LMFDB - Embedded newform 378.3.q.a.197.8

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			197.8
Character	$\chi$	$=$	378.197
Dual form			378.3.q.a.71.8

$q$-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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

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

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	−0.920109	−	0.391663i	$-0.871900\pi$
$5$	−5.20486	+	3.00503i	−1.04097	+	0.601006i	−0.120864	+	0.992669i	$0.538566\pi$
$6$		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	−0.419525	−	0.907744i	$-0.637803\pi$
$11$	−15.5696	−	8.98910i	−1.41542	−	0.817191i	−0.995892	+	0.0905531i	$0.971137\pi$
$12$		0			0
$13$	−1.24017	−	2.14804i	−0.0953979	−	0.165234i	0.814377	−	0.580337i	$-0.197079\pi$
$13$	−1.24017	−	2.14804i	−0.0953979	−	0.165234i	−0.909775	+	0.415103i	$0.863746\pi$
$14$	−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	$-0.717244\pi$
$17$		−	26.3841i		−	1.55201i	0.630728	−	0.776004i	$-0.282756\pi$
$18$		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	−0.980390	−	0.197066i	$-0.936859\pi$
$23$	−29.8982	+	17.2617i	−1.29992	+	0.750510i	−0.319531	+	0.947576i	$0.603525\pi$
$24$		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	0.769609	−	0.638516i	$-0.220451\pi$
$29$	17.4418	+	10.0700i	0.601442	+	0.347243i	−0.168167	+	0.985759i	$0.553785\pi$
$30$		0			0
$31$	0.457601	+	0.792588i	0.0147613	+	0.0255673i	0.873312	−	0.487162i	$-0.161968\pi$
$31$	0.457601	+	0.792588i	0.0147613	+	0.0255673i	−0.858550	+	0.512729i	$0.828634\pi$
$32$	−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	−0.926745	−	0.375690i	$-0.877406\pi$
$41$	−43.6552	+	25.2043i	−1.06476	+	0.614740i	−0.138016	+	0.990430i	$0.544072\pi$
$42$		0			0
$43$	1.22348	−	2.11914i	0.0284531	−	0.0492823i	−0.851448	−	0.524439i	$-0.824275\pi$
$43$	1.22348	−	2.11914i	0.0284531	−	0.0492823i	0.879901	+	0.475156i	$0.157609\pi$
$44$		−	35.9564i		−	0.817191i
$45$		0			0
$46$	−48.8235			−1.06138
$47$	45.5238	+	26.2832i	0.968592	+	0.559217i	0.898807	−	0.438345i	$-0.144435\pi$
$47$	45.5238	+	26.2832i	0.968592	+	0.559217i	0.0697853	+	0.997562i	$0.477769\pi$
$48$		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	$0.329860\pi$
$53$			91.2148i			1.72103i	−0.509421	+	0.860517i	$0.670140\pi$
$54$		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	−0.611199	−	0.791477i	$-0.709312\pi$
$59$	−13.6502	+	7.88092i	−0.231359	+	0.133575i	0.379840	+	0.925052i	$0.375979\pi$
$60$		0			0
$61$	39.3826	−	68.2126i	0.645616	−	1.11824i	−0.338543	−	0.940951i	$-0.609934\pi$
$61$	39.3826	−	68.2126i	0.645616	−	1.11824i	0.984159	−	0.177289i	$-0.0567327\pi$
$62$			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	0.854428	−	0.519570i	$-0.173908\pi$
$67$	−1.52405	−	2.63973i	−0.0227470	−	0.0393990i	−0.877175	+	0.480171i	$0.840575\pi$
$68$	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	$0.135880\pi$
$71$			58.7927i			0.828066i	−0.910262	+	0.414033i	$0.864120\pi$
$72$		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	−0.974165	−	0.225839i	$-0.927488\pi$
$79$	−23.0285	+	39.8865i	−0.291500	+	0.504892i	0.682665	+	0.730732i	$0.260821\pi$
$80$		−	24.0402i		−	0.300503i
