LMFDB - Embedded newform 144.3.j.a.53.12

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			53.12
Character	$\chi$	$=$	144.53
Dual form			144.3.j.a.125.12

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

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

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 $

$2$	1.13812	+	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	$-0.936146\pi$
$5$	−3.90343	+	3.90343i	−0.780685	+	0.780685i	0.199261	+	0.979946i	$0.436146\pi$
$6$		0			0
$7$			0.778757i			0.111251i	0.998452	+	0.0556255i	$0.0177153\pi$
$7$			0.778757i			0.111251i	−0.998452	+	0.0556255i	$0.982285\pi$
$8$	−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	$-0.838954\pi$
$11$	−4.29098	+	4.29098i	−0.390089	+	0.390089i	0.484630	+	0.874719i	$0.338954\pi$
$12$		0			0
$13$	6.44007	−	6.44007i	0.495390	−	0.495390i	−0.414610	−	0.909999i	$-0.636082\pi$
$13$	6.44007	−	6.44007i	0.495390	−	0.495390i	0.909999	+	0.414610i	$0.136082\pi$
$14$	−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	−0.677044	−	0.735942i	$-0.736739\pi$
$19$	1.11906	−	1.11906i	0.0588979	−	0.0588979i	0.735942	+	0.677044i	$0.236739\pi$
$20$	−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	$-0.232971\pi$
$23$	34.2197			1.48781			0.743906	+	0.668285i	$0.232971\pi$
$24$		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	$-0.318634\pi$
$29$	−8.77471	−	8.77471i	−0.302576	−	0.302576i	−0.842021	+	0.539445i	$0.818634\pi$
$30$		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	0.189765	−	0.981830i	$-0.439227\pi$
$37$	−29.3064	−	29.3064i	−0.792065	−	0.792065i	−0.981830	+	0.189765i	$0.939227\pi$
$38$	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	$-0.625198\pi$
$41$	−31.4271			−0.766513			−0.383257	+	0.923642i	$0.625198\pi$
$42$		0			0
$43$	55.9022	+	55.9022i	1.30005	+	1.30005i	0.928354	+	0.371696i	$0.121224\pi$
$43$	55.9022	+	55.9022i	1.30005	+	1.30005i	0.371696	+	0.928354i	$0.378776\pi$
$44$	−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	$-0.791583\pi$
$53$	−9.76389	+	9.76389i	−0.184224	+	0.184224i	0.608969	+	0.793194i	$0.291583\pi$
$54$		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	$-0.524088\pi$
$59$	54.3706	−	54.3706i	0.921535	−	0.921535i	0.997138	+	0.0756026i	$0.0240881\pi$
$60$		0			0
$61$	−47.1104	+	47.1104i	−0.772302	+	0.772302i	−0.978508	−	0.206207i	$-0.933888\pi$
$61$	−47.1104	+	47.1104i	−0.772302	+	0.772302i	0.206207	+	0.978508i	$0.433888\pi$
$62$	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	−0.999918	−	0.0128446i	$-0.995911\pi$
$67$	−66.1339	+	66.1339i	−0.987073	+	0.987073i	0.0128446	+	0.999918i	$0.495911\pi$
$68$	−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	$-0.320391\pi$
$71$	75.9403			1.06958			0.534791	+	0.844985i	$0.320391\pi$
$72$		0			0
$73$		−	24.1992i		−	0.331497i	−0.986168	−	0.165748i	$-0.946996\pi$
$73$		−	24.1992i		−	0.331497i	0.986168	−	0.165748i	$-0.0530039\pi$
$74$	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	$-0.498591\pi$
$83$	−82.6319	−	82.6319i	−0.995565	−	0.995565i	−0.999990	+	0.00442530i	$0.998591\pi$
$84$		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	$-0.653692\pi$
$89$	−82.6445			−0.928590			−0.464295	+	0.885681i	$0.653692\pi$
$90$		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	$-0.656681\pi$
$101$	41.2778	−	41.2778i	0.408691	−	0.408691i	0.881282	+	0.472591i	$0.156681\pi$
$102$		0			0
$103$		−	173.236i		−	1.68190i	−0.541111	−	0.840951i	$-0.681996\pi$
$103$		−	173.236i		−	1.68190i	0.541111	−	0.840951i	$-0.318004\pi$
$104$	−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	$-0.864523\pi$
$107$	−53.2761	+	53.2761i	−0.497907	+	0.497907i	0.412879	+	0.910786i	$0.364523\pi$
