LMFDB - Embedded newform 336.4.bc.d.17.3

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			17.3
Root			$-2.23014 - 2.00661i$ of defining polynomial
Character	$\chi$	$=$	336.17
Dual form			336.4.bc.d.257.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.60743 + 4.94127i) q^{3} +(-0.623706 - 1.08029i) q^{5} +(-10.0808 - 15.5363i) q^{7} +(-21.8323 - 15.8855i) q^{9} +(35.2392 + 20.3453i) q^{11} +19.5973i q^{13} +(6.34057 - 1.34540i) q^{15} +(52.3592 - 90.6889i) q^{17} +(-35.0345 + 20.2272i) q^{19} +(92.9734 - 24.8386i) q^{21} +(69.6324 - 40.2023i) q^{23} +(61.7220 - 106.906i) q^{25} +(113.589 - 82.3444i) q^{27} +211.712i q^{29} +(86.6242 + 50.0125i) q^{31} +(-157.176 + 141.422i) q^{33} +(-10.4962 + 20.5803i) q^{35} +(94.9875 + 164.523i) q^{37} +(-96.8355 - 31.5014i) q^{39} +186.753 q^{41} -158.618 q^{43} +(-3.54405 + 33.4931i) q^{45} +(179.034 + 310.097i) q^{47} +(-139.753 + 313.238i) q^{49} +(363.954 + 404.498i) q^{51} +(366.460 + 211.576i) q^{53} -50.7580i q^{55} +(-43.6323 - 205.629i) q^{57} +(312.781 - 541.753i) q^{59} +(699.575 - 403.900i) q^{61} +(-26.7144 + 499.333i) q^{63} +(21.1708 - 12.2229i) q^{65} +(149.272 - 258.547i) q^{67} +(86.7208 + 408.695i) q^{69} +455.386i q^{71} +(-434.467 - 250.840i) q^{73} +(429.035 + 476.829i) q^{75} +(-39.1491 - 752.584i) q^{77} +(-30.9561 - 53.6176i) q^{79} +(224.299 + 693.636i) q^{81} -73.1180 q^{83} -130.627 q^{85} +(-1046.13 - 340.313i) q^{87} +(-57.3723 - 99.3717i) q^{89} +(304.469 - 197.557i) q^{91} +(-386.368 + 347.642i) q^{93} +(43.7025 + 25.2316i) q^{95} -1416.51i q^{97} +(-446.156 - 1003.98i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9} - 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}+ \cdots + 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

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
$3$	−1.60743	+	4.94127i	−0.309351	+	0.950948i
$3$	−1.60743	+	4.94127i	−0.309351	+	0.950948i
$4$		0			0
$5$	−0.623706	−	1.08029i	−0.0557859	−	0.0966240i	0.836784	−	0.547533i	$-0.184433\pi$
$5$	−0.623706	−	1.08029i	−0.0557859	−	0.0966240i	−0.892570	+	0.450909i	$0.851100\pi$
$6$		0			0
$7$	−10.0808	−	15.5363i	−0.544314	−	0.838881i
$7$	−10.0808	−	15.5363i	−0.544314	−	0.838881i
$8$		0			0
$9$	−21.8323	−	15.8855i	−0.808604	−	0.588353i
$10$		0			0
$11$	35.2392	+	20.3453i	0.965910	+	0.557668i	0.897987	−	0.440022i	$-0.145029\pi$
$11$	35.2392	+	20.3453i	0.965910	+	0.557668i	0.0679230	+	0.997691i	$0.478363\pi$
$12$		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	$-0.564827\pi$
$17$	52.3592	−	90.6889i	0.746999	−	1.29384i	0.949255	−	0.314507i	$-0.101839\pi$
$18$		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
$21$	92.9734	−	24.8386i	0.966117	−	0.258106i
$22$		0			0
$23$	69.6324	−	40.2023i	0.631276	−	0.364467i	−0.149970	−	0.988691i	$-0.547918\pi$
$23$	69.6324	−	40.2023i	0.631276	−	0.364467i	0.781246	+	0.624223i	$0.214584\pi$
$24$		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	$0.237078\pi$
$29$			211.712i			1.35565i	−0.735222	+	0.677827i	$0.762922\pi$
$30$		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
$33$	−157.176	+	141.422i	−0.829119	+	0.746015i
$34$		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
$39$	−96.8355	−	31.5014i	−0.397592	−	0.129340i
$40$		0			0
$41$	186.753			0.711362			0.355681	−	0.934607i	$-0.384249\pi$
$41$	186.753			0.711362			0.355681	+	0.934607i	$0.384249\pi$
$42$		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
$45$	−3.54405	+	33.4931i	−0.0117404	+	0.110952i
$46$		0			0
$47$	179.034	+	310.097i	0.555635	+	0.962388i	0.997854	+	0.0654808i	$0.0208581\pi$
$47$	179.034	+	310.097i	0.555635	+	0.962388i	−0.442219	+	0.896907i	$0.645809\pi$
$48$		0			0
$49$	−139.753	+	313.238i	−0.407444	+	0.913230i
$50$		0			0
$51$	363.954	+	404.498i	0.999290	+	1.11061i
$52$		0			0
$53$	366.460	+	211.576i	0.949758	+	0.548343i	0.893006	−	0.450045i	$-0.148592\pi$
$53$	366.460	+	211.576i	0.949758	+	0.548343i	0.0567521	+	0.998388i	$0.481926\pi$
