169i	0.224337	+	0.388562i	0.956120	−	0.292975i	$-0.0946451\pi$
$617$	5.57241	+	9.65169i	0.224337	+	0.388562i	−0.731784	+	0.681537i	$0.761312\pi$
$618$		0			0
$619$	−9.54119	+	16.5258i	−0.383493	+	0.664229i	−0.991559	−	0.129658i	$-0.958612\pi$
$619$	−9.54119	+	16.5258i	−0.383493	+	0.664229i	0.608066	+	0.793886i	$0.291946\pi$
$620$		0			0
$621$	27.2089	+	3.18989i	1.09185	+	0.128006i
$622$		0			0
$623$	4.24980	−	7.36086i	0.170265	−	0.294907i
$624$		0			0
$625$	10.9727	+	19.0053i	0.438908	+	0.760211i
$626$		0			0
$627$	−19.4745	−	17.6763i	−0.777736	−	0.705923i
$628$		0			0
$629$	−50.7813			−2.02478
$630$		0			0
$631$	29.7049			1.18253			0.591267	−	0.806476i	$-0.298628\pi$
$631$	29.7049			1.18253			0.591267	+	0.806476i	$0.298628\pi$
$632$		0			0
$633$	−27.4785	+	8.80712i	−1.09217	+	0.350051i
$634$		0			0
$635$	−8.51984	−	14.7568i	−0.338099	−	0.585605i
$636$		0			0
$637$	−4.23898	+	7.34214i	−0.167955	+	0.290906i
$638$		0			0
$639$	15.9067	+	7.23493i	0.629258	+	0.286209i
$640$		0			0
$641$	−9.60138	+	16.6301i	−0.379232	+	0.656848i	−0.990951	−	0.134227i	$-0.957145\pi$
$641$	−9.60138	+	16.6301i	−0.379232	+	0.656848i	0.611719	+	0.791075i	$0.290478\pi$
$642$		0			0
$643$	−3.52181	−	6.09995i	−0.138887	−	0.240559i	0.788189	−	0.615434i	$-0.211019\pi$
$643$	−3.52181	−	6.09995i	−0.138887	−	0.240559i	−0.927075	+	0.374875i	$0.877686\pi$
$644$		0			0
$645$	4.83797	−	22.3220i	0.190495	−	0.878929i
$646$		0			0
$647$	−36.8474			−1.44862			−0.724311	−	0.689473i	$-0.757842\pi$
$647$	−36.8474			−1.44862			−0.724311	+	0.689473i	$0.757842\pi$
$648$		0			0
$649$	−23.5252			−0.923446
$650$		0			0
$651$	3.78123	−	17.4463i	0.148198	−	0.683774i
$652$		0			0
$653$	−20.6354	−	35.7416i	−0.807526	−	1.39868i	−0.914572	−	0.404422i	$-0.867473\pi$
$653$	−20.6354	−	35.7416i	−0.807526	−	1.39868i	0.107046	−	0.994254i	$-0.465861\pi$
$654$		0			0
$655$	23.4839	−	40.6754i	0.917593	−	1.58932i
$656$		0			0
$657$	13.6874	+	6.22552i	0.533995	+	0.242881i
$658$		0			0
$659$	7.79606	−	13.5032i	0.303691	−	0.526009i	−0.673278	−	0.739390i	$-0.735114\pi$
$659$	7.79606	−	13.5032i	0.303691	−	0.526009i	0.976969	+	0.213381i	$0.0684475\pi$
$660$		0			0
$661$	0.273228	+	0.473246i	0.0106274	+	0.0184071i	0.871290	−	0.490768i	$-0.163284\pi$
$661$	0.273228	+	0.473246i	0.0106274	+	0.0184071i	−0.860663	+	0.509175i	$0.829950\pi$
$662$		0			0
$663$	−82.3929	+	26.4076i	−3.19987	+	1.02559i
$664$		0			0
$665$	37.9942			1.47335
$666$		0			0
$667$	16.6413			0.644353
$668$		0			0
$669$	11.5235	+	10.4595i	0.445525	+	0.404387i
$670$		0			0
$671$	6.25601	+	10.8357i	0.241510	+	0.418308i
$672$		0			0
$673$	7.71994	−	13.3713i	0.297582	−	0.515427i	−0.678000	−	0.735061i	$-0.737153\pi$
