LMFDB - Embedded newform 336.4.bc.f.17.15

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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.15
Character	$\chi$	$=$	336.17
Dual form			336.4.bc.f.257.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40845 - 5.00163i) q^{3} +(-0.263312 - 0.456070i) q^{5} +(16.6747 + 8.05944i) q^{7} +(-23.0325 - 14.0891i) q^{9} +O(q^{10})$	\(q+(1.40845 - 5.00163i) q^{3} +(-0.263312 - 0.456070i) q^{5} +(16.6747 + 8.05944i) q^{7} +(-23.0325 - 14.0891i) q^{9} +(-9.84572 - 5.68443i) q^{11} -65.8264i q^{13} +(-2.65195 + 0.674638i) q^{15} +(-0.339033 + 0.587223i) q^{17} +(19.0112 - 10.9761i) q^{19} +(63.7957 - 72.0493i) q^{21} +(-6.60693 + 3.81451i) q^{23} +(62.3613 - 108.013i) q^{25} +(-102.908 + 95.3565i) q^{27} -165.699i q^{29} +(110.323 + 63.6953i) q^{31} +(-42.2986 + 41.2384i) q^{33} +(-0.714981 - 9.72697i) q^{35} +(-95.9053 - 166.113i) q^{37} +(-329.239 - 92.7131i) q^{39} -508.434 q^{41} +25.2052 q^{43} +(-0.360849 + 14.2143i) q^{45} +(-167.209 - 289.614i) q^{47} +(213.091 + 268.777i) q^{49} +(2.45956 + 2.52279i) q^{51} +(-376.298 - 217.256i) q^{53} +5.98711i q^{55} +(-28.1222 - 110.546i) q^{57} +(208.919 - 361.858i) q^{59} +(-288.511 + 166.572i) q^{61} +(-270.511 - 420.560i) q^{63} +(-30.0214 + 17.3329i) q^{65} +(68.6985 - 118.989i) q^{67} +(9.77326 + 38.4180i) q^{69} +718.257i q^{71} +(1009.78 + 582.997i) q^{73} +(-452.408 - 464.039i) q^{75} +(-118.361 - 174.137i) q^{77} +(-189.187 - 327.682i) q^{79} +(331.997 + 649.014i) q^{81} +539.610 q^{83} +0.357086 q^{85} +(-828.766 - 233.379i) q^{87} +(-457.610 - 792.604i) q^{89} +(530.524 - 1097.64i) q^{91} +(473.965 - 462.085i) q^{93} +(-10.0117 - 5.78029i) q^{95} -29.2850i q^{97} +(146.684 + 269.644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{7} + 14 q^{9}+O(q^{10}) $ 48 * q - 12 * q^7 + 14 * q^9	$ 48 q - 12 q^{7} + 14 q^{9} + 88 q^{15} + 270 q^{19} + 50 q^{21} - 438 q^{25} - 216 q^{31} - 372 q^{33} + 66 q^{37} - 242 q^{39} - 900 q^{43} - 294 q^{45} + 60 q^{49} + 138 q^{51} + 1384 q^{57} + 108 q^{61} - 1096 q^{63} - 6 q^{67} - 1206 q^{73} + 594 q^{75} + 588 q^{79} - 54 q^{81} - 240 q^{85} + 3522 q^{87} - 234 q^{91} - 608 q^{93} - 1988 q^{99}+O(q^{100}) $ 48 * q - 12 * q^7 + 14 * q^9 + 88 * q^15 + 270 * q^19 + 50 * q^21 - 438 * q^25 - 216 * q^31 - 372 * q^33 + 66 * q^37 - 242 * q^39 - 900 * q^43 - 294 * q^45 + 60 * q^49 + 138 * q^51 + 1384 * q^57 + 108 * q^61 - 1096 * q^63 - 6 * q^67 - 1206 * q^73 + 594 * q^75 + 588 * q^79 - 54 * q^81 - 240 * q^85 + 3522 * q^87 - 234 * q^91 - 608 * q^93 - 1988 * 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
$3$	1.40845	−	5.00163i	0.271056	−	0.962564i
$3$	1.40845	−	5.00163i	0.271056	−	0.962564i
$4$		0			0
$5$	−0.263312	−	0.456070i	−0.0235513	−	0.0407921i	0.854010	−	0.520257i	$-0.174164\pi$
$5$	−0.263312	−	0.456070i	−0.0235513	−	0.0407921i	−0.877561	+	0.479465i	$0.840831\pi$
$6$		0			0
$7$	16.6747	+	8.05944i	0.900349	+	0.435169i
$7$	16.6747	+	8.05944i	0.900349	+	0.435169i
$8$		0			0
$9$	−23.0325	−	14.0891i	−0.853057	−	0.521817i
$10$		0			0
$11$	−9.84572	−	5.68443i	−0.269872	−	0.155811i	0.358957	−	0.933354i	$-0.383132\pi$
$11$	−9.84572	−	5.68443i	−0.269872	−	0.155811i	−0.628830	+	0.777543i	$0.716466\pi$
$12$		0			0
$13$		−	65.8264i		−	1.40438i	−0.711989	−	0.702191i	$-0.752205\pi$
$13$		−	65.8264i		−	1.40438i	0.711989	−	0.702191i	$-0.247795\pi$
$14$		0			0
$15$	−2.65195	+	0.674638i	−0.0456487	+	0.0116127i
$16$		0			0
$17$	−0.339033	+	0.587223i	−0.00483692	+	0.00837779i	−0.868434	−	0.495805i	$-0.834873\pi$
$17$	−0.339033	+	0.587223i	−0.00483692	+	0.00837779i	0.863597	+	0.504183i	$0.168206\pi$
$18$		0			0
$19$	19.0112	−	10.9761i	0.229551	−	0.132531i	−0.380814	−	0.924652i	$-0.624356\pi$
$19$	19.0112	−	10.9761i	0.229551	−	0.132531i	0.610365	+	0.792120i	$0.291023\pi$
$20$		0			0
$21$	63.7957	−	72.0493i	0.662923	−	0.748688i
$22$		0			0
$23$	−6.60693	+	3.81451i	−0.0598974	+	0.0345818i	−0.529650	−	0.848217i	$-0.677677\pi$
$23$	−6.60693	+	3.81451i	−0.0598974	+	0.0345818i	0.469752	+	0.882798i	$0.344343\pi$
$24$		0			0
$25$	62.3613	−	108.013i	0.498891	−	0.864104i
$26$		0			0
$27$	−102.908	+	95.3565i	−0.733508	+	0.679680i
$28$		0			0
$29$		−	165.699i		−	1.06102i	−0.847679	−	0.530510i	$-0.822000\pi$
$29$		−	165.699i		−	1.06102i	0.847679	−	0.530510i	$-0.178000\pi$
$30$		0			0
$31$	110.323	+	63.6953i	0.639183	+	0.369033i	0.784300	−	0.620382i	$-0.213022\pi$
$31$	110.323	+	63.6953i	0.639183	+	0.369033i	−0.145117	+	0.989415i	$0.546356\pi$
$32$		0			0
$33$	−42.2986	+	41.2384i	−0.223128	+	0.217536i
$34$		0			0
$35$	−0.714981	−	9.72697i	−0.00345297	−	0.0469759i
$36$		0			0
$37$	−95.9053	−	166.113i	−0.426128	−	0.738075i	0.570397	−	0.821369i	$-0.306789\pi$
$37$	−95.9053	−	166.113i	−0.426128	−	0.738075i	−0.996525	+	0.0832937i	$0.973456\pi$
$38$		0			0
$39$	−329.239	−	92.7131i	−1.35181	−	0.380666i
$40$		0			0
$41$	−508.434			−1.93668			−0.968342	−	0.249627i	$-0.919692\pi$
$41$	−508.434			−1.93668			−0.968342	+	0.249627i	$0.919692\pi$
$42$		0			0
$43$	25.2052			0.0893898			0.0446949	−	0.999001i	$-0.485768\pi$
$43$	25.2052			0.0893898			0.0446949	+	0.999001i	$0.485768\pi$
$44$		0			0
$45$	−0.360849	+	14.2143i	−0.00119538	+	0.0470875i
$46$		0			0
$47$	−167.209	−	289.614i	−0.518934	−	0.898820i	−0.999758	−	0.0220031i	$-0.992996\pi$
$47$	−167.209	−	289.614i	−0.518934	−	0.898820i	0.480824	−	0.876817i	$-0.340338\pi$
$48$		0			0
$49$	213.091	+	268.777i	0.621256	+	0.783607i
$50$		0			0
$51$	2.45956	+	2.52279i	0.00675308	+	0.00692669i
$52$		0			0
$53$	−376.298	−	217.256i	−0.975255	−	0.563064i	−0.0744207	−	0.997227i	$-0.523711\pi$
$53$	−376.298	−	217.256i	−0.975255	−	0.563064i	−0.900834	+	0.434163i	$0.857044\pi$
$54$		0			0
$55$			5.98711i			0.0146782i
$56$		0			0
$57$	−28.1222	−	110.546i	−0.0653487	−	0.256881i
$58$		0			0
$59$	208.919	−	361.858i	0.460998	−	0.798473i	−0.538012	−	0.842937i	$-0.680825\pi$
$59$	208.919	−	361.858i	0.460998	−	0.798473i	0.999011	+	0.0444641i	$0.0141580\pi$
$60$		0			0
$61$	−288.511	+	166.572i	−0.605576	+	0.349629i	−0.771232	−	0.636554i	$-0.780359\pi$
$61$	−288.511	+	166.572i	−0.605576	+	0.349629i	0.165656	+	0.986184i	$0.447026\pi$
$62$		0			0
$63$	−270.511	−	420.560i	−0.540971	−	0.841041i
$64$		0			0
$65$	−30.0214	+	17.3329i	−0.0572877	+	0.0330751i
$66$		0			0
$67$	68.6985	−	118.989i	0.125266	−	0.216968i	−0.796571	−	0.604546i	$-0.793355\pi$
$67$	68.6985	−	118.989i	0.125266	−	0.216968i	0.921837	+	0.387578i	$0.126688\pi$
$68$		0			0
$69$	9.77326	+	38.4180i	0.0170516	+	0.0670287i
$70$		0			0
$71$			718.257i			1.20058i	0.799781	+	0.600292i	$0.204949\pi$
$71$			718.257i			1.20058i	−0.799781	+	0.600292i	$0.795051\pi$
$72$		0			0
