LMFDB - Embedded newform 92.3.f.a.5.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [92,3,Mod(5,92)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("92.5"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(92, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	92.f (of order $22$, degree $10$, 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:	$2.50681843211$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.2
Character	$\chi$	$=$	92.5
Dual form			92.3.f.a.37.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.710283 + 0.819710i) q^{3} +(-9.64449 - 1.38667i) q^{5} +(-4.98879 + 2.27830i) q^{7} +(1.11341 + 7.74394i) q^{9} +(-3.69536 - 12.5852i) q^{11} +(0.537204 - 1.17631i) q^{13} +(7.98699 - 6.92076i) q^{15} +(3.26150 + 5.07499i) q^{17} +(-16.9355 + 26.3522i) q^{19} +(1.67590 - 5.70760i) q^{21} +(-15.3675 - 17.1126i) q^{23} +(67.1061 + 19.7041i) q^{25} +(-15.3507 - 9.86528i) q^{27} +(28.7783 - 18.4947i) q^{29} +(-5.00573 - 5.77692i) q^{31} +(12.9410 + 5.90996i) q^{33} +(51.2736 - 15.0553i) q^{35} +(-21.1877 + 3.04634i) q^{37} +(0.582669 + 1.27587i) q^{39} +(-8.71362 + 60.6045i) q^{41} +(-12.7175 - 11.0198i) q^{43} -76.2303i q^{45} -40.1246 q^{47} +(-12.3909 + 14.2998i) q^{49} +(-6.47661 - 0.931196i) q^{51} +(-60.6602 + 27.7026i) q^{53} +(18.1883 + 126.503i) q^{55} +(-9.57214 - 32.5997i) q^{57} +(28.2210 - 61.7953i) q^{59} +(2.76812 - 2.39859i) q^{61} +(-23.1976 - 36.0962i) q^{63} +(-6.81222 + 10.6000i) q^{65} +(3.79860 - 12.9368i) q^{67} +(24.9426 - 0.442086i) q^{69} +(-43.2131 - 12.6885i) q^{71} +(-51.5883 - 33.1538i) q^{73} +(-63.8160 + 41.0121i) q^{75} +(47.1083 + 54.3659i) q^{77} +(15.2696 + 6.97338i) q^{79} +(-48.5700 + 14.2614i) q^{81} +(-109.753 + 15.7802i) q^{83} +(-24.4182 - 53.4684i) q^{85} +(-5.28045 + 36.7263i) q^{87} +(38.5581 + 33.4108i) q^{89} +7.09229i q^{91} +8.29089 q^{93} +(199.876 - 230.669i) q^{95} +(136.770 + 19.6645i) q^{97} +(93.3449 - 42.6292i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{3} - 6 q^{9} - 2 q^{13} + 77 q^{15} + 55 q^{17} + 33 q^{19} + 33 q^{21} - 50 q^{23} - 54 q^{25} - 191 q^{27} + q^{29} - 53 q^{31} - 121 q^{33} - 156 q^{35} - 352 q^{37} - 306 q^{39} + 6 q^{41}+ \cdots + 1353 q^{99}+O(q^{100}) $ 40 * q - 2 * q^3 - 6 * q^9 - 2 * q^13 + 77 * q^15 + 55 * q^17 + 33 * q^19 + 33 * q^21 - 50 * q^23 - 54 * q^25 - 191 * q^27 + q^29 - 53 * q^31 - 121 * q^33 - 156 * q^35 - 352 * q^37 - 306 * q^39 + 6 * q^41 - 88 * q^43 - 58 * q^47 + 292 * q^49 + 264 * q^51 + 176 * q^53 + 518 * q^55 + 891 * q^57 + 696 * q^59 + 308 * q^61 + 275 * q^63 + 231 * q^65 + 22 * q^67 - 233 * q^69 - 215 * q^71 - 400 * q^73 - 557 * q^75 - 239 * q^77 - 748 * q^79 - 684 * q^81 - 671 * q^83 - 794 * q^85 + 62 * q^87 - 44 * q^89 - 346 * q^93 + 561 * q^95 + 693 * q^97 + 1353 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$1$

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
$3$	−0.710283	+	0.819710i	−0.236761	+	0.273237i	−0.861679	−	0.507454i	$-0.830587\pi$
$3$	−0.710283	+	0.819710i	−0.236761	+	0.273237i	0.624918	+	0.780690i	$0.285132\pi$
$4$		0			0
$5$	−9.64449	−	1.38667i	−1.92890	−	0.277334i	−0.932434	−	0.361341i	$-0.882319\pi$
$5$	−9.64449	−	1.38667i	−1.92890	−	0.277334i	−0.996465	+	0.0840073i	$0.973228\pi$
$6$		0			0
$7$	−4.98879	+	2.27830i	−0.712684	+	0.325472i	−0.738555	−	0.674194i	$-0.764491\pi$
$7$	−4.98879	+	2.27830i	−0.712684	+	0.325472i	0.0258711	+	0.999665i	$0.491764\pi$
$8$		0			0
$9$	1.11341	+	7.74394i	0.123712	+	0.860438i
$10$		0			0
$11$	−3.69536	−	12.5852i	−0.335942	−	1.14411i	−0.938281	−	0.345873i	$-0.887583\pi$
$11$	−3.69536	−	12.5852i	−0.335942	−	1.14411i	0.602339	−	0.798240i	$-0.294235\pi$
$12$		0			0
$13$	0.537204	−	1.17631i	0.0413234	−	0.0904856i	−0.887844	−	0.460144i	$-0.847798\pi$
$13$	0.537204	−	1.17631i	0.0413234	−	0.0904856i	0.929168	+	0.369658i	$0.120525\pi$
$14$		0			0
$15$	7.98699	−	6.92076i	0.532466	−	0.461384i
$16$		0			0
$17$	3.26150	+	5.07499i	0.191853	+	0.298529i	0.923832	−	0.382798i	$-0.125040\pi$
$17$	3.26150	+	5.07499i	0.191853	+	0.298529i	−0.731979	+	0.681327i	$0.761403\pi$
$18$		0			0
$19$	−16.9355	+	26.3522i	−0.891342	+	1.38696i	0.0305598	+	0.999533i	$0.490271\pi$
$19$	−16.9355	+	26.3522i	−0.891342	+	1.38696i	−0.921902	+	0.387423i	$0.873365\pi$
$20$		0			0
$21$	1.67590	−	5.70760i	0.0798049	−	0.271790i
$22$		0			0
$23$	−15.3675	−	17.1126i	−0.668151	−	0.744026i
$23$	−15.3675	−	17.1126i	−0.668151	−	0.744026i
$24$		0			0
$25$	67.1061	+	19.7041i	2.68424	+	0.788165i
$26$		0			0
$27$	−15.3507	−	9.86528i	−0.568544	−	0.365381i
$28$		0			0
$29$	28.7783	−	18.4947i	0.992354	−	0.637747i	0.0595858	−	0.998223i	$-0.481022\pi$
$29$	28.7783	−	18.4947i	0.992354	−	0.637747i	0.932769	+	0.360476i	$0.117386\pi$
$30$		0			0
$31$	−5.00573	−	5.77692i	−0.161475	−	0.186352i	0.669246	−	0.743041i	$-0.266617\pi$
$31$	−5.00573	−	5.77692i	−0.161475	−	0.186352i	−0.830721	+	0.556688i	$0.812072\pi$
$32$		0			0
$33$	12.9410	+	5.90996i	0.392152	+	0.179090i
$34$		0			0
$35$	51.2736	−	15.0553i	1.46496	−	0.430151i
$36$		0			0
$37$	−21.1877	+	3.04634i	−0.572641	+	0.0823334i	−0.422551	−	0.906339i	$-0.638865\pi$
$37$	−21.1877	+	3.04634i	−0.572641	+	0.0823334i	−0.150090	+	0.988672i	$0.547956\pi$
$38$		0			0
$39$	0.582669	+	1.27587i	0.0149402	+	0.0327145i
$40$		0			0
$41$	−8.71362	+	60.6045i	−0.212527	+	1.47816i	0.552149	+	0.833745i	$0.313808\pi$
$41$	−8.71362	+	60.6045i	−0.212527	+	1.47816i	−0.764677	+	0.644414i	$0.777101\pi$
$42$		0			0
$43$	−12.7175	−	11.0198i	−0.295756	−	0.256274i	0.494324	−	0.869278i	$-0.335416\pi$
$43$	−12.7175	−	11.0198i	−0.295756	−	0.256274i	−0.790080	+	0.613004i	$0.789961\pi$
$44$		0			0
$45$		−	76.2303i		−	1.69401i
$46$		0			0
$47$	−40.1246			−0.853716			−0.426858	−	0.904319i	$-0.640380\pi$
$47$	−40.1246			−0.853716			−0.426858	+	0.904319i	$0.640380\pi$
$48$		0			0
$49$	−12.3909	+	14.2998i	−0.252875	+	0.291833i
$50$		0			0
$51$	−6.47661	−	0.931196i	−0.126992	−	0.0182588i
$52$		0			0
$53$	−60.6602	+	27.7026i	−1.14453	+	0.522690i	−0.895172	−	0.445721i	$-0.852947\pi$
$53$	−60.6602	+	27.7026i	−1.14453	+	0.522690i	−0.249360	+	0.968411i	$0.580220\pi$
$54$		0			0
$55$	18.1883	+	126.503i	0.330697	+	2.30005i
$56$		0			0
$57$	−9.57214	−	32.5997i	−0.167932	−	0.571925i
$58$		0			0
$59$	28.2210	−	61.7953i	0.478322	−	1.04738i	−0.504600	−	0.863353i	$-0.668360\pi$
$59$	28.2210	−	61.7953i	0.478322	−	1.04738i	0.982922	−	0.184025i	$-0.0589128\pi$
$60$		0			0
$61$	2.76812	−	2.39859i	0.0453790	−	0.0393211i	−0.631876	−	0.775069i	$-0.717715\pi$
$61$	2.76812	−	2.39859i	0.0453790	−	0.0393211i	0.677255	+	0.735748i	$0.263169\pi$
$62$		0			0
$63$	−23.1976	−	36.0962i	−0.368216	−	0.572955i
$64$		0			0
$65$	−6.81222	+	10.6000i	−0.104803	+	0.163077i
$66$		0			0
$67$	3.79860	−	12.9368i	0.0566955	−	0.193087i	−0.926276	−	0.376846i	$-0.877008\pi$
$67$	3.79860	−	12.9368i	0.0566955	−	0.193087i	0.982971	+	0.183759i	$0.0588267\pi$
$68$		0			0
$69$	24.9426	−	0.442086i	0.361487	−	0.00640705i
