LMFDB - Embedded newform 252.3.p.a.157.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [252,3,Mod(61,252)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(252, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 5])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("252.61"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	252.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.86650266188$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			157.4
Character	$\chi$	$=$	252.157
Dual form			252.3.p.a.61.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.37299 + 1.83546i) q^{3} +5.22643i q^{5} +(-2.36655 + 6.58783i) q^{7} +(2.26216 - 8.71106i) q^{9} +4.86821 q^{11} +(-3.87803 - 2.23898i) q^{13} +(-9.59291 - 12.4023i) q^{15} +(-22.8086 - 13.1686i) q^{17} +(-15.6393 + 9.02938i) q^{19} +(-6.47591 - 19.9766i) q^{21} +2.10501 q^{23} -2.31556 q^{25} +(10.6207 + 24.8234i) q^{27} +(-13.8523 - 23.9929i) q^{29} +(-24.7272 + 14.2763i) q^{31} +(-11.5522 + 8.93540i) q^{33} +(-34.4308 - 12.3686i) q^{35} +(13.5493 + 23.4681i) q^{37} +(13.3121 - 1.80489i) q^{39} +(-59.9799 - 34.6294i) q^{41} +(0.983471 + 1.70342i) q^{43} +(45.5278 + 11.8230i) q^{45} +(38.7995 + 22.4009i) q^{47} +(-37.7989 - 31.1808i) q^{49} +(78.2950 - 10.6155i) q^{51} +(6.39788 - 11.0815i) q^{53} +25.4433i q^{55} +(20.5389 - 50.1320i) q^{57} +(-48.4028 + 27.9454i) q^{59} +(91.6937 + 52.9394i) q^{61} +(52.0335 + 35.5179i) q^{63} +(11.7019 - 20.2682i) q^{65} +(10.4104 + 18.0313i) q^{67} +(-4.99518 + 3.86367i) q^{69} -23.1583 q^{71} +(116.548 + 67.2890i) q^{73} +(5.49480 - 4.25012i) q^{75} +(-11.5208 + 32.0709i) q^{77} +(-55.8622 + 96.7561i) q^{79} +(-70.7652 - 39.4117i) q^{81} +(16.3728 - 9.45285i) q^{83} +(68.8245 - 119.208i) q^{85} +(76.9093 + 31.5095i) q^{87} +(49.5248 - 28.5932i) q^{89} +(23.9275 - 20.2491i) q^{91} +(32.4739 - 79.2633i) q^{93} +(-47.1914 - 81.7379i) q^{95} +(-165.209 + 95.3837i) q^{97} +(11.0127 - 42.4072i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + q^{7} - 6 q^{9} - 12 q^{11} + 15 q^{13} + 9 q^{15} - 27 q^{17} - 36 q^{21} + 30 q^{23} - 160 q^{25} - 9 q^{27} + 24 q^{29} - 24 q^{31} + 81 q^{33} + 141 q^{35} + 11 q^{37} - 21 q^{39} - 90 q^{41}+ \cdots - 45 q^{99}+O(q^{100}) $ 32 * q + q^7 - 6 * q^9 - 12 * q^11 + 15 * q^13 + 9 * q^15 - 27 * q^17 - 36 * q^21 + 30 * q^23 - 160 * q^25 - 9 * q^27 + 24 * q^29 - 24 * q^31 + 81 * q^33 + 141 * q^35 + 11 * q^37 - 21 * q^39 - 90 * q^41 - 16 * q^43 + 39 * q^45 + 108 * q^47 - 61 * q^49 + 117 * q^51 + 54 * q^53 + 51 * q^57 + 45 * q^59 - 165 * q^61 - 93 * q^63 - 33 * q^65 - 35 * q^67 + 105 * q^69 + 138 * q^71 - 195 * q^75 - 123 * q^77 + 37 * q^79 + 126 * q^81 + 378 * q^83 + 30 * q^85 - 237 * q^87 - 261 * q^89 + 45 * q^91 + 111 * q^93 - 48 * q^95 - 57 * q^97 - 45 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.37299	+	1.83546i	−0.790997	+	0.611820i
$3$	−2.37299	+	1.83546i	−0.790997	+	0.611820i
$4$		0			0
$5$			5.22643i			1.04529i	0.852552	+	0.522643i	$0.175054\pi$
$5$			5.22643i			1.04529i	−0.852552	+	0.522643i	$0.824946\pi$
$6$		0			0
$7$	−2.36655	+	6.58783i	−0.338078	+	0.941118i
$7$	−2.36655	+	6.58783i	−0.338078	+	0.941118i
$8$		0			0
$9$	2.26216	−	8.71106i	0.251351	−	0.967896i
$10$		0			0
$11$	4.86821			0.442564			0.221282	−	0.975210i	$-0.428976\pi$
$11$	4.86821			0.442564			0.221282	+	0.975210i	$0.428976\pi$
$12$		0			0
$13$	−3.87803	−	2.23898i	−0.298310	−	0.172229i	0.343374	−	0.939199i	$-0.388430\pi$
$13$	−3.87803	−	2.23898i	−0.298310	−	0.172229i	−0.641683	+	0.766970i	$0.721764\pi$
$14$		0			0
$15$	−9.59291	−	12.4023i	−0.639527	−	0.826818i
$16$		0			0
$17$	−22.8086	−	13.1686i	−1.34168	−	0.774621i	−0.354629	−	0.935007i	$-0.615393\pi$
$17$	−22.8086	−	13.1686i	−1.34168	−	0.774621i	−0.987054	+	0.160386i	$0.948726\pi$
$18$		0			0
$19$	−15.6393	+	9.02938i	−0.823123	+	0.475231i	−0.851492	−	0.524367i	$-0.824302\pi$
$19$	−15.6393	+	9.02938i	−0.823123	+	0.475231i	0.0283690	+	0.999598i	$0.490969\pi$
$20$		0			0
$21$	−6.47591	−	19.9766i	−0.308377	−	0.951264i
$22$		0			0
$23$	2.10501			0.0915223			0.0457612	−	0.998952i	$-0.485429\pi$
$23$	2.10501			0.0915223			0.0457612	+	0.998952i	$0.485429\pi$
$24$		0			0
$25$	−2.31556			−0.0926224
$26$		0			0
$27$	10.6207	+	24.8234i	0.393360	+	0.919384i
$28$		0			0
$29$	−13.8523	−	23.9929i	−0.477665	−	0.827341i	0.522007	−	0.852941i	$-0.325183\pi$
$29$	−13.8523	−	23.9929i	−0.477665	−	0.827341i	−0.999672	+	0.0256007i	$0.991850\pi$
$30$		0			0
$31$	−24.7272	+	14.2763i	−0.797653	+	0.460525i	−0.842650	−	0.538462i	$-0.819005\pi$
$31$	−24.7272	+	14.2763i	−0.797653	+	0.460525i	0.0449971	+	0.998987i	$0.485672\pi$
$32$		0			0
$33$	−11.5522	+	8.93540i	−0.350067	+	0.270770i
$34$		0			0
$35$	−34.4308	−	12.3686i	−0.983737	−	0.353388i
$36$		0			0
$37$	13.5493	+	23.4681i	0.366198	+	0.634273i	0.988968	−	0.148132i	$-0.0473260\pi$
$37$	13.5493	+	23.4681i	0.366198	+	0.634273i	−0.622770	+	0.782405i	$0.713993\pi$
$38$		0			0
$39$	13.3121	−	1.80489i	0.341335	−	0.0462793i
$40$		0			0
$41$	−59.9799	−	34.6294i	−1.46292	−	0.844620i	−0.463779	−	0.885951i	$-0.653507\pi$
$41$	−59.9799	−	34.6294i	−1.46292	−	0.844620i	−0.999146	+	0.0413310i	$0.986840\pi$
$42$		0			0
$43$	0.983471	+	1.70342i	0.0228714	+	0.0396145i	0.877235	−	0.480062i	$-0.159386\pi$
$43$	0.983471	+	1.70342i	0.0228714	+	0.0396145i	−0.854363	+	0.519676i	$0.826052\pi$
$44$		0			0
$45$	45.5278	+	11.8230i	1.01173	+	0.262734i
$46$		0			0
$47$	38.7995	+	22.4009i	0.825522	+	0.476615i	0.852317	−	0.523026i	$-0.175197\pi$
$47$	38.7995	+	22.4009i	0.825522	+	0.476615i	−0.0267949	+	0.999641i	$0.508530\pi$
$48$		0			0
$49$	−37.7989	−	31.1808i	−0.771406	−	0.636343i
$50$		0			0
$51$	78.2950	−	10.6155i	1.53520	−	0.208146i
$52$		0			0
$53$	6.39788	−	11.0815i	0.120715	−	0.209084i	−0.799335	−	0.600886i	$-0.794815\pi$
$53$	6.39788	−	11.0815i	0.120715	−	0.209084i	0.920050	+	0.391802i	$0.128148\pi$
$54$		0			0
$55$			25.4433i			0.462606i
$56$		0			0
$57$	20.5389	−	50.1320i	0.360332	−	0.879509i
$58$		0			0
$59$	−48.4028	+	27.9454i	−0.820387	+	0.473650i	−0.850550	−	0.525895i	$-0.823731\pi$
$59$	−48.4028	+	27.9454i	−0.820387	+	0.473650i	0.0301632	+	0.999545i	$0.490397\pi$
$60$		0			0
$61$	91.6937	+	52.9394i	1.50318	+	0.867859i	0.999993	+	0.00367844i	$0.00117089\pi$
$61$	91.6937	+	52.9394i	1.50318	+	0.867859i	0.503182	+	0.864180i	$0.332162\pi$
$62$		0			0
$63$	52.0335	+	35.5179i	0.825928	+	0.563776i
$64$		0			0
$65$	11.7019	−	20.2682i	0.180029	−	0.311819i
$66$		0			0
$67$	10.4104	+	18.0313i	0.155378	+	0.269123i	0.933197	−	0.359366i	$-0.117007\pi$
$67$	10.4104	+	18.0313i	0.155378	+	0.269123i	−0.777818	+	0.628489i	$0.783674\pi$
$68$		0			0
$69$	−4.99518	+	3.86367i	−0.0723939	+	0.0559952i
