LMFDB - Embedded newform 224.3.r.c.191.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(95,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4]))

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

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

chi := DirichletCharacter("224.95");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.r (of order $6$, 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:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 28 x^{9} - 100 x^{8} + 140 x^{7} + 392 x^{6} + 1400 x^{5} + 8040 x^{4} + 11256 x^{3} + \cdots + 9604 $ x^12 - 28x^9 - 100x^8 + 140x^7 + 392x^6 + 1400x^5 + 8040x^4 + 11256x^3 + 9800x^2 + 13720*x + 9604
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.6
Root			$-2.35362 + 0.630651i$ of defining polynomial
Character	$\chi$	$=$	224.191
Dual form			224.3.r.c.95.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.85030 - 2.22297i) q^{3} +(2.88318 - 4.99382i) q^{5} +(5.85985 - 3.82912i) q^{7} +(5.38318 - 9.32395i) q^{9} +O(q^{10})$	\(q+(3.85030 - 2.22297i) q^{3} +(2.88318 - 4.99382i) q^{5} +(5.85985 - 3.82912i) q^{7} +(5.38318 - 9.32395i) q^{9} +(-16.6383 + 9.60615i) q^{11} -5.23363 q^{13} -25.6369i q^{15} +(14.5414 + 25.1865i) q^{17} +(-9.49276 - 5.48065i) q^{19} +(14.0501 - 27.7695i) q^{21} +(-11.3335 - 6.54340i) q^{23} +(-4.12551 - 7.14559i) q^{25} -7.85317i q^{27} +46.5849 q^{29} +(-10.8201 + 6.24702i) q^{31} +(-42.7084 + 73.9731i) q^{33} +(-2.22694 - 40.3031i) q^{35} +(3.90723 - 6.76752i) q^{37} +(-20.1510 + 11.6342i) q^{39} +34.5154 q^{41} -22.6330i q^{43} +(-31.0414 - 53.7653i) q^{45} +(32.2200 + 18.6022i) q^{47} +(19.6756 - 44.8762i) q^{49} +(111.978 + 64.6503i) q^{51} +(-38.6002 - 66.8576i) q^{53} +110.785i q^{55} -48.7332 q^{57} +(34.2179 - 19.7557i) q^{59} +(-23.8418 + 41.2951i) q^{61} +(-4.15791 - 75.2498i) q^{63} +(-15.0895 + 26.1358i) q^{65} +(-77.1378 + 44.5355i) q^{67} -58.1831 q^{69} +92.5129i q^{71} +(14.4093 + 24.9576i) q^{73} +(-31.7688 - 18.3418i) q^{75} +(-60.7150 + 120.001i) q^{77} +(-37.4277 - 21.6089i) q^{79} +(30.9913 + 53.6785i) q^{81} +6.88400i q^{83} +167.703 q^{85} +(179.366 - 103.557i) q^{87} +(-57.2838 + 99.2184i) q^{89} +(-30.6683 + 20.0402i) q^{91} +(-27.7738 + 48.1057i) q^{93} +(-54.7387 + 31.6034i) q^{95} -117.928 q^{97} +206.847i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{5} + 32 q^{9}+O(q^{10}) $ 12 * q + 2 * q^5 + 32 * q^9	$ 12 q + 2 q^{5} + 32 q^{9} - 128 q^{13} - 6 q^{17} - 62 q^{21} - 32 q^{25} + 128 q^{29} - 134 q^{33} - 66 q^{37} + 384 q^{41} - 192 q^{45} - 12 q^{49} - 2 q^{53} + 468 q^{57} - 434 q^{61} + 160 q^{65} + 124 q^{69} - 10 q^{73} - 370 q^{77} + 422 q^{81} + 1020 q^{85} - 522 q^{89} + 306 q^{93} - 768 q^{97}+O(q^{100}) $ 12 * q + 2 * q^5 + 32 * q^9 - 128 * q^13 - 6 * q^17 - 62 * q^21 - 32 * q^25 + 128 * q^29 - 134 * q^33 - 66 * q^37 + 384 * q^41 - 192 * q^45 - 12 * q^49 - 2 * q^53 + 468 * q^57 - 434 * q^61 + 160 * q^65 + 124 * q^69 - 10 * q^73 - 370 * q^77 + 422 * q^81 + 1020 * q^85 - 522 * q^89 + 306 * q^93 - 768 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	3.85030	−	2.22297i	1.28343	−	0.740990i	0.305958	−	0.952045i	$-0.401023\pi$
$3$	3.85030	−	2.22297i	1.28343	−	0.740990i	0.977474	+	0.211055i	$0.0676900\pi$
$4$		0			0
$5$	2.88318	−	4.99382i	0.576637	−	0.998764i	−0.419225	−	0.907882i	$-0.637698\pi$
$5$	2.88318	−	4.99382i	0.576637	−	0.998764i	0.995862	−	0.0908820i	$-0.0289686\pi$
$6$		0			0
$7$	5.85985	−	3.82912i	0.837121	−	0.547018i
$7$	5.85985	−	3.82912i	0.837121	−	0.547018i
$8$		0			0
$9$	5.38318	−	9.32395i	0.598132	−	1.03599i
$10$		0			0
$11$	−16.6383	+	9.60615i	−1.51258	+	0.873287i	−0.512685	+	0.858577i	$0.671349\pi$
$11$	−16.6383	+	9.60615i	−1.51258	+	0.873287i	−0.999892	+	0.0147100i	$0.995317\pi$
$12$		0			0
$13$	−5.23363			−0.402587			−0.201293	−	0.979531i	$-0.564514\pi$
$13$	−5.23363			−0.402587			−0.201293	+	0.979531i	$0.564514\pi$
$14$		0			0
$15$		−	25.6369i		−	1.70913i
$16$		0			0
$17$	14.5414	+	25.1865i	0.855378	+	1.48156i	0.876294	+	0.481777i	$0.160009\pi$
$17$	14.5414	+	25.1865i	0.855378	+	1.48156i	−0.0209153	+	0.999781i	$0.506658\pi$
$18$		0			0
$19$	−9.49276	−	5.48065i	−0.499619	−	0.288455i	0.228937	−	0.973441i	$-0.426475\pi$
$19$	−9.49276	−	5.48065i	−0.499619	−	0.288455i	−0.728556	+	0.684986i	$0.759808\pi$
$20$		0			0
$21$	14.0501	−	27.7695i	0.669053	−	1.32236i
$22$		0			0
$23$	−11.3335	−	6.54340i	−0.492761	−	0.284496i	0.232958	−	0.972487i	$-0.425159\pi$
$23$	−11.3335	−	6.54340i	−0.492761	−	0.284496i	−0.725719	+	0.687991i	$0.758493\pi$
$24$		0			0
$25$	−4.12551	−	7.14559i	−0.165020	−	0.285824i
$26$		0			0
$27$		−	7.85317i		−	0.290858i
$28$		0			0
$29$	46.5849			1.60638			0.803188	−	0.595726i	$-0.203136\pi$
$29$	46.5849			1.60638			0.803188	+	0.595726i	$0.203136\pi$
$30$		0			0
$31$	−10.8201	+	6.24702i	−0.349037	+	0.201517i	−0.664261	−	0.747501i	$-0.731254\pi$
$31$	−10.8201	+	6.24702i	−0.349037	+	0.201517i	0.315224	+	0.949017i	$0.397920\pi$
$32$		0			0
$33$	−42.7084	+	73.9731i	−1.29419	+	2.24161i
$34$		0			0
$35$	−2.22694	−	40.3031i	−0.0636268	−	1.15152i
$36$		0			0
$37$	3.90723	−	6.76752i	0.105601	−	0.182906i	−0.808383	−	0.588657i	$-0.799657\pi$
$37$	3.90723	−	6.76752i	0.105601	−	0.182906i	0.913984	+	0.405751i	$0.132990\pi$
$38$		0			0
$39$	−20.1510	+	11.6342i	−0.516693	+	0.298313i
$40$		0			0
$41$	34.5154			0.841838			0.420919	−	0.907098i	$-0.361708\pi$
$41$	34.5154			0.841838			0.420919	+	0.907098i	$0.361708\pi$
$42$		0			0
$43$		−	22.6330i		−	0.526349i	−0.964748	−	0.263174i	$-0.915231\pi$
$43$		−	22.6330i		−	0.526349i	0.964748	−	0.263174i	$-0.0847694\pi$
$44$		0			0
$45$	−31.0414	−	53.7653i	−0.689810	−	1.19479i
$46$		0			0
$47$	32.2200	+	18.6022i	0.685532	+	0.395792i	0.801936	−	0.597410i	$-0.203804\pi$
$47$	32.2200	+	18.6022i	0.685532	+	0.395792i	−0.116404	+	0.993202i	$0.537137\pi$
$48$		0			0
$49$	19.6756	−	44.8762i	0.401543	−	0.915840i
$50$		0			0
$51$	111.978	+	64.6503i	2.19564	+	1.26765i
$52$		0			0
$53$	−38.6002	−	66.8576i	−0.728307	−	1.26146i	−0.957598	−	0.288106i	$-0.906974\pi$
$53$	−38.6002	−	66.8576i	−0.728307	−	1.26146i	0.229292	−	0.973358i	$-0.426359\pi$
$54$		0			0
$55$			110.785i			2.01428i
$56$		0			0
$57$	−48.7332			−0.854969
$58$		0			0
$59$	34.2179	−	19.7557i	0.579964	−	0.334843i	−0.181155	−	0.983455i	$-0.557984\pi$
$59$	34.2179	−	19.7557i	0.579964	−	0.334843i	0.761119	+	0.648612i	$0.224650\pi$
$60$		0			0
$61$	−23.8418	+	41.2951i	−0.390848	+	0.676969i	−0.992562	−	0.121743i	$-0.961152\pi$
$61$	−23.8418	+	41.2951i	−0.390848	+	0.676969i	0.601713	+	0.798712i	$0.294485\pi$
$62$		0			0
$63$	−4.15791	−	75.2498i	−0.0659985	−	1.19444i