$673$	7.71994	−	13.3713i	0.297582	−	0.515427i	0.975582	+	0.219635i	$0.0704866\pi$
$674$		0			0
$675$	−1.13174	−	2.62619i	−0.0435607	−	0.101082i
$676$		0			0
$677$	20.7394	−	35.9216i	0.797079	−	1.38058i	−0.124432	−	0.992228i	$-0.539711\pi$
$677$	20.7394	−	35.9216i	0.797079	−	1.38058i	0.921511	−	0.388353i	$-0.126956\pi$
$678$		0			0
$679$	−15.8663	−	27.4812i	−0.608893	−	1.05463i
$680$		0			0
$681$	−13.6575	−	12.3965i	−0.523358	−	0.475033i
$682$		0			0
$683$	−7.83506			−0.299800			−0.149900	−	0.988701i	$-0.547895\pi$
$683$	−7.83506			−0.299800			−0.149900	+	0.988701i	$0.547895\pi$
$684$		0			0
$685$	−19.5064			−0.745303
$686$		0			0
$687$	−18.1693	+	5.82344i	−0.693204	+	0.222178i
$688$		0			0
$689$	3.14500	+	5.44730i	0.119815	+	0.207526i
$690$		0			0
$691$	−11.8366	+	20.5016i	−0.450286	+	0.779918i	−0.998404	−	0.0564831i	$-0.982011\pi$
$691$	−11.8366	+	20.5016i	−0.450286	+	0.779918i	0.548118	+	0.836401i	$0.315345\pi$
$692$		0			0
$693$	−2.02357	−	20.8545i	−0.0768691	−	0.792196i
$694$		0			0
$695$	8.86497	−	15.3546i	0.336267	−	0.582432i
$696$		0			0
$697$	13.2098	+	22.8800i	0.500356	+	0.866642i
$698$		0			0
$699$	−10.0009	+	46.1435i	−0.378270	+	1.74531i
$700$		0			0
$701$	7.14909			0.270017			0.135009	−	0.990844i	$-0.456894\pi$
$701$	7.14909			0.270017			0.135009	+	0.990844i	$0.456894\pi$
$702$		0			0
$703$	−41.9871			−1.58357
$704$		0			0
$705$	2.05815	−	9.49612i	0.0775143	−	0.357645i
$706$		0			0
$707$	−5.24876	−	9.09111i	−0.197400	−	0.341906i
$708$		0			0
$709$	−19.3826	+	33.5716i	−0.727928	+	1.26081i	0.229830	+	0.973231i	$0.426183\pi$
$709$	−19.3826	+	33.5716i	−0.727928	+	1.26081i	−0.957757	+	0.287577i	$0.907150\pi$
$710$		0			0
$711$	31.7336	−	22.6707i	1.19010	−	0.850217i
$712$		0			0
$713$	−9.43931	+	16.3494i	−0.353505	+	0.612289i
$714$		0			0
$715$	−16.8914	−	29.2568i	−0.631704	−	1.09414i
$716$		0			0
$717$	19.2088	−	6.15659i	0.717365	−	0.229922i
$718$		0			0
$719$	38.3429			1.42995			0.714975	−	0.699151i	$-0.246438\pi$
$719$	38.3429			1.42995			0.714975	+	0.699151i	$0.246438\pi$
$720$		0			0
$721$	−31.3108			−1.16607
$722$		0			0
$723$	25.2286	+	22.8991i	0.938263	+	0.851627i
$724$		0			0
$725$	−0.868556	−	1.50438i	−0.0322574	−	0.0558714i
$726$		0			0
$727$	21.9734	−	38.0591i	0.814950	−	1.41154i	−0.0944136	−	0.995533i	$-0.530098\pi$
$727$	21.9734	−	38.0591i	0.814950	−	1.41154i	0.909364	−	0.416002i	$-0.136569\pi$
$728$		0			0
$729$	−7.72564	−	25.8711i	−0.286135	−	0.958189i
$730$		0			0
$731$	23.6568	−	40.9748i	0.874979	−	1.51551i
$732$		0			0
$733$	24.7222	+	42.8202i	0.913137	+	1.58160i	0.809606	+	0.586973i	$0.199681\pi$
$733$	24.7222	+	42.8202i	0.913137	+	1.58160i	0.103531	+	0.994626i	$0.466986\pi$
