LMFDB - Embedded newform 495.3.j.c.397.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [495,3,Mod(298,495)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(495, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 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("495.298"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	495.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4877730858$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			397.8
Character	$\chi$	$=$	495.397
Dual form			495.3.j.c.298.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.762894 - 0.762894i) q^{2} -2.83599i q^{4} +(4.94835 - 0.716812i) q^{5} +(-5.64620 - 5.64620i) q^{7} +(-5.21513 + 5.21513i) q^{8} +(-4.32192 - 3.22822i) q^{10} -3.31662 q^{11} +(-13.3014 + 13.3014i) q^{13} +8.61491i q^{14} -3.38676 q^{16} +(-21.6782 - 21.6782i) q^{17} +34.8757i q^{19} +(-2.03287 - 14.0335i) q^{20} +(2.53023 + 2.53023i) q^{22} +(15.6380 - 15.6380i) q^{23} +(23.9724 - 7.09407i) q^{25} +20.2951 q^{26} +(-16.0126 + 16.0126i) q^{28} +11.8667i q^{29} -24.8833 q^{31} +(23.4443 + 23.4443i) q^{32} +33.0763i q^{34} +(-31.9867 - 23.8921i) q^{35} +(-9.97802 - 9.97802i) q^{37} +(26.6065 - 26.6065i) q^{38} +(-22.0680 + 29.5446i) q^{40} +13.0596 q^{41} +(-2.85546 + 2.85546i) q^{43} +9.40590i q^{44} -23.8603 q^{46} +(-21.6085 - 21.6085i) q^{47} +14.7592i q^{49} +(-23.7004 - 12.8763i) q^{50} +(37.7225 + 37.7225i) q^{52} +(7.24110 - 7.24110i) q^{53} +(-16.4118 + 2.37739i) q^{55} +58.8914 q^{56} +(9.05302 - 9.05302i) q^{58} +57.4972i q^{59} -52.6576 q^{61} +(18.9834 + 18.9834i) q^{62} -22.2239i q^{64} +(-56.2853 + 75.3545i) q^{65} +(-35.3923 - 35.3923i) q^{67} +(-61.4789 + 61.4789i) q^{68} +(6.17527 + 42.6296i) q^{70} -94.5007 q^{71} +(-72.5959 + 72.5959i) q^{73} +15.2243i q^{74} +98.9071 q^{76} +(18.7263 + 18.7263i) q^{77} +84.9764i q^{79} +(-16.7589 + 2.42767i) q^{80} +(-9.96309 - 9.96309i) q^{82} +(68.0357 - 68.0357i) q^{83} +(-122.810 - 91.7320i) q^{85} +4.35682 q^{86} +(17.2966 - 17.2966i) q^{88} -22.9837i q^{89} +150.205 q^{91} +(-44.3492 - 44.3492i) q^{92} +32.9700i q^{94} +(24.9993 + 172.577i) q^{95} +(-27.4864 - 27.4864i) q^{97} +(11.2597 - 11.2597i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{10} - 88 q^{13} - 296 q^{16} + 168 q^{25} + 248 q^{28} - 32 q^{31} - 24 q^{37} + 296 q^{40} - 48 q^{43} + 48 q^{46} + 64 q^{52} + 104 q^{58} + 576 q^{61} - 544 q^{67} - 1048 q^{70} - 408 q^{73}+ \cdots + 712 q^{97}+O(q^{100}) $ 40 * q + 24 * q^10 - 88 * q^13 - 296 * q^16 + 168 * q^25 + 248 * q^28 - 32 * q^31 - 24 * q^37 + 296 * q^40 - 48 * q^43 + 48 * q^46 + 64 * q^52 + 104 * q^58 + 576 * q^61 - 544 * q^67 - 1048 * q^70 - 408 * q^73 - 96 * q^76 - 280 * q^82 + 160 * q^85 + 264 * q^88 + 528 * q^91 + 712 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.762894	−	0.762894i	−0.381447	−	0.381447i	0.490176	−	0.871623i	$-0.336932\pi$
$2$	−0.762894	−	0.762894i	−0.381447	−	0.381447i	−0.871623	+	0.490176i	$0.836932\pi$
$3$		0			0
$3$		0			0
$4$		−	2.83599i		−	0.708996i
$5$	4.94835	−	0.716812i	0.989670	−	0.143362i
$5$	4.94835	−	0.716812i	0.989670	−	0.143362i
$6$		0			0
$7$	−5.64620	−	5.64620i	−0.806600	−	0.806600i	0.177517	−	0.984118i	$-0.443193\pi$
$7$	−5.64620	−	5.64620i	−0.806600	−	0.806600i	−0.984118	+	0.177517i	$0.943193\pi$
$8$	−5.21513	+	5.21513i	−0.651891	+	0.651891i
$9$		0			0
$10$	−4.32192	−	3.22822i	−0.432192	−	0.322822i
$11$	−3.31662			−0.301511
$11$	−3.31662			−0.301511
$12$		0			0
$13$	−13.3014	+	13.3014i	−1.02318	+	1.02318i	−0.0234586	+	0.999725i	$0.507468\pi$
$13$	−13.3014	+	13.3014i	−1.02318	+	1.02318i	−0.999725	+	0.0234586i	$0.992532\pi$
$14$			8.61491i			0.615351i
$15$		0			0
$16$	−3.38676			−0.211672
$17$	−21.6782	−	21.6782i	−1.27519	−	1.27519i	−0.943330	−	0.331855i	$-0.892325\pi$
$17$	−21.6782	−	21.6782i	−1.27519	−	1.27519i	−0.331855	−	0.943330i	$-0.607675\pi$
$18$		0			0
$19$			34.8757i			1.83556i	0.397084	+	0.917782i	$0.370022\pi$
$19$			34.8757i			1.83556i	−0.397084	+	0.917782i	$0.629978\pi$
$20$	−2.03287	−	14.0335i	−0.101643	−	0.701673i
$21$		0			0
$22$	2.53023	+	2.53023i	0.115011	+	0.115011i
$23$	15.6380	−	15.6380i	0.679913	−	0.679913i	−0.280067	−	0.959980i	$-0.590357\pi$
$23$	15.6380	−	15.6380i	0.679913	−	0.679913i	0.959980	+	0.280067i	$0.0903567\pi$
$24$		0			0
$25$	23.9724	−	7.09407i	0.958894	−	0.283763i
$26$	20.2951			0.780580
$27$		0			0
$28$	−16.0126	+	16.0126i	−0.571877	+	0.571877i
$29$			11.8667i			0.409196i	0.978846	+	0.204598i	$0.0655887\pi$
$29$			11.8667i			0.409196i	−0.978846	+	0.204598i	$0.934411\pi$
$30$		0			0
$31$	−24.8833			−0.802689			−0.401344	−	0.915927i	$-0.631457\pi$
$31$	−24.8833			−0.802689			−0.401344	+	0.915927i	$0.631457\pi$
$32$	23.4443	+	23.4443i	0.732633	+	0.732633i
$33$		0			0
$34$			33.0763i			0.972831i
$35$	−31.9867	−	23.8921i	−0.913905	−	0.682632i
$36$		0			0
$37$	−9.97802	−	9.97802i	−0.269676	−	0.269676i	0.559293	−	0.828970i	$-0.311073\pi$
$37$	−9.97802	−	9.97802i	−0.269676	−	0.269676i	−0.828970	+	0.559293i	$0.811073\pi$
$38$	26.6065	−	26.6065i	0.700170	−	0.700170i
$39$		0			0
$40$	−22.0680	+	29.5446i	−0.551701	+	0.738614i
$41$	13.0596			0.318527			0.159263	−	0.987236i	$-0.449088\pi$
$41$	13.0596			0.318527			0.159263	+	0.987236i	$0.449088\pi$
$42$		0			0
$43$	−2.85546	+	2.85546i	−0.0664060	+	0.0664060i	−0.739530	−	0.673124i	$-0.764952\pi$
$43$	−2.85546	+	2.85546i	−0.0664060	+	0.0664060i	0.673124	+	0.739530i	$0.264952\pi$
$44$			9.40590i			0.213770i
$45$		0			0
$46$	−23.8603			−0.518702
$47$	−21.6085	−	21.6085i	−0.459755	−	0.459755i	0.438820	−	0.898575i	$-0.355397\pi$
$47$	−21.6085	−	21.6085i	−0.459755	−	0.459755i	−0.898575	+	0.438820i	$0.855397\pi$
$48$		0			0
$49$			14.7592i			0.301208i
$50$	−23.7004	−	12.8763i	−0.474008	−	0.257527i
$51$		0			0
$52$	37.7225	+	37.7225i	0.725433	+	0.725433i
$53$	7.24110	−	7.24110i	0.136624	−	0.136624i	−0.635487	−	0.772112i	$-0.719201\pi$
$53$	7.24110	−	7.24110i	0.136624	−	0.136624i	0.772112	+	0.635487i	$0.219201\pi$
$54$		0			0
$55$	−16.4118	+	2.37739i	−0.298397	+	0.0432254i
$56$	58.8914			1.05163
$57$		0			0
$58$	9.05302	−	9.05302i	0.156087	−	0.156087i
$59$			57.4972i			0.974528i	0.873255	+	0.487264i	$0.162005\pi$
$59$			57.4972i			0.974528i	−0.873255	+	0.487264i	$0.837995\pi$
$60$		0			0
$61$	−52.6576			−0.863239			−0.431620	−	0.902056i	$-0.642058\pi$
$61$	−52.6576			−0.863239			−0.431620	+	0.902056i	$0.642058\pi$
$62$	18.9834	+	18.9834i	0.306183	+	0.306183i
$63$		0			0
$64$		−	22.2239i		−	0.347249i
$65$	−56.2853	+	75.3545i	−0.865928	+	1.15930i
$66$		0			0
$67$	−35.3923	−	35.3923i	−0.528243	−	0.528243i	0.391805	−	0.920048i	$-0.371851\pi$
$67$	−35.3923	−	35.3923i	−0.528243	−	0.528243i	−0.920048	+	0.391805i	$0.871851\pi$
$68$	−61.4789	+	61.4789i	−0.904102	+	0.904102i
$69$		0			0
$70$	6.17527	+	42.6296i	0.0882181	+	0.608994i
$71$	−94.5007			−1.33100			−0.665498	−	0.746400i	$-0.731781\pi$