$64$		0			0
$65$	−15.0895	+	26.1358i	−0.232147	+	0.402090i
$66$		0			0
$67$	−77.1378	+	44.5355i	−1.15131	+	0.664709i	−0.949206	−	0.314655i	$-0.898111\pi$
$67$	−77.1378	+	44.5355i	−1.15131	+	0.664709i	−0.202104	+	0.979364i	$0.564778\pi$
$68$		0			0
$69$	−58.1831			−0.843233
$70$		0			0
$71$			92.5129i			1.30300i	0.758649	+	0.651499i	$0.225860\pi$
$71$			92.5129i			1.30300i	−0.758649	+	0.651499i	$0.774140\pi$
$72$		0			0
$73$	14.4093	+	24.9576i	0.197387	+	0.341885i	0.947680	−	0.319221i	$-0.103421\pi$
$73$	14.4093	+	24.9576i	0.197387	+	0.341885i	−0.750293	+	0.661105i	$0.770088\pi$
$74$		0			0
$75$	−31.7688	−	18.3418i	−0.423585	−	0.244557i
$76$		0			0
$77$	−60.7150	+	120.001i	−0.788507	+	1.55845i
$78$		0			0
$79$	−37.4277	−	21.6089i	−0.473768	−	0.273530i	0.244048	−	0.969763i	$-0.421525\pi$
$79$	−37.4277	−	21.6089i	−0.473768	−	0.273530i	−0.717816	+	0.696233i	$0.754858\pi$
$80$		0			0
$81$	30.9913	+	53.6785i	0.382609	+	0.662698i
$82$		0			0
$83$			6.88400i			0.0829398i	0.999140	+	0.0414699i	$0.0132041\pi$
$83$			6.88400i			0.0829398i	−0.999140	+	0.0414699i	$0.986796\pi$
$84$		0			0
$85$	167.703			1.97297
$86$		0			0
$87$	179.366	−	103.557i	2.06167	−	1.19031i
$88$		0			0
$89$	−57.2838	+	99.2184i	−0.643638	+	1.11481i	0.340977	+	0.940072i	$0.389242\pi$
$89$	−57.2838	+	99.2184i	−0.643638	+	1.11481i	−0.984614	+	0.174741i	$0.944091\pi$
$90$		0			0
$91$	−30.6683	+	20.0402i	−0.337014	+	0.220222i
$92$		0			0
$93$	−27.7738	+	48.1057i	−0.298644	+	0.517266i
$94$		0			0
$95$	−54.7387	+	31.6034i	−0.576197	+	0.332668i
$96$		0			0
$97$	−117.928			−1.21575			−0.607876	−	0.794032i	$-0.707978\pi$
$97$	−117.928			−1.21575			−0.607876	+	0.794032i	$0.707978\pi$
$98$		0			0
$99$			206.847i			2.08936i
$100$		0			0
$101$	−48.9353	−	84.7585i	−0.484508	−	0.839193i	0.515333	−	0.856990i	$-0.327668\pi$
$101$	−48.9353	−	84.7585i	−0.484508	−	0.839193i	−0.999842	+	0.0177968i	$0.994335\pi$
$102$		0			0
$103$	−132.855	−	76.7037i	−1.28985	−	0.744696i	−0.311224	−	0.950337i	$-0.600739\pi$
$103$	−132.855	−	76.7037i	−1.28985	−	0.744696i	−0.978628	+	0.205641i	$0.934072\pi$
$104$		0			0
$105$	−98.1669	−	150.228i	−0.934923	−	1.43075i
$106$		0			0
$107$	−78.6271	−	45.3954i	−0.734832	−	0.424256i	0.0853551	−	0.996351i	$-0.472798\pi$
$107$	−78.6271	−	45.3954i	−0.734832	−	0.424256i	−0.820187	+	0.572095i	$0.806131\pi$
$108$		0			0
$109$	19.0087	+	32.9240i	0.174392	+	0.302055i	0.939951	−	0.341311i	$-0.110871\pi$
$109$	19.0087	+	32.9240i	0.174392	+	0.302055i	−0.765559	+	0.643366i	$0.777537\pi$
$110$		0			0
$111$		−	34.7426i		−	0.312997i
$112$		0			0
$113$	118.024			1.04446			0.522231	−	0.852804i	$-0.325100\pi$
$113$	118.024			1.04446			0.522231	+	0.852804i	$0.325100\pi$
$114$		0			0
$115$	−65.3532	+	37.7317i	−0.568288	+	0.328101i
$116$		0			0
$117$	−28.1736	+	48.7981i	−0.240800	+	0.417078i
$118$		0			0
$119$	181.653	+	91.9081i	1.52649	+	0.772337i
$120$		0			0
$121$	124.056	−	214.872i	1.02526	−	1.77580i
$122$		0			0
$123$	132.894	−	76.7266i	1.08044	−	0.623793i
$124$		0			0
$125$	96.5808			0.772647
$126$		0			0
$127$		−	8.58246i		−	0.0675785i	−0.999429	−	0.0337892i	$-0.989243\pi$
$127$		−	8.58246i		−	0.0675785i	0.999429	−	0.0337892i	$-0.0107575\pi$
$128$		0			0
$129$	−50.3124	−	87.1437i	−0.390019	−	0.675532i
$130$		0			0
$131$	55.8213	+	32.2284i	0.426116	+	0.246018i	0.697691	−	0.716399i	$-0.254211\pi$
$131$	55.8213	+	32.2284i	0.426116	+	0.246018i	−0.271574	+	0.962417i	$0.587544\pi$
$132$		0			0
$133$	−76.6122	+	4.23319i	−0.576031	+	0.0318285i
$134$		0			0
$135$	−39.2173	−	22.6421i	−0.290499	−	0.167720i
$136$		0			0
$137$	49.0782	+	85.0060i	0.358235	+	0.620482i	0.987666	−	0.156575i	$-0.0500452\pi$
$137$	49.0782	+	85.0060i	0.358235	+	0.620482i	−0.629431	+	0.777057i	$0.716712\pi$
$138$		0			0
$139$		−	245.848i		−	1.76869i	−0.466830	−	0.884347i	$-0.654604\pi$
$139$		−	245.848i		−	1.76869i	0.466830	−	0.884347i	$-0.345396\pi$
$140$		0			0
$141$	165.409			1.17311
$142$		0			0
$143$	87.0790	−	50.2751i	0.608944	−	0.351574i
$144$		0			0
$145$	134.313	−	232.637i	0.926296	−	1.60439i
$146$		0			0
$147$	−24.0013	−	216.525i	−0.163274	−	1.47296i
$148$		0			0
$149$	−79.0663	+	136.947i	−0.530646	+	0.919106i	0.468714	+	0.883350i	$0.344717\pi$
$149$	−79.0663	+	136.947i	−0.530646	+	0.919106i	−0.999361	+	0.0357565i	$0.988616\pi$
$150$		0			0
$151$	−1.71809	+	0.991939i	−0.0113781	+	0.00656913i	−0.505678	−	0.862722i	$-0.668758\pi$
$151$	−1.71809	+	0.991939i	−0.0113781	+	0.00656913i	0.494300	+	0.869291i	$0.335424\pi$
$152$		0			0
$153$	313.117			2.04652
$154$		0			0
$155$			72.0452i			0.464808i
$156$		0			0
$157$	−129.791	−	224.805i	−0.826696	−	1.43188i	−0.900616	−	0.434615i	$-0.856884\pi$
$157$	−129.791	−	224.805i	−0.826696	−	1.43188i	0.0739206	−	0.997264i	$-0.476449\pi$
$158$		0			0
$159$	−297.245	−	171.614i	−1.86946	−	1.07934i
$160$		0			0
$161$	−91.4681	+	5.05404i	−0.568125	+	0.0313916i
$162$		0			0
$163$	150.961	+	87.1575i	0.926142	+	0.534709i	0.885589	−	0.464469i	$-0.153755\pi$
$163$	150.961	+	87.1575i	0.926142	+	0.534709i	0.0405529	+	0.999177i	$0.487088\pi$
$164$		0			0
$165$	246.272	+	426.556i	1.49256	+	2.58519i
$166$		0			0
$167$			16.5232i			0.0989415i	0.998776	+	0.0494707i	$0.0157535\pi$
$167$			16.5232i			0.0989415i	−0.998776	+	0.0494707i	$0.984247\pi$
$168$		0			0
$169$	−141.609			−0.837924
$170$		0			0
$171$	−102.203	+	59.0067i	−0.597676	+	0.345068i
$172$		0			0
$173$	−0.148738	+	0.257621i	−0.000859756	+	0.00148914i	−0.866455	−	0.499255i	$-0.833607\pi$
$173$	−0.148738	+	0.257621i	−0.000859756	+	0.00148914i	0.865595	+	0.500744i	$0.166940\pi$
$174$		0			0
$175$	−51.5362	−	26.0750i	−0.294492	−	0.149000i
$176$		0			0
$177$	87.8327	−	152.131i	0.496230	−	0.859495i
$178$		0			0
$179$	107.052	−	61.8065i	0.598056	−	0.345288i	−0.170220	−	0.985406i	$-0.554448\pi$
$179$	107.052	−	61.8065i	0.598056	−	0.345288i	0.768276	+	0.640118i	$0.221115\pi$
$180$		0			0
$181$	65.0497			0.359391			0.179695	−	0.983722i	$-0.442489\pi$
$181$	65.0497			0.359391			0.179695	+	0.983722i	$0.442489\pi$
$182$		0			0
$183$			211.998i			1.15846i
$184$		0			0
$185$	−22.5305	−	39.0240i	−0.121787	−	0.210941i
$186$		0			0
$187$	−483.891	−	279.374i	−2.58765	−	1.49398i
$188$		0			0
$189$	−30.0708	−	46.0184i	−0.159105	−	0.243483i
$190$		0			0
$191$	10.2515	+	5.91871i	0.0536728	+	0.0309880i	0.526596	−	0.850115i	$-0.323468\pi$
$191$	10.2515	+	5.91871i	0.0536728	+	0.0309880i	−0.472923	+	0.881104i	$0.656801\pi$
$192$		0			0
$193$	−29.4292	−	50.9730i	−0.152483	−	0.264109i	0.779657	−	0.626207i	$-0.215394\pi$
$193$	−29.4292	−	50.9730i	−0.152483	−	0.264109i	−0.932140	+	0.362099i	$0.882060\pi$
$194$		0			0
