LMFDB - Embedded newform 135.2.e.b.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(46,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("135.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			91.1
Root			$1.71903 - 0.211943i$ of defining polynomial
Character	$\chi$	$=$	135.91
Dual form			135.2.e.b.46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04307 - 1.80664i) q^{2} +(-1.17597 + 2.03684i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.04307 - 3.53869i) q^{7} +0.734191 q^{8} +O(q^{10})$	\(q+(-1.04307 - 1.80664i) q^{2} +(-1.17597 + 2.03684i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.04307 - 3.53869i) q^{7} +0.734191 q^{8} -2.08613 q^{10} +(-0.675970 - 1.17081i) q^{11} +(-0.324030 + 0.561237i) q^{13} +(-4.26210 + 7.38217i) q^{14} +(1.58613 + 2.74726i) q^{16} +1.35194 q^{17} +0.648061 q^{19} +(1.17597 + 2.03684i) q^{20} +(-1.41016 + 2.44247i) q^{22} +(2.39500 - 4.14827i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.35194 q^{26} +9.61033 q^{28} +(1.93807 + 3.35683i) q^{29} +(3.84823 - 6.66533i) q^{31} +(4.04307 - 7.00279i) q^{32} +(-1.41016 - 2.44247i) q^{34} -4.08613 q^{35} +7.52420 q^{37} +(-0.675970 - 1.17081i) q^{38} +(0.367095 - 0.635828i) q^{40} +(-0.0898394 + 0.155606i) q^{41} +(0.410161 + 0.710419i) q^{43} +3.17968 q^{44} -9.99258 q^{46} +(5.45323 + 9.44526i) q^{47} +(-4.84823 + 8.39738i) q^{49} +(-1.04307 + 1.80664i) q^{50} +(-0.762100 - 1.32000i) q^{52} -4.17226 q^{53} -1.35194 q^{55} +(-1.50000 - 2.59808i) q^{56} +(4.04307 - 7.00279i) q^{58} +(2.08613 - 3.61328i) q^{59} +(1.91016 + 3.30850i) q^{61} -16.0558 q^{62} -10.5242 q^{64} +(0.324030 + 0.561237i) q^{65} +(-4.07097 + 7.05113i) q^{67} +(-1.58984 + 2.75368i) q^{68} +(4.26210 + 7.38217i) q^{70} +6.11644 q^{71} -12.3445 q^{73} +(-7.84823 - 13.5935i) q^{74} +(-0.762100 + 1.32000i) q^{76} +(-2.76210 + 4.78410i) q^{77} +(-5.17226 - 8.95862i) q^{79} +3.17226 q^{80} +0.374833 q^{82} +(-6.12920 - 10.6161i) q^{83} +(0.675970 - 1.17081i) q^{85} +(0.855648 - 1.48203i) q^{86} +(-0.496291 - 0.859601i) q^{88} +3.00000 q^{89} +2.64806 q^{91} +(5.63290 + 9.75648i) q^{92} +(11.3761 - 19.7041i) q^{94} +(0.324030 - 0.561237i) q^{95} +(6.79001 + 11.7606i) q^{97} +20.2281 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 5 q^{4} + 3 q^{5} - 5 q^{7} - 6 q^{8}+O(q^{10}) $ 6 * q + q^2 - 5 * q^4 + 3 * q^5 - 5 * q^7 - 6 * q^8	$ 6 q + q^{2} - 5 q^{4} + 3 q^{5} - 5 q^{7} - 6 q^{8} + 2 q^{10} - 2 q^{11} - 4 q^{13} - 9 q^{14} - 5 q^{16} + 4 q^{17} + 8 q^{19} + 5 q^{20} + 4 q^{22} + 3 q^{23} - 3 q^{25} + 4 q^{26} + 10 q^{28} - 7 q^{29} - 8 q^{31} + 17 q^{32} + 4 q^{34} - 10 q^{35} + 12 q^{37} - 2 q^{38} - 3 q^{40} - 13 q^{41} - 10 q^{43} + 44 q^{44} - 6 q^{46} + 13 q^{47} + 2 q^{49} + q^{50} + 12 q^{52} + 4 q^{53} - 4 q^{55} - 9 q^{56} + 17 q^{58} - 2 q^{59} - q^{61} - 84 q^{62} - 30 q^{64} + 4 q^{65} - 11 q^{67} - 22 q^{68} + 9 q^{70} + 20 q^{71} - 16 q^{73} - 16 q^{74} + 12 q^{76} - 2 q^{79} - 10 q^{80} - 58 q^{82} - 15 q^{83} + 2 q^{85} + 28 q^{86} + 24 q^{88} + 18 q^{89} + 20 q^{91} + 39 q^{92} + 31 q^{94} + 4 q^{95} + 18 q^{97} + 80 q^{98}+O(q^{100}) $ 6 * q + q^2 - 5 * q^4 + 3 * q^5 - 5 * q^7 - 6 * q^8 + 2 * q^10 - 2 * q^11 - 4 * q^13 - 9 * q^14 - 5 * q^16 + 4 * q^17 + 8 * q^19 + 5 * q^20 + 4 * q^22 + 3 * q^23 - 3 * q^25 + 4 * q^26 + 10 * q^28 - 7 * q^29 - 8 * q^31 + 17 * q^32 + 4 * q^34 - 10 * q^35 + 12 * q^37 - 2 * q^38 - 3 * q^40 - 13 * q^41 - 10 * q^43 + 44 * q^44 - 6 * q^46 + 13 * q^47 + 2 * q^49 + q^50 + 12 * q^52 + 4 * q^53 - 4 * q^55 - 9 * q^56 + 17 * q^58 - 2 * q^59 - q^61 - 84 * q^62 - 30 * q^64 + 4 * q^65 - 11 * q^67 - 22 * q^68 + 9 * q^70 + 20 * q^71 - 16 * q^73 - 16 * q^74 + 12 * q^76 - 2 * q^79 - 10 * q^80 - 58 * q^82 - 15 * q^83 + 2 * q^85 + 28 * q^86 + 24 * q^88 + 18 * q^89 + 20 * q^91 + 39 * q^92 + 31 * q^94 + 4 * q^95 + 18 * q^97 + 80 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.04307	−	1.80664i	−0.737558	−	1.27749i	−0.953592	−	0.301103i	$-0.902645\pi$
$2$	−1.04307	−	1.80664i	−0.737558	−	1.27749i	0.216033	−	0.976386i	$-0.430688\pi$
$3$		0			0
$3$		0			0
$4$	−1.17597	+	2.03684i	−0.587985	+	1.01842i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−2.04307	−	3.53869i	−0.772206	−	1.33750i	−0.936351	−	0.351064i	$-0.885820\pi$
$7$	−2.04307	−	3.53869i	−0.772206	−	1.33750i	0.164145	−	0.986436i	$-0.447513\pi$
$8$	0.734191			0.259576
$9$		0			0
$10$	−2.08613			−0.659692
$11$	−0.675970	−	1.17081i	−0.203813	−	0.353014i	0.745941	−	0.666012i	$-0.232000\pi$
$11$	−0.675970	−	1.17081i	−0.203813	−	0.353014i	−0.949754	+	0.312998i	$0.898667\pi$
$12$		0			0
$13$	−0.324030	+	0.561237i	−0.0898699	+	0.155659i	−0.907456	−	0.420147i	$-0.861978\pi$
$13$	−0.324030	+	0.561237i	−0.0898699	+	0.155659i	0.817586	+	0.575806i	$0.195312\pi$
$14$	−4.26210	+	7.38217i	−1.13909	+	1.97297i
$15$		0			0
$16$	1.58613	+	2.74726i	0.396533	+	0.686815i
$17$	1.35194			0.327893			0.163947	−	0.986469i	$-0.447577\pi$
$17$	1.35194			0.327893			0.163947	+	0.986469i	$0.447577\pi$
$18$		0			0
$19$	0.648061			0.148675			0.0743377	−	0.997233i	$-0.476316\pi$
$19$	0.648061			0.148675			0.0743377	+	0.997233i	$0.476316\pi$
$20$	1.17597	+	2.03684i	0.262955	+	0.455451i
$21$		0			0
$22$	−1.41016	+	2.44247i	−0.300647	+	0.520736i
$23$	2.39500	−	4.14827i	0.499393	−	0.864974i	−0.500607	−	0.865675i	$-0.666890\pi$
$23$	2.39500	−	4.14827i	0.499393	−	0.864974i	1.00000		0.000700856i	$0.000223089\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.35194			0.265137
$27$		0			0
$28$	9.61033			1.81618
$29$	1.93807	+	3.35683i	0.359890	+	0.623349i	0.987942	−	0.154823i	$-0.0494807\pi$
$29$	1.93807	+	3.35683i	0.359890	+	0.623349i	−0.628052	+	0.778172i	$0.716147\pi$
$30$		0			0
$31$	3.84823	−	6.66533i	0.691163	−	1.19713i	−0.280295	−	0.959914i	$-0.590432\pi$
$31$	3.84823	−	6.66533i	0.691163	−	1.19713i	0.971457	−	0.237215i	$-0.0762345\pi$
$32$	4.04307	−	7.00279i	0.714720	−	1.23793i
$33$		0			0
$34$	−1.41016	−	2.44247i	−0.241841	−	0.418880i
$35$	−4.08613			−0.690682
$36$		0			0
$37$	7.52420			1.23697			0.618485	−	0.785796i	$-0.287747\pi$
$37$	7.52420			1.23697			0.618485	+	0.785796i	$0.287747\pi$
$38$	−0.675970	−	1.17081i	−0.109657	−	0.189931i
$39$		0			0
$40$	0.367095	−	0.635828i	0.0580429	−	0.100533i
$41$	−0.0898394	+	0.155606i	−0.0140306	+	0.0243016i	−0.872955	−	0.487800i	$-0.837800\pi$
$41$	−0.0898394	+	0.155606i	−0.0140306	+	0.0243016i	0.858925	+	0.512102i	$0.171133\pi$
$42$		0			0
$43$	0.410161	+	0.710419i	0.0625489	+	0.108338i	0.895604	−	0.444852i	$-0.146744\pi$
$43$	0.410161	+	0.710419i	0.0625489	+	0.108338i	−0.833055	+	0.553190i	$0.813410\pi$
$44$	3.17968			0.479355
$45$		0			0
$46$	−9.99258			−1.47333
$47$	5.45323	+	9.44526i	0.795435	+	1.37773i	0.922563	+	0.385847i	$0.126091\pi$
$47$	5.45323	+	9.44526i	0.795435	+	1.37773i	−0.127128	+	0.991886i	$0.540576\pi$
$48$		0			0
$49$	−4.84823	+	8.39738i	−0.692604	+	1.19963i
$50$	−1.04307	+	1.80664i	−0.147512	+	0.255498i
$51$		0			0
$52$	−0.762100	−	1.32000i	−0.105684	−	0.183050i
$53$	−4.17226			−0.573104			−0.286552	−	0.958065i	$-0.592509\pi$
$53$	−4.17226			−0.573104			−0.286552	+	0.958065i	$0.592509\pi$
$54$		0			0
$55$	−1.35194			−0.182295
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$		0			0
$58$	4.04307	−	7.00279i	0.530880	−	0.919512i
$59$	2.08613	−	3.61328i	0.271591	−	0.470409i	−0.697678	−	0.716411i	$-0.745784\pi$
$59$	2.08613	−	3.61328i	0.271591	−	0.470409i	0.969269	+	0.246002i	$0.0791169\pi$
$60$		0			0