$108$		0			0
$109$	−93.1537	+	93.1537i	−0.854621	+	0.854621i	−0.990698	−	0.136077i	$-0.956551\pi$
$109$	−93.1537	+	93.1537i	−0.854621	+	0.854621i	0.136077	+	0.990698i	$0.456551\pi$
$110$	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	$-0.212092\pi$
$131$	22.0108	+	22.0108i	0.168021	+	0.168021i	−0.618088	+	0.786109i	$0.712092\pi$
$132$		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	$-0.367495\pi$
$137$	110.794			0.808715			0.404358	+	0.914601i	$0.367495\pi$
$138$		0			0
$139$	30.3862	+	30.3862i	0.218605	+	0.218605i	0.807911	−	0.589305i	$-0.200598\pi$
$139$	30.3862	+	30.3862i	0.218605	+	0.218605i	−0.589305	+	0.807911i	$0.700598\pi$
$140$	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	0.184428	−	0.982846i	$-0.440957\pi$
$149$	173.924	−	173.924i	1.16727	−	1.16727i	0.982846	−	0.184428i	$-0.0590433\pi$
$150$		0			0
$151$			26.2521i			0.173855i	0.996215	+	0.0869274i	$0.0277048\pi$
$151$			26.2521i			0.173855i	−0.996215	+	0.0869274i	$0.972295\pi$
$152$	−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	−0.423009	−	0.906126i	$-0.639026\pi$
$157$	75.8493	−	75.8493i	0.483117	−	0.483117i	0.906126	+	0.423009i	$0.139026\pi$
$158$	−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	−0.0462578	−	0.998930i	$-0.514730\pi$
$163$	155.285	−	155.285i	0.952672	−	0.952672i	0.998930	+	0.0462578i	$0.0147296\pi$
$164$	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	$-0.249017\pi$
$167$	236.902			1.41857			0.709286	+	0.704920i	$0.249017\pi$
$168$		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	$-0.340153\pi$
$173$	−68.3708	−	68.3708i	−0.395207	−	0.395207i	−0.876539	+	0.481332i	$0.840153\pi$
$174$		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	$-0.421120\pi$
$179$	−129.626	−	129.626i	−0.724170	−	0.724170i	−0.969452	+	0.245282i	$0.921120\pi$
$180$		0			0
$181$	157.641	+	157.641i	0.870947	+	0.870947i	0.992576	−	0.121629i	$-0.0388118\pi$
$181$	157.641	+	157.641i	0.870947	+	0.870947i	−0.121629	+	0.992576i	$0.538812\pi$
$182$	−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	$-0.698556\pi$
$197$	44.8306	−	44.8306i	0.227567	−	0.227567i	0.811675	+	0.584109i	$0.198556\pi$
$198$		0			0
$199$		−	157.131i		−	0.789601i	−0.918767	−	0.394801i	$-0.870814\pi$
$199$		−	157.131i		−	0.789601i	0.918767	−	0.394801i	$-0.129186\pi$
$200$	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	−0.850262	−	0.526360i	$-0.823556\pi$
$211$	−68.3433	+	68.3433i	−0.323902	+	0.323902i	0.526360	+	0.850262i	$0.323556\pi$
$212$	−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	$-0.00284313\pi$
$227$	224.963	+	224.963i	0.991028	+	0.991028i	−0.00893184	+	0.999960i	$0.502843\pi$
$228$		0			0
$229$	26.3030	+	26.3030i	0.114860	+	0.114860i	0.762201	−	0.647341i	$-0.224119\pi$
$229$	26.3030	+	26.3030i	0.114860	+	0.114860i	−0.647341	+	0.762201i	$0.724119\pi$
$230$	−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	$-0.616295\pi$
$233$	−166.492			−0.714557			−0.357279	+	0.933998i	$0.616295\pi$
$234$		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	$-0.787350\pi$
$251$	−41.5560	+	41.5560i	−0.165562	+	0.165562i	0.619464	+	0.785025i	$0.287350\pi$
$252$		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	$-0.534883\pi$
$263$	−57.5273			−0.218735			−0.109368	+	0.994001i	$0.534883\pi$
$264$		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	$-0.146602\pi$
$269$	121.413	+	121.413i	0.451350	+	0.451350i	−0.444452	+	0.895803i	$0.646602\pi$
$270$		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	0.802167	−	0.597100i	$-0.203680\pi$
$277$	56.8037	+	56.8037i	0.205068	+	0.205068i	−0.597100	+	0.802167i	$0.703680\pi$