$70$		0			0
$71$	−23.1583			−0.326174			−0.163087	−	0.986612i	$-0.552145\pi$
$71$	−23.1583			−0.326174			−0.163087	+	0.986612i	$0.552145\pi$
$72$		0			0
$73$	116.548	+	67.2890i	1.59655	+	0.921767i	0.992146	+	0.125086i	$0.0399207\pi$
$73$	116.548	+	67.2890i	1.59655	+	0.921767i	0.604401	+	0.796680i	$0.293413\pi$
$74$		0			0
$75$	5.49480	−	4.25012i	0.0732640	−	0.0566683i
$76$		0			0
$77$	−11.5208	+	32.0709i	−0.149621	+	0.416505i
$78$		0			0
$79$	−55.8622	+	96.7561i	−0.707116	+	1.22476i	0.258807	+	0.965929i	$0.416671\pi$
$79$	−55.8622	+	96.7561i	−0.707116	+	1.22476i	−0.965922	+	0.258832i	$0.916663\pi$
$80$		0			0
$81$	−70.7652	−	39.4117i	−0.873645	−	0.486564i
$82$		0			0
$83$	16.3728	−	9.45285i	0.197263	−	0.113890i	−0.398115	−	0.917335i	$-0.630336\pi$
$83$	16.3728	−	9.45285i	0.197263	−	0.113890i	0.595378	+	0.803446i	$0.297002\pi$
$84$		0			0
$85$	68.8245	−	119.208i	0.809700	−	1.40244i
$86$		0			0
$87$	76.9093	+	31.5095i	0.884016	+	0.362178i
$88$		0			0
$89$	49.5248	−	28.5932i	0.556459	−	0.321272i	−0.195264	−	0.980751i	$-0.562556\pi$
$89$	49.5248	−	28.5932i	0.556459	−	0.321272i	0.751723	+	0.659479i	$0.229223\pi$
$90$		0			0
$91$	23.9275	−	20.2491i	0.262940	−	0.222518i
$92$		0			0
$93$	32.4739	−	79.2633i	0.349182	−	0.852294i
$94$		0			0
$95$	−47.1914	−	81.7379i	−0.496752	−	0.860399i
$96$		0			0
$97$	−165.209	+	95.3837i	−1.70319	+	0.983337i	−0.760698	+	0.649106i	$0.775143\pi$
$97$	−165.209	+	95.3837i	−1.70319	+	0.983337i	−0.942491	+	0.334231i	$0.891523\pi$
$98$		0			0
$99$	11.0127	−	42.4072i	0.111239	−	0.428356i
$100$		0			0
$101$		−	113.735i		−	1.12609i	−0.826427	−	0.563044i	$-0.809630\pi$
$101$		−	113.735i		−	1.12609i	0.826427	−	0.563044i	$-0.190370\pi$
$102$		0			0
$103$			120.883i			1.17362i	0.809724	+	0.586811i	$0.199617\pi$
$103$			120.883i			1.17362i	−0.809724	+	0.586811i	$0.800383\pi$
$104$		0			0
$105$	104.406	−	33.8459i	0.994343	−	0.322342i
$106$		0			0
$107$	57.2792	+	99.2104i	0.535319	+	0.927200i	0.999148	+	0.0412752i	$0.0131420\pi$
$107$	57.2792	+	99.2104i	0.535319	+	0.927200i	−0.463829	+	0.885925i	$0.653525\pi$
$108$		0			0
$109$	1.44744	−	2.50705i	0.0132793	−	0.0230004i	−0.859309	−	0.511456i	$-0.829106\pi$
$109$	1.44744	−	2.50705i	0.0132793	−	0.0230004i	0.872589	+	0.488456i	$0.162440\pi$
$110$		0			0
$111$	−75.2272	−	30.8203i	−0.677723	−	0.277661i
$112$		0			0
$113$	−60.3613	+	104.549i	−0.534171	+	0.925211i	0.465032	+	0.885294i	$0.346043\pi$
$113$	−60.3613	+	104.549i	−0.534171	+	0.925211i	−0.999203	+	0.0399175i	$0.987290\pi$
$114$		0			0
$115$			11.0017i			0.0956670i
$116$		0			0
$117$	−28.2766	+	28.7168i	−0.241681	+	0.245443i
$118$		0			0
$119$	140.730	−	119.095i	1.18260	−	1.00080i
$120$		0			0
$121$	−97.3006			−0.804137
$122$		0			0
$123$	205.893	−	27.9155i	1.67392	−	0.226956i
$124$		0			0
$125$			118.559i			0.948469i
$126$		0			0
$127$	−146.347			−1.15234			−0.576168	−	0.817331i	$-0.695453\pi$
$127$	−146.347			−1.15234			−0.576168	+	0.817331i	$0.695453\pi$
$128$		0			0
$129$	−5.46033	−	2.23708i	−0.0423282	−	0.0173417i
$130$		0			0
$131$		−	83.9330i		−	0.640710i	−0.947298	−	0.320355i	$-0.896198\pi$
$131$		−	83.9330i		−	0.640710i	0.947298	−	0.320355i	$-0.103802\pi$
$132$		0			0
$133$	−22.4727	−	124.398i	−0.168968	−	0.935321i
$134$		0			0
$135$	−129.738	+	55.5085i	−0.961019	+	0.411174i
$136$		0			0
$137$	−19.1092			−0.139483			−0.0697415	−	0.997565i	$-0.522217\pi$
$137$	−19.1092			−0.139483			−0.0697415	+	0.997565i	$0.522217\pi$
$138$		0			0
$139$	121.699	+	70.2632i	0.875535	+	0.505490i	0.869184	−	0.494490i	$-0.164645\pi$
$139$	121.699	+	70.2632i	0.875535	+	0.505490i	0.00635130	+	0.999980i	$0.497978\pi$
$140$		0			0
$141$	−133.187	+	18.0579i	−0.944588	+	0.128070i
$142$		0			0
$143$	−18.8790	−	10.8998i	−0.132021	−	0.0762225i
$144$		0			0
$145$	125.397	−	72.3980i	0.864807	−	0.499297i
$146$		0			0
$147$	146.928	+	4.61329i	0.999507	+	0.0313829i
$148$		0			0
$149$	−127.289			−0.854288			−0.427144	−	0.904184i	$-0.640480\pi$
$149$	−127.289			−0.854288			−0.427144	+	0.904184i	$0.640480\pi$
$150$		0			0
$151$	153.984			1.01976			0.509880	−	0.860245i	$-0.329690\pi$
$151$	153.984			1.01976			0.509880	+	0.860245i	$0.329690\pi$
$152$		0			0
$153$	−166.309	+	168.898i	−1.08699	+	1.10391i
$154$		0			0
$155$	−74.6139	−	129.235i	−0.481380	−	0.833775i
$156$		0			0
$157$	−123.023	+	71.0276i	−0.783589	+	0.452405i	−0.837701	−	0.546130i	$-0.816101\pi$
$157$	−123.023	+	71.0276i	−0.783589	+	0.452405i	0.0541119	+	0.998535i	$0.482767\pi$
$158$		0			0
$159$	5.15747	+	38.0392i	0.0324369	+	0.239241i
$160$		0			0
$161$	−4.98161	+	13.8675i	−0.0309417	+	0.0861333i
$162$		0			0
$163$	−28.1059	−	48.6808i	−0.172429	−	0.298655i	0.766840	−	0.641839i	$-0.221828\pi$
$163$	−28.1059	−	48.6808i	−0.172429	−	0.298655i	−0.939268	+	0.343183i	$0.888495\pi$
$164$		0			0
$165$	−46.7002	−	60.3768i	−0.283032	−	0.365920i
$166$		0			0
$167$	−149.022	−	86.0380i	−0.892348	−	0.515197i	−0.0176382	−	0.999844i	$-0.505615\pi$
$167$	−149.022	−	86.0380i	−0.892348	−	0.515197i	−0.874710	+	0.484647i	$0.838948\pi$
$168$		0			0
$169$	−74.4739	−	128.993i	−0.440674	−	0.763270i
$170$		0			0
$171$	43.2767	+	156.661i	0.253080	+	0.916148i
$172$		0			0
$173$	259.109	+	149.597i	1.49774	+	0.864722i	0.999997	−	0.00260137i	$-0.000828042\pi$
$173$	259.109	+	149.597i	1.49774	+	0.864722i	0.497745	+	0.867323i	$0.334161\pi$
$174$		0			0
$175$	5.47988	−	15.2545i	0.0313136	−	0.0871686i
$176$		0			0
$177$	63.5667	−	155.156i	0.359134	−	0.876585i
$178$		0			0
$179$	−105.294	+	182.374i	−0.588234	+	1.01885i	0.406230	+	0.913771i	$0.366843\pi$
$179$	−105.294	+	182.374i	−0.588234	+	1.01885i	−0.994464	+	0.105080i	$0.966490\pi$
$180$		0			0
$181$		−	109.297i		−	0.603849i	−0.953332	−	0.301924i	$-0.902371\pi$
$181$		−	109.297i		−	0.603849i	0.953332	−	0.301924i	$-0.0976290\pi$
$182$		0			0
$183$	−314.756	+	42.6756i	−1.71998	+	0.233200i
$184$		0			0
$185$	−122.654	+	70.8146i	−0.662997	+	0.382782i
$186$		0			0
$187$	−111.037	−	64.1072i	−0.593781	−	0.342820i
$188$		0			0
$189$	−188.667	+	11.2218i	−0.998236	+	0.0593747i
$190$		0			0
$191$	−80.0424	+	138.637i	−0.419070	+	0.725850i	−0.995846	−	0.0910518i	$-0.970977\pi$
$191$	−80.0424	+	138.637i	−0.419070	+	0.725850i	0.576776	+	0.816902i	$0.304310\pi$
$192$		0			0
$193$	128.950	+	223.348i	0.668135	+	1.15724i	0.978425	+	0.206602i	$0.0662404\pi$
$193$	128.950	+	223.348i	0.668135	+	1.15724i	−0.310290	+	0.950642i	$0.600426\pi$
$194$		0			0
$195$	9.43314	+	69.5747i	0.0483751	+	0.356793i
$196$		0			0
$197$	48.3615			0.245490			0.122745	−	0.992438i	$-0.460830\pi$
$197$	48.3615			0.245490			0.122745	+	0.992438i	$0.460830\pi$
$198$		0			0
$199$	−242.500	−	140.007i	−1.21859	−	0.703555i	−0.253976	−	0.967211i	$-0.581738\pi$
