LMFDB - Embedded newform 375.3.j.b.26.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [375,3,Mod(26,375)] 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("375.26"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(375, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 4])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	375.j (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [144] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$10.2180099135$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			26.11
Character	$\chi$	$=$	375.26
Dual form			375.3.j.b.101.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.81520 + 0.589794i) q^{2} +(-2.32377 - 1.89739i) q^{3} +(-0.288978 + 0.209955i) q^{4} +(5.33718 + 2.07358i) q^{6} -4.41289 q^{7} +(4.88814 - 6.72795i) q^{8} +(1.79986 + 8.81819i) q^{9} +(10.5279 - 3.42072i) q^{11} +(1.06988 + 0.0604149i) q^{12} +(2.29360 - 7.05898i) q^{13} +(8.01027 - 2.60269i) q^{14} +(-4.46333 + 13.7367i) q^{16} +(7.26868 - 10.0045i) q^{17} +(-8.46802 - 14.9452i) q^{18} +(-3.31483 - 2.40836i) q^{19} +(10.2546 + 8.37295i) q^{21} +(-17.0927 + 12.4186i) q^{22} +(-19.6017 + 6.36898i) q^{23} +(-24.1244 + 6.35955i) q^{24} +14.1662i q^{26} +(12.5490 - 23.9065i) q^{27} +(1.27523 - 0.926506i) q^{28} +(-10.1555 - 13.9778i) q^{29} +(35.5401 + 25.8214i) q^{31} +5.69751i q^{32} +(-30.9548 - 12.0265i) q^{33} +(-7.29352 + 22.4471i) q^{34} +(-2.37154 - 2.17037i) q^{36} +(-15.4731 + 47.6213i) q^{37} +(7.43751 + 2.41659i) q^{38} +(-18.7234 + 12.0516i) q^{39} +(-61.9322 - 20.1230i) q^{41} +(-23.5524 - 9.15049i) q^{42} -71.9655 q^{43} +(-2.32413 + 3.19889i) q^{44} +(31.8246 - 23.1219i) q^{46} +(-16.2566 - 22.3753i) q^{47} +(36.4356 - 23.4524i) q^{48} -29.5264 q^{49} +(-35.8731 + 9.45667i) q^{51} +(0.819266 + 2.52144i) q^{52} +(34.7232 + 47.7924i) q^{53} +(-8.67909 + 50.7964i) q^{54} +(-21.5708 + 29.6897i) q^{56} +(3.13332 + 11.8860i) q^{57} +(26.6782 + 19.3828i) q^{58} +(-49.4896 - 16.0801i) q^{59} +(11.2398 + 34.5926i) q^{61} +(-79.7417 - 25.9096i) q^{62} +(-7.94257 - 38.9137i) q^{63} +(-21.2137 - 65.2889i) q^{64} +(63.2823 + 3.57347i) q^{66} +(-66.1816 - 48.0837i) q^{67} +4.41716i q^{68} +(57.6344 + 22.3919i) q^{69} +(-76.9924 - 105.971i) q^{71} +(68.1263 + 30.9952i) q^{72} +(40.4118 + 124.375i) q^{73} -95.5681i q^{74} +1.46356 q^{76} +(-46.4584 + 15.0952i) q^{77} +(26.8788 - 32.9191i) q^{78} +(89.4854 - 65.0149i) q^{79} +(-74.5210 + 31.7430i) q^{81} +124.288 q^{82} +(-63.7909 + 87.8007i) q^{83} +(-4.72128 - 0.266604i) q^{84} +(130.632 - 42.4448i) q^{86} +(-2.92226 + 51.7501i) q^{87} +(28.4474 - 87.5520i) q^{88} +(57.5511 - 18.6995i) q^{89} +(-10.1214 + 31.1505i) q^{91} +(4.32726 - 5.95596i) q^{92} +(-33.5941 - 127.436i) q^{93} +(42.7058 + 31.0276i) q^{94} +(10.8104 - 13.2397i) q^{96} +(24.1988 - 17.5814i) q^{97} +(53.5963 - 17.4145i) q^{98} +(49.1132 + 86.6801i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 76 q^{4} + 10 q^{6} + 26 q^{9} + 44 q^{16} + 72 q^{19} + 108 q^{21} + 40 q^{24} - 252 q^{31} - 420 q^{34} - 426 q^{36} + 382 q^{39} - 420 q^{46} + 448 q^{49} - 120 q^{51} - 640 q^{54} + 588 q^{61}+ \cdots - 120 q^{99}+O(q^{100}) $ 144 * q + 76 * q^4 + 10 * q^6 + 26 * q^9 + 44 * q^16 + 72 * q^19 + 108 * q^21 + 40 * q^24 - 252 * q^31 - 420 * q^34 - 426 * q^36 + 382 * q^39 - 420 * q^46 + 448 * q^49 - 120 * q^51 - 640 * q^54 + 588 * q^61 - 724 * q^64 - 940 * q^66 - 670 * q^69 - 32 * q^76 + 692 * q^79 + 1014 * q^81 + 912 * q^84 + 1076 * q^91 + 1120 * q^94 + 1480 * q^96 - 120 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$

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 $

$2$	−1.81520	+	0.589794i	−0.907599	+	0.294897i	−0.725370	−	0.688359i	$-0.758331\pi$
$2$	−1.81520	+	0.589794i	−0.907599	+	0.294897i	−0.182229	+	0.983256i	$0.558331\pi$
$3$	−2.32377	−	1.89739i	−0.774592	−	0.632462i
$3$	−2.32377	−	1.89739i	−0.774592	−	0.632462i
$4$	−0.288978	+	0.209955i	−0.0722445	+	0.0524887i
$5$		0			0
$5$		0			0
$6$	5.33718	+	2.07358i	0.889530	+	0.345597i
$7$	−4.41289			−0.630412			−0.315206	−	0.949023i	$-0.602074\pi$
$7$	−4.41289			−0.630412			−0.315206	+	0.949023i	$0.602074\pi$
$8$	4.88814	−	6.72795i	0.611018	−	0.840994i
$9$	1.79986	+	8.81819i	0.199984	+	0.979799i
$10$		0			0
$11$	10.5279	−	3.42072i	0.957080	−	0.310974i	0.211491	−	0.977380i	$-0.432168\pi$
$11$	10.5279	−	3.42072i	0.957080	−	0.310974i	0.745589	+	0.666406i	$0.232168\pi$
$12$	1.06988	+	0.0604149i	0.0891570	+	0.00503458i
$13$	2.29360	−	7.05898i	0.176431	−	0.542999i	−0.823265	−	0.567657i	$-0.807850\pi$
$13$	2.29360	−	7.05898i	0.176431	−	0.542999i	0.999696	+	0.0246587i	$0.00784990\pi$
$14$	8.01027	−	2.60269i	0.572162	−	0.185907i
$15$		0			0
$16$	−4.46333	+	13.7367i	−0.278958	+	0.858544i
$17$	7.26868	−	10.0045i	0.427569	−	0.588499i	−0.539824	−	0.841778i	$-0.681509\pi$
$17$	7.26868	−	10.0045i	0.427569	−	0.588499i	0.967393	+	0.253279i	$0.0815092\pi$
$18$	−8.46802	−	14.9452i	−0.470445	−	0.830290i
$19$	−3.31483	−	2.40836i	−0.174465	−	0.126756i	0.497126	−	0.867678i	$-0.334389\pi$
$19$	−3.31483	−	2.40836i	−0.174465	−	0.126756i	−0.671591	+	0.740922i	$0.734389\pi$
$20$		0			0
$21$	10.2546	+	8.37295i	0.488312	+	0.398712i
$22$	−17.0927	+	12.4186i	−0.776940	+	0.564480i
$23$	−19.6017	+	6.36898i	−0.852248	+	0.276912i	−0.702387	−	0.711795i	$-0.747883\pi$
$23$	−19.6017	+	6.36898i	−0.852248	+	0.276912i	−0.149861	+	0.988707i	$0.547883\pi$
$24$	−24.1244	+	6.35955i	−1.00519	+	0.264981i
$25$		0			0
$26$			14.1662i			0.544854i
$27$	12.5490	−	23.9065i	0.464779	−	0.885427i
$28$	1.27523	−	0.926506i	0.0455438	−	0.0330895i
$29$	−10.1555	−	13.9778i	−0.350188	−	0.481993i	0.597194	−	0.802097i	$-0.296282\pi$
$29$	−10.1555	−	13.9778i	−0.350188	−	0.481993i	−0.947382	+	0.320104i	$0.896282\pi$
$30$		0			0
$31$	35.5401	+	25.8214i	1.14646	+	0.832949i	0.988006	−	0.154418i	$-0.0493504\pi$
$31$	35.5401	+	25.8214i	1.14646	+	0.832949i	0.158450	+	0.987367i	$0.449350\pi$
$32$			5.69751i			0.178047i
$33$	−30.9548	−	12.0265i	−0.938026	−	0.364439i
$34$	−7.29352	+	22.4471i	−0.214515	+	0.660210i
$35$		0			0
$36$	−2.37154	−	2.17037i	−0.0658761	−	0.0602882i
$37$	−15.4731	+	47.6213i	−0.418192	+	1.28706i	0.491173	+	0.871062i	$0.336568\pi$
$37$	−15.4731	+	47.6213i	−0.418192	+	1.28706i	−0.909365	+	0.416000i	$0.863432\pi$
$38$	7.43751	+	2.41659i	0.195724	+	0.0635946i
$39$	−18.7234	+	12.0516i	−0.480088	+	0.309016i
$40$		0			0
$41$	−61.9322	−	20.1230i	−1.51054	−	0.490805i	−0.567470	−	0.823394i	$-0.692078\pi$
$41$	−61.9322	−	20.1230i	−1.51054	−	0.490805i	−0.943072	+	0.332589i	$0.892078\pi$
$42$	−23.5524	−	9.15049i	−0.560771	−	0.217869i
$43$	−71.9655			−1.67362			−0.836808	−	0.547497i	$-0.815581\pi$
$43$	−71.9655			−1.67362			−0.836808	+	0.547497i	$0.815581\pi$
$44$	−2.32413	+	3.19889i	−0.0528211	+	0.0727020i
$45$		0			0
$46$	31.8246	−	23.1219i	0.691839	−	0.502651i
$47$	−16.2566	−	22.3753i	−0.345885	−	0.476070i	0.600263	−	0.799802i	$-0.295062\pi$
$47$	−16.2566	−	22.3753i	−0.345885	−	0.476070i	−0.946149	+	0.323732i	$0.895062\pi$
$48$	36.4356	−	23.4524i	0.759075	−	0.488591i
$49$	−29.5264			−0.602580
$50$		0			0
$51$	−35.8731	+	9.45667i	−0.703394	+	0.185425i
$52$	0.819266	+	2.52144i	0.0157551	+	0.0484893i
$53$	34.7232	+	47.7924i	0.655155	+	0.901743i	0.999309	−	0.0371699i	$-0.0118343\pi$
$53$	34.7232	+	47.7924i	0.655155	+	0.901743i	−0.344154	+	0.938913i	$0.611834\pi$
$54$	−8.67909	+	50.7964i	−0.160724	+	0.940675i
$55$		0			0
$56$	−21.5708	+	29.6897i	−0.385193	+	0.530173i
$57$	3.13332	+	11.8860i	0.0549706	+	0.208526i
$58$	26.6782	+	19.3828i	0.459969	+	0.334187i
$59$	−49.4896	−	16.0801i	−0.838806	−	0.272545i	−0.142056	−	0.989859i	$-0.545371\pi$
$59$	−49.4896	−	16.0801i	−0.838806	−	0.272545i	−0.696750	+	0.717314i	$0.745371\pi$
$60$		0			0
$61$	11.2398	+	34.5926i	0.184259	+	0.567091i	0.999935	−	0.0114181i	$-0.00363457\pi$
$61$	11.2398	+	34.5926i	0.184259	+	0.567091i	−0.815676	+	0.578510i	$0.803635\pi$
$62$	−79.7417	−	25.9096i	−1.28616	−	0.417897i
$63$	−7.94257	−	38.9137i	−0.126073	−	0.617677i
$64$	−21.2137	−	65.2889i	−0.331463	−	1.02014i
$65$		0			0
$66$	63.2823	+	3.57347i	0.958823	+	0.0541434i
$67$	−66.1816	−	48.0837i	−0.987785	−	0.717668i	−0.0283498	−	0.999598i	$-0.509025\pi$
$67$	−66.1816	−	48.0837i	−0.987785	−	0.717668i	−0.959435	+	0.281931i	$0.909025\pi$
$68$			4.41716i			0.0649583i
