LMFDB - Embedded newform 144.3.j.a.125.5

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			125.5
Character	$\chi$	$=$	144.125
Dual form			144.3.j.a.53.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13812 + 1.64459i) q^{2} +(-1.40936 - 3.74349i) q^{4} +(3.90343 + 3.90343i) q^{5} -0.778757i q^{7} +(7.76053 + 1.94271i) q^{8} +O(q^{10})$	\(q+(-1.13812 + 1.64459i) q^{2} +(-1.40936 - 3.74349i) q^{4} +(3.90343 + 3.90343i) q^{5} -0.778757i q^{7} +(7.76053 + 1.94271i) q^{8} +(-10.8621 + 1.97697i) q^{10} +(4.29098 + 4.29098i) q^{11} +(6.44007 + 6.44007i) q^{13} +(1.28074 + 0.886319i) q^{14} +(-12.0274 + 10.5519i) q^{16} +31.3383i q^{17} +(1.11906 + 1.11906i) q^{19} +(9.11108 - 20.1138i) q^{20} +(-11.9406 + 2.17326i) q^{22} -34.2197 q^{23} +5.47346i q^{25} +(-17.9208 + 3.26171i) q^{26} +(-2.91526 + 1.09755i) q^{28} +(8.77471 - 8.77471i) q^{29} +50.8507 q^{31} +(-3.66490 - 31.7894i) q^{32} +(-51.5386 - 35.6667i) q^{34} +(3.03982 - 3.03982i) q^{35} +(-29.3064 + 29.3064i) q^{37} +(-3.11402 + 0.566772i) q^{38} +(22.7094 + 37.8759i) q^{40} +31.4271 q^{41} +(55.9022 - 55.9022i) q^{43} +(10.0157 - 22.1108i) q^{44} +(38.9461 - 56.2774i) q^{46} -26.5249i q^{47} +48.3935 q^{49} +(-9.00161 - 6.22946i) q^{50} +(15.0319 - 33.1847i) q^{52} +(9.76389 + 9.76389i) q^{53} +33.4991i q^{55} +(1.51290 - 6.04357i) q^{56} +(4.44414 + 24.4175i) q^{58} +(-54.3706 - 54.3706i) q^{59} +(-47.1104 - 47.1104i) q^{61} +(-57.8742 + 83.6287i) q^{62} +(56.4517 + 30.1530i) q^{64} +50.2766i q^{65} +(-66.1339 - 66.1339i) q^{67} +(117.314 - 44.1670i) q^{68} +(1.53958 + 8.45894i) q^{70} -75.9403 q^{71} +24.1992i q^{73} +(-14.8428 - 81.5513i) q^{74} +(2.61202 - 5.76635i) q^{76} +(3.34163 - 3.34163i) q^{77} -80.5454 q^{79} +(-88.1365 - 5.75959i) q^{80} +(-35.7678 + 51.6847i) q^{82} +(82.6319 - 82.6319i) q^{83} +(-122.327 + 122.327i) q^{85} +(28.3128 + 155.560i) q^{86} +(24.9642 + 41.6365i) q^{88} +82.6445 q^{89} +(5.01524 - 5.01524i) q^{91} +(48.2279 + 128.101i) q^{92} +(43.6226 + 30.1885i) q^{94} +8.73634i q^{95} +48.9478 q^{97} +(-55.0777 + 79.5876i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.13812	+	1.64459i	−0.569060	+	0.822296i
$2$	−1.13812	+	1.64459i	−0.569060	+	0.822296i
$3$		0			0
$3$		0			0
$4$	−1.40936	−	3.74349i	−0.352341	−	0.935872i
$5$	3.90343	+	3.90343i	0.780685	+	0.780685i	0.979946	−	0.199261i	$-0.0638542\pi$
$5$	3.90343	+	3.90343i	0.780685	+	0.780685i	−0.199261	+	0.979946i	$0.563854\pi$
$6$		0			0
$7$		−	0.778757i		−	0.111251i	−0.998452	−	0.0556255i	$-0.982285\pi$
$7$		−	0.778757i		−	0.111251i	0.998452	−	0.0556255i	$-0.0177153\pi$
$8$	7.76053	+	1.94271i	0.970067	+	0.242839i
$9$		0			0
$10$	−10.8621	+	1.97697i	−1.08621	+	0.197697i
$11$	4.29098	+	4.29098i	0.390089	+	0.390089i	0.874719	−	0.484630i	$-0.161046\pi$
$11$	4.29098	+	4.29098i	0.390089	+	0.390089i	−0.484630	+	0.874719i	$0.661046\pi$
$12$		0			0
$13$	6.44007	+	6.44007i	0.495390	+	0.495390i	0.909999	−	0.414610i	$-0.136082\pi$
$13$	6.44007	+	6.44007i	0.495390	+	0.495390i	−0.414610	+	0.909999i	$0.636082\pi$
$14$	1.28074	+	0.886319i	0.0914812	+	0.0633085i
$15$		0			0
$16$	−12.0274	+	10.5519i	−0.751712	+	0.659492i
$17$			31.3383i			1.84343i	0.387872	+	0.921713i	$0.373210\pi$
$17$			31.3383i			1.84343i	−0.387872	+	0.921713i	$0.626790\pi$
$18$		0			0
$19$	1.11906	+	1.11906i	0.0588979	+	0.0588979i	0.735942	−	0.677044i	$-0.236739\pi$
$19$	1.11906	+	1.11906i	0.0588979	+	0.0588979i	−0.677044	+	0.735942i	$0.736739\pi$
$20$	9.11108	−	20.1138i	0.455554	−	1.00569i
$21$		0			0
$22$	−11.9406	+	2.17326i	−0.542753	+	0.0987845i
$23$	−34.2197			−1.48781			−0.743906	−	0.668285i	$-0.767029\pi$
$23$	−34.2197			−1.48781			−0.743906	+	0.668285i	$0.767029\pi$
$24$		0			0
$25$			5.47346i			0.218939i
$26$	−17.9208	+	3.26171i	−0.689263	+	0.125450i
$27$		0			0
$28$	−2.91526	+	1.09755i	−0.104117	+	0.0391983i
$29$	8.77471	−	8.77471i	0.302576	−	0.302576i	−0.539445	−	0.842021i	$-0.681366\pi$
$29$	8.77471	−	8.77471i	0.302576	−	0.302576i	0.842021	+	0.539445i	$0.181366\pi$
$30$		0			0
$31$	50.8507			1.64035			0.820173	−	0.572116i	$-0.193877\pi$
$31$	50.8507			1.64035			0.820173	+	0.572116i	$0.193877\pi$
$32$	−3.66490	−	31.7894i	−0.114528	−	0.993420i
$33$		0			0
$34$	−51.5386	−	35.6667i	−1.51584	−	1.04902i
$35$	3.03982	−	3.03982i	0.0868520	−	0.0868520i
$36$		0			0
$37$	−29.3064	+	29.3064i	−0.792065	+	0.792065i	−0.981830	−	0.189765i	$-0.939227\pi$
$37$	−29.3064	+	29.3064i	−0.792065	+	0.792065i	0.189765	+	0.981830i	$0.439227\pi$
$38$	−3.11402	+	0.566772i	−0.0819480	+	0.0149150i
$39$		0			0
$40$	22.7094	+	37.8759i	0.567736	+	0.946897i
$41$	31.4271			0.766513			0.383257	−	0.923642i	$-0.374802\pi$
$41$	31.4271			0.766513			0.383257	+	0.923642i	$0.374802\pi$
$42$		0			0
$43$	55.9022	−	55.9022i	1.30005	−	1.30005i	0.371696	−	0.928354i	$-0.378776\pi$
$43$	55.9022	−	55.9022i	1.30005	−	1.30005i	0.928354	−	0.371696i	$-0.121224\pi$
$44$	10.0157	−	22.1108i	0.227629	−	0.502518i
$45$		0			0
$46$	38.9461	−	56.2774i	0.846654	−	1.22342i
$47$		−	26.5249i		−	0.564359i	−0.959362	−	0.282180i	$-0.908943\pi$
$47$		−	26.5249i		−	0.564359i	0.959362	−	0.282180i	$-0.0910574\pi$
$48$		0			0
$49$	48.3935			0.987623
$50$	−9.00161	−	6.22946i	−0.180032	−	0.124589i
$51$		0			0
$52$	15.0319	−	33.1847i	0.289075	−	0.638167i
$53$	9.76389	+	9.76389i	0.184224	+	0.184224i	0.793194	−	0.608969i	$-0.208417\pi$
$53$	9.76389	+	9.76389i	0.184224	+	0.184224i	−0.608969	+	0.793194i	$0.708417\pi$
$54$		0			0
$55$			33.4991i			0.609074i
$56$	1.51290	−	6.04357i	0.0270161	−	0.107921i
$57$		0			0
$58$	4.44414	+	24.4175i	0.0766231	+	0.420991i
$59$	−54.3706	−	54.3706i	−0.921535	−	0.921535i	0.0756026	−	0.997138i	$-0.475912\pi$
$59$	−54.3706	−	54.3706i	−0.921535	−	0.921535i	−0.997138	+	0.0756026i	$0.975912\pi$
$60$		0			0
$61$	−47.1104	−	47.1104i	−0.772302	−	0.772302i	0.206207	−	0.978508i	$-0.433888\pi$
$61$	−47.1104	−	47.1104i	−0.772302	−	0.772302i	−0.978508	+	0.206207i	$0.933888\pi$
$62$	−57.8742	+	83.6287i	−0.933455	+	1.34885i
$63$		0			0
$64$	56.4517	+	30.1530i	0.882058	+	0.471140i
$65$			50.2766i			0.773487i
$66$		0			0
$67$	−66.1339	−	66.1339i	−0.987073	−	0.987073i	0.0128446	−	0.999918i	$-0.495911\pi$
$67$	−66.1339	−	66.1339i	−0.987073	−	0.987073i	−0.999918	+	0.0128446i	$0.995911\pi$
$68$	117.314	−	44.1670i	1.72521	−	0.649515i
$69$		0			0
$70$	1.53958	+	8.45894i	0.0219940	+	0.120842i
$71$	−75.9403			−1.06958			−0.534791	−	0.844985i	$-0.679609\pi$
$71$	−75.9403			−1.06958			−0.534791	+	0.844985i	$0.679609\pi$
$72$		0			0
$73$			24.1992i			0.331497i	0.986168	+	0.165748i	$0.0530039\pi$
$73$			24.1992i			0.331497i	−0.986168	+	0.165748i	$0.946996\pi$
$74$	−14.8428	−	81.5513i	−0.200579	−	1.10204i
$75$		0			0
$76$	2.61202	−	5.76635i	0.0343687	−	0.0758730i
$77$	3.34163	−	3.34163i	0.0433978	−	0.0433978i
$78$		0			0
$79$	−80.5454			−1.01956			−0.509781	−	0.860304i	$-0.670274\pi$
$79$	−80.5454			−1.01956			−0.509781	+	0.860304i	$0.670274\pi$
$80$	−88.1365	−	5.75959i	−1.10171	−	0.0719949i
$81$		0			0
$82$	−35.7678	+	51.6847i	−0.436192	+	0.630301i
$83$	82.6319	−	82.6319i	0.995565	−	0.995565i	−0.00442530	−	0.999990i	$-0.501409\pi$