$71$	−94.5007			−1.33100			−0.665498	+	0.746400i	$0.731781\pi$
$72$		0			0
$73$	−72.5959	+	72.5959i	−0.994465	+	0.994465i	−0.999985	−	0.00552010i	$-0.998243\pi$
$73$	−72.5959	+	72.5959i	−0.994465	+	0.994465i	0.00552010	+	0.999985i	$0.498243\pi$
$74$			15.2243i			0.205734i
$75$		0			0
$76$	98.9071			1.30141
$77$	18.7263	+	18.7263i	0.243199	+	0.243199i
$78$		0			0
$79$			84.9764i			1.07565i	0.843056	+	0.537825i	$0.180754\pi$
$79$			84.9764i			1.07565i	−0.843056	+	0.537825i	$0.819246\pi$
$80$	−16.7589	+	2.42767i	−0.209486	+	0.0303458i
$81$		0			0
$82$	−9.96309	−	9.96309i	−0.121501	−	0.121501i
$83$	68.0357	−	68.0357i	0.819707	−	0.819707i	−0.166358	−	0.986065i	$-0.553201\pi$
$83$	68.0357	−	68.0357i	0.819707	−	0.819707i	0.986065	+	0.166358i	$0.0532008\pi$
$84$		0			0
$85$	−122.810	−	91.7320i	−1.44483	−	1.07920i
$86$	4.35682			0.0506607
$87$		0			0
$88$	17.2966	−	17.2966i	0.196553	−	0.196553i
$89$		−	22.9837i		−	0.258244i	−0.991629	−	0.129122i	$-0.958784\pi$
$89$		−	22.9837i		−	0.258244i	0.991629	−	0.129122i	$-0.0412158\pi$
$90$		0			0
$91$	150.205			1.65060
$92$	−44.3492	−	44.3492i	−0.482056	−	0.482056i
$93$		0			0
$94$			32.9700i			0.350744i
$95$	24.9993	+	172.577i	0.263151	+	1.81660i
$96$		0			0
$97$	−27.4864	−	27.4864i	−0.283365	−	0.283365i	0.551084	−	0.834449i	$-0.314214\pi$
$97$	−27.4864	−	27.4864i	−0.283365	−	0.283365i	−0.834449	+	0.551084i	$0.814214\pi$
$98$	11.2597	−	11.2597i	0.114895	−	0.114895i
$99$		0			0
$100$	−20.1187	−	67.9853i	−0.201187	−	0.679853i
$101$	134.985			1.33648			0.668240	−	0.743946i	$-0.267048\pi$
$101$	134.985			1.33648			0.668240	+	0.743946i	$0.267048\pi$
$102$		0			0
$103$	−141.839	+	141.839i	−1.37708	+	1.37708i	−0.527561	+	0.849517i	$0.676893\pi$
$103$	−141.839	+	141.839i	−1.37708	+	1.37708i	−0.849517	+	0.527561i	$0.823107\pi$
$104$		−	138.737i		−	1.33401i
$105$		0			0
$106$	−11.0484			−0.104230
$107$	−81.1330	−	81.1330i	−0.758253	−	0.758253i	0.217752	−	0.976004i	$-0.430128\pi$
$107$	−81.1330	−	81.1330i	−0.758253	−	0.758253i	−0.976004	+	0.217752i	$0.930128\pi$
$108$		0			0
$109$		−	214.556i		−	1.96840i	−0.177060	−	0.984200i	$-0.556659\pi$
$109$		−	214.556i		−	1.96840i	0.177060	−	0.984200i	$-0.443341\pi$
$110$	14.3342	+	10.7068i	0.130311	+	0.0973344i
$111$		0			0
$112$	19.1223	+	19.1223i	0.170735	+	0.170735i
$113$	74.6983	−	74.6983i	0.661047	−	0.661047i	−0.294580	−	0.955627i	$-0.595180\pi$
$113$	74.6983	−	74.6983i	0.661047	−	0.661047i	0.955627	+	0.294580i	$0.0951797\pi$
$114$		0			0
$115$	66.1729	−	88.5919i	0.575416	−	0.770364i
$116$	33.6538			0.290119
$117$		0			0
$118$	43.8642	−	43.8642i	0.371731	−	0.371731i
$119$			244.799i			2.05713i
$120$		0			0
$121$	11.0000			0.0909091
$122$	40.1722	+	40.1722i	0.329280	+	0.329280i
$123$		0			0
$124$			70.5688i			0.569103i
$125$	113.539	−	52.2876i	0.908308	−	0.418301i
$126$		0			0
$127$	−19.2265	−	19.2265i	−0.151390	−	0.151390i	0.627349	−	0.778739i	$-0.284140\pi$
$127$	−19.2265	−	19.2265i	−0.151390	−	0.151390i	−0.778739	+	0.627349i	$0.784140\pi$
$128$	76.8225	−	76.8225i	0.600176	−	0.600176i
$129$		0			0
$130$	100.427	−	14.5478i	0.772517	−	0.111906i
$131$	−142.166			−1.08524			−0.542620	−	0.839979i	$-0.682567\pi$
$131$	−142.166			−1.08524			−0.542620	+	0.839979i	$0.682567\pi$
$132$		0			0
$133$	196.915	−	196.915i	1.48057	−	1.48057i
$134$			54.0011i			0.402994i
$135$		0			0
$136$	226.109			1.66257
$137$	−67.9414	−	67.9414i	−0.495923	−	0.495923i	0.414243	−	0.910166i	$-0.364046\pi$
$137$	−67.9414	−	67.9414i	−0.495923	−	0.495923i	−0.910166	+	0.414243i	$0.864046\pi$
$138$		0			0
$139$		−	68.3755i		−	0.491910i	−0.969281	−	0.245955i	$-0.920898\pi$
$139$		−	68.3755i		−	0.491910i	0.969281	−	0.245955i	$-0.0791015\pi$
$140$	−67.7577	+	90.7137i	−0.483984	+	0.647955i
$141$		0			0
$142$	72.0940	+	72.0940i	0.507704	+	0.507704i
$143$	44.1157	−	44.1157i	0.308501	−	0.308501i
$144$		0			0
$145$	8.50618	+	58.7205i	0.0586633	+	0.404969i
$146$	110.766			0.758671
$147$		0			0
$148$	−28.2975	+	28.2975i	−0.191200	+	0.191200i
$149$		−	158.915i		−	1.06654i	−0.845945	−	0.533270i	$-0.820963\pi$
$149$		−	158.915i		−	1.06654i	0.845945	−	0.533270i	$-0.179037\pi$
$150$		0			0
$151$	−36.4129			−0.241145			−0.120573	−	0.992705i	$-0.538473\pi$
$151$	−36.4129			−0.241145			−0.120573	+	0.992705i	$0.538473\pi$
$152$	−181.881	−	181.881i	−1.19659	−	1.19659i
$153$		0			0
$154$		−	28.5724i		−	0.185535i
$155$	−123.132	+	17.8367i	−0.794397	+	0.115075i
$156$		0			0
$157$	−81.3870	−	81.3870i	−0.518389	−	0.518389i	0.398695	−	0.917084i	$-0.369463\pi$
$157$	−81.3870	−	81.3870i	−0.518389	−	0.518389i	−0.917084	+	0.398695i	$0.869463\pi$
$158$	64.8280	−	64.8280i	0.410304	−	0.410304i
$159$		0			0
$160$	132.816	+	99.2053i	0.830097	+	0.620033i
$161$	−176.591			−1.09684
$162$		0			0
$163$	51.1071	−	51.1071i	0.313540	−	0.313540i	−0.532739	−	0.846279i	$-0.678837\pi$
$163$	51.1071	−	51.1071i	0.313540	−	0.313540i	0.846279	+	0.532739i	$0.178837\pi$
$164$		−	37.0369i		−	0.225834i
$165$		0			0
$166$	−103.808			−0.625350
$167$	−25.6226	−	25.6226i	−0.153429	−	0.153429i	0.626219	−	0.779647i	$-0.284602\pi$
$167$	−25.6226	−	25.6226i	−0.153429	−	0.153429i	−0.779647	+	0.626219i	$0.784602\pi$
$168$		0			0
$169$		−	184.854i		−	1.09381i
$170$	23.7094	+	163.673i	0.139467	+	0.962782i
$171$		0			0
$172$	8.09804	+	8.09804i	0.0470816	+	0.0470816i
$173$	19.5766	−	19.5766i	0.113160	−	0.113160i	−0.648260	−	0.761419i	$-0.724503\pi$
$173$	19.5766	−	19.5766i	0.113160	−	0.113160i	0.761419	+	0.648260i	$0.224503\pi$
$174$		0			0
$175$	−175.407	−	95.2983i	−1.00233	−	0.544561i
$176$	11.2326			0.0638216
$177$		0			0
$178$	−17.5341	+	17.5341i	−0.0985063	+	0.0985063i
$179$			296.275i			1.65517i	0.561340	+	0.827585i	$0.310286\pi$
$179$			296.275i			1.65517i	−0.561340	+	0.827585i	$0.689714\pi$
$180$		0			0
$181$	60.5675			0.334627			0.167314	−	0.985904i	$-0.446491\pi$
$181$	60.5675			0.334627			0.167314	+	0.985904i	$0.446491\pi$
$182$	−114.590	−	114.590i	−0.629616	−	0.629616i
$183$		0			0
$184$			163.109i			0.886460i
$185$	−56.5271	−	42.2224i	−0.305552	−	0.228229i
$186$		0			0
$187$	71.8983	+	71.8983i	0.384483	+	0.384483i
$188$	−61.2814	+	61.2814i	−0.325965	+	0.325965i
$189$		0			0
$190$	112.586	−	150.730i	0.592560	−	0.793316i
$191$	282.738			1.48030			0.740152	−	0.672439i	$-0.234753\pi$
$191$	282.738			1.48030			0.740152	+	0.672439i	$0.234753\pi$
$192$		0			0
$193$	224.475	−	224.475i	1.16308	−	1.16308i	0.179284	−	0.983797i	$-0.442622\pi$
$193$	224.475	−	224.475i	1.16308	−	1.16308i	0.983797	−	0.179284i	$-0.0573782\pi$
$194$			41.9384i			0.216177i
$195$		0			0
$196$	41.8569			0.213556
$197$	−86.0459	−	86.0459i	−0.436781	−	0.436781i	0.454146	−	0.890927i	$-0.349944\pi$
$197$	−86.0459	−	86.0459i	−0.436781	−	0.436781i	−0.890927	+	0.454146i	$0.849944\pi$
$198$		0			0
$199$			100.165i			0.503343i	0.967813	+	0.251672i	$0.0809803\pi$
$199$			100.165i			0.503343i	−0.967813	+	0.251672i	$0.919020\pi$
