LMFDB - Embedded newform 336.4.bc.d.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,4,Mod(17,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("336.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.bc (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441 $ x^12 - x^11 - 29x^9 + 6x^8 - 49x^7 + 1564x^6 - 441x^5 + 486x^4 - 21141x^3 - 59049x + 531441
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.5
Root			$2.85284 + 0.928053i$ of defining polynomial
Character	$\chi$	$=$	336.17
Dual form			336.4.bc.d.257.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.47555 - 3.86271i) q^{3} +(0.623706 + 1.08029i) q^{5} +(-10.0808 - 15.5363i) q^{7} +(-2.84113 - 26.8501i) q^{9} +O(q^{10})$	\(q+(3.47555 - 3.86271i) q^{3} +(0.623706 + 1.08029i) q^{5} +(-10.0808 - 15.5363i) q^{7} +(-2.84113 - 26.8501i) q^{9} +(-35.2392 - 20.3453i) q^{11} +19.5973i q^{13} +(6.34057 + 1.34540i) q^{15} +(-52.3592 + 90.6889i) q^{17} +(-35.0345 + 20.2272i) q^{19} +(-95.0487 - 15.0578i) q^{21} +(-69.6324 + 40.2023i) q^{23} +(61.7220 - 106.906i) q^{25} +(-113.589 - 82.3444i) q^{27} -211.712i q^{29} +(86.6242 + 50.0125i) q^{31} +(-201.064 + 65.4076i) q^{33} +(10.4962 - 20.5803i) q^{35} +(94.9875 + 164.523i) q^{37} +(75.6987 + 68.1113i) q^{39} -186.753 q^{41} -158.618 q^{43} +(27.2339 - 19.8158i) q^{45} +(-179.034 - 310.097i) q^{47} +(-139.753 + 313.238i) q^{49} +(168.328 + 517.442i) q^{51} +(-366.460 - 211.576i) q^{53} -50.7580i q^{55} +(-43.6323 + 205.629i) q^{57} +(-312.781 + 541.753i) q^{59} +(699.575 - 403.900i) q^{61} +(-388.510 + 314.812i) q^{63} +(-21.1708 + 12.2229i) q^{65} +(149.272 - 258.547i) q^{67} +(-86.7208 + 408.695i) q^{69} -455.386i q^{71} +(-434.467 - 250.840i) q^{73} +(-198.428 - 609.970i) q^{75} +(39.1491 + 752.584i) q^{77} +(-30.9561 - 53.6176i) q^{79} +(-712.856 + 152.569i) q^{81} +73.1180 q^{83} -130.627 q^{85} +(-817.783 - 735.816i) q^{87} +(57.3723 + 99.3717i) q^{89} +(304.469 - 197.557i) q^{91} +(494.251 - 160.784i) q^{93} +(-43.7025 - 25.2316i) q^{95} -1416.51i q^{97} +(-446.156 + 1003.98i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 + 56 * q^7 - 3 * q^9	$ 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9} - 6 q^{15} - 300 q^{19} + 357 q^{21} - 42 q^{25} + 930 q^{31} - 855 q^{33} + 764 q^{37} + 426 q^{39} + 1012 q^{43} + 2367 q^{45} - 336 q^{49} + 1341 q^{51} + 270 q^{57} + 2358 q^{61} - 1071 q^{63} - 792 q^{67} - 2904 q^{73} + 2418 q^{75} - 1674 q^{79} + 837 q^{81} + 348 q^{85} - 1638 q^{87} + 1218 q^{91} - 1479 q^{93} + 3354 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 + 56 * q^7 - 3 * q^9 - 6 * q^15 - 300 * q^19 + 357 * q^21 - 42 * q^25 + 930 * q^31 - 855 * q^33 + 764 * q^37 + 426 * q^39 + 1012 * q^43 + 2367 * q^45 - 336 * q^49 + 1341 * q^51 + 270 * q^57 + 2358 * q^61 - 1071 * q^63 - 792 * q^67 - 2904 * q^73 + 2418 * q^75 - 1674 * q^79 + 837 * q^81 + 348 * q^85 - 1638 * q^87 + 1218 * q^91 - 1479 * q^93 + 3354 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	3.47555	−	3.86271i	0.668870	−	0.743380i
$3$	3.47555	−	3.86271i	0.668870	−	0.743380i
$4$		0			0
$5$	0.623706	+	1.08029i	0.0557859	+	0.0966240i	0.892570	−	0.450909i	$-0.148900\pi$
$5$	0.623706	+	1.08029i	0.0557859	+	0.0966240i	−0.836784	+	0.547533i	$0.815567\pi$
$6$		0			0
$7$	−10.0808	−	15.5363i	−0.544314	−	0.838881i
$7$	−10.0808	−	15.5363i	−0.544314	−	0.838881i
$8$		0			0
$9$	−2.84113	−	26.8501i	−0.105227	−	0.994448i
$10$		0			0
$11$	−35.2392	−	20.3453i	−0.965910	−	0.557668i	−0.0679230	−	0.997691i	$-0.521637\pi$
$11$	−35.2392	−	20.3453i	−0.965910	−	0.557668i	−0.897987	+	0.440022i	$0.854971\pi$
$12$		0			0
$13$			19.5973i			0.418101i	0.977905	+	0.209050i	$0.0670373\pi$
$13$			19.5973i			0.418101i	−0.977905	+	0.209050i	$0.932963\pi$
$14$		0			0
$15$	6.34057	+	1.34540i	0.109142	+	0.0231588i
$16$		0			0
$17$	−52.3592	+	90.6889i	−0.746999	+	1.29384i	0.202256	+	0.979333i	$0.435173\pi$
$17$	−52.3592	+	90.6889i	−0.746999	+	1.29384i	−0.949255	+	0.314507i	$0.898161\pi$
$18$		0			0
$19$	−35.0345	+	20.2272i	−0.423025	+	0.244234i	−0.696371	−	0.717682i	$-0.745203\pi$
$19$	−35.0345	+	20.2272i	−0.423025	+	0.244234i	0.273346	+	0.961916i	$0.411870\pi$
$20$		0			0
$21$	−95.0487	−	15.0578i	−0.987683	−	0.156470i
$22$		0			0
$23$	−69.6324	+	40.2023i	−0.631276	+	0.364467i	−0.781246	−	0.624223i	$-0.785416\pi$
$23$	−69.6324	+	40.2023i	−0.631276	+	0.364467i	0.149970	+	0.988691i	$0.452082\pi$
$24$		0			0
$25$	61.7220	−	106.906i	0.493776	−	0.855245i
$26$		0			0
$27$	−113.589	−	82.3444i	−0.809636	−	0.586933i
$28$		0			0
$29$		−	211.712i		−	1.35565i	−0.735222	−	0.677827i	$-0.762922\pi$
$29$		−	211.712i		−	1.35565i	0.735222	−	0.677827i	$-0.237078\pi$
$30$		0			0
$31$	86.6242	+	50.0125i	0.501876	+	0.289758i	0.729488	−	0.683994i	$-0.239758\pi$
$31$	86.6242	+	50.0125i	0.501876	+	0.289758i	−0.227612	+	0.973752i	$0.573092\pi$
$32$		0			0
$33$	−201.064	+	65.4076i	−1.06063	+	0.345030i
$34$		0			0
$35$	10.4962	−	20.5803i	0.0506910	−	0.0993916i
$36$		0			0
$37$	94.9875	+	164.523i	0.422050	+	0.731012i	0.996140	−	0.0877801i	$-0.0279773\pi$
$37$	94.9875	+	164.523i	0.422050	+	0.731012i	−0.574090	+	0.818792i	$0.694644\pi$
$38$		0			0
$39$	75.6987	+	68.1113i	0.310808	+	0.279655i
$40$		0			0
$41$	−186.753			−0.711362			−0.355681	−	0.934607i	$-0.615751\pi$
$41$	−186.753			−0.711362			−0.355681	+	0.934607i	$0.615751\pi$
$42$		0			0
$43$	−158.618			−0.562536			−0.281268	−	0.959629i	$-0.590755\pi$
$43$	−158.618			−0.562536			−0.281268	+	0.959629i	$0.590755\pi$
$44$		0			0
$45$	27.2339	−	19.8158i	0.0902174	−	0.0656437i
$46$		0			0
$47$	−179.034	−	310.097i	−0.555635	−	0.962388i	−0.997854	−	0.0654808i	$-0.979142\pi$
$47$	−179.034	−	310.097i	−0.555635	−	0.962388i	0.442219	−	0.896907i	$-0.354191\pi$
$48$		0			0
$49$	−139.753	+	313.238i	−0.407444	+	0.913230i
$50$		0			0
$51$	168.328	+	517.442i	0.462170	+	1.42071i
$52$		0			0
$53$	−366.460	−	211.576i	−0.949758	−	0.548343i	−0.0567521	−	0.998388i	$-0.518074\pi$
$53$	−366.460	−	211.576i	−0.949758	−	0.548343i	−0.893006	+	0.450045i	$0.851408\pi$
$54$		0			0
$55$		−	50.7580i		−	0.124440i
$56$		0			0
$57$	−43.6323	+	205.629i	−0.101390	+	0.477829i
$58$		0			0
$59$	−312.781	+	541.753i	−0.690180	+	1.19543i	0.281599	+	0.959532i	$0.409135\pi$
$59$	−312.781	+	541.753i	−0.690180	+	1.19543i	−0.971779	+	0.235895i	$0.924198\pi$
$60$		0			0
$61$	699.575	−	403.900i	1.46838	−	0.847772i	0.469011	−	0.883192i	$-0.344611\pi$
$61$	699.575	−	403.900i	1.46838	−	0.847772i	0.999372	+	0.0354209i	$0.0112772\pi$
$62$		0			0
$63$	−388.510	+	314.812i	−0.776948	+	0.629565i
$64$		0			0
$65$	−21.1708	+	12.2229i	−0.0403986	+	0.0233241i
$66$		0			0
$67$	149.272	−	258.547i	0.272187	−	0.471441i	−0.697235	−	0.716843i	$-0.745587\pi$
$67$	149.272	−	258.547i	0.272187	−	0.471441i	0.969421	+	0.245402i	$0.0789199\pi$
$68$		0			0