$195$			134.174i			0.688073i
$196$		0			0
$197$	−329.405			−1.67211			−0.836054	−	0.548647i	$-0.815143\pi$
$197$	−329.405			−1.67211			−0.836054	+	0.548647i	$0.815143\pi$
$198$		0			0
$199$	−7.92070	+	4.57302i	−0.0398025	+	0.0229800i	−0.519769	−	0.854307i	$-0.673982\pi$
$199$	−7.92070	+	4.57302i	−0.0398025	+	0.0229800i	0.479967	+	0.877287i	$0.340649\pi$
$200$		0			0
$201$	−198.002	+	342.950i	−0.985086	+	1.70622i
$202$		0			0
$203$	272.980	−	178.379i	1.34473	−	0.878716i
$204$		0			0
$205$	99.5141	−	172.364i	0.485435	−	0.840798i
$206$		0			0
$207$	−122.021	+	70.4487i	−0.589472	+	0.340332i
$208$		0			0
$209$	210.592			1.00762
$210$		0			0
$211$			56.1119i			0.265933i	0.991121	+	0.132967i	$0.0424503\pi$
$211$			56.1119i			0.265933i	−0.991121	+	0.132967i	$0.957550\pi$
$212$		0			0
$213$	205.653	+	356.202i	0.965509	+	1.67231i
$214$		0			0
$215$	−113.025	−	65.2551i	−0.525698	−	0.303512i
$216$		0			0
$217$	−39.4838	+	78.0382i	−0.181953	+	0.359623i
$218$		0			0
$219$	110.960	+	64.0627i	0.506666	+	0.292524i
$220$		0			0
$221$	−76.1045	−	131.817i	−0.344364	−	0.596456i
$222$		0			0
$223$			67.9891i			0.304884i	0.988312	+	0.152442i	$0.0487137\pi$
$223$			67.9891i			0.304884i	−0.988312	+	0.152442i	$0.951286\pi$
$224$		0			0
$225$	−88.8335			−0.394815
$226$		0			0
$227$	−214.074	+	123.596i	−0.943059	+	0.544475i	−0.890918	−	0.454165i	$-0.849938\pi$
$227$	−214.074	+	123.596i	−0.943059	+	0.544475i	−0.0521408	+	0.998640i	$0.516604\pi$
$228$		0			0
$229$	−11.8058	+	20.4482i	−0.0515536	+	0.0892934i	−0.890651	−	0.454688i	$-0.849751\pi$
$229$	−11.8058	+	20.4482i	−0.0515536	+	0.0892934i	0.839097	+	0.543982i	$0.183084\pi$
$230$		0			0
$231$	32.9874	+	597.007i	0.142803	+	2.58444i
$232$		0			0
$233$	−69.4830	+	120.348i	−0.298210	+	0.516516i	−0.975727	−	0.218992i	$-0.929723\pi$
$233$	−69.4830	+	120.348i	−0.298210	+	0.516516i	0.677516	+	0.735508i	$0.263056\pi$
$234$		0			0
$235$	185.792	−	107.267i	0.790606	−	0.456456i
$236$		0			0
$237$	−192.143			−0.810732
$238$		0			0
$239$		−	423.627i		−	1.77250i	−0.463210	−	0.886248i	$-0.653303\pi$
$239$		−	423.627i		−	1.77250i	0.463210	−	0.886248i	$-0.346697\pi$
$240$		0			0
$241$	−122.283	−	211.800i	−0.507398	−	0.878839i	−0.999963	−	0.00856384i	$-0.997274\pi$
$241$	−122.283	−	211.800i	−0.507398	−	0.878839i	0.492565	−	0.870276i	$-0.336059\pi$
$242$		0			0
$243$	299.861	+	173.125i	1.23400	+	0.712447i
$244$		0			0
$245$	−167.375	−	227.643i	−0.683164	−	0.929155i
$246$		0			0
$247$	49.6816	+	28.6837i	0.201140	+	0.116128i
$248$		0			0
$249$	15.3029	+	26.5054i	0.0614575	+	0.106448i
$250$		0			0
$251$			176.193i			0.701964i	0.936382	+	0.350982i	$0.114152\pi$
$251$			176.193i			0.701964i	−0.936382	+	0.350982i	$0.885848\pi$
$252$		0			0
$253$	251.428			0.993785
$254$		0			0
$255$	645.704	−	372.798i	2.53217	−	1.46195i
$256$		0			0
$257$	−25.5390	+	44.2348i	−0.0993735	+	0.172120i	−0.911426	−	0.411465i	$-0.865017\pi$
$257$	−25.5390	+	44.2348i	−0.0993735	+	0.172120i	0.812052	+	0.583585i	$0.198351\pi$
$258$		0			0
$259$	−3.01790	−	54.6179i	−0.0116521	−	0.210880i
$260$		0			0
$261$	250.775	−	434.355i	0.960824	−	1.66420i
$262$		0			0
$263$	167.852	−	96.9095i	0.638221	−	0.368477i	−0.145708	−	0.989328i	$-0.546546\pi$
$263$	167.852	−	96.9095i	0.638221	−	0.368477i	0.783929	+	0.620851i	$0.213213\pi$
$264$		0			0
$265$	−445.167			−1.67987
$266$		0			0
$267$			509.360i			1.90772i
$268$		0			0
$269$	−3.00342	−	5.20207i	−0.0111651	−	0.0193385i	0.860389	−	0.509638i	$-0.170221\pi$
$269$	−3.00342	−	5.20207i	−0.0111651	−	0.0193385i	−0.871554	+	0.490300i	$0.836887\pi$
$270$		0			0
$271$	341.760	+	197.315i	1.26111	+	0.728101i	0.973289	−	0.229584i	$-0.0737366\pi$
$271$	341.760	+	197.315i	1.26111	+	0.728101i	0.287819	+	0.957685i	$0.407070\pi$
$272$		0			0
$273$	−73.5332	+	145.335i	−0.269352	+	0.532364i
$274$		0			0
$275$	137.283	+	79.2605i	0.499212	+	0.288220i
$276$		0			0
$277$	−148.982	−	258.045i	−0.537842	−	0.931570i	−0.999020	−	0.0442619i	$-0.985906\pi$
$277$	−148.982	−	258.045i	−0.537842	−	0.931570i	0.461178	−	0.887308i	$-0.347427\pi$
$278$		0			0
$279$			134.515i			0.482134i
$280$		0			0
$281$	431.477			1.53551			0.767753	−	0.640746i	$-0.221375\pi$
$281$	431.477			1.53551			0.767753	+	0.640746i	$0.221375\pi$
$282$		0			0
$283$	−383.084	+	221.174i	−1.35365	+	0.781532i	−0.988759	−	0.149516i	$-0.952228\pi$
$283$	−383.084	+	221.174i	−1.35365	+	0.781532i	−0.364895	+	0.931049i	$0.618895\pi$
$284$		0			0
$285$	−140.507	+	243.365i	−0.493007	+	0.853913i
$286$		0			0
$287$	202.255	−	132.164i	0.704720	−	0.460500i
$288$		0			0
$289$	−278.406	+	482.214i	−0.963344	+	1.66856i
$290$		0			0
$291$	−454.058	+	262.150i	−1.56034	+	0.900860i
$292$		0			0
$293$	66.8335			0.228101			0.114050	−	0.993475i	$-0.463617\pi$
$293$	66.8335			0.228101			0.114050	+	0.993475i	$0.463617\pi$
$294$		0			0
$295$		−	227.837i		−	0.772330i
$296$		0			0
$297$	75.4388	+	130.664i	0.254003	+	0.439945i
$298$		0			0
$299$	59.3154	+	34.2457i	0.198379	+	0.114534i
$300$		0			0
$301$	−86.6645	−	132.626i	−0.287922	−	0.440617i
$302$		0			0
$303$	−376.831	−	217.564i	−1.24367	−	0.718031i
$304$		0			0
$305$	137.480	+	238.123i	0.450755	+	0.780731i
$306$		0			0
$307$		−	135.049i		−	0.439900i	−0.975511	−	0.219950i	$-0.929411\pi$
$307$		−	135.049i		−	0.439900i	0.975511	−	0.219950i	$-0.0705894\pi$
$308$		0			0
$309$	−682.040			−2.20725
$310$		0			0
$311$	−269.408	+	155.543i	−0.866263	+	0.500137i	−0.866104	−	0.499863i	$-0.833384\pi$
$311$	−269.408	+	155.543i	−0.866263	+	0.500137i	−0.000158189		1.00000i	$0.500050\pi$
$312$		0			0
$313$	64.6255	−	111.935i	0.206471	−	0.357619i	−0.744129	−	0.668036i	$-0.767135\pi$
$313$	64.6255	−	111.935i	0.206471	−	0.357619i	0.950600	+	0.310417i	$0.100469\pi$
$314$		0			0
$315$	−387.772	−	196.195i	−1.23102	−	0.622842i
$316$		0			0
$317$	−177.441	+	307.337i	−0.559752	+	0.969519i	0.437765	+	0.899089i	$0.355770\pi$
$317$	−177.441	+	307.337i	−0.559752	+	0.969519i	−0.997517	+	0.0704293i	$0.977563\pi$
$318$		0			0
$319$	−775.096	+	447.502i	−2.42977	+	1.40283i
$320$		0			0
$321$	−403.650			−1.25748
$322$		0			0
$323$		−	318.786i		−	0.986953i
$324$		0			0
$325$	21.5914	+	37.3974i	0.0664350	+	0.115069i
$326$		0			0
$327$	146.378	+	84.5115i	0.447640	+	0.258445i
$328$		0			0
$329$	260.034	−	14.3681i	0.790378	−	0.0436721i
$330$		0			0
$331$	219.277	+	126.599i	0.662468	+	0.382476i	0.793217	−	0.608940i	$-0.208405\pi$
$331$	219.277	+	126.599i	0.662468	+	0.382476i	−0.130749	+	0.991416i	$0.541738\pi$
$332$		0			0
$333$	−42.0667	−	72.8616i	−0.126326	−	0.218804i
$334$		0			0
$335$			513.617i			1.53318i
$336$		0			0
$337$	395.788			1.17444			0.587222	−	0.809426i	$-0.300221\pi$
