LMFDB - Embedded newform 675.3.i.c.449.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,3,Mod(224,675)] 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("675.224"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	675.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,-32,0,0,0,0,0,0,36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$18.3924178443$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			449.12
Character	$\chi$	$=$	675.449
Dual form			675.3.i.c.224.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.916957 + 1.58822i) q^{2} +(0.318381 - 0.551452i) q^{4} +(5.60142 - 3.23398i) q^{7} +8.50342 q^{8} +(-9.24701 + 5.33876i) q^{11} +(-9.58473 - 5.53374i) q^{13} +(10.2725 + 5.93084i) q^{14} +(6.52374 + 11.2995i) q^{16} +12.6328 q^{17} +32.1403 q^{19} +(-16.9582 - 9.79083i) q^{22} +(-5.67112 + 9.82266i) q^{23} -20.2968i q^{26} -4.11855i q^{28} +(35.2234 - 20.3362i) q^{29} +(15.9429 - 27.6139i) q^{31} +(5.04286 - 8.73448i) q^{32} +(11.5837 + 20.0635i) q^{34} -45.4499i q^{37} +(29.4713 + 51.0457i) q^{38} +(25.4781 + 14.7098i) q^{41} +(-32.5786 + 18.8093i) q^{43} +6.79904i q^{44} -20.8007 q^{46} +(-28.7589 - 49.8119i) q^{47} +(-3.58274 + 6.20548i) q^{49} +(-6.10319 + 3.52368i) q^{52} +33.3940 q^{53} +(47.6312 - 27.4999i) q^{56} +(64.5966 + 37.2949i) q^{58} +(3.54909 + 2.04907i) q^{59} +(33.1195 + 57.3647i) q^{61} +58.4757 q^{62} +70.6863 q^{64} +(61.4687 + 35.4890i) q^{67} +(4.02203 - 6.96635i) q^{68} +13.1123i q^{71} +109.273i q^{73} +(72.1842 - 41.6756i) q^{74} +(10.2328 - 17.7238i) q^{76} +(-34.5309 + 59.8093i) q^{77} +(49.8891 + 86.4104i) q^{79} +53.9530i q^{82} +(-42.8667 - 74.2472i) q^{83} +(-59.7463 - 34.4945i) q^{86} +(-78.6312 + 45.3977i) q^{88} -63.6372i q^{89} -71.5841 q^{91} +(3.61115 + 6.25469i) q^{92} +(52.7414 - 91.3507i) q^{94} +(-74.8357 + 43.2064i) q^{97} -13.1409 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} + 36 q^{11} - 108 q^{14} - 64 q^{16} + 104 q^{19} - 108 q^{29} + 64 q^{31} - 108 q^{34} - 288 q^{41} - 216 q^{46} + 108 q^{49} + 36 q^{56} - 972 q^{59} + 124 q^{61} - 512 q^{64} + 1080 q^{74}+ \cdots + 300 q^{94}+O(q^{100}) $ 32 * q - 32 * q^4 + 36 * q^11 - 108 * q^14 - 64 * q^16 + 104 * q^19 - 108 * q^29 + 64 * q^31 - 108 * q^34 - 288 * q^41 - 216 * q^46 + 108 * q^49 + 36 * q^56 - 972 * q^59 + 124 * q^61 - 512 * q^64 + 1080 * q^74 - 212 * q^76 + 80 * q^79 - 108 * q^86 + 272 * q^91 + 300 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.916957	+	1.58822i	0.458478	+	0.794108i	0.998881	−	0.0472989i	$-0.0150613\pi$
$2$	0.916957	+	1.58822i	0.458478	+	0.794108i	−0.540402	+	0.841407i	$0.681728\pi$
$3$		0			0
$3$		0			0
$4$	0.318381	−	0.551452i	0.0795952	−	0.137863i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	5.60142	−	3.23398i	0.800203	−	0.461997i	−0.0433393	−	0.999060i	$-0.513800\pi$
$7$	5.60142	−	3.23398i	0.800203	−	0.461997i	0.843542	+	0.537063i	$0.180466\pi$
$8$	8.50342			1.06293
$9$		0			0
$10$		0			0
$11$	−9.24701	+	5.33876i	−0.840637	+	0.485342i	−0.857481	−	0.514516i	$-0.827972\pi$
$11$	−9.24701	+	5.33876i	−0.840637	+	0.485342i	0.0168436	+	0.999858i	$0.494638\pi$
$12$		0			0
$13$	−9.58473	−	5.53374i	−0.737287	−	0.425673i	0.0837952	−	0.996483i	$-0.473296\pi$
$13$	−9.58473	−	5.53374i	−0.737287	−	0.425673i	−0.821082	+	0.570810i	$0.806629\pi$
$14$	10.2725	+	5.93084i	0.733751	+	0.423631i
$15$		0			0
$16$	6.52374	+	11.2995i	0.407734	+	0.706216i
$17$	12.6328			0.743103			0.371552	−	0.928412i	$-0.378826\pi$
$17$	12.6328			0.743103			0.371552	+	0.928412i	$0.378826\pi$
$18$		0			0
$19$	32.1403			1.69159			0.845797	−	0.533505i	$-0.179125\pi$
$19$	32.1403			1.69159			0.845797	+	0.533505i	$0.179125\pi$
$20$		0			0
$21$		0			0
$22$	−16.9582	−	9.79083i	−0.770828	−	0.445038i
$23$	−5.67112	+	9.82266i	−0.246570	+	0.427072i	−0.962572	−	0.271026i	$-0.912637\pi$
$23$	−5.67112	+	9.82266i	−0.246570	+	0.427072i	0.716002	+	0.698099i	$0.245970\pi$
$24$		0			0
$25$		0			0
$26$		−	20.2968i		−	0.780647i
$27$		0			0
$28$		−	4.11855i		−	0.147091i
$29$	35.2234	−	20.3362i	1.21460	−	0.701249i	0.250841	−	0.968028i	$-0.419293\pi$
$29$	35.2234	−	20.3362i	1.21460	−	0.701249i	0.963758	+	0.266779i	$0.0859594\pi$
$30$		0			0
$31$	15.9429	−	27.6139i	0.514286	−	0.890770i	−0.485576	−	0.874194i	$-0.661390\pi$
$31$	15.9429	−	27.6139i	0.514286	−	0.890770i	0.999863	−	0.0165759i	$-0.00527652\pi$
$32$	5.04286	−	8.73448i	0.157589	−	0.272953i
$33$		0			0
$34$	11.5837	+	20.0635i	0.340697	+	0.590104i
$35$		0			0
$36$		0			0
$37$		−	45.4499i		−	1.22837i	−0.789160	−	0.614187i	$-0.789484\pi$
$37$		−	45.4499i		−	1.22837i	0.789160	−	0.614187i	$-0.210516\pi$
$38$	29.4713	+	51.0457i	0.775559	+	1.34331i
$39$		0			0
$40$		0			0
$41$	25.4781	+	14.7098i	0.621418	+	0.358776i	0.777421	−	0.628981i	$-0.216528\pi$
$41$	25.4781	+	14.7098i	0.621418	+	0.358776i	−0.156003	+	0.987757i	$0.549861\pi$
$42$		0			0
$43$	−32.5786	+	18.8093i	−0.757641	+	0.437424i	−0.828448	−	0.560066i	$-0.810776\pi$
$43$	−32.5786	+	18.8093i	−0.757641	+	0.437424i	0.0708069	+	0.997490i	$0.477443\pi$
$44$			6.79904i			0.154524i
$45$		0			0
$46$	−20.8007			−0.452188
$47$	−28.7589	−	49.8119i	−0.611892	−	1.05983i	−0.990921	−	0.134443i	$-0.957075\pi$
$47$	−28.7589	−	49.8119i	−0.611892	−	1.05983i	0.379029	−	0.925385i	$-0.376258\pi$
$48$		0			0
$49$	−3.58274	+	6.20548i	−0.0731171	+	0.126642i
$50$		0			0
$51$		0			0
$52$	−6.10319	+	3.52368i	−0.117369	+	0.0677630i
$53$	33.3940			0.630075			0.315038	−	0.949079i	$-0.397983\pi$
$53$	33.3940			0.630075			0.315038	+	0.949079i	$0.397983\pi$
$54$		0			0
$55$		0			0
$56$	47.6312	−	27.4999i	0.850557	−	0.491070i
$57$		0			0
$58$	64.5966	+	37.2949i	1.11373	+	0.643015i
$59$	3.54909	+	2.04907i	0.0601541	+	0.0347300i	0.529775	−	0.848138i	$-0.322276\pi$
$59$	3.54909	+	2.04907i	0.0601541	+	0.0347300i	−0.469621	+	0.882868i	$0.655610\pi$
$60$		0			0
$61$	33.1195	+	57.3647i	0.542943	+	0.940404i	0.998733	+	0.0503172i	$0.0160232\pi$
$61$	33.1195	+	57.3647i	0.542943	+	0.940404i	−0.455791	+	0.890087i	$0.650643\pi$
$62$	58.4757			0.943157
$63$		0			0
$64$	70.6863			1.10447
$65$		0			0
$66$		0			0
$67$	61.4687	+	35.4890i	0.917444	+	0.529686i	0.882819	−	0.469714i	$-0.155643\pi$
$67$	61.4687	+	35.4890i	0.917444	+	0.529686i	0.0346251	+	0.999400i	$0.488976\pi$
$68$	4.02203	−	6.96635i	0.0591474	−	0.102446i
$69$		0			0
$70$		0			0
$71$			13.1123i			0.184680i	0.995728	+	0.0923400i	$0.0294347\pi$
$71$			13.1123i			0.184680i	−0.995728	+	0.0923400i	$0.970565\pi$
$72$		0			0
$73$			109.273i			1.49688i	0.663200	+	0.748442i	$0.269198\pi$
$73$			109.273i			1.49688i	−0.663200	+	0.748442i	$0.730802\pi$
$74$	72.1842	−	41.6756i	0.975462	−	0.563183i
$75$		0			0
