LMFDB - Embedded newform 144.3.j.a.125.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(53,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("144.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			125.2
Character	$\chi$	$=$	144.125
Dual form			144.3.j.a.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95704 + 0.412300i) q^{2} +(3.66002 - 1.61377i) q^{4} +(5.52702 + 5.52702i) q^{5} -7.79421i q^{7} +(-6.49745 + 4.66725i) q^{8} +O(q^{10})$	\(q+(-1.95704 + 0.412300i) q^{2} +(3.66002 - 1.61377i) q^{4} +(5.52702 + 5.52702i) q^{5} -7.79421i q^{7} +(-6.49745 + 4.66725i) q^{8} +(-13.0954 - 8.53782i) q^{10} +(-2.48521 - 2.48521i) q^{11} +(13.3242 + 13.3242i) q^{13} +(3.21355 + 15.2536i) q^{14} +(10.7915 - 11.8129i) q^{16} -5.86338i q^{17} +(18.5712 + 18.5712i) q^{19} +(29.1484 + 11.3096i) q^{20} +(5.88832 + 3.83901i) q^{22} +34.3136 q^{23} +36.0959i q^{25} +(-31.5696 - 20.5825i) q^{26} +(-12.5781 - 28.5269i) q^{28} +(-21.4872 + 21.4872i) q^{29} -30.6117 q^{31} +(-16.2489 + 27.5676i) q^{32} +(2.41747 + 11.4749i) q^{34} +(43.0788 - 43.0788i) q^{35} +(30.3274 - 30.3274i) q^{37} +(-44.0016 - 28.6877i) q^{38} +(-61.7075 - 10.1156i) q^{40} -3.12709 q^{41} +(-9.94981 + 9.94981i) q^{43} +(-13.1065 - 5.08535i) q^{44} +(-67.1531 + 14.1475i) q^{46} -38.4052i q^{47} -11.7497 q^{49} +(-14.8823 - 70.6412i) q^{50} +(70.2692 + 27.2646i) q^{52} +(-61.1826 - 61.1826i) q^{53} -27.4717i q^{55} +(36.3775 + 50.6425i) q^{56} +(33.1922 - 50.9106i) q^{58} +(-2.98892 - 2.98892i) q^{59} +(3.88659 + 3.88659i) q^{61} +(59.9083 - 12.6212i) q^{62} +(20.4336 - 60.6504i) q^{64} +147.287i q^{65} +(-47.0242 - 47.0242i) q^{67} +(-9.46217 - 21.4601i) q^{68} +(-66.5455 + 102.068i) q^{70} -97.5416 q^{71} +106.904i q^{73} +(-46.8481 + 71.8560i) q^{74} +(97.9408 + 38.0013i) q^{76} +(-19.3703 + 19.3703i) q^{77} -96.8255 q^{79} +(124.935 - 5.64541i) q^{80} +(6.11984 - 1.28930i) q^{82} +(88.8242 - 88.8242i) q^{83} +(32.4070 - 32.4070i) q^{85} +(15.3699 - 23.5745i) q^{86} +(27.7467 + 4.54844i) q^{88} +54.8651 q^{89} +(103.852 - 103.852i) q^{91} +(125.588 - 55.3744i) q^{92} +(15.8345 + 75.1606i) q^{94} +205.287i q^{95} -5.00194 q^{97} +(22.9946 - 4.84439i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 40 q^{10} + 48 q^{16} + 64 q^{19} - 88 q^{22} - 120 q^{28} - 248 q^{34} - 184 q^{40} + 128 q^{43} + 24 q^{46} - 224 q^{49} + 632 q^{52} + 456 q^{58} + 64 q^{61} - 48 q^{64} - 64 q^{67} - 312 q^{70} - 576 q^{76} - 512 q^{79} - 720 q^{82} + 320 q^{85} - 400 q^{88} - 192 q^{91} + 696 q^{94}+O(q^{100}) $ 32 * q + 40 * q^10 + 48 * q^16 + 64 * q^19 - 88 * q^22 - 120 * q^28 - 248 * q^34 - 184 * q^40 + 128 * q^43 + 24 * q^46 - 224 * q^49 + 632 * q^52 + 456 * q^58 + 64 * q^61 - 48 * q^64 - 64 * q^67 - 312 * q^70 - 576 * q^76 - 512 * q^79 - 720 * q^82 + 320 * q^85 - 400 * q^88 - 192 * q^91 + 696 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.95704	+	0.412300i	−0.978520	+	0.206150i
$2$	−1.95704	+	0.412300i	−0.978520	+	0.206150i
$3$		0			0
$3$		0			0
$4$	3.66002	−	1.61377i	0.915005	−	0.403444i
$5$	5.52702	+	5.52702i	1.10540	+	1.10540i	0.993747	+	0.111658i	$0.0356160\pi$
$5$	5.52702	+	5.52702i	1.10540	+	1.10540i	0.111658	+	0.993747i	$0.464384\pi$
$6$		0			0
$7$		−	7.79421i		−	1.11346i	−0.830694	−	0.556729i	$-0.812056\pi$
$7$		−	7.79421i		−	1.11346i	0.830694	−	0.556729i	$-0.187944\pi$
$8$	−6.49745	+	4.66725i	−0.812181	+	0.583406i
$9$		0			0
$10$	−13.0954	−	8.53782i	−1.30954	−	0.853782i
$11$	−2.48521	−	2.48521i	−0.225929	−	0.225929i	0.585061	−	0.810989i	$-0.301071\pi$
$11$	−2.48521	−	2.48521i	−0.225929	−	0.225929i	−0.810989	+	0.585061i	$0.801071\pi$
$12$		0			0
$13$	13.3242	+	13.3242i	1.02494	+	1.02494i	0.999681	+	0.0252590i	$0.00804105\pi$
$13$	13.3242	+	13.3242i	1.02494	+	1.02494i	0.0252590	+	0.999681i	$0.491959\pi$
$14$	3.21355	+	15.2536i	0.229539	+	1.08954i
$15$		0			0
$16$	10.7915	−	11.8129i	0.674467	−	0.738305i
$17$		−	5.86338i		−	0.344905i	−0.985018	−	0.172452i	$-0.944831\pi$
$17$		−	5.86338i		−	0.344905i	0.985018	−	0.172452i	$-0.0551691\pi$
$18$		0			0
$19$	18.5712	+	18.5712i	0.977433	+	0.977433i	0.999751	−	0.0223177i	$-0.00710453\pi$
$19$	18.5712	+	18.5712i	0.977433	+	0.977433i	−0.0223177	+	0.999751i	$0.507105\pi$
$20$	29.1484	+	11.3096i	1.45742	+	0.565482i
$21$		0			0
$22$	5.88832	+	3.83901i	0.267651	+	0.174501i
$23$	34.3136			1.49190			0.745948	−	0.666004i	$-0.231997\pi$
$23$	34.3136			1.49190			0.745948	+	0.666004i	$0.231997\pi$
$24$		0			0
$25$			36.0959i			1.44384i
$26$	−31.5696	−	20.5825i	−1.21422	−	0.791634i
$27$		0			0
$28$	−12.5781	−	28.5269i	−0.449218	−	1.01882i
$29$	−21.4872	+	21.4872i	−0.740939	+	0.740939i	−0.972759	−	0.231820i	$-0.925532\pi$
$29$	−21.4872	+	21.4872i	−0.740939	+	0.740939i	0.231820	+	0.972759i	$0.425532\pi$
$30$		0			0
$31$	−30.6117			−0.987473			−0.493737	−	0.869612i	$-0.664369\pi$
$31$	−30.6117			−0.987473			−0.493737	+	0.869612i	$0.664369\pi$
$32$	−16.2489	+	27.5676i	−0.507778	+	0.861488i
$33$		0			0
$34$	2.41747	+	11.4749i	0.0711021	+	0.337496i
$35$	43.0788	−	43.0788i	1.23082	−	1.23082i
$36$		0			0
$37$	30.3274	−	30.3274i	0.819661	−	0.819661i	−0.166398	−	0.986059i	$-0.553214\pi$
$37$	30.3274	−	30.3274i	0.819661	−	0.819661i	0.986059	+	0.166398i	$0.0532137\pi$
$38$	−44.0016	−	28.6877i	−1.15794	−	0.754941i
$39$		0			0
$40$	−61.7075	−	10.1156i	−1.54269	−	0.252889i
$41$	−3.12709			−0.0762704			−0.0381352	−	0.999273i	$-0.512142\pi$
$41$	−3.12709			−0.0762704			−0.0381352	+	0.999273i	$0.512142\pi$
$42$		0			0
$43$	−9.94981	+	9.94981i	−0.231391	+	0.231391i	−0.813273	−	0.581882i	$-0.802316\pi$
$43$	−9.94981	+	9.94981i	−0.231391	+	0.231391i	0.581882	+	0.813273i	$0.302316\pi$
$44$	−13.1065	−	5.08535i	−0.297875	−	0.115576i
$45$		0			0
$46$	−67.1531	+	14.1475i	−1.45985	+	0.307554i
$47$		−	38.4052i		−	0.817132i	−0.912729	−	0.408566i	$-0.866029\pi$
$47$		−	38.4052i		−	0.817132i	0.912729	−	0.408566i	$-0.133971\pi$
$48$		0			0
$49$	−11.7497			−0.239790
$50$	−14.8823	−	70.6412i	−0.297647	−	1.41282i
$51$		0			0
$52$	70.2692	+	27.2646i	1.35133	+	0.524319i
$53$	−61.1826	−	61.1826i	−1.15439	−	1.15439i	−0.985663	−	0.168725i	$-0.946035\pi$
$53$	−61.1826	−	61.1826i	−1.15439	−	1.15439i	−0.168725	−	0.985663i	$-0.553965\pi$
$54$		0			0
$55$		−	27.4717i		−	0.499485i
$56$	36.3775	+	50.6425i	0.649598	+	0.904330i
$57$		0			0
$58$	33.1922	−	50.9106i	0.572280	−	0.877768i
$59$	−2.98892	−	2.98892i	−0.0506596	−	0.0506596i	0.681323	−	0.731983i	$-0.261405\pi$
$59$	−2.98892	−	2.98892i	−0.0506596	−	0.0506596i	−0.731983	+	0.681323i	$0.761405\pi$
$60$		0			0
$61$	3.88659	+	3.88659i	0.0637146	+	0.0637146i	0.738246	−	0.674531i	$-0.235654\pi$
$61$	3.88659	+	3.88659i	0.0637146	+	0.0637146i	−0.674531	+	0.738246i	$0.735654\pi$
$62$	59.9083	−	12.6212i	0.966263	−	0.203567i
$63$		0			0
$64$	20.4336	−	60.6504i	0.319275	−	0.947662i
$65$			147.287i			2.26595i
$66$		0			0
$67$	−47.0242	−	47.0242i	−0.701853	−	0.701853i	0.262955	−	0.964808i	$-0.415303\pi$
$67$	−47.0242	−	47.0242i	−0.701853	−	0.701853i	−0.964808	+	0.262955i	$0.915303\pi$
$68$	−9.46217	−	21.4601i	−0.139150	−	0.315589i
$69$		0			0
$70$	−66.5455	+	102.068i	−0.950651	+	1.45812i
$71$	−97.5416			−1.37383			−0.686913	−	0.726740i	$-0.741035\pi$
$71$	−97.5416			−1.37383			−0.686913	+	0.726740i	$0.741035\pi$
$72$		0			0