$337$	395.788			1.17444			0.587222	+	0.809426i	$0.300221\pi$
$338$		0			0
$339$	454.428	−	262.364i	1.34050	−	0.773936i
$340$		0			0
$341$	120.020	−	207.880i	0.351964	−	0.609619i
$342$		0			0
$343$	−56.5401	−	338.308i	−0.164840	−	0.986320i
$344$		0			0
$345$	−167.753	+	290.556i	−0.486240	+	0.842192i
$346$		0			0
$347$	266.808	−	154.041i	0.768898	−	0.443924i	−0.0635832	−	0.997977i	$-0.520253\pi$
$347$	266.808	−	154.041i	0.768898	−	0.443924i	0.832481	+	0.554053i	$0.186919\pi$
$348$		0			0
$349$	336.754			0.964911			0.482455	−	0.875921i	$-0.339745\pi$
$349$	336.754			0.964911			0.482455	+	0.875921i	$0.339745\pi$
$350$		0			0
$351$			41.1006i			0.117096i
$352$		0			0
$353$	86.4268	+	149.696i	0.244835	+	0.424067i	0.962085	−	0.272749i	$-0.0879328\pi$
$353$	86.4268	+	149.696i	0.244835	+	0.424067i	−0.717250	+	0.696816i	$0.754599\pi$
$354$		0			0
$355$	461.993	+	266.732i	1.30139	+	0.751357i
$356$		0			0
$357$	903.726	−	49.9351i	2.53144	−	0.139874i
$358$		0			0
$359$	−205.407	−	118.592i	−0.572163	−	0.330339i	0.185850	−	0.982578i	$-0.440496\pi$
$359$	−205.407	−	118.592i	−0.572163	−	0.330339i	−0.758013	+	0.652240i	$0.773830\pi$
$360$		0			0
$361$	−120.425	−	208.582i	−0.333587	−	0.577790i
$362$		0			0
$363$		−	1103.09i		−	3.03883i
$364$		0			0
$365$	166.178			0.455283
$366$		0			0
$367$	44.1618	−	25.4968i	0.120332	−	0.0694736i	−0.438626	−	0.898670i	$-0.644535\pi$
$367$	44.1618	−	25.4968i	0.120332	−	0.0694736i	0.558958	+	0.829196i	$0.311201\pi$
$368$		0			0
$369$	185.803	−	321.819i	0.503530	−	0.872139i
$370$		0			0
$371$	−482.198	−	243.970i	−1.29972	−	0.657602i
$372$		0			0
$373$	82.9591	−	143.689i	0.222411	−	0.385226i	−0.733129	−	0.680090i	$-0.761941\pi$
$373$	82.9591	−	143.689i	0.222411	−	0.385226i	0.955539	+	0.294863i	$0.0952741\pi$
$374$		0			0
$375$	371.865	−	214.696i	0.991639	−	0.572523i
$376$		0			0
$377$	−243.808			−0.646706
$378$		0			0
$379$			107.108i			0.282608i	0.989966	+	0.141304i	$0.0451295\pi$
$379$			107.108i			0.282608i	−0.989966	+	0.141304i	$0.954870\pi$
$380$		0			0
$381$	−19.0786	−	33.0450i	−0.0500749	−	0.0867323i
$382$		0			0
$383$	−2.24980	−	1.29892i	−0.00587415	−	0.00339144i	0.497060	−	0.867716i	$-0.334413\pi$
$383$	−2.24980	−	1.29892i	−0.00587415	−	0.00339144i	−0.502934	+	0.864325i	$0.667746\pi$
$384$		0			0
$385$	424.210	+	649.185i	1.10185	+	1.68619i
$386$		0			0
$387$	−211.029	−	121.838i	−0.545294	−	0.314826i
$388$		0			0
$389$	−382.629	−	662.733i	−0.983622	−	1.70368i	−0.647907	−	0.761720i	$-0.724355\pi$
$389$	−382.629	−	662.733i	−0.983622	−	1.70368i	−0.335715	−	0.941964i	$-0.608978\pi$
$390$		0			0
$391$		−	380.602i		−	0.973406i
$392$		0			0
$393$	286.571			0.729189
$394$		0			0
$395$	−215.822	+	124.605i	−0.546384	+	0.315455i
$396$		0			0
$397$	−58.4121	+	101.173i	−0.147134	+	0.254843i	−0.930167	−	0.367137i	$-0.880338\pi$
$397$	−58.4121	+	101.173i	−0.147134	+	0.254843i	0.783033	+	0.621980i	$0.213671\pi$
$398$		0			0
$399$	−285.569	+	186.606i	−0.715713	+	0.467683i
$400$		0			0
$401$	−161.192	+	279.192i	−0.401975	+	0.696240i	−0.993964	−	0.109705i	$-0.965009\pi$
$401$	−161.192	+	279.192i	−0.401975	+	0.696240i	0.591990	+	0.805946i	$0.298343\pi$
$402$		0			0
$403$	56.6287	−	32.6946i	0.140518	−	0.0811280i
$404$		0			0
$405$	357.415			0.882505
$406$		0			0
$407$			150.134i			0.368879i
$408$		0			0
$409$	−150.890	−	261.350i	−0.368925	−	0.638997i	0.620473	−	0.784228i	$-0.286941\pi$
$409$	−150.890	−	261.350i	−0.368925	−	0.638997i	−0.989398	+	0.145231i	$0.953607\pi$
$410$		0			0
$411$	377.931	+	218.199i	0.919541	+	0.530897i
$412$		0			0
$413$	124.865	−	246.790i	0.302336	−	0.597554i
$414$		0			0
$415$	34.3775	+	19.8478i	0.0828373	+	0.0478261i
$416$		0			0
$417$	−546.514	−	946.589i	−1.31058	−	2.27000i
$418$		0			0
$419$			384.000i			0.916468i	0.888832	+	0.458234i	$0.151518\pi$
$419$			384.000i			0.916468i	−0.888832	+	0.458234i	$0.848482\pi$
$420$		0			0
$421$	168.193			0.399509			0.199754	−	0.979846i	$-0.435986\pi$
$421$	168.193			0.399509			0.199754	+	0.979846i	$0.435986\pi$
$422$		0			0
$423$	346.892	−	200.278i	0.820076	−	0.473471i
$424$		0			0
$425$	119.982	−	207.814i	0.282310	−	0.488975i
$426$		0			0
$427$	18.4151	+	333.276i	0.0431267	+	0.780506i
$428$		0			0
$429$	223.520	−	387.148i	0.521025	−	0.902442i
$430$		0			0
$431$	32.9644	−	19.0320i	0.0764836	−	0.0441578i	−0.461270	−	0.887260i	$-0.652606\pi$
$431$	32.9644	−	19.0320i	0.0764836	−	0.0441578i	0.537754	+	0.843102i	$0.319273\pi$
$432$		0			0
$433$	77.8536			0.179801			0.0899003	−	0.995951i	$-0.471345\pi$
$433$	77.8536			0.179801			0.0899003	+	0.995951i	$0.471345\pi$
$434$		0			0
$435$		−	1194.29i		−	2.74550i
$436$		0			0
$437$	71.7241	+	124.230i	0.164128	+	0.284279i
$438$		0			0
$439$	−235.201	−	135.793i	−0.535765	−	0.309324i	0.207596	−	0.978215i	$-0.433436\pi$
$439$	−235.201	−	135.793i	−0.535765	−	0.309324i	−0.743361	+	0.668891i	$0.766769\pi$
$440$		0			0
$441$	−312.505	−	425.031i	−0.708629	−	0.963790i
$442$		0			0
$443$	402.570	+	232.424i	0.908735	+	0.524659i	0.880024	−	0.474929i	$-0.157526\pi$
$443$	402.570	+	232.424i	0.908735	+	0.524659i	0.0287113	+	0.999588i	$0.490860\pi$
$444$		0			0
$445$	330.319	+	572.130i	0.742291	+	1.28568i
$446$		0			0
$447$			703.048i			1.57281i
$448$		0			0
$449$	211.810			0.471736			0.235868	−	0.971785i	$-0.424207\pi$
$449$	211.810			0.471736			0.235868	+	0.971785i	$0.424207\pi$
$450$		0			0
$451$	−574.278	+	331.560i	−1.27334	+	0.735166i
$452$		0			0
$453$	−4.41010	+	7.63851i	−0.00973532	+	0.0168621i
$454$		0			0
$455$	11.6550	+	210.932i	0.0256153	+	0.463586i
$456$		0			0
$457$	442.640	−	766.674i	0.968577	−	1.67762i	0.268896	−	0.963169i	$-0.413341\pi$
$457$	442.640	−	766.674i	0.968577	−	1.67762i	0.699681	−	0.714455i	$-0.253325\pi$
$458$		0			0
$459$	197.794	−	114.196i	0.430923	−	0.248794i
$460$		0			0
$461$	−622.030			−1.34931			−0.674653	−	0.738135i	$-0.735707\pi$
$461$	−622.030			−1.34931			−0.674653	+	0.738135i	$0.735707\pi$
$462$		0			0
$463$		−	799.125i		−	1.72597i	−0.505227	−	0.862986i	$-0.668591\pi$
$463$		−	799.125i		−	1.72597i	0.505227	−	0.862986i	$-0.331409\pi$
$464$		0			0
$465$	160.154	+	277.395i	0.344418	+	0.596549i
$466$		0			0
$467$	−139.052	−	80.2818i	−0.297756	−	0.171910i	0.343678	−	0.939087i	$-0.388327\pi$
$467$	−139.052	−	80.2818i	−0.297756	−	0.171910i	−0.641435	+	0.767178i	$0.721660\pi$
$468$		0			0
$469$	−281.484	+	556.341i	−0.600178	+	1.18623i
$470$		0			0
$471$	−999.469	−	577.044i	−2.12202	−	1.22515i
$472$		0			0
$473$	217.416	+	376.575i	0.459653	+	0.796143i
$474$		0			0
$475$			90.4418i			0.190404i
$476$		0			0
$477$	−831.169			−1.74249
$478$		0			0