$54$		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	$-0.590865\pi$
$59$	312.781	−	541.753i	0.690180	−	1.19543i	0.971779	−	0.235895i	$-0.0758020\pi$
$60$		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
$63$	−26.7144	+	499.333i	−0.0534239	+	0.998572i
$64$		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	$0.124281\pi$
$71$			455.386i			0.761189i	−0.924742	+	0.380594i	$0.875719\pi$
$72$		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
$75$	429.035	+	476.829i	0.660543	+	0.734126i
$76$		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
$81$	224.299	+	693.636i	0.307681	+	0.951490i
$82$		0			0
$83$	−73.1180			−0.0966957			−0.0483478	−	0.998831i	$-0.515396\pi$
$83$	−73.1180			−0.0966957			−0.0483478	+	0.998831i	$0.515396\pi$
$84$		0			0
$85$	−130.627			−0.166688
$86$		0			0
$87$	−1046.13	−	340.313i	−1.28916	−	0.419373i
$88$		0			0
$89$	−57.3723	−	99.3717i	−0.0683309	−	0.118353i	0.829836	−	0.558008i	$-0.188434\pi$
$89$	−57.3723	−	99.3717i	−0.0683309	−	0.118353i	−0.898167	+	0.439655i	$0.855101\pi$
$90$		0			0
$91$	304.469	−	197.557i	0.350737	−	0.227578i
$92$		0			0
$93$	−386.368	+	347.642i	−0.430801	+	0.387621i
$94$		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	−0.919222	−	0.393740i	$-0.871181\pi$
$101$	−120.406	+	208.549i	−0.118622	+	0.205459i	0.800600	+	0.599199i	$0.204514\pi$
$102$		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
$105$	−84.8209	−	84.9462i	−0.0788349	−	0.0789514i
$106$		0			0
$107$	924.644	−	533.843i	0.835408	−	0.482323i	−0.0202926	−	0.999794i	$-0.506460\pi$
$107$	924.644	−	533.843i	0.835408	−	0.482323i	0.855701	+	0.517471i	$0.173126\pi$
$108$		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	$0.119987\pi$
$113$			884.294i			0.736171i	−0.929792	+	0.368086i	$0.880013\pi$
$114$		0			0
$115$	−86.8602	−	50.1487i	−0.0704326	−	0.0406643i
$116$		0			0
$117$	311.314	−	427.854i	0.245991	−	0.338078i
$118$		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
$123$	−300.192	+	922.795i	−0.220061	+	0.676468i
$124$		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
$129$	254.968	−	783.776i	0.174021	−	0.534943i
$130$		0			0
$131$	−258.951	−	448.517i	−0.172707	−	0.299138i	0.766658	−	0.642056i	$-0.221918\pi$
$131$	−258.951	−	448.517i	−0.172707	−	0.299138i	−0.939366	+	0.342918i	$0.888585\pi$
$132$		0			0
$133$	667.434	+	340.400i	0.435142	+	0.221928i
$134$		0			0
$135$	−159.802	−	71.3501i	−0.101878	−	0.0454877i
$136$		0			0
$137$	−950.957	−	549.035i	−0.593034	−	0.342389i	0.173262	−	0.984876i	$-0.444569\pi$
$137$	−950.957	−	549.035i	−0.593034	−	0.342389i	−0.766296	+	0.642487i	$0.777903\pi$
$138$		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
$147$	−1323.15	−	1194.07i	−0.742391	−	0.669967i
$148$		0			0
$149$	−773.007	+	446.296i	−0.425015	+	0.245382i	−0.697221	−	0.716857i	$-0.745580\pi$
$149$	−773.007	+	446.296i	−0.425015	+	0.245382i	0.272206	+	0.962239i	$0.412247\pi$
$150$		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
$159$	−1634.51	+	1470.68i	−0.815254	+	0.733540i
$160$		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
$165$	250.809	+	81.5902i	0.118336	+	0.0384957i
$166$		0			0
$167$	−2344.70			−1.08646			−0.543229	−	0.839585i	$-0.682798\pi$
$167$	−2344.70			−1.08646			−0.543229	+	0.839585i	$0.682798\pi$
$168$		0			0
$169$	1812.95			0.825192
$170$		0			0
$171$	1086.21	+	114.936i	0.485755	+	0.0513999i
$172$		0			0
$173$	−516.901	−	895.298i	−0.227163	−	0.393458i	0.729803	−	0.683657i	$-0.239612\pi$
$173$	−516.901	−	895.298i	−0.227163	−	0.393458i	−0.956966	+	0.290199i	$0.906278\pi$
$174$		0			0
$175$	−2283.13	+	118.767i	−0.986218	+	0.0513026i
$176$		0			0
$177$	2174.17	+	2416.37i	0.923281	+	1.02613i
$178$		0			0
$179$	−125.472	−	72.4412i	−0.0523922	−	0.0302486i	0.473575	−	0.880753i	$-0.342963\pi$
$179$	−125.472	−	72.4412i	−0.0523922	−	0.0302486i	−0.525967	+	0.850505i	$0.676297\pi$