$73$			106.904i			1.46444i	0.681069	+	0.732219i	$0.261515\pi$
$73$			106.904i			1.46444i	−0.681069	+	0.732219i	$0.738485\pi$
$74$	−46.8481	+	71.8560i	−0.633082	+	0.971028i
$75$		0			0
$76$	97.9408	+	38.0013i	1.28869	+	0.500017i
$77$	−19.3703	+	19.3703i	−0.251562	+	0.251562i
$78$		0			0
$79$	−96.8255			−1.22564			−0.612820	−	0.790223i	$-0.709965\pi$
$79$	−96.8255			−1.22564			−0.612820	+	0.790223i	$0.709965\pi$
$80$	124.935	−	5.64541i	1.56168	−	0.0705677i
$81$		0			0
$82$	6.11984	−	1.28930i	0.0746321	−	0.0157231i
$83$	88.8242	−	88.8242i	1.07017	−	1.07017i	0.0728268	−	0.997345i	$-0.476798\pi$
$83$	88.8242	−	88.8242i	1.07017	−	1.07017i	0.997345	−	0.0728268i	$-0.0232020\pi$
$84$		0			0
$85$	32.4070	−	32.4070i	0.381259	−	0.381259i
$86$	15.3699	−	23.5745i	0.178720	−	0.274122i
$87$		0			0
$88$	27.7467	+	4.54844i	0.315303	+	0.0516868i
$89$	54.8651			0.616462			0.308231	−	0.951311i	$-0.400263\pi$
$89$	54.8651			0.616462			0.308231	+	0.951311i	$0.400263\pi$
$90$		0			0
$91$	103.852	−	103.852i	1.14123	−	1.14123i
$92$	125.588	−	55.3744i	1.36509	−	0.601896i
$93$		0			0
$94$	15.8345	+	75.1606i	0.168452	+	0.799581i
$95$			205.287i			2.16092i
$96$		0			0
$97$	−5.00194			−0.0515664			−0.0257832	−	0.999668i	$-0.508208\pi$
$97$	−5.00194			−0.0515664			−0.0257832	+	0.999668i	$0.508208\pi$
$98$	22.9946	−	4.84439i	0.234639	−	0.0494326i
$99$		0			0
$100$	58.2507	+	132.112i	0.582507	+	1.32112i
$101$	−37.2481	−	37.2481i	−0.368793	−	0.368793i	0.498244	−	0.867037i	$-0.333978\pi$
$101$	−37.2481	−	37.2481i	−0.368793	−	0.368793i	−0.867037	+	0.498244i	$0.833978\pi$
$102$		0			0
$103$		−	188.028i		−	1.82551i	−0.408505	−	0.912756i	$-0.633950\pi$
$103$		−	188.028i		−	1.82551i	0.408505	−	0.912756i	$-0.366050\pi$
$104$	−148.761	−	24.3860i	−1.43039	−	0.234481i
$105$		0			0
$106$	144.962	+	94.5113i	1.36757	+	0.891616i
$107$	35.2253	+	35.2253i	0.329208	+	0.329208i	0.852285	−	0.523077i	$-0.175216\pi$
$107$	35.2253	+	35.2253i	0.329208	+	0.329208i	−0.523077	+	0.852285i	$0.675216\pi$
$108$		0			0
$109$	−93.0073	−	93.0073i	−0.853278	−	0.853278i	0.137257	−	0.990535i	$-0.456171\pi$
$109$	−93.0073	−	93.0073i	−0.853278	−	0.853278i	−0.990535	+	0.137257i	$0.956171\pi$
$110$	11.3266	+	53.7632i	0.102969	+	0.488756i
$111$		0			0
$112$	−92.0721	−	84.1109i	−0.822072	−	0.750990i
$113$			3.80833i			0.0337021i	0.999858	+	0.0168510i	$0.00536410\pi$
$113$			3.80833i			0.0337021i	−0.999858	+	0.0168510i	$0.994636\pi$
$114$		0			0
$115$	189.652	+	189.652i	1.64915	+	1.64915i
$116$	−43.9681	+	113.319i	−0.379036	+	0.976890i
$117$		0			0
$118$	7.08176	+	4.61710i	0.0600149	+	0.0391280i
$119$	−45.7004			−0.384037
$120$		0			0
$121$		−	108.647i		−	0.897913i
$122$	−9.20866	−	6.00378i	−0.0754808	−	0.0492113i
$123$		0			0
$124$	−112.039	+	49.4003i	−0.903542	+	0.398390i
$125$	−61.3275	+	61.3275i	−0.490620	+	0.490620i
$126$		0			0
$127$	−173.704			−1.36775			−0.683875	−	0.729600i	$-0.739706\pi$
$127$	−173.704			−1.36775			−0.683875	+	0.729600i	$0.739706\pi$
$128$	−14.9833	+	127.120i	−0.117057	+	0.993125i
$129$		0			0
$130$	−60.7262	−	288.246i	−0.467124	−	2.21727i
$131$	−59.8594	+	59.8594i	−0.456942	+	0.456942i	−0.897650	−	0.440708i	$-0.854727\pi$
$131$	−59.8594	+	59.8594i	−0.456942	+	0.456942i	0.440708	+	0.897650i	$0.354727\pi$
$132$		0			0
$133$	144.748	−	144.748i	1.08833	−	1.08833i
$134$	111.416	+	72.6402i	0.831465	+	0.542091i
$135$		0			0
$136$	27.3658	+	38.0970i	0.201219	+	0.280125i
$137$	−13.0602			−0.0953299			−0.0476649	−	0.998863i	$-0.515178\pi$
$137$	−13.0602			−0.0953299			−0.0476649	+	0.998863i	$0.515178\pi$
$138$		0			0
$139$	−132.497	+	132.497i	−0.953219	+	0.953219i	−0.998954	−	0.0457344i	$-0.985437\pi$
$139$	−132.497	+	132.497i	−0.953219	+	0.953219i	0.0457344	+	0.998954i	$0.485437\pi$
$140$	88.1497	−	227.188i	0.629640	−	1.62277i
$141$		0			0
$142$	190.893	−	40.2164i	1.34432	−	0.283214i
$143$		−	66.2271i		−	0.463126i
$144$		0			0
$145$	−237.521			−1.63807
$146$	−44.0765	−	209.215i	−0.301894	−	1.43298i
$147$		0			0
$148$	62.0573	−	159.941i	0.419306	−	1.08068i
$149$	10.4768	+	10.4768i	0.0703142	+	0.0703142i	0.741389	−	0.671075i	$-0.234167\pi$
$149$	10.4768	+	10.4768i	0.0703142	+	0.0703142i	−0.671075	+	0.741389i	$0.734167\pi$
$150$		0			0
$151$			181.207i			1.20005i	0.799982	+	0.600024i	$0.204842\pi$
$151$			181.207i			1.20005i	−0.799982	+	0.600024i	$0.795158\pi$
$152$	−207.342	−	33.9891i	−1.36409	−	0.223612i
$153$		0			0
$154$	29.9221	−	45.8948i	0.194299	−	0.298018i
$155$	−169.191	−	169.191i	−1.09156	−	1.09156i
$156$		0			0
$157$	57.9518	+	57.9518i	0.369120	+	0.369120i	0.867156	−	0.498036i	$-0.165945\pi$
$157$	57.9518	+	57.9518i	0.369120	+	0.369120i	−0.498036	+	0.867156i	$0.665945\pi$
$158$	189.491	−	39.9211i	1.19931	−	0.252665i
$159$		0			0
$160$	−242.175	+	62.5588i	−1.51359	+	0.390993i
$161$		−	267.447i		−	1.66116i
$162$		0			0
$163$	87.8044	+	87.8044i	0.538677	+	0.538677i	0.923140	−	0.384463i	$-0.125613\pi$
$163$	87.8044	+	87.8044i	0.538677	+	0.538677i	−0.384463	+	0.923140i	$0.625613\pi$
$164$	−11.4452	+	5.04641i	−0.0697878	+	0.0307708i
$165$		0			0
$166$	−137.210	+	210.455i	−0.826569	+	1.26780i
$167$	86.9131			0.520438			0.260219	−	0.965550i	$-0.416205\pi$
$167$	86.9131			0.520438			0.260219	+	0.965550i	$0.416205\pi$
$168$		0			0
$169$			186.070i			1.10100i
$170$	−50.0605	+	76.7833i	−0.294474	+	0.451667i
$171$		0			0
$172$	−20.3597	+	52.4732i	−0.118371	+	0.305077i
$173$	216.007	−	216.007i	1.24860	−	1.24860i	0.292258	−	0.956339i	$-0.405593\pi$
$173$	216.007	−	216.007i	1.24860	−	1.24860i	0.956339	−	0.292258i	$-0.0944067\pi$
$174$		0			0
$175$	281.339			1.60765
$176$	−56.1766	+	2.53845i	−0.319186	+	0.0144230i
$177$		0			0
$178$	−107.373	+	22.6209i	−0.603221	+	0.127084i
$179$	−86.1380	+	86.1380i	−0.481218	+	0.481218i	−0.905520	−	0.424303i	$-0.860519\pi$
$179$	−86.1380	+	86.1380i	−0.481218	+	0.481218i	0.424303	+	0.905520i	$0.360519\pi$
$180$		0			0
$181$	1.84265	−	1.84265i	0.0101804	−	0.0101804i	−0.701998	−	0.712179i	$-0.747709\pi$
$181$	1.84265	−	1.84265i	0.0101804	−	0.0101804i	0.712179	+	0.701998i	$0.247709\pi$
$182$	−160.424	+	246.060i	−0.881451	+	1.35198i
$183$		0			0
$184$	−222.951	+	160.150i	−1.21169	+	0.870381i
$185$	335.241			1.81211
$186$		0			0
$187$	−14.5718	+	14.5718i	−0.0779238	+	0.0779238i
$188$	−61.9773	−	140.564i	−0.329667	−	0.747680i
$189$		0			0
$190$	−84.6398	−	401.755i	−0.445473	−	2.11450i
$191$			82.0328i			0.429491i	0.976670	+	0.214746i	$0.0688922\pi$
$191$			82.0328i			0.429491i	−0.976670	+	0.214746i	$0.931108\pi$
$192$		0			0
$193$	−91.2193			−0.472639			−0.236319	−	0.971675i	$-0.575941\pi$
$193$	−91.2193			−0.472639			−0.236319	+	0.971675i	$0.575941\pi$
$194$	9.78901	−	2.06230i	0.0504588	−	0.0106304i
$195$		0			0
$196$	−43.0041	+	18.9613i	−0.219409	+	0.0967416i
$197$	8.74282	+	8.74282i	0.0443798	+	0.0443798i	0.728948	−	0.684569i	$-0.240009\pi$
$197$	8.74282	+	8.74282i	0.0443798	+	0.0443798i	−0.684569	+	0.728948i	$0.740009\pi$
$198$		0			0
$199$		−	128.824i		−	0.647357i	−0.946167	−	0.323679i	$-0.895080\pi$
$199$		−	128.824i		−	0.647357i	0.946167	−	0.323679i	$-0.104920\pi$
$200$	−168.469	−	234.531i	−0.842343	−	1.17266i
$201$		0			0
$202$	88.2533	+	57.5386i	0.436898	+	0.284845i
$203$	167.476	+	167.476i	0.825005	+	0.825005i
$204$		0			0
$205$	−17.2835	−	17.2835i	−0.0843096	−	0.0843096i