$83$	82.6319	−	82.6319i	0.995565	−	0.995565i	0.999990	+	0.00442530i	$0.00140862\pi$
$84$		0			0
$85$	−122.327	+	122.327i	−1.43914	+	1.43914i
$86$	28.3128	+	155.560i	0.329219	+	1.80883i
$87$		0			0
$88$	24.9642	+	41.6365i	0.283684	+	0.473142i
$89$	82.6445			0.928590			0.464295	−	0.885681i	$-0.346308\pi$
$89$	82.6445			0.928590			0.464295	+	0.885681i	$0.346308\pi$
$90$		0			0
$91$	5.01524	−	5.01524i	0.0551126	−	0.0551126i
$92$	48.2279	+	128.101i	0.524217	+	1.39240i
$93$		0			0
$94$	43.6226	+	30.1885i	0.464070	+	0.321154i
$95$			8.73634i			0.0919614i
$96$		0			0
$97$	48.9478			0.504617			0.252308	−	0.967647i	$-0.418810\pi$
$97$	48.9478			0.504617			0.252308	+	0.967647i	$0.418810\pi$
$98$	−55.0777	+	79.5876i	−0.562017	+	0.812118i
$99$		0			0
$100$	20.4898	−	7.71410i	0.204898	−	0.0771410i
$101$	−41.2778	−	41.2778i	−0.408691	−	0.408691i	0.472591	−	0.881282i	$-0.343319\pi$
$101$	−41.2778	−	41.2778i	−0.408691	−	0.408691i	−0.881282	+	0.472591i	$0.843319\pi$
$102$		0			0
$103$			173.236i			1.68190i	0.541111	+	0.840951i	$0.318004\pi$
$103$			173.236i			1.68190i	−0.541111	+	0.840951i	$0.681996\pi$
$104$	37.4671	+	62.4895i	0.360261	+	0.600861i
$105$		0			0
$106$	−27.1701	+	4.94513i	−0.256322	+	0.0466521i
$107$	53.2761	+	53.2761i	0.497907	+	0.497907i	0.910786	−	0.412879i	$-0.135477\pi$
$107$	53.2761	+	53.2761i	0.497907	+	0.497907i	−0.412879	+	0.910786i	$0.635477\pi$
$108$		0			0
$109$	−93.1537	−	93.1537i	−0.854621	−	0.854621i	0.136077	−	0.990698i	$-0.456551\pi$
$109$	−93.1537	−	93.1537i	−0.854621	−	0.854621i	−0.990698	+	0.136077i	$0.956551\pi$
$110$	−55.0923	−	38.1260i	−0.500839	−	0.346600i
$111$		0			0
$112$	8.21734	+	9.36641i	0.0733691	+	0.0836286i
$113$			40.8189i			0.361229i	0.983554	+	0.180615i	$0.0578087\pi$
$113$			40.8189i			0.361229i	−0.983554	+	0.180615i	$0.942191\pi$
$114$		0			0
$115$	−133.574	−	133.574i	−1.16151	−	1.16151i
$116$	−45.2148	−	20.4813i	−0.389782	−	0.176563i
$117$		0			0
$118$	151.298	−	27.5371i	1.28218	−	0.233366i
$119$	24.4049			0.205083
$120$		0			0
$121$		−	84.1749i		−	0.695661i
$122$	131.095	−	23.8601i	1.07455	−	0.195574i
$123$		0			0
$124$	−71.6671	−	190.359i	−0.577961	−	1.53515i
$125$	76.2204	−	76.2204i	0.609763	−	0.609763i
$126$		0			0
$127$	88.9136			0.700107			0.350054	−	0.936730i	$-0.386163\pi$
$127$	88.9136			0.700107			0.350054	+	0.936730i	$0.386163\pi$
$128$	−113.838	+	58.5224i	−0.889361	+	0.457206i
$129$		0			0
$130$	−82.6845	−	57.2209i	−0.636035	−	0.440161i
$131$	−22.0108	+	22.0108i	−0.168021	+	0.168021i	−0.786109	−	0.618088i	$-0.787908\pi$
$131$	−22.0108	+	22.0108i	−0.168021	+	0.168021i	0.618088	+	0.786109i	$0.287908\pi$
$132$		0			0
$133$	0.871475	−	0.871475i	0.00655245	−	0.00655245i
$134$	184.032	−	33.4949i	1.37337	−	0.249962i
$135$		0			0
$136$	−60.8812	+	243.202i	−0.447656	+	1.78825i
$137$	−110.794			−0.808715			−0.404358	−	0.914601i	$-0.632505\pi$
$137$	−110.794			−0.808715			−0.404358	+	0.914601i	$0.632505\pi$
$138$		0			0
$139$	30.3862	−	30.3862i	0.218605	−	0.218605i	−0.589305	−	0.807911i	$-0.700598\pi$
$139$	30.3862	−	30.3862i	0.218605	−	0.218605i	0.807911	+	0.589305i	$0.200598\pi$
$140$	−15.6637	−	7.09531i	−0.111884	−	0.0506808i
$141$		0			0
$142$	86.4292	−	124.891i	0.608656	−	0.879512i
$143$			55.2684i			0.386493i
$144$		0			0
$145$	68.5029			0.472433
$146$	−39.7979	−	27.5417i	−0.272588	−	0.188641i
$147$		0			0
$148$	151.012	+	68.4048i	1.02035	+	0.462194i
$149$	−173.924	−	173.924i	−1.16727	−	1.16727i	−0.982846	−	0.184428i	$-0.940957\pi$
$149$	−173.924	−	173.924i	−1.16727	−	1.16727i	−0.184428	−	0.982846i	$-0.559043\pi$
$150$		0			0
$151$		−	26.2521i		−	0.173855i	−0.996215	−	0.0869274i	$-0.972295\pi$
$151$		−	26.2521i		−	0.173855i	0.996215	−	0.0869274i	$-0.0277048\pi$
$152$	6.51049	+	10.8585i	0.0428322	+	0.0714376i
$153$		0			0
$154$	1.69244	+	9.29880i	0.0109899	+	0.0603818i
$155$	198.492	+	198.492i	1.28059	+	1.28059i
$156$		0			0
$157$	75.8493	+	75.8493i	0.483117	+	0.483117i	0.906126	−	0.423009i	$-0.139026\pi$
$157$	75.8493	+	75.8493i	0.483117	+	0.483117i	−0.423009	+	0.906126i	$0.639026\pi$
$158$	91.6703	−	132.464i	0.580192	−	0.838381i
$159$		0			0
$160$	109.782	−	138.393i	0.686138	−	0.864959i
$161$			26.6488i			0.165520i
$162$		0			0
$163$	155.285	+	155.285i	0.952672	+	0.952672i	0.998930	−	0.0462578i	$-0.0147296\pi$
$163$	155.285	+	155.285i	0.952672	+	0.952672i	−0.0462578	+	0.998930i	$0.514730\pi$
$164$	−44.2921	−	117.647i	−0.270074	−	0.717358i
$165$		0			0
$166$	41.8507	+	229.941i	0.252112	+	1.38519i
$167$	−236.902			−1.41857			−0.709286	−	0.704920i	$-0.750983\pi$
$167$	−236.902			−1.41857			−0.709286	+	0.704920i	$0.750983\pi$
$168$		0			0
$169$		−	86.0511i		−	0.509178i
$170$	−61.9549	−	340.400i	−0.364440	−	2.00235i
$171$		0			0
$172$	−288.056	−	130.483i	−1.67474	−	0.758620i
$173$	68.3708	−	68.3708i	0.395207	−	0.395207i	−0.481332	−	0.876539i	$-0.659847\pi$
$173$	68.3708	−	68.3708i	0.395207	−	0.395207i	0.876539	+	0.481332i	$0.159847\pi$
$174$		0			0
$175$	4.26250			0.0243571
$176$	−96.8872	−	6.33144i	−0.550496	−	0.0359741i
$177$		0			0
$178$	−94.0595	+	135.917i	−0.528424	+	0.763576i
$179$	129.626	−	129.626i	0.724170	−	0.724170i	−0.245282	−	0.969452i	$-0.578880\pi$
$179$	129.626	−	129.626i	0.724170	−	0.724170i	0.969452	+	0.245282i	$0.0788804\pi$
$180$		0			0
$181$	157.641	−	157.641i	0.870947	−	0.870947i	−0.121629	−	0.992576i	$-0.538812\pi$
$181$	157.641	−	157.641i	0.870947	−	0.870947i	0.992576	+	0.121629i	$0.0388118\pi$
$182$	2.54008	+	13.9560i	0.0139565	+	0.0766812i
$183$		0			0
$184$	−265.563	−	66.4789i	−1.44328	−	0.361299i
$185$	−228.791			−1.23671
$186$		0			0
$187$	−134.472	+	134.472i	−0.719101	+	0.719101i
$188$	−99.2955	+	37.3832i	−0.528168	+	0.198847i
$189$		0			0
$190$	−14.3677	−	9.94300i	−0.0756195	−	0.0523316i
$191$			58.1217i			0.304302i	0.988357	+	0.152151i	$0.0486200\pi$
$191$			58.1217i			0.304302i	−0.988357	+	0.152151i	$0.951380\pi$
$192$		0			0
$193$	312.491			1.61912			0.809561	−	0.587035i	$-0.199705\pi$
$193$	312.491			1.61912			0.809561	+	0.587035i	$0.199705\pi$
$194$	−55.7085	+	80.4991i	−0.287157	+	0.414944i
$195$		0			0
$196$	−68.2041	−	181.161i	−0.347980	−	0.924289i
$197$	−44.8306	−	44.8306i	−0.227567	−	0.227567i	0.584109	−	0.811675i	$-0.301444\pi$
$197$	−44.8306	−	44.8306i	−0.227567	−	0.227567i	−0.811675	+	0.584109i	$0.801444\pi$
$198$		0			0
$199$			157.131i			0.789601i	0.918767	+	0.394801i	$0.129186\pi$
$199$			157.131i			0.789601i	−0.918767	+	0.394801i	$0.870814\pi$
$200$	−10.6334	+	42.4770i	−0.0531668	+	0.212385i
$201$		0			0
$202$	114.864	−	20.9060i	0.568635	−	0.103495i
$203$	−6.83336	−	6.83336i	−0.0336619	−	0.0336619i
$204$		0			0
$205$	122.673	+	122.673i	0.598406	+	0.598406i
$206$	−284.902	−	197.163i	−1.38302	−	0.957103i
$207$		0			0
$208$	−145.412	−	9.50246i	−0.699096	−	0.0456849i
$209$			9.60374i			0.0459509i
$210$		0			0
$211$	−68.3433	−	68.3433i	−0.323902	−	0.323902i	0.526360	−	0.850262i	$-0.323556\pi$
$211$	−68.3433	−	68.3433i	−0.323902	−	0.323902i	−0.850262	+	0.526360i	$0.823556\pi$
$212$	22.7901	−	50.3119i	0.107501	−	0.237320i
$213$		0			0
$214$	−148.252	+	26.9828i	−0.692766	+	0.126088i
$215$	436.420			2.02986
$216$		0			0