$69$	−86.7208	+	408.695i	−0.151304	+	0.713059i
$70$		0			0
$71$		−	455.386i		−	0.761189i	−0.924742	−	0.380594i	$-0.875719\pi$
$71$		−	455.386i		−	0.761189i	0.924742	−	0.380594i	$-0.124281\pi$
$72$		0			0
$73$	−434.467	−	250.840i	−0.696582	−	0.402172i	0.109491	−	0.993988i	$-0.465078\pi$
$73$	−434.467	−	250.840i	−0.696582	−	0.402172i	−0.806073	+	0.591816i	$0.798411\pi$
$74$		0			0
$75$	−198.428	−	609.970i	−0.305500	−	0.939110i
$76$		0			0
$77$	39.1491	+	752.584i	0.0579410	+	1.11383i
$78$		0			0
$79$	−30.9561	−	53.6176i	−0.0440865	−	0.0763601i	0.843140	−	0.537694i	$-0.180704\pi$
$79$	−30.9561	−	53.6176i	−0.0440865	−	0.0763601i	−0.887227	+	0.461334i	$0.847371\pi$
$80$		0			0
$81$	−712.856	+	152.569i	−0.977855	+	0.209285i
$82$		0			0
$83$	73.1180			0.0966957			0.0483478	−	0.998831i	$-0.484604\pi$
$83$	73.1180			0.0966957			0.0483478	+	0.998831i	$0.484604\pi$
$84$		0			0
$85$	−130.627			−0.166688
$86$		0			0
$87$	−817.783	−	735.816i	−1.00777	−	0.906755i
$88$		0			0
$89$	57.3723	+	99.3717i	0.0683309	+	0.118353i	0.898167	−	0.439655i	$-0.144899\pi$
$89$	57.3723	+	99.3717i	0.0683309	+	0.118353i	−0.829836	+	0.558008i	$0.811566\pi$
$90$		0			0
$91$	304.469	−	197.557i	0.350737	−	0.227578i
$92$		0			0
$93$	494.251	−	160.784i	0.551090	−	0.179274i
$94$		0			0
$95$	−43.7025	−	25.2316i	−0.0471977	−	0.0272496i
$96$		0			0
$97$		−	1416.51i		−	1.48273i	−0.671101	−	0.741366i	$-0.734178\pi$
$97$		−	1416.51i		−	1.48273i	0.671101	−	0.741366i	$-0.265822\pi$
$98$		0			0
$99$	−446.156	+	1003.98i	−0.452933	+	1.01923i
$100$		0			0
$101$	120.406	−	208.549i	0.118622	−	0.205459i	−0.800600	−	0.599199i	$-0.795486\pi$
$101$	120.406	−	208.549i	0.118622	−	0.205459i	0.919222	+	0.393740i	$0.128819\pi$
$102$		0			0
$103$	960.453	−	554.518i	0.918799	−	0.530469i	0.0355471	−	0.999368i	$-0.488683\pi$
$103$	960.453	−	554.518i	0.918799	−	0.530469i	0.883252	+	0.468899i	$0.155349\pi$
$104$		0			0
$105$	−43.0157	−	112.072i	−0.0399800	−	0.104163i
$106$		0			0
$107$	−924.644	+	533.843i	−0.835408	+	0.482323i	−0.855701	−	0.517471i	$-0.826874\pi$
$107$	−924.644	+	533.843i	−0.835408	+	0.482323i	0.0202926	+	0.999794i	$0.493540\pi$
$108$		0			0
$109$	−5.04376	+	8.73604i	−0.00443215	+	0.00767671i	−0.868233	−	0.496157i	$-0.834744\pi$
$109$	−5.04376	+	8.73604i	−0.00443215	+	0.00767671i	0.863801	+	0.503833i	$0.168077\pi$
$110$		0			0
$111$	965.640	+	204.899i	0.825716	+	0.175208i
$112$		0			0
$113$		−	884.294i		−	0.736171i	−0.929792	−	0.368086i	$-0.880013\pi$
$113$		−	884.294i		−	0.736171i	0.929792	−	0.368086i	$-0.119987\pi$
$114$		0			0
$115$	−86.8602	−	50.1487i	−0.0704326	−	0.0406643i
$116$		0			0
$117$	526.189	−	55.6784i	0.415780	−	0.0439954i
$118$		0			0
$119$	1936.79	−	100.751i	1.49198	−	0.0776122i
$120$		0			0
$121$	162.366	+	281.226i	0.121988	+	0.211289i
$122$		0			0
$123$	−649.067	+	721.372i	−0.475808	+	0.528812i
$124$		0			0
$125$	309.912			0.221755
$126$		0			0
$127$	840.132			0.587005			0.293503	−	0.955958i	$-0.405179\pi$
$127$	840.132			0.587005			0.293503	+	0.955958i	$0.405179\pi$
$128$		0			0
$129$	−551.285	+	612.697i	−0.376263	+	0.418178i
$130$		0			0
$131$	258.951	+	448.517i	0.172707	+	0.299138i	0.939366	−	0.342918i	$-0.111415\pi$
$131$	258.951	+	448.517i	0.172707	+	0.299138i	−0.766658	+	0.642056i	$0.778082\pi$
$132$		0			0
$133$	667.434	+	340.400i	0.435142	+	0.221928i
$134$		0			0
$135$	18.1098	−	174.067i	0.0115455	−	0.110973i
$136$		0			0
$137$	950.957	+	549.035i	0.593034	+	0.342389i	0.766296	−	0.642487i	$-0.222097\pi$
$137$	950.957	+	549.035i	0.593034	+	0.342389i	−0.173262	+	0.984876i	$0.555431\pi$
$138$		0			0
$139$		−	828.268i		−	0.505416i	−0.967543	−	0.252708i	$-0.918679\pi$
$139$		−	828.268i		−	0.505416i	0.967543	−	0.252708i	$-0.0813212\pi$
$140$		0			0
$141$	−1820.06	−	386.197i	−1.08707	−	0.230664i
$142$		0			0
$143$	398.714	−	690.592i	0.233162	−	0.403848i
$144$		0			0
$145$	228.710	−	132.046i	0.130989	−	0.0756264i
$146$		0			0
$147$	724.230	+	1628.50i	0.406350	+	0.913717i
$148$		0			0
$149$	773.007	−	446.296i	0.425015	−	0.245382i	−0.272206	−	0.962239i	$-0.587753\pi$
$149$	773.007	−	446.296i	0.425015	−	0.245382i	0.697221	+	0.716857i	$0.254420\pi$
$150$		0			0
$151$	712.518	−	1234.12i	0.383999	−	0.665106i	−0.607630	−	0.794220i	$-0.707880\pi$
$151$	712.518	−	1234.12i	0.383999	−	0.665106i	0.991630	+	0.129113i	$0.0412131\pi$
$152$		0			0
$153$	2583.76	+	1148.19i	1.36526	+	0.606705i
$154$		0			0
$155$			124.772i			0.0646577i
$156$		0			0
$157$	−244.872	−	141.377i	−0.124477	−	0.0718670i	0.436468	−	0.899720i	$-0.356229\pi$
$157$	−244.872	−	141.377i	−0.124477	−	0.0718670i	−0.560946	+	0.827853i	$0.689562\pi$
$158$		0			0
$159$	−2090.91	+	680.189i	−1.04289	+	0.339261i
$160$		0			0
$161$	1326.55	+	676.557i	0.649358	+	0.331181i
$162$		0			0
$163$	1158.07	+	2005.83i	0.556484	+	0.963858i	0.997786	+	0.0664997i	$0.0211832\pi$
$163$	1158.07	+	2005.83i	0.556484	+	0.963858i	−0.441303	+	0.897358i	$0.645484\pi$
$164$		0			0
$165$	−196.064	−	176.412i	−0.0925063	−	0.0832342i
$166$		0			0
$167$	2344.70			1.08646			0.543229	−	0.839585i	$-0.317202\pi$
$167$	2344.70			1.08646			0.543229	+	0.839585i	$0.317202\pi$
$168$		0			0
$169$	1812.95			0.825192
$170$		0			0
$171$	642.640	+	883.213i	0.287391	+	0.394977i
$172$		0			0
$173$	516.901	+	895.298i	0.227163	+	0.393458i	0.956966	−	0.290199i	$-0.0937216\pi$
$173$	516.901	+	895.298i	0.227163	+	0.393458i	−0.729803	+	0.683657i	$0.760388\pi$
$174$		0			0
$175$	−2283.13	+	118.767i	−0.986218	+	0.0513026i
$176$		0			0
$177$	1005.55	+	3091.07i	0.427016	+	1.31265i
$178$		0			0
$179$	125.472	+	72.4412i	0.0523922	+	0.0302486i	0.525967	−	0.850505i	$-0.323703\pi$
$179$	125.472	+	72.4412i	0.0523922	+	0.0302486i	−0.473575	+	0.880753i	$0.657037\pi$
$180$		0			0
$181$		−	2057.17i		−	0.844797i	−0.906410	−	0.422398i	$-0.861188\pi$
$181$		−	2057.17i		−	0.844797i	0.906410	−	0.422398i	$-0.138812\pi$
$182$		0			0
$183$	871.257	−	4106.03i	0.351941	−	1.65862i
$184$		0			0
$185$	−118.489	+	205.228i	−0.0470889	+	0.0815604i
$186$		0			0
$187$	3690.19	−	2130.53i	1.44307	−	0.833155i
$188$		0			0
$189$	−134.257	+	2594.85i	−0.0516706	+	0.998664i
$190$		0			0
$191$	2553.66	−	1474.36i	0.967417	−	0.558538i	0.0689690	−	0.997619i	$-0.478029\pi$
$191$	2553.66	−	1474.36i	0.967417	−	0.558538i	0.898448	+	0.439080i	$0.144696\pi$
$192$		0			0
$193$	1135.40	−	1966.57i	0.423460	−	0.733455i	−0.572815	−	0.819685i	$-0.694149\pi$
$193$	1135.40	−	1966.57i	0.423460	−	0.733455i	0.996275	+	0.0862300i	$0.0274820\pi$
$194$		0			0
$195$	−26.3662	+	124.258i	−0.00968270	+	0.0456323i
$196$		0			0
$197$		−	495.849i		−	0.179329i	−0.995972	−	0.0896645i	$-0.971421\pi$
$197$		−	495.849i		−	0.179329i	0.995972	−	0.0896645i	$-0.0285795\pi$
$198$		0			0
$199$	−727.207	−	419.853i	−0.259047	−	0.149561i	0.364853	−	0.931065i	$-0.381119\pi$