$61$	1.91016	+	3.30850i	0.244571	+	0.423609i	0.962011	−	0.273011i	$-0.0880195\pi$
$61$	1.91016	+	3.30850i	0.244571	+	0.423609i	−0.717440	+	0.696620i	$0.754686\pi$
$62$	−16.0558			−2.03909
$63$		0			0
$64$	−10.5242			−1.31552
$65$	0.324030	+	0.561237i	0.0401910	+	0.0696129i
$66$		0			0
$67$	−4.07097	+	7.05113i	−0.497349	+	0.861433i	−0.999995	−	0.00305885i	$-0.999026\pi$
$67$	−4.07097	+	7.05113i	−0.497349	+	0.861433i	0.502647	+	0.864492i	$0.332360\pi$
$68$	−1.58984	+	2.75368i	−0.192796	+	0.333933i
$69$		0			0
$70$	4.26210	+	7.38217i	0.509418	+	0.882338i
$71$	6.11644			0.725888			0.362944	−	0.931811i	$-0.381772\pi$
$71$	6.11644			0.725888			0.362944	+	0.931811i	$0.381772\pi$
$72$		0			0
$73$	−12.3445			−1.44482			−0.722408	−	0.691467i	$-0.756965\pi$
$73$	−12.3445			−1.44482			−0.722408	+	0.691467i	$0.756965\pi$
$74$	−7.84823	−	13.5935i	−0.912338	−	1.58022i
$75$		0			0
$76$	−0.762100	+	1.32000i	−0.0874188	+	0.151414i
$77$	−2.76210	+	4.78410i	−0.314770	+	0.545198i
$78$		0			0
$79$	−5.17226	−	8.95862i	−0.581925	−	1.00792i	−0.995251	−	0.0973403i	$-0.968966\pi$
$79$	−5.17226	−	8.95862i	−0.581925	−	1.00792i	0.413326	−	0.910583i	$-0.364367\pi$
$80$	3.17226			0.354669
$81$		0			0
$82$	0.374833			0.0413934
$83$	−6.12920	−	10.6161i	−0.672767	−	1.16527i	−0.977116	−	0.212706i	$-0.931772\pi$
$83$	−6.12920	−	10.6161i	−0.672767	−	1.16527i	0.304350	−	0.952560i	$-0.401561\pi$
$84$		0			0
$85$	0.675970	−	1.17081i	0.0733192	−	0.126993i
$86$	0.855648	−	1.48203i	0.0922669	−	0.159811i
$87$		0			0
$88$	−0.496291	−	0.859601i	−0.0529048	−	0.0916338i
$89$	3.00000			0.317999			0.159000	−	0.987279i	$-0.449173\pi$
$89$	3.00000			0.317999			0.159000	+	0.987279i	$0.449173\pi$
$90$		0			0
$91$	2.64806			0.277592
$92$	5.63290	+	9.75648i	0.587271	+	1.01718i
$93$		0			0
$94$	11.3761	−	19.7041i	1.17336	−	2.03232i
$95$	0.324030	−	0.561237i	0.0332448	−	0.0575817i
$96$		0			0
$97$	6.79001	+	11.7606i	0.689421	+	1.19411i	0.972025	+	0.234876i	$0.0754683\pi$
$97$	6.79001	+	11.7606i	0.689421	+	1.19411i	−0.282605	+	0.959237i	$0.591198\pi$
$98$	20.2281			2.04334
$99$		0			0
$100$	2.35194			0.235194
$101$	−0.734191	−	1.27166i	−0.0730547	−	0.126535i	0.827184	−	0.561931i	$-0.189941\pi$
$101$	−0.734191	−	1.27166i	−0.0730547	−	0.126535i	−0.900239	+	0.435397i	$0.856608\pi$
$102$		0			0
$103$	−3.76210	+	6.51615i	−0.370691	+	0.642055i	−0.989672	−	0.143351i	$-0.954212\pi$
$103$	−3.76210	+	6.51615i	−0.370691	+	0.642055i	0.618981	+	0.785406i	$0.287546\pi$
$104$	−0.237900	+	0.412055i	−0.0233280	+	0.0404053i
$105$		0			0
$106$	4.35194	+	7.53778i	0.422698	+	0.732134i
$107$	−1.20999			−0.116974			−0.0584871	−	0.998288i	$-0.518628\pi$
$107$	−1.20999			−0.116974			−0.0584871	+	0.998288i	$0.518628\pi$
$108$		0			0
$109$	14.1042			1.35094			0.675469	−	0.737388i	$-0.263941\pi$
$109$	14.1042			1.35094			0.675469	+	0.737388i	$0.263941\pi$
$110$	1.41016	+	2.44247i	0.134454	+	0.232880i
$111$		0			0
$112$	6.48113	−	11.2257i	0.612410	−	1.06072i
$113$	−5.96227	+	10.3270i	−0.560883	+	0.971478i	0.436537	+	0.899687i	$0.356205\pi$
$113$	−5.96227	+	10.3270i	−0.560883	+	0.971478i	−0.997420	+	0.0717915i	$0.977128\pi$
$114$		0			0
$115$	−2.39500	−	4.14827i	−0.223335	−	0.386828i
$116$	−9.11644			−0.846440
$117$		0			0
$118$	−8.70388			−0.801257
$119$	−2.76210	−	4.78410i	−0.253201	−	0.438557i
$120$		0			0
$121$	4.58613	−	7.94341i	0.416921	−	0.722128i
$122$	3.98484	−	6.90195i	0.360771	−	0.624873i
$123$		0			0
$124$	9.05080	+	15.6765i	0.812786	+	1.40779i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−7.07871			−0.628134			−0.314067	−	0.949401i	$-0.601692\pi$
$127$	−7.07871			−0.628134			−0.314067	+	0.949401i	$0.601692\pi$
$128$	2.89130	+	5.00787i	0.255557	+	0.442637i
$129$		0			0
$130$	0.675970	−	1.17081i	0.0592865	−	0.102687i
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	−0.966803	−	0.255524i	$-0.917752\pi$
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	0.704692	+	0.709514i	$0.251085\pi$
$132$		0			0
$133$	−1.32403	−	2.29329i	−0.114808	−	0.198853i
$134$	16.9852			1.46729
$135$		0			0
$136$	0.992582			0.0851132
$137$	−3.73419	−	6.46781i	−0.319033	−	0.552582i	0.661253	−	0.750163i	$-0.270025\pi$
$137$	−3.73419	−	6.46781i	−0.319033	−	0.552582i	−0.980287	+	0.197581i	$0.936692\pi$
$138$		0			0
$139$	−4.00000	+	6.92820i	−0.339276	+	0.587643i	−0.984297	−	0.176522i	$-0.943515\pi$
$139$	−4.00000	+	6.92820i	−0.339276	+	0.587643i	0.645021	+	0.764165i	$0.276849\pi$
$140$	4.80516	−	8.32279i	0.406111	−	0.703404i
$141$		0			0
$142$	−6.37985	−	11.0502i	−0.535385	−	0.927314i
$143$	0.876139			0.0732664
$144$		0			0
$145$	3.87614			0.321896
$146$	12.8761	+	22.3021i	1.06564	+	1.84574i
$147$		0			0
$148$	−8.84823	+	15.3256i	−0.727320	+	1.25976i
$149$	−5.29241	+	9.16673i	−0.433571	+	0.750968i	−0.997178	−	0.0750759i	$-0.976080\pi$
$149$	−5.29241	+	9.16673i	−0.433571	+	0.750968i	0.563607	+	0.826043i	$0.309413\pi$
$150$		0			0
$151$	−8.84823	−	15.3256i	−0.720059	−	1.24718i	−0.960976	−	0.276633i	$-0.910781\pi$
$151$	−8.84823	−	15.3256i	−0.720059	−	1.24718i	0.240917	−	0.970546i	$-0.422552\pi$
$152$	0.475800			0.0385925
$153$		0			0
$154$	11.5242			0.928646
$155$	−3.84823	−	6.66533i	−0.309097	−	0.535372i
$156$		0			0
$157$	1.26581	−	2.19245i	0.101023	−	0.174976i	−0.811084	−	0.584930i	$-0.801122\pi$
$157$	1.26581	−	2.19245i	0.101023	−	0.174976i	0.912106	+	0.409954i	$0.134455\pi$
$158$	−10.7900	+	18.6888i	−0.858407	+	1.48680i
$159$		0			0
$160$	−4.04307	−	7.00279i	−0.319632	−	0.553619i
$161$	−19.5726			−1.54254
$162$		0			0
$163$	8.47580			0.663876			0.331938	−	0.943301i	$-0.392298\pi$
$163$	8.47580			0.663876			0.331938	+	0.943301i	$0.392298\pi$
$164$	−0.211297	−	0.365977i	−0.0164995	−	0.0285780i
$165$		0			0
$166$	−12.7863	+	22.1465i	−0.992409	+	1.71890i
$167$	6.36710	−	11.0281i	0.492701	−	0.853383i	−0.507264	−	0.861791i	$-0.669343\pi$
$167$	6.36710	−	11.0281i	0.492701	−	0.853383i	0.999965	+	0.00840816i	$0.00267643\pi$
$168$		0			0
$169$	6.29001	+	10.8946i	0.483847	+	0.838047i
$170$	−2.82032			−0.216309
$171$		0			0
$172$	−1.92935			−0.147111
$173$	11.5242	+	19.9605i	0.876169	+	1.51757i	0.855513	+	0.517782i	$0.173242\pi$
$173$	11.5242	+	19.9605i	0.876169	+	1.51757i	0.0206561	+	0.999787i	$0.493424\pi$
$174$		0			0
$175$	−2.04307	+	3.53869i	−0.154441	+	0.267500i
$176$	2.14435	−	3.71413i	0.161637	−	0.279963i
$177$		0			0
$178$	−3.12920	−	5.41993i	−0.234543	−	0.406241i
$179$	−2.22808			−0.166534			−0.0832672	−	0.996527i	$-0.526535\pi$
$179$	−2.22808			−0.166534			−0.0832672	+	0.996527i	$0.526535\pi$
$180$		0			0
$181$	0.468382			0.0348146			0.0174073	−	0.999848i	$-0.494459\pi$
$181$	0.468382			0.0348146			0.0174073	+	0.999848i	$0.494459\pi$
$182$	−2.76210	−	4.78410i	−0.204740	−	0.354621i
$183$		0			0
$184$	1.75839	−	3.04562i	0.129630	−	0.224526i
$185$	3.76210	−	6.51615i	0.276595	−	0.479077i
$186$		0			0
$187$	−0.913870	−	1.58287i	−0.0668288	−	0.115751i
$188$	−25.6513			−1.87081
$189$		0			0
$190$	−1.35194			−0.0980800
$191$	−10.1140	−	17.5180i	−0.731826	−	1.26756i	−0.956102	−	0.293034i	$-0.905335\pi$
$191$	−10.1140	−	17.5180i	−0.731826	−	1.26756i	0.224276	−	0.974526i	$-0.427998\pi$
$192$		0			0
$193$	9.96467	−	17.2593i	0.717273	−	1.24235i	−0.244804	−	0.969573i	$-0.578723\pi$
$193$	9.96467	−	17.2593i	0.717273	−	1.24235i	0.962076	−	0.272780i	$-0.0879432\pi$
$194$	14.1648	−	24.5342i	1.01698	−	1.76145i
$195$		0			0
$196$	−11.4027	−	19.7501i	−0.814482	−	1.41072i
$197$	15.5800			1.11003			0.555015	−	0.831840i	$-0.312712\pi$
$197$	15.5800			1.11003			0.555015	+	0.831840i	$0.312712\pi$