$206$	77.5238	+	367.978i	0.376329	+	1.78630i
$207$		0			0
$208$	301.185	−	13.6096i	1.44801	−	0.0654309i
$209$		−	92.3070i		−	0.441660i
$210$		0			0
$211$	96.2826	+	96.2826i	0.456316	+	0.456316i	0.897444	−	0.441128i	$-0.145422\pi$
$211$	96.2826	+	96.2826i	0.456316	+	0.456316i	−0.441128	+	0.897444i	$0.645422\pi$
$212$	−322.664	−	125.194i	−1.52200	−	0.590540i
$213$		0			0
$214$	−83.4607	−	54.4140i	−0.390003	−	0.254271i
$215$	−109.986			−0.511561
$216$		0			0
$217$			238.594i			1.09951i
$218$	220.366	+	143.672i	1.01085	+	0.659047i
$219$		0			0
$220$	−44.3331	−	100.547i	−0.201514	−	0.457031i
$221$	78.1250	−	78.1250i	0.353507	−	0.353507i
$222$		0			0
$223$	−15.9317			−0.0714424			−0.0357212	−	0.999362i	$-0.511373\pi$
$223$	−15.9317			−0.0714424			−0.0357212	+	0.999362i	$0.511373\pi$
$224$	214.868	+	126.647i	0.959231	+	0.565390i
$225$		0			0
$226$	−1.57017	−	7.45306i	−0.00694767	−	0.0329782i
$227$	−66.7298	+	66.7298i	−0.293964	+	0.293964i	−0.838644	−	0.544680i	$-0.816651\pi$
$227$	−66.7298	+	66.7298i	−0.293964	+	0.293964i	0.544680	+	0.838644i	$0.316651\pi$
$228$		0			0
$229$	−109.514	+	109.514i	−0.478229	+	0.478229i	−0.904565	−	0.426336i	$-0.859804\pi$
$229$	−109.514	+	109.514i	−0.478229	+	0.478229i	0.426336	+	0.904565i	$0.359804\pi$
$230$	−449.350	−	292.963i	−1.95370	−	1.27375i
$231$		0			0
$232$	39.3259	−	239.898i	0.169508	−	1.03404i
$233$	85.9062			0.368696			0.184348	−	0.982861i	$-0.440983\pi$
$233$	85.9062			0.368696			0.184348	+	0.982861i	$0.440983\pi$
$234$		0			0
$235$	212.266	−	212.266i	0.903261	−	0.903261i
$236$	−15.7629	−	6.11605i	−0.0667921	−	0.0259155i
$237$		0			0
$238$	89.4376	−	18.8423i	0.375788	−	0.0791692i
$239$			47.0157i			0.196718i	0.995151	+	0.0983592i	$0.0313594\pi$
$239$			47.0157i			0.196718i	−0.995151	+	0.0983592i	$0.968641\pi$
$240$		0			0
$241$	312.627			1.29721			0.648603	−	0.761127i	$-0.275354\pi$
$241$	312.627			1.29721			0.648603	+	0.761127i	$0.275354\pi$
$242$	44.7953	+	212.627i	0.185104	+	0.878626i
$243$		0			0
$244$	20.4971	+	7.95291i	0.0840044	+	0.0325939i
$245$	−64.9408	−	64.9408i	−0.265064	−	0.265064i
$246$		0			0
$247$			494.894i			2.00362i
$248$	198.898	−	142.872i	0.802007	−	0.576097i
$249$		0			0
$250$	94.7352	−	145.306i	0.378941	−	0.581223i
$251$	−125.339	−	125.339i	−0.499360	−	0.499360i	0.411878	−	0.911239i	$-0.364873\pi$
$251$	−125.339	−	125.339i	−0.499360	−	0.499360i	−0.911239	+	0.411878i	$0.864873\pi$
$252$		0			0
$253$	−85.2767	−	85.2767i	−0.337062	−	0.337062i
$254$	339.946	−	71.6181i	1.33837	−	0.281961i
$255$		0			0
$256$	−23.0885	−	254.957i	−0.0901896	−	0.995925i
$257$			341.153i			1.32744i	0.747980	+	0.663722i	$0.231024\pi$
$257$			341.153i			1.32744i	−0.747980	+	0.663722i	$0.768976\pi$
$258$		0			0
$259$	−236.378	−	236.378i	−0.912658	−	0.912658i
$260$	237.687	+	539.071i	0.914181	+	2.07335i
$261$		0			0
$262$	92.4673	−	141.827i	0.352929	−	0.541326i
$263$	−161.903			−0.615599			−0.307799	−	0.951451i	$-0.599593\pi$
$263$	−161.903			−0.615599			−0.307799	+	0.951451i	$0.599593\pi$
$264$		0			0
$265$		−	676.315i		−	2.55213i
$266$	−223.598	+	342.957i	−0.840595	+	1.28931i
$267$		0			0
$268$	−247.996	−	96.2229i	−0.925357	−	0.359041i
$269$	−65.6610	+	65.6610i	−0.244093	+	0.244093i	−0.818541	−	0.574448i	$-0.805217\pi$
$269$	−65.6610	+	65.6610i	−0.244093	+	0.244093i	0.574448	+	0.818541i	$0.305217\pi$
$270$		0			0
$271$	200.090			0.738339			0.369170	−	0.929362i	$-0.379642\pi$
$271$	200.090			0.738339			0.369170	+	0.929362i	$0.379642\pi$
$272$	−69.2635	−	63.2745i	−0.254645	−	0.232627i
$273$		0			0
$274$	25.5593	−	5.38471i	0.0932822	−	0.0196522i
$275$	89.7061	−	89.7061i	0.326204	−	0.326204i
$276$		0			0
$277$	−70.7882	+	70.7882i	−0.255553	+	0.255553i	−0.823243	−	0.567690i	$-0.807837\pi$
$277$	−70.7882	+	70.7882i	−0.255553	+	0.255553i	0.567690	+	0.823243i	$0.307837\pi$
$278$	204.674	−	313.932i	0.736239	−	1.12925i
$279$		0			0
$280$	−78.8428	+	480.961i	−0.281581	+	1.71772i
$281$	−448.021			−1.59438			−0.797190	−	0.603729i	$-0.793681\pi$
$281$	−448.021			−1.59438			−0.797190	+	0.603729i	$0.793681\pi$
$282$		0			0
$283$	−187.254	+	187.254i	−0.661676	+	0.661676i	−0.955775	−	0.294099i	$-0.904980\pi$
$283$	−187.254	+	187.254i	−0.661676	+	0.661676i	0.294099	+	0.955775i	$0.404980\pi$
$284$	−357.004	+	157.410i	−1.25706	+	0.554261i
$285$		0			0
$286$	27.3054	+	129.609i	0.0954734	+	0.453179i
$287$			24.3732i			0.0849239i
$288$		0			0
$289$	254.621			0.881041
$290$	464.838	−	97.9297i	1.60289	−	0.337689i
$291$		0			0
$292$	172.519	+	391.271i	0.590818	+	1.33997i
$293$	200.350	+	200.350i	0.683788	+	0.683788i	0.960852	−	0.277063i	$-0.0893612\pi$
$293$	200.350	+	200.350i	0.683788	+	0.683788i	−0.277063	+	0.960852i	$0.589361\pi$
$294$		0			0
$295$		−	33.0396i		−	0.111999i
$296$	−55.5053	+	338.597i	−0.187518	+	1.14391i
$297$		0			0
$298$	−24.8231	−	16.1840i	−0.0832992	−	0.0543086i
$299$	457.202	+	457.202i	1.52910	+	1.52910i
$300$		0			0
$301$	77.5509	+	77.5509i	0.257644	+	0.257644i
$302$	−74.7116	−	354.630i	−0.247390	−	1.17427i
$303$		0			0
$304$	419.791	−	18.9690i	1.38089	−	0.0623981i
$305$			42.9625i			0.140861i
$306$		0			0
$307$	−118.542	−	118.542i	−0.386130	−	0.386130i	0.487174	−	0.873305i	$-0.338028\pi$
$307$	−118.542	−	118.542i	−0.386130	−	0.386130i	−0.873305	+	0.487174i	$0.838028\pi$
$308$	−39.6363	+	102.155i	−0.128689	+	0.331671i
$309$		0			0
$310$	400.872	+	261.357i	1.29314	+	0.843087i
$311$	3.29491			0.0105946			0.00529729	−	0.999986i	$-0.498314\pi$
$311$	3.29491			0.0105946			0.00529729	+	0.999986i	$0.498314\pi$
$312$		0			0
$313$		−	492.839i		−	1.57457i	−0.616592	−	0.787283i	$-0.711487\pi$
$313$		−	492.839i		−	1.57457i	0.616592	−	0.787283i	$-0.288513\pi$
$314$	−137.308	−	89.5205i	−0.437285	−	0.285097i
$315$		0			0
$316$	−354.383	+	156.255i	−1.12147	+	0.494476i
$317$	118.311	−	118.311i	0.373222	−	0.373222i	−0.495427	−	0.868649i	$-0.664988\pi$
$317$	118.311	−	118.311i	0.373222	−	0.373222i	0.868649	+	0.495427i	$0.164988\pi$
$318$		0			0
$319$	106.801			0.334799
$320$	448.153	−	222.279i	1.40048	−	0.694621i
$321$		0			0
$322$	110.268	+	523.406i	0.342449	+	1.62548i
$323$	108.890	−	108.890i	0.337121	−	0.337121i
$324$		0			0
$325$	−480.950	+	480.950i	−1.47985	+	1.47985i
$326$	−208.039	−	135.635i	−0.638155	−	0.416059i
$327$		0			0
$328$	20.3181	−	14.5949i	0.0619454	−	0.0444966i
$329$	−299.338			−0.909843
$330$		0			0
$331$	−52.2818	+	52.2818i	−0.157951	+	0.157951i	−0.781658	−	0.623707i	$-0.785626\pi$
$331$	−52.2818	+	52.2818i	−0.157951	+	0.157951i	0.623707	+	0.781658i	$0.285626\pi$
$332$	181.756	−	468.441i	0.547458	−	1.41097i
$333$		0			0
$334$	−170.092	+	35.8342i	−0.509259	+	0.107288i
$335$		−	519.807i		−	1.55166i
$336$		0			0
$337$	104.504			0.310100			0.155050	−	0.987907i	$-0.450446\pi$
$337$	104.504			0.310100			0.155050	+	0.987907i	$0.450446\pi$
$338$	−76.7164	−	364.146i	−0.226972	−	1.07735i
$339$		0			0
$340$	66.3127	−	170.908i	0.195037	−	0.502671i
$341$	76.0765	+	76.0765i	0.223098	+	0.223098i
$342$		0			0
$343$		−	290.337i		−	0.846463i
$344$	18.2101	−	111.087i	0.0529365	−	0.322926i
$345$		0			0
$346$	−333.676	+	511.795i	−0.964380	+	1.47918i
$347$	−312.769	−	312.769i	−0.901351	−	0.901351i	0.0942021	−	0.995553i	$-0.469970\pi$
$347$	−312.769	−	312.769i	−0.901351	−	0.901351i	−0.995553	+	0.0942021i	$0.969970\pi$
$348$		0			0