$199$	−242.500	−	140.007i	−1.21859	−	0.703555i	−0.964617	+	0.263656i	$0.915072\pi$
$200$		0			0
$201$	−57.7994	−	23.6802i	−0.287559	−	0.117812i
$202$		0			0
$203$	190.843	−	34.4762i	0.940113	−	0.169834i
$204$		0			0
$205$	180.988	−	313.481i	0.882869	−	1.52917i
$206$		0			0
$207$	4.76188	−	18.3369i	0.0230043	−	0.0885841i
$208$		0			0
$209$	−76.1355	+	43.9569i	−0.364285	+	0.210320i
$210$		0			0
$211$	116.083	−	201.061i	0.550155	−	0.952897i	−0.448108	−	0.893980i	$-0.647902\pi$
$211$	116.083	−	201.061i	0.550155	−	0.952897i	0.998263	−	0.0589170i	$-0.0187647\pi$
$212$		0			0
$213$	54.9545	−	42.5062i	0.258002	−	0.199560i
$214$		0			0
$215$	−8.90282	+	5.14004i	−0.0414085	+	0.0239072i
$216$		0			0
$217$	−35.5315	−	196.684i	−0.163739	−	0.906379i
$218$		0			0
$219$	−400.073	+	54.2431i	−1.82682	+	0.247686i
$220$		0			0
$221$	58.9683	+	102.136i	0.266825	+	0.462154i
$222$		0			0
$223$	40.4870	−	23.3752i	0.181556	−	0.104822i	−0.406467	−	0.913665i	$-0.633240\pi$
$223$	40.4870	−	23.3752i	0.181556	−	0.104822i	0.588024	+	0.808844i	$0.299906\pi$
$224$		0			0
$225$	−5.23817	+	20.1710i	−0.0232808	+	0.0896488i
$226$		0			0
$227$		−	194.745i		−	0.857905i	−0.903327	−	0.428953i	$-0.858883\pi$
$227$		−	194.745i		−	0.857905i	0.903327	−	0.428953i	$-0.141117\pi$
$228$		0			0
$229$		−	323.593i		−	1.41307i	−0.707679	−	0.706534i	$-0.750258\pi$
$229$		−	323.593i		−	1.41307i	0.707679	−	0.706534i	$-0.249742\pi$
$230$		0			0
$231$	−31.5260	−	97.2500i	−0.136476	−	0.420995i
$232$		0			0
$233$	118.761	+	205.701i	0.509706	+	0.882836i	0.999937	+	0.0112437i	$0.00357907\pi$
$233$	118.761	+	205.701i	0.509706	+	0.882836i	−0.490231	+	0.871593i	$0.663088\pi$
$234$		0			0
$235$	−117.077	+	202.783i	−0.498199	+	0.862907i
$236$		0			0
$237$	−45.0317	−	332.134i	−0.190007	−	1.40141i
$238$		0			0
$239$	208.192	−	360.600i	0.871098	−	1.50879i	0.0102362	−	0.999948i	$-0.496742\pi$
$239$	208.192	−	360.600i	0.871098	−	1.50879i	0.860862	−	0.508839i	$-0.169925\pi$
$240$		0			0
$241$			193.161i			0.801500i	0.916187	+	0.400750i	$0.131250\pi$
$241$			193.161i			0.801500i	−0.916187	+	0.400750i	$0.868750\pi$
$242$		0			0
$243$	240.264	−	36.3633i	0.988740	−	0.149643i
$244$		0			0
$245$	162.964	−	197.553i	0.665160	−	0.806340i
$246$		0			0
$247$	80.8664			0.327394
$248$		0			0
$249$	−21.5022	+	52.4832i	−0.0863542	+	0.210776i
$250$		0			0
$251$			398.689i			1.58840i	0.607654	+	0.794202i	$0.292111\pi$
$251$			398.689i			1.58840i	−0.607654	+	0.794202i	$0.707889\pi$
$252$		0			0
$253$	10.2476			0.0405045
$254$		0			0
$255$	55.4810	+	409.203i	0.217573	+	1.60472i
$256$		0			0
$257$		−	62.2823i		−	0.242343i	−0.992632	−	0.121172i	$-0.961335\pi$
$257$		−	62.2823i		−	0.242343i	0.992632	−	0.121172i	$-0.0386652\pi$
$258$		0			0
$259$	−186.669	+	33.7222i	−0.720730	+	0.130202i
$260$		0			0
$261$	−240.340	+	66.3924i	−0.920841	+	0.254377i
$262$		0			0
$263$	19.4267			0.0738658			0.0369329	−	0.999318i	$-0.488241\pi$
$263$	19.4267			0.0738658			0.0369329	+	0.999318i	$0.488241\pi$
$264$		0			0
$265$	57.9164	+	33.4381i	0.218553	+	0.126181i
$266$		0			0
$267$	−65.0402	+	158.752i	−0.243596	+	0.594577i
$268$		0			0
$269$	402.278	+	232.255i	1.49546	+	0.863402i	0.999986	−	0.00522340i	$-0.00166267\pi$
$269$	402.278	+	232.255i	1.49546	+	0.863402i	0.495470	+	0.868625i	$0.334996\pi$
$270$		0			0
$271$	−79.6131	+	45.9646i	−0.293775	+	0.169611i	−0.639643	−	0.768672i	$-0.720918\pi$
$271$	−79.6131	+	45.9646i	−0.293775	+	0.169611i	0.345868	+	0.938283i	$0.387585\pi$
$272$		0			0
$273$	−19.6134	+	91.9690i	−0.0718438	+	0.336883i
$274$		0			0
$275$	−11.2726			−0.0409913
$276$		0			0
$277$	477.953			1.72546			0.862730	−	0.505664i	$-0.168752\pi$
$277$	477.953			1.72546			0.862730	+	0.505664i	$0.168752\pi$
$278$		0			0
$279$	68.4245	+	247.696i	0.245249	+	0.887798i
$280$		0			0
$281$	256.938	+	445.030i	0.914371	+	1.58374i	0.807820	+	0.589429i	$0.200647\pi$
$281$	256.938	+	445.030i	0.914371	+	1.58374i	0.106550	+	0.994307i	$0.466019\pi$
$282$		0			0
$283$	−308.150	+	177.910i	−1.08887	+	0.628659i	−0.933275	−	0.359162i	$-0.883062\pi$
$283$	−308.150	+	177.910i	−1.08887	+	0.628659i	−0.155594	+	0.987821i	$0.549729\pi$
$284$		0			0
$285$	262.012	+	107.345i	0.919339	+	0.376650i
$286$		0			0
$287$	370.078	−	313.185i	1.28947	−	1.09124i
$288$		0			0
$289$	202.322	+	350.432i	0.700076	+	1.21257i
$290$		0			0
$291$	216.967	−	529.580i	0.745592	−	1.81986i
$292$		0			0
$293$	117.030	+	67.5671i	0.399419	+	0.230604i	0.686233	−	0.727382i	$-0.259263\pi$
$293$	117.030	+	67.5671i	0.399419	+	0.230604i	−0.286815	+	0.957986i	$0.592596\pi$
$294$		0			0
$295$	−146.055	−	252.974i	−0.495100	−	0.857538i
$296$		0			0
$297$	51.7039	+	120.845i	0.174087	+	0.406887i
$298$		0			0
$299$	−8.16330	−	4.71308i	−0.0273020	−	0.0157628i
$300$		0			0
$301$	−13.5493	+	2.44771i	−0.0450142	+	0.00813193i
$302$		0			0
$303$	208.756	+	269.892i	0.688964	+	0.890732i
$304$		0			0
$305$	−276.684	+	479.231i	−0.907160	+	1.57125i
$306$		0			0
$307$		−	39.5279i		−	0.128755i	−0.997926	−	0.0643776i	$-0.979494\pi$
$307$		−	39.5279i		−	0.128755i	0.997926	−	0.0643776i	$-0.0205062\pi$
$308$		0			0
$309$	−221.876	−	286.854i	−0.718046	−	0.928331i
$310$		0			0
$311$	300.456	−	173.468i	0.966095	−	0.557775i	0.0680515	−	0.997682i	$-0.478322\pi$
$311$	300.456	−	173.468i	0.966095	−	0.557775i	0.898044	+	0.439907i	$0.144988\pi$
$312$		0			0
$313$	111.454	+	64.3478i	0.356082	+	0.205584i	0.667361	−	0.744735i	$-0.267424\pi$
$313$	111.454	+	64.3478i	0.356082	+	0.205584i	−0.311279	+	0.950319i	$0.600757\pi$
$314$		0			0
$315$	−185.632	+	271.949i	−0.589307	+	0.863331i
$316$		0			0
$317$	98.3572	−	170.360i	0.310275	−	0.537412i	−0.668147	−	0.744030i	$-0.732912\pi$
$317$	98.3572	−	170.360i	0.310275	−	0.537412i	0.978422	+	0.206617i	$0.0662455\pi$
$318$		0			0
$319$	−67.4358	−	116.802i	−0.211398	−	0.366151i
$320$		0			0
$321$	−318.020	−	130.292i	−0.990716	−	0.405893i
$322$		0			0
$323$	475.616			1.47249
$324$		0			0
$325$	8.97980	+	5.18449i	0.0276302	+	0.0159523i
$326$		0			0
$327$	1.16682	+	8.60593i	0.00356825	+	0.0263178i
$328$		0			0
$329$	−239.394	+	202.592i	−0.727642	+	0.615781i
$330$		0			0
$331$	255.022	−	441.712i	0.770461	−	1.33448i	−0.166850	−	0.985982i	$-0.553360\pi$
$331$	255.022	−	441.712i	0.770461	−	1.33448i	0.937311	−	0.348495i	$-0.113307\pi$
$332$		0			0
$333$	235.083	−	64.9403i	0.705955	−	0.195016i
$334$		0			0
$335$	−94.2392	+	54.4090i	−0.281311	+	0.162415i
$336$		0			0
$337$	162.206	−	280.949i	0.481324	−	0.833678i	−0.518446	−	0.855110i	$-0.673489\pi$
$337$	162.206	−	280.949i	0.481324	−	0.833678i	0.999770	+	0.0214324i	$0.00682267\pi$
$338$		0			0
$339$	−48.6586	−	358.884i	−0.143536	−	1.05866i
$340$		0			0
$341$	−120.377	+	69.4998i	−0.353012	+	0.203812i