$198$		0			0
$199$	3.58482			0.254121			0.127061	−	0.991895i	$-0.459446\pi$
$199$	3.58482			0.254121			0.127061	+	0.991895i	$0.459446\pi$
$200$	−0.367095	−	0.635828i	−0.0259576	−	0.0449598i
$201$		0			0
$202$	−1.53162	+	2.65284i	−0.107764	+	0.186653i
$203$	7.91920	−	13.7165i	0.555819	−	0.962707i
$204$		0			0
$205$	0.0898394	+	0.155606i	0.00627466	+	0.0108680i
$206$	15.6965			1.09362
$207$		0			0
$208$	−2.05582			−0.142545
$209$	−0.438069	−	0.758758i	−0.0303019	−	0.0524844i
$210$		0			0
$211$	−7.49629	+	12.9840i	−0.516066	+	0.893852i	0.483760	+	0.875201i	$0.339271\pi$
$211$	−7.49629	+	12.9840i	−0.516066	+	0.893852i	−0.999826	+	0.0186518i	$0.994063\pi$
$212$	4.90645	−	8.49822i	0.336976	−	0.583660i
$213$		0			0
$214$	1.26210	+	2.18602i	0.0862754	+	0.149433i
$215$	0.820321			0.0559454
$216$		0			0
$217$	−31.4487			−2.13488
$218$	−14.7116	−	25.4813i	−0.996396	−	1.72581i
$219$		0			0
$220$	1.58984	−	2.75368i	0.107187	−	0.185653i
$221$	−0.438069	+	0.758758i	−0.0294677	+	0.0510396i
$222$		0			0
$223$	13.4155	+	23.2363i	0.898368	+	1.55602i	0.829580	+	0.558388i	$0.188580\pi$
$223$	13.4155	+	23.2363i	0.898368	+	1.55602i	0.0687878	+	0.997631i	$0.478087\pi$
$224$	−33.0410			−2.20764
$225$		0			0
$226$	24.8761			1.65474
$227$	0.675970	+	1.17081i	0.0448657	+	0.0777096i	0.887586	−	0.460642i	$-0.152381\pi$
$227$	0.675970	+	1.17081i	0.0448657	+	0.0777096i	−0.842721	+	0.538351i	$0.819047\pi$
$228$		0			0
$229$	4.11775	−	7.13215i	0.272108	−	0.471306i	−0.697293	−	0.716786i	$-0.745612\pi$
$229$	4.11775	−	7.13215i	0.272108	−	0.471306i	0.969402	+	0.245480i	$0.0789457\pi$
$230$	−4.99629	+	8.65383i	−0.329446	+	0.570617i
$231$		0			0
$232$	1.42291	+	2.46456i	0.0934188	+	0.161806i
$233$	−8.58744			−0.562582			−0.281291	−	0.959623i	$-0.590763\pi$
$233$	−8.58744			−0.562582			−0.281291	+	0.959623i	$0.590763\pi$
$234$		0			0
$235$	10.9065			0.711458
$236$	4.90645	+	8.49822i	0.319383	+	0.553187i
$237$		0			0
$238$	−5.76210	+	9.98025i	−0.373501	+	0.646923i
$239$	−11.9623	+	20.7193i	−0.773775	+	1.34022i	0.161706	+	0.986839i	$0.448300\pi$
$239$	−11.9623	+	20.7193i	−0.773775	+	1.34022i	−0.935480	+	0.353378i	$0.885033\pi$
$240$		0			0
$241$	3.12015	+	5.40426i	0.200987	+	0.348119i	0.948847	−	0.315737i	$-0.102252\pi$
$241$	3.12015	+	5.40426i	0.200987	+	0.348119i	−0.747860	+	0.663857i	$0.768919\pi$
$242$	−19.1345			−1.23001
$243$		0			0
$244$	−8.98516			−0.575216
$245$	4.84823	+	8.39738i	0.309742	+	0.536489i
$246$		0			0
$247$	−0.209991	+	0.363716i	−0.0133614	+	0.0231427i
$248$	2.82534	−	4.89363i	0.179409	−	0.310746i
$249$		0			0
$250$	1.04307	+	1.80664i	0.0659692	+	0.114262i
$251$	28.5726			1.80349			0.901743	−	0.432272i	$-0.142288\pi$
$251$	28.5726			1.80349			0.901743	+	0.432272i	$0.142288\pi$
$252$		0			0
$253$	−6.47580			−0.407130
$254$	7.38356	+	12.7887i	0.463286	+	0.802434i
$255$		0			0
$256$	−4.49258	+	7.78138i	−0.280786	+	0.486336i
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	0.435970	+	0.899961i	$0.356405\pi$
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	−0.997374	+	0.0724199i	$0.976928\pi$
$258$		0			0
$259$	−15.3724	−	26.6258i	−0.955196	−	1.65445i
$260$	−1.52420			−0.0945268
$261$		0			0
$262$	12.5168			0.773289
$263$	15.9344	+	27.5991i	0.982555	+	1.70183i	0.652335	+	0.757931i	$0.273789\pi$
$263$	15.9344	+	27.5991i	0.982555	+	1.70183i	0.330220	+	0.943904i	$0.392877\pi$
$264$		0			0
$265$	−2.08613	+	3.61328i	−0.128150	+	0.221962i
$266$	−2.76210	+	4.78410i	−0.169355	+	0.293332i
$267$		0			0
$268$	−9.57468	−	16.5838i	−0.584867	−	1.01302i
$269$	31.4971			1.92041			0.960207	−	0.279289i	$-0.0900987\pi$
$269$	31.4971			1.92041			0.960207	+	0.279289i	$0.0900987\pi$
$270$		0			0
$271$	−3.24030			−0.196834			−0.0984172	−	0.995145i	$-0.531378\pi$
$271$	−3.24030			−0.196834			−0.0984172	+	0.995145i	$0.531378\pi$
$272$	2.14435	+	3.71413i	0.130020	+	0.225202i
$273$		0			0
$274$	−7.79001	+	13.4927i	−0.470612	+	0.815123i
$275$	−0.675970	+	1.17081i	−0.0407625	+	0.0706027i
$276$		0			0
$277$	2.79241	+	4.83660i	0.167780	+	0.290603i	0.937639	−	0.347611i	$-0.113007\pi$
$277$	2.79241	+	4.83660i	0.167780	+	0.290603i	−0.769859	+	0.638214i	$0.779674\pi$
$278$	16.6890			1.00094
$279$		0			0
$280$	−3.00000			−0.179284
$281$	−12.0521	−	20.8749i	−0.718969	−	1.24529i	−0.961409	−	0.275124i	$-0.911281\pi$
$281$	−12.0521	−	20.8749i	−0.718969	−	1.24529i	0.242440	−	0.970166i	$-0.422052\pi$
$282$		0			0
$283$	5.27114	−	9.12989i	0.313337	−	0.542715i	−0.665746	−	0.746179i	$-0.731886\pi$
$283$	5.27114	−	9.12989i	0.313337	−	0.542715i	0.979083	+	0.203463i	$0.0652197\pi$
$284$	−7.19275	+	12.4582i	−0.426811	+	0.739259i
$285$		0			0
$286$	−0.913870	−	1.58287i	−0.0540383	−	0.0935970i
$287$	0.734191			0.0433379
$288$		0			0
$289$	−15.1723			−0.892486
$290$	−4.04307	−	7.00279i	−0.237417	−	0.411218i
$291$		0			0
$292$	14.5168	−	25.1438i	0.849530	−	1.47143i
$293$	9.49629	−	16.4481i	0.554779	−	0.960906i	−0.443141	−	0.896452i	$-0.646136\pi$
$293$	9.49629	−	16.4481i	0.554779	−	0.960906i	0.997921	−	0.0644541i	$-0.0205306\pi$
$294$		0			0
$295$	−2.08613	−	3.61328i	−0.121459	−	0.210373i
$296$	5.52420			0.321088
$297$		0			0
$298$	22.0813			1.27914
$299$	1.55211	+	2.68833i	0.0897607	+	0.155470i
$300$		0			0
$301$	1.67597	−	2.90286i	0.0966013	−	0.167318i
$302$	−18.4586	+	31.9712i	−1.06217	+	1.83973i
$303$		0			0
$304$	1.02791	+	1.78039i	0.0589546	+	0.102112i
$305$	3.82032			0.218751
$306$		0			0
$307$	29.4791			1.68246			0.841229	−	0.540679i	$-0.181833\pi$
$307$	29.4791			1.68246			0.841229	+	0.540679i	$0.181833\pi$
$308$	−6.49629	−	11.2519i	−0.370161	−	0.641137i
$309$		0			0
$310$	−8.02791	+	13.9047i	−0.455955	+	0.789736i
$311$	−4.70628	+	8.15152i	−0.266869	+	0.462230i	−0.968052	−	0.250751i	$-0.919322\pi$
$311$	−4.70628	+	8.15152i	−0.266869	+	0.462230i	0.701183	+	0.712982i	$0.252656\pi$
$312$		0			0
$313$	−5.81050	−	10.0641i	−0.328429	−	0.568855i	0.653771	−	0.756692i	$-0.273186\pi$
$313$	−5.81050	−	10.0641i	−0.328429	−	0.568855i	−0.982200	+	0.187837i	$0.939852\pi$
$314$	−5.28128			−0.298040
$315$		0			0
$316$	24.3297			1.36865
$317$	−4.58984	−	7.94984i	−0.257791	−	0.446507i	0.707859	−	0.706354i	$-0.249661\pi$
$317$	−4.58984	−	7.94984i	−0.257791	−	0.446507i	−0.965650	+	0.259847i	$0.916328\pi$
$318$		0			0
$319$	2.62015	−	4.53824i	0.146700	−	0.254092i
$320$	−5.26210	+	9.11422i	−0.294160	+	0.509501i
$321$		0			0
$322$	20.4155	+	35.3607i	1.13771	+	1.97057i
$323$	0.876139			0.0487497
$324$		0			0
$325$	0.648061			0.0359479
$326$	−8.84081	−	15.3127i	−0.489647	−	0.848094i
$327$		0			0
$328$	−0.0659593	+	0.114245i	−0.00364199	+	0.00630812i
$329$	22.2826	−	38.5946i	1.22848	−	2.12779i
$330$		0			0
$331$	3.61033	+	6.25327i	0.198442	+	0.343711i	0.948023	−	0.318201i	$-0.103079\pi$
$331$	3.61033	+	6.25327i	0.198442	+	0.343711i	−0.749582	+	0.661912i	$0.769745\pi$
$332$	28.8310			1.58231
$333$		0			0
$334$	−26.5652			−1.45358
$335$	4.07097	+	7.05113i	0.222421	+	0.385245i
$336$		0			0
$337$	−1.14195	+	1.97791i	−0.0622059	+	0.107744i	−0.895451	−	0.445160i	$-0.853147\pi$
$337$	−1.14195	+	1.97791i	−0.0622059	+	0.107744i	0.833245	+	0.552904i	$0.186480\pi$
$338$	13.1218	−	22.7276i	0.713731	−	1.23622i
$339$		0			0
$340$	1.58984	+	2.75368i	0.0862211	+	0.149339i
$341$	−10.4051			−0.563470
$342$		0			0
$343$	11.0181			0.594921
$344$	0.301136	+	0.521583i	0.0162362	+	0.0281219i
$345$		0			0
$346$	24.0410	−	41.6402i	1.29245	−	2.23859i
$347$	−0.354343	+	0.613740i	−0.0190221	+	0.0329473i	−0.875380	−	0.483436i	$-0.839389\pi$
