LMFDB - Embedded newform 378.3.q.a.71.6

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			71.6
Character	$\chi$	$=$	378.71
Dual form			378.3.q.a.197.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(5.52056 + 3.18729i) q^{5} +(1.32288 + 2.29129i) q^{7} +2.82843i q^{8} -9.01503 q^{10} +(-14.5856 + 8.42098i) q^{11} +(-8.77375 + 15.1966i) q^{13} +(-3.24037 - 1.87083i) q^{14} +(-2.00000 - 3.46410i) q^{16} -13.4343i q^{17} +34.1905 q^{19} +(11.0411 - 6.37459i) q^{20} +(11.9091 - 20.6271i) q^{22} +(3.08155 + 1.77914i) q^{23} +(7.81769 + 13.5406i) q^{25} -24.8159i q^{26} +5.29150 q^{28} +(-29.4139 + 16.9821i) q^{29} +(-15.0078 + 25.9943i) q^{31} +(4.89898 + 2.82843i) q^{32} +(9.49945 + 16.4535i) q^{34} +16.8656i q^{35} -37.7845 q^{37} +(-41.8747 + 24.1764i) q^{38} +(-9.01503 + 15.6145i) q^{40} +(-28.4844 - 16.4455i) q^{41} +(34.9160 + 60.4762i) q^{43} +33.6839i q^{44} -5.03215 q^{46} +(22.9154 - 13.2302i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(-19.1493 - 11.0559i) q^{50} +(17.5475 + 30.3931i) q^{52} +8.14401i q^{53} -107.360 q^{55} +(-6.48074 + 3.74166i) q^{56} +(24.0163 - 41.5975i) q^{58} +(87.5730 + 50.5603i) q^{59} +(8.32503 + 14.4194i) q^{61} -42.4484i q^{62} -8.00000 q^{64} +(-96.8719 + 55.9290i) q^{65} +(-21.0059 + 36.3833i) q^{67} +(-23.2688 - 13.4343i) q^{68} +(-11.9258 - 20.6560i) q^{70} +14.4296i q^{71} -42.4557 q^{73} +(46.2764 - 26.7177i) q^{74} +(34.1905 - 59.2197i) q^{76} +(-38.5898 - 22.2798i) q^{77} +(-27.1440 - 47.0147i) q^{79} -25.4984i q^{80} +46.5148 q^{82} +(33.4110 - 19.2899i) q^{83} +(42.8189 - 74.1645i) q^{85} +(-85.5263 - 49.3786i) q^{86} +(-23.8181 - 41.2542i) q^{88} +98.5144i q^{89} -46.4263 q^{91} +(6.16311 - 3.55827i) q^{92} +(-18.7103 + 32.4072i) q^{94} +(188.751 + 108.975i) q^{95} +(10.5777 + 18.3210i) q^{97} -9.89949i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	5.52056	+	3.18729i	1.10411	+	0.637459i	0.937298	−	0.348530i	$-0.113319\pi$
$5$	5.52056	+	3.18729i	1.10411	+	0.637459i	0.166813	+	0.985989i	$0.446652\pi$
$6$		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
$10$	−9.01503			−0.901503
$11$	−14.5856	+	8.42098i	−1.32596	+	0.765543i	−0.984672	−	0.174416i	$-0.944196\pi$
$11$	−14.5856	+	8.42098i	−1.32596	+	0.765543i	−0.341288	+	0.939959i	$0.610863\pi$
$12$		0			0
$13$	−8.77375	+	15.1966i	−0.674904	+	1.16897i	0.301594	+	0.953437i	$0.402481\pi$
$13$	−8.77375	+	15.1966i	−0.674904	+	1.16897i	−0.976497	+	0.215531i	$0.930852\pi$
$14$	−3.24037	−	1.87083i	−0.231455	−	0.133631i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$		−	13.4343i		−	0.790250i	−0.918627	−	0.395125i	$-0.870701\pi$
$17$		−	13.4343i		−	0.790250i	0.918627	−	0.395125i	$-0.129299\pi$
$18$		0			0
$19$	34.1905			1.79950			0.899751	−	0.436404i	$-0.143748\pi$
$19$	34.1905			1.79950			0.899751	+	0.436404i	$0.143748\pi$
$20$	11.0411	−	6.37459i	0.552056	−	0.318729i
$21$		0			0
$22$	11.9091	−	20.6271i	0.541321	−	0.937595i
$23$	3.08155	+	1.77914i	0.133981	+	0.0773537i	0.565492	−	0.824754i	$-0.308686\pi$
$23$	3.08155	+	1.77914i	0.133981	+	0.0773537i	−0.431512	+	0.902107i	$0.642020\pi$
$24$		0			0
$25$	7.81769	+	13.5406i	0.312707	+	0.541625i
$26$		−	24.8159i		−	0.954458i
$27$		0			0
$28$	5.29150			0.188982
$29$	−29.4139	+	16.9821i	−1.01427	+	0.585590i	−0.912440	−	0.409211i	$-0.865804\pi$
$29$	−29.4139	+	16.9821i	−1.01427	+	0.585590i	−0.101832	+	0.994802i	$0.532470\pi$
$30$		0			0
$31$	−15.0078	+	25.9943i	−0.484122	+	0.838524i	−0.999834	−	0.0182380i	$-0.994194\pi$
$31$	−15.0078	+	25.9943i	−0.484122	+	0.838524i	0.515711	+	0.856762i	$0.327528\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$		0			0
$34$	9.49945	+	16.4535i	0.279396	+	0.483927i
$35$			16.8656i			0.481874i
$36$		0			0
$37$	−37.7845			−1.02120			−0.510601	−	0.859818i	$-0.670577\pi$
$37$	−37.7845			−1.02120			−0.510601	+	0.859818i	$0.670577\pi$
$38$	−41.8747	+	24.1764i	−1.10197	+	0.636220i
$39$		0			0
$40$	−9.01503	+	15.6145i	−0.225376	+	0.390362i
$41$	−28.4844	−	16.4455i	−0.694742	−	0.401109i	0.110644	−	0.993860i	$-0.464709\pi$
$41$	−28.4844	−	16.4455i	−0.694742	−	0.401109i	−0.805386	+	0.592751i	$0.798042\pi$
$42$		0			0
$43$	34.9160	+	60.4762i	0.811999	+	1.40642i	0.911463	+	0.411383i	$0.134954\pi$
$43$	34.9160	+	60.4762i	0.811999	+	1.40642i	−0.0994634	+	0.995041i	$0.531713\pi$
$44$			33.6839i			0.765543i
$45$		0			0
$46$	−5.03215			−0.109395
$47$	22.9154	−	13.2302i	0.487561	−	0.281494i	−0.236001	−	0.971753i	$-0.575837\pi$
$47$	22.9154	−	13.2302i	0.487561	−	0.281494i	0.723562	+	0.690259i	$0.242503\pi$
$48$		0			0
$49$	−3.50000	+	6.06218i	−0.0714286	+	0.123718i
$50$	−19.1493	−	11.0559i	−0.382987	−	0.221118i
$51$		0			0
$52$	17.5475	+	30.3931i	0.337452	+	0.584484i
$53$			8.14401i			0.153661i	0.997044	+	0.0768303i	$0.0244800\pi$
$53$			8.14401i			0.153661i	−0.997044	+	0.0768303i	$0.975520\pi$
$54$		0			0
$55$	−107.360			−1.95201
$56$	−6.48074	+	3.74166i	−0.115728	+	0.0668153i
$57$		0			0
$58$	24.0163	−	41.5975i	0.414075	−	0.717198i
$59$	87.5730	+	50.5603i	1.48429	+	0.856954i	0.999840	−	0.0178665i	$-0.00568740\pi$
$59$	87.5730	+	50.5603i	1.48429	+	0.856954i	0.484447	+	0.874820i	$0.339021\pi$
$60$		0			0
$61$	8.32503	+	14.4194i	0.136476	+	0.236383i	0.926160	−	0.377130i	$-0.123089\pi$
$61$	8.32503	+	14.4194i	0.136476	+	0.236383i	−0.789684	+	0.613513i	$0.789756\pi$
$62$		−	42.4484i		−	0.684652i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−96.8719	+	55.9290i	−1.49034	+	0.860446i
$66$		0			0
$67$	−21.0059	+	36.3833i	−0.313521	+	0.543035i	−0.979122	−	0.203273i	$-0.934842\pi$
$67$	−21.0059	+	36.3833i	−0.313521	+	0.543035i	0.665601	+	0.746308i	$0.268175\pi$
$68$	−23.2688	−	13.4343i	−0.342188	−	0.197563i
$69$		0			0
$70$	−11.9258	−	20.6560i	−0.170368	−	0.295086i
$71$			14.4296i			0.203234i	0.994824	+	0.101617i	$0.0324017\pi$
$71$			14.4296i			0.203234i	−0.994824	+	0.101617i	$0.967598\pi$
$72$		0			0
$73$	−42.4557			−0.581584			−0.290792	−	0.956786i	$-0.593919\pi$
$73$	−42.4557			−0.581584			−0.290792	+	0.956786i	$0.593919\pi$
$74$	46.2764	−	26.7177i	0.625357	−	0.361050i
$75$		0			0
$76$	34.1905	−	59.2197i	0.449875	−	0.779207i
$77$	−38.5898	−	22.2798i	−0.501166	−	0.289348i
$78$		0			0
$79$	−27.1440	−	47.0147i	−0.343594	−	0.595123i	0.641503	−	0.767121i	$-0.278311\pi$
$79$	−27.1440	−	47.0147i	−0.343594	−	0.595123i	−0.985097	+	0.171998i	$0.944978\pi$
$80$		−	25.4984i		−	0.318729i
$81$		0			0
$82$	46.5148			0.567254
$83$	33.4110	−	19.2899i	0.402543	−	0.232408i	−0.285038	−	0.958516i	$-0.592006\pi$
$83$	33.4110	−	19.2899i	0.402543	−	0.232408i	0.687580	+	0.726108i	$0.258673\pi$
$84$		0			0
$85$	42.8189	−	74.1645i	0.503752	−	0.872524i
$86$	−85.5263	−	49.3786i	−0.994492	−	0.574170i
$87$		0			0
$88$	−23.8181	−	41.2542i	−0.270660	−	0.468798i
$89$			98.5144i			1.10690i	0.832881	+	0.553452i	$0.186690\pi$
$89$			98.5144i			1.10690i	−0.832881	+	0.553452i	$0.813310\pi$
$90$		0			0
$91$	−46.4263			−0.510179