$73$	1009.78	+	582.997i	1.61898	+	0.934721i	0.987183	+	0.159591i	$0.0510176\pi$
$73$	1009.78	+	582.997i	1.61898	+	0.934721i	0.631802	+	0.775130i	$0.282316\pi$
$74$		0			0
$75$	−452.408	−	464.039i	−0.696528	−	0.714435i
$76$		0			0
$77$	−118.361	−	174.137i	−0.175175	−	0.257724i
$78$		0			0
$79$	−189.187	−	327.682i	−0.269433	−	0.466672i	0.699282	−	0.714846i	$-0.253503\pi$
$79$	−189.187	−	327.682i	−0.269433	−	0.466672i	−0.968716	+	0.248174i	$0.920170\pi$
$80$		0			0
$81$	331.997	+	649.014i	0.455414	+	0.890280i
$82$		0			0
$83$	539.610			0.713613			0.356806	−	0.934178i	$-0.383866\pi$
$83$	539.610			0.713613			0.356806	+	0.934178i	$0.383866\pi$
$84$		0			0
$85$	0.357086			0.000455663
$86$		0			0
$87$	−828.766	−	233.379i	−1.02130	−	0.287596i
$88$		0			0
$89$	−457.610	−	792.604i	−0.545018	−	0.943998i	−0.998606	−	0.0527868i	$-0.983190\pi$
$89$	−457.610	−	792.604i	−0.545018	−	0.943998i	0.453588	−	0.891211i	$-0.350144\pi$
$90$		0			0
$91$	530.524	−	1097.64i	0.611143	−	1.26443i
$92$		0			0
$93$	473.965	−	462.085i	0.528472	−	0.515226i
$94$		0			0
$95$	−10.0117	−	5.78029i	−0.0108125	−	0.00624258i
$96$		0			0
$97$		−	29.2850i		−	0.0306541i	−0.999883	−	0.0153270i	$-0.995121\pi$
$97$		−	29.2850i		−	0.0306541i	0.999883	−	0.0153270i	$-0.00487894\pi$
$98$		0			0
$99$	146.684	+	269.644i	0.148912	+	0.273740i
$100$		0			0
$101$	−502.651	+	870.617i	−0.495204	+	0.857719i	−0.999985	−	0.00552879i	$-0.998240\pi$
$101$	−502.651	+	870.617i	−0.495204	+	0.857719i	0.504780	+	0.863248i	$0.331573\pi$
$102$		0			0
$103$	209.321	−	120.852i	0.200243	−	0.115610i	−0.396526	−	0.918024i	$-0.629784\pi$
$103$	209.321	−	120.852i	0.200243	−	0.115610i	0.596769	+	0.802413i	$0.296451\pi$
$104$		0			0
$105$	−49.6577	−	10.1239i	−0.0461533	−	0.00940940i
$106$		0			0
$107$	1253.93	−	723.958i	1.13292	−	0.654090i	0.188250	−	0.982121i	$-0.439718\pi$
$107$	1253.93	−	723.958i	1.13292	−	0.654090i	0.944667	+	0.328031i	$0.106385\pi$
$108$		0			0
$109$	945.124	−	1637.00i	0.830518	−	1.43850i	−0.0671095	−	0.997746i	$-0.521378\pi$
$109$	945.124	−	1637.00i	0.830518	−	1.43850i	0.897628	−	0.440754i	$-0.145289\pi$
$110$		0			0
$111$	−965.912	+	245.721i	−0.825949	+	0.210116i
$112$		0			0
$113$			751.341i			0.625488i	0.949837	+	0.312744i	$0.101248\pi$
$113$			751.341i			0.625488i	−0.949837	+	0.312744i	$0.898752\pi$
$114$		0			0
$115$	3.47937	+	2.00881i	0.00282133	+	0.00162889i
$116$		0			0
$117$	−927.433	+	1516.15i	−0.732830	+	1.19802i
$118$		0			0
$119$	−10.3860	+	7.05934i	−0.00800066	+	0.00543806i
$120$		0			0
$121$	−600.875	−	1040.75i	−0.451446	−	0.781927i
$122$		0			0
$123$	−716.103	+	2543.00i	−0.524950	+	1.86418i
$124$		0			0
$125$	−131.510			−0.0941008
$126$		0			0
$127$	2243.48			1.56753			0.783767	−	0.621054i	$-0.213295\pi$
$127$	2243.48			1.56753			0.783767	+	0.621054i	$0.213295\pi$
$128$		0			0
$129$	35.5002	−	126.067i	0.0242296	−	0.0860434i
$130$		0			0
$131$	1038.92	+	1799.47i	0.692909	+	1.20015i	0.970881	+	0.239564i	$0.0770044\pi$
$131$	1038.92	+	1799.47i	0.692909	+	1.20015i	−0.277972	+	0.960589i	$0.589662\pi$
$132$		0			0
$133$	405.467	−	29.8039i	0.264349	−	0.0194310i
$134$		0			0
$135$	70.5862	+	21.8249i	0.0450007	+	0.0139140i
$136$		0			0
$137$	1954.66	+	1128.52i	1.21896	+	0.703767i	0.964696	−	0.263367i	$-0.0848332\pi$
$137$	1954.66	+	1128.52i	1.21896	+	0.703767i	0.254265	+	0.967135i	$0.418166\pi$
$138$		0			0
$139$			1086.52i			0.663004i	0.943455	+	0.331502i	$0.107555\pi$
$139$			1086.52i			0.663004i	−0.943455	+	0.331502i	$0.892445\pi$
$140$		0			0
$141$	−1684.05	+	428.410i	−1.00583	+	0.255877i
$142$		0			0
$143$	−374.186	+	648.108i	−0.218818	+	0.379004i
$144$		0			0
$145$	−75.5704	+	43.6306i	−0.0432813	+	0.0249884i
$146$		0			0
$147$	1644.45	−	687.242i	0.922667	−	0.385597i
$148$		0			0
$149$	2547.94	−	1471.06i	1.40091	−	0.808816i	0.406424	−	0.913685i	$-0.366776\pi$
$149$	2547.94	−	1471.06i	1.40091	−	0.808816i	0.994486	+	0.104869i	$0.0334422\pi$
$150$		0			0
$151$	−1167.06	+	2021.40i	−0.628965	+	1.08940i	0.358795	+	0.933417i	$0.383188\pi$
$151$	−1167.06	+	2021.40i	−0.628965	+	1.08940i	−0.987760	+	0.155983i	$0.950145\pi$
$152$		0			0
$153$	16.0822	−	8.74857i	0.00849784	−	0.00462275i
$154$		0			0
$155$		−	67.0869i		−	0.0347648i
$156$		0			0
$157$	2616.30	+	1510.52i	1.32996	+	0.767852i	0.985293	−	0.170873i	$-0.0546588\pi$
$157$	2616.30	+	1510.52i	1.32996	+	0.767852i	0.344666	+	0.938725i	$0.387992\pi$
$158$		0			0
$159$	−1616.63	+	1576.11i	−0.806333	+	0.786123i
$160$		0			0
$161$	−140.911	+	10.3577i	−0.0689775	+	0.00507019i
$162$		0			0
$163$	1190.49	+	2061.98i	0.572062	+	0.990840i	0.996354	+	0.0853146i	$0.0271895\pi$
$163$	1190.49	+	2061.98i	0.572062	+	0.990840i	−0.424292	+	0.905525i	$0.639477\pi$
$164$		0			0
$165$	29.9453	+	8.43253i	0.0141287	+	0.00397862i
$166$		0			0
$167$	−3474.90			−1.61015			−0.805077	−	0.593171i	$-0.797876\pi$
$167$	−3474.90			−1.61015			−0.805077	+	0.593171i	$0.797876\pi$
$168$		0			0
$169$	−2136.12			−0.972288
$170$		0			0
$171$	−592.520	−	15.0419i	−0.264977	−	0.00672682i
$172$		0			0
$173$	231.181	+	400.417i	0.101597	+	0.175972i	0.912343	−	0.409427i	$-0.134271\pi$
$173$	231.181	+	400.417i	0.101597	+	0.175972i	−0.810746	+	0.585399i	$0.800938\pi$
$174$		0			0
$175$	1910.38	−	1298.49i	0.825207	−	0.560893i
$176$		0			0
$177$	−1515.63	−	1554.59i	−0.643624	−	0.660171i
$178$		0			0
$179$	1687.55	+	974.309i	0.704657	+	0.406834i	0.809080	−	0.587699i	$-0.199966\pi$
$179$	1687.55	+	974.309i	0.704657	+	0.406834i	−0.104423	+	0.994533i	$0.533299\pi$
$180$		0			0
$181$		−	615.018i		−	0.252563i	−0.991994	−	0.126282i	$-0.959696\pi$
$181$		−	615.018i		−	0.252563i	0.991994	−	0.126282i	$-0.0403043\pi$
$182$		0			0
$183$	426.779	+	1677.64i	0.172396	+	0.677674i
$184$		0			0
$185$	−50.5060	+	87.4790i	−0.0200718	+	0.0347653i
$186$		0			0
$187$	6.67605	−	3.85442i	0.00261070	−	0.00150729i
$188$		0			0
$189$	−2484.49	+	760.657i	−0.956189	+	0.292750i
$190$		0			0
$191$	−1933.30	+	1116.19i	−0.732400	+	0.422851i	−0.819300	−	0.573366i	$-0.805637\pi$
$191$	−1933.30	+	1116.19i	−0.732400	+	0.422851i	0.0868995	+	0.996217i	$0.472304\pi$
$192$		0			0
$193$	692.298	−	1199.09i	0.258200	−	0.447216i	−0.707559	−	0.706654i	$-0.750204\pi$
$193$	692.298	−	1199.09i	0.258200	−	0.447216i	0.965760	+	0.259438i	$0.0835372\pi$
$194$		0			0
$195$	44.4090	+	174.568i	0.0163087	+	0.0641082i
$196$		0			0
$197$			3912.85i			1.41512i	0.706652	+	0.707562i	$0.250205\pi$
$197$			3912.85i			1.41512i	−0.706652	+	0.707562i	$0.749795\pi$
$198$		0			0
$199$	−3069.79	−	1772.34i	−1.09353	−	0.631347i	−0.159013	−	0.987277i	$-0.550831\pi$
$199$	−3069.79	−	1772.34i	−1.09353	−	0.631347i	−0.934513	+	0.355929i	$0.884164\pi$
$200$		0			0
$201$	−498.382	−	511.194i	−0.174891	−	0.179387i
$202$		0			0
