LMFDB - Embedded newform 144.3.j.a.53.2

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			53.2
Character	$\chi$	$=$	144.53
Dual form			144.3.j.a.125.2

$q$-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 $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−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	0.111658	−	0.993747i	$-0.464384\pi$
$5$	5.52702	−	5.52702i	1.10540	−	1.10540i	0.993747	−	0.111658i	$-0.0356160\pi$
$6$		0			0
$7$			7.79421i			1.11346i	0.830694	+	0.556729i	$0.187944\pi$
$7$			7.79421i			1.11346i	−0.830694	+	0.556729i	$0.812056\pi$
$8$	−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	−0.810989	−	0.585061i	$-0.801071\pi$
$11$	−2.48521	+	2.48521i	−0.225929	+	0.225929i	0.585061	+	0.810989i	$0.301071\pi$
$12$		0			0
$13$	13.3242	−	13.3242i	1.02494	−	1.02494i	0.0252590	−	0.999681i	$-0.491959\pi$
$13$	13.3242	−	13.3242i	1.02494	−	1.02494i	0.999681	−	0.0252590i	$-0.00804105\pi$
$14$	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	$0.0551691\pi$
$17$			5.86338i			0.344905i	−0.985018	+	0.172452i	$0.944831\pi$
$18$		0			0
$19$	18.5712	−	18.5712i	0.977433	−	0.977433i	−0.0223177	−	0.999751i	$-0.507105\pi$
$19$	18.5712	−	18.5712i	0.977433	−	0.977433i	0.999751	+	0.0223177i	$0.00710453\pi$
$20$	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	0.231820	−	0.972759i	$-0.425532\pi$
$29$	−21.4872	−	21.4872i	−0.740939	−	0.740939i	−0.972759	+	0.231820i	$0.925532\pi$
$30$		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	0.986059	−	0.166398i	$-0.0532137\pi$
$37$	30.3274	+	30.3274i	0.819661	+	0.819661i	−0.166398	+	0.986059i	$0.553214\pi$
$38$	−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	0.581882	−	0.813273i	$-0.302316\pi$
$43$	−9.94981	−	9.94981i	−0.231391	−	0.231391i	−0.813273	+	0.581882i	$0.802316\pi$
$44$	−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	$0.133971\pi$
$47$			38.4052i			0.817132i	−0.912729	+	0.408566i	$0.866029\pi$
$48$		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	−0.168725	+	0.985663i	$0.553965\pi$
$53$	−61.1826	+	61.1826i	−1.15439	+	1.15439i	−0.985663	+	0.168725i	$0.946035\pi$
$54$		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	−0.731983	−	0.681323i	$-0.761405\pi$
$59$	−2.98892	+	2.98892i	−0.0506596	+	0.0506596i	0.681323	+	0.731983i	$0.261405\pi$
$60$		0			0
$61$	3.88659	−	3.88659i	0.0637146	−	0.0637146i	−0.674531	−	0.738246i	$-0.735654\pi$
$61$	3.88659	−	3.88659i	0.0637146	−	0.0637146i	0.738246	+	0.674531i	$0.235654\pi$
$62$	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	−0.964808	−	0.262955i	$-0.915303\pi$
$67$	−47.0242	+	47.0242i	−0.701853	+	0.701853i	0.262955	+	0.964808i	$0.415303\pi$
$68$	−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	$-0.738485\pi$
$73$		−	106.904i		−	1.46444i	0.681069	−	0.732219i	$-0.261515\pi$
$74$	−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	0.997345	+	0.0728268i	$0.0232020\pi$
$83$	88.8242	+	88.8242i	1.07017	+	1.07017i	0.0728268	+	0.997345i	$0.476798\pi$
$84$		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	−0.867037	−	0.498244i	$-0.833978\pi$
$101$	−37.2481	+	37.2481i	−0.368793	+	0.368793i	0.498244	+	0.867037i	$0.333978\pi$
$102$		0			0
$103$			188.028i			1.82551i	0.408505	+	0.912756i	$0.366050\pi$
$103$			188.028i			1.82551i	−0.408505	+	0.912756i	$0.633950\pi$
$104$	−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	−0.523077	−	0.852285i	$-0.675216\pi$
$107$	35.2253	−	35.2253i	0.329208	−	0.329208i	0.852285	+	0.523077i	$0.175216\pi$
$108$		0			0
$109$	−93.0073	+	93.0073i	−0.853278	+	0.853278i	−0.990535	−	0.137257i	$-0.956171\pi$
$109$	−93.0073	+	93.0073i	−0.853278	+	0.853278i	0.137257	+	0.990535i	$0.456171\pi$