$92$	6.16311	−	3.55827i	0.0669903	−	0.0386769i
$93$		0			0
$94$	−18.7103	+	32.4072i	−0.199046	+	0.344758i
$95$	188.751	+	108.975i	1.98685	+	1.14711i
$96$		0			0
$97$	10.5777	+	18.3210i	0.109048	+	0.188877i	0.915385	−	0.402580i	$-0.131886\pi$
$97$	10.5777	+	18.3210i	0.109048	+	0.188877i	−0.806337	+	0.591457i	$0.798553\pi$
$98$		−	9.89949i		−	0.101015i
$99$		0			0
$100$	31.2707			0.312707
$101$	43.8679	−	25.3272i	0.434336	−	0.250764i	−0.266856	−	0.963736i	$-0.585985\pi$
$101$	43.8679	−	25.3272i	0.434336	−	0.250764i	0.701192	+	0.712972i	$0.252652\pi$
$102$		0			0
$103$	100.159	−	173.480i	0.972413	−	1.68427i	0.284193	−	0.958767i	$-0.408274\pi$
$103$	100.159	−	173.480i	0.972413	−	1.68427i	0.688220	−	0.725502i	$-0.258392\pi$
$104$	−42.9824	−	24.8159i	−0.413292	−	0.238614i
$105$		0			0
$106$	−5.75869	−	9.97434i	−0.0543272	−	0.0940975i
$107$		−	49.8812i		−	0.466180i	−0.972455	−	0.233090i	$-0.925116\pi$
$107$		−	49.8812i		−	0.466180i	0.972455	−	0.233090i	$-0.0748836\pi$
$108$		0			0
$109$	120.571			1.10616			0.553080	−	0.833128i	$-0.313452\pi$
$109$	120.571			1.10616			0.553080	+	0.833128i	$0.313452\pi$
$110$	131.489	−	75.9153i	1.19536	−	0.690139i
$111$		0			0
$112$	5.29150	−	9.16515i	0.0472456	−	0.0818317i
$113$	−18.6422	−	10.7631i	−0.164975	−	0.0952482i	0.415239	−	0.909712i	$-0.363698\pi$
$113$	−18.6422	−	10.7631i	−0.164975	−	0.0952482i	−0.580214	+	0.814464i	$0.697031\pi$
$114$		0			0
$115$	11.3413	+	19.6436i	0.0986196	+	0.170814i
$116$			67.9285i			0.585590i
$117$		0			0
$118$	−143.006			−1.21192
$119$	30.7817	−	17.7718i	0.258670	−	0.149343i
$120$		0			0
$121$	81.3256	−	140.860i	0.672113	−	1.16413i
$122$	−20.3921	−	11.7734i	−0.167148	−	0.0965030i
$123$		0			0
$124$	30.0156	+	51.9885i	0.242061	+	0.419262i
$125$		−	59.6957i		−	0.477565i
$126$		0			0
$127$	−71.9765			−0.566744			−0.283372	−	0.959010i	$-0.591453\pi$
$127$	−71.9765			−0.566744			−0.283372	+	0.959010i	$0.591453\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$		0			0
$130$	79.0956	−	136.998i	0.608427	−	1.05383i
$131$	81.3545	+	46.9700i	0.621027	+	0.358550i	0.777269	−	0.629169i	$-0.216605\pi$
$131$	81.3545	+	46.9700i	0.621027	+	0.358550i	−0.156242	+	0.987719i	$0.549938\pi$
$132$		0			0
$133$	45.2298	+	78.3403i	0.340074	+	0.589025i
$134$		−	59.4137i		−	0.443386i
$135$		0			0
$136$	37.9978			0.279396
$137$	166.155	−	95.9298i	1.21281	−	0.700218i	0.249442	−	0.968390i	$-0.419753\pi$
$137$	166.155	−	95.9298i	1.21281	−	0.700218i	0.963371	+	0.268172i	$0.0864195\pi$
$138$		0			0
$139$	−65.4130	+	113.299i	−0.470597	+	0.815098i	−0.999435	−	0.0336248i	$-0.989295\pi$
$139$	−65.4130	+	113.299i	−0.470597	+	0.815098i	0.528837	+	0.848723i	$0.322628\pi$
$140$	29.2120	+	16.8656i	0.208657	+	0.120468i
$141$		0			0
$142$	−10.2033	−	17.6726i	−0.0718541	−	0.124455i
$143$		−	295.534i		−	2.06667i
$144$		0			0
$145$	−216.508			−1.49316
$146$	51.9974	−	30.0207i	0.356146	−	0.205621i
$147$		0			0
$148$	−37.7845	+	65.4447i	−0.255301	+	0.442194i
$149$	−14.0716	−	8.12426i	−0.0944405	−	0.0545253i	0.452036	−	0.892000i	$-0.350698\pi$
$149$	−14.0716	−	8.12426i	−0.0944405	−	0.0545253i	−0.546476	+	0.837474i	$0.684031\pi$
$150$		0			0
$151$	63.1067	+	109.304i	0.417925	+	0.723868i	0.995731	−	0.0923066i	$-0.0294240\pi$
$151$	63.1067	+	109.304i	0.417925	+	0.723868i	−0.577805	+	0.816175i	$0.696091\pi$
$152$			96.7054i			0.636220i
$153$		0			0
$154$	63.0168			0.409200
$155$	−165.703	+	95.6685i	−1.06905	+	0.617216i
$156$		0			0
$157$	−13.6184	+	23.5878i	−0.0867414	+	0.150241i	−0.906132	−	0.422995i	$-0.860979\pi$
$157$	−13.6184	+	23.5878i	−0.0867414	+	0.150241i	0.819391	+	0.573236i	$0.194312\pi$
$158$	66.4888	+	38.3874i	0.420815	+	0.242958i
$159$		0			0
$160$	18.0301	+	31.2290i	0.112688	+	0.195181i
$161$			9.41430i			0.0584739i
$162$		0			0
$163$	178.576			1.09556			0.547778	−	0.836624i	$-0.315474\pi$
$163$	178.576			1.09556			0.547778	+	0.836624i	$0.315474\pi$
$164$	−56.9688	+	32.8910i	−0.347371	+	0.200555i
$165$		0			0
$166$	−27.2800	+	47.2503i	−0.164337	+	0.284641i
$167$	−52.9322	−	30.5604i	−0.316959	−	0.182997i	0.333077	−	0.942900i	$-0.391913\pi$
$167$	−52.9322	−	30.5604i	−0.316959	−	0.182997i	−0.650036	+	0.759903i	$0.725246\pi$
$168$		0			0
$169$	−69.4572	−	120.303i	−0.410990	−	0.711855i
$170$			121.110i			0.712413i
$171$		0			0
$172$	139.664			0.811999
$173$	−52.4568	+	30.2860i	−0.303219	+	0.175063i	−0.643888	−	0.765120i	$-0.722680\pi$
$173$	−52.4568	+	30.2860i	−0.303219	+	0.175063i	0.340669	+	0.940183i	$0.389346\pi$
$174$		0			0
$175$	−20.6837	+	35.8251i	−0.118192	+	0.204715i
$176$	58.3422	+	33.6839i	0.331490	+	0.191386i
$177$		0			0
$178$	−69.6602	−	120.655i	−0.391349	−	0.677837i
$179$		−	180.309i		−	1.00731i	−0.863904	−	0.503657i	$-0.831988\pi$
$179$		−	180.309i		−	1.00731i	0.863904	−	0.503657i	$-0.168012\pi$
$180$		0			0
$181$	−85.1609			−0.470502			−0.235251	−	0.971935i	$-0.575591\pi$
$181$	−85.1609			−0.470502			−0.235251	+	0.971935i	$0.575591\pi$
$182$	56.8604	−	32.8284i	0.312420	−	0.180376i
$183$		0			0
$184$	−5.03215	+	8.71595i	−0.0273487	+	0.0473693i
$185$	−208.591	−	120.430i	−1.12752	−	0.650975i
$186$		0			0
$187$	113.129	+	195.946i	0.604971	+	1.04784i
$188$		−	52.9208i		−	0.281494i
$189$		0			0
$190$	−308.229			−1.62226
$191$	318.289	−	183.764i	1.66643	−	0.962117i	0.696898	−	0.717170i	$-0.254563\pi$
$191$	318.289	−	183.764i	1.66643	−	0.962117i	0.969537	−	0.244946i	$-0.0787704\pi$
$192$		0			0
$193$	134.549	−	233.045i	0.697144	−	1.20749i	−0.272308	−	0.962210i	$-0.587787\pi$
$193$	134.549	−	233.045i	0.697144	−	1.20749i	0.969453	−	0.245279i	$-0.0788796\pi$
$194$	−25.9099	−	14.9591i	−0.133556	−	0.0771086i
$195$		0			0
$196$	7.00000	+	12.1244i	0.0357143	+	0.0618590i
$197$		−	272.308i		−	1.38228i	−0.722723	−	0.691138i	$-0.757110\pi$
$197$		−	272.308i		−	1.38228i	0.722723	−	0.691138i	$-0.242890\pi$
$198$		0			0
$199$	111.789			0.561752			0.280876	−	0.959744i	$-0.409375\pi$
$199$	111.789			0.561752			0.280876	+	0.959744i	$0.409375\pi$
$200$	−38.2987	+	22.1118i	−0.191493	+	0.110559i
$201$		0			0
$202$	−35.8180	+	62.0386i	−0.177317	+	0.307122i
$203$	−77.8218	−	44.9304i	−0.383359	−	0.221332i
$204$		0			0
$205$	−104.833	−	181.576i	−0.511381	−	0.885738i
$206$			283.291i			1.37520i
$207$		0			0
$208$	70.1900			0.337452
$209$	−498.688	+	287.918i	−2.38607	+	1.37760i
$210$		0			0
$211$	−8.51986	+	14.7568i	−0.0403785	+	0.0699376i	−0.885508	−	0.464623i	$-0.846190\pi$
$211$	−8.51986	+	14.7568i	−0.0403785	+	0.0699376i	0.845130	+	0.534561i	$0.179523\pi$
$212$	14.1058	+	8.14401i	0.0665370	+	0.0384152i
$213$		0			0
$214$	35.2713	+	61.0918i	0.164819	+	0.285476i
$215$			445.150i			2.07046i
$216$		0			0
$217$	−79.4138			−0.365962
$218$	−147.669	+	85.2569i	−0.677382	+	0.391087i
$219$		0			0
$220$	−107.360	+	185.954i	−0.488002	+	0.845245i
$221$	204.155	+	117.869i	0.923776	+	0.533343i
$222$		0			0
$223$	−161.354	−	279.474i	−0.723563	−	1.25325i	−0.959563	−	0.281494i	$-0.909170\pi$