$69$	57.6344	+	22.3919i	0.835281	+	0.324520i
$70$		0			0
$71$	−76.9924	−	105.971i	−1.08440	−	1.49255i	−0.854584	−	0.519314i	$-0.826188\pi$
$71$	−76.9924	−	105.971i	−1.08440	−	1.49255i	−0.229816	−	0.973234i	$-0.573812\pi$
$72$	68.1263	+	30.9952i	0.946199	+	0.430489i
$73$	40.4118	+	124.375i	0.553586	+	1.70376i	0.699648	+	0.714488i	$0.253340\pi$
$73$	40.4118	+	124.375i	0.553586	+	1.70376i	−0.146061	+	0.989276i	$0.546660\pi$
$74$		−	95.5681i		−	1.29146i
$75$		0			0
$76$	1.46356			0.0192574
$77$	−46.4584	+	15.0952i	−0.603355	+	0.196042i
$78$	26.8788	−	32.9191i	0.344599	−	0.422039i
$79$	89.4854	−	65.0149i	1.13273	−	0.822974i	0.146637	−	0.989190i	$-0.453155\pi$
$79$	89.4854	−	65.0149i	1.13273	−	0.822974i	0.986089	+	0.166217i	$0.0531552\pi$
$80$		0			0
$81$	−74.5210	+	31.7430i	−0.920013	+	0.391889i
$82$	124.288			1.51570
$83$	−63.7909	+	87.8007i	−0.768565	+	1.05784i	0.227888	+	0.973687i	$0.426818\pi$
$83$	−63.7909	+	87.8007i	−0.768565	+	1.05784i	−0.996453	+	0.0841518i	$0.973182\pi$
$84$	−4.72128	−	0.266604i	−0.0562057	−	0.00317386i
$85$		0			0
$86$	130.632	−	42.4448i	1.51897	−	0.493544i
$87$	−2.92226	+	51.7501i	−0.0335891	+	0.594828i
$88$	28.4474	−	87.5520i	0.323266	−	0.994909i
$89$	57.5511	−	18.6995i	0.646642	−	0.210107i	0.0327090	−	0.999465i	$-0.489587\pi$
$89$	57.5511	−	18.6995i	0.646642	−	0.210107i	0.613933	+	0.789358i	$0.289587\pi$
$90$		0			0
$91$	−10.1214	+	31.1505i	−0.111224	+	0.342313i
$92$	4.32726	−	5.95596i	0.0470354	−	0.0647387i
$93$	−33.5941	−	127.436i	−0.361227	−	1.37028i
$94$	42.7058	+	31.0276i	0.454317	+	0.330081i
$95$		0			0
$96$	10.8104	−	13.2397i	0.112608	−	0.137914i
$97$	24.1988	−	17.5814i	0.249472	−	0.181252i	−0.456021	−	0.889969i	$-0.650726\pi$
$97$	24.1988	−	17.5814i	0.249472	−	0.181252i	0.705493	+	0.708717i	$0.250726\pi$
$98$	53.5963	−	17.4145i	0.546901	−	0.177699i
$99$	49.1132	+	86.6801i	0.496093	+	0.875557i
$100$		0			0
$101$			43.9076i			0.434729i	0.976091	+	0.217364i	$0.0697460\pi$
$101$			43.9076i			0.434729i	−0.976091	+	0.217364i	$0.930254\pi$
$102$	59.5394	−	38.3235i	0.583719	−	0.375720i
$103$	11.4024	−	8.28434i	0.110703	−	0.0804305i	−0.531056	−	0.847336i	$-0.678205\pi$
$103$	11.4024	−	8.28434i	0.110703	−	0.0804305i	0.641759	+	0.766906i	$0.278205\pi$
$104$	−36.2810	−	49.9365i	−0.348856	−	0.480159i
$105$		0			0
$106$	−91.2172	−	66.2732i	−0.860540	−	0.625219i
$107$			37.3527i			0.349091i	0.984649	+	0.174546i	$0.0558456\pi$
$107$			37.3527i			0.349091i	−0.984649	+	0.174546i	$0.944154\pi$
$108$	1.39289	+	9.54318i	0.0128971	+	0.0883628i
$109$	−12.8306	+	39.4885i	−0.117712	+	0.362280i	−0.992503	−	0.122220i	$-0.960999\pi$
$109$	−12.8306	+	39.4885i	−0.117712	+	0.362280i	0.874791	+	0.484500i	$0.160999\pi$
$110$		0			0
$111$	126.312	−	81.3027i	1.13795	−	0.732457i
$112$	19.6962	−	60.6185i	0.175858	−	0.541237i
$113$	−89.1295	−	28.9599i	−0.788756	−	0.256282i	−0.113182	−	0.993574i	$-0.536104\pi$
$113$	−89.1295	−	28.9599i	−0.788756	−	0.256282i	−0.675574	+	0.737292i	$0.736104\pi$
$114$	−12.6979	−	19.7275i	−0.111385	−	0.173048i
$115$		0			0
$116$	5.86941	+	1.90709i	0.0505983	+	0.0164404i
$117$	66.3756	+	7.52026i	0.567313	+	0.0642757i
$118$	99.3174			0.841673
$119$	−32.0758	+	44.1486i	−0.269545	+	0.370997i
$120$		0			0
$121$	1.24398	−	0.903807i	0.0102809	−	0.00746948i
$122$	−40.8050	−	56.1632i	−0.334467	−	0.460354i
$123$	105.735	+	164.271i	0.859638	+	1.33553i
$124$	−15.6916			−0.126545
$125$		0			0
$126$	37.3684	+	65.9516i	0.296575	+	0.523425i
$127$	2.52112	+	7.75921i	0.0198513	+	0.0610962i	0.960491	−	0.278309i	$-0.0897741\pi$
$127$	2.52112	+	7.75921i	0.0198513	+	0.0610962i	−0.940640	+	0.339406i	$0.889774\pi$
$128$	63.6184	+	87.5632i	0.497019	+	0.684087i
$129$	167.232	+	136.546i	1.29637	+	1.05850i
$130$		0			0
$131$	−36.9420	+	50.8463i	−0.282000	+	0.388140i	−0.926395	−	0.376553i	$-0.877109\pi$
$131$	−36.9420	+	50.8463i	−0.282000	+	0.388140i	0.644395	+	0.764693i	$0.277109\pi$
$132$	11.4703	−	3.02373i	0.0868961	−	0.0229070i
$133$	14.6280	+	10.6278i	0.109985	+	0.0799086i
$134$	148.492	+	48.2480i	1.10815	+	0.360060i
$135$		0			0
$136$	−31.7793	−	97.8066i	−0.233671	−	0.719166i
$137$	147.501	+	47.9259i	1.07665	+	0.349824i	0.793073	−	0.609126i	$-0.208480\pi$
$137$	147.501	+	47.9259i	1.07665	+	0.349824i	0.283574	+	0.958950i	$0.408480\pi$
$138$	−117.824	−	6.65338i	−0.853800	−	0.0482129i
$139$	2.53894	+	7.81406i	0.0182658	+	0.0562163i	0.959774	−	0.280774i	$-0.0905911\pi$
$139$	2.53894	+	7.81406i	0.0182658	+	0.0562163i	−0.941508	+	0.336990i	$0.890591\pi$
$140$		0			0
$141$	−4.67788	+	82.8402i	−0.0331764	+	0.587519i
$142$	202.257	+	146.949i	1.42435	+	1.03485i
$143$		−	82.1619i		−	0.574559i
$144$	−129.166	−	14.6343i	−0.896988	−	0.101627i
$145$		0			0
$146$	−146.711	−	201.930i	−1.00487	−	1.38308i
$147$	68.6128	+	56.0230i	0.466754	+	0.381109i
$148$	−5.52693	−	17.0101i	−0.0373441	−	0.114933i
$149$			93.4274i			0.627030i	0.949583	+	0.313515i	$0.101507\pi$
$149$			93.4274i			0.627030i	−0.949583	+	0.313515i	$0.898493\pi$
$150$		0			0
$151$	−209.930			−1.39027			−0.695133	−	0.718882i	$-0.744654\pi$
$151$	−209.930			−1.39027			−0.695133	+	0.718882i	$0.744654\pi$
$152$	−32.4067	+	10.5296i	−0.213202	+	0.0692735i
$153$	101.304	+	46.0900i	0.662118	+	0.301242i
$154$	75.4281	−	54.8017i	0.489793	−	0.355855i
$155$		0			0
$156$	2.88036	−	7.41373i	0.0184638	−	0.0475239i
$157$	−184.544			−1.17544			−0.587720	−	0.809064i	$-0.699975\pi$
$157$	−184.544			−1.17544			−0.587720	+	0.809064i	$0.699975\pi$
$158$	−124.088	+	170.793i	−0.785369	+	1.08097i
$159$	9.99168	−	176.942i	0.0628407	−	1.11284i
$160$		0			0
$161$	86.5001	−	28.1056i	0.537268	−	0.174569i
$162$	116.549	−	101.572i	0.719436	−	0.626987i
$163$	45.7029	−	140.659i	0.280386	−	0.862938i	−0.707358	−	0.706855i	$-0.750113\pi$
$163$	45.7029	−	140.659i	0.280386	−	0.862938i	0.987744	−	0.156083i	$-0.0498867\pi$
$164$	22.1220	−	7.18786i	0.134890	−	0.0438284i
$165$		0			0
$166$	64.0089	−	196.999i	0.385596	−	1.18674i
$167$	5.79243	−	7.97260i	0.0346852	−	0.0477401i	−0.791322	−	0.611399i	$-0.790607\pi$
$167$	5.79243	−	7.97260i	0.0346852	−	0.0477401i	0.826007	+	0.563659i	$0.190607\pi$
$168$	106.458	−	28.0640i	0.633681	−	0.167047i
$169$	92.1553	+	66.9547i	0.545297	+	0.396182i
$170$		0			0
$171$	15.2712	−	33.5655i	0.0893053	−	0.196290i
$172$	20.7964	−	15.1095i	0.120909	−	0.0878459i
$173$	26.5053	−	8.61208i	0.153210	−	0.0497808i	−0.231408	−	0.972857i	$-0.574333\pi$
$173$	26.5053	−	8.61208i	0.153210	−	0.0497808i	0.384618	+	0.923076i	$0.374333\pi$
$174$	−25.2174	−	95.6602i	−0.144928	−	0.549771i
$175$		0			0
$176$			159.886i			0.908444i
$177$	84.4924	+	131.267i	0.477358	+	0.741624i
$178$	−93.4379	+	67.8866i	−0.524932	+	0.381385i
$179$	−164.237	−	226.053i	−0.917527	−	1.26287i	−0.964530	−	0.263973i	$-0.914967\pi$
$179$	−164.237	−	226.053i	−0.917527	−	1.26287i	0.0470028	−	0.998895i	$-0.485033\pi$
$180$		0			0
$181$	−46.9496	−	34.1109i	−0.259390	−	0.188458i	0.450488	−	0.892782i	$-0.351250\pi$
$181$	−46.9496	−	34.1109i	−0.259390	−	0.188458i	−0.709878	+	0.704325i	$0.751250\pi$
$182$		−	62.5139i		−	0.343483i
$183$	39.5167	−	101.712i	0.215938	−	0.555801i
$184$	−52.9657	+	163.012i	−0.287857	+	0.885933i
$185$		0			0
$186$	136.141	+	211.509i	0.731942	+	1.13714i
$187$	42.3013	−	130.190i	0.226210	−	0.696203i
$188$	9.39560	+	3.05282i	0.0499766	+	0.0162384i
$189$	−55.3775	+	105.497i	−0.293003	+	0.558184i
$190$		0			0
$191$	−21.7540	−	7.06832i	−0.113895	−	0.0370069i	0.251515	−	0.967853i	$-0.419071\pi$
$191$	−21.7540	−	7.06832i	−0.113895	−	0.0370069i	−0.365410	+	0.930847i	$0.619071\pi$
$192$	−74.5825	+	191.967i	−0.388451	+	0.999830i
$193$	−223.265			−1.15681			−0.578407	−	0.815748i	$-0.696326\pi$
$193$	−223.265			−1.15681			−0.578407	+	0.815748i	$0.696326\pi$
$194$	−33.5561	+	46.1861i	−0.172970	+	0.238072i
$195$		0			0
$196$	8.53248	−	6.19921i	0.0435331	−	0.0316286i
$197$	−113.906	−	156.779i	−0.578204	−	0.795830i	0.415293	−	0.909688i	$-0.363679\pi$
$197$	−113.906	−	156.779i	−0.578204	−	0.795830i	−0.993497	+	0.113858i	$0.963679\pi$
$198$	−140.274	−	128.375i	−0.708453	−	0.648358i
$199$	−32.3854			−0.162741			−0.0813703	−	0.996684i	$-0.525930\pi$
$199$	−32.3854			−0.162741			−0.0813703	+	0.996684i	$0.525930\pi$
$200$		0			0
$201$	62.5577	+	237.308i	0.311232	+	1.18064i
$202$	−25.8964	−	79.7011i	−0.128200	−	0.394560i
$203$	44.8149	+	61.6824i	0.220763	+	0.303854i