$349$	−114.172	−	114.172i	−0.327141	−	0.327141i	0.524357	−	0.851498i	$-0.324306\pi$
$349$	−114.172	−	114.172i	−0.327141	−	0.327141i	−0.851498	+	0.524357i	$0.824306\pi$
$350$	−550.593	+	115.996i	−1.57312	+	0.331417i
$351$		0			0
$352$	108.893	−	28.1295i	0.309356	−	0.0799132i
$353$		−	312.848i		−	0.886255i	−0.896459	−	0.443127i	$-0.853869\pi$
$353$		−	312.848i		−	0.886255i	0.896459	−	0.443127i	$-0.146131\pi$
$354$		0			0
$355$	−539.115	−	539.115i	−1.51863	−	1.51863i
$356$	200.807	−	88.5400i	0.564066	−	0.248708i
$357$		0			0
$358$	133.061	−	204.090i	0.371679	−	0.570085i
$359$	670.421			1.86747			0.933734	−	0.357967i	$-0.116530\pi$
$359$	670.421			1.86747			0.933734	+	0.357967i	$0.116530\pi$
$360$		0			0
$361$			328.781i			0.910751i
$362$	−2.84641	+	4.36586i	−0.00786302	+	0.0120604i
$363$		0			0
$364$	212.506	−	547.693i	0.583808	−	1.50465i
$365$	−590.861	+	590.861i	−1.61880	+	1.61880i
$366$		0			0
$367$	−531.445			−1.44808			−0.724039	−	0.689759i	$-0.757717\pi$
$367$	−531.445			−1.44808			−0.724039	+	0.689759i	$0.757717\pi$
$368$	370.294	−	405.343i	1.00623	−	1.10147i
$369$		0			0
$370$	−656.080	+	138.220i	−1.77319	+	0.373567i
$371$	−476.870	+	476.870i	−1.28536	+	1.28536i
$372$		0			0
$373$	25.9291	−	25.9291i	0.0695151	−	0.0695151i	−0.671494	−	0.741010i	$-0.734347\pi$
$373$	25.9291	−	25.9291i	0.0695151	−	0.0695151i	0.741010	+	0.671494i	$0.234347\pi$
$374$	22.5096	−	34.5255i	0.0601861	−	0.0923141i
$375$		0			0
$376$	179.247	+	249.536i	0.476720	+	0.663659i
$377$	−572.601			−1.51884
$378$		0			0
$379$	109.268	−	109.268i	0.288307	−	0.288307i	−0.548103	−	0.836411i	$-0.684650\pi$
$379$	109.268	−	109.268i	0.288307	−	0.288307i	0.836411	+	0.548103i	$0.184650\pi$
$380$	331.287	+	751.355i	0.871808	+	1.97725i
$381$		0			0
$382$	−33.8221	−	160.542i	−0.0885395	−	0.420266i
$383$		−	93.3821i		−	0.243818i	−0.992541	−	0.121909i	$-0.961098\pi$
$383$		−	93.3821i		−	0.243818i	0.992541	−	0.121909i	$-0.0389015\pi$
$384$		0			0
$385$	−214.120			−0.556156
$386$	178.520	−	37.6097i	0.462487	−	0.0974344i
$387$		0			0
$388$	−18.3072	+	8.07201i	−0.0471835	+	0.0208041i
$389$	−66.8268	−	66.8268i	−0.171791	−	0.171791i	0.615975	−	0.787766i	$-0.288762\pi$
$389$	−66.8268	−	66.8268i	−0.171791	−	0.171791i	−0.787766	+	0.615975i	$0.788762\pi$
$390$		0			0
$391$		−	201.194i		−	0.514562i
$392$	76.3430	−	54.8387i	0.194753	−	0.139895i
$393$		0			0
$394$	−20.7147	−	13.5054i	−0.0525754	−	0.0342776i
$395$	−535.157	−	535.157i	−1.35483	−	1.35483i
$396$		0			0
$397$	329.309	+	329.309i	0.829494	+	0.829494i	0.987447	−	0.157953i	$-0.0504893\pi$
$397$	329.309	+	329.309i	0.829494	+	0.829494i	−0.157953	+	0.987447i	$0.550489\pi$
$398$	53.1141	+	252.114i	0.133453	+	0.633452i
$399$		0			0
$400$	426.397	+	389.528i	1.06599	+	0.973820i
$401$		−	129.336i		−	0.322534i	−0.986911	−	0.161267i	$-0.948442\pi$
$401$		−	129.336i		−	0.322534i	0.986911	−	0.161267i	$-0.0515581\pi$
$402$		0			0
$403$	−407.877	−	407.877i	−1.01210	−	1.01210i
$404$	−196.439	−	76.2186i	−0.486234	−	0.188660i
$405$		0			0
$406$	−396.808	−	258.707i	−0.977359	−	0.637210i
$407$	−150.740			−0.370369
$408$		0			0
$409$			567.479i			1.38748i	0.720226	+	0.693739i	$0.244038\pi$
$409$			567.479i			1.38748i	−0.720226	+	0.693739i	$0.755962\pi$
$410$	40.9504	+	26.6985i	0.0998791	+	0.0651183i
$411$		0			0
$412$	−303.434	−	688.185i	−0.736491	−	1.67035i
$413$	−23.2962	+	23.2962i	−0.0564074	+	0.0564074i
$414$		0			0
$415$	981.867			2.36594
$416$	−583.821	+	150.813i	−1.40342	+	0.362532i
$417$		0			0
$418$	38.0581	+	180.649i	0.0910481	+	0.432173i
$419$	11.9979	−	11.9979i	0.0286346	−	0.0286346i	−0.692645	−	0.721279i	$-0.743555\pi$
$419$	11.9979	−	11.9979i	0.0286346	−	0.0286346i	0.721279	+	0.692645i	$0.243555\pi$
$420$		0			0
$421$	301.310	−	301.310i	0.715700	−	0.715700i	−0.252022	−	0.967722i	$-0.581095\pi$
$421$	301.310	−	301.310i	0.715700	−	0.715700i	0.967722	+	0.252022i	$0.0810954\pi$
$422$	−228.126	−	148.732i	−0.540583	−	0.352445i
$423$		0			0
$424$	683.085	+	111.976i	1.61105	+	0.264095i
$425$	211.644			0.497987
$426$		0			0
$427$	30.2929	−	30.2929i	0.0709436	−	0.0709436i
$428$	185.771	+	72.0795i	0.434044	+	0.168410i
$429$		0			0
$430$	215.246	−	45.3470i	0.500573	−	0.105458i
$431$		−	700.273i		−	1.62476i	−0.583126	−	0.812382i	$-0.698171\pi$
$431$		−	700.273i		−	1.62476i	0.583126	−	0.812382i	$-0.301829\pi$
$432$		0			0
$433$	−93.2906			−0.215452			−0.107726	−	0.994181i	$-0.534357\pi$
$433$	−93.2906			−0.215452			−0.107726	+	0.994181i	$0.534357\pi$
$434$	−98.3721	−	466.938i	−0.226664	−	1.07589i
$435$		0			0
$436$	−490.501	−	190.316i	−1.12500	−	0.436504i
$437$	637.246	+	637.246i	1.45823	+	1.45823i
$438$		0			0
$439$			98.5794i			0.224554i	0.993677	+	0.112277i	$0.0358145\pi$
$439$			98.5794i			0.224554i	−0.993677	+	0.112277i	$0.964186\pi$
$440$	128.217	+	178.496i	0.291402	+	0.405672i
$441$		0			0
$442$	−120.683	+	185.105i	−0.273038	+	0.418789i
$443$	574.790	+	574.790i	1.29749	+	1.29749i	0.930043	+	0.367450i	$0.119769\pi$
$443$	574.790	+	574.790i	1.29749	+	1.29749i	0.367450	+	0.930043i	$0.380231\pi$
$444$		0			0
$445$	303.241	+	303.241i	0.681440	+	0.681440i
$446$	31.1789	−	6.56861i	0.0699079	−	0.0147278i
$447$		0			0
$448$	−472.722	−	159.264i	−1.05518	−	0.355500i
$449$		−	79.1258i		−	0.176227i	−0.996110	−	0.0881133i	$-0.971916\pi$
$449$		−	79.1258i		−	0.176227i	0.996110	−	0.0881133i	$-0.0280838\pi$
$450$		0			0
$451$	7.77148	+	7.77148i	0.0172317	+	0.0172317i
$452$	6.14579	+	13.9386i	0.0135969	+	0.0308375i
$453$		0			0
$454$	103.080	−	158.106i	0.227049	−	0.348250i
$455$	1147.98			2.52304
$456$		0			0
$457$		−	721.867i		−	1.57958i	−0.613380	−	0.789788i	$-0.710190\pi$
$457$		−	721.867i		−	1.57958i	0.613380	−	0.789788i	$-0.289810\pi$
$458$	169.171	−	259.477i	0.369370	−	0.566543i
$459$		0			0
$460$	1000.19	+	388.074i	2.17432	+	0.843640i
$461$	57.6748	−	57.6748i	0.125108	−	0.125108i	−0.641780	−	0.766888i	$-0.721804\pi$
$461$	57.6748	−	57.6748i	0.125108	−	0.125108i	0.766888	+	0.641780i	$0.221804\pi$
$462$		0			0
$463$	−469.888			−1.01488			−0.507438	−	0.861688i	$-0.669407\pi$
$463$	−469.888			−1.01488			−0.507438	+	0.861688i	$0.669407\pi$
$464$	21.9475	+	485.705i	0.0473006	+	1.04678i
$465$		0			0
$466$	−168.122	+	35.4191i	−0.360777	+	0.0760066i
$467$	−284.381	+	284.381i	−0.608954	+	0.608954i	−0.942673	−	0.333719i	$-0.891696\pi$
$467$	−284.381	+	284.381i	−0.608954	+	0.608954i	0.333719	+	0.942673i	$0.391696\pi$
$468$		0			0
$469$	−366.516	+	366.516i	−0.781485	+	0.781485i
$470$	−327.897	+	502.931i	−0.697653	+	1.07007i
$471$		0			0
$472$	33.3703	+	5.47032i	0.0706999	+	0.0115897i
$473$	49.4548			0.104556
$474$		0			0
$475$	−670.346	+	670.346i	−1.41126	+	1.41126i
$476$	−167.264	+	73.7502i	−0.351396	+	0.154937i
$477$		0			0
$478$	−19.3846	−	92.0116i	−0.0405535	−	0.192493i
$479$		−	74.7175i		−	0.155986i	−0.996954	−	0.0779932i	$-0.975149\pi$
$479$		−	74.7175i		−	0.155986i	0.996954	−	0.0779932i	$-0.0248512\pi$
$480$		0			0
$481$	808.179			1.68021
$482$	−611.823	+	128.896i	−1.26934	+	0.267419i
$483$		0			0
$484$	−175.332	−	397.652i	−0.362257	−	0.821594i
$485$	−27.6458	−	27.6458i	−0.0570017	−	0.0570017i
$486$		0			0
$487$			465.139i			0.955111i	0.878602	+	0.477555i	$0.158477\pi$
$487$			465.139i			0.955111i	−0.878602	+	0.477555i	$0.841523\pi$
$488$	−43.3926	−	7.11324i	−0.0889193	−	0.0145763i
$489$		0			0