$223$	−161.354	−	279.474i	−0.723563	−	1.25325i	0.236000	−	0.971753i	$-0.424163\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	30.4425			0.134701
$227$	−137.968	+	79.6559i	−0.607789	+	0.350907i	−0.772099	−	0.635502i	$-0.780793\pi$
$227$	−137.968	+	79.6559i	−0.607789	+	0.350907i	0.164311	+	0.986409i	$0.447460\pi$
$228$		0			0
$229$	124.634	−	215.872i	0.544253	−	0.942674i	−0.454400	−	0.890798i	$-0.650146\pi$
$229$	124.634	−	215.872i	0.544253	−	0.942674i	0.998653	−	0.0518768i	$-0.0165203\pi$
$230$	−27.7803	−	16.0390i	−0.120784	−	0.0697346i
$231$		0			0
$232$	−48.0327	−	83.1950i	−0.207037	−	0.358599i
$233$			344.778i			1.47973i	0.672753	+	0.739867i	$0.265112\pi$
$233$			344.778i			1.47973i	−0.672753	+	0.739867i	$0.734888\pi$
$234$		0			0
$235$	168.674			0.717763
$236$	175.146	−	101.121i	0.742144	−	0.428477i
$237$		0			0
$238$	−25.1332	+	43.5319i	−0.105602	+	0.182907i
$239$	−43.0470	−	24.8532i	−0.180113	−	0.103988i	0.407233	−	0.913324i	$-0.366494\pi$
$239$	−43.0470	−	24.8532i	−0.180113	−	0.103988i	−0.587346	+	0.809336i	$0.699827\pi$
$240$		0			0
$241$	83.6027	+	144.804i	0.346899	+	0.600847i	0.985697	−	0.168528i	$-0.0539012\pi$
$241$	83.6027	+	144.804i	0.346899	+	0.600847i	−0.638798	+	0.769375i	$0.720568\pi$
$242$			230.024i			0.950511i
$243$		0			0
$244$	33.3001			0.136476
$245$	−38.6439	+	22.3111i	−0.157730	+	0.0910655i
$246$		0			0
$247$	−299.979	+	519.579i	−1.21449	+	2.10356i
$248$	−73.5229	−	42.4484i	−0.296463	−	0.171163i
$249$		0			0
$250$	42.2112	+	73.1119i	0.168845	+	0.292448i
$251$			107.145i			0.426871i	0.976957	+	0.213436i	$0.0684653\pi$
$251$			107.145i			0.426871i	−0.976957	+	0.213436i	$0.931535\pi$
$252$		0			0
$253$	−59.9282			−0.236870
$254$	88.1528	−	50.8951i	0.347058	−	0.200374i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−36.6340	−	21.1507i	−0.142545	−	0.0822983i	0.427031	−	0.904237i	$-0.359559\pi$
$257$	−36.6340	−	21.1507i	−0.142545	−	0.0822983i	−0.569576	+	0.821938i	$0.692893\pi$
$258$		0			0
$259$	−49.9842	−	86.5752i	−0.192989	−	0.334267i
$260$			223.716i			0.860446i
$261$		0			0
$262$	−132.851			−0.507066
$263$	−118.330	+	68.3177i	−0.449923	+	0.259763i	−0.707798	−	0.706415i	$-0.750311\pi$
$263$	−118.330	+	68.3177i	−0.449923	+	0.259763i	0.257875	+	0.966178i	$0.416978\pi$
$264$		0			0
$265$	−25.9574	+	44.9595i	−0.0979523	+	0.169658i
$266$	−110.790	−	63.9646i	−0.416504	−	0.240469i
$267$		0			0
$268$	42.0118	+	72.7666i	0.156761	+	0.271517i
$269$			11.4676i			0.0426306i	0.999773	+	0.0213153i	$0.00678539\pi$
$269$			11.4676i			0.0426306i	−0.999773	+	0.0213153i	$0.993215\pi$
$270$		0			0
$271$	127.282			0.469677			0.234839	−	0.972034i	$-0.424544\pi$
$271$	127.282			0.469677			0.234839	+	0.972034i	$0.424544\pi$
$272$	−46.5376	+	26.8685i	−0.171094	+	0.0987813i
$273$		0			0
$274$	−135.665	+	234.979i	−0.495129	+	0.857588i
$275$	−228.051	−	131.665i	−0.829275	−	0.478782i
$276$		0			0
$277$	−26.2499	−	45.4661i	−0.0947649	−	0.164138i	0.814746	−	0.579819i	$-0.196877\pi$
$277$	−26.2499	−	45.4661i	−0.0947649	−	0.164138i	−0.909510	+	0.415681i	$0.863543\pi$
$278$		−	185.016i		−	0.665525i
$279$		0			0
$280$	−47.7030			−0.170368
$281$	434.613	−	250.924i	1.54667	−	0.892967i	0.548272	−	0.836300i	$-0.315286\pi$
$281$	434.613	−	250.924i	1.54667	−	0.892967i	0.998393	−	0.0566674i	$-0.0180475\pi$
$282$		0			0
$283$	−168.127	+	291.204i	−0.594088	+	1.02899i	0.399587	+	0.916695i	$0.369154\pi$
$283$	−168.127	+	291.204i	−0.594088	+	1.02899i	−0.993675	+	0.112295i	$0.964180\pi$
$284$	24.9928	+	14.4296i	0.0880030	+	0.0508085i
$285$		0			0
$286$	208.974	+	361.954i	0.730679	+	1.26557i
$287$		−	87.0213i		−	0.303210i
$288$		0			0
$289$	108.521			0.375505
$290$	265.167	−	153.094i	0.914369	−	0.527911i
$291$		0			0
$292$	−42.4557	+	73.5354i	−0.145396	+	0.251833i
$293$	−263.780	−	152.293i	−0.900272	−	0.519772i	−0.0229833	−	0.999736i	$-0.507316\pi$
$293$	−263.780	−	152.293i	−0.900272	−	0.519772i	−0.877288	+	0.479964i	$0.840650\pi$
$294$		0			0
$295$	322.301	+	558.242i	1.09255	+	1.89234i
$296$		−	106.871i		−	0.361050i
$297$		0			0
$298$	22.9789			0.0771104
$299$	−54.0735	+	31.2194i	−0.180848	+	0.104413i
$300$		0			0
$301$	−92.3790	+	160.005i	−0.306907	+	0.531578i
$302$	−154.579	−	89.2464i	−0.511852	−	0.295518i
$303$		0			0
$304$	−68.3811	−	118.439i	−0.224938	−	0.389604i
$305$			106.137i			0.347991i
$306$		0			0
$307$	317.423			1.03395			0.516975	−	0.856000i	$-0.327058\pi$
$307$	317.423			1.03395			0.516975	+	0.856000i	$0.327058\pi$
$308$	−77.1795	+	44.5596i	−0.250583	+	0.144674i
$309$		0			0
$310$	135.296	−	234.339i	0.436438	−	0.755932i
$311$	37.3570	+	21.5681i	0.120119	+	0.0693507i	0.558856	−	0.829265i	$-0.311241\pi$
$311$	37.3570	+	21.5681i	0.120119	+	0.0693507i	−0.438737	+	0.898616i	$0.644574\pi$
$312$		0			0
$313$	−152.356	−	263.888i	−0.486759	−	0.843091i	0.513125	−	0.858314i	$-0.328488\pi$
$313$	−152.356	−	263.888i	−0.486759	−	0.843091i	−0.999884	+	0.0152225i	$0.995154\pi$
$314$		−	38.5187i		−	0.122671i
$315$		0			0
$316$	−108.576			−0.343594
$317$	−104.314	+	60.2259i	−0.329067	+	0.189987i	−0.655427	−	0.755259i	$-0.727511\pi$
$317$	−104.314	+	60.2259i	−0.329067	+	0.189987i	0.326360	+	0.945246i	$0.394178\pi$
$318$		0			0
$319$	286.012	−	495.387i	0.896589	−	1.55294i
$320$	−44.1644	−	25.4984i	−0.138014	−	0.0796823i
$321$		0			0
$322$	−6.65692	−	11.5301i	−0.0206737	−	0.0358078i
$323$		−	459.324i		−	1.42206i
$324$		0			0
$325$	−274.362			−0.844189
$326$	−218.709	+	126.272i	−0.670888	+	0.387337i
$327$		0			0
$328$	46.5148	−	80.5661i	0.141814	−	0.245628i
$329$	60.6284	+	35.0038i	0.184281	+	0.106395i
$330$		0			0
$331$	−72.4842	−	125.546i	−0.218985	−	0.379294i	0.735513	−	0.677511i	$-0.236941\pi$
$331$	−72.4842	−	125.546i	−0.218985	−	0.379294i	−0.954498	+	0.298217i	$0.903608\pi$
$332$		−	77.1595i		−	0.232408i
$333$		0			0
$334$	86.4379			0.258796
$335$	−231.929	+	133.904i	−0.692324	+	0.399714i
$336$		0			0
$337$	45.0515	−	78.0314i	0.133684	−	0.231547i	−0.791410	−	0.611286i	$-0.790653\pi$
$337$	45.0515	−	78.0314i	0.133684	−	0.231547i	0.925094	+	0.379738i	$0.123986\pi$
$338$	170.135	+	98.2274i	0.503357	+	0.290614i
$339$		0			0
$340$	−85.6378	−	148.329i	−0.251876	−	0.436262i
$341$		−	505.521i		−	1.48247i
$342$		0			0
$343$	−18.5203			−0.0539949
$344$	−171.053	+	98.7573i	−0.497246	+	0.287085i
$345$		0			0
$346$	42.8308	−	74.1851i	0.123788	−	0.214408i
$347$	474.135	+	273.742i	1.36638	+	0.788882i	0.990464	−	0.137771i	$-0.0439938\pi$
$347$	474.135	+	273.742i	1.36638	+	0.788882i	0.375919	+	0.926653i	$0.377327\pi$
$348$		0			0
$349$	15.0822	+	26.1231i	0.0432154	+	0.0748513i	0.886824	−	0.462107i	$-0.152906\pi$
$349$	15.0822	+	26.1231i	0.0432154	+	0.0748513i	−0.843609	+	0.536959i	$0.819573\pi$
$350$		−	58.5022i		−	0.167149i
$351$		0			0
$352$	−95.2725			−0.270660
$353$	−274.034	+	158.214i	−0.776302	+	0.448198i	−0.835118	−	0.550071i	$-0.814601\pi$