$203$	1335.44	−	2762.99i	0.461723	−	0.955289i
$204$		0			0
$205$	133.877	+	231.881i	0.0456115	+	0.0790014i
$206$		0			0
$207$	205.917	+	5.22750i	0.0691413	+	0.00175525i
$208$		0			0
$209$	−249.572			−0.0825993
$210$		0			0
$211$	2180.84			0.711542			0.355771	−	0.934573i	$-0.384218\pi$
$211$	2180.84			0.711542			0.355771	+	0.934573i	$0.384218\pi$
$212$		0			0
$213$	3592.45	+	1011.63i	1.15564	+	0.325425i
$214$		0			0
$215$	−6.63684	−	11.4953i	−0.00210525	−	0.00364640i
$216$		0			0
$217$	1326.26	+	1951.24i	0.414896	+	0.610411i
$218$		0			0
$219$	4338.16	−	4229.43i	1.33856	−	1.30501i
$220$		0			0
$221$	38.6548	+	22.3173i	0.0117656	+	0.00679288i
$222$		0			0
$223$		−	3793.00i		−	1.13900i	−0.821990	−	0.569502i	$-0.807136\pi$
$223$		−	3793.00i		−	1.13900i	0.821990	−	0.569502i	$-0.192864\pi$
$224$		0			0
$225$	−2958.14	+	1609.20i	−0.876487	+	0.476801i
$226$		0			0
$227$	2487.54	−	4308.54i	0.727329	−	1.25977i	−0.230680	−	0.973030i	$-0.574095\pi$
$227$	2487.54	−	4308.54i	0.727329	−	1.25977i	0.958008	−	0.286740i	$-0.0925717\pi$
$228$		0			0
$229$	226.277	−	130.641i	0.0652961	−	0.0376987i	−0.466997	−	0.884259i	$-0.654664\pi$
$229$	226.277	−	130.641i	0.0652961	−	0.0376987i	0.532293	+	0.846560i	$0.321331\pi$
$230$		0			0
$231$	−1037.67	+	346.735i	−0.295558	+	0.0987597i
$232$		0			0
$233$	3952.64	−	2282.06i	1.11136	−	0.641643i	0.172177	−	0.985066i	$-0.444920\pi$
$233$	3952.64	−	2282.06i	1.11136	−	0.641643i	0.939181	+	0.343423i	$0.111587\pi$
$234$		0			0
$235$	−88.0561	+	152.518i	−0.0244432	+	0.0423368i
$236$		0			0
$237$	−1905.40	+	484.721i	−0.522233	+	0.132852i
$238$		0			0
$239$			4367.13i			1.18195i	0.806689	+	0.590976i	$0.201257\pi$
$239$			4367.13i			1.18195i	−0.806689	+	0.590976i	$0.798743\pi$
$240$		0			0
$241$	1154.96	+	666.815i	0.308703	+	0.178230i	0.646346	−	0.763045i	$-0.276296\pi$
$241$	1154.96	+	666.815i	0.308703	+	0.178230i	−0.337643	+	0.941274i	$0.609630\pi$
$242$		0			0
$243$	3713.73	−	746.421i	0.980394	−	0.197049i
$244$		0			0
$245$	66.4718	−	167.957i	0.0173336	−	0.0437973i
$246$		0			0
$247$	−722.519	−	1251.44i	−0.186125	−	0.322377i
$248$		0			0
$249$	760.012	−	2698.93i	0.193429	−	0.686898i
$250$		0			0
$251$	−3117.15			−0.783875			−0.391938	−	0.919992i	$-0.628195\pi$
$251$	−3117.15			−0.783875			−0.391938	+	0.919992i	$0.628195\pi$
$252$		0			0
$253$	86.7333			0.0215529
$254$		0			0
$255$	0.502937	−	1.78601i	0.000123510	−	0.000438605i
$256$		0			0
$257$	−554.639	−	960.663i	−0.134620	−	0.233169i	0.790832	−	0.612033i	$-0.209648\pi$
$257$	−554.639	−	960.663i	−0.134620	−	0.233169i	−0.925452	+	0.378864i	$0.876315\pi$
$258$		0			0
$259$	−260.415	−	3542.82i	−0.0624766	−	0.849963i
$260$		0			0
$261$	−2334.55	+	3816.48i	−0.553659	+	0.905111i
$262$		0			0
$263$	−4538.61	−	2620.37i	−1.06412	−	0.614368i	−0.137549	−	0.990495i	$-0.543922\pi$
$263$	−4538.61	−	2620.37i	−1.06412	−	0.614368i	−0.926568	+	0.376127i	$0.877256\pi$
$264$		0			0
$265$			228.824i			0.0530436i
$266$		0			0
$267$	−4608.83	+	1172.45i	−1.05639	+	0.268738i
$268$		0			0
$269$	1654.06	−	2864.92i	0.374907	−	0.649358i	−0.615406	−	0.788210i	$-0.711008\pi$
$269$	1654.06	−	2864.92i	0.374907	−	0.649358i	0.990313	+	0.138852i	$0.0443412\pi$
$270$		0			0
$271$	2978.05	−	1719.38i	0.667541	−	0.385405i	−0.127603	−	0.991825i	$-0.540728\pi$
$271$	2978.05	−	1719.38i	0.667541	−	0.385405i	0.795144	+	0.606420i	$0.207395\pi$
$272$		0			0
$273$	−4742.75	−	4199.45i	−1.05144	−	0.930996i
$274$		0			0
$275$	−1227.98	+	708.977i	−0.269274	+	0.155465i
$276$		0			0
$277$	1792.98	−	3105.53i	0.388915	−	0.673621i	−0.603389	−	0.797447i	$-0.706183\pi$
$277$	1792.98	−	3105.53i	0.388915	−	0.673621i	0.992304	+	0.123826i	$0.0395166\pi$
$278$		0			0
$279$	−1643.62	−	3021.42i	−0.352692	−	0.648343i
$280$		0			0
$281$			536.879i			0.113977i	0.998375	+	0.0569884i	$0.0181498\pi$
$281$			536.879i			0.113977i	−0.998375	+	0.0569884i	$0.981850\pi$
$282$		0			0
$283$	−1693.93	−	977.990i	−0.355808	−	0.205426i	0.311433	−	0.950268i	$-0.399191\pi$
$283$	−1693.93	−	977.990i	−0.355808	−	0.205426i	−0.667240	+	0.744843i	$0.732525\pi$
$284$		0			0
$285$	−43.0119	+	41.9338i	−0.00893966	+	0.00871559i
$286$		0			0
$287$	−8477.98	−	4097.69i	−1.74369	−	0.842784i
$288$		0			0
$289$	2456.27	+	4254.38i	0.499953	+	0.865944i
$290$		0			0
$291$	−146.473	−	41.2464i	−0.0295065	−	0.00830896i
$292$		0			0
$293$	−8428.11			−1.68046			−0.840232	−	0.542228i	$-0.817581\pi$
$293$	−8428.11			−1.68046			−0.840232	+	0.542228i	$0.817581\pi$
$294$		0			0
$295$	−220.043			−0.0434285
$296$		0			0
$297$	1555.25	−	353.878i	0.303855	−	0.0691383i
$298$		0			0
$299$	251.096	+	434.911i	0.0485660	+	0.0841188i
$300$		0			0
$301$	420.289	+	203.140i	0.0804820	+	0.0388996i
$302$		0			0
$303$	3646.54	+	3740.29i	0.691381	+	0.709155i
$304$		0			0
$305$	151.937	+	87.7209i	0.0285242	+	0.0164685i
$306$		0			0
$307$			4651.20i			0.864684i	0.901710	+	0.432342i	$0.142313\pi$
$307$			4651.20i			0.864684i	−0.901710	+	0.432342i	$0.857687\pi$
$308$		0			0
$309$	−309.637	−	1217.16i	−0.0570053	−	0.224084i
$310$		0			0
$311$	1839.99	−	3186.96i	0.335486	−	0.581080i	−0.648092	−	0.761562i	$-0.724433\pi$
$311$	1839.99	−	3186.96i	0.335486	−	0.581080i	0.983578	+	0.180483i	$0.0577660\pi$
$312$		0			0
$313$	−929.740	+	536.786i	−0.167898	+	0.0969358i	−0.581594	−	0.813479i	$-0.697571\pi$
$313$	−929.740	+	536.786i	−0.167898	+	0.0969358i	0.413696	+	0.910415i	$0.364237\pi$
$314$		0			0
$315$	−120.576	+	234.110i	−0.0215673	+	0.0418750i
$316$		0			0
$317$	2312.94	−	1335.38i	0.409804	−	0.236600i	−0.280902	−	0.959737i	$-0.590633\pi$
$317$	2312.94	−	1335.38i	0.409804	−	0.236600i	0.690706	+	0.723136i	$0.257300\pi$
$318$		0			0
$319$	−941.906	+	1631.43i	−0.165319	+	0.286340i
$320$		0			0
$321$	−1854.87	−	7291.36i	−0.322519	−	1.26780i
$322$		0			0
$323$			14.8851i			0.00256417i
$324$		0			0
$325$	−7110.11	−	4105.02i	−1.21353	−	0.700633i
$326$		0			0
$327$	−6856.52	−	7032.79i	−1.15953	−	1.18934i
$328$		0			0
$329$	−454.029	−	6176.84i	−0.0760833	−	1.03508i
$330$		0			0
$331$	4779.06	+	8277.58i	0.793599	+	1.37455i	0.923725	+	0.383056i	$0.125128\pi$
$331$	4779.06	+	8277.58i	0.793599	+	1.37455i	−0.130127	+	0.991497i	$0.541538\pi$
$332$		0			0
$333$	−131.431	+	5177.22i	−0.0216287	+	0.851982i
$334$		0			0
$335$	−72.3565			−0.0118008
$336$		0			0
$337$	−305.593			−0.0493968			−0.0246984	−	0.999695i	$-0.507863\pi$
$337$	−305.593			−0.0493968			−0.0246984	+	0.999695i	$0.507863\pi$
$338$		0			0
$339$	3757.93	+	1058.22i	0.602072	+	0.169542i
$340$		0			0
$341$	−724.143	−	1254.25i	−0.114999	−	0.199183i
$342$		0			0
$343$	1387.03	+	6199.17i	0.218346	+	0.975871i
$344$		0			0
$345$	14.9478	−	14.5732i	0.00233265	−	0.00227419i
$346$		0			0