$342$		0			0
$343$	294.867	−	175.222i	0.859669	−	0.510851i
$344$		0			0
$345$	−20.1932	−	26.1069i	−0.0585310	−	0.0756723i
$346$		0			0
$347$	−344.996	−	597.550i	−0.994224	−	1.72205i	−0.590060	−	0.807359i	$-0.700896\pi$
$347$	−344.996	−	597.550i	−0.994224	−	1.72205i	−0.404164	−	0.914687i	$-0.632437\pi$
$348$		0			0
$349$	−99.8806	+	57.6661i	−0.286191	+	0.165232i	−0.636223	−	0.771505i	$-0.719504\pi$
$349$	−99.8806	+	57.6661i	−0.286191	+	0.165232i	0.350032	+	0.936738i	$0.386171\pi$
$350$		0			0
$351$	14.3916	−	120.045i	0.0410016	−	0.342010i
$352$		0			0
$353$		−	534.239i		−	1.51342i	−0.653749	−	0.756712i	$-0.726805\pi$
$353$		−	534.239i		−	1.51342i	0.653749	−	0.756712i	$-0.273195\pi$
$354$		0			0
$355$		−	121.035i		−	0.340945i
$356$		0			0
$357$	−115.356	+	540.916i	−0.323126	+	1.51517i
$358$		0			0
$359$	−37.1151	−	64.2853i	−0.103385	−	0.179068i	0.809692	−	0.586855i	$-0.199634\pi$
$359$	−37.1151	−	64.2853i	−0.103385	−	0.179068i	−0.913077	+	0.407787i	$0.866301\pi$
$360$		0			0
$361$	−17.4406	+	30.2080i	−0.0483119	+	0.0836787i
$362$		0			0
$363$	230.893	−	178.591i	0.636070	−	0.491987i
$364$		0			0
$365$	−351.681	+	609.129i	−0.963510	+	1.66885i
$366$		0			0
$367$			221.060i			0.602344i	0.953570	+	0.301172i	$0.0973778\pi$
$367$			221.060i			0.602344i	−0.953570	+	0.301172i	$0.902622\pi$
$368$		0			0
$369$	−437.343	+	444.151i	−1.18521	+	1.20366i
$370$		0			0
$371$	57.8618	+	68.3729i	0.155962	+	0.184294i
$372$		0			0
$373$	308.603			0.827355			0.413677	−	0.910424i	$-0.364244\pi$
$373$	308.603			0.827355			0.413677	+	0.910424i	$0.364244\pi$
$374$		0			0
$375$	−217.610	−	281.338i	−0.580293	−	0.750236i
$376$		0			0
$377$			124.060i			0.329072i
$378$		0			0
$379$	−183.496			−0.484159			−0.242080	−	0.970256i	$-0.577830\pi$
$379$	−183.496			−0.484159			−0.242080	+	0.970256i	$0.577830\pi$
$380$		0			0
$381$	347.279	−	268.614i	0.911494	−	0.705023i
$382$		0			0
$383$			304.720i			0.795614i	0.917469	+	0.397807i	$0.130229\pi$
$383$			304.720i			0.795614i	−0.917469	+	0.397807i	$0.869771\pi$
$384$		0			0
$385$	−167.616	−	60.2128i	−0.435367	−	0.156397i
$386$		0			0
$387$	17.0634	−	4.71366i	0.0440915	−	0.0121800i
$388$		0			0
$389$	−530.534			−1.36384			−0.681920	−	0.731427i	$-0.738855\pi$
$389$	−530.534			−1.36384			−0.681920	+	0.731427i	$0.738855\pi$
$390$		0			0
$391$	−48.0124	−	27.7200i	−0.122794	−	0.0708951i
$392$		0			0
$393$	154.056	+	199.172i	0.391999	+	0.506799i
$394$		0			0
$395$	−505.689	−	291.960i	−1.28022	−	0.739138i
$396$		0			0
$397$	−34.4462	+	19.8875i	−0.0867662	+	0.0500945i	−0.542755	−	0.839891i	$-0.682619\pi$
$397$	−34.4462	+	19.8875i	−0.0867662	+	0.0500945i	0.455989	+	0.889985i	$0.349286\pi$
$398$		0			0
$399$	281.655	+	253.947i	0.705902	+	0.636458i
$400$		0			0
$401$	−137.340			−0.342493			−0.171246	−	0.985228i	$-0.554779\pi$
$401$	−137.340			−0.342493			−0.171246	+	0.985228i	$0.554779\pi$
$402$		0			0
$403$	127.857			0.317263
$404$		0			0
$405$	205.982	−	369.849i	0.508599	−	0.913209i
$406$		0			0
$407$	65.9609	+	114.248i	0.162066	+	0.280707i
$408$		0			0
$409$	−250.540	+	144.649i	−0.612568	+	0.353666i	−0.773970	−	0.633223i	$-0.781732\pi$
$409$	−250.540	+	144.649i	−0.612568	+	0.353666i	0.161402	+	0.986889i	$0.448398\pi$
$410$		0			0
$411$	45.3459	−	35.0742i	0.110331	−	0.0853386i
$412$		0			0
$413$	−69.5518	−	385.003i	−0.168406	−	0.932211i
$414$		0			0
$415$	49.4047	+	85.5714i	0.119047	+	0.206196i
$416$		0			0
$417$	−417.757	+	56.6407i	−1.00181	+	0.135829i
$418$		0			0
$419$	−276.096	−	159.404i	−0.658940	−	0.380439i	0.132933	−	0.991125i	$-0.457561\pi$
$419$	−276.096	−	159.404i	−0.658940	−	0.380439i	−0.791873	+	0.610686i	$0.790894\pi$
$420$		0			0
$421$	151.715	+	262.779i	0.360369	+	0.624178i	0.988022	−	0.154316i	$-0.0493174\pi$
$421$	151.715	+	262.779i	0.360369	+	0.624178i	−0.627652	+	0.778494i	$0.715984\pi$
$422$		0			0
$423$	282.907	−	287.311i	0.668810	−	0.679221i
$424$		0			0
$425$	52.8147	+	30.4926i	0.124270	+	0.0717472i
$426$		0			0
$427$	−565.753	+	478.779i	−1.32495	+	1.12126i
$428$		0			0
$429$	64.8059	−	8.78658i	0.151063	−	0.0204815i
$430$		0			0
$431$	95.1177	−	164.749i	0.220691	−	0.382248i	−0.734327	−	0.678796i	$-0.762502\pi$
$431$	95.1177	−	164.749i	0.220691	−	0.382248i	0.955018	+	0.296548i	$0.0958355\pi$
$432$		0			0
$433$		−	174.100i		−	0.402080i	−0.979583	−	0.201040i	$-0.935568\pi$
$433$		−	174.100i		−	0.402080i	0.979583	−	0.201040i	$-0.0644320\pi$
$434$		0			0
$435$	−164.682	+	401.961i	−0.378580	+	0.924049i
$436$		0			0
$437$	−32.9210	+	19.0070i	−0.0753342	+	0.0434942i
$438$		0			0
$439$	−328.255	−	189.518i	−0.747734	−	0.431705i	0.0771404	−	0.997020i	$-0.475421\pi$
$439$	−328.255	−	189.518i	−0.747734	−	0.431705i	−0.824875	+	0.565316i	$0.808754\pi$
$440$		0			0
$441$	−357.125	+	258.733i	−0.809808	+	0.586695i
$442$		0			0
$443$	−225.787	+	391.075i	−0.509678	+	0.882788i	0.490259	+	0.871577i	$0.336902\pi$
$443$	−225.787	+	391.075i	−0.509678	+	0.882788i	−0.999937	+	0.0112115i	$0.996431\pi$
$444$		0			0
$445$	149.440	+	258.838i	0.335821	+	0.581658i
$446$		0			0
$447$	302.055	−	233.634i	0.675739	−	0.522671i
$448$		0			0
$449$	210.442			0.468690			0.234345	−	0.972154i	$-0.424705\pi$
$449$	210.442			0.468690			0.234345	+	0.972154i	$0.424705\pi$
$450$		0			0
$451$	−291.995	−	168.583i	−0.647438	−	0.373798i
$452$		0			0
$453$	−365.402	+	282.631i	−0.806627	+	0.623910i
$454$		0			0
$455$	105.831	+	125.056i	0.232595	+	0.274848i
$456$		0			0
$457$	−169.499	+	293.580i	−0.370894	+	0.642407i	−0.989703	−	0.143134i	$-0.954282\pi$
$457$	−169.499	+	293.580i	−0.370894	+	0.642407i	0.618809	+	0.785541i	$0.287615\pi$
$458$		0			0
$459$	84.6441	−	706.047i	0.184410	−	1.53823i
$460$		0			0
$461$	667.078	−	385.138i	1.44702	−	0.835439i	0.448720	−	0.893672i	$-0.351880\pi$
$461$	667.078	−	385.138i	1.44702	−	0.835439i	0.998303	+	0.0582329i	$0.0185466\pi$
$462$		0			0
$463$	19.3898	−	33.5841i	0.0418786	−	0.0725359i	−0.844326	−	0.535829i	$-0.819999\pi$
$463$	19.3898	−	33.5841i	0.0418786	−	0.0725359i	0.886205	+	0.463293i	$0.153332\pi$
$464$		0			0
$465$	414.264	+	169.723i	0.890891	+	0.364995i
$466$		0			0
$467$	−664.728	+	383.781i	−1.42340	+	0.821801i	−0.996588	−	0.0825394i	$-0.973697\pi$
$467$	−664.728	+	383.781i	−1.42340	+	0.821801i	−0.426813	+	0.904340i	$0.640364\pi$
$468$		0			0
$469$	−143.423	+	25.9098i	−0.305807	+	0.0552448i
$470$		0			0
$471$	161.565	−	394.353i	0.343025	−	0.837267i
$472$		0			0
$473$	4.78774	+	8.29261i	0.0101221	+	0.0175319i
$474$		0			0
$475$	36.2138	−	20.9081i	0.0762396	−	0.0440170i
$476$		0			0
$477$	−82.0582	−	80.8004i	−0.172030	−	0.169393i
$478$		0			0
$479$		−	690.530i		−	1.44161i	−0.693139	−	0.720804i	$-0.743773\pi$