$180$		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
$189$	−2424.40	−	934.648i	−0.933063	−	0.359712i
$190$		0			0
$191$	−2553.66	+	1474.36i	−0.967417	+	0.558538i	−0.898448	−	0.439080i	$-0.855304\pi$
$191$	−2553.66	+	1474.36i	−0.967417	+	0.558538i	−0.0689690	+	0.997619i	$0.521971\pi$
$192$		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	$0.0285795\pi$
$197$			495.849i			0.179329i	−0.995972	+	0.0896645i	$0.971421\pi$
$198$		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
$201$	1037.61	+	1153.19i	0.364115	+	0.404676i
$202$		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
$207$	−2158.87	−	228.439i	−0.724888	−	0.0767035i
$208$		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
$213$	−2250.19	−	732.004i	−0.723851	−	0.235474i
$214$		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
$219$	1937.84	−	1743.61i	0.597933	−	0.538001i
$220$		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	$-0.611131\pi$
$227$	2198.24	−	3807.46i	0.642741	−	1.11326i	0.984818	−	0.173588i	$-0.0555360\pi$
$228$		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
$231$	3781.65	+	1016.28i	1.07712	+	0.289466i
$232$		0			0
$233$	3787.78	−	2186.87i	1.06500	−	0.614879i	0.138191	−	0.990406i	$-0.455871\pi$
$233$	3787.78	−	2186.87i	1.06500	−	0.614879i	0.926812	+	0.375526i	$0.122538\pi$
$234$		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	$0.173250\pi$
$239$			3826.41i			1.03561i	−0.855500	+	0.517803i	$0.826750\pi$
$240$		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
$243$	−3787.99	−	6.65062i	−0.999998	−	0.00175571i
$244$		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
$249$	117.532	−	361.296i	0.0299129	−	0.0919525i
$250$		0			0
$251$	−2046.61			−0.514664			−0.257332	−	0.966323i	$-0.582843\pi$
$251$	−2046.61			−0.514664			−0.257332	+	0.966323i	$0.582843\pi$
$252$		0			0
$253$	3271.72			0.813008
$254$		0			0
$255$	209.974	−	645.463i	0.0515651	−	0.158512i
$256$		0			0
$257$	3025.57	+	5240.44i	0.734357	+	1.27194i	0.955005	+	0.296590i	$0.0958496\pi$
$257$	3025.57	+	5240.44i	0.734357	+	1.27194i	−0.220648	+	0.975354i	$0.570817\pi$
$258$		0			0
$259$	1598.53	−	3134.29i	0.383505	−	0.751950i
$260$		0			0
$261$	3363.16	−	4622.16i	0.797603	−	1.09619i
$262$		0			0
$263$	5433.69	+	3137.14i	1.27398	+	0.735530i	0.975734	−	0.218960i	$-0.0702665\pi$
$263$	5433.69	+	3137.14i	1.27398	+	0.735530i	0.298242	+	0.954490i	$0.403600\pi$
$264$		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	−0.612681	−	0.790331i	$-0.709909\pi$
$269$	1668.18	−	2889.37i	0.378106	−	0.654899i	0.990787	+	0.135432i	$0.0432421\pi$
$270$		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
$273$	486.769	+	1822.03i	0.107914	+	0.403934i
$274$		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	$0.129794\pi$
$281$			3735.88i			0.793110i	−0.918011	+	0.396555i	$0.870206\pi$
$282$		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
$285$	−194.925	+	175.388i	−0.0405136	+	0.0364529i
$286$		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
$291$	6999.37	+	2276.95i	1.41000	+	0.458685i
$292$		0			0
$293$	−7574.50			−1.51026			−0.755131	−	0.655574i	$-0.772427\pi$
$293$	−7574.50			−1.51026			−0.755131	+	0.655574i	$0.772427\pi$
$294$		0			0
$295$	−780.333			−0.154009
$296$		0			0
$297$	5678.10	−	590.745i	1.10935	−	0.115416i
$298$		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
$303$	−836.951	−	930.184i	−0.158685	−	0.176362i
$304$		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	$0.343025\pi$
$311$	−2885.59	+	4997.99i	−0.526132	+	0.911287i	−0.999537	+	0.0304419i	$0.990309\pi$
$312$		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
$315$	556.086	−	282.577i	0.0994664	−	0.0505442i
$316$		0			0
$317$	6852.10	−	3956.06i	1.21405	−	0.700929i	0.250407	−	0.968141i	$-0.419435\pi$
$317$	6852.10	−	3956.06i	1.21405	−	0.700929i	0.963638	+	0.267211i	$0.0861021\pi$
$318$		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