$217$		−	39.6003i		−	0.182490i
$218$	259.220	−	47.1797i	1.18908	−	0.216421i
$219$		0			0
$220$	125.403	−	47.2124i	0.570015	−	0.214602i
$221$	−201.820	+	201.820i	−0.913214	+	0.913214i
$222$		0			0
$223$	−3.75135			−0.0168222			−0.00841111	−	0.999965i	$-0.502677\pi$
$223$	−3.75135			−0.0168222			−0.00841111	+	0.999965i	$0.502677\pi$
$224$	−24.7562	+	2.85406i	−0.110519	+	0.0127413i
$225$		0			0
$226$	−67.1304	−	46.4568i	−0.297037	−	0.205561i
$227$	−224.963	+	224.963i	−0.991028	+	0.991028i	−0.999960	−	0.00893184i	$-0.997157\pi$
$227$	−224.963	+	224.963i	−0.991028	+	0.991028i	0.00893184	+	0.999960i	$0.497157\pi$
$228$		0			0
$229$	26.3030	−	26.3030i	0.114860	−	0.114860i	−0.647341	−	0.762201i	$-0.724119\pi$
$229$	26.3030	−	26.3030i	0.114860	−	0.114860i	0.762201	+	0.647341i	$0.224119\pi$
$230$	371.698	−	67.6513i	1.61608	−	0.294136i
$231$		0			0
$232$	85.1432	−	51.0497i	0.366996	−	0.220042i
$233$	166.492			0.714557			0.357279	−	0.933998i	$-0.383705\pi$
$233$	166.492			0.714557			0.357279	+	0.933998i	$0.383705\pi$
$234$		0			0
$235$	103.538	−	103.538i	0.440587	−	0.440587i
$236$	−126.908	+	280.164i	−0.537744	+	1.18713i
$237$		0			0
$238$	−27.7757	+	40.1360i	−0.116705	+	0.168639i
$239$			247.174i			1.03420i	0.855925	+	0.517100i	$0.172989\pi$
$239$			247.174i			1.03420i	−0.855925	+	0.517100i	$0.827011\pi$
$240$		0			0
$241$	14.7552			0.0612247			0.0306124	−	0.999531i	$-0.490254\pi$
$241$	14.7552			0.0612247			0.0306124	+	0.999531i	$0.490254\pi$
$242$	138.433	+	95.8012i	0.572039	+	0.395873i
$243$		0			0
$244$	−109.962	+	242.753i	−0.450662	+	0.994889i
$245$	188.901	+	188.901i	0.771023	+	0.771023i
$246$		0			0
$247$			14.4136i			0.0583548i
$248$	394.629	+	98.7883i	1.59124	+	0.398340i
$249$		0			0
$250$	38.6034	+	212.099i	0.154414	+	0.848398i
$251$	41.5560	+	41.5560i	0.165562	+	0.165562i	0.785025	−	0.619464i	$-0.212650\pi$
$251$	41.5560	+	41.5560i	0.165562	+	0.165562i	−0.619464	+	0.785025i	$0.712650\pi$
$252$		0			0
$253$	−146.836	−	146.836i	−0.580379	−	0.580379i
$254$	−101.194	+	146.227i	−0.398403	+	0.575695i
$255$		0			0
$256$	33.3162	−	253.823i	0.130141	−	0.991495i
$257$		−	189.265i		−	0.736439i	−0.929739	−	0.368220i	$-0.879967\pi$
$257$		−	189.265i		−	0.736439i	0.929739	−	0.368220i	$-0.120033\pi$
$258$		0			0
$259$	22.8226	+	22.8226i	0.0881180	+	0.0881180i
$260$	188.210	−	70.8581i	0.723884	−	0.272531i
$261$		0			0
$262$	−11.1478	−	61.2496i	−0.0425489	−	0.233777i
$263$	57.5273			0.218735			0.109368	−	0.994001i	$-0.465117\pi$
$263$	57.5273			0.218735			0.109368	+	0.994001i	$0.465117\pi$
$264$		0			0
$265$			76.2252i			0.287642i
$266$	0.441377	+	2.42507i	0.00165931	+	0.00911679i
$267$		0			0
$268$	−154.365	+	340.778i	−0.575988	+	1.27156i
$269$	−121.413	+	121.413i	−0.451350	+	0.451350i	−0.895803	−	0.444452i	$-0.853398\pi$
$269$	−121.413	+	121.413i	−0.451350	+	0.451350i	0.444452	+	0.895803i	$0.353398\pi$
$270$		0			0
$271$	−217.759			−0.803539			−0.401769	−	0.915741i	$-0.631605\pi$
$271$	−217.759			−0.803539			−0.401769	+	0.915741i	$0.631605\pi$
$272$	−330.677	−	376.917i	−1.21572	−	1.38573i
$273$		0			0
$274$	126.097	−	182.211i	0.460208	−	0.665003i
$275$	−23.4865	+	23.4865i	−0.0854056	+	0.0854056i
$276$		0			0
$277$	56.8037	−	56.8037i	0.205068	−	0.205068i	−0.597100	−	0.802167i	$-0.703680\pi$
$277$	56.8037	−	56.8037i	0.205068	−	0.205068i	0.802167	+	0.597100i	$0.203680\pi$
$278$	15.3897	+	84.5559i	0.0553587	+	0.304158i
$279$		0			0
$280$	29.4961	−	17.6851i	0.105343	−	0.0631611i
$281$	58.9828			0.209903			0.104952	−	0.994477i	$-0.466531\pi$
$281$	58.9828			0.209903			0.104952	+	0.994477i	$0.466531\pi$
$282$		0			0
$283$	−170.002	+	170.002i	−0.600713	+	0.600713i	−0.940502	−	0.339789i	$-0.889644\pi$
$283$	−170.002	+	170.002i	−0.600713	+	0.600713i	0.339789	+	0.940502i	$0.389644\pi$
$284$	107.027	+	284.281i	0.376857	+	1.00099i
$285$		0			0
$286$	−90.8940	−	62.9021i	−0.317811	−	0.219938i
$287$		−	24.4740i		−	0.0852753i
$288$		0			0
$289$	−693.086			−2.39822
$290$	−77.9645	+	112.659i	−0.268843	+	0.388480i
$291$		0			0
$292$	90.5896	−	34.1055i	0.310238	−	0.116800i
$293$	−46.1968	−	46.1968i	−0.157668	−	0.157668i	0.623864	−	0.781533i	$-0.285562\pi$
$293$	−46.1968	−	46.1968i	−0.157668	−	0.157668i	−0.781533	+	0.623864i	$0.785562\pi$
$294$		0			0
$295$		−	424.463i		−	1.43886i
$296$	−284.367	+	170.499i	−0.960700	+	0.576012i
$297$		0			0
$298$	483.980	−	88.0874i	1.62409	−	0.295595i
$299$	−220.377	−	220.377i	−0.737046	−	0.737046i
$300$		0			0
$301$	−43.5342	−	43.5342i	−0.144632	−	0.144632i
$302$	43.1740	+	29.8780i	0.142960	+	0.0989339i
$303$		0			0
$304$	−25.2675	−	1.65120i	−0.0831169	−	0.00543157i
$305$		−	367.784i		−	1.20585i
$306$		0			0
$307$	361.635	+	361.635i	1.17796	+	1.17796i	0.980262	+	0.197701i	$0.0633474\pi$
$307$	361.635	+	361.635i	1.17796	+	1.17796i	0.197701	+	0.980262i	$0.436653\pi$
$308$	−17.2189	−	7.79978i	−0.0559056	−	0.0253240i
$309$		0			0
$310$	−552.346	+	100.530i	−1.78176	+	0.324292i
$311$	175.216			0.563395			0.281697	−	0.959503i	$-0.409103\pi$
$311$	175.216			0.563395			0.281697	+	0.959503i	$0.409103\pi$
$312$		0			0
$313$			432.899i			1.38307i	0.722345	+	0.691533i	$0.243064\pi$
$313$			432.899i			1.38307i	−0.722345	+	0.691533i	$0.756936\pi$
$314$	−211.067	+	38.4155i	−0.672187	+	0.122342i
$315$		0			0
$316$	113.518	+	301.521i	0.359233	+	0.954179i
$317$	180.916	−	180.916i	0.570714	−	0.570714i	−0.361614	−	0.932328i	$-0.617774\pi$
$317$	180.916	−	180.916i	0.570714	−	0.570714i	0.932328	+	0.361614i	$0.117774\pi$
$318$		0			0
$319$	75.3043			0.236064
$320$	102.655	+	338.055i	0.320798	+	1.05642i
$321$		0			0
$322$	−43.8264	−	30.3295i	−0.136107	−	0.0941911i
$323$	−35.0694	+	35.0694i	−0.108574	+	0.108574i
$324$		0			0
$325$	−35.2495	+	35.2495i	−0.108460	+	0.108460i
$326$	−432.115	+	78.6476i	−1.32551	+	0.241250i
$327$		0			0
$328$	243.891	+	61.0537i	0.743569	+	0.186139i
$329$	−20.6564			−0.0627855
$330$		0			0
$331$	98.3525	−	98.3525i	0.297137	−	0.297137i	−0.542754	−	0.839892i	$-0.682618\pi$
$331$	98.3525	−	98.3525i	0.297137	−	0.297137i	0.839892	+	0.542754i	$0.182618\pi$
$332$	−425.790	−	192.873i	−1.28250	−	0.580943i
$333$		0			0
$334$	269.623	−	389.607i	0.807253	−	1.16649i
$335$		−	516.297i		−	1.54119i
$336$		0			0
$337$	−384.266			−1.14026			−0.570128	−	0.821556i	$-0.693106\pi$
$337$	−384.266			−1.14026			−0.570128	+	0.821556i	$0.693106\pi$
$338$	141.519	+	97.9365i	0.418695	+	0.289753i
$339$		0			0
$340$	630.330	+	285.525i	1.85391	+	0.839780i
$341$	218.200	+	218.200i	0.639881	+	0.639881i
$342$		0			0
$343$		−	75.8459i		−	0.221125i
$344$	542.433	−	325.229i	1.57684	−	0.945433i
$345$		0			0
$346$	34.6278	+	190.256i	0.100080	+	0.549873i
$347$	−380.232	−	380.232i	−1.09577	−	1.09577i	−0.994900	−	0.100869i	$-0.967838\pi$
$347$	−380.232	−	380.232i	−1.09577	−	1.09577i	−0.100869	−	0.994900i	$-0.532162\pi$
$348$		0			0
$349$	260.199	+	260.199i	0.745555	+	0.745555i	0.973641	−	0.228086i	$-0.0732466\pi$
$349$	260.199	+	260.199i	0.745555	+	0.745555i	−0.228086	+	0.973641i	$0.573247\pi$
$350$	−4.85123	+	7.01007i	−0.0138607	+	0.0200288i
$351$		0			0
$352$	120.682	−	152.134i	0.342846	−	0.432199i
