LMFDB - Embedded newform 378.3.q.a.71.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,3,Mod(71,378)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.71"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$10.2997539928$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.8
Character	$\chi$	$=$	378.71
Dual form			378.3.q.a.197.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-5.20486 - 3.00503i) q^{5} +(-1.32288 - 2.29129i) q^{7} -2.82843i q^{8} -8.49950 q^{10} +(-15.5696 + 8.98910i) q^{11} +(-1.24017 + 2.14804i) q^{13} +(-3.24037 - 1.87083i) q^{14} +(-2.00000 - 3.46410i) q^{16} +26.3841i q^{17} +5.05223 q^{19} +(-10.4097 + 6.01006i) q^{20} +(-12.7125 + 22.0187i) q^{22} +(-29.8982 - 17.2617i) q^{23} +(5.56039 + 9.63088i) q^{25} +3.50774i q^{26} -5.29150 q^{28} +(17.4418 - 10.0700i) q^{29} +(0.457601 - 0.792588i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(18.6564 + 32.3138i) q^{34} +15.9011i q^{35} -69.8690 q^{37} +(6.18769 - 3.57247i) q^{38} +(-8.49950 + 14.7216i) q^{40} +(-43.6552 - 25.2043i) q^{41} +(1.22348 + 2.11914i) q^{43} +35.9564i q^{44} -48.8235 q^{46} +(45.5238 - 26.2832i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(13.6201 + 7.86358i) q^{50} +(2.48035 + 4.29609i) q^{52} -91.2148i q^{53} +108.050 q^{55} +(-6.48074 + 3.74166i) q^{56} +(14.2412 - 24.6664i) q^{58} +(-13.6502 - 7.88092i) q^{59} +(39.3826 + 68.2126i) q^{61} -1.29429i q^{62} -8.00000 q^{64} +(12.9099 - 7.45351i) q^{65} +(-1.52405 + 2.63973i) q^{67} +(45.6987 + 26.3841i) q^{68} +(11.2438 + 19.4748i) q^{70} -58.7927i q^{71} -8.20759 q^{73} +(-85.5717 + 49.4049i) q^{74} +(5.05223 - 8.75072i) q^{76} +(41.1932 + 23.7829i) q^{77} +(-23.0285 - 39.8865i) q^{79} +24.0402i q^{80} -71.2887 q^{82} +(-33.1885 + 19.1614i) q^{83} +(79.2851 - 137.326i) q^{85} +(2.99691 + 1.73027i) q^{86} +(25.4250 + 44.0374i) q^{88} +88.0689i q^{89} +6.56238 q^{91} +(-59.7964 + 34.5235i) q^{92} +(37.1700 - 64.3804i) q^{94} +(-26.2962 - 15.1821i) q^{95} +(2.91032 + 5.04083i) q^{97} +9.89949i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} - 36 q^{5} - 48 q^{16} + 24 q^{19} - 72 q^{20} + 24 q^{22} + 72 q^{23} + 72 q^{25} + 108 q^{29} - 60 q^{31} - 48 q^{34} - 168 q^{37} - 144 q^{38} - 108 q^{41} + 60 q^{43} + 324 q^{47} - 84 q^{49}+ \cdots + 48 q^{97}+O(q^{100}) $ 24 * q + 24 * q^4 - 36 * q^5 - 48 * q^16 + 24 * q^19 - 72 * q^20 + 24 * q^22 + 72 * q^23 + 72 * q^25 + 108 * q^29 - 60 * q^31 - 48 * q^34 - 168 * q^37 - 144 * q^38 - 108 * q^41 + 60 * q^43 + 324 * q^47 - 84 * q^49 - 144 * q^50 + 264 * q^55 + 432 * q^59 - 192 * q^64 + 180 * q^65 + 72 * q^67 - 72 * q^68 + 24 * q^73 - 288 * q^74 + 24 * q^76 + 12 * q^79 - 288 * q^82 - 756 * q^83 - 156 * q^85 - 360 * q^86 - 48 * q^88 - 168 * q^91 + 144 * q^92 + 936 * q^95 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	−5.20486	−	3.00503i	−1.04097	−	0.601006i	−0.120864	−	0.992669i	$-0.538566\pi$
$5$	−5.20486	−	3.00503i	−1.04097	−	0.601006i	−0.920109	+	0.391663i	$0.871900\pi$
$6$		0			0
$7$	−1.32288	−	2.29129i	−0.188982	−	0.327327i
$7$	−1.32288	−	2.29129i	−0.188982	−	0.327327i
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	−8.49950			−0.849950
$11$	−15.5696	+	8.98910i	−1.41542	+	0.817191i	−0.995892	−	0.0905531i	$-0.971137\pi$
$11$	−15.5696	+	8.98910i	−1.41542	+	0.817191i	−0.419525	+	0.907744i	$0.637803\pi$
$12$		0			0
$13$	−1.24017	+	2.14804i	−0.0953979	+	0.165234i	−0.909775	−	0.415103i	$-0.863746\pi$
$13$	−1.24017	+	2.14804i	−0.0953979	+	0.165234i	0.814377	+	0.580337i	$0.197079\pi$
$14$	−3.24037	−	1.87083i	−0.231455	−	0.133631i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$			26.3841i			1.55201i	0.630728	+	0.776004i	$0.282756\pi$
$17$			26.3841i			1.55201i	−0.630728	+	0.776004i	$0.717244\pi$
$18$		0			0
$19$	5.05223			0.265907			0.132953	−	0.991122i	$-0.457554\pi$
$19$	5.05223			0.265907			0.132953	+	0.991122i	$0.457554\pi$
$20$	−10.4097	+	6.01006i	−0.520486	+	0.300503i
$21$		0			0
$22$	−12.7125	+	22.0187i	−0.577841	+	1.00085i
$23$	−29.8982	−	17.2617i	−1.29992	−	0.750510i	−0.319531	−	0.947576i	$-0.603525\pi$
$23$	−29.8982	−	17.2617i	−1.29992	−	0.750510i	−0.980390	+	0.197066i	$0.936859\pi$
$24$		0			0
$25$	5.56039	+	9.63088i	0.222416	+	0.385235i
$26$			3.50774i			0.134913i
$27$		0			0
$28$	−5.29150			−0.188982
$29$	17.4418	−	10.0700i	0.601442	−	0.347243i	−0.168167	−	0.985759i	$-0.553785\pi$
$29$	17.4418	−	10.0700i	0.601442	−	0.347243i	0.769609	+	0.638516i	$0.220451\pi$
$30$		0			0
$31$	0.457601	−	0.792588i	0.0147613	−	0.0255673i	−0.858550	−	0.512729i	$-0.828634\pi$
$31$	0.457601	−	0.792588i	0.0147613	−	0.0255673i	0.873312	+	0.487162i	$0.161968\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$		0			0
$34$	18.6564	+	32.3138i	0.548718	+	0.950407i
$35$			15.9011i			0.454318i
$36$		0			0
$37$	−69.8690			−1.88835			−0.944176	−	0.329441i	$-0.893140\pi$
$37$	−69.8690			−1.88835			−0.944176	+	0.329441i	$0.893140\pi$
$38$	6.18769	−	3.57247i	0.162834	−	0.0940123i
$39$		0			0
$40$	−8.49950	+	14.7216i	−0.212488	+	0.368039i
$41$	−43.6552	−	25.2043i	−1.06476	−	0.614740i	−0.138016	−	0.990430i	$-0.544072\pi$
$41$	−43.6552	−	25.2043i	−1.06476	−	0.614740i	−0.926745	+	0.375690i	$0.877406\pi$
$42$		0			0
$43$	1.22348	+	2.11914i	0.0284531	+	0.0492823i	0.879901	−	0.475156i	$-0.157609\pi$
$43$	1.22348	+	2.11914i	0.0284531	+	0.0492823i	−0.851448	+	0.524439i	$0.824275\pi$
$44$			35.9564i			0.817191i
$45$		0			0
$46$	−48.8235			−1.06138
$47$	45.5238	−	26.2832i	0.968592	−	0.559217i	0.0697853	−	0.997562i	$-0.477769\pi$
$47$	45.5238	−	26.2832i	0.968592	−	0.559217i	0.898807	+	0.438345i	$0.144435\pi$
$48$		0			0
$49$	−3.50000	+	6.06218i	−0.0714286	+	0.123718i
$50$	13.6201	+	7.86358i	0.272402	+	0.157272i
$51$		0			0
$52$	2.48035	+	4.29609i	0.0476990	+	0.0826170i
$53$		−	91.2148i		−	1.72103i	−0.509421	−	0.860517i	$-0.670140\pi$
$53$		−	91.2148i		−	1.72103i	0.509421	−	0.860517i	$-0.329860\pi$
$54$		0			0
$55$	108.050			1.96455
$56$	−6.48074	+	3.74166i	−0.115728	+	0.0668153i
$57$		0			0
$58$	14.2412	−	24.6664i	0.245538	−	0.425284i
$59$	−13.6502	−	7.88092i	−0.231359	−	0.133575i	0.379840	−	0.925052i	$-0.375979\pi$
$59$	−13.6502	−	7.88092i	−0.231359	−	0.133575i	−0.611199	+	0.791477i	$0.709312\pi$
$60$		0			0
$61$	39.3826	+	68.2126i	0.645616	+	1.11824i	0.984159	+	0.177289i	$0.0567327\pi$
$61$	39.3826	+	68.2126i	0.645616	+	1.11824i	−0.338543	+	0.940951i	$0.609934\pi$
$62$		−	1.29429i		−	0.0208757i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	12.9099	−	7.45351i	0.198613	−	0.114669i
$66$		0			0
$67$	−1.52405	+	2.63973i	−0.0227470	+	0.0393990i	−0.877175	−	0.480171i	$-0.840575\pi$
$67$	−1.52405	+	2.63973i	−0.0227470	+	0.0393990i	0.854428	+	0.519570i	$0.173908\pi$
$68$	45.6987	+	26.3841i	0.672039	+	0.388002i
$69$		0			0
$70$	11.2438	+	19.4748i	0.160626	+	0.278212i
$71$		−	58.7927i		−	0.828066i	−0.910262	−	0.414033i	$-0.864120\pi$
$71$		−	58.7927i		−	0.828066i	0.910262	−	0.414033i	$-0.135880\pi$
$72$		0			0
$73$	−8.20759			−0.112433			−0.0562164	−	0.998419i	$-0.517904\pi$
$73$	−8.20759			−0.112433			−0.0562164	+	0.998419i	$0.517904\pi$