$479$	244.409	−	141.109i	0.510248	−	0.294592i	−0.222688	−	0.974890i	$-0.571483\pi$
$479$	244.409	−	141.109i	0.510248	−	0.294592i	0.732935	+	0.680298i	$0.238150\pi$
$480$		0			0
$481$	−20.4490	+	35.4187i	−0.0425135	+	0.0736356i
$482$		0			0
$483$	−340.944	+	222.790i	−0.705889	+	0.461264i
$484$		0			0
$485$	−340.008	+	588.912i	−0.701048	+	1.21425i
$486$		0			0
$487$	389.490	−	224.872i	0.799773	−	0.461749i	−0.0436185	−	0.999048i	$-0.513889\pi$
$487$	389.490	−	224.872i	0.799773	−	0.461749i	0.843392	+	0.537299i	$0.180555\pi$
$488$		0			0
$489$	774.994			1.58485
$490$		0			0
$491$		−	253.137i		−	0.515554i	−0.966204	−	0.257777i	$-0.917010\pi$
$491$		−	253.137i		−	0.515554i	0.966204	−	0.257777i	$-0.0829901\pi$
$492$		0			0
$493$	677.411	+	1173.31i	1.37406	+	2.37994i
$494$		0			0
$495$	1032.96	+	596.378i	2.08678	+	1.20480i
$496$		0			0
$497$	354.243	+	542.112i	0.712763	+	1.09077i
$498$		0			0
$499$	261.296	+	150.859i	0.523639	+	0.302323i	0.738422	−	0.674339i	$-0.235571\pi$
$499$	261.296	+	150.859i	0.523639	+	0.302323i	−0.214783	+	0.976662i	$0.568905\pi$
$500$		0			0
$501$	36.7306	+	63.6193i	0.0733146	+	0.126985i
$502$		0			0
$503$		−	115.146i		−	0.228918i	−0.993428	−	0.114459i	$-0.963486\pi$
$503$		−	115.146i		−	0.228918i	0.993428	−	0.114459i	$-0.0365135\pi$
$504$		0			0
$505$	−564.358			−1.11754
$506$		0			0
$507$	−545.237	+	314.793i	−1.07542	+	0.620893i
$508$		0			0
$509$	217.015	−	375.880i	0.426355	−	0.738468i	−0.570191	−	0.821512i	$-0.693131\pi$
$509$	217.015	−	375.880i	0.426355	−	0.738468i	0.996546	+	0.0830438i	$0.0264641\pi$
$510$		0			0
$511$	180.002	+	91.0727i	0.352254	+	0.178225i
$512$		0			0
$513$	−43.0404	+	74.5482i	−0.0838995	+	0.145318i
$514$		0			0
$515$	−766.089	+	442.302i	−1.48755	+	0.858838i
$516$		0			0
$517$	−714.783			−1.38256
$518$		0			0
$519$			1.32256i			0.00254828i
$520$		0			0
$521$	−298.700	−	517.363i	−0.573320	−	0.993019i	−0.996222	−	0.0868439i	$-0.972322\pi$
$521$	−298.700	−	517.363i	−0.573320	−	0.993019i	0.422902	−	0.906175i	$-0.361011\pi$
$522$		0			0
$523$	134.862	+	77.8625i	0.257862	+	0.148877i	0.623359	−	0.781936i	$-0.285768\pi$
$523$	134.862	+	77.8625i	0.257862	+	0.148877i	−0.365497	+	0.930813i	$0.619101\pi$
$524$		0			0
$525$	−256.393	+	14.1670i	−0.488368	+	0.0269847i
$526$		0			0
$527$	−314.681	−	181.681i	−0.597117	−	0.344746i
$528$		0			0
$529$	−178.868	−	309.808i	−0.338124	−	0.585649i
$530$		0			0
$531$		−	425.394i		−	0.801120i
$532$		0			0
$533$	−180.641			−0.338913
$534$		0			0
$535$	−453.393	+	261.766i	−0.847463	+	0.489283i
$536$		0			0
$537$	274.788	−	475.947i	0.511710	−	0.886307i
$538$		0			0
$539$	103.717	+	935.672i	0.192425	+	1.73594i
$540$		0			0
$541$	−328.050	+	568.199i	−0.606377	+	1.05028i	0.385456	+	0.922726i	$0.374044\pi$
$541$	−328.050	+	568.199i	−0.606377	+	1.05028i	−0.991832	+	0.127549i	$0.959289\pi$
$542$		0			0
$543$	250.461	−	144.604i	0.461254	−	0.266305i
$544$		0			0
$545$	219.222			0.402243
$546$		0			0
$547$			765.118i			1.39875i	0.714754	+	0.699376i	$0.246539\pi$
$547$			765.118i			1.39875i	−0.714754	+	0.699376i	$0.753461\pi$
$548$		0			0
$549$	256.689	+	444.599i	0.467558	+	0.809834i
$550$		0			0
$551$	−442.219	−	255.315i	−0.802576	−	0.463367i
$552$		0			0
$553$	−302.064	+	16.6904i	−0.546227	+	0.0301816i
$554$		0			0
$555$	−173.498	−	100.169i	−0.312610	−	0.180485i
$556$		0			0
$557$	294.325	+	509.786i	0.528411	+	0.915236i	0.999451	+	0.0331235i	$0.0105455\pi$
$557$	294.325	+	509.786i	0.528411	+	0.915236i	−0.471040	+	0.882112i	$0.656121\pi$
$558$		0			0
$559$			118.453i			0.211901i
$560$		0			0
$561$	−2484.16			−4.42810
$562$		0			0
$563$	480.746	−	277.559i	0.853901	−	0.493000i	−0.00806399	−	0.999967i	$-0.502567\pi$
$563$	480.746	−	277.559i	0.853901	−	0.493000i	0.861965	+	0.506967i	$0.169234\pi$
$564$		0			0
$565$	340.286	−	589.392i	0.602275	−	1.04317i
$566$		0			0
$567$	387.146	+	195.878i	0.682797	+	0.345465i
$568$		0			0
$569$	−64.1433	+	111.099i	−0.112730	+	0.195254i	−0.916870	−	0.399186i	$-0.869293\pi$
$569$	−64.1433	+	111.099i	−0.112730	+	0.195254i	0.804140	+	0.594440i	$0.202626\pi$
$570$		0			0
$571$	744.272	−	429.705i	1.30345	−	0.752549i	0.322458	−	0.946584i	$-0.395491\pi$
$571$	744.272	−	429.705i	1.30345	−	0.752549i	0.980995	+	0.194035i	$0.0621574\pi$
$572$		0			0
$573$	52.6284			0.0918472
$574$		0			0
$575$			107.979i			0.187790i
$576$		0			0
$577$	316.372	+	547.972i	0.548305	+	0.949692i	0.998391	+	0.0567065i	$0.0180599\pi$
$577$	316.372	+	547.972i	0.548305	+	0.949692i	−0.450086	+	0.892985i	$0.648607\pi$
$578$		0			0
$579$	−226.623	−	130.841i	−0.391403	−	0.225977i
$580$		0			0
$581$	26.3597	+	40.3392i	0.0453695	+	0.0694306i
$582$		0			0
$583$	1284.49	+	741.600i	2.20324	+	1.27204i
$584$		0			0
$585$	162.459	+	281.388i	0.277708	+	0.481005i
$586$		0			0
$587$			647.488i			1.10305i	0.834160	+	0.551523i	$0.185953\pi$
$587$			647.488i			1.10305i	−0.834160	+	0.551523i	$0.814047\pi$
$588$		0			0
$589$	136.951			0.232514
$590$		0			0
$591$	−1268.31	+	732.258i	−2.14604	+	1.23902i
$592$		0			0
$593$	339.014	−	587.190i	0.571693	−	0.990202i	−0.424699	−	0.905335i	$-0.639620\pi$
$593$	339.014	−	587.190i	0.571693	−	0.990202i	0.996392	−	0.0848672i	$-0.0270466\pi$
$594$		0			0
$595$	982.711	−	642.154i	1.65162	−	1.07925i
$596$		0			0
$597$	−20.3314	+	35.2149i	−0.0340559	+	0.0589865i
$598$		0			0
$599$	93.3584	−	53.9005i	0.155857	−	0.0899841i	−0.420043	−	0.907504i	$-0.637985\pi$
$599$	93.3584	−	53.9005i	0.155857	−	0.0899841i	0.575900	+	0.817520i	$0.304652\pi$
$600$		0			0
$601$	−690.543			−1.14899			−0.574495	−	0.818508i	$-0.694802\pi$
$601$	−690.543			−1.14899			−0.574495	+	0.818508i	$0.694802\pi$
$602$		0			0
$603$			958.972i			1.59033i
$604$		0			0
$605$	−715.355	−	1239.03i	−1.18240	−	2.04799i
$606$		0			0
$607$	552.137	+	318.776i	0.909615	+	0.525167i	0.880307	−	0.474404i	$-0.157336\pi$
$607$	552.137	+	318.776i	0.909615	+	0.525167i	0.0293080	+	0.999570i	$0.490670\pi$
$608$		0			0
$609$	654.523	−	1293.64i	1.07475	−	2.12420i
$610$		0			0
$611$	−168.627	−	97.3571i	−0.275986	−	0.159341i
$612$		0			0
$613$	−56.4517	−	97.7773i	−0.0920909	−	0.159506i	0.816300	−	0.577628i	$-0.196022\pi$
$613$	−56.4517	−	97.7773i	−0.0920909	−	0.159506i	−0.908391	+	0.418122i	$0.862688\pi$
$614$		0			0
$615$		−	884.867i		−	1.43881i
$616$		0			0
$617$	0.582311			0.000943779			0.000471889	−	1.00000i	$-0.499850\pi$
$617$	0.582311			0.000943779			0.000471889		1.00000i	$0.499850\pi$
$618$		0			0
$619$	−192.651	+	111.227i	−0.311230	+	0.179688i	−0.647477	−	0.762085i	$-0.724176\pi$
$619$	−192.651	+	111.227i	−0.311230	+	0.179688i	0.336247	+	0.941774i	$0.390842\pi$
$620$		0			0
$621$	−51.3864	+	89.0039i	−0.0827479	+	0.143324i