$70$		0			0
$71$	−43.2131	−	12.6885i	−0.608636	−	0.178712i	−0.0371311	−	0.999310i	$-0.511822\pi$
$71$	−43.2131	−	12.6885i	−0.608636	−	0.178712i	−0.571505	+	0.820599i	$0.693640\pi$
$72$		0			0
$73$	−51.5883	−	33.1538i	−0.706689	−	0.454161i	0.137295	−	0.990530i	$-0.456159\pi$
$73$	−51.5883	−	33.1538i	−0.706689	−	0.454161i	−0.843984	+	0.536369i	$0.819796\pi$
$74$		0			0
$75$	−63.8160	+	41.0121i	−0.850880	+	0.546827i
$76$		0			0
$77$	47.1083	+	54.3659i	0.611797	+	0.706051i
$78$		0			0
$79$	15.2696	+	6.97338i	0.193286	+	0.0882706i	0.509707	−	0.860348i	$-0.329754\pi$
$79$	15.2696	+	6.97338i	0.193286	+	0.0882706i	−0.316421	+	0.948619i	$0.602481\pi$
$80$		0			0
$81$	−48.5700	+	14.2614i	−0.599629	+	0.176067i
$82$		0			0
$83$	−109.753	+	15.7802i	−1.32233	+	0.190122i	−0.767075	−	0.641557i	$-0.778289\pi$
$83$	−109.753	+	15.7802i	−1.32233	+	0.190122i	−0.555255	+	0.831680i	$0.687379\pi$
$84$		0			0
$85$	−24.4182	−	53.4684i	−0.287273	−	0.629040i
$86$		0			0
$87$	−5.28045	+	36.7263i	−0.0606948	+	0.422141i
$88$		0			0
$89$	38.5581	+	33.4108i	0.433238	+	0.375402i	0.844003	−	0.536339i	$-0.180193\pi$
$89$	38.5581	+	33.4108i	0.433238	+	0.375402i	−0.410765	+	0.911741i	$0.634738\pi$
$90$		0			0
$91$			7.09229i			0.0779372i
$92$		0			0
$93$	8.29089			0.0891493
$94$		0			0
$95$	199.876	−	230.669i	2.10396	−	2.42810i
$96$		0			0
$97$	136.770	+	19.6645i	1.41000	+	0.202727i	0.804894	−	0.593419i	$-0.202222\pi$
$97$	136.770	+	19.6645i	1.41000	+	0.202727i	0.605105	+	0.796146i	$0.293131\pi$
$98$		0			0
$99$	93.3449	−	42.6292i	0.942878	−	0.430598i
$100$		0			0
$101$	−1.03115	−	7.17178i	−0.0102094	−	0.0710078i	0.984080	−	0.177727i	$-0.0568744\pi$
$101$	−1.03115	−	7.17178i	−0.0102094	−	0.0710078i	−0.994289	+	0.106719i	$0.965965\pi$
$102$		0			0
$103$	44.8592	+	152.776i	0.435526	+	1.48327i	0.826538	+	0.562880i	$0.190307\pi$
$103$	44.8592	+	152.776i	0.435526	+	1.48327i	−0.391012	+	0.920386i	$0.627875\pi$
$104$		0			0
$105$	−24.0778	+	52.7230i	−0.229312	+	0.502124i
$106$		0			0
$107$	42.7593	−	37.0511i	0.399620	−	0.346272i	−0.431749	−	0.901994i	$-0.642103\pi$
$107$	42.7593	−	37.0511i	0.399620	−	0.346272i	0.831369	+	0.555721i	$0.187558\pi$
$108$		0			0
$109$	42.9550	+	66.8393i	0.394083	+	0.613205i	0.980433	−	0.196853i	$-0.0630721\pi$
$109$	42.9550	+	66.8393i	0.394083	+	0.613205i	−0.586350	+	0.810058i	$0.699436\pi$
$110$		0			0
$111$	12.5522	−	19.5316i	0.113083	−	0.175960i
$112$		0			0
$113$	43.5287	−	148.245i	0.385209	−	1.31190i	−0.507649	−	0.861564i	$-0.669485\pi$
$113$	43.5287	−	148.245i	0.385209	−	1.31190i	0.892858	−	0.450338i	$-0.148697\pi$
$114$		0			0
$115$	124.482	+	186.352i	1.08245	+	1.62045i
$116$		0			0
$117$	9.70743	+	2.85036i	0.0829695	+	0.0243620i
$118$		0			0
$119$	−27.8333	−	17.8874i	−0.233893	−	0.150314i
$120$		0			0
$121$	−42.9410	+	27.5965i	−0.354884	+	0.228070i
$122$		0			0
$123$	−43.4890	−	50.1890i	−0.353569	−	0.408041i
$124$		0			0
$125$	−398.302	−	181.899i	−3.18642	−	1.45519i
$126$		0			0
$127$	−76.8418	+	22.5628i	−0.605054	+	0.177660i	−0.569889	−	0.821722i	$-0.693014\pi$
$127$	−76.8418	+	22.5628i	−0.605054	+	0.177660i	−0.0351647	+	0.999382i	$0.511196\pi$
$128$		0			0
$129$	18.0661	−	2.59751i	0.140047	−	0.0201357i
$130$		0			0
$131$	72.3984	+	158.530i	0.552660	+	1.21016i	0.955529	+	0.294898i	$0.0952858\pi$
$131$	72.3984	+	158.530i	0.552660	+	1.21016i	−0.402869	+	0.915258i	$0.631987\pi$
$132$		0			0
$133$	24.4494	−	170.049i	0.183830	−	1.27857i
$134$		0			0
$135$	134.370	+	116.432i	0.995331	+	0.862459i
$136$		0			0
$137$		−	67.7953i		−	0.494856i	−0.968906	−	0.247428i	$-0.920415\pi$
$137$		−	67.7953i		−	0.494856i	0.968906	−	0.247428i	$-0.0795854\pi$
$138$		0			0
$139$	157.883			1.13585			0.567926	−	0.823080i	$-0.307746\pi$
$139$	157.883			1.13585			0.567926	+	0.823080i	$0.307746\pi$
$140$		0			0
$141$	28.4999	−	32.8906i	0.202127	−	0.233267i
$142$		0			0
$143$	−16.7894	−	2.41394i	−0.117408	−	0.0168807i
$144$		0			0
$145$	−303.198	+	138.466i	−2.09102	+	0.954937i
$146$		0			0
$147$	−2.92069	−	20.3138i	−0.0198686	−	0.138189i
$148$		0			0
$149$	34.5129	+	117.540i	0.231630	+	0.788861i	0.990487	+	0.137603i	$0.0439399\pi$
$149$	34.5129	+	117.540i	0.231630	+	0.788861i	−0.758857	+	0.651257i	$0.774242\pi$
$150$		0			0
$151$	74.0365	−	162.117i	0.490308	−	1.07363i	−0.489191	−	0.872177i	$-0.662708\pi$
$151$	74.0365	−	162.117i	0.490308	−	1.07363i	0.979499	−	0.201448i	$-0.0645648\pi$
$152$		0			0
$153$	−35.6691	+	30.9074i	−0.233131	+	0.202009i
$154$		0			0
$155$	40.2671	+	62.6568i	0.259788	+	0.404237i
$156$		0			0
$157$	46.9851	−	73.1102i	0.299268	−	0.465670i	−0.658757	−	0.752356i	$-0.728917\pi$
$157$	46.9851	−	73.1102i	0.299268	−	0.465670i	0.958025	+	0.286686i	$0.0925536\pi$
$158$		0			0
$159$	20.3778	−	69.4005i	0.128162	−	0.436481i
$160$		0			0
$161$	115.653	+	50.3593i	0.718339	+	0.312791i
$162$		0			0
$163$	−149.584	−	43.9217i	−0.917691	−	0.269458i	−0.211416	−	0.977396i	$-0.567807\pi$
$163$	−149.584	−	43.9217i	−0.917691	−	0.269458i	−0.706275	+	0.707938i	$0.749626\pi$
$164$		0			0
$165$	−116.614	−	74.9435i	−0.706753	−	0.454203i
$166$		0			0
$167$	−216.593	+	139.196i	−1.29696	+	0.833507i	−0.992878	−	0.119138i	$-0.961987\pi$
$167$	−216.593	+	139.196i	−1.29696	+	0.833507i	−0.304085	+	0.952645i	$0.598351\pi$
$168$		0			0
$169$	109.576	+	126.458i	0.648381	+	0.748271i
$170$		0			0
$171$	−222.926	−	101.807i	−1.30366	−	0.595361i
$172$		0			0
$173$	−123.293	+	36.2020i	−0.712675	+	0.209260i	−0.617921	−	0.786240i	$-0.712025\pi$
$173$	−123.293	+	36.2020i	−0.712675	+	0.209260i	−0.0947545	+	0.995501i	$0.530207\pi$
$174$		0			0
$175$	−379.670	+	54.5883i	−2.16954	+	0.311933i
$176$		0			0
$177$	30.6094	+	67.0252i	0.172934	+	0.378674i
$178$		0			0
$179$	−8.29392	+	57.6855i	−0.0463348	+	0.322265i	0.953451	+	0.301549i	$0.0975037\pi$
$179$	−8.29392	+	57.6855i	−0.0463348	+	0.322265i	−0.999785	+	0.0207162i	$0.993405\pi$
$180$		0			0
$181$	−141.302	−	122.439i	−0.780673	−	0.676457i	0.170417	−	0.985372i	$-0.445489\pi$
$181$	−141.302	−	122.439i	−0.780673	−	0.676457i	−0.951090	+	0.308915i	$0.900034\pi$
$182$		0			0
$183$			3.97273i			0.0217089i
$184$		0			0
$185$	208.569			1.12740
$186$		0			0
$187$	51.8176	−	59.8007i	0.277100	−	0.319790i
$188$		0			0
$189$	99.0573	+	14.2423i	0.524113	+	0.0753561i
$190$		0			0
$191$	158.834	−	72.5373i	0.831594	−	0.379776i	0.0463215	−	0.998927i	$-0.485250\pi$
$191$	158.834	−	72.5373i	0.831594	−	0.379776i	0.785272	+	0.619150i	$0.212523\pi$
$192$		0			0
$193$	33.8920	+	235.724i	0.175606	+	1.22137i	0.866785	+	0.498683i	$0.166183\pi$
$193$	33.8920	+	235.724i	0.175606	+	1.22137i	−0.691178	+	0.722684i	$0.742908\pi$
$194$		0			0
$195$	−3.85034	−	13.1131i	−0.0197453	−	0.0672465i
$196$		0			0
$197$	−68.3206	+	149.601i	−0.346805	+	0.759397i	0.653193	+	0.757192i	$0.273429\pi$
$197$	−68.3206	+	149.601i	−0.346805	+	0.759397i	−0.999998	+	0.00220521i	$0.999298\pi$
$198$		0			0
$199$	129.980	−	112.628i	0.653165	−	0.565971i	−0.263978	−	0.964529i	$-0.585035\pi$