$110$	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	$-0.994636\pi$
$113$		−	3.80833i		−	0.0337021i	0.999858	−	0.0168510i	$-0.00536410\pi$
$114$		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	0.440708	−	0.897650i	$-0.354727\pi$
$131$	−59.8594	−	59.8594i	−0.456942	−	0.456942i	−0.897650	+	0.440708i	$0.854727\pi$
$132$		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	0.0457344	−	0.998954i	$-0.485437\pi$
$139$	−132.497	−	132.497i	−0.953219	−	0.953219i	−0.998954	+	0.0457344i	$0.985437\pi$
$140$	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	−0.671075	−	0.741389i	$-0.734167\pi$
$149$	10.4768	−	10.4768i	0.0703142	−	0.0703142i	0.741389	+	0.671075i	$0.234167\pi$
$150$		0			0
$151$		−	181.207i		−	1.20005i	−0.799982	−	0.600024i	$-0.795158\pi$
$151$		−	181.207i		−	1.20005i	0.799982	−	0.600024i	$-0.204842\pi$
$152$	−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	−0.498036	−	0.867156i	$-0.665945\pi$
$157$	57.9518	−	57.9518i	0.369120	−	0.369120i	0.867156	+	0.498036i	$0.165945\pi$
$158$	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	−0.384463	−	0.923140i	$-0.625613\pi$
$163$	87.8044	−	87.8044i	0.538677	−	0.538677i	0.923140	+	0.384463i	$0.125613\pi$
$164$	−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	0.956339	+	0.292258i	$0.0944067\pi$
$173$	216.007	+	216.007i	1.24860	+	1.24860i	0.292258	+	0.956339i	$0.405593\pi$
$174$		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	0.424303	−	0.905520i	$-0.360519\pi$
$179$	−86.1380	−	86.1380i	−0.481218	−	0.481218i	−0.905520	+	0.424303i	$0.860519\pi$
$180$		0			0
$181$	1.84265	+	1.84265i	0.0101804	+	0.0101804i	0.712179	−	0.701998i	$-0.247709\pi$
$181$	1.84265	+	1.84265i	0.0101804	+	0.0101804i	−0.701998	+	0.712179i	$0.747709\pi$
$182$	−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	$-0.931108\pi$
$191$		−	82.0328i		−	0.429491i	0.976670	−	0.214746i	$-0.0688922\pi$
$192$		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	−0.684569	−	0.728948i	$-0.740009\pi$
$197$	8.74282	−	8.74282i	0.0443798	−	0.0443798i	0.728948	+	0.684569i	$0.240009\pi$
$198$		0			0
$199$			128.824i			0.647357i	0.946167	+	0.323679i	$0.104920\pi$
$199$			128.824i			0.647357i	−0.946167	+	0.323679i	$0.895080\pi$
$200$	−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	−0.441128	−	0.897444i	$-0.645422\pi$
$211$	96.2826	−	96.2826i	0.456316	−	0.456316i	0.897444	+	0.441128i	$0.145422\pi$
$212$	−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	0.544680	−	0.838644i	$-0.316651\pi$
$227$	−66.7298	−	66.7298i	−0.293964	−	0.293964i	−0.838644	+	0.544680i	$0.816651\pi$
$228$		0			0
$229$	−109.514	−	109.514i	−0.478229	−	0.478229i	0.426336	−	0.904565i	$-0.359804\pi$
$229$	−109.514	−	109.514i	−0.478229	−	0.478229i	−0.904565	+	0.426336i	$0.859804\pi$
$230$	−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	$-0.968641\pi$
$239$		−	47.0157i		−	0.196718i	0.995151	−	0.0983592i	$-0.0313594\pi$
$240$		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	−0.911239	−	0.411878i	$-0.864873\pi$
$251$	−125.339	+	125.339i	−0.499360	+	0.499360i	0.411878	+	0.911239i	$0.364873\pi$
$252$		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	$-0.768976\pi$
$257$		−	341.153i		−	1.32744i	0.747980	−	0.663722i	$-0.231024\pi$
$258$		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	0.574448	−	0.818541i	$-0.305217\pi$
$269$	−65.6610	−	65.6610i	−0.244093	−	0.244093i	−0.818541	+	0.574448i	$0.805217\pi$
$270$		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	0.567690	−	0.823243i	$-0.307837\pi$
$277$	−70.7882	−	70.7882i	−0.255553	−	0.255553i	−0.823243	+	0.567690i	$0.807837\pi$