$490$	153.867	+	100.317i	0.314014	+	0.204728i
$491$	165.364	+	165.364i	0.336791	+	0.336791i	0.855158	−	0.518367i	$-0.173460\pi$
$491$	165.364	+	165.364i	0.336791	+	0.336791i	−0.518367	+	0.855158i	$0.673460\pi$
$492$		0			0
$493$	125.988	+	125.988i	0.255553	+	0.255553i
$494$	−204.045	−	968.528i	−0.413046	−	1.96058i
$495$		0			0
$496$	−330.345	+	361.612i	−0.666018	+	0.729057i
$497$			760.260i			1.52970i
$498$		0			0
$499$	502.645	+	502.645i	1.00730	+	1.00730i	0.999973	+	0.00733057i	$0.00233342\pi$
$499$	502.645	+	502.645i	1.00730	+	1.00730i	0.00733057	+	0.999973i	$0.497667\pi$
$500$	−125.491	+	323.429i	−0.250982	+	0.646857i
$501$		0			0
$502$	296.972	+	193.617i	0.591577	+	0.385691i
$503$	−19.2713			−0.0383127			−0.0191563	−	0.999817i	$-0.506098\pi$
$503$	−19.2713			−0.0383127			−0.0191563	+	0.999817i	$0.506098\pi$
$504$		0			0
$505$		−	411.742i		−	0.815330i
$506$	202.049	+	131.730i	0.399307	+	0.260337i
$507$		0			0
$508$	−635.760	+	280.319i	−1.25150	+	0.551810i
$509$	−136.252	+	136.252i	−0.267686	+	0.267686i	−0.828167	−	0.560481i	$-0.810616\pi$
$509$	−136.252	+	136.252i	−0.267686	+	0.267686i	0.560481	+	0.828167i	$0.310616\pi$
$510$		0			0
$511$	833.232			1.63059
$512$	150.304	+	489.441i	0.293562	+	0.955940i
$513$		0			0
$514$	−140.657	−	667.650i	−0.273652	−	1.29893i
$515$	1039.23	−	1039.23i	2.01793	−	2.01793i
$516$		0			0
$517$	−95.4452	+	95.4452i	−0.184613	+	0.184613i
$518$	560.061	+	365.144i	1.08120	+	0.704910i
$519$		0			0
$520$	−687.422	−	956.986i	−1.32197	−	1.84036i
$521$	−196.906			−0.377939			−0.188969	−	0.981983i	$-0.560515\pi$
$521$	−196.906			−0.377939			−0.188969	+	0.981983i	$0.560515\pi$
$522$		0			0
$523$	481.313	−	481.313i	0.920293	−	0.920293i	−0.0767569	−	0.997050i	$-0.524457\pi$
$523$	481.313	−	481.313i	0.920293	−	0.920293i	0.997050	+	0.0767569i	$0.0244565\pi$
$524$	−122.487	+	315.686i	−0.233754	+	0.602455i
$525$		0			0
$526$	316.850	−	66.7523i	0.602376	−	0.126906i
$527$			179.488i			0.340584i
$528$		0			0
$529$	648.424			1.22575
$530$	278.844	+	1323.58i	0.526121	+	2.49731i
$531$		0			0
$532$	296.190	−	763.371i	0.556748	−	1.43491i
$533$	−41.6660	−	41.6660i	−0.0781726	−	0.0781726i
$534$		0			0
$535$			389.382i			0.727817i
$536$	525.010	+	86.0637i	0.979497	+	0.160567i
$537$		0			0
$538$	101.429	−	155.573i	0.188530	−	0.289170i
$539$	29.2005	+	29.2005i	0.0541753	+	0.0541753i
$540$		0			0
$541$	−38.4319	−	38.4319i	−0.0710387	−	0.0710387i	0.670695	−	0.741733i	$-0.265996\pi$
$541$	−38.4319	−	38.4319i	−0.0710387	−	0.0710387i	−0.741733	+	0.670695i	$0.765996\pi$
$542$	−391.584	+	82.4970i	−0.722480	+	0.152208i
$543$		0			0
$544$	161.639	+	95.2735i	0.297131	+	0.175135i
$545$		−	1028.11i		−	1.88643i
$546$		0			0
$547$	249.883	+	249.883i	0.456824	+	0.456824i	0.897611	−	0.440788i	$-0.145301\pi$
$547$	249.883	+	249.883i	0.456824	+	0.456824i	−0.440788	+	0.897611i	$0.645301\pi$
$548$	−47.8006	+	21.0762i	−0.0872273	+	0.0384602i
$549$		0			0
$550$	−138.573	+	212.544i	−0.251951	+	0.386444i
$551$	−798.089			−1.44844
$552$		0			0
$553$			754.678i			1.36470i
$554$	109.349	−	167.721i	0.197382	−	0.302746i
$555$		0			0
$556$	−271.122	+	698.764i	−0.487630	+	1.25677i
$557$	561.819	−	561.819i	1.00865	−	1.00865i	0.00868977	−	0.999962i	$-0.497234\pi$
$557$	561.819	−	561.819i	1.00865	−	1.00865i	0.999962	−	0.00868977i	$-0.00276607\pi$
$558$		0			0
$559$	−265.147			−0.474323
$560$	−44.0015	−	973.768i	−0.0785741	−	1.73887i
$561$		0			0
$562$	876.795	−	184.719i	1.56013	−	0.328681i
$563$	−512.028	+	512.028i	−0.909464	+	0.909464i	−0.996229	−	0.0867652i	$-0.972347\pi$
$563$	−512.028	+	512.028i	−0.909464	+	0.909464i	0.0867652	+	0.996229i	$0.472347\pi$
$564$		0			0
$565$	−21.0487	+	21.0487i	−0.0372544	+	0.0372544i
$566$	289.259	−	443.669i	0.511059	−	0.783868i
$567$		0			0
$568$	633.771	−	455.251i	1.11579	−	0.801498i
$569$	−278.458			−0.489382			−0.244691	−	0.969601i	$-0.578686\pi$
$569$	−278.458			−0.489382			−0.244691	+	0.969601i	$0.578686\pi$
$570$		0			0
$571$	83.1512	−	83.1512i	0.145624	−	0.145624i	−0.630536	−	0.776160i	$-0.717165\pi$
$571$	83.1512	−	83.1512i	0.145624	−	0.145624i	0.776160	+	0.630536i	$0.217165\pi$
$572$	−106.876	−	242.392i	−0.186845	−	0.423763i
$573$		0			0
$574$	−10.0490	−	47.6993i	−0.0175070	−	0.0830998i
$575$			1238.58i			2.15406i
$576$		0			0
$577$	−1079.23			−1.87042			−0.935208	−	0.354098i	$-0.884788\pi$
$577$	−1079.23			−1.87042			−0.935208	+	0.354098i	$0.884788\pi$
$578$	−498.303	+	104.980i	−0.862116	+	0.181626i
$579$		0			0
$580$	−869.331	+	383.305i	−1.49885	+	0.660871i
$581$	−692.315	−	692.315i	−1.19159	−	1.19159i
$582$		0			0
$583$			304.104i			0.521619i
$584$	−498.947	−	694.603i	−0.854362	−	1.18939i
$585$		0			0
$586$	−474.697	−	309.489i	−0.810063	−	0.528138i
$587$	197.819	+	197.819i	0.337000	+	0.337000i	0.855237	−	0.518237i	$-0.173412\pi$
$587$	197.819	+	197.819i	0.337000	+	0.337000i	−0.518237	+	0.855237i	$0.673412\pi$
$588$		0			0
$589$	−568.496	−	568.496i	−0.965189	−	0.965189i
$590$	13.6222	+	64.6599i	0.0230885	+	0.109593i
$591$		0			0
$592$	−30.9771	−	685.532i	−0.0523261	−	1.15799i
$593$			313.761i			0.529108i	0.964371	+	0.264554i	$0.0852248\pi$
$593$			313.761i			0.529108i	−0.964371	+	0.264554i	$0.914775\pi$
$594$		0			0
$595$	−252.587	−	252.587i	−0.424516	−	0.424516i
$596$	55.2526	+	21.4381i	0.0927056	+	0.0359700i
$597$		0			0
$598$	−1083.27	−	706.259i	−1.81148	−	1.18104i
$599$	−1076.31			−1.79684			−0.898422	−	0.439133i	$-0.855286\pi$
$599$	−1076.31			−1.79684			−0.898422	+	0.439133i	$0.855286\pi$
$600$		0			0
$601$		−	25.5949i		−	0.0425873i	−0.999773	−	0.0212936i	$-0.993222\pi$
$601$		−	25.5949i		−	0.0425873i	0.999773	−	0.0212936i	$-0.00677848\pi$
$602$	−183.744	−	119.796i	−0.305223	−	0.198997i
$603$		0			0
$604$	292.427	+	663.222i	0.484151	+	1.09805i
$605$	600.497	−	600.497i	0.992557	−	0.992557i
$606$		0			0
$607$	−576.415			−0.949612			−0.474806	−	0.880090i	$-0.657482\pi$
$607$	−576.415			−0.949612			−0.474806	+	0.880090i	$0.657482\pi$
$608$	−813.727	+	210.203i	−1.33837	+	0.345728i
$609$		0			0
$610$	−17.7134	−	84.0795i	−0.0290384	−	0.137835i
$611$	511.719	−	511.719i	0.837511	−	0.837511i
$612$		0			0
$613$	−478.265	+	478.265i	−0.780205	+	0.780205i	−0.979865	−	0.199660i	$-0.936016\pi$
$613$	−478.265	+	478.265i	−0.780205	+	0.780205i	0.199660	+	0.979865i	$0.436016\pi$
$614$	280.866	+	183.117i	0.457437	+	0.298236i
$615$		0			0
$616$	35.4515	−	216.263i	0.0575511	−	0.351077i
$617$	1106.10			1.79271			0.896357	−	0.443334i	$-0.146204\pi$
$617$	1106.10			1.79271			0.896357	+	0.443334i	$0.146204\pi$
$618$		0			0
$619$	592.514	−	592.514i	0.957212	−	0.957212i	−0.0419094	−	0.999121i	$-0.513344\pi$
$619$	592.514	−	592.514i	0.957212	−	0.957212i	0.999121	+	0.0419094i	$0.0133441\pi$
$620$	−892.280	−	346.207i	−1.43916	−	0.558398i
$621$		0			0
$622$	−6.44828	+	1.35849i	−0.0103670	+	0.00218407i
$623$		−	427.630i		−	0.686405i
$624$		0			0
$625$	224.481			0.359170
$626$	203.197	+	964.506i	0.324596	+	1.54075i
$627$		0			0
$628$	305.626	+	118.584i	0.486665	+	0.188827i
$629$	−177.821	−	177.821i	−0.282705	−	0.282705i
$630$		0			0
$631$		−	845.724i		−	1.34029i	−0.742229	−	0.670146i	$-0.766231\pi$
$631$		−	845.724i		−	1.34029i	0.742229	−	0.670146i	$-0.233769\pi$
$632$	629.119	−	451.908i	0.995441	−	0.715045i
$633$		0			0
$634$	−182.761	+	280.320i	−0.288266	+	0.442145i