$347$	−0.354343	+	0.613740i	−0.0190221	+	0.0329473i	0.856358	+	0.516383i	$0.172722\pi$
$348$		0			0
$349$	10.6723	+	18.4849i	0.571273	+	0.989474i	0.996436	+	0.0843569i	$0.0268836\pi$
$349$	10.6723	+	18.4849i	0.571273	+	0.989474i	−0.425163	+	0.905117i	$0.639783\pi$
$350$	8.52420			0.455638
$351$		0			0
$352$	−10.9320			−0.582675
$353$	−5.04840	−	8.74408i	−0.268699	−	0.465401i	0.699827	−	0.714312i	$-0.253260\pi$
$353$	−5.04840	−	8.74408i	−0.268699	−	0.465401i	−0.968526	+	0.248912i	$0.919927\pi$
$354$		0			0
$355$	3.05822	−	5.29699i	0.162314	−	0.281135i
$356$	−3.52791	+	6.11052i	−0.186979	+	0.323857i
$357$		0			0
$358$	2.32403	+	4.02534i	0.122829	+	0.212746i
$359$	−30.5578			−1.61278			−0.806388	−	0.591386i	$-0.798581\pi$
$359$	−30.5578			−1.61278			−0.806388	+	0.591386i	$0.798581\pi$
$360$		0			0
$361$	−18.5800			−0.977896
$362$	−0.488553	−	0.846198i	−0.0256778	−	0.0444752i
$363$		0			0
$364$	−3.11404	+	5.39367i	−0.163220	+	0.282705i
$365$	−6.17226	+	10.6907i	−0.323071	+	0.559575i
$366$		0			0
$367$	3.58984	+	6.21778i	0.187388	+	0.324566i	0.944379	−	0.328860i	$-0.106664\pi$
$367$	3.58984	+	6.21778i	0.187388	+	0.324566i	−0.756991	+	0.653426i	$0.773331\pi$
$368$	15.1952			0.792102
$369$		0			0
$370$	−15.6965			−0.816020
$371$	8.52420	+	14.7643i	0.442554	+	0.766527i
$372$		0			0
$373$	10.9623	−	18.9872i	0.567605	−	0.983120i	−0.429197	−	0.903211i	$-0.641204\pi$
$373$	10.9623	−	18.9872i	0.567605	−	0.983120i	0.996802	−	0.0799096i	$-0.0254632\pi$
$374$	−1.90645	+	3.30207i	−0.0985803	+	0.170746i
$375$		0			0
$376$	4.00371	+	6.93463i	0.206476	+	0.357626i
$377$	−2.51197			−0.129373
$378$		0			0
$379$	−17.3929			−0.893414			−0.446707	−	0.894680i	$-0.647403\pi$
$379$	−17.3929			−0.893414			−0.446707	+	0.894680i	$0.647403\pi$
$380$	0.762100	+	1.32000i	0.0390949	+	0.0677143i
$381$		0			0
$382$	−21.0992	+	36.5449i	−1.07953	+	1.86980i
$383$	0.237900	−	0.412055i	0.0121561	−	0.0210550i	−0.859883	−	0.510491i	$-0.829464\pi$
$383$	0.237900	−	0.412055i	0.0121561	−	0.0210550i	0.872039	+	0.489436i	$0.162797\pi$
$384$		0			0
$385$	2.76210	+	4.78410i	0.140770	+	0.243820i
$386$	−41.5752			−2.11612
$387$		0			0
$388$	−31.9394			−1.62148
$389$	−2.79372	−	4.83886i	−0.141647	−	0.245340i	0.786470	−	0.617629i	$-0.211906\pi$
$389$	−2.79372	−	4.83886i	−0.141647	−	0.245340i	−0.928117	+	0.372289i	$0.878573\pi$
$390$		0			0
$391$	3.23790	−	5.60821i	0.163748	−	0.283619i
$392$	−3.55953	+	6.16528i	−0.179783	+	0.311394i
$393$		0			0
$394$	−16.2510	−	28.1475i	−0.818712	−	1.41805i
$395$	−10.3445			−0.520489
$396$		0			0
$397$	3.75228			0.188321			0.0941607	−	0.995557i	$-0.469983\pi$
$397$	3.75228			0.188321			0.0941607	+	0.995557i	$0.469983\pi$
$398$	−3.73921	−	6.47649i	−0.187429	−	0.324637i
$399$		0			0
$400$	1.58613	−	2.74726i	0.0793065	−	0.137363i
$401$	11.7826	−	20.4080i	0.588394	−	1.01913i	−0.406048	−	0.913852i	$-0.633094\pi$
$401$	11.7826	−	20.4080i	0.588394	−	1.01913i	0.994443	−	0.105278i	$-0.0335731\pi$
$402$		0			0
$403$	2.49389	+	4.31954i	0.124229	+	0.215172i
$404$	3.45355			0.171820
$405$		0			0
$406$	−33.0410			−1.63980
$407$	−5.08613	−	8.80944i	−0.252110	−	0.436668i
$408$		0			0
$409$	−0.524200	+	0.907940i	−0.0259200	+	0.0448948i	−0.878694	−	0.477385i	$-0.841585\pi$
$409$	−0.524200	+	0.907940i	−0.0259200	+	0.0448948i	0.852774	+	0.522279i	$0.174918\pi$
$410$	0.187417	−	0.324615i	0.00925585	−	0.0160316i
$411$		0			0
$412$	−8.84823	−	15.3256i	−0.435921	−	0.755037i
$413$	−17.0484			−0.838897
$414$		0			0
$415$	−12.2584			−0.601741
$416$	2.62015	+	4.53824i	0.128464	+	0.222505i
$417$		0			0
$418$	−0.913870	+	1.58287i	−0.0446988	+	0.0774207i
$419$	−12.9599	+	22.4471i	−0.633131	+	1.09661i	0.353777	+	0.935330i	$0.384897\pi$
$419$	−12.9599	+	22.4471i	−0.633131	+	1.09661i	−0.986908	+	0.161285i	$0.948436\pi$
$420$		0			0
$421$	−3.82032	−	6.61699i	−0.186191	−	0.322492i	0.757786	−	0.652503i	$-0.226281\pi$
$421$	−3.82032	−	6.61699i	−0.186191	−	0.322492i	−0.943977	+	0.330011i	$0.892948\pi$
$422$	31.2765			1.52252
$423$		0			0
$424$	−3.06324			−0.148764
$425$	−0.675970	−	1.17081i	−0.0327893	−	0.0567928i
$426$		0			0
$427$	7.80516	−	13.5189i	0.377718	−	0.654227i
$428$	1.42291	−	2.46456i	0.0687791	−	0.119129i
$429$		0			0
$430$	−0.855648	−	1.48203i	−0.0412630	−	0.0714697i
$431$	−7.98516			−0.384632			−0.192316	−	0.981333i	$-0.561600\pi$
$431$	−7.98516			−0.384632			−0.192316	+	0.981333i	$0.561600\pi$
$432$		0			0
$433$	−12.5120			−0.601287			−0.300644	−	0.953737i	$-0.597201\pi$
$433$	−12.5120			−0.601287			−0.300644	+	0.953737i	$0.597201\pi$
$434$	32.8031	+	56.8166i	1.57460	+	2.72728i
$435$		0			0
$436$	−16.5861	+	28.7280i	−0.794332	+	1.37582i
$437$	1.55211	−	2.68833i	0.0742474	−	0.128600i
$438$		0			0
$439$	4.38225	+	7.59028i	0.209153	+	0.362264i	0.951448	−	0.307809i	$-0.0995958\pi$
$439$	4.38225	+	7.59028i	0.209153	+	0.362264i	−0.742295	+	0.670074i	$0.766263\pi$
$440$	−0.992582			−0.0473195
$441$		0			0
$442$	1.82774			0.0869367
$443$	1.83548	+	3.17914i	0.0872062	+	0.151046i	0.906329	−	0.422572i	$-0.138873\pi$
$443$	1.83548	+	3.17914i	0.0872062	+	0.151046i	−0.819123	+	0.573618i	$0.805539\pi$
$444$		0			0
$445$	1.50000	−	2.59808i	0.0711068	−	0.123161i
$446$	27.9865	−	48.4740i	1.32520	−	2.29531i
$447$		0			0
$448$	21.5016	+	37.2419i	1.01586	+	1.75951i
$449$	−28.1723			−1.32953			−0.664766	−	0.747052i	$-0.731469\pi$
$449$	−28.1723			−1.32953			−0.664766	+	0.747052i	$0.731469\pi$
$450$		0			0
$451$	0.242915			0.0114384
$452$	−14.0229	−	24.2884i	−0.659581	−	1.14243i
$453$		0			0
$454$	1.41016	−	2.44247i	0.0661821	−	0.114631i
$455$	1.32403	−	2.29329i	0.0620715	−	0.107511i
$456$		0			0
$457$	−17.6308	−	30.5375i	−0.824735	−	1.42848i	−0.902122	−	0.431482i	$-0.857991\pi$
$457$	−17.6308	−	30.5375i	−0.824735	−	1.42848i	0.0773867	−	0.997001i	$-0.475342\pi$
$458$	−17.1803			−0.802784
$459$		0			0
$460$	11.2658			0.525271
$461$	17.3384	+	30.0310i	0.807530	+	1.39868i	0.914570	+	0.404428i	$0.132530\pi$
$461$	17.3384	+	30.0310i	0.807530	+	1.39868i	−0.107039	+	0.994255i	$0.534137\pi$
$462$		0			0
$463$	−3.72437	+	6.45080i	−0.173086	+	0.299794i	−0.939497	−	0.342556i	$-0.888707\pi$
$463$	−3.72437	+	6.45080i	−0.173086	+	0.299794i	0.766411	+	0.642350i	$0.222041\pi$
$464$	−6.14806	+	10.6488i	−0.285417	+	0.494356i
$465$		0			0
$466$	8.95725	+	15.5144i	0.414937	+	0.718692i
$467$	−29.9655			−1.38664			−0.693319	−	0.720630i	$-0.743852\pi$
$467$	−29.9655			−1.38664			−0.693319	+	0.720630i	$0.743852\pi$
$468$		0			0
$469$	33.2691			1.53622
$470$	−11.3761	−	19.7041i	−0.524742	−	0.908880i
$471$		0			0
$472$	1.53162	−	2.65284i	0.0704984	−	0.122107i
$473$	0.554512	−	0.960443i	0.0254965	−	0.0441612i
$474$		0			0
$475$	−0.324030	−	0.561237i	−0.0148675	−	0.0257513i
$476$	12.9926			0.595514
$477$		0			0
$478$	49.9097			2.28282
$479$	−3.99258	−	6.91535i	−0.182426	−	0.315971i	0.760280	−	0.649595i	$-0.225062\pi$
$479$	−3.99258	−	6.91535i	−0.182426	−	0.315971i	−0.942706	+	0.333625i	$0.891728\pi$
$480$		0			0
$481$	−2.43807	+	4.22286i	−0.111166	+	0.192546i
$482$	6.50904	−	11.2740i	0.296479	−	0.513516i
$483$		0			0
$484$	10.7863	+	18.6824i	0.490286	+	0.849201i
$485$	13.5800			0.616637
$486$		0			0
$487$	−11.9442			−0.541243			−0.270621	−	0.962686i	$-0.587229\pi$
$487$	−11.9442			−0.541243			−0.270621	+	0.962686i	$0.587229\pi$
$488$	1.40242	+	2.42907i	0.0634847	+	0.109959i
$489$		0			0
$490$	10.1140	−	17.5180i	0.456906	−	0.791384i
$491$	−4.61033	+	7.98533i	−0.208061	+	0.360373i	−0.951104	−	0.308872i	$-0.900049\pi$