$199$	129.980	−	112.628i	0.653165	−	0.565971i	0.917143	+	0.398558i	$0.130489\pi$
$200$		0			0
$201$	7.90638	+	12.3026i	0.0393352	+	0.0612068i
$202$		0			0
$203$	−101.432	+	157.832i	−0.499666	+	0.777495i
$204$		0			0
$205$	168.077	−	572.417i	0.819887	−	2.79228i
$206$		0			0
$207$	115.409	−	138.058i	0.557530	−	0.666947i
$208$		0			0
$209$	394.231	+	115.757i	1.88627	+	0.553860i
$210$		0			0
$211$	−201.305	−	129.371i	−0.954052	−	0.613132i	−0.0317064	−	0.999497i	$-0.510094\pi$
$211$	−201.305	−	129.371i	−0.954052	−	0.613132i	−0.922346	+	0.386365i	$0.873731\pi$
$212$		0			0
$213$	41.0945	−	26.4098i	0.192932	−	0.123990i
$214$		0			0
$215$	107.373	+	123.915i	0.499410	+	0.576350i
$216$		0			0
$217$	38.1341	+	17.4153i	0.175733	+	0.0802546i
$218$		0			0
$219$	63.8188	−	18.7389i	0.291410	−	0.0855656i
$220$		0			0
$221$	7.72187	−	1.11024i	0.0349406	−	0.00502370i
$222$		0			0
$223$	−109.776	−	240.377i	−0.492271	−	1.07792i	−0.978905	−	0.204317i	$-0.934503\pi$
$223$	−109.776	−	240.377i	−0.492271	−	1.07792i	0.486634	−	0.873606i	$-0.338224\pi$
$224$		0			0
$225$	−77.8710	+	541.604i	−0.346093	+	2.40713i
$226$		0			0
$227$	−52.0480	−	45.0999i	−0.229286	−	0.198678i	0.532639	−	0.846342i	$-0.321200\pi$
$227$	−52.0480	−	45.0999i	−0.229286	−	0.198678i	−0.761925	+	0.647665i	$0.775746\pi$
$228$		0			0
$229$		−	39.8188i		−	0.173881i	−0.996214	−	0.0869405i	$-0.972291\pi$
$229$		−	39.8188i		−	0.173881i	0.996214	−	0.0869405i	$-0.0277090\pi$
$230$		0			0
$231$	−78.0246			−0.337769
$232$		0			0
$233$	−28.8433	+	33.2870i	−0.123791	+	0.142863i	−0.814262	−	0.580498i	$-0.802858\pi$
$233$	−28.8433	+	33.2870i	−0.123791	+	0.142863i	0.690471	+	0.723360i	$0.257403\pi$
$234$		0			0
$235$	386.982	+	55.6396i	1.64673	+	0.236764i
$236$		0			0
$237$	−16.5619	+	7.56355i	−0.0698813	+	0.0319137i
$238$		0			0
$239$	29.9181	+	208.085i	0.125180	+	0.870649i	0.951544	+	0.307512i	$0.0994966\pi$
$239$	29.9181	+	208.085i	0.125180	+	0.870649i	−0.826364	+	0.563137i	$0.809594\pi$
$240$		0			0
$241$	−93.0411	−	316.869i	−0.386063	−	1.31481i	−0.891921	−	0.452192i	$-0.850642\pi$
$241$	−93.0411	−	316.869i	−0.386063	−	1.31481i	0.505858	−	0.862617i	$-0.331176\pi$
$242$		0			0
$243$	91.0303	−	199.329i	0.374610	−	0.820282i
$244$		0			0
$245$	139.333	−	120.732i	0.568705	−	0.492785i
$246$		0			0
$247$	21.9006	+	34.0780i	0.0886663	+	0.137967i
$248$		0			0
$249$	65.0208	−	101.174i	0.261128	−	0.406323i
$250$		0			0
$251$	−119.193	+	405.934i	−0.474872	+	1.61727i	0.279032	+	0.960282i	$0.409987\pi$
$251$	−119.193	+	405.934i	−0.474872	+	1.61727i	−0.753904	+	0.656985i	$0.771832\pi$
$252$		0			0
$253$	−158.578	+	256.641i	−0.626790	+	1.01439i
$254$		0			0
$255$	61.1724	+	17.9618i	0.239892	+	0.0704386i
$256$		0			0
$257$	−213.072	−	136.933i	−0.829073	−	0.532813i	0.0559105	−	0.998436i	$-0.482194\pi$
$257$	−213.072	−	136.933i	−0.829073	−	0.532813i	−0.884983	+	0.465623i	$0.845830\pi$
$258$		0			0
$259$	98.7606	−	63.4696i	0.381315	−	0.245056i
$260$		0			0
$261$	175.264	+	202.265i	0.671508	+	0.774962i
$262$		0			0
$263$	132.210	+	60.3782i	0.502699	+	0.229575i	0.650591	−	0.759429i	$-0.274521\pi$
$263$	132.210	+	60.3782i	0.502699	+	0.229575i	−0.147891	+	0.989004i	$0.547249\pi$
$264$		0			0
$265$	623.451	−	183.062i	2.35265	−	0.690799i
$266$		0			0
$267$	−54.7744	+	7.87537i	−0.205148	+	0.0294958i
$268$		0			0
$269$	46.0007	+	100.727i	0.171006	+	0.374451i	0.975659	−	0.219295i	$-0.0703756\pi$
$269$	46.0007	+	100.727i	0.171006	+	0.374451i	−0.804652	+	0.593746i	$0.797648\pi$
$270$		0			0
$271$	−18.6757	+	129.892i	−0.0689141	+	0.479308i	0.925914	+	0.377734i	$0.123297\pi$
$271$	−18.6757	+	129.892i	−0.0689141	+	0.479308i	−0.994828	+	0.101573i	$0.967612\pi$
$272$		0			0
$273$	−5.81362	−	5.03753i	−0.0212953	−	0.0184525i
$274$		0			0
$275$		−	917.360i		−	3.33586i
$276$		0			0
$277$	−87.1222			−0.314520			−0.157260	−	0.987557i	$-0.550266\pi$
$277$	−87.1222			−0.314520			−0.157260	+	0.987557i	$0.550266\pi$
$278$		0			0
$279$	39.1627	−	45.1962i	0.140368	−	0.161993i
$280$		0			0
$281$	−362.793	−	52.1618i	−1.29108	−	0.185629i	−0.537656	−	0.843164i	$-0.680690\pi$
$281$	−362.793	−	52.1618i	−1.29108	−	0.185629i	−0.753424	+	0.657535i	$0.771599\pi$
$282$		0			0
$283$	−448.212	+	204.692i	−1.58379	+	0.723292i	−0.996300	−	0.0859397i	$-0.972611\pi$
$283$	−448.212	+	204.692i	−1.58379	+	0.723292i	−0.587489	+	0.809232i	$0.699883\pi$
$284$		0			0
$285$	47.1134	+	327.681i	0.165310	+	1.14976i
$286$		0			0
$287$	−94.6051	−	322.195i	−0.329634	−	1.12263i
$288$		0			0
$289$	104.937	−	229.779i	0.363103	−	0.795085i
$290$		0			0
$291$	−113.265	+	98.1443i	−0.389225	+	0.337266i
$292$		0			0
$293$	23.3005	+	36.2564i	0.0795241	+	0.123742i	0.878737	−	0.477306i	$-0.158387\pi$
$293$	23.3005	+	36.2564i	0.0795241	+	0.123742i	−0.799213	+	0.601048i	$0.794750\pi$
$294$		0			0
$295$	−357.867	+	556.852i	−1.21311	+	1.88763i
$296$		0			0
$297$	−67.4307	+	229.648i	−0.227039	+	0.773225i
$298$		0			0
$299$	−28.3852	+	8.88400i	−0.0949339	+	0.0297124i
$300$		0			0
$301$	88.5513	+	26.0010i	0.294190	+	0.0863821i
$302$		0			0
$303$	6.61119	+	4.24875i	0.0218191	+	0.0140223i
$304$		0			0
$305$	−30.0231	+	19.2947i	−0.0984365	+	0.0632613i
$306$		0			0
$307$	−343.003	−	395.847i	−1.11727	−	1.28940i	−0.952994	−	0.302988i	$-0.902016\pi$
$307$	−343.003	−	395.847i	−1.11727	−	1.28940i	−0.164279	−	0.986414i	$-0.552530\pi$
$308$		0			0
$309$	−157.095	−	71.7429i	−0.508398	−	0.232178i
$310$		0			0
$311$	−90.8754	+	26.6834i	−0.292204	+	0.0857988i	−0.424549	−	0.905405i	$-0.639567\pi$
$311$	−90.8754	+	26.6834i	−0.292204	+	0.0857988i	0.132345	+	0.991204i	$0.457749\pi$
$312$		0			0
$313$	−392.994	+	56.5040i	−1.25557	+	0.180524i	−0.737815	−	0.675003i	$-0.764142\pi$
$313$	−392.994	+	56.5040i	−1.25557	+	0.180524i	−0.517758	+	0.855527i	$0.673233\pi$
$314$		0			0
$315$	173.676	+	380.297i	0.551351	+	1.20729i
$316$		0			0
$317$	−20.7687	+	144.450i	−0.0655166	+	0.455678i	0.930484	+	0.366332i	$0.119387\pi$
$317$	−20.7687	+	144.450i	−0.0655166	+	0.455678i	−0.996001	+	0.0893455i	$0.971522\pi$
$318$		0			0
$319$	−339.106	−	293.837i	−1.06303	−	0.921120i
$320$		0			0
$321$			61.3670i			0.191175i
$322$		0			0
$323$	−188.972			−0.585053
$324$		0			0
$325$	59.2279	−	68.3527i	0.182240	−	0.210316i
$326$		0			0
$327$	−85.2991	−	12.2642i	−0.260854	−	0.0375051i
$328$		0			0
$329$	200.173	−	91.4161i	0.608429	−	0.277860i
$330$		0			0
$331$	12.8119	+	89.1086i	0.0387066	+	0.269210i	0.999980	−	0.00638766i	$-0.00203327\pi$
$331$	12.8119	+	89.1086i	0.0387066	+	0.269210i	−0.961273	+	0.275598i	$0.911124\pi$
$332$		0			0
$333$	−47.1813	−	160.685i	−0.141686	−	0.482537i
$334$		0			0
$335$	−54.5746	+	119.502i	−0.162909	+	0.356722i
$336$		0			0
$337$	321.002	−	278.150i	0.952528	−	0.825371i	−0.0321977	−	0.999482i	$-0.510251\pi$
$337$	321.002	−	278.150i	0.952528	−	0.825371i	0.984726	+	0.174111i	$0.0557052\pi$
$338$		0			0
$339$	90.6003	+	140.977i	0.267257	+	0.415861i
$340$		0			0