$347$	4993.59	+	2883.05i	0.772536	+	0.446024i	0.833778	−	0.552099i	$-0.186173\pi$
$347$	4993.59	+	2883.05i	0.772536	+	0.446024i	−0.0612428	+	0.998123i	$0.519506\pi$
$348$		0			0
$349$		−	6896.44i		−	1.05776i	−0.848697	−	0.528880i	$-0.822612\pi$
$349$		−	6896.44i		−	1.05776i	0.848697	−	0.528880i	$-0.177388\pi$
$350$		0			0
$351$	6276.98	+	6774.09i	0.954531	+	1.03013i
$352$		0			0
$353$	−4688.32	+	8120.40i	−0.706895	+	1.22438i	0.259108	+	0.965848i	$0.416571\pi$
$353$	−4688.32	+	8120.40i	−0.706895	+	1.22438i	−0.966003	+	0.258530i	$0.916762\pi$
$354$		0			0
$355$	327.575	−	189.126i	0.0489743	−	0.0282753i
$356$		0			0
$357$	20.6801	+	61.8894i	0.00306585	+	0.00917517i
$358$		0			0
$359$	1644.06	−	949.198i	0.241700	−	0.139545i	−0.374258	−	0.927325i	$-0.622103\pi$
$359$	1644.06	−	949.198i	0.241700	−	0.139545i	0.615958	+	0.787779i	$0.288769\pi$
$360$		0			0
$361$	−3188.55	+	5522.73i	−0.464871	+	0.805180i
$362$		0			0
$363$	−6051.72	+	1539.52i	−0.875022	+	0.222599i
$364$		0			0
$365$		−	614.040i		−	0.0880557i
$366$		0			0
$367$	−3072.05	−	1773.65i	−0.436947	−	0.252271i	0.265355	−	0.964151i	$-0.414511\pi$
$367$	−3072.05	−	1773.65i	−0.436947	−	0.252271i	−0.702302	+	0.711879i	$0.747844\pi$
$368$		0			0
$369$	11710.5	+	7163.36i	1.65210	+	1.01060i
$370$		0			0
$371$	−4523.70	−	6655.42i	−0.633042	−	0.931354i
$372$		0			0
$373$	−2099.26	−	3636.02i	−0.291408	−	0.504734i	0.682735	−	0.730666i	$-0.260791\pi$
$373$	−2099.26	−	3636.02i	−0.291408	−	0.504734i	−0.974143	+	0.225932i	$0.927457\pi$
$374$		0			0
$375$	−185.225	+	657.763i	−0.0255066	+	0.0905780i
$376$		0			0
$377$	−10907.4			−1.49008
$378$		0			0
$379$	−11748.8			−1.59233			−0.796165	−	0.605080i	$-0.793141\pi$
$379$	−11748.8			−1.59233			−0.796165	+	0.605080i	$0.793141\pi$
$380$		0			0
$381$	3159.83	−	11221.1i	0.424890	−	1.50885i
$382$		0			0
$383$	5111.95	+	8854.16i	0.682006	+	1.18127i	0.974368	+	0.224962i	$0.0722257\pi$
$383$	5111.95	+	8854.16i	0.682006	+	1.18127i	−0.292361	+	0.956308i	$0.594441\pi$
$384$		0			0
$385$	−48.2527	+	99.8332i	−0.00638750	+	0.0132155i
$386$		0			0
$387$	−580.541	−	355.118i	−0.0762546	−	0.0466451i
$388$		0			0
$389$	3605.15	+	2081.43i	0.469893	+	0.271293i	0.716195	−	0.697901i	$-0.245882\pi$
$389$	3605.15	+	2081.43i	0.469893	+	0.271293i	−0.246302	+	0.969193i	$0.579216\pi$
$390$		0			0
$391$		−	5.17299i		−	0.000669077i
$392$		0			0
$393$	10463.5	−	2661.85i	1.34304	−	0.341660i
$394$		0			0
$395$	−99.6305	+	172.565i	−0.0126910	+	0.0219815i
$396$		0			0
$397$	3962.92	−	2287.99i	0.500991	−	0.289247i	−0.228132	−	0.973630i	$-0.573262\pi$
$397$	3962.92	−	2287.99i	0.500991	−	0.289247i	0.729123	+	0.684383i	$0.239928\pi$
$398$		0			0
$399$	422.012	−	2069.97i	0.0529499	−	0.259720i
$400$		0			0
$401$	5375.54	−	3103.57i	0.669430	−	0.386496i	−0.126431	−	0.991975i	$-0.540352\pi$
$401$	5375.54	−	3103.57i	0.669430	−	0.386496i	0.795861	+	0.605480i	$0.207019\pi$
$402$		0			0
$403$	4192.83	−	7262.20i	0.518263	−	0.897657i
$404$		0			0
$405$	208.577	−	322.307i	0.0255908	−	0.0395446i
$406$		0			0
$407$			2180.67i			0.265582i
$408$		0			0
$409$	−10290.0	−	5940.92i	−1.24403	−	0.718238i	−0.274114	−	0.961697i	$-0.588385\pi$
$409$	−10290.0	−	5940.92i	−1.24403	−	0.718238i	−0.969911	+	0.243459i	$0.921718\pi$
$410$		0			0
$411$	8397.48	−	8187.00i	1.00783	−	0.982567i
$412$		0			0
$413$	6400.03	−	4350.10i	0.762530	−	0.518292i
$414$		0			0
$415$	−142.086	−	246.100i	−0.0168065	−	0.0291098i
$416$		0			0
$417$	5434.37	+	1530.31i	0.638183	+	0.179711i
$418$		0			0
$419$	−347.837			−0.0405560			−0.0202780	−	0.999794i	$-0.506455\pi$
$419$	−347.837			−0.0405560			−0.0202780	+	0.999794i	$0.506455\pi$
$420$		0			0
$421$	−7639.03			−0.884331			−0.442166	−	0.896933i	$-0.645790\pi$
$421$	−7639.03			−0.884331			−0.442166	+	0.896933i	$0.645790\pi$
$422$		0			0
$423$	−229.147	+	9026.37i	−0.0263392	+	1.03753i
$424$		0			0
$425$	42.2851	+	73.2400i	0.00482619	+	0.00835920i
$426$		0			0
$427$	−6153.32	+	452.300i	−0.697377	+	0.0512607i
$428$		0			0
$429$	2714.58	+	2784.36i	0.305503	+	0.313357i
$430$		0			0
$431$	13282.3	+	7668.55i	1.48442	+	0.857032i	0.999843	−	0.0177146i	$-0.00563903\pi$
$431$	13282.3	+	7668.55i	1.48442	+	0.857032i	0.484580	+	0.874747i	$0.338972\pi$
$432$		0			0
$433$			11113.0i			1.23339i	0.787202	+	0.616696i	$0.211529\pi$
$433$			11113.0i			1.23339i	−0.787202	+	0.616696i	$0.788471\pi$
$434$		0			0
$435$	111.787	+	439.426i	0.0123213	+	0.0484342i
$436$		0			0
$437$	−83.7371	+	145.037i	−0.00916634	+	0.0158766i
$438$		0			0
$439$	−7997.97	+	4617.63i	−0.869527	+	0.502022i	−0.867191	−	0.497976i	$-0.834077\pi$
$439$	−7997.97	+	4617.63i	−0.869527	+	0.502022i	−0.00233599	+	0.999997i	$0.500744\pi$
$440$		0			0
$441$	−1121.21	−	9192.88i	−0.121067	−	0.992644i
$442$		0			0
$443$	2636.02	−	1521.91i	0.282712	−	0.163224i	−0.351939	−	0.936023i	$-0.614477\pi$
$443$	2636.02	−	1521.91i	0.282712	−	0.163224i	0.634650	+	0.772799i	$0.281144\pi$
$444$		0			0
$445$	−240.988	+	417.404i	−0.0256718	+	0.0444648i
$446$		0			0
$447$	−3769.03	−	14815.8i	−0.398812	−	1.56770i
$448$		0			0
$449$			9732.40i			1.02294i	0.859301	+	0.511470i	$0.170899\pi$
$449$			9732.40i			1.02294i	−0.859301	+	0.511470i	$0.829101\pi$
$450$		0			0
$451$	5005.90	+	2890.16i	0.522657	+	0.301756i
$452$		0			0
$453$	8466.56	+	8684.22i	0.878132	+	0.900707i
$454$		0			0
$455$	−640.291	+	47.0646i	−0.0659721	+	0.00484928i
$456$		0			0
$457$	9550.15	+	16541.3i	0.977543	+	1.69315i	0.671274	+	0.741210i	$0.265748\pi$
$457$	9550.15	+	16541.3i	0.977543	+	1.69315i	0.306270	+	0.951945i	$0.400919\pi$
$458$		0			0
$459$	−21.1061	−	92.7591i	−0.00214630	−	0.00943274i
$460$		0			0
$461$	−1672.67			−0.168989			−0.0844946	−	0.996424i	$-0.526928\pi$
$461$	−1672.67			−0.168989			−0.0844946	+	0.996424i	$0.526928\pi$
$462$		0			0
$463$	−12242.9			−1.22889			−0.614445	−	0.788960i	$-0.710620\pi$
$463$	−12242.9			−1.22889			−0.614445	+	0.788960i	$0.710620\pi$
$464$		0			0
$465$	−335.544	−	94.4884i	−0.0334634	−	0.00942322i
$466$		0			0
$467$	8378.07	+	14511.2i	0.830173	+	1.43790i	0.897901	+	0.440197i	$0.145092\pi$
$467$	8378.07	+	14511.2i	0.830173	+	1.43790i	−0.0677283	+	0.997704i	$0.521575\pi$
$468$		0			0
$469$	2104.51	−	1430.44i	0.207201	−	0.140835i
$470$		0			0
$471$	11240.0	−	10958.3i	1.09960	−	1.07204i
$472$		0			0
$473$	−248.164	−	143.277i	−0.0241238	−	0.0139279i
$474$		0			0
$475$		−	2737.94i		−	0.264474i
$476$		0			0
$477$	5606.17	+	10305.6i	0.538132	+	0.989230i
$478$		0			0
$479$	8971.99	−	15539.9i	0.855826	−	1.48233i	−0.0200500	−	0.999799i	$-0.506383\pi$
$479$	8971.99	−	15539.9i	0.855826	−	1.48233i	0.875876	−	0.482536i	$-0.160284\pi$
$480$		0			0
$481$	−10934.6	+	6313.10i	−1.03654	+	0.598446i
$482$		0			0
$483$	−146.661	+	719.375i	−0.0138164	+	0.0677695i
$484$		0			0