$74$	−85.5717	+	49.4049i	−1.15637	+	0.667633i
$75$		0			0
$76$	5.05223	−	8.75072i	0.0664767	−	0.115141i
$77$	41.1932	+	23.7829i	0.534977	+	0.308869i
$78$		0			0
$79$	−23.0285	−	39.8865i	−0.291500	−	0.504892i	0.682665	−	0.730732i	$-0.260821\pi$
$79$	−23.0285	−	39.8865i	−0.291500	−	0.504892i	−0.974165	+	0.225839i	$0.927488\pi$
$80$			24.0402i			0.300503i
$81$		0			0
$82$	−71.2887			−0.869374
$83$	−33.1885	+	19.1614i	−0.399861	+	0.230860i	−0.686424	−	0.727202i	$-0.740821\pi$
$83$	−33.1885	+	19.1614i	−0.399861	+	0.230860i	0.286563	+	0.958061i	$0.407487\pi$
$84$		0			0
$85$	79.2851	−	137.326i	0.932765	−	1.61560i
$86$	2.99691	+	1.73027i	0.0348478	+	0.0201194i
$87$		0			0
$88$	25.4250	+	44.0374i	0.288921	+	0.500425i
$89$			88.0689i			0.989538i	0.869025	+	0.494769i	$0.164747\pi$
$89$			88.0689i			0.989538i	−0.869025	+	0.494769i	$0.835253\pi$
$90$		0			0
$91$	6.56238			0.0721141
$92$	−59.7964	+	34.5235i	−0.649961	+	0.375255i
$93$		0			0
$94$	37.1700	−	64.3804i	0.395426	−	0.684898i
$95$	−26.2962	−	15.1821i	−0.276802	−	0.159812i
$96$		0			0
$97$	2.91032	+	5.04083i	0.0300033	+	0.0519673i	0.880637	−	0.473791i	$-0.157115\pi$
$97$	2.91032	+	5.04083i	0.0300033	+	0.0519673i	−0.850634	+	0.525759i	$0.823782\pi$
$98$			9.89949i			0.101015i
$99$		0			0
$100$	22.2416			0.222416
$101$	49.6443	−	28.6621i	0.491528	−	0.283784i	−0.233680	−	0.972313i	$-0.575077\pi$
$101$	49.6443	−	28.6621i	0.491528	−	0.283784i	0.725208	+	0.688530i	$0.241744\pi$
$102$		0			0
$103$	2.65907	−	4.60565i	0.0258162	−	0.0447150i	−0.852829	−	0.522191i	$-0.825115\pi$
$103$	2.65907	−	4.60565i	0.0258162	−	0.0447150i	0.878645	+	0.477476i	$0.158448\pi$
$104$	6.07558	+	3.50774i	0.0584191	+	0.0337283i
$105$		0			0
$106$	−64.4986	−	111.715i	−0.608478	−	1.05391i
$107$			9.07038i			0.0847699i	0.999101	+	0.0423850i	$0.0134956\pi$
$107$			9.07038i			0.0847699i	−0.999101	+	0.0423850i	$0.986504\pi$
$108$		0			0
$109$	−137.837			−1.26456			−0.632281	−	0.774739i	$-0.717881\pi$
$109$	−137.837			−1.26456			−0.632281	+	0.774739i	$0.717881\pi$
$110$	132.334	−	76.4029i	1.20303	−	0.694572i
$111$		0			0
$112$	−5.29150	+	9.16515i	−0.0472456	+	0.0818317i
$113$	172.652	+	99.6806i	1.52789	+	0.882129i	0.999450	+	0.0331605i	$0.0105573\pi$
$113$	172.652	+	99.6806i	1.52789	+	0.882129i	0.528443	+	0.848969i	$0.322776\pi$
$114$		0			0
$115$	103.744	+	179.690i	0.902122	+	1.56252i
$116$		−	40.2801i		−	0.347243i
$117$		0			0
$118$	−22.2906			−0.188903
$119$	60.4536	−	34.9029i	0.508014	−	0.293302i
$120$		0			0
$121$	101.108	−	175.124i	0.835602	−	1.44731i
$122$	96.4672	+	55.6954i	0.790715	+	0.456520i
$123$		0			0
$124$	−0.915201	−	1.58518i	−0.00738066	−	0.0127837i
$125$			83.4149i			0.667319i
$126$		0			0
$127$	28.7480			0.226362			0.113181	−	0.993574i	$-0.463896\pi$
$127$	28.7480			0.226362			0.113181	+	0.993574i	$0.463896\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	10.5409	−	18.2573i	0.0810835	−	0.140441i
$131$	−213.887	−	123.488i	−1.63272	−	0.942654i	−0.983248	−	0.182272i	$-0.941655\pi$
$131$	−213.887	−	123.488i	−1.63272	−	0.942654i	−0.649476	−	0.760382i	$-0.725012\pi$
$132$		0			0
$133$	−6.68347	−	11.5761i	−0.0502517	−	0.0870385i
$134$			4.31066i			0.0321691i
$135$		0			0
$136$	74.6256			0.548718
$137$	170.567	−	98.4768i	1.24501	−	0.718809i	0.274903	−	0.961472i	$-0.411354\pi$
$137$	170.567	−	98.4768i	1.24501	−	0.718809i	0.970111	+	0.242663i	$0.0780209\pi$
$138$		0			0
$139$	113.493	−	196.575i	0.816496	−	1.41421i	−0.0917531	−	0.995782i	$-0.529247\pi$
$139$	113.493	−	196.575i	0.816496	−	1.41421i	0.908249	−	0.418430i	$-0.137420\pi$
$140$	27.5415	+	15.9011i	0.196725	+	0.113579i
$141$		0			0
$142$	−41.5727	−	72.0061i	−0.292766	−	0.507085i
$143$		−	44.5922i		−	0.311833i
$144$		0			0
$145$	−121.043			−0.834779
$146$	−10.0522	+	5.80364i	−0.0688507	+	0.0397510i
$147$		0			0
$148$	−69.8690	+	121.017i	−0.472088	+	0.817681i
$149$	−130.827	−	75.5330i	−0.878034	−	0.506933i	−0.00802404	−	0.999968i	$-0.502554\pi$
$149$	−130.827	−	75.5330i	−0.878034	−	0.506933i	−0.870010	+	0.493035i	$0.835887\pi$
$150$		0			0
$151$	−42.0460	−	72.8259i	−0.278451	−	0.482291i	0.692549	−	0.721371i	$-0.256488\pi$
$151$	−42.0460	−	72.8259i	−0.278451	−	0.482291i	−0.971000	+	0.239080i	$0.923154\pi$
$152$		−	14.2899i		−	0.0940123i
$153$		0			0
$154$	67.2683			0.436807
$155$	−4.76350	+	2.75021i	−0.0307322	+	0.0177433i
$156$		0			0
$157$	−11.6141	+	20.1162i	−0.0739751	+	0.128129i	−0.900640	−	0.434566i	$-0.856902\pi$
$157$	−11.6141	+	20.1162i	−0.0739751	+	0.128129i	0.826665	+	0.562694i	$0.190235\pi$
$158$	−56.4080	−	32.5672i	−0.357013	−	0.206121i
$159$		0			0
$160$	16.9990	+	29.4431i	0.106244	+	0.184020i
$161$			91.3405i			0.567332i
$162$		0			0
$163$	−244.894			−1.50242			−0.751209	−	0.660064i	$-0.770529\pi$
$163$	−244.894			−1.50242			−0.751209	+	0.660064i	$0.770529\pi$
$164$	−87.3104	+	50.4087i	−0.532381	+	0.307370i
$165$		0			0
$166$	−27.0983	+	46.9356i	−0.163243	+	0.282744i
$167$	80.3710	+	46.4022i	0.481263	+	0.277858i	0.720943	−	0.692995i	$-0.243709\pi$
$167$	80.3710	+	46.4022i	0.481263	+	0.277858i	−0.239679	+	0.970852i	$0.577042\pi$
$168$		0			0
$169$	81.4239	+	141.030i	0.481798	+	0.834499i
$170$		−	224.252i		−	1.31913i
$171$		0			0
$172$	4.89394			0.0284531
$173$	−155.555	+	89.8099i	−0.899164	+	0.519132i	−0.876929	−	0.480620i	$-0.840412\pi$
$173$	−155.555	+	89.8099i	−0.899164	+	0.519132i	−0.0222350	+	0.999753i	$0.507078\pi$
$174$		0			0
$175$	14.7114	−	25.4809i	0.0840652	−	0.145605i
$176$	62.2783	+	35.9564i	0.353854	+	0.204298i
$177$		0			0
$178$	62.2741	+	107.862i	0.349854	+	0.605966i
$179$		−	62.3812i		−	0.348498i	−0.984702	−	0.174249i	$-0.944250\pi$
$179$		−	62.3812i		−	0.348498i	0.984702	−	0.174249i	$-0.0557498\pi$
$180$		0			0
$181$	128.060			0.707513			0.353756	−	0.935338i	$-0.384904\pi$
$181$	128.060			0.707513			0.353756	+	0.935338i	$0.384904\pi$
$182$	8.03724	−	4.64030i	0.0441607	−	0.0254962i
$183$		0			0
$184$	−48.8235	+	84.5649i	−0.265345	+	0.459592i
$185$	363.659	+	209.958i	1.96572	+	1.13491i
$186$		0			0
$187$	−237.170	−	410.790i	−1.26829	−	2.19674i
$188$		−	105.133i		−	0.559217i
$189$		0			0
$190$	−42.9415			−0.226008
$191$	126.673	−	73.1348i	0.663210	−	0.382904i	−0.130289	−	0.991476i	$-0.541591\pi$
$191$	126.673	−	73.1348i	0.663210	−	0.382904i	0.793499	+	0.608572i	$0.208257\pi$
$192$		0			0
$193$	−112.684	+	195.175i	−0.583856	+	1.01127i	0.411161	+	0.911563i	$0.365123\pi$
$193$	−112.684	+	195.175i	−0.583856	+	1.01127i	−0.995017	+	0.0997058i	$0.968210\pi$
$194$	7.12881	+	4.11582i	0.0367464	+	0.0212156i
$195$		0			0
$196$	7.00000	+	12.1244i	0.0357143	+	0.0618590i
$197$			219.974i			1.11662i	0.829632	+	0.558311i	$0.188550\pi$
$197$			219.974i			1.11662i	−0.829632	+	0.558311i	$0.811450\pi$
$198$		0			0
$199$	168.217			0.845309			0.422655	−	0.906291i	$-0.361098\pi$
$199$	168.217			0.845309			0.422655	+	0.906291i	$0.361098\pi$
$200$	27.2402	−	15.7272i	0.136201	−	0.0786358i
$201$		0			0
$202$	40.5344	−	70.2076i	0.200665	−	0.347563i
$203$	−46.1467	−	26.6428i	−0.227324	−	0.131245i
$204$		0			0
$205$	151.480	+	262.370i	0.738925	+	1.27986i
$206$		−	7.52099i		−	0.0365097i