$278$	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	0.294099	−	0.955775i	$-0.404980\pi$
$283$	−187.254	−	187.254i	−0.661676	−	0.661676i	−0.955775	+	0.294099i	$0.904980\pi$
$284$	−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	−0.277063	−	0.960852i	$-0.589361\pi$
$293$	200.350	−	200.350i	0.683788	−	0.683788i	0.960852	+	0.277063i	$0.0893612\pi$
$294$		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	−0.873305	−	0.487174i	$-0.838028\pi$
$307$	−118.542	+	118.542i	−0.386130	+	0.386130i	0.487174	+	0.873305i	$0.338028\pi$
$308$	−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	$0.288513\pi$
$313$			492.839i			1.57457i	−0.616592	+	0.787283i	$0.711487\pi$
$314$	−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	0.868649	−	0.495427i	$-0.164988\pi$
$317$	118.311	+	118.311i	0.373222	+	0.373222i	−0.495427	+	0.868649i	$0.664988\pi$
$318$		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	0.623707	−	0.781658i	$-0.285626\pi$
$331$	−52.2818	−	52.2818i	−0.157951	−	0.157951i	−0.781658	+	0.623707i	$0.785626\pi$
$332$	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	−0.995553	−	0.0942021i	$-0.969970\pi$
$347$	−312.769	+	312.769i	−0.901351	+	0.901351i	0.0942021	+	0.995553i	$0.469970\pi$
$348$		0			0
$349$	−114.172	+	114.172i	−0.327141	+	0.327141i	−0.851498	−	0.524357i	$-0.824306\pi$
$349$	−114.172	+	114.172i	−0.327141	+	0.327141i	0.524357	+	0.851498i	$0.324306\pi$
$350$	−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	$0.146131\pi$
$353$			312.848i			0.886255i	−0.896459	+	0.443127i	$0.853869\pi$
$354$		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	0.741010	−	0.671494i	$-0.234347\pi$
$373$	25.9291	+	25.9291i	0.0695151	+	0.0695151i	−0.671494	+	0.741010i	$0.734347\pi$
$374$	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	0.836411	−	0.548103i	$-0.184650\pi$
$379$	109.268	+	109.268i	0.288307	+	0.288307i	−0.548103	+	0.836411i	$0.684650\pi$
$380$	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	$0.0389015\pi$
$383$			93.3821i			0.243818i	−0.992541	+	0.121909i	$0.961098\pi$
$384$		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	−0.787766	−	0.615975i	$-0.788762\pi$
$389$	−66.8268	+	66.8268i	−0.171791	+	0.171791i	0.615975	+	0.787766i	$0.288762\pi$
$390$		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	−0.157953	−	0.987447i	$-0.550489\pi$
$397$	329.309	−	329.309i	0.829494	−	0.829494i	0.987447	+	0.157953i	$0.0504893\pi$
$398$	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	$0.0515581\pi$
$401$			129.336i			0.322534i	−0.986911	+	0.161267i	$0.948442\pi$
$402$		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	$-0.755962\pi$
$409$		−	567.479i		−	1.38748i	0.720226	−	0.693739i	$-0.244038\pi$
$410$	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	0.721279	−	0.692645i	$-0.243555\pi$
$419$	11.9979	+	11.9979i	0.0286346	+	0.0286346i	−0.692645	+	0.721279i	$0.743555\pi$
$420$		0			0
$421$	301.310	+	301.310i	0.715700	+	0.715700i	0.967722	−	0.252022i	$-0.0810954\pi$
$421$	301.310	+	301.310i	0.715700	+	0.715700i	−0.252022	+	0.967722i	$0.581095\pi$
$422$	−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	$0.301829\pi$
$431$			700.273i			1.62476i	−0.583126	+	0.812382i	$0.698171\pi$
$432$		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	$-0.964186\pi$
$439$		−	98.5794i		−	0.224554i	0.993677	−	0.112277i	$-0.0358145\pi$
$440$	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	0.367450	−	0.930043i	$-0.380231\pi$
$443$	574.790	−	574.790i	1.29749	−	1.29749i	0.930043	−	0.367450i	$-0.119769\pi$
$444$		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	$0.0280838\pi$
$449$			79.1258i			0.176227i	−0.996110	+	0.0881133i	$0.971916\pi$