$353$		−	97.9162i		−	0.277383i	−0.990336	−	0.138692i	$-0.955710\pi$
$353$		−	97.9162i		−	0.277383i	0.990336	−	0.138692i	$-0.0442897\pi$
$354$		0			0
$355$	−296.427	−	296.427i	−0.835006	−	0.835006i
$356$	−116.476	−	309.379i	−0.327180	−	0.869042i
$357$		0			0
$358$	65.6521	+	360.713i	0.183386	+	1.00758i
$359$	−126.839			−0.353311			−0.176656	−	0.984273i	$-0.556528\pi$
$359$	−126.839			−0.353311			−0.176656	+	0.984273i	$0.556528\pi$
$360$		0			0
$361$		−	358.495i		−	0.993062i
$362$	79.8408	+	438.670i	0.220555	+	1.21180i
$363$		0			0
$364$	−25.8428	−	11.7062i	−0.0709967	−	0.0321599i
$365$	−94.4600	+	94.4600i	−0.258794	+	0.258794i
$366$		0			0
$367$	−354.084			−0.964807			−0.482404	−	0.875949i	$-0.660236\pi$
$367$	−354.084			−0.964807			−0.482404	+	0.875949i	$0.660236\pi$
$368$	411.573	−	361.081i	1.11841	−	0.981199i
$369$		0			0
$370$	260.391	−	376.267i	0.703761	−	1.01694i
$371$	7.60369	−	7.60369i	0.0204951	−	0.0204951i
$372$		0			0
$373$	77.4388	−	77.4388i	0.207611	−	0.207611i	−0.595640	−	0.803251i	$-0.703102\pi$
$373$	77.4388	−	77.4388i	0.207611	−	0.207611i	0.803251	+	0.595640i	$0.203102\pi$
$374$	−68.1062	−	374.197i	−0.182102	−	1.00053i
$375$		0			0
$376$	51.5302	−	205.847i	0.137048	−	0.547466i
$377$	113.019			0.299786
$378$		0			0
$379$	−209.955	+	209.955i	−0.553971	+	0.553971i	−0.927584	−	0.373614i	$-0.878119\pi$
$379$	−209.955	+	209.955i	−0.553971	+	0.553971i	0.373614	+	0.927584i	$0.378119\pi$
$380$	32.7044	−	12.3127i	0.0860641	−	0.0324018i
$381$		0			0
$382$	−95.5865	−	66.1495i	−0.250226	−	0.173166i
$383$		−	579.620i		−	1.51337i	−0.653781	−	0.756684i	$-0.726818\pi$
$383$		−	579.620i		−	1.51337i	0.653781	−	0.756684i	$-0.273182\pi$
$384$		0			0
$385$	26.0876			0.0677601
$386$	−355.652	+	513.920i	−0.921378	+	1.33140i
$387$		0			0
$388$	−68.9852	−	183.235i	−0.177797	−	0.472256i
$389$	420.113	+	420.113i	1.07998	+	1.07998i	0.996510	+	0.0834708i	$0.0266005\pi$
$389$	420.113	+	420.113i	1.07998	+	1.07998i	0.0834708	+	0.996510i	$0.473399\pi$
$390$		0			0
$391$		−	1072.38i		−	2.74267i
$392$	375.560	+	94.0147i	0.958060	+	0.239833i
$393$		0			0
$394$	124.751	−	22.7054i	0.316626	−	0.0576280i
$395$	−314.403	−	314.403i	−0.795957	−	0.795957i
$396$		0			0
$397$	13.0474	+	13.0474i	0.0328650	+	0.0328650i	0.723348	−	0.690483i	$-0.242602\pi$
$397$	13.0474	+	13.0474i	0.0328650	+	0.0328650i	−0.690483	+	0.723348i	$0.742602\pi$
$398$	−258.416	−	178.834i	−0.649286	−	0.449331i
$399$		0			0
$400$	−57.7553	−	65.8315i	−0.144388	−	0.164579i
$401$			152.424i			0.380110i	0.981773	+	0.190055i	$0.0608666\pi$
$401$			152.424i			0.380110i	−0.981773	+	0.190055i	$0.939133\pi$
$402$		0			0
$403$	327.482	+	327.482i	0.812610	+	0.812610i
$404$	−96.3475	+	212.698i	−0.238484	+	0.526481i
$405$		0			0
$406$	19.0153	−	3.46090i	0.0468357	−	0.00852439i
$407$	−251.507			−0.617952
$408$		0			0
$409$		−	43.2426i		−	0.105728i	−0.998602	−	0.0528639i	$-0.983165\pi$
$409$		−	43.2426i		−	0.105728i	0.998602	−	0.0528639i	$-0.0168349\pi$
$410$	−341.364	+	62.1304i	−0.832595	+	0.151538i
$411$		0			0
$412$	648.506	−	244.152i	1.57404	−	0.592603i
$413$	−42.3415	+	42.3415i	−0.102522	+	0.102522i
$414$		0			0
$415$	645.095			1.55445
$416$	181.124	−	228.328i	0.435394	−	0.548866i
$417$		0			0
$418$	−15.7942	−	10.9302i	−0.0377852	−	0.0261488i
$419$	−81.3896	+	81.3896i	−0.194247	+	0.194247i	−0.797528	−	0.603281i	$-0.793860\pi$
$419$	−81.3896	+	81.3896i	−0.194247	+	0.194247i	0.603281	+	0.797528i	$0.293860\pi$
$420$		0			0
$421$	198.570	−	198.570i	0.471663	−	0.471663i	−0.430789	−	0.902452i	$-0.641765\pi$
$421$	198.570	−	198.570i	0.471663	−	0.471663i	0.902452	+	0.430789i	$0.141765\pi$
$422$	190.180	−	34.6139i	0.450663	−	0.0820235i
$423$		0			0
$424$	56.8045	+	94.7414i	0.133973	+	0.223447i
$425$	−171.529			−0.403597
$426$		0			0
$427$	−36.6875	+	36.6875i	−0.0859193	+	0.0859193i
$428$	124.353	−	274.524i	0.290544	−	0.641410i
$429$		0			0
$430$	−496.699	+	717.733i	−1.15511	+	1.66915i
$431$			395.497i			0.917627i	0.888533	+	0.458813i	$0.151725\pi$
$431$			395.497i			0.917627i	−0.888533	+	0.458813i	$0.848275\pi$
$432$		0			0
$433$	−672.683			−1.55354			−0.776770	−	0.629784i	$-0.783143\pi$
$433$	−672.683			−1.55354			−0.776770	+	0.629784i	$0.783143\pi$
$434$	65.1264	+	45.0699i	0.150061	+	0.103848i
$435$		0			0
$436$	−217.432	+	480.007i	−0.498698	+	1.10093i
$437$	−38.2939	−	38.2939i	−0.0876290	−	0.0876290i
$438$		0			0
$439$			26.8920i			0.0612574i	0.999531	+	0.0306287i	$0.00975095\pi$
$439$			26.8920i			0.0612574i	−0.999531	+	0.0306287i	$0.990249\pi$
$440$	−65.0790	+	259.971i	−0.147907	+	0.590842i
$441$		0			0
$442$	−102.216	−	561.608i	−0.231258	−	1.27061i
$443$	524.214	+	524.214i	1.18333	+	1.18333i	0.978877	+	0.204451i	$0.0655408\pi$
$443$	524.214	+	524.214i	1.18333	+	1.18333i	0.204451	+	0.978877i	$0.434459\pi$
$444$		0			0
$445$	322.597	+	322.597i	0.724937	+	0.724937i
$446$	4.26949	−	6.16944i	0.00957285	−	0.0138328i
$447$		0			0
$448$	23.4818	−	43.9622i	0.0524148	−	0.0981298i
$449$			518.381i			1.15452i	0.816559	+	0.577262i	$0.195879\pi$
$449$			518.381i			1.15452i	−0.816559	+	0.577262i	$0.804121\pi$
$450$		0			0
$451$	134.853	+	134.853i	0.299009	+	0.299009i
$452$	152.805	−	57.5287i	0.338064	−	0.127276i
$453$		0			0
$454$	−113.937	−	626.008i	−0.250964	−	1.37887i
$455$	39.1533			0.0860511
$456$		0			0
$457$			853.516i			1.86765i	0.357729	+	0.933825i	$0.383551\pi$
$457$			853.516i			1.86765i	−0.357729	+	0.933825i	$0.616449\pi$
$458$	13.3217	+	73.1936i	0.0290867	+	0.159811i
$459$		0			0
$460$	−311.778	+	688.286i	−0.677778	+	1.49627i
$461$	331.810	−	331.810i	0.719761	−	0.719761i	−0.248795	−	0.968556i	$-0.580034\pi$
$461$	331.810	−	331.810i	0.719761	−	0.719761i	0.968556	+	0.248795i	$0.0800345\pi$
$462$		0			0
$463$	−164.893			−0.356141			−0.178070	−	0.984018i	$-0.556986\pi$
$463$	−164.893			−0.356141			−0.178070	+	0.984018i	$0.556986\pi$
$464$	−12.9473	+	198.126i	−0.0279036	+	0.426997i
$465$		0			0
$466$	−189.488	+	273.811i	−0.406626	+	0.587577i
$467$	−105.253	+	105.253i	−0.225380	+	0.225380i	−0.810760	−	0.585379i	$-0.800946\pi$
$467$	−105.253	+	105.253i	−0.225380	+	0.225380i	0.585379	+	0.810760i	$0.300946\pi$
$468$		0			0
$469$	−51.5022	+	51.5022i	−0.109813	+	0.109813i
$470$	52.4390	+	288.116i	0.111572	+	0.613013i
$471$		0			0
$472$	−316.318	−	527.571i	−0.670166	−	1.11774i
$473$	479.751			1.01427
$474$		0			0
$475$	−6.12514	+	6.12514i	−0.0128950	+	0.0128950i
$476$	−34.3953	−	91.3593i	−0.0722591	−	0.191931i
$477$		0			0
$478$	−406.500	−	281.314i	−0.850419	−	0.588523i
$479$		−	678.054i		−	1.41556i	−0.706432	−	0.707781i	$-0.749696\pi$
$479$		−	678.054i		−	1.41556i	0.706432	−	0.707781i	$-0.250304\pi$
$480$		0			0
$481$	−377.470			−0.784762
$482$	−16.7932	+	24.2662i	−0.0348406	+	0.0503449i
$483$		0			0
$484$	−315.108	+	118.633i	−0.651049	+	0.245110i
$485$	191.064	+	191.064i	0.393947	+	0.393947i
$486$		0			0
$487$		−	7.72273i		−	0.0158578i	−0.999969	−	0.00792888i	$-0.997476\pi$
$487$		−	7.72273i		−	0.0158578i	0.999969	−	0.00792888i	$-0.00252387\pi$
$488$	−274.080	−	457.124i	−0.561639	−	0.936729i
$489$		0			0
$490$	−525.656	+	95.6727i	−1.07277	+	0.195250i