$341$	−54.2060	+	84.3462i	−0.158962	+	0.247349i
$342$		0			0
$343$	104.948	−	357.419i	0.305970	−	1.04204i
$344$		0			0
$345$	−241.172	−	30.3235i	−0.699049	−	0.0878941i
$346$		0			0
$347$	427.315	+	125.471i	1.23145	+	0.361588i	0.831798	−	0.555078i	$-0.187312\pi$
$347$	427.315	+	125.471i	1.23145	+	0.361588i	0.399656	+	0.916665i	$0.369130\pi$
$348$		0			0
$349$	427.647	+	274.832i	1.22535	+	0.787485i	0.983160	−	0.182744i	$-0.0584980\pi$
$349$	427.647	+	274.832i	1.22535	+	0.787485i	0.242190	+	0.970229i	$0.422134\pi$
$350$		0			0
$351$	−19.8511	+	12.7575i	−0.0565559	+	0.0363463i
$352$		0			0
$353$	1.68290	+	1.94217i	0.00476742	+	0.00550189i	0.758128	−	0.652105i	$-0.226114\pi$
$353$	1.68290	+	1.94217i	0.00476742	+	0.00550189i	−0.753361	+	0.657607i	$0.771569\pi$
$354$		0			0
$355$	399.174	+	182.297i	1.12443	+	0.513512i
$356$		0			0
$357$	34.4320	−	10.1101i	0.0964481	−	0.0283197i
$358$		0			0
$359$	−384.256	+	55.2477i	−1.07035	+	0.153893i	−0.654895	−	0.755720i	$-0.727287\pi$
$359$	−384.256	+	55.2477i	−1.07035	+	0.153893i	−0.415457	+	0.909613i	$0.636378\pi$
$360$		0			0
$361$	−257.660	−	564.197i	−0.713740	−	1.56287i
$362$		0			0
$363$	7.87912	−	54.8005i	0.0217056	−	0.150966i
$364$		0			0
$365$	451.569	+	391.287i	1.23718	+	1.07202i
$366$		0			0
$367$			533.350i			1.45327i	0.687024	+	0.726635i	$0.258917\pi$
$367$			533.350i			1.45327i	−0.687024	+	0.726635i	$0.741083\pi$
$368$		0			0
$369$	−479.020			−1.29816
$370$		0			0
$371$	239.506	−	276.404i	0.645568	−	0.745026i
$372$		0			0
$373$	4.46095	+	0.641388i	0.0119597	+	0.00171954i	0.148292	−	0.988944i	$-0.452622\pi$
$373$	4.46095	+	0.641388i	0.0119597	+	0.00171954i	−0.136332	+	0.990663i	$0.543532\pi$
$374$		0			0
$375$	432.012	−	197.293i	1.15203	−	0.526115i
$376$		0			0
$377$	−6.29572	−	43.7877i	−0.0166995	−	0.116148i
$378$		0			0
$379$	125.271	+	426.633i	0.330529	+	1.12568i	0.942335	+	0.334672i	$0.108625\pi$
$379$	125.271	+	426.633i	0.330529	+	1.12568i	−0.611805	+	0.791008i	$0.709556\pi$
$380$		0			0
$381$	36.0845	−	79.0140i	0.0947099	−	0.207386i
$382$		0			0
$383$	285.064	−	247.010i	0.744293	−	0.644934i	−0.197816	−	0.980239i	$-0.563385\pi$
$383$	285.064	−	247.010i	0.744293	−	0.644934i	0.942109	+	0.335305i	$0.108840\pi$
$384$		0			0
$385$	−378.949	−	589.656i	−0.984282	−	1.53157i
$386$		0			0
$387$	71.1767	−	110.753i	0.183919	−	0.286184i
$388$		0			0
$389$	−119.130	+	405.718i	−0.306246	+	1.04298i	0.652281	+	0.757977i	$0.273812\pi$
$389$	−119.130	+	405.718i	−0.306246	+	1.04298i	−0.958527	+	0.285001i	$0.908006\pi$
$390$		0			0
$391$	36.7253	−	133.803i	0.0939266	−	0.342206i
$392$		0			0
$393$	−181.372	−	53.2558i	−0.461507	−	0.135511i
$394$		0			0
$395$	−137.598	−	88.4286i	−0.348348	−	0.223870i
$396$		0			0
$397$	−264.755	+	170.147i	−0.666888	+	0.428583i	−0.829802	−	0.558057i	$-0.811547\pi$
$397$	−264.755	+	170.147i	−0.666888	+	0.428583i	0.162914	+	0.986640i	$0.447911\pi$
$398$		0			0
$399$	122.025	+	140.825i	0.305828	+	0.352944i
$400$		0			0
$401$	−378.168	−	172.704i	−0.943064	−	0.430683i	−0.116289	−	0.993215i	$-0.537100\pi$
$401$	−378.168	−	172.704i	−0.943064	−	0.430683i	−0.826775	+	0.562533i	$0.809827\pi$
$402$		0			0
$403$	−9.48457	+	2.78492i	−0.0235349	+	0.00691048i
$404$		0			0
$405$	488.209	−	70.1938i	1.20545	−	0.173318i
$406$		0			0
$407$	116.635	+	255.395i	0.286573	+	0.627507i
$408$		0			0
$409$	73.5327	−	511.431i	0.179787	−	1.25044i	−0.677469	−	0.735551i	$-0.736923\pi$
$409$	73.5327	−	511.431i	0.179787	−	1.25044i	0.857255	−	0.514891i	$-0.172168\pi$
$410$		0			0
$411$	55.5725	+	48.1539i	0.135213	+	0.117163i
$412$		0			0
$413$			372.580i			0.902130i
$414$		0			0
$415$	1080.40			2.60337
$416$		0			0
$417$	−112.142	+	129.419i	−0.268925	+	0.310356i
$418$		0			0
$419$	−25.3403	−	3.64339i	−0.0604782	−	0.00869545i	0.112009	−	0.993707i	$-0.464271\pi$
$419$	−25.3403	−	3.64339i	−0.0604782	−	0.00869545i	−0.172487	+	0.985012i	$0.555180\pi$
$420$		0			0
$421$	−72.3201	+	33.0275i	−0.171782	+	0.0784500i	−0.499450	−	0.866343i	$-0.666464\pi$
$421$	−72.3201	+	33.0275i	−0.171782	+	0.0784500i	0.327668	+	0.944793i	$0.393737\pi$
$422$		0			0
$423$	−44.6752	−	310.723i	−0.105615	−	0.734569i
$424$		0			0
$425$	118.868	+	404.828i	0.279690	+	0.952537i
$426$		0			0
$427$	−8.34484	+	18.2726i	−0.0195429	+	0.0427931i
$428$		0			0
$429$	13.9039	−	12.0478i	0.0324101	−	0.0280835i
$430$		0			0
$431$	300.432	+	467.481i	0.697058	+	1.08464i	0.991642	+	0.129018i	$0.0411825\pi$
$431$	300.432	+	467.481i	0.697058	+	1.08464i	−0.294584	+	0.955626i	$0.595181\pi$
$432$		0			0
$433$	91.2867	−	142.045i	0.210824	−	0.328048i	−0.719696	−	0.694289i	$-0.755719\pi$
$433$	91.2867	−	142.045i	0.210824	−	0.328048i	0.930520	+	0.366241i	$0.119355\pi$
$434$		0			0
$435$	101.854	−	346.884i	0.234148	−	0.797435i
$436$		0			0
$437$	711.210	−	115.156i	1.62748	−	0.263514i
$438$		0			0
$439$	−369.745	−	108.567i	−0.842243	−	0.247305i	−0.167975	−	0.985791i	$-0.553723\pi$
$439$	−369.745	−	108.567i	−0.842243	−	0.247305i	−0.674268	+	0.738486i	$0.735541\pi$
$440$		0			0
$441$	−124.533	−	80.0325i	−0.282388	−	0.181480i
$442$		0			0
$443$	449.845	−	289.098i	1.01545	−	0.652592i	0.0766537	−	0.997058i	$-0.475576\pi$
$443$	449.845	−	289.098i	1.01545	−	0.652592i	0.938799	+	0.344466i	$0.111940\pi$
$444$		0			0
$445$	−325.544	−	375.698i	−0.731560	−	0.844265i
$446$		0			0
$447$	−120.863	−	55.1962i	−0.270387	−	0.123481i
$448$		0			0
$449$	−281.535	+	82.6663i	−0.627028	+	0.184112i	−0.579782	−	0.814771i	$-0.696862\pi$
$449$	−281.535	+	82.6663i	−0.627028	+	0.184112i	−0.0472453	+	0.998883i	$0.515044\pi$
$450$		0			0
$451$	794.923	−	114.293i	1.76258	−	0.253421i
$452$		0			0
$453$	80.3024	+	175.838i	0.177268	+	0.388163i
$454$		0			0
$455$	9.83466	−	68.4015i	0.0216146	−	0.150333i
$456$		0			0
$457$	283.148	+	245.350i	0.619581	+	0.536870i	0.907105	−	0.420903i	$-0.138287\pi$
$457$	283.148	+	245.350i	0.619581	+	0.536870i	−0.287525	+	0.957773i	$0.592832\pi$
$458$		0			0
$459$		−	110.080i		−	0.239826i
$460$		0			0
$461$	−245.044			−0.531549			−0.265774	−	0.964035i	$-0.585628\pi$
$461$	−245.044			−0.531549			−0.265774	+	0.964035i	$0.585628\pi$
$462$		0			0
$463$	−255.131	+	294.437i	−0.551039	+	0.635933i	−0.961125	−	0.276114i	$-0.910953\pi$
$463$	−255.131	+	294.437i	−0.551039	+	0.635933i	0.410086	+	0.912047i	$0.365499\pi$
$464$		0			0
$465$	−79.9614	−	11.4967i	−0.171960	−	0.0247241i
$466$		0			0
$467$	−592.416	+	270.547i	−1.26856	+	0.579330i	−0.932043	−	0.362348i	$-0.881975\pi$
$467$	−592.416	+	270.547i	−1.26856	+	0.579330i	−0.336514	+	0.941679i	$0.609248\pi$
$468$		0			0
$469$	10.5236	+	73.1934i	0.0224384	+	0.156063i
$470$		0			0
$471$	26.5565	+	90.4431i	0.0563832	+	0.192024i
$472$		0			0
$473$	−91.6908	+	200.775i	−0.193850	+	0.424471i
$474$		0			0
$475$	−1655.72	+	1434.69i	−3.48573	+	3.02040i
$476$		0			0
$477$	−282.067	−	438.905i	−0.591335	−	0.920135i
$478$		0			0
$479$	418.447	−	651.117i	0.873585	−	1.35933i	−0.0589552	−	0.998261i	$-0.518777\pi$