$278$	−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	$-0.533469\pi$
$281$	−58.9828			−0.209903			−0.104952	+	0.994477i	$0.533469\pi$
$282$		0			0
$283$	−170.002	−	170.002i	−0.600713	−	0.600713i	0.339789	−	0.940502i	$-0.389644\pi$
$283$	−170.002	−	170.002i	−0.600713	−	0.600713i	−0.940502	+	0.339789i	$0.889644\pi$
$284$	−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	$-0.714438\pi$
$293$	46.1968	−	46.1968i	0.157668	−	0.157668i	0.781533	+	0.623864i	$0.214438\pi$
$294$		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	0.197701	−	0.980262i	$-0.436653\pi$
$307$	361.635	−	361.635i	1.17796	−	1.17796i	0.980262	−	0.197701i	$-0.0633474\pi$
$308$	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	$-0.590897\pi$
$311$	−175.216			−0.563395			−0.281697	+	0.959503i	$0.590897\pi$
$312$		0			0
$313$		−	432.899i		−	1.38307i	−0.722345	−	0.691533i	$-0.756936\pi$
$313$		−	432.899i		−	1.38307i	0.722345	−	0.691533i	$-0.243064\pi$
$314$	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	$-0.382226\pi$
$317$	−180.916	−	180.916i	−0.570714	−	0.570714i	−0.932328	+	0.361614i	$0.882226\pi$
$318$		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	0.839892	−	0.542754i	$-0.182618\pi$
$331$	98.3525	+	98.3525i	0.297137	+	0.297137i	−0.542754	+	0.839892i	$0.682618\pi$
$332$	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	0.100869	−	0.994900i	$-0.467838\pi$
$347$	380.232	−	380.232i	1.09577	−	1.09577i	0.994900	−	0.100869i	$-0.0321623\pi$
$348$		0			0
$349$	260.199	−	260.199i	0.745555	−	0.745555i	−0.228086	−	0.973641i	$-0.573247\pi$
$349$	260.199	−	260.199i	0.745555	−	0.745555i	0.973641	+	0.228086i	$0.0732466\pi$
$350$	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	$-0.443472\pi$
$359$	126.839			0.353311			0.176656	+	0.984273i	$0.443472\pi$
$360$		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	0.803251	−	0.595640i	$-0.203102\pi$
$373$	77.4388	+	77.4388i	0.207611	+	0.207611i	−0.595640	+	0.803251i	$0.703102\pi$
$374$	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	0.373614	−	0.927584i	$-0.378119\pi$
$379$	−209.955	−	209.955i	−0.553971	−	0.553971i	−0.927584	+	0.373614i	$0.878119\pi$
$380$	−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	−0.0834708	+	0.996510i	$0.526601\pi$
$389$	−420.113	+	420.113i	−1.07998	+	1.07998i	−0.996510	+	0.0834708i	$0.973399\pi$
$390$		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	−0.690483	−	0.723348i	$-0.742602\pi$
$397$	13.0474	−	13.0474i	0.0328650	−	0.0328650i	0.723348	+	0.690483i	$0.242602\pi$
$398$	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	$0.0168349\pi$
$409$			43.2426i			0.105728i	−0.998602	+	0.0528639i	$0.983165\pi$
$410$	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	$-0.206140\pi$
$419$	81.3896	+	81.3896i	0.194247	+	0.194247i	−0.603281	+	0.797528i	$0.706140\pi$
$420$		0			0
$421$	198.570	+	198.570i	0.471663	+	0.471663i	0.902452	−	0.430789i	$-0.141765\pi$
$421$	198.570	+	198.570i	0.471663	+	0.471663i	−0.430789	+	0.902452i	$0.641765\pi$
$422$	−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	$-0.990249\pi$
$439$		−	26.8920i		−	0.0612574i	0.999531	−	0.0306287i	$-0.00975095\pi$
$440$	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	−0.204451	+	0.978877i	$0.565541\pi$
$443$	−524.214	+	524.214i	−1.18333	+	1.18333i	−0.978877	+	0.204451i	$0.934459\pi$
$444$		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	$-0.616449\pi$
$457$		−	853.516i		−	1.86765i	0.357729	−	0.933825i	$-0.383551\pi$
$458$	−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	$-0.419966\pi$
$461$	−331.810	−	331.810i	−0.719761	−	0.719761i	−0.968556	+	0.248795i	$0.919966\pi$