$81$		0			0
$82$	−71.2887			−0.869374
$83$	−33.1885	−	19.1614i	−0.399861	−	0.230860i	0.286563	−	0.958061i	$-0.407487\pi$
$83$	−33.1885	−	19.1614i	−0.399861	−	0.230860i	−0.686424	+	0.727202i	$0.740821\pi$
$84$		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	$-0.835253\pi$
$89$		−	88.0689i		−	0.989538i	0.869025	−	0.494769i	$-0.164747\pi$
$90$		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	−0.850634	−	0.525759i	$-0.823782\pi$
$97$	2.91032	−	5.04083i	0.0300033	−	0.0519673i	0.880637	+	0.473791i	$0.157115\pi$
$98$		−	9.89949i		−	0.101015i
$99$		0			0
$100$	22.2416			0.222416
$101$	49.6443	+	28.6621i	0.491528	+	0.283784i	0.725208	−	0.688530i	$-0.241744\pi$
$101$	49.6443	+	28.6621i	0.491528	+	0.283784i	−0.233680	+	0.972313i	$0.575077\pi$
$102$		0			0
$103$	2.65907	+	4.60565i	0.0258162	+	0.0447150i	0.878645	−	0.477476i	$-0.158448\pi$
$103$	2.65907	+	4.60565i	0.0258162	+	0.0447150i	−0.852829	+	0.522191i	$0.825115\pi$
$104$	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	$-0.986504\pi$
$107$		−	9.07038i		−	0.0847699i	0.999101	−	0.0423850i	$-0.0134956\pi$
$108$		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	0.528443	−	0.848969i	$-0.322776\pi$
$113$	172.652	−	99.6806i	1.52789	−	0.882129i	0.999450	−	0.0331605i	$-0.0105573\pi$
$114$		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	−0.649476	+	0.760382i	$0.725012\pi$
$131$	−213.887	+	123.488i	−1.63272	+	0.942654i	−0.983248	+	0.182272i	$0.941655\pi$
$132$		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	0.970111	−	0.242663i	$-0.0780209\pi$
$137$	170.567	+	98.4768i	1.24501	+	0.718809i	0.274903	+	0.961472i	$0.411354\pi$
$138$		0			0
$139$	113.493	+	196.575i	0.816496	+	1.41421i	0.908249	+	0.418430i	$0.137420\pi$
$139$	113.493	+	196.575i	0.816496	+	1.41421i	−0.0917531	+	0.995782i	$0.529247\pi$
$140$	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	−0.870010	−	0.493035i	$-0.835887\pi$
$149$	−130.827	+	75.5330i	−0.878034	+	0.506933i	−0.00802404	+	0.999968i	$0.502554\pi$
$150$		0			0
$151$	−42.0460	+	72.8259i	−0.278451	+	0.482291i	−0.971000	−	0.239080i	$-0.923154\pi$
$151$	−42.0460	+	72.8259i	−0.278451	+	0.482291i	0.692549	+	0.721371i	$0.256488\pi$
$152$			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	0.826665	−	0.562694i	$-0.190235\pi$
$157$	−11.6141	−	20.1162i	−0.0739751	−	0.128129i	−0.900640	+	0.434566i	$0.856902\pi$
$158$	−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	−0.239679	−	0.970852i	$-0.577042\pi$
$167$	80.3710	−	46.4022i	0.481263	−	0.277858i	0.720943	+	0.692995i	$0.243709\pi$
$168$		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	−0.0222350	−	0.999753i	$-0.507078\pi$
$173$	−155.555	−	89.8099i	−0.899164	−	0.519132i	−0.876929	+	0.480620i	$0.840412\pi$
$174$		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	$0.0557498\pi$
$179$			62.3812i			0.348498i	−0.984702	+	0.174249i	$0.944250\pi$
$180$		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	0.793499	−	0.608572i	$-0.208257\pi$
$191$	126.673	+	73.1348i	0.663210	+	0.382904i	−0.130289	+	0.991476i	$0.541591\pi$
$192$		0			0
$193$	−112.684	−	195.175i	−0.583856	−	1.01127i	−0.995017	−	0.0997058i	$-0.968210\pi$