$479$		−	690.530i		−	1.44161i	0.693139	−	0.720804i	$-0.256227\pi$
$480$		0			0
$481$		−	121.347i		−	0.252280i
$482$		0			0
$483$	−13.6319	−	42.0509i	−0.0282233	−	0.0870619i
$484$		0			0
$485$	−498.516	−	863.455i	−1.02787	−	1.78032i
$486$		0			0
$487$	−240.644	+	416.807i	−0.494135	+	0.855867i	−0.999977	−	0.00675930i	$-0.997848\pi$
$487$	−240.644	+	416.807i	−0.494135	+	0.855867i	0.505842	+	0.862626i	$0.331182\pi$
$488$		0			0
$489$	156.047	+	63.9318i	0.319114	+	0.130740i
$490$		0			0
$491$	−87.9273	+	152.295i	−0.179078	+	0.310172i	−0.941565	−	0.336831i	$-0.890645\pi$
$491$	−87.9273	+	152.295i	−0.179078	+	0.310172i	0.762487	+	0.647004i	$0.223978\pi$
$492$		0			0
$493$			729.659i			1.48004i
$494$		0			0
$495$	221.638	+	57.5570i	0.447754	+	0.116277i
$496$		0			0
$497$	54.8053	−	152.563i	0.110272	−	0.306968i
$498$		0			0
$499$	441.085			0.883938			0.441969	−	0.897030i	$-0.354280\pi$
$499$	441.085			0.883938			0.441969	+	0.897030i	$0.354280\pi$
$500$		0			0
$501$	511.547	−	69.3571i	1.02105	−	0.138437i
$502$		0			0
$503$		−	574.435i		−	1.14202i	−0.820944	−	0.571009i	$-0.806552\pi$
$503$		−	574.435i		−	1.14202i	0.820944	−	0.571009i	$-0.193448\pi$
$504$		0			0
$505$	594.428			1.17708
$506$		0			0
$507$	413.487	+	169.404i	0.815556	+	0.334131i
$508$		0			0
$509$		−	204.871i		−	0.402497i	−0.979540	−	0.201248i	$-0.935500\pi$
$509$		−	204.871i		−	0.402497i	0.979540	−	0.201248i	$-0.0644998\pi$
$510$		0			0
$511$	−719.104	+	608.555i	−1.40725	+	1.19091i
$512$		0			0
$513$	−390.241	−	292.323i	−0.760704	−	0.569830i
$514$		0			0
$515$	−631.787			−1.22677
$516$		0			0
$517$	188.884	+	109.052i	0.365346	+	0.210933i
$518$		0			0
$519$	−889.443	+	120.593i	−1.71376	+	0.232357i
$520$		0			0
$521$	−353.441	−	204.059i	−0.678389	−	0.391668i	0.120858	−	0.992670i	$-0.461435\pi$
$521$	−353.441	−	204.059i	−0.678389	−	0.391668i	−0.799248	+	0.601001i	$0.794769\pi$
$522$		0			0
$523$	48.8115	−	28.1814i	0.0933299	−	0.0538841i	−0.452609	−	0.891709i	$-0.649507\pi$
$523$	48.8115	−	28.1814i	0.0933299	−	0.0538841i	0.545939	+	0.837825i	$0.316173\pi$
$524$		0			0
$525$	14.9953	+	46.2569i	0.0285626	+	0.0881083i
$526$		0			0
$527$	751.992			1.42693
$528$		0			0
$529$	−524.569			−0.991624
$530$		0			0
$531$	133.939	+	484.857i	0.252239	+	0.913102i
$532$		0			0
$533$	155.069	+	268.588i	0.290937	+	0.503917i
$534$		0			0
$535$	−518.516	+	299.365i	−0.969189	+	0.559562i
$536$		0			0
$537$	−84.8797	−	626.035i	−0.158063	−	1.16580i
$538$		0			0
$539$	−184.013	−	151.795i	−0.341397	−	0.281623i
$540$		0			0
$541$	−12.8446	−	22.2475i	−0.0237424	−	0.0411230i	0.853910	−	0.520421i	$-0.174225\pi$
$541$	−12.8446	−	22.2475i	−0.0237424	−	0.0411230i	−0.877652	+	0.479298i	$0.840891\pi$
$542$		0			0
$543$	200.610	+	259.360i	0.369447	+	0.477642i
$544$		0			0
$545$	13.1029	+	7.56497i	0.0240420	+	0.0138807i
$546$		0			0
$547$	382.531	+	662.563i	0.699326	+	1.21127i	0.968701	+	0.248232i	$0.0798496\pi$
$547$	382.531	+	662.563i	0.699326	+	1.21127i	−0.269375	+	0.963035i	$0.586817\pi$
$548$		0			0
$549$	668.584	−	678.992i	1.21782	−	1.23678i
$550$		0			0
$551$	433.282	+	250.155i	0.786355	+	0.454002i
$552$		0			0
$553$	−505.212	−	596.988i	−0.913584	−	1.07954i
$554$		0			0
$555$	161.080	−	393.170i	0.290235	−	0.708414i
$556$		0			0
$557$	−268.114	+	464.386i	−0.481353	+	0.833728i	−0.999771	−	0.0213996i	$-0.993188\pi$
$557$	−268.114	+	464.386i	−0.481353	+	0.833728i	0.518418	+	0.855127i	$0.326521\pi$
$558$		0			0
$559$		−	8.80789i		−	0.0157565i
$560$		0			0
$561$	381.156	−	51.6783i	0.679423	−	0.0921181i
$562$		0			0
$563$	−292.335	+	168.780i	−0.519245	+	0.299786i	−0.736626	−	0.676301i	$-0.763582\pi$
$563$	−292.335	+	168.780i	−0.519245	+	0.299786i	0.217381	+	0.976087i	$0.430249\pi$
$564$		0			0
$565$	−546.417	−	315.474i	−0.967110	−	0.558361i
$566$		0			0
$567$	427.107	−	372.919i	0.753275	−	0.657706i
$568$		0			0
$569$	−518.116	+	897.403i	−0.910572	+	1.57716i	−0.0973144	+	0.995254i	$0.531025\pi$
$569$	−518.116	+	897.403i	−0.910572	+	1.57716i	−0.813258	+	0.581904i	$0.802308\pi$
$570$		0			0
$571$	339.020	+	587.200i	0.593730	+	1.02837i	0.993725	+	0.111853i	$0.0356787\pi$
$571$	339.020	+	587.200i	0.593730	+	1.02837i	−0.399995	+	0.916518i	$0.630988\pi$
$572$		0			0
$573$	−64.5239	−	475.900i	−0.112607	−	0.830541i
$574$		0			0
$575$	−4.87428			−0.00847701
$576$		0			0
$577$	392.667	+	226.706i	0.680532	+	0.392906i	0.800056	−	0.599926i	$-0.204803\pi$
$577$	392.667	+	226.706i	0.680532	+	0.392906i	−0.119523	+	0.992831i	$0.538137\pi$
$578$		0			0
$579$	−715.944	−	293.320i	−1.23652	−	0.506597i
$580$		0			0
$581$	23.5267	+	130.232i	0.0404935	+	0.224151i
$582$		0			0
$583$	31.1462	−	53.9468i	0.0534240	−	0.0925331i
$584$		0			0
$585$	−150.086	−	147.786i	−0.256558	−	0.252625i
$586$		0			0
$587$	−244.807	+	141.339i	−0.417047	+	0.240782i	−0.693813	−	0.720155i	$-0.744071\pi$
$587$	−244.807	+	141.339i	−0.417047	+	0.240782i	0.276766	+	0.960937i	$0.410737\pi$
$588$		0			0
$589$	257.812	−	446.543i	0.437711	−	0.758138i
$590$		0			0
$591$	−114.761	+	88.7657i	−0.194182	+	0.150196i
$592$		0			0
$593$	612.297	−	353.510i	1.03254	−	0.596138i	0.114830	−	0.993385i	$-0.463368\pi$
$593$	612.297	−	353.510i	1.03254	−	0.596138i	0.917712	+	0.397247i	$0.130034\pi$
$594$		0			0
$595$	622.442	+	735.514i	1.04612	+	1.23616i
$596$		0			0
$597$	832.428	−	112.863i	1.39435	−	0.189050i
$598$		0			0
$599$	210.290	+	364.234i	0.351069	+	0.608069i	0.986437	−	0.164140i	$-0.0524849\pi$
$599$	210.290	+	364.234i	0.351069	+	0.608069i	−0.635368	+	0.772210i	$0.719152\pi$
$600$		0			0
$601$	493.506	−	284.926i	0.821142	−	0.474086i	−0.0296684	−	0.999560i	$-0.509445\pi$
$601$	493.506	−	284.926i	0.821142	−	0.474086i	0.850810	+	0.525473i	$0.176112\pi$
$602$		0			0
$603$	180.621	−	49.8956i	0.299538	−	0.0827456i
$604$		0			0
$605$		−	508.535i		−	0.840553i
$606$		0			0
$607$		−	229.484i		−	0.378062i	−0.981971	−	0.189031i	$-0.939465\pi$
$607$		−	229.484i		−	0.378062i	0.981971	−	0.189031i	$-0.0605347\pi$
$608$		0			0
$609$	−389.589	+	432.097i	−0.639719	+	0.709518i
$610$		0			0
$611$	−100.310	−	173.743i	−0.164174	−	0.284358i
$612$		0			0
$613$	303.077	−	524.944i	0.494415	−	0.856353i	−0.505564	−	0.862789i	$-0.668716\pi$
$613$	303.077	−	524.944i	0.494415	−	0.856353i	0.999979	+	0.00643661i	$0.00204885\pi$
$614$		0			0
$615$	145.899	+	1076.08i	0.237234	+	1.74973i
$616$		0			0
$617$	8.50305	−	14.7277i	0.0137813	−	0.0238699i	−0.859053	−	0.511887i	$-0.828946\pi$
$617$	8.50305	−	14.7277i	0.0137813	−	0.0238699i	0.872834	+	0.488018i	$0.162280\pi$
$618$		0			0
$619$		−	221.345i		−	0.357584i	−0.983887	−	0.178792i	$-0.942781\pi$
$619$		−	221.345i		−	0.357584i	0.983887	−	0.178792i	$-0.0572189\pi$
$620$		0			0
$621$	22.3568	+	52.2535i	0.0360012	+	0.0841442i