$204$	8.38106	−	10.2645i	0.0410836	−	0.0503162i
$205$		0			0
$206$	−15.8116	+	21.7628i	−0.0767553	+	0.105645i
$207$	−91.4432	−	161.388i	−0.441754	−	0.779654i
$208$	86.7300	+	63.0131i	0.416971	+	0.302947i
$209$	−43.1365	−	14.0159i	−0.206395	−	0.0670617i
$210$		0			0
$211$	81.5984	+	251.134i	0.386722	+	1.19021i	0.935223	+	0.354059i	$0.115199\pi$
$211$	81.5984	+	251.134i	0.386722	+	1.19021i	−0.548501	+	0.836150i	$0.684801\pi$
$212$	−20.0685	−	6.52064i	−0.0946626	−	0.0307577i
$213$	−22.1547	+	392.337i	−0.104013	+	1.84196i
$214$	−22.0304	−	67.8027i	−0.102946	−	0.316835i
$215$		0			0
$216$	−99.5003	−	201.288i	−0.460650	−	0.931888i
$217$	−156.834	−	113.947i	−0.722740	−	0.525101i
$218$		−	79.2469i		−	0.363518i
$219$	142.079	−	365.696i	0.648762	−	1.66984i
$220$		0			0
$221$	−53.9500	−	74.2557i	−0.244117	−	0.335999i
$222$	−181.329	+	222.079i	−0.816799	+	1.00035i
$223$	−75.5301	−	232.458i	−0.338700	−	1.04241i	−0.964871	−	0.262726i	$-0.915379\pi$
$223$	−75.5301	−	232.458i	−0.338700	−	1.04241i	0.626170	−	0.779686i	$-0.284621\pi$
$224$		−	25.1425i		−	0.112243i
$225$		0			0
$226$	178.868			0.791452
$227$	−293.361	+	95.3189i	−1.29234	+	0.419907i	−0.872911	−	0.487880i	$-0.837770\pi$
$227$	−293.361	+	95.3189i	−1.29234	+	0.419907i	−0.419431	+	0.907787i	$0.637770\pi$
$228$	−3.40098	−	2.77694i	−0.0149166	−	0.0121795i
$229$	−329.863	+	239.660i	−1.44045	+	1.04655i	−0.452502	+	0.891763i	$0.649469\pi$
$229$	−329.863	+	239.660i	−1.44045	+	1.04655i	−0.987948	+	0.154785i	$0.950531\pi$
$230$		0			0
$231$	136.600	+	53.0715i	0.591343	+	0.229747i
$232$	−143.683			−0.619324
$233$	42.2218	−	58.1134i	0.181210	−	0.249414i	−0.708743	−	0.705467i	$-0.750737\pi$
$233$	42.2218	−	58.1134i	0.181210	−	0.249414i	0.889952	+	0.456053i	$0.150737\pi$
$234$	−124.920	+	25.4972i	−0.533848	+	0.108962i
$235$		0			0
$236$	17.6775	−	5.74376i	0.0749046	−	0.0243380i
$237$	−331.302	−	18.7082i	−1.39790	−	0.0789375i
$238$	32.1855	−	99.0567i	0.135233	−	0.416204i
$239$	29.9013	−	9.71552i	0.125110	−	0.0406507i	−0.245793	−	0.969322i	$-0.579048\pi$
$239$	29.9013	−	9.71552i	0.125110	−	0.0406507i	0.370903	+	0.928672i	$0.379048\pi$
$240$		0			0
$241$	−32.6481	+	100.481i	−0.135469	+	0.416932i	−0.995663	−	0.0930360i	$-0.970343\pi$
$241$	−32.6481	+	100.481i	−0.135469	+	0.416932i	0.860193	+	0.509968i	$0.170343\pi$
$242$	−1.72502	+	2.37428i	−0.00712817	+	0.00981109i
$243$	233.399	+	67.6315i	0.960489	+	0.278319i
$244$	−10.5109	−	7.63664i	−0.0430776	−	0.0312977i
$245$		0			0
$246$	−288.817	−	235.822i	−1.17405	−	0.958625i
$247$	−24.6035	+	17.8755i	−0.0996093	+	0.0723704i
$248$	347.450	−	112.893i	1.40101	−	0.455215i
$249$	314.827	−	82.9930i	1.26437	−	0.333305i
$250$		0			0
$251$		−	18.8308i		−	0.0750233i	−0.999296	−	0.0375116i	$-0.988057\pi$
$251$		−	18.8308i		−	0.0750233i	0.999296	−	0.0375116i	$-0.0119431\pi$
$252$	10.4653	+	9.57761i	0.0415291	+	0.0380064i
$253$	−184.578	+	134.104i	−0.729557	+	0.530054i
$254$	−9.15267	−	12.5976i	−0.0360341	−	0.0495967i
$255$		0			0
$256$	55.0281	+	39.9803i	0.214954	+	0.156173i
$257$			165.627i			0.644461i	0.946661	+	0.322231i	$0.104433\pi$
$257$			165.627i			0.644461i	−0.946661	+	0.322231i	$0.895567\pi$
$258$	−384.093	−	149.226i	−1.48873	−	0.578397i
$259$	68.2810	−	210.147i	0.263633	−	0.811380i
$260$		0			0
$261$	104.980	−	114.711i	0.402224	−	0.439505i
$262$	37.0683	−	114.084i	0.141482	−	0.435437i
$263$	−221.773	−	72.0585i	−0.843244	−	0.273987i	−0.144630	−	0.989486i	$-0.546199\pi$
$263$	−221.773	−	72.0585i	−0.843244	−	0.273987i	−0.698614	+	0.715499i	$0.746199\pi$
$264$	−232.225	+	149.476i	−0.879641	+	0.566195i
$265$		0			0
$266$	−32.8209	−	10.6642i	−0.123387	−	0.0400908i
$267$	−169.216	−	65.7432i	−0.633768	−	0.246229i
$268$	29.2204			0.109031
$269$	−36.2442	+	49.8858i	−0.134737	+	0.185449i	−0.871054	−	0.491187i	$-0.836563\pi$
$269$	−36.2442	+	49.8858i	−0.134737	+	0.185449i	0.736317	+	0.676636i	$0.236563\pi$
$270$		0			0
$271$	−29.1365	+	21.1689i	−0.107515	+	0.0781140i	−0.640244	−	0.768172i	$-0.721167\pi$
$271$	−29.1365	+	21.1689i	−0.107515	+	0.0781140i	0.532729	+	0.846286i	$0.321167\pi$
$272$	104.986	+	144.501i	0.385978	+	0.531253i
$273$	82.6243	−	53.1825i	0.302653	−	0.194808i
$274$	−296.010			−1.08033
$275$		0			0
$276$	−21.3563	+	5.62984i	−0.0773780	+	0.0203980i
$277$	26.5323	+	81.6581i	0.0957845	+	0.294794i	0.987457	−	0.157886i	$-0.0504678\pi$
$277$	26.5323	+	81.6581i	0.0957845	+	0.294794i	−0.891673	+	0.452680i	$0.850468\pi$
$278$	−9.21737	−	12.6866i	−0.0331560	−	0.0456354i
$279$	−163.731	+	359.874i	−0.586849	+	1.28987i
$280$		0			0
$281$	−55.9474	+	77.0049i	−0.199101	+	0.274039i	−0.896880	−	0.442274i	$-0.854172\pi$
$281$	−55.9474	+	77.0049i	−0.199101	+	0.274039i	0.697779	+	0.716313i	$0.254172\pi$
$282$	−40.3674	−	153.131i	−0.143147	−	0.543016i
$283$	−67.8613	−	49.3041i	−0.239792	−	0.174219i	0.461398	−	0.887193i	$-0.347348\pi$
$283$	−67.8613	−	49.3041i	−0.239792	−	0.174219i	−0.701191	+	0.712974i	$0.747348\pi$
$284$	44.4982	+	14.4583i	0.156684	+	0.0509096i
$285$		0			0
$286$	48.4586	+	149.140i	0.169436	+	0.521469i
$287$	273.300	+	88.8005i	0.952264	+	0.309409i
$288$	−50.2418	+	10.2547i	−0.174451	+	0.0356067i
$289$	42.0500	+	129.417i	0.145502	+	0.447809i
$290$		0			0
$291$	−89.5912	−	5.05909i	−0.307873	−	0.0173852i
$292$	−37.7912	−	27.4569i	−0.129422	−	0.0940305i
$293$		−	123.416i		−	0.421214i	−0.977571	−	0.210607i	$-0.932456\pi$
$293$		−	123.416i		−	0.421214i	0.977571	−	0.210607i	$-0.0675440\pi$
$294$	−157.588	−	61.2255i	−0.536013	−	0.208250i
$295$		0			0
$296$	244.759	+	336.882i	0.826888	+	1.13811i
$297$	50.3375	−	294.612i	0.169486	−	0.991959i
$298$	−55.1029	−	169.589i	−0.184909	−	0.569092i
$299$			152.976i			0.511625i
$300$		0			0
$301$	317.575			1.05507
$302$	381.065	−	123.815i	1.26180	−	0.409985i
$303$	83.3097	−	102.031i	0.274949	−	0.336737i
$304$	47.8782	−	34.7855i	0.157494	−	0.114426i
$305$		0			0
$306$	−211.070	−	23.9140i	−0.689773	−	0.0781502i
$307$	65.2670			0.212596			0.106298	−	0.994334i	$-0.466100\pi$
$307$	65.2670			0.212596			0.106298	+	0.994334i	$0.466100\pi$
$308$	10.2561	−	14.1163i	0.0332991	−	0.0458323i
$309$	−42.2152	−	2.38384i	−0.136619	−	0.00771468i
$310$		0			0
$311$	19.6525	−	6.38548i	0.0631913	−	0.0205321i	−0.277251	−	0.960798i	$-0.589423\pi$
$311$	19.6525	−	6.38548i	0.0631913	−	0.0205321i	0.340442	+	0.940266i	$0.389423\pi$
$312$	−10.4399	+	184.880i	−0.0334613	+	0.592565i
$313$	−24.2172	+	74.5328i	−0.0773711	+	0.238124i	−0.982260	−	0.187524i	$-0.939954\pi$
$313$	−24.2172	+	74.5328i	−0.0773711	+	0.238124i	0.904889	+	0.425648i	$0.139954\pi$
$314$	334.984	−	108.843i	1.06683	−	0.346634i
$315$		0			0
$316$	−12.2091	+	37.5757i	−0.0386364	+	0.118911i
$317$	277.943	−	382.556i	0.876793	−	1.20680i	−0.100506	−	0.994936i	$-0.532046\pi$
$317$	277.943	−	382.556i	0.876793	−	1.20680i	0.977299	−	0.211865i	$-0.0679538\pi$
$318$	86.2225	+	327.078i	0.271140	+	1.02855i
$319$	−154.730	−	112.418i	−0.485046	−	0.352406i
$320$		0			0
$321$	70.8725	−	86.7994i	0.220787	−	0.270403i
$322$	−140.438	+	102.034i	−0.436144	+	0.316877i
$323$	−48.1889	+	15.6575i	−0.149192	+	0.0484753i
$324$	14.8703	−	24.8191i	0.0458961	−	0.0766020i
$325$		0			0
$326$			282.279i			0.865887i
$327$	104.740	−	67.4178i	0.320307	−	0.206171i
$328$	−438.120	+	318.313i	−1.33573	+	0.970466i
$329$	71.7386	+	98.7397i	0.218050	+	0.300121i
$330$		0			0
$331$	70.6578	+	51.3359i	0.213468	+	0.155093i	0.689381	−	0.724399i	$-0.257883\pi$
$331$	70.6578	+	51.3359i	0.213468	+	0.155093i	−0.475914	+	0.879492i	$0.657883\pi$
$332$		−	38.7656i		−	0.116764i
$333$	−447.783	−	50.7332i	−1.34469	−	0.152352i
$334$	−5.81223	+	17.8882i	−0.0174019	+	0.0535575i
$335$		0			0
$336$	−160.786	+	103.493i	−0.478530	+	0.308014i
$337$	−193.716	+	596.196i	−0.574824	+	1.76913i	0.0619517	+	0.998079i	$0.480268\pi$
$337$	−193.716	+	596.196i	−0.574824	+	1.76913i	−0.636776	+	0.771049i	$0.719732\pi$
$338$	−206.770	−	67.1835i	−0.611744	−	0.198768i
$339$	152.169	+	236.409i	0.448875	+	0.697373i
$340$		0			0
$341$	462.490	+	150.272i	1.35628	+	0.440681i
$342$	−7.92353	+	69.9350i	−0.0231682	+	0.204488i
$343$	346.528			1.01029
$344$	−351.777	+	484.180i	−1.02261	+	1.40750i
$345$		0			0
$346$	−43.0330	+	31.2653i	−0.124373	+	0.0903621i
$347$	152.183	+	209.462i	0.438568	+	0.603638i	0.969893	−	0.243531i	$-0.0783056\pi$
$347$	152.183	+	209.462i	0.438568	+	0.603638i	−0.531325	+	0.847168i	$0.678306\pi$