$622$		0			0
$623$	44.2453	+	800.751i	0.0710197	+	1.28531i
$624$		0			0
$625$	381.598	−	660.947i	0.610557	−	1.05752i
$626$		0			0
$627$	810.840	−	468.139i	1.29321	−	0.746633i
$628$		0			0
$629$	227.267			0.361315
$630$		0			0
$631$		−	133.261i		−	0.211190i	−0.994409	−	0.105595i	$-0.966325\pi$
$631$		−	133.261i		−	0.211190i	0.994409	−	0.105595i	$-0.0336746\pi$
$632$		0			0
$633$	124.735	+	216.048i	0.197054	+	0.341307i
$634$		0			0
$635$	−42.8593	−	24.7448i	−0.0674950	−	0.0389682i
$636$		0			0
$637$	−102.975	+	234.865i	−0.161656	+	0.368705i
$638$		0			0
$639$	862.586	+	498.014i	1.34990	+	0.779365i
$640$		0			0
$641$	90.8335	+	157.328i	0.141706	+	0.245442i	0.928139	−	0.372233i	$-0.121408\pi$
$641$	90.8335	+	157.328i	0.141706	+	0.245442i	−0.786433	+	0.617675i	$0.788075\pi$
$642$		0			0
$643$		−	872.108i		−	1.35631i	−0.734919	−	0.678155i	$-0.762780\pi$
$643$		−	872.108i		−	1.35631i	0.734919	−	0.678155i	$-0.237220\pi$
$644$		0			0
$645$	−580.240			−0.899597
$646$		0			0
$647$	−491.471	+	283.751i	−0.759615	+	0.438564i	−0.829157	−	0.559015i	$-0.811179\pi$
$647$	−491.471	+	283.751i	−0.759615	+	0.438564i	0.0695427	+	0.997579i	$0.477846\pi$
$648$		0			0
$649$	−379.553	+	657.405i	−0.584827	+	1.01295i
$650$		0			0
$651$	21.4522	+	388.242i	0.0329527	+	0.596377i
$652$		0			0
$653$	77.1434	−	133.616i	0.118137	−	0.204619i	−0.800892	−	0.598808i	$-0.795641\pi$
$653$	77.1434	−	133.616i	0.118137	−	0.204619i	0.919029	+	0.394189i	$0.128975\pi$
$654$		0			0
$655$	321.886	−	185.841i	0.491429	−	0.283727i
$656$		0			0
$657$	310.271			0.472254
$658$		0			0
$659$		−	643.809i		−	0.976948i	−0.872578	−	0.488474i	$-0.837554\pi$
$659$		−	643.809i		−	0.976948i	0.872578	−	0.488474i	$-0.162446\pi$
$660$		0			0
$661$	73.7811	+	127.793i	0.111620	+	0.193332i	0.916424	−	0.400209i	$-0.131063\pi$
$661$	73.7811	+	127.793i	0.111620	+	0.193332i	−0.804803	+	0.593542i	$0.797729\pi$
$662$		0			0
$663$	−586.050	−	338.356i	−0.883936	−	0.510341i
$664$		0			0
$665$	−199.747	+	394.793i	−0.300372	+	0.593673i
$666$		0			0
$667$	−527.970	−	304.824i	−0.791559	−	0.457007i
$668$		0			0
$669$	151.138	+	261.778i	0.225916	+	0.391298i
$670$		0			0
$671$		−	916.110i		−	1.36529i
$672$		0			0
$673$	200.134			0.297375			0.148688	−	0.988884i	$-0.452495\pi$
$673$	200.134			0.297375			0.148688	+	0.988884i	$0.452495\pi$
$674$		0			0
$675$	−56.1155	+	32.3983i	−0.0831341	+	0.0479975i
$676$		0			0
$677$	302.267	−	523.542i	0.446480	−	0.773326i	−0.551674	−	0.834060i	$-0.686011\pi$
$677$	302.267	−	523.542i	0.446480	−	0.773326i	0.998154	+	0.0607337i	$0.0193440\pi$
$678$		0			0
$679$	−691.040	+	451.561i	−1.01773	+	0.665038i
$680$		0			0
$681$	−549.500	+	951.761i	−0.806901	+	1.39759i
$682$		0			0
$683$	282.520	−	163.113i	0.413645	−	0.238818i	−0.278710	−	0.960375i	$-0.589907\pi$
$683$	282.520	−	163.113i	0.413645	−	0.238818i	0.692355	+	0.721557i	$0.256573\pi$
$684$		0			0
$685$	566.006			0.826287
$686$		0			0
$687$			104.975i			0.152803i
$688$		0			0
$689$	202.019	+	349.908i	0.293207	+	0.507849i
$690$		0			0
$691$	−37.8620	−	21.8596i	−0.0547931	−	0.0316348i	0.472353	−	0.881409i	$-0.343405\pi$
$691$	−37.8620	−	21.8596i	−0.0547931	−	0.0316348i	−0.527146	+	0.849775i	$0.676738\pi$
$692$		0			0
$693$	792.042	+	1212.09i	1.14292	+	1.74905i
$694$		0			0
$695$	−1227.72	−	708.826i	−1.76651	−	1.01989i
$696$		0			0
$697$	501.903	+	869.321i	0.720090	+	1.24723i
$698$		0			0
$699$			617.835i			0.883884i
$700$		0			0
$701$	765.890			1.09257			0.546284	−	0.837600i	$-0.316042\pi$
$701$	765.890			1.09257			0.546284	+	0.837600i	$0.316042\pi$
$702$		0			0
$703$	−74.1808	+	42.8283i	−0.105520	+	0.0609222i
$704$		0			0
$705$	476.904	−	826.021i	0.676459	−	1.17166i
$706$		0			0
$707$	−611.304	−	309.292i	−0.864645	−	0.437472i
$708$		0			0
$709$	−657.627	+	1139.04i	−0.927542	+	1.60655i	−0.140121	+	0.990134i	$0.544749\pi$
$709$	−657.627	+	1139.04i	−0.927542	+	1.60655i	−0.787421	+	0.616415i	$0.788584\pi$
$710$		0			0
$711$	−402.960	+	232.649i	−0.566751	+	0.327214i
$712$		0			0
$713$	163.507			0.229322
$714$		0			0
$715$		−	579.809i		−	0.810922i
$716$		0			0
$717$	−941.709	−	1631.09i	−1.31340	−	2.27488i
$718$		0			0
$719$	154.245	+	89.0534i	0.214527	+	0.123857i	0.603414	−	0.797428i	$-0.293807\pi$
$719$	154.245	+	89.0534i	0.214527	+	0.123857i	−0.388886	+	0.921286i	$0.627140\pi$
$720$		0			0
$721$	−1072.22	+	59.2450i	−1.48712	+	0.0821706i
$722$		0			0
$723$	−941.651	−	543.663i	−1.30242	−	0.751954i
$724$		0			0
$725$	−192.186	−	332.876i	−0.265085	−	0.459140i
$726$		0			0
$727$			760.723i			1.04639i	0.852214	+	0.523193i	$0.175259\pi$
$727$			760.723i			1.04639i	−0.852214	+	0.523193i	$0.824741\pi$
$728$		0			0
$729$	981.560			1.34645
$730$		0			0
$731$	570.046	−	329.116i	0.779816	−	0.450227i
$732$		0			0
$733$	−37.2538	+	64.5255i	−0.0508238	+	0.0880294i	−0.890318	−	0.455339i	$-0.849518\pi$
$733$	−37.2538	+	64.5255i	−0.0508238	+	0.0880294i	0.839494	+	0.543369i	$0.182851\pi$
$734$		0			0
$735$	−1150.49	−	504.423i	−1.56529	−	0.686289i
$736$		0			0
$737$	855.630	−	1481.99i	1.16096	−	2.01085i
$738$		0			0
$739$	292.777	−	169.035i	0.396180	−	0.228735i	−0.288654	−	0.957433i	$-0.593208\pi$
$739$	292.777	−	169.035i	0.396180	−	0.228735i	0.684835	+	0.728699i	$0.259874\pi$
$740$		0			0
$741$	255.052			0.344199
$742$		0			0
$743$		−	681.343i		−	0.917016i	−0.888690	−	0.458508i	$-0.848384\pi$
$743$		−	681.343i		−	0.917016i	0.888690	−	0.458508i	$-0.151616\pi$
$744$		0			0
$745$	455.925	+	789.686i	0.611980	+	1.05998i
$746$		0			0
$747$	64.1861	+	37.0578i	0.0859251	+	0.0496089i
$748$		0			0
$749$	−634.567	+	35.0628i	−0.847219	+	0.0468129i
$750$		0			0
$751$	386.501	+	223.147i	0.514649	+	0.297133i	0.734743	−	0.678346i	$-0.237303\pi$
$751$	386.501	+	223.147i	0.514649	+	0.297133i	−0.220094	+	0.975479i	$0.570636\pi$
$752$		0			0
$753$	391.672	+	678.395i	0.520148	+	0.900923i
$754$		0			0
$755$			11.4398i			0.0151520i
$756$		0			0
$757$	455.207			0.601330			0.300665	−	0.953730i	$-0.402791\pi$
$757$	455.207			0.601330			0.300665	+	0.953730i	$0.402791\pi$
$758$		0			0
$759$	968.071	−	558.916i	1.27546	−	0.736385i
$760$		0			0
$761$	−408.242	+	707.095i	−0.536454	+	0.929166i	0.462637	+	0.886548i	$0.346903\pi$
$761$	−408.242	+	707.095i	−0.536454	+	0.929166i	−0.999091	+	0.0426181i	$0.986430\pi$
$762$		0			0
$763$	237.458	+	120.143i	0.311216	+	0.157462i
$764$		0			0
$765$	902.774	−	1563.65i	1.18010	−	2.04399i
$766$		0			0
$767$	−179.084	+	103.394i	−0.233486	+	0.134803i
$768$		0			0
$769$	−203.680			−0.264863			−0.132431	−	0.991192i	$-0.542278\pi$
$769$	−203.680			−0.264863			−0.132431	+	0.991192i	$0.542278\pi$
$770$		0			0