$200$	−88.0225	+	162.016i	−0.440113	+	0.810078i
$201$		0			0
$202$	−102.979	−	102.979i	−0.509796	−	0.509796i
$203$	67.0017	−	67.0017i	0.330058	−	0.330058i
$204$		0			0
$205$	64.6235	−	9.36128i	0.315237	−	0.0456648i
$206$	216.416			1.05056
$207$		0			0
$208$	45.0486	−	45.0486i	0.216580	−	0.216580i
$209$		−	115.670i		−	0.553443i
$210$		0			0
$211$	20.2391			0.0959201			0.0479601	−	0.998849i	$-0.484728\pi$
$211$	20.2391			0.0959201			0.0479601	+	0.998849i	$0.484728\pi$
$212$	−20.5356	−	20.5356i	−0.0968663	−	0.0968663i
$213$		0			0
$214$			123.792i			0.578466i
$215$	−12.0830	+	16.1766i	−0.0561999	+	0.0752402i
$216$		0			0
$217$	140.496	+	140.496i	0.647449	+	0.647449i
$218$	−163.683	+	163.683i	−0.750840	+	0.750840i
$219$		0			0
$220$	6.74226	+	46.5437i	0.0306466	+	0.211562i
$221$	576.699			2.60950
$222$		0			0
$223$	−209.064	+	209.064i	−0.937509	+	0.937509i	−0.998159	−	0.0606503i	$-0.980683\pi$
$223$	−209.064	+	209.064i	−0.937509	+	0.937509i	0.0606503	+	0.998159i	$0.480683\pi$
$224$		−	264.742i		−	1.18188i
$225$		0			0
$226$	−113.974			−0.504309
$227$	−141.036	−	141.036i	−0.621305	−	0.621305i	0.324560	−	0.945865i	$-0.394784\pi$
$227$	−141.036	−	141.036i	−0.621305	−	0.621305i	−0.945865	+	0.324560i	$0.894784\pi$
$228$		0			0
$229$		−	454.192i		−	1.98337i	−0.128678	−	0.991686i	$-0.541073\pi$
$229$		−	454.192i		−	1.98337i	0.128678	−	0.991686i	$-0.458927\pi$
$230$	−118.069	+	17.1033i	−0.513344	+	0.0743623i
$231$		0			0
$232$	−61.8863	−	61.8863i	−0.266751	−	0.266751i
$233$	−242.026	+	242.026i	−1.03874	+	1.03874i	−0.0395211	+	0.999219i	$0.512583\pi$
$233$	−242.026	+	242.026i	−1.03874	+	1.03874i	−0.999219	+	0.0395211i	$0.987417\pi$
$234$		0			0
$235$	−122.416	−	91.4372i	−0.520918	−	0.389094i
$236$	163.061			0.690937
$237$		0			0
$238$	186.755	−	186.755i	0.784686	−	0.784686i
$239$		−	316.920i		−	1.32603i	−0.748608	−	0.663013i	$-0.769277\pi$
$239$		−	316.920i		−	1.32603i	0.748608	−	0.663013i	$-0.230723\pi$
$240$		0			0
$241$	79.5916			0.330256			0.165128	−	0.986272i	$-0.447196\pi$
$241$	79.5916			0.330256			0.165128	+	0.986272i	$0.447196\pi$
$242$	−8.39183	−	8.39183i	−0.0346770	−	0.0346770i
$243$		0			0
$244$			149.336i			0.612034i
$245$	10.5796	+	73.0338i	0.0431819	+	0.298097i
$246$		0			0
$247$	−463.895	−	463.895i	−1.87812	−	1.87812i
$248$	129.770	−	129.770i	0.523266	−	0.523266i
$249$		0			0
$250$	−126.508	−	46.7280i	−0.506031	−	0.186912i
$251$	125.487			0.499948			0.249974	−	0.968253i	$-0.419578\pi$
$251$	125.487			0.499948			0.249974	+	0.968253i	$0.419578\pi$
$252$		0			0
$253$	−51.8654	+	51.8654i	−0.205002	+	0.205002i
$254$			29.3356i			0.115495i
$255$		0			0
$256$	−206.111			−0.805120
$257$	−267.818	−	267.818i	−1.04210	−	1.04210i	−0.999074	−	0.0430210i	$-0.986302\pi$
$257$	−267.818	−	267.818i	−1.04210	−	1.04210i	−0.0430210	−	0.999074i	$-0.513698\pi$
$258$		0			0
$259$			112.676i			0.435042i
$260$	213.704	+	159.624i	0.821940	+	0.613940i
$261$		0			0
$262$	108.458	+	108.458i	0.413961	+	0.413961i
$263$	87.0542	−	87.0542i	0.331004	−	0.331004i	−0.521963	−	0.852968i	$-0.674800\pi$
$263$	87.0542	−	87.0542i	0.331004	−	0.331004i	0.852968	+	0.521963i	$0.174800\pi$
$264$		0			0
$265$	30.6410	−	41.0220i	0.115626	−	0.154800i
$266$	−300.451			−1.12952
$267$		0			0
$268$	−100.372	+	100.372i	−0.374523	+	0.374523i
$269$			398.129i			1.48004i	0.672588	+	0.740018i	$0.265183\pi$
$269$			398.129i			1.48004i	−0.672588	+	0.740018i	$0.734817\pi$
$270$		0			0
$271$	−70.6482			−0.260695			−0.130347	−	0.991468i	$-0.541609\pi$
$271$	−70.6482			−0.260695			−0.130347	+	0.991468i	$0.541609\pi$
$272$	73.4187	+	73.4187i	0.269922	+	0.269922i
$273$		0			0
$274$			103.664i			0.378337i
$275$	−79.5073	+	23.5284i	−0.289118	+	0.0855577i
$276$		0			0
$277$	126.191	+	126.191i	0.455563	+	0.455563i	0.897196	−	0.441633i	$-0.145601\pi$
$277$	126.191	+	126.191i	0.455563	+	0.455563i	−0.441633	+	0.897196i	$0.645601\pi$
$278$	−52.1632	+	52.1632i	−0.187638	+	0.187638i
$279$		0			0
$280$	291.415	−	42.2140i	1.04077	−	0.150764i
$281$	369.039			1.31330			0.656652	−	0.754193i	$-0.271972\pi$
$281$	369.039			1.31330			0.656652	+	0.754193i	$0.271972\pi$
$282$		0			0
$283$	−90.3144	+	90.3144i	−0.319132	+	0.319132i	−0.848434	−	0.529301i	$-0.822454\pi$
$283$	−90.3144	+	90.3144i	−0.319132	+	0.319132i	0.529301	+	0.848434i	$0.322454\pi$
$284$			268.003i			0.943671i
$285$		0			0
$286$	−67.3112			−0.235354
$287$	−73.7372	−	73.7372i	−0.256924	−	0.256924i
$288$		0			0
$289$			650.885i			2.25220i
$290$	38.3082	−	51.2869i	0.132097	−	0.176851i
$291$		0			0
$292$	205.881	+	205.881i	0.705072	+	0.705072i
$293$	−228.045	+	228.045i	−0.778311	+	0.778311i	−0.979543	−	0.201233i	$-0.935505\pi$
$293$	−228.045	+	228.045i	−0.778311	+	0.778311i	0.201233	+	0.979543i	$0.435505\pi$
$294$		0			0
$295$	41.2146	+	284.516i	0.139711	+	0.964462i
$296$	104.073			0.351599
$297$		0			0
$298$	−121.235	+	121.235i	−0.406829	+	0.406829i
$299$			416.014i			1.39135i
$300$		0			0
$301$	32.2450			0.107126
$302$	27.7792	+	27.7792i	0.0919840	+	0.0919840i
$303$		0			0
$304$		−	118.116i		−	0.388538i
$305$	−260.568	+	37.7456i	−0.854322	+	0.123756i
$306$		0			0
$307$	−166.353	−	166.353i	−0.541866	−	0.541866i	0.382209	−	0.924076i	$-0.375163\pi$
$307$	−166.353	−	166.353i	−0.541866	−	0.541866i	−0.924076	+	0.382209i	$0.875163\pi$
$308$	53.1076	−	53.1076i	0.172427	−	0.172427i
$309$		0			0
$310$	107.544	+	80.3288i	0.346915	+	0.259125i
$311$	−538.220			−1.73061			−0.865305	−	0.501246i	$-0.832875\pi$
$311$	−538.220			−1.73061			−0.865305	+	0.501246i	$0.832875\pi$
$312$		0			0
$313$	−157.952	+	157.952i	−0.504639	+	0.504639i	−0.912876	−	0.408237i	$-0.866144\pi$
$313$	−157.952	+	157.952i	−0.504639	+	0.504639i	0.408237	+	0.912876i	$0.366144\pi$
$314$			124.179i			0.395476i
$315$		0			0
$316$	240.992			0.762632
$317$	138.919	+	138.919i	0.438229	+	0.438229i	0.891416	−	0.453187i	$-0.149713\pi$
$317$	138.919	+	138.919i	0.438229	+	0.438229i	−0.453187	+	0.891416i	$0.649713\pi$
$318$		0			0
$319$		−	39.3574i		−	0.123377i
$320$	−15.9304	−	109.972i	−0.0497824	−	0.343662i
$321$		0			0
$322$	134.720	+	134.720i	0.418385	+	0.418385i
$323$	756.041	−	756.041i	2.34069	−	2.34069i
$324$		0			0
$325$	−224.505	+	413.227i	−0.690783	+	1.27147i
$326$	−77.9785			−0.239198
$327$		0			0
$328$	−68.1076	+	68.1076i	−0.207645	+	0.207645i
$329$			244.012i			0.741677i
$330$		0			0
$331$	8.14051			0.0245937			0.0122968	−	0.999924i	$-0.496086\pi$
$331$	8.14051			0.0245937			0.0122968	+	0.999924i	$0.496086\pi$
$332$	−192.948	−	192.948i	−0.581169	−	0.581169i
$333$		0			0
$334$			39.0946i			0.117050i
$335$	−200.503	−	149.764i	−0.598517	−	0.447056i
$336$		0			0
$337$	224.968	+	224.968i	0.667560	+	0.667560i	0.957151	−	0.289591i	$-0.0935193\pi$
$337$	224.968	+	224.968i	0.667560	+	0.667560i	−0.289591	+	0.957151i	$0.593519\pi$
$338$	−141.024	+	141.024i	−0.417230	+	0.417230i
$339$		0			0
$340$	−260.151	+	348.288i	−0.765149	+	1.02438i
$341$	82.5287			0.242020