$193$	−112.684	−	195.175i	−0.583856	−	1.01127i	0.411161	−	0.911563i	$-0.365123\pi$
$194$	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	$-0.811450\pi$
$197$		−	219.974i		−	1.11662i	0.829632	−	0.558311i	$-0.188550\pi$
$198$		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	0.682331	−	0.731043i	$-0.260966\pi$
$211$	−61.5985	−	106.692i	−0.291936	−	0.505648i	−0.974268	+	0.225395i	$0.927633\pi$
$212$	−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	−0.972487	−	0.232959i	$-0.925159\pi$
$223$	−63.4424	+	109.886i	−0.284495	+	0.492760i	0.687991	+	0.725719i	$0.258493\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	281.939			1.24752
$227$	−230.462	−	133.058i	−1.01525	−	0.586156i	−0.102527	−	0.994730i	$-0.532693\pi$
$227$	−230.462	−	133.058i	−1.01525	−	0.586156i	−0.912725	+	0.408574i	$0.866026\pi$
$228$		0			0
$229$	−165.524	−	286.696i	−0.722813	−	1.25195i	−0.959868	−	0.280452i	$-0.909515\pi$
$229$	−165.524	−	286.696i	−0.722813	−	1.25195i	0.237055	−	0.971496i	$-0.423818\pi$
$230$	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	$-0.997367\pi$
$233$		−	3.85475i		−	0.0165440i	0.999966	−	0.00827199i	$-0.00263309\pi$
$234$		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	−0.987604	−	0.156964i	$-0.949829\pi$
$239$	−321.568	+	185.657i	−1.34547	+	0.776808i	−0.357867	+	0.933772i	$0.616496\pi$
$240$		0			0
$241$	75.9784	−	131.598i	0.315263	−	0.546051i	−0.664230	−	0.747528i	$-0.731241\pi$
$241$	75.9784	−	131.598i	0.315263	−	0.546051i	0.979493	+	0.201476i	$0.0645739\pi$
$242$			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	$-0.851426\pi$
$251$		−	225.897i		−	0.899989i	0.893031	−	0.449995i	$-0.148574\pi$
$252$		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	−0.790234	−	0.612805i	$-0.790041\pi$
$257$	−168.244	+	97.1359i	−0.654647	+	0.377961i	0.135587	+	0.990765i	$0.456708\pi$
$258$		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	0.0697963	−	0.997561i	$-0.477765\pi$
$263$	−199.675	−	115.282i	−0.759219	−	0.438335i	−0.829015	+	0.559226i	$0.811098\pi$
$264$		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	$-0.980913\pi$
$269$		−	32.2412i		−	0.119856i	0.998203	−	0.0599279i	$-0.0190871\pi$
$270$		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	−0.991926	−	0.126821i	$-0.959523\pi$
$277$	−106.959	+	185.258i	−0.386132	+	0.668801i	0.605793	+	0.795622i	$0.292856\pi$
$278$			321.006i			1.15470i
$279$		0			0
$280$	44.9751			0.160626
$281$	57.3099	+	33.0879i	0.203950	+	0.117750i	0.598497	−	0.801125i	$-0.295765\pi$
$281$	57.3099	+	33.0879i	0.203950	+	0.117750i	−0.394547	+	0.918876i	$0.629098\pi$
$282$		0			0
$283$	74.7213	+	129.421i	0.264033	+	0.457318i	0.967310	−	0.253598i	$-0.0816140\pi$
$283$	74.7213	+	129.421i	0.264033	+	0.457318i	−0.703277	+	0.710916i	$0.748281\pi$
$284$	−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	0.123248	−	0.992376i	$-0.460669\pi$
$293$	305.978	−	176.657i	1.04430	−	0.602924i	0.921047	+	0.389452i	$0.127336\pi$
$294$		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	−0.0231572	−	0.999732i	$-0.507372\pi$
$311$	258.459	−	149.221i	0.831057	−	0.479811i	0.854215	+	0.519921i	$0.174038\pi$
$312$		0			0