$491$	−296.311	−	296.311i	−0.603484	−	0.603484i	0.337751	−	0.941235i	$-0.390334\pi$
$491$	−296.311	−	296.311i	−0.603484	−	0.603484i	−0.941235	+	0.337751i	$0.890334\pi$
$492$		0			0
$493$	274.984	+	274.984i	0.557777	+	0.557777i
$494$	−23.7046	−	16.4045i	−0.0479849	−	0.0332074i
$495$		0			0
$496$	−611.601	+	536.570i	−1.23307	+	1.08179i
$497$			59.1390i			0.118992i
$498$		0			0
$499$	555.542	+	555.542i	1.11331	+	1.11331i	0.992700	+	0.120612i	$0.0384856\pi$
$499$	555.542	+	555.542i	1.11331	+	1.11331i	0.120612	+	0.992700i	$0.461514\pi$
$500$	−392.752	−	177.908i	−0.785504	−	0.355816i
$501$		0			0
$502$	−115.638	+	21.0469i	−0.230356	+	0.0419262i
$503$	322.916			0.641979			0.320990	−	0.947083i	$-0.395985\pi$
$503$	322.916			0.641979			0.320990	+	0.947083i	$0.395985\pi$
$504$		0			0
$505$		−	322.250i		−	0.638118i
$506$	408.602	−	74.3682i	0.807514	−	0.146973i
$507$		0			0
$508$	−125.312	−	332.847i	−0.246676	−	0.655210i
$509$	−522.344	+	522.344i	−1.02622	+	1.02622i	−0.0265686	+	0.999647i	$0.508458\pi$
$509$	−522.344	+	522.344i	−1.02622	+	1.02622i	−0.999647	+	0.0265686i	$0.991542\pi$
$510$		0			0
$511$	18.8453			0.0368793
$512$	379.517	+	343.672i	0.741244	+	0.671235i
$513$		0			0
$514$	311.264	+	215.406i	0.605571	+	0.419078i
$515$	−676.213	+	676.213i	−1.31304	+	1.31304i
$516$		0			0
$517$	113.818	−	113.818i	0.220150	−	0.220150i
$518$	−63.5086	+	11.5590i	−0.122603	+	0.0223146i
$519$		0			0
$520$	−97.6730	+	390.173i	−0.187833	+	0.750334i
$521$	−80.4109			−0.154340			−0.0771698	−	0.997018i	$-0.524588\pi$
$521$	−80.4109			−0.154340			−0.0771698	+	0.997018i	$0.524588\pi$
$522$		0			0
$523$	133.868	−	133.868i	0.255962	−	0.255962i	−0.567447	−	0.823410i	$-0.692069\pi$
$523$	133.868	−	133.868i	0.255962	−	0.255962i	0.823410	+	0.567447i	$0.192069\pi$
$524$	113.418	+	51.3758i	0.216447	+	0.0980454i
$525$		0			0
$526$	−65.4731	+	94.6090i	−0.124473	+	0.179865i
$527$			1593.57i			3.02386i
$528$		0			0
$529$	641.985			1.21358
$530$	−125.359	−	86.7535i	−0.236527	−	0.163686i
$531$		0			0
$532$	−4.49058	−	2.03413i	−0.00844094	−	0.00382355i
$533$	202.392	+	202.392i	0.379723	+	0.379723i
$534$		0			0
$535$			415.918i			0.777417i
$536$	−384.755	−	641.713i	−0.717827	−	1.19723i
$537$		0			0
$538$	−61.4923	−	337.858i	−0.114298	−	0.627989i
$539$	207.656	+	207.656i	0.385261	+	0.385261i
$540$		0			0
$541$	−643.791	−	643.791i	−1.19000	−	1.19000i	−0.977066	−	0.212936i	$-0.931698\pi$
$541$	−643.791	−	643.791i	−1.19000	−	1.19000i	−0.212936	−	0.977066i	$-0.568302\pi$
$542$	247.836	−	358.125i	0.457262	−	0.660747i
$543$		0			0
$544$	996.226	−	114.851i	1.83130	−	0.211124i
$545$		−	727.237i		−	1.33438i
$546$		0			0
$547$	−543.953	−	543.953i	−0.994429	−	0.994429i	0.00555539	−	0.999985i	$-0.498232\pi$
$547$	−543.953	−	543.953i	−0.994429	−	0.994429i	−0.999985	+	0.00555539i	$0.998232\pi$
$548$	156.149	+	414.756i	0.284943	+	0.756854i
$549$		0			0
$550$	−11.8953	−	65.3563i	−0.0216277	−	0.118830i
$551$	19.6389			0.0356422
$552$		0			0
$553$			62.7252i			0.113427i
$554$	28.7695	+	158.068i	0.0519304	+	0.285322i
$555$		0			0
$556$	−156.575	−	70.9250i	−0.281610	−	0.127563i
$557$	−436.430	+	436.430i	−0.783537	+	0.783537i	−0.980426	−	0.196889i	$-0.936916\pi$
$557$	−436.430	+	436.430i	−0.783537	+	0.783537i	0.196889	+	0.980426i	$0.436916\pi$
$558$		0			0
$559$	720.027			1.28806
$560$	−4.48532	+	68.6368i	−0.00800950	+	0.122566i
$561$		0			0
$562$	−67.1295	+	97.0026i	−0.119448	+	0.172602i
$563$	525.339	−	525.339i	0.933107	−	0.933107i	−0.0647918	−	0.997899i	$-0.520638\pi$
$563$	525.339	−	525.339i	0.933107	−	0.933107i	0.997899	+	0.0647918i	$0.0206383\pi$
$564$		0			0
$565$	−159.334	+	159.334i	−0.282006	+	0.282006i
$566$	−86.1010	−	473.066i	−0.152122	−	0.835806i
$567$		0			0
$568$	−589.337	−	147.530i	−1.03756	−	0.259736i
$569$	−848.985			−1.49207			−0.746033	−	0.665909i	$-0.768044\pi$
$569$	−848.985			−1.49207			−0.746033	+	0.665909i	$0.768044\pi$
$570$		0			0
$571$	503.454	−	503.454i	0.881706	−	0.881706i	−0.112002	−	0.993708i	$-0.535726\pi$
$571$	503.454	−	503.454i	0.881706	−	0.881706i	0.993708	+	0.112002i	$0.0357264\pi$
$572$	206.897	−	77.8933i	0.361707	−	0.136177i
$573$		0			0
$574$	40.2498	+	27.8544i	0.0701216	+	0.0485268i
$575$		−	187.300i		−	0.325739i
$576$		0			0
$577$	891.580			1.54520			0.772600	−	0.634894i	$-0.218956\pi$
$577$	891.580			1.54520			0.772600	+	0.634894i	$0.218956\pi$
$578$	788.816	−	1139.84i	1.36473	−	1.97205i
$579$		0			0
$580$	−96.5454	−	256.440i	−0.166458	−	0.442137i
$581$	−64.3501	−	64.3501i	−0.110758	−	0.110758i
$582$		0			0
$583$			83.7934i			0.143728i
$584$	−47.0122	+	187.799i	−0.0805003	+	0.321574i
$585$		0			0
$586$	128.552	−	23.3974i	0.219373	−	0.0399272i
$587$	−121.737	−	121.737i	−0.207388	−	0.207388i	0.595768	−	0.803156i	$-0.296848\pi$
$587$	−121.737	−	121.737i	−0.207388	−	0.207388i	−0.803156	+	0.595768i	$0.796848\pi$
$588$		0			0
$589$	56.9050	+	56.9050i	0.0966129	+	0.0966129i
$590$	698.068	+	483.090i	1.18317	+	0.818797i
$591$		0			0
$592$	43.2422	−	661.717i	0.0730443	−	1.11776i
$593$		−	207.925i		−	0.350632i	−0.984512	−	0.175316i	$-0.943905\pi$
$593$		−	207.925i		−	0.350632i	0.984512	−	0.175316i	$-0.0560947\pi$
$594$		0			0
$595$	95.2626	+	95.2626i	0.160105	+	0.160105i
$596$	−405.960	+	896.204i	−0.681141	+	1.50370i
$597$		0			0
$598$	613.245	−	111.615i	1.02549	−	0.186646i
$599$	689.528			1.15113			0.575566	−	0.817755i	$-0.304782\pi$
$599$	689.528			1.15113			0.575566	+	0.817755i	$0.304782\pi$
$600$		0			0
$601$		−	542.421i		−	0.902531i	−0.892390	−	0.451266i	$-0.850973\pi$
$601$		−	542.421i		−	0.902531i	0.892390	−	0.451266i	$-0.149027\pi$
$602$	121.143	−	22.0488i	0.201234	−	0.0366259i
$603$		0			0
$604$	−98.2743	+	36.9987i	−0.162706	+	0.0612562i
$605$	328.571	−	328.571i	0.543092	−	0.543092i
$606$		0			0
$607$	−1018.93			−1.67864			−0.839318	−	0.543641i	$-0.817045\pi$
$607$	−1018.93			−1.67864			−0.839318	+	0.543641i	$0.817045\pi$
$608$	31.4731	−	39.6755i	0.0517649	−	0.0652558i
$609$		0			0
$610$	604.855	+	418.583i	0.991565	+	0.686201i
$611$	170.822	−	170.822i	0.279578	−	0.279578i
$612$		0			0
$613$	169.481	−	169.481i	0.276478	−	0.276478i	−0.555223	−	0.831701i	$-0.687367\pi$
$613$	169.481	−	169.481i	0.276478	−	0.276478i	0.831701	+	0.555223i	$0.187367\pi$
$614$	−1006.33	+	183.158i	−1.63897	+	0.298302i
$615$		0			0
$616$	32.4247	−	19.4410i	0.0526374	−	0.0315601i
$617$	834.597			1.35267			0.676335	−	0.736594i	$-0.263567\pi$
$617$	834.597			1.35267			0.676335	+	0.736594i	$0.263567\pi$
$618$		0			0
$619$	−322.772	+	322.772i	−0.521441	+	0.521441i	−0.918007	−	0.396565i	$-0.870202\pi$
$619$	−322.772	+	322.772i	−0.521441	+	0.521441i	0.396565	+	0.918007i	$0.370202\pi$
$620$	463.305	−	1022.80i	0.747266	−	1.64968i
$621$		0			0
$622$	−199.417	+	288.158i	−0.320606	+	0.463277i
$623$		−	64.3600i		−	0.103307i
$624$		0			0
$625$	731.878			1.17100
$626$	−711.943	−	492.692i	−1.13729	−	0.787048i
$627$		0			0
$628$	177.042	−	390.840i	0.281913	−	0.622357i
$629$	−918.411	−	918.411i	−1.46011	−	1.46011i
$630$		0			0
$631$			1006.06i			1.59439i	0.603723	+	0.797194i	$0.293683\pi$
$631$			1006.06i			1.59439i	−0.603723	+	0.797194i	$0.706317\pi$
$632$	−625.075	−	156.476i	−0.989043	−	0.247589i