$342$		0			0
$343$	−193.330	+	193.330i	−0.563646	+	0.563646i
$344$		−	29.7832i		−	0.0865790i
$345$		0			0
$346$	−29.8698			−0.0863288
$347$	91.0351	+	91.0351i	0.262349	+	0.262349i	0.826008	−	0.563659i	$-0.190607\pi$
$347$	91.0351	+	91.0351i	0.262349	+	0.262349i	−0.563659	+	0.826008i	$0.690607\pi$
$348$		0			0
$349$		−	331.235i		−	0.949096i	−0.880230	−	0.474548i	$-0.842612\pi$
$349$		−	331.235i		−	0.949096i	0.880230	−	0.474548i	$-0.157388\pi$
$350$	61.1148	+	206.520i	0.174614	+	0.590056i
$351$		0			0
$352$	−77.7558	−	77.7558i	−0.220897	−	0.220897i
$353$	277.162	−	277.162i	0.785161	−	0.785161i	−0.195536	−	0.980697i	$-0.562645\pi$
$353$	277.162	−	277.162i	0.785161	−	0.785161i	0.980697	+	0.195536i	$0.0626446\pi$
$354$		0			0
$355$	−467.623	+	67.7392i	−1.31725	+	0.190815i
$356$	−65.1814			−0.183094
$357$		0			0
$358$	226.027	−	226.027i	0.631360	−	0.631360i
$359$			524.643i			1.46140i	0.682699	+	0.730700i	$0.260806\pi$
$359$			524.643i			1.46140i	−0.682699	+	0.730700i	$0.739194\pi$
$360$		0			0
$361$	−855.316			−2.36930
$362$	−46.2066	−	46.2066i	−0.127642	−	0.127642i
$363$		0			0
$364$		−	425.978i		−	1.17027i
$365$	−307.193	+	411.268i	−0.841623	+	1.12676i
$366$		0			0
$367$	373.653	+	373.653i	1.01813	+	1.01813i	0.999833	+	0.0182967i	$0.00582436\pi$
$367$	373.653	+	373.653i	1.01813	+	1.01813i	0.0182967	+	0.999833i	$0.494176\pi$
$368$	−52.9622	+	52.9622i	−0.143919	+	0.143919i
$369$		0			0
$370$	10.9130	+	75.3354i	0.0294946	+	0.203609i
$371$	−81.7694			−0.220403
$372$		0			0
$373$	−178.188	+	178.188i	−0.477716	+	0.477716i	−0.904400	−	0.426685i	$-0.859681\pi$
$373$	−178.188	+	178.188i	−0.477716	+	0.477716i	0.426685	+	0.904400i	$0.359681\pi$
$374$		−	109.702i		−	0.293320i
$375$		0			0
$376$	225.382			0.599421
$377$	−157.843	−	157.843i	−0.418683	−	0.418683i
$378$		0			0
$379$		−	98.4759i		−	0.259831i	−0.991525	−	0.129915i	$-0.958529\pi$
$379$		−	98.4759i		−	0.259831i	0.991525	−	0.129915i	$-0.0414706\pi$
$380$	489.427	−	70.8977i	1.28797	−	0.186573i
$381$		0			0
$382$	−215.699	−	215.699i	−0.564658	−	0.564658i
$383$	48.4087	−	48.4087i	0.126393	−	0.126393i	−0.641080	−	0.767474i	$-0.721513\pi$
$383$	48.4087	−	48.4087i	0.126393	−	0.126393i	0.767474	+	0.641080i	$0.221513\pi$
$384$		0			0
$385$	106.088	+	79.2412i	0.275553	+	0.205821i
$386$	−342.501			−0.887308
$387$		0			0
$388$	−77.9510	+	77.9510i	−0.200905	+	0.200905i
$389$		−	160.956i		−	0.413769i	−0.978365	−	0.206884i	$-0.933668\pi$
$389$		−	160.956i		−	0.413769i	0.978365	−	0.206884i	$-0.0663324\pi$
$390$		0			0
$391$	−678.006			−1.73403
$392$	−76.9713	−	76.9713i	−0.196355	−	0.196355i
$393$		0			0
$394$			131.288i			0.333218i
$395$	60.9121	+	420.493i	0.154208	+	1.06454i
$396$		0			0
$397$	−81.4640	−	81.4640i	−0.205199	−	0.205199i	0.597024	−	0.802223i	$-0.296350\pi$
$397$	−81.4640	−	81.4640i	−0.205199	−	0.205199i	−0.802223	+	0.597024i	$0.796350\pi$
$398$	76.4155	−	76.4155i	0.191999	−	0.191999i
$399$		0			0
$400$	−81.1886	+	24.0259i	−0.202971	+	0.0600648i
$401$	707.539			1.76444			0.882219	−	0.470840i	$-0.156049\pi$
$401$	707.539			1.76444			0.882219	+	0.470840i	$0.156049\pi$
$402$		0			0
$403$	330.983	−	330.983i	0.821298	−	0.821298i
$404$		−	382.814i		−	0.947560i
$405$		0			0
$406$	−102.230			−0.251799
$407$	33.0934	+	33.0934i	0.0813105	+	0.0813105i
$408$		0			0
$409$		−	578.569i		−	1.41459i	−0.706917	−	0.707297i	$-0.749914\pi$
$409$		−	578.569i		−	1.41459i	0.706917	−	0.707297i	$-0.250086\pi$
$410$	−56.4425	−	42.1592i	−0.137665	−	0.102827i
$411$		0			0
$412$	402.254	+	402.254i	0.976344	+	0.976344i
$413$	324.641	−	324.641i	0.786055	−	0.786055i
$414$		0			0
$415$	287.896	−	385.433i	0.693725	−	0.928755i
$416$	−623.682			−1.49924
$417$		0			0
$418$	−88.2437	+	88.2437i	−0.211109	+	0.211109i
$419$		−	641.532i		−	1.53110i	−0.643374	−	0.765552i	$-0.722466\pi$
$419$		−	641.532i		−	1.53110i	0.643374	−	0.765552i	$-0.277534\pi$
$420$		0			0
$421$	175.632			0.417177			0.208589	−	0.978003i	$-0.433113\pi$
$421$	175.632			0.417177			0.208589	+	0.978003i	$0.433113\pi$
$422$	−15.4403	−	15.4403i	−0.0365884	−	0.0365884i
$423$		0			0
$424$			75.5266i			0.178129i
$425$	−673.463	−	365.890i	−1.58462	−	0.860918i
$426$		0			0
$427$	297.316	+	297.316i	0.696289	+	0.696289i
$428$	−230.092	+	230.092i	−0.537598	+	0.537598i
$429$		0			0
$430$	21.5591	−	3.12302i	0.0501374	−	0.00726284i
$431$	−160.285			−0.371890			−0.185945	−	0.982560i	$-0.559535\pi$
$431$	−160.285			−0.371890			−0.185945	+	0.982560i	$0.559535\pi$
$432$		0			0
$433$	318.636	−	318.636i	0.735880	−	0.735880i	−0.235898	−	0.971778i	$-0.575803\pi$
$433$	318.636	−	318.636i	0.735880	−	0.735880i	0.971778	+	0.235898i	$0.0758031\pi$
$434$		−	214.368i		−	0.493935i
$435$		0			0
$436$	−608.477			−1.39559
$437$	545.387	+	545.387i	1.24802	+	1.24802i
$438$		0			0
$439$			145.324i			0.331034i	0.986207	+	0.165517i	$0.0529293\pi$
$439$			145.324i			0.331034i	−0.986207	+	0.165517i	$0.947071\pi$
$440$	73.1914	−	97.9883i	0.166344	−	0.222701i
$441$		0			0
$442$	−439.960	−	439.960i	−0.995385	−	0.995385i
$443$	180.836	−	180.836i	0.408208	−	0.408208i	−0.472905	−	0.881113i	$-0.656795\pi$
$443$	180.836	−	180.836i	0.408208	−	0.408208i	0.881113	+	0.472905i	$0.156795\pi$
$444$		0			0
$445$	−16.4750	−	113.731i	−0.0370224	−	0.255576i
$446$	318.988			0.715220
$447$		0			0
$448$	−125.481	+	125.481i	−0.280091	+	0.280091i
$449$		−	343.266i		−	0.764512i	−0.924057	−	0.382256i	$-0.875147\pi$
$449$		−	343.266i		−	0.764512i	0.924057	−	0.382256i	$-0.124853\pi$
$450$		0			0
$451$	−43.3138			−0.0960395
$452$	−211.843	−	211.843i	−0.468680	−	0.468680i
$453$		0			0
$454$			215.192i			0.473990i
$455$	743.265	−	107.668i	1.63355	−	0.236634i
$456$		0			0
$457$	−122.346	−	122.346i	−0.267716	−	0.267716i	0.560463	−	0.828179i	$-0.310623\pi$
$457$	−122.346	−	122.346i	−0.267716	−	0.267716i	−0.828179	+	0.560463i	$0.810623\pi$
$458$	−346.501	+	346.501i	−0.756552	+	0.756552i
$459$		0			0
$460$	−251.245	−	187.665i	−0.546185	−	0.407968i
$461$	−677.352			−1.46931			−0.734655	−	0.678441i	$-0.762656\pi$
$461$	−677.352			−1.46931			−0.734655	+	0.678441i	$0.762656\pi$
$462$		0			0
$463$	−13.6180	+	13.6180i	−0.0294126	+	0.0294126i	−0.721660	−	0.692248i	$-0.756621\pi$
$463$	−13.6180	+	13.6180i	−0.0294126	+	0.0294126i	0.692248	+	0.721660i	$0.256621\pi$
$464$		−	40.1896i		−	0.0866155i
$465$		0			0
$466$	369.281			0.792448
$467$	−102.513	−	102.513i	−0.219513	−	0.219513i	0.588780	−	0.808293i	$-0.299608\pi$
$467$	−102.513	−	102.513i	−0.219513	−	0.219513i	−0.808293	+	0.588780i	$0.799608\pi$
$468$		0			0
$469$			399.664i			0.852162i
$470$	23.6333	+	163.147i	0.0502835	+	0.347121i
$471$		0			0
$472$	−299.855	−	299.855i	−0.635287	−	0.635287i
$473$	9.47048	−	9.47048i	0.0200222	−	0.0200222i
$474$		0			0
$475$	247.411	+	836.053i	0.520865	+	1.76011i
$476$	694.245			1.45850
$477$		0			0
$478$	−241.776	+	241.776i	−0.505809	+	0.505809i
$479$		−	558.469i		−	1.16591i	−0.812506	−	0.582953i	$-0.801897\pi$