$462$		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	$-0.199054\pi$
$467$	105.253	+	105.253i	0.225380	+	0.225380i	−0.585379	+	0.810760i	$0.699054\pi$
$468$		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	$0.00252387\pi$
$487$			7.72273i			0.0158578i	−0.999969	+	0.00792888i	$0.997476\pi$
$488$	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	$-0.609666\pi$
$491$	296.311	−	296.311i	0.603484	−	0.603484i	0.941235	+	0.337751i	$0.109666\pi$
$492$		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	0.120612	−	0.992700i	$-0.461514\pi$
$499$	555.542	−	555.542i	1.11331	−	1.11331i	0.992700	−	0.120612i	$-0.0384856\pi$
$500$	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	$-0.604015\pi$
$503$	−322.916			−0.641979			−0.320990	+	0.947083i	$0.604015\pi$
$504$		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	0.999647	+	0.0265686i	$0.00845804\pi$
$509$	522.344	+	522.344i	1.02622	+	1.02622i	0.0265686	+	0.999647i	$0.491542\pi$
$510$		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	$-0.475412\pi$
$521$	80.4109			0.154340			0.0771698	+	0.997018i	$0.475412\pi$
$522$		0			0
$523$	133.868	+	133.868i	0.255962	+	0.255962i	0.823410	−	0.567447i	$-0.192069\pi$
$523$	133.868	+	133.868i	0.255962	+	0.255962i	−0.567447	+	0.823410i	$0.692069\pi$
$524$	−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	−0.212936	+	0.977066i	$0.568302\pi$
$541$	−643.791	+	643.791i	−1.19000	+	1.19000i	−0.977066	+	0.212936i	$0.931698\pi$
$542$	−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	−0.999985	−	0.00555539i	$-0.998232\pi$
$547$	−543.953	+	543.953i	−0.994429	+	0.994429i	0.00555539	+	0.999985i	$0.498232\pi$
$548$	−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	$-0.0630838\pi$
$557$	436.430	+	436.430i	0.783537	+	0.783537i	−0.196889	+	0.980426i	$0.563084\pi$
$558$		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	$-0.479362\pi$
$563$	−525.339	−	525.339i	−0.933107	−	0.933107i	−0.997899	+	0.0647918i	$0.979362\pi$
$564$		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	$-0.231956\pi$
$569$	848.985			1.49207			0.746033	+	0.665909i	$0.231956\pi$
$570$		0			0
$571$	503.454	+	503.454i	0.881706	+	0.881706i	0.993708	−	0.112002i	$-0.0357264\pi$
$571$	503.454	+	503.454i	0.881706	+	0.881706i	−0.112002	+	0.993708i	$0.535726\pi$
$572$	−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	$-0.703152\pi$
$587$	121.737	−	121.737i	0.207388	−	0.207388i	0.803156	+	0.595768i	$0.203152\pi$
$588$		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	$-0.695218\pi$
$599$	−689.528			−1.15113			−0.575566	+	0.817755i	$0.695218\pi$
$600$		0			0
$601$			542.421i			0.902531i	0.892390	+	0.451266i	$0.149027\pi$
$601$			542.421i			0.902531i	−0.892390	+	0.451266i	$0.850973\pi$
$602$	−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	0.831701	−	0.555223i	$-0.187367\pi$
$613$	169.481	+	169.481i	0.276478	+	0.276478i	−0.555223	+	0.831701i	$0.687367\pi$
$614$	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	$-0.736433\pi$
$617$	−834.597			−1.35267			−0.676335	+	0.736594i	$0.736433\pi$
$618$		0			0
$619$	−322.772	−	322.772i	−0.521441	−	0.521441i	0.396565	−	0.918007i	$-0.370202\pi$
$619$	−322.772	−	322.772i	−0.521441	−	0.521441i	−0.918007	+	0.396565i	$0.870202\pi$
$620$	−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	$-0.706317\pi$
$631$		−	1006.06i		−	1.59439i	0.603723	−	0.797194i	$-0.293683\pi$
$632$	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	−0.906742	−	0.421686i	$-0.861438\pi$
$643$	−311.891	+	311.891i	−0.485056	+	0.485056i	0.421686	+	0.906742i	$0.361438\pi$
$644$	−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	$-0.270158\pi$