$633$		0			0
$634$	91.6290	+	503.438i	0.144525	+	0.794067i
$635$	347.068	+	347.068i	0.546563	+	0.546563i
$636$		0			0
$637$	311.658	+	311.658i	0.489258	+	0.489258i
$638$	−85.7053	+	123.845i	−0.134334	+	0.194114i
$639$		0			0
$640$	−672.797	−	215.921i	−1.05124	−	0.337377i
$641$			257.206i			0.401257i	0.979667	+	0.200628i	$0.0642984\pi$
$641$			257.206i			0.401257i	−0.979667	+	0.200628i	$0.935702\pi$
$642$		0			0
$643$	−311.891	−	311.891i	−0.485056	−	0.485056i	0.421686	−	0.906742i	$-0.361438\pi$
$643$	−311.891	−	311.891i	−0.485056	−	0.485056i	−0.906742	+	0.421686i	$0.861438\pi$
$644$	99.7594	−	37.5578i	0.154906	−	0.0583196i
$645$		0			0
$646$	−17.7616	−	97.5880i	−0.0274948	−	0.151065i
$647$	−855.255			−1.32188			−0.660939	−	0.750440i	$-0.729842\pi$
$647$	−855.255			−1.32188			−0.660939	+	0.750440i	$0.729842\pi$
$648$		0			0
$649$		−	466.607i		−	0.718962i
$650$	−17.8528	−	98.0891i	−0.0274659	−	0.150906i
$651$		0			0
$652$	362.456	−	800.163i	0.555913	−	1.22724i
$653$	171.197	−	171.197i	0.262170	−	0.262170i	−0.563765	−	0.825935i	$-0.690648\pi$
$653$	171.197	−	171.197i	0.262170	−	0.262170i	0.825935	+	0.563765i	$0.190648\pi$
$654$		0			0
$655$	−171.835			−0.262343
$656$	−377.985	+	331.614i	−0.576197	+	0.505509i
$657$		0			0
$658$	23.5095	−	33.9714i	0.0357287	−	0.0516282i
$659$	510.283	−	510.283i	0.774330	−	0.774330i	−0.204530	−	0.978860i	$-0.565567\pi$
$659$	510.283	−	510.283i	0.774330	−	0.774330i	0.978860	+	0.204530i	$0.0655667\pi$
$660$		0			0
$661$	491.063	−	491.063i	0.742910	−	0.742910i	−0.230227	−	0.973137i	$-0.573947\pi$
$661$	491.063	−	491.063i	0.742910	−	0.742910i	0.973137	+	0.230227i	$0.0739470\pi$
$662$	49.8127	+	273.687i	0.0752458	+	0.413424i
$663$		0			0
$664$	801.797	−	480.738i	1.20753	−	0.724002i
$665$	6.80348			0.0102308
$666$		0			0
$667$	−300.268	+	300.268i	−0.450176	+	0.450176i
$668$	333.881	+	886.838i	0.499821	+	1.32760i
$669$		0			0
$670$	849.098	+	587.609i	1.26731	+	0.877028i
$671$		−	404.300i		−	0.602534i
$672$		0			0
$673$	−200.282			−0.297596			−0.148798	−	0.988868i	$-0.547540\pi$
$673$	−200.282			−0.297596			−0.148798	+	0.988868i	$0.547540\pi$
$674$	437.341	−	631.961i	0.648874	−	0.937628i
$675$		0			0
$676$	−322.131	+	121.277i	−0.476525	+	0.179404i
$677$	−818.346	−	818.346i	−1.20878	−	1.20878i	−0.971422	−	0.237361i	$-0.923718\pi$
$677$	−818.346	−	818.346i	−1.20878	−	1.20878i	−0.237361	−	0.971422i	$-0.576282\pi$
$678$		0			0
$679$		−	38.1184i		−	0.0561391i
$680$	−1186.96	+	711.674i	−1.74554	+	1.04658i
$681$		0			0
$682$	−607.187	+	110.512i	−0.890303	+	0.162041i
$683$	−559.041	−	559.041i	−0.818508	−	0.818508i	0.167383	−	0.985892i	$-0.446468\pi$
$683$	−559.041	−	559.041i	−0.818508	−	0.818508i	−0.985892	+	0.167383i	$0.946468\pi$
$684$		0			0
$685$	−432.476	−	432.476i	−0.631352	−	0.631352i
$686$	124.735	+	86.3217i	0.181830	+	0.125833i
$687$		0			0
$688$	−82.4849	+	1262.23i	−0.119891	+	1.83464i
$689$			125.760i			0.182526i
$690$		0			0
$691$	−558.744	−	558.744i	−0.808602	−	0.808602i	0.175820	−	0.984422i	$-0.443742\pi$
$691$	−558.744	−	558.744i	−0.808602	−	0.808602i	−0.984422	+	0.175820i	$0.943742\pi$
$692$	−352.304	−	159.586i	−0.509110	−	0.230615i
$693$		0			0
$694$	1058.08	−	192.576i	1.52460	−	0.277488i
$695$	237.220			0.341324
$696$		0			0
$697$			984.869i			1.41301i
$698$	−724.059	+	131.783i	−1.03733	+	0.188801i
$699$		0			0
$700$	−6.00741	−	15.9566i	−0.00858201	−	0.0227951i
$701$	452.428	−	452.428i	0.645404	−	0.645404i	−0.306475	−	0.951879i	$-0.599149\pi$
$701$	452.428	−	452.428i	0.645404	−	0.645404i	0.951879	+	0.306475i	$0.0991495\pi$
$702$		0			0
$703$	−65.5913			−0.0933019
$704$	112.848	+	371.619i	0.160295	+	0.527868i
$705$		0			0
$706$	161.032	+	111.440i	0.228091	+	0.157848i
$707$	−32.1454	+	32.1454i	−0.0454673	+	0.0454673i
$708$		0			0
$709$	−693.360	+	693.360i	−0.977941	+	0.977941i	−0.999762	−	0.0218205i	$-0.993054\pi$
$709$	−693.360	+	693.360i	−0.977941	+	0.977941i	0.0218205	+	0.999762i	$0.493054\pi$
$710$	824.871	−	150.132i	1.16179	−	0.211453i
$711$		0			0
$712$	641.366	+	160.555i	0.900795	+	0.225498i
$713$	−1740.09			−2.44052
$714$		0			0
$715$	−215.736	+	215.736i	−0.301729	+	0.301729i
$716$	−667.946	−	302.564i	−0.932885	−	0.422576i
$717$		0			0
$718$	144.358	−	208.598i	0.201055	−	0.290526i
$719$			641.528i			0.892251i	0.894970	+	0.446125i	$0.147196\pi$
$719$			641.528i			0.892251i	−0.894970	+	0.446125i	$0.852804\pi$
$720$		0			0
$721$	134.909			0.187113
$722$	589.579	+	408.011i	0.816591	+	0.565112i
$723$		0			0
$724$	−812.302	−	367.954i	−1.12196	−	0.508224i
$725$	48.0281	+	48.0281i	0.0662456	+	0.0662456i
$726$		0			0
$727$			644.665i			0.886747i	0.896337	+	0.443373i	$0.146218\pi$
$727$			644.665i			0.886747i	−0.896337	+	0.443373i	$0.853782\pi$
$728$	48.6641	−	29.1778i	0.0668463	−	0.0400794i
$729$		0			0
$730$	−47.8412	−	262.855i	−0.0655360	−	0.360075i
$731$	1751.88	+	1751.88i	2.39655	+	2.39655i
$732$		0			0
$733$	−748.983	−	748.983i	−1.02180	−	1.02180i	−0.999757	−	0.0220473i	$-0.992982\pi$
$733$	−748.983	−	748.983i	−1.02180	−	1.02180i	−0.0220473	−	0.999757i	$-0.507018\pi$
$734$	402.991	−	582.324i	0.549034	−	0.793357i
$735$		0			0
$736$	125.411	+	1087.82i	0.170396	+	1.47802i
$737$		−	567.559i		−	0.770093i
$738$		0			0
$739$	−387.245	−	387.245i	−0.524013	−	0.524013i	0.394768	−	0.918781i	$-0.370825\pi$
$739$	−387.245	−	387.245i	−0.524013	−	0.524013i	−0.918781	+	0.394768i	$0.870825\pi$
$740$	322.449	+	856.475i	0.435742	+	1.15740i
$741$		0			0
$742$	3.85105	+	21.1589i	0.00519009	+	0.0285160i
$743$	−245.165			−0.329966			−0.164983	−	0.986296i	$-0.552757\pi$
$743$	−245.165			−0.329966			−0.164983	+	0.986296i	$0.552757\pi$
$744$		0			0
$745$		−	1357.80i		−	1.82255i
$746$	39.2205	+	215.490i	0.0525744	+	0.288860i
$747$		0			0
$748$	692.914	+	313.874i	0.926355	+	0.419618i
$749$	41.4891	−	41.4891i	0.0553926	−	0.0553926i
$750$		0			0
$751$	−547.753			−0.729365			−0.364683	−	0.931132i	$-0.618822\pi$
$751$	−547.753			−0.729365			−0.364683	+	0.931132i	$0.618822\pi$
$752$	279.887	+	319.025i	0.372190	+	0.424235i
$753$		0			0
$754$	−128.630	+	185.871i	−0.170596	+	0.246513i
$755$	102.473	−	102.473i	0.135726	−	0.135726i
$756$		0			0
$757$	−876.755	+	876.755i	−1.15820	+	1.15820i	−0.173334	+	0.984863i	$0.555454\pi$
$757$	−876.755	+	876.755i	−1.15820	+	1.15820i	−0.984863	+	0.173334i	$0.944546\pi$
$758$	−106.336	−	584.244i	−0.140285	−	0.770770i
$759$		0			0
$760$	−16.9722	+	67.7986i	−0.0223318	+	0.0892087i
$761$	876.682			1.15201			0.576007	−	0.817445i	$-0.304610\pi$
$761$	876.682			1.15201			0.576007	+	0.817445i	$0.304610\pi$
$762$		0			0
$763$	−72.5441	+	72.5441i	−0.0950774	+	0.0950774i
$764$	217.578	−	81.9146i	0.284788	−	0.107218i
$765$		0			0
$766$	953.238	+	659.677i	1.24444	+	0.861198i
$767$		−	700.300i		−	0.913038i
$768$		0			0
$769$	−155.364			−0.202034			−0.101017	−	0.994885i	$-0.532210\pi$
$769$	−155.364			−0.202034			−0.101017	+	0.994885i	$0.532210\pi$
$770$	−29.6909	+	42.9035i	−0.0385596	+	0.0557188i
$771$		0			0
$772$	−440.413	−	1169.80i	−0.570483	−	1.51529i
$773$	−336.932	−	336.932i	−0.435876	−	0.435876i	0.454746	−	0.890621i	$-0.349730\pi$