$479$		−	558.469i		−	1.16591i	0.812506	−	0.582953i	$-0.198103\pi$
$480$		0			0
$481$	265.443			0.551857
$482$	−60.7199	−	60.7199i	−0.125975	−	0.125975i
$483$		0			0
$484$		−	31.1958i		−	0.0644542i
$485$	−155.715	−	116.310i	−0.321062	−	0.239814i
$486$		0			0
$487$	289.688	+	289.688i	0.594841	+	0.594841i	0.938935	−	0.344094i	$-0.111814\pi$
$487$	289.688	+	289.688i	0.594841	+	0.594841i	−0.344094	+	0.938935i	$0.611814\pi$
$488$	274.616	−	274.616i	0.562738	−	0.562738i
$489$		0			0
$490$	47.6459	−	63.7881i	0.0972366	−	0.130180i
$491$	−111.574			−0.227238			−0.113619	−	0.993524i	$-0.536244\pi$
$491$	−111.574			−0.227238			−0.113619	+	0.993524i	$0.536244\pi$
$492$		0			0
$493$	257.248	−	257.248i	0.521801	−	0.521801i
$494$			707.806i			1.43281i
$495$		0			0
$496$	84.2739			0.169907
$497$	533.570	+	533.570i	1.07358	+	1.07358i
$498$		0			0
$499$			319.712i			0.640705i	0.947298	+	0.320353i	$0.103801\pi$
$499$			319.712i			0.640705i	−0.947298	+	0.320353i	$0.896199\pi$
$500$	−148.287	−	321.994i	−0.296574	−	0.643987i
$501$		0			0
$502$	−95.7332	−	95.7332i	−0.190704	−	0.190704i
$503$	240.825	−	240.825i	0.478777	−	0.478777i	−0.425964	−	0.904740i	$-0.640065\pi$
$503$	240.825	−	240.825i	0.478777	−	0.478777i	0.904740	+	0.425964i	$0.140065\pi$
$504$		0			0
$505$	667.951	−	96.7585i	1.32268	−	0.191601i
$506$	79.1356			0.156394
$507$		0			0
$508$	−54.5262	+	54.5262i	−0.107335	+	0.107335i
$509$			110.965i			0.218005i	0.994041	+	0.109003i	$0.0347657\pi$
$509$			110.965i			0.218005i	−0.994041	+	0.109003i	$0.965234\pi$
$510$		0			0
$511$	819.783			1.60427
$512$	−150.050	−	150.050i	−0.293066	−	0.293066i
$513$		0			0
$514$			408.634i			0.795008i
$515$	−600.198	+	803.541i	−1.16543	+	1.56027i
$516$		0			0
$517$	71.6673	+	71.6673i	0.138621	+	0.138621i
$518$	85.9597	−	85.9597i	0.165945	−	0.165945i
$519$		0			0
$520$	−99.4482	−	686.519i	−0.191247	−	1.32023i
$521$	−341.847			−0.656136			−0.328068	−	0.944654i	$-0.606397\pi$
$521$	−341.847			−0.656136			−0.328068	+	0.944654i	$0.606397\pi$
$522$		0			0
$523$	92.5568	−	92.5568i	0.176973	−	0.176973i	−0.613062	−	0.790035i	$-0.710062\pi$
$523$	92.5568	−	92.5568i	0.176973	−	0.176973i	0.790035	+	0.613062i	$0.210062\pi$
$524$			403.182i			0.769431i
$525$		0			0
$526$	−132.826			−0.252521
$527$	539.425	+	539.425i	1.02358	+	1.02358i
$528$		0			0
$529$			39.9053i			0.0754354i
$530$	−54.6713	+	7.91961i	−0.103153	+	0.0149427i
$531$		0			0
$532$	−558.449	−	558.449i	−1.04972	−	1.04972i
$533$	−173.711	+	173.711i	−0.325911	+	0.325911i
$534$		0			0
$535$	−459.632	−	343.318i	−0.859125	−	0.641715i
$536$	369.151			0.688714
$537$		0			0
$538$	303.731	−	303.731i	0.564555	−	0.564555i
$539$		−	48.9508i		−	0.0908178i
$540$		0			0
$541$	388.779			0.718631			0.359315	−	0.933216i	$-0.383010\pi$
$541$	388.779			0.718631			0.359315	+	0.933216i	$0.383010\pi$
$542$	53.8971	+	53.8971i	0.0994411	+	0.0994411i
$543$		0			0
$544$		−	1016.46i		−	1.86849i
$545$	−153.796	−	1061.70i	−0.282194	−	1.94807i
$546$		0			0
$547$	460.867	+	460.867i	0.842536	+	0.842536i	0.989188	−	0.146652i	$-0.0468497\pi$
$547$	460.867	+	460.867i	0.842536	+	0.842536i	−0.146652	+	0.989188i	$0.546850\pi$
$548$	−192.681	+	192.681i	−0.351608	+	0.351608i
$549$		0			0
$550$	78.6053	+	42.7060i	0.142919	+	0.0776473i
$551$	−413.859			−0.751106
$552$		0			0
$553$	479.794	−	479.794i	0.867620	−	0.867620i
$554$		−	192.540i		−	0.347546i
$555$		0			0
$556$	−193.912			−0.348762
$557$	−252.526	−	252.526i	−0.453369	−	0.453369i	0.443102	−	0.896471i	$-0.353878\pi$
$557$	−252.526	−	252.526i	−0.453369	−	0.453369i	−0.896471	+	0.443102i	$0.853878\pi$
$558$		0			0
$559$		−	75.9631i		−	0.135891i
$560$	108.331	+	80.9169i	0.193448	+	0.144494i
$561$		0			0
$562$	−281.537	−	281.537i	−0.500956	−	0.500956i
$563$	−637.910	+	637.910i	−1.13306	+	1.13306i	−0.143389	+	0.989666i	$0.545800\pi$
$563$	−637.910	+	637.910i	−1.13306	+	1.13306i	−0.989666	+	0.143389i	$0.954200\pi$
$564$		0			0
$565$	316.089	−	423.178i	0.559449	−	0.748988i
$566$	137.801			0.243464
$567$		0			0
$568$	492.834	−	492.834i	0.867665	−	0.867665i
$569$			748.048i			1.31467i	0.753598	+	0.657335i	$0.228317\pi$
$569$			748.048i			1.31467i	−0.753598	+	0.657335i	$0.771683\pi$
$570$		0			0
$571$	98.2879			0.172133			0.0860665	−	0.996289i	$-0.472570\pi$
$571$	98.2879			0.172133			0.0860665	+	0.996289i	$0.472570\pi$
$572$	−125.111	−	125.111i	−0.218726	−	0.218726i
$573$		0			0
$574$			112.507i			0.196006i
$575$	263.943	−	485.817i	0.459031	−	0.844899i
$576$		0			0
$577$	6.74285	+	6.74285i	0.0116861	+	0.0116861i	0.712926	−	0.701240i	$-0.247370\pi$
$577$	6.74285	+	6.74285i	0.0116861	+	0.0116861i	−0.701240	+	0.712926i	$0.747370\pi$
$578$	496.556	−	496.556i	0.859093	−	0.859093i
$579$		0			0
$580$	166.531	−	24.1234i	0.287122	−	0.0415921i
$581$	−768.287			−1.32235
$582$		0			0
$583$	−24.0160	+	24.0160i	−0.0411938	+	0.0411938i
$584$		−	757.195i		−	1.29657i
$585$		0			0
$586$	347.948			0.593769
$587$	535.346	+	535.346i	0.912003	+	0.912003i	0.996430	−	0.0844269i	$-0.0269059\pi$
$587$	535.346	+	535.346i	0.912003	+	0.912003i	−0.0844269	+	0.996430i	$0.526906\pi$
$588$		0			0
$589$		−	867.825i		−	1.47339i
$590$	185.613	−	248.498i	0.314599	−	0.421183i
$591$		0			0
$592$	33.7931	+	33.7931i	0.0570830	+	0.0570830i
$593$	−652.415	+	652.415i	−1.10019	+	1.10019i	−0.105808	+	0.994387i	$0.533743\pi$
$593$	−652.415	+	652.415i	−1.10019	+	1.10019i	−0.994387	+	0.105808i	$0.966257\pi$
$594$		0			0
$595$	175.474	+	1211.35i	0.294915	+	2.03588i
$596$	−450.679			−0.756174
$597$		0			0
$598$	317.375	−	317.375i	0.530727	−	0.530727i
$599$			340.966i			0.569225i	0.958643	+	0.284613i	$0.0918649\pi$
$599$			340.966i			0.569225i	−0.958643	+	0.284613i	$0.908135\pi$
$600$		0			0
$601$	467.606			0.778047			0.389023	−	0.921228i	$-0.372813\pi$
$601$	467.606			0.778047			0.389023	+	0.921228i	$0.372813\pi$
$602$	−24.5995	−	24.5995i	−0.0408630	−	0.0408630i
$603$		0			0
$604$			103.266i			0.170971i
$605$	54.4319	−	7.88493i	0.0899700	−	0.0130329i
$606$		0			0
$607$	−182.070	−	182.070i	−0.299951	−	0.299951i	0.541044	−	0.840994i	$-0.318029\pi$
$607$	−182.070	−	182.070i	−0.299951	−	0.299951i	−0.840994	+	0.541044i	$0.818029\pi$
$608$	−817.636	+	817.636i	−1.34480	+	1.34480i
$609$		0			0
$610$	227.582	+	169.990i	0.373085	+	0.278672i
$611$	574.846			0.940828
$612$		0			0
$613$	183.193	−	183.193i	0.298847	−	0.298847i	−0.541715	−	0.840562i	$-0.682225\pi$
$613$	183.193	−	183.193i	0.298847	−	0.298847i	0.840562	+	0.541715i	$0.182225\pi$
$614$			253.819i			0.413387i
$615$		0			0
$616$	−195.321			−0.317079
$617$	164.004	+	164.004i	0.265809	+	0.265809i	0.827409	−	0.561600i	$-0.189814\pi$
$617$	164.004	+	164.004i	0.265809	+	0.265809i	−0.561600	+	0.827409i	$0.689814\pi$
$618$		0			0
$619$		−	657.075i		−	1.06151i	−0.847525	−	0.530755i	$-0.821908\pi$
$619$		−	657.075i		−	1.06151i	0.847525	−	0.530755i	$-0.178092\pi$