$348$	−10.0207	−	15.5682i	−0.0287951	−	0.0447361i
$349$	110.570			0.316818			0.158409	−	0.987374i	$-0.449364\pi$
$349$	110.570			0.316818			0.158409	+	0.987374i	$0.449364\pi$
$350$		0			0
$351$	−139.973	−	143.415i	−0.398784	−	0.408591i
$352$	19.4896	+	59.9828i	0.0553681	+	0.170406i
$353$	−115.355	−	158.773i	−0.326785	−	0.449781i	0.613739	−	0.789509i	$-0.289665\pi$
$353$	−115.355	−	158.773i	−0.326785	−	0.449781i	−0.940524	+	0.339728i	$0.889665\pi$
$354$	−230.791	−	188.443i	−0.651953	−	0.532326i
$355$		0			0
$356$	−12.7050	+	17.4869i	−0.0356881	+	0.0491204i
$357$	158.304	−	41.7312i	0.443429	−	0.116894i
$358$	431.448	+	313.466i	1.20516	+	0.875602i
$359$	279.715	+	90.8849i	0.779150	+	0.253161i	0.671477	−	0.741025i	$-0.265660\pi$
$359$	279.715	+	90.8849i	0.779150	+	0.253161i	0.107673	+	0.994186i	$0.465660\pi$
$360$		0			0
$361$	−106.367	−	327.365i	−0.294646	−	0.906828i
$362$	105.341	+	34.2274i	0.290998	+	0.0945509i
$363$	−4.60561	−	0.260072i	−0.0126876	−	0.000716453i
$364$	−3.61533	−	11.1268i	−0.00993222	−	0.0305682i
$365$		0			0
$366$	−11.7417	+	207.933i	−0.0320812	+	0.568124i
$367$	122.465	+	88.9759i	0.333692	+	0.242441i	0.741995	−	0.670405i	$-0.233880\pi$
$367$	122.465	+	88.9759i	0.333692	+	0.242441i	−0.408304	+	0.912846i	$0.633880\pi$
$368$		−	297.690i		−	0.808939i
$369$	65.9793	−	582.349i	0.178806	−	1.57818i
$370$		0			0
$371$	−153.230	−	210.902i	−0.413018	−	0.568470i
$372$	36.4638	+	29.7731i	0.0980210	+	0.0800351i
$373$	−25.8861	−	79.6692i	−0.0693997	−	0.213590i	0.910342	−	0.413858i	$-0.135819\pi$
$373$	−25.8861	−	79.6692i	−0.0693997	−	0.213590i	−0.979741	+	0.200267i	$0.935819\pi$
$374$			261.270i			0.698583i
$375$		0			0
$376$	−230.005			−0.611714
$377$	−121.962	+	39.6277i	−0.323506	+	0.105113i
$378$	38.2999	−	224.159i	0.101322	−	0.593013i
$379$	404.648	−	293.994i	1.06767	−	0.775709i	0.0921796	−	0.995742i	$-0.470617\pi$
$379$	404.648	−	293.994i	1.06767	−	0.775709i	0.975492	+	0.220033i	$0.0706166\pi$
$380$		0			0
$381$	8.86370	−	22.8142i	0.0232643	−	0.0598798i
$382$	43.6568			0.114285
$383$	153.550	−	211.343i	0.400913	−	0.551810i	−0.560060	−	0.828452i	$-0.689222\pi$
$383$	153.550	−	211.343i	0.400913	−	0.551810i	0.960973	+	0.276643i	$0.0892218\pi$
$384$	18.3063	−	324.186i	0.0476727	−	0.844233i
$385$		0			0
$386$	405.271	−	131.680i	1.04992	−	0.341141i
$387$	−129.528	−	634.605i	−0.334697	−	1.63981i
$388$	−3.30160	+	10.1613i	−0.00850928	+	0.0261889i
$389$	−292.261	+	94.9613i	−0.751313	+	0.244117i	−0.659546	−	0.751664i	$-0.729252\pi$
$389$	−292.261	+	94.9613i	−0.751313	+	0.244117i	−0.0917672	+	0.995780i	$0.529252\pi$
$390$		0			0
$391$	−78.7602	+	242.399i	−0.201433	+	0.619946i
$392$	−144.329	+	198.652i	−0.368187	+	0.506766i
$393$	182.320	−	48.0622i	0.463919	−	0.122296i
$394$	299.230	+	217.403i	0.759466	+	0.551784i
$395$		0			0
$396$	−32.3915	−	14.7371i	−0.0817968	−	0.0372148i
$397$	323.187	−	234.809i	0.814073	−	0.591459i	−0.100935	−	0.994893i	$-0.532184\pi$
$397$	323.187	−	234.809i	0.814073	−	0.591459i	0.915009	+	0.403434i	$0.132184\pi$
$398$	58.7859	−	19.1007i	0.147703	−	0.0479917i
$399$	−13.8270	−	52.4516i	−0.0346541	−	0.131458i
$400$		0			0
$401$		−	411.484i		−	1.02614i	−0.858345	−	0.513072i	$-0.828507\pi$
$401$		−	411.484i		−	1.02614i	0.858345	−	0.513072i	$-0.171493\pi$
$402$	−253.517	−	393.864i	−0.630640	−	0.979762i
$403$	263.788	−	191.653i	0.654560	−	0.475566i
$404$	−9.21861	−	12.6883i	−0.0228183	−	0.0314068i
$405$		0			0
$406$	−117.728	−	85.5343i	−0.289970	−	0.210676i
$407$			554.281i			1.36187i
$408$	−111.729	+	287.578i	−0.273845	+	0.704848i
$409$	−29.9193	+	92.0821i	−0.0731523	+	0.225140i	−0.980947	−	0.194275i	$-0.937765\pi$
$409$	−29.9193	+	92.0821i	−0.0731523	+	0.225140i	0.907795	+	0.419414i	$0.137765\pi$
$410$		0			0
$411$	−251.825	−	391.235i	−0.612712	−	0.951909i
$412$	−1.55571	+	4.78798i	−0.00377599	+	0.0116213i
$413$	218.392	+	70.9598i	0.528794	+	0.171816i
$414$	261.173	+	239.019i	0.630854	+	0.577341i
$415$		0			0
$416$	40.2186	+	13.0678i	0.0966794	+	0.0314130i
$417$	8.92636	−	22.9755i	0.0214061	−	0.0550971i
$418$	86.5678			0.207100
$419$	62.6472	−	86.2265i	0.149516	−	0.205791i	−0.727689	−	0.685907i	$-0.759405\pi$
$419$	62.6472	−	86.2265i	0.149516	−	0.205791i	0.877205	+	0.480116i	$0.159405\pi$
$420$		0			0
$421$	527.139	−	382.989i	1.25211	−	0.909713i	0.253770	−	0.967265i	$-0.418329\pi$
$421$	527.139	−	382.989i	1.25211	−	0.909713i	0.998343	+	0.0575516i	$0.0183294\pi$
$422$	−296.235	−	407.732i	−0.701978	−	0.966190i
$423$	168.050	−	183.626i	0.397282	−	0.434105i
$424$	491.277			1.15867
$425$		0			0
$426$	−191.183	−	725.236i	−0.448785	−	1.70243i
$427$	−49.6000	−	152.653i	−0.116159	−	0.357501i
$428$	−7.84238	−	10.7941i	−0.0183233	−	0.0252199i
$429$	−155.893	+	190.926i	−0.363386	+	0.445048i
$430$		0			0
$431$	−66.7077	+	91.8153i	−0.154774	+	0.213029i	−0.879362	−	0.476154i	$-0.842030\pi$
$431$	−66.7077	+	91.8153i	−0.154774	+	0.213029i	0.724587	+	0.689183i	$0.242030\pi$
$432$	272.386	+	279.085i	0.630524	+	0.646030i
$433$	556.211	+	404.111i	1.28455	+	0.933281i	0.999680	−	0.0252849i	$-0.00804929\pi$
$433$	556.211	+	404.111i	1.28455	+	0.933281i	0.284871	+	0.958566i	$0.408049\pi$
$434$	351.891	+	114.336i	0.810809	+	0.263448i
$435$		0			0
$436$	−4.58304	−	14.1052i	−0.0105116	−	0.0323513i
$437$	80.3151	+	26.0960i	0.183788	+	0.0597162i
$438$	−42.2164	+	747.608i	−0.0963844	+	1.70687i
$439$	−200.112	−	615.882i	−0.455836	−	1.40292i	−0.870151	−	0.492786i	$-0.835979\pi$
$439$	−200.112	−	615.882i	−0.455836	−	1.40292i	0.414314	−	0.910134i	$-0.364021\pi$
$440$		0			0
$441$	−53.1434	−	260.370i	−0.120507	−	0.590408i
$442$	141.725	+	102.970i	0.320646	+	0.232963i
$443$			517.544i			1.16827i	0.811656	+	0.584136i	$0.198566\pi$
$443$			517.544i			1.16827i	−0.811656	+	0.584136i	$0.801434\pi$
$444$	−19.4315	+	50.0145i	−0.0437646	+	0.112645i
$445$		0			0
$446$	274.204	+	377.410i	0.614808	+	0.846211i
$447$	177.268	−	217.104i	0.396572	−	0.485692i
$448$	93.6135	+	288.113i	0.208959	+	0.643109i
$449$		−	139.654i		−	0.311034i	−0.987833	−	0.155517i	$-0.950296\pi$
$449$		−	139.654i		−	0.311034i	0.987833	−	0.155517i	$-0.0497044\pi$
$450$		0			0
$451$	−720.850			−1.59834
$452$	31.8367	−	10.3444i	0.0704352	−	0.0228858i
$453$	487.830	+	398.318i	1.07689	+	0.879290i
$454$	476.291	−	346.046i	1.04910	−	0.762215i
$455$		0			0
$456$	95.2846	+	37.0196i	0.208957	+	0.0811834i
$457$	672.235			1.47097			0.735487	−	0.677539i	$-0.236953\pi$
$457$	672.235			1.47097			0.735487	+	0.677539i	$0.236953\pi$
$458$	457.417	−	629.581i	0.998728	−	1.37463i
$459$	−147.957	−	299.315i	−0.322347	−	0.652103i
$460$		0			0
$461$	−362.835	+	117.892i	−0.787060	+	0.255731i	−0.674852	−	0.737953i	$-0.735792\pi$
$461$	−362.835	+	117.892i	−0.787060	+	0.255731i	−0.112208	+	0.993685i	$0.535792\pi$
$462$	−279.258	−	15.7693i	−0.604454	−	0.0341327i
$463$	168.981	−	520.070i	0.364970	−	1.12326i	−0.585030	−	0.811012i	$-0.698917\pi$
$463$	168.981	−	520.070i	0.364970	−	1.12326i	0.950000	−	0.312250i	$-0.101083\pi$
$464$	237.336	−	77.1151i	0.511500	−	0.166196i
$465$		0			0
$466$	−42.3661	+	130.389i	−0.0909144	+	0.279806i
$467$	−26.7323	+	36.7939i	−0.0572427	+	0.0787878i	−0.836679	−	0.547694i	$-0.815506\pi$
$467$	−26.7323	+	36.7939i	−0.0572427	+	0.0787878i	0.779436	+	0.626482i	$0.215506\pi$
$468$	−20.7600	+	11.7627i	−0.0443590	+	0.0251339i
$469$	292.052	+	212.188i	0.622712	+	0.452427i
$470$		0			0
$471$	428.839	+	350.152i	0.910487	+	0.743421i
$472$	−350.098	+	254.361i	−0.741734	+	0.538901i
$473$	−757.644	+	246.174i	−1.60178	+	0.520451i
$474$	612.413	−	161.441i	1.29201	−	0.340593i
$475$		0			0
$476$		−	19.4924i		−	0.0409505i
$477$	−358.946	+	392.215i	−0.752507	+	0.822255i
$478$	−48.5467	+	35.2712i	−0.101562	+	0.0737891i
$479$	35.7422	+	49.1949i	0.0746183	+	0.102703i	0.844695	−	0.535248i	$-0.179782\pi$
$479$	35.7422	+	49.1949i	0.0746183	+	0.102703i	−0.770076	+	0.637952i	$0.779782\pi$
$480$		0			0
$481$	300.669	+	218.449i	0.625091	+	0.454155i
$482$		−	201.648i		−	0.418357i
$483$	−254.334	−	98.8130i	−0.526571	−	0.204582i
$484$	−0.169725	+	0.522361i	−0.000350672	+	0.00107926i
$485$		0			0
$486$	−463.554	+	14.8925i	−0.953814	+	0.0306429i
$487$	64.1507	−	197.436i	0.131726	−	0.405412i	−0.863340	−	0.504622i	$-0.831632\pi$
$487$	64.1507	−	197.436i	0.131726	−	0.405412i	0.995066	+	0.0992105i	$0.0316317\pi$