$771$			227.090i			0.294539i
$772$		0			0
$773$	−257.358	−	445.756i	−0.332934	−	0.576658i	0.650152	−	0.759804i	$-0.274705\pi$
$773$	−257.358	−	445.756i	−0.332934	−	0.576658i	−0.983086	+	0.183146i	$0.941372\pi$
$774$		0			0
$775$	89.2772	+	51.5442i	0.115196	+	0.0665087i
$776$		0			0
$777$	−133.034	−	203.586i	−0.171215	−	0.262016i
$778$		0			0
$779$	−327.646	−	189.166i	−0.420598	−	0.242832i
$780$		0			0
$781$	−888.693	−	1539.26i	−1.13789	−	1.97089i
$782$		0			0
$783$		−	365.839i		−	0.467227i
$784$		0			0
$785$	−1496.85			−1.90681
$786$		0			0
$787$	−53.6099	+	30.9517i	−0.0681193	+	0.0393287i	−0.533673	−	0.845691i	$-0.679189\pi$
$787$	−53.6099	+	30.9517i	−0.0681193	+	0.0393287i	0.465554	+	0.885020i	$0.345855\pi$
$788$		0			0
$789$	430.854	−	746.260i	0.546076	−	0.945831i
$790$		0			0
$791$	691.604	−	451.929i	0.874341	−	0.571339i
$792$		0			0
$793$	124.779	−	216.123i	0.157350	−	0.272539i
$794$		0			0
$795$	−1714.02	+	989.592i	−2.15600	+	1.24477i
$796$		0			0
$797$	674.547			0.846357			0.423179	−	0.906046i	$-0.360914\pi$
$797$	674.547			0.846357			0.423179	+	0.906046i	$0.360914\pi$
$798$		0			0
$799$			1082.01i			1.35421i
$800$		0			0
$801$	616.738	+	1068.22i	0.769960	+	1.33361i
$802$		0			0
$803$	−479.493	−	276.835i	−0.597127	−	0.344751i
$804$		0			0
$805$	−238.480	+	471.347i	−0.296249	+	0.585524i
$806$		0			0
$807$	−23.1281	−	13.3530i	−0.0286593	−	0.0165465i
$808$		0			0
$809$	−613.272	−	1062.22i	−0.758062	−	1.31300i	−0.943838	−	0.330409i	$-0.892813\pi$
$809$	−613.272	−	1062.22i	−0.758062	−	1.31300i	0.185776	−	0.982592i	$-0.440520\pi$
$810$		0			0
$811$			920.398i			1.13489i	0.823410	+	0.567446i	$0.192069\pi$
$811$			920.398i			1.13489i	−0.823410	+	0.567446i	$0.807931\pi$
$812$		0			0
$813$	1754.50			2.15806
$814$		0			0
$815$	870.498	−	502.582i	1.06810	−	0.616665i
$816$		0			0
$817$	−124.043	+	214.849i	−0.151828	+	0.262974i
$818$		0			0
$819$	21.7610	+	393.830i	0.0265702	+	0.480867i
$820$		0			0
$821$	85.1028	−	147.402i	0.103657	−	0.179540i	−0.809531	−	0.587077i	$-0.800279\pi$
$821$	85.1028	−	147.402i	0.103657	−	0.179540i	0.913189	+	0.407537i	$0.133612\pi$
$822$		0			0
$823$	974.415	−	562.579i	1.18398	−	0.683571i	0.227047	−	0.973884i	$-0.427093\pi$
$823$	974.415	−	562.579i	1.18398	−	0.683571i	0.956932	+	0.290313i	$0.0937594\pi$
$824$		0			0
$825$	704.775			0.854273
$826$		0			0
$827$		−	749.693i		−	0.906521i	−0.891378	−	0.453261i	$-0.850261\pi$
$827$		−	749.693i		−	0.906521i	0.891378	−	0.453261i	$-0.149739\pi$
$828$		0			0
$829$	397.023	+	687.664i	0.478918	+	0.829510i	0.999708	−	0.0241749i	$-0.00769586\pi$
$829$	397.023	+	687.664i	0.478918	+	0.829510i	−0.520790	+	0.853685i	$0.674363\pi$
$830$		0			0
$831$	−1147.25	−	662.366i	−1.38057	−	0.797071i
$832$		0			0
$833$	1416.39	−	157.003i	1.70034	−	0.188479i
$834$		0			0
$835$	82.5141	+	47.6395i	0.0988193	+	0.0570533i
$836$		0			0
$837$	49.0589	+	84.9725i	0.0586128	+	0.101520i
$838$		0			0
$839$		−	1580.69i		−	1.88402i	−0.335586	−	0.942010i	$-0.608934\pi$
$839$		−	1580.69i		−	1.88402i	0.335586	−	0.942010i	$-0.391066\pi$
$840$		0			0
$841$	1329.15			1.58044
$842$		0			0
$843$	1661.31	−	959.160i	1.97072	−	1.13779i
$844$		0			0
$845$	−408.285	+	707.171i	−0.483178	+	0.836888i
$846$		0			0
$847$	−95.8197	−	1734.14i	−0.113128	−	2.04740i
$848$		0			0
$849$	−983.325	+	1703.17i	−1.15821	+	2.00609i
$850$		0			0
$851$	−88.5652	+	51.1332i	−0.104072	+	0.0600860i
$852$		0			0
$853$	−1404.70			−1.64678			−0.823389	−	0.567477i	$-0.807920\pi$
$853$	−1404.70			−1.64678			−0.823389	+	0.567477i	$0.807920\pi$
$854$		0			0
$855$			680.508i			0.795916i
$856$		0			0
$857$	−630.820	−	1092.61i	−0.736079	−	1.27493i	−0.954248	−	0.299016i	$-0.903342\pi$
$857$	−630.820	−	1092.61i	−0.736079	−	1.27493i	0.218169	−	0.975911i	$-0.429992\pi$
$858$		0			0
$859$	145.467	+	83.9852i	0.169344	+	0.0977709i	0.582277	−	0.812991i	$-0.302162\pi$
$859$	145.467	+	83.9852i	0.169344	+	0.0977709i	−0.412932	+	0.910762i	$0.635495\pi$
$860$		0			0
$861$	484.945	−	958.475i	0.563235	−	1.11321i
$862$		0			0
$863$	1316.73	+	760.214i	1.52576	+	0.880897i	0.999533	+	0.0305517i	$0.00972642\pi$
$863$	1316.73	+	760.214i	1.52576	+	0.880897i	0.526225	+	0.850345i	$0.323607\pi$
$864$		0			0
$865$	0.857677	+	1.48554i	0.000991534	+	0.00171739i
$866$		0			0
$867$			2475.56i			2.85531i
$868$		0			0
$869$	830.313			0.955481
$870$		0			0
$871$	403.711	−	233.082i	0.463503	−	0.267603i
$872$		0			0
$873$	−634.828	+	1099.55i	−0.727180	+	1.25951i
$874$		0			0
$875$	565.949	−	369.820i	0.646799	−	0.422651i
$876$		0			0
$877$	−19.5472	+	33.8568i	−0.0222887	+	0.0386052i	−0.876955	−	0.480573i	$-0.840429\pi$
$877$	−19.5472	+	33.8568i	−0.0222887	+	0.0386052i	0.854666	+	0.519178i	$0.173762\pi$
$878$		0			0
$879$	257.329	−	148.569i	0.292752	−	0.169020i
$880$		0			0
$881$	−915.577			−1.03925			−0.519624	−	0.854395i	$-0.673928\pi$
$881$	−915.577			−1.03925			−0.519624	+	0.854395i	$0.673928\pi$
$882$		0			0
$883$			331.093i			0.374963i	0.982268	+	0.187482i	$0.0600325\pi$
$883$			331.093i			0.374963i	−0.982268	+	0.187482i	$0.939967\pi$
$884$		0			0
$885$	−506.476	−	877.241i	−0.572289	−	0.991233i
$886$		0			0
$887$	1039.22	+	599.992i	1.17161	+	0.676428i	0.954058	−	0.299621i	$-0.0968601\pi$
$887$	1039.22	+	599.992i	1.17161	+	0.676428i	0.217550	+	0.976049i	$0.430193\pi$
$888$		0			0
$889$	−32.8633	−	50.2919i	−0.0369666	−	0.0565714i
$890$		0			0
$891$	−1031.29	−	595.415i	−1.15745	−	0.668254i
$892$		0			0
$893$	−203.904	−	353.173i	−0.228336	−	0.395490i
$894$		0			0
$895$		−	712.798i		−	0.796423i
$896$		0			0
$897$	304.509			0.339475
$898$		0			0
$899$	−504.055	+	291.017i	−0.560685	+	0.323711i
$900$		0			0
$901$	1122.61	−	1944.41i	1.24596	−	2.15806i
$902$		0			0
$903$	−628.507	−	317.996i	−0.696021	−	0.352155i
$904$		0			0
$905$	187.550	−	324.847i	0.207238	−	0.358947i
$906$		0			0
$907$	263.969	−	152.402i	0.291035	−	0.168029i	−0.347374	−	0.937727i	$-0.612926\pi$
$907$	263.969	−	152.402i	0.291035	−	0.168029i	0.638408	+	0.769698i	$0.279593\pi$
$908$		0			0
$909$	−1053.71			−1.15920
$910$		0			0
$911$			1743.29i			1.91360i	0.290753	+	0.956798i	$0.406094\pi$
$911$			1743.29i			1.91360i	−0.290753	+	0.956798i	$0.593906\pi$
$912$		0			0
$913$	−66.1288	−	114.538i	−0.0724302	−	0.125453i
$914$		0			0
$915$	1058.68	+	611.229i	1.15703	+	0.668010i
$916$		0			0
$917$	450.511	−	24.8928i	0.491287	−	0.0271460i
$918$		0			0
$919$	1069.37	+	617.403i	1.16363	+	0.671821i	0.952171	−	0.305567i	$-0.0988459\pi$
$919$	1069.37	+	617.403i	1.16363	+	0.671821i	0.211457	+	0.977387i	$0.432179\pi$
$920$		0			0
$921$	−300.210	−	519.979i	−0.325961	−	0.564581i
$922$		0			0
$923$		−	484.178i		−	0.524570i