$353$	−274.034	+	158.214i	−0.776302	+	0.448198i	0.0588164	+	0.998269i	$0.481267\pi$
$354$		0			0
$355$	−45.9915	+	79.6596i	−0.129553	+	0.224393i
$356$	170.632	+	98.5144i	0.479303	+	0.276726i
$357$		0			0
$358$	127.498	+	220.833i	0.356139	+	0.616851i
$359$		−	154.111i		−	0.429278i	−0.976693	−	0.214639i	$-0.931143\pi$
$359$		−	154.111i		−	0.429278i	0.976693	−	0.214639i	$-0.0688575\pi$
$360$		0			0
$361$	807.992			2.23821
$362$	104.300	−	60.2178i	0.288123	−	0.166348i
$363$		0			0
$364$	−46.4263	+	80.4127i	−0.127545	+	0.220914i
$365$	−234.379	−	135.319i	−0.642134	−	0.370736i
$366$		0			0
$367$	−306.965	−	531.680i	−0.836418	−	1.44872i	−0.892871	−	0.450314i	$-0.851312\pi$
$367$	−306.965	−	531.680i	−0.836418	−	1.44872i	0.0564523	−	0.998405i	$-0.482021\pi$
$368$		−	14.2331i		−	0.0386769i
$369$		0			0
$370$	340.628			0.920617
$371$	−18.6603	+	10.7735i	−0.0502973	+	0.0290391i
$372$		0			0
$373$	−277.865	+	481.276i	−0.744946	+	1.29028i	0.205274	+	0.978705i	$0.434192\pi$
$373$	−277.865	+	481.276i	−0.744946	+	1.29028i	−0.950220	+	0.311580i	$0.899142\pi$
$374$	−277.110	−	159.989i	−0.740935	−	0.427779i
$375$		0			0
$376$	37.4207	+	64.8145i	0.0995230	+	0.172379i
$377$		−	595.987i		−	1.58087i
$378$		0			0
$379$	404.691			1.06779			0.533893	−	0.845552i	$-0.320729\pi$
$379$	404.691			1.06779			0.533893	+	0.845552i	$0.320729\pi$
$380$	377.501	−	217.951i	0.993425	−	0.573554i
$381$		0			0
$382$	−259.882	+	450.129i	−0.680319	+	1.17835i
$383$	491.091	+	283.531i	1.28222	+	0.740291i	0.977254	−	0.212072i	$-0.0680212\pi$
$383$	491.091	+	283.531i	1.28222	+	0.740291i	0.304967	+	0.952363i	$0.401355\pi$
$384$		0			0
$385$	−142.025	−	245.994i	−0.368895	−	0.638945i
$386$			380.561i			0.985911i
$387$		0			0
$388$	42.3107			0.109048
$389$	−144.479	+	83.4149i	−0.371411	+	0.214434i	−0.674075	−	0.738663i	$-0.735457\pi$
$389$	−144.479	+	83.4149i	−0.371411	+	0.214434i	0.302664	+	0.953097i	$0.402124\pi$
$390$		0			0
$391$	23.9014	−	41.3984i	0.0611288	−	0.105878i
$392$	−17.1464	−	9.89949i	−0.0437409	−	0.0252538i
$393$		0			0
$394$	192.551	+	333.508i	0.488708	+	0.846468i
$395$		−	346.063i		−	0.876109i
$396$		0			0
$397$	−413.385			−1.04127			−0.520636	−	0.853779i	$-0.674305\pi$
$397$	−413.385			−1.04127			−0.520636	+	0.853779i	$0.674305\pi$
$398$	−136.913	+	79.0466i	−0.344002	+	0.198609i
$399$		0			0
$400$	31.2707	−	54.1625i	0.0781769	−	0.135406i
$401$	506.285	+	292.303i	1.26255	+	0.728936i	0.973568	−	0.228397i	$-0.0733483\pi$
$401$	506.285	+	292.303i	1.26255	+	0.728936i	0.288987	+	0.957333i	$0.406682\pi$
$402$		0			0
$403$	−263.349	−	456.134i	−0.653472	−	1.13185i
$404$		−	101.309i		−	0.250764i
$405$		0			0
$406$	127.082			0.313011
$407$	551.108	−	318.182i	1.35407	−	0.781775i
$408$		0			0
$409$	−20.5437	+	35.5827i	−0.0502290	+	0.0869992i	−0.890047	−	0.455869i	$-0.849328\pi$
$409$	−20.5437	+	35.5827i	−0.0502290	+	0.0869992i	0.839818	+	0.542868i	$0.182662\pi$
$410$	256.788	+	148.256i	0.626311	+	0.361601i
$411$		0			0
$412$	−200.317	−	346.959i	−0.486207	−	0.842135i
$413$			267.540i			0.647796i
$414$		0			0
$415$	245.930			0.592602
$416$	−85.9648	+	49.6318i	−0.206646	+	0.119307i
$417$		0			0
$418$	407.177	−	705.251i	0.974108	−	1.68720i
$419$	604.987	+	349.289i	1.44388	+	0.833626i	0.998106	−	0.0615188i	$-0.0195944\pi$
$419$	604.987	+	349.289i	1.44388	+	0.833626i	0.445776	+	0.895144i	$0.352928\pi$
$420$		0			0
$421$	−332.730	−	576.305i	−0.790332	−	1.36890i	−0.925761	−	0.378109i	$-0.876574\pi$
$421$	−332.730	−	576.305i	−0.790332	−	1.36890i	0.135429	−	0.990787i	$-0.456759\pi$
$422$		−	24.0978i		−	0.0571038i
$423$		0			0
$424$	−23.0348			−0.0543272
$425$	181.908	−	105.025i	0.428019	−	0.247117i
$426$		0			0
$427$	−22.0260	+	38.1501i	−0.0515830	+	0.0893444i
$428$	−86.3968	−	49.8812i	−0.201862	−	0.116545i
$429$		0			0
$430$	−314.768	−	545.195i	−0.732020	−	1.26790i
$431$			542.351i			1.25836i	0.777261	+	0.629178i	$0.216608\pi$
$431$			542.351i			1.25836i	−0.777261	+	0.629178i	$0.783392\pi$
$432$		0			0
$433$	−796.313			−1.83906			−0.919530	−	0.393020i	$-0.871430\pi$
$433$	−796.313			−1.83906			−0.919530	+	0.393020i	$0.871430\pi$
$434$	97.2616	−	56.1540i	0.224105	−	0.129387i
$435$		0			0
$436$	120.571	−	208.836i	0.276540	−	0.478982i
$437$	105.360	+	60.8296i	0.241098	+	0.139198i
$438$		0			0
$439$	352.125	+	609.898i	0.802107	+	1.38929i	0.918227	+	0.396055i	$0.129621\pi$
$439$	352.125	+	609.898i	0.802107	+	1.38929i	−0.116120	+	0.993235i	$0.537046\pi$
$440$		−	303.661i		−	0.690139i
$441$		0			0
$442$	−333.383			−0.754260
$443$	−171.456	+	98.9901i	−0.387034	+	0.223454i	−0.680874	−	0.732401i	$-0.738400\pi$
$443$	−171.456	+	98.9901i	−0.387034	+	0.223454i	0.293840	+	0.955854i	$0.405067\pi$
$444$		0			0
$445$	−313.994	+	543.854i	−0.705605	+	1.22214i
$446$	395.236	+	228.190i	0.886180	+	0.511636i
$447$		0			0
$448$	−10.5830	−	18.3303i	−0.0236228	−	0.0409159i
$449$			764.577i			1.70284i	0.524482	+	0.851422i	$0.324259\pi$
$449$			764.577i			1.70284i	−0.524482	+	0.851422i	$0.675741\pi$
$450$		0			0
$451$	553.948			1.22827
$452$	−37.2843	+	21.5261i	−0.0824874	+	0.0476241i
$453$		0			0
$454$	112.650	−	195.116i	0.248129	−	0.429771i
$455$	−256.299	−	147.974i	−0.563294	−	0.325218i
$456$		0			0
$457$	−74.3456	−	128.770i	−0.162682	−	0.281773i	0.773148	−	0.634226i	$-0.218681\pi$
$457$	−74.3456	−	128.770i	−0.162682	−	0.281773i	−0.935830	+	0.352453i	$0.885348\pi$
$458$			352.518i			0.769690i
$459$		0			0
$460$	45.3650			0.0986196
$461$	289.359	−	167.061i	0.627677	−	0.362389i	−0.152175	−	0.988354i	$-0.548628\pi$
$461$	289.359	−	167.061i	0.627677	−	0.362389i	0.779852	+	0.625964i	$0.215294\pi$
$462$		0			0
$463$	200.250	−	346.843i	0.432505	−	0.749121i	−0.564583	−	0.825376i	$-0.690963\pi$
$463$	200.250	−	346.843i	0.432505	−	0.749121i	0.997088	+	0.0762549i	$0.0242963\pi$
$464$	117.656	+	67.9285i	0.253568	+	0.146398i
$465$		0			0
$466$	−243.795	−	422.265i	−0.523165	−	0.906148i
$467$		−	108.547i		−	0.232434i	−0.993224	−	0.116217i	$-0.962923\pi$
$467$		−	108.547i		−	0.232434i	0.993224	−	0.116217i	$-0.0370768\pi$
$468$		0			0
$469$	−111.153			−0.237000
$470$	−206.583	+	119.271i	−0.439538	+	0.253767i
$471$		0			0
$472$	−143.006	+	247.694i	−0.302979	+	0.524775i
$473$	−1018.54	−	588.053i	−2.15336	−	1.24324i
$474$		0			0
$475$	267.291	+	462.961i	0.562717	+	0.974655i
$476$		−	71.0874i		−	0.149343i
$477$		0			0
$478$	70.2955			0.147062
$479$	−564.239	+	325.764i	−1.17795	+	0.680091i	−0.955540	−	0.294862i	$-0.904726\pi$
$479$	−564.239	+	325.764i	−1.17795	+	0.680091i	−0.222412	+	0.974953i	$0.571393\pi$
$480$		0			0
$481$	331.512	−	574.195i	0.689213	−	1.19375i
$482$	−204.784	−	118.232i	−0.424863	−	0.245295i
$483$		0			0
$484$	−162.651	−	281.720i	−0.336056	−	0.582067i
$485$			134.856i			0.278055i
$486$		0			0
$487$	−462.741			−0.950188			−0.475094	−	0.879935i	$-0.657586\pi$
$487$	−462.741			−0.950188			−0.475094	+	0.879935i	$0.657586\pi$