$450$		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	$0.289810\pi$
$457$			721.867i			1.57958i	−0.613380	+	0.789788i	$0.710190\pi$
$458$	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	0.766888	−	0.641780i	$-0.221804\pi$
$461$	57.6748	+	57.6748i	0.125108	+	0.125108i	−0.641780	+	0.766888i	$0.721804\pi$
$462$		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	0.333719	−	0.942673i	$-0.391696\pi$
$467$	−284.381	−	284.381i	−0.608954	−	0.608954i	−0.942673	+	0.333719i	$0.891696\pi$
$468$		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	$0.0248512\pi$
$479$			74.7175i			0.155986i	−0.996954	+	0.0779932i	$0.975149\pi$
$480$		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	$-0.841523\pi$
$487$		−	465.139i		−	0.955111i	0.878602	−	0.477555i	$-0.158477\pi$
$488$	−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	−0.518367	−	0.855158i	$-0.673460\pi$
$491$	165.364	−	165.364i	0.336791	−	0.336791i	0.855158	+	0.518367i	$0.173460\pi$
$492$		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	0.00733057	−	0.999973i	$-0.497667\pi$
$499$	502.645	−	502.645i	1.00730	−	1.00730i	0.999973	−	0.00733057i	$-0.00233342\pi$
$500$	−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	0.560481	−	0.828167i	$-0.310616\pi$
$509$	−136.252	−	136.252i	−0.267686	−	0.267686i	−0.828167	+	0.560481i	$0.810616\pi$
$510$		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	0.997050	−	0.0767569i	$-0.0244565\pi$
$523$	481.313	+	481.313i	0.920293	+	0.920293i	−0.0767569	+	0.997050i	$0.524457\pi$
$524$	−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	−0.741733	−	0.670695i	$-0.765996\pi$
$541$	−38.4319	+	38.4319i	−0.0710387	+	0.0710387i	0.670695	+	0.741733i	$0.265996\pi$
$542$	−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	−0.440788	−	0.897611i	$-0.645301\pi$
$547$	249.883	−	249.883i	0.456824	−	0.456824i	0.897611	+	0.440788i	$0.145301\pi$
$548$	−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	0.999962	+	0.00868977i	$0.00276607\pi$
$557$	561.819	+	561.819i	1.00865	+	1.00865i	0.00868977	+	0.999962i	$0.497234\pi$
$558$		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	0.0867652	−	0.996229i	$-0.472347\pi$
$563$	−512.028	−	512.028i	−0.909464	−	0.909464i	−0.996229	+	0.0867652i	$0.972347\pi$
$564$		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	0.776160	−	0.630536i	$-0.217165\pi$
$571$	83.1512	+	83.1512i	0.145624	+	0.145624i	−0.630536	+	0.776160i	$0.717165\pi$
$572$	−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	−0.518237	−	0.855237i	$-0.673412\pi$
$587$	197.819	−	197.819i	0.337000	−	0.337000i	0.855237	+	0.518237i	$0.173412\pi$
$588$		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	$-0.914775\pi$
$593$		−	313.761i		−	0.529108i	0.964371	−	0.264554i	$-0.0852248\pi$
$594$		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	$0.00677848\pi$
$601$			25.5949i			0.0425873i	−0.999773	+	0.0212936i	$0.993222\pi$
$602$	−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	0.199660	−	0.979865i	$-0.436016\pi$
$613$	−478.265	−	478.265i	−0.780205	−	0.780205i	−0.979865	+	0.199660i	$0.936016\pi$
$614$	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	0.999121	−	0.0419094i	$-0.0133441\pi$
$619$	592.514	+	592.514i	0.957212	+	0.957212i	−0.0419094	+	0.999121i	$0.513344\pi$
$620$	−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	$0.233769\pi$
$631$			845.724i			1.34029i	−0.742229	+	0.670146i	$0.766231\pi$
$632$	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	$-0.635531\pi$
$641$		−	1167.54i		−	1.82143i	0.413035	−	0.910715i	$-0.364469\pi$
$642$		0			0
$643$	296.182	−	296.182i	0.460626	−	0.460626i	−0.438235	−	0.898861i	$-0.644396\pi$