$734$		0			0
$735$	3.47510	+	3.15422i	0.128181	+	0.116345i
$736$		0			0
$737$	−4.60814			−0.169743
$738$		0			0
$739$	−9.25073			−0.340294			−0.170147	−	0.985419i	$-0.554424\pi$
$739$	−9.25073			−0.340294			−0.170147	+	0.985419i	$0.554424\pi$
$740$		0			0
$741$	−68.1242	+	21.8344i	−2.50261	+	0.802107i
$742$		0			0
$743$	20.6473	+	35.7621i	0.757475	+	1.31198i	0.944135	+	0.329560i	$0.106900\pi$
$743$	20.6473	+	35.7621i	0.757475	+	1.31198i	−0.186660	+	0.982425i	$0.559766\pi$
$744$		0			0
$745$	13.0328	−	22.5734i	0.477483	−	0.827025i
$746$		0			0
$747$	7.54299	−	5.38875i	0.275984	−	0.197164i
$748$		0			0
$749$	−8.56178	+	14.8294i	−0.312840	+	0.541856i
$750$		0			0
$751$	−10.2101	−	17.6845i	−0.372573	−	0.645315i	0.617388	−	0.786659i	$-0.288191\pi$
$751$	−10.2101	−	17.6845i	−0.372573	−	0.645315i	−0.989961	+	0.141344i	$0.954858\pi$
$752$		0			0
$753$	8.57770	−	39.5768i	0.312589	−	1.44226i
$754$		0			0
$755$	20.7324			0.754529
$756$		0			0
$757$	−7.74944			−0.281658			−0.140829	−	0.990034i	$-0.544977\pi$
$757$	−7.74944			−0.281658			−0.140829	+	0.990034i	$0.544977\pi$
$758$		0			0
$759$	−4.69348	+	21.6554i	−0.170363	+	0.786039i
$760$		0			0
$761$	13.3416	+	23.1084i	0.483634	+	0.837679i	0.999823	−	0.0187955i	$-0.00598315\pi$
$761$	13.3416	+	23.1084i	0.483634	+	0.837679i	−0.516189	+	0.856475i	$0.672650\pi$
$762$		0			0
$763$	14.2059	−	24.6054i	0.514290	−	0.890776i
$764$		0			0
$765$	4.62570	+	47.6714i	0.167243	+	1.72356i
$766$		0			0
$767$	−31.9947	+	55.4165i	−1.15526	+	2.00097i
$768$		0			0
$769$	−24.5226	−	42.4744i	−0.884307	−	1.53166i	−0.846506	−	0.532379i	$-0.821298\pi$
$769$	−24.5226	−	42.4744i	−0.884307	−	1.53166i	−0.0378010	−	0.999285i	$-0.512035\pi$
$770$		0			0
$771$	6.23596	−	1.99868i	0.224583	−	0.0719807i
$772$		0			0
$773$	−12.1406			−0.436665			−0.218333	−	0.975874i	$-0.570062\pi$
$773$	−12.1406			−0.436665			−0.218333	+	0.975874i	$0.570062\pi$
$774$		0			0
$775$	1.97066			0.0707881
$776$		0			0
$777$	−24.7682	−	22.4812i	−0.888553	−	0.806508i
$778$		0			0
$779$	10.9221	+	18.9177i	0.391326	+	0.677796i
$780$		0			0
$781$	−7.06706	+	12.2405i	−0.252879	+	0.438000i
$782$		0			0
$783$	−6.49093	−	15.0621i	−0.231967	−	0.538276i
$784$		0			0
$785$	−0.227993	+	0.394895i	−0.00813742	+	0.0140944i
$786$		0			0
$787$	−24.2553	−	42.0114i	−0.864608	−	1.49754i	−0.867436	−	0.497549i	$-0.834234\pi$
$787$	−24.2553	−	42.0114i	−0.864608	−	1.49754i	0.00282812	−	0.999996i	$-0.499100\pi$
$788$		0			0
$789$	−26.5837	−	24.1291i	−0.946405	−	0.859017i
$790$		0			0
$791$	43.2616			1.53821
$792$		0			0
$793$	34.0331			1.20855
$794$		0			0
$795$	3.31579	−	1.06274i	0.117599	−	0.0376915i