$327$	−35.0596	−	38.9652i	−0.00592906	−	0.00658954i
$328$		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
$333$	539.743	−	5100.85i	0.0888220	−	0.839414i
$334$		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
$339$	−4369.53	−	1421.44i	−0.700061	−	0.227735i
$340$		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
$345$	387.421	−	348.589i	0.0604580	−	0.0543982i
$346$		0			0
$347$	2009.83	+	1160.38i	0.310933	+	0.179517i	0.647344	−	0.762198i	$-0.275880\pi$
$347$	2009.83	+	1160.38i	0.310933	+	0.179517i	−0.336411	+	0.941715i	$0.609213\pi$
$348$		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	−0.916579	−	0.399854i	$-0.869061\pi$
$353$	−742.854	+	1286.66i	−0.112006	+	0.194000i	0.804573	+	0.593854i	$0.202394\pi$
$354$		0			0
$355$	491.949	−	284.027i	0.0735491	−	0.0424636i
$356$		0			0
$357$	2615.43	−	9732.18i	0.387740	−	1.44280i
$358$		0			0
$359$	9419.94	−	5438.60i	1.38486	−	0.799550i	0.392131	−	0.919909i	$-0.371738\pi$
$359$	9419.94	−	5438.60i	1.38486	−	0.799550i	0.992730	+	0.120359i	$0.0384045\pi$
$360$		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
$369$	−4077.24	−	2966.66i	−0.575210	−	0.418532i
$370$		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
$375$	498.163	−	1531.36i	0.0686001	−	0.210877i
$376$		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
$381$	−1350.46	+	4151.32i	−0.181591	+	0.558211i
$382$		0			0
$383$	−2185.13	−	3784.75i	−0.291527	−	0.504939i	0.682644	−	0.730751i	$-0.260830\pi$
$383$	−2185.13	−	3784.75i	−0.291527	−	0.504939i	−0.974171	+	0.225812i	$0.927497\pi$
$384$		0			0
$385$	−788.592	+	511.683i	−0.104391	+	0.0677346i
$386$		0			0
$387$	3463.00	+	2519.74i	0.454869	+	0.330970i
$388$		0			0
$389$	11877.4	+	6857.42i	1.54809	+	0.893791i	0.998288	+	0.0584981i	$0.0186311\pi$
$389$	11877.4	+	6857.42i	1.54809	+	0.893791i	0.549805	+	0.835293i	$0.314702\pi$
$390$		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
$399$	−2754.86	+	2750.80i	−0.345653	+	0.345143i
$400$		0			0
$401$	2268.96	−	1309.98i	0.282560	−	0.163136i	−0.352022	−	0.935992i	$-0.614506\pi$
$401$	2268.96	−	1309.98i	0.282560	−	0.163136i	0.634582	+	0.772856i	$0.281172\pi$
$402$		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
$411$	4241.53	−	3816.40i	0.509049	−	0.458027i
$412$		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
$417$	4092.70	+	1331.39i	0.480624	+	0.156351i
$418$		0			0
$419$	−15171.1			−1.76887			−0.884433	−	0.466666i	$-0.845455\pi$
$419$	−15171.1			−1.76887			−0.884433	+	0.466666i	$0.845455\pi$
$420$		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
$423$	1017.32	−	9614.18i	0.116935	−	1.10510i
$424$		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
$429$	−2771.50	−	3080.23i	−0.311909	−	0.346655i
$430$		0			0
$431$	−6923.58	−	3997.33i	−0.773776	−	0.446740i	0.0604442	−	0.998172i	$-0.480748\pi$
$431$	−6923.58	−	3997.33i	−0.773776	−	0.446740i	−0.834220	+	0.551432i	$0.814082\pi$
$432$		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
$441$	8027.09	−	4618.65i	0.866763	−	0.498721i
$442$		0			0
$443$	−3432.16	+	1981.56i	−0.368097	+	0.212521i	−0.672627	−	0.739982i	$-0.734834\pi$
$443$	−3432.16	+	1981.56i	−0.368097	+	0.212521i	0.304530	+	0.952503i	$0.401501\pi$
$444$		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	$0.250570\pi$
$449$			13479.1i			1.41675i	−0.705838	+	0.708373i	$0.749430\pi$
$450$		0			0
$451$	6581.00	+	3799.54i	0.687112	+	0.396704i
$452$		0			0
$453$	4952.78	+	5504.51i	0.513691	+	0.570915i
$454$		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
$459$	−1520.30	−	14612.7i	−0.154600	−	1.48598i
$460$		0			0
$461$	−9053.72			−0.914694			−0.457347	−	0.889288i	$-0.651200\pi$
$461$	−9053.72			−0.914694			−0.457347	+	0.889288i	$0.651200\pi$
$462$		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
$465$	616.534	+	200.563i	0.0614862	+	0.0200019i
$466$		0			0
$467$	6196.30	+	10732.3i	0.613984	+	1.06345i	0.990562	+	0.137067i	$0.0437675\pi$