$488$	287.679	+	93.4725i	0.589506	+	0.191542i
$489$	−373.087	+	240.144i	−0.762960	+	0.491091i
$490$		0			0
$491$	−620.755	−	201.696i	−1.26427	−	0.410785i	−0.401254	−	0.915967i	$-0.631425\pi$
$491$	−620.755	−	201.696i	−1.26427	−	0.410785i	−0.863013	+	0.505182i	$0.831425\pi$
$492$	−65.0446	−	25.2709i	−0.132204	−	0.0513636i
$493$	−213.657			−0.433382
$494$	34.1174	−	46.9586i	0.0690635	−	0.0950578i
$495$		0			0
$496$	−513.328	+	372.955i	−1.03494	+	0.751925i
$497$	339.759	+	467.638i	0.683619	+	0.940921i
$498$	−522.526	+	336.332i	−1.04925	+	0.675366i
$499$	−574.409			−1.15112			−0.575560	−	0.817759i	$-0.695216\pi$
$499$	−574.409			−1.15112			−0.575560	+	0.817759i	$0.695216\pi$
$500$		0			0
$501$	−28.5874	+	7.53605i	−0.0570607	+	0.0150420i
$502$	11.1063	+	34.1817i	0.0221241	+	0.0680911i
$503$	−207.267	−	285.279i	−0.412062	−	0.567155i	0.551657	−	0.834071i	$-0.313996\pi$
$503$	−207.267	−	285.279i	−0.412062	−	0.567155i	−0.963720	+	0.266915i	$0.913996\pi$
$504$	−300.634	−	136.778i	−0.596495	−	0.271386i
$505$		0			0
$506$	255.952	−	352.288i	0.505834	−	0.696221i
$507$	−87.1092	−	330.442i	−0.171813	−	0.651759i
$508$	−2.35763	−	1.71292i	−0.00464101	−	0.00337189i
$509$	−952.599	−	309.518i	−1.87151	−	0.608091i	−0.990963	−	0.134134i	$-0.957175\pi$
$509$	−952.599	−	309.518i	−1.87151	−	0.608091i	−0.880548	−	0.473957i	$-0.842825\pi$
$510$		0			0
$511$	−178.333	−	548.852i	−0.348988	−	1.07407i
$512$	−535.214	−	173.902i	−1.04534	−	0.339651i
$513$	−99.1736	+	49.0234i	−0.193321	+	0.0955621i
$514$	−97.6855	−	300.645i	−0.190050	−	0.584913i
$515$		0			0
$516$	−76.9947	−	4.34779i	−0.149215	−	0.00842594i
$517$	−247.687	−	179.955i	−0.479086	−	0.348076i
$518$			421.731i			0.814153i
$519$	−77.9327	−	30.2781i	−0.150159	−	0.0583394i
$520$		0			0
$521$	435.711	+	599.705i	0.836298	+	1.15107i	0.986718	+	0.162443i	$0.0519374\pi$
$521$	435.711	+	599.705i	0.836298	+	1.15107i	−0.150420	+	0.988622i	$0.548063\pi$
$522$	−122.905	+	270.140i	−0.235450	+	0.517509i
$523$	60.6901	+	186.785i	0.116042	+	0.357141i	0.992163	−	0.124950i	$-0.0398772\pi$
$523$	60.6901	+	186.785i	0.116042	+	0.357141i	−0.876121	+	0.482092i	$0.839877\pi$
$524$		−	22.4496i		−	0.0428428i
$525$		0			0
$526$	445.062			0.846126
$527$	516.659	−	167.873i	0.980378	−	0.318544i
$528$	303.366	−	371.540i	0.574556	−	0.703673i
$529$	−84.3071	+	61.2527i	−0.159371	+	0.115790i
$530$		0			0
$531$	52.7235	−	465.350i	0.0992910	−	0.876366i
$532$	−6.45852			−0.0121401
$533$	−284.096	+	391.024i	−0.533013	+	0.733629i
$534$	345.936	+	19.5345i	0.647820	+	0.0365815i
$535$		0			0
$536$	−647.010	+	210.226i	−1.20711	+	0.392213i
$537$	−47.2597	+	836.919i	−0.0880068	+	1.55851i
$538$	36.3680	−	111.929i	0.0675985	−	0.208047i
$539$	−310.851	+	101.002i	−0.576718	+	0.187387i
$540$		0			0
$541$	256.106	−	788.212i	0.473393	−	1.45695i	−0.374719	−	0.927138i	$-0.622261\pi$
$541$	256.106	−	788.212i	0.473393	−	1.45695i	0.848113	−	0.529816i	$-0.177739\pi$
$542$	40.4032	−	55.6103i	0.0745447	−	0.102602i
$543$	44.3788	+	168.347i	0.0817289	+	0.310032i
$544$	57.0006	+	41.4134i	0.104781	+	0.0761276i
$545$		0			0
$546$	−118.613	+	145.268i	−0.217240	+	0.266059i
$547$	440.386	−	319.959i	0.805093	−	0.584934i	−0.107311	−	0.994225i	$-0.534224\pi$
$547$	440.386	−	319.959i	0.805093	−	0.584934i	0.912404	+	0.409292i	$0.134224\pi$
$548$	−52.6867	+	17.1190i	−0.0961436	+	0.0312390i
$549$	−284.814	+	161.377i	−0.518787	+	0.293946i
$550$		0			0
$551$			70.7921i			0.128479i
$552$	432.376	−	278.306i	0.783291	−	0.504178i
$553$	−394.889	+	286.903i	−0.714084	+	0.518813i
$554$	−96.3229	−	132.577i	−0.173868	−	0.239309i
$555$		0			0
$556$	−2.37430	−	1.72503i	−0.00427032	−	0.00310257i
$557$			346.841i			0.622695i	0.950296	+	0.311347i	$0.100780\pi$
$557$			346.841i			0.622695i	−0.950296	+	0.311347i	$0.899220\pi$
$558$	84.9525	−	749.811i	0.152245	−	1.34375i
$559$	−165.060	+	508.003i	−0.295278	+	0.908771i
$560$		0			0
$561$	−345.319	+	222.270i	−0.615543	+	0.396204i
$562$	56.1385	−	172.777i	0.0998906	−	0.307432i
$563$	887.774	+	288.455i	1.57686	+	0.512354i	0.961246	−	0.275692i	$-0.0889069\pi$
$563$	887.774	+	288.455i	1.57686	+	0.512354i	0.615617	+	0.788045i	$0.288907\pi$
$564$	−16.0409	−	24.9211i	−0.0284413	−	0.0441864i
$565$		0			0
$566$	152.261	+	49.4726i	0.269012	+	0.0874074i
$567$	328.853	−	140.078i	0.579987	−	0.247052i
$568$	−1089.32			−1.91781
$569$	164.196	−	225.997i	0.288570	−	0.397182i	−0.639979	−	0.768392i	$-0.721057\pi$
$569$	164.196	−	225.997i	0.288570	−	0.397182i	0.928549	+	0.371210i	$0.121057\pi$
$570$		0			0
$571$	−368.214	+	267.523i	−0.644859	+	0.468517i	−0.861516	−	0.507730i	$-0.830485\pi$
$571$	−368.214	+	267.523i	−0.644859	+	0.468517i	0.216657	+	0.976248i	$0.430485\pi$
$572$	17.2503	+	23.7430i	0.0301578	+	0.0415087i
$573$	37.1402	+	57.7010i	0.0648170	+	0.100700i
$574$	−548.468			−0.955518
$575$		0			0
$576$	537.549	−	304.577i	0.933244	−	0.528779i
$577$	75.5479	+	232.512i	0.130932	+	0.402968i	0.994935	−	0.100519i	$-0.0320503\pi$
$577$	75.5479	+	232.512i	0.130932	+	0.402968i	−0.864003	+	0.503487i	$0.832050\pi$
$578$	−152.658	−	210.116i	−0.264115	−	0.363523i
$579$	518.818	+	423.620i	0.896059	+	0.731641i
$580$		0			0
$581$	281.502	−	387.454i	0.484513	−	0.666875i
$582$	165.610	−	43.6571i	0.284553	−	0.0750121i
$583$	529.046	+	384.375i	0.907455	+	0.659305i
$584$	1034.33	+	336.073i	1.77111	+	0.575467i
$585$		0			0
$586$	72.7898	+	224.024i	0.124215	+	0.382294i
$587$	539.288	+	175.225i	0.918719	+	0.298510i	0.729941	−	0.683510i	$-0.239547\pi$
$587$	539.288	+	175.225i	0.918719	+	0.298510i	0.188778	+	0.982020i	$0.439547\pi$
$588$	−31.5899	−	1.78384i	−0.0537243	−	0.00303374i
$589$	−55.6221	−	171.187i	−0.0944348	−	0.290640i
$590$		0			0
$591$	−32.7768	+	580.442i	−0.0554598	+	0.982136i
$592$	−585.098	−	425.099i	−0.988342	−	0.718072i
$593$		−	41.5540i		−	0.0700743i	−0.999386	−	0.0350371i	$-0.988845\pi$
$593$		−	41.5540i		−	0.0700743i	0.999386	−	0.0350371i	$-0.0111549\pi$
$594$	82.3877	+	564.468i	0.138700	+	0.950282i
$595$		0			0
$596$	−19.6155	−	26.9985i	−0.0329120	−	0.0452994i
$597$	75.2564	+	61.4476i	0.126058	+	0.102927i
$598$	−90.2243	−	277.682i	−0.150877	−	0.464351i
$599$			558.815i			0.932914i	0.884544	+	0.466457i	$0.154470\pi$
$599$			558.815i			0.932914i	−0.884544	+	0.466457i	$0.845530\pi$
$600$		0			0
$601$	706.508			1.17555			0.587777	−	0.809023i	$-0.300003\pi$
$601$	706.508			1.17555			0.587777	+	0.809023i	$0.300003\pi$
$602$	−576.463	+	187.304i	−0.957579	+	0.311136i
$603$	304.894	−	670.146i	0.505629	−	1.11135i
$604$	60.6651	−	44.0758i	0.100439	−	0.0729732i
$605$		0			0
$606$	−91.0461	+	234.343i	−0.150241	+	0.386704i
$607$	−250.439			−0.412585			−0.206293	−	0.978490i	$-0.566140\pi$
$607$	−250.439			−0.412585			−0.206293	+	0.978490i	$0.566140\pi$
$608$	13.7217	−	18.8863i	0.0225686	−	0.0310630i
$609$	12.8956	−	228.367i	0.0211750	−	0.374987i
$610$		0			0
$611$	−195.233	+	63.4351i	−0.319530	+	0.103822i
$612$	−38.9514	+	7.95027i	−0.0636461	+	0.0129906i
$613$	212.509	−	654.036i	0.346671	−	1.06694i	−0.614012	−	0.789296i	$-0.710446\pi$
$613$	212.509	−	654.036i	0.346671	−	1.06694i	0.960683	−	0.277647i	$-0.0895544\pi$
$614$	−118.473	+	38.4941i	−0.192952	+	0.0626939i
$615$		0			0
$616$	−125.535	+	386.357i	−0.203791	+	0.627203i
$617$	19.3389	−	26.6177i	0.0313434	−	0.0431405i	−0.793058	−	0.609147i	$-0.791512\pi$
$617$	19.3389	−	26.6177i	0.0313434	−	0.0431405i	0.824401	+	0.566006i	$0.191512\pi$
$618$	78.0350	−	20.5711i	0.126270	−	0.0332866i
$619$	−1.70484	−	1.23864i	−0.00275419	−	0.00200104i	0.586407	−	0.810016i	$-0.300542\pi$
$619$	−1.70484	−	1.23864i	−0.00275419	−	0.00200104i	−0.589161	+	0.808015i	$0.700542\pi$
$620$		0			0
$621$	−93.7225	+	548.533i	−0.150922	+	0.883306i
$622$	−31.9070	+	23.1818i	−0.0512975	+	0.0372698i
$623$	−253.967	+	82.5187i	−0.407651	+	0.132454i
$624$	−81.9810	−	310.988i	−0.131380	−	0.498379i
$625$		0			0
$626$		−	149.575i		−	0.238938i
$627$	73.6459	+	114.416i	0.117458	+	0.182482i
$628$	53.3292	−	38.7459i	0.0849191	−	0.0616973i
$629$	363.957	+	500.944i	0.578628	+	0.796414i
$630$		0			0
$631$	−30.5285	−	22.1803i	−0.0483812	−	0.0351510i	0.563332	−	0.826231i	$-0.309519\pi$
$631$	−30.5285	−	22.1803i	−0.0483812	−	0.0351510i	−0.611713	+	0.791080i	$0.709519\pi$
$632$		−	919.855i		−	1.45547i
$633$	286.882	−	738.403i	0.453210	−	1.16651i