$773$	−336.932	−	336.932i	−0.435876	−	0.435876i	−0.890621	+	0.454746i	$0.849730\pi$
$774$		0			0
$775$			278.330i			0.359135i
$776$	379.861	+	95.0915i	0.489512	+	0.122541i
$777$		0			0
$778$	−1169.05	+	212.775i	−1.50264	+	0.273490i
$779$	35.1688	+	35.1688i	0.0451460	+	0.0451460i
$780$		0			0
$781$	−325.858	−	325.858i	−0.417232	−	0.417232i
$782$	1763.63	+	1220.50i	2.25529	+	1.56074i
$783$		0			0
$784$	−582.048	+	510.642i	−0.742408	+	0.651329i
$785$			592.144i			0.754324i
$786$		0			0
$787$	201.318	+	201.318i	0.255804	+	0.255804i	0.823345	−	0.567541i	$-0.192105\pi$
$787$	201.318	+	201.318i	0.255804	+	0.255804i	−0.567541	+	0.823345i	$0.692105\pi$
$788$	−104.640	+	231.006i	−0.132792	+	0.293154i
$789$		0			0
$790$	874.893	−	159.236i	1.10746	−	0.201565i
$791$	31.7880			0.0401871
$792$		0			0
$793$		−	606.788i		−	0.765181i
$794$	−36.3071	+	6.60812i	−0.0457268	+	0.00832257i
$795$		0			0
$796$	588.216	−	221.454i	0.738965	−	0.278209i
$797$	571.213	−	571.213i	0.716704	−	0.716704i	−0.251225	−	0.967929i	$-0.580833\pi$
$797$	571.213	−	571.213i	0.716704	−	0.716704i	0.967929	+	0.251225i	$0.0808333\pi$
$798$		0			0
$799$	831.243			1.04035
$800$	173.998	−	20.0597i	0.217498	−	0.0250746i
$801$		0			0
$802$	−250.675	−	173.477i	−0.312563	−	0.216306i
$803$	−103.839	+	103.839i	−0.129313	+	0.129313i
$804$		0			0
$805$	−104.022	+	104.022i	−0.129219	+	0.129219i
$806$	−911.288	+	165.860i	−1.13063	+	0.205782i
$807$		0			0
$808$	−240.147	−	400.529i	−0.297212	−	0.495704i
$809$	554.891			0.685898			0.342949	−	0.939354i	$-0.388574\pi$
$809$	554.891			0.685898			0.342949	+	0.939354i	$0.388574\pi$
$810$		0			0
$811$	570.087	−	570.087i	0.702944	−	0.702944i	−0.262098	−	0.965041i	$-0.584414\pi$
$811$	570.087	−	570.087i	0.702944	−	0.702944i	0.965041	+	0.262098i	$0.0844143\pi$
$812$	−15.9499	+	35.2113i	−0.0196427	+	0.0433637i
$813$		0			0
$814$	286.245	−	413.626i	0.351652	−	0.508140i
$815$			1212.29i			1.48747i
$816$		0			0
$817$	125.116			0.153141
$818$	71.1165	+	49.2153i	0.0869395	+	0.0601655i
$819$		0			0
$820$	286.334	−	632.116i	0.349188	−	0.770874i
$821$	150.698	+	150.698i	0.183554	+	0.183554i	0.792903	−	0.609348i	$-0.208569\pi$
$821$	150.698	+	150.698i	0.183554	+	0.183554i	−0.609348	+	0.792903i	$0.708569\pi$
$822$		0			0
$823$			742.019i			0.901603i	0.892624	+	0.450801i	$0.148862\pi$
$823$			742.019i			0.901603i	−0.892624	+	0.450801i	$0.851138\pi$
$824$	−336.547	+	1344.40i	−0.408431	+	1.63156i
$825$		0			0
$826$	−21.4447	−	117.824i	−0.0259621	−	0.142644i
$827$	248.150	+	248.150i	0.300061	+	0.300061i	0.841037	−	0.540977i	$-0.181945\pi$
$827$	248.150	+	248.150i	0.300061	+	0.300061i	−0.540977	+	0.841037i	$0.681945\pi$
$828$		0			0
$829$	373.174	+	373.174i	0.450150	+	0.450150i	0.895404	−	0.445255i	$-0.146887\pi$
$829$	373.174	+	373.174i	0.450150	+	0.450150i	−0.445255	+	0.895404i	$0.646887\pi$
$830$	−734.196	+	1060.92i	−0.884573	+	1.27821i
$831$		0			0
$832$	169.366	+	557.740i	0.203565	+	0.670361i
$833$			1516.57i			1.82061i
$834$		0			0
$835$	−924.728	−	924.728i	−1.10746	−	1.10746i
$836$	35.9515	−	13.5352i	0.0430041	−	0.0161904i
$837$		0			0
$838$	−41.2215	−	226.484i	−0.0491903	−	0.270267i
$839$	−1227.49			−1.46304			−0.731520	−	0.681820i	$-0.761189\pi$
$839$	−1227.49			−1.46304			−0.731520	+	0.681820i	$0.761189\pi$
$840$		0			0
$841$			687.009i			0.816895i
$842$	100.570	+	552.563i	0.119442	+	0.656251i
$843$		0			0
$844$	−159.522	+	352.163i	−0.189007	+	0.417255i
$845$	335.894	−	335.894i	0.397508	−	0.397508i
$846$		0			0
$847$	−65.5518			−0.0773929
$848$	−220.461	−	14.4068i	−0.259978	−	0.0169892i
$849$		0			0
$850$	195.220	−	282.095i	0.229671	−	0.331876i
$851$	1002.86	−	1002.86i	1.17844	−	1.17844i
$852$		0			0
$853$	24.4613	−	24.4613i	0.0286768	−	0.0286768i	−0.692623	−	0.721300i	$-0.743545\pi$
$853$	24.4613	−	24.4613i	0.0286768	−	0.0286768i	0.721300	+	0.692623i	$0.243545\pi$
$854$	−18.5812	−	102.091i	−0.0217578	−	0.119544i
$855$		0			0
$856$	309.951	+	516.951i	0.362092	+	0.603914i
$857$	−839.732			−0.979850			−0.489925	−	0.871764i	$-0.662976\pi$
$857$	−839.732			−0.979850			−0.489925	+	0.871764i	$0.662976\pi$
$858$		0			0
$859$	−483.229	+	483.229i	−0.562548	+	0.562548i	−0.930031	−	0.367482i	$-0.880220\pi$
$859$	−483.229	+	483.229i	−0.562548	+	0.562548i	0.367482	+	0.930031i	$0.380220\pi$
$860$	−615.074	−	1633.73i	−0.715203	−	1.89969i
$861$		0			0
$862$	−650.431	−	450.123i	−0.754561	−	0.522185i
$863$			21.1881i			0.0245517i	0.999925	+	0.0122758i	$0.00390761\pi$
$863$			21.1881i			0.0245517i	−0.999925	+	0.0122758i	$0.996092\pi$
$864$		0			0
$865$	533.761			0.617064
$866$	765.595	−	1106.29i	0.884058	−	1.27747i
$867$		0			0
$868$	−148.243	+	55.8113i	−0.170787	+	0.0642987i
$869$	−345.619	−	345.619i	−0.397720	−	0.397720i
$870$		0			0
$871$		−	851.813i		−	0.977971i
$872$	−541.952	−	903.893i	−0.621504	−	1.03658i
$873$		0			0
$874$	106.561	−	19.3947i	0.121923	−	0.0221908i
$875$	−59.3571	−	59.3571i	−0.0678367	−	0.0678367i
$876$		0			0
$877$	350.528	+	350.528i	0.399690	+	0.399690i	0.878124	−	0.478434i	$-0.158795\pi$
$877$	350.528	+	350.528i	0.399690	+	0.399690i	−0.478434	+	0.878124i	$0.658795\pi$
$878$	−44.2264	−	30.6063i	−0.0503717	−	0.0348592i
$879$		0			0
$880$	−353.478	−	402.906i	−0.401679	−	0.457848i
$881$			472.491i			0.536312i	0.963375	+	0.268156i	$0.0864143\pi$
$881$			472.491i			0.536312i	−0.963375	+	0.268156i	$0.913586\pi$
$882$		0			0
$883$	294.850	+	294.850i	0.333919	+	0.333919i	0.854073	−	0.520154i	$-0.174125\pi$
$883$	294.850	+	294.850i	0.333919	+	0.333919i	−0.520154	+	0.854073i	$0.674125\pi$
$884$	1039.95	+	471.074i	1.17641	+	0.532889i
$885$		0			0
$886$	−1458.74	+	265.499i	−1.64643	+	0.299661i
$887$	−189.405			−0.213535			−0.106767	−	0.994284i	$-0.534050\pi$
$887$	−189.405			−0.213535			−0.106767	+	0.994284i	$0.534050\pi$
$888$		0			0
$889$		−	69.2421i		−	0.0778876i
$890$	−897.694	+	163.386i	−1.00865	+	0.183580i
$891$		0			0
$892$	5.28702	+	14.0431i	0.00592715	+	0.0157434i
$893$	29.6829	−	29.6829i	0.0332396	−	0.0332396i
$894$		0			0
$895$	1011.97			1.13070
$896$	45.5747	+	88.6522i	0.0508646	+	0.0989422i
$897$		0			0
$898$	−852.526	−	589.980i	−0.949360	−	0.656994i
$899$	446.200	−	446.200i	0.496330	−	0.496330i
$900$		0			0
$901$	−305.983	+	305.983i	−0.339604	+	0.339604i
$902$	−375.257	+	68.2991i	−0.416028	+	0.0757197i
$903$		0			0
$904$	−79.2994	+	316.776i	−0.0877206	+	0.350416i
$905$	1230.68			1.35987
$906$		0			0
$907$	1025.20	−	1025.20i	1.13032	−	1.13032i	0.140200	−	0.990123i	$-0.455226\pi$
$907$	1025.20	−	1025.20i	1.13032	−	1.13032i	0.990123	−	0.140200i	$-0.0447744\pi$
$908$	1159.20	+	525.092i	1.27666	+	0.578296i
$909$		0			0
$910$	−44.5611	+	64.3911i	−0.0489683	+	0.0707595i
$911$		−	1115.84i		−	1.22485i	−0.790528	−	0.612426i	$-0.790194\pi$
$911$		−	1115.84i		−	1.22485i	0.790528	−	0.612426i	$-0.209806\pi$
$912$		0			0
$913$	709.144			0.776719
$914$	−1403.69	−	971.405i	−1.53576	−	1.06281i
$915$		0			0
$916$	−135.535	−	61.3944i	−0.147964	−	0.0670244i
$917$	17.1410	+	17.1410i	0.0186925	+	0.0186925i
$918$		0			0
$919$			1169.50i			1.27258i	0.771450	+	0.636290i	$0.219532\pi$
$919$			1169.50i			1.27258i	−0.771450	+	0.636290i	$0.780468\pi$