$647$	855.255			1.32188			0.660939	+	0.750440i	$0.270158\pi$
$648$		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	$-0.309352\pi$
$653$	−171.197	−	171.197i	−0.262170	−	0.262170i	−0.825935	+	0.563765i	$0.809352\pi$
$654$		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	$-0.434433\pi$
$659$	−510.283	−	510.283i	−0.774330	−	0.774330i	−0.978860	+	0.204530i	$0.934433\pi$
$660$		0			0
$661$	491.063	+	491.063i	0.742910	+	0.742910i	0.973137	−	0.230227i	$-0.0739470\pi$
$661$	491.063	+	491.063i	0.742910	+	0.742910i	−0.230227	+	0.973137i	$0.573947\pi$
$662$	−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	0.237361	−	0.971422i	$-0.423718\pi$
$677$	818.346	−	818.346i	1.20878	−	1.20878i	0.971422	−	0.237361i	$-0.0762823\pi$
$678$		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	$-0.553532\pi$
$683$	559.041	−	559.041i	0.818508	−	0.818508i	0.985892	+	0.167383i	$0.0535318\pi$
$684$		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	−0.984422	−	0.175820i	$-0.943742\pi$
$691$	−558.744	+	558.744i	−0.808602	+	0.808602i	0.175820	+	0.984422i	$0.443742\pi$
$692$	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	$-0.400851\pi$
$701$	−452.428	−	452.428i	−0.645404	−	0.645404i	−0.951879	+	0.306475i	$0.900851\pi$
$702$		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	0.0218205	−	0.999762i	$-0.493054\pi$
$709$	−693.360	−	693.360i	−0.977941	−	0.977941i	−0.999762	+	0.0218205i	$0.993054\pi$
$710$	−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	$-0.853782\pi$
$727$		−	644.665i		−	0.886747i	0.896337	−	0.443373i	$-0.146218\pi$
$728$	−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	−0.0220473	+	0.999757i	$0.507018\pi$
$733$	−748.983	+	748.983i	−1.02180	+	1.02180i	−0.999757	+	0.0220473i	$0.992982\pi$
$734$	−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	−0.918781	−	0.394768i	$-0.870825\pi$
$739$	−387.245	+	387.245i	−0.524013	+	0.524013i	0.394768	+	0.918781i	$0.370825\pi$
$740$	−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	$-0.447243\pi$
$743$	245.165			0.329966			0.164983	+	0.986296i	$0.447243\pi$
$744$		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	−0.984863	−	0.173334i	$-0.944546\pi$
$757$	−876.755	−	876.755i	−1.15820	−	1.15820i	−0.173334	−	0.984863i	$-0.555454\pi$
$758$	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	$-0.695390\pi$
$761$	−876.682			−1.15201			−0.576007	+	0.817445i	$0.695390\pi$
$762$		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	$-0.650270\pi$
$773$	336.932	−	336.932i	0.435876	−	0.435876i	0.890621	+	0.454746i	$0.150270\pi$
$774$		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	−0.567541	−	0.823345i	$-0.692105\pi$
$787$	201.318	−	201.318i	0.255804	−	0.255804i	0.823345	+	0.567541i	$0.192105\pi$
$788$	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	$-0.419167\pi$
$797$	−571.213	−	571.213i	−0.716704	−	0.716704i	−0.967929	+	0.251225i	$0.919167\pi$
$798$		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	$-0.611426\pi$
$809$	−554.891			−0.685898			−0.342949	+	0.939354i	$0.611426\pi$
$810$		0			0
$811$	570.087	+	570.087i	0.702944	+	0.702944i	0.965041	−	0.262098i	$-0.0844143\pi$
$811$	570.087	+	570.087i	0.702944	+	0.702944i	−0.262098	+	0.965041i	$0.584414\pi$
$812$	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	$-0.791431\pi$
$821$	−150.698	+	150.698i	−0.183554	+	0.183554i	0.609348	+	0.792903i	$0.291431\pi$
$822$		0			0
$823$		−	742.019i		−	0.901603i	−0.892624	−	0.450801i	$-0.851138\pi$
$823$		−	742.019i		−	0.901603i	0.892624	−	0.450801i	$-0.148862\pi$
$824$	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	$-0.818055\pi$
$827$	−248.150	+	248.150i	−0.300061	+	0.300061i	0.540977	+	0.841037i	$0.318055\pi$