$635$	−960.067	−	960.067i	−1.51192	−	1.51192i
$636$		0			0
$637$	−156.555	−	156.555i	−0.245770	−	0.245770i
$638$	−209.013	+	44.0339i	−0.327607	+	0.0690187i
$639$		0			0
$640$	−785.408	+	619.782i	−1.22720	+	0.968409i
$641$			1167.54i			1.82143i	0.413035	+	0.910715i	$0.364469\pi$
$641$			1167.54i			1.82143i	−0.413035	+	0.910715i	$0.635531\pi$
$642$		0			0
$643$	296.182	+	296.182i	0.460626	+	0.460626i	0.898861	−	0.438235i	$-0.144396\pi$
$643$	296.182	+	296.182i	0.460626	+	0.460626i	−0.438235	+	0.898861i	$0.644396\pi$
$644$	−431.600	−	978.863i	−0.670186	−	1.51997i
$645$		0			0
$646$	−168.207	+	257.998i	−0.260383	+	0.399378i
$647$	113.278			0.175082			0.0875412	−	0.996161i	$-0.472099\pi$
$647$	113.278			0.175082			0.0875412	+	0.996161i	$0.472099\pi$
$648$		0			0
$649$			14.8562i			0.0228909i
$650$	742.944	−	1139.54i	1.14299	−	1.75313i
$651$		0			0
$652$	463.062	+	179.669i	0.710218	+	0.275566i
$653$	24.6005	−	24.6005i	0.0376730	−	0.0376730i	−0.688019	−	0.725692i	$-0.741520\pi$
$653$	24.6005	−	24.6005i	0.0376730	−	0.0376730i	0.725692	+	0.688019i	$0.241520\pi$
$654$		0			0
$655$	−661.689			−1.01021
$656$	−33.7458	+	36.9399i	−0.0514418	+	0.0563108i
$657$		0			0
$658$	585.817	−	123.417i	0.890300	−	0.187564i
$659$	−430.149	+	430.149i	−0.652730	+	0.652730i	−0.953650	−	0.300919i	$-0.902707\pi$
$659$	−430.149	+	430.149i	−0.652730	+	0.652730i	0.300919	+	0.953650i	$0.402707\pi$
$660$		0			0
$661$	755.093	−	755.093i	1.14235	−	1.14235i	0.154330	−	0.988019i	$-0.450678\pi$
$661$	755.093	−	755.093i	1.14235	−	1.14235i	0.988019	−	0.154330i	$-0.0493221\pi$
$662$	80.7618	−	123.873i	0.121997	−	0.187120i
$663$		0			0
$664$	−162.566	+	991.695i	−0.244829	+	1.49352i
$665$	1600.05			2.40609
$666$		0			0
$667$	−737.305	+	737.305i	−1.10540	+	1.10540i
$668$	318.103	−	140.258i	0.476203	−	0.209967i
$669$		0			0
$670$	214.316	+	1017.28i	0.319875	+	1.51833i
$671$		−	19.3180i		−	0.0287899i
$672$		0			0
$673$	−148.466			−0.220604			−0.110302	−	0.993898i	$-0.535182\pi$
$673$	−148.466			−0.220604			−0.110302	+	0.993898i	$0.535182\pi$
$674$	−204.518	+	43.0868i	−0.303439	+	0.0639270i
$675$		0			0
$676$	300.274	+	681.018i	0.444193	+	1.00742i
$677$	422.759	+	422.759i	0.624459	+	0.624459i	0.946668	−	0.322209i	$-0.104425\pi$
$677$	422.759	+	422.759i	0.624459	+	0.624459i	−0.322209	+	0.946668i	$0.604425\pi$
$678$		0			0
$679$			38.9862i			0.0574171i
$680$	−59.3114	+	361.815i	−0.0872226	+	0.532080i
$681$		0			0
$682$	−180.251	−	117.519i	−0.264298	−	0.172315i
$683$	473.364	+	473.364i	0.693066	+	0.693066i	0.962905	−	0.269839i	$-0.0869705\pi$
$683$	473.364	+	473.364i	0.693066	+	0.693066i	−0.269839	+	0.962905i	$0.586971\pi$
$684$		0			0
$685$	−72.1840	−	72.1840i	−0.105378	−	0.105378i
$686$	119.706	+	568.201i	0.174498	+	0.828281i
$687$		0			0
$688$	10.1629	+	224.909i	0.0147717	+	0.326903i
$689$		−	1630.42i		−	2.36636i
$690$		0			0
$691$	286.969	+	286.969i	0.415295	+	0.415295i	0.883579	−	0.468283i	$-0.155127\pi$
$691$	286.969	+	286.969i	0.415295	+	0.415295i	−0.468283	+	0.883579i	$0.655127\pi$
$692$	442.004	−	1139.18i	0.638734	−	1.64621i
$693$		0			0
$694$	741.056	+	483.147i	1.06780	+	0.696177i
$695$	−1464.63			−2.10739
$696$		0			0
$697$			18.3353i			0.0263060i
$698$	270.513	+	176.367i	0.387554	+	0.252674i
$699$		0			0
$700$	1029.71	−	454.018i	1.47101	−	0.648597i
$701$	−490.554	+	490.554i	−0.699791	+	0.699791i	−0.964365	−	0.264574i	$-0.914769\pi$
$701$	−490.554	+	490.554i	−0.699791	+	0.699791i	0.264574	+	0.964365i	$0.414769\pi$
$702$		0			0
$703$	1126.44			1.60233
$704$	−201.511	+	99.9472i	−0.286237	+	0.141970i
$705$		0			0
$706$	128.987	+	612.256i	0.182701	+	0.867218i
$707$	−290.319	+	290.319i	−0.410635	+	0.410635i
$708$		0			0
$709$	471.995	−	471.995i	0.665719	−	0.665719i	−0.291003	−	0.956722i	$-0.593989\pi$
$709$	471.995	−	471.995i	0.665719	−	0.665719i	0.956722	+	0.291003i	$0.0939890\pi$
$710$	1277.35	+	832.793i	1.79908	+	1.17295i
$711$		0			0
$712$	−356.483	+	256.069i	−0.500679	+	0.359648i
$713$	−1050.40			−1.47321
$714$		0			0
$715$	366.038	−	366.038i	0.511942	−	0.511942i
$716$	−176.259	+	454.274i	−0.246172	+	0.634461i
$717$		0			0
$718$	−1312.04	+	276.414i	−1.82736	+	0.384978i
$719$			1035.64i			1.44040i	0.693769	+	0.720198i	$0.255949\pi$
$719$			1035.64i			1.44040i	−0.693769	+	0.720198i	$0.744051\pi$
$720$		0			0
$721$	−1465.53			−2.03263
$722$	−135.556	−	643.438i	−0.187751	−	0.891189i
$723$		0			0
$724$	3.77051	−	9.71774i	0.00520788	−	0.0134223i
$725$	−775.602	−	775.602i	−1.06980	−	1.06980i
$726$		0			0
$727$			172.311i			0.237016i	0.992953	+	0.118508i	$0.0378112\pi$
$727$			172.311i			0.237016i	−0.992953	+	0.118508i	$0.962189\pi$
$728$	−190.070	+	1159.47i	−0.261085	+	1.59268i
$729$		0			0
$730$	912.727	−	1399.95i	1.25031	−	1.91774i
$731$	58.3395	+	58.3395i	0.0798078	+	0.0798078i
$732$		0			0
$733$	−729.510	−	729.510i	−0.995239	−	0.995239i	0.00474987	−	0.999989i	$-0.498488\pi$
$733$	−729.510	−	729.510i	−0.995239	−	0.995239i	−0.999989	+	0.00474987i	$0.998488\pi$
$734$	1040.06	−	219.114i	1.41697	−	0.298521i
$735$		0			0
$736$	−557.558	+	945.945i	−0.757552	+	1.28525i
$737$			233.730i			0.317137i
$738$		0			0
$739$	183.822	+	183.822i	0.248745	+	0.248745i	0.820455	−	0.571711i	$-0.193720\pi$
$739$	183.822	+	183.822i	0.248745	+	0.248745i	−0.571711	+	0.820455i	$0.693720\pi$
$740$	1226.99	−	541.003i	1.65809	−	0.731085i
$741$		0			0
$742$	736.641	−	1129.87i	0.992777	−	1.52273i
$743$	1276.92			1.71860			0.859300	−	0.511471i	$-0.170899\pi$
$743$	1276.92			1.71860			0.859300	+	0.511471i	$0.170899\pi$
$744$		0			0
$745$			115.811i			0.155451i
$746$	−40.0538	+	61.4349i	−0.0536914	+	0.0823525i
$747$		0			0
$748$	−29.8174	+	76.8484i	−0.0398628	+	0.102739i
$749$	274.553	−	274.553i	0.366560	−	0.366560i
$750$		0			0
$751$	−841.133			−1.12002			−0.560009	−	0.828487i	$-0.689202\pi$
$751$	−841.133			−1.12002			−0.560009	+	0.828487i	$0.689202\pi$
$752$	−453.676	−	414.449i	−0.603293	−	0.551128i
$753$		0			0
$754$	1120.60	−	236.083i	1.48621	−	0.313108i
$755$	−1001.54	+	1001.54i	−1.32654	+	1.32654i
$756$		0			0
$757$	695.488	−	695.488i	0.918743	−	0.918743i	−0.0781952	−	0.996938i	$-0.524916\pi$
$757$	695.488	−	695.488i	0.918743	−	0.918743i	0.996938	+	0.0781952i	$0.0249157\pi$
$758$	−168.792	+	258.894i	−0.222680	+	0.341549i
$759$		0			0
$760$	−958.126	−	1333.84i	−1.26069	−	1.75506i
$761$	−449.501			−0.590671			−0.295335	−	0.955394i	$-0.595431\pi$
$761$	−449.501			−0.590671			−0.295335	+	0.955394i	$0.595431\pi$
$762$		0			0
$763$	−724.918	+	724.918i	−0.950090	+	0.950090i
$764$	132.382	+	300.242i	0.173275	+	0.392986i
$765$		0			0
$766$	38.5014	+	182.753i	0.0502629	+	0.238580i
$767$		−	79.6500i		−	0.103846i
$768$		0			0
$769$	−1445.97			−1.88033			−0.940163	−	0.340725i	$-0.889328\pi$
$769$	−1445.97			−1.88033			−0.940163	+	0.340725i	$0.889328\pi$
$770$	419.041	−	88.2815i	0.544210	−	0.114651i
$771$		0			0
$772$	−333.864	+	147.207i	−0.432467	+	0.190683i
$773$	186.543	+	186.543i	0.241323	+	0.241323i	0.817397	−	0.576074i	$-0.195416\pi$
$773$	186.543	+	186.543i	0.241323	+	0.241323i	−0.576074	+	0.817397i	$0.695416\pi$
$774$		0			0
$775$		−	1104.96i		−	1.42575i
$776$	32.4999	−	23.3453i	0.0418813	−	0.0300841i
$777$		0			0
$778$	158.335	+	103.230i	0.203516	+	0.132687i
$779$	−58.0738	−	58.0738i	−0.0745492	−	0.0745492i