$796$		0			0
$797$	2.54989	+	4.41654i	0.0903218	+	0.156442i	0.907647	−	0.419735i	$-0.137877\pi$
$797$	2.54989	+	4.41654i	0.0903218	+	0.156442i	−0.817325	+	0.576177i	$0.804544\pi$
$798$		0			0
$799$	10.0640	−	17.4313i	0.356037	−	0.616675i
$800$		0			0
$801$	8.06408	+	3.66784i	0.284930	+	0.129597i
$802$		0			0
$803$	−6.08107	+	10.5327i	−0.214596	+	0.371692i
$804$		0			0
$805$	−16.0051	−	27.7217i	−0.564107	−	0.977063i
$806$		0			0
$807$	0.354321	−	1.63481i	0.0124727	−	0.0575480i
$808$		0			0
$809$	−38.1416			−1.34099			−0.670494	−	0.741915i	$-0.733918\pi$
$809$	−38.1416			−1.34099			−0.670494	+	0.741915i	$0.733918\pi$
$810$		0			0
$811$	2.88343			0.101251			0.0506255	−	0.998718i	$-0.483878\pi$
$811$	2.88343			0.101251			0.0506255	+	0.998718i	$0.483878\pi$
$812$		0			0
$813$	1.57104	−	7.24867i	0.0550989	−	0.254222i
$814$		0			0
$815$	6.09745	+	10.5611i	0.213584	+	0.369939i
$816$		0			0
$817$	19.5600	−	33.8789i	0.684317	−	1.18527i
$818$		0			0
$819$	−51.8773	−	23.5957i	−1.81274	−	0.824500i
$820$		0			0
$821$	5.84327	−	10.1208i	0.203931	−	0.353220i	−0.745860	−	0.666102i	$-0.767961\pi$
$821$	5.84327	−	10.1208i	0.203931	−	0.353220i	0.949792	+	0.312883i	$0.101295\pi$
$822$		0			0
$823$	5.91203	+	10.2399i	0.206080	+	0.356942i	0.950476	−	0.310797i	$-0.100596\pi$
$823$	5.91203	+	10.2399i	0.206080	+	0.356942i	−0.744396	+	0.667738i	$0.767262\pi$
$824$		0			0
$825$	2.20262	−	0.705961i	0.0766855	−	0.0245784i
$826$		0			0
$827$	27.5265			0.957192			0.478596	−	0.878035i	$-0.341146\pi$
$827$	27.5265			0.957192			0.478596	+	0.878035i	$0.341146\pi$
$828$		0			0
$829$	27.7398			0.963443			0.481721	−	0.876324i	$-0.340012\pi$
$829$	27.7398			0.963443			0.481721	+	0.876324i	$0.340012\pi$
$830$		0			0
$831$	−12.4051	−	11.2596i	−0.430327	−	0.390592i
$832$		0			0
$833$	4.86090	+	8.41932i	0.168420	+	0.291712i
$834$		0			0
$835$	1.72687	−	2.99102i	0.0597608	−	0.103509i
$836$		0			0
$837$	18.4797	+	2.16650i	0.638752	+	0.0748853i
$838$		0			0
$839$	12.7349	−	22.0574i	0.439656	−	0.761507i	−0.558007	−	0.829837i	$-0.688434\pi$
$839$	12.7349	−	22.0574i	0.439656	−	0.761507i	0.997663	+	0.0683295i	$0.0217669\pi$
$840$		0			0
$841$	9.51853	+	16.4866i	0.328225	+	0.568503i
$842$		0			0
$843$	18.8492	+	17.1087i	0.649201	+	0.589256i
$844$		0			0
$845$	−64.4682			−2.21777
$846$		0			0
$847$	−14.7141			−0.505583
$848$		0			0
$849$	−26.0663	+	8.35448i	−0.894594	+	0.286725i
$850$		0			0
$851$	17.6872	+	30.6351i	0.606308	+	1.05016i
$852$		0			0
$853$	−15.2819	+	26.4690i	−0.523241	+	0.906280i	0.476393	+	0.879232i	$0.341944\pi$
$853$	−15.2819	+	26.4690i	−0.523241	+	0.906280i	−0.999634	+	0.0270477i	$0.991389\pi$
$854$		0			0