$467$	6196.30	+	10732.3i	0.613984	+	1.06345i	−0.376578	+	0.926385i	$0.622899\pi$
$468$		0			0
$469$	−5521.65	+	287.234i	−0.543638	+	0.0282798i
$470$		0			0
$471$	1092.20	−	982.726i	0.106849	−	0.0961393i
$472$		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	−0.598691	−	0.800980i	$-0.704312\pi$
$479$	4133.87	−	7160.07i	0.394324	−	0.682989i	0.993015	+	0.117991i	$0.0376455\pi$
$480$		0			0
$481$	−3224.21	+	1861.50i	−0.305637	+	0.176460i
$482$		0			0
$483$	5475.39	−	5467.31i	0.515815	−	0.515054i
$484$		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	$0.0154728\pi$
$491$			1057.30i			0.0971801i	−0.998819	+	0.0485900i	$0.984527\pi$
$492$		0			0
$493$	19199.9	+	11085.1i	1.75400	+	1.01267i
$494$		0			0
$495$	−806.318	+	1108.16i	−0.0732148	+	0.100623i
$496$		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
$501$	3768.95	−	11585.8i	0.336097	−	1.03316i
$502$		0			0
$503$	−4284.28			−0.379775			−0.189887	−	0.981806i	$-0.560812\pi$
$503$	−4284.28			−0.379775			−0.189887	+	0.981806i	$0.560812\pi$
$504$		0			0
$505$	300.390			0.0264697
$506$		0			0
$507$	−2914.19	+	8958.26i	−0.255274	+	0.784714i
$508$		0			0
$509$	−7550.52	−	13077.9i	−0.657507	−	1.13884i	−0.981259	−	0.192693i	$-0.938278\pi$
$509$	−7550.52	−	13077.9i	−0.657507	−	1.13884i	0.323752	−	0.946142i	$-0.395056\pi$
$510$		0			0
$511$	482.673	+	9278.68i	0.0417851	+	0.803258i
$512$		0			0
$513$	−2313.93	+	5182.48i	−0.199148	+	0.446028i
$514$		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	$-0.636497\pi$
$521$	6894.00	−	11940.8i	0.579715	−	1.00410i	0.995512	−	0.0946385i	$-0.0301695\pi$
$522$		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
$525$	3083.12	−	11472.5i	0.256301	−	0.953713i
$526$		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
$537$	559.639	−	503.545i	0.0449724	−	0.0404648i
$538$		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
$543$	10165.0	+	3306.77i	0.803358	+	0.261339i
$544$		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
$549$	−21689.5	−	2295.06i	−1.68613	−	0.178417i
$550$		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
$555$	823.625	+	915.375i	0.0629927	+	0.0700099i
$556$		0			0
$557$	−5908.09	−	3411.04i	−0.449432	−	0.259480i	0.258158	−	0.966103i	$-0.416884\pi$
$557$	−5908.09	−	3411.04i	−0.449432	−	0.259480i	−0.707590	+	0.706623i	$0.750218\pi$
$558$		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	−0.996437	−	0.0843399i	$-0.973122\pi$
$563$	−5679.80	+	9837.71i	−0.425178	+	0.736430i	0.571259	+	0.820770i	$0.306455\pi$
$564$		0			0
$565$	955.293	−	551.539i	0.0711318	−	0.0410680i
$566$		0			0
$567$	8515.41	−	10477.2i	0.630712	−	0.776017i
$568$		0			0
$569$	−18467.2	+	10662.1i	−1.36061	+	0.785549i	−0.989705	−	0.143122i	$-0.954286\pi$
$569$	−18467.2	+	10662.1i	−1.36061	+	0.785549i	−0.370905	+	0.928671i	$0.620953\pi$
$570$		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
$579$	7892.27	+	8771.45i	0.566479	+	0.629584i
$580$		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
$585$	−656.374	−	69.4538i	−0.0463893	−	0.00490865i
$586$		0			0
$587$	4397.46			0.309204			0.154602	−	0.987977i	$-0.450590\pi$
$587$	4397.46			0.309204			0.154602	+	0.987977i	$0.450590\pi$
$588$		0			0
$589$	−4046.45			−0.283075
$590$		0			0
$591$	−2450.13	−	797.045i	−0.170532	−	0.0554756i
$592$		0			0
$593$	10970.1	+	19000.8i	0.759677	+	1.31580i	0.943015	+	0.332749i	$0.107976\pi$
$593$	10970.1	+	19000.8i	0.759677	+	1.31580i	−0.183339	+	0.983050i	$0.558691\pi$
$594$		0			0
$595$	1316.83	+	2029.46i	0.0907307	+	0.139832i
$596$		0			0
$597$	3243.54	−	2918.44i	0.222361	−	0.200073i
$598$		0			0
$599$	−4765.07	−	2751.12i	−0.325034	−	0.187659i	0.328600	−	0.944469i	$-0.393423\pi$
$599$	−4765.07	−	2751.12i	−0.325034	−	0.187659i	−0.653634	+	0.756810i	$0.726757\pi$
$600$		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
$609$	5258.63	+	19683.6i	0.349902	+	1.30972i
$610$		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	$-0.996382\pi$