$488$	−40.7841	+	23.5467i	−0.0835741	+	0.0482515i
$489$		0			0
$490$	31.5526	−	54.6507i	0.0643931	−	0.111532i
$491$	76.4160	+	44.1188i	0.155633	+	0.0898550i	0.575794	−	0.817595i	$-0.304693\pi$
$491$	76.4160	+	44.1188i	0.155633	+	0.0898550i	−0.420161	+	0.907450i	$0.638026\pi$
$492$		0			0
$493$	228.142	+	395.153i	0.462763	+	0.801528i
$494$		−	848.469i		−	1.71755i
$495$		0			0
$496$	120.062			0.242061
$497$	−33.0624	+	19.0886i	−0.0665240	+	0.0384077i
$498$		0			0
$499$	82.9999	−	143.760i	0.166332	−	0.288096i	−0.770795	−	0.637083i	$-0.780141\pi$
$499$	82.9999	−	143.760i	0.166332	−	0.288096i	0.937128	+	0.348987i	$0.113474\pi$
$500$	−103.396	−	59.6957i	−0.206792	−	0.119391i
$501$		0			0
$502$	−75.7627	−	131.225i	−0.150922	−	0.261404i
$503$		−	30.6263i		−	0.0608872i	−0.999536	−	0.0304436i	$-0.990308\pi$
$503$		−	30.6263i		−	0.0608872i	0.999536	−	0.0304436i	$-0.00969200\pi$
$504$		0			0
$505$	322.900			0.639407
$506$	73.3968	−	42.3757i	0.145053	−	0.0837463i
$507$		0			0
$508$	−71.9765	+	124.667i	−0.141686	+	0.245407i
$509$	−717.965	−	414.518i	−1.41054	−	0.814376i	−0.415102	−	0.909775i	$-0.636254\pi$
$509$	−717.965	−	414.518i	−1.41054	−	0.814376i	−0.995439	+	0.0953985i	$0.969587\pi$
$510$		0			0
$511$	−56.1636	−	97.2781i	−0.109909	−	0.190368i
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$	59.8231			0.116387
$515$	1105.86	−	638.470i	2.14730	−	1.23975i
$516$		0			0
$517$	−222.822	+	385.940i	−0.430991	+	0.746499i
$518$	122.436	+	70.6883i	0.236363	+	0.136464i
$519$		0			0
$520$	−158.191	−	273.995i	−0.304214	−	0.526914i
$521$		−	40.5567i		−	0.0778439i	−0.999242	−	0.0389220i	$-0.987608\pi$
$521$		−	40.5567i		−	0.0778439i	0.999242	−	0.0389220i	$-0.0123924\pi$
$522$		0			0
$523$	−658.989			−1.26002			−0.630008	−	0.776588i	$-0.716949\pi$
$523$	−658.989			−1.26002			−0.630008	+	0.776588i	$0.716949\pi$
$524$	162.709	−	93.9401i	0.310513	−	0.179275i
$525$		0			0
$526$	96.6158	−	167.343i	0.183680	−	0.318143i
$527$	349.213	+	201.618i	0.662644	+	0.382578i
$528$		0			0
$529$	−258.169	−	447.162i	−0.488033	−	0.845298i
$530$		−	73.4185i		−	0.138526i
$531$		0			0
$532$	180.919			0.340074
$533$	499.830	−	288.577i	0.937767	−	0.541420i
$534$		0			0
$535$	158.986	−	275.372i	0.297170	−	0.514714i
$536$	−102.908	−	59.4137i	−0.191992	−	0.110846i
$537$		0			0
$538$	−8.10884	−	14.0449i	−0.0150722	−	0.0261058i
$539$		−	117.894i		−	0.218727i
$540$		0			0
$541$	513.937			0.949976			0.474988	−	0.879992i	$-0.342452\pi$
$541$	513.937			0.949976			0.474988	+	0.879992i	$0.342452\pi$
$542$	−155.889	+	90.0023i	−0.287617	+	0.166056i
$543$		0			0
$544$	37.9978	−	65.8141i	0.0698489	−	0.120982i
$545$	665.622	+	384.297i	1.22132	+	0.705132i
$546$		0			0
$547$	412.329	+	714.174i	0.753800	+	1.30562i	0.945969	+	0.324258i	$0.105115\pi$
$547$	412.329	+	714.174i	0.753800	+	1.30562i	−0.192169	+	0.981362i	$0.561552\pi$
$548$		−	383.719i		−	0.700218i
$549$		0			0
$550$	372.405			0.677100
$551$	−1005.68	+	580.627i	−1.82518	+	1.05377i
$552$		0			0
$553$	71.8162	−	124.389i	0.129866	−	0.224935i
$554$	64.2988	+	37.1229i	0.116063	+	0.0670089i
$555$		0			0
$556$	130.826	+	226.597i	0.235299	+	0.407549i
$557$			301.569i			0.541416i	0.962661	+	0.270708i	$0.0872579\pi$
$557$			301.569i			0.541416i	−0.962661	+	0.270708i	$0.912742\pi$
$558$		0			0
$559$	−1225.38			−2.19208
$560$	58.4241	−	33.7311i	0.104329	−	0.0602342i
$561$		0			0
$562$	−354.860	+	614.635i	−0.631423	+	1.09366i
$563$	218.538	+	126.173i	0.388166	+	0.224108i	0.681365	−	0.731944i	$-0.261387\pi$
$563$	218.538	+	126.173i	0.388166	+	0.224108i	−0.293199	+	0.956051i	$0.594720\pi$
$564$		0			0
$565$	−68.6100	−	118.836i	−0.121434	−	0.210329i
$566$		−	475.535i		−	0.840168i
$567$		0			0
$568$	−40.8132			−0.0718541
$569$	−44.4483	+	25.6622i	−0.0781165	+	0.0451006i	−0.538549	−	0.842594i	$-0.681027\pi$
$569$	−44.4483	+	25.6622i	−0.0781165	+	0.0451006i	0.460433	+	0.887694i	$0.347694\pi$
$570$		0			0
$571$	−327.899	+	567.938i	−0.574254	+	0.994637i	0.421868	+	0.906657i	$0.361374\pi$
$571$	−327.899	+	567.938i	−0.574254	+	0.994637i	−0.996122	+	0.0879797i	$0.971959\pi$
$572$	−511.880	−	295.534i	−0.894895	−	0.516668i
$573$		0			0
$574$	61.5333	+	106.579i	0.107201	+	0.185677i
$575$			55.6349i			0.0967563i
$576$		0			0
$577$	496.760			0.860936			0.430468	−	0.902606i	$-0.358348\pi$
$577$	496.760			0.860936			0.430468	+	0.902606i	$0.358348\pi$
$578$	−132.910	+	76.7359i	−0.229949	+	0.132761i
$579$		0			0
$580$	−216.508	+	375.003i	−0.373290	+	0.646556i
$581$	88.3973	+	51.0362i	0.152147	+	0.0878420i
$582$		0			0
$583$	−68.5805	−	118.785i	−0.117634	−	0.203748i
$584$		−	120.083i		−	0.205621i
$585$		0			0
$586$	430.750			0.735069
$587$	17.2048	−	9.93319i	0.0293097	−	0.0169220i	−0.485274	−	0.874362i	$-0.661280\pi$
$587$	17.2048	−	9.93319i	0.0293097	−	0.0169220i	0.514583	+	0.857440i	$0.327947\pi$
$588$		0			0
$589$	−513.124	+	888.757i	−0.871179	+	1.50893i
$590$	−789.473	−	455.802i	−1.33809	−	0.772546i
$591$		0			0
$592$	75.5690	+	130.889i	0.127650	+	0.221097i
$593$			798.534i			1.34660i	0.739369	+	0.673300i	$0.235124\pi$
$593$			798.534i			1.34660i	−0.739369	+	0.673300i	$0.764876\pi$
$594$		0			0
$595$	226.576			0.380801
$596$	−28.1433	+	16.2485i	−0.0472203	+	0.0272626i
$597$		0			0
$598$	44.1509	−	76.4715i	0.0738309	−	0.127879i
$599$	−41.6471	−	24.0450i	−0.0695277	−	0.0401419i	0.464833	−	0.885398i	$-0.346114\pi$
$599$	−41.6471	−	24.0450i	−0.0695277	−	0.0401419i	−0.534361	+	0.845256i	$0.679448\pi$
$600$		0			0
$601$	212.193	+	367.529i	0.353066	+	0.611529i	0.986785	−	0.162035i	$-0.0518056\pi$
$601$	212.193	+	367.529i	0.353066	+	0.611529i	−0.633719	+	0.773564i	$0.718472\pi$
$602$		−	261.287i		−	0.434032i
$603$		0			0
$604$	252.427			0.417925
$605$	897.925	−	518.417i	1.48417	−	0.856888i
$606$		0			0
$607$	−414.986	+	718.776i	−0.683667	+	1.18415i	0.290187	+	0.956970i	$0.406282\pi$
$607$	−414.986	+	718.776i	−0.683667	+	1.18415i	−0.973854	+	0.227176i	$0.927051\pi$
$608$	167.499	+	96.7054i	0.275491	+	0.159055i
$609$		0			0
$610$	−75.0504	−	129.991i	−0.123033	−	0.213100i
$611$			464.314i			0.759924i
$612$		0			0
$613$	866.351			1.41330			0.706648	−	0.707565i	$-0.250206\pi$
$613$	866.351			1.41330			0.706648	+	0.707565i	$0.250206\pi$
$614$	−388.762	+	224.452i	−0.633163	+	0.365557i
$615$		0			0
$616$	63.0168	−	109.148i	0.102300	−	0.177189i
$617$	−577.560	−	333.455i	−0.936078	−	0.540445i	−0.0473494	−	0.998878i	$-0.515077\pi$
$617$	−577.560	−	333.455i	−0.936078	−	0.540445i	−0.888729	+	0.458433i	$0.848411\pi$
$618$		0			0
$619$	107.809	+	186.731i	0.174167	+	0.301666i	0.939873	−	0.341525i	$-0.110943\pi$
$619$	107.809	+	186.731i	0.174167	+	0.301666i	−0.765706	+	0.643191i	$0.777610\pi$
$620$			382.674i			0.617216i
$621$		0			0
$622$	−61.0037			−0.0980766
$623$	−225.725	+	130.322i	−0.362319	+	0.209185i
$624$		0			0
$625$	385.710	−	668.069i	0.617136	−	1.06891i
$626$	373.193	+	215.463i	0.596156	+	0.344191i
$627$		0			0