$780$		0			0
$781$	242.412	+	242.412i	0.310386	+	0.310386i
$782$	82.9521	+	393.745i	0.106077	+	0.503510i
$783$		0			0
$784$	−126.796	+	138.798i	−0.161730	+	0.177038i
$785$			640.602i			0.816053i
$786$		0			0
$787$	753.754	+	753.754i	0.957756	+	0.957756i	0.999143	−	0.0413871i	$-0.0131777\pi$
$787$	753.754	+	753.754i	0.957756	+	0.957756i	−0.0413871	+	0.999143i	$0.513178\pi$
$788$	46.1078	+	17.8899i	0.0585124	+	0.0227030i
$789$		0			0
$790$	1267.97	+	826.679i	1.60502	+	1.04643i
$791$	29.6829			0.0375258
$792$		0			0
$793$			103.572i			0.130607i
$794$	−780.245	−	508.697i	−0.982677	−	0.640677i
$795$		0			0
$796$	−207.893	−	471.498i	−0.261172	−	0.592335i
$797$	−531.870	+	531.870i	−0.667340	+	0.667340i	−0.957100	−	0.289759i	$-0.906425\pi$
$797$	−531.870	+	531.870i	−0.667340	+	0.667340i	0.289759	+	0.957100i	$0.406425\pi$
$798$		0			0
$799$	−225.184			−0.281833
$800$	−995.079	−	586.519i	−1.24385	−	0.733149i
$801$		0			0
$802$	53.3253	+	253.116i	0.0664903	+	0.315606i
$803$	265.679	−	265.679i	0.330858	−	0.330858i
$804$		0			0
$805$	1478.19	−	1478.19i	1.83626	−	1.83626i
$806$	966.398	+	630.064i	1.19901	+	0.781717i
$807$		0			0
$808$	415.863	+	68.1714i	0.514682	+	0.0843706i
$809$	540.279			0.667836			0.333918	−	0.942602i	$-0.391629\pi$
$809$	540.279			0.667836			0.333918	+	0.942602i	$0.391629\pi$
$810$		0			0
$811$	702.871	−	702.871i	0.866672	−	0.866672i	−0.125430	−	0.992102i	$-0.540031\pi$
$811$	702.871	−	702.871i	0.866672	−	0.866672i	0.992102	+	0.125430i	$0.0400311\pi$
$812$	883.234	+	342.697i	1.08773	+	0.422040i
$813$		0			0
$814$	295.005	−	62.1502i	0.362414	−	0.0763516i
$815$			970.594i			1.19091i
$816$		0			0
$817$	−369.560			−0.452338
$818$	−233.971	−	1110.58i	−0.286028	−	1.35768i
$819$		0			0
$820$	−91.1495	−	35.3662i	−0.111158	−	0.0431295i
$821$	−286.031	−	286.031i	−0.348393	−	0.348393i	0.511117	−	0.859511i	$-0.329232\pi$
$821$	−286.031	−	286.031i	−0.348393	−	0.348393i	−0.859511	+	0.511117i	$0.829232\pi$
$822$		0			0
$823$		−	215.600i		−	0.261969i	−0.991384	−	0.130984i	$-0.958186\pi$
$823$		−	215.600i		−	0.261969i	0.991384	−	0.130984i	$-0.0418138\pi$
$824$	877.572	+	1221.70i	1.06501	+	1.48265i
$825$		0			0
$826$	35.9867	−	55.1967i	0.0435674	−	0.0668241i
$827$	−375.162	−	375.162i	−0.453642	−	0.453642i	0.442920	−	0.896561i	$-0.353943\pi$
$827$	−375.162	−	375.162i	−0.453642	−	0.453642i	−0.896561	+	0.442920i	$0.853943\pi$
$828$		0			0
$829$	22.5151	+	22.5151i	0.0271594	+	0.0271594i	0.720556	−	0.693397i	$-0.243887\pi$
$829$	22.5151	+	22.5151i	0.0271594	+	0.0271594i	−0.693397	+	0.720556i	$0.743887\pi$
$830$	−1921.55	+	404.823i	−2.31512	+	0.487739i
$831$		0			0
$832$	1080.38	−	535.857i	1.29853	−	0.644058i
$833$			68.8929i			0.0827046i
$834$		0			0
$835$	480.370	+	480.370i	0.575294	+	0.575294i
$836$	−148.963	−	337.845i	−0.178185	−	0.404121i
$837$		0			0
$838$	−18.5337	+	28.4271i	−0.0221165	+	0.0339226i
$839$	1139.61			1.35830			0.679151	−	0.733999i	$-0.262348\pi$
$839$	1139.61			1.35830			0.679151	+	0.733999i	$0.262348\pi$
$840$		0			0
$841$		−	82.4023i		−	0.0979814i
$842$	−465.445	+	713.905i	−0.552786	+	0.847868i
$843$		0			0
$844$	507.774	+	197.018i	0.601628	+	0.233433i
$845$	−1028.41	+	1028.41i	−1.21705	+	1.21705i
$846$		0			0
$847$	−846.821			−0.999788
$848$	−1382.99	+	62.4931i	−1.63089	+	0.0736947i
$849$		0			0
$850$	−414.197	+	87.2609i	−0.487290	+	0.102660i
$851$	1040.64	−	1040.64i	1.22285	−	1.22285i
$852$		0			0
$853$	−405.464	+	405.464i	−0.475339	+	0.475339i	−0.903637	−	0.428298i	$-0.859113\pi$
$853$	−405.464	+	405.464i	−0.475339	+	0.475339i	0.428298	+	0.903637i	$0.359113\pi$
$854$	−46.7947	+	71.7742i	−0.0547947	+	0.0840447i
$855$		0			0
$856$	−393.280	−	64.4694i	−0.459439	−	0.0753147i
$857$	1006.21			1.17411			0.587056	−	0.809546i	$-0.300287\pi$
$857$	1006.21			1.17411			0.587056	+	0.809546i	$0.300287\pi$
$858$		0			0
$859$	626.283	−	626.283i	0.729083	−	0.729083i	−0.241354	−	0.970437i	$-0.577591\pi$
$859$	626.283	−	626.283i	0.729083	−	0.729083i	0.970437	+	0.241354i	$0.0775914\pi$
$860$	−402.549	+	177.492i	−0.468081	+	0.206386i
$861$		0			0
$862$	288.722	+	1370.46i	0.334945	+	1.58986i
$863$			926.795i			1.07392i	0.843607	+	0.536961i	$0.180428\pi$
$863$			926.795i			1.07392i	−0.843607	+	0.536961i	$0.819572\pi$
$864$		0			0
$865$	2387.76			2.76041
$866$	182.573	−	38.4637i	0.210824	−	0.0444153i
$867$		0			0
$868$	385.036	+	873.257i	0.443590	+	1.00606i
$869$	240.632	+	240.632i	0.276907	+	0.276907i
$870$		0			0
$871$		−	1253.12i		−	1.43872i
$872$	1038.40	+	170.222i	1.19082	+	0.195209i
$873$		0			0
$874$	−1509.85	−	984.380i	−1.72752	−	1.12629i
$875$	478.000	+	478.000i	0.546285	+	0.546285i
$876$		0			0
$877$	−558.537	−	558.537i	−0.636872	−	0.636872i	0.312911	−	0.949783i	$-0.398696\pi$
$877$	−558.537	−	558.537i	−0.636872	−	0.636872i	−0.949783	+	0.312911i	$0.898696\pi$
$878$	−40.6442	−	192.924i	−0.0462918	−	0.219731i
$879$		0			0
$880$	−324.520	−	296.460i	−0.368772	−	0.336886i
$881$		−	969.827i		−	1.10083i	−0.834893	−	0.550413i	$-0.814470\pi$
$881$		−	969.827i		−	1.10083i	0.834893	−	0.550413i	$-0.185530\pi$
$882$		0			0
$883$	549.585	+	549.585i	0.622407	+	0.622407i	0.946146	−	0.323739i	$-0.104940\pi$
$883$	549.585	+	549.585i	0.622407	+	0.622407i	−0.323739	+	0.946146i	$0.604940\pi$
$884$	159.863	−	412.015i	0.180840	−	0.466080i
$885$		0			0
$886$	−1361.87	−	887.901i	−1.53710	−	1.00215i
$887$	−1552.40			−1.75017			−0.875086	−	0.483968i	$-0.839195\pi$
$887$	−1552.40			−1.75017			−0.875086	+	0.483968i	$0.839195\pi$
$888$		0			0
$889$			1353.89i			1.52293i
$890$	−718.481	−	468.429i	−0.807282	−	0.526324i
$891$		0			0
$892$	−58.3101	+	25.7101i	−0.0653701	+	0.0288230i
$893$	713.232	−	713.232i	0.798692	−	0.798692i
$894$		0			0
$895$	−952.173			−1.06388
$896$	990.800	+	116.783i	1.10580	+	0.130338i
$897$		0			0
$898$	32.6235	+	154.852i	0.0363291	+	0.172441i
$899$	657.760	−	657.760i	0.731657	−	0.731657i
$900$		0			0
$901$	−358.737	+	358.737i	−0.398154	+	0.398154i
$902$	−18.4133	−	12.0049i	−0.0204138	−	0.0133092i
$903$		0			0
$904$	−17.7744	−	24.7444i	−0.0196620	−	0.0273722i
$905$	20.3687			0.0225069
$906$		0			0
$907$	−451.019	+	451.019i	−0.497265	+	0.497265i	−0.910586	−	0.413321i	$-0.864369\pi$
$907$	−451.019	+	451.019i	−0.497265	+	0.497265i	0.413321	+	0.910586i	$0.364369\pi$
$908$	−136.545	+	351.919i	−0.150380	+	0.387576i
$909$		0			0
$910$	−2246.65	+	473.312i	−2.46884	+	0.520124i
$911$		−	1490.19i		−	1.63578i	−0.575378	−	0.817888i	$-0.695145\pi$
$911$		−	1490.19i		−	1.63578i	0.575378	−	0.817888i	$-0.304855\pi$
$912$		0			0
$913$	−441.494			−0.483565
$914$	297.625	+	1412.72i	0.325629	+	1.54565i
$915$		0			0
$916$	−224.093	+	577.556i	−0.244643	+	0.630520i
$917$	466.557	+	466.557i	0.508786	+	0.508786i
$918$		0			0
$919$			949.287i			1.03296i	0.856300	+	0.516478i	$0.172757\pi$
$919$			949.287i			1.03296i	−0.856300	+	0.516478i	$0.827243\pi$
$920$	−2117.41	−	347.101i	−2.30153	−	0.377284i
$921$		0			0
$922$	−89.0926	+	136.651i	−0.0966297	+	0.148212i
$923$	−1299.67	−	1299.67i	−1.40809	−	1.40809i
$924$		0			0
$925$	1094.70	+	1094.70i	1.18346	+	1.18346i
$926$	919.589	−	193.734i	0.993077	−	0.209216i
$927$		0			0
$928$	−243.208	−	941.496i	−0.262078	−	1.01454i
$929$			1078.41i			1.16083i	0.814322	+	0.580413i	$0.197109\pi$
$929$			1078.41i			1.16083i	−0.814322	+	0.580413i	$0.802891\pi$