$491$	−4.61033	+	7.98533i	−0.208061	+	0.360373i	0.743042	+	0.669244i	$0.233382\pi$
$492$		0			0
$493$	2.62015	+	4.53824i	0.118006	+	0.204392i
$494$	0.876139			0.0394193
$495$		0			0
$496$	24.4152			1.09627
$497$	−12.4963	−	21.6442i	−0.560535	−	0.970876i
$498$		0			0
$499$	−15.0861	+	26.1299i	−0.675348	+	1.16974i	0.301019	+	0.953618i	$0.402673\pi$
$499$	−15.0861	+	26.1299i	−0.675348	+	1.16974i	−0.976367	+	0.216119i	$0.930660\pi$
$500$	1.17597	−	2.03684i	0.0525910	−	0.0910902i
$501$		0			0
$502$	−29.8031	−	51.6204i	−1.33018	−	2.30393i
$503$	10.5981			0.472546			0.236273	−	0.971687i	$-0.424074\pi$
$503$	10.5981			0.472546			0.236273	+	0.971687i	$0.424074\pi$
$504$		0			0
$505$	−1.46838			−0.0653421
$506$	6.75468	+	11.6995i	0.300282	+	0.520104i
$507$		0			0
$508$	8.32435	−	14.4182i	0.369333	−	0.639704i
$509$	14.3761	−	24.9002i	0.637211	−	1.10368i	−0.348831	−	0.937186i	$-0.613421\pi$
$509$	14.3761	−	24.9002i	0.637211	−	1.10368i	0.986042	−	0.166496i	$-0.0532454\pi$
$510$		0			0
$511$	25.2207	+	43.6835i	1.11570	+	1.93244i
$512$	30.3094			1.33950
$513$		0			0
$514$	37.5503			1.65627
$515$	3.76210	+	6.51615i	0.165778	+	0.287136i
$516$		0			0
$517$	7.37243	−	12.7694i	0.324239	−	0.561599i
$518$	−32.0689	+	55.5449i	−1.40903	+	2.44050i
$519$		0			0
$520$	0.237900	+	0.412055i	0.0104326	+	0.0180698i
$521$	36.0942			1.58132			0.790658	−	0.612259i	$-0.209739\pi$
$521$	36.0942			1.58132			0.790658	+	0.612259i	$0.209739\pi$
$522$		0			0
$523$	11.1297			0.486669			0.243334	−	0.969942i	$-0.421759\pi$
$523$	11.1297			0.486669			0.243334	+	0.969942i	$0.421759\pi$
$524$	−7.05582	−	12.2210i	−0.308235	−	0.533878i
$525$		0			0
$526$	33.2411	−	57.5754i	1.44938	−	2.51041i
$527$	5.20257	−	9.01112i	0.226628	−	0.392531i
$528$		0			0
$529$	0.0279088	+	0.0483395i	0.00121343	+	0.00210172i
$530$	8.70388			0.378072
$531$		0			0
$532$	6.22808			0.270021
$533$	−0.0582214	−	0.100842i	−0.00252185	−	0.00436797i
$534$		0			0
$535$	−0.604996	+	1.04788i	−0.0261562	+	0.0453039i
$536$	−2.98887	+	5.17688i	−0.129100	+	0.223607i
$537$		0			0
$538$	−32.8536	−	56.9040i	−1.41642	−	2.45331i
$539$	13.1090			0.564646
$540$		0			0
$541$	−34.7374			−1.49348			−0.746740	−	0.665116i	$-0.768382\pi$
$541$	−34.7374			−1.49348			−0.746740	+	0.665116i	$0.768382\pi$
$542$	3.37985	+	5.85407i	0.145177	+	0.251454i
$543$		0			0
$544$	5.46598	−	9.46735i	0.234352	−	0.405909i
$545$	7.05211	−	12.2146i	0.302079	−	0.523216i
$546$		0			0
$547$	1.35727	+	2.35087i	0.0580328	+	0.100516i	0.893582	−	0.448899i	$-0.148184\pi$
$547$	1.35727	+	2.35087i	0.0580328	+	0.100516i	−0.835549	+	0.549415i	$0.814851\pi$
$548$	17.5652			0.750347
$549$		0			0
$550$	2.82032			0.120259
$551$	1.25599	+	2.17543i	0.0535068	+	0.0926766i
$552$		0			0
$553$	−21.1345	+	36.6061i	−0.898732	+	1.55665i
$554$	5.82534	−	10.0898i	0.247495	−	0.428674i
$555$		0			0
$556$	−9.40776	−	16.2947i	−0.398978	−	0.691050i
$557$	8.93676			0.378663			0.189331	−	0.981913i	$-0.439368\pi$
$557$	8.93676			0.378663			0.189331	+	0.981913i	$0.439368\pi$
$558$		0			0
$559$	−0.531618			−0.0224850
$560$	−6.48113	−	11.2257i	−0.273878	−	0.474370i
$561$		0			0
$562$	−25.1423	+	43.5477i	−1.06056	+	1.83695i
$563$	−4.68130	+	8.10826i	−0.197293	+	0.341722i	−0.947650	−	0.319311i	$-0.896549\pi$
$563$	−4.68130	+	8.10826i	−0.197293	+	0.341722i	0.750357	+	0.661033i	$0.229882\pi$
$564$		0			0
$565$	5.96227	+	10.3270i	0.250835	+	0.434458i
$566$	−21.9926			−0.924417
$567$		0			0
$568$	4.49064			0.188423
$569$	17.9368	+	31.0674i	0.751948	+	1.30241i	0.946877	+	0.321595i	$0.104219\pi$
$569$	17.9368	+	31.0674i	0.751948	+	1.30241i	−0.194929	+	0.980817i	$0.562448\pi$
$570$		0			0
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$	−1.03031	+	1.78455i	−0.0430795	+	0.0746159i
$573$		0			0
$574$	−0.765809	−	1.32642i	−0.0319643	−	0.0553637i
$575$	−4.79001			−0.199757
$576$		0			0
$577$	1.35675			0.0564821			0.0282411	−	0.999601i	$-0.491009\pi$
$577$	1.35675			0.0564821			0.0282411	+	0.999601i	$0.491009\pi$
$578$	15.8257	+	27.4108i	0.658260	+	1.14014i
$579$		0			0
$580$	−4.55822	+	7.89507i	−0.189270	+	0.327825i
$581$	−25.0447	+	43.3787i	−1.03903	+	1.79965i
$582$		0			0
$583$	2.82032	+	4.88494i	0.116806	+	0.202314i
$584$	−9.06324			−0.375039
$585$		0			0
$586$	−39.6210			−1.63673
$587$	14.3950	+	24.9329i	0.594145	+	1.02909i	0.993667	+	0.112366i	$0.0358430\pi$
$587$	14.3950	+	24.9329i	0.594145	+	1.02909i	−0.399521	+	0.916724i	$0.630824\pi$
$588$		0			0
$589$	2.49389	−	4.31954i	0.102759	−	0.177984i
$590$	−4.35194	+	7.53778i	−0.179167	+	0.310325i
$591$		0			0
$592$	11.9344	+	20.6709i	0.490499	+	0.849570i
$593$	−30.9171			−1.26961			−0.634807	−	0.772671i	$-0.718920\pi$
$593$	−30.9171			−1.26961			−0.634807	+	0.772671i	$0.718920\pi$
$594$		0			0
$595$	−5.52420			−0.226470
$596$	−12.4474	−	21.5596i	−0.509867	−	0.883115i
$597$		0			0
$598$	3.23790	−	5.60821i	0.132408	−	0.229337i
$599$	0.696460	−	1.20630i	0.0284566	−	0.0492882i	−0.851446	−	0.524442i	$-0.824274\pi$
$599$	0.696460	−	1.20630i	0.0284566	−	0.0492882i	0.879903	+	0.475153i	$0.157607\pi$
$600$		0			0
$601$	−4.41256	−	7.64279i	−0.179992	−	0.311756i	0.761885	−	0.647712i	$-0.224274\pi$
$601$	−4.41256	−	7.64279i	−0.179992	−	0.311756i	−0.941878	+	0.335956i	$0.890941\pi$
$602$	−6.99258			−0.284996
$603$		0			0
$604$	41.6210			1.69353
$605$	−4.58613	−	7.94341i	−0.186453	−	0.322946i
$606$		0			0
$607$	1.07839	−	1.86783i	0.0437706	−	0.0758129i	−0.843310	−	0.537427i	$-0.819396\pi$
$607$	1.07839	−	1.86783i	0.0437706	−	0.0758129i	0.887081	+	0.461614i	$0.152730\pi$
$608$	2.62015	−	4.53824i	0.106261	−	0.184050i
$609$		0			0
$610$	−3.98484	−	6.90195i	−0.161342	−	0.279452i
$611$	−7.06804			−0.285942
$612$		0			0
$613$	−9.57521			−0.386739			−0.193370	−	0.981126i	$-0.561942\pi$
$613$	−9.57521			−0.386739			−0.193370	+	0.981126i	$0.561942\pi$
$614$	−30.7486	−	53.2581i	−1.24091	−	2.14932i
$615$		0			0
$616$	−2.02791	+	3.51244i	−0.0817068	+	0.141520i
$617$	−18.8384	+	32.6291i	−0.758406	+	1.31360i	0.185258	+	0.982690i	$0.440688\pi$
$617$	−18.8384	+	32.6291i	−0.758406	+	1.31360i	−0.943663	+	0.330907i	$0.892645\pi$
$618$		0			0
$619$	−8.55211	−	14.8127i	−0.343738	−	0.595372i	0.641385	−	0.767219i	$-0.278360\pi$
$619$	−8.55211	−	14.8127i	−0.343738	−	0.595372i	−0.985124	+	0.171847i	$0.945027\pi$
$620$	18.1016			0.726978
$621$		0			0
$622$	19.6358			0.787325
$623$	−6.12920	−	10.6161i	−0.245561	−	0.425324i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−12.1215	+	20.9950i	−0.484471	+	0.839128i
$627$		0			0
$628$	2.97711	+	5.15650i	0.118799	+	0.205767i
$629$	10.1723			0.405595
$630$		0			0
$631$	33.1090			1.31805			0.659025	−	0.752121i	$-0.270969\pi$
$631$	33.1090			1.31805			0.659025	+	0.752121i	$0.270969\pi$
$632$	−3.79743	−	6.57734i	−0.151054	−	0.261632i
$633$		0			0
$634$	−9.57500	+	16.5844i	−0.380272	+	0.658650i
$635$	−3.53936	+	6.13034i	−0.140455	+	0.243275i
$636$		0			0
$637$	−3.14195	−	5.44201i	−0.124489	−	0.215620i
$638$	−10.9320			−0.432800
$639$		0			0
$640$	5.78259			0.228577
$641$	−11.5763	−	20.0508i	−0.457237	−	0.791957i	0.541577	−	0.840651i	$-0.317827\pi$
$641$	−11.5763	−	20.0508i	−0.457237	−	0.791957i	−0.998814	+	0.0486939i	$0.984494\pi$
$642$		0			0
$643$	−21.5319	+	37.2944i	−0.849137	+	1.47075i	0.0328430	+	0.999461i	$0.489544\pi$
$643$	−21.5319	+	37.2944i	−0.849137	+	1.47075i	−0.881980	+	0.471287i	$0.843789\pi$
$644$	23.0168	−	39.8662i	0.906988	−	1.57095i
$645$		0			0
$646$	−0.913870	−	1.58287i	−0.0359557	−	0.0622771i
$647$	20.6439			0.811595			0.405798	−	0.913963i	$-0.366994\pi$