$628$	27.2368	+	47.1755i	0.0433707	+	0.0751203i
$629$			507.607i			0.807006i
$630$		0			0
$631$	−10.1283			−0.0160512			−0.00802562	−	0.999968i	$-0.502555\pi$
$631$	−10.1283			−0.0160512			−0.00802562	+	0.999968i	$0.502555\pi$
$632$	132.978	−	76.7747i	0.210408	−	0.121479i
$633$		0			0
$634$	85.1723	−	147.523i	0.134341	−	0.232686i
$635$	−397.350	−	229.410i	−0.625748	−	0.361276i
$636$		0			0
$637$	−61.4162	−	106.376i	−0.0964148	−	0.166995i
$638$			808.964i			1.26797i
$639$		0			0
$640$	72.1202			0.112688
$641$	−225.657	+	130.283i	−0.352038	+	0.203249i	−0.665583	−	0.746324i	$-0.731817\pi$
$641$	−225.657	+	130.283i	−0.352038	+	0.203249i	0.313544	+	0.949574i	$0.398484\pi$
$642$		0			0
$643$	300.852	−	521.092i	0.467889	−	0.810407i	−0.531438	−	0.847097i	$-0.678348\pi$
$643$	300.852	−	521.092i	0.467889	−	0.810407i	0.999327	+	0.0366903i	$0.0116815\pi$
$644$	16.3060	+	9.41430i	0.0253199	+	0.0146185i
$645$		0			0
$646$	324.791	+	562.555i	0.502773	+	0.870828i
$647$		−	338.311i		−	0.522891i	−0.965218	−	0.261446i	$-0.915801\pi$
$647$		−	338.311i		−	0.522891i	0.965218	−	0.261446i	$-0.0841992\pi$
$648$		0			0
$649$	−1703.07			−2.62414
$650$	336.023	−	194.003i	0.516958	−	0.298466i
$651$		0			0
$652$	178.576	−	309.302i	0.273889	−	0.474389i
$653$	−93.7725	−	54.1396i	−0.143603	−	0.0829090i	0.426477	−	0.904498i	$-0.359754\pi$
$653$	−93.7725	−	54.1396i	−0.143603	−	0.0829090i	−0.570080	+	0.821589i	$0.693088\pi$
$654$		0			0
$655$	299.415	+	518.601i	0.457122	+	0.791758i
$656$			131.564i			0.200555i
$657$		0			0
$658$	−99.0058			−0.150465
$659$	469.638	−	271.146i	0.712653	−	0.411450i	−0.0993897	−	0.995049i	$-0.531689\pi$
$659$	469.638	−	271.146i	0.712653	−	0.411450i	0.812043	+	0.583598i	$0.198356\pi$
$660$		0			0
$661$	211.097	−	365.630i	0.319360	−	0.553147i	−0.660995	−	0.750390i	$-0.729865\pi$
$661$	211.097	−	365.630i	0.319360	−	0.553147i	0.980355	+	0.197243i	$0.0631988\pi$
$662$	177.549	+	102.508i	0.268201	+	0.154846i
$663$		0			0
$664$	54.5600	+	94.5007i	0.0821687	+	0.142320i
$665$			576.643i			0.867132i
$666$		0			0
$667$	−120.854			−0.181190
$668$	−105.864	+	61.1209i	−0.158480	+	0.0914983i
$669$		0			0
$670$	189.369	−	327.997i	0.282640	−	0.489547i
$671$	−242.850	−	140.210i	−0.361923	−	0.208956i
$672$		0			0
$673$	516.283	+	894.228i	0.767137	+	1.32872i	0.939109	+	0.343618i	$0.111653\pi$
$673$	516.283	+	894.228i	0.767137	+	1.32872i	−0.171973	+	0.985102i	$0.555014\pi$
$674$			127.425i			0.189058i
$675$		0			0
$676$	−277.829			−0.410990
$677$	253.223	−	146.198i	0.374037	−	0.215950i	−0.301184	−	0.953566i	$-0.597382\pi$
$677$	253.223	−	146.198i	0.374037	−	0.215950i	0.675221	+	0.737616i	$0.264048\pi$
$678$		0			0
$679$	−27.9859	+	48.4729i	−0.0412163	+	0.0713887i
$680$	209.769	+	121.110i	0.308484	+	0.178103i
$681$		0			0
$682$	357.457	+	619.134i	0.524131	+	0.907821i
$683$		−	893.737i		−	1.30855i	−0.756258	−	0.654273i	$-0.772975\pi$
$683$		−	893.737i		−	1.30855i	0.756258	−	0.654273i	$-0.227025\pi$
$684$		0			0
$685$	1223.03			1.78544
$686$	22.6826	−	13.0958i	0.0330650	−	0.0190901i
$687$		0			0
$688$	139.664	−	241.905i	0.203000	−	0.351606i
$689$	−123.761	−	71.4535i	−0.179624	−	0.103706i
$690$		0			0
$691$	57.0433	+	98.8019i	0.0825518	+	0.142984i	0.904345	−	0.426801i	$-0.140360\pi$
$691$	57.0433	+	98.8019i	0.0825518	+	0.142984i	−0.821794	+	0.569785i	$0.807026\pi$
$692$			121.144i			0.175063i
$693$		0			0
$694$	−774.259			−1.11565
$695$	−722.232	+	416.981i	−1.03918	+	0.599973i
$696$		0			0
$697$	−220.933	+	382.667i	−0.316977	+	0.549020i
$698$	−36.9436	−	21.3294i	−0.0529279	−	0.0305579i
$699$		0			0
$700$	41.3673	+	71.6503i	0.0590961	+	0.102358i
$701$			1007.65i			1.43744i	0.695300	+	0.718720i	$0.255272\pi$
$701$			1007.65i			1.43744i	−0.695300	+	0.718720i	$0.744728\pi$
$702$		0			0
$703$	−1291.87			−1.83766
$704$	116.684	−	67.3678i	0.165745	−	0.0956929i
$705$		0			0
$706$	223.748	−	387.543i	0.316924	−	0.548928i
$707$	116.064	+	67.0094i	0.164164	+	0.0947799i
$708$		0			0
$709$	−152.837	−	264.722i	−0.215567	−	0.373373i	0.737881	−	0.674931i	$-0.235827\pi$
$709$	−152.837	−	264.722i	−0.215567	−	0.373373i	−0.953448	+	0.301558i	$0.902493\pi$
$710$		−	130.084i		−	0.183216i
$711$		0			0
$712$	−278.641			−0.391349
$713$	−92.4946	+	53.4018i	−0.129726	+	0.0748973i
$714$		0			0
$715$	941.954	−	1631.51i	1.31742	−	2.28183i
$716$	−312.305	−	180.309i	−0.436180	−	0.251829i
$717$		0			0
$718$	108.973	+	188.746i	0.151773	+	0.262878i
$719$			53.5870i			0.0745299i	0.999305	+	0.0372649i	$0.0118645\pi$
$719$			53.5870i			0.0745299i	−0.999305	+	0.0372649i	$0.988135\pi$
$720$		0			0
$721$	529.989			0.735075
$722$	−989.584	+	571.337i	−1.37062	+	0.791325i
$723$		0			0
$724$	−85.1609	+	147.503i	−0.117626	+	0.203733i
$725$	−459.897	−	265.522i	−0.634341	−	0.366237i
$726$		0			0
$727$	−445.717	−	772.004i	−0.613090	−	1.06190i	−0.990716	−	0.135945i	$-0.956593\pi$
$727$	−445.717	−	772.004i	−0.613090	−	1.06190i	0.377626	−	0.925958i	$-0.376740\pi$
$728$		−	131.313i		−	0.180376i
$729$		0			0
$730$	382.739			0.524300
$731$	812.453	−	469.070i	1.11143	−	0.641682i
$732$		0			0
$733$	227.950	−	394.821i	0.310982	−	0.538637i	−0.667593	−	0.744526i	$-0.732675\pi$
$733$	227.950	−	394.821i	0.310982	−	0.538637i	0.978575	+	0.205890i	$0.0660088\pi$
$734$	751.909	+	434.115i	1.02440	+	0.591437i
$735$		0			0
$736$	10.0643	+	17.4319i	0.0136743	+	0.0236846i
$737$		−	707.561i		−	0.960056i
$738$		0			0
$739$	−1246.08			−1.68617			−0.843084	−	0.537781i	$-0.819263\pi$
$739$	−1246.08			−1.68617			−0.843084	+	0.537781i	$0.819263\pi$
$740$	−417.183	+	240.861i	−0.563761	+	0.325487i
$741$		0			0
$742$	15.2361	−	26.3896i	0.0205338	−	0.0355655i
$743$	−936.983	−	540.968i	−1.26108	−	0.728086i	−0.287797	−	0.957691i	$-0.592923\pi$
$743$	−936.983	−	540.968i	−1.26108	−	0.728086i	−0.973284	+	0.229606i	$0.926256\pi$
$744$		0			0
$745$	−51.7888	−	89.7009i	−0.0695152	−	0.120404i
$746$		−	785.921i		−	1.05351i
$747$		0			0
$748$	452.518			0.604971
$749$	114.292	−	65.9866i	0.152593	−	0.0880997i
$750$		0			0
$751$	−611.914	+	1059.87i	−0.814799	+	1.41127i	0.0946726	+	0.995508i	$0.469820\pi$
$751$	−611.914	+	1059.87i	−0.814799	+	1.41127i	−0.909472	+	0.415765i	$0.863514\pi$
$752$	−91.6615	−	52.9208i	−0.121890	−	0.0703734i
$753$		0			0
$754$	421.426	+	729.932i	0.558921	+	0.968080i
$755$			804.559i			1.06564i
$756$		0			0
$757$	334.860			0.442352			0.221176	−	0.975234i	$-0.429010\pi$
$757$	334.860			0.442352			0.221176	+	0.975234i	$0.429010\pi$
$758$	−495.643	+	286.159i	−0.653882	+	0.377519i
$759$		0			0
$760$	−308.229	+	533.868i	−0.405564	+	0.702457i
$761$	853.330	+	492.671i	1.12133	+	0.647399i	0.941740	−	0.336343i	$-0.109190\pi$
$761$	853.330	+	492.671i	1.12133	+	0.647399i	0.179588	+	0.983742i	$0.442523\pi$
$762$		0			0
$763$	159.501	+	276.264i	0.209045	+	0.362076i
$764$		−	735.057i		−	0.962117i
$765$		0			0
$766$	−801.948			−1.04693
$767$	−1536.69	+	887.206i	−2.00350	+	1.15672i