$855$	3.82463	+	39.4158i	0.130800	+	1.34799i
$856$		0			0
$857$	7.69252	−	13.3238i	0.262772	−	0.455134i	−0.704206	−	0.709996i	$-0.748697\pi$
$857$	7.69252	−	13.3238i	0.262772	−	0.455134i	0.966977	+	0.254862i	$0.0820301\pi$
$858$		0			0
$859$	−9.19471	−	15.9257i	−0.313720	−	0.543378i	0.665445	−	0.746447i	$-0.268242\pi$
$859$	−9.19471	−	15.9257i	−0.313720	−	0.543378i	−0.979164	+	0.203069i	$0.934909\pi$
$860$		0			0
$861$	−3.68615	+	17.0076i	−0.125624	+	0.579617i
$862$		0			0
$863$	35.5698			1.21081			0.605404	−	0.795918i	$-0.293011\pi$
$863$	35.5698			1.21081			0.605404	+	0.795918i	$0.293011\pi$
$864$		0			0
$865$	12.6240			0.429227
$866$		0			0
$867$	−14.7786	+	68.1871i	−0.501907	+	2.31576i
$868$		0			0
$869$	15.7721	+	27.3181i	0.535033	+	0.926704i
$870$		0			0
$871$	−6.26715	+	10.8550i	−0.212354	+	0.367808i
$872$		0			0
$873$	26.9123	−	19.2263i	0.910844	−	0.650712i
$874$		0			0
$875$	−16.8495	+	29.1842i	−0.569616	+	0.986605i
$876$		0			0
$877$	−11.1127	−	19.2477i	−0.375249	−	0.649950i	0.615115	−	0.788437i	$-0.289109\pi$
$877$	−11.1127	−	19.2477i	−0.375249	−	0.649950i	−0.990364	+	0.138487i	$0.955776\pi$
$878$		0			0
$879$	−9.89201	+	3.17048i	−0.333649	+	0.106937i
$880$		0			0
$881$	38.5586			1.29907			0.649536	−	0.760331i	$-0.274963\pi$
$881$	38.5586			1.29907			0.649536	+	0.760331i	$0.274963\pi$
$882$		0			0
$883$	−10.4984			−0.353298			−0.176649	−	0.984274i	$-0.556526\pi$
$883$	−10.4984			−0.353298			−0.176649	+	0.984274i	$0.556526\pi$
$884$		0			0
$885$	26.2291	+	23.8072i	0.881681	+	0.800270i
$886$		0			0
$887$	−23.0186	−	39.8693i	−0.772888	−	1.33868i	−0.935974	−	0.352069i	$-0.885478\pi$
$887$	−23.0186	−	39.8693i	−0.772888	−	1.33868i	0.163087	−	0.986612i	$-0.447855\pi$
$888$		0			0
$889$	11.6252	−	20.1355i	0.389898	−	0.675322i
$890$		0			0
$891$	21.4311	−	4.19857i	0.717968	−	0.140657i
$892$		0			0
$893$	8.32111	−	14.4126i	0.278455	−	0.482299i
$894$		0			0
$895$	−10.0336	−	17.3787i	−0.335386	−	0.580906i
$896$		0			0
$897$	44.6285	+	40.5077i	1.49010	+	1.35251i
$898$		0			0
$899$	11.3024			0.376956
$900$		0			0
$901$	7.21283			0.240294
$902$		0			0
$903$	29.6782	−	9.51213i	0.987630	−	0.316544i
$904$		0			0
$905$	25.0521	+	43.3914i	0.832759	+	1.44238i
$906$		0			0
$907$	8.68354	−	15.0403i	0.288332	−	0.499406i	−0.685080	−	0.728468i	$-0.740233\pi$
$907$	8.68354	−	15.0403i	0.288332	−	0.499406i	0.973412	+	0.229062i	$0.0735659\pi$
$908$		0			0
$909$	8.90291	−	6.36029i	0.295291	−	0.210957i
$910$		0			0
$911$	1.29095	−	2.23599i	0.0427711	−	0.0740817i	−0.843847	−	0.536583i	$-0.819715\pi$
$911$	1.29095	−	2.23599i	0.0427711	−	0.0740817i	0.886618	+	0.462502i	$0.153048\pi$
$912$		0			0
$913$	3.74899	+	6.49344i	0.124073	+	0.214902i