$76$	10.2328	−	17.7238i	0.134643	−	0.233208i
$77$	−34.5309	+	59.8093i	−0.448453	+	0.776744i
$78$		0			0
$79$	49.8891	+	86.4104i	0.631507	+	1.09380i	0.987244	+	0.159217i	$0.0508968\pi$
$79$	49.8891	+	86.4104i	0.631507	+	1.09380i	−0.355736	+	0.934586i	$0.615770\pi$
$80$		0			0
$81$		0			0
$82$			53.9530i			0.657964i
$83$	−42.8667	−	74.2472i	−0.516466	−	0.894545i	−0.999817	−	0.0191187i	$-0.993914\pi$
$83$	−42.8667	−	74.2472i	−0.516466	−	0.894545i	0.483351	−	0.875426i	$-0.339419\pi$
$84$		0			0
$85$		0			0
$86$	−59.7463	−	34.4945i	−0.694724	−	0.401099i
$87$		0			0
$88$	−78.6312	+	45.3977i	−0.893536	+	0.515883i
$89$		−	63.6372i		−	0.715025i	−0.933908	−	0.357513i	$-0.883625\pi$
$89$		−	63.6372i		−	0.715025i	0.933908	−	0.357513i	$-0.116375\pi$
$90$		0			0
$91$	−71.5841			−0.786638
$92$	3.61115	+	6.25469i	0.0392516	+	0.0679858i
$93$		0			0
$94$	52.7414	−	91.3507i	0.561078	−	0.971816i
$95$		0			0
$96$		0			0
$97$	−74.8357	+	43.2064i	−0.771503	+	0.445427i	−0.833410	−	0.552655i	$-0.813615\pi$
$97$	−74.8357	+	43.2064i	−0.771503	+	0.445427i	0.0619078	+	0.998082i	$0.480282\pi$
$98$	−13.1409			−0.134090
$99$		0			0
$100$		0			0
$101$	38.1796	−	22.0430i	0.378015	−	0.218247i	−0.298939	−	0.954272i	$-0.596633\pi$
$101$	38.1796	−	22.0430i	0.378015	−	0.218247i	0.676954	+	0.736025i	$0.263299\pi$
$102$		0			0
$103$	−81.2952	−	46.9358i	−0.789274	−	0.455688i	0.0504329	−	0.998727i	$-0.483940\pi$
$103$	−81.2952	−	46.9358i	−0.789274	−	0.455688i	−0.839707	+	0.543040i	$0.817273\pi$
$104$	−81.5030	−	47.0558i	−0.783682	−	0.452459i
$105$		0			0
$106$	30.6208	+	53.0369i	0.288876	+	0.500348i
$107$	−138.518			−1.29456			−0.647280	−	0.762252i	$-0.724094\pi$
$107$	−138.518			−1.29456			−0.647280	+	0.762252i	$0.724094\pi$
$108$		0			0
$109$	−176.733			−1.62140			−0.810700	−	0.585461i	$-0.800913\pi$
$109$	−176.733			−1.62140			−0.810700	+	0.585461i	$0.800913\pi$
$110$		0			0
$111$		0			0
$112$	73.0845	+	42.1953i	0.652540	+	0.376744i
$113$	−44.3653	+	76.8430i	−0.392613	+	0.680026i	−0.992793	−	0.119839i	$-0.961762\pi$
$113$	−44.3653	+	76.8430i	−0.392613	+	0.680026i	0.600180	+	0.799865i	$0.295096\pi$
$114$		0			0
$115$		0			0
$116$		−	25.8986i		−	0.223264i
$117$		0			0
$118$			7.51564i			0.0636918i
$119$	70.7613	−	40.8541i	0.594633	−	0.343312i
$120$		0			0
$121$	−3.49522	+	6.05390i	−0.0288861	+	0.0500323i
$122$	−60.7383	+	105.202i	−0.497855	+	0.862310i
$123$		0			0
$124$	−10.1518	−	17.5835i	−0.0818695	−	0.141802i
$125$		0			0
$126$		0			0
$127$		−	92.0203i		−	0.724569i	−0.932068	−	0.362285i	$-0.881997\pi$
$127$		−	92.0203i		−	0.724569i	0.932068	−	0.362285i	$-0.118003\pi$
$128$	44.6448	+	77.3271i	0.348788	+	0.604118i
$129$		0			0
$130$		0			0
$131$	138.979	+	80.2398i	1.06091	+	0.612518i	0.925684	−	0.378297i	$-0.123490\pi$
$131$	138.979	+	80.2398i	1.06091	+	0.612518i	0.135228	+	0.990815i	$0.456823\pi$
$132$		0			0
$133$	180.031	−	103.941i	1.35362	−	0.781512i
$134$			130.167i			0.971399i
$135$		0			0
$136$	107.422			0.789865
$137$	−45.4321	−	78.6907i	−0.331621	−	0.574385i	0.651209	−	0.758899i	$-0.274262\pi$
$137$	−45.4321	−	78.6907i	−0.331621	−	0.574385i	−0.982830	+	0.184514i	$0.940929\pi$
$138$		0			0
$139$	−32.4865	+	56.2682i	−0.233716	+	0.404807i	−0.958899	−	0.283749i	$-0.908422\pi$
$139$	−32.4865	+	56.2682i	−0.233716	+	0.404807i	0.725183	+	0.688556i	$0.241755\pi$
$140$		0			0
$141$		0			0
$142$	−20.8251	+	12.0234i	−0.146656	+	0.0846718i
$143$	118.173			0.826387
$144$		0			0
$145$		0			0
$146$	−173.548	+	100.198i	−1.18869	+	0.686289i
$147$		0			0
$148$	−25.0634	−	14.4704i	−0.169347	−	0.0977727i
$149$	−124.965	−	72.1483i	−0.838688	−	0.484217i	0.0181301	−	0.999836i	$-0.494229\pi$
$149$	−124.965	−	72.1483i	−0.838688	−	0.484217i	−0.856818	+	0.515619i	$0.827562\pi$
$150$		0			0
$151$	−68.3876	−	118.451i	−0.452898	−	0.784442i	0.545667	−	0.838002i	$-0.316276\pi$
$151$	−68.3876	−	118.451i	−0.452898	−	0.784442i	−0.998565	+	0.0535600i	$0.982943\pi$
$152$	273.302			1.79804
$153$		0			0
$154$	−126.653			−0.822425
$155$		0			0
$156$		0			0
$157$	−45.2004	−	26.0965i	−0.287901	−	0.166220i	0.349094	−	0.937088i	$-0.386489\pi$
$157$	−45.2004	−	26.0965i	−0.287901	−	0.166220i	−0.636995	+	0.770868i	$0.719823\pi$
$158$	−91.4923	+	158.469i	−0.579065	+	1.00297i
$159$		0			0
$160$		0			0
$161$			73.3611i			0.455659i
$162$		0			0
$163$		−	103.226i		−	0.633287i	−0.948545	−	0.316643i	$-0.897444\pi$
$163$		−	103.226i		−	0.633287i	0.948545	−	0.316643i	$-0.102556\pi$
$164$	16.2235	−	9.36664i	0.0989238	−	0.0571137i
$165$		0			0
$166$	78.6138	−	136.163i	0.473577	−	0.820259i
$167$	−56.4096	+	97.7044i	−0.337782	+	0.585056i	−0.984015	−	0.178084i	$-0.943010\pi$
$167$	−56.4096	+	97.7044i	−0.337782	+	0.585056i	0.646233	+	0.763140i	$0.276343\pi$
$168$		0			0
$169$	−23.2553	−	40.2794i	−0.137606	−	0.238340i
$170$		0			0
$171$		0			0
$172$			23.9540i			0.139268i
$173$	−65.6580	−	113.723i	−0.379526	−	0.657359i	0.611467	−	0.791270i	$-0.290580\pi$
$173$	−65.6580	−	113.723i	−0.379526	−	0.657359i	−0.990993	+	0.133911i	$0.957246\pi$
$174$		0			0
$175$		0			0
$176$	−120.650	−	69.6574i	−0.685513	−	0.395781i
$177$		0			0
$178$	101.070	−	58.3526i	0.567807	−	0.327824i
$179$			297.076i			1.65964i	0.558028	+	0.829822i	$0.311558\pi$
$179$			297.076i			1.65964i	−0.558028	+	0.829822i	$0.688442\pi$
$180$		0			0
$181$	28.1168			0.155342			0.0776708	−	0.996979i	$-0.475252\pi$
$181$	28.1168			0.155342			0.0776708	+	0.996979i	$0.475252\pi$
$182$	−65.6395	−	113.691i	−0.360657	−	0.624676i
$183$		0			0
$184$	−48.2239	+	83.5262i	−0.262086	+	0.453947i
$185$		0			0
$186$		0			0
$187$	−116.815	+	67.4433i	−0.624680	+	0.360659i
$188$	−36.6252			−0.194815
$189$		0			0
$190$		0			0
$191$	−7.94176	+	4.58518i	−0.0415799	+	0.0240062i	−0.520646	−	0.853773i	$-0.674309\pi$
$191$	−7.94176	+	4.58518i	−0.0415799	+	0.0240062i	0.479066	+	0.877779i	$0.340975\pi$
$192$		0			0
$193$	−82.0697	−	47.3830i	−0.425232	−	0.245508i	0.272082	−	0.962274i	$-0.412288\pi$
$193$	−82.0697	−	47.3830i	−0.425232	−	0.245508i	−0.697313	+	0.716767i	$0.745621\pi$
$194$	−137.242	−	79.2369i	−0.707434	−	0.408437i
$195$		0			0
$196$	2.28135	+	3.95141i	0.0116395	+	0.0201603i
$197$	267.330			1.35701			0.678504	−	0.734597i	$-0.262629\pi$
$197$	267.330			1.35701			0.678504	+	0.734597i	$0.262629\pi$
$198$		0			0
$199$	158.327			0.795615			0.397808	−	0.917469i	$-0.369771\pi$
$199$	158.327			0.795615			0.397808	+	0.917469i	$0.369771\pi$
$200$		0			0
$201$		0			0
$202$	70.0180	+	40.4249i	0.346624	+	0.200123i
$203$	131.534	−	227.823i	0.647950	−	1.12228i
$204$		0			0
$205$		0			0
$206$		−	172.152i		−	0.835692i
$207$		0			0
$208$		−	144.403i		−	0.694245i
$209$	−297.202	+	171.589i	−1.42202	+	0.821002i