$479$	418.447	−	651.117i	0.873585	−	1.35933i	0.932541	−	0.361065i	$-0.117587\pi$
$480$		0			0
$481$	−7.79869	+	26.5599i	−0.0162135	+	0.0552181i
$482$		0			0
$483$	−123.426	+	59.0323i	−0.255541	+	0.122220i
$484$		0			0
$485$	−1291.81	−	379.309i	−2.66352	−	0.782080i
$486$		0			0
$487$	145.125	+	93.2661i	0.297998	+	0.191511i	0.681092	−	0.732198i	$-0.261505\pi$
$487$	145.125	+	93.2661i	0.297998	+	0.191511i	−0.383095	+	0.923709i	$0.625142\pi$
$488$		0			0
$489$	142.250	−	91.4184i	0.290899	−	0.186950i
$490$		0			0
$491$	166.334	+	191.960i	0.338766	+	0.390957i	0.899414	−	0.437097i	$-0.143994\pi$
$491$	166.334	+	191.960i	0.338766	+	0.390957i	−0.560648	+	0.828054i	$0.689448\pi$
$492$		0			0
$493$	187.721	+	85.7292i	0.380772	+	0.173893i
$494$		0			0
$495$	−959.377	+	281.699i	−1.93814	+	0.569088i
$496$		0			0
$497$	244.489	−	35.1523i	0.491930	−	0.0707289i
$498$		0			0
$499$	−3.97095	−	8.69516i	−0.00795781	−	0.0174252i	0.905611	−	0.424109i	$-0.139412\pi$
$499$	−3.97095	−	8.69516i	−0.00795781	−	0.0174252i	−0.913569	+	0.406683i	$0.866685\pi$
$500$		0			0
$501$	39.7420	−	276.412i	0.0793254	−	0.551720i
$502$		0			0
$503$	−289.603	−	250.942i	−0.575752	−	0.498892i	0.317615	−	0.948220i	$-0.397118\pi$
$503$	−289.603	−	250.942i	−0.575752	−	0.498892i	−0.893367	+	0.449328i	$0.851663\pi$
$504$		0			0
$505$			70.5981i			0.139798i
$506$		0			0
$507$	−181.489			−0.357966
$508$		0			0
$509$	−94.8920	+	109.511i	−0.186428	+	0.215150i	−0.841268	−	0.540618i	$-0.818191\pi$
$509$	−94.8920	+	109.511i	−0.186428	+	0.215150i	0.654840	+	0.755767i	$0.272736\pi$
$510$		0			0
$511$	332.897	+	47.8634i	0.651462	+	0.0936661i
$512$		0			0
$513$	519.943	−	237.450i	1.01353	−	0.462866i
$514$		0			0
$515$	−220.794	−	1535.66i	−0.428726	−	2.98186i
$516$		0			0
$517$	148.275	+	504.979i	0.286799	+	0.976748i
$518$		0			0
$519$	57.8976	−	126.778i	0.111556	−	0.244274i
$520$		0			0
$521$	−85.0830	+	73.7249i	−0.163307	+	0.141506i	−0.732681	−	0.680572i	$-0.761731\pi$
$521$	−85.0830	+	73.7249i	−0.163307	+	0.141506i	0.569374	+	0.822079i	$0.307186\pi$
$522$		0			0
$523$	223.828	+	348.283i	0.427969	+	0.665932i	0.986539	−	0.163525i	$-0.0522864\pi$
$523$	223.828	+	348.283i	0.427969	+	0.665932i	−0.558571	+	0.829457i	$0.688650\pi$
$524$		0			0
$525$	224.926	−	349.992i	0.428431	−	0.666652i
$526$		0			0
$527$	12.9916	−	44.2455i	0.0246521	−	0.0839573i
$528$		0			0
$529$	−56.6818	+	525.955i	−0.107149	+	0.994243i
$530$		0			0
$531$	509.961	+	149.738i	0.960378	+	0.281993i
$532$		0			0
$533$	66.6089	+	42.8070i	0.124970	+	0.0803132i
$534$		0			0
$535$	−463.769	+	298.047i	−0.866859	+	0.557096i
$536$		0			0
$537$	−41.3944	−	47.7716i	−0.0770845	−	0.0889602i
$538$		0			0
$539$	225.755	+	103.099i	0.418841	+	0.191278i
$540$		0			0
$541$	−211.401	+	62.0730i	−0.390760	+	0.114737i	−0.471210	−	0.882021i	$-0.656183\pi$
$541$	−211.401	+	62.0730i	−0.390760	+	0.114737i	0.0804498	+	0.996759i	$0.474364\pi$
$542$		0			0
$543$	200.728	−	28.8604i	0.369666	−	0.0531499i
$544$		0			0
$545$	−321.596	−	704.196i	−0.590083	−	1.29210i
$546$		0			0
$547$	106.135	−	738.184i	0.194031	−	1.34951i	−0.627173	−	0.778880i	$-0.715788\pi$
$547$	106.135	−	738.184i	0.194031	−	1.34951i	0.821204	−	0.570634i	$-0.193303\pi$
$548$		0			0
$549$	21.6566	+	18.7655i	0.0394473	+	0.0341813i
$550$		0			0
$551$			1071.59i			1.94480i
$552$		0			0
$553$	−92.0641			−0.166481
$554$		0			0
$555$	−148.143	+	170.966i	−0.266925	+	0.308047i
$556$		0			0
$557$	39.2228	+	5.63938i	0.0704179	+	0.0101246i	0.177434	−	0.984133i	$-0.443220\pi$
$557$	39.2228	+	5.63938i	0.0704179	+	0.0101246i	−0.107016	+	0.994257i	$0.534130\pi$
$558$		0			0
$559$	−19.7946	+	9.03990i	−0.0354108	+	0.0161715i
$560$		0			0
$561$	12.2141	+	84.9509i	0.0217720	+	0.151428i
$562$		0			0
$563$	138.220	+	470.734i	0.245506	+	0.836117i	0.986381	+	0.164474i	$0.0525928\pi$
$563$	138.220	+	470.734i	0.245506	+	0.836117i	−0.740875	+	0.671643i	$0.765589\pi$
$564$		0			0
$565$	−625.379	+	1369.39i	−1.10686	+	2.42370i
$566$		0			0
$567$	209.813	−	181.804i	0.370041	−	0.320642i
$568$		0			0
$569$	−200.604	−	312.146i	−0.352555	−	0.548586i	0.619003	−	0.785389i	$-0.287537\pi$
$569$	−200.604	−	312.146i	−0.352555	−	0.548586i	−0.971558	+	0.236803i	$0.923901\pi$
$570$		0			0
$571$	127.635	−	198.603i	0.223528	−	0.347817i	−0.711318	−	0.702871i	$-0.751901\pi$
$571$	127.635	−	198.603i	0.223528	−	0.347817i	0.934846	+	0.355054i	$0.115538\pi$
$572$		0			0
$573$	−53.3579	+	181.720i	−0.0931202	+	0.317138i
$574$		0			0
$575$	−694.062	−	1451.16i	−1.20706	−	2.52376i
$576$		0			0
$577$	−3.75169	−	1.10160i	−0.00650207	−	0.00190918i	0.278480	−	0.960442i	$-0.410169\pi$
$577$	−3.75169	−	1.10160i	−0.00650207	−	0.00190918i	−0.284982	+	0.958533i	$0.591988\pi$
$578$		0			0
$579$	−217.298	−	139.649i	−0.375299	−	0.241190i
$580$		0			0
$581$	511.584	−	328.775i	0.880524	−	0.565878i
$582$		0			0
$583$	572.805	+	661.052i	0.982513	+	1.13388i
$584$		0			0
$585$	−89.6707	−	40.9513i	−0.153283	−	0.0700021i
$586$		0			0
$587$	161.624	−	47.4572i	0.275340	−	0.0808471i	−0.141148	−	0.989989i	$-0.545079\pi$
$587$	161.624	−	47.4572i	0.275340	−	0.0808471i	0.416487	+	0.909142i	$0.363261\pi$
$588$		0			0
$589$	237.009	−	34.0767i	0.402392	−	0.0578553i
$590$		0			0
$591$	−74.1027	−	162.262i	−0.125385	−	0.274555i
$592$		0			0
$593$	33.6439	−	233.999i	0.0567351	−	0.394601i	−0.941591	−	0.336760i	$-0.890669\pi$
$593$	33.6439	−	233.999i	0.0567351	−	0.394601i	0.998326	−	0.0578417i	$-0.0184219\pi$
$594$		0			0
$595$	243.634	+	211.110i	0.409469	+	0.354807i
$596$		0			0
$597$			186.544i			0.312468i
$598$		0			0
$599$	−156.510			−0.261285			−0.130643	−	0.991430i	$-0.541704\pi$
$599$	−156.510			−0.261285			−0.130643	+	0.991430i	$0.541704\pi$
$600$		0			0
$601$	16.6631	−	19.2302i	0.0277256	−	0.0319970i	−0.741717	−	0.670712i	$-0.765988\pi$
$601$	16.6631	−	19.2302i	0.0277256	−	0.0319970i	0.769443	+	0.638715i	$0.220534\pi$
$602$		0			0
$603$	104.411	+	15.0121i	0.173153	+	0.0248957i
$604$		0			0
$605$	452.411	−	206.609i	0.747788	−	0.341503i
$606$		0			0
$607$	−0.153618	−	1.06844i	−0.000253077	−	0.00176019i	0.989695	−	0.143195i	$-0.0457376\pi$
$607$	−0.153618	−	1.06844i	−0.000253077	−	0.00176019i	−0.989948	+	0.141435i	$0.954828\pi$
$608$		0			0
$609$	−57.3306	−	195.250i	−0.0941389	−	0.320608i
$610$		0			0
$611$	−21.5551	+	47.1992i	−0.0352785	+	0.0772490i
$612$		0			0
$613$	817.788	−	708.617i	1.33408	−	1.15598i	0.359192	−	0.933264i	$-0.383052\pi$
$613$	817.788	−	708.617i	1.33408	−	1.15598i	0.974883	−	0.222719i	$-0.0714933\pi$
$614$		0			0
$615$	349.834	+	544.353i	0.568836	+	0.885126i
$616$		0			0
$617$	304.084	−	473.165i	0.492843	−	0.766879i	−0.502365	−	0.864656i	$-0.667537\pi$
$617$	304.084	−	473.165i	0.492843	−	0.766879i	0.995208	+	0.0977763i	$0.0311730\pi$
$618$		0			0
$619$	−1.25984	+	4.29062i	−0.00203528	+	0.00693154i	−0.960504	−	0.278265i	$-0.910241\pi$
$619$	−1.25984	+	4.29062i	−0.00203528	+	0.00693154i	0.958469	+	0.285196i	$0.0920589\pi$
$620$		0			0