$313$	−26.7197	+	46.2799i	−0.0853664	+	0.147859i	−0.905547	−	0.424245i	$-0.860539\pi$
$313$	−26.7197	+	46.2799i	−0.0853664	+	0.147859i	0.820181	+	0.572104i	$0.193873\pi$
$314$		−	32.8496i		−	0.104617i
$315$		0			0
$316$	−92.1139			−0.291500
$317$	−220.308	−	127.195i	−0.694978	−	0.401246i	0.110496	−	0.993877i	$-0.464756\pi$
$317$	−220.308	−	127.195i	−0.694978	−	0.401246i	−0.805474	+	0.592631i	$0.798089\pi$
$318$		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	−0.954614	−	0.297847i	$-0.903731\pi$
$331$	−72.6094	+	125.763i	−0.219364	+	0.379949i	0.735250	+	0.677796i	$0.237065\pi$
$332$		−	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	−0.932774	−	0.360460i	$-0.882620\pi$
$337$	−262.373	−	454.444i	−0.778555	−	1.34850i	0.154219	−	0.988037i	$-0.450714\pi$
$338$	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	−0.978716	−	0.205220i	$-0.934209\pi$
$347$	−447.751	+	258.509i	−1.29035	+	0.744983i	−0.311632	+	0.950203i	$0.600876\pi$
$348$		0			0
$349$	26.3750	−	45.6828i	0.0755731	−	0.130896i	−0.825762	−	0.564018i	$-0.809255\pi$
$349$	26.3750	−	45.6828i	0.0755731	−	0.130896i	0.901335	+	0.433122i	$0.142588\pi$
$350$			41.6102i			0.118886i
$351$		0			0
$352$	101.700			0.288921
$353$	422.969	+	244.201i	1.19821	+	0.691788i	0.960156	−	0.279464i	$-0.0901567\pi$
$353$	422.969	+	244.201i	1.19821	+	0.691788i	0.238055	+	0.971252i	$0.423490\pi$
$354$		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	$-0.884052\pi$
$359$		−	255.794i		−	0.712518i	0.934387	−	0.356259i	$-0.115948\pi$
$360$		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	0.0970209	+	0.995282i	$0.469069\pi$
$367$	−298.529	+	517.067i	−0.813429	+	1.40890i	−0.910450	+	0.413619i	$0.864265\pi$
$368$		−	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	0.925634	−	0.378419i	$-0.123532\pi$
$373$	50.3910	+	87.2798i	0.135097	+	0.233994i	−0.790538	+	0.612413i	$0.790199\pi$
$374$	−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	−0.594039	−	0.804436i	$-0.702467\pi$
$383$	−74.4535	+	42.9858i	−0.194396	+	0.112234i	0.399643	+	0.916671i	$0.369134\pi$
$384$		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	0.719336	−	0.694662i	$-0.244446\pi$
$389$	185.712	+	107.221i	0.477409	+	0.275632i	−0.241927	+	0.970294i	$0.577779\pi$
$390$		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	−0.314232	−	0.949346i	$-0.601747\pi$
$401$	140.675	−	81.2186i	0.350810	−	0.202540i	0.665042	+	0.746806i	$0.268414\pi$
$402$		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	0.997297	+	0.0734799i	$0.0234105\pi$
$409$	229.974	+	398.327i	0.562284	+	0.973904i	−0.435013	+	0.900424i	$0.643256\pi$
$410$	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	−0.467160	−	0.884173i	$-0.654723\pi$
$419$	27.2249	−	15.7183i	0.0649759	−	0.0375138i	0.532136	+	0.846659i	$0.321390\pi$
$420$		0			0
$421$	72.8545	−	126.188i	0.173051	−	0.299733i	−0.766434	−	0.642323i	$-0.777971\pi$
$421$	72.8545	−	126.188i	0.173051	−	0.299733i	0.939485	+	0.342590i	$0.111304\pi$
$422$		−	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	$-0.867397\pi$
$431$		−	348.799i		−	0.809278i	0.914477	−	0.404639i	$-0.132603\pi$
$432$		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	0.207231	+	0.978292i	$0.433555\pi$