$617$		−	348.388i		−	0.0227319i	0.999935	−	0.0113660i	$-0.00361797\pi$
$618$		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
$621$	4599.02	−	10300.4i	0.297186	−	0.665602i
$622$		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
$627$	2646.03	−	8133.91i	0.168536	−	0.518082i
$628$		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
$633$	6432.49	−	19773.6i	0.403900	−	1.24159i
$634$		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
$639$	7234.06	−	9942.13i	0.447848	−	0.615500i
$640$		0			0
$641$	2433.38	+	1404.91i	0.149942	+	0.0865689i	0.573094	−	0.819490i	$-0.305743\pi$
$641$	2433.38	+	1404.91i	0.149942	+	0.0865689i	−0.423152	+	0.906059i	$0.639076\pi$
$642$		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	$-0.483485\pi$
$647$	14659.9	−	25391.7i	0.890790	−	1.54289i	0.838930	−	0.544239i	$-0.183181\pi$
$648$		0			0
$649$	22044.3	−	12727.3i	1.33330	−	0.769783i
$650$		0			0
$651$	9295.98	+	2498.21i	0.559659	+	0.150403i
$652$		0			0
$653$	14500.6	−	8371.91i	0.868992	−	0.501713i	0.00197863	−	0.999998i	$-0.499370\pi$
$653$	14500.6	−	8371.91i	0.868992	−	0.501713i	0.867013	+	0.498285i	$0.166037\pi$
$654$		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	$0.0907937\pi$
$659$			9520.47i			0.562769i	−0.959595	+	0.281385i	$0.909206\pi$
$660$		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
$663$	−7927.06	+	7132.51i	−0.464346	+	0.417804i
$664$		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
$669$	15024.1	+	4887.46i	0.868260	+	0.282452i
$670$		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
$675$	−1792.15	−	17225.7i	−0.102193	−	0.982250i
$676$		0			0
$677$	6495.88	+	11251.2i	0.368769	+	0.638727i	0.989373	−	0.145397i	$-0.0464459\pi$
$677$	6495.88	+	11251.2i	0.368769	+	0.638727i	−0.620604	+	0.784124i	$0.713113\pi$
$678$		0			0
$679$	−22007.4	+	14279.6i	−1.24384	+	0.807072i
$680$		0			0
$681$	15280.2	+	16982.3i	0.859819	+	0.955601i
$682$		0			0
$683$	7366.62	+	4253.12i	0.412703	+	0.238274i	0.691950	−	0.721945i	$-0.256752\pi$
$683$	7366.62	+	4253.12i	0.412703	+	0.238274i	−0.279248	+	0.960219i	$0.590085\pi$
$684$		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
$693$	−11100.5	+	17052.6i	−0.608475	+	0.934738i
$694$		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	$-0.791552\pi$
$701$		−	22607.8i		−	1.21810i	0.793134	−	0.609048i	$-0.208448\pi$
$702$		0			0
$703$	−6655.69	−	3842.67i	−0.357076	−	0.206158i
$704$		0			0
$705$	1552.38	+	1725.32i	0.0829308	+	0.0921690i
$706$		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
$711$	−175.900	+	1662.35i	−0.00927818	+	0.0876835i
$712$		0			0
$713$	8042.46			0.422430
$714$		0			0
$715$	994.720			0.0520285
$716$		0			0
$717$	−18907.3	−	6150.70i	−0.984808	−	0.320366i
$718$		0			0
$719$	12885.3	+	22317.9i	0.668344	+	1.15761i	0.978367	+	0.206877i	$0.0663299\pi$
$719$	12885.3	+	22317.9i	0.668344	+	1.15761i	−0.310023	+	0.950729i	$0.600337\pi$
$720$		0			0
$721$	−18297.3	−	9331.88i	−0.945116	−	0.482021i
$722$		0			0
$723$	−13287.3	+	11955.5i	−0.683486	+	0.614979i
$724$		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
$735$	−464.684	+	2174.13i	−0.0233199	+	0.109108i
$736$		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	$0.0641577\pi$
$743$			8109.00i			0.400391i	−0.979756	+	0.200195i	$0.935842\pi$
$744$		0			0
$745$	964.258	+	556.715i	0.0474197	+	0.0273778i
$746$		0			0
$747$	1596.33	+	1161.52i	0.0781885	+	0.0568912i
$748$		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
$753$	3289.79	−	10112.8i	0.159212	−	0.489419i
$754$		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
$759$	−5259.07	+	16166.4i	−0.251505	+	0.773128i
$760$		0			0
$761$	−5014.38	−	8685.16i	−0.238858	−	0.413715i	0.721529	−	0.692385i	$-0.243440\pi$
$761$	−5014.38	−	8685.16i	−0.238858	−	0.413715i	−0.960387	+	0.278670i	$0.910106\pi$
$762$		0			0
$763$	186.571	−	9.70535i	0.00885233	−	0.000460494i
$764$		0			0