$210$		0			0
$211$	−158.786	+	275.026i	−0.752542	+	1.30344i	0.194045	+	0.980993i	$0.437839\pi$
$211$	−158.786	+	275.026i	−0.752542	+	1.30344i	−0.946587	+	0.322448i	$0.895494\pi$
$212$	10.6320	−	18.4152i	0.0501510	−	0.0868640i
$213$		0			0
$214$	−127.015	−	219.996i	−0.593528	−	1.02802i
$215$		0			0
$216$		0			0
$217$		−	206.236i		−	0.950396i
$218$	−162.056	−	280.690i	−0.743377	−	1.28757i
$219$		0			0
$220$		0			0
$221$	−121.081	−	69.9064i	−0.547880	−	0.316319i
$222$		0			0
$223$	−107.379	+	61.9955i	−0.481522	+	0.278007i	−0.721050	−	0.692883i	$-0.756340\pi$
$223$	−107.379	+	61.9955i	−0.481522	+	0.278007i	0.239529	+	0.970889i	$0.423007\pi$
$224$		−	65.2340i		−	0.291223i
$225$		0			0
$226$	−162.724			−0.720019
$227$	−108.739	−	188.341i	−0.479025	−	0.829695i	0.520686	−	0.853748i	$-0.325676\pi$
$227$	−108.739	−	188.341i	−0.479025	−	0.829695i	−0.999711	+	0.0240532i	$0.992343\pi$
$228$		0			0
$229$	37.4773	−	64.9126i	0.163656	−	0.283461i	−0.772521	−	0.634989i	$-0.781005\pi$
$229$	37.4773	−	64.9126i	0.163656	−	0.283461i	0.936177	+	0.351528i	$0.114338\pi$
$230$		0			0
$231$		0			0
$232$	299.519	−	172.927i	1.29103	−	0.745377i
$233$	−142.781			−0.612792			−0.306396	−	0.951904i	$-0.599123\pi$
$233$	−142.781			−0.612792			−0.306396	+	0.951904i	$0.599123\pi$
$234$		0			0
$235$		0			0
$236$	2.25993	−	1.30477i	0.00957596	−	0.00552868i
$237$		0			0
$238$	129.770	+	74.9229i	0.545253	+	0.314802i
$239$	173.362	+	100.090i	0.725363	+	0.418789i	0.816723	−	0.577029i	$-0.195788\pi$
$239$	173.362	+	100.090i	0.725363	+	0.418789i	−0.0913604	+	0.995818i	$0.529122\pi$
$240$		0			0
$241$	−96.9600	−	167.940i	−0.402324	−	0.696845i	0.591682	−	0.806171i	$-0.298464\pi$
$241$	−96.9600	−	167.940i	−0.402324	−	0.696845i	−0.994006	+	0.109326i	$0.965131\pi$
$242$	−12.8199			−0.0529747
$243$		0			0
$244$	42.1784			0.172862
$245$		0			0
$246$		0			0
$247$	−308.056	−	177.856i	−1.24719	−	0.720065i
$248$	135.569	−	234.812i	0.546649	−	0.946824i
$249$		0			0
$250$		0			0
$251$			301.288i			1.20035i	0.799868	+	0.600176i	$0.204903\pi$
$251$			301.288i			1.20035i	−0.799868	+	0.600176i	$0.795097\pi$
$252$		0			0
$253$		−	121.107i		−	0.478684i
$254$	146.148	−	84.3786i	0.575386	−	0.332199i
$255$		0			0
$256$	59.4978	−	103.053i	0.232413	−	0.402552i
$257$	−105.005	+	181.874i	−0.408579	+	0.707679i	−0.994731	−	0.102522i	$-0.967309\pi$
$257$	−105.005	+	181.874i	−0.408579	+	0.707679i	0.586152	+	0.810201i	$0.300642\pi$
$258$		0			0
$259$	−146.984	−	254.584i	−0.567506	−	0.982949i
$260$		0			0
$261$		0			0
$262$			294.306i			1.12330i
$263$	−75.7092	−	131.132i	−0.287868	−	0.498601i	0.685433	−	0.728136i	$-0.259613\pi$
$263$	−75.7092	−	131.132i	−0.287868	−	0.498601i	−0.973301	+	0.229534i	$0.926280\pi$
$264$		0			0
$265$		0			0
$266$	330.162	+	190.619i	1.24121	+	0.716613i
$267$		0			0
$268$	39.1409	−	22.5980i	0.146048	−	0.0843210i
$269$			411.264i			1.52886i	0.644706	+	0.764431i	$0.276980\pi$
$269$			411.264i			1.52886i	−0.644706	+	0.764431i	$0.723020\pi$
$270$		0			0
$271$	−255.156			−0.941534			−0.470767	−	0.882257i	$-0.656023\pi$
$271$	−255.156			−0.941534			−0.470767	+	0.882257i	$0.656023\pi$
$272$	82.4129	+	142.743i	0.302988	+	0.524791i
$273$		0			0
$274$	83.3186	−	144.312i	0.304082	−	0.526686i
$275$		0			0
$276$		0			0
$277$	160.699	−	92.7798i	0.580142	−	0.334945i	−0.181048	−	0.983474i	$-0.557949\pi$
$277$	160.699	−	92.7798i	0.580142	−	0.334945i	0.761190	+	0.648529i	$0.224615\pi$
$278$	−119.155			−0.428614
$279$		0			0
$280$		0			0
$281$	−90.1892	+	52.0708i	−0.320958	+	0.185305i	−0.651820	−	0.758374i	$-0.725994\pi$
$281$	−90.1892	+	52.0708i	−0.320958	+	0.185305i	0.330862	+	0.943679i	$0.392661\pi$
$282$		0			0
$283$	44.9089	+	25.9282i	0.158689	+	0.0916189i	0.577241	−	0.816574i	$-0.304129\pi$
$283$	44.9089	+	25.9282i	0.158689	+	0.0916189i	−0.418553	+	0.908192i	$0.637463\pi$
$284$	7.23079	+	4.17470i	0.0254605	+	0.0146996i
$285$		0			0
$286$	108.360	+	187.685i	0.378881	+	0.656241i
$287$	190.285			0.663014
$288$		0			0
$289$	−129.414			−0.447798
$290$		0			0
$291$		0			0
$292$	60.2586	+	34.7903i	0.206365	+	0.119145i
$293$	−165.835	+	287.235i	−0.565990	+	0.980323i	0.430967	+	0.902368i	$0.358172\pi$
$293$	−165.835	+	287.235i	−0.565990	+	0.980323i	−0.996957	+	0.0779553i	$0.975161\pi$
$294$		0			0
$295$		0			0
$296$		−	386.479i		−	1.30567i
$297$		0			0
$298$		−	264.627i		−	0.888012i
$299$	108.712	−	62.7650i	0.363586	−	0.209916i
$300$		0			0
$301$	−121.658	+	210.717i	−0.404178	+	0.700057i
$302$	125.417	−	217.228i	0.415288	−	0.719300i
$303$		0			0
$304$	209.675	+	363.168i	0.689720	+	1.19463i
$305$		0			0
$306$		0			0
$307$			292.274i			0.952031i	0.879437	+	0.476016i	$0.157919\pi$
$307$			292.274i			0.952031i	−0.879437	+	0.476016i	$0.842081\pi$
$308$	21.9880	+	38.0843i	0.0713895	+	0.123650i
$309$		0			0
$310$		0			0
$311$	−171.292	−	98.8956i	−0.550779	−	0.317992i	0.198657	−	0.980069i	$-0.436342\pi$
$311$	−171.292	−	98.8956i	−0.550779	−	0.317992i	−0.749436	+	0.662077i	$0.769675\pi$
$312$		0			0
$313$	186.800	−	107.849i	0.596804	−	0.344565i	−0.170979	−	0.985275i	$-0.554693\pi$
$313$	186.800	−	107.849i	0.596804	−	0.344565i	0.767783	+	0.640710i	$0.221360\pi$
$314$		−	95.7173i		−	0.304832i
$315$		0			0
$316$	63.5349			0.201060
$317$	−101.818	−	176.354i	−0.321192	−	0.556321i	0.659542	−	0.751668i	$-0.270750\pi$
$317$	−101.818	−	176.354i	−0.321192	−	0.556321i	−0.980734	+	0.195346i	$0.937417\pi$
$318$		0			0
$319$	−217.141	+	376.098i	−0.680691	+	1.17899i
$320$		0			0
$321$		0			0
$322$	−116.513	+	67.2690i	−0.361842	+	0.208910i
$323$	406.020			1.25703
$324$		0			0
$325$		0			0
$326$	163.945	−	94.6536i	0.502898	−	0.290348i
$327$		0			0
$328$	216.651	+	125.084i	0.660522	+	0.381353i
$329$	−322.182	−	186.012i	−0.979275	−	0.565385i
$330$		0			0
$331$	−47.0115	−	81.4264i	−0.142029	−	0.246001i	0.786232	−	0.617932i	$-0.212029\pi$
$331$	−47.0115	−	81.4264i	−0.142029	−	0.246001i	−0.928260	+	0.371931i	$0.878696\pi$
$332$	−54.5917			−0.164433
$333$		0			0
$334$	−206.901			−0.619464
$335$		0			0
$336$		0			0
$337$	−291.103	−	168.068i	−0.863807	−	0.498719i	0.00147845	−	0.999999i	$-0.499529\pi$
$337$	−291.103	−	168.068i	−0.863807	−	0.498719i	−0.865285	+	0.501280i	$0.832863\pi$
$338$	42.6483	−	73.8690i	0.126178	−	0.218547i
$339$		0			0
$340$		0			0
$341$			340.461i			0.998419i
$342$		0			0
$343$			363.276i			1.05911i
$344$	−277.029	+	159.943i	−0.805318	+	0.464950i
$345$		0			0
$346$	120.411	−	208.558i	0.348009	−	0.602769i
$347$	−31.2617	+	54.1469i	−0.0900914	+	0.156043i	−0.907549	−	0.419945i	$-0.862049\pi$
$347$	−31.2617	+	54.1469i	−0.0900914	+	0.156043i	0.817458	+	0.575988i	$0.195383\pi$
$348$		0			0