$439$	−326.445	+	565.419i	−0.743610	+	1.28797i	−0.950841	+	0.309679i	$0.899778\pi$
$440$			305.612i			0.694572i
$441$		0			0
$442$	−92.5486			−0.209386
$443$	120.348	+	69.4828i	0.271665	+	0.156846i	0.629644	−	0.776884i	$-0.283201\pi$
$443$	120.348	+	69.4828i	0.271665	+	0.156846i	−0.357979	+	0.933730i	$0.616534\pi$
$444$		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	$0.0188116\pi$
$449$			53.0394i			0.118128i	−0.998254	+	0.0590639i	$0.981188\pi$
$450$		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	−0.949919	−	0.312497i	$-0.898834\pi$
$457$	−93.3782	+	161.736i	−0.204329	+	0.353908i	0.745590	+	0.666405i	$0.232168\pi$
$458$		−	468.173i		−	1.02221i
$459$		0			0
$460$	414.976			0.902122
$461$	−369.166	−	213.138i	−0.800794	−	0.462338i	0.0429550	−	0.999077i	$-0.486323\pi$
$461$	−369.166	−	213.138i	−0.800794	−	0.462338i	−0.843749	+	0.536739i	$0.819656\pi$
$462$		0			0
$463$	97.4829	+	168.845i	0.210546	+	0.364677i	0.951886	−	0.306454i	$-0.0991424\pi$
$463$	97.4829	+	168.845i	0.210546	+	0.364677i	−0.741339	+	0.671130i	$0.765809\pi$
$464$	−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	$0.197177\pi$
$467$			542.269i			1.16118i	−0.814197	+	0.580588i	$0.802823\pi$
$468$		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	0.807929	−	0.589280i	$-0.200588\pi$
$479$	336.048	+	194.018i	0.701562	+	0.405047i	−0.106367	+	0.994327i	$0.533922\pi$
$480$		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	0.120918	−	0.992663i	$-0.461416\pi$
$491$	511.155	−	295.115i	1.04105	−	0.601049i	0.920130	+	0.391613i	$0.128083\pi$
$492$		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	0.627252	−	0.778816i	$-0.284180\pi$
$499$	−180.064	−	311.879i	−0.360849	−	0.625008i	−0.988101	+	0.153808i	$0.950846\pi$
$500$	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	$-0.998843\pi$
$503$		−	3.65643i		−	0.00726925i	0.999993	−	0.00363462i	$-0.00115694\pi$
$504$		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	−0.189900	−	0.981803i	$-0.560816\pi$
$509$	287.797	−	166.160i	0.565417	−	0.326444i	0.755317	+	0.655360i	$0.227483\pi$
$510$		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	$0.204093\pi$
$521$			623.260i			1.19628i	−0.801393	+	0.598138i	$0.795907\pi$
$522$		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	−0.999797	−	0.0201394i	$-0.993589\pi$
$547$	−263.904	+	457.095i	−0.482457	+	0.835641i	0.517340	+	0.855780i	$0.326922\pi$
$548$			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	$0.132317\pi$
$557$			449.852i			0.807634i	−0.914840	+	0.403817i	$0.867683\pi$
$558$		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	−0.985950	−	0.167042i	$-0.946579\pi$
$563$	−751.190	+	433.700i	−1.33426	+	0.770337i	−0.348313	+	0.937378i	$0.613245\pi$
$564$		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	0.768490	−	0.639862i	$-0.221008\pi$
$569$	340.603	+	196.647i	0.598599	+	0.345601i	−0.169891	+	0.985463i	$0.554342\pi$
$570$		0			0
$571$	548.804	+	950.557i	0.961129	+	1.66472i	0.719675	+	0.694311i	$0.244291\pi$
$571$	548.804	+	950.557i	0.961129	+	1.66472i	0.241454	+	0.970412i	$0.422376\pi$
$572$	−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	−0.999763	−	0.0217812i	$-0.993066\pi$