$914$		0			0
$915$	3.99056	−	18.4121i	0.131924	−	0.608685i
$916$		0			0
$917$	64.0871			2.11634
$918$		0			0
$919$	34.8909			1.15095			0.575473	−	0.817821i	$-0.304818\pi$
$919$	34.8909			1.15095			0.575473	+	0.817821i	$0.304818\pi$
$920$		0			0
$921$	−4.31330	+	19.9012i	−0.142128	+	0.655768i
$922$		0			0
$923$	19.2226	+	33.2946i	0.632721	+	1.09591i
$924$		0			0
$925$	1.84629	−	3.19786i	0.0607055	−	0.105145i
$926$		0			0
$927$	−3.15185	−	32.4823i	−0.103520	−	1.06686i
$928$		0			0
$929$	4.38201	−	7.58986i	0.143769	−	0.249015i	−0.785144	−	0.619313i	$-0.787411\pi$
$929$	4.38201	−	7.58986i	0.143769	−	0.249015i	0.928913	+	0.370298i	$0.120744\pi$
$930$		0			0
$931$	4.01910	+	6.96128i	0.131721	+	0.228147i
$932$		0			0
$933$	53.3736	−	17.1067i	1.74737	−	0.560049i
$934$		0			0
$935$	−38.7393			−1.26691
$936$		0			0
$937$	39.6212			1.29437			0.647184	−	0.762334i	$-0.275946\pi$
$937$	39.6212			1.29437			0.647184	+	0.762334i	$0.275946\pi$
$938$		0			0
$939$	−37.4656	−	34.0062i	−1.22264	−	1.10975i
$940$		0			0
$941$	13.5675	+	23.4995i	0.442287	+	0.766063i	0.997859	−	0.0654053i	$-0.0208340\pi$
$941$	13.5675	+	23.4995i	0.442287	+	0.766063i	−0.555572	+	0.831468i	$0.687501\pi$
$942$		0			0
$943$	9.20195	−	15.9382i	0.299657	−	0.519020i
$944$		0			0
$945$	−18.8483	+	25.2992i	−0.613135	+	0.822983i
$946$		0			0
$947$	1.06166	−	1.83886i	0.0344995	−	0.0597548i	−0.848260	−	0.529580i	$-0.822350\pi$
$947$	1.06166	−	1.83886i	0.0344995	−	0.0597548i	0.882760	+	0.469825i	$0.155683\pi$
$948$		0			0
$949$	16.5407	+	28.6494i	0.536934	+	0.929998i
$950$		0			0
$951$	−35.1440	−	31.8989i	−1.13962	−	1.03439i
$952$		0			0
$953$	−0.523434			−0.0169557			−0.00847784	−	0.999964i	$-0.502699\pi$
$953$	−0.523434			−0.0169557			−0.00847784	+	0.999964i	$0.502699\pi$
$954$		0			0
$955$	−17.4729			−0.565410
$956$		0			0
$957$	12.6328	−	4.04893i	0.408361	−	0.130883i
$958$		0			0
$959$	−13.3082	−	23.0504i	−0.429743	−	0.744337i
$960$		0			0
$961$	9.08902	−	15.7426i	0.293194	−	0.507827i
$962$		0			0
$963$	−16.2461	−	7.38934i	−0.523525	−	0.238118i
$964$		0			0
$965$	−10.5538	+	18.2796i	−0.339737	+	0.588442i
$966$		0			0
$967$	−2.74196	−	4.74922i	−0.0881756	−	0.152725i	0.818564	−	0.574415i	$-0.194770\pi$
$967$	−2.74196	−	4.74922i	−0.0881756	−	0.152725i	−0.906740	+	0.421690i	$0.861437\pi$
$968$		0			0
$969$	−17.3761	+	80.1719i	−0.558200	+	2.57549i
$970$		0			0
$971$	0.813501			0.0261065			0.0130532	−	0.999915i	$-0.495845\pi$
$971$	0.813501			0.0261065			0.0130532	+	0.999915i	$0.495845\pi$
$972$		0			0
$973$	24.1923			0.775570
$974$		0			0
$975$	1.33263	−	6.14866i	0.0426784	−	0.196915i
$976$		0			0