$485$	−13.3560	+	7.71109i	−0.00125044	+	0.000721944i
$486$		0			0
$487$	4293.67	−	7436.85i	0.399517	−	0.691983i	−0.594150	−	0.804355i	$-0.702511\pi$
$487$	4293.67	−	7436.85i	0.399517	−	0.691983i	0.993666	+	0.112371i	$0.0358446\pi$
$488$		0			0
$489$	11990.0	−	3050.17i	1.10881	−	0.282073i
$490$		0			0
$491$			7844.47i			0.721010i	0.932757	+	0.360505i	$0.117396\pi$
$491$			7844.47i			0.721010i	−0.932757	+	0.360505i	$0.882604\pi$
$492$		0			0
$493$	97.3024	+	56.1776i	0.00888900	+	0.00513207i
$494$		0			0
$495$	84.3528	−	137.898i	0.00765934	−	0.0125214i
$496$		0			0
$497$	−5788.75	+	11976.7i	−0.522456	+	1.08094i
$498$		0			0
$499$	−7889.58	−	13665.2i	−0.707788	−	1.22593i	−0.965676	−	0.259750i	$-0.916360\pi$
$499$	−7889.58	−	13665.2i	−0.707788	−	1.22593i	0.257888	−	0.966175i	$-0.416974\pi$
$500$		0			0
$501$	−4894.21	+	17380.1i	−0.436442	+	1.54988i
$502$		0			0
$503$	15535.1			1.37709			0.688543	−	0.725196i	$-0.258251\pi$
$503$	15535.1			1.37709			0.688543	+	0.725196i	$0.258251\pi$
$504$		0			0
$505$	529.416			0.0466509
$506$		0			0
$507$	−3008.61	+	10684.1i	−0.263544	+	0.935889i
$508$		0			0
$509$	−5913.59	−	10242.6i	−0.514961	−	0.891939i	−0.999849	−	0.0173626i	$-0.994473\pi$
$509$	−5913.59	−	10242.6i	−0.514961	−	0.891939i	0.484888	−	0.874576i	$-0.338860\pi$
$510$		0			0
$511$	12139.2	+	17859.6i	1.05089	+	1.54611i
$512$		0			0
$513$	−909.767	+	2942.38i	−0.0782986	+	0.253234i
$514$		0			0
$515$	−110.234	−	63.6434i	−0.00943199	−	0.00544556i
$516$		0			0
$517$			3801.94i			0.323422i
$518$		0			0
$519$	2328.34	−	592.314i	0.196923	−	0.0500957i
$520$		0			0
$521$	4803.81	−	8320.44i	0.403951	−	0.699664i	−0.590248	−	0.807222i	$-0.700970\pi$
$521$	4803.81	−	8320.44i	0.403951	−	0.699664i	0.994199	+	0.107558i	$0.0343032\pi$
$522$		0			0
$523$	−6854.71	+	3957.57i	−0.573108	+	0.330884i	−0.758390	−	0.651801i	$-0.774014\pi$
$523$	−6854.71	+	3957.57i	−0.573108	+	0.330884i	0.185282	+	0.982685i	$0.440680\pi$
$524$		0			0
$525$	−3803.87	−	11383.9i	−0.316218	−	0.946347i
$526$		0			0
$527$	−74.8066	+	43.1896i	−0.00618335	+	0.00356996i
$528$		0			0
$529$	−6054.40	+	10486.5i	−0.497608	+	0.861883i
$530$		0			0
$531$	−9910.17	+	5391.04i	−0.809915	+	0.440586i
$532$		0			0
$533$			33468.4i			2.71984i
$534$		0			0
$535$	−660.350	−	381.253i	−0.0533634	−	0.0308094i
$536$		0			0
$537$	7249.96	−	7068.24i	0.582605	−	0.568002i
$538$		0			0
$539$	−570.188	−	3857.61i	−0.0455653	−	0.308272i
$540$		0			0
$541$	−2198.76	−	3808.36i	−0.174736	−	0.302651i	0.765334	−	0.643633i	$-0.222574\pi$
$541$	−2198.76	−	3808.36i	−0.174736	−	0.302651i	−0.940070	+	0.340982i	$0.889240\pi$
$542$		0			0
$543$	−3076.09	−	866.221i	−0.243108	−	0.0684587i
$544$		0			0
$545$	−995.450			−0.0782392
$546$		0			0
$547$	−16800.1			−1.31320			−0.656598	−	0.754240i	$-0.728005\pi$
$547$	−16800.1			−1.31320			−0.656598	+	0.754240i	$0.728005\pi$
$548$		0			0
$549$	8992.00	+	228.274i	0.699033	+	0.0177459i
$550$		0			0
$551$	−1818.74	−	3150.14i	−0.140618	−	0.243558i
$552$		0			0
$553$	−513.707	−	6988.74i	−0.0395028	−	0.537416i
$554$		0			0
$555$	366.402	+	375.822i	0.0280233	+	0.0287437i
$556$		0			0
$557$	−18844.8	−	10880.1i	−1.43354	−	0.827654i	−0.436150	−	0.899874i	$-0.643658\pi$
$557$	−18844.8	−	10880.1i	−1.43354	−	0.827654i	−0.997389	+	0.0722198i	$0.976992\pi$
$558$		0			0
$559$		−	1659.17i		−	0.125537i
$560$		0			0
$561$	−9.87550	−	38.8199i	−0.000743215	−	0.00292152i
$562$		0			0
$563$	−4741.56	+	8212.63i	−0.354943	+	0.614780i	−0.987108	−	0.160054i	$-0.948833\pi$
$563$	−4741.56	+	8212.63i	−0.354943	+	0.614780i	0.632165	+	0.774834i	$0.282167\pi$
$564$		0			0
$565$	342.664	−	197.837i	0.0255150	−	0.0147311i
$566$		0			0
$567$	305.254	+	13497.8i	0.0226093	+	0.999744i
$568$		0			0
$569$	17650.5	−	10190.5i	1.30043	−	0.750805i	0.319955	−	0.947433i	$-0.396332\pi$
$569$	17650.5	−	10190.5i	1.30043	−	0.750805i	0.980478	+	0.196627i	$0.0629989\pi$
$570$		0			0
$571$	8194.57	−	14193.4i	0.600582	−	1.04024i	−0.392151	−	0.919901i	$-0.628269\pi$
$571$	8194.57	−	14193.4i	0.600582	−	1.04024i	0.992733	−	0.120337i	$-0.0383977\pi$
$572$		0			0
$573$	2859.81	+	11241.7i	0.208500	+	0.819598i
$574$		0			0
$575$			951.513i			0.0690101i
$576$		0			0
$577$	−3432.41	−	1981.70i	−0.247648	−	0.142980i	0.371039	−	0.928617i	$-0.379002\pi$
$577$	−3432.41	−	1981.70i	−0.247648	−	0.142980i	−0.618687	+	0.785638i	$0.712335\pi$
$578$		0			0
$579$	−5022.36	−	5151.48i	−0.360487	−	0.369755i
$580$		0			0
$581$	8997.83	+	4348.95i	0.642501	+	0.310542i
$582$		0			0
$583$	2469.95	+	4278.08i	0.175463	+	0.303911i
$584$		0			0
$585$	935.674	+	23.7534i	0.0661288	+	0.00167877i
$586$		0			0
$587$	−25463.9			−1.79047			−0.895236	−	0.445593i	$-0.852993\pi$
$587$	−25463.9			−1.79047			−0.895236	+	0.445593i	$0.852993\pi$
$588$		0			0
$589$	2796.51			0.195633
$590$		0			0
$591$	19570.6	+	5511.05i	1.36215	+	0.383578i
$592$		0			0
$593$	−5111.63	−	8853.61i	−0.353979	−	0.613110i	0.632964	−	0.774182i	$-0.281838\pi$
$593$	−5111.63	−	8853.61i	−0.353979	−	0.613110i	−0.986943	+	0.161072i	$0.948505\pi$
$594$		0			0
$595$	5.95430	+	2.87791i	0.000410256	+	0.000198290i
$596$		0			0
$597$	−13188.2	+	12857.7i	−0.904119	+	0.881458i
$598$		0			0
$599$	9148.27	+	5281.76i	0.624020	+	0.360278i	0.778433	−	0.627728i	$-0.216015\pi$
$599$	9148.27	+	5281.76i	0.624020	+	0.360278i	−0.154412	+	0.988007i	$0.549348\pi$
$600$		0			0
$601$			8886.76i			0.603159i	0.953441	+	0.301579i	$0.0975138\pi$
$601$			8886.76i			0.603159i	−0.953441	+	0.301579i	$0.902486\pi$
$602$		0			0
$603$	−3258.75	+	1772.73i	−0.220077	+	0.119720i
$604$		0			0
$605$	−316.435	+	548.081i	−0.0212643	+	0.0368309i
$606$		0			0
$607$	−20595.0	+	11890.5i	−1.37714	+	0.795093i	−0.991815	−	0.127686i	$-0.959245\pi$
$607$	−20595.0	+	11890.5i	−1.37714	+	0.795093i	−0.385328	+	0.922780i	$0.625912\pi$
$608$		0			0
$609$	−11938.5	−	10570.9i	−0.794373	−	0.703374i
$610$		0			0
$611$	−19064.3	+	11006.8i	−1.26229	+	0.728782i
$612$		0			0
$613$	6975.41	−	12081.8i	0.459599	−	0.796048i	−0.539341	−	0.842088i	$-0.681327\pi$
$613$	6975.41	−	12081.8i	0.459599	−	0.796048i	0.998940	+	0.0460392i	$0.0146599\pi$
$614$		0			0
$615$	1348.34	−	343.009i	0.0884072	−	0.0224902i
$616$		0			0
$617$		−	17793.8i		−	1.16103i	−0.814251	−	0.580513i	$-0.802852\pi$
$617$		−	17793.8i		−	1.16103i	0.814251	−	0.580513i	$-0.197148\pi$
$618$		0			0
$619$	15053.4	+	8691.09i	0.977459	+	0.564336i	0.901502	−	0.432775i	$-0.142465\pi$
$619$	15053.4	+	8691.09i	0.977459	+	0.564336i	0.0759571	+	0.997111i	$0.475799\pi$
$620$		0			0
$621$	316.170	−	1022.56i	0.0204307	−	0.0660771i
$622$		0			0
$623$	−1242.57	−	16904.5i	−0.0799075	−	1.08710i
$624$		0			0
$625$	−7760.54	−	13441.6i	−0.496674	−	0.860265i
$626$		0			0