$587$	−891.364	−	514.629i	−1.51851	−	0.876711i	−0.518744	−	0.854929i	$-0.673600\pi$
$588$		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	$-0.875340\pi$
$593$		−	452.693i		−	0.763395i	0.924287	−	0.381698i	$-0.124660\pi$
$594$		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	−0.265224	−	0.964187i	$-0.585446\pi$
$599$	261.867	−	151.189i	0.437174	−	0.252403i	0.702398	+	0.711784i	$0.252113\pi$
$600$		0			0
$601$	−69.7673	+	120.841i	−0.116085	+	0.201066i	−0.918213	−	0.396087i	$-0.870368\pi$
$601$	−69.7673	+	120.841i	−0.116085	+	0.201066i	0.802128	+	0.597153i	$0.203701\pi$
$602$			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	−0.909325	−	0.416087i	$-0.863401\pi$
$607$	−494.708	−	856.859i	−0.815004	−	1.41163i	0.0943203	−	0.995542i	$-0.469932\pi$
$608$	−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	−0.809192	−	0.587545i	$-0.800095\pi$
$617$	−434.960	+	251.124i	−0.704959	+	0.407008i	0.104233	+	0.994553i	$0.466761\pi$
$618$		0			0
$619$	112.854	−	195.468i	0.182316	−	0.315781i	−0.760353	−	0.649510i	$-0.774974\pi$
$619$	112.854	−	195.468i	0.182316	−	0.315781i	0.942669	+	0.333730i	$0.108307\pi$
$620$		−	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	0.402719	−	0.915324i	$-0.368065\pi$
$641$	−120.902	−	69.8031i	−0.188615	−	0.108897i	−0.591334	+	0.806427i	$0.701399\pi$
$642$		0			0
$643$	34.3711	+	59.5325i	0.0534543	+	0.0925855i	0.891514	−	0.452992i	$-0.149644\pi$
$643$	34.3711	+	59.5325i	0.0534543	+	0.0925855i	−0.838060	+	0.545578i	$0.816310\pi$
$644$	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	$0.268163\pi$
$647$			965.690i			1.49257i	−0.665629	+	0.746283i	$0.731837\pi$
$648$		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	0.306690	−	0.951809i	$-0.400778\pi$
$653$	838.665	−	484.204i	1.28433	−	0.741506i	0.977636	+	0.210303i	$0.0674451\pi$
$654$		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	0.775574	−	0.631257i	$-0.217461\pi$
$659$	406.390	+	234.629i	0.616676	+	0.356038i	−0.158898	+	0.987295i	$0.550794\pi$
$660$		0			0
$661$	−274.083	−	474.726i	−0.414649	−	0.718193i	0.580743	−	0.814087i	$-0.302762\pi$
$661$	−274.083	−	474.726i	−0.414649	−	0.718193i	−0.995392	+	0.0958941i	$0.969429\pi$
$662$	−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	−0.896768	−	0.442500i	$-0.854092\pi$
$673$	−43.8580	+	75.9643i	−0.0651679	+	0.112874i	0.831601	+	0.555374i	$0.187425\pi$
$674$		−	742.103i		−	1.10104i
$675$		0			0
$676$	325.696			0.481798
$677$	−507.524	−	293.019i	−0.749666	−	0.432820i	0.0759074	−	0.997115i	$-0.475815\pi$
$677$	−507.524	−	293.019i	−0.749666	−	0.432820i	−0.825573	+	0.564295i	$0.809148\pi$
$678$		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	$-0.816208\pi$
$683$		−	745.627i		−	1.09169i	0.837885	−	0.545847i	$-0.183792\pi$
$684$		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	−0.961018	−	0.276486i	$-0.910830\pi$
$691$	−166.576	+	288.518i	−0.241065	+	0.417537i	0.719953	+	0.694023i	$0.244163\pi$
$692$		−	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	$-0.747294\pi$
$701$		−	999.755i		−	1.42618i	0.701070	−	0.713092i	$-0.252706\pi$
$702$		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	−0.232113	+	0.972689i	$0.574564\pi$