$920$	−777.109	−	1296.10i	−0.844684	−	1.40880i
$921$		0			0
$922$	168.052	+	923.332i	0.182269	+	1.00144i
$923$	−489.060	−	489.060i	−0.529859	−	0.529859i
$924$		0			0
$925$	−160.408	−	160.408i	−0.173414	−	0.173414i
$926$	187.668	−	271.182i	0.202666	−	0.292853i
$927$		0			0
$928$	−311.102	−	246.785i	−0.335239	−	0.265932i
$929$			115.506i			0.124334i	0.998066	+	0.0621671i	$0.0198012\pi$
$929$			115.506i			0.124334i	−0.998066	+	0.0621671i	$0.980199\pi$
$930$		0			0
$931$	54.1553	+	54.1553i	0.0581689	+	0.0581689i
$932$	−234.647	−	623.260i	−0.251768	−	0.668734i
$933$		0			0
$934$	−53.3074	−	292.888i	−0.0570743	−	0.313584i
$935$	−1049.80			−1.12278
$936$		0			0
$937$			666.120i			0.710907i	0.934694	+	0.355454i	$0.115674\pi$
$937$			666.120i			0.710907i	−0.934694	+	0.355454i	$0.884326\pi$
$938$	−26.0844	−	143.316i	−0.0278085	−	0.152789i
$939$		0			0
$940$	−533.515	−	241.670i	−0.567569	−	0.257096i
$941$	−559.735	+	559.735i	−0.594830	+	0.594830i	−0.938932	−	0.344102i	$-0.888183\pi$
$941$	−559.735	+	559.735i	−0.594830	+	0.594830i	0.344102	+	0.938932i	$0.388183\pi$
$942$		0			0
$943$	−1075.42			−1.14043
$944$	1227.65	+	80.2250i	1.30047	+	0.0849841i
$945$		0			0
$946$	−546.014	+	788.994i	−0.577182	+	0.834032i
$947$	−871.120	+	871.120i	−0.919873	+	0.919873i	−0.997020	−	0.0771466i	$-0.975419\pi$
$947$	−871.120	+	871.120i	−0.919873	+	0.919873i	0.0771466	+	0.997020i	$0.475419\pi$
$948$		0			0
$949$	−155.845	+	155.845i	−0.164220	+	0.164220i
$950$	−3.10220	−	17.0445i	−0.00326548	−	0.0179416i
$951$		0			0
$952$	189.395	+	47.4116i	0.198944	+	0.0498021i
$953$	−264.384			−0.277423			−0.138711	−	0.990333i	$-0.544296\pi$
$953$	−264.384			−0.277423			−0.138711	+	0.990333i	$0.544296\pi$
$954$		0			0
$955$	−226.874	+	226.874i	−0.237564	+	0.237564i
$956$	925.293	−	348.358i	0.967879	−	0.364391i
$957$		0			0
$958$	1115.12	+	771.707i	1.16401	+	0.805540i
$959$			86.2816i			0.0899703i
$960$		0			0
$961$	1624.80			1.69073
$962$	429.607	−	620.785i	0.446577	−	0.645306i
$963$		0			0
$964$	−20.7954	−	55.2358i	−0.0215720	−	0.0572985i
$965$	1219.78	+	1219.78i	1.26402	+	1.26402i
$966$		0			0
$967$		−	92.8445i		−	0.0960129i	−0.998847	−	0.0480065i	$-0.984713\pi$
$967$		−	92.8445i		−	0.0960129i	0.998847	−	0.0480065i	$-0.0152868\pi$
$968$	163.528	−	653.242i	0.168933	−	0.674837i
$969$		0			0
$970$	−531.676	+	96.7685i	−0.548120	+	0.0997613i
$971$	−1086.25	−	1086.25i	−1.11870	−	1.11870i	−0.991933	−	0.126764i	$-0.959541\pi$
$971$	−1086.25	−	1086.25i	−1.11870	−	1.11870i	−0.126764	−	0.991933i	$-0.540459\pi$
$972$		0			0
$973$	−23.6634	−	23.6634i	−0.0243201	−	0.0243201i
$974$	12.7007	+	8.78939i	0.0130398	+	0.00902402i
$975$		0			0
$976$	1063.72	+	69.5124i	1.08988	+	0.0712218i
$977$		−	626.473i		−	0.641222i	−0.947211	−	0.320611i	$-0.896112\pi$
$977$		−	626.473i		−	0.641222i	0.947211	−	0.320611i	$-0.103888\pi$
$978$		0			0
$979$	354.626	+	354.626i	0.362233	+	0.362233i
$980$	440.917	−	973.376i	0.449916	−	0.993241i
$981$		0			0
$982$	824.548	−	150.073i	0.839662	−	0.152824i
$983$	204.267			0.207800			0.103900	−	0.994588i	$-0.466868\pi$
$983$	204.267			0.207800			0.103900	+	0.994588i	$0.466868\pi$
$984$		0			0
$985$		−	349.986i		−	0.355316i
$986$	−765.202	+	139.272i	−0.776066	+	0.141249i
$987$		0			0
$988$	53.9573	−	20.3141i	0.0546126	−	0.0205608i
$989$	−1912.95	+	1912.95i	−1.93423	+	1.93423i
$990$		0			0
$991$	1147.30			1.15772			0.578859	−	0.815428i	$-0.303498\pi$
$991$	1147.30			1.15772			0.578859	+	0.815428i	$0.303498\pi$
$992$	−186.363	−	1616.52i	−0.187865	−	1.62955i
$993$		0			0
$994$	−97.2595	−	67.3073i	−0.0978465	−	0.0677136i
$995$	−613.348	+	613.348i	−0.616430	+	0.616430i
$996$		0			0
$997$	514.690	−	514.690i	0.516239	−	0.516239i	−0.400192	−	0.916431i	$-0.631057\pi$
$997$	514.690	−	514.690i	0.516239	−	0.516239i	0.916431	+	0.400192i	$0.131057\pi$
$998$	−1545.91	+	281.366i	−1.54901	+	0.281930i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.j.a.125.5	yes	32
3.2	odd	2	inner	144.3.j.a.125.12	yes	32
4.3	odd	2		576.3.j.a.17.13		32
8.3	odd	2		1152.3.j.b.161.4		32
8.5	even	2		1152.3.j.a.161.4		32
12.11	even	2		576.3.j.a.17.4		32
16.3	odd	4		1152.3.j.b.737.13		32
16.5	even	4	inner	144.3.j.a.53.12	yes	32
16.11	odd	4		576.3.j.a.305.4		32
16.13	even	4		1152.3.j.a.737.13		32
24.5	odd	2		1152.3.j.a.161.13		32
24.11	even	2		1152.3.j.b.161.13		32
48.5	odd	4	inner	144.3.j.a.53.5	✓	32
48.11	even	4		576.3.j.a.305.13		32
48.29	odd	4		1152.3.j.a.737.4		32
48.35	even	4		1152.3.j.b.737.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.j.a.53.5	✓	32	48.5	odd	4	inner
144.3.j.a.53.12	yes	32	16.5	even	4	inner
144.3.j.a.125.5	yes	32	1.1	even	1	trivial
144.3.j.a.125.12	yes	32	3.2	odd	2	inner
576.3.j.a.17.4		32	12.11	even	2
576.3.j.a.17.13		32	4.3	odd	2
576.3.j.a.305.4		32	16.11	odd	4
576.3.j.a.305.13		32	48.11	even	4
1152.3.j.a.161.4		32	8.5	even	2
1152.3.j.a.161.13		32	24.5	odd	2
1152.3.j.a.737.4		32	48.29	odd	4
1152.3.j.a.737.13		32	16.13	even	4
1152.3.j.b.161.4		32	8.3	odd	2
1152.3.j.b.161.13		32	24.11	even	2
1152.3.j.b.737.4		32	48.35	even	4
1152.3.j.b.737.13		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)

\(f(q)\)	\(=\)	\(q+(-1.13812 + 1.64459i) q^{2} +(-1.40936 - 3.74349i) q^{4} +(3.90343 + 3.90343i) q^{5} -0.778757i q^{7} +(7.76053 + 1.94271i) q^{8} +O(q^{10})\)	\(q+(-1.13812 + 1.64459i) q^{2} +(-1.40936 - 3.74349i) q^{4} +(3.90343 + 3.90343i) q^{5} -0.778757i q^{7} +(7.76053 + 1.94271i) q^{8} +(-10.8621 + 1.97697i) q^{10} +(4.29098 + 4.29098i) q^{11} +(6.44007 + 6.44007i) q^{13} +(1.28074 + 0.886319i) q^{14} +(-12.0274 + 10.5519i) q^{16} +31.3383i q^{17} +(1.11906 + 1.11906i) q^{19} +(9.11108 - 20.1138i) q^{20} +(-11.9406 + 2.17326i) q^{22} -34.2197 q^{23} +5.47346i q^{25} +(-17.9208 + 3.26171i) q^{26} +(-2.91526 + 1.09755i) q^{28} +(8.77471 - 8.77471i) q^{29} +50.8507 q^{31} +(-3.66490 - 31.7894i) q^{32} +(-51.5386 - 35.6667i) q^{34} +(3.03982 - 3.03982i) q^{35} +(-29.3064 + 29.3064i) q^{37} +(-3.11402 + 0.566772i) q^{38} +(22.7094 + 37.8759i) q^{40} +31.4271 q^{41} +(55.9022 - 55.9022i) q^{43} +(10.0157 - 22.1108i) q^{44} +(38.9461 - 56.2774i) q^{46} -26.5249i q^{47} +48.3935 q^{49} +(-9.00161 - 6.22946i) q^{50} +(15.0319 - 33.1847i) q^{52} +(9.76389 + 9.76389i) q^{53} +33.4991i q^{55} +(1.51290 - 6.04357i) q^{56} +(4.44414 + 24.4175i) q^{58} +(-54.3706 - 54.3706i) q^{59} +(-47.1104 - 47.1104i) q^{61} +(-57.8742 + 83.6287i) q^{62} +(56.4517 + 30.1530i) q^{64} +50.2766i q^{65} +(-66.1339 - 66.1339i) q^{67} +(117.314 - 44.1670i) q^{68} +(1.53958 + 8.45894i) q^{70} -75.9403 q^{71} +24.1992i q^{73} +(-14.8428 - 81.5513i) q^{74} +(2.61202 - 5.76635i) q^{76} +(3.34163 - 3.34163i) q^{77} -80.5454 q^{79} +(-88.1365 - 5.75959i) q^{80} +(-35.7678 + 51.6847i) q^{82} +(82.6319 - 82.6319i) q^{83} +(-122.327 + 122.327i) q^{85} +(28.3128 + 155.560i) q^{86} +(24.9642 + 41.6365i) q^{88} +82.6445 q^{89} +(5.01524 - 5.01524i) q^{91} +(48.2279 + 128.101i) q^{92} +(43.6226 + 30.1885i) q^{94} +8.73634i q^{95} +48.9478 q^{97} +(-55.0777 + 79.5876i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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