$930$		0			0
$931$	−218.206	−	218.206i	−0.234378	−	0.234378i
$932$	314.418	−	138.633i	0.337359	−	0.148748i
$933$		0			0
$934$	439.296	−	673.797i	0.470338	−	0.721410i
$935$	−161.077			−0.172275
$936$		0			0
$937$			1158.42i			1.23631i	0.786056	+	0.618155i	$0.212120\pi$
$937$			1158.42i			1.23631i	−0.786056	+	0.618155i	$0.787880\pi$
$938$	566.173	−	868.402i	0.603596	−	0.925801i
$939$		0			0
$940$	434.349	−	1119.45i	0.462073	−	1.19090i
$941$	1027.40	−	1027.40i	1.09181	−	1.09181i	0.0964770	−	0.995335i	$-0.469243\pi$
$941$	1027.40	−	1027.40i	1.09181	−	1.09181i	0.995335	−	0.0964770i	$-0.0307574\pi$
$942$		0			0
$943$	−107.302			−0.113788
$944$	−67.5625	+	3.05294i	−0.0715705	+	0.00323405i
$945$		0			0
$946$	−96.7851	+	20.3902i	−0.102310	+	0.0215541i
$947$	890.208	−	890.208i	0.940030	−	0.940030i	−0.0582710	−	0.998301i	$-0.518559\pi$
$947$	890.208	−	890.208i	0.940030	−	0.940030i	0.998301	+	0.0582710i	$0.0185588\pi$
$948$		0			0
$949$	−1424.41	+	1424.41i	−1.50096	+	1.50096i
$950$	1035.51	−	1588.28i	1.09001	−	1.67187i
$951$		0			0
$952$	296.936	−	213.295i	0.311908	−	0.224049i
$953$	−566.070			−0.593987			−0.296994	−	0.954879i	$-0.595984\pi$
$953$	−566.070			−0.593987			−0.296994	+	0.954879i	$0.595984\pi$
$954$		0			0
$955$	−453.397	+	453.397i	−0.474761	+	0.474761i
$956$	75.8727	+	172.078i	0.0793648	+	0.179998i
$957$		0			0
$958$	30.8060	+	146.225i	0.0321566	+	0.152636i
$959$			101.794i			0.106146i
$960$		0			0
$961$	−23.9259			−0.0248968
$962$	−1581.64	+	333.212i	−1.64412	+	0.346374i
$963$		0			0
$964$	1144.22	−	504.509i	1.18695	−	0.523349i
$965$	−504.171	−	504.171i	−0.522457	−	0.522457i
$966$		0			0
$967$		−	461.918i		−	0.477682i	−0.971059	−	0.238841i	$-0.923233\pi$
$967$		−	461.918i		−	0.477682i	0.971059	−	0.238841i	$-0.0767674\pi$
$968$	507.084	+	705.931i	0.523847	+	0.729267i
$969$		0			0
$970$	65.5024	+	42.7057i	0.0675283	+	0.0440265i
$971$	703.059	+	703.059i	0.724057	+	0.724057i	0.969429	−	0.245372i	$-0.0789101\pi$
$971$	703.059	+	703.059i	0.724057	+	0.724057i	−0.245372	+	0.969429i	$0.578910\pi$
$972$		0			0
$973$	1032.71	+	1032.71i	1.06137	+	1.06137i
$974$	−191.777	−	910.296i	−0.196896	−	0.934595i
$975$		0			0
$976$	87.8539	−	3.96984i	0.0900142	−	0.00406746i
$977$			1020.60i			1.04462i	0.852755	+	0.522311i	$0.174930\pi$
$977$			1020.60i			1.04462i	−0.852755	+	0.522311i	$0.825070\pi$
$978$		0			0
$979$	−136.352	−	136.352i	−0.139276	−	0.139276i
$980$	−342.484	−	132.885i	−0.349474	−	0.135597i
$981$		0			0
$982$	−391.805	−	255.445i	−0.398987	−	0.260128i
$983$	−837.639			−0.852125			−0.426063	−	0.904694i	$-0.640100\pi$
$983$	−837.639			−0.852125			−0.426063	+	0.904694i	$0.640100\pi$
$984$		0			0
$985$			96.6435i			0.0981152i
$986$	−298.508	−	194.619i	−0.302747	−	0.197382i
$987$		0			0
$988$	798.648	+	1811.32i	0.808348	+	1.83332i
$989$	−341.414	+	341.414i	−0.345211	+	0.345211i
$990$		0			0
$991$	273.535			0.276019			0.138009	−	0.990431i	$-0.455930\pi$
$991$	273.535			0.276019			0.138009	+	0.990431i	$0.455930\pi$
$992$	497.406	−	843.891i	0.501417	−	0.850696i
$993$		0			0
$994$	−313.455	−	1487.86i	−0.315347	−	1.49684i
$995$	712.013	−	712.013i	0.715591	−	0.715591i
$996$		0			0
$997$	77.9043	−	77.9043i	0.0781387	−	0.0781387i	−0.666957	−	0.745096i	$-0.732404\pi$
$997$	77.9043	−	77.9043i	0.0781387	−	0.0781387i	0.745096	+	0.666957i	$0.232404\pi$
$998$	−1190.94	−	776.456i	−1.19332	−	0.778012i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.j.a.125.2	yes	32
3.2	odd	2	inner	144.3.j.a.125.15	yes	32
4.3	odd	2		576.3.j.a.17.15		32
8.3	odd	2		1152.3.j.b.161.2		32
8.5	even	2		1152.3.j.a.161.2		32
12.11	even	2		576.3.j.a.17.2		32
16.3	odd	4		1152.3.j.b.737.15		32
16.5	even	4	inner	144.3.j.a.53.15	yes	32
16.11	odd	4		576.3.j.a.305.2		32
16.13	even	4		1152.3.j.a.737.15		32
24.5	odd	2		1152.3.j.a.161.15		32
24.11	even	2		1152.3.j.b.161.15		32
48.5	odd	4	inner	144.3.j.a.53.2	✓	32
48.11	even	4		576.3.j.a.305.15		32
48.29	odd	4		1152.3.j.a.737.2		32
48.35	even	4		1152.3.j.b.737.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.j.a.53.2	✓	32	48.5	odd	4	inner
144.3.j.a.53.15	yes	32	16.5	even	4	inner
144.3.j.a.125.2	yes	32	1.1	even	1	trivial
144.3.j.a.125.15	yes	32	3.2	odd	2	inner
576.3.j.a.17.2		32	12.11	even	2
576.3.j.a.17.15		32	4.3	odd	2
576.3.j.a.305.2		32	16.11	odd	4
576.3.j.a.305.15		32	48.11	even	4
1152.3.j.a.161.2		32	8.5	even	2
1152.3.j.a.161.15		32	24.5	odd	2
1152.3.j.a.737.2		32	48.29	odd	4
1152.3.j.a.737.15		32	16.13	even	4
1152.3.j.b.161.2		32	8.3	odd	2
1152.3.j.b.161.15		32	24.11	even	2
1152.3.j.b.737.2		32	48.35	even	4
1152.3.j.b.737.15		32	16.3	odd	4

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.95704 + 0.412300i) q^{2} +(3.66002 - 1.61377i) q^{4} +(5.52702 + 5.52702i) q^{5} -7.79421i q^{7} +(-6.49745 + 4.66725i) q^{8} +O(q^{10})\)	\(q+(-1.95704 + 0.412300i) q^{2} +(3.66002 - 1.61377i) q^{4} +(5.52702 + 5.52702i) q^{5} -7.79421i q^{7} +(-6.49745 + 4.66725i) q^{8} +(-13.0954 - 8.53782i) q^{10} +(-2.48521 - 2.48521i) q^{11} +(13.3242 + 13.3242i) q^{13} +(3.21355 + 15.2536i) q^{14} +(10.7915 - 11.8129i) q^{16} -5.86338i q^{17} +(18.5712 + 18.5712i) q^{19} +(29.1484 + 11.3096i) q^{20} +(5.88832 + 3.83901i) q^{22} +34.3136 q^{23} +36.0959i q^{25} +(-31.5696 - 20.5825i) q^{26} +(-12.5781 - 28.5269i) q^{28} +(-21.4872 + 21.4872i) q^{29} -30.6117 q^{31} +(-16.2489 + 27.5676i) q^{32} +(2.41747 + 11.4749i) q^{34} +(43.0788 - 43.0788i) q^{35} +(30.3274 - 30.3274i) q^{37} +(-44.0016 - 28.6877i) q^{38} +(-61.7075 - 10.1156i) q^{40} -3.12709 q^{41} +(-9.94981 + 9.94981i) q^{43} +(-13.1065 - 5.08535i) q^{44} +(-67.1531 + 14.1475i) q^{46} -38.4052i q^{47} -11.7497 q^{49} +(-14.8823 - 70.6412i) q^{50} +(70.2692 + 27.2646i) q^{52} +(-61.1826 - 61.1826i) q^{53} -27.4717i q^{55} +(36.3775 + 50.6425i) q^{56} +(33.1922 - 50.9106i) q^{58} +(-2.98892 - 2.98892i) q^{59} +(3.88659 + 3.88659i) q^{61} +(59.9083 - 12.6212i) q^{62} +(20.4336 - 60.6504i) q^{64} +147.287i q^{65} +(-47.0242 - 47.0242i) q^{67} +(-9.46217 - 21.4601i) q^{68} +(-66.5455 + 102.068i) q^{70} -97.5416 q^{71} +106.904i q^{73} +(-46.8481 + 71.8560i) q^{74} +(97.9408 + 38.0013i) q^{76} +(-19.3703 + 19.3703i) q^{77} -96.8255 q^{79} +(124.935 - 5.64541i) q^{80} +(6.11984 - 1.28930i) q^{82} +(88.8242 - 88.8242i) q^{83} +(32.4070 - 32.4070i) q^{85} +(15.3699 - 23.5745i) q^{86} +(27.7467 + 4.54844i) q^{88} +54.8651 q^{89} +(103.852 - 103.852i) q^{91} +(125.588 - 55.3744i) q^{92} +(15.8345 + 75.1606i) q^{94} +205.287i q^{95} -5.00194 q^{97} +(22.9946 - 4.84439i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 40 q^{10} + 48 q^{16} + 64 q^{19} - 88 q^{22} - 120 q^{28} - 248 q^{34} - 184 q^{40} + 128 q^{43} + 24 q^{46} - 224 q^{49} + 632 q^{52} + 456 q^{58} + 64 q^{61} - 48 q^{64} - 64 q^{67} - 312 q^{70} - 576 q^{76} - 512 q^{79} - 720 q^{82} + 320 q^{85} - 400 q^{88} - 192 q^{91} + 696 q^{94}+O(q^{100}) \) 32 * q + 40 * q^10 + 48 * q^16 + 64 * q^19 - 88 * q^22 - 120 * q^28 - 248 * q^34 - 184 * q^40 + 128 * q^43 + 24 * q^46 - 224 * q^49 + 632 * q^52 + 456 * q^58 + 64 * q^61 - 48 * q^64 - 64 * q^67 - 312 * q^70 - 576 * q^76 - 512 * q^79 - 720 * q^82 + 320 * q^85 - 400 * q^88 - 192 * q^91 + 696 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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