$349$	−160.475	−	277.951i	−0.459815	−	0.796422i	0.539136	−	0.842219i	$-0.318751\pi$
$349$	−160.475	−	277.951i	−0.459815	−	0.796422i	−0.998951	+	0.0457962i	$0.985418\pi$
$350$		0			0
$351$		0			0
$352$			107.690i			0.305939i
$353$	83.1067	+	143.945i	0.235430	+	0.407776i	0.959397	−	0.282058i	$-0.0910170\pi$
$353$	83.1067	+	143.945i	0.235430	+	0.407776i	−0.723968	+	0.689834i	$0.757684\pi$
$354$		0			0
$355$		0			0
$356$	−35.0929	−	20.2609i	−0.0985754	−	0.0569126i
$357$		0			0
$358$	−471.821	+	272.406i	−1.31794	+	0.760911i
$359$		−	199.670i		−	0.556183i	−0.960555	−	0.278091i	$-0.910298\pi$
$359$		−	199.670i		−	0.556183i	0.960555	−	0.278091i	$-0.0897018\pi$
$360$		0			0
$361$	671.998			1.86149
$362$	25.7819	+	44.6556i	0.0712208	+	0.123358i
$363$		0			0
$364$	−22.7910	+	39.4752i	−0.0626126	+	0.108448i
$365$		0			0
$366$		0			0
$367$	139.120	−	80.3209i	0.379073	−	0.218858i	−0.298342	−	0.954459i	$-0.596433\pi$
$367$	139.120	−	80.3209i	0.379073	−	0.218858i	0.677415	+	0.735601i	$0.263100\pi$
$368$	−147.988			−0.402140
$369$		0			0
$370$		0			0
$371$	187.054	−	107.996i	0.504188	−	0.291093i
$372$		0			0
$373$	148.296	+	85.6188i	0.397577	+	0.229541i	0.685438	−	0.728131i	$-0.259611\pi$
$373$	148.296	+	85.6188i	0.397577	+	0.229541i	−0.287861	+	0.957672i	$0.592944\pi$
$374$	−214.229	−	123.685i	−0.572805	−	0.330709i
$375$		0			0
$376$	−244.549	−	423.572i	−0.650397	−	1.12652i
$377$	−450.142			−1.19401
$378$		0			0
$379$	297.486			0.784922			0.392461	−	0.919769i	$-0.371624\pi$
$379$	297.486			0.784922			0.392461	+	0.919769i	$0.371624\pi$
$380$		0			0
$381$		0			0
$382$	−14.5645	−	8.40882i	−0.0381270	−	0.0220126i
$383$	−240.374	+	416.340i	−0.627608	+	1.08705i	0.360423	+	0.932789i	$0.382632\pi$
$383$	−240.374	+	416.340i	−0.627608	+	1.08705i	−0.988030	+	0.154259i	$0.950701\pi$
$384$		0			0
$385$		0			0
$386$		−	173.793i		−	0.450240i
$387$		0			0
$388$			55.0244i			0.141815i
$389$	514.801	−	297.220i	1.32340	−	0.764062i	0.339126	−	0.940741i	$-0.389869\pi$
$389$	514.801	−	297.220i	1.32340	−	0.764062i	0.984269	+	0.176678i	$0.0565352\pi$
$390$		0			0
$391$	−71.6418	+	124.087i	−0.183227	+	0.317359i
$392$	−30.4655	+	52.7678i	−0.0777181	+	0.134612i
$393$		0			0
$394$	245.130	+	424.578i	0.622158	+	1.07761i
$395$		0			0
$396$		0			0
$397$			106.303i			0.267765i	0.990997	+	0.133883i	$0.0427445\pi$
$397$			106.303i			0.267765i	−0.990997	+	0.133883i	$0.957255\pi$
$398$	145.179	+	251.458i	0.364772	+	0.631804i
$399$		0			0
$400$		0			0
$401$	26.3207	+	15.1963i	0.0656376	+	0.0378959i	0.532460	−	0.846455i	$-0.321268\pi$
$401$	26.3207	+	15.1963i	0.0656376	+	0.0378959i	−0.466822	+	0.884351i	$0.654601\pi$
$402$		0			0
$403$	−305.616	+	176.448i	−0.758353	+	0.437835i
$404$		−	28.0722i		−	0.0694857i
$405$		0			0
$406$	482.444			1.18828
$407$	242.646	+	420.275i	0.596182	+	1.03262i
$408$		0			0
$409$	36.7195	−	63.6000i	0.0897787	−	0.155501i	−0.817639	−	0.575732i	$-0.804717\pi$
$409$	36.7195	−	63.6000i	0.0897787	−	0.155501i	0.907418	+	0.420230i	$0.138051\pi$
$410$		0			0
$411$		0			0
$412$	−51.7657	+	29.8869i	−0.125645	+	0.0725411i
$413$	26.5066			0.0641807
$414$		0			0
$415$		0			0
$416$	−96.6688	+	55.8118i	−0.232377	+	0.134163i
$417$		0			0
$418$	−545.042	−	314.680i	−1.30393	−	0.752823i
$419$	144.551	+	83.4568i	0.344992	+	0.199181i	0.662477	−	0.749082i	$-0.269505\pi$
$419$	144.551	+	83.4568i	0.344992	+	0.199181i	−0.317486	+	0.948263i	$0.602838\pi$
$420$		0			0
$421$	152.746	+	264.563i	0.362816	+	0.628416i	0.988423	−	0.151722i	$-0.0484820\pi$
$421$	152.746	+	264.563i	0.362816	+	0.628416i	−0.625607	+	0.780138i	$0.715149\pi$
$422$	−582.401			−1.38010
$423$		0			0
$424$	283.963			0.669724
$425$		0			0
$426$		0			0
$427$	371.032	+	214.216i	0.868928	+	0.501676i
$428$	−44.1014	+	76.3859i	−0.103041	+	0.178472i
$429$		0			0
$430$		0			0
$431$			221.026i			0.512820i	0.966568	+	0.256410i	$0.0825398\pi$
$431$			221.026i			0.512820i	−0.966568	+	0.256410i	$0.917460\pi$
$432$		0			0
$433$			194.055i			0.448164i	0.974570	+	0.224082i	$0.0719384\pi$
$433$			194.055i			0.448164i	−0.974570	+	0.224082i	$0.928062\pi$
$434$	327.547	−	189.109i	0.754717	−	0.435736i
$435$		0			0
$436$	−56.2683	+	97.4595i	−0.129056	+	0.223531i
$437$	−182.271	+	315.703i	−0.417097	+	0.722433i
$438$		0			0
$439$	−77.3450	−	133.965i	−0.176184	−	0.305160i	0.764386	−	0.644759i	$-0.223042\pi$
$439$	−77.3450	−	133.965i	−0.176184	−	0.305160i	−0.940571	+	0.339598i	$0.889709\pi$
$440$		0			0
$441$		0			0
$442$		−	256.405i		−	0.580101i
$443$	241.573	+	418.418i	0.545313	+	0.944509i	0.998587	+	0.0531381i	$0.0169224\pi$
$443$	241.573	+	418.418i	0.545313	+	0.944509i	−0.453275	+	0.891371i	$0.649744\pi$
$444$		0			0
$445$		0			0
$446$	−196.924	−	113.694i	−0.441535	−	0.254920i
$447$		0			0
$448$	395.943	−	228.598i	0.883802	−	0.510264i
$449$		−	679.146i		−	1.51257i	−0.654240	−	0.756287i	$-0.727011\pi$
$449$		−	679.146i		−	1.51257i	0.654240	−	0.756287i	$-0.272989\pi$
$450$		0			0
$451$	−314.129			−0.696516
$452$	28.2501	+	48.9306i	0.0625003	+	0.108254i
$453$		0			0
$454$	199.417	−	345.401i	0.439245	−	0.760794i
$455$		0			0
$456$		0			0
$457$	69.7270	−	40.2569i	0.152576	−	0.0880896i	−0.421768	−	0.906704i	$-0.638590\pi$
$457$	69.7270	−	40.2569i	0.152576	−	0.0880896i	0.574344	+	0.818614i	$0.305257\pi$
$458$	137.460			0.300131
$459$		0			0
$460$		0			0
$461$	−535.846	+	309.371i	−1.16236	+	0.671087i	−0.951868	−	0.306510i	$-0.900839\pi$
$461$	−535.846	+	309.371i	−1.16236	+	0.671087i	−0.210489	+	0.977596i	$0.567505\pi$
$462$		0			0
$463$	−285.318	−	164.729i	−0.616238	−	0.355785i	0.159165	−	0.987252i	$-0.449120\pi$
$463$	−285.318	−	164.729i	−0.616238	−	0.355785i	−0.775403	+	0.631467i	$0.782453\pi$
$464$	459.577	+	265.337i	0.990467	+	0.571846i
$465$		0			0
$466$	−130.924	−	226.766i	−0.280952	−	0.486623i
$467$	216.349			0.463275			0.231637	−	0.972802i	$-0.425592\pi$
$467$	216.349			0.463275			0.231637	+	0.972802i	$0.425592\pi$
$468$		0			0
$469$	459.083			0.978855
$470$		0			0
$471$		0			0
$472$	30.1794	+	17.4241i	0.0639395	+	0.0369155i
$473$	200.836	−	347.859i	0.424601	−	0.735430i
$474$		0			0
$475$		0			0
$476$		−	52.0286i		−	0.109304i
$477$		0			0
$478$			367.114i			0.768022i
$479$	−119.965	+	69.2617i	−0.250448	+	0.144596i	−0.619970	−	0.784626i	$-0.712855\pi$
$479$	−119.965	+	69.2617i	−0.250448	+	0.144596i	0.369521	+	0.929222i	$0.379522\pi$
$480$		0			0
$481$	−251.508	+	435.625i	−0.522886	+	0.905665i
$482$	177.816	−	307.987i	0.368913	−	0.638977i
$483$		0			0
$484$	2.22562	+	3.85489i	0.00459840	+	0.00796466i
$485$		0			0
$486$		0			0
$487$		−	93.0290i		−	0.191025i	−0.995428	−	0.0955123i	$-0.969551\pi$
$487$		−	93.0290i		−	0.191025i	0.995428	−	0.0955123i	$-0.0304489\pi$