$709$	−679.527	+	1176.97i	−0.958430	+	1.66005i	−0.726317	+	0.687360i	$0.758769\pi$
$710$		−	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	$-0.835855\pi$
$719$		−	709.113i		−	0.986249i	0.869959	−	0.493125i	$-0.164145\pi$
$720$		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	−0.822432	−	0.568864i	$-0.807383\pi$
$727$	59.2031	−	102.543i	0.0814347	−	0.141049i	0.903866	+	0.427815i	$0.140716\pi$
$728$			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	−0.966661	−	0.256061i	$-0.917575\pi$
$733$	−516.828	−	895.172i	−0.705085	−	1.22124i	0.261575	−	0.965183i	$-0.415758\pi$
$734$	−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	−0.829286	−	0.558825i	$-0.811252\pi$
$743$	−564.659	+	326.006i	−0.759972	+	0.438770i	0.0693136	+	0.997595i	$0.477919\pi$
$744$		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	0.873366	−	0.487064i	$-0.161932\pi$
$751$	11.1700	+	19.3470i	0.0148735	+	0.0257617i	−0.858493	+	0.512826i	$0.828599\pi$
$752$	−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	0.201322	−	0.979525i	$-0.435476\pi$
$761$	875.361	−	505.390i	1.15028	−	0.664113i	0.948955	+	0.315413i	$0.102143\pi$
$762$		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	0.949183	−	0.314726i	$-0.101913\pi$
$769$	155.362	+	269.094i	0.202031	+	0.349928i	−0.747152	+	0.664653i	$0.768579\pi$
$770$	−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	$0.0836891\pi$
$773$			401.803i			0.519797i	−0.965636	+	0.259899i	$0.916311\pi$
$774$		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	0.637185	−	0.770711i	$-0.280099\pi$
$787$	−274.555	−	475.543i	−0.348863	−	0.604248i	−0.986048	+	0.166463i	$0.946765\pi$
$788$	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	−0.997245	−	0.0741765i	$-0.976367\pi$
$797$	−1141.01	+	658.761i	−1.43163	+	0.826551i	−0.434384	+	0.900728i	$0.643034\pi$
$798$		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	$-0.923880\pi$
$809$		−	383.248i		−	0.473731i	0.971542	−	0.236865i	$-0.0761201\pi$
$810$		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	−0.0336771	−	0.999433i	$-0.510722\pi$
$821$	−752.077	−	434.212i	−0.916050	−	0.528882i	−0.882373	+	0.470551i	$0.844055\pi$
$822$		0			0
$823$	−177.628	−	307.660i	−0.215829	−	0.373828i	0.737699	−	0.675129i	$-0.235912\pi$
$823$	−177.628	−	307.660i	−0.215829	−	0.373828i	−0.953529	+	0.301302i	$0.902579\pi$
$824$	−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	$0.109670\pi$
$827$			558.661i			0.675527i	−0.941231	+	0.337763i	$0.890330\pi$
$828$		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	0.968870	−	0.247572i	$-0.0796327\pi$
$839$	1039.44	+	600.120i	1.23890	+	0.715280i	0.270031	+	0.962852i	$0.412966\pi$
$840$		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	0.0247485	+	0.999694i	$0.492122\pi$
$853$	−727.938	+	1260.83i	−0.853386	+	1.47811i	−0.878134	+	0.478414i	$0.841212\pi$
$854$			294.712i			0.345096i
$855$		0			0
$856$	25.6549			0.0299707
$857$	−883.035	−	509.821i	−1.03038	−	0.594890i	−0.113286	−	0.993562i	$-0.536138\pi$
$857$	−883.035	−	509.821i	−1.03038	−	0.594890i	−0.917093	+	0.398672i	$0.869471\pi$
$858$		0			0