$621$	67.0805	+	414.294i	0.108020	+	0.667141i
$622$		0			0
$623$	−268.478	−	78.8323i	−0.430944	−	0.126537i
$624$		0			0
$625$	2118.28	+	1361.33i	3.38925	+	2.17814i
$626$		0			0
$627$	−374.903	+	240.935i	−0.597931	+	0.384267i
$628$		0			0
$629$	−84.5639	−	97.5920i	−0.134442	−	0.155154i
$630$		0			0
$631$	1086.25	+	496.073i	1.72147	+	0.786170i	0.995101	+	0.0988668i	$0.0315218\pi$
$631$	1086.25	+	496.073i	1.72147	+	0.786170i	0.726371	+	0.687303i	$0.241205\pi$
$632$		0			0
$633$	249.030	−	73.1219i	0.393413	−	0.115516i
$634$		0			0
$635$	772.387	−	111.053i	1.21636	−	0.174886i
$636$		0			0
$637$	10.1646	+	22.2575i	0.0159570	+	0.0349411i
$638$		0			0
$639$	50.1452	−	348.767i	0.0784745	−	0.545802i
$640$		0			0
$641$	−392.038	−	339.703i	−0.611604	−	0.529958i	0.293054	−	0.956096i	$-0.405328\pi$
$641$	−392.038	−	339.703i	−0.611604	−	0.529958i	−0.904658	+	0.426138i	$0.859874\pi$
$642$		0			0
$643$		−	589.547i		−	0.916870i	−0.888728	−	0.458435i	$-0.848410\pi$
$643$		−	589.547i		−	0.916870i	0.888728	−	0.458435i	$-0.151590\pi$
$644$		0			0
$645$	−177.840			−0.275721
$646$		0			0
$647$	−126.868	+	146.413i	−0.196086	+	0.226295i	−0.845275	−	0.534332i	$-0.820563\pi$
$647$	−126.868	+	146.413i	−0.196086	+	0.226295i	0.649189	+	0.760627i	$0.275109\pi$
$648$		0			0
$649$	−881.996	−	126.812i	−1.35901	−	0.195396i
$650$		0			0
$651$	−41.3615	+	18.8891i	−0.0635353	+	0.0290156i
$652$		0			0
$653$	−44.6845	−	310.787i	−0.0684295	−	0.475938i	−0.995005	−	0.0998281i	$-0.968171\pi$
$653$	−44.6845	−	310.787i	−0.0684295	−	0.475938i	0.926575	−	0.376110i	$-0.122738\pi$
$654$		0			0
$655$	−478.417	−	1629.34i	−0.730408	−	2.48754i
$656$		0			0
$657$	199.302	−	436.410i	0.303351	−	0.664247i
$658$		0			0
$659$	−344.770	+	298.744i	−0.523171	+	0.453330i	−0.875968	−	0.482370i	$-0.839776\pi$
$659$	−344.770	+	298.744i	−0.523171	+	0.453330i	0.352797	+	0.935700i	$0.385231\pi$
$660$		0			0
$661$	−224.445	−	349.243i	−0.339553	−	0.528355i	0.628921	−	0.777469i	$-0.283497\pi$
$661$	−224.445	−	349.243i	−0.339553	−	0.528355i	−0.968474	+	0.249114i	$0.919860\pi$
$662$		0			0
$663$	−4.57464	+	7.11828i	−0.00689991	+	0.0107365i
$664$		0			0
$665$	−471.605	+	1606.14i	−0.709180	+	2.41524i
$666$		0			0
$667$	−758.741	−	208.255i	−1.13754	−	0.312226i
$668$		0			0
$669$	275.012	+	80.7507i	0.411079	+	0.120704i
$670$		0			0
$671$	−40.4160	−	25.9738i	−0.0602325	−	0.0387091i
$672$		0			0
$673$	707.819	−	454.887i	1.05174	−	0.675910i	0.103874	−	0.994590i	$-0.466876\pi$
$673$	707.819	−	454.887i	1.05174	−	0.675910i	0.947862	+	0.318681i	$0.103240\pi$
$674$		0			0
$675$	−835.737	−	964.492i	−1.23813	−	1.42888i
$676$		0			0
$677$	1088.90	+	497.286i	1.60843	+	0.734544i	0.998329	−	0.0577829i	$-0.0184031\pi$
$677$	1088.90	+	497.286i	1.60843	+	0.734544i	0.610097	+	0.792327i	$0.291130\pi$
$678$		0			0
$679$	−727.117	+	213.501i	−1.07086	+	0.314434i
$680$		0			0
$681$	73.9376	−	10.6306i	0.108572	−	0.0156103i
$682$		0			0
$683$	518.548	+	1135.46i	0.759221	+	1.66246i	0.749050	+	0.662514i	$0.230510\pi$
$683$	518.548	+	1135.46i	0.759221	+	1.66246i	0.0101711	+	0.999948i	$0.496762\pi$
$684$		0			0
$685$	−94.0096	+	653.851i	−0.137240	+	0.954528i
$686$		0			0
$687$	32.6398	+	28.2826i	0.0475107	+	0.0411682i
$688$		0			0
$689$			86.2373i			0.125163i
$690$		0			0
$691$	−276.558			−0.400229			−0.200114	−	0.979773i	$-0.564131\pi$
$691$	−276.558			−0.400229			−0.200114	+	0.979773i	$0.564131\pi$
$692$		0			0
$693$	−368.556	+	425.336i	−0.531826	+	0.613760i
$694$		0			0
$695$	−1522.70	−	218.932i	−2.19094	−	0.315010i
$696$		0			0
$697$	−335.987	+	153.440i	−0.482047	+	0.220144i
$698$		0			0
$699$	−6.79875	−	47.2864i	−0.00972640	−	0.0676486i
$700$		0			0
$701$	9.28316	+	31.6155i	0.0132427	+	0.0451006i	0.965849	−	0.259104i	$-0.0834274\pi$
$701$	9.28316	+	31.6155i	0.0132427	+	0.0451006i	−0.952607	+	0.304205i	$0.901609\pi$
$702$		0			0
$703$	278.547	−	609.934i	0.396227	−	0.867615i
$704$		0			0
$705$	−320.475	+	277.693i	−0.454575	+	0.393891i
$706$		0			0
$707$	21.4837	+	33.4292i	0.0303871	+	0.0472832i
$708$		0			0
$709$	−523.286	+	814.249i	−0.738062	+	1.14845i	0.245766	+	0.969329i	$0.420961\pi$
$709$	−523.286	+	814.249i	−0.738062	+	1.14845i	−0.983828	+	0.179118i	$0.942676\pi$
$710$		0			0
$711$	−37.0001	+	126.011i	−0.0520396	+	0.177230i
$712$		0			0
$713$	−21.9327	+	174.438i	−0.0307612	+	0.244653i
$714$		0			0
$715$	158.577	+	46.5626i	0.221787	+	0.0651225i
$716$		0			0
$717$	−191.820	−	123.275i	−0.267531	−	0.171932i
$718$		0			0
$719$	205.244	−	131.902i	0.285457	−	0.183452i	−0.390074	−	0.920783i	$-0.627551\pi$
$719$	205.244	−	131.902i	0.285457	−	0.183452i	0.675531	+	0.737331i	$0.263914\pi$
$720$		0			0
$721$	−571.864	−	659.966i	−0.793153	−	0.915348i
$722$		0			0
$723$	325.826	+	148.800i	0.450659	+	0.205809i
$724$		0			0
$725$	2295.62	−	674.055i	3.16637	−	0.929731i
$726$		0			0
$727$	−67.6966	+	9.73330i	−0.0931178	+	0.0133883i	−0.188716	−	0.982032i	$-0.560433\pi$
$727$	−67.6966	+	9.73330i	−0.0931178	+	0.0133883i	0.0955984	+	0.995420i	$0.469524\pi$
$728$		0			0
$729$	−90.5220	−	198.216i	−0.124173	−	0.271901i
$730$		0			0
$731$	14.4472	−	100.482i	0.0197636	−	0.137459i
$732$		0			0
$733$	255.484	+	221.378i	0.348546	+	0.302017i	0.811485	−	0.584373i	$-0.198660\pi$
$733$	255.484	+	221.378i	0.348546	+	0.302017i	−0.462939	+	0.886390i	$0.653205\pi$
$734$		0			0
$735$			199.967i			0.272063i
$736$		0			0
$737$	−176.850			−0.239960
$738$		0			0
$739$	−817.589	+	943.548i	−1.10635	+	1.27679i	−0.148687	+	0.988884i	$0.547505\pi$
$739$	−817.589	+	943.548i	−1.10635	+	1.27679i	−0.957659	+	0.287906i	$0.907041\pi$
$740$		0			0
$741$	−43.4897	−	6.25287i	−0.0586905	−	0.00843842i
$742$		0			0
$743$	796.172	−	363.599i	1.07156	−	0.489367i	0.200074	−	0.979781i	$-0.435882\pi$
$743$	796.172	−	363.599i	1.07156	−	0.489367i	0.871490	+	0.490414i	$0.163154\pi$
$744$		0			0
$745$	−169.870	−	1181.47i	−0.228014	−	1.58587i
$746$		0			0
$747$	−244.401	−	832.354i	−0.327177	−	1.11426i
$748$		0			0
$749$	−128.903	+	282.259i	−0.172100	+	0.376848i
$750$		0			0
$751$	−3.74018	+	3.24089i	−0.00498027	+	0.00431543i	−0.657347	−	0.753588i	$-0.728322\pi$
$751$	−3.74018	+	3.24089i	−0.00498027	+	0.00431543i	0.652367	+	0.757903i	$0.273776\pi$
$752$		0			0
$753$	−248.087	−	386.032i	−0.329465	−	0.512658i
$754$		0			0
$755$	−938.848	+	1460.88i	−1.24351	+	1.93494i
$756$		0			0
$757$	−289.651	+	986.461i	−0.382630	+	1.30312i	0.513026	+	0.858373i	$0.328524\pi$
$757$	−289.651	+	986.461i	−0.382630	+	1.30312i	−0.895657	+	0.444746i	$0.853294\pi$
$758$		0			0
$759$	−97.7358	−	312.275i	−0.128769	−	0.411430i
$760$		0			0
$761$	119.024	+	34.9486i	0.156405	+	0.0459246i	0.358998	−	0.933338i	$-0.383119\pi$
$761$	119.024	+	34.9486i	0.156405	+	0.0459246i	−0.202593	+	0.979263i	$0.564937\pi$
$762$		0			0
$763$	−366.574	−	235.583i	−0.480437	−	0.308758i
$764$		0			0
$765$	386.868	−	248.625i	0.505710	−	0.325000i
$766$		0			0
$767$	−57.5302	−	66.3934i	−0.0750068	−	0.0865625i