$199$	−727.207	−	419.853i	−0.259047	−	0.149561i	−0.623900	+	0.781504i	$0.714453\pi$
$200$		0			0
$201$	−479.890	−	1475.19i	−0.168402	−	0.517670i
$202$		0			0
$203$	−3289.22	+	2134.24i	−1.13723	+	0.737902i
$204$		0			0
$205$	−116.479	−	201.747i	−0.0396840	−	0.0687347i
$206$		0			0
$207$	1277.27	+	1755.42i	0.428871	+	0.589420i
$208$		0			0
$209$	1646.12			0.544805
$210$		0			0
$211$	−4001.71			−1.30564			−0.652818	−	0.757514i	$-0.726414\pi$
$211$	−4001.71			−1.30564			−0.652818	+	0.757514i	$0.726414\pi$
$212$		0			0
$213$	−1759.03	−	1582.72i	−0.565852	−	0.509136i
$214$		0			0
$215$	−98.9311	−	171.354i	−0.0313816	−	0.0543545i
$216$		0			0
$217$	−96.2355	−	1849.99i	−0.0301055	−	0.578734i
$218$		0			0
$219$	−2478.93	+	806.416i	−0.764889	+	0.248825i
$220$		0			0
$221$	−1777.26	−	1026.10i	−0.540955	−	0.312321i
$222$		0			0
$223$		−	3040.54i		−	0.913047i	−0.889711	−	0.456523i	$-0.849095\pi$
$223$		−	3040.54i		−	0.913047i	0.889711	−	0.456523i	$-0.150905\pi$
$224$		0			0
$225$	−3045.79	−	1353.51i	−0.902455	−	0.401040i
$226$		0			0
$227$	−2198.24	+	3807.46i	−0.642741	+	1.11326i	0.342078	+	0.939672i	$0.388869\pi$
$227$	−2198.24	+	3807.46i	−0.642741	+	1.11326i	−0.984818	+	0.173588i	$0.944464\pi$
$228$		0			0
$229$	−1717.81	+	991.778i	−0.495703	+	0.286194i	−0.726937	−	0.686704i	$-0.759057\pi$
$229$	−1717.81	+	991.778i	−0.495703	+	0.286194i	0.231234	+	0.972898i	$0.425724\pi$
$230$		0			0
$231$	3043.08	+	2464.42i	0.866754	+	0.701935i
$232$		0			0
$233$	−3787.78	+	2186.87i	−1.06500	+	0.614879i	−0.926812	−	0.375526i	$-0.877462\pi$
$233$	−3787.78	+	2186.87i	−1.06500	+	0.614879i	−0.138191	+	0.990406i	$0.544129\pi$
$234$		0			0
$235$	223.329	−	386.818i	0.0619932	−	0.107375i
$236$		0			0
$237$	−314.699	−	66.7758i	−0.0862527	−	0.0183019i
$238$		0			0
$239$		−	3826.41i		−	1.03561i	−0.855500	−	0.517803i	$-0.826750\pi$
$239$		−	3826.41i		−	1.03561i	0.855500	−	0.517803i	$-0.173250\pi$
$240$		0			0
$241$	2979.03	+	1719.94i	0.796250	+	0.459715i	0.842158	−	0.539231i	$-0.181285\pi$
$241$	2979.03	+	1719.94i	0.796250	+	0.459715i	−0.0459083	+	0.998946i	$0.514618\pi$
$242$		0			0
$243$	−1888.24	+	3283.82i	−0.498479	+	0.866902i
$244$		0			0
$245$	−425.553	+	44.3943i	−0.110970	+	0.0115765i
$246$		0			0
$247$	−396.398	−	686.582i	−0.102114	−	0.176867i
$248$		0			0
$249$	254.125	−	282.434i	0.0646768	−	0.0718816i
$250$		0			0
$251$	2046.61			0.514664			0.257332	−	0.966323i	$-0.417157\pi$
$251$	2046.61			0.514664			0.257332	+	0.966323i	$0.417157\pi$
$252$		0			0
$253$	3271.72			0.813008
$254$		0			0
$255$	−454.000	+	504.575i	−0.111493	+	0.123913i
$256$		0			0
$257$	−3025.57	−	5240.44i	−0.734357	−	1.27194i	−0.955005	−	0.296590i	$-0.904150\pi$
$257$	−3025.57	−	5240.44i	−0.734357	−	1.27194i	0.220648	−	0.975354i	$-0.429183\pi$
$258$		0			0
$259$	1598.53	−	3134.29i	0.383505	−	0.751950i
$260$		0			0
$261$	−5684.49	+	601.501i	−1.34813	+	0.142651i
$262$		0			0
$263$	−5433.69	−	3137.14i	−1.27398	−	0.735530i	−0.298242	−	0.954490i	$-0.596400\pi$
$263$	−5433.69	−	3137.14i	−1.27398	−	0.735530i	−0.975734	+	0.218960i	$0.929733\pi$
$264$		0			0
$265$		−	527.844i		−	0.122359i
$266$		0			0
$267$	583.245	+	123.758i	0.133685	+	0.0283666i
$268$		0			0
$269$	−1668.18	+	2889.37i	−0.378106	+	0.654899i	−0.990787	−	0.135432i	$-0.956758\pi$
$269$	−1668.18	+	2889.37i	−0.378106	+	0.654899i	0.612681	+	0.790331i	$0.290091\pi$
$270$		0			0
$271$	−2462.26	+	1421.59i	−0.551925	+	0.318654i	−0.749898	−	0.661553i	$-0.769897\pi$
$271$	−2462.26	+	1421.59i	−0.551925	+	0.318654i	0.197973	+	0.980207i	$0.436564\pi$
$272$		0			0
$273$	295.091	−	1862.70i	0.0654202	−	0.412951i
$274$		0			0
$275$	−4350.06	+	2511.51i	−0.953886	+	0.550726i
$276$		0			0
$277$	−3174.17	+	5497.82i	−0.688510	+	1.19253i	0.283809	+	0.958881i	$0.408402\pi$
$277$	−3174.17	+	5497.82i	−0.688510	+	1.19253i	−0.972320	+	0.233654i	$0.924932\pi$
$278$		0			0
$279$	1096.73	−	2467.96i	0.235339	−	0.529580i
$280$		0			0
$281$		−	3735.88i		−	0.793110i	−0.918011	−	0.396555i	$-0.870206\pi$
$281$		−	3735.88i		−	0.793110i	0.918011	−	0.396555i	$-0.129794\pi$
$282$		0			0
$283$	4777.96	+	2758.56i	1.00361	+	0.579432i	0.909313	−	0.416112i	$-0.136608\pi$
$283$	4777.96	+	2758.56i	1.00361	+	0.579432i	0.0942927	+	0.995545i	$0.469941\pi$
$284$		0			0
$285$	−249.353	+	81.1164i	−0.0518259	+	0.0168594i
$286$		0			0
$287$	1882.62	+	2901.44i	0.387205	+	0.596748i
$288$		0			0
$289$	−3026.48	−	5242.01i	−0.616014	−	1.06697i
$290$		0			0
$291$	−5471.58	−	4923.16i	−1.10223	−	0.991755i
$292$		0			0
$293$	7574.50			1.51026			0.755131	−	0.655574i	$-0.227573\pi$
$293$	7574.50			1.51026			0.755131	+	0.655574i	$0.227573\pi$
$294$		0			0
$295$	−780.333			−0.154009
$296$		0			0
$297$	2327.45	+	5212.75i	0.454721	+	1.01843i
$298$		0			0
$299$	−787.855	−	1364.61i	−0.152384	−	0.263937i
$300$		0			0
$301$	1599.01	+	2464.34i	0.306196	+	0.471901i
$302$		0			0
$303$	−387.088	−	1189.91i	−0.0733915	−	0.225606i
$304$		0			0
$305$	872.657	+	503.829i	0.163830	+	0.0945874i
$306$		0			0
$307$			10635.6i			1.97723i	0.150480	+	0.988613i	$0.451918\pi$
$307$			10635.6i			1.97723i	−0.150480	+	0.988613i	$0.548082\pi$
$308$		0			0
$309$	1196.16	−	5637.21i	0.220217	−	1.03783i
$310$		0			0
$311$	2885.59	−	4997.99i	0.526132	−	0.911287i	−0.473405	−	0.880845i	$-0.656975\pi$
$311$	2885.59	−	4997.99i	0.526132	−	0.911287i	0.999537	−	0.0304419i	$-0.00969146\pi$
$312$		0			0
$313$	−2030.41	+	1172.26i	−0.366664	+	0.211694i	−0.672000	−	0.740551i	$-0.734565\pi$
$313$	−2030.41	+	1172.26i	−0.366664	+	0.211694i	0.305336	+	0.952245i	$0.401231\pi$
$314$		0			0
$315$	−582.404	−	223.354i	−0.104174	−	0.0399509i
$316$		0			0
$317$	−6852.10	+	3956.06i	−1.21405	+	0.700929i	−0.963638	−	0.267211i	$-0.913898\pi$
$317$	−6852.10	+	3956.06i	−1.21405	+	0.700929i	−0.250407	+	0.968141i	$0.580565\pi$
$318$		0			0
$319$	−4307.36	+	7460.56i	−0.756005	+	1.30944i
$320$		0			0
$321$	−1151.56	+	5427.03i	−0.200230	+	0.943637i
$322$		0			0
$323$		−	4236.32i		−	0.729769i
$324$		0			0
$325$	2095.06	+	1209.58i	0.357579	+	0.206448i
$326$		0			0
$327$	16.2150	+	49.8451i	0.00274218	+	0.00842949i
$328$		0			0
$329$	−3012.94	+	5907.57i	−0.504889	+	0.989953i
$330$		0			0
$331$	−2440.02	−	4226.23i	−0.405182	−	0.701797i	0.589160	−	0.808016i	$-0.299459\pi$
$331$	−2440.02	−	4226.23i	−0.405182	−	0.701797i	−0.994343	+	0.106220i	$0.966125\pi$
$332$		0			0
$333$	4147.59	−	3017.86i	0.682543	−	0.496629i
$334$		0			0
$335$	372.407			0.0607367
$336$		0			0
$337$	−4136.39			−0.668616			−0.334308	−	0.942464i	$-0.608503\pi$
$337$	−4136.39			−0.668616			−0.334308	+	0.942464i	$0.608503\pi$
$338$		0			0
$339$	−3415.77	−	3073.41i	−0.547255	−	0.492403i
$340$		0			0
$341$	−2035.04	−	3524.80i	−0.323178	−	0.559761i
$342$		0			0
$343$	6275.39	−	986.454i	0.987869	−	0.155287i
$344$		0			0
$345$	−495.597	+	161.222i	−0.0773393	+	0.0251591i
$346$		0			0