$634$	−278.893	+	858.345i	−0.439895	+	1.35386i
$635$		0			0
$636$	34.2624	+	53.2301i	0.0538718	+	0.0836952i
$637$	−67.7219	+	208.427i	−0.106314	+	0.327200i
$638$	347.168	+	112.802i	0.544151	+	0.176805i
$639$	795.896	−	869.666i	1.24553	−	1.36098i
$640$		0			0
$641$	58.5879	+	19.0363i	0.0914007	+	0.0296979i	0.354360	−	0.935109i	$-0.384699\pi$
$641$	58.5879	+	19.0363i	0.0914007	+	0.0296979i	−0.262960	+	0.964807i	$0.584699\pi$
$642$	−77.4540	+	199.358i	−0.120645	+	0.310527i
$643$	−1083.43			−1.68496			−0.842479	−	0.538729i	$-0.818905\pi$
$643$	−1083.43			−1.68496			−0.842479	+	0.538729i	$0.818905\pi$
$644$	−19.0957	+	26.2830i	−0.0296517	+	0.0408121i
$645$		0			0
$646$	78.2377	−	56.8430i	0.121111	−	0.0879922i
$647$	−550.697	−	757.970i	−0.851155	−	1.17151i	−0.983607	−	0.180325i	$-0.942285\pi$
$647$	−550.697	−	757.970i	−0.851155	−	1.17151i	0.132452	−	0.991189i	$-0.457715\pi$
$648$	−150.704	+	656.538i	−0.232568	+	1.01318i
$649$	−576.026			−0.887559
$650$		0			0
$651$	148.247	+	562.362i	0.227722	+	0.863844i
$652$	16.3249	+	50.2428i	0.0250382	+	0.0770596i
$653$	−551.268	−	758.755i	−0.844208	−	1.16195i	−0.985109	−	0.171928i	$-0.945000\pi$
$653$	−551.268	−	758.755i	−0.844208	−	1.16195i	0.140902	−	0.990024i	$-0.455000\pi$
$654$	−150.362	+	184.152i	−0.229911	+	0.281578i
$655$		0			0
$656$	552.847	−	760.929i	0.842755	−	1.15995i
$657$	−1024.02	+	580.216i	−1.55864	+	0.883129i
$658$	−188.456	−	136.921i	−0.286407	−	0.208087i
$659$	−928.888	−	301.814i	−1.40954	−	0.457988i	−0.497278	−	0.867591i	$-0.665667\pi$
$659$	−928.888	−	301.814i	−1.40954	−	0.457988i	−0.912264	+	0.409603i	$0.865667\pi$
$660$		0			0
$661$	155.647	+	479.033i	0.235472	+	0.724710i	0.997058	+	0.0766458i	$0.0244211\pi$
$661$	155.647	+	479.033i	0.235472	+	0.724710i	−0.761586	+	0.648064i	$0.775579\pi$
$662$	−158.536	−	51.5113i	−0.239480	−	0.0778116i
$663$	−15.5242	+	274.917i	−0.0234151	+	0.414657i
$664$	278.899	+	858.364i	0.420029	+	1.29272i
$665$		0			0
$666$	842.738	−	172.009i	1.26537	−	0.258272i
$667$	288.089	+	209.309i	0.431917	+	0.313806i
$668$			3.52005i			0.00526954i
$669$	−265.547	+	683.489i	−0.396931	+	1.02166i
$670$		0			0
$671$	236.663	+	325.738i	0.352702	+	0.485452i
$672$	−47.7050	+	58.4255i	−0.0709895	+	0.0869427i
$673$	15.4934	+	47.6838i	0.0230214	+	0.0708527i	0.961907	−	0.273376i	$-0.0881404\pi$
$673$	15.4934	+	47.6838i	0.0230214	+	0.0708527i	−0.938886	+	0.344229i	$0.888140\pi$
$674$		−	1196.47i		−	1.77517i
$675$		0			0
$676$	−40.6883			−0.0601898
$677$	−217.093	+	70.5379i	−0.320670	+	0.104192i	−0.464929	−	0.885348i	$-0.653920\pi$
$677$	−217.093	+	70.5379i	−0.320670	+	0.104192i	0.144259	+	0.989540i	$0.453920\pi$
$678$	−415.649	−	339.382i	−0.613052	−	0.500563i
$679$	−106.786	+	77.5848i	−0.157270	+	0.114263i
$680$		0			0
$681$	862.563	+	335.120i	1.26661	+	0.492100i
$682$	−928.141			−1.36091
$683$	414.477	−	570.478i	0.606847	−	0.835253i	−0.389466	−	0.921041i	$-0.627341\pi$
$683$	414.477	−	570.478i	0.606847	−	0.835253i	0.996313	+	0.0857872i	$0.0273405\pi$
$684$	2.63420	+	12.9060i	0.00385117	+	0.0188684i
$685$		0			0
$686$	−629.018	+	204.380i	−0.916935	+	0.297930i
$687$	1221.25	+	68.9626i	1.77766	+	0.100382i
$688$	321.205	−	988.568i	0.466868	−	1.43687i
$689$	417.007	−	135.494i	0.605235	−	0.196653i
$690$		0			0
$691$	33.1187	−	101.929i	0.0479287	−	0.147509i	−0.924228	−	0.381841i	$-0.875290\pi$
$691$	33.1187	−	101.929i	0.0479287	−	0.147509i	0.972157	+	0.234332i	$0.0752902\pi$
$692$	−5.85128	+	8.05360i	−0.00845561	+	0.0116382i
$693$	−216.731	−	382.509i	−0.312743	−	0.551962i
$694$	−399.782	−	290.459i	−0.576055	−	0.418529i
$695$		0			0
$696$	333.887	+	272.622i	0.479723	+	0.391699i
$697$	−651.485	+	473.332i	−0.934699	+	0.679099i
$698$	−200.706	+	65.2132i	−0.287544	+	0.0934287i
$699$	−208.377	+	54.9313i	−0.298108	+	0.0785855i
$700$		0			0
$701$		−	1254.29i		−	1.78929i	−0.446779	−	0.894644i	$-0.647429\pi$
$701$		−	1254.29i		−	1.78929i	0.446779	−	0.894644i	$-0.352571\pi$
$702$	338.665	+	177.772i	0.482428	+	0.253237i
$703$	165.980	−	120.592i	0.236103	−	0.171539i
$704$	−446.670	−	614.788i	−0.634474	−	0.873279i
$705$		0			0
$706$	303.036	+	220.168i	0.429229	+	0.311853i
$707$		−	193.759i		−	0.274059i
$708$	−51.9766	−	20.1938i	−0.0734133	−	0.0285223i
$709$	−306.972	+	944.763i	−0.432965	+	1.33253i	0.462193	+	0.886779i	$0.347063\pi$
$709$	−306.972	+	944.763i	−0.432965	+	1.33253i	−0.895158	+	0.445749i	$0.852937\pi$
$710$		0			0
$711$	734.375	+	672.081i	1.03288	+	0.945262i
$712$	155.509	−	478.607i	0.218411	−	0.672200i
$713$	−861.103	−	279.789i	−1.20772	−	0.392411i
$714$	−262.740	+	169.117i	−0.367984	+	0.236859i
$715$		0			0
$716$	94.9219	+	30.8420i	0.132573	+	0.0430754i
$717$	−87.9180	−	34.1576i	−0.122619	−	0.0476396i
$718$	−561.342			−0.781813
$719$	637.051	−	876.825i	0.886024	−	1.21951i	−0.0886923	−	0.996059i	$-0.528269\pi$
$719$	637.051	−	876.825i	0.886024	−	1.21951i	0.974716	−	0.223448i	$-0.0717312\pi$
$720$		0			0
$721$	−50.3176	+	36.5578i	−0.0697886	+	0.0507044i
$722$	386.155	+	531.497i	0.534841	+	0.736146i
$723$	266.517	−	171.548i	0.368627	−	0.237273i
$724$	20.7291			0.0286314
$725$		0			0
$726$	8.51349	−	2.24428i	0.0117266	−	0.00309129i
$727$	−244.810	−	753.449i	−0.336741	−	1.03638i	−0.965858	−	0.259071i	$-0.916584\pi$
$727$	−244.810	−	753.449i	−0.336741	−	1.03638i	0.629118	−	0.777310i	$-0.283416\pi$
$728$	160.104	+	220.364i	0.219923	+	0.302698i
$729$	−414.043	−	600.008i	−0.567960	−	0.823056i
$730$		0			0
$731$	−523.094	+	719.977i	−0.715587	+	0.984920i
$732$	9.93539	+	37.6891i	0.0135729	+	0.0514879i
$733$	−170.984	−	124.227i	−0.233266	−	0.169478i	0.465012	−	0.885305i	$-0.346050\pi$
$733$	−170.984	−	124.227i	−0.233266	−	0.169478i	−0.698278	+	0.715827i	$0.746050\pi$
$734$	−274.776	−	89.2800i	−0.374354	−	0.121635i
$735$		0			0
$736$	−36.2874	−	111.681i	−0.0493035	−	0.151740i
$737$	−861.233	−	279.831i	−1.16857	−	0.379690i
$738$	223.700	+	1095.99i	0.303117	+	1.48509i
$739$	−149.389	−	459.772i	−0.202150	−	0.622154i	−0.999818	−	0.0190574i	$-0.993933\pi$
$739$	−149.389	−	459.772i	−0.202150	−	0.622154i	0.797668	−	0.603096i	$-0.206067\pi$
$740$		0			0
$741$	91.0897	+	5.14371i	0.122928	+	0.00694158i
$742$	402.531	+	292.456i	0.542495	+	0.394146i
$743$			819.254i			1.10263i	0.834297	+	0.551315i	$0.185874\pi$
$743$			819.254i			1.10263i	−0.834297	+	0.551315i	$0.814126\pi$
$744$	−1021.60	−	396.908i	−1.37312	−	0.533478i
$745$		0			0
$746$	93.9768	+	129.348i	0.125974	+	0.173389i
$747$	−889.058	−	404.492i	−1.19017	−	0.541488i
$748$	15.1099	+	46.5034i	0.0202004	+	0.0621703i
$749$		−	164.833i		−	0.220071i
$750$		0			0
$751$	108.581			0.144582			0.0722909	−	0.997384i	$-0.476969\pi$
$751$	108.581			0.144582			0.0722909	+	0.997384i	$0.476969\pi$
$752$	379.922	−	123.444i	0.505215	−	0.164154i
$753$	−35.7294	+	43.7586i	−0.0474494	+	0.0581124i
$754$	198.012	−	143.864i	0.262616	−	0.190802i
$755$		0			0
$756$	−6.14666	−	42.1130i	−0.00813051	−	0.0557050i
$757$	15.3279			0.0202482			0.0101241	−	0.999949i	$-0.496777\pi$
$757$	15.3279			0.0202482			0.0101241	+	0.999949i	$0.496777\pi$
$758$	−561.120	+	772.316i	−0.740264	+	1.01889i
$759$	683.364	+	38.5886i	0.900348	+	0.0508414i
$760$		0			0
$761$	−1336.61	+	434.292i	−1.75639	+	0.570685i	−0.996816	−	0.0797369i	$-0.974592\pi$
$761$	−1336.61	+	434.292i	−1.75639	+	0.570685i	−0.759573	+	0.650422i	$0.774592\pi$
$762$	−2.63370	+	46.6401i	−0.00345630	+	0.0612074i
$763$	56.6200	−	174.258i	0.0742070	−	0.228386i
$764$	7.77046	−	2.52478i	0.0101708	−	0.00330468i
$765$		0			0
$766$	−154.074	+	474.192i	−0.201142	+	0.619050i
$767$	−227.019	+	312.464i	−0.295983	+	0.407385i
$768$	−52.0150	−	197.315i	−0.0677279	−	0.256920i
$769$	1078.89	+	783.857i	1.40297	+	1.01932i	0.994298	+	0.106639i	$0.0340090\pi$
$769$	1078.89	+	783.857i	1.40297	+	1.01932i	0.408675	+	0.912680i	$0.365991\pi$
$770$		0			0
$771$	314.257	−	384.879i	0.407597	−	0.499194i
$772$	64.5187	−	46.8756i	0.0835734	−	0.0607197i
$773$	672.222	−	218.418i	0.869628	−	0.282559i	0.159984	−	0.987120i	$-0.448856\pi$
$773$	672.222	−	218.418i	0.869628	−	0.282559i	0.709644	+	0.704561i	$0.248856\pi$
$774$	609.405	+	1075.54i	0.787345	+	1.38959i
$775$		0			0
$776$		−	248.748i		−	0.320552i
$777$	−557.400	+	358.780i	−0.717375	+	0.461750i
$778$	474.504	−	344.747i	0.609902	−	0.443120i
$779$	156.831	+	215.860i	0.201324	+	0.277098i
$780$		0			0
$781$	−1173.06	−	852.280i	−1.50200	−	1.09127i