$977$	9.85335	+	17.0665i	0.315237	+	0.546006i	0.979488	−	0.201504i	$-0.0645828\pi$
$977$	9.85335	+	17.0665i	0.315237	+	0.546006i	−0.664251	+	0.747509i	$0.731249\pi$
$978$		0			0
$979$	−3.58273	+	6.20547i	−0.114505	+	0.198328i
$980$		0			0
$981$	26.9561	+	12.2606i	0.860641	+	0.391451i
$982$		0			0
$983$	27.9588	−	48.4261i	0.891747	−	1.54455i	0.0539681	−	0.998543i	$-0.482813\pi$
$983$	27.9588	−	48.4261i	0.891747	−	1.54455i	0.837779	−	0.546009i	$-0.183854\pi$
$984$		0			0
$985$	−0.586692	−	1.01618i	−0.0186936	−	0.0323782i
$986$		0			0
$987$	12.6256	−	4.04660i	0.401876	−	0.128805i
$988$		0			0
$989$	−32.9588			−1.04803
$990$		0			0
$991$	−22.4053			−0.711727			−0.355863	−	0.934538i	$-0.615813\pi$
$991$	−22.4053			−0.711727			−0.355863	+	0.934538i	$0.615813\pi$
$992$		0			0
$993$	2.79412	+	2.53612i	0.0886686	+	0.0804813i
$994$		0			0
$995$	−22.7318	−	39.3726i	−0.720646	−	1.24819i
$996$		0			0
$997$	−16.6132	+	28.7749i	−0.526146	+	0.911311i	0.473390	+	0.880853i	$0.343030\pi$
$997$	−16.6132	+	28.7749i	−0.526146	+	0.911311i	−0.999536	+	0.0304585i	$0.990303\pi$
$998$		0			0
$999$	20.8291	−	27.9579i	0.659003	−	0.884550i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.i.j.385.4	yes	12
3.2	odd	2		3456.2.i.j.1153.3		12
4.3	odd	2		1152.2.i.l.385.3	yes	12
8.3	odd	2		1152.2.i.i.385.4	✓	12
8.5	even	2		1152.2.i.k.385.3	yes	12
9.4	even	3	inner	1152.2.i.j.769.4	yes	12
9.5	odd	6		3456.2.i.j.2305.3		12
12.11	even	2		3456.2.i.i.1153.3		12
24.5	odd	2		3456.2.i.l.1153.4		12
24.11	even	2		3456.2.i.k.1153.4		12
36.23	even	6		3456.2.i.i.2305.3		12
36.31	odd	6		1152.2.i.l.769.3	yes	12
72.5	odd	6		3456.2.i.l.2305.4		12
72.13	even	6		1152.2.i.k.769.3	yes	12
72.59	even	6		3456.2.i.k.2305.4		12
72.67	odd	6		1152.2.i.i.769.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.i.i.385.4	✓	12	8.3	odd	2
1152.2.i.i.769.4	yes	12	72.67	odd	6
1152.2.i.j.385.4	yes	12	1.1	even	1	trivial
1152.2.i.j.769.4	yes	12	9.4	even	3	inner
1152.2.i.k.385.3	yes	12	8.5	even	2
1152.2.i.k.769.3	yes	12	72.13	even	6
1152.2.i.l.385.3	yes	12	4.3	odd	2
1152.2.i.l.769.3	yes	12	36.31	odd	6
3456.2.i.i.1153.3		12	12.11	even	2
3456.2.i.i.2305.3		12	36.23	even	6
3456.2.i.j.1153.3		12	3.2	odd	2
3456.2.i.j.2305.3		12	9.5	odd	6
3456.2.i.k.1153.4		12	24.11	even	2
3456.2.i.k.2305.4		12	72.59	even	6
3456.2.i.l.1153.4		12	24.5	odd	2