$765$	2851.89	+	2075.08i	0.134785	+	0.0980715i
$766$		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	$0.348936\pi$
$773$	−11644.9	+	20169.5i	−0.541833	+	0.938482i	−0.998799	+	0.0489979i	$0.984397\pi$
$774$		0			0
$775$	10693.2	−	6173.74i	0.495629	−	0.286151i
$776$		0			0
$777$	12917.8	+	12936.9i	0.596428	+	0.597310i
$778$		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
$789$	−24235.8	+	21806.6i	−1.09356	+	0.983947i
$790$		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
$795$	2608.22	+	848.475i	0.116357	+	0.0378519i
$796$		0			0
$797$	12609.3			0.560406			0.280203	−	0.959941i	$-0.409598\pi$
$797$	12609.3			0.560406			0.280203	+	0.959941i	$0.409598\pi$
$798$		0			0
$799$	37496.4			1.66023
$800$		0			0
$801$	−326.004	+	3080.90i	−0.0143805	+	0.135903i
$802$		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
$807$	11595.7	+	12887.4i	0.505807	+	0.562153i
$808$		0			0
$809$	−30281.4	−	17483.0i	−1.31599	−	0.759789i	−0.332912	−	0.942958i	$-0.608031\pi$
$809$	−30281.4	−	17483.0i	−1.31599	−	0.759789i	−0.983082	+	0.183169i	$0.941365\pi$
$810$		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
$819$	−9785.57	−	523.531i	−0.417504	−	0.0223366i
$820$		0			0
$821$	−10487.0	+	6054.70i	−0.445798	+	0.257382i	−0.706054	−	0.708158i	$-0.749526\pi$
$821$	−10487.0	+	6054.70i	−0.445798	+	0.257382i	0.260256	+	0.965540i	$0.416193\pi$
$822$		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	$-0.722587\pi$
$827$		−	36401.9i		−	1.53061i	0.643666	−	0.765307i	$-0.277413\pi$
$828$		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
$831$	−22064.0	−	24521.8i	−0.921047	−	1.02365i
$832$		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
$837$	13957.8	−	1452.16i	0.576406	−	0.0599688i
$838$		0			0
$839$	−13781.4			−0.567090			−0.283545	−	0.958959i	$-0.591510\pi$
$839$	−13781.4			−0.567090			−0.283545	+	0.958959i	$0.591510\pi$
$840$		0			0
$841$	−20433.0			−0.837796
$842$		0			0
$843$	−18460.0	−	6005.18i	−0.754206	−	0.245349i
$844$		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
$849$	−21311.0	+	19175.0i	−0.861476	+	0.775129i
$850$		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	$-0.504203\pi$
$857$	21559.6	−	37342.3i	0.859349	−	1.48844i	0.872551	−	0.488523i	$-0.162464\pi$
$858$		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
$861$	17363.0	−	4638.67i	0.687259	−	0.183607i
$862$		0			0
$863$	−30262.7	+	17472.2i	−1.19369	+	0.689176i	−0.959141	−	0.282929i	$-0.908694\pi$
$863$	−30262.7	+	17472.2i	−1.19369	+	0.689176i	−0.234547	+	0.972105i	$0.575361\pi$
$864$		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
$873$	−22502.1	+	30925.7i	−0.872370	+	1.19894i
$874$		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
$879$	12175.5	−	37427.6i	0.467201	−	1.43618i
$880$		0			0
$881$	−15697.6			−0.600301			−0.300151	−	0.953892i	$-0.597037\pi$
$881$	−15697.6			−0.600301			−0.300151	+	0.953892i	$0.597037\pi$
$882$		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
$885$	1254.33	−	3855.84i	0.0476429	−	0.146455i
$886$		0			0
$887$	−14164.5	−	24533.5i	−0.536185	−	0.928699i	−0.999105	−	0.0422991i	$-0.986532\pi$
$887$	−14164.5	−	24533.5i	−0.536185	−	0.928699i	0.462920	−	0.886400i	$-0.346802\pi$
$888$		0			0
$889$	−8469.24	−	13052.5i	−0.319515	−	0.492428i
$890$		0			0
$891$	−6208.14	+	29006.6i	−0.233424	+	1.09064i
$892$		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
$903$	−14747.3	+	3939.85i	−0.543476	+	0.145194i
$904$		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	$-0.894127\pi$
$911$		−	17955.9i		−	0.653025i	0.945193	−	0.326512i	$-0.105873\pi$
$912$		0			0
$913$	−2576.62	−	1487.61i	−0.0933993	−	0.0539241i
$914$		0			0
$915$	3892.30	−	3502.16i	0.140629	−	0.126533i
$916$		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
$921$	−52553.6	−	17096.1i	−1.88024	−	0.611657i
$922$		0			0
$923$	−8924.34			−0.318254
$924$		0			0
$925$	23451.3			0.833593
$926$		0			0