$207$		0			0
$208$	9.92138			0.0476990
$209$	−78.6611	+	45.4150i	−0.376369	+	0.217297i
$210$		0			0
$211$	−61.5985	+	106.692i	−0.291936	+	0.505648i	−0.974268	−	0.225395i	$-0.927633\pi$
$211$	−61.5985	+	106.692i	−0.291936	+	0.505648i	0.682331	+	0.731043i	$0.260966\pi$
$212$	−157.989	−	91.2148i	−0.745230	−	0.430259i
$213$		0			0
$214$	6.41373	+	11.1089i	0.0299707	+	0.0519108i
$215$		−	14.7064i		−	0.0684020i
$216$		0			0
$217$	−2.42140			−0.0111585
$218$	−168.815	+	97.4657i	−0.774383	+	0.447090i
$219$		0			0
$220$	108.050	−	187.148i	0.491136	−	0.850673i
$221$	−56.6742	−	32.7209i	−0.256445	−	0.148058i
$222$		0			0
$223$	−63.4424	−	109.886i	−0.284495	−	0.492760i	0.687991	−	0.725719i	$-0.258493\pi$
$223$	−63.4424	−	109.886i	−0.284495	−	0.492760i	−0.972487	+	0.232959i	$0.925159\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	281.939			1.24752
$227$	−230.462	+	133.058i	−1.01525	+	0.586156i	−0.912725	−	0.408574i	$-0.866026\pi$
$227$	−230.462	+	133.058i	−1.01525	+	0.586156i	−0.102527	+	0.994730i	$0.532693\pi$
$228$		0			0
$229$	−165.524	+	286.696i	−0.722813	+	1.25195i	0.237055	+	0.971496i	$0.423818\pi$
$229$	−165.524	+	286.696i	−0.722813	+	1.25195i	−0.959868	+	0.280452i	$0.909515\pi$
$230$	254.120	+	146.716i	1.10487	+	0.637896i
$231$		0			0
$232$	−28.4824	−	49.3329i	−0.122769	−	0.212642i
$233$			3.85475i			0.0165440i	0.999966	+	0.00827199i	$0.00263309\pi$
$233$			3.85475i			0.0165440i	−0.999966	+	0.00827199i	$0.997367\pi$
$234$		0			0
$235$	−315.927			−1.34437
$236$	−27.3003	+	15.7618i	−0.115679	+	0.0667875i
$237$		0			0
$238$	49.3602	−	85.4943i	0.207396	−	0.359220i
$239$	−321.568	−	185.657i	−1.34547	−	0.776808i	−0.357867	−	0.933772i	$-0.616496\pi$
$239$	−321.568	−	185.657i	−1.34547	−	0.776808i	−0.987604	+	0.156964i	$0.949829\pi$
$240$		0			0
$241$	75.9784	+	131.598i	0.315263	+	0.546051i	0.979493	−	0.201476i	$-0.0645739\pi$
$241$	75.9784	+	131.598i	0.315263	+	0.546051i	−0.664230	+	0.747528i	$0.731241\pi$
$242$		−	285.976i		−	1.18172i
$243$		0			0
$244$	157.530			0.645616
$245$	36.4340	−	21.0352i	0.148710	−	0.0858580i
$246$		0			0
$247$	−6.26564	+	10.8524i	−0.0253670	+	0.0439369i
$248$	−2.24178	−	1.29429i	−0.00903942	−	0.00521891i
$249$		0			0
$250$	58.9832	+	102.162i	0.235933	+	0.408648i
$251$			225.897i			0.899989i	0.893031	+	0.449995i	$0.148574\pi$
$251$			225.897i			0.899989i	−0.893031	+	0.449995i	$0.851426\pi$
$252$		0			0
$253$	620.670			2.45324
$254$	35.2089	−	20.3279i	0.138618	−	0.0800310i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−168.244	−	97.1359i	−0.654647	−	0.377961i	0.135587	−	0.990765i	$-0.456708\pi$
$257$	−168.244	−	97.1359i	−0.654647	−	0.377961i	−0.790234	+	0.612805i	$0.790041\pi$
$258$		0			0
$259$	92.4281	+	160.090i	0.356865	+	0.618108i
$260$		−	29.8140i		−	0.114669i
$261$		0			0
$262$	−349.276			−1.33311
$263$	−199.675	+	115.282i	−0.759219	+	0.438335i	−0.829015	−	0.559226i	$-0.811098\pi$
$263$	−199.675	+	115.282i	−0.759219	+	0.438335i	0.0697963	+	0.997561i	$0.477765\pi$
$264$		0			0
$265$	−274.103	+	474.761i	−1.03435	+	1.79155i
$266$	−16.3711	−	9.45186i	−0.0615455	−	0.0355333i
$267$		0			0
$268$	3.04810	+	5.27946i	0.0113735	+	0.0196995i
$269$			32.2412i			0.119856i	0.998203	+	0.0599279i	$0.0190871\pi$
$269$			32.2412i			0.119856i	−0.998203	+	0.0599279i	$0.980913\pi$
$270$		0			0
$271$	216.052			0.797238			0.398619	−	0.917117i	$-0.369490\pi$
$271$	216.052			0.797238			0.398619	+	0.917117i	$0.369490\pi$
$272$	91.3973	−	52.7683i	0.336019	−	0.194001i
$273$		0			0
$274$	139.267	−	241.218i	0.508275	−	0.880358i
$275$	−173.146	−	99.9658i	−0.629621	−	0.363512i
$276$		0			0
$277$	−106.959	−	185.258i	−0.386132	−	0.668801i	0.605793	−	0.795622i	$-0.292856\pi$
$277$	−106.959	−	185.258i	−0.386132	−	0.668801i	−0.991926	+	0.126821i	$0.959523\pi$
$278$		−	321.006i		−	1.15470i
$279$		0			0
$280$	44.9751			0.160626
$281$	57.3099	−	33.0879i	0.203950	−	0.117750i	−0.394547	−	0.918876i	$-0.629098\pi$
$281$	57.3099	−	33.0879i	0.203950	−	0.117750i	0.598497	+	0.801125i	$0.295765\pi$
$282$		0			0
$283$	74.7213	−	129.421i	0.264033	−	0.457318i	−0.703277	−	0.710916i	$-0.748281\pi$
$283$	74.7213	−	129.421i	0.264033	−	0.457318i	0.967310	+	0.253598i	$0.0816140\pi$
$284$	−101.832	−	58.7927i	−0.358563	−	0.207017i
$285$		0			0
$286$	−31.5314	−	54.6140i	−0.110250	−	0.190958i
$287$			133.369i			0.464700i
$288$		0			0
$289$	−407.122			−1.40873
$290$	−148.247	+	85.5903i	−0.511196	+	0.295139i
$291$		0			0
$292$	−8.20759	+	14.2160i	−0.0281082	+	0.0486848i
$293$	305.978	+	176.657i	1.04430	+	0.602924i	0.921047	−	0.389452i	$-0.127336\pi$
$293$	305.978	+	176.657i	1.04430	+	0.602924i	0.123248	+	0.992376i	$0.460669\pi$
$294$		0			0
$295$	47.3648	+	82.0382i	0.160559	+	0.278096i
$296$			197.619i			0.667633i
$297$		0			0
$298$	−213.640			−0.716911
$299$	74.1579	−	42.8151i	0.248020	−	0.143194i
$300$		0			0
$301$	3.23704	−	5.60671i	0.0107543	−	0.0186269i
$302$	−102.991	−	59.4621i	−0.341031	−	0.196894i
$303$		0			0
$304$	−10.1045	−	17.5014i	−0.0332384	−	0.0575705i
$305$		−	473.383i		−	1.55208i
$306$		0			0
$307$	−534.432			−1.74082			−0.870410	−	0.492328i	$-0.836146\pi$
$307$	−534.432			−1.74082			−0.870410	+	0.492328i	$0.836146\pi$
$308$	82.3865	−	47.5658i	0.267489	−	0.154435i
$309$		0			0
$310$	−3.88938	+	6.73660i	−0.0125464	+	0.0217310i
$311$	258.459	+	149.221i	0.831057	+	0.479811i	0.854215	−	0.519921i	$-0.174038\pi$
$311$	258.459	+	149.221i	0.831057	+	0.479811i	−0.0231572	+	0.999732i	$0.507372\pi$
$312$		0			0
$313$	−26.7197	−	46.2799i	−0.0853664	−	0.147859i	0.820181	−	0.572104i	$-0.193873\pi$
$313$	−26.7197	−	46.2799i	−0.0853664	−	0.147859i	−0.905547	+	0.424245i	$0.860539\pi$
$314$			32.8496i			0.104617i
$315$		0			0
$316$	−92.1139			−0.291500
$317$	−220.308	+	127.195i	−0.694978	+	0.401246i	−0.805474	−	0.592631i	$-0.798089\pi$
$317$	−220.308	+	127.195i	−0.694978	+	0.401246i	0.110496	+	0.993877i	$0.464756\pi$
$318$		0			0
$319$	−181.041	+	313.572i	−0.567527	+	0.982986i
$320$	41.6389	+	24.0402i	0.130122	+	0.0751257i
$321$		0			0
$322$	64.5875	+	111.869i	0.200582	+	0.347419i
$323$			133.299i			0.412690i
$324$		0			0
$325$	−27.5834			−0.0848720
$326$	−299.933	+	173.166i	−0.920040	+	0.531185i
$327$		0			0
$328$	−71.2887	+	123.476i	−0.217343	+	0.376450i
$329$	−120.445	−	69.5388i	−0.366093	−	0.211364i
$330$		0			0
$331$	−72.6094	−	125.763i	−0.219364	−	0.379949i	0.735250	−	0.677796i	$-0.237065\pi$
$331$	−72.6094	−	125.763i	−0.219364	−	0.379949i	−0.954614	+	0.297847i	$0.903731\pi$
$332$			76.6455i			0.230860i
$333$		0			0
$334$	131.245			0.392950
$335$	15.8649	−	9.15963i	0.0473580	−	0.0273422i
$336$		0			0
$337$	−262.373	+	454.444i	−0.778555	+	1.34850i	0.154219	+	0.988037i	$0.450714\pi$
$337$	−262.373	+	454.444i	−0.778555	+	1.34850i	−0.932774	+	0.360460i	$0.882620\pi$
$338$	199.447	+	115.151i	0.590080	+	0.340683i
$339$		0			0
$340$	−158.570	−	274.651i	−0.466383	−	0.807798i
$341$			16.4537i			0.0482512i
$342$		0			0
$343$	18.5203			0.0539949
$344$	5.99383	−	3.46054i	0.0174239	−	0.0100597i
$345$		0			0
$346$	−127.010	+	219.988i	−0.367082	+	0.635805i