3456.2.i.l.2305.4		12	72.5	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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366879 + 1.69275i) q^{3} +(1.05471 + 1.82681i) q^{5} +(-1.43914 + 2.49267i) q^{7} +(-2.73080 - 1.24207i) q^{9} +O(q^{10})\)	\(q+(-0.366879 + 1.69275i) q^{3} +(1.05471 + 1.82681i) q^{5} +(-1.43914 + 2.49267i) q^{7} +(-2.73080 - 1.24207i) q^{9} +(1.21325 - 2.10141i) q^{11} +(-3.30008 - 5.71590i) q^{13} +(-3.47929 + 1.11514i) q^{15} -7.56848 q^{17} -6.25779 q^{19} +(-3.69147 - 3.35061i) q^{21} +(2.63611 + 4.56587i) q^{23} +(0.275172 - 0.476612i) q^{25} +(3.10438 - 4.16687i) q^{27} +(1.57821 - 2.73353i) q^{29} +(1.79039 + 3.10104i) q^{31} +(3.11204 + 2.82469i) q^{33} -6.07151 q^{35} +6.70957 q^{37} +(10.8863 - 3.48916i) q^{39} +(-1.74537 - 3.02306i) q^{41} +(-3.12570 + 5.41388i) q^{43} +(-0.611180 - 6.29868i) q^{45} +(-1.32972 + 2.30314i) q^{47} +(-0.642255 - 1.11242i) q^{49} +(2.77671 - 12.8115i) q^{51} -0.953009 q^{53} +5.11850 q^{55} +(2.29585 - 10.5929i) q^{57} +(-4.84757 - 8.39624i) q^{59} +(-2.57821 + 4.46558i) q^{61} +(7.02607 - 5.01946i) q^{63} +(6.96125 - 12.0572i) q^{65} +(-0.949546 - 1.64466i) q^{67} +(-8.69601 + 2.78715i) q^{69} -5.82491 q^{71} -5.01222 q^{73} +(0.705829 + 0.640656i) q^{75} +(3.49207 + 6.04844i) q^{77} +(-6.49996 + 11.2583i) q^{79} +(5.91454 + 6.78368i) q^{81} +(-1.54502 + 2.67606i) q^{83} +(-7.98256 - 13.8262i) q^{85} +(4.04818 + 3.67438i) q^{87} -2.95301 q^{89} +18.9971 q^{91} +(-5.90614 + 1.89297i) q^{93} +(-6.60015 - 11.4318i) q^{95} +(-5.51242 + 9.54779i) q^{97} +(-5.92323 + 4.23159i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} + 2 q^{5} + 6 q^{7} - 2 q^{9}+O(q^{10}) \) 12 * q - 4 * q^3 + 2 * q^5 + 6 * q^7 - 2 * q^9	\( 12 q - 4 q^{3} + 2 q^{5} + 6 q^{7} - 2 q^{9} - 4 q^{11} - 10 q^{13} + 4 q^{15} + 4 q^{17} - 4 q^{19} - 2 q^{21} + 8 q^{23} - 14 q^{25} + 14 q^{27} + 2 q^{29} + 8 q^{31} - 10 q^{33} - 8 q^{35} + 22 q^{39} - 2 q^{41} + 2 q^{43} - 10 q^{45} - 14 q^{47} - 18 q^{49} + 38 q^{51} - 24 q^{53} - 16 q^{55} - 38 q^{57} - 6 q^{59} - 14 q^{61} - 16 q^{63} - 8 q^{65} - 4 q^{67} + 50 q^{69} - 28 q^{71} + 60 q^{73} - 50 q^{75} - 2 q^{77} + 16 q^{79} + 22 q^{81} - 24 q^{83} - 16 q^{85} - 36 q^{87} - 48 q^{89} + 52 q^{91} - 42 q^{93} - 20 q^{95} - 14 q^{97} - 68 q^{99}+O(q^{100}) \) 12 * q - 4 * q^3 + 2 * q^5 + 6 * q^7 - 2 * q^9 - 4 * q^11 - 10 * q^13 + 4 * q^15 + 4 * q^17 - 4 * q^19 - 2 * q^21 + 8 * q^23 - 14 * q^25 + 14 * q^27 + 2 * q^29 + 8 * q^31 - 10 * q^33 - 8 * q^35 + 22 * q^39 - 2 * q^41 + 2 * q^43 - 10 * q^45 - 14 * q^47 - 18 * q^49 + 38 * q^51 - 24 * q^53 - 16 * q^55 - 38 * q^57 - 6 * q^59 - 14 * q^61 - 16 * q^63 - 8 * q^65 - 4 * q^67 + 50 * q^69 - 28 * q^71 + 60 * q^73 - 50 * q^75 - 2 * q^77 + 16 * q^79 + 22 * q^81 - 24 * q^83 - 16 * q^85 - 36 * q^87 - 48 * q^89 + 52 * q^91 - 42 * q^93 - 20 * q^95 - 14 * q^97 - 68 * q^99

Introduction

L-functions

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Database

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