$647$	20.6439			0.811595			0.405798	+	0.913963i	$0.366994\pi$
$648$		0			0
$649$	−5.64064			−0.221415
$650$	−0.675970	−	1.17081i	−0.0265137	−	0.0459231i
$651$		0			0
$652$	−9.96728	+	17.2638i	−0.390349	+	0.676104i
$653$	3.41758	−	5.91942i	0.133740	−	0.231645i	−0.791375	−	0.611331i	$-0.790635\pi$
$653$	3.41758	−	5.91942i	0.133740	−	0.231645i	0.925116	+	0.379686i	$0.123968\pi$
$654$		0			0
$655$	3.00000	+	5.19615i	0.117220	+	0.203030i
$656$	−0.569988			−0.0222543
$657$		0			0
$658$	−92.9688			−3.62430
$659$	−13.4307	−	23.2626i	−0.523184	−	0.906181i	−0.999636	−	0.0269806i	$-0.991411\pi$
$659$	−13.4307	−	23.2626i	−0.523184	−	0.906181i	0.476452	−	0.879200i	$-0.341923\pi$
$660$		0			0
$661$	1.06063	−	1.83706i	0.0412535	−	0.0714532i	−0.844661	−	0.535301i	$-0.820198\pi$
$661$	1.06063	−	1.83706i	0.0412535	−	0.0714532i	0.885915	+	0.463848i	$0.153532\pi$
$662$	7.53162	−	13.0451i	0.292725	−	0.507014i
$663$		0			0
$664$	−4.50000	−	7.79423i	−0.174634	−	0.302475i
$665$	−2.64806			−0.102687
$666$		0			0
$667$	18.5667			0.718907
$668$	14.9750	+	25.9375i	0.579401	+	1.00355i
$669$		0			0
$670$	8.49258	−	14.7096i	0.328097	−	0.568281i
$671$	2.58242	−	4.47288i	0.0996933	−	0.172674i
$672$		0			0
$673$	−17.4102	−	30.1553i	−0.671112	−	1.16240i	−0.977589	−	0.210523i	$-0.932483\pi$
$673$	−17.4102	−	30.1553i	−0.671112	−	1.16240i	0.306477	−	0.951878i	$-0.400850\pi$
$674$	4.76450			0.183522
$675$		0			0
$676$	−29.5874			−1.13798
$677$	−12.3421	−	21.3772i	−0.474346	−	0.821592i	0.525222	−	0.850965i	$-0.323982\pi$
$677$	−12.3421	−	21.3772i	−0.474346	−	0.821592i	−0.999569	+	0.0293735i	$0.990649\pi$
$678$		0			0
$679$	27.7449	−	48.0555i	1.06475	−	1.84420i
$680$	0.496291	−	0.859601i	0.0190319	−	0.0329642i
$681$		0			0
$682$	10.8532	+	18.7984i	0.415592	+	0.719827i
$683$	38.4610			1.47167			0.735834	−	0.677162i	$-0.236790\pi$
$683$	38.4610			1.47167			0.735834	+	0.677162i	$0.236790\pi$
$684$		0			0
$685$	−7.46838			−0.285352
$686$	−11.4926	−	19.9057i	−0.438789	−	0.760005i
$687$		0			0
$688$	−1.30114	+	2.25363i	−0.0496054	+	0.0859190i
$689$	1.35194	−	2.34163i	0.0515048	−	0.0892089i
$690$		0			0
$691$	−0.240304	−	0.416219i	−0.00914159	−	0.0158337i	0.861418	−	0.507896i	$-0.169577\pi$
$691$	−0.240304	−	0.416219i	−0.00914159	−	0.0158337i	−0.870560	+	0.492062i	$0.836243\pi$
$692$	−54.2084			−2.06070
$693$		0			0
$694$	1.47841			0.0561197
$695$	4.00000	+	6.92820i	0.151729	+	0.262802i
$696$		0			0
$697$	−0.121457	+	0.210370i	−0.00460053	+	0.00796835i
$698$	22.2637	−	38.5619i	0.842694	−	1.45959i
$699$		0			0
$700$	−4.80516	−	8.32279i	−0.181618	−	0.314572i
$701$	18.1797			0.686637			0.343318	−	0.939219i	$-0.388449\pi$
$701$	18.1797			0.686637			0.343318	+	0.939219i	$0.388449\pi$
$702$		0			0
$703$	4.87614			0.183907
$704$	7.11404	+	12.3219i	0.268120	+	0.464398i
$705$		0			0
$706$	−10.5316	+	18.2413i	−0.396363	+	0.686520i
$707$	−3.00000	+	5.19615i	−0.112827	+	0.195421i
$708$		0			0
$709$	−3.59355	−	6.22421i	−0.134959	−	0.233755i	0.790623	−	0.612303i	$-0.209757\pi$
$709$	−3.59355	−	6.22421i	−0.134959	−	0.233755i	−0.925582	+	0.378548i	$0.876423\pi$
$710$	−12.7597			−0.478863
$711$		0			0
$712$	2.20257			0.0825449
$713$	−18.4331	−	31.9270i	−0.690323	−	1.19568i
$714$		0			0
$715$	0.438069	−	0.758758i	0.0163829	−	0.0283760i
$716$	2.62015	−	4.53824i	0.0979197	−	0.169602i
$717$		0			0
$718$	31.8737	+	55.2069i	1.18952	+	2.06030i
$719$	−12.5168			−0.466797			−0.233399	−	0.972381i	$-0.574985\pi$
$719$	−12.5168			−0.466797			−0.233399	+	0.972381i	$0.574985\pi$
$720$		0			0
$721$	30.7449			1.14500
$722$	19.3802	+	33.5674i	0.721255	+	1.24925i
$723$		0			0
$724$	−0.550803	+	0.954019i	−0.0204704	+	0.0354558i
$725$	1.93807	−	3.35683i	0.0719781	−	0.124670i
$726$		0			0
$727$	−4.21292	−	7.29699i	−0.156249	−	0.270631i	0.777264	−	0.629174i	$-0.216607\pi$
$727$	−4.21292	−	7.29699i	−0.156249	−	0.270631i	−0.933513	+	0.358544i	$0.883273\pi$
$728$	1.94418			0.0720562
$729$		0			0
$730$	25.7523			0.953135
$731$	0.554512	+	0.960443i	0.0205094	+	0.0355233i
$732$		0			0
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$	7.48887	−	12.9711i	0.276419	−	0.478772i
$735$		0			0
$736$	−19.3663	−	33.5434i	−0.713852	−	1.23643i
$737$	11.0074			0.405463
$738$		0			0
$739$	−1.81290			−0.0666887			−0.0333444	−	0.999444i	$-0.510616\pi$
$739$	−1.81290			−0.0666887			−0.0333444	+	0.999444i	$0.510616\pi$
$740$	8.84823	+	15.3256i	0.325267	+	0.563380i
$741$		0			0
$742$	17.7826	−	30.8003i	0.652819	−	1.13072i
$743$	10.0686	−	17.4393i	0.369380	−	0.639785i	−0.620089	−	0.784532i	$-0.712903\pi$
$743$	10.0686	−	17.4393i	0.369380	−	0.639785i	0.989469	+	0.144747i	$0.0462367\pi$
$744$		0			0
$745$	5.29241	+	9.16673i	0.193899	+	0.335843i
$746$	−45.7374			−1.67457
$747$		0			0
$748$	4.29873			0.157177
$749$	2.47209	+	4.28179i	0.0903282	+	0.156453i
$750$		0			0
$751$	−6.10662	+	10.5770i	−0.222834	+	0.385959i	−0.955667	−	0.294449i	$-0.904864\pi$
$751$	−6.10662	+	10.5770i	−0.222834	+	0.385959i	0.732834	+	0.680408i	$0.238197\pi$
$752$	−17.2991	+	29.9628i	−0.630832	+	1.09263i
$753$		0			0
$754$	2.62015	+	4.53824i	0.0954203	+	0.165273i
$755$	−17.6965			−0.644040
$756$		0			0
$757$	52.9533			1.92462			0.962310	−	0.271955i	$-0.0876701\pi$
$757$	52.9533			1.92462			0.962310	+	0.271955i	$0.0876701\pi$
$758$	18.1419	+	31.4228i	0.658945	+	1.14133i
$759$		0			0
$760$	0.237900	−	0.412055i	0.00862955	−	0.0149468i
$761$	−9.22677	+	15.9812i	−0.334470	+	0.579319i	−0.983383	−	0.181543i	$-0.941891\pi$
$761$	−9.22677	+	15.9812i	−0.334470	+	0.579319i	0.648913	+	0.760863i	$0.275224\pi$
$762$		0			0
$763$	−28.8158	−	49.9105i	−1.04320	−	1.80688i
$764$	47.5752			1.72121
$765$		0			0
$766$	−0.992582			−0.0358634
$767$	1.35194	+	2.34163i	0.0488157	+	0.0845513i
$768$		0			0
$769$	2.22677	−	3.85688i	0.0802995	−	0.139083i	−0.823079	−	0.567927i	$-0.807746\pi$
$769$	2.22677	−	3.85688i	0.0802995	−	0.139083i	0.903379	+	0.428844i	$0.141079\pi$
$770$	5.76210	−	9.98025i	0.207652	−	0.359663i
$771$		0			0
$772$	23.4363	+	40.5929i	0.843491	+	1.46097i
$773$	−38.9368			−1.40046			−0.700229	−	0.713918i	$-0.746919\pi$
$773$	−38.9368			−1.40046			−0.700229	+	0.713918i	$0.746919\pi$
$774$		0			0
$775$	−7.69646			−0.276465
$776$	4.98516	+	8.63456i	0.178957	+	0.309962i
$777$		0			0
$778$	−5.82806	+	10.0945i	−0.208946	+	0.361905i
$779$	−0.0582214	+	0.100842i	−0.00208600	+	0.00361305i
$780$		0			0
$781$	−4.13453	−	7.16121i	−0.147945	−	0.256248i
$782$	−13.5094			−0.483094
$783$		0			0
$784$	−30.7597			−1.09856
$785$	−1.26581	−	2.19245i	−0.0451787	−	0.0782517i
$786$		0			0
$787$	−17.1140	+	29.6424i	−0.610050	+	1.05664i	0.381182	+	0.924500i	$0.375517\pi$
$787$	−17.1140	+	29.6424i	−0.610050	+	1.05664i	−0.991231	+	0.132137i	$0.957816\pi$
$788$	−18.3216	+	31.7340i	−0.652681	+	1.13048i
$789$		0			0
$790$	10.7900	+	18.6888i	0.383891	+	0.664919i
$791$	48.7252			1.73247
$792$		0			0
$793$	−2.47580			−0.0879183
$794$	−3.91387	−	6.77902i	−0.138898	−	0.240578i
$795$		0			0
$796$	−4.21564	+	7.30171i	−0.149420	+	0.258802i
$797$	11.9828	−	20.7547i	0.424451	−	0.735171i	−0.571918	−	0.820311i	$-0.693800\pi$
$797$	11.9828	−	20.7547i	0.424451	−	0.735171i	0.996369	+	0.0851400i	$0.0271337\pi$
$798$		0			0
$799$	7.37243	+	12.7694i	0.260818	+	0.451750i
$800$	−8.08613			−0.285888
$801$		0			0
$802$	−49.1600			−1.73590
$803$	8.34452	+	14.4531i	0.294472	+	0.510040i
$804$		0			0
$805$	−9.78630	+	16.9504i	−0.344922	+	0.597422i
$806$	5.20257	−	9.01112i	0.183253	−	0.317403i
$807$		0			0