$347$	−447.751	−	258.509i	−1.29035	−	0.744983i	−0.311632	−	0.950203i	$-0.600876\pi$
$347$	−447.751	−	258.509i	−1.29035	−	0.744983i	−0.978716	+	0.205220i	$0.934209\pi$
$348$		0			0
$349$	26.3750	+	45.6828i	0.0755731	+	0.130896i	0.901335	−	0.433122i	$-0.142588\pi$
$349$	26.3750	+	45.6828i	0.0755731	+	0.130896i	−0.825762	+	0.564018i	$0.809255\pi$
$350$		−	41.6102i		−	0.118886i
$351$		0			0
$352$	101.700			0.288921
$353$	422.969	−	244.201i	1.19821	−	0.691788i	0.238055	−	0.971252i	$-0.423490\pi$
$353$	422.969	−	244.201i	1.19821	−	0.691788i	0.960156	+	0.279464i	$0.0901567\pi$
$354$		0			0
$355$	−176.674	+	306.008i	−0.497673	+	0.861994i
$356$	152.540	+	88.0689i	0.428482	+	0.247384i
$357$		0			0
$358$	−44.1101	−	76.4010i	−0.123213	−	0.213411i
$359$			255.794i			0.712518i	0.934387	+	0.356259i	$0.115948\pi$
$359$			255.794i			0.712518i	−0.934387	+	0.356259i	$0.884052\pi$
$360$		0			0
$361$	−335.475			−0.929294
$362$	156.841	−	90.5520i	0.433261	−	0.250144i
$363$		0			0
$364$	6.56238	−	11.3664i	0.0180285	−	0.0312263i
$365$	42.7194	+	24.6640i	0.117039	+	0.0675727i
$366$		0			0
$367$	−298.529	−	517.067i	−0.813429	−	1.40890i	−0.910450	−	0.413619i	$-0.864265\pi$
$367$	−298.529	−	517.067i	−0.813429	−	1.40890i	0.0970209	−	0.995282i	$-0.469069\pi$
$368$			138.094i			0.375255i
$369$		0			0
$370$	593.852			1.60501
$371$	−208.999	+	120.666i	−0.563341	+	0.325245i
$372$		0			0
$373$	50.3910	−	87.2798i	0.135097	−	0.233994i	−0.790538	−	0.612413i	$-0.790199\pi$
$373$	50.3910	−	87.2798i	0.135097	−	0.233994i	0.925634	+	0.378419i	$0.123532\pi$
$374$	−580.944	−	335.408i	−1.55333	−	0.896814i
$375$		0			0
$376$	−74.3401	−	128.761i	−0.197713	−	0.342449i
$377$			49.9543i			0.132505i
$378$		0			0
$379$	547.449			1.44446			0.722228	−	0.691655i	$-0.243118\pi$
$379$	547.449			1.44446			0.722228	+	0.691655i	$0.243118\pi$
$380$	−52.5923	+	30.3642i	−0.138401	+	0.0799058i
$381$		0			0
$382$	103.428	−	179.143i	0.270754	−	0.468960i
$383$	−74.4535	−	42.9858i	−0.194396	−	0.112234i	0.399643	−	0.916671i	$-0.369134\pi$
$383$	−74.4535	−	42.9858i	−0.194396	−	0.112234i	−0.594039	+	0.804436i	$0.702467\pi$
$384$		0			0
$385$	−142.937	−	247.574i	−0.371264	−	0.643048i
$386$			318.719i			0.825697i
$387$		0			0
$388$	11.6413			0.0300033
$389$	185.712	−	107.221i	0.477409	−	0.275632i	−0.241927	−	0.970294i	$-0.577779\pi$
$389$	185.712	−	107.221i	0.477409	−	0.275632i	0.719336	+	0.694662i	$0.244446\pi$
$390$		0			0
$391$	455.436	−	788.838i	1.16480	−	2.01749i
$392$	17.1464	+	9.89949i	0.0437409	+	0.0252538i
$393$		0			0
$394$	155.545	+	269.412i	0.394785	+	0.683788i
$395$			276.805i			0.700772i
$396$		0			0
$397$	552.294			1.39117			0.695585	−	0.718444i	$-0.255145\pi$
$397$	552.294			1.39117			0.695585	+	0.718444i	$0.255145\pi$
$398$	206.022	−	118.947i	0.517644	−	0.298862i
$399$		0			0
$400$	22.2416	−	38.5235i	0.0556039	−	0.0963088i
$401$	140.675	+	81.2186i	0.350810	+	0.202540i	0.665042	−	0.746806i	$-0.268414\pi$
$401$	140.675	+	81.2186i	0.350810	+	0.202540i	−0.314232	+	0.949346i	$0.601747\pi$
$402$		0			0
$403$	1.13501	+	1.96589i	0.00281640	+	0.00487814i
$404$		−	114.649i		−	0.283784i
$405$		0			0
$406$	−75.3572			−0.185609
$407$	1087.83	−	628.060i	2.67280	−	1.54314i
$408$		0			0
$409$	229.974	−	398.327i	0.562284	−	0.973904i	−0.435013	−	0.900424i	$-0.643256\pi$
$409$	229.974	−	398.327i	0.562284	−	0.973904i	0.997297	−	0.0734799i	$-0.0234105\pi$
$410$	371.048	+	214.224i	0.904994	+	0.522499i
$411$		0			0
$412$	−5.31814	−	9.21129i	−0.0129081	−	0.0223575i
$413$			41.7019i			0.100973i
$414$		0			0
$415$	230.322			0.554992
$416$	12.1512	−	7.01548i	0.0292095	−	0.0168641i
$417$		0			0
$418$	−64.2265	+	111.244i	−0.153652	+	0.266133i
$419$	27.2249	+	15.7183i	0.0649759	+	0.0375138i	0.532136	−	0.846659i	$-0.321390\pi$
$419$	27.2249	+	15.7183i	0.0649759	+	0.0375138i	−0.467160	+	0.884173i	$0.654723\pi$
$420$		0			0
$421$	72.8545	+	126.188i	0.173051	+	0.299733i	0.939485	−	0.342590i	$-0.111304\pi$
$421$	72.8545	+	126.188i	0.173051	+	0.299733i	−0.766434	+	0.642323i	$0.777971\pi$
$422$			174.227i			0.412860i
$423$		0			0
$424$	−257.995			−0.608478
$425$	−254.102	+	146.706i	−0.597888	+	0.345191i
$426$		0			0
$427$	104.197	−	180.474i	0.244020	−	0.422655i
$428$	15.7104	+	9.07038i	0.0367064	+	0.0211925i
$429$		0			0
$430$	−10.3990	−	18.0116i	−0.0241837	−	0.0418875i
$431$			348.799i			0.809278i	0.914477	+	0.404639i	$0.132603\pi$
$431$			348.799i			0.809278i	−0.914477	+	0.404639i	$0.867397\pi$
$432$		0			0
$433$	570.342			1.31719			0.658594	−	0.752499i	$-0.271152\pi$
$433$	570.342			1.31719			0.658594	+	0.752499i	$0.271152\pi$
$434$	−2.96559	+	1.71219i	−0.00683316	+	0.00394513i
$435$		0			0
$436$	−137.837	+	238.741i	−0.316141	+	0.547571i
$437$	−151.053	−	87.2103i	−0.345658	−	0.199566i
$438$		0			0
$439$	−326.445	−	565.419i	−0.743610	−	1.28797i	−0.950841	−	0.309679i	$-0.899778\pi$
$439$	−326.445	−	565.419i	−0.743610	−	1.28797i	0.207231	−	0.978292i	$-0.433555\pi$
$440$		−	305.612i		−	0.694572i
$441$		0			0
$442$	−92.5486			−0.209386
$443$	120.348	−	69.4828i	0.271665	−	0.156846i	−0.357979	−	0.933730i	$-0.616534\pi$
$443$	120.348	−	69.4828i	0.271665	−	0.156846i	0.629644	+	0.776884i	$0.283201\pi$
$444$		0			0
$445$	264.649	−	458.386i	0.594718	−	1.03008i
$446$	−155.402	−	89.7211i	−0.348434	−	0.201168i
$447$		0			0
$448$	10.5830	+	18.3303i	0.0236228	+	0.0409159i
$449$		−	53.0394i		−	0.118128i	−0.998254	−	0.0590639i	$-0.981188\pi$
$449$		−	53.0394i		−	0.118128i	0.998254	−	0.0590639i	$-0.0188116\pi$
$450$		0			0
$451$	906.258			2.00944
$452$	345.304	−	199.361i	0.763946	−	0.441065i
$453$		0			0
$454$	−188.172	+	325.923i	−0.414475	+	0.717892i
$455$	−34.1563	−	19.7201i	−0.0750687	−	0.0433410i
$456$		0			0
$457$	−93.3782	−	161.736i	−0.204329	−	0.353908i	0.745590	−	0.666405i	$-0.232168\pi$
$457$	−93.3782	−	161.736i	−0.204329	−	0.353908i	−0.949919	+	0.312497i	$0.898834\pi$
$458$			468.173i			1.02221i
$459$		0			0
$460$	414.976			0.902122
$461$	−369.166	+	213.138i	−0.800794	+	0.462338i	−0.843749	−	0.536739i	$-0.819656\pi$
$461$	−369.166	+	213.138i	−0.800794	+	0.462338i	0.0429550	+	0.999077i	$0.486323\pi$
$462$		0			0
$463$	97.4829	−	168.845i	0.210546	−	0.364677i	−0.741339	−	0.671130i	$-0.765809\pi$
$463$	97.4829	−	168.845i	0.210546	−	0.364677i	0.951886	+	0.306454i	$0.0991424\pi$
$464$	−69.7673	−	40.2801i	−0.150360	−	0.0868107i
$465$		0			0
$466$	2.72572	+	4.72108i	0.00584918	+	0.0101311i
$467$		−	542.269i		−	1.16118i	−0.814197	−	0.580588i	$-0.802823\pi$
$467$		−	542.269i		−	1.16118i	0.814197	−	0.580588i	$-0.197177\pi$
$468$		0			0
$469$	8.06451			0.0171951
$470$	−386.930	+	223.394i	−0.823255	+	0.475307i
$471$		0			0
$472$	−22.2906	+	38.6085i	−0.0472259	+	0.0817976i
$473$	−38.0983	−	21.9960i	−0.0805460	−	0.0465033i
$474$		0			0
$475$	28.0924	+	48.6574i	0.0591419	+	0.102437i
$476$		−	139.612i		−	0.293302i
$477$		0			0
$478$	−525.118			−1.09857
$479$	336.048	−	194.018i	0.701562	−	0.405047i	−0.106367	−	0.994327i	$-0.533922\pi$
$479$	336.048	−	194.018i	0.701562	−	0.405047i	0.807929	+	0.589280i	$0.200588\pi$
$480$		0			0
$481$	86.6497	−	150.082i	0.180145	−	0.312020i
$482$	186.108	+	107.450i	0.386117	+	0.222925i