$620$	50.5845	+	349.199i	0.0815880	+	0.563225i
$621$		0			0
$622$	410.605	+	410.605i	0.660136	+	0.660136i
$623$	−129.771	+	129.771i	−0.208299	+	0.208299i
$624$		0			0
$625$	524.348	−	340.123i	0.838957	−	0.544197i
$626$	241.001			0.384986
$627$		0			0
$628$	−230.812	+	230.812i	−0.367536	+	0.367536i
$629$			432.610i			0.687775i
$630$		0			0
$631$	−919.159			−1.45667			−0.728335	−	0.685221i	$-0.759706\pi$
$631$	−919.159			−1.45667			−0.728335	+	0.685221i	$0.759706\pi$
$632$	−443.163	−	443.163i	−0.701207	−	0.701207i
$633$		0			0
$634$		−	211.960i		−	0.334322i
$635$	−108.921	−	81.3578i	−0.171530	−	0.128123i
$636$		0			0
$637$	−196.318	−	196.318i	−0.308191	−	0.308191i
$638$	−30.0255	+	30.0255i	−0.0470619	+	0.0470619i
$639$		0			0
$640$	325.078	−	435.212i	0.507934	−	0.680019i
$641$	61.4913			0.0959303			0.0479651	−	0.998849i	$-0.484726\pi$
$641$	61.4913			0.0959303			0.0479651	+	0.998849i	$0.484726\pi$
$642$		0			0
$643$	−570.327	+	570.327i	−0.886978	+	0.886978i	−0.994232	−	0.107254i	$-0.965794\pi$
$643$	−570.327	+	570.327i	−0.886978	+	0.886978i	0.107254	+	0.994232i	$0.465794\pi$
$644$			500.809i			0.777653i
$645$		0			0
$646$	−1153.56			−1.78569
$647$	611.891	+	611.891i	0.945736	+	0.945736i	0.998602	−	0.0528656i	$-0.0168355\pi$
$647$	611.891	+	611.891i	0.945736	+	0.945736i	−0.0528656	+	0.998602i	$0.516835\pi$
$648$		0			0
$649$		−	190.697i		−	0.293831i
$650$	486.521	−	143.975i	0.748494	−	0.221500i
$651$		0			0
$652$	−144.939	−	144.939i	−0.222299	−	0.222299i
$653$	734.878	−	734.878i	1.12539	−	1.12539i	0.134470	−	0.990918i	$-0.457067\pi$
$653$	734.878	−	734.878i	1.12539	−	1.12539i	0.990918	−	0.134470i	$-0.0429331\pi$
$654$		0			0
$655$	−703.489	+	101.906i	−1.07403	+	0.155582i
$656$	−44.2297			−0.0674234
$657$		0			0
$658$	186.155	−	186.155i	0.282911	−	0.282911i
$659$		−	630.823i		−	0.957243i	−0.878021	−	0.478621i	$-0.841137\pi$
$659$		−	630.823i		−	0.957243i	0.878021	−	0.478621i	$-0.158863\pi$
$660$		0			0
$661$	1194.50			1.80711			0.903554	−	0.428474i	$-0.140949\pi$
$661$	1194.50			1.80711			0.903554	+	0.428474i	$0.140949\pi$
$662$	−6.21035	−	6.21035i	−0.00938119	−	0.00938119i
$663$		0			0
$664$			709.630i			1.06872i
$665$	833.255	−	1115.56i	1.25302	−	1.67753i
$666$		0			0
$667$	185.571	+	185.571i	0.278218	+	0.278218i
$668$	−72.6652	+	72.6652i	−0.108780	+	0.108780i
$669$		0			0
$670$	38.7086	+	267.217i	0.0577741	+	0.398831i
$671$	174.646			0.260277
$672$		0			0
$673$	78.8533	−	78.8533i	0.117167	−	0.117167i	−0.646092	−	0.763259i	$-0.723598\pi$
$673$	78.8533	−	78.8533i	0.117167	−	0.117167i	0.763259	+	0.646092i	$0.223598\pi$
$674$		−	343.253i		−	0.509277i
$675$		0			0
$676$	−524.242			−0.775506
$677$	107.293	+	107.293i	0.158483	+	0.158483i	0.781894	−	0.623411i	$-0.214254\pi$
$677$	107.293	+	107.293i	0.158483	+	0.158483i	−0.623411	+	0.781894i	$0.714254\pi$
$678$		0			0
$679$			310.388i			0.457125i
$680$	1118.87	−	162.077i	1.64539	−	0.238349i
$681$		0			0
$682$	−62.9607	−	62.9607i	−0.0923177	−	0.0923177i
$683$	82.9789	−	82.9789i	0.121492	−	0.121492i	−0.643747	−	0.765239i	$-0.722621\pi$
$683$	82.9789	−	82.9789i	0.121492	−	0.121492i	0.765239	+	0.643747i	$0.222621\pi$
$684$		0			0
$685$	−384.899	−	287.497i	−0.561897	−	0.419703i
$686$	294.981			0.430002
$687$		0			0
$688$	9.67075	−	9.67075i	0.0140563	−	0.0140563i
$689$			192.633i			0.279584i
$690$		0			0
$691$	−256.614			−0.371366			−0.185683	−	0.982610i	$-0.559450\pi$
$691$	−256.614			−0.371366			−0.185683	+	0.982610i	$0.559450\pi$
$692$	−55.5190	−	55.5190i	−0.0802298	−	0.0802298i
$693$		0			0
$694$		−	138.900i		−	0.200144i
$695$	−49.0123	−	338.346i	−0.0705213	−	0.486829i
$696$		0			0
$697$	−283.108	−	283.108i	−0.406181	−	0.406181i
$698$	−252.697	+	252.697i	−0.362030	+	0.362030i
$699$		0			0
$700$	−270.265	+	497.453i	−0.386092	+	0.710647i
$701$	−1015.74			−1.44898			−0.724491	−	0.689284i	$-0.757925\pi$
$701$	−1015.74			−1.44898			−0.724491	+	0.689284i	$0.757925\pi$
$702$		0			0
$703$	347.991	−	347.991i	0.495008	−	0.495008i
$704$			73.7085i			0.104700i
$705$		0			0
$706$	−422.890			−0.598994
$707$	−762.150	−	762.150i	−1.07801	−	1.07801i
$708$		0			0
$709$		−	20.1332i		−	0.0283966i	−0.999899	−	0.0141983i	$-0.995480\pi$
$709$		−	20.1332i		−	0.0283966i	0.999899	−	0.0141983i	$-0.00451961\pi$
$710$	408.424	+	305.069i	0.575246	+	0.429674i
$711$		0			0
$712$	119.863	+	119.863i	0.168347	+	0.168347i
$713$	−389.126	+	389.126i	−0.545759	+	0.545759i
$714$		0			0
$715$	186.677	−	249.923i	0.261087	−	0.349542i
$716$	840.233			1.17351
$717$		0			0
$718$	400.247	−	400.247i	0.557446	−	0.557446i
$719$		−	1372.93i		−	1.90950i	−0.297414	−	0.954748i	$-0.596124\pi$
$719$		−	1372.93i		−	1.90950i	0.297414	−	0.954748i	$-0.403876\pi$
$720$		0			0
$721$	1601.70			2.22150
$722$	652.515	+	652.515i	0.903761	+	0.903761i
$723$		0			0
$724$		−	171.769i		−	0.237249i
$725$	84.1831	+	284.473i	0.116115	+	0.392376i
$726$		0			0
$727$	86.3075	+	86.3075i	0.118717	+	0.118717i	0.763970	−	0.645252i	$-0.223248\pi$
$727$	86.3075	+	86.3075i	0.118717	+	0.118717i	−0.645252	+	0.763970i	$0.723248\pi$
$728$	−783.337	+	783.337i	−1.07601	+	1.07601i
$729$		0			0
$730$	548.109	−	79.3983i	0.750834	−	0.108765i
$731$	123.802			0.169360
$732$		0			0
$733$	−949.251	+	949.251i	−1.29502	+	1.29502i	−0.363381	+	0.931640i	$0.618378\pi$
$733$	−949.251	+	949.251i	−1.29502	+	1.29502i	−0.931640	+	0.363381i	$0.881622\pi$
$734$		−	570.116i		−	0.776725i
$735$		0			0
$736$	733.243			0.996254
$737$	117.383	+	117.383i	0.159271	+	0.159271i
$738$		0			0
$739$		−	654.872i		−	0.886160i	−0.896482	−	0.443080i	$-0.853886\pi$
$739$		−	654.872i		−	0.886160i	0.896482	−	0.443080i	$-0.146114\pi$
$740$	−119.742	+	160.310i	−0.161814	+	0.216635i
$741$		0			0
$742$	62.3814	+	62.3814i	0.0840719	+	0.0840719i
$743$	−516.440	+	516.440i	−0.695073	+	0.695073i	−0.963344	−	0.268270i	$-0.913548\pi$
$743$	−516.440	+	516.440i	−0.695073	+	0.695073i	0.268270	+	0.963344i	$0.413548\pi$
$744$		0			0
$745$	−113.912	−	786.365i	−0.152902	−	1.05552i
$746$	271.877			0.364446
$747$		0			0
$748$	203.903	−	203.903i	0.272597	−	0.272597i
$749$			916.187i			1.22321i
$750$		0			0
$751$	457.318			0.608946			0.304473	−	0.952521i	$-0.401520\pi$
$751$	457.318			0.608946			0.304473	+	0.952521i	$0.401520\pi$
$752$	73.1827	+	73.1827i	0.0973175	+	0.0973175i
$753$		0			0
$754$			240.836i			0.319410i
$755$	−180.184	+	26.1012i	−0.238654	+	0.0345711i
$756$		0			0
$757$	648.074	+	648.074i	0.856108	+	0.856108i	0.990877	−	0.134769i	$-0.0430292\pi$
$757$	648.074	+	648.074i	0.856108	+	0.856108i	−0.134769	+	0.990877i	$0.543029\pi$
$758$	−75.1267	+	75.1267i	−0.0991117	+	0.0991117i
$759$		0			0
$760$	−1030.39	−	769.639i	−1.35577	−	1.01268i
$761$	−1042.24			−1.36957			−0.684784	−	0.728746i	$-0.740103\pi$
$761$	−1042.24			−1.36957			−0.684784	+	0.728746i	$0.740103\pi$
$762$		0			0
$763$	−1211.42	+	1211.42i	−1.58771	+	1.58771i
$764$		−	801.841i		−	1.04953i
$765$		0			0
$766$	−73.8613			−0.0964247