$808$	−0.539036	−	0.933638i	−0.0189632	−	0.0328453i
$809$	0.283896			0.00998124			0.00499062	−	0.999988i	$-0.498411\pi$
$809$	0.283896			0.00998124			0.00499062	+	0.999988i	$0.498411\pi$
$810$		0			0
$811$	32.4413			1.13917			0.569584	−	0.821933i	$-0.307104\pi$
$811$	32.4413			1.13917			0.569584	+	0.821933i	$0.307104\pi$
$812$	18.6255	+	32.2603i	0.653626	+	1.13211i
$813$		0			0
$814$	−10.6103	+	18.3776i	−0.371892	+	0.644136i
$815$	4.23790	−	7.34026i	0.148447	−	0.257118i
$816$		0			0
$817$	0.265809	+	0.460395i	0.00929948	+	0.0161072i
$818$	2.18710			0.0764701
$819$		0			0
$820$	−0.422594			−0.0147576
$821$	20.8347	+	36.0868i	0.727136	+	1.25944i	0.958089	+	0.286472i	$0.0924824\pi$
$821$	20.8347	+	36.0868i	0.727136	+	1.25944i	−0.230953	+	0.972965i	$0.574184\pi$
$822$		0			0
$823$	9.68130	−	16.7685i	0.337469	−	0.584514i	−0.646487	−	0.762925i	$-0.723763\pi$
$823$	9.68130	−	16.7685i	0.337469	−	0.584514i	0.983956	+	0.178412i	$0.0570958\pi$
$824$	−2.76210	+	4.78410i	−0.0962223	+	0.166662i
$825$		0			0
$826$	17.7826	+	30.8003i	0.618735	+	1.07168i
$827$	−18.8097			−0.654076			−0.327038	−	0.945011i	$-0.606050\pi$
$827$	−18.8097			−0.654076			−0.327038	+	0.945011i	$0.606050\pi$
$828$		0			0
$829$	−33.1016			−1.14967			−0.574833	−	0.818271i	$-0.694933\pi$
$829$	−33.1016			−1.14967			−0.574833	+	0.818271i	$0.694933\pi$
$830$	12.7863	+	22.1465i	0.443819	+	0.768717i
$831$		0			0
$832$	3.41016	−	5.90657i	0.118226	−	0.204774i
$833$	−6.55451	+	11.3527i	−0.227100	+	0.393349i
$834$		0			0
$835$	−6.36710	−	11.0281i	−0.220342	−	0.381644i
$836$	2.06063			0.0712682
$837$		0			0
$838$	54.0719			1.86788
$839$	−19.8482	−	34.3781i	−0.685237	−	1.18687i	−0.973362	−	0.229273i	$-0.926365\pi$
$839$	−19.8482	−	34.3781i	−0.685237	−	1.18687i	0.288125	−	0.957593i	$-0.406968\pi$
$840$		0			0
$841$	6.98777	−	12.1032i	0.240958	−	0.417351i
$842$	−7.96969	+	13.8039i	−0.274654	+	0.475714i
$843$		0			0
$844$	−17.6308	−	30.5375i	−0.606878	−	1.05114i
$845$	12.5800			0.432766
$846$		0			0
$847$	−37.4791			−1.28780
$848$	−6.61775	−	11.4623i	−0.227254	−	0.393616i
$849$		0			0
$850$	−1.41016	+	2.44247i	−0.0483681	+	0.0837760i
$851$	18.0205	−	31.2124i	0.617734	−	1.06995i
$852$		0			0
$853$	2.05822	+	3.56494i	0.0704722	+	0.122061i	0.899108	−	0.437726i	$-0.144216\pi$
$853$	2.05822	+	3.56494i	0.0704722	+	0.122061i	−0.828636	+	0.559788i	$0.810883\pi$
$854$	−32.5652			−1.11436
$855$		0			0
$856$	−0.888365			−0.0303637
$857$	7.37243	+	12.7694i	0.251837	+	0.436195i	0.964032	−	0.265787i	$-0.0856319\pi$
$857$	7.37243	+	12.7694i	0.251837	+	0.436195i	−0.712194	+	0.701982i	$0.752299\pi$
$858$		0			0
$859$	18.9269	−	32.7824i	0.645779	−	1.11852i	−0.338342	−	0.941023i	$-0.609866\pi$
$859$	18.9269	−	32.7824i	0.645779	−	1.11852i	0.984121	−	0.177499i	$-0.0568006\pi$
$860$	−0.964673	+	1.67086i	−0.0328951	+	0.0569759i
$861$		0			0
$862$	8.32905	+	14.4263i	0.283688	+	0.491363i
$863$	−26.7704			−0.911274			−0.455637	−	0.890166i	$-0.650588\pi$
$863$	−26.7704			−0.911274			−0.455637	+	0.890166i	$0.650588\pi$
$864$		0			0
$865$	23.0484			0.783669
$866$	13.0508	+	22.6047i	0.443484	+	0.768137i
$867$		0			0
$868$	36.9828	−	64.0560i	1.25528	−	2.17420i
$869$	−6.99258	+	12.1115i	−0.237207	+	0.410855i
$870$		0			0
$871$	−2.63824	−	4.56956i	−0.0893933	−	0.154834i
$872$	10.3552			0.350671
$873$		0			0
$874$	−6.47580			−0.219047
$875$	2.04307	+	3.53869i	0.0690682	+	0.119630i
$876$		0			0
$877$	23.4841	−	40.6756i	0.793001	−	1.37352i	−0.131101	−	0.991369i	$-0.541851\pi$
$877$	23.4841	−	40.6756i	0.793001	−	1.37352i	0.924101	−	0.382148i	$-0.124816\pi$
$878$	9.14195	−	15.8343i	0.308526	−	0.534382i
$879$		0			0
$880$	−2.14435	−	3.71413i	−0.0722861	−	0.125203i
$881$	19.8055			0.667264			0.333632	−	0.942703i	$-0.391726\pi$
$881$	19.8055			0.667264			0.333632	+	0.942703i	$0.391726\pi$
$882$		0			0
$883$	−6.20257			−0.208733			−0.104367	−	0.994539i	$-0.533282\pi$
$883$	−6.20257			−0.208733			−0.104367	+	0.994539i	$0.533282\pi$
$884$	−1.03031	−	1.78455i	−0.0346532	−	0.0600210i
$885$		0			0
$886$	3.82905	−	6.63210i	0.128639	−	0.222810i
$887$	6.71370	−	11.6285i	0.225424	−	0.390446i	−0.731023	−	0.682353i	$-0.760957\pi$
$887$	6.71370	−	11.6285i	0.225424	−	0.390446i	0.956447	+	0.291907i	$0.0942899\pi$
$888$		0			0
$889$	14.4623	+	25.0494i	0.485049	+	0.840129i
$890$	−6.25839			−0.209782
$891$		0			0
$892$	−63.1049			−2.11291
$893$	3.53402	+	6.12111i	0.118262	+	0.204835i
$894$		0			0
$895$	−1.11404	+	1.92957i	−0.0372382	+	0.0644985i
$896$	11.8142	−	20.4628i	0.394685	−	0.683614i
$897$		0			0
$898$	29.3855	+	50.8972i	0.980607	+	1.69846i
$899$	29.8325			0.994971
$900$		0			0
$901$	−5.64064			−0.187917
$902$	−0.253376	−	0.438860i	−0.00843650	−	0.0146124i
$903$		0			0
$904$	−4.37744	+	7.58196i	−0.145592	+	0.252172i
$905$	0.234191	−	0.405631i	0.00778477	−	0.0134836i
$906$		0			0
$907$	−0.336783	−	0.583325i	−0.0111827	−	0.0193690i	0.860380	−	0.509653i	$-0.170226\pi$
$907$	−0.336783	−	0.583325i	−0.0111827	−	0.0193690i	−0.871563	+	0.490284i	$0.836893\pi$
$908$	−3.17968			−0.105521
$909$		0			0
$910$	−5.52420			−0.183125
$911$	−3.95485	−	6.85000i	−0.131030	−	0.226951i	0.793044	−	0.609165i	$-0.208495\pi$
$911$	−3.95485	−	6.85000i	−0.131030	−	0.226951i	−0.924074	+	0.382214i	$0.875162\pi$
$912$		0			0
$913$	−8.28630	+	14.3523i	−0.274236	+	0.474992i
$914$	−36.7802	+	63.7052i	−1.21658	+	2.10718i
$915$		0			0
$916$	9.68469	+	16.7744i	0.319991	+	0.554241i
$917$	24.5168			0.809615
$918$		0			0
$919$	−8.58263			−0.283115			−0.141557	−	0.989930i	$-0.545211\pi$
$919$	−8.58263			−0.283115			−0.141557	+	0.989930i	$0.545211\pi$
$920$	−1.75839	−	3.04562i	−0.0579724	−	0.100411i
$921$		0			0
$922$	36.1702	−	62.6486i	1.19120	−	2.06322i
$923$	−1.98191	+	3.43277i	−0.0652355	+	0.112991i
$924$		0			0
$925$	−3.76210	−	6.51615i	−0.123697	−	0.214250i
$926$	15.5390			0.510644
$927$		0			0
$928$	31.3430			1.02888
$929$	14.8081	+	25.6484i	0.485838	+	0.841496i	0.999868	−	0.0162766i	$-0.00518122\pi$
$929$	14.8081	+	25.6484i	0.485838	+	0.841496i	−0.514030	+	0.857772i	$0.671848\pi$
$930$		0			0
$931$	−3.14195	+	5.44201i	−0.102973	+	0.178355i
$932$	10.0986	−	17.4912i	0.330789	−	0.572944i
$933$		0			0
$934$	31.2560	+	54.1370i	1.02273	+	1.77142i
$935$	−1.82774			−0.0597735
$936$		0			0
$937$	−15.2058			−0.496753			−0.248376	−	0.968664i	$-0.579897\pi$
$937$	−15.2058			−0.496753			−0.248376	+	0.968664i	$0.579897\pi$
$938$	−34.7018	−	60.1053i	−1.13305	−	1.96251i
$939$		0			0
$940$	−12.8257	+	22.2147i	−0.418327	+	0.724563i
$941$	2.82643	−	4.89553i	0.0921391	−	0.159590i	−0.816272	−	0.577668i	$-0.803963\pi$
$941$	2.82643	−	4.89553i	0.0921391	−	0.159590i	0.908411	+	0.418078i	$0.137296\pi$
$942$		0			0
$943$	0.430332	+	0.745356i	0.0140135	+	0.0242721i
$944$	13.2355			0.430779
$945$		0			0
$946$	−2.31357			−0.0752206
$947$	−20.1981	−	34.9841i	−0.656350	−	1.13683i	−0.981554	−	0.191187i	$-0.938766\pi$
$947$	−20.1981	−	34.9841i	−0.656350	−	1.13683i	0.325204	−	0.945644i	$-0.394567\pi$
$948$		0			0
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$	−0.675970	+	1.17081i	−0.0219313	+	0.0379862i
$951$		0			0
$952$	−2.02791	−	3.51244i	−0.0657249	−	0.113839i
$953$	22.9320			0.742839			0.371419	−	0.928465i	$-0.378871\pi$
$953$	22.9320			0.742839			0.371419	+	0.928465i	$0.378871\pi$
$954$		0			0
$955$	−20.2281			−0.654565
$956$	−28.1345	−	48.7304i	−0.909936	−	1.57605i
$957$		0			0
$958$	−8.32905	+	14.4263i	−0.269099	+	0.466094i
$959$	−15.2584	+	26.4283i	−0.492719	+	0.853415i
$960$		0			0
$961$	−14.1177	−	24.4527i	−0.455411	−	0.788795i