$622$		0			0
$623$	71.1640	+	393.928i	0.114228	+	0.632308i
$624$		0			0
$625$	−677.527			−1.08404
$626$		0			0
$627$	99.9877	−	244.053i	0.159470	−	0.389239i
$628$		0			0
$629$		−	713.700i		−	1.13466i
$630$		0			0
$631$	947.169			1.50106			0.750530	−	0.660837i	$-0.229798\pi$
$631$	947.169			1.50106			0.750530	+	0.660837i	$0.229798\pi$
$632$		0			0
$633$	93.5769	+	690.181i	0.147831	+	1.09033i
$634$		0			0
$635$		−	764.871i		−	1.20452i
$636$		0			0
$637$	76.7720	+	205.551i	0.120521	+	0.322686i
$638$		0			0
$639$	−52.3879	+	201.734i	−0.0819842	+	0.315702i
$640$		0			0
$641$	−639.570			−0.997769			−0.498884	−	0.866669i	$-0.666257\pi$
$641$	−639.570			−0.997769			−0.498884	+	0.866669i	$0.666257\pi$
$642$		0			0
$643$	790.540	+	456.419i	1.22946	+	0.709827i	0.966916	−	0.255094i	$-0.0821065\pi$
$643$	790.540	+	456.419i	1.22946	+	0.709827i	0.262540	+	0.964921i	$0.415440\pi$
$644$		0			0
$645$	11.6919	−	28.5380i	0.0181270	−	0.0442450i
$646$		0			0
$647$	−921.679	−	532.131i	−1.42454	−	0.822460i	−0.427859	−	0.903845i	$-0.640732\pi$
$647$	−921.679	−	532.131i	−1.42454	−	0.822460i	−0.996683	+	0.0813857i	$0.974065\pi$
$648$		0			0
$649$	−235.635	+	136.044i	−0.363074	+	0.209621i
$650$		0			0
$651$	445.322	+	401.513i	0.684058	+	0.616763i
$652$		0			0
$653$	238.535			0.365291			0.182646	−	0.983179i	$-0.441534\pi$
$653$	238.535			0.365291			0.182646	+	0.983179i	$0.441534\pi$
$654$		0			0
$655$	438.670			0.669725
$656$		0			0
$657$	849.809	−	863.037i	1.29347	−	1.31360i
$658$		0			0
$659$	538.673	+	933.010i	0.817410	+	1.41580i	0.907584	+	0.419870i	$0.137924\pi$
$659$	538.673	+	933.010i	0.817410	+	1.41580i	−0.0901739	+	0.995926i	$0.528742\pi$
$660$		0			0
$661$	−95.1790	+	54.9516i	−0.143992	+	0.0831341i	−0.570265	−	0.821460i	$-0.693160\pi$
$661$	−95.1790	+	54.9516i	−0.143992	+	0.0831341i	0.426273	+	0.904595i	$0.359826\pi$
$662$		0			0
$663$	−327.398	−	134.134i	−0.493813	−	0.202314i
$664$		0			0
$665$	650.156	−	117.452i	0.977678	−	0.176620i
$666$		0			0
$667$	−29.1593	−	50.5053i	−0.0437170	−	0.0757201i
$668$		0			0
$669$	−53.1711	+	129.782i	−0.0794784	+	0.193993i
$670$		0			0
$671$	446.384	+	257.720i	0.665252	+	0.384083i
$672$		0			0
$673$	−133.564	−	231.339i	−0.198460	−	0.343743i	0.749569	−	0.661926i	$-0.230261\pi$
$673$	−133.564	−	231.339i	−0.198460	−	0.343743i	−0.948029	+	0.318183i	$0.896927\pi$
$674$		0			0
$675$	−24.5929	−	57.4800i	−0.0364340	−	0.0851556i
$676$		0			0
$677$	−512.469	−	295.874i	−0.756970	−	0.437037i	0.0712366	−	0.997459i	$-0.477305\pi$
$677$	−512.469	−	295.874i	−0.756970	−	0.437037i	−0.828207	+	0.560422i	$0.810639\pi$
$678$		0			0
$679$	−237.395	−	1314.10i	−0.349625	−	1.93535i
$680$		0			0
$681$	357.446	+	462.127i	0.524884	+	0.678600i
$682$		0			0
$683$	299.478	−	518.712i	0.438475	−	0.759461i	−0.559097	−	0.829102i	$-0.688852\pi$
$683$	299.478	−	518.712i	0.438475	−	0.759461i	0.997572	+	0.0696413i	$0.0221855\pi$
$684$		0			0
$685$		−	99.8728i		−	0.145800i
$686$		0			0
$687$	593.942	+	767.882i	0.864544	+	1.11773i
$688$		0			0
$689$	−49.6223	+	28.6495i	−0.0720208	+	0.0415812i
$690$		0			0
$691$	577.667	+	333.516i	0.835987	+	0.482657i	0.855898	−	0.517144i	$-0.173005\pi$
$691$	577.667	+	333.516i	0.835987	+	0.482657i	−0.0199111	+	0.999802i	$0.506338\pi$
$692$		0			0
$693$	253.310	+	172.908i	0.365526	+	0.249507i
$694$		0			0
$695$	−367.225	+	636.053i	−0.528382	+	0.915184i
$696$		0			0
$697$	912.039	+	1579.70i	1.30852	+	2.26642i
$698$		0			0
$699$	−659.376	−	270.144i	−0.943313	−	0.386472i
$700$		0			0
$701$	938.173			1.33834			0.669168	−	0.743111i	$-0.266651\pi$
$701$	938.173			1.33834			0.669168	+	0.743111i	$0.266651\pi$
$702$		0			0
$703$	−423.805	−	244.684i	−0.602852	−	0.348057i
$704$		0			0
$705$	−94.3782	−	696.092i	−0.133870	−	0.987365i
$706$		0			0
$707$	749.266	+	269.159i	1.05978	+	0.380706i
$708$		0			0
$709$	−331.078	+	573.444i	−0.466964	+	0.808806i	−0.999288	−	0.0377350i	$-0.987986\pi$
$709$	−331.078	+	573.444i	−0.466964	+	0.808806i	0.532323	+	0.846541i	$0.321319\pi$
$710$		0			0
$711$	716.479	+	705.497i	1.00771	+	0.992260i
$712$		0			0
$713$	−52.0511	+	30.0517i	−0.0730030	+	0.0421483i
$714$		0			0
$715$	56.9671	−	98.6699i	0.0796743	−	0.138000i
$716$		0			0
$717$	167.829	+	1237.83i	0.234071	+	1.72640i
$718$		0			0
$719$	−417.149	+	240.841i	−0.580179	+	0.334966i	−0.761204	−	0.648512i	$-0.775392\pi$
$719$	−417.149	+	240.841i	−0.580179	+	0.334966i	0.181026	+	0.983478i	$0.442058\pi$
$720$		0			0
$721$	−796.357	−	286.076i	−1.10452	−	0.396776i
$722$		0			0
$723$	−354.540	−	458.370i	−0.490374	−	0.633984i
$724$		0			0
$725$	32.0758	+	55.5569i	0.0442425	+	0.0766302i
$726$		0			0
$727$	158.111	−	91.2852i	0.217484	−	0.125564i	−0.387301	−	0.921953i	$-0.626593\pi$
$727$	158.111	−	91.2852i	0.217484	−	0.125564i	0.604785	+	0.796389i	$0.293259\pi$
$728$		0			0
$729$	−503.400	+	527.285i	−0.690535	+	0.723299i
$730$		0			0
$731$		−	51.8036i		−	0.0708668i
$732$		0			0
$733$		−	309.155i		−	0.421767i	−0.977511	−	0.210883i	$-0.932366\pi$
$733$		−	309.155i		−	0.421767i	0.977511	−	0.210883i	$-0.0676341\pi$
$734$		0			0
$735$	−24.1110	+	767.907i	−0.0328041	+	1.04477i
$736$		0			0
$737$	50.6798	+	87.7799i	0.0687649	+	0.119104i
$738$		0			0
$739$	153.566	−	265.984i	0.207803	−	0.359925i	−0.743219	−	0.669048i	$-0.766702\pi$
$739$	153.566	−	265.984i	0.207803	−	0.359925i	0.951022	+	0.309123i	$0.100036\pi$
$740$		0			0
$741$	−191.895	+	148.427i	−0.258968	+	0.200307i
$742$		0			0
$743$	−333.563	+	577.749i	−0.448941	+	0.777589i	−0.998317	−	0.0579859i	$-0.981532\pi$
$743$	−333.563	+	577.749i	−0.448941	+	0.777589i	0.549376	+	0.835575i	$0.314865\pi$
$744$		0			0
$745$		−	665.266i		−	0.892975i
$746$		0			0
$747$	−45.3064	−	164.009i	−0.0606511	−	0.219556i
$748$		0			0
$749$	−789.135	+	142.559i	−1.05358	+	0.190333i
$750$		0			0
$751$	−165.828			−0.220809			−0.110405	−	0.993887i	$-0.535215\pi$
$751$	−165.828			−0.220809			−0.110405	+	0.993887i	$0.535215\pi$
$752$		0			0
$753$	−731.779	−	946.086i	−0.971818	−	1.25642i
$754$		0			0
$755$			804.785i			1.06594i
$756$		0			0
$757$	−1445.23			−1.90916			−0.954580	−	0.297954i	$-0.903696\pi$
$757$	−1445.23			−1.90916			−0.954580	+	0.297954i	$0.903696\pi$
$758$		0			0
$759$	−24.3175	+	18.8091i	−0.0320389	+	0.0247815i
$760$		0			0
$761$		−	1385.00i		−	1.81997i	−0.414639	−	0.909986i	$-0.636092\pi$
$761$		−	1385.00i		−	1.81997i	0.414639	−	0.909986i	$-0.363908\pi$
$762$		0			0
$763$	13.0905	+	15.4686i	0.0171567	+	0.0202733i
$764$		0			0
$765$	−882.733	−	869.202i	−1.15390	−	1.13621i
$766$		0			0
$767$	250.277			0.326306
$768$		0			0
$769$	−278.900	−	161.023i	−0.362679	−	0.209393i	0.307576	−	0.951523i	$-0.400482\pi$
$769$	−278.900	−	161.023i	−0.362679	−	0.209393i	−0.670255	+	0.742131i	$0.733815\pi$