$782$		−	486.454i		−	0.622064i
$783$	−461.602	+	67.3738i	−0.589530	+	0.0860457i
$784$	131.786	−	405.596i	0.168094	−	0.517342i
$785$		0			0
$786$	−302.600	+	194.774i	−0.384988	+	0.247804i
$787$	245.077	−	754.271i	0.311407	−	0.958413i	−0.665801	−	0.746129i	$-0.731910\pi$
$787$	245.077	−	754.271i	0.311407	−	0.958413i	0.977208	−	0.212283i	$-0.0680900\pi$
$788$	65.8328	+	21.3904i	0.0835441	+	0.0271451i
$789$	378.628	+	588.237i	0.479884	+	0.745547i
$790$		0			0
$791$	393.318	+	127.797i	0.497242	+	0.161564i
$792$	823.252	+	93.2732i	1.03946	+	0.117769i
$793$	269.968			0.340439
$794$	−448.160	+	616.839i	−0.564433	+	0.776875i
$795$		0			0
$796$	9.35866	−	6.79946i	0.0117571	−	0.00854204i
$797$	−102.490	−	141.066i	−0.128595	−	0.176996i	0.739865	−	0.672756i	$-0.234890\pi$
$797$	−102.490	−	141.066i	−0.128595	−	0.176996i	−0.868460	+	0.495760i	$0.834890\pi$
$798$	56.0344	+	87.0550i	0.0702185	+	0.109091i
$799$	−342.017			−0.428057
$800$		0			0
$801$	268.480	+	473.840i	0.335180	+	0.591561i
$802$	242.691	+	746.925i	0.302607	+	0.931328i
$803$	850.902	+	1171.17i	1.05965	+	1.45849i
$804$	−67.9017	−	55.4424i	−0.0844548	−	0.0689582i
$805$		0			0
$806$	−365.791	+	503.469i	−0.453835	+	0.624651i
$807$	178.876	−	47.1542i	0.221655	−	0.0584315i
$808$	295.408	+	214.627i	0.365604	+	0.265627i
$809$	−351.459	−	114.196i	−0.434437	−	0.141157i	0.0836306	−	0.996497i	$-0.473348\pi$
$809$	−351.459	−	114.196i	−0.434437	−	0.141157i	−0.518068	+	0.855340i	$0.673348\pi$
$810$		0			0
$811$	−80.0619	−	246.405i	−0.0987200	−	0.303829i	0.889485	−	0.456964i	$-0.151063\pi$
$811$	−80.0619	−	246.405i	−0.0987200	−	0.303829i	−0.988205	+	0.153135i	$0.951063\pi$
$812$	−25.9010	−	8.41575i	−0.0318978	−	0.0103642i
$813$	107.872	+	6.09139i	0.132684	+	0.00749249i
$814$	−326.911	−	1006.13i	−0.401611	−	1.23603i
$815$		0			0
$816$	30.2100	−	534.987i	0.0370220	−	0.655621i
$817$	238.553	+	173.319i	0.291987	+	0.212141i
$818$		−	184.793i		−	0.225909i
$819$	−292.908	−	33.1860i	−0.357641	−	0.0405202i
$820$		0			0
$821$	−555.657	−	764.796i	−0.676805	−	0.931542i	0.323085	−	0.946370i	$-0.395280\pi$
$821$	−555.657	−	764.796i	−0.676805	−	0.931542i	−0.999890	+	0.0148281i	$0.995280\pi$
$822$	687.860	+	561.644i	0.836812	+	0.683266i
$823$	−62.1170	−	191.176i	−0.0754762	−	0.232292i	0.906200	−	0.422850i	$-0.138970\pi$
$823$	−62.1170	−	191.176i	−0.0754762	−	0.232292i	−0.981676	+	0.190558i	$0.938970\pi$
$824$		−	117.210i		−	0.142245i
$825$		0			0
$826$	−438.276			−0.530601
$827$	−1166.14	+	378.900i	−1.41008	+	0.458162i	−0.912436	−	0.409219i	$-0.865801\pi$
$827$	−1166.14	+	378.900i	−1.41008	+	0.458162i	−0.497643	+	0.867382i	$0.665801\pi$
$828$	60.3093	+	27.4387i	0.0728373	+	0.0331386i
$829$	610.245	−	443.369i	0.736122	−	0.534824i	−0.155372	−	0.987856i	$-0.549658\pi$
$829$	610.245	−	443.369i	0.736122	−	0.534824i	0.891494	+	0.453032i	$0.149658\pi$
$830$		0			0
$831$	93.2817	−	240.097i	0.112252	−	0.288925i
$832$	−509.529			−0.612415
$833$	−214.618	+	295.396i	−0.257645	+	0.354618i
$834$	−2.65232	+	46.9698i	−0.00318024	+	0.0563187i
$835$		0			0
$836$	15.4082	−	5.00642i	0.0184308	−	0.00598855i
$837$	1063.29	−	525.606i	1.27036	−	0.627965i
$838$	−62.8613	+	193.467i	−0.0750135	+	0.230868i
$839$	−919.271	+	298.689i	−1.09567	+	0.356006i	−0.800437	−	0.599417i	$-0.795399\pi$
$839$	−919.271	+	298.689i	−1.09567	+	0.356006i	−0.295238	+	0.955424i	$0.595399\pi$
$840$		0			0
$841$	167.638	−	515.937i	0.199332	−	0.613480i
$842$	−730.978	+	1006.11i	−0.868145	+	1.19490i
$843$	276.117	−	72.7884i	0.327541	−	0.0863445i
$844$	−76.3069	−	55.4402i	−0.0904110	−	0.0656875i
$845$		0			0
$846$	−196.743	+	432.433i	−0.232557	+	0.511150i
$847$	−5.48956	+	3.98840i	−0.00648118	+	0.00470885i
$848$	−811.491	+	263.669i	−0.956947	+	0.310931i
$849$	64.1454	+	243.331i	0.0755541	+	0.286608i
$850$		0			0
$851$		−	1032.01i		−	1.21270i
$852$	−75.9707	−	118.028i	−0.0891675	−	0.138531i
$853$	−819.440	+	595.358i	−0.960657	+	0.697958i	−0.953303	−	0.302015i	$-0.902341\pi$
$853$	−819.440	+	595.358i	−0.960657	+	0.697958i	−0.00735340	+	0.999973i	$0.502341\pi$
$854$	180.068	+	247.842i	0.210852	+	0.290213i
$855$		0			0
$856$	251.307	+	182.585i	0.293583	+	0.213301i
$857$		−	360.896i		−	0.421115i	−0.977581	−	0.210558i	$-0.932472\pi$
$857$		−	360.896i		−	0.421115i	0.977581	−	0.210558i	$-0.0675280\pi$
$858$	170.370	−	438.513i	0.198566	−	0.511087i
$859$	310.248	−	954.844i	0.361173	−	1.11158i	−0.591170	−	0.806547i	$-0.701334\pi$
$859$	310.248	−	954.844i	0.361173	−	1.11158i	0.952343	−	0.305029i	$-0.0986662\pi$
$860$		0			0
$861$	−466.598	−	724.907i	−0.541926	−	0.841937i
$862$	66.9357	−	206.007i	0.0776516	−	0.238987i
$863$	966.963	+	314.185i	1.12047	+	0.364062i	0.809946	−	0.586505i	$-0.199496\pi$
$863$	966.963	+	314.185i	1.12047	+	0.364062i	0.310521	+	0.950566i	$0.399496\pi$
$864$	136.208	+	71.4983i	0.157648	+	0.0827527i
$865$		0			0
$866$	−1247.97	−	405.492i	−1.44108	−	0.468235i
$867$	147.839	−	380.520i	0.170517	−	0.438893i
$868$	69.2454			0.0797758
$869$	719.694	−	990.574i	0.828186	−	1.13990i
$870$		0			0
$871$	−491.216	+	356.890i	−0.563968	+	0.409747i
$872$	202.959	+	279.349i	0.232751	+	0.320354i
$873$	198.591	+	181.745i	0.227481	+	0.208185i
$874$	−161.179			−0.184416
$875$		0			0
$876$	35.7219	+	135.508i	0.0407784	+	0.154690i
$877$	−35.0090	−	107.747i	−0.0399190	−	0.122858i	0.929111	−	0.369801i	$-0.120574\pi$
$877$	−35.0090	−	107.747i	−0.0399190	−	0.122858i	−0.969030	+	0.246943i	$0.920574\pi$
$878$	726.487	+	999.923i	0.827433	+	1.13886i
$879$	−234.167	+	286.790i	−0.266402	+	0.326269i
$880$		0			0
$881$	310.612	−	427.520i	0.352567	−	0.485267i	−0.595492	−	0.803361i	$-0.703043\pi$
$881$	310.612	−	427.520i	0.352567	−	0.485267i	0.948059	+	0.318094i	$0.103043\pi$
$882$	250.030	+	441.279i	0.283481	+	0.500317i
$883$	827.989	+	601.570i	0.937700	+	0.681279i	0.947866	−	0.318669i	$-0.103236\pi$
$883$	827.989	+	601.570i	0.937700	+	0.681279i	−0.0101656	+	0.999948i	$0.503236\pi$
$884$	31.1807	+	10.1312i	0.0352723	+	0.0114607i
$885$		0			0
$886$	−305.244	−	939.446i	−0.344520	−	1.06032i
$887$	−292.421	−	95.0134i	−0.329674	−	0.107118i	0.139503	−	0.990222i	$-0.455450\pi$
$887$	−292.421	−	95.0134i	−0.329674	−	0.107118i	−0.469177	+	0.883104i	$0.655450\pi$
$888$	70.4299	−	1247.24i	0.0793130	−	1.40455i
$889$	−11.1254	−	34.2405i	−0.0125145	−	0.0385158i
$890$		0			0
$891$	−675.965	+	589.102i	−0.758659	+	0.661169i
$892$	70.6322	+	51.3173i	0.0791840	+	0.0575306i
$893$			113.322i			0.126901i
$894$	−193.730	+	498.639i	−0.216700	+	0.557762i
$895$		0			0
$896$	−280.741	−	386.406i	−0.313327	−	0.431257i
$897$	290.254	−	355.482i	0.323583	−	0.396301i
$898$	82.3674	+	253.501i	0.0917231	+	0.282295i
$899$		−	759.001i		−	0.844272i
$900$		0			0
$901$	730.530			0.810799
$902$	1308.49	−	425.153i	1.45065	−	0.471345i
$903$	−737.974	−	602.563i	−0.817247	−	0.667290i
$904$	−630.518	+	458.098i	−0.697476	+	0.506746i
$905$		0			0
$906$	−1120.43	−	435.307i	−1.23668	−	0.480472i
$907$	356.635			0.393203			0.196601	−	0.980483i	$-0.437009\pi$
$907$	356.635			0.393203			0.196601	+	0.980483i	$0.437009\pi$
$908$	64.7623	−	89.1377i	0.0713241	−	0.0981692i
$909$	−387.186	+	79.0275i	−0.425947	+	0.0869389i
$910$		0			0
$911$	695.250	−	225.900i	0.763172	−	0.247970i	0.0985326	−	0.995134i	$-0.468585\pi$
$911$	695.250	−	225.900i	0.763172	−	0.247970i	0.664640	+	0.747164i	$0.268585\pi$
$912$	−177.260	−	10.0096i	−0.194364	−	0.0109754i
$913$	−371.242	+	1142.57i	−0.406618	+	1.25144i
$914$	−1220.24	+	396.480i	−1.33506	+	0.433786i
$915$		0			0
$916$	45.0055	−	138.513i	0.0491326	−	0.151215i
$917$	163.021	−	224.379i	0.177776	−	0.244688i
$918$	445.106	+	456.053i	0.484865	+	0.496789i
$919$	1012.43	+	735.573i	1.10166	+	0.800405i	0.981331	−	0.192328i	$-0.0616038\pi$
$919$	1012.43	+	735.573i	1.10166	+	0.800405i	0.120333	+	0.992734i	$0.461604\pi$
$920$		0			0
$921$	−151.666	−	123.837i	−0.164675	−	0.134459i
$922$	589.085	−	427.995i	0.638921	−	0.464203i
$923$	−924.636	+	300.433i	−1.00177	+	0.325496i
$924$	−50.6170	+	13.3434i	−0.0547804	+	0.0144409i
$925$		0			0
$926$			1043.69i			1.12710i
$927$	93.5756	+	85.6380i	0.100945	+	0.0923819i
$928$	79.6387	−	57.8609i	0.0858175	−	0.0623501i
$929$	653.571	+	899.563i	0.703521	+	0.968313i	0.999912	+	0.0132469i	$0.00421674\pi$
$929$	653.571	+	899.563i	0.703521	+	0.968313i	−0.296391	+	0.955067i	$0.595783\pi$