$859$	219.697	+	380.527i	0.255759	+	0.442988i	0.965101	−	0.261876i	$-0.0843413\pi$
$859$	219.697	+	380.527i	0.255759	+	0.442988i	−0.709342	+	0.704864i	$0.751008\pi$
$860$	−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	$0.273682\pi$
$863$			1307.81i			1.51542i	−0.652591	+	0.757711i	$0.726318\pi$
$864$		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	0.999987	+	0.00516691i	$0.00164468\pi$
$877$	442.418	+	766.291i	0.504468	+	0.873764i	−0.495519	+	0.868597i	$0.665022\pi$
$878$	−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	$-0.665461\pi$
$881$		−	1529.26i		−	1.73583i	0.496716	−	0.867913i	$-0.334539\pi$
$882$		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	0.103490	−	0.994630i	$-0.466999\pi$
$887$	901.733	−	520.616i	1.01661	−	0.586940i	0.913120	+	0.407690i	$0.133666\pi$
$888$		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	−0.994416	−	0.105528i	$-0.966347\pi$
$907$	−368.077	+	637.528i	−0.405818	+	0.702897i	0.588598	+	0.808426i	$0.299680\pi$
$908$		−	532.230i		−	0.586156i
$909$		0			0
$910$	−55.7770			−0.0612934
$911$	688.026	+	397.232i	0.755242	+	0.436039i	0.827585	−	0.561340i	$-0.189714\pi$
$911$	688.026	+	397.232i	0.755242	+	0.436039i	−0.0723426	+	0.997380i	$0.523047\pi$
$912$		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	0.315301	−	0.948992i	$-0.397894\pi$
$929$	−324.127	−	187.135i	−0.348899	−	0.201437i	−0.664200	+	0.747555i	$0.731228\pi$
$930$		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	−0.201691	−	0.979449i	$-0.564644\pi$
$941$	513.495	−	296.466i	0.545691	−	0.315055i	0.747382	+	0.664394i	$0.231310\pi$
$942$		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	0.597927	−	0.801550i	$-0.295991\pi$
$947$	191.983	+	110.842i	0.202728	+	0.117045i	−0.395199	+	0.918595i	$0.629324\pi$
$948$		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	$0.206872\pi$
$953$			1153.34i			1.21022i	−0.796140	+	0.605112i	$0.793128\pi$
$954$		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	0.796973	−	0.604015i	$-0.206433\pi$
$967$	−120.494	−	208.702i	−0.124606	−	0.215824i	−0.921579	+	0.388191i	$0.873100\pi$
$968$	−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	$-0.608780\pi$
$971$		−	1829.70i		−	1.88434i	0.335131	−	0.942172i	$-0.391220\pi$
$972$		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	−0.781735	−	0.623610i	$-0.785665\pi$
$977$	−617.992	+	356.798i	−0.632540	+	0.365197i	0.149195	+	0.988808i	$0.452332\pi$
$978$		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	0.506663	−	0.862144i	$-0.330879\pi$
$983$	13.1289	+	7.57997i	0.0133559	+	0.00771106i	−0.493307	+	0.869855i	$0.664212\pi$
$984$		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	−0.953034	−	0.302865i	$-0.902057\pi$
$997$	−213.586	+	369.941i	−0.214228	+	0.371054i	0.738805	+	0.673919i	$0.235390\pi$
$998$		−	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.197.8		24
3.2	odd	2		126.3.q.a.29.5	✓	24
9.2	odd	6		1134.3.b.c.323.22		24
9.4	even	3		126.3.q.a.113.5	yes	24
9.5	odd	6	inner	378.3.q.a.71.8		24
9.7	even	3		1134.3.b.c.323.3		24

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

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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