$483$		0			0
$484$	−202.216	−	350.248i	−0.417801	−	0.723653i
$485$		−	34.9824i		−	0.0721287i
$486$		0			0
$487$	299.064			0.614095			0.307047	−	0.951694i	$-0.400659\pi$
$487$	299.064			0.614095			0.307047	+	0.951694i	$0.400659\pi$
$488$	192.934	−	111.391i	0.395358	−	0.228260i
$489$		0			0
$490$	29.7483	−	51.5255i	0.0607107	−	0.105154i
$491$	511.155	+	295.115i	1.04105	+	0.601049i	0.920130	−	0.391613i	$-0.128083\pi$
$491$	511.155	+	295.115i	1.04105	+	0.601049i	0.120918	+	0.992663i	$0.461416\pi$
$492$		0			0
$493$	265.689	+	460.187i	0.538923	+	0.933442i
$494$			17.7219i			0.0358743i
$495$		0			0
$496$	−3.66081			−0.00738066
$497$	−134.711	+	77.7755i	−0.271048	+	0.156490i
$498$		0			0
$499$	−180.064	+	311.879i	−0.360849	+	0.625008i	−0.988101	−	0.153808i	$-0.950846\pi$
$499$	−180.064	+	311.879i	−0.360849	+	0.625008i	0.627252	+	0.778816i	$0.284180\pi$
$500$	144.479	+	83.4149i	0.288958	+	0.166830i
$501$		0			0
$502$	159.734	+	276.667i	0.318194	+	0.551129i
$503$			3.65643i			0.00726925i	0.999993	+	0.00363462i	$0.00115694\pi$
$503$			3.65643i			0.00726925i	−0.999993	+	0.00363462i	$0.998843\pi$
$504$		0			0
$505$	−344.522			−0.682222
$506$	760.162	−	438.880i	1.50230	−	0.867351i
$507$		0			0
$508$	28.7480	−	49.7929i	0.0565905	−	0.0980175i
$509$	287.797	+	166.160i	0.565417	+	0.326444i	0.755317	−	0.655360i	$-0.227483\pi$
$509$	287.797	+	166.160i	0.565417	+	0.326444i	−0.189900	+	0.981803i	$0.560816\pi$
$510$		0			0
$511$	10.8576	+	18.8059i	0.0212478	+	0.0368022i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	−274.742			−0.534517
$515$	−27.6802	+	15.9812i	−0.0537480	+	0.0310314i
$516$		0			0
$517$	−472.525	+	818.436i	−0.913974	+	1.58305i
$518$	226.402	+	130.713i	0.437069	+	0.252342i
$519$		0			0
$520$	−21.0817	−	36.5146i	−0.0405418	−	0.0702204i
$521$		−	623.260i		−	1.19628i	−0.801393	−	0.598138i	$-0.795907\pi$
$521$		−	623.260i		−	1.19628i	0.801393	−	0.598138i	$-0.204093\pi$
$522$		0			0
$523$	−646.966			−1.23703			−0.618514	−	0.785774i	$-0.712265\pi$
$523$	−646.966			−1.23703			−0.618514	+	0.785774i	$0.712265\pi$
$524$	−427.774	+	246.975i	−0.816362	+	0.471327i
$525$		0			0
$526$	−163.034	+	282.383i	−0.309950	+	0.536849i
$527$	20.9117	+	12.0734i	0.0396807	+	0.0229097i
$528$		0			0
$529$	331.435	+	574.062i	0.626531	+	1.08518i
$530$			775.281i			1.46279i
$531$		0			0
$532$	−26.7339			−0.0502517
$533$	108.280	−	62.5155i	0.203152	−	0.117290i
$534$		0			0
$535$	27.2567	−	47.2101i	0.0509472	−	0.0882431i
$536$	7.46629	+	4.31066i	0.0139296	+	0.00804228i
$537$		0			0
$538$	22.7980	+	39.4872i	0.0423754	+	0.0733963i
$539$		−	125.847i		−	0.233483i
$540$		0			0
$541$	241.271			0.445972			0.222986	−	0.974822i	$-0.428420\pi$
$541$	241.271			0.445972			0.222986	+	0.974822i	$0.428420\pi$
$542$	264.608	−	152.772i	0.488207	−	0.281866i
$543$		0			0
$544$	74.6256	−	129.255i	0.137179	−	0.237602i
$545$	717.424	+	414.205i	1.31637	+	0.760009i
$546$		0			0
$547$	−263.904	−	457.095i	−0.482457	−	0.835641i	0.517340	−	0.855780i	$-0.326922\pi$
$547$	−263.904	−	457.095i	−0.482457	−	0.835641i	−0.999797	+	0.0201394i	$0.993589\pi$
$548$		−	393.907i		−	0.718809i
$549$		0			0
$550$	−282.746			−0.514084
$551$	88.1201	−	50.8762i	0.159928	−	0.0923342i
$552$		0			0
$553$	−60.9276	+	105.530i	−0.110176	+	0.190831i
$554$	−261.994	−	151.262i	−0.472914	−	0.273037i
$555$		0			0
$556$	−226.986	−	393.151i	−0.408248	−	0.707106i
$557$		−	449.852i		−	0.807634i	−0.914840	−	0.403817i	$-0.867683\pi$
$557$		−	449.852i		−	0.807634i	0.914840	−	0.403817i	$-0.132317\pi$
$558$		0			0
$559$	−6.06933			−0.0108575
$560$	55.0831	−	31.8022i	0.0983626	−	0.0567897i
$561$		0			0
$562$	46.7933	−	81.0484i	0.0832622	−	0.144214i
$563$	−751.190	−	433.700i	−1.33426	−	0.770337i	−0.348313	−	0.937378i	$-0.613245\pi$
$563$	−751.190	−	433.700i	−1.33426	−	0.770337i	−0.985950	+	0.167042i	$0.946579\pi$
$564$		0			0
$565$	−599.086	−	1037.65i	−1.06033	−	1.83654i
$566$		−	211.344i		−	0.373399i
$567$		0			0
$568$	−166.291			−0.292766
$569$	340.603	−	196.647i	0.598599	−	0.345601i	−0.169891	−	0.985463i	$-0.554342\pi$
$569$	340.603	−	196.647i	0.598599	−	0.345601i	0.768490	+	0.639862i	$0.221008\pi$
$570$		0			0
$571$	548.804	−	950.557i	0.961129	−	1.66472i	0.241454	−	0.970412i	$-0.422376\pi$
$571$	548.804	−	950.557i	0.961129	−	1.66472i	0.719675	−	0.694311i	$-0.244291\pi$
$572$	−77.2359	−	44.5922i	−0.135028	−	0.0779583i
$573$		0			0
$574$	94.3060	+	163.343i	0.164296	+	0.284569i
$575$		−	383.928i		−	0.667701i
$576$		0			0
$577$	−643.623			−1.11546			−0.557732	−	0.830021i	$-0.688328\pi$
$577$	−643.623			−1.11546			−0.557732	+	0.830021i	$0.688328\pi$
$578$	−498.621	+	287.879i	−0.862666	+	0.498060i
$579$		0			0
$580$	−121.043	+	209.653i	−0.208695	+	0.361470i
$581$	87.8084	+	50.6962i	0.151133	+	0.0872568i
$582$		0			0
$583$	819.939	+	1420.18i	1.40641	+	2.43598i
$584$			23.2146i			0.0397510i
$585$		0			0
$586$	499.661			0.852663
$587$	−891.364	+	514.629i	−1.51851	+	0.876711i	−0.518744	+	0.854929i	$0.673600\pi$
$587$	−891.364	+	514.629i	−1.51851	+	0.876711i	−0.999763	+	0.0217812i	$0.993066\pi$
$588$		0			0
$589$	2.31190	−	4.00434i	0.00392514	−	0.00679853i
$590$	116.020	+	66.9839i	0.196643	+	0.113532i
$591$		0			0
$592$	139.738	+	242.033i	0.236044	+	0.408840i
$593$			452.693i			0.763395i	0.924287	+	0.381698i	$0.124660\pi$
$593$			452.693i			0.763395i	−0.924287	+	0.381698i	$0.875340\pi$
$594$		0			0
$595$	−419.537			−0.705104
$596$	−261.654	+	151.066i	−0.439017	+	0.253466i
$597$		0			0
$598$	60.5497	−	104.875i	0.101254	−	0.175376i
$599$	261.867	+	151.189i	0.437174	+	0.252403i	0.702398	−	0.711784i	$-0.252113\pi$
$599$	261.867	+	151.189i	0.437174	+	0.252403i	−0.265224	+	0.964187i	$0.585446\pi$
$600$		0			0
$601$	−69.7673	−	120.841i	−0.116085	−	0.201066i	0.802128	−	0.597153i	$-0.203701\pi$
$601$	−69.7673	−	120.841i	−0.116085	−	0.201066i	−0.918213	+	0.396087i	$0.870368\pi$
$602$		−	9.15572i		−	0.0152088i
$603$		0			0
$604$	−168.184			−0.278451
$605$	−1052.50	+	607.664i	−1.73968	+	1.00440i
$606$		0			0
$607$	−494.708	+	856.859i	−0.815004	+	1.41163i	0.0943203	+	0.995542i	$0.469932\pi$
$607$	−494.708	+	856.859i	−0.815004	+	1.41163i	−0.909325	+	0.416087i	$0.863401\pi$
$608$	−24.7508	−	14.2899i	−0.0407085	−	0.0235031i
$609$		0			0
$610$	−334.732	−	579.774i	−0.548742	−	0.950449i
$611$			130.383i			0.213393i
$612$		0			0
$613$	536.913			0.875877			0.437939	−	0.899005i	$-0.355709\pi$
$613$	536.913			0.875877			0.437939	+	0.899005i	$0.355709\pi$
$614$	−654.542	+	377.900i	−1.06603	+	0.615473i
$615$		0			0
$616$	67.2683	−	116.512i	0.109202	−	0.189143i
$617$	−434.960	−	251.124i	−0.704959	−	0.407008i	0.104233	−	0.994553i	$-0.466761\pi$
$617$	−434.960	−	251.124i	−0.704959	−	0.407008i	−0.809192	+	0.587545i	$0.800095\pi$
$618$		0			0
$619$	112.854	+	195.468i	0.182316	+	0.315781i	0.942669	−	0.333730i	$-0.108307\pi$
$619$	112.854	+	195.468i	0.182316	+	0.315781i	−0.760353	+	0.649510i	$0.774974\pi$
$620$			11.0008i			0.0177433i
$621$		0			0
$622$	422.062			0.678556
$623$	201.791	−	116.504i	0.323902	−	0.187005i
$624$		0			0
$625$	389.674	−	674.935i	0.623478	−	1.07990i