$488$	281.629	+	487.796i	0.577109	+	0.999581i
$489$		0			0
$490$		0			0
$491$	203.168	+	117.299i	0.413783	+	0.238898i	0.692414	−	0.721501i	$-0.256547\pi$
$491$	203.168	+	117.299i	0.413783	+	0.238898i	−0.278631	+	0.960398i	$0.589881\pi$
$492$		0			0
$493$	444.968	−	256.902i	0.902572	−	0.521100i
$494$		−	652.346i		−	1.32054i
$495$		0			0
$496$	416.029			0.838768
$497$	42.4049	+	73.4474i	0.0853217	+	0.147781i
$498$		0			0
$499$	−330.575	+	572.573i	−0.662476	+	1.14744i	0.317487	+	0.948262i	$0.397161\pi$
$499$	−330.575	+	572.573i	−0.662476	+	1.14744i	−0.979963	+	0.199179i	$0.936172\pi$
$500$		0			0
$501$		0			0
$502$	−478.511	+	276.268i	−0.953209	+	0.550336i
$503$	−184.352			−0.366504			−0.183252	−	0.983066i	$-0.558662\pi$
$503$	−184.352			−0.366504			−0.183252	+	0.983066i	$0.558662\pi$
$504$		0			0
$505$		0			0
$506$	192.344	−	111.050i	0.380126	−	0.219466i
$507$		0			0
$508$	−50.7447	−	29.2975i	−0.0998912	−	0.0576722i
$509$	702.274	+	405.458i	1.37971	+	0.796578i	0.992125	−	0.125255i	$-0.0399749\pi$
$509$	702.274	+	405.458i	1.37971	+	0.796578i	0.387588	+	0.921833i	$0.373308\pi$
$510$		0			0
$511$	353.385	+	612.082i	0.691557	+	1.19781i
$512$	575.386			1.12380
$513$		0			0
$514$	−385.139			−0.749298
$515$		0			0
$516$		0			0
$517$	531.868	+	307.074i	1.02876	+	0.593954i
$518$	269.556	−	466.885i	0.520378	−	0.901322i
$519$		0			0
$520$		0			0
$521$		−	787.925i		−	1.51233i	−0.654379	−	0.756167i	$-0.727070\pi$
$521$		−	787.925i		−	1.51233i	0.654379	−	0.756167i	$-0.272930\pi$
$522$		0			0
$523$			495.806i			0.948004i	0.880524	+	0.474002i	$0.157191\pi$
$523$			495.806i			0.948004i	−0.880524	+	0.474002i	$0.842809\pi$
$524$	88.4968	−	51.0936i	0.168887	−	0.0975070i
$525$		0			0
$526$	138.844	−	240.485i	0.263962	−	0.457196i
$527$	201.402	−	348.839i	0.382168	−	0.661934i
$528$		0			0
$529$	200.177	+	346.717i	0.378406	+	0.655419i
$530$		0			0
$531$		0			0
$532$		−	132.371i		−	0.248818i
$533$	−162.801	−	281.979i	−0.305442	−	0.529041i
$534$		0			0
$535$		0			0
$536$	522.694	+	301.778i	0.975176	+	0.563018i
$537$		0			0
$538$	−653.175	+	377.111i	−1.21408	+	0.700950i
$539$		−	76.5095i		−	0.141947i
$540$		0			0
$541$	−395.636			−0.731305			−0.365652	−	0.930751i	$-0.619154\pi$
$541$	−395.636			−0.731305			−0.365652	+	0.930751i	$0.619154\pi$
$542$	−233.967	−	405.242i	−0.431673	−	0.747680i
$543$		0			0
$544$	63.7052	−	110.341i	0.117105	−	0.202832i
$545$		0			0
$546$		0			0
$547$	−140.121	+	80.8992i	−0.256164	+	0.147896i	−0.622583	−	0.782554i	$-0.713917\pi$
$547$	−140.121	+	80.8992i	−0.256164	+	0.147896i	0.366420	+	0.930450i	$0.380583\pi$
$548$	−57.8589			−0.105582
$549$		0			0
$550$		0			0
$551$	1132.09	−	653.612i	2.05461	−	1.18623i
$552$		0			0
$553$	558.899	+	322.681i	1.01067	+	0.583509i
$554$	294.709	+	170.150i	0.531965	+	0.307130i
$555$		0			0
$556$	20.6861	+	35.8294i	0.0372053	+	0.0644414i
$557$	−199.042			−0.357347			−0.178673	−	0.983908i	$-0.557181\pi$
$557$	−199.042			−0.357347			−0.178673	+	0.983908i	$0.557181\pi$
$558$		0			0
$559$	416.342			0.744799
$560$		0			0
$561$		0			0
$562$	−165.399	−	95.4933i	−0.294305	−	0.169917i
$563$	−453.792	+	785.990i	−0.806024	+	1.39608i	0.109573	+	0.993979i	$0.465052\pi$
$563$	−453.792	+	785.990i	−0.806024	+	1.39608i	−0.915597	+	0.402096i	$0.868282\pi$
$564$		0			0
$565$		0			0
$566$			95.1000i			0.168021i
$567$		0			0
$568$			111.499i			0.196301i
$569$	−776.399	+	448.254i	−1.36450	+	0.787793i	−0.990219	−	0.139523i	$-0.955443\pi$
$569$	−776.399	+	448.254i	−1.36450	+	0.787793i	−0.374279	+	0.927316i	$0.622110\pi$
$570$		0			0
$571$	304.808	−	527.943i	0.533815	−	0.924594i	−0.465405	−	0.885098i	$-0.654091\pi$
$571$	304.808	−	527.943i	0.533815	−	0.924594i	0.999220	−	0.0394965i	$-0.0125754\pi$
$572$	37.6241	−	65.1669i	0.0657765	−	0.113928i
$573$		0			0
$574$	174.483	+	302.214i	0.303977	+	0.526504i
$575$		0			0
$576$		0			0
$577$		−	477.854i		−	0.828170i	−0.910238	−	0.414085i	$-0.864102\pi$
$577$		−	477.854i		−	0.828170i	0.910238	−	0.414085i	$-0.135898\pi$
$578$	−118.667	−	205.537i	−0.205306	−	0.355600i
$579$		0			0
$580$		0			0
$581$	−480.228	−	277.260i	−0.826555	−	0.477212i
$582$		0			0
$583$	−308.795	+	178.283i	−0.529665	+	0.305802i
$584$			929.191i			1.59108i
$585$		0			0
$586$	−608.254			−1.03798
$587$	−127.420	−	220.698i	−0.217070	−	0.375976i	0.736841	−	0.676066i	$-0.236317\pi$
$587$	−127.420	−	220.698i	−0.217070	−	0.375976i	−0.953911	+	0.300090i	$0.902983\pi$
$588$		0			0
$589$	512.409	−	887.518i	0.869964	−	1.50682i
$590$		0			0
$591$		0			0
$592$	513.559	−	296.503i	0.867498	−	0.500850i
$593$	604.184			1.01886			0.509430	−	0.860512i	$-0.329856\pi$
$593$	604.184			1.01886			0.509430	+	0.860512i	$0.329856\pi$
$594$		0			0
$595$		0			0
$596$	−79.5726	+	45.9413i	−0.133511	+	0.0770826i
$597$		0			0
$598$	199.369	+	115.106i	0.333393	+	0.192484i
$599$	−164.832	−	95.1657i	−0.275178	−	0.158874i	0.356060	−	0.934463i	$-0.384120\pi$
$599$	−164.832	−	95.1657i	−0.275178	−	0.158874i	−0.631239	+	0.775589i	$0.717453\pi$
$600$		0			0
$601$	−468.662	−	811.746i	−0.779804	−	1.35066i	−0.932055	−	0.362318i	$-0.881986\pi$
$601$	−468.662	−	811.746i	−0.779804	−	1.35066i	0.152251	−	0.988342i	$-0.451348\pi$
$602$	−446.219			−0.741227
$603$		0			0
$604$	−87.0932			−0.144194
$605$		0			0
$606$		0			0
$607$	−838.308	−	483.997i	−1.38107	−	0.797360i	−0.388781	−	0.921330i	$-0.627104\pi$
$607$	−838.308	−	483.997i	−1.38107	−	0.797360i	−0.992286	+	0.123970i	$0.960437\pi$
$608$	162.079	−	280.729i	0.266577	−	0.461725i
$609$		0			0
$610$		0			0
$611$			636.578i			1.04186i
$612$		0			0
$613$			14.3244i			0.0233677i	0.999932	+	0.0116839i	$0.00371918\pi$
$613$			14.3244i			0.0233677i	−0.999932	+	0.0116839i	$0.996281\pi$
$614$	−464.194	+	268.002i	−0.756016	+	0.436486i
$615$		0			0
$616$	−293.631	+	508.584i	−0.476673	+	0.825623i
$617$	533.807	−	924.580i	0.865165	−	1.49851i	−0.00171906	−	0.999999i	$-0.500547\pi$
$617$	533.807	−	924.580i	0.865165	−	1.49851i	0.866884	−	0.498511i	$-0.166119\pi$
$618$		0			0
$619$	582.166	+	1008.34i	0.940494	+	1.62898i	0.764531	+	0.644586i	$0.222970\pi$
$619$	582.166	+	1008.34i	0.940494	+	1.62898i	0.175963	+	0.984397i	$0.443696\pi$
$620$		0			0
$621$		0			0
$622$		−	362.732i		−	0.583170i
$623$	−205.802	−	356.459i	−0.330340	−	0.572165i
$624$		0			0
$625$		0			0
$626$	342.574	+	197.785i	0.547243	+	0.315951i
$627$		0			0
$628$	−28.7819	+	16.6172i	−0.0458310	+	0.0264605i
$629$		−	574.157i		−	0.912809i
$630$		0			0
$631$	−88.9538			−0.140973			−0.0704864	−	0.997513i	$-0.522455\pi$
$631$	−88.9538			−0.140973			−0.0704864	+	0.997513i	$0.522455\pi$
$632$	424.228	+	734.784i	0.671247	+	1.16263i
$633$		0			0
$634$	186.725	−	323.418i	0.294519	−	0.510123i