$770$		0			0
$771$	114.317	+	147.795i	0.148271	+	0.191693i
$772$		0			0
$773$	691.055	+	398.981i	0.893991	+	0.516146i	0.875246	−	0.483678i	$-0.160700\pi$
$773$	691.055	+	398.981i	0.893991	+	0.516146i	0.0187451	+	0.999824i	$0.494033\pi$
$774$		0			0
$775$	57.2574	−	33.0575i	0.0738805	−	0.0426549i
$776$		0			0
$777$	381.068	−	422.646i	0.490435	−	0.543946i
$778$		0			0
$779$	1250.73			1.60556
$780$		0			0
$781$	−112.740			−0.144353
$782$		0			0
$783$	448.463	−	598.683i	0.572749	−	0.764601i
$784$		0			0
$785$	−371.221	−	642.973i	−0.472893	−	0.819074i
$786$		0			0
$787$	17.0107	−	9.82112i	0.0216146	−	0.0124792i	−0.489154	−	0.872198i	$-0.662694\pi$
$787$	17.0107	−	9.82112i	0.0216146	−	0.0124792i	0.510768	+	0.859718i	$0.329361\pi$
$788$		0			0
$789$	−46.0994	+	35.6570i	−0.0584276	+	0.0451926i
$790$		0			0
$791$	−545.902	−	645.070i	−0.690142	−	0.815512i
$792$		0			0
$793$	−237.060	−	410.601i	−0.298941	−	0.517782i
$794$		0			0
$795$	−198.809	+	26.9552i	−0.250075	+	0.0339059i
$796$		0			0
$797$	47.9342	+	27.6748i	0.0601433	+	0.0347238i	0.529770	−	0.848141i	$-0.322278\pi$
$797$	47.9342	+	27.6748i	0.0601433	+	0.0347238i	−0.469627	+	0.882865i	$0.655612\pi$
$798$		0			0
$799$	−589.976	−	1021.87i	−0.738393	−	1.27893i
$800$		0			0
$801$	−137.044	−	496.096i	−0.171091	−	0.619346i
$802$		0			0
$803$	567.379	+	327.576i	0.706574	+	0.407941i
$804$		0			0
$805$	−72.4773	−	26.0360i	−0.0900339	−	0.0323429i
$806$		0			0
$807$	−1380.90	+	187.226i	−1.71115	+	0.232002i
$808$		0			0
$809$	−476.140	+	824.699i	−0.588554	+	1.01941i	0.405868	+	0.913932i	$0.366969\pi$
$809$	−476.140	+	824.699i	−0.588554	+	1.01941i	−0.994422	+	0.105474i	$0.966364\pi$
$810$		0			0
$811$			1053.01i			1.29841i	0.760615	+	0.649204i	$0.224898\pi$
$811$			1053.01i			1.29841i	−0.760615	+	0.649204i	$0.775102\pi$
$812$		0			0
$813$	104.555	−	255.200i	0.128604	−	0.313900i
$814$		0			0
$815$	254.427	−	146.893i	0.312180	−	0.180237i
$816$		0			0
$817$	−30.7617	−	17.7603i	−0.0376520	−	0.0217384i
$818$		0			0
$819$	−122.263	−	254.241i	−0.149284	−	0.310429i
$820$		0			0
$821$	−73.9349	+	128.059i	−0.0900547	+	0.155979i	−0.907534	−	0.419979i	$-0.862038\pi$
$821$	−73.9349	+	128.059i	−0.0900547	+	0.155979i	0.817479	+	0.575958i	$0.195371\pi$
$822$		0			0
$823$	−708.750	−	1227.59i	−0.861179	−	1.49161i	−0.870792	−	0.491652i	$-0.836393\pi$
$823$	−708.750	−	1227.59i	−0.861179	−	1.49161i	0.00961253	−	0.999954i	$-0.496940\pi$
$824$		0			0
$825$	26.7498	−	20.6905i	0.0324240	−	0.0250793i
$826$		0			0
$827$	−620.518			−0.750323			−0.375162	−	0.926959i	$-0.622413\pi$
$827$	−620.518			−0.750323			−0.375162	+	0.926959i	$0.622413\pi$
$828$		0			0
$829$	239.434	+	138.237i	0.288823	+	0.166752i	0.637411	−	0.770524i	$-0.280005\pi$
$829$	239.434	+	138.237i	0.288823	+	0.166752i	−0.348588	+	0.937276i	$0.613339\pi$
$830$		0			0
$831$	−1134.18	+	877.264i	−1.36483	+	1.05567i
$832$		0			0
$833$	451.535	+	1208.95i	0.542058	+	1.45132i
$834$		0			0
$835$	449.671	−	778.853i	0.538528	−	0.932759i
$836$		0			0
$837$	−617.006	−	462.189i	−0.737164	−	0.552197i
$838$		0			0
$839$	517.588	−	298.830i	0.616911	−	0.356174i	−0.158755	−	0.987318i	$-0.550748\pi$
$839$	517.588	−	298.830i	0.616911	−	0.356174i	0.775665	+	0.631145i	$0.217415\pi$
$840$		0			0
$841$	36.7279	−	63.6147i	0.0436718	−	0.0756417i
$842$		0			0
$843$	−1426.55	−	584.452i	−1.69223	−	0.693300i
$844$		0			0
$845$	674.171	−	389.233i	0.797835	−	0.460630i
$846$		0			0
$847$	230.266	−	640.999i	0.271861	−	0.756788i
$848$		0			0
$849$	404.689	−	987.777i	0.476665	−	1.16346i
$850$		0			0
$851$	28.5215	+	49.4007i	0.0335153	+	0.0580502i
$852$		0			0
$853$	832.688	−	480.753i	0.976187	−	0.563602i	0.0750705	−	0.997178i	$-0.476082\pi$
$853$	832.688	−	480.753i	0.976187	−	0.563602i	0.901117	+	0.433576i	$0.142748\pi$
$854$		0			0
$855$	−818.779	+	226.183i	−0.957636	+	0.264541i
$856$		0			0
$857$		−	1136.54i		−	1.32618i	−0.748538	−	0.663092i	$-0.769244\pi$
$857$		−	1136.54i		−	1.32618i	0.748538	−	0.663092i	$-0.230756\pi$
$858$		0			0
$859$			934.897i			1.08836i	0.838970	+	0.544178i	$0.183158\pi$
$859$			934.897i			1.08836i	−0.838970	+	0.544178i	$0.816842\pi$
$860$		0			0
$861$	−303.352	+	1422.45i	−0.352325	+	1.65209i
$862$		0			0
$863$	−127.595	−	221.001i	−0.147850	−	0.256084i	0.782582	−	0.622547i	$-0.213902\pi$
$863$	−127.595	−	221.001i	−0.147850	−	0.256084i	−0.930433	+	0.366463i	$0.880569\pi$
$864$		0			0
$865$	−781.857	+	1354.22i	−0.903881	+	1.56557i
$866$		0			0
$867$	−1123.31	−	460.217i	−1.29563	−	0.530816i
$868$		0			0
$869$	−271.948	+	471.029i	−0.312944	+	0.542035i
$870$		0			0
$871$		−	93.2344i		−	0.107043i
$872$		0			0
$873$	457.163	+	1654.92i	0.523668	+	1.89567i
$874$		0			0
$875$	−781.044	−	280.575i	−0.892621	−	0.320657i
$876$		0			0
$877$	201.993			0.230323			0.115161	−	0.993347i	$-0.463261\pi$
$877$	201.993			0.230323			0.115161	+	0.993347i	$0.463261\pi$
$878$		0			0
$879$	−401.727	+	54.4673i	−0.457027	+	0.0619651i
$880$		0			0
$881$		−	63.7012i		−	0.0723056i	−0.999346	−	0.0361528i	$-0.988490\pi$
$881$		−	63.7012i		−	0.0723056i	0.999346	−	0.0361528i	$-0.0115103\pi$
$882$		0			0
$883$	480.739			0.544438			0.272219	−	0.962235i	$-0.412242\pi$
$883$	480.739			0.544438			0.272219	+	0.962235i	$0.412242\pi$
$884$		0			0
$885$	810.910	+	332.227i	0.916282	+	0.375398i
$886$		0			0
$887$			910.655i			1.02667i	0.858189	+	0.513334i	$0.171590\pi$
$887$			910.655i			1.02667i	−0.858189	+	0.513334i	$0.828410\pi$
$888$		0			0
$889$	346.336	−	964.107i	0.389580	−	1.08448i
$890$		0			0
$891$	−344.500	−	191.864i	−0.386644	−	0.215336i
$892$		0			0
$893$	−809.066			−0.906009
$894$		0			0
$895$	−953.166	−	550.311i	−1.06499	−	0.614872i
$896$		0			0
$897$	28.0221	−	3.79932i	0.0312398	−	0.00423559i
$898$		0			0
$899$	685.058	+	395.518i	0.762022	+	0.439954i
$900$		0			0
$901$	−291.854	+	168.502i	−0.323922	+	0.187016i
$902$		0			0
$903$	27.6596	−	30.6776i	0.0306308	−	0.0339730i
$904$		0			0
$905$	571.231			0.631194
$906$		0			0
$907$	864.974			0.953664			0.476832	−	0.878994i	$-0.341785\pi$
$907$	864.974			0.953664			0.476832	+	0.878994i	$0.341785\pi$
$908$		0			0
$909$	−990.752	−	257.287i	−1.08994	−	0.283044i
$910$		0			0
$911$	674.624	+	1168.48i	0.740532	+	1.28264i	0.952254	+	0.305308i	$0.0987595\pi$
$911$	674.624	+	1168.48i	0.740532	+	1.28264i	−0.211722	+	0.977330i	$0.567907\pi$
$912$		0			0
$913$	79.7063	−	46.0184i	0.0873015	−	0.0504035i
$914$		0			0
$915$	−223.041	−	1645.05i	−0.243761	−	1.79787i
$916$		0			0
$917$	552.936	+	198.631i	0.602984	+	0.216610i
$918$		0			0
$919$	−343.774	−	595.433i	−0.374073	−	0.647914i	0.616114	−	0.787657i	$-0.288706\pi$
$919$	−343.774	−	595.433i	−0.374073	−	0.647914i	−0.990188	+	0.139742i	$0.955373\pi$