$626$	−65.4496	−	37.7874i	−0.104552	−	0.0603632i
$627$		0			0
$628$	23.2282	+	40.2324i	0.0369876	+	0.0640643i
$629$		−	1843.43i		−	2.93074i
$630$		0			0
$631$	−17.8821			−0.0283393			−0.0141696	−	0.999900i	$-0.504510\pi$
$631$	−17.8821			−0.0283393			−0.0141696	+	0.999900i	$0.504510\pi$
$632$	−112.816	+	65.1343i	−0.178506	+	0.103061i
$633$		0			0
$634$	−179.881	+	311.562i	−0.283723	+	0.491423i
$635$	−149.629	−	86.3884i	−0.235636	−	0.136045i
$636$		0			0
$637$	−8.68121	−	15.0363i	−0.0136283	−	0.0236049i
$638$			512.062i			0.802604i
$639$		0			0
$640$	67.9960			0.106244
$641$	−120.902	+	69.8031i	−0.188615	+	0.108897i	−0.591334	−	0.806427i	$-0.701399\pi$
$641$	−120.902	+	69.8031i	−0.188615	+	0.108897i	0.402719	+	0.915324i	$0.368065\pi$
$642$		0			0
$643$	34.3711	−	59.5325i	0.0534543	−	0.0925855i	−0.838060	−	0.545578i	$-0.816310\pi$
$643$	34.3711	−	59.5325i	0.0534543	−	0.0925855i	0.891514	+	0.452992i	$0.149644\pi$
$644$	158.206	+	91.3405i	0.245662	+	0.141833i
$645$		0			0
$646$	94.2564	+	163.257i	0.145908	+	0.252720i
$647$		−	965.690i		−	1.49257i	−0.665629	−	0.746283i	$-0.731837\pi$
$647$		−	965.690i		−	1.49257i	0.665629	−	0.746283i	$-0.268163\pi$
$648$		0			0
$649$	283.370			0.436625
$650$	−33.7826	+	19.5044i	−0.0519732	+	0.0300068i
$651$		0			0
$652$	−244.894	+	424.169i	−0.375605	+	0.650566i
$653$	838.665	+	484.204i	1.28433	+	0.741506i	0.977636	−	0.210303i	$-0.0674451\pi$
$653$	838.665	+	484.204i	1.28433	+	0.741506i	0.306690	+	0.951809i	$0.400778\pi$
$654$		0			0
$655$	742.168	+	1285.47i	1.13308	+	1.96255i
$656$			201.635i			0.307370i
$657$		0			0
$658$	−196.685			−0.298914
$659$	406.390	−	234.629i	0.616676	−	0.356038i	−0.158898	−	0.987295i	$-0.550794\pi$
$659$	406.390	−	234.629i	0.616676	−	0.356038i	0.775574	+	0.631257i	$0.217461\pi$
$660$		0			0
$661$	−274.083	+	474.726i	−0.414649	+	0.718193i	−0.995392	−	0.0958941i	$-0.969429\pi$
$661$	−274.083	+	474.726i	−0.414649	+	0.718193i	0.580743	+	0.814087i	$0.302762\pi$
$662$	−177.856	−	102.685i	−0.268664	−	0.155113i
$663$		0			0
$664$	54.1965	+	93.8711i	0.0816213	+	0.141372i
$665$			80.3361i			0.120806i
$666$		0			0
$667$	−695.305			−1.04244
$668$	160.742	−	92.8044i	0.240632	−	0.138929i
$669$		0			0
$670$	12.9537	−	22.4364i	0.0193338	−	0.0334872i
$671$	−1226.34	−	708.028i	−1.82763	−	1.05518i
$672$		0			0
$673$	−43.8580	−	75.9643i	−0.0651679	−	0.112874i	0.831601	−	0.555374i	$-0.187425\pi$
$673$	−43.8580	−	75.9643i	−0.0651679	−	0.112874i	−0.896768	+	0.442500i	$0.854092\pi$
$674$			742.103i			1.10104i
$675$		0			0
$676$	325.696			0.481798
$677$	−507.524	+	293.019i	−0.749666	+	0.432820i	−0.825573	−	0.564295i	$-0.809148\pi$
$677$	−507.524	+	293.019i	−0.749666	+	0.432820i	0.0759074	+	0.997115i	$0.475815\pi$
$678$		0			0
$679$	7.69999	−	13.3368i	0.0113402	−	0.0196418i
$680$	−388.416	−	224.252i	−0.571200	−	0.329782i
$681$		0			0
$682$	11.6345	+	20.1516i	0.0170594	+	0.0295477i
$683$			745.627i			1.09169i	0.837885	+	0.545847i	$0.183792\pi$
$683$			745.627i			1.09169i	−0.837885	+	0.545847i	$0.816208\pi$
$684$		0			0
$685$	−1183.70			−1.72803
$686$	22.6826	−	13.0958i	0.0330650	−	0.0190901i
$687$		0			0
$688$	4.89394	−	8.47655i	0.00711328	−	0.0123206i
$689$	195.933	+	113.122i	0.284374	+	0.164183i
$690$		0			0
$691$	−166.576	−	288.518i	−0.241065	−	0.417537i	0.719953	−	0.694023i	$-0.244163\pi$
$691$	−166.576	−	288.518i	−0.241065	−	0.417537i	−0.961018	+	0.276486i	$0.910830\pi$
$692$			359.240i			0.519132i
$693$		0			0
$694$	−731.174			−1.05356
$695$	−1181.43	+	682.099i	−1.69990	+	0.981437i
$696$		0			0
$697$	664.995	−	1151.80i	0.954081	−	1.65252i
$698$	64.6053	+	37.2999i	0.0925577	+	0.0534382i
$699$		0			0
$700$	−29.4228	−	50.9618i	−0.0420326	−	0.0728026i
$701$			999.755i			1.42618i	0.701070	+	0.713092i	$0.252706\pi$
$701$			999.755i			1.42618i	−0.701070	+	0.713092i	$0.747294\pi$
$702$		0			0
$703$	−352.995			−0.502126
$704$	124.557	−	71.9128i	0.176927	−	0.102149i
$705$		0			0
$706$	345.353	−	598.168i	0.489168	−	0.847264i
$707$	−131.346	−	75.8329i	−0.185780	−	0.107260i
$708$		0			0
$709$	−679.527	−	1176.97i	−0.958430	−	1.66005i	−0.726317	−	0.687360i	$-0.758769\pi$
$709$	−679.527	−	1176.97i	−0.958430	−	1.66005i	−0.232113	−	0.972689i	$-0.574564\pi$
$710$			499.709i			0.703815i
$711$		0			0
$712$	249.096			0.349854
$713$	−27.3629	+	15.7980i	−0.0383771	+	0.0221570i
$714$		0			0
$715$	−134.001	+	232.096i	−0.187414	+	0.324610i
$716$	−108.047	−	62.3812i	−0.150904	−	0.0871245i
$717$		0			0
$718$	180.874	+	313.282i	0.251913	+	0.436326i
$719$			709.113i			0.986249i	0.869959	+	0.493125i	$0.164145\pi$
$719$			709.113i			0.986249i	−0.869959	+	0.493125i	$0.835855\pi$
$720$		0			0
$721$	−14.0705			−0.0195152
$722$	−410.871	+	237.217i	−0.569074	+	0.328555i
$723$		0			0
$724$	128.060	−	221.806i	0.176878	−	0.306362i
$725$	193.967	+	111.987i	0.267540	+	0.154464i
$726$		0			0
$727$	59.2031	+	102.543i	0.0814347	+	0.141049i	0.903866	−	0.427815i	$-0.140716\pi$
$727$	59.2031	+	102.543i	0.0814347	+	0.141049i	−0.822432	+	0.568864i	$0.807383\pi$
$728$		−	18.5612i		−	0.0254962i
$729$		0			0
$730$	69.7604			0.0955622
$731$	−55.9116	+	32.2806i	−0.0764864	+	0.0441595i
$732$		0			0
$733$	−516.828	+	895.172i	−0.705085	+	1.22124i	0.261575	+	0.965183i	$0.415758\pi$
$733$	−516.828	+	895.172i	−0.705085	+	1.22124i	−0.966661	+	0.256061i	$0.917575\pi$
$734$	−731.243	−	422.183i	−0.996243	−	0.575181i
$735$		0			0
$736$	97.6471	+	169.130i	0.132673	+	0.229796i
$737$		−	54.7993i		−	0.0743546i
$738$		0			0
$739$	−862.977			−1.16776			−0.583882	−	0.811839i	$-0.698467\pi$
$739$	−862.977			−1.16776			−0.583882	+	0.811839i	$0.698467\pi$
$740$	727.317	−	419.917i	0.982861	−	0.567455i
$741$		0			0
$742$	−170.647	+	295.570i	−0.229983	+	0.398342i
$743$	−564.659	−	326.006i	−0.759972	−	0.438770i	0.0693136	−	0.997595i	$-0.477919\pi$
$743$	−564.659	−	326.006i	−0.759972	−	0.438770i	−0.829286	+	0.558825i	$0.811252\pi$
$744$		0			0
$745$	453.958	+	786.278i	0.609339	+	1.05541i
$746$		−	142.527i		−	0.191055i
$747$		0			0
$748$	−948.678			−1.26829
$749$	20.7829	−	11.9990i	0.0277475	−	0.0160200i
$750$		0			0
$751$	11.1700	−	19.3470i	0.0148735	−	0.0257617i	−0.858493	−	0.512826i	$-0.828599\pi$
$751$	11.1700	−	19.3470i	0.0148735	−	0.0257617i	0.873366	+	0.487064i	$0.161932\pi$
$752$	−182.095	−	105.133i	−0.242148	−	0.139804i
$753$		0			0
$754$	35.3231	+	61.1813i	0.0468476	+	0.0811423i
$755$			505.398i			0.669402i
$756$		0			0
$757$	117.194			0.154813			0.0774067	−	0.997000i	$-0.475336\pi$
$757$	117.194			0.154813			0.0774067	+	0.997000i	$0.475336\pi$
$758$	670.485	−	387.105i	0.884545	−	0.510692i
$759$		0			0
$760$	−42.9415	+	74.3768i	−0.0565019	+	0.0978642i
$761$	875.361	+	505.390i	1.15028	+	0.664113i	0.948955	−	0.315413i	$-0.102143\pi$
$761$	875.361	+	505.390i	1.15028	+	0.664113i	0.201322	+	0.979525i	$0.435476\pi$
$762$		0			0
$763$	182.342	+	315.825i	0.238980	+	0.413925i
$764$		−	292.539i		−	0.382904i
$765$		0			0
$766$	−121.582			−0.158723
$767$	33.8571	−	19.5474i	0.0441422	−	0.0254855i
$768$		0			0
$769$	155.362	−	269.094i	0.202031	−	0.349928i	−0.747152	−	0.664653i	$-0.768579\pi$