$635$		0			0
$636$		0			0
$637$	68.6791	−	39.6519i	0.107816	−	0.0622479i
$638$	−796.434			−1.24833
$639$		0			0
$640$		0			0
$641$	−115.362	+	66.6040i	−0.179971	+	0.103906i	−0.587279	−	0.809384i	$-0.699801\pi$
$641$	−115.362	+	66.6040i	−0.179971	+	0.103906i	0.407308	+	0.913291i	$0.366468\pi$
$642$		0			0
$643$	418.686	+	241.729i	0.651145	+	0.375939i	0.788895	−	0.614528i	$-0.210654\pi$
$643$	418.686	+	241.729i	0.651145	+	0.375939i	−0.137750	+	0.990467i	$0.543987\pi$
$644$	40.4551	+	23.3568i	0.0628185	+	0.0362683i
$645$		0			0
$646$	372.303	+	644.848i	0.576321	+	0.998216i
$647$	−347.759			−0.537495			−0.268748	−	0.963211i	$-0.586610\pi$
$647$	−347.759			−0.537495			−0.268748	+	0.963211i	$0.586610\pi$
$648$		0			0
$649$	−43.7580			−0.0674237
$650$		0			0
$651$		0			0
$652$	−56.9240	−	32.8651i	−0.0873068	−	0.0504066i
$653$	433.872	−	751.488i	0.664428	−	1.15082i	−0.315011	−	0.949088i	$-0.602008\pi$
$653$	433.872	−	751.488i	0.664428	−	1.15082i	0.979440	−	0.201736i	$-0.0646583\pi$
$654$		0			0
$655$		0			0
$656$			383.852i			0.585140i
$657$		0			0
$658$		−	682.258i		−	1.03687i
$659$	804.603	−	464.538i	1.22095	−	0.704913i	0.255826	−	0.966723i	$-0.417653\pi$
$659$	804.603	−	464.538i	1.22095	−	0.704913i	0.965120	+	0.261810i	$0.0843193\pi$
$660$		0			0
$661$	463.561	−	802.912i	0.701303	−	1.21469i	−0.266706	−	0.963778i	$-0.585935\pi$
$661$	463.561	−	802.912i	0.701303	−	1.21469i	0.968009	−	0.250915i	$-0.0807314\pi$
$662$	86.2151	−	149.329i	0.130234	−	0.225572i
$663$		0			0
$664$	−364.513	−	631.355i	−0.548966	−	0.950837i
$665$		0			0
$666$		0			0
$667$			461.316i			0.691629i
$668$	35.9195	+	62.2144i	0.0537717	+	0.0931353i
$669$		0			0
$670$		0			0
$671$	−612.513	−	353.634i	−0.912836	−	0.527026i
$672$		0			0
$673$	819.253	−	472.996i	1.21732	−	0.702817i	0.252973	−	0.967473i	$-0.418592\pi$
$673$	819.253	−	472.996i	1.21732	−	0.702817i	0.964343	+	0.264656i	$0.0852584\pi$
$674$		−	616.446i		−	0.914608i
$675$		0			0
$676$	−29.6162			−0.0438110
$677$	307.292	+	532.245i	0.453902	+	0.786182i	0.998624	−	0.0524349i	$-0.0166982\pi$
$677$	307.292	+	532.245i	0.453902	+	0.786182i	−0.544722	+	0.838617i	$0.683365\pi$
$678$		0			0
$679$	−279.458	+	484.035i	−0.411572	+	0.712864i
$680$		0			0
$681$		0			0
$682$	−540.726	+	312.188i	−0.792853	+	0.457754i
$683$	258.893			0.379053			0.189527	−	0.981876i	$-0.439305\pi$
$683$	258.893			0.379053			0.189527	+	0.981876i	$0.439305\pi$
$684$		0			0
$685$		0			0
$686$	−576.961	+	333.108i	−0.841051	+	0.485581i
$687$		0			0
$688$	−425.069	−	245.414i	−0.617832	−	0.356706i
$689$	−320.072	−	184.794i	−0.464546	−	0.268206i
$690$		0			0
$691$	485.487	+	840.888i	0.702586	+	1.21691i	0.967556	+	0.252658i	$0.0813048\pi$
$691$	485.487	+	840.888i	0.702586	+	1.21691i	−0.264969	+	0.964257i	$0.585362\pi$
$692$	−83.6170			−0.120834
$693$		0			0
$694$	−114.663			−0.165220
$695$		0			0
$696$		0			0
$697$	321.859	+	185.825i	0.461778	+	0.266607i
$698$	294.298	−	509.739i	0.421630	−	0.730285i
$699$		0			0
$700$		0			0
$701$		−	718.418i		−	1.02485i	−0.858733	−	0.512424i	$-0.828748\pi$
$701$		−	718.418i		−	1.02485i	0.858733	−	0.512424i	$-0.171252\pi$
$702$		0			0
$703$		−	1460.77i		−	2.07791i
$704$	−653.637	+	377.377i	−0.928461	+	0.536047i
$705$		0			0
$706$	−152.410	+	263.983i	−0.215879	+	0.373913i
$707$	142.573	−	246.944i	0.201659	−	0.349284i
$708$		0			0
$709$	−494.222	−	856.018i	−0.697070	−	1.20736i	−0.969478	−	0.245178i	$-0.921153\pi$
$709$	−494.222	−	856.018i	−0.697070	−	1.20736i	0.272408	−	0.962182i	$-0.412180\pi$
$710$		0			0
$711$		0			0
$712$		−	541.134i		−	0.760020i
$713$	180.828	+	313.203i	0.253615	+	0.439275i
$714$		0			0
$715$		0			0
$716$	163.823	+	94.5834i	0.228803	+	0.132100i
$717$		0			0
$718$	317.118	−	183.088i	0.441669	−	0.254998i
$719$			1280.53i			1.78099i	0.454994	+	0.890495i	$0.349642\pi$
$719$			1280.53i			1.78099i	−0.454994	+	0.890495i	$0.650358\pi$
$720$		0			0
$721$	−607.158			−0.842106
$722$	616.193	+	1067.28i	0.853453	+	1.47822i
$723$		0			0
$724$	8.95186	−	15.5051i	0.0123644	−	0.0214158i
$725$		0			0
$726$		0			0
$727$	562.611	−	324.824i	0.773881	−	0.446800i	−0.0603766	−	0.998176i	$-0.519230\pi$
$727$	562.611	−	324.824i	0.773881	−	0.446800i	0.834257	+	0.551376i	$0.185897\pi$
$728$	−608.710			−0.836140
$729$		0			0
$730$		0			0
$731$	−411.557	+	237.613i	−0.563006	+	0.325052i
$732$		0			0
$733$	−1013.33	−	585.044i	−1.38244	−	0.798150i	−0.389989	−	0.920820i	$-0.627521\pi$
$733$	−1013.33	−	585.044i	−1.38244	−	0.798150i	−0.992448	+	0.122669i	$0.960855\pi$
$734$	255.134	+	147.302i	0.347594	+	0.200683i
$735$		0			0
$736$	57.1972	+	99.0685i	0.0777136	+	0.134604i
$737$	−757.869			−1.02832
$738$		0			0
$739$	−1175.25			−1.59033			−0.795164	−	0.606394i	$-0.792615\pi$
$739$	−1175.25			−1.59033			−0.795164	+	0.606394i	$0.792615\pi$
$740$		0			0
$741$		0			0
$742$	343.040	+	198.054i	0.462319	+	0.266920i
$743$	−508.717	+	881.124i	−0.684680	+	1.18590i	0.288858	+	0.957372i	$0.406725\pi$
$743$	−508.717	+	881.124i	−0.684680	+	1.18590i	−0.973537	+	0.228528i	$0.926609\pi$
$744$		0			0
$745$		0			0
$746$			314.035i			0.420958i
$747$		0			0
$748$			85.8906i			0.114827i
$749$	−775.897	+	447.964i	−1.03591	+	0.598083i
$750$		0			0
$751$	497.229	−	861.226i	0.662089	−	1.14677i	−0.317977	−	0.948099i	$-0.603003\pi$
$751$	497.229	−	861.226i	0.662089	−	1.14677i	0.980066	−	0.198673i	$-0.0636633\pi$
$752$	375.232	−	649.920i	0.498978	−	0.864256i
$753$		0			0
$754$	−412.761	−	714.922i	−0.547428	−	0.948173i
$755$		0			0
$756$		0			0
$757$			659.088i			0.870658i	0.900271	+	0.435329i	$0.143368\pi$
$757$			659.088i			0.870658i	−0.900271	+	0.435329i	$0.856632\pi$
$758$	272.781	+	472.471i	0.359870	+	0.623313i
$759$		0			0
$760$		0			0
$761$	−559.677	−	323.130i	−0.735450	−	0.424612i	0.0849628	−	0.996384i	$-0.472923\pi$
$761$	−559.677	−	323.130i	−0.735450	−	0.424612i	−0.820413	+	0.571772i	$0.806256\pi$
$762$		0			0
$763$	−989.954	+	571.550i	−1.29745	+	0.749083i
$764$			5.83933i			0.00764310i
$765$		0			0
$766$	−881.649			−1.15098
$767$	−22.6781	−	39.2796i	−0.0295672	−	0.0512119i
$768$		0			0
$769$	−123.429	+	213.784i	−0.160505	+	0.278003i	−0.935050	−	0.354516i	$-0.884646\pi$
$769$	−123.429	+	213.784i	−0.160505	+	0.278003i	0.774545	+	0.632519i	$0.217979\pi$
$770$		0			0
$771$		0			0
$772$	−52.2588	+	30.1717i	−0.0676928	+	0.0390824i
$773$	−263.071			−0.340325			−0.170162	−	0.985416i	$-0.554429\pi$
$773$	−263.071			−0.340325			−0.170162	+	0.985416i	$0.554429\pi$
$774$		0			0
$775$		0			0
$776$	−636.360	+	367.402i	−0.820051	+	0.473457i
$777$		0			0
$778$	944.100	+	545.076i	1.21350	+	0.700612i
$779$	818.875	+	472.777i	1.05119	+	0.606903i
$780$		0			0
$781$	−70.0034	−	121.249i	−0.0896330	−	0.155249i