$930$		0			0
$931$	97.8751	+	71.1104i	0.105129	+	0.0763807i
$932$			25.6581i			0.0275302i
$933$	−57.7837	−	22.4499i	−0.0619332	−	0.0240621i
$934$	26.8237	−	82.5548i	0.0287191	−	0.0883884i
$935$		0			0
$936$	375.049	−	409.812i	0.400694	−	0.437833i
$937$	−442.429	+	1361.66i	−0.472176	+	1.45321i	0.377553	+	0.925988i	$0.376766\pi$
$937$	−442.429	+	1361.66i	−0.472176	+	1.45321i	−0.849729	+	0.527220i	$0.823234\pi$
$938$	−655.279	−	212.913i	−0.698592	−	0.226986i
$939$	197.693	−	127.248i	0.210535	−	0.135514i
$940$		0			0
$941$	1462.96	+	475.344i	1.55469	+	0.505148i	0.955382	−	0.295374i	$-0.0954443\pi$
$941$	1462.96	+	475.344i	1.55469	+	0.505148i	0.599303	+	0.800522i	$0.295444\pi$
$942$	−984.946	−	382.668i	−1.04559	−	0.406229i
$943$	1342.14			1.42327
$944$	441.776	−	608.053i	0.467983	−	0.644124i
$945$		0			0
$946$	1230.08	−	893.708i	1.30030	−	0.944723i
$947$	−281.343	−	387.235i	−0.297088	−	0.408907i	0.634212	−	0.773159i	$-0.281325\pi$
$947$	−281.343	−	387.235i	−0.297088	−	0.408907i	−0.931300	+	0.364252i	$0.881325\pi$
$948$	99.6668	−	64.1522i	0.105134	−	0.0676711i
$949$	970.648			1.02281
$950$		0			0
$951$	−1371.73	+	361.609i	−1.44241	+	0.380241i
$952$	140.238	+	431.609i	0.147309	+	0.453371i
$953$	−554.511	−	763.219i	−0.581858	−	0.800859i	0.412039	−	0.911166i	$-0.364817\pi$
$953$	−554.511	−	763.219i	−0.581858	−	0.800859i	−0.993898	+	0.110307i	$0.964817\pi$
$954$	420.232	−	923.653i	0.440494	−	0.968190i
$955$		0			0
$956$	−6.60099	+	9.08549i	−0.00690481	+	0.00950365i
$957$	146.257	+	554.815i	0.152829	+	0.579744i
$958$	−93.8940	−	68.2180i	−0.0980105	−	0.0712088i
$959$	−650.904	−	211.492i	−0.678732	−	0.220533i
$960$		0			0
$961$	299.389	+	921.426i	0.311540	+	0.958820i
$962$	−674.613	−	219.195i	−0.701261	−	0.227854i
$963$	−329.384	+	67.2296i	−0.342039	+	0.0698127i
$964$	−11.6618	−	35.8913i	−0.0120973	−	0.0372317i
$965$		0			0
$966$	519.946	+	29.3606i	0.538246	+	0.0303940i
$967$	999.326	+	726.053i	1.03343	+	0.750830i	0.968992	−	0.247091i	$-0.0794748\pi$
$967$	999.326	+	726.053i	1.03343	+	0.750830i	0.0644372	+	0.997922i	$0.479475\pi$
$968$		−	12.7874i		−	0.0132101i
$969$	141.688	+	55.0483i	0.146221	+	0.0568094i
$970$		0			0
$971$	384.963	+	529.856i	0.396460	+	0.545681i	0.959851	−	0.280510i	$-0.0905034\pi$
$971$	384.963	+	529.856i	0.396460	+	0.545681i	−0.563391	+	0.826191i	$0.690503\pi$
$972$	−81.6466	+	29.4591i	−0.0839986	+	0.0303078i
$973$	−11.2041	−	34.4826i	−0.0115150	−	0.0354394i
$974$			396.221i			0.406797i
$975$		0			0
$976$	−525.355			−0.538273
$977$	508.240	−	165.137i	0.520205	−	0.169025i	−0.0371334	−	0.999310i	$-0.511823\pi$
$977$	508.240	−	165.137i	0.520205	−	0.169025i	0.557338	+	0.830285i	$0.311823\pi$
$978$	535.592	−	655.953i	0.547640	−	0.670709i
$979$	541.926	−	393.732i	0.553550	−	0.402178i
$980$		0			0
$981$	−371.311	−	42.0689i	−0.378502	−	0.0428837i
$982$	1245.75			1.26859
$983$	157.054	−	216.167i	0.159770	−	0.219905i	−0.721625	−	0.692284i	$-0.756605\pi$
$983$	157.054	−	216.167i	0.159770	−	0.219905i	0.881396	+	0.472379i	$0.156605\pi$
$984$	1622.05	+	91.5951i	1.64843	+	0.0930845i
$985$		0			0
$986$	387.830	−	126.014i	0.393337	−	0.127803i
$987$	20.6429	−	365.565i	0.0209148	−	0.370380i
$988$	3.35682	−	10.3312i	0.00339759	−	0.0104567i
$989$	1410.65	−	458.347i	1.42634	−	0.463445i
$990$		0			0
$991$	−252.029	+	775.666i	−0.254318	+	0.782710i	0.739645	+	0.672997i	$0.234993\pi$
$991$	−252.029	+	775.666i	−0.254318	+	0.782710i	−0.993963	+	0.109713i	$0.965007\pi$
$992$	−147.118	+	202.490i	−0.148304	+	0.204123i
$993$	−66.7888	−	253.358i	−0.0672596	−	0.255144i
$994$	−892.539	−	648.468i	−0.897927	−	0.652382i
$995$		0			0
$996$	−73.5534	+	90.0826i	−0.0738488	+	0.0904444i
$997$	183.378	−	133.232i	0.183930	−	0.133633i	−0.492010	−	0.870589i	$-0.663738\pi$
$997$	183.378	−	133.232i	0.183930	−	0.133633i	0.675940	+	0.736957i	$0.263738\pi$
$998$	1042.67	−	338.783i	1.04476	−	0.339462i
$999$	944.287	+	967.510i	0.945232	+	0.968478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.3.j.b.26.11		144
3.2	odd	2	inner	375.3.j.b.26.25		144
5.2	odd	4		75.3.h.a.44.6	yes	72
5.3	odd	4		375.3.h.a.224.13		72
5.4	even	2	inner	375.3.j.b.26.26		144
15.2	even	4		75.3.h.a.44.13	yes	72
15.8	even	4		375.3.h.a.224.6		72
15.14	odd	2	inner	375.3.j.b.26.12		144
25.3	odd	20		75.3.h.a.29.13	yes	72
25.4	even	10	inner	375.3.j.b.101.12		144
25.21	even	5	inner	375.3.j.b.101.25		144
25.22	odd	20		375.3.h.a.149.6		72
75.29	odd	10	inner	375.3.j.b.101.26		144
75.47	even	20		375.3.h.a.149.13		72
75.53	even	20		75.3.h.a.29.6	✓	72
75.71	odd	10	inner	375.3.j.b.101.11		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.h.a.29.6	✓	72	75.53	even	20
75.3.h.a.29.13	yes	72	25.3	odd	20
75.3.h.a.44.6	yes	72	5.2	odd	4
75.3.h.a.44.13	yes	72	15.2	even	4
375.3.h.a.149.6		72	25.22	odd	20
375.3.h.a.149.13		72	75.47	even	20
375.3.h.a.224.6		72	15.8	even	4
375.3.h.a.224.13		72	5.3	odd	4
375.3.j.b.26.11		144	1.1	even	1	trivial
375.3.j.b.26.12		144	15.14	odd	2	inner
375.3.j.b.26.25		144	3.2	odd	2	inner
375.3.j.b.26.26		144	5.4	even	2	inner
375.3.j.b.101.11		144	75.71	odd	10	inner
375.3.j.b.101.12		144	25.4	even	10	inner
375.3.j.b.101.25		144	25.21	even	5	inner
375.3.j.b.101.26		144	75.29	odd	10	inner

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	375.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.81520 + 0.589794i) q^{2} +(-2.32377 - 1.89739i) q^{3} +(-0.288978 + 0.209955i) q^{4} +(5.33718 + 2.07358i) q^{6} -4.41289 q^{7} +(4.88814 - 6.72795i) q^{8} +(1.79986 + 8.81819i) q^{9} +(10.5279 - 3.42072i) q^{11} +(1.06988 + 0.0604149i) q^{12} +(2.29360 - 7.05898i) q^{13} +(8.01027 - 2.60269i) q^{14} +(-4.46333 + 13.7367i) q^{16} +(7.26868 - 10.0045i) q^{17} +(-8.46802 - 14.9452i) q^{18} +(-3.31483 - 2.40836i) q^{19} +(10.2546 + 8.37295i) q^{21} +(-17.0927 + 12.4186i) q^{22} +(-19.6017 + 6.36898i) q^{23} +(-24.1244 + 6.35955i) q^{24} +14.1662i q^{26} +(12.5490 - 23.9065i) q^{27} +(1.27523 - 0.926506i) q^{28} +(-10.1555 - 13.9778i) q^{29} +(35.5401 + 25.8214i) q^{31} +5.69751i q^{32} +(-30.9548 - 12.0265i) q^{33} +(-7.29352 + 22.4471i) q^{34} +(-2.37154 - 2.17037i) q^{36} +(-15.4731 + 47.6213i) q^{37} +(7.43751 + 2.41659i) q^{38} +(-18.7234 + 12.0516i) q^{39} +(-61.9322 - 20.1230i) q^{41} +(-23.5524 - 9.15049i) q^{42} -71.9655 q^{43} +(-2.32413 + 3.19889i) q^{44} +(31.8246 - 23.1219i) q^{46} +(-16.2566 - 22.3753i) q^{47} +(36.4356 - 23.4524i) q^{48} -29.5264 q^{49} +(-35.8731 + 9.45667i) q^{51} +(0.819266 + 2.52144i) q^{52} +(34.7232 + 47.7924i) q^{53} +(-8.67909 + 50.7964i) q^{54} +(-21.5708 + 29.6897i) q^{56} +(3.13332 + 11.8860i) q^{57} +(26.6782 + 19.3828i) q^{58} +(-49.4896 - 16.0801i) q^{59} +(11.2398 + 34.5926i) q^{61} +(-79.7417 - 25.9096i) q^{62} +(-7.94257 - 38.9137i) q^{63} +(-21.2137 - 65.2889i) q^{64} +(63.2823 + 3.57347i) q^{66} +(-66.1816 - 48.0837i) q^{67} +4.41716i q^{68} +(57.6344 + 22.3919i) q^{69} +(-76.9924 - 105.971i) q^{71} +(68.1263 + 30.9952i) q^{72} +(40.4118 + 124.375i) q^{73} -95.5681i q^{74} +1.46356 q^{76} +(-46.4584 + 15.0952i) q^{77} +(26.8788 - 32.9191i) q^{78} +(89.4854 - 65.0149i) q^{79} +(-74.5210 + 31.7430i) q^{81} +124.288 q^{82} +(-63.7909 + 87.8007i) q^{83} +(-4.72128 - 0.266604i) q^{84} +(130.632 - 42.4448i) q^{86} +(-2.92226 + 51.7501i) q^{87} +(28.4474 - 87.5520i) q^{88} +(57.5511 - 18.6995i) q^{89} +(-10.1214 + 31.1505i) q^{91} +(4.32726 - 5.95596i) q^{92} +(-33.5941 - 127.436i) q^{93} +(42.7058 + 31.0276i) q^{94} +(10.8104 - 13.2397i) q^{96} +(24.1988 - 17.5814i) q^{97} +(53.5963 - 17.4145i) q^{98} +(49.1132 + 86.6801i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 76 q^{4} + 10 q^{6} + 26 q^{9} + 44 q^{16} + 72 q^{19} + 108 q^{21} + 40 q^{24} - 252 q^{31} - 420 q^{34} - 426 q^{36} + 382 q^{39} - 420 q^{46} + 448 q^{49} - 120 q^{51} - 640 q^{54} + 588 q^{61}+ \cdots - 120 q^{99}+O(q^{100}) \) 144 * q + 76 * q^4 + 10 * q^6 + 26 * q^9 + 44 * q^16 + 72 * q^19 + 108 * q^21 + 40 * q^24 - 252 * q^31 - 420 * q^34 - 426 * q^36 + 382 * q^39 - 420 * q^46 + 448 * q^49 - 120 * q^51 - 640 * q^54 + 588 * q^61 - 724 * q^64 - 940 * q^66 - 670 * q^69 - 32 * q^76 + 692 * q^79 + 1014 * q^81 + 912 * q^84 + 1076 * q^91 + 1120 * q^94 + 1480 * q^96 - 120 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

Properties

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