$347$	−2009.83	−	1160.38i	−0.310933	−	0.179517i	0.336411	−	0.941715i	$-0.390787\pi$
$347$	−2009.83	−	1160.38i	−0.310933	−	0.179517i	−0.647344	+	0.762198i	$0.724120\pi$
$348$		0			0
$349$		−	226.795i		−	0.0347853i	−0.999849	−	0.0173926i	$-0.994463\pi$
$349$		−	226.795i		−	0.0347853i	0.999849	−	0.0173926i	$-0.00553653\pi$
$350$		0			0
$351$	1613.73	−	2226.03i	0.245397	−	0.338509i
$352$		0			0
$353$	742.854	−	1286.66i	0.112006	−	0.194000i	−0.804573	−	0.593854i	$-0.797606\pi$
$353$	742.854	−	1286.66i	0.112006	−	0.194000i	0.916579	+	0.399854i	$0.130939\pi$
$354$		0			0
$355$	491.949	−	284.027i	0.0735491	−	0.0424636i
$356$		0			0
$357$	6342.25	−	7831.45i	0.940245	−	1.16102i
$358$		0			0
$359$	−9419.94	+	5438.60i	−1.38486	+	0.799550i	−0.992730	−	0.120359i	$-0.961595\pi$
$359$	−9419.94	+	5438.60i	−1.38486	+	0.799550i	−0.392131	+	0.919909i	$0.628262\pi$
$360$		0			0
$361$	−2611.22	+	4522.77i	−0.380700	+	0.659392i
$362$		0			0
$363$	1650.61	+	350.241i	0.238662	+	0.0506416i
$364$		0			0
$365$		−	625.800i		−	0.0897421i
$366$		0			0
$367$	3299.69	+	1905.08i	0.469325	+	0.270965i	0.715957	−	0.698144i	$-0.245991\pi$
$367$	3299.69	+	1905.08i	0.469325	+	0.270965i	−0.246632	+	0.969109i	$0.579324\pi$
$368$		0			0
$369$	530.587	+	5014.32i	0.0748544	+	0.707413i
$370$		0			0
$371$	407.121	+	7826.30i	0.0569721	+	1.09521i
$372$		0			0
$373$	4869.55	+	8434.30i	0.675967	+	1.17081i	0.976185	+	0.216938i	$0.0696070\pi$
$373$	4869.55	+	8434.30i	0.675967	+	1.17081i	−0.300219	+	0.953870i	$0.597060\pi$
$374$		0			0
$375$	1077.11	−	1197.10i	0.148325	−	0.164848i
$376$		0			0
$377$	4148.98			0.566800
$378$		0			0
$379$	−320.171			−0.0433933			−0.0216967	−	0.999765i	$-0.506907\pi$
$379$	−320.171			−0.0433933			−0.0216967	+	0.999765i	$0.506907\pi$
$380$		0			0
$381$	2919.92	−	3245.19i	0.392630	−	0.436368i
$382$		0			0
$383$	2185.13	+	3784.75i	0.291527	+	0.504939i	0.974171	−	0.225812i	$-0.0725034\pi$
$383$	2185.13	+	3784.75i	0.291527	+	0.504939i	−0.682644	+	0.730751i	$0.739170\pi$
$384$		0			0
$385$	−788.592	+	511.683i	−0.104391	+	0.0677346i
$386$		0			0
$387$	450.654	+	4258.92i	0.0591939	+	0.559413i
$388$		0			0
$389$	−11877.4	−	6857.42i	−1.54809	−	0.893791i	−0.998288	−	0.0584981i	$-0.981369\pi$
$389$	−11877.4	−	6857.42i	−1.54809	−	0.893791i	−0.549805	−	0.835293i	$-0.685298\pi$
$390$		0			0
$391$		−	8419.84i		−	1.08903i
$392$		0			0
$393$	2632.49	+	558.587i	0.337892	+	0.0716971i
$394$		0			0
$395$	38.6150	−	66.8832i	0.00491882	−	0.00851964i
$396$		0			0
$397$	−2181.61	+	1259.55i	−0.275798	+	0.159232i	−0.631520	−	0.775360i	$-0.717568\pi$
$397$	−2181.61	+	1259.55i	−0.275798	+	0.159232i	0.355722	+	0.934592i	$0.384235\pi$
$398$		0			0
$399$	3634.57	−	1395.03i	0.456030	−	0.175035i
$400$		0			0
$401$	−2268.96	+	1309.98i	−0.282560	+	0.163136i	−0.634582	−	0.772856i	$-0.718828\pi$
$401$	−2268.96	+	1309.98i	−0.282560	+	0.163136i	0.352022	+	0.935992i	$0.385494\pi$
$402$		0			0
$403$	−980.109	+	1697.60i	−0.121148	+	0.209835i
$404$		0			0
$405$	−609.431	−	674.933i	−0.0747725	−	0.0828091i
$406$		0			0
$407$		−	7730.22i		−	0.941456i
$408$		0			0
$409$	−12058.7	−	6962.09i	−1.45786	−	0.841694i	−0.458952	−	0.888461i	$-0.651775\pi$
$409$	−12058.7	−	6962.09i	−1.45786	−	0.841694i	−0.998906	+	0.0467669i	$0.985108\pi$
$410$		0			0
$411$	5425.86	−	1765.08i	0.651187	−	0.211836i
$412$		0			0
$413$	11569.9	−	601.863i	1.37850	−	0.0717088i
$414$		0			0
$415$	45.6041	+	78.9886i	0.00539426	+	0.00934313i
$416$		0			0
$417$	−3199.36	−	2878.69i	−0.375716	−	0.338057i
$418$		0			0
$419$	15171.1			1.76887			0.884433	−	0.466666i	$-0.154545\pi$
$419$	15171.1			1.76887			0.884433	+	0.466666i	$0.154545\pi$
$420$		0			0
$421$	−1052.53			−0.121846			−0.0609228	−	0.998142i	$-0.519404\pi$
$421$	−1052.53			−0.121846			−0.0609228	+	0.998142i	$0.519404\pi$
$422$		0			0
$423$	−7817.47	+	5688.11i	−0.898577	+	0.653819i
$424$		0			0
$425$	6463.43	+	11195.0i	0.737700	+	1.27773i
$426$		0			0
$427$	−13327.4	−	6797.16i	−1.51044	−	0.770345i
$428$		0			0
$429$	−1281.81	−	3940.30i	−0.144258	−	0.443449i
$430$		0			0
$431$	6923.58	+	3997.33i	0.773776	+	0.446740i	0.834220	−	0.551432i	$-0.185918\pi$
$431$	6923.58	+	3997.33i	0.773776	+	0.446740i	−0.0604442	+	0.998172i	$0.519252\pi$
$432$		0			0
$433$		−	12889.4i		−	1.43055i	−0.698845	−	0.715273i	$-0.746303\pi$
$433$		−	12889.4i		−	1.43055i	0.698845	−	0.715273i	$-0.253697\pi$
$434$		0			0
$435$	284.838	−	1342.38i	0.0313953	−	0.147959i
$436$		0			0
$437$	1626.36	−	2816.94i	0.178030	−	0.308358i
$438$		0			0
$439$	−12456.7	+	7191.89i	−1.35427	+	0.781891i	−0.988845	−	0.148948i	$-0.952411\pi$
$439$	−12456.7	+	7191.89i	−1.35427	+	0.781891i	−0.365430	+	0.930839i	$0.619078\pi$
$440$		0			0
$441$	8807.53	+	2862.44i	0.951034	+	0.309085i
$442$		0			0
$443$	3432.16	−	1981.56i	0.368097	−	0.212521i	−0.304530	−	0.952503i	$-0.598499\pi$
$443$	3432.16	−	1981.56i	0.368097	−	0.212521i	0.672627	+	0.739982i	$0.265166\pi$
$444$		0			0
$445$	−71.5668	+	123.957i	−0.00762380	+	0.0132048i
$446$		0			0
$447$	962.710	−	4537.03i	0.101867	−	0.480076i
$448$		0			0
$449$		−	13479.1i		−	1.41675i	−0.705838	−	0.708373i	$-0.749430\pi$
$449$		−	13479.1i		−	1.41675i	0.705838	−	0.708373i	$-0.250570\pi$
$450$		0			0
$451$	6581.00	+	3799.54i	0.687112	+	0.396704i
$452$		0			0
$453$	−2290.65	−	7041.49i	−0.237581	−	0.730327i
$454$		0			0
$455$	403.318	+	205.698i	0.0415557	+	0.0211940i
$456$		0			0
$457$	−1989.79	−	3446.42i	−0.203673	−	0.352772i	0.746036	−	0.665905i	$-0.231955\pi$
$457$	−1989.79	−	3446.42i	−0.203673	−	0.352772i	−0.949709	+	0.313134i	$0.898621\pi$
$458$		0			0
$459$	13415.1	−	5989.74i	1.36419	−	0.609101i
$460$		0			0
$461$	9053.72			0.914694			0.457347	−	0.889288i	$-0.348800\pi$
$461$	9053.72			0.914694			0.457347	+	0.889288i	$0.348800\pi$
$462$		0			0
$463$	5736.10			0.575764			0.287882	−	0.957666i	$-0.407049\pi$
$463$	5736.10			0.575764			0.287882	+	0.957666i	$0.407049\pi$
$464$		0			0
$465$	481.960	+	433.652i	0.0480653	+	0.0432476i
$466$		0			0
$467$	−6196.30	−	10732.3i	−0.613984	−	1.06345i	−0.990562	−	0.137067i	$-0.956232\pi$
$467$	−6196.30	−	10732.3i	−0.613984	−	1.06345i	0.376578	−	0.926385i	$-0.377101\pi$
$468$		0			0
$469$	−5521.65	+	287.234i	−0.543638	+	0.0282798i
$470$		0			0
$471$	−1397.17	+	454.509i	−0.136684	+	0.0444643i
$472$		0			0
$473$	5589.57	+	3227.14i	0.543359	+	0.313709i
$474$		0			0
$475$			4993.85i			0.482387i
$476$		0			0
$477$	−4639.67	+	10440.6i	−0.445359	+	1.00219i
$478$		0			0
$479$	−4133.87	+	7160.07i	−0.394324	+	0.682989i	−0.993015	−	0.117991i	$-0.962355\pi$
$479$	−4133.87	+	7160.07i	−0.394324	+	0.682989i	0.598691	+	0.800980i	$0.295688\pi$
$480$		0			0
$481$	−3224.21	+	1861.50i	−0.305637	+	0.176460i
$482$		0			0
$483$	7223.82	−	2772.67i	0.680529	−	0.261202i
$484$		0			0
$485$	1530.24	−	883.487i	0.143268	−	0.0827156i
$486$		0			0