$627$	−351.509	+	1248.27i	−0.0223890	+	0.0795070i
$628$		0			0
$629$	130.060			0.00824459
$630$		0			0
$631$	23727.0			1.49692			0.748461	−	0.663178i	$-0.230793\pi$
$631$	23727.0			1.49692			0.748461	+	0.663178i	$0.230793\pi$
$632$		0			0
$633$	3071.60	−	10907.8i	0.192868	−	0.684904i
$634$		0			0
$635$	−590.736	−	1023.18i	−0.0369175	−	0.0639430i
$636$		0			0
$637$	17692.6	−	14027.0i	1.10048	−	0.872481i
$638$		0			0
$639$	10119.6	−	16543.3i	0.626485	−	1.02417i
$640$		0			0
$641$	17207.0	+	9934.44i	1.06027	+	0.612148i	0.925507	−	0.378730i	$-0.123639\pi$
$641$	17207.0	+	9934.44i	1.06027	+	0.612148i	0.134764	+	0.990878i	$0.456972\pi$
$642$		0			0
$643$			12150.0i			0.745178i	0.927997	+	0.372589i	$0.121530\pi$
$643$			12150.0i			0.745178i	−0.927997	+	0.372589i	$0.878470\pi$
$644$		0			0
$645$	−66.8430	+	17.0044i	−0.00408053	+	0.00103806i
$646$		0			0
$647$	−1830.02	+	3169.69i	−0.111199	+	0.192602i	−0.916254	−	0.400598i	$-0.868802\pi$
$647$	−1830.02	+	3169.69i	−0.111199	+	0.192602i	0.805055	+	0.593200i	$0.202136\pi$
$648$		0			0
$649$	−4113.91	+	2375.17i	−0.248821	+	0.143657i
$650$		0			0
$651$	11627.4	−	3885.24i	0.700019	−	0.233909i
$652$		0			0
$653$	12672.4	−	7316.41i	0.759432	−	0.438458i	−0.0696600	−	0.997571i	$-0.522191\pi$
$653$	12672.4	−	7316.41i	0.759432	−	0.438458i	0.829092	+	0.559113i	$0.188858\pi$
$654$		0			0
$655$	547.121	−	947.641i	0.0326378	−	0.0565304i
$656$		0			0
$657$	−15043.9	−	27654.8i	−0.893333	−	1.64218i
$658$		0			0
$659$		−	28047.8i		−	1.65795i	−0.559286	−	0.828975i	$-0.688925\pi$
$659$		−	28047.8i		−	1.65795i	0.559286	−	0.828975i	$-0.311075\pi$
$660$		0			0
$661$	−25318.8	−	14617.8i	−1.48985	−	0.860162i	−0.489912	−	0.871772i	$-0.662971\pi$
$661$	−25318.8	−	14617.8i	−1.48985	−	0.860162i	−0.999933	+	0.0116092i	$0.996305\pi$
$662$		0			0
$663$	166.066	−	161.904i	0.00972772	−	0.00948390i
$664$		0			0
$665$	−120.357	−	177.074i	−0.00701841	−	0.0103257i
$666$		0			0
$667$	632.062	+	1094.76i	0.0366920	+	0.0635524i
$668$		0			0
$669$	−18971.2	−	5342.24i	−1.09636	−	0.308734i
$670$		0			0
$671$	3787.47			0.217904
$672$		0			0
$673$	8911.77			0.510436			0.255218	−	0.966883i	$-0.417853\pi$
$673$	8911.77			0.510436			0.255218	+	0.966883i	$0.417853\pi$
$674$		0			0
$675$	3882.24	+	17062.0i	0.221374	+	0.972914i
$676$		0			0
$677$	4990.32	+	8643.48i	0.283299	+	0.490688i	0.972195	−	0.234172i	$-0.0752378\pi$
$677$	4990.32	+	8643.48i	0.283299	+	0.490688i	−0.688896	+	0.724860i	$0.741904\pi$
$678$		0			0
$679$	236.021	−	488.319i	0.0133397	−	0.0275993i
$680$		0			0
$681$	−18046.1	−	18510.1i	−1.01546	−	1.04157i
$682$		0			0
$683$	−15066.1	−	8698.39i	−0.844051	−	0.487313i	0.0145884	−	0.999894i	$-0.495356\pi$
$683$	−15066.1	−	8698.39i	−0.844051	−	0.487313i	−0.858639	+	0.512581i	$0.828690\pi$
$684$		0			0
$685$		−	1188.61i		−	0.0662986i
$686$		0			0
$687$	−334.719	−	1315.75i	−0.0185885	−	0.0730701i
$688$		0			0
$689$	−14301.2	+	24770.4i	−0.790756	+	1.36963i
$690$		0			0
$691$	5002.68	−	2888.30i	0.275414	−	0.159010i	−0.355932	−	0.934512i	$-0.615836\pi$
$691$	5002.68	−	2888.30i	0.275414	−	0.159010i	0.631345	+	0.775502i	$0.282503\pi$
$692$		0			0
$693$	272.729	+	5678.42i	0.0149497	+	0.311263i
$694$		0			0
$695$	495.529	−	286.094i	0.0270453	−	0.0156146i
$696$		0			0
$697$	172.376	−	298.564i	0.00936758	−	0.0162251i
$698$		0			0
$699$	−5846.92	−	22983.8i	−0.316382	−	1.24367i
$700$		0			0
$701$		−	15013.5i		−	0.808916i	−0.914557	−	0.404458i	$-0.867460\pi$
$701$		−	15013.5i		−	0.808916i	0.914557	−	0.404458i	$-0.132540\pi$
$702$		0			0
$703$	−3646.55	−	2105.34i	−0.195636	−	0.112951i
$704$		0			0
$705$	638.814	+	655.237i	0.0341264	+	0.0350038i
$706$		0			0
$707$	−15398.2	+	10466.2i	−0.819109	+	0.556749i
$708$		0			0
$709$	2499.40	+	4329.10i	0.132394	+	0.229313i	0.924599	−	0.380942i	$-0.124400\pi$
$709$	2499.40	+	4329.10i	0.132394	+	0.229313i	−0.792205	+	0.610255i	$0.791067\pi$
$710$		0			0
$711$	−259.267	+	10212.8i	−0.0136755	+	0.538693i
$712$		0			0
$713$	−971.866			−0.0510472
$714$		0			0
$715$	394.110			0.0206138
$716$		0			0
$717$	21842.8	+	6150.88i	1.13770	+	0.320375i
$718$		0			0
$719$	−3748.62	−	6492.79i	−0.194436	−	0.336774i	0.752279	−	0.658844i	$-0.228954\pi$
$719$	−3748.62	−	6492.79i	−0.194436	−	0.336774i	−0.946716	+	0.322071i	$0.895621\pi$
$720$		0			0
$721$	4464.37	−	328.154i	0.230599	−	0.0169502i
$722$		0			0
$723$	4961.86	−	4837.49i	0.255233	−	0.248836i
$724$		0			0
$725$	−17897.7	−	10333.2i	−0.916832	−	0.529333i
$726$		0			0
$727$			2079.71i			0.106096i	0.998592	+	0.0530482i	$0.0168937\pi$
$727$			2079.71i			0.106096i	−0.998592	+	0.0530482i	$0.983106\pi$
$728$		0			0
$729$	1497.27	−	19626.0i	0.0760693	−	0.997103i
$730$		0			0
$731$	−8.54541	+	14.8011i	−0.000432371	+	0.000748889i
$732$		0			0
$733$	−331.894	+	191.619i	−0.0167241	+	0.00965567i	−0.508339	−	0.861157i	$-0.669740\pi$
$733$	−331.894	+	191.619i	−0.0167241	+	0.00965567i	0.491615	+	0.870813i	$0.336407\pi$
$734$		0			0
$735$	−746.434	−	569.025i	−0.0374594	−	0.0285562i
$736$		0			0
$737$	−1352.77	+	781.023i	−0.0676119	+	0.0390358i
$738$		0			0
$739$	−1523.42	+	2638.64i	−0.0758320	+	0.131345i	−0.901448	−	0.432888i	$-0.857495\pi$
$739$	−1523.42	+	2638.64i	−0.0758320	+	0.131345i	0.825616	+	0.564233i	$0.190828\pi$
$740$		0			0
$741$	−7276.86	+	1851.18i	−0.360759	+	0.0917745i
$742$		0			0
$743$		−	7608.81i		−	0.375694i	−0.982198	−	0.187847i	$-0.939849\pi$
$743$		−	7608.81i		−	0.375694i	0.982198	−	0.187847i	$-0.0601508\pi$
$744$		0			0
$745$	−1341.81	−	774.693i	−0.0659866	−	0.0380974i
$746$		0			0
$747$	−12428.6	−	7602.60i	−0.608753	−	0.372375i
$748$		0			0
$749$	26743.6	−	1965.79i	1.30466	−	0.0958991i
$750$		0			0
$751$	−6607.85	−	11445.1i	−0.321070	−	0.556110i	0.659639	−	0.751583i	$-0.270709\pi$
$751$	−6607.85	−	11445.1i	−0.321070	−	0.556110i	−0.980709	+	0.195473i	$0.937376\pi$
$752$		0			0
$753$	−4390.34	+	15590.8i	−0.212474	+	0.754530i
$754$		0			0
$755$	1229.20			0.0592519
$756$		0			0
$757$	24928.8			1.19690			0.598449	−	0.801161i	$-0.295784\pi$
$757$	24928.8			1.19690			0.598449	+	0.801161i	$0.295784\pi$
$758$		0			0
$759$	122.159	−	433.808i	0.00584203	−	0.0207460i
$760$		0			0
$761$	−18141.8	−	31422.6i	−0.864179	−	1.49680i	−0.867860	−	0.496810i	$-0.834505\pi$
$761$	−18141.8	−	31422.6i	−0.864179	−	1.49680i	0.00368010	−	0.999993i	$-0.498829\pi$
$762$		0			0
$763$	28953.0	−	19679.4i	1.37375	−	0.933736i
$764$		0			0
$765$	−8.22460	−	5.03100i	−0.000388707	−	0.000237773i
$766$		0			0
$767$	−23819.8	−	13752.4i	−1.12136	−	0.647418i
$768$		0			0
$769$			19079.7i			0.894708i	0.894357	+	0.447354i	$0.147634\pi$
$769$			19079.7i			0.894708i	−0.894357	+	0.447354i	$0.852366\pi$
$770$		0			0
$771$	−5586.06	+	1421.05i	−0.260930	+	0.0663787i
$772$		0			0