$767$	−764.792	−	764.792i	−0.997121	−	0.997121i
$768$		0			0
$769$			1312.56i			1.70684i	0.521227	+	0.853418i	$0.325474\pi$
$769$			1312.56i			1.70684i	−0.521227	+	0.853418i	$0.674526\pi$
$770$	−20.4810	−	141.386i	−0.0265988	−	0.183619i
$771$		0			0
$772$	−636.607	−	636.607i	−0.824621	−	0.824621i
$773$	−441.630	+	441.630i	−0.571319	+	0.571319i	−0.932497	−	0.361178i	$-0.882375\pi$
$773$	−441.630	+	441.630i	−0.571319	+	0.571319i	0.361178	+	0.932497i	$0.382375\pi$
$774$		0			0
$775$	−596.513	+	176.524i	−0.769694	+	0.227773i
$776$	286.690			0.369446
$777$		0			0
$778$	−122.792	+	122.792i	−0.157831	+	0.157831i
$779$			455.463i			0.584677i
$780$		0			0
$781$	313.423			0.401310
$782$	517.247	+	517.247i	0.661441	+	0.661441i
$783$		0			0
$784$		−	49.9859i		−	0.0637575i
$785$	−461.071	−	344.392i	−0.587351	−	0.438716i
$786$		0			0
$787$	113.137	+	113.137i	0.143758	+	0.143758i	0.775323	−	0.631565i	$-0.217587\pi$
$787$	113.137	+	113.137i	0.143758	+	0.143758i	−0.631565	+	0.775323i	$0.717587\pi$
$788$	−244.025	+	244.025i	−0.309676	+	0.309676i
$789$		0			0
$790$	274.322	−	367.261i	0.347243	−	0.464887i
$791$	−843.524			−1.06640
$792$		0			0
$793$	700.419	−	700.419i	0.883252	−	0.883252i
$794$			124.297i			0.156545i
$795$		0			0
$796$	284.068			0.356869
$797$	954.456	+	954.456i	1.19756	+	1.19756i	0.974895	+	0.222667i	$0.0714761\pi$
$797$	954.456	+	954.456i	1.19756	+	1.19756i	0.222667	+	0.974895i	$0.428524\pi$
$798$		0			0
$799$			936.865i			1.17255i
$800$	728.330	+	395.699i	0.910412	+	0.494624i
$801$		0			0
$802$	−539.777	−	539.777i	−0.673039	−	0.673039i
$803$	240.773	−	240.773i	0.299842	−	0.299842i
$804$		0			0
$805$	−873.833	+	126.582i	−1.08551	+	0.157245i
$806$	−505.010			−0.626563
$807$		0			0
$808$	−703.962	+	703.962i	−0.871240	+	0.871240i
$809$		−	1343.80i		−	1.66107i	−0.556968	−	0.830534i	$-0.688036\pi$
$809$		−	1343.80i		−	1.66107i	0.556968	−	0.830534i	$-0.311964\pi$
$810$		0			0
$811$	−1283.38			−1.58246			−0.791231	−	0.611518i	$-0.790559\pi$
$811$	−1283.38			−1.58246			−0.791231	+	0.611518i	$0.790559\pi$
$812$	−190.016	−	190.016i	−0.234010	−	0.234010i
$813$		0			0
$814$		−	50.4934i		−	0.0620313i
$815$	216.262	−	289.530i	0.265352	−	0.355251i
$816$		0			0
$817$	−99.5862	−	99.5862i	−0.121893	−	0.121893i
$818$	−441.387	+	441.387i	−0.539593	+	0.539593i
$819$		0			0
$820$	−26.5484	−	183.271i	−0.0323761	−	0.223502i
$821$	−358.759			−0.436978			−0.218489	−	0.975839i	$-0.570113\pi$
$821$	−358.759			−0.436978			−0.218489	+	0.975839i	$0.570113\pi$
$822$		0			0
$823$	−1075.11	+	1075.11i	−1.30633	+	1.30633i	−0.382281	+	0.924046i	$0.624861\pi$
$823$	−1075.11	+	1075.11i	−1.30633	+	1.30633i	−0.924046	+	0.382281i	$0.875139\pi$
$824$		−	1479.42i		−	1.79541i
$825$		0			0
$826$	−495.333			−0.599677
$827$	356.469	+	356.469i	0.431039	+	0.431039i	0.888982	−	0.457943i	$-0.151414\pi$
$827$	356.469	+	356.469i	0.431039	+	0.431039i	−0.457943	+	0.888982i	$0.651414\pi$
$828$		0			0
$829$		−	22.4556i		−	0.0270876i	−0.999908	−	0.0135438i	$-0.995689\pi$
$829$		−	22.4556i		−	0.0270876i	0.999908	−	0.0135438i	$-0.00431126\pi$
$830$	−513.679	+	74.4108i	−0.618890	+	0.0896516i
$831$		0			0
$832$	295.609	+	295.609i	0.355300	+	0.355300i
$833$	319.953	−	319.953i	0.384097	−	0.384097i
$834$		0			0
$835$	−145.156	−	108.423i	−0.173840	−	0.129848i
$836$	−328.038			−0.392389
$837$		0			0
$838$	−489.421	+	489.421i	−0.584035	+	0.584035i
$839$			402.649i			0.479915i	0.970783	+	0.239958i	$0.0771335\pi$
$839$			402.649i			0.479915i	−0.970783	+	0.239958i	$0.922866\pi$
$840$		0			0
$841$	700.182			0.832559
$842$	−133.988	−	133.988i	−0.159131	−	0.159131i
$843$		0			0
$844$		−	57.3979i		−	0.0680070i
$845$	−132.505	−	914.721i	−0.156811	−	1.08251i
$846$		0			0
$847$	−62.1082	−	62.1082i	−0.0733273	−	0.0733273i
$848$	−24.5238	+	24.5238i	−0.0289196	+	0.0289196i
$849$		0			0
$850$	234.645	+	792.916i	0.276053	+	0.932843i
$851$	−312.073			−0.366713
$852$		0			0
$853$	553.945	−	553.945i	0.649409	−	0.649409i	−0.303442	−	0.952850i	$-0.598136\pi$
$853$	553.945	−	553.945i	0.649409	−	0.649409i	0.952850	+	0.303442i	$0.0981357\pi$
$854$		−	453.640i		−	0.531195i
$855$		0			0
$856$	846.239			0.988597
$857$	188.069	+	188.069i	0.219451	+	0.219451i	0.808267	−	0.588816i	$-0.200406\pi$
$857$	188.069	+	188.069i	0.219451	+	0.219451i	−0.588816	+	0.808267i	$0.700406\pi$
$858$		0			0
$859$			1327.36i			1.54524i	0.634870	+	0.772619i	$0.281054\pi$
$859$			1327.36i			1.54524i	−0.634870	+	0.772619i	$0.718946\pi$
$860$	45.8767	+	34.2672i	0.0533450	+	0.0398456i
$861$		0			0
$862$	122.280	+	122.280i	0.141856	+	0.141856i
$863$	−102.826	+	102.826i	−0.119150	+	0.119150i	−0.764168	−	0.645018i	$-0.776850\pi$
$863$	−102.826	+	102.826i	−0.119150	+	0.119150i	0.645018	+	0.764168i	$0.276850\pi$
$864$		0			0
$865$	82.8393	−	110.905i	0.0957679	−	0.128214i
$866$	−486.171			−0.561398
$867$		0			0
$868$	398.446	−	398.446i	0.459039	−	0.459039i
$869$		−	281.835i		−	0.324321i
$870$		0			0
$871$	941.533			1.08098
$872$	1118.94	+	1118.94i	1.28318	+	1.28318i
$873$		0			0
$874$		−	832.145i		−	0.952111i
$875$	−936.288	−	345.835i	−1.07004	−	0.395240i
$876$		0			0
$877$	563.350	+	563.350i	0.642360	+	0.642360i	0.951135	−	0.308775i	$-0.0999190\pi$
$877$	563.350	+	563.350i	0.642360	+	0.642360i	−0.308775	+	0.951135i	$0.599919\pi$
$878$	110.867	−	110.867i	0.126272	−	0.126272i
$879$		0			0
$880$	55.5829	−	8.05166i	0.0631624	−	0.00914962i
$881$	914.185			1.03767			0.518834	−	0.854875i	$-0.326366\pi$
$881$	914.185			1.03767			0.518834	+	0.854875i	$0.326366\pi$
$882$		0			0
$883$	−653.317	+	653.317i	−0.739884	+	0.739884i	−0.972555	−	0.232672i	$-0.925253\pi$
$883$	−653.317	+	653.317i	−0.739884	+	0.739884i	0.232672	+	0.972555i	$0.425253\pi$
$884$		−	1635.51i		−	1.85012i
$885$		0			0
$886$	−275.917			−0.311419
$887$	682.260	+	682.260i	0.769177	+	0.769177i	0.977962	−	0.208785i	$-0.0669509\pi$
$887$	682.260	+	682.260i	0.769177	+	0.769177i	−0.208785	+	0.977962i	$0.566951\pi$
$888$		0			0
$889$			217.114i			0.244222i
$890$	−74.1963	+	99.3336i	−0.0833666	+	0.111611i
$891$		0			0
$892$	592.904	+	592.904i	0.664690	+	0.664690i
$893$	753.612	−	753.612i	0.843910	−	0.843910i
$894$		0			0
$895$	212.374	+	1466.08i	0.237289	+	1.63807i
$896$	−867.511			−0.968205
$897$		0			0
$898$	−261.875	+	261.875i	−0.291621	+	0.291621i
$899$		−	295.283i		−	0.328457i
$900$		0			0
$901$	−313.947			−0.348443
$902$	33.0438	+	33.0438i	0.0366340	+	0.0366340i
$903$		0			0
$904$			779.123i			0.861862i
$905$	299.709	−	43.4155i	0.331170	−	0.0479729i
$906$		0			0
$907$	614.819	+	614.819i	0.677860	+	0.677860i	0.959516	−	0.281655i	$-0.0908835\pi$
$907$	614.819	+	614.819i	0.677860	+	0.677860i	−0.281655	+	0.959516i	$0.590883\pi$
$908$	−399.977	+	399.977i	−0.440503	+	0.440503i
$909$		0			0
$910$	−649.172	−	484.893i	−0.713376	−	0.532849i
$911$	−726.132			−0.797071			−0.398536	−	0.917153i	$-0.630482\pi$