$768$		0			0
$769$	−184.398	+	319.386i	−0.239789	+	0.415327i	−0.960654	−	0.277749i	$-0.910412\pi$
$769$	−184.398	+	319.386i	−0.239789	+	0.415327i	0.720865	+	0.693076i	$0.243745\pi$
$770$	347.888	+	200.853i	0.451802	+	0.260848i
$771$		0			0
$772$	−269.098	−	466.091i	−0.348572	−	0.603744i
$773$			1132.76i			1.46540i	0.680550	+	0.732701i	$0.261741\pi$
$773$			1132.76i			1.46540i	−0.680550	+	0.732701i	$0.738259\pi$
$774$		0			0
$775$	−469.305			−0.605554
$776$	−51.8198	+	29.9181i	−0.0667780	+	0.0385543i
$777$		0			0
$778$	117.967	−	204.324i	0.151628	−	0.262627i
$779$	−973.897	−	562.280i	−1.25019	−	0.721797i
$780$		0			0
$781$	−121.512	−	210.464i	−0.155585	−	0.269480i
$782$			67.6032i			0.0864491i
$783$		0			0
$784$	28.0000			0.0357143
$785$	−150.362	+	86.8117i	−0.191544	+	0.110588i
$786$		0			0
$787$	644.116	−	1115.64i	0.818445	−	1.41759i	−0.0883822	−	0.996087i	$-0.528170\pi$
$787$	644.116	−	1115.64i	0.818445	−	1.41759i	0.906827	−	0.421502i	$-0.138497\pi$
$788$	−471.652	−	272.308i	−0.598543	−	0.345569i
$789$		0			0
$790$	244.704	+	423.839i	0.309751	+	0.536505i
$791$		−	56.9527i		−	0.0720009i
$792$		0			0
$793$	−292.167			−0.368432
$794$	506.291	−	292.307i	0.637646	−	0.368145i
$795$		0			0
$796$	111.789	−	193.624i	0.140438	−	0.243246i
$797$	−782.130	−	451.563i	−0.981342	−	0.566578i	−0.0786672	−	0.996901i	$-0.525066\pi$
$797$	−782.130	−	451.563i	−0.981342	−	0.566578i	−0.902675	+	0.430323i	$0.858400\pi$
$798$		0			0
$799$	−177.738	−	307.851i	−0.222450	−	0.385295i
$800$			88.4470i			0.110559i
$801$		0			0
$802$	−826.759			−1.03087
$803$	619.239	−	357.518i	0.771157	−	0.445228i
$804$		0			0
$805$	−30.0061	+	51.9722i	−0.0372747	+	0.0645617i
$806$	645.071	+	372.432i	0.800336	+	0.462074i
$807$		0			0
$808$	71.6360	+	124.077i	0.0886584	+	0.153561i
$809$		−	1114.49i		−	1.37762i	−0.724942	−	0.688810i	$-0.758133\pi$
$809$		−	1114.49i		−	1.37762i	0.724942	−	0.688810i	$-0.241867\pi$
$810$		0			0
$811$	620.916			0.765618			0.382809	−	0.923828i	$-0.374957\pi$
$811$	620.916			0.765618			0.382809	+	0.923828i	$0.374957\pi$
$812$	−155.644	+	89.8609i	−0.191679	+	0.110666i
$813$		0			0
$814$	−449.978	+	779.385i	−0.552798	+	0.957475i
$815$	985.836	+	569.173i	1.20961	+	0.698371i
$816$		0			0
$817$	1193.80	+	2067.71i	1.46119	+	2.53086i
$818$		−	58.1063i		−	0.0710345i
$819$		0			0
$820$	−419.333			−0.511381
$821$	69.7444	−	40.2669i	0.0849505	−	0.0490462i	−0.456923	−	0.889506i	$-0.651049\pi$
$821$	69.7444	−	40.2669i	0.0849505	−	0.0490462i	0.541874	+	0.840460i	$0.317715\pi$
$822$		0			0
$823$	−767.625	+	1329.56i	−0.932715	+	1.61551i	−0.154057	+	0.988062i	$0.549234\pi$
$823$	−767.625	+	1329.56i	−0.932715	+	1.61551i	−0.778658	+	0.627448i	$0.784099\pi$
$824$	490.675	+	283.291i	0.595479	+	0.343800i
$825$		0			0
$826$	−189.179	−	327.668i	−0.229031	−	0.396693i
$827$		−	708.693i		−	0.856944i	−0.903555	−	0.428472i	$-0.859052\pi$
$827$		−	708.693i		−	0.856944i	0.903555	−	0.428472i	$-0.140948\pi$
$828$		0			0
$829$	1376.20			1.66008			0.830038	−	0.557706i	$-0.188318\pi$
$829$	1376.20			1.66008			0.830038	+	0.557706i	$0.188318\pi$
$830$	−301.201	+	173.899i	−0.362893	+	0.209517i
$831$		0			0
$832$	70.1900	−	121.573i	0.0843629	−	0.146121i
$833$	81.4408	+	47.0199i	0.0977681	+	0.0564464i
$834$		0			0
$835$	−194.810	−	337.421i	−0.233306	−	0.404097i
$836$			1151.67i			1.37760i
$837$		0			0
$838$	−987.939			−1.17892
$839$	−78.2013	+	45.1496i	−0.0932078	+	0.0538135i	−0.545879	−	0.837864i	$-0.683804\pi$
$839$	−78.2013	+	45.1496i	−0.0932078	+	0.0538135i	0.452672	+	0.891677i	$0.350471\pi$
$840$		0			0
$841$	156.284	−	270.692i	0.185832	−	0.321870i
$842$	815.019	+	470.551i	0.967956	+	0.558849i
$843$		0			0
$844$	17.0397	+	29.5137i	0.0201892	+	0.0349688i
$845$		−	885.523i		−	1.04796i
$846$		0			0
$847$	430.335			0.508069
$848$	28.2117	−	16.2880i	0.0332685	−	0.0192076i
$849$		0			0
$850$	−148.527	+	257.257i	−0.174738	+	0.302655i
$851$	−116.435	−	67.2238i	−0.136821	−	0.0789938i
$852$		0			0
$853$	560.003	+	969.954i	0.656510	+	1.13711i	0.981513	+	0.191396i	$0.0613014\pi$
$853$	560.003	+	969.954i	0.656510	+	1.13711i	−0.325003	+	0.945713i	$0.605365\pi$
$854$		−	62.2988i		−	0.0729494i
$855$		0			0
$856$	141.085			0.164819
$857$	−175.676	+	101.427i	−0.204990	+	0.118351i	−0.598981	−	0.800763i	$-0.704427\pi$
$857$	−175.676	+	101.427i	−0.204990	+	0.118351i	0.393991	+	0.919114i	$0.371094\pi$
$858$		0			0
$859$	238.933	−	413.844i	0.278152	−	0.481774i	−0.692773	−	0.721155i	$-0.743611\pi$
$859$	238.933	−	413.844i	0.278152	−	0.481774i	0.970926	+	0.239382i	$0.0769447\pi$
$860$	771.022	+	445.150i	0.896537	+	0.517616i
$861$		0			0
$862$	−383.500	−	664.242i	−0.444896	−	0.770583i
$863$			100.180i			0.116083i	0.998314	+	0.0580417i	$0.0184856\pi$
$863$			100.180i			0.116083i	−0.998314	+	0.0580417i	$0.981514\pi$
$864$		0			0
$865$	−386.121			−0.446383
$866$	975.280	−	563.078i	1.12619	−	0.650206i
$867$		0			0
$868$	−79.4138	+	137.549i	−0.0914905	+	0.158466i
$869$	791.819	+	457.157i	0.911185	+	0.526073i
$870$		0			0
$871$	−368.601	−	638.436i	−0.423193	−	0.732992i
$872$			341.028i			0.391087i
$873$		0			0
$874$	−172.052			−0.196856
$875$	136.780	−	78.9699i	0.156320	−	0.0902513i
$876$		0			0
$877$	170.603	−	295.493i	0.194530	−	0.336936i	−0.752216	−	0.658916i	$-0.771015\pi$
$877$	170.603	−	295.493i	0.194530	−	0.336936i	0.946746	+	0.321980i	$0.104349\pi$
$878$	−862.526	−	497.980i	−0.982376	−	0.567175i
$879$		0			0
$880$	214.721	+	371.908i	0.244001	+	0.422622i
$881$			248.995i			0.282628i	0.989965	+	0.141314i	$0.0451328\pi$
$881$			248.995i			0.282628i	−0.989965	+	0.141314i	$0.954867\pi$
$882$		0			0
$883$	−847.157			−0.959408			−0.479704	−	0.877430i	$-0.659256\pi$
$883$	−847.157			−0.959408			−0.479704	+	0.877430i	$0.659256\pi$
$884$	408.309	−	235.737i	0.461888	−	0.266671i
$885$		0			0
$886$	139.993	−	242.475i	0.158006	−	0.273674i
$887$	−687.128	−	396.713i	−0.774665	−	0.447253i	0.0598712	−	0.998206i	$-0.480931\pi$
$887$	−687.128	−	396.713i	−0.774665	−	0.447253i	−0.834536	+	0.550953i	$0.814264\pi$
$888$		0			0
$889$	−95.2160	−	164.919i	−0.107105	−	0.185511i
$890$		−	888.110i		−	0.997877i
$891$		0			0
$892$	−645.418			−0.723563
$893$	783.489	−	452.348i	0.877367	−	0.506548i
$894$		0			0
$895$	574.698	−	995.407i	0.642121	−	1.11219i
$896$	25.9230	+	14.9666i	0.0289319	+	0.0167038i
$897$		0			0
$898$	−540.637	−	936.411i	−0.602046	−	1.04277i
$899$		−	1019.46i		−	1.13399i
$900$		0			0
$901$	109.409			0.121430
$902$	−678.445	+	391.700i	−0.752156	+	0.434257i
$903$		0			0
$904$	30.4425	−	52.7280i	0.0336753	−	0.0583274i
$905$	−470.135	−	271.433i	−0.519487	−	0.299926i
$906$		0			0
$907$	−256.266	−	443.865i	−0.282542	−	0.489377i	0.689468	−	0.724316i	$-0.257844\pi$
$907$	−256.266	−	443.865i	−0.282542	−	0.489377i	−0.972010	+	0.234939i	$0.924511\pi$
$908$			318.623i			0.350907i
$909$		0			0
$910$	418.534			0.459928