$920$		0			0
$921$	72.5518	+	93.7992i	0.0787751	+	0.101845i
$922$		0			0
$923$	89.8087	+	51.8511i	0.0973008	+	0.0561767i
$924$		0			0
$925$	−31.3743	−	54.3418i	−0.0339181	−	0.0587479i
$926$		0			0
$927$	1053.02	+	273.457i	1.13594	+	0.294992i
$928$		0			0
$929$	836.461	+	482.931i	0.900389	+	0.519840i	0.877326	−	0.479894i	$-0.159325\pi$
$929$	836.461	+	482.931i	0.900389	+	0.519840i	0.0230626	+	0.999734i	$0.492658\pi$
$930$		0			0
$931$	872.693	+	146.347i	0.937372	+	0.157193i
$932$		0			0
$933$	−394.584	+	963.113i	−0.422920	+	1.03228i
$934$		0			0
$935$	335.052	−	580.327i	0.358344	−	0.620671i
$936$		0			0
$937$		−	1227.11i		−	1.30962i	−0.755795	−	0.654808i	$-0.772749\pi$
$937$		−	1227.11i		−	1.30962i	0.755795	−	0.654808i	$-0.227251\pi$
$938$		0			0
$939$	−382.586	+	51.8722i	−0.407440	+	0.0552419i
$940$		0			0
$941$	247.826	−	143.082i	0.263364	−	0.152053i	−0.362504	−	0.931982i	$-0.618078\pi$
$941$	247.826	−	143.082i	0.263364	−	0.152053i	0.625868	+	0.779929i	$0.284745\pi$
$942$		0			0
$943$	−126.259	−	72.8954i	−0.133890	−	0.0773016i
$944$		0			0
$945$	−58.6500	−	986.052i	−0.0620635	−	1.04344i
$946$		0			0
$947$	−804.293	+	1393.08i	−0.849306	+	1.47104i	0.0325231	+	0.999471i	$0.489646\pi$
$947$	−804.293	+	1393.08i	−0.849306	+	1.47104i	−0.881829	+	0.471570i	$0.843688\pi$
$948$		0			0
$949$	−301.317	−	521.897i	−0.317510	−	0.549944i
$950$		0			0
$951$	79.2879	+	584.793i	0.0833732	+	0.614924i
$952$		0			0
$953$	809.469			0.849390			0.424695	−	0.905336i	$-0.360381\pi$
$953$	809.469			0.849390			0.424695	+	0.905336i	$0.360381\pi$
$954$		0			0
$955$	−724.579	−	418.336i	−0.758721	−	0.438048i
$956$		0			0
$957$	374.410	+	153.395i	0.391234	+	0.160287i
$958$		0			0
$959$	45.2228	−	125.888i	0.0471562	−	0.131270i
$960$		0			0
$961$	−72.8761	+	126.225i	−0.0758336	+	0.131348i
$962$		0			0
$963$	993.803	−	274.532i	1.03199	−	0.285080i
$964$		0			0
$965$	−1167.31	+	673.948i	−1.20965	+	0.698392i
$966$		0			0
$967$	−582.505	+	1008.93i	−0.602384	+	1.04336i	0.390076	+	0.920783i	$0.372449\pi$
$967$	−582.505	+	1008.93i	−0.602384	+	1.04336i	−0.992459	+	0.122576i	$0.960884\pi$
$968$		0			0
$969$	−1128.63	+	872.974i	−1.16474	+	0.900902i
$970$		0			0
$971$	−1065.16	+	614.970i	−1.09697	+	0.633337i	−0.935424	−	0.353528i	$-0.884982\pi$
$971$	−1065.16	+	614.970i	−1.09697	+	0.633337i	−0.161548	+	0.986865i	$0.551649\pi$
$972$		0			0
$973$	−750.889	+	635.453i	−0.771725	+	0.653086i
$974$		0			0
$975$	−30.8249	+	4.17933i	−0.0316153	+	0.00428650i
$976$		0			0
$977$	−102.611	−	177.728i	−0.105027	−	0.181912i	0.808722	−	0.588191i	$-0.200160\pi$
$977$	−102.611	−	177.728i	−0.105027	−	0.181912i	−0.913749	+	0.406279i	$0.866826\pi$
$978$		0			0
$979$	241.097	−	139.197i	0.246269	−	0.142183i
$980$		0			0
$981$	−18.5647	−	18.2801i	−0.0189243	−	0.0186342i
$982$		0			0
$983$			571.168i			0.581046i	0.956868	+	0.290523i	$0.0938292\pi$
$983$			571.168i			0.581046i	−0.956868	+	0.290523i	$0.906171\pi$
$984$		0			0
$985$			252.758i			0.256607i
$986$		0			0
$987$	196.231	−	920.147i	0.198816	−	0.932267i
$988$		0			0
$989$	2.07022	+	3.58573i	0.00209325	+	0.00362561i
$990$		0			0
$991$	513.419	−	889.268i	0.518082	−	0.897344i	−0.481698	−	0.876338i	$-0.659980\pi$
$991$	513.419	−	889.268i	0.518082	−	0.897344i	0.999779	−	0.0210064i	$-0.00668704\pi$
$992$		0			0
$993$	205.579	+	1516.26i	0.207028	+	1.52695i
$994$		0			0
$995$	731.739	−	1267.41i	0.735416	−	1.27378i
$996$		0			0
$997$		−	361.272i		−	0.362359i	−0.983450	−	0.181180i	$-0.942008\pi$
$997$		−	361.272i		−	0.362359i	0.983450	−	0.181180i	$-0.0579916\pi$
$998$		0			0
$999$	−438.654	+	585.589i	−0.439093	+	0.586175i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.3.p.a.157.4	yes	32
3.2	odd	2		756.3.p.a.577.3		32
7.5	odd	6		252.3.bd.a.229.9	yes	32
9.2	odd	6		756.3.bd.a.73.14		32
9.7	even	3		252.3.bd.a.241.9	yes	32
21.5	even	6		756.3.bd.a.145.14		32
63.47	even	6		756.3.p.a.397.14		32
63.61	odd	6	inner	252.3.p.a.61.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.3.p.a.61.4	✓	32	63.61	odd	6	inner
252.3.p.a.157.4	yes	32	1.1	even	1	trivial
252.3.bd.a.229.9	yes	32	7.5	odd	6
252.3.bd.a.241.9	yes	32	9.7	even	3
756.3.p.a.397.14		32	63.47	even	6
756.3.p.a.577.3		32	3.2	odd	2
756.3.bd.a.73.14		32	9.2	odd	6
756.3.bd.a.145.14		32	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	252.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.37299 + 1.83546i) q^{3} +5.22643i q^{5} +(-2.36655 + 6.58783i) q^{7} +(2.26216 - 8.71106i) q^{9} +4.86821 q^{11} +(-3.87803 - 2.23898i) q^{13} +(-9.59291 - 12.4023i) q^{15} +(-22.8086 - 13.1686i) q^{17} +(-15.6393 + 9.02938i) q^{19} +(-6.47591 - 19.9766i) q^{21} +2.10501 q^{23} -2.31556 q^{25} +(10.6207 + 24.8234i) q^{27} +(-13.8523 - 23.9929i) q^{29} +(-24.7272 + 14.2763i) q^{31} +(-11.5522 + 8.93540i) q^{33} +(-34.4308 - 12.3686i) q^{35} +(13.5493 + 23.4681i) q^{37} +(13.3121 - 1.80489i) q^{39} +(-59.9799 - 34.6294i) q^{41} +(0.983471 + 1.70342i) q^{43} +(45.5278 + 11.8230i) q^{45} +(38.7995 + 22.4009i) q^{47} +(-37.7989 - 31.1808i) q^{49} +(78.2950 - 10.6155i) q^{51} +(6.39788 - 11.0815i) q^{53} +25.4433i q^{55} +(20.5389 - 50.1320i) q^{57} +(-48.4028 + 27.9454i) q^{59} +(91.6937 + 52.9394i) q^{61} +(52.0335 + 35.5179i) q^{63} +(11.7019 - 20.2682i) q^{65} +(10.4104 + 18.0313i) q^{67} +(-4.99518 + 3.86367i) q^{69} -23.1583 q^{71} +(116.548 + 67.2890i) q^{73} +(5.49480 - 4.25012i) q^{75} +(-11.5208 + 32.0709i) q^{77} +(-55.8622 + 96.7561i) q^{79} +(-70.7652 - 39.4117i) q^{81} +(16.3728 - 9.45285i) q^{83} +(68.8245 - 119.208i) q^{85} +(76.9093 + 31.5095i) q^{87} +(49.5248 - 28.5932i) q^{89} +(23.9275 - 20.2491i) q^{91} +(32.4739 - 79.2633i) q^{93} +(-47.1914 - 81.7379i) q^{95} +(-165.209 + 95.3837i) q^{97} +(11.0127 - 42.4072i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + q^{7} - 6 q^{9} - 12 q^{11} + 15 q^{13} + 9 q^{15} - 27 q^{17} - 36 q^{21} + 30 q^{23} - 160 q^{25} - 9 q^{27} + 24 q^{29} - 24 q^{31} + 81 q^{33} + 141 q^{35} + 11 q^{37} - 21 q^{39} - 90 q^{41}+ \cdots - 45 q^{99}+O(q^{100}) \) 32 * q + q^7 - 6 * q^9 - 12 * q^11 + 15 * q^13 + 9 * q^15 - 27 * q^17 - 36 * q^21 + 30 * q^23 - 160 * q^25 - 9 * q^27 + 24 * q^29 - 24 * q^31 + 81 * q^33 + 141 * q^35 + 11 * q^37 - 21 * q^39 - 90 * q^41 - 16 * q^43 + 39 * q^45 + 108 * q^47 - 61 * q^49 + 117 * q^51 + 54 * q^53 + 51 * q^57 + 45 * q^59 - 165 * q^61 - 93 * q^63 - 33 * q^65 - 35 * q^67 + 105 * q^69 + 138 * q^71 - 195 * q^75 - 123 * q^77 + 37 * q^79 + 126 * q^81 + 378 * q^83 + 30 * q^85 - 237 * q^87 - 261 * q^89 + 45 * q^91 + 111 * q^93 - 48 * q^95 - 57 * q^97 - 45 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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