$768$		0			0
$769$	−464.642	−	212.195i	−0.604216	−	0.275936i	0.0897268	−	0.995966i	$-0.471401\pi$
$769$	−464.642	−	212.195i	−0.604216	−	0.275936i	−0.693943	+	0.720030i	$0.744128\pi$
$770$		0			0
$771$	263.586	−	77.3960i	0.341876	−	0.100384i
$772$		0			0
$773$	228.610	−	32.8692i	0.295744	−	0.0425216i	0.00715434	−	0.999974i	$-0.497723\pi$
$773$	228.610	−	32.8692i	0.295744	−	0.0425216i	0.288590	+	0.957453i	$0.406814\pi$
$774$		0			0
$775$	−222.086	−	486.300i	−0.286562	−	0.627484i
$776$		0			0
$777$	−18.1213	+	126.036i	−0.0233221	+	0.162209i
$778$		0			0
$779$	−1449.49	−	1255.99i	−1.86071	−	1.61231i
$780$		0			0
$781$			590.737i			0.756385i
$782$		0			0
$783$	−624.221			−0.797218
$784$		0			0
$785$	−554.527	+	639.958i	−0.706404	+	0.815234i
$786$		0			0
$787$	1117.11	+	160.616i	1.41946	+	0.204087i	0.808928	−	0.587908i	$-0.200048\pi$
$787$	1117.11	+	160.616i	1.41946	+	0.204087i	0.610528	+	0.791995i	$0.290957\pi$
$788$		0			0
$789$	−143.399	+	65.4882i	−0.181748	+	0.0830015i
$790$		0			0
$791$	120.592	+	838.734i	0.152455	+	1.06035i
$792$		0			0
$793$	−1.33445	−	4.54471i	−0.00168278	−	0.00573103i
$794$		0			0
$795$	−292.769	+	641.075i	−0.368263	+	0.806384i
$796$		0			0
$797$	166.097	−	143.924i	0.208403	−	0.180582i	−0.544405	−	0.838823i	$-0.683244\pi$
$797$	166.097	−	143.924i	0.208403	−	0.180582i	0.752808	+	0.658241i	$0.228699\pi$
$798$		0			0
$799$	−130.867	−	203.632i	−0.163788	−	0.254859i
$800$		0			0
$801$	−215.800	+	335.792i	−0.269414	+	0.419216i
$802$		0			0
$803$	−226.611	+	771.766i	−0.282205	+	0.961103i
$804$		0			0
$805$	−1045.58	−	646.062i	−1.29886	−	0.802562i
$806$		0			0
$807$	−115.241	−	33.8377i	−0.142801	−	0.0419303i
$808$		0			0
$809$	−834.474	−	536.284i	−1.03149	−	0.662898i	−0.0886213	−	0.996065i	$-0.528246\pi$
$809$	−834.474	−	536.284i	−1.03149	−	0.662898i	−0.942868	+	0.333168i	$0.891882\pi$
$810$		0			0
$811$	890.044	−	571.996i	1.09746	−	0.705298i	0.138938	−	0.990301i	$-0.455631\pi$
$811$	890.044	−	571.996i	1.09746	−	0.705298i	0.958526	+	0.285004i	$0.0919948\pi$
$812$		0			0
$813$	−93.2091	−	107.569i	−0.114648	−	0.132311i
$814$		0			0
$815$	1381.75	+	631.025i	1.69540	+	0.774264i
$816$		0			0
$817$	505.772	−	148.508i	0.619060	−	0.181773i
$818$		0			0
$819$	−54.9223	+	7.89663i	−0.0670601	+	0.00964179i
$820$		0			0
$821$	−594.946	−	1302.75i	−0.724661	−	1.58679i	−0.807255	−	0.590202i	$-0.799048\pi$
$821$	−594.946	−	1302.75i	−0.724661	−	1.58679i	0.0825949	−	0.996583i	$-0.473679\pi$
$822$		0			0
$823$	−170.052	+	1182.74i	−0.206625	+	1.43710i	0.577444	+	0.816430i	$0.304050\pi$
$823$	−170.052	+	1182.74i	−0.206625	+	1.43710i	−0.784068	+	0.620675i	$0.786859\pi$
$824$		0			0
$825$	751.970	+	651.586i	0.911479	+	0.789801i
$826$		0			0
$827$		−	224.413i		−	0.271357i	−0.990753	−	0.135679i	$-0.956679\pi$
$827$		−	224.413i		−	0.271357i	0.990753	−	0.135679i	$-0.0433215\pi$
$828$		0			0
$829$	−808.176			−0.974881			−0.487440	−	0.873156i	$-0.662069\pi$
$829$	−808.176			−0.974881			−0.487440	+	0.873156i	$0.662069\pi$
$830$		0			0
$831$	61.8814	−	71.4149i	0.0744662	−	0.0859386i
$832$		0			0
$833$	−112.984	−	16.2447i	−0.135635	−	0.0195014i
$834$		0			0
$835$	2281.95	−	1042.13i	2.73287	−	1.24806i
$836$		0			0
$837$	19.8504	+	138.063i	0.0237161	+	0.164949i
$838$		0			0
$839$	233.691	+	795.877i	0.278535	+	0.948602i	0.973333	+	0.229397i	$0.0736755\pi$
$839$	233.691	+	795.877i	0.278535	+	0.948602i	−0.694798	+	0.719205i	$0.744506\pi$
$840$		0			0
$841$	136.772	−	299.489i	0.162630	−	0.356111i
$842$		0			0
$843$	300.444	−	260.336i	0.356398	−	0.308821i
$844$		0			0
$845$	−881.453	−	1371.57i	−1.04314	−	1.62316i
$846$		0			0
$847$	151.350	−	235.506i	0.178690	−	0.278047i
$848$		0			0
$849$	150.570	−	512.793i	0.177350	−	0.603997i
$850$		0			0
$851$	377.732	+	315.763i	0.443869	+	0.371049i
$852$		0			0
$853$	419.396	+	123.146i	0.491672	+	0.144368i	0.518164	−	0.855281i	$-0.326616\pi$
$853$	419.396	+	123.146i	0.491672	+	0.144368i	−0.0264925	+	0.999649i	$0.508434\pi$
$854$		0			0
$855$	2008.83	+	1291.00i	2.34951	+	1.50994i
$856$		0			0
$857$	−461.799	+	296.780i	−0.538856	+	0.346301i	−0.781591	−	0.623791i	$-0.785592\pi$
$857$	−461.799	+	296.780i	−0.538856	+	0.346301i	0.242736	+	0.970092i	$0.421955\pi$
$858$		0			0
$859$	−614.654	−	709.349i	−0.715547	−	0.825785i	0.275218	−	0.961382i	$-0.411250\pi$
$859$	−614.654	−	709.349i	−0.715547	−	0.825785i	−0.990764	+	0.135597i	$0.956705\pi$
$860$		0			0
$861$	331.303	+	151.301i	0.384789	+	0.175727i
$862$		0			0
$863$	−396.306	+	116.366i	−0.459219	+	0.134839i	−0.503156	−	0.864196i	$-0.667828\pi$
$863$	−396.306	+	116.366i	−0.459219	+	0.134839i	0.0439375	+	0.999034i	$0.486010\pi$
$864$		0			0
$865$	1239.30	−	178.184i	1.43271	−	0.205993i
$866$		0			0
$867$	113.818	+	249.226i	0.131278	+	0.287458i
$868$		0			0
$869$	31.3351	−	217.940i	0.0360588	−	0.250795i
$870$		0			0
$871$	−13.1771	−	11.4181i	−0.0151288	−	0.0131091i
$872$		0			0
$873$			1081.03i			1.23830i
$874$		0			0
$875$	2401.46			2.74453
$876$		0			0
$877$	−767.799	+	886.087i	−0.875483	+	1.01036i	0.124352	+	0.992238i	$0.460315\pi$
$877$	−767.799	+	886.087i	−0.875483	+	1.01036i	−0.999836	+	0.0181235i	$0.994231\pi$
$878$		0			0
$879$	−46.2697	−	6.65258i	−0.0526390	−	0.00756835i
$880$		0			0
$881$	−32.3562	+	14.7766i	−0.0367267	+	0.0167725i	−0.433694	−	0.901060i	$-0.642790\pi$
$881$	−32.3562	+	14.7766i	−0.0367267	+	0.0167725i	0.396967	+	0.917833i	$0.370063\pi$
$882$		0			0
$883$	−68.1316	−	473.866i	−0.0771592	−	0.536654i	−0.991337	−	0.131341i	$-0.958072\pi$
$883$	−68.1316	−	473.866i	−0.0771592	−	0.536654i	0.914178	−	0.405313i	$-0.132837\pi$
$884$		0			0
$885$	−202.270	−	688.869i	−0.228554	−	0.778383i
$886$		0			0
$887$	324.788	−	711.186i	0.366165	−	0.801788i	−0.633443	−	0.773789i	$-0.718359\pi$
$887$	324.788	−	711.186i	0.366165	−	0.801788i	0.999608	−	0.0279994i	$-0.00891367\pi$
$888$		0			0
$889$	331.942	−	287.630i	0.373389	−	0.323543i
$890$		0			0
$891$	358.967	+	558.564i	0.402881	+	0.626895i
$892$		0			0
$893$	679.531	−	1057.37i	0.760953	−	1.18407i
$894$		0			0
$895$	159.981	−	544.847i	0.178750	−	0.608767i
$896$		0			0
$897$	12.8793	−	29.5778i	0.0143581	−	0.0329742i
$898$		0			0
$899$	−250.899	−	73.6705i	−0.279086	−	0.0819472i
$900$		0			0
$901$	−338.434	−	217.498i	−0.375620	−	0.241396i
$902$		0			0
$903$	−84.2098	+	54.1183i	−0.0932555	+	0.0599317i
$904$		0			0
$905$	1193.00	+	1376.80i	1.31823	+	1.52132i
$906$		0			0
$907$	−21.6209	−	9.87392i	−0.0238378	−	0.0108863i	0.403460	−	0.914997i	$-0.367807\pi$
$907$	−21.6209	−	9.87392i	−0.0238378	−	0.0108863i	−0.427298	+	0.904111i	$0.640535\pi$
$908$		0			0
$909$	54.3898	−	15.9703i	0.0598347	−	0.0175691i
$910$		0			0
$911$	−1017.38	+	146.278i	−1.11678	+	0.160568i	−0.675895	−	0.736998i	$-0.736243\pi$
$911$	−1017.38	+	146.278i	−1.11678	+	0.160568i	−0.440881	+	0.897566i	$0.645334\pi$
$912$		0			0
$913$	604.176	+	1322.96i	0.661748	+	1.44903i
$914$		0			0
$915$	5.50886	−	38.3150i	0.00602061	−	0.0418743i
$916$		0			0