$924$		0			0
$925$	−64.4772			−0.0697051
$926$		0			0
$927$	−1430.36	+	825.820i	−1.54300	+	0.890852i
$928$		0			0
$929$	−664.417	+	1150.80i	−0.715196	+	1.23876i	0.247688	+	0.968840i	$0.420329\pi$
$929$	−664.417	+	1150.80i	−0.715196	+	1.23876i	−0.962884	+	0.269916i	$0.913004\pi$
$930$		0			0
$931$	−432.726	+	318.163i	−0.464797	+	0.341744i
$932$		0			0
$933$	−691.533	+	1197.77i	−0.741193	+	1.28378i
$934$		0			0
$935$	−2790.29	+	1610.98i	−2.98427	+	1.72297i
$936$		0			0
$937$	−206.866			−0.220775			−0.110387	−	0.993889i	$-0.535209\pi$
$937$	−206.866			−0.220775			−0.110387	+	0.993889i	$0.535209\pi$
$938$		0			0
$939$		−	574.642i		−	0.611972i
$940$		0			0
$941$	500.890	+	867.566i	0.532295	+	0.921962i	0.999289	+	0.0377016i	$0.0120036\pi$
$941$	500.890	+	867.566i	0.532295	+	0.921962i	−0.466994	+	0.884261i	$0.654663\pi$
$942$		0			0
$943$	−391.180	−	225.848i	−0.414825	−	0.239499i
$944$		0			0
$945$	−316.507	+	17.4885i	−0.334928	+	0.0185064i
$946$		0			0
$947$	162.584	+	93.8677i	0.171683	+	0.0991212i	0.583379	−	0.812200i	$-0.301730\pi$
$947$	162.584	+	93.8677i	0.171683	+	0.0991212i	−0.411696	+	0.911321i	$0.635064\pi$
$948$		0			0
$949$	−75.4128	−	130.619i	−0.0794655	−	0.137638i
$950$		0			0
$951$			1577.79i			1.65908i
$952$		0			0
$953$	−876.232			−0.919446			−0.459723	−	0.888062i	$-0.652051\pi$
$953$	−876.232			−0.919446			−0.459723	+	0.888062i	$0.652051\pi$
$954$		0			0
$955$	59.1140	−	34.1295i	0.0618994	−	0.0357377i
$956$		0			0
$957$	−1989.56	+	3446.03i	−2.07896	+	3.60086i
$958$		0			0
$959$	613.089	+	310.196i	0.639301	+	0.323457i
$960$		0			0
$961$	−402.450	+	697.063i	−0.418782	+	0.725352i
$962$		0			0
$963$	−846.528	+	488.743i	−0.879053	+	0.507521i
$964$		0			0
$965$	−339.400			−0.351710
$966$		0			0
$967$		−	311.857i		−	0.322499i	−0.986914	−	0.161250i	$-0.948448\pi$
$967$		−	311.857i		−	0.322499i	0.986914	−	0.161250i	$-0.0515524\pi$
$968$		0			0
$969$	−708.651	−	1227.42i	−0.731322	−	1.26669i
$970$		0			0
$971$	−346.856	−	200.257i	−0.357215	−	0.206238i	0.310643	−	0.950527i	$-0.399456\pi$
$971$	−346.856	−	200.257i	−0.357215	−	0.206238i	−0.667858	+	0.744288i	$0.732789\pi$
$972$		0			0
$973$	−941.384	−	1440.63i	−0.967507	−	1.48061i
$974$		0			0
$975$	166.266	+	95.9940i	0.170530	+	0.0984553i
$976$		0			0
$977$	488.351	+	845.848i	0.499847	+	0.865761i	1.00000		0.000176296i	$-5.61167e-5\pi$
$977$	488.351	+	845.848i	0.499847	+	0.865761i	−0.500153	+	0.865937i	$0.666723\pi$
$978$		0			0
$979$		−	2201.11i		−	2.24832i
$980$		0			0
$981$	409.309			0.417237
$982$		0			0
$983$	−1388.31	+	801.539i	−1.41232	+	0.815401i	−0.995606	−	0.0936386i	$-0.970150\pi$
$983$	−1388.31	+	801.539i	−1.41232	+	0.815401i	−0.416710	+	0.909040i	$0.636817\pi$
$984$		0			0
$985$	−949.737	+	1644.99i	−0.964200	+	1.67004i
$986$		0			0
$987$	969.269	−	633.370i	0.982036	−	0.641712i
$988$		0			0
$989$	−148.097	+	256.511i	−0.149744	+	0.259364i
$990$		0			0
$991$	−796.867	+	460.071i	−0.804104	+	0.464250i	−0.844904	−	0.534918i	$-0.820343\pi$
$991$	−796.867	+	460.071i	−0.804104	+	0.464250i	0.0408003	+	0.999167i	$0.487009\pi$
$992$		0			0
$993$	1125.71			1.13364
$994$		0			0
$995$			52.7394i			0.0530044i
$996$		0			0
$997$	193.081	+	334.427i	0.193662	+	0.335433i	0.946461	−	0.322818i	$-0.104630\pi$
$997$	193.081	+	334.427i	0.193662	+	0.335433i	−0.752799	+	0.658251i	$0.771297\pi$
$998$		0			0
$999$	−53.1465	−	30.6841i	−0.0531997	−	0.0307149i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.r.c.191.6	yes	12
4.3	odd	2	inner	224.3.r.c.191.1	yes	12
7.2	even	3		1568.3.d.j.1471.6		6
7.4	even	3	inner	224.3.r.c.95.1	✓	12
7.5	odd	6		1568.3.d.k.1471.1		6
8.3	odd	2		448.3.r.g.191.6		12
8.5	even	2		448.3.r.g.191.1		12
28.11	odd	6	inner	224.3.r.c.95.6	yes	12
28.19	even	6		1568.3.d.k.1471.6		6
28.23	odd	6		1568.3.d.j.1471.1		6
56.11	odd	6		448.3.r.g.319.1		12
56.53	even	6		448.3.r.g.319.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.r.c.95.1	✓	12	7.4	even	3	inner
224.3.r.c.95.6	yes	12	28.11	odd	6	inner
224.3.r.c.191.1	yes	12	4.3	odd	2	inner
224.3.r.c.191.6	yes	12	1.1	even	1	trivial
448.3.r.g.191.1		12	8.5	even	2
448.3.r.g.191.6		12	8.3	odd	2
448.3.r.g.319.1		12	56.11	odd	6
448.3.r.g.319.6		12	56.53	even	6
1568.3.d.j.1471.1		6	28.23	odd	6
1568.3.d.j.1471.6		6	7.2	even	3
1568.3.d.k.1471.1		6	7.5	odd	6
1568.3.d.k.1471.6		6	28.19	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.85030 - 2.22297i) q^{3} +(2.88318 - 4.99382i) q^{5} +(5.85985 - 3.82912i) q^{7} +(5.38318 - 9.32395i) q^{9} +O(q^{10})\)	\(q+(3.85030 - 2.22297i) q^{3} +(2.88318 - 4.99382i) q^{5} +(5.85985 - 3.82912i) q^{7} +(5.38318 - 9.32395i) q^{9} +(-16.6383 + 9.60615i) q^{11} -5.23363 q^{13} -25.6369i q^{15} +(14.5414 + 25.1865i) q^{17} +(-9.49276 - 5.48065i) q^{19} +(14.0501 - 27.7695i) q^{21} +(-11.3335 - 6.54340i) q^{23} +(-4.12551 - 7.14559i) q^{25} -7.85317i q^{27} +46.5849 q^{29} +(-10.8201 + 6.24702i) q^{31} +(-42.7084 + 73.9731i) q^{33} +(-2.22694 - 40.3031i) q^{35} +(3.90723 - 6.76752i) q^{37} +(-20.1510 + 11.6342i) q^{39} +34.5154 q^{41} -22.6330i q^{43} +(-31.0414 - 53.7653i) q^{45} +(32.2200 + 18.6022i) q^{47} +(19.6756 - 44.8762i) q^{49} +(111.978 + 64.6503i) q^{51} +(-38.6002 - 66.8576i) q^{53} +110.785i q^{55} -48.7332 q^{57} +(34.2179 - 19.7557i) q^{59} +(-23.8418 + 41.2951i) q^{61} +(-4.15791 - 75.2498i) q^{63} +(-15.0895 + 26.1358i) q^{65} +(-77.1378 + 44.5355i) q^{67} -58.1831 q^{69} +92.5129i q^{71} +(14.4093 + 24.9576i) q^{73} +(-31.7688 - 18.3418i) q^{75} +(-60.7150 + 120.001i) q^{77} +(-37.4277 - 21.6089i) q^{79} +(30.9913 + 53.6785i) q^{81} +6.88400i q^{83} +167.703 q^{85} +(179.366 - 103.557i) q^{87} +(-57.2838 + 99.2184i) q^{89} +(-30.6683 + 20.0402i) q^{91} +(-27.7738 + 48.1057i) q^{93} +(-54.7387 + 31.6034i) q^{95} -117.928 q^{97} +206.847i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{5} + 32 q^{9}+O(q^{10}) \) 12 * q + 2 * q^5 + 32 * q^9	\( 12 q + 2 q^{5} + 32 q^{9} - 128 q^{13} - 6 q^{17} - 62 q^{21} - 32 q^{25} + 128 q^{29} - 134 q^{33} - 66 q^{37} + 384 q^{41} - 192 q^{45} - 12 q^{49} - 2 q^{53} + 468 q^{57} - 434 q^{61} + 160 q^{65} + 124 q^{69} - 10 q^{73} - 370 q^{77} + 422 q^{81} + 1020 q^{85} - 522 q^{89} + 306 q^{93} - 768 q^{97}+O(q^{100}) \) 12 * q + 2 * q^5 + 32 * q^9 - 128 * q^13 - 6 * q^17 - 62 * q^21 - 32 * q^25 + 128 * q^29 - 134 * q^33 - 66 * q^37 + 384 * q^41 - 192 * q^45 - 12 * q^49 - 2 * q^53 + 468 * q^57 - 434 * q^61 + 160 * q^65 + 124 * q^69 - 10 * q^73 - 370 * q^77 + 422 * q^81 + 1020 * q^85 - 522 * q^89 + 306 * q^93 - 768 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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