$782$	−262.770			−0.336023
$783$		0			0
$784$	−93.4914			−0.119249
$785$		0			0
$786$		0			0
$787$	932.515	+	538.388i	1.18490	+	0.684102i	0.957143	−	0.289617i	$-0.0935278\pi$
$787$	932.515	+	538.388i	1.18490	+	0.684102i	0.227756	+	0.973718i	$0.426861\pi$
$788$	85.1129	−	147.420i	0.108011	−	0.187081i
$789$		0			0
$790$		0			0
$791$			573.906i			0.725545i
$792$		0			0
$793$		−	733.100i		−	0.924463i
$794$	−168.832	+	97.4751i	−0.212635	+	0.122765i
$795$		0			0
$796$	50.4084	−	87.3099i	0.0633271	−	0.109686i
$797$	−456.965	+	791.487i	−0.573356	+	0.993082i	0.422862	+	0.906194i	$0.361026\pi$
$797$	−456.965	+	791.487i	−0.573356	+	0.993082i	−0.996218	+	0.0868882i	$0.972308\pi$
$798$		0			0
$799$	−363.304	−	629.262i	−0.454699	−	0.787562i
$800$		0			0
$801$		0			0
$802$			55.7373i			0.0694978i
$803$	−583.381	−	1010.44i	−0.726501	−	1.25834i
$804$		0			0
$805$		0			0
$806$	−560.474	−	323.590i	−0.695377	−	0.401476i
$807$		0			0
$808$	324.657	−	187.441i	0.401803	−	0.231981i
$809$		−	1008.67i		−	1.24681i	−0.781897	−	0.623407i	$-0.785748\pi$
$809$		−	1008.67i		−	1.24681i	0.781897	−	0.623407i	$-0.214252\pi$
$810$		0			0
$811$	952.468			1.17444			0.587218	−	0.809429i	$-0.300223\pi$
$811$	952.468			1.17444			0.587218	+	0.809429i	$0.300223\pi$
$812$	−83.7557	−	145.069i	−0.103147	−	0.178657i
$813$		0			0
$814$	−444.992	+	770.749i	−0.546673	+	0.946866i
$815$		0			0
$816$		0			0
$817$	−1047.08	+	604.535i	−1.28162	+	0.739945i
$818$	134.681			0.164646
$819$		0			0
$820$		0			0
$821$	1222.35	−	705.724i	1.48885	−	0.859590i	0.488935	−	0.872320i	$-0.337385\pi$
$821$	1222.35	−	705.724i	1.48885	−	0.859590i	0.999919	+	0.0127295i	$0.00405205\pi$
$822$		0			0
$823$	−659.680	−	380.867i	−0.801556	−	0.462778i	0.0424591	−	0.999098i	$-0.486481\pi$
$823$	−659.680	−	380.867i	−0.801556	−	0.462778i	−0.844015	+	0.536320i	$0.819814\pi$
$824$	−691.287	−	399.115i	−0.838941	−	0.484363i
$825$		0			0
$826$	24.3054	+	42.0982i	0.0294255	+	0.0509664i
$827$	718.144			0.868373			0.434186	−	0.900823i	$-0.357036\pi$
$827$	718.144			0.868373			0.434186	+	0.900823i	$0.357036\pi$
$828$		0			0
$829$	−400.411			−0.483005			−0.241503	−	0.970400i	$-0.577640\pi$
$829$	−400.411			−0.483005			−0.241503	+	0.970400i	$0.577640\pi$
$830$		0			0
$831$		0			0
$832$	−677.509	−	391.160i	−0.814313	−	0.470144i
$833$	−45.2598	+	78.3923i	−0.0543335	+	0.0941084i
$834$		0			0
$835$		0			0
$836$			218.523i			0.261391i
$837$		0			0
$838$			306.105i			0.365281i
$839$	−614.302	+	354.667i	−0.732183	+	0.422726i	−0.819220	−	0.573479i	$-0.805593\pi$
$839$	−614.302	+	354.667i	−0.732183	+	0.422726i	0.0870370	+	0.996205i	$0.472260\pi$
$840$		0			0
$841$	406.624	−	704.293i	0.483500	−	0.837447i
$842$	−280.122	+	485.186i	−0.332687	+	0.576230i
$843$		0			0
$844$	101.109	+	175.126i	0.119797	+	0.207495i
$845$		0			0
$846$		0			0
$847$			45.2139i			0.0533813i
$848$	217.854	+	377.334i	0.256903	+	0.444969i
$849$		0			0
$850$		0			0
$851$	446.439	+	257.751i	0.524605	+	0.302881i
$852$		0			0
$853$	767.495	−	443.113i	0.899760	−	0.519476i	0.0226375	−	0.999744i	$-0.492794\pi$
$853$	767.495	−	443.113i	0.899760	−	0.519476i	0.877122	+	0.480267i	$0.159460\pi$
$854$			785.706i			0.920030i
$855$		0			0
$856$	−1177.88			−1.37602
$857$	163.757	+	283.635i	0.191081	+	0.330963i	0.945609	−	0.325306i	$-0.105467\pi$
$857$	163.757	+	283.635i	0.191081	+	0.330963i	−0.754527	+	0.656268i	$0.772134\pi$
$858$		0			0
$859$	−35.0835	+	60.7664i	−0.0408423	+	0.0707409i	−0.885724	−	0.464212i	$-0.846337\pi$
$859$	−35.0835	+	60.7664i	−0.0408423	+	0.0707409i	0.844882	+	0.534953i	$0.179671\pi$
$860$		0			0
$861$		0			0
$862$	−351.036	+	202.671i	−0.407235	+	0.235117i
$863$	−982.709			−1.13871			−0.569356	−	0.822091i	$-0.692807\pi$
$863$	−982.709			−1.13871			−0.569356	+	0.822091i	$0.692807\pi$
$864$		0			0
$865$		0			0
$866$	−308.201	+	177.940i	−0.355891	+	0.205474i
$867$		0			0
$868$	−113.729	−	65.6615i	−0.131024	−	0.0756469i
$869$	−922.650	−	532.692i	−1.06174	−	0.612994i
$870$		0			0
$871$	−392.774	−	680.305i	−0.450946	−	0.781062i
$872$	−1502.83			−1.72343
$873$		0			0
$874$	−668.539			−0.764919
$875$		0			0
$876$		0			0
$877$	802.714	+	463.447i	0.915296	+	0.528446i	0.882131	−	0.471004i	$-0.156108\pi$
$877$	802.714	+	463.447i	0.915296	+	0.528446i	0.0331646	+	0.999450i	$0.489441\pi$
$878$	141.844	−	245.681i	0.161553	−	0.279819i
$879$		0			0
$880$		0			0
$881$			766.920i			0.870510i	0.900307	+	0.435255i	$0.143342\pi$
$881$			766.920i			0.870510i	−0.900307	+	0.435255i	$0.856658\pi$
$882$		0			0
$883$			1206.08i			1.36589i	0.730469	+	0.682946i	$0.239301\pi$
$883$			1206.08i			1.36589i	−0.730469	+	0.682946i	$0.760699\pi$
$884$	−77.1000	+	44.5137i	−0.0872172	+	0.0503549i
$885$		0			0
$886$	−443.025	+	767.341i	−0.500028	+	0.866074i
$887$	−376.283	+	651.741i	−0.424220	+	0.734771i	−0.996347	−	0.0853943i	$-0.972785\pi$
$887$	−376.283	+	651.741i	−0.424220	+	0.734771i	0.572127	+	0.820165i	$0.306118\pi$
$888$		0			0
$889$	−297.592	−	515.444i	−0.334749	−	0.579802i
$890$		0			0
$891$		0			0
$892$			78.9527i			0.0885120i
$893$	−924.320	−	1600.97i	−1.03507	−	1.79280i
$894$		0			0
$895$		0			0
$896$	500.149	+	288.761i	0.558202	+	0.322278i
$897$		0			0
$898$	1078.63	−	622.747i	1.20115	−	0.693482i
$899$		−	1296.87i		−	1.44257i
$900$		0			0
$901$	421.858			0.468211
$902$	−288.042	−	498.904i	−0.319338	−	0.553109i
$903$		0			0
$904$	−377.257	+	653.428i	−0.417319	+	0.722818i
$905$		0			0
$906$		0			0
$907$	307.213	−	177.370i	0.338713	−	0.195556i	−0.320989	−	0.947083i	$-0.604015\pi$
$907$	307.213	−	177.370i	0.338713	−	0.195556i	0.659703	+	0.751526i	$0.270682\pi$
$908$	−138.481			−0.152512
$909$		0			0
$910$		0			0
$911$	−280.940	+	162.201i	−0.308387	+	0.178047i	−0.646204	−	0.763164i	$-0.723645\pi$
$911$	−280.940	+	162.201i	−0.308387	+	0.178047i	0.337818	+	0.941212i	$0.390311\pi$
$912$		0			0
$913$	792.777	+	457.710i	0.868321	+	0.501325i
$914$	127.873	+	73.8277i	0.139905	+	0.0807743i
$915$		0			0
$916$	−23.8641	−	41.3338i	−0.0260525	−	0.0451243i
$917$	1037.98			1.13193
$918$		0			0
$919$	604.200			0.657453			0.328727	−	0.944425i	$-0.393381\pi$
$919$	604.200			0.657453			0.328727	+	0.944425i	$0.393381\pi$
$920$		0			0
$921$		0			0
$922$	−982.696	−	567.360i	−1.06583	−	0.615357i
$923$	72.5600	−	125.678i	0.0786133	−	0.136162i
$924$		0			0
$925$		0			0
$926$		−	604.196i		−	0.652479i
$927$		0			0
$928$		−	410.211i		−	0.442037i
$929$	−1417.48	+	818.384i	−1.52582	+	0.880930i	−0.526285	+	0.850308i	$0.676415\pi$
$929$	−1417.48	+	818.384i	−1.52582	+	0.880930i	−0.999531	+	0.0306220i	$0.990251\pi$
$930$		0			0
$931$	−115.150	+	199.446i	−0.123684	+	0.214228i
$932$	−45.4586	+	78.7366i	−0.0487753	+	0.0844813i