$769$	155.362	−	269.094i	0.202031	−	0.349928i	0.949183	+	0.314726i	$0.101913\pi$
$770$	−350.122	−	202.143i	−0.454704	−	0.262523i
$771$		0			0
$772$	225.369	+	390.350i	0.291928	+	0.505634i
$773$		−	401.803i		−	0.519797i	−0.965636	−	0.259899i	$-0.916311\pi$
$773$		−	401.803i		−	0.519797i	0.965636	−	0.259899i	$-0.0836891\pi$
$774$		0			0
$775$	10.1778			0.0131326
$776$	14.2576	−	8.23164i	0.0183732	−	0.0106078i
$777$		0			0
$778$	151.633	−	262.637i	0.194902	−	0.337579i
$779$	−220.556	−	127.338i	−0.283127	−	0.163464i
$780$		0			0
$781$	528.494	+	915.378i	0.676688	+	1.17206i
$782$		−	1288.17i		−	1.64727i
$783$		0			0
$784$	28.0000			0.0357143
$785$	120.900	−	69.8014i	0.154012	−	0.0889189i
$786$		0			0
$787$	−274.555	+	475.543i	−0.348863	+	0.604248i	−0.986048	−	0.166463i	$-0.946765\pi$
$787$	−274.555	+	475.543i	−0.348863	+	0.604248i	0.637185	+	0.770711i	$0.280099\pi$
$788$	381.007	+	219.974i	0.483511	+	0.279155i
$789$		0			0
$790$	195.731	+	339.015i	0.247760	+	0.429133i
$791$		−	527.460i		−	0.666827i
$792$		0			0
$793$	−195.365			−0.246362
$794$	676.420	−	390.531i	0.851914	−	0.491853i
$795$		0			0
$796$	168.217	−	291.360i	0.211327	−	0.366030i
$797$	−1141.01	−	658.761i	−1.43163	−	0.826551i	−0.434384	−	0.900728i	$-0.643034\pi$
$797$	−1141.01	−	658.761i	−1.43163	−	0.826551i	−0.997245	+	0.0741765i	$0.976367\pi$
$798$		0			0
$799$	693.459	+	1201.11i	0.867909	+	1.50326i
$800$		−	62.9086i		−	0.0786358i
$801$		0			0
$802$	229.721			0.286435
$803$	127.789	−	73.7788i	0.159139	−	0.0918790i
$804$		0			0
$805$	274.481	−	475.415i	0.340970	−	0.590577i
$806$	2.78019	+	1.60514i	0.00344937	+	0.00199149i
$807$		0			0
$808$	−81.0688	−	140.415i	−0.100333	−	0.173781i
$809$			383.248i			0.473731i	0.971542	+	0.236865i	$0.0761201\pi$
$809$			383.248i			0.473731i	−0.971542	+	0.236865i	$0.923880\pi$
$810$		0			0
$811$	854.626			1.05379			0.526896	−	0.849929i	$-0.323356\pi$
$811$	854.626			1.05379			0.526896	+	0.849929i	$0.323356\pi$
$812$	−92.2934	+	53.2856i	−0.113662	+	0.0656227i
$813$		0			0
$814$	888.211	−	1538.43i	1.09117	−	1.88996i
$815$	1274.64	+	735.914i	1.56398	+	0.902962i
$816$		0			0
$817$	6.18133	+	10.7064i	0.00756588	+	0.0131045i
$818$		−	650.465i		−	0.795189i
$819$		0			0
$820$	605.918			0.738925
$821$	−752.077	+	434.212i	−0.916050	+	0.528882i	−0.882373	−	0.470551i	$-0.844055\pi$
$821$	−752.077	+	434.212i	−0.916050	+	0.528882i	−0.0336771	+	0.999433i	$0.510722\pi$
$822$		0			0
$823$	−177.628	+	307.660i	−0.215829	+	0.373828i	−0.953529	−	0.301302i	$-0.902579\pi$
$823$	−177.628	+	307.660i	−0.215829	+	0.373828i	0.737699	+	0.675129i	$0.235912\pi$
$824$	−13.0267	−	7.52099i	−0.0158091	−	0.00912741i
$825$		0			0
$826$	29.4877	+	51.0742i	0.0356994	+	0.0618332i
$827$		−	558.661i		−	0.675527i	−0.941231	−	0.337763i	$-0.890330\pi$
$827$		−	558.661i		−	0.675527i	0.941231	−	0.337763i	$-0.109670\pi$
$828$		0			0
$829$	−838.199			−1.01110			−0.505548	−	0.862798i	$-0.668710\pi$
$829$	−838.199			−1.01110			−0.505548	+	0.862798i	$0.668710\pi$
$830$	282.085	−	162.862i	0.339862	−	0.196219i
$831$		0			0
$832$	9.92138	−	17.1843i	0.0119247	−	0.0206543i
$833$	−159.945	−	92.3444i	−0.192011	−	0.110858i
$834$		0			0
$835$	−278.880	−	483.034i	−0.333988	−	0.578484i
$836$			181.660i			0.217297i
$837$		0			0
$838$	44.4580			0.0530526
$839$	1039.44	−	600.120i	1.23890	−	0.715280i	0.270031	−	0.962852i	$-0.412966\pi$
$839$	1039.44	−	600.120i	1.23890	−	0.715280i	0.968870	+	0.247572i	$0.0796327\pi$
$840$		0			0
$841$	−217.689	+	377.048i	−0.258845	+	0.448333i
$842$	178.456	+	103.032i	0.211943	+	0.122366i
$843$		0			0
$844$	123.197	+	213.384i	0.145968	+	0.252824i
$845$		−	978.725i		−	1.15825i
$846$		0			0
$847$	−535.012			−0.631656
$848$	−315.977	+	182.430i	−0.372615	+	0.215129i
$849$		0			0
$850$	−207.474	+	359.355i	−0.244087	+	0.422771i
$851$	2088.96	+	1206.06i	2.45471	+	1.41723i
$852$		0			0
$853$	−727.938	−	1260.83i	−0.853386	−	1.47811i	−0.878134	−	0.478414i	$-0.841212\pi$
$853$	−727.938	−	1260.83i	−0.853386	−	1.47811i	0.0247485	−	0.999694i	$-0.492122\pi$
$854$		−	294.712i		−	0.345096i
$855$		0			0
$856$	25.6549			0.0299707
$857$	−883.035	+	509.821i	−1.03038	+	0.594890i	−0.917093	−	0.398672i	$-0.869471\pi$
$857$	−883.035	+	509.821i	−1.03038	+	0.594890i	−0.113286	+	0.993562i	$0.536138\pi$
$858$		0			0
$859$	219.697	−	380.527i	0.255759	−	0.442988i	−0.709342	−	0.704864i	$-0.751008\pi$
$859$	219.697	−	380.527i	0.255759	−	0.442988i	0.965101	+	0.261876i	$0.0843413\pi$
$860$	−25.4723	−	14.7064i	−0.0296189	−	0.0171005i
$861$		0			0
$862$	246.638	+	427.189i	0.286123	+	0.495579i
$863$		−	1307.81i		−	1.51542i	−0.652591	−	0.757711i	$-0.726318\pi$
$863$		−	1307.81i		−	1.51542i	0.652591	−	0.757711i	$-0.273682\pi$
$864$		0			0
$865$	1079.53			1.24801
$866$	698.524	−	403.293i	0.806609	−	0.465696i
$867$		0			0
$868$	−2.42140	+	4.19398i	−0.00278963	+	0.00483177i
$869$	717.087	+	414.010i	0.825187	+	0.476422i
$870$		0			0
$871$	−3.78017	−	6.54745i	−0.00434004	−	0.00751716i
$872$			389.863i			0.447090i
$873$		0			0
$874$	−246.668			−0.282229
$875$	191.128	−	110.348i	0.218431	−	0.126111i
$876$		0			0
$877$	442.418	−	766.291i	0.504468	−	0.873764i	−0.495519	−	0.868597i	$-0.665022\pi$
$877$	442.418	−	766.291i	0.504468	−	0.873764i	0.999987	−	0.00516691i	$-0.00164468\pi$
$878$	−799.624	−	461.663i	−0.910733	−	0.525812i
$879$		0			0
$880$	−216.100	−	374.296i	−0.245568	−	0.425337i
$881$			1529.26i			1.73583i	0.496716	+	0.867913i	$0.334539\pi$
$881$			1529.26i			1.73583i	−0.496716	+	0.867913i	$0.665461\pi$
$882$		0			0
$883$	116.662			0.132120			0.0660600	−	0.997816i	$-0.478957\pi$
$883$	116.662			0.132120			0.0660600	+	0.997816i	$0.478957\pi$
$884$	−113.348	+	65.4418i	−0.128222	+	0.0740292i
$885$		0			0
$886$	98.2635	−	170.197i	0.110907	−	0.192096i
$887$	901.733	+	520.616i	1.01661	+	0.586940i	0.913120	−	0.407690i	$-0.133666\pi$
$887$	901.733	+	520.616i	1.01661	+	0.586940i	0.103490	+	0.994630i	$0.466999\pi$
$888$		0			0
$889$	−38.0300	−	65.8698i	−0.0427784	−	0.0740943i
$890$		−	748.542i		−	0.841058i
$891$		0			0
$892$	−253.770			−0.284495
$893$	229.997	−	132.789i	0.257555	−	0.148700i
$894$		0			0
$895$	−187.457	+	324.685i	−0.209449	+	0.362777i
$896$	25.9230	+	14.9666i	0.0289319	+	0.0167038i
$897$		0			0
$898$	−37.5045	−	64.9598i	−0.0417645	−	0.0723383i
$899$		−	18.4322i		−	0.0205030i
$900$		0			0
$901$	2406.62			2.67106
$902$	1109.93	−	640.821i	1.23053	−	0.710445i
$903$		0			0
$904$	281.939	−	488.333i	0.311880	−	0.540192i
$905$	−666.534	−	384.823i	−0.736501	−	0.425219i
$906$		0			0
$907$	−368.077	−	637.528i	−0.405818	−	0.702897i	0.588598	−	0.808426i	$-0.299680\pi$
$907$	−368.077	−	637.528i	−0.405818	−	0.702897i	−0.994416	+	0.105528i	$0.966347\pi$
$908$			532.230i			0.586156i
$909$		0			0
$910$	−55.7770			−0.0612934
$911$	688.026	−	397.232i	0.755242	−	0.436039i	−0.0723426	−	0.997380i	$-0.523047\pi$
$911$	688.026	−	397.232i	0.755242	−	0.436039i	0.827585	+	0.561340i	$0.189714\pi$
$912$		0			0
$913$	344.487	−	596.669i	0.377313	−	0.653525i
$914$	−228.729	−	132.057i	−0.250251	−	0.144482i
$915$		0			0
$916$	331.048	+	573.393i	0.361406	+	0.625974i