$911$	−78.6763	+	45.4238i	−0.0863626	+	0.0498615i	−0.542559	−	0.840017i	$-0.682545\pi$
$911$	−78.6763	+	45.4238i	−0.0863626	+	0.0498615i	0.456197	+	0.889879i	$0.349211\pi$
$912$		0			0
$913$	−324.879	+	562.707i	−0.355837	+	0.616327i
$914$	182.109	+	105.141i	0.199244	+	0.115033i
$915$		0			0
$916$	−249.268	−	431.745i	−0.272127	−	0.471337i
$917$			248.542i			0.271038i
$918$		0			0
$919$	−480.491			−0.522841			−0.261421	−	0.965225i	$-0.584191\pi$
$919$	−480.491			−0.522841			−0.261421	+	0.965225i	$0.584191\pi$
$920$	−55.5606	+	32.0779i	−0.0603919	+	0.0348673i
$921$		0			0
$922$	−236.261	+	409.215i	−0.256248	+	0.443834i
$923$	−219.281	−	126.602i	−0.237574	−	0.137163i
$924$		0			0
$925$	−295.387	−	511.626i	−0.319338	−	0.553109i
$926$			566.393i			0.611655i
$927$		0			0
$928$	−192.131			−0.207037
$929$	215.475	−	124.405i	0.231943	−	0.133912i	−0.379525	−	0.925181i	$-0.623913\pi$
$929$	215.475	−	124.405i	0.231943	−	0.133912i	0.611468	+	0.791269i	$0.290579\pi$
$930$		0			0
$931$	−119.667	+	207.269i	−0.128536	+	0.222631i
$932$	597.173	+	344.778i	0.640744	+	0.369934i
$933$		0			0
$934$	76.7541	+	132.942i	0.0821778	+	0.142336i
$935$			1442.31i			1.54258i
$936$		0			0
$937$	−849.151			−0.906245			−0.453122	−	0.891448i	$-0.649690\pi$
$937$	−849.151			−0.906245			−0.453122	+	0.891448i	$0.649690\pi$
$938$	136.134	−	78.5969i	0.145132	−	0.0837921i
$939$		0			0
$940$	168.674	−	292.152i	0.179441	−	0.310800i
$941$	1092.43	+	630.716i	1.16093	+	0.670261i	0.951526	−	0.307569i	$-0.0995154\pi$
$941$	1092.43	+	630.716i	1.16093	+	0.670261i	0.209401	+	0.977830i	$0.432849\pi$
$942$		0			0
$943$	−58.5175	−	101.355i	−0.0620546	−	0.107482i
$944$		−	404.482i		−	0.428477i
$945$		0			0
$946$	1663.27			1.75821
$947$	−282.167	+	162.909i	−0.297958	+	0.172026i	−0.641525	−	0.767102i	$-0.721698\pi$
$947$	−282.167	+	162.909i	−0.297958	+	0.172026i	0.343567	+	0.939128i	$0.388365\pi$
$948$		0			0
$949$	372.495	−	645.181i	0.392513	−	0.679853i
$950$	−654.726	−	378.006i	−0.689185	−	0.397901i
$951$		0			0
$952$	50.2664	+	87.0639i	0.0528008	+	0.0914537i
$953$		−	1730.60i		−	1.81594i	−0.419030	−	0.907972i	$-0.637630\pi$
$953$		−	1730.60i		−	1.81594i	0.419030	−	0.907972i	$-0.362370\pi$
$954$		0			0
$955$	2342.84			2.45324
$956$	−86.0940	+	49.7064i	−0.0900565	+	0.0519941i
$957$		0			0
$958$	460.699	−	797.955i	0.480897	−	0.832938i
$959$	439.606	+	253.807i	0.458400	+	0.264657i
$960$		0			0
$961$	30.0325	+	52.0178i	0.0312513	+	0.0541289i
$962$			937.657i			0.974695i
$963$		0			0
$964$	334.411			0.346899
$965$	1485.57	−	857.693i	1.53945	−	0.888801i
$966$		0			0
$967$	433.499	−	750.843i	0.448293	−	0.776466i	−0.549982	−	0.835177i	$-0.685365\pi$
$967$	433.499	−	750.843i	0.448293	−	0.776466i	0.998275	+	0.0587101i	$0.0186988\pi$
$968$	398.413	+	230.024i	0.411583	+	0.237628i
$969$		0			0
$970$	−95.3579	−	165.165i	−0.0983072	−	0.170273i
$971$		−	1235.27i		−	1.27216i	−0.771623	−	0.636080i	$-0.780555\pi$
$971$		−	1235.27i		−	1.27216i	0.771623	−	0.636080i	$-0.219445\pi$
$972$		0			0
$973$	−346.133			−0.355738
$974$	566.740	−	327.208i	0.581869	−	0.335942i
$975$		0			0
$976$	33.3001	−	57.6775i	0.0341190	−	0.0590958i
$977$	−1405.24	−	811.318i	−1.43833	−	0.830418i	−0.440592	−	0.897708i	$-0.645231\pi$
$977$	−1405.24	−	811.318i	−1.43833	−	0.830418i	−0.997733	+	0.0672900i	$0.978565\pi$
$978$		0			0
$979$	−829.587	−	1436.89i	−0.847382	−	1.46771i
$980$			89.2442i			0.0910655i
$981$		0			0
$982$	−124.787			−0.127074
$983$	421.673	−	243.453i	0.428965	−	0.247663i	−0.269941	−	0.962877i	$-0.587004\pi$
$983$	421.673	−	243.453i	0.428965	−	0.247663i	0.698906	+	0.715214i	$0.253671\pi$
$984$		0			0
$985$	867.927	−	1503.29i	0.881144	−	1.52619i
$986$	−558.831	−	322.641i	−0.566766	−	0.327223i
$987$		0			0
$988$	599.958	+	1039.16i	0.607245	+	1.05178i
$989$			248.481i			0.251245i
$990$		0			0
$991$	558.514			0.563587			0.281793	−	0.959475i	$-0.409071\pi$
$991$	558.514			0.563587			0.281793	+	0.959475i	$0.409071\pi$
$992$	−147.046	+	84.8969i	−0.148232	+	0.0855815i
$993$		0			0
$994$	26.9954	−	46.7573i	0.0271583	−	0.0470396i
$995$	617.136	+	356.304i	0.620237	+	0.358094i
$996$		0			0
$997$	−234.505	−	406.174i	−0.235210	−	0.407396i	0.724124	−	0.689670i	$-0.242245\pi$
$997$	−234.505	−	406.174i	−0.235210	−	0.407396i	−0.959334	+	0.282274i	$0.908911\pi$
$998$			234.759i			0.235230i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.q.a.71.6		24
3.2	odd	2		126.3.q.a.113.11	yes	24
9.2	odd	6	inner	378.3.q.a.197.6		24
9.4	even	3		1134.3.b.c.323.2		24
9.5	odd	6		1134.3.b.c.323.23		24
9.7	even	3		126.3.q.a.29.11	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.q.a.29.11	✓	24	9.7	even	3
126.3.q.a.113.11	yes	24	3.2	odd	2
378.3.q.a.71.6		24	1.1	even	1	trivial
378.3.q.a.197.6		24	9.2	odd	6	inner
1134.3.b.c.323.2		24	9.4	even	3
1134.3.b.c.323.23		24	9.5	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)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(5.52056 + 3.18729i) q^{5} +(1.32288 + 2.29129i) q^{7} +2.82843i q^{8} -9.01503 q^{10} +(-14.5856 + 8.42098i) q^{11} +(-8.77375 + 15.1966i) q^{13} +(-3.24037 - 1.87083i) q^{14} +(-2.00000 - 3.46410i) q^{16} -13.4343i q^{17} +34.1905 q^{19} +(11.0411 - 6.37459i) q^{20} +(11.9091 - 20.6271i) q^{22} +(3.08155 + 1.77914i) q^{23} +(7.81769 + 13.5406i) q^{25} -24.8159i q^{26} +5.29150 q^{28} +(-29.4139 + 16.9821i) q^{29} +(-15.0078 + 25.9943i) q^{31} +(4.89898 + 2.82843i) q^{32} +(9.49945 + 16.4535i) q^{34} +16.8656i q^{35} -37.7845 q^{37} +(-41.8747 + 24.1764i) q^{38} +(-9.01503 + 15.6145i) q^{40} +(-28.4844 - 16.4455i) q^{41} +(34.9160 + 60.4762i) q^{43} +33.6839i q^{44} -5.03215 q^{46} +(22.9154 - 13.2302i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(-19.1493 - 11.0559i) q^{50} +(17.5475 + 30.3931i) q^{52} +8.14401i q^{53} -107.360 q^{55} +(-6.48074 + 3.74166i) q^{56} +(24.0163 - 41.5975i) q^{58} +(87.5730 + 50.5603i) q^{59} +(8.32503 + 14.4194i) q^{61} -42.4484i q^{62} -8.00000 q^{64} +(-96.8719 + 55.9290i) q^{65} +(-21.0059 + 36.3833i) q^{67} +(-23.2688 - 13.4343i) q^{68} +(-11.9258 - 20.6560i) q^{70} +14.4296i q^{71} -42.4557 q^{73} +(46.2764 - 26.7177i) q^{74} +(34.1905 - 59.2197i) q^{76} +(-38.5898 - 22.2798i) q^{77} +(-27.1440 - 47.0147i) q^{79} -25.4984i q^{80} +46.5148 q^{82} +(33.4110 - 19.2899i) q^{83} +(42.8189 - 74.1645i) q^{85} +(-85.5263 - 49.3786i) q^{86} +(-23.8181 - 41.2542i) q^{88} +98.5144i q^{89} -46.4263 q^{91} +(6.16311 - 3.55827i) q^{92} +(-18.7103 + 32.4072i) q^{94} +(188.751 + 108.975i) q^{95} +(10.5777 + 18.3210i) q^{97} -9.89949i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} - 36 q^{5} - 48 q^{16} + 24 q^{19} - 72 q^{20} + 24 q^{22} + 72 q^{23} + 72 q^{25} + 108 q^{29} - 60 q^{31} - 48 q^{34} - 168 q^{37} - 144 q^{38} - 108 q^{41} + 60 q^{43} + 324 q^{47} - 84 q^{49}+ \cdots + 48 q^{97}+O(q^{100}) \) 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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