$911$	−726.132			−0.797071			−0.398536	+	0.917153i	$0.630482\pi$
$912$		0			0
$913$	−225.649	+	225.649i	−0.247151	+	0.247151i
$914$			186.675i			0.204239i
$915$		0			0
$916$	−1288.08			−1.40620
$917$	802.700	+	802.700i	0.875354	+	0.875354i
$918$		0			0
$919$			1208.30i			1.31480i	0.753544	+	0.657398i	$0.228343\pi$
$919$			1208.30i			1.31480i	−0.753544	+	0.657398i	$0.771657\pi$
$920$	116.918	+	807.118i	0.127085	+	0.877303i
$921$		0			0
$922$	516.748	+	516.748i	0.560464	+	0.560464i
$923$	1256.99	−	1256.99i	1.36185	−	1.36185i
$924$		0			0
$925$	−309.982	−	168.412i	−0.335115	−	0.182067i
$926$	20.7783			0.0224387
$927$		0			0
$928$	−278.206	+	278.206i	−0.299791	+	0.299791i
$929$			1704.41i			1.83468i	0.398109	+	0.917338i	$0.369667\pi$
$929$			1704.41i			1.83468i	−0.398109	+	0.917338i	$0.630333\pi$
$930$		0			0
$931$	−514.738			−0.552888
$932$	686.383	+	686.383i	0.736463	+	0.736463i
$933$		0			0
$934$			156.412i			0.167465i
$935$	407.316	+	304.241i	0.435632	+	0.325391i
$936$		0			0
$937$	−526.665	−	526.665i	−0.562076	−	0.562076i	0.367821	−	0.929897i	$-0.380104\pi$
$937$	−526.665	−	526.665i	−0.562076	−	0.562076i	−0.929897	+	0.367821i	$0.880104\pi$
$938$	304.901	−	304.901i	0.325055	−	0.325055i
$939$		0			0
$940$	−259.315	+	347.169i	−0.275867	+	0.369329i
$941$	−326.805			−0.347296			−0.173648	−	0.984808i	$-0.555555\pi$
$941$	−326.805			−0.347296			−0.173648	+	0.984808i	$0.555555\pi$
$942$		0			0
$943$	204.226	−	204.226i	0.216571	−	0.216571i
$944$		−	194.729i		−	0.206281i
$945$		0			0
$946$	−14.4499			−0.0152748
$947$	−388.018	−	388.018i	−0.409734	−	0.409734i	0.471912	−	0.881646i	$-0.343564\pi$
$947$	−388.018	−	388.018i	−0.409734	−	0.409734i	−0.881646	+	0.471912i	$0.843564\pi$
$948$		0			0
$949$		−	1931.25i		−	2.03504i
$950$	449.072	−	826.568i	0.472707	−	0.870072i
$951$		0			0
$952$	−1276.66	−	1276.66i	−1.34103	−	1.34103i
$953$	427.472	−	427.472i	0.448554	−	0.448554i	−0.446320	−	0.894874i	$-0.647266\pi$
$953$	427.472	−	427.472i	0.448554	−	0.448554i	0.894874	+	0.446320i	$0.147266\pi$
$954$		0			0
$955$	1399.09	−	202.670i	1.46501	−	0.212220i
$956$	−898.781			−0.940148
$957$		0			0
$958$	−426.053	+	426.053i	−0.444732	+	0.444732i
$959$			767.222i			0.800023i
$960$		0			0
$961$	−341.819			−0.355691
$962$	−202.505	−	202.505i	−0.210504	−	0.210504i
$963$		0			0
$964$		−	225.721i		−	0.234150i
$965$	949.874	−	1271.69i	0.984325	−	1.31781i
$966$		0			0
$967$	−320.030	−	320.030i	−0.330951	−	0.330951i	0.521997	−	0.852948i	$-0.325187\pi$
$967$	−320.030	−	320.030i	−0.330951	−	0.330951i	−0.852948	+	0.521997i	$0.825187\pi$
$968$	−57.3665	+	57.3665i	−0.0592629	+	0.0592629i
$969$		0			0
$970$	30.0619	+	207.526i	0.0309917	+	0.213944i
$971$	975.264			1.00439			0.502196	−	0.864754i	$-0.332526\pi$
$971$	975.264			1.00439			0.502196	+	0.864754i	$0.332526\pi$
$972$		0			0
$973$	−386.062	+	386.062i	−0.396775	+	0.396775i
$974$		−	442.002i		−	0.453801i
$975$		0			0
$976$	178.339			0.182724
$977$	−448.672	−	448.672i	−0.459235	−	0.459235i	0.439169	−	0.898404i	$-0.355273\pi$
$977$	−448.672	−	448.672i	−0.459235	−	0.459235i	−0.898404	+	0.439169i	$0.855273\pi$
$978$		0			0
$979$			76.2283i			0.0778634i
$980$	207.123	−	30.0035i	0.211350	−	0.0306158i
$981$		0			0
$982$	85.1190	+	85.1190i	0.0866792	+	0.0866792i
$983$	220.567	−	220.567i	0.224382	−	0.224382i	−0.585959	−	0.810341i	$-0.699282\pi$
$983$	220.567	−	220.567i	0.224382	−	0.224382i	0.810341	+	0.585959i	$0.199282\pi$
$984$		0			0
$985$	−487.464	−	364.107i	−0.494888	−	0.369652i
$986$	−392.506			−0.398079
$987$		0			0
$988$	−1315.60	+	1315.60i	−1.33158	+	1.33158i
$989$			89.3074i			0.0903007i
$990$		0			0
$991$	−716.915			−0.723425			−0.361713	−	0.932290i	$-0.617808\pi$
$991$	−716.915			−0.723425			−0.361713	+	0.932290i	$0.617808\pi$
$992$	−583.372	−	583.372i	−0.588076	−	0.588076i
$993$		0			0
$994$		−	814.115i		−	0.819029i
$995$	71.7997	+	495.653i	0.0721605	+	0.498144i
$996$		0			0
$997$	−1001.73	−	1001.73i	−1.00475	−	1.00475i	−0.999989	−	0.00475731i	$-0.998486\pi$
$997$	−1001.73	−	1001.73i	−1.00475	−	1.00475i	−0.00475731	−	0.999989i	$-0.501514\pi$
$998$	243.906	−	243.906i	0.244395	−	0.244395i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.3.j.c.397.8	yes	40
3.2	odd	2	inner	495.3.j.c.397.13	yes	40
5.3	odd	4	inner	495.3.j.c.298.8	✓	40
15.8	even	4	inner	495.3.j.c.298.13	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.3.j.c.298.8	✓	40	5.3	odd	4	inner
495.3.j.c.298.13	yes	40	15.8	even	4	inner
495.3.j.c.397.8	yes	40	1.1	even	1	trivial
495.3.j.c.397.13	yes	40	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	495.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.762894 - 0.762894i) q^{2} -2.83599i q^{4} +(4.94835 - 0.716812i) q^{5} +(-5.64620 - 5.64620i) q^{7} +(-5.21513 + 5.21513i) q^{8} +(-4.32192 - 3.22822i) q^{10} -3.31662 q^{11} +(-13.3014 + 13.3014i) q^{13} +8.61491i q^{14} -3.38676 q^{16} +(-21.6782 - 21.6782i) q^{17} +34.8757i q^{19} +(-2.03287 - 14.0335i) q^{20} +(2.53023 + 2.53023i) q^{22} +(15.6380 - 15.6380i) q^{23} +(23.9724 - 7.09407i) q^{25} +20.2951 q^{26} +(-16.0126 + 16.0126i) q^{28} +11.8667i q^{29} -24.8833 q^{31} +(23.4443 + 23.4443i) q^{32} +33.0763i q^{34} +(-31.9867 - 23.8921i) q^{35} +(-9.97802 - 9.97802i) q^{37} +(26.6065 - 26.6065i) q^{38} +(-22.0680 + 29.5446i) q^{40} +13.0596 q^{41} +(-2.85546 + 2.85546i) q^{43} +9.40590i q^{44} -23.8603 q^{46} +(-21.6085 - 21.6085i) q^{47} +14.7592i q^{49} +(-23.7004 - 12.8763i) q^{50} +(37.7225 + 37.7225i) q^{52} +(7.24110 - 7.24110i) q^{53} +(-16.4118 + 2.37739i) q^{55} +58.8914 q^{56} +(9.05302 - 9.05302i) q^{58} +57.4972i q^{59} -52.6576 q^{61} +(18.9834 + 18.9834i) q^{62} -22.2239i q^{64} +(-56.2853 + 75.3545i) q^{65} +(-35.3923 - 35.3923i) q^{67} +(-61.4789 + 61.4789i) q^{68} +(6.17527 + 42.6296i) q^{70} -94.5007 q^{71} +(-72.5959 + 72.5959i) q^{73} +15.2243i q^{74} +98.9071 q^{76} +(18.7263 + 18.7263i) q^{77} +84.9764i q^{79} +(-16.7589 + 2.42767i) q^{80} +(-9.96309 - 9.96309i) q^{82} +(68.0357 - 68.0357i) q^{83} +(-122.810 - 91.7320i) q^{85} +4.35682 q^{86} +(17.2966 - 17.2966i) q^{88} -22.9837i q^{89} +150.205 q^{91} +(-44.3492 - 44.3492i) q^{92} +32.9700i q^{94} +(24.9993 + 172.577i) q^{95} +(-27.4864 - 27.4864i) q^{97} +(11.2597 - 11.2597i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{10} - 88 q^{13} - 296 q^{16} + 168 q^{25} + 248 q^{28} - 32 q^{31} - 24 q^{37} + 296 q^{40} - 48 q^{43} + 48 q^{46} + 64 q^{52} + 104 q^{58} + 576 q^{61} - 544 q^{67} - 1048 q^{70} - 408 q^{73}+ \cdots + 712 q^{97}+O(q^{100}) \) 40 * q + 24 * q^10 - 88 * q^13 - 296 * q^16 + 168 * q^25 + 248 * q^28 - 32 * q^31 - 24 * q^37 + 296 * q^40 - 48 * q^43 + 48 * q^46 + 64 * q^52 + 104 * q^58 + 576 * q^61 - 544 * q^67 - 1048 * q^70 - 408 * q^73 - 96 * q^76 - 280 * q^82 + 160 * q^85 + 264 * q^88 + 528 * q^91 + 712 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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