$962$	10.1723			0.327967
$963$		0			0
$964$	−14.6768			−0.472708
$965$	−9.96467	−	17.2593i	−0.320774	−	0.555597i
$966$		0			0
$967$	−5.18501	+	8.98071i	−0.166739	+	0.288800i	−0.937271	−	0.348601i	$-0.886657\pi$
$967$	−5.18501	+	8.98071i	−0.166739	+	0.288800i	0.770533	+	0.637401i	$0.219990\pi$
$968$	3.36710	−	5.83198i	0.108223	−	0.187447i
$969$		0			0
$970$	−14.1648	−	24.5342i	−0.454806	−	0.787747i
$971$	−48.0410			−1.54171			−0.770854	−	0.637012i	$-0.780170\pi$
$971$	−48.0410			−1.54171			−0.770854	+	0.637012i	$0.780170\pi$
$972$		0			0
$973$	32.6890			1.04796
$974$	12.4586	+	21.5789i	0.399198	+	0.691431i
$975$		0			0
$976$	−6.05953	+	10.4954i	−0.193961	+	0.335950i
$977$	13.5266	−	23.4288i	0.432754	−	0.749553i	−0.564355	−	0.825532i	$-0.690875\pi$
$977$	13.5266	−	23.4288i	0.432754	−	0.749553i	0.997109	+	0.0759796i	$0.0242084\pi$
$978$		0			0
$979$	−2.02791	−	3.51244i	−0.0648122	−	0.112258i
$980$	−22.8055			−0.728494
$981$		0			0
$982$	19.2355			0.613829
$983$	−11.2408	−	19.4697i	−0.358527	−	0.620987i	0.629188	−	0.777253i	$-0.283388\pi$
$983$	−11.2408	−	19.4697i	−0.358527	−	0.620987i	−0.987715	+	0.156266i	$0.950054\pi$
$984$		0			0
$985$	7.79001	−	13.4927i	0.248210	−	0.429913i
$986$	5.46598	−	9.46735i	0.174072	−	0.301502i
$987$		0			0
$988$	−0.493887	−	0.855437i	−0.0157126	−	0.0272151i
$989$	3.92935			0.124946
$990$		0			0
$991$	−26.5316			−0.842805			−0.421402	−	0.906874i	$-0.638462\pi$
$991$	−26.5316			−0.842805			−0.421402	+	0.906874i	$0.638462\pi$
$992$	−31.1173	−	53.8967i	−0.987975	−	1.71122i
$993$		0			0
$994$	−26.0689	+	45.1526i	−0.826855	+	1.43215i
$995$	1.79241	−	3.10455i	0.0568233	−	0.0984208i
$996$		0			0
$997$	14.1829	+	24.5656i	0.449178	+	0.777999i	0.998333	−	0.0577217i	$-0.0183836\pi$
$997$	14.1829	+	24.5656i	0.449178	+	0.777999i	−0.549155	+	0.835721i	$0.685050\pi$
$998$	62.9433			1.99243
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.e.b.91.1		6
3.2	odd	2		45.2.e.b.31.3	yes	6
4.3	odd	2		2160.2.q.k.1441.3		6
5.2	odd	4		675.2.k.b.199.5		12
5.3	odd	4		675.2.k.b.199.2		12
5.4	even	2		675.2.e.b.226.3		6
9.2	odd	6		45.2.e.b.16.3	✓	6
9.4	even	3		405.2.a.i.1.3		3
9.5	odd	6		405.2.a.j.1.1		3
9.7	even	3	inner	135.2.e.b.46.1		6
12.11	even	2		720.2.q.i.481.3		6
15.2	even	4		225.2.k.b.49.2		12
15.8	even	4		225.2.k.b.49.5		12
15.14	odd	2		225.2.e.b.76.1		6
36.7	odd	6		2160.2.q.k.721.3		6
36.11	even	6		720.2.q.i.241.3		6
36.23	even	6		6480.2.a.bv.1.1		3
36.31	odd	6		6480.2.a.bs.1.1		3
45.2	even	12		225.2.k.b.124.5		12
45.4	even	6		2025.2.a.o.1.1		3
45.7	odd	12		675.2.k.b.424.2		12
45.13	odd	12		2025.2.b.m.649.2		6
45.14	odd	6		2025.2.a.n.1.3		3
45.22	odd	12		2025.2.b.m.649.5		6
45.23	even	12		2025.2.b.l.649.5		6
45.29	odd	6		225.2.e.b.151.1		6
45.32	even	12		2025.2.b.l.649.2		6
45.34	even	6		675.2.e.b.451.3		6
45.38	even	12		225.2.k.b.124.2		12
45.43	odd	12		675.2.k.b.424.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.e.b.16.3	✓	6	9.2	odd	6
45.2.e.b.31.3	yes	6	3.2	odd	2
135.2.e.b.46.1		6	9.7	even	3	inner
135.2.e.b.91.1		6	1.1	even	1	trivial
225.2.e.b.76.1		6	15.14	odd	2
225.2.e.b.151.1		6	45.29	odd	6
225.2.k.b.49.2		12	15.2	even	4
225.2.k.b.49.5		12	15.8	even	4
225.2.k.b.124.2		12	45.38	even	12
225.2.k.b.124.5		12	45.2	even	12
405.2.a.i.1.3		3	9.4	even	3
405.2.a.j.1.1		3	9.5	odd	6
675.2.e.b.226.3		6	5.4	even	2
675.2.e.b.451.3		6	45.34	even	6
675.2.k.b.199.2		12	5.3	odd	4
675.2.k.b.199.5		12	5.2	odd	4
675.2.k.b.424.2		12	45.7	odd	12
675.2.k.b.424.5		12	45.43	odd	12
720.2.q.i.241.3		6	36.11	even	6
720.2.q.i.481.3		6	12.11	even	2
2025.2.a.n.1.3		3	45.14	odd	6
2025.2.a.o.1.1		3	45.4	even	6
2025.2.b.l.649.2		6	45.32	even	12
2025.2.b.l.649.5		6	45.23	even	12
2025.2.b.m.649.2		6	45.13	odd	12
2025.2.b.m.649.5		6	45.22	odd	12
2160.2.q.k.721.3		6	36.7	odd	6
2160.2.q.k.1441.3		6	4.3	odd	2
6480.2.a.bs.1.1		3	36.31	odd	6
6480.2.a.bv.1.1		3	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.04307 - 1.80664i) q^{2} +(-1.17597 + 2.03684i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.04307 - 3.53869i) q^{7} +0.734191 q^{8} +O(q^{10})\)	\(q+(-1.04307 - 1.80664i) q^{2} +(-1.17597 + 2.03684i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.04307 - 3.53869i) q^{7} +0.734191 q^{8} -2.08613 q^{10} +(-0.675970 - 1.17081i) q^{11} +(-0.324030 + 0.561237i) q^{13} +(-4.26210 + 7.38217i) q^{14} +(1.58613 + 2.74726i) q^{16} +1.35194 q^{17} +0.648061 q^{19} +(1.17597 + 2.03684i) q^{20} +(-1.41016 + 2.44247i) q^{22} +(2.39500 - 4.14827i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.35194 q^{26} +9.61033 q^{28} +(1.93807 + 3.35683i) q^{29} +(3.84823 - 6.66533i) q^{31} +(4.04307 - 7.00279i) q^{32} +(-1.41016 - 2.44247i) q^{34} -4.08613 q^{35} +7.52420 q^{37} +(-0.675970 - 1.17081i) q^{38} +(0.367095 - 0.635828i) q^{40} +(-0.0898394 + 0.155606i) q^{41} +(0.410161 + 0.710419i) q^{43} +3.17968 q^{44} -9.99258 q^{46} +(5.45323 + 9.44526i) q^{47} +(-4.84823 + 8.39738i) q^{49} +(-1.04307 + 1.80664i) q^{50} +(-0.762100 - 1.32000i) q^{52} -4.17226 q^{53} -1.35194 q^{55} +(-1.50000 - 2.59808i) q^{56} +(4.04307 - 7.00279i) q^{58} +(2.08613 - 3.61328i) q^{59} +(1.91016 + 3.30850i) q^{61} -16.0558 q^{62} -10.5242 q^{64} +(0.324030 + 0.561237i) q^{65} +(-4.07097 + 7.05113i) q^{67} +(-1.58984 + 2.75368i) q^{68} +(4.26210 + 7.38217i) q^{70} +6.11644 q^{71} -12.3445 q^{73} +(-7.84823 - 13.5935i) q^{74} +(-0.762100 + 1.32000i) q^{76} +(-2.76210 + 4.78410i) q^{77} +(-5.17226 - 8.95862i) q^{79} +3.17226 q^{80} +0.374833 q^{82} +(-6.12920 - 10.6161i) q^{83} +(0.675970 - 1.17081i) q^{85} +(0.855648 - 1.48203i) q^{86} +(-0.496291 - 0.859601i) q^{88} +3.00000 q^{89} +2.64806 q^{91} +(5.63290 + 9.75648i) q^{92} +(11.3761 - 19.7041i) q^{94} +(0.324030 - 0.561237i) q^{95} +(6.79001 + 11.7606i) q^{97} +20.2281 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 5 q^{4} + 3 q^{5} - 5 q^{7} - 6 q^{8}+O(q^{10}) \) 6 * q + q^2 - 5 * q^4 + 3 * q^5 - 5 * q^7 - 6 * q^8	\( 6 q + q^{2} - 5 q^{4} + 3 q^{5} - 5 q^{7} - 6 q^{8} + 2 q^{10} - 2 q^{11} - 4 q^{13} - 9 q^{14} - 5 q^{16} + 4 q^{17} + 8 q^{19} + 5 q^{20} + 4 q^{22} + 3 q^{23} - 3 q^{25} + 4 q^{26} + 10 q^{28} - 7 q^{29} - 8 q^{31} + 17 q^{32} + 4 q^{34} - 10 q^{35} + 12 q^{37} - 2 q^{38} - 3 q^{40} - 13 q^{41} - 10 q^{43} + 44 q^{44} - 6 q^{46} + 13 q^{47} + 2 q^{49} + q^{50} + 12 q^{52} + 4 q^{53} - 4 q^{55} - 9 q^{56} + 17 q^{58} - 2 q^{59} - q^{61} - 84 q^{62} - 30 q^{64} + 4 q^{65} - 11 q^{67} - 22 q^{68} + 9 q^{70} + 20 q^{71} - 16 q^{73} - 16 q^{74} + 12 q^{76} - 2 q^{79} - 10 q^{80} - 58 q^{82} - 15 q^{83} + 2 q^{85} + 28 q^{86} + 24 q^{88} + 18 q^{89} + 20 q^{91} + 39 q^{92} + 31 q^{94} + 4 q^{95} + 18 q^{97} + 80 q^{98}+O(q^{100}) \) 6 * q + q^2 - 5 * q^4 + 3 * q^5 - 5 * q^7 - 6 * q^8 + 2 * q^10 - 2 * q^11 - 4 * q^13 - 9 * q^14 - 5 * q^16 + 4 * q^17 + 8 * q^19 + 5 * q^20 + 4 * q^22 + 3 * q^23 - 3 * q^25 + 4 * q^26 + 10 * q^28 - 7 * q^29 - 8 * q^31 + 17 * q^32 + 4 * q^34 - 10 * q^35 + 12 * q^37 - 2 * q^38 - 3 * q^40 - 13 * q^41 - 10 * q^43 + 44 * q^44 - 6 * q^46 + 13 * q^47 + 2 * q^49 + q^50 + 12 * q^52 + 4 * q^53 - 4 * q^55 - 9 * q^56 + 17 * q^58 - 2 * q^59 - q^61 - 84 * q^62 - 30 * q^64 + 4 * q^65 - 11 * q^67 - 22 * q^68 + 9 * q^70 + 20 * q^71 - 16 * q^73 - 16 * q^74 + 12 * q^76 - 2 * q^79 - 10 * q^80 - 58 * q^82 - 15 * q^83 + 2 * q^85 + 28 * q^86 + 24 * q^88 + 18 * q^89 + 20 * q^91 + 39 * q^92 + 31 * q^94 + 4 * q^95 + 18 * q^97 + 80 * q^98

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