$773$	1279.58	−	2216.29i	0.0595383	−	0.103123i	−0.834720	−	0.550675i	$-0.814370\pi$
$773$	1279.58	−	2216.29i	0.0595383	−	0.103123i	0.894258	+	0.447551i	$0.147704\pi$
$774$		0			0
$775$	13759.8	−	7944.25i	0.637765	−	0.368214i
$776$		0			0
$777$	−18086.7	−	3687.38i	−0.835078	−	0.170250i
$778$		0			0
$779$	−9665.94	+	5580.63i	−0.444568	+	0.256671i
$780$		0			0
$781$	4082.88	−	7071.76i	0.187064	−	0.324004i
$782$		0			0
$783$	15800.5	+	17051.8i	0.721155	+	0.778267i
$784$		0			0
$785$		−	1590.95i		−	0.0723358i
$786$		0			0
$787$	−32921.5	−	19007.2i	−1.49114	−	0.860908i	−0.491188	−	0.871053i	$-0.663437\pi$
$787$	−32921.5	−	19007.2i	−1.49114	−	0.860908i	−0.999949	+	0.0101450i	$0.996771\pi$
$788$		0			0
$789$	−19498.5	+	19009.8i	−0.879804	+	0.857752i
$790$		0			0
$791$	−6055.38	+	12528.4i	−0.272193	+	0.563158i
$792$		0			0
$793$	10964.9	+	18991.7i	0.491013	+	0.850459i
$794$		0			0
$795$	1144.49	+	322.287i	0.0510578	+	0.0143778i
$796$		0			0
$797$	−264.307			−0.0117468			−0.00587342	−	0.999983i	$-0.501870\pi$
$797$	−264.307			−0.0117468			−0.00587342	+	0.999983i	$0.501870\pi$
$798$		0			0
$799$	226.757			0.0100402
$800$		0			0
$801$	−627.120	+	24703.0i	−0.0276631	+	1.08968i
$802$		0			0
$803$	−6628.01	−	11480.1i	−0.291279	−	0.504511i
$804$		0			0
$805$	41.8275	+	61.5381i	0.00183134	+	0.00269433i
$806$		0			0
$807$	−11999.6	−	12308.1i	−0.523428	−	0.536884i
$808$		0			0
$809$	22385.9	+	12924.5i	0.972865	+	0.561684i	0.900109	−	0.435666i	$-0.143487\pi$
$809$	22385.9	+	12924.5i	0.972865	+	0.561684i	0.0727566	+	0.997350i	$0.476820\pi$
$810$		0			0
$811$			29501.8i			1.27737i	0.769468	+	0.638686i	$0.220522\pi$
$811$			29501.8i			1.27737i	−0.769468	+	0.638686i	$0.779478\pi$
$812$		0			0
$813$	−4405.26	−	17316.7i	−0.190036	−	0.747017i
$814$		0			0
$815$	626.938	−	1085.89i	0.0269456	−	0.0466712i
$816$		0			0
$817$	479.182	−	276.656i	0.0205195	−	0.0118469i
$818$		0			0
$819$	−27684.0	+	17806.8i	−1.18114	+	0.759729i
$820$		0			0
$821$	−19688.6	+	11367.2i	−0.836953	+	0.483215i	−0.856227	−	0.516599i	$-0.827198\pi$
$821$	−19688.6	+	11367.2i	−0.836953	+	0.483215i	0.0192746	+	0.999814i	$0.493864\pi$
$822$		0			0
$823$	10968.7	−	18998.4i	0.464577	−	0.804670i	−0.534606	−	0.845102i	$-0.679540\pi$
$823$	10968.7	−	18998.4i	0.464577	−	0.804670i	0.999182	+	0.0404314i	$0.0128732\pi$
$824$		0			0
$825$	1816.49	+	7140.48i	0.0766569	+	0.301333i
$826$		0			0
$827$			14680.4i			0.617276i	0.951180	+	0.308638i	$0.0998731\pi$
$827$			14680.4i			0.617276i	−0.951180	+	0.308638i	$0.900127\pi$
$828$		0			0
$829$	22703.0	+	13107.6i	0.951155	+	0.549150i	0.893440	−	0.449183i	$-0.148285\pi$
$829$	22703.0	+	13107.6i	0.951155	+	0.549150i	0.0577157	+	0.998333i	$0.481618\pi$
$830$		0			0
$831$	−13007.4	−	13341.8i	−0.542985	−	0.556944i
$832$		0			0
$833$	−230.077	+	34.0074i	−0.00956986	+	0.00141451i
$834$		0			0
$835$	914.982	+	1584.79i	0.0379213	+	0.0656815i
$836$		0			0
$837$	−17427.0	+	3965.28i	−0.719671	+	0.163752i
$838$		0			0
$839$	20763.2			0.854382			0.427191	−	0.904161i	$-0.359503\pi$
$839$	20763.2			0.854382			0.427191	+	0.904161i	$0.359503\pi$
$840$		0			0
$841$	−3067.27			−0.125764
$842$		0			0
$843$	2685.27	+	756.166i	0.109710	+	0.0308941i
$844$		0			0
$845$	562.465	+	974.218i	0.0228987	+	0.0396617i
$846$		0			0
$847$	−1631.58	−	22196.8i	−0.0661885	−	0.900463i
$848$		0			0
$849$	−7277.35	+	7094.95i	−0.294179	+	0.286806i
$850$		0			0
$851$	1267.28	+	731.664i	0.0510479	+	0.0294725i
$852$		0			0
$853$			36.8279i			0.00147827i	1.00000		0.000739134i	$0.000235274\pi$
$853$			36.8279i			0.00147827i	−1.00000		0.000739134i	$0.999765\pi$
$854$		0			0
$855$	149.157	+	274.191i	0.00596616	+	0.0109674i
$856$		0			0
$857$	−12324.1	+	21345.9i	−0.491228	+	0.850832i	−0.999949	−	0.0100996i	$-0.996785\pi$
$857$	−12324.1	+	21345.9i	−0.491228	+	0.850832i	0.508721	+	0.860931i	$0.330118\pi$
$858$		0			0
$859$	16681.8	−	9631.21i	0.662601	−	0.382553i	−0.130666	−	0.991426i	$-0.541712\pi$
$859$	16681.8	−	9631.21i	0.662601	−	0.382553i	0.793267	+	0.608874i	$0.208378\pi$
$860$		0			0
$861$	−32435.9	+	36632.3i	−1.28387	+	1.44997i
$862$		0			0
$863$	1795.72	−	1036.76i	0.0708307	−	0.0408941i	−0.464166	−	0.885748i	$-0.653646\pi$
$863$	1795.72	−	1036.76i	0.0708307	−	0.0408941i	0.534997	+	0.844854i	$0.320313\pi$
$864$		0			0
$865$	121.745	−	210.869i	0.00478551	−	0.00828874i
$866$		0			0
$867$	24738.4	−	6293.27i	0.969042	−	0.246517i
$868$		0			0
$869$			4301.68i			0.167922i
$870$		0			0
$871$	−7832.64	−	4522.17i	−0.304706	−	0.175922i
$872$		0			0
$873$	−412.598	+	674.509i	−0.0159958	+	0.0261497i
$874$		0			0
$875$	−2192.89	−	1059.90i	−0.0847236	−	0.0409497i
$876$		0			0
$877$	−9254.98	−	16030.1i	−0.356349	−	0.617215i	0.630999	−	0.775784i	$-0.282645\pi$
$877$	−9254.98	−	16030.1i	−0.356349	−	0.617215i	−0.987348	+	0.158569i	$0.949312\pi$
$878$		0			0
$879$	−11870.6	+	42154.3i	−0.455499	+	1.61755i
$880$		0			0
$881$	18519.0			0.708197			0.354098	−	0.935208i	$-0.384788\pi$
$881$	18519.0			0.708197			0.354098	+	0.935208i	$0.384788\pi$
$882$		0			0
$883$	17433.5			0.664421			0.332210	−	0.943205i	$-0.392206\pi$
$883$	17433.5			0.664421			0.332210	+	0.943205i	$0.392206\pi$
$884$		0			0
$885$	−309.919	+	1100.57i	−0.0117716	+	0.0418027i
$886$		0			0
$887$	6522.36	+	11297.1i	0.246899	+	0.427642i	0.962664	−	0.270700i	$-0.0872551\pi$
$887$	6522.36	+	11297.1i	0.246899	+	0.427642i	−0.715765	+	0.698341i	$0.753922\pi$
$888$		0			0
$889$	37409.4	+	18081.2i	1.41133	+	0.682142i
$890$		0			0
$891$	420.529	−	8277.22i	0.0158117	−	0.311220i
$892$		0			0
$893$	−6357.68	−	3670.61i	−0.238244	−	0.137550i
$894$		0			0
$895$		−	1026.19i		−	0.0383259i
$896$		0			0
$897$	2528.92	−	643.338i	0.0941338	−	0.0239470i
$898$		0			0
$899$	10554.3	−	18280.5i	0.391551	−	0.678186i
$900$		0			0
$901$	255.155	−	147.314i	0.00943446	−	0.00544699i
$902$		0			0
$903$	1607.99	−	1816.02i	0.0592585	−	0.0669251i
$904$		0			0
$905$	−280.491	+	161.941i	−0.0103026	+	0.00594820i
$906$		0			0
$907$	−4239.49	+	7343.01i	−0.155204	+	0.268821i	−0.933133	−	0.359531i	$-0.882937\pi$
$907$	−4239.49	+	7343.01i	−0.155204	+	0.268821i	0.777929	+	0.628352i	$0.216270\pi$
$908$		0			0
$909$	23843.5	−	12970.6i	0.870010	−	0.473277i
$910$		0			0
$911$		−	2461.64i		−	0.0895256i	−0.998998	−	0.0447628i	$-0.985747\pi$
$911$		−	2461.64i		−	0.0895256i	0.998998	−	0.0447628i	$-0.0142532\pi$
$912$		0			0
$913$	−5312.85	−	3067.37i	−0.192584	−	0.111189i
$914$		0			0
$915$	652.742	−	636.382i	0.0235836	−	0.0229925i
$916$		0			0
$917$	2821.02	+	38378.7i	0.101590	+	1.38209i
$918$		0			0
$919$	19763.8	+	34232.0i	0.709411	+	1.22874i	0.965076	+	0.261970i	$0.0843722\pi$
$919$	19763.8	+	34232.0i	0.709411	+	1.22874i	−0.255665	+	0.966765i	$0.582294\pi$