$643$	296.182	−	296.182i	0.460626	−	0.460626i	0.898861	+	0.438235i	$0.144396\pi$
$644$	−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	0.725692	−	0.688019i	$-0.241520\pi$
$653$	24.6005	+	24.6005i	0.0376730	+	0.0376730i	−0.688019	+	0.725692i	$0.741520\pi$
$654$		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	0.300919	−	0.953650i	$-0.402707\pi$
$659$	−430.149	−	430.149i	−0.652730	−	0.652730i	−0.953650	+	0.300919i	$0.902707\pi$
$660$		0			0
$661$	755.093	+	755.093i	1.14235	+	1.14235i	0.988019	+	0.154330i	$0.0493221\pi$
$661$	755.093	+	755.093i	1.14235	+	1.14235i	0.154330	+	0.988019i	$0.450678\pi$
$662$	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	−0.322209	−	0.946668i	$-0.604425\pi$
$677$	422.759	−	422.759i	0.624459	−	0.624459i	0.946668	+	0.322209i	$0.104425\pi$
$678$		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	−0.269839	−	0.962905i	$-0.586971\pi$
$683$	473.364	−	473.364i	0.693066	−	0.693066i	0.962905	+	0.269839i	$0.0869705\pi$
$684$		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	−0.468283	−	0.883579i	$-0.655127\pi$
$691$	286.969	−	286.969i	0.415295	−	0.415295i	0.883579	+	0.468283i	$0.155127\pi$
$692$	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	0.264574	−	0.964365i	$-0.414769\pi$
$701$	−490.554	−	490.554i	−0.699791	−	0.699791i	−0.964365	+	0.264574i	$0.914769\pi$
$702$		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	0.956722	−	0.291003i	$-0.0939890\pi$
$709$	471.995	+	471.995i	0.665719	+	0.665719i	−0.291003	+	0.956722i	$0.593989\pi$
$710$	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	$-0.744051\pi$
$719$		−	1035.64i		−	1.44040i	0.693769	−	0.720198i	$-0.255949\pi$
$720$		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	$-0.962189\pi$
$727$		−	172.311i		−	0.237016i	0.992953	−	0.118508i	$-0.0378112\pi$
$728$	−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	−0.999989	−	0.00474987i	$-0.998488\pi$
$733$	−729.510	+	729.510i	−0.995239	+	0.995239i	0.00474987	+	0.999989i	$0.498488\pi$
$734$	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	−0.571711	−	0.820455i	$-0.693720\pi$
$739$	183.822	−	183.822i	0.248745	−	0.248745i	0.820455	+	0.571711i	$0.193720\pi$
$740$	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	0.996938	−	0.0781952i	$-0.0249157\pi$
$757$	695.488	+	695.488i	0.918743	+	0.918743i	−0.0781952	+	0.996938i	$0.524916\pi$
$758$	−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	−0.576074	−	0.817397i	$-0.695416\pi$
$773$	186.543	−	186.543i	0.241323	−	0.241323i	0.817397	+	0.576074i	$0.195416\pi$
$774$		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	−0.0413871	−	0.999143i	$-0.513178\pi$
$787$	753.754	−	753.754i	0.957756	−	0.957756i	0.999143	+	0.0413871i	$0.0131777\pi$
$788$	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	0.289759	−	0.957100i	$-0.406425\pi$
$797$	−531.870	−	531.870i	−0.667340	−	0.667340i	−0.957100	+	0.289759i	$0.906425\pi$
$798$		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	0.992102	−	0.125430i	$-0.0400311\pi$
$811$	702.871	+	702.871i	0.866672	+	0.866672i	−0.125430	+	0.992102i	$0.540031\pi$
$812$	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	−0.859511	−	0.511117i	$-0.829232\pi$
$821$	−286.031	+	286.031i	−0.348393	+	0.348393i	0.511117	+	0.859511i	$0.329232\pi$
$822$		0			0
$823$			215.600i			0.261969i	0.991384	+	0.130984i	$0.0418138\pi$
$823$			215.600i			0.261969i	−0.991384	+	0.130984i	$0.958186\pi$
$824$	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	−0.896561	−	0.442920i	$-0.853943\pi$
$827$	−375.162	+	375.162i	−0.453642	+	0.453642i	0.442920	+	0.896561i	$0.353943\pi$
$828$		0			0
$829$	22.5151	−	22.5151i	0.0271594	−	0.0271594i	−0.693397	−	0.720556i	$-0.743887\pi$