$487$	470.075	−	814.194i	0.0437395	−	0.0757590i	−0.843327	−	0.537401i	$-0.819406\pi$
$487$	470.075	−	814.194i	0.0437395	−	0.0757590i	0.887066	+	0.461642i	$0.152740\pi$
$488$		0			0
$489$	11772.9	+	2498.08i	1.08873	+	0.231017i
$490$		0			0
$491$		−	1057.30i		−	0.0971801i	−0.998819	−	0.0485900i	$-0.984527\pi$
$491$		−	1057.30i		−	0.0971801i	0.998819	−	0.0485900i	$-0.0154728\pi$
$492$		0			0
$493$	19199.9	+	11085.1i	1.75400	+	1.01267i
$494$		0			0
$495$	−1362.86	+	144.210i	−0.123749	+	0.0130944i
$496$		0			0
$497$	−7075.02	+	4590.68i	−0.638547	+	0.414326i
$498$		0			0
$499$	−3086.65	−	5346.23i	−0.276909	−	0.479620i	0.693706	−	0.720258i	$-0.255977\pi$
$499$	−3086.65	−	5346.23i	−0.276909	−	0.479620i	−0.970615	+	0.240638i	$0.922643\pi$
$500$		0			0
$501$	8149.12	−	9056.91i	0.726699	−	0.807651i
$502$		0			0
$503$	4284.28			0.379775			0.189887	−	0.981806i	$-0.439188\pi$
$503$	4284.28			0.379775			0.189887	+	0.981806i	$0.439188\pi$
$504$		0			0
$505$	300.390			0.0264697
$506$		0			0
$507$	6300.98	−	7002.89i	0.551946	−	0.613431i
$508$		0			0
$509$	7550.52	+	13077.9i	0.657507	+	1.13884i	0.981259	+	0.192693i	$0.0617223\pi$
$509$	7550.52	+	13077.9i	0.657507	+	1.13884i	−0.323752	+	0.946142i	$0.604944\pi$
$510$		0			0
$511$	482.673	+	9278.68i	0.0417851	+	0.803258i
$512$		0			0
$513$	5645.13	+	587.315i	0.485845	+	0.0505470i
$514$		0			0
$515$	1198.08	+	691.712i	0.102512	+	0.0591854i
$516$		0			0
$517$			14570.1i			1.23944i
$518$		0			0
$519$	5254.79	+	1115.01i	0.444431	+	0.0943037i
$520$		0			0
$521$	−6894.00	+	11940.8i	−0.579715	+	1.00410i	0.415796	+	0.909458i	$0.363503\pi$
$521$	−6894.00	+	11940.8i	−0.579715	+	1.00410i	−0.995512	+	0.0946385i	$0.969830\pi$
$522$		0			0
$523$	832.513	−	480.652i	0.0696047	−	0.0401863i	−0.464794	−	0.885419i	$-0.653872\pi$
$523$	832.513	−	480.652i	0.0696047	−	0.0401863i	0.534398	+	0.845233i	$0.320538\pi$
$524$		0			0
$525$	−7476.36	+	9231.85i	−0.621514	+	0.767449i
$526$		0			0
$527$	−9071.15	+	5237.23i	−0.749802	+	0.432898i
$528$		0			0
$529$	−2851.06	+	4938.17i	−0.234327	+	0.405866i
$530$		0			0
$531$	15434.8	+	6859.02i	1.26142	+	0.560557i
$532$		0			0
$533$		−	3659.84i		−	0.297421i
$534$		0			0
$535$	−1153.41	−	665.922i	−0.0932080	−	0.0538137i
$536$		0			0
$537$	715.903	−	232.889i	0.0575298	−	0.0187149i
$538$		0			0
$539$	11297.7	−	8194.92i	0.902834	−	0.654880i
$540$		0			0
$541$	597.846	+	1035.50i	0.0475109	+	0.0822913i	0.888803	−	0.458290i	$-0.151538\pi$
$541$	597.846	+	1035.50i	0.0475109	+	0.0822913i	−0.841292	+	0.540581i	$0.818204\pi$
$542$		0			0
$543$	−7946.26	−	7149.79i	−0.628005	−	0.565059i
$544$		0			0
$545$	−12.5833			−0.000989006
$546$		0			0
$547$	−18601.8			−1.45403			−0.727014	−	0.686622i	$-0.759093\pi$
$547$	−18601.8			−1.45403			−0.727014	+	0.686622i	$0.759093\pi$
$548$		0			0
$549$	−12832.3	−	17636.1i	−0.997578	−	1.37102i
$550$		0			0
$551$	4282.34	+	7417.24i	0.331096	+	0.573475i
$552$		0			0
$553$	−520.955	+	1021.45i	−0.0400601	+	0.0785473i
$554$		0			0
$555$	380.925	+	1170.97i	0.0291340	+	0.0895582i
$556$		0			0
$557$	5908.09	+	3411.04i	0.449432	+	0.259480i	0.707590	−	0.706623i	$-0.249782\pi$
$557$	5908.09	+	3411.04i	0.449432	+	0.259480i	−0.258158	+	0.966103i	$0.583116\pi$
$558$		0			0
$559$		−	3108.49i		−	0.235197i
$560$		0			0
$561$	4595.80	−	21658.9i	0.345873	−	1.63002i
$562$		0			0
$563$	5679.80	−	9837.71i	0.425178	−	0.736430i	−0.571259	−	0.820770i	$-0.693545\pi$
$563$	5679.80	−	9837.71i	0.425178	−	0.736430i	0.996437	+	0.0843399i	$0.0268782\pi$
$564$		0			0
$565$	955.293	−	551.539i	0.0711318	−	0.0410680i
$566$		0			0
$567$	9556.55	+	9537.12i	0.707826	+	0.706387i
$568$		0			0
$569$	18467.2	−	10662.1i	1.36061	−	0.785549i	0.370905	−	0.928671i	$-0.379047\pi$
$569$	18467.2	−	10662.1i	1.36061	−	0.785549i	0.989705	+	0.143122i	$0.0457141\pi$
$570$		0			0
$571$	−7384.00	+	12789.5i	−0.541175	+	0.937343i	0.457662	+	0.889126i	$0.348687\pi$
$571$	−7384.00	+	12789.5i	−0.541175	+	0.937343i	−0.998837	+	0.0482163i	$0.984646\pi$
$572$		0			0
$573$	3180.36	−	14988.3i	0.231870	−	1.09275i
$574$		0			0
$575$			9925.45i			0.719861i
$576$		0			0
$577$	16718.5	+	9652.44i	1.20624	+	0.696424i	0.961936	−	0.273275i	$-0.0881068\pi$
$577$	16718.5	+	9652.44i	1.20624	+	0.696424i	0.244305	+	0.969698i	$0.421440\pi$
$578$		0			0
$579$	−3650.16	−	11220.6i	−0.261996	−	0.805377i
$580$		0			0
$581$	−737.091	−	1135.98i	−0.0526328	−	0.0811162i
$582$		0			0
$583$	8609.17	+	14911.5i	0.611587	+	1.05930i
$584$		0			0
$585$	388.336	+	533.710i	0.0274457	+	0.0377200i
$586$		0			0
$587$	−4397.46			−0.309204			−0.154602	−	0.987977i	$-0.549410\pi$
$587$	−4397.46			−0.309204			−0.154602	+	0.987977i	$0.549410\pi$
$588$		0			0
$589$	−4046.45			−0.283075
$590$		0			0
$591$	−1915.32	−	1723.35i	−0.133310	−	0.119948i
$592$		0			0
$593$	−10970.1	−	19000.8i	−0.759677	−	1.31580i	−0.943015	−	0.332749i	$-0.892024\pi$
$593$	−10970.1	−	19000.8i	−0.759677	−	1.31580i	0.183339	−	0.983050i	$-0.441309\pi$
$594$		0			0
$595$	1316.83	+	2029.46i	0.0907307	+	0.139832i
$596$		0			0
$597$	−4149.21	+	1349.77i	−0.284449	+	0.0925335i
$598$		0			0
$599$	4765.07	+	2751.12i	0.325034	+	0.187659i	0.653634	−	0.756810i	$-0.273243\pi$
$599$	4765.07	+	2751.12i	0.325034	+	0.187659i	−0.328600	+	0.944469i	$0.606577\pi$
$600$		0			0
$601$		−	5814.58i		−	0.394645i	−0.980339	−	0.197322i	$-0.936775\pi$
$601$		−	5814.58i		−	0.394645i	0.980339	−	0.197322i	$-0.0632246\pi$
$602$		0			0
$603$	−7366.11	−	3273.41i	−0.497465	−	0.221067i
$604$		0			0
$605$	−202.537	+	350.804i	−0.0136104	+	0.0235739i
$606$		0			0
$607$	11510.7	−	6645.69i	0.769693	−	0.444382i	−0.0630721	−	0.998009i	$-0.520090\pi$
$607$	11510.7	−	6645.69i	0.769693	−	0.444382i	0.832765	+	0.553627i	$0.186756\pi$
$608$		0			0
$609$	−3187.91	+	20123.0i	−0.212119	+	1.33896i
$610$		0			0
$611$	6077.05	−	3508.59i	0.402375	−	0.232311i
$612$		0			0
$613$	−9797.17	+	16969.2i	−0.645520	+	1.11807i	0.338661	+	0.940909i	$0.390026\pi$
$613$	−9797.17	+	16969.2i	−0.645520	+	1.11807i	−0.984181	+	0.177166i	$0.943307\pi$
$614$		0			0
$615$	−1184.12	−	251.257i	−0.0776394	−	0.0164743i
$616$		0			0
$617$			348.388i			0.0227319i	0.999935	+	0.0113660i	$0.00361797\pi$
$617$			348.388i			0.0227319i	−0.999935	+	0.0113660i	$0.996382\pi$
$618$		0			0
$619$	−5867.68	−	3387.71i	−0.381005	−	0.219973i	0.297251	−	0.954799i	$-0.403930\pi$
$619$	−5867.68	−	3387.71i	−0.381005	−	0.219973i	−0.678255	+	0.734826i	$0.737264\pi$
$620$		0			0
$621$	11219.9	+	1167.31i	0.725022	+	0.0754307i
$622$		0			0
$623$	965.508	−	1893.10i	0.0620903	−	0.121742i
$624$		0			0
$625$	−7521.95	−	13028.4i	−0.481405	−	0.833818i
$626$		0			0
$627$	5721.16	−	6358.48i	0.364404	−	0.404997i
$628$		0			0
$629$	−19893.9			−1.26108
$630$		0			0
$631$	7326.82			0.462244			0.231122	−	0.972925i	$-0.425760\pi$
$631$	7326.82			0.462244			0.231122	+	0.972925i	$0.425760\pi$