$920$		0			0
$921$	23263.6	+	6550.97i	0.832313	+	0.234378i
$922$		0			0
$923$	47280.3			1.68608
$924$		0			0
$925$	−23923.1			−0.850365
$926$		0			0
$927$	−6523.89	−	165.618i	−0.231147	−	0.00586798i
$928$		0			0
$929$	16359.4	+	28335.2i	0.577754	+	1.00070i	0.995736	+	0.0922440i	$0.0294040\pi$
$929$	16359.4	+	28335.2i	0.577754	+	1.00070i	−0.417983	+	0.908455i	$0.637263\pi$
$930$		0			0
$931$	7001.25	+	2770.87i	0.246462	+	0.0975419i
$932$		0			0
$933$	−13348.4	−	13691.6i	−0.468390	−	0.480432i
$934$		0			0
$935$	−3.51577	−	2.02983i	−0.000122971	−	7.09973e-5i
$936$		0			0
$937$			21523.1i			0.750406i	0.926943	+	0.375203i	$0.122427\pi$
$937$			21523.1i			0.750406i	−0.926943	+	0.375203i	$0.877573\pi$
$938$		0			0
$939$	1375.31	+	5406.25i	0.0477972	+	0.187887i
$940$		0			0
$941$	21454.9	−	37161.0i	0.743263	−	1.28737i	−0.207738	−	0.978184i	$-0.566610\pi$
$941$	21454.9	−	37161.0i	0.743263	−	1.28737i	0.951002	−	0.309186i	$-0.100056\pi$
$942$		0			0
$943$	3359.19	−	1939.43i	0.116002	−	0.0669740i
$944$		0			0
$945$	1001.11	+	932.808i	0.0344614	+	0.0321103i
$946$		0			0
$947$	−8938.35	+	5160.56i	−0.306713	+	0.177081i	−0.645455	−	0.763798i	$-0.723332\pi$
$947$	−8938.35	+	5160.56i	−0.306713	+	0.177081i	0.338741	+	0.940879i	$0.389999\pi$
$948$		0			0
$949$	38376.6	−	66470.2i	1.31271	−	2.27367i
$950$		0			0
$951$	−3421.41	−	13449.3i	−0.116663	−	0.458594i
$952$		0			0
$953$		−	55448.9i		−	1.88475i	−0.334558	−	0.942375i	$-0.608587\pi$
$953$		−	55448.9i		−	1.88475i	0.334558	−	0.942375i	$-0.391413\pi$
$954$		0			0
$955$	1018.12	+	587.812i	0.0344980	+	0.0199174i
$956$		0			0
$957$	6833.17	+	7008.84i	0.230810	+	0.236744i
$958$		0			0
$959$	23498.1	+	34571.2i	0.791232	+	1.16409i
$960$		0			0
$961$	−6781.32	−	11745.6i	−0.227630	−	0.394266i
$962$		0			0
$963$	−39081.1	−	992.129i	−1.30776	−	0.0331993i
$964$		0			0
$965$	−729.161			−0.0243239
$966$		0			0
$967$	14843.5			0.493626			0.246813	−	0.969063i	$-0.420617\pi$
$967$	14843.5			0.493626			0.246813	+	0.969063i	$0.420617\pi$
$968$		0			0
$969$	74.4496	+	20.9648i	0.00246818	+	0.000695034i
$970$		0			0
$971$	11922.3	+	20650.1i	0.394033	+	0.682485i	0.992977	−	0.118306i	$-0.0377463\pi$
$971$	11922.3	+	20650.1i	0.394033	+	0.682485i	−0.598944	+	0.800791i	$0.704413\pi$
$972$		0			0
$973$	−8756.75	+	18117.4i	−0.288519	+	0.596935i
$974$		0			0
$975$	−30546.0	+	29780.4i	−1.00334	+	0.978191i
$976$		0			0
$977$	−11571.6	−	6680.87i	−0.378923	−	0.218772i	0.298426	−	0.954433i	$-0.403538\pi$
$977$	−11571.6	−	6680.87i	−0.378923	−	0.218772i	−0.677350	+	0.735661i	$0.736872\pi$
$978$		0			0
$979$			10405.0i			0.339679i
$980$		0			0
$981$	−44832.5	+	24388.4i	−1.45911	+	0.793744i
$982$		0			0
$983$	−2649.18	+	4588.51i	−0.0859569	+	0.148882i	−0.905799	−	0.423709i	$-0.860728\pi$
$983$	−2649.18	+	4588.51i	−0.0859569	+	0.148882i	0.819842	+	0.572590i	$0.194061\pi$
$984$		0			0
$985$	1784.53	−	1030.30i	0.0577258	−	0.0333280i
$986$		0			0
$987$	−31533.7	−	6428.87i	−1.01695	−	0.207328i
$988$		0			0
$989$	−166.529	+	96.1457i	−0.00535422	+	0.00309126i
$990$		0			0
$991$	8526.29	−	14768.0i	0.273306	−	0.473381i	−0.696400	−	0.717654i	$-0.745216\pi$
$991$	8526.29	−	14768.0i	0.273306	−	0.473381i	0.969706	+	0.244273i	$0.0785494\pi$
$992$		0			0
$993$	48132.4	−	12244.6i	1.53820	−	0.391308i
$994$		0			0
$995$			1866.72i			0.0594763i
$996$		0			0
$997$	2682.03	+	1548.47i	0.0851963	+	0.0491881i	0.541993	−	0.840383i	$-0.317670\pi$
$997$	2682.03	+	1548.47i	0.0851963	+	0.0491881i	−0.456797	+	0.889571i	$0.651003\pi$
$998$		0			0
$999$	25709.4	+	7949.21i	0.814224	+	0.251754i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bc.f.17.15		48
3.2	odd	2	inner	336.4.bc.f.17.6		48
4.3	odd	2		168.4.u.a.17.10	✓	48
7.5	odd	6	inner	336.4.bc.f.257.6		48
12.11	even	2		168.4.u.a.17.19	yes	48
21.5	even	6	inner	336.4.bc.f.257.15		48
28.19	even	6		168.4.u.a.89.19	yes	48
84.47	odd	6		168.4.u.a.89.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.u.a.17.10	✓	48	4.3	odd	2
168.4.u.a.17.19	yes	48	12.11	even	2
168.4.u.a.89.10	yes	48	84.47	odd	6
168.4.u.a.89.19	yes	48	28.19	even	6
336.4.bc.f.17.6		48	3.2	odd	2	inner
336.4.bc.f.17.15		48	1.1	even	1	trivial
336.4.bc.f.257.6		48	7.5	odd	6	inner
336.4.bc.f.257.15		48	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)

\(f(q)\)	\(=\)	\(q+(1.40845 - 5.00163i) q^{3} +(-0.263312 - 0.456070i) q^{5} +(16.6747 + 8.05944i) q^{7} +(-23.0325 - 14.0891i) q^{9} +O(q^{10})\)	\(q+(1.40845 - 5.00163i) q^{3} +(-0.263312 - 0.456070i) q^{5} +(16.6747 + 8.05944i) q^{7} +(-23.0325 - 14.0891i) q^{9} +(-9.84572 - 5.68443i) q^{11} -65.8264i q^{13} +(-2.65195 + 0.674638i) q^{15} +(-0.339033 + 0.587223i) q^{17} +(19.0112 - 10.9761i) q^{19} +(63.7957 - 72.0493i) q^{21} +(-6.60693 + 3.81451i) q^{23} +(62.3613 - 108.013i) q^{25} +(-102.908 + 95.3565i) q^{27} -165.699i q^{29} +(110.323 + 63.6953i) q^{31} +(-42.2986 + 41.2384i) q^{33} +(-0.714981 - 9.72697i) q^{35} +(-95.9053 - 166.113i) q^{37} +(-329.239 - 92.7131i) q^{39} -508.434 q^{41} +25.2052 q^{43} +(-0.360849 + 14.2143i) q^{45} +(-167.209 - 289.614i) q^{47} +(213.091 + 268.777i) q^{49} +(2.45956 + 2.52279i) q^{51} +(-376.298 - 217.256i) q^{53} +5.98711i q^{55} +(-28.1222 - 110.546i) q^{57} +(208.919 - 361.858i) q^{59} +(-288.511 + 166.572i) q^{61} +(-270.511 - 420.560i) q^{63} +(-30.0214 + 17.3329i) q^{65} +(68.6985 - 118.989i) q^{67} +(9.77326 + 38.4180i) q^{69} +718.257i q^{71} +(1009.78 + 582.997i) q^{73} +(-452.408 - 464.039i) q^{75} +(-118.361 - 174.137i) q^{77} +(-189.187 - 327.682i) q^{79} +(331.997 + 649.014i) q^{81} +539.610 q^{83} +0.357086 q^{85} +(-828.766 - 233.379i) q^{87} +(-457.610 - 792.604i) q^{89} +(530.524 - 1097.64i) q^{91} +(473.965 - 462.085i) q^{93} +(-10.0117 - 5.78029i) q^{95} -29.2850i q^{97} +(146.684 + 269.644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{7} + 14 q^{9}+O(q^{10}) \) 48 * q - 12 * q^7 + 14 * q^9	\( 48 q - 12 q^{7} + 14 q^{9} + 88 q^{15} + 270 q^{19} + 50 q^{21} - 438 q^{25} - 216 q^{31} - 372 q^{33} + 66 q^{37} - 242 q^{39} - 900 q^{43} - 294 q^{45} + 60 q^{49} + 138 q^{51} + 1384 q^{57} + 108 q^{61} - 1096 q^{63} - 6 q^{67} - 1206 q^{73} + 594 q^{75} + 588 q^{79} - 54 q^{81} - 240 q^{85} + 3522 q^{87} - 234 q^{91} - 608 q^{93} - 1988 q^{99}+O(q^{100}) \) 48 * q - 12 * q^7 + 14 * q^9 + 88 * q^15 + 270 * q^19 + 50 * q^21 - 438 * q^25 - 216 * q^31 - 372 * q^33 + 66 * q^37 - 242 * q^39 - 900 * q^43 - 294 * q^45 + 60 * q^49 + 138 * q^51 + 1384 * q^57 + 108 * q^61 - 1096 * q^63 - 6 * q^67 - 1206 * q^73 + 594 * q^75 + 588 * q^79 - 54 * q^81 - 240 * q^85 + 3522 * q^87 - 234 * q^91 - 608 * q^93 - 1988 * q^99

Introduction

L-functions

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