$917$	−722.361	−	625.929i	−0.787743	−	0.682583i
$918$		0			0
$919$			536.305i			0.583575i	0.956483	+	0.291787i	$0.0942499\pi$
$919$			536.305i			0.583575i	−0.956483	+	0.291787i	$0.905750\pi$
$920$		0			0
$921$	568.109			0.616839
$922$		0			0
$923$	−38.1400	+	44.0159i	−0.0413217	+	0.0476878i
$924$		0			0
$925$	−1481.85	−	213.058i	−1.60200	−	0.230333i
$926$		0			0
$927$	−1133.14	+	517.490i	−1.22238	+	0.558241i
$928$		0			0
$929$	8.88967	+	61.8290i	0.00956907	+	0.0665543i	0.994046	−	0.108957i	$-0.0347512\pi$
$929$	8.88967	+	61.8290i	0.00956907	+	0.0665543i	−0.984477	+	0.175512i	$0.943842\pi$
$930$		0			0
$931$	−166.985	−	568.700i	−0.179361	−	0.610849i
$932$		0			0
$933$	42.6746	−	93.4443i	0.0457391	−	0.100155i
$934$		0			0
$935$	−582.678	+	504.894i	−0.623186	+	0.539993i
$936$		0			0
$937$	489.441	+	761.586i	0.522349	+	0.812792i	0.997755	−	0.0669754i	$-0.0213349\pi$
$937$	489.441	+	761.586i	0.522349	+	0.812792i	−0.475405	+	0.879767i	$0.657699\pi$
$938$		0			0
$939$	232.820	−	362.275i	0.247945	−	0.385810i
$940$		0			0
$941$	22.9597	−	78.1936i	0.0243993	−	0.0830963i	−0.946393	−	0.323016i	$-0.895303\pi$
$941$	22.9597	−	78.1936i	0.0243993	−	0.0830963i	0.970793	+	0.239920i	$0.0771213\pi$
$942$		0			0
$943$	1171.01	−	782.226i	1.24179	−	0.829508i
$944$		0			0
$945$	−935.609	−	274.719i	−0.990062	−	0.290708i
$946$		0			0
$947$	104.456	+	67.1298i	0.110302	+	0.0708867i	0.594629	−	0.804000i	$-0.297299\pi$
$947$	104.456	+	67.1298i	0.110302	+	0.0708867i	−0.484327	+	0.874887i	$0.660935\pi$
$948$		0			0
$949$	−66.7127	+	42.8736i	−0.0702978	+	0.0451777i
$950$		0			0
$951$	−103.655	−	119.625i	−0.108996	−	0.125788i
$952$		0			0
$953$	−274.614	−	125.412i	−0.288157	−	0.131597i	0.266092	−	0.963948i	$-0.414267\pi$
$953$	−274.614	−	125.412i	−0.288157	−	0.131597i	−0.554249	+	0.832351i	$0.686995\pi$
$954$		0			0
$955$	−1632.46	+	479.334i	−1.70939	+	0.501921i
$956$		0			0
$957$	481.723	−	69.2613i	0.503367	−	0.0723733i
$958$		0			0
$959$	154.458	+	338.216i	0.161062	+	0.352676i
$960$		0			0
$961$	128.449	−	893.383i	0.133662	−	0.929639i
$962$		0			0
$963$	334.531	+	289.872i	0.347384	+	0.301010i
$964$		0			0
$965$		−	2320.43i		−	2.40459i
$966$		0			0
$967$	−1349.94			−1.39601			−0.698003	−	0.716095i	$-0.745928\pi$
$967$	−1349.94			−1.39601			−0.698003	+	0.716095i	$0.745928\pi$
$968$		0			0
$969$	134.224	−	154.902i	0.138518	−	0.159858i
$970$		0			0
$971$	668.685	+	96.1423i	0.688656	+	0.0990137i	0.477754	−	0.878494i	$-0.341451\pi$
$971$	668.685	+	96.1423i	0.688656	+	0.0990137i	0.210902	+	0.977507i	$0.432360\pi$
$972$		0			0
$973$	−787.646	+	359.706i	−0.809502	+	0.369687i
$974$		0			0
$975$	13.9608	+	97.0995i	0.0143188	+	0.0995892i
$976$		0			0
$977$	360.340	+	1227.21i	0.368823	+	1.25610i	0.909796	+	0.415056i	$0.136238\pi$
$977$	360.340	+	1227.21i	0.368823	+	1.25610i	−0.540973	+	0.841040i	$0.681944\pi$
$978$		0			0
$979$	277.997	−	608.729i	0.283960	−	0.621786i
$980$		0			0
$981$	−469.773	+	407.061i	−0.478872	+	0.414945i
$982$		0			0
$983$	539.680	+	839.758i	0.549013	+	0.854281i	0.999254	−	0.0386263i	$-0.0122982\pi$
$983$	539.680	+	839.758i	0.549013	+	0.854281i	−0.450241	+	0.892907i	$0.648662\pi$
$984$		0			0
$985$	866.365	−	1348.09i	0.879558	−	1.36862i
$986$		0			0
$987$	−67.2450	+	229.015i	−0.0681307	+	0.232032i
$988$		0			0
$989$	6.85881	+	386.976i	0.00693509	+	0.391280i
$990$		0			0
$991$	−1096.32	−	321.909i	−1.10628	−	0.324833i	−0.322935	−	0.946421i	$-0.604669\pi$
$991$	−1096.32	−	321.909i	−1.10628	−	0.324833i	−0.783344	+	0.621589i	$0.786488\pi$
$992$		0			0
$993$	−82.1433	−	52.7903i	−0.0827223	−	0.0531624i
$994$		0			0
$995$	−1409.77	+	906.002i	−1.41685	+	0.910555i
$996$		0			0
$997$	868.971	+	1002.85i	0.871586	+	1.00586i	0.999900	+	0.0141299i	$0.00449785\pi$
$997$	868.971	+	1002.85i	0.871586	+	1.00586i	−0.128315	+	0.991734i	$0.540957\pi$
$998$		0			0
$999$	355.299	+	162.260i	0.355655	+	0.162422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.3.f.a.5.2	✓	40
4.3	odd	2		368.3.p.c.97.3		40
23.3	even	11		2116.3.d.c.1057.26		40
23.14	odd	22	inner	92.3.f.a.37.2	yes	40
23.20	odd	22		2116.3.d.c.1057.25		40
92.83	even	22		368.3.p.c.129.3		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.3.f.a.5.2	✓	40	1.1	even	1	trivial
92.3.f.a.37.2	yes	40	23.14	odd	22	inner
368.3.p.c.97.3		40	4.3	odd	2
368.3.p.c.129.3		40	92.83	even	22
2116.3.d.c.1057.25		40	23.20	odd	22
2116.3.d.c.1057.26		40	23.3	even	11

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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	92.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.710283 + 0.819710i) q^{3} +(-9.64449 - 1.38667i) q^{5} +(-4.98879 + 2.27830i) q^{7} +(1.11341 + 7.74394i) q^{9} +(-3.69536 - 12.5852i) q^{11} +(0.537204 - 1.17631i) q^{13} +(7.98699 - 6.92076i) q^{15} +(3.26150 + 5.07499i) q^{17} +(-16.9355 + 26.3522i) q^{19} +(1.67590 - 5.70760i) q^{21} +(-15.3675 - 17.1126i) q^{23} +(67.1061 + 19.7041i) q^{25} +(-15.3507 - 9.86528i) q^{27} +(28.7783 - 18.4947i) q^{29} +(-5.00573 - 5.77692i) q^{31} +(12.9410 + 5.90996i) q^{33} +(51.2736 - 15.0553i) q^{35} +(-21.1877 + 3.04634i) q^{37} +(0.582669 + 1.27587i) q^{39} +(-8.71362 + 60.6045i) q^{41} +(-12.7175 - 11.0198i) q^{43} -76.2303i q^{45} -40.1246 q^{47} +(-12.3909 + 14.2998i) q^{49} +(-6.47661 - 0.931196i) q^{51} +(-60.6602 + 27.7026i) q^{53} +(18.1883 + 126.503i) q^{55} +(-9.57214 - 32.5997i) q^{57} +(28.2210 - 61.7953i) q^{59} +(2.76812 - 2.39859i) q^{61} +(-23.1976 - 36.0962i) q^{63} +(-6.81222 + 10.6000i) q^{65} +(3.79860 - 12.9368i) q^{67} +(24.9426 - 0.442086i) q^{69} +(-43.2131 - 12.6885i) q^{71} +(-51.5883 - 33.1538i) q^{73} +(-63.8160 + 41.0121i) q^{75} +(47.1083 + 54.3659i) q^{77} +(15.2696 + 6.97338i) q^{79} +(-48.5700 + 14.2614i) q^{81} +(-109.753 + 15.7802i) q^{83} +(-24.4182 - 53.4684i) q^{85} +(-5.28045 + 36.7263i) q^{87} +(38.5581 + 33.4108i) q^{89} +7.09229i q^{91} +8.29089 q^{93} +(199.876 - 230.669i) q^{95} +(136.770 + 19.6645i) q^{97} +(93.3449 - 42.6292i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{3} - 6 q^{9} - 2 q^{13} + 77 q^{15} + 55 q^{17} + 33 q^{19} + 33 q^{21} - 50 q^{23} - 54 q^{25} - 191 q^{27} + q^{29} - 53 q^{31} - 121 q^{33} - 156 q^{35} - 352 q^{37} - 306 q^{39} + 6 q^{41}+ \cdots + 1353 q^{99}+O(q^{100}) \) 40 * q - 2 * q^3 - 6 * q^9 - 2 * q^13 + 77 * q^15 + 55 * q^17 + 33 * q^19 + 33 * q^21 - 50 * q^23 - 54 * q^25 - 191 * q^27 + q^29 - 53 * q^31 - 121 * q^33 - 156 * q^35 - 352 * q^37 - 306 * q^39 + 6 * q^41 - 88 * q^43 - 58 * q^47 + 292 * q^49 + 264 * q^51 + 176 * q^53 + 518 * q^55 + 891 * q^57 + 696 * q^59 + 308 * q^61 + 275 * q^63 + 231 * q^65 + 22 * q^67 - 233 * q^69 - 215 * q^71 - 400 * q^73 - 557 * q^75 - 239 * q^77 - 748 * q^79 - 684 * q^81 - 671 * q^83 - 794 * q^85 + 62 * q^87 - 44 * q^89 - 346 * q^93 + 561 * q^95 + 693 * q^97 + 1353 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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