$632$		0			0
$633$	−13908.2	+	15457.5i	−0.873301	+	0.970584i
$634$		0			0
$635$	523.995	+	907.586i	0.0327466	+	0.0567188i
$636$		0			0
$637$	−6138.62	−	2738.79i	−0.381822	−	0.170353i
$638$		0			0
$639$	−12227.2	+	1293.81i	−0.756963	+	0.0800975i
$640$		0			0
$641$	−2433.38	−	1404.91i	−0.149942	−	0.0865689i	0.423152	−	0.906059i	$-0.360924\pi$
$641$	−2433.38	−	1404.91i	−0.149942	−	0.0865689i	−0.573094	+	0.819490i	$0.694257\pi$
$642$		0			0
$643$		−	27485.5i		−	1.68573i	−0.538128	−	0.842863i	$-0.680868\pi$
$643$		−	27485.5i		−	1.68573i	0.538128	−	0.842863i	$-0.319132\pi$
$644$		0			0
$645$	−1005.73	−	213.405i	−0.0613962	−	0.0130276i
$646$		0			0
$647$	−14659.9	+	25391.7i	−0.890790	+	1.54289i	−0.0518595	+	0.998654i	$0.516515\pi$
$647$	−14659.9	+	25391.7i	−0.890790	+	1.54289i	−0.838930	+	0.544239i	$0.816819\pi$
$648$		0			0
$649$	22044.3	−	12727.3i	1.33330	−	0.769783i
$650$		0			0
$651$	−7480.44	−	6057.99i	−0.450356	−	0.364718i
$652$		0			0
$653$	−14500.6	+	8371.91i	−0.868992	+	0.501713i	−0.867013	−	0.498285i	$-0.833963\pi$
$653$	−14500.6	+	8371.91i	−0.868992	+	0.501713i	−0.00197863	+	0.999998i	$0.500630\pi$
$654$		0			0
$655$	−323.019	+	559.485i	−0.0192693	+	0.0333754i
$656$		0			0
$657$	−5500.69	+	12378.1i	−0.326640	+	0.735034i
$658$		0			0
$659$		−	9520.47i		−	0.562769i	−0.959595	−	0.281385i	$-0.909206\pi$
$659$		−	9520.47i		−	0.562769i	0.959595	−	0.281385i	$-0.0907937\pi$
$660$		0			0
$661$	−20217.5	−	11672.6i	−1.18966	−	0.686853i	−0.231434	−	0.972851i	$-0.574342\pi$
$661$	−20217.5	−	11672.6i	−1.18966	−	0.686853i	−0.958230	+	0.285998i	$0.907675\pi$
$662$		0			0
$663$	−10140.5	+	3298.77i	−0.594002	+	0.193233i
$664$		0			0
$665$	48.5515	+	933.331i	0.00283120	+	0.0544256i
$666$		0			0
$667$	8511.31	+	14742.0i	0.494092	+	0.855792i
$668$		0			0
$669$	−11744.7	−	10567.5i	−0.678740	−	0.610709i
$670$		0			0
$671$	−32869.9			−1.89110
$672$		0			0
$673$	−12283.5			−0.703559			−0.351780	−	0.936083i	$-0.614423\pi$
$673$	−12283.5			−0.703559			−0.351780	+	0.936083i	$0.614423\pi$
$674$		0			0
$675$	−15814.0	+	7060.82i	−0.901750	+	0.402624i
$676$		0			0
$677$	−6495.88	−	11251.2i	−0.368769	−	0.638727i	0.620604	−	0.784124i	$-0.286887\pi$
$677$	−6495.88	−	11251.2i	−0.368769	−	0.638727i	−0.989373	+	0.145397i	$0.953554\pi$
$678$		0			0
$679$	−22007.4	+	14279.6i	−1.24384	+	0.807072i
$680$		0			0
$681$	7067.05	+	21724.2i	0.397665	+	1.22243i
$682$		0			0
$683$	−7366.62	−	4253.12i	−0.412703	−	0.238274i	0.279248	−	0.960219i	$-0.409915\pi$
$683$	−7366.62	−	4253.12i	−0.412703	−	0.238274i	−0.691950	+	0.721945i	$0.743248\pi$
$684$		0			0
$685$			1369.74i			0.0764018i
$686$		0			0
$687$	−2139.38	+	10082.4i	−0.118810	+	0.559923i
$688$		0			0
$689$	4146.31	−	7181.62i	0.229263	−	0.397095i
$690$		0			0
$691$	22372.0	−	12916.5i	1.23165	−	0.711093i	0.264276	−	0.964447i	$-0.414867\pi$
$691$	22372.0	−	12916.5i	1.23165	−	0.711093i	0.967374	+	0.253354i	$0.0815336\pi$
$692$		0			0
$693$	20095.7	−	3189.34i	1.10155	−	0.174824i
$694$		0			0
$695$	894.770	−	516.595i	0.0488353	−	0.0281951i
$696$		0			0
$697$	9778.22	−	16936.4i	0.531387	−	0.920389i
$698$		0			0
$699$	−4717.33	+	22231.7i	−0.255259	+	1.20298i
$700$		0			0
$701$			22607.8i			1.21810i	0.793134	+	0.609048i	$0.208448\pi$
$701$			22607.8i			1.21810i	−0.793134	+	0.609048i	$0.791552\pi$
$702$		0			0
$703$	−6655.69	−	3842.67i	−0.357076	−	0.206158i
$704$		0			0
$705$	−717.975	−	2207.06i	−0.0383553	−	0.117905i
$706$		0			0
$707$	−4453.86	+	231.688i	−0.236923	+	0.0123246i
$708$		0			0
$709$	5472.41	+	9478.50i	0.289874	+	0.502077i	0.973779	−	0.227494i	$-0.0730532\pi$
$709$	5472.41	+	9478.50i	0.289874	+	0.502077i	−0.683905	+	0.729571i	$0.739720\pi$
$710$		0			0
$711$	−1351.69	+	983.509i	−0.0712971	+	0.0518769i
$712$		0			0
$713$	−8042.46			−0.422430
$714$		0			0
$715$	994.720			0.0520285
$716$		0			0
$717$	−14780.3	−	13298.9i	−0.769849	−	0.692685i
$718$		0			0
$719$	−12885.3	−	22317.9i	−0.668344	−	1.15761i	−0.978367	−	0.206877i	$-0.933670\pi$
$719$	−12885.3	−	22317.9i	−0.668344	−	1.15761i	0.310023	−	0.950729i	$-0.399663\pi$
$720$		0			0
$721$	−18297.3	−	9331.88i	−0.945116	−	0.482021i
$722$		0			0
$723$	16997.4	−	5529.40i	0.874330	−	0.284427i
$724$		0			0
$725$	−22633.2	−	13067.3i	−1.15942	−	0.669389i
$726$		0			0
$727$		−	15593.1i		−	0.795485i	−0.917497	−	0.397742i	$-0.869794\pi$
$727$		−	15593.1i		−	0.795485i	0.917497	−	0.397742i	$-0.130206\pi$
$728$		0			0
$729$	6121.81	+	18706.8i	0.311020	+	0.950403i
$730$		0			0
$731$	8305.13	−	14384.9i	0.420214	−	0.727832i
$732$		0			0
$733$	692.858	−	400.022i	0.0349131	−	0.0201571i	−0.482442	−	0.875928i	$-0.660250\pi$
$733$	692.858	−	400.022i	0.0349131	−	0.0201571i	0.517355	+	0.855771i	$0.326917\pi$
$734$		0			0
$735$	−1307.55	+	1798.08i	−0.0656185	+	0.0902358i
$736$		0			0
$737$	−10520.5	+	6073.99i	−0.525815	+	0.303580i
$738$		0			0
$739$	−454.445	+	787.122i	−0.0226211	+	0.0391810i	−0.877114	−	0.480282i	$-0.840534\pi$
$739$	−454.445	+	787.122i	−0.0226211	+	0.0391810i	0.854493	+	0.519463i	$0.173868\pi$
$740$		0			0
$741$	−4029.77	−	855.076i	−0.199781	−	0.0423914i
$742$		0			0
$743$		−	8109.00i		−	0.400391i	−0.979756	−	0.200195i	$-0.935842\pi$
$743$		−	8109.00i		−	0.400391i	0.979756	−	0.200195i	$-0.0641577\pi$
$744$		0			0
$745$	964.258	+	556.715i	0.0474197	+	0.0273778i
$746$		0			0
$747$	−207.737	−	1963.22i	−0.0101750	−	0.0961588i
$748$		0			0
$749$	17615.1	+	8983.95i	0.859337	+	0.438273i
$750$		0			0
$751$	−10382.2	−	17982.5i	−0.504463	−	0.873756i	−0.999987	−	0.00516122i	$-0.998357\pi$
$751$	−10382.2	−	17982.5i	−0.504463	−	0.873756i	0.495524	−	0.868594i	$-0.334976\pi$
$752$		0			0
$753$	7113.09	−	7905.46i	0.344243	−	0.382591i
$754$		0			0
$755$	1777.61			0.0856870
$756$		0			0
$757$	23295.6			1.11848			0.559242	−	0.829005i	$-0.311092\pi$
$757$	23295.6			1.11848			0.559242	+	0.829005i	$0.311092\pi$
$758$		0			0
$759$	11371.0	−	12637.7i	0.543796	−	0.604374i
$760$		0			0
$761$	5014.38	+	8685.16i	0.238858	+	0.413715i	0.960387	−	0.278670i	$-0.0898935\pi$
$761$	5014.38	+	8685.16i	0.238858	+	0.413715i	−0.721529	+	0.692385i	$0.756560\pi$
$762$		0			0
$763$	186.571	−	9.70535i	0.00885233	−	0.000460494i
$764$		0			0
$765$	371.128	+	3507.35i	0.0175401	+	0.165763i
$766$		0			0
$767$	−10616.9	−	6129.66i	−0.499809	−	0.288565i
$768$		0			0
$769$		−	13500.3i		−	0.633074i	−0.948580	−	0.316537i	$-0.897480\pi$
$769$		−	13500.3i		−	0.633074i	0.948580	−	0.316537i	$-0.102520\pi$
$770$		0			0
$771$	−30757.8	−	6526.49i	−1.43673	−	0.304858i
$772$		0			0
$773$	11644.9	−	20169.5i	0.541833	−	0.938482i	−0.456966	−	0.889484i	$-0.651064\pi$
$773$	11644.9	−	20169.5i	0.541833	−	0.938482i	0.998799	−	0.0489979i	$-0.0156028\pi$
$774$		0			0
$775$	10693.2	−	6173.74i	0.495629	−	0.286151i
$776$		0			0
$777$	−6551.10	−	17068.0i	−0.302470	−	0.788046i