$829$	22.5151	−	22.5151i	0.0271594	−	0.0271594i	0.720556	+	0.693397i	$0.243887\pi$
$830$	−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	0.428298	−	0.903637i	$-0.359113\pi$
$853$	−405.464	−	405.464i	−0.475339	−	0.475339i	−0.903637	+	0.428298i	$0.859113\pi$
$854$	−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	0.970437	−	0.241354i	$-0.0775914\pi$
$859$	626.283	+	626.283i	0.729083	+	0.729083i	−0.241354	+	0.970437i	$0.577591\pi$
$860$	−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	$-0.819572\pi$
$863$		−	926.795i		−	1.07392i	0.843607	−	0.536961i	$-0.180428\pi$
$864$		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	−0.949783	−	0.312911i	$-0.898696\pi$
$877$	−558.537	+	558.537i	−0.636872	+	0.636872i	0.312911	+	0.949783i	$0.398696\pi$
$878$	−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	$0.185530\pi$
$881$			969.827i			1.10083i	−0.834893	+	0.550413i	$0.814470\pi$
$882$		0			0
$883$	549.585	−	549.585i	0.622407	−	0.622407i	−0.323739	−	0.946146i	$-0.604940\pi$
$883$	549.585	−	549.585i	0.622407	−	0.622407i	0.946146	+	0.323739i	$0.104940\pi$
$884$	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	0.413321	−	0.910586i	$-0.364369\pi$
$907$	−451.019	−	451.019i	−0.497265	−	0.497265i	−0.910586	+	0.413321i	$0.864369\pi$
$908$	−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	$0.304855\pi$
$911$			1490.19i			1.63578i	−0.575378	+	0.817888i	$0.695145\pi$
$912$		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	$-0.827243\pi$
$919$		−	949.287i		−	1.03296i	0.856300	−	0.516478i	$-0.172757\pi$
$920$	−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	$-0.802891\pi$
$929$		−	1078.41i		−	1.16083i	0.814322	−	0.580413i	$-0.197109\pi$
$930$		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	$-0.787880\pi$
$937$		−	1158.42i		−	1.23631i	0.786056	−	0.618155i	$-0.212120\pi$
$938$	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	0.995335	+	0.0964770i	$0.0307574\pi$
$941$	1027.40	+	1027.40i	1.09181	+	1.09181i	0.0964770	+	0.995335i	$0.469243\pi$
$942$		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	0.998301	−	0.0582710i	$-0.0185588\pi$
$947$	890.208	+	890.208i	0.940030	+	0.940030i	−0.0582710	+	0.998301i	$0.518559\pi$
$948$		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	$0.0767674\pi$
$967$			461.918i			0.477682i	−0.971059	+	0.238841i	$0.923233\pi$
$968$	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	−0.245372	−	0.969429i	$-0.578910\pi$
$971$	703.059	−	703.059i	0.724057	−	0.724057i	0.969429	+	0.245372i	$0.0789101\pi$
$972$		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	$-0.825070\pi$
$977$		−	1020.60i		−	1.04462i	0.852755	−	0.522311i	$-0.174930\pi$
$978$		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	0.745096	−	0.666957i	$-0.232404\pi$
$997$	77.9043	+	77.9043i	0.0781387	+	0.0781387i	−0.666957	+	0.745096i	$0.732404\pi$
$998$	−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.53.2	✓	32
3.2	odd	2	inner	144.3.j.a.53.15	yes	32
4.3	odd	2		576.3.j.a.305.15		32
8.3	odd	2		1152.3.j.b.737.2		32
8.5	even	2		1152.3.j.a.737.2		32
12.11	even	2		576.3.j.a.305.2		32
16.3	odd	4		576.3.j.a.17.2		32
16.5	even	4		1152.3.j.a.161.15		32
16.11	odd	4		1152.3.j.b.161.15		32
16.13	even	4	inner	144.3.j.a.125.15	yes	32
24.5	odd	2		1152.3.j.a.737.15		32
24.11	even	2		1152.3.j.b.737.15		32
48.5	odd	4		1152.3.j.a.161.2		32
48.11	even	4		1152.3.j.b.161.2		32
48.29	odd	4	inner	144.3.j.a.125.2	yes	32
48.35	even	4		576.3.j.a.17.15		32

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

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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