$927$	−29777.7	−	3150.91i	−1.05505	−	0.111639i
$928$		0			0
$929$	22338.1	+	38690.6i	0.788900	+	1.36641i	0.926642	+	0.375946i	$0.122682\pi$
$929$	22338.1	+	38690.6i	0.788900	+	1.36641i	−0.137742	+	0.990468i	$0.543984\pi$
$930$		0			0
$931$	−1439.74	−	13801.0i	−0.0506826	−	0.485831i
$932$		0			0
$933$	−20058.0	−	22292.4i	−0.703827	−	0.782231i
$934$		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	$0.429091\pi$
$941$	−21192.2	+	36706.0i	−0.734162	+	1.27161i	−0.955090	+	0.296316i	$0.904242\pi$
$942$		0			0
$943$	13004.0	−	7507.87i	0.449066	−	0.259268i
$944$		0			0
$945$	502.419	+	3202.00i	0.0172949	+	0.110223i
$946$		0			0
$947$	10648.1	−	6147.69i	0.365383	−	0.210954i	−0.306057	−	0.952013i	$-0.599010\pi$
$947$	10648.1	−	6147.69i	0.365383	−	0.210954i	0.671439	+	0.741060i	$0.265676\pi$
$948$		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	$-0.992843\pi$
$953$		−	1322.78i		−	0.0449621i	0.999747	−	0.0224811i	$-0.00715655\pi$
$954$		0			0
$955$	3185.47	+	1839.13i	0.107936	+	0.0623171i
$956$		0			0
$957$	−29940.8	−	33276.2i	−1.01134	−	1.12400i
$958$		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
$963$	−28667.5	−	3033.43i	−0.959291	−	0.101507i
$964$		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
$969$	−20932.8	−	6809.61i	−0.693972	−	0.225755i
$970$		0			0
$971$	3409.79	+	5905.93i	0.112693	+	0.195191i	0.916855	−	0.399220i	$-0.130719\pi$
$971$	3409.79	+	5905.93i	0.112693	+	0.195191i	−0.804162	+	0.594410i	$0.797386\pi$
$972$		0			0
$973$	−12868.2	+	8349.64i	−0.423984	+	0.275105i
$974$		0			0
$975$	−9344.55	+	8407.93i	−0.306939	+	0.276174i
$976$		0			0
$977$	−42700.8	−	24653.3i	−1.39828	−	0.807298i	−0.404068	−	0.914729i	$-0.632404\pi$
$977$	−42700.8	−	24653.3i	−1.39828	−	0.807298i	−0.994213	+	0.107431i	$0.965738\pi$
$978$		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	−0.979831	−	0.199828i	$-0.935962\pi$
$983$	−9765.55	+	16914.4i	−0.316859	+	0.548816i	0.662972	+	0.748644i	$0.269295\pi$
$984$		0			0
$985$	535.661	−	309.264i	0.0173275	−	0.0100040i
$986$		0			0
$987$	24347.8	+	24383.8i	0.785206	+	0.786366i
$988$		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
$999$	24337.1	+	10866.3i	0.770762	+	0.344139i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.60743 + 4.94127i) q^{3} +(-0.623706 - 1.08029i) q^{5} +(-10.0808 - 15.5363i) q^{7} +(-21.8323 - 15.8855i) q^{9} +(35.2392 + 20.3453i) q^{11} +19.5973i q^{13} +(6.34057 - 1.34540i) q^{15} +(52.3592 - 90.6889i) q^{17} +(-35.0345 + 20.2272i) q^{19} +(92.9734 - 24.8386i) q^{21} +(69.6324 - 40.2023i) q^{23} +(61.7220 - 106.906i) q^{25} +(113.589 - 82.3444i) q^{27} +211.712i q^{29} +(86.6242 + 50.0125i) q^{31} +(-157.176 + 141.422i) q^{33} +(-10.4962 + 20.5803i) q^{35} +(94.9875 + 164.523i) q^{37} +(-96.8355 - 31.5014i) q^{39} +186.753 q^{41} -158.618 q^{43} +(-3.54405 + 33.4931i) q^{45} +(179.034 + 310.097i) q^{47} +(-139.753 + 313.238i) q^{49} +(363.954 + 404.498i) q^{51} +(366.460 + 211.576i) q^{53} -50.7580i q^{55} +(-43.6323 - 205.629i) q^{57} +(312.781 - 541.753i) q^{59} +(699.575 - 403.900i) q^{61} +(-26.7144 + 499.333i) q^{63} +(21.1708 - 12.2229i) q^{65} +(149.272 - 258.547i) q^{67} +(86.7208 + 408.695i) q^{69} +455.386i q^{71} +(-434.467 - 250.840i) q^{73} +(429.035 + 476.829i) q^{75} +(-39.1491 - 752.584i) q^{77} +(-30.9561 - 53.6176i) q^{79} +(224.299 + 693.636i) q^{81} -73.1180 q^{83} -130.627 q^{85} +(-1046.13 - 340.313i) q^{87} +(-57.3723 - 99.3717i) q^{89} +(304.469 - 197.557i) q^{91} +(-386.368 + 347.642i) q^{93} +(43.7025 + 25.2316i) q^{95} -1416.51i q^{97} +(-446.156 - 1003.98i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9} - 6 q^{15} - 300 q^{19} + 357 q^{21} - 42 q^{25} + 930 q^{31} - 855 q^{33} + 764 q^{37} + 426 q^{39} + 1012 q^{43} + 2367 q^{45} - 336 q^{49} + 1341 q^{51} + 270 q^{57}+ \cdots + 3354 q^{99}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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