$778$		0			0
$779$	6542.79	−	3777.48i	0.300924	−	0.173739i
$780$		0			0
$781$	−9264.99	+	16047.4i	−0.424491	+	0.735240i
$782$		0			0
$783$	−17433.3	+	24048.1i	−0.795677	+	1.09759i
$784$		0			0
$785$		−	352.711i		−	0.0160367i
$786$		0			0
$787$	20635.4	+	11913.8i	0.934653	+	0.539622i	0.888280	−	0.459302i	$-0.151901\pi$
$787$	20635.4	+	11913.8i	0.934653	+	0.539622i	0.0463726	+	0.998924i	$0.485234\pi$
$788$		0			0
$789$	−31002.9	+	10085.5i	−1.39890	+	0.455074i
$790$		0			0
$791$	−13738.7	+	8914.42i	−0.617560	+	0.400709i
$792$		0			0
$793$	7915.34	+	13709.8i	0.354454	+	0.613932i
$794$		0			0
$795$	−2038.91	−	1834.55i	−0.0909594	−	0.0818424i
$796$		0			0
$797$	−12609.3			−0.560406			−0.280203	−	0.959941i	$-0.590402\pi$
$797$	−12609.3			−0.560406			−0.280203	+	0.959941i	$0.590402\pi$
$798$		0			0
$799$	37496.4			1.66023
$800$		0			0
$801$	2505.14	−	1822.78i	0.110505	−	0.0804054i
$802$		0			0
$803$	10206.8	+	17678.8i	0.448557	+	0.776924i
$804$		0			0
$805$	96.4977	+	1855.03i	0.00422497	+	0.0812188i
$806$		0			0
$807$	5362.97	+	16485.8i	0.233935	+	0.719118i
$808$		0			0
$809$	30281.4	+	17483.0i	1.31599	+	0.759789i	0.983082	−	0.183169i	$-0.0586354\pi$
$809$	30281.4	+	17483.0i	1.31599	+	0.759789i	0.332912	+	0.942958i	$0.391969\pi$
$810$		0			0
$811$		−	5691.42i		−	0.246428i	−0.992380	−	0.123214i	$-0.960680\pi$
$811$		−	5691.42i		−	0.246428i	0.992380	−	0.123214i	$-0.0393201\pi$
$812$		0			0
$813$	−3066.52	+	14451.8i	−0.132285	+	0.623428i
$814$		0			0
$815$	−1444.59	+	2502.10i	−0.0620879	+	0.107539i
$816$		0			0
$817$	5557.12	−	3208.40i	0.237967	−	0.137390i
$818$		0			0
$819$	−6169.47	−	7613.75i	−0.263222	−	0.324842i
$820$		0			0
$821$	10487.0	−	6054.70i	0.445798	−	0.257382i	−0.260256	−	0.965540i	$-0.583807\pi$
$821$	10487.0	−	6054.70i	0.445798	−	0.257382i	0.706054	+	0.708158i	$0.250474\pi$
$822$		0			0
$823$	−15861.0	+	27472.0i	−0.671784	+	1.16356i	0.305614	+	0.952155i	$0.401138\pi$
$823$	−15861.0	+	27472.0i	−0.671784	+	1.16356i	−0.977398	+	0.211408i	$0.932195\pi$
$824$		0			0
$825$	−5417.61	+	25531.9i	−0.228627	+	1.07746i
$826$		0			0
$827$			36401.9i			1.53061i	0.643666	+	0.765307i	$0.277413\pi$
$827$			36401.9i			1.53061i	−0.643666	+	0.765307i	$0.722587\pi$
$828$		0			0
$829$	27287.8	+	15754.6i	1.14324	+	0.660049i	0.947230	−	0.320554i	$-0.103869\pi$
$829$	27287.8	+	15754.6i	1.14324	+	0.660049i	0.196007	+	0.980602i	$0.437202\pi$
$830$		0			0
$831$	10204.5	+	31368.9i	0.425983	+	1.30948i
$832$		0			0
$833$	−21089.8	−	29075.0i	−0.877214	−	1.20935i
$834$		0			0
$835$	1462.40	+	2532.96i	0.0606090	+	0.104978i
$836$		0			0
$837$	−5721.28	−	12813.9i	−0.236268	−	0.529166i
$838$		0			0
$839$	13781.4			0.567090			0.283545	−	0.958959i	$-0.408490\pi$
$839$	13781.4			0.567090			0.283545	+	0.958959i	$0.408490\pi$
$840$		0			0
$841$	−20433.0			−0.837796
$842$		0			0
$843$	−14430.6	−	12984.2i	−0.589582	−	0.530487i
$844$		0			0
$845$	1130.74	+	1958.51i	0.0460341	+	0.0797334i
$846$		0			0
$847$	2732.43	−	5357.56i	0.110847	−	0.217341i
$848$		0			0
$849$	27261.6	−	8868.40i	1.10202	−	0.358496i
$850$		0			0
$851$	−13228.4	−	7637.43i	−0.532860	−	0.307647i
$852$		0			0
$853$		−	11376.3i		−	0.456645i	−0.973586	−	0.228322i	$-0.926676\pi$
$853$		−	11376.3i		−	0.456645i	0.973586	−	0.228322i	$-0.0733240\pi$
$854$		0			0
$855$	−553.308	+	1245.10i	−0.0221318	+	0.0498030i
$856$		0			0
$857$	−21559.6	+	37342.3i	−0.859349	+	1.48844i	0.0132022	+	0.999913i	$0.495797\pi$
$857$	−21559.6	+	37342.3i	−0.859349	+	1.48844i	−0.872551	+	0.488523i	$0.837536\pi$
$858$		0			0
$859$	−32325.9	+	18663.4i	−1.28399	+	0.741311i	−0.977575	−	0.210588i	$-0.932462\pi$
$859$	−32325.9	+	18663.4i	−1.28399	+	0.741311i	−0.306413	+	0.951899i	$0.599129\pi$
$860$		0			0
$861$	17750.6	+	2812.07i	0.702600	+	0.111307i
$862$		0			0
$863$	30262.7	−	17472.2i	1.19369	−	0.689176i	0.234547	−	0.972105i	$-0.424639\pi$
$863$	30262.7	−	17472.2i	1.19369	−	0.689176i	0.959141	+	0.282929i	$0.0913060\pi$
$864$		0			0
$865$	−644.788	+	1116.80i	−0.0253450	+	0.0438988i
$866$		0			0
$867$	−30767.1	−	6528.45i	−1.20520	−	0.255730i
$868$		0			0
$869$			2519.25i			0.0983426i
$870$		0			0
$871$	5066.82	+	2925.33i	0.197110	+	0.113801i
$872$		0			0
$873$	−38033.5	+	4024.49i	−1.47450	+	0.156023i
$874$		0			0
$875$	−3124.17	−	4814.88i	−0.120704	−	0.186026i
$876$		0			0
$877$	−2054.59	−	3558.66i	−0.0791092	−	0.137021i	0.823757	−	0.566944i	$-0.191874\pi$
$877$	−2054.59	−	3558.66i	−0.0791092	−	0.137021i	−0.902866	+	0.429922i	$0.858541\pi$
$878$		0			0
$879$	26325.5	−	29258.1i	1.01017	−	1.12270i
$880$		0			0
$881$	15697.6			0.600301			0.300151	−	0.953892i	$-0.402963\pi$
$881$	15697.6			0.600301			0.300151	+	0.953892i	$0.402963\pi$
$882$		0			0
$883$	44102.6			1.68083			0.840413	−	0.541946i	$-0.182312\pi$
$883$	44102.6			1.68083			0.840413	+	0.541946i	$0.182312\pi$
$884$		0			0
$885$	−2712.09	+	3014.20i	−0.103012	+	0.114487i
$886$		0			0
$887$	14164.5	+	24533.5i	0.536185	+	0.928699i	0.999105	+	0.0422991i	$0.0134682\pi$
$887$	14164.5	+	24533.5i	0.536185	+	0.928699i	−0.462920	+	0.886400i	$0.653198\pi$
$888$		0			0
$889$	−8469.24	−	13052.5i	−0.319515	−	0.492428i
$890$		0			0
$891$	28224.5	+	9126.89i	1.06123	+	0.343168i
$892$		0			0
$893$	12544.8	+	7242.73i	0.470095	+	0.271409i
$894$		0			0
$895$			180.728i			0.00674979i
$896$		0			0
$897$	−8009.31	−	1699.49i	−0.298131	−	0.0632602i
$898$		0			0
$899$	10588.3	−	18339.4i	0.392812	−	0.680370i
$900$		0			0
$901$	38375.1	−	22155.9i	1.41894	−	0.819223i
$902$		0			0
$903$	15076.5	+	2388.43i	0.555607	+	0.0880201i
$904$		0			0
$905$	2222.34	−	1283.07i	0.0816277	−	0.0471278i
$906$		0			0
$907$	7102.79	−	12302.4i	0.260027	−	0.450380i	−0.706222	−	0.707991i	$-0.749602\pi$
$907$	7102.79	−	12302.4i	0.260027	−	0.450380i	0.966249	+	0.257611i	$0.0829353\pi$
$908$		0			0
$909$	−5941.64	−	2640.39i	−0.216800	−	0.0963434i
$910$		0			0
$911$			17955.9i			0.653025i	0.945193	+	0.326512i	$0.105873\pi$
$911$			17955.9i			0.653025i	−0.945193	+	0.326512i	$0.894127\pi$
$912$		0			0
$913$	−2576.62	−	1487.61i	−0.0933993	−	0.0539241i
$914$		0			0
$915$	4979.11	−	1619.74i	0.179895	−	0.0585214i
$916$		0			0
$917$	4357.84	−	8544.57i	0.156934	−	0.307706i
$918$		0			0
$919$	−21121.3	−	36583.1i	−0.758135	−	1.31313i	−0.943800	−	0.330516i	$-0.892777\pi$
$919$	−21121.3	−	36583.1i	−0.758135	−	1.31313i	0.185665	−	0.982613i	$-0.440556\pi$
$920$		0			0
$921$	41082.5	+	36964.7i	1.46983	+	1.32251i
$922$		0			0
$923$	8924.34			0.318254
$924$		0			0
$925$	23451.3			0.833593
$926$		0			0
$927$	−17617.6	−	24212.8i	−0.624206	−	0.857878i
$928$		0			0
$929$	−22338.1	−	38690.6i	−0.788900	−	1.36641i	−0.926642	−	0.375946i	$-0.877318\pi$
$929$	−22338.1	−	38690.6i	−0.788900	−	1.36641i	0.137742	−	0.990468i	$-0.456016\pi$
$930$		0			0
$931$	−1439.74	−	13801.0i	−0.0506826	−	0.485831i
$932$		0			0