$828$		0			0
$829$	373.174	−	373.174i	0.450150	−	0.450150i	−0.445255	−	0.895404i	$-0.646887\pi$
$829$	373.174	−	373.174i	0.450150	−	0.450150i	0.895404	+	0.445255i	$0.146887\pi$
$830$	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	$-0.238811\pi$
$839$	1227.49			1.46304			0.731520	+	0.681820i	$0.238811\pi$
$840$		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	0.721300	−	0.692623i	$-0.243545\pi$
$853$	24.4613	+	24.4613i	0.0286768	+	0.0286768i	−0.692623	+	0.721300i	$0.743545\pi$
$854$	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	$-0.337024\pi$
$857$	839.732			0.979850			0.489925	+	0.871764i	$0.337024\pi$
$858$		0			0
$859$	−483.229	−	483.229i	−0.562548	−	0.562548i	0.367482	−	0.930031i	$-0.380220\pi$
$859$	−483.229	−	483.229i	−0.562548	−	0.562548i	−0.930031	+	0.367482i	$0.880220\pi$
$860$	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	−0.478434	−	0.878124i	$-0.658795\pi$
$877$	350.528	−	350.528i	0.399690	−	0.399690i	0.878124	+	0.478434i	$0.158795\pi$
$878$	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	−0.520154	−	0.854073i	$-0.674125\pi$
$883$	294.850	−	294.850i	0.333919	−	0.333919i	0.854073	+	0.520154i	$0.174125\pi$
$884$	−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	$-0.465950\pi$
$887$	189.405			0.213535			0.106767	+	0.994284i	$0.465950\pi$
$888$		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	0.990123	+	0.140200i	$0.0447744\pi$
$907$	1025.20	+	1025.20i	1.13032	+	1.13032i	0.140200	+	0.990123i	$0.455226\pi$
$908$	−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	$-0.780468\pi$
$919$		−	1169.50i		−	1.27258i	0.771450	−	0.636290i	$-0.219532\pi$
$920$	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	$-0.884326\pi$
$937$		−	666.120i		−	0.710907i	0.934694	−	0.355454i	$-0.115674\pi$
$938$	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	$-0.111817\pi$
$941$	559.735	+	559.735i	0.594830	+	0.594830i	−0.344102	+	0.938932i	$0.611817\pi$
$942$		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	$-0.0245809\pi$
$947$	871.120	+	871.120i	0.919873	+	0.919873i	−0.0771466	+	0.997020i	$0.524581\pi$
$948$		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	$-0.455704\pi$
$953$	264.384			0.277423			0.138711	+	0.990333i	$0.455704\pi$
$954$		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	$0.0152868\pi$
$967$			92.8445i			0.0960129i	−0.998847	+	0.0480065i	$0.984713\pi$
$968$	−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	0.126764	−	0.991933i	$-0.459541\pi$
$971$	1086.25	−	1086.25i	1.11870	−	1.11870i	0.991933	−	0.126764i	$-0.0404592\pi$
$972$		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	$-0.533132\pi$
$983$	−204.267			−0.207800			−0.103900	+	0.994588i	$0.533132\pi$
$984$		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	0.916431	−	0.400192i	$-0.131057\pi$
$997$	514.690	+	514.690i	0.516239	+	0.516239i	−0.400192	+	0.916431i	$0.631057\pi$
$998$	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.53.12	yes	32
3.2	odd	2	inner	144.3.j.a.53.5	✓	32
4.3	odd	2		576.3.j.a.305.4		32
8.3	odd	2		1152.3.j.b.737.13		32
8.5	even	2		1152.3.j.a.737.13		32
12.11	even	2		576.3.j.a.305.13		32
16.3	odd	4		576.3.j.a.17.13		32
16.5	even	4		1152.3.j.a.161.4		32
16.11	odd	4		1152.3.j.b.161.4		32
16.13	even	4	inner	144.3.j.a.125.5	yes	32
24.5	odd	2		1152.3.j.a.737.4		32
24.11	even	2		1152.3.j.b.737.4		32
48.5	odd	4		1152.3.j.a.161.13		32
48.11	even	4		1152.3.j.b.161.13		32
48.29	odd	4	inner	144.3.j.a.125.12	yes	32
48.35	even	4		576.3.j.a.17.4		32

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

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