$917$			653.435i			0.712579i
$918$		0			0
$919$	−623.915			−0.678907			−0.339453	−	0.940623i	$-0.610242\pi$
$919$	−623.915			−0.678907			−0.339453	+	0.940623i	$0.610242\pi$
$920$	508.240	−	293.432i	0.552434	−	0.318948i
$921$		0			0
$922$	−301.423	+	522.079i	−0.326923	+	0.566247i
$923$	126.289	+	72.9131i	0.136825	+	0.0789958i
$924$		0			0
$925$	−388.499	−	672.900i	−0.419999	−	0.727460i
$926$		−	275.723i		−	0.297757i
$927$		0			0
$928$	−113.929			−0.122769
$929$	−324.127	+	187.135i	−0.348899	+	0.201437i	−0.664200	−	0.747555i	$-0.731228\pi$
$929$	−324.127	+	187.135i	−0.348899	+	0.201437i	0.315301	+	0.948992i	$0.397894\pi$
$930$		0			0
$931$	−17.6828	+	30.6275i	−0.0189934	+	0.0328974i
$932$	6.67662	+	3.85475i	0.00716376	+	0.00413600i
$933$		0			0
$934$	−383.442	−	664.142i	−0.410538	−	0.711073i
$935$			2850.81i			3.04899i
$936$		0			0
$937$	−1287.98			−1.37458			−0.687288	−	0.726385i	$-0.741199\pi$
$937$	−1287.98			−1.37458			−0.687288	+	0.726385i	$0.741199\pi$
$938$	9.87697	−	5.70247i	0.0105298	−	0.00607939i
$939$		0			0
$940$	−315.927	+	547.202i	−0.336093	+	0.582129i
$941$	513.495	+	296.466i	0.545691	+	0.315055i	0.747382	−	0.664394i	$-0.231310\pi$
$941$	513.495	+	296.466i	0.545691	+	0.315055i	−0.201691	+	0.979449i	$0.564644\pi$
$942$		0			0
$943$	870.141	+	1507.13i	0.922737	+	1.59823i
$944$			63.0474i			0.0667875i
$945$		0			0
$946$	−62.2142			−0.0657656
$947$	191.983	−	110.842i	0.202728	−	0.117045i	−0.395199	−	0.918595i	$-0.629324\pi$
$947$	191.983	−	110.842i	0.202728	−	0.117045i	0.597927	+	0.801550i	$0.295991\pi$
$948$		0			0
$949$	10.1788	−	17.6303i	0.0107258	−	0.0185777i
$950$	68.8120	+	39.7286i	0.0724337	+	0.0418196i
$951$		0			0
$952$	−98.7204	−	170.989i	−0.103698	−	0.179610i
$953$		−	1153.34i		−	1.21022i	−0.796140	−	0.605112i	$-0.793128\pi$
$953$		−	1153.34i		−	1.21022i	0.796140	−	0.605112i	$-0.206872\pi$
$954$		0			0
$955$	−879.088			−0.920511
$956$	−643.135	+	371.314i	−0.672736	+	0.388404i
$957$		0			0
$958$	274.382	−	475.244i	0.286412	−	0.496079i
$959$	−451.278	−	260.545i	−0.470571	−	0.271684i
$960$		0			0
$961$	480.081	+	831.525i	0.499564	+	0.865271i
$962$		−	245.082i		−	0.254763i
$963$		0			0
$964$	303.914			0.315263
$965$	1173.01	−	677.239i	1.21556	−	0.701802i
$966$		0			0
$967$	−120.494	+	208.702i	−0.124606	+	0.215824i	−0.921579	−	0.388191i	$-0.873100\pi$
$967$	−120.494	+	208.702i	−0.124606	+	0.215824i	0.796973	+	0.604015i	$0.206433\pi$
$968$	−495.325	−	285.976i	−0.511700	−	0.295430i
$969$		0			0
$970$	−24.7363	−	42.8445i	−0.0255013	−	0.0441696i
$971$			1829.70i			1.88434i	0.335131	+	0.942172i	$0.391220\pi$
$971$			1829.70i			1.88434i	−0.335131	+	0.942172i	$0.608780\pi$
$972$		0			0
$973$	−600.548			−0.617213
$974$	366.277	−	211.470i	0.376055	−	0.217115i
$975$		0			0
$976$	157.530	−	272.851i	0.161404	−	0.279560i
$977$	−617.992	−	356.798i	−0.632540	−	0.365197i	0.149195	−	0.988808i	$-0.452332\pi$
$977$	−617.992	−	356.798i	−0.632540	−	0.365197i	−0.781735	+	0.623610i	$0.785665\pi$
$978$		0			0
$979$	−791.660	−	1371.20i	−0.808641	−	1.40061i
$980$		−	84.1408i		−	0.0858580i
$981$		0			0
$982$	834.712			0.850012
$983$	13.1289	−	7.57997i	0.0133559	−	0.00771106i	−0.493307	−	0.869855i	$-0.664212\pi$
$983$	13.1289	−	7.57997i	0.0133559	−	0.00771106i	0.506663	+	0.862144i	$0.330879\pi$
$984$		0			0
$985$	661.029	−	1144.94i	0.671096	−	1.16237i
$986$	650.803	+	375.741i	0.660043	+	0.381076i
$987$		0			0
$988$	12.5313	+	21.7048i	0.0126835	+	0.0219684i
$989$		−	84.4778i		−	0.0854174i
$990$		0			0
$991$	1059.57			1.06919			0.534597	−	0.845107i	$-0.320463\pi$
$991$	1059.57			1.06919			0.534597	+	0.845107i	$0.320463\pi$
$992$	−4.48355	+	2.58858i	−0.00451971	+	0.00260946i
$993$		0			0
$994$	−109.991	+	190.510i	−0.110655	+	0.191660i
$995$	−875.544	−	505.495i	−0.879944	−	0.508036i
$996$		0			0
$997$	−213.586	−	369.941i	−0.214228	−	0.371054i	0.738805	−	0.673919i	$-0.235390\pi$
$997$	−213.586	−	369.941i	−0.214228	−	0.371054i	−0.953034	+	0.302865i	$0.902057\pi$
$998$			509.297i			0.510317i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.q.a.71.8		24
3.2	odd	2		126.3.q.a.113.5	yes	24
9.2	odd	6	inner	378.3.q.a.197.8		24
9.4	even	3		1134.3.b.c.323.22		24
9.5	odd	6		1134.3.b.c.323.3		24
9.7	even	3		126.3.q.a.29.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.q.a.29.5	✓	24	9.7	even	3
126.3.q.a.113.5	yes	24	3.2	odd	2
378.3.q.a.71.8		24	1.1	even	1	trivial
378.3.q.a.197.8		24	9.2	odd	6	inner
1134.3.b.c.323.3		24	9.5	odd	6
1134.3.b.c.323.22		24	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	378.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-5.20486 - 3.00503i) q^{5} +(-1.32288 - 2.29129i) q^{7} -2.82843i q^{8} -8.49950 q^{10} +(-15.5696 + 8.98910i) q^{11} +(-1.24017 + 2.14804i) q^{13} +(-3.24037 - 1.87083i) q^{14} +(-2.00000 - 3.46410i) q^{16} +26.3841i q^{17} +5.05223 q^{19} +(-10.4097 + 6.01006i) q^{20} +(-12.7125 + 22.0187i) q^{22} +(-29.8982 - 17.2617i) q^{23} +(5.56039 + 9.63088i) q^{25} +3.50774i q^{26} -5.29150 q^{28} +(17.4418 - 10.0700i) q^{29} +(0.457601 - 0.792588i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(18.6564 + 32.3138i) q^{34} +15.9011i q^{35} -69.8690 q^{37} +(6.18769 - 3.57247i) q^{38} +(-8.49950 + 14.7216i) q^{40} +(-43.6552 - 25.2043i) q^{41} +(1.22348 + 2.11914i) q^{43} +35.9564i q^{44} -48.8235 q^{46} +(45.5238 - 26.2832i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(13.6201 + 7.86358i) q^{50} +(2.48035 + 4.29609i) q^{52} -91.2148i q^{53} +108.050 q^{55} +(-6.48074 + 3.74166i) q^{56} +(14.2412 - 24.6664i) q^{58} +(-13.6502 - 7.88092i) q^{59} +(39.3826 + 68.2126i) q^{61} -1.29429i q^{62} -8.00000 q^{64} +(12.9099 - 7.45351i) q^{65} +(-1.52405 + 2.63973i) q^{67} +(45.6987 + 26.3841i) q^{68} +(11.2438 + 19.4748i) q^{70} -58.7927i q^{71} -8.20759 q^{73} +(-85.5717 + 49.4049i) q^{74} +(5.05223 - 8.75072i) q^{76} +(41.1932 + 23.7829i) q^{77} +(-23.0285 - 39.8865i) q^{79} +24.0402i q^{80} -71.2887 q^{82} +(-33.1885 + 19.1614i) q^{83} +(79.2851 - 137.326i) q^{85} +(2.99691 + 1.73027i) q^{86} +(25.4250 + 44.0374i) q^{88} +88.0689i q^{89} +6.56238 q^{91} +(-59.7964 + 34.5235i) q^{92} +(37.1700 - 64.3804i) q^{94} +(-26.2962 - 15.1821i) q^{95} +(2.91032 + 5.04083i) q^{97} +9.89949i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} - 36 q^{5} - 48 q^{16} + 24 q^{19} - 72 q^{20} + 24 q^{22} + 72 q^{23} + 72 q^{25} + 108 q^{29} - 60 q^{31} - 48 q^{34} - 168 q^{37} - 144 q^{38} - 108 q^{41} + 60 q^{43} + 324 q^{47} - 84 q^{49}+ \cdots + 48 q^{97}+O(q^{100}) \) 24 * q + 24 * q^4 - 36 * q^5 - 48 * q^16 + 24 * q^19 - 72 * q^20 + 24 * q^22 + 72 * q^23 + 72 * q^25 + 108 * q^29 - 60 * q^31 - 48 * q^34 - 168 * q^37 - 144 * q^38 - 108 * q^41 + 60 * q^43 + 324 * q^47 - 84 * q^49 - 144 * q^50 + 264 * q^55 + 432 * q^59 - 192 * q^64 + 180 * q^65 + 72 * q^67 - 72 * q^68 + 24 * q^73 - 288 * q^74 + 24 * q^76 + 12 * q^79 - 288 * q^82 - 756 * q^83 - 156 * q^85 - 360 * q^86 - 48 * q^88 - 168 * q^91 + 144 * q^92 + 936 * q^95 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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