$933$	−9276.80	−	28517.0i	−0.325519	−	1.00065i
$934$		0			0
$935$	4603.19	+	2657.65i	0.161006	+	0.0929566i
$936$		0			0
$937$		−	15309.3i		−	0.533761i	−0.963730	−	0.266880i	$-0.914007\pi$
$937$		−	15309.3i		−	0.533761i	0.963730	−	0.266880i	$-0.0859929\pi$
$938$		0			0
$939$	−2528.70	+	11917.2i	−0.0878817	+	0.414166i
$940$		0			0
$941$	21192.2	−	36706.0i	0.734162	−	1.27161i	−0.220928	−	0.975290i	$-0.570909\pi$
$941$	21192.2	−	36706.0i	0.734162	−	1.27161i	0.955090	−	0.296316i	$-0.0957582\pi$
$942$		0			0
$943$	13004.0	−	7507.87i	0.449066	−	0.259268i
$944$		0			0
$945$	−2886.93	+	1473.39i	−0.0993775	+	0.0507188i
$946$		0			0
$947$	−10648.1	+	6147.69i	−0.365383	+	0.210954i	−0.671439	−	0.741060i	$-0.734324\pi$
$947$	−10648.1	+	6147.69i	−0.365383	+	0.210954i	0.306057	+	0.952013i	$0.400990\pi$
$948$		0			0
$949$	4915.78	−	8514.37i	0.168148	−	0.291242i
$950$		0			0
$951$	−8533.67	+	40217.2i	−0.290981	+	1.37133i
$952$		0			0
$953$			1322.78i			0.0449621i	0.999747	+	0.0224811i	$0.00715655\pi$
$953$			1322.78i			0.0449621i	−0.999747	+	0.0224811i	$0.992843\pi$
$954$		0			0
$955$	3185.47	+	1839.13i	0.107936	+	0.0623171i
$956$		0			0
$957$	13847.6	+	42567.6i	0.467742	+	1.43784i
$958$		0			0
$959$	−1056.47	−	20309.1i	−0.0355737	−	0.683852i
$960$		0			0
$961$	−9893.00	−	17135.2i	−0.332080	−	0.575180i
$962$		0			0
$963$	16960.8	+	23310.1i	0.567553	+	0.780017i
$964$		0			0
$965$	2832.62			0.0944925
$966$		0			0
$967$	−36887.2			−1.22669			−0.613346	−	0.789814i	$-0.710177\pi$
$967$	−36887.2			−1.22669			−0.613346	+	0.789814i	$0.710177\pi$
$968$		0			0
$969$	−16363.7	−	14723.5i	−0.542495	−	0.488120i
$970$		0			0
$971$	−3409.79	−	5905.93i	−0.112693	−	0.195191i	0.804162	−	0.594410i	$-0.202614\pi$
$971$	−3409.79	−	5905.93i	−0.112693	−	0.195191i	−0.916855	+	0.399220i	$0.869281\pi$
$972$		0			0
$973$	−12868.2	+	8349.64i	−0.423984	+	0.275105i
$974$		0			0
$975$	11953.8	−	3888.65i	0.392643	−	0.127730i
$976$		0			0
$977$	42700.8	+	24653.3i	1.39828	+	0.807298i	0.994213	−	0.107431i	$-0.0342624\pi$
$977$	42700.8	+	24653.3i	1.39828	+	0.807298i	0.404068	+	0.914729i	$0.367596\pi$
$978$		0			0
$979$		−	4669.03i		−	0.152424i
$980$		0			0
$981$	248.894	+	110.605i	0.00810047	+	0.00359975i
$982$		0			0
$983$	9765.55	−	16914.4i	0.316859	−	0.548816i	−0.662972	−	0.748644i	$-0.730705\pi$
$983$	9765.55	−	16914.4i	0.316859	−	0.548816i	0.979831	+	0.199828i	$0.0640384\pi$
$984$		0			0
$985$	535.661	−	309.264i	0.0173275	−	0.0100040i
$986$		0			0
$987$	12347.6	+	32170.1i	0.398206	+	1.03747i
$988$		0			0
$989$	11045.0	−	6376.81i	0.355116	−	0.205026i
$990$		0			0
$991$	9285.39	−	16082.8i	0.297639	−	0.515526i	−0.677956	−	0.735102i	$-0.737134\pi$
$991$	9285.39	−	16082.8i	0.297639	−	0.515526i	0.975595	+	0.219576i	$0.0704675\pi$
$992$		0			0
$993$	−24805.1	−	5263.39i	−0.792716	−	0.168206i
$994$		0			0
$995$		−	1047.46i		−	0.0333735i
$996$		0			0
$997$	19389.3	+	11194.4i	0.615913	+	0.355598i	0.775276	−	0.631622i	$-0.217611\pi$
$997$	19389.3	+	11194.4i	0.615913	+	0.355598i	−0.159363	+	0.987220i	$0.550944\pi$
$998$		0			0
$999$	2758.05	−	26509.7i	0.0873481	−	0.839569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bc.d.17.5		12
3.2	odd	2	inner	336.4.bc.d.17.3		12
4.3	odd	2		21.4.g.a.17.3	yes	12
7.5	odd	6	inner	336.4.bc.d.257.3		12
12.11	even	2		21.4.g.a.17.4	yes	12
21.5	even	6	inner	336.4.bc.d.257.5		12
28.3	even	6		147.4.c.a.146.5		12
28.11	odd	6		147.4.c.a.146.6		12
28.19	even	6		21.4.g.a.5.4	yes	12
28.23	odd	6		147.4.g.d.68.4		12
28.27	even	2		147.4.g.d.80.3		12
84.11	even	6		147.4.c.a.146.7		12
84.23	even	6		147.4.g.d.68.3		12
84.47	odd	6		21.4.g.a.5.3	✓	12
84.59	odd	6		147.4.c.a.146.8		12
84.83	odd	2		147.4.g.d.80.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.g.a.5.3	✓	12	84.47	odd	6
21.4.g.a.5.4	yes	12	28.19	even	6
21.4.g.a.17.3	yes	12	4.3	odd	2
21.4.g.a.17.4	yes	12	12.11	even	2
147.4.c.a.146.5		12	28.3	even	6
147.4.c.a.146.6		12	28.11	odd	6
147.4.c.a.146.7		12	84.11	even	6
147.4.c.a.146.8		12	84.59	odd	6
147.4.g.d.68.3		12	84.23	even	6
147.4.g.d.68.4		12	28.23	odd	6
147.4.g.d.80.3		12	28.27	even	2
147.4.g.d.80.4		12	84.83	odd	2
336.4.bc.d.17.3		12	3.2	odd	2	inner
336.4.bc.d.17.5		12	1.1	even	1	trivial
336.4.bc.d.257.3		12	7.5	odd	6	inner
336.4.bc.d.257.5		12	21.5	even	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.bc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.47555 - 3.86271i) q^{3} +(0.623706 + 1.08029i) q^{5} +(-10.0808 - 15.5363i) q^{7} +(-2.84113 - 26.8501i) q^{9} +O(q^{10})\)	\(q+(3.47555 - 3.86271i) q^{3} +(0.623706 + 1.08029i) q^{5} +(-10.0808 - 15.5363i) q^{7} +(-2.84113 - 26.8501i) q^{9} +(-35.2392 - 20.3453i) q^{11} +19.5973i q^{13} +(6.34057 + 1.34540i) q^{15} +(-52.3592 + 90.6889i) q^{17} +(-35.0345 + 20.2272i) q^{19} +(-95.0487 - 15.0578i) q^{21} +(-69.6324 + 40.2023i) q^{23} +(61.7220 - 106.906i) q^{25} +(-113.589 - 82.3444i) q^{27} -211.712i q^{29} +(86.6242 + 50.0125i) q^{31} +(-201.064 + 65.4076i) q^{33} +(10.4962 - 20.5803i) q^{35} +(94.9875 + 164.523i) q^{37} +(75.6987 + 68.1113i) q^{39} -186.753 q^{41} -158.618 q^{43} +(27.2339 - 19.8158i) q^{45} +(-179.034 - 310.097i) q^{47} +(-139.753 + 313.238i) q^{49} +(168.328 + 517.442i) q^{51} +(-366.460 - 211.576i) q^{53} -50.7580i q^{55} +(-43.6323 + 205.629i) q^{57} +(-312.781 + 541.753i) q^{59} +(699.575 - 403.900i) q^{61} +(-388.510 + 314.812i) q^{63} +(-21.1708 + 12.2229i) q^{65} +(149.272 - 258.547i) q^{67} +(-86.7208 + 408.695i) q^{69} -455.386i q^{71} +(-434.467 - 250.840i) q^{73} +(-198.428 - 609.970i) q^{75} +(39.1491 + 752.584i) q^{77} +(-30.9561 - 53.6176i) q^{79} +(-712.856 + 152.569i) q^{81} +73.1180 q^{83} -130.627 q^{85} +(-817.783 - 735.816i) q^{87} +(57.3723 + 99.3717i) q^{89} +(304.469 - 197.557i) q^{91} +(494.251 - 160.784i) q^{93} +(-43.7025 - 25.2316i) q^{95} -1416.51i q^{97} +(-446.156 + 1003.98i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 + 56 * q^7 - 3 * q^9	\( 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9} - 6 q^{15} - 300 q^{19} + 357 q^{21} - 42 q^{25} + 930 q^{31} - 855 q^{33} + 764 q^{37} + 426 q^{39} + 1012 q^{43} + 2367 q^{45} - 336 q^{49} + 1341 q^{51} + 270 q^{57} + 2358 q^{61} - 1071 q^{63} - 792 q^{67} - 2904 q^{73} + 2418 q^{75} - 1674 q^{79} + 837 q^{81} + 348 q^{85} - 1638 q^{87} + 1218 q^{91} - 1479 q^{93} + 3354 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 + 56 * q^7 - 3 * q^9 - 6 * q^15 - 300 * q^19 + 357 * q^21 - 42 * q^25 + 930 * q^31 - 855 * q^33 + 764 * q^37 + 426 * q^39 + 1012 * q^43 + 2367 * q^45 - 336 * q^49 + 1341 * q^51 + 270 * q^57 + 2358 * q^61 - 1071 * q^63 - 792 * q^67 - 2904 * q^73 + 2418 * q^75 - 1674 * q^79 + 837 * q^81 + 348 * q^85 - 1638 * q^87 + 1218 * q^91 - 1479 * q^93 + 3354 * q^99

Introduction

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