$933$		0			0
$934$	198.383	+	343.609i	0.212401	+	0.367890i
$935$		0			0
$936$		0			0
$937$			266.212i			0.284111i	0.989859	+	0.142055i	$0.0453711\pi$
$937$			266.212i			0.284111i	−0.989859	+	0.142055i	$0.954629\pi$
$938$	420.959	+	729.123i	0.448784	+	0.777316i
$939$		0			0
$940$		0			0
$941$	−140.374	−	81.0449i	−0.149175	−	0.0861264i	0.423554	−	0.905871i	$-0.360782\pi$
$941$	−140.374	−	81.0449i	−0.149175	−	0.0861264i	−0.572730	+	0.819744i	$0.694116\pi$
$942$		0			0
$943$	−288.979	+	166.842i	−0.306446	+	0.176927i
$944$			53.4704i			0.0566424i
$945$		0			0
$946$	736.633			0.778681
$947$	−398.717	−	690.598i	−0.421032	−	0.729248i	0.575009	−	0.818147i	$-0.304999\pi$
$947$	−398.717	−	690.598i	−0.421032	−	0.729248i	−0.996041	+	0.0888989i	$0.971665\pi$
$948$		0			0
$949$	604.687	−	1047.35i	0.637183	−	1.10363i
$950$		0			0
$951$		0			0
$952$	601.713	−	347.399i	0.632052	−	0.364915i
$953$	1382.90			1.45110			0.725551	−	0.688168i	$-0.241585\pi$
$953$	1382.90			1.45110			0.725551	+	0.688168i	$0.241585\pi$
$954$		0			0
$955$		0			0
$956$	110.390	−	63.7338i	0.115471	−	0.0666671i
$957$		0			0
$958$	−220.005	−	127.020i	−0.229650	−	0.132589i
$959$	−508.969	−	293.853i	−0.530729	−	0.306416i
$960$		0			0
$961$	−27.8509	−	48.2391i	−0.0289811	−	0.0501968i
$962$	−922.488			−0.958927
$963$		0			0
$964$	−123.481			−0.128092
$965$		0			0
$966$		0			0
$967$	320.006	+	184.756i	0.330927	+	0.191061i	0.656252	−	0.754541i	$-0.272141\pi$
$967$	320.006	+	184.756i	0.330927	+	0.191061i	−0.325326	+	0.945602i	$0.605474\pi$
$968$	−29.7214	+	51.4789i	−0.0307039	+	0.0531807i
$969$		0			0
$970$		0			0
$971$		−	961.450i		−	0.990165i	−0.868846	−	0.495082i	$-0.835138\pi$
$971$		−	961.450i		−	0.990165i	0.868846	−	0.495082i	$-0.164862\pi$
$972$		0			0
$973$			420.243i			0.431904i
$974$	147.750	−	85.3036i	0.151694	−	0.0875807i
$975$		0			0
$976$	−432.126	+	748.465i	−0.442752	+	0.766870i
$977$	859.076	−	1487.96i	0.879300	−	1.52299i	0.0271901	−	0.999630i	$-0.491344\pi$
$977$	859.076	−	1487.96i	0.879300	−	1.52299i	0.852110	−	0.523362i	$-0.175323\pi$
$978$		0			0
$979$	339.744	+	588.454i	0.347032	+	0.601077i
$980$		0			0
$981$		0			0
$982$			430.232i			0.438118i
$983$	640.833	+	1109.96i	0.651915	+	1.12915i	0.982658	+	0.185430i	$0.0593676\pi$
$983$	640.833	+	1109.96i	0.651915	+	1.12915i	−0.330742	+	0.943721i	$0.607299\pi$
$984$		0			0
$985$		0			0
$986$	816.033	+	471.137i	0.827620	+	0.477826i
$987$		0			0
$988$	−196.158	+	113.252i	−0.198541	+	0.114627i
$989$		−	426.678i		−	0.431423i
$990$		0			0
$991$	952.926			0.961581			0.480790	−	0.876836i	$-0.340350\pi$
$991$	952.926			0.961581			0.480790	+	0.876836i	$0.340350\pi$
$992$	−160.795	−	278.506i	−0.162092	−	0.280752i
$993$		0			0
$994$	−77.7669	+	134.696i	−0.0782363	+	0.135509i
$995$		0			0
$996$		0			0
$997$	−1532.57	+	884.833i	−1.53719	+	0.887495i	−0.538185	+	0.842827i	$0.680890\pi$
$997$	−1532.57	+	884.833i	−1.53719	+	0.887495i	−0.999002	+	0.0446679i	$0.985777\pi$
$998$	−1212.49			−1.21492
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.3.i.c.449.12		32
3.2	odd	2		225.3.i.b.149.5		32
5.2	odd	4		135.3.i.a.71.3		16
5.3	odd	4		675.3.j.b.476.6		16
5.4	even	2	inner	675.3.i.c.449.5		32
9.2	odd	6	inner	675.3.i.c.224.5		32
9.7	even	3		225.3.i.b.74.12		32
15.2	even	4		45.3.i.a.41.6	yes	16
15.8	even	4		225.3.j.b.176.3		16
15.14	odd	2		225.3.i.b.149.12		32
20.7	even	4		2160.3.bs.c.881.6		16
45.2	even	12		135.3.i.a.116.3		16
45.7	odd	12		45.3.i.a.11.6	✓	16
45.22	odd	12		405.3.c.a.161.5		16
45.29	odd	6	inner	675.3.i.c.224.12		32
45.32	even	12		405.3.c.a.161.12		16
45.34	even	6		225.3.i.b.74.5		32
45.38	even	12		675.3.j.b.251.6		16
45.43	odd	12		225.3.j.b.101.3		16
60.47	odd	4		720.3.bs.c.401.4		16
180.7	even	12		720.3.bs.c.641.4		16
180.47	odd	12		2160.3.bs.c.1601.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.i.a.11.6	✓	16	45.7	odd	12
45.3.i.a.41.6	yes	16	15.2	even	4
135.3.i.a.71.3		16	5.2	odd	4
135.3.i.a.116.3		16	45.2	even	12
225.3.i.b.74.5		32	45.34	even	6
225.3.i.b.74.12		32	9.7	even	3
225.3.i.b.149.5		32	3.2	odd	2
225.3.i.b.149.12		32	15.14	odd	2
225.3.j.b.101.3		16	45.43	odd	12
225.3.j.b.176.3		16	15.8	even	4
405.3.c.a.161.5		16	45.22	odd	12
405.3.c.a.161.12		16	45.32	even	12
675.3.i.c.224.5		32	9.2	odd	6	inner
675.3.i.c.224.12		32	45.29	odd	6	inner
675.3.i.c.449.5		32	5.4	even	2	inner
675.3.i.c.449.12		32	1.1	even	1	trivial
675.3.j.b.251.6		16	45.38	even	12
675.3.j.b.476.6		16	5.3	odd	4
720.3.bs.c.401.4		16	60.47	odd	4
720.3.bs.c.641.4		16	180.7	even	12
2160.3.bs.c.881.6		16	20.7	even	4
2160.3.bs.c.1601.6		16	180.47	odd	12

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	675.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.916957 + 1.58822i) q^{2} +(0.318381 - 0.551452i) q^{4} +(5.60142 - 3.23398i) q^{7} +8.50342 q^{8} +(-9.24701 + 5.33876i) q^{11} +(-9.58473 - 5.53374i) q^{13} +(10.2725 + 5.93084i) q^{14} +(6.52374 + 11.2995i) q^{16} +12.6328 q^{17} +32.1403 q^{19} +(-16.9582 - 9.79083i) q^{22} +(-5.67112 + 9.82266i) q^{23} -20.2968i q^{26} -4.11855i q^{28} +(35.2234 - 20.3362i) q^{29} +(15.9429 - 27.6139i) q^{31} +(5.04286 - 8.73448i) q^{32} +(11.5837 + 20.0635i) q^{34} -45.4499i q^{37} +(29.4713 + 51.0457i) q^{38} +(25.4781 + 14.7098i) q^{41} +(-32.5786 + 18.8093i) q^{43} +6.79904i q^{44} -20.8007 q^{46} +(-28.7589 - 49.8119i) q^{47} +(-3.58274 + 6.20548i) q^{49} +(-6.10319 + 3.52368i) q^{52} +33.3940 q^{53} +(47.6312 - 27.4999i) q^{56} +(64.5966 + 37.2949i) q^{58} +(3.54909 + 2.04907i) q^{59} +(33.1195 + 57.3647i) q^{61} +58.4757 q^{62} +70.6863 q^{64} +(61.4687 + 35.4890i) q^{67} +(4.02203 - 6.96635i) q^{68} +13.1123i q^{71} +109.273i q^{73} +(72.1842 - 41.6756i) q^{74} +(10.2328 - 17.7238i) q^{76} +(-34.5309 + 59.8093i) q^{77} +(49.8891 + 86.4104i) q^{79} +53.9530i q^{82} +(-42.8667 - 74.2472i) q^{83} +(-59.7463 - 34.4945i) q^{86} +(-78.6312 + 45.3977i) q^{88} -63.6372i q^{89} -71.5841 q^{91} +(3.61115 + 6.25469i) q^{92} +(52.7414 - 91.3507i) q^{94} +(-74.8357 + 43.2064i) q^{97} -13.1409 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} + 36 q^{11} - 108 q^{14} - 64 q^{16} + 104 q^{19} - 108 q^{29} + 64 q^{31} - 108 q^{34} - 288 q^{41} - 216 q^{46} + 108 q^{49} + 36 q^{56} - 972 q^{59} + 124 q^{61} - 512 q^{64} + 1080 q^{74}+ \cdots + 300 q^{94}+O(q^{100}) \) 32 * q - 32 * q^4 + 36 * q^11 - 108 * q^14 - 64 * q^16 + 104 * q^19 - 108 * q^29 + 64 * q^31 - 108 * q^34 - 288 * q^41 - 216 * q^46 + 108 * q^49 + 36 * q^56 - 972 * q^59 + 124 * q^61 - 512 * q^64 + 1080 * q^74 - 212 * q^76 + 80 * q^79 - 108 * q^86 + 272 * q^91 + 300 * q^94

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