LMFDB - Embedded newform 405.3.h.k.269.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(134,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.134"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,-48,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.22
Character	$\chi$	$=$	405.269
Dual form			405.3.h.k.134.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.74200 - 3.01723i) q^{2} +(-4.06913 - 7.04793i) q^{4} +(3.55914 + 3.51177i) q^{5} +(-11.0647 - 6.38818i) q^{7} -14.4177 q^{8} +(16.7958 - 4.62123i) q^{10} +(-12.2871 - 7.09395i) q^{11} +(3.89787 - 2.25044i) q^{13} +(-38.5493 + 22.2564i) q^{14} +(-8.83907 + 15.3097i) q^{16} +9.20574 q^{17} -15.8342 q^{19} +(10.2682 - 39.3744i) q^{20} +(-42.8082 + 24.7153i) q^{22} +(-2.12146 - 3.67447i) q^{23} +(0.334886 + 24.9978i) q^{25} -15.6810i q^{26} +103.977i q^{28} +(-22.9719 - 13.2628i) q^{29} +(-15.7179 - 27.2242i) q^{31} +(1.95998 + 3.39479i) q^{32} +(16.0364 - 27.7759i) q^{34} +(-16.9468 - 61.5930i) q^{35} +14.6355i q^{37} +(-27.5831 + 47.7753i) q^{38} +(-51.3144 - 50.6316i) q^{40} +(38.6673 - 22.3246i) q^{41} +(56.6228 + 32.6912i) q^{43} +115.465i q^{44} -14.7823 q^{46} +(28.2856 - 48.9921i) q^{47} +(57.1178 + 98.9309i) q^{49} +(76.0074 + 42.5357i) q^{50} +(-31.7218 - 18.3146i) q^{52} +17.8840 q^{53} +(-18.8190 - 68.3978i) q^{55} +(159.527 + 92.1027i) q^{56} +(-80.0340 + 46.2076i) q^{58} +(-41.8306 + 24.1509i) q^{59} +(45.7349 - 79.2151i) q^{61} -109.522 q^{62} -57.0554 q^{64} +(21.7761 + 5.67883i) q^{65} +(43.8758 - 25.3317i) q^{67} +(-37.4593 - 64.8815i) q^{68} +(-215.362 - 56.1627i) q^{70} -67.7587i q^{71} +52.6768i q^{73} +(44.1586 + 25.4950i) q^{74} +(64.4312 + 111.598i) q^{76} +(90.6349 + 156.984i) q^{77} +(27.4481 - 47.5415i) q^{79} +(-85.2237 + 23.4485i) q^{80} -155.558i q^{82} +(1.27876 - 2.21487i) q^{83} +(32.7645 + 32.3285i) q^{85} +(197.274 - 113.896i) q^{86} +(177.151 + 102.278i) q^{88} -82.7313i q^{89} -57.5048 q^{91} +(-17.2650 + 29.9038i) q^{92} +(-98.5469 - 170.688i) q^{94} +(-56.3559 - 55.6060i) q^{95} +(55.3388 + 31.9499i) q^{97} +397.997 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} + 24 q^{10} - 96 q^{16} - 48 q^{25} - 144 q^{34} - 72 q^{40} - 336 q^{46} + 288 q^{49} - 264 q^{55} + 360 q^{61} - 144 q^{64} + 156 q^{70} - 48 q^{76} + 480 q^{79} + 456 q^{85} - 96 q^{91}+ \cdots - 384 q^{94}+O(q^{100}) $ 48 * q - 48 * q^4 + 24 * q^10 - 96 * q^16 - 48 * q^25 - 144 * q^34 - 72 * q^40 - 336 * q^46 + 288 * q^49 - 264 * q^55 + 360 * q^61 - 144 * q^64 + 156 * q^70 - 48 * q^76 + 480 * q^79 + 456 * q^85 - 96 * q^91 - 384 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.74200	−	3.01723i	0.871000	−	1.50862i	0.0100362	−	0.999950i	$-0.496805\pi$
$2$	1.74200	−	3.01723i	0.871000	−	1.50862i	0.860964	−	0.508666i	$-0.169861\pi$
$3$		0			0
$3$		0			0
$4$	−4.06913	−	7.04793i	−1.01728	−	1.76198i
$5$	3.55914	+	3.51177i	0.711827	+	0.702355i
$5$	3.55914	+	3.51177i	0.711827	+	0.702355i
$6$		0			0
$7$	−11.0647	−	6.38818i	−1.58067	−	0.912598i	−0.994762	−	0.102217i	$-0.967406\pi$
$7$	−11.0647	−	6.38818i	−1.58067	−	0.912598i	−0.585903	−	0.810381i	$-0.699260\pi$
$8$	−14.4177			−1.80221
$9$		0			0
$10$	16.7958	−	4.62123i	1.67958	−	0.462123i
$11$	−12.2871	−	7.09395i	−1.11701	−	0.644905i	−0.176372	−	0.984324i	$-0.556436\pi$
$11$	−12.2871	−	7.09395i	−1.11701	−	0.644905i	−0.940635	+	0.339419i	$0.889770\pi$
$12$		0			0
$13$	3.89787	−	2.25044i	0.299836	−	0.173110i	−0.342533	−	0.939506i	$-0.611285\pi$
$13$	3.89787	−	2.25044i	0.299836	−	0.173110i	0.642369	+	0.766395i	$0.277952\pi$
$14$	−38.5493	+	22.2564i	−2.75352	+	1.58974i
$15$		0			0
$16$	−8.83907	+	15.3097i	−0.552442	+	0.956857i
$17$	9.20574			0.541514			0.270757	−	0.962648i	$-0.412726\pi$
$17$	9.20574			0.541514			0.270757	+	0.962648i	$0.412726\pi$
$18$		0			0
$19$	−15.8342			−0.833376			−0.416688	−	0.909049i	$-0.636809\pi$
$19$	−15.8342			−0.833376			−0.416688	+	0.909049i	$0.636809\pi$
$20$	10.2682	−	39.3744i	0.513409	−	1.96872i
$21$		0			0
$22$	−42.8082	+	24.7153i	−1.94583	+	1.12342i
$23$	−2.12146	−	3.67447i	−0.0922373	−	0.159760i	0.816215	−	0.577748i	$-0.196068\pi$
$23$	−2.12146	−	3.67447i	−0.0922373	−	0.159760i	−0.908452	+	0.417989i	$0.862735\pi$
$24$		0			0
$25$	0.334886	+	24.9978i	0.0133954	+	0.999910i
$26$		−	15.6810i		−	0.603117i
$27$		0			0
$28$			103.977i			3.71348i
$29$	−22.9719	−	13.2628i	−0.792133	−	0.457338i	0.0485796	−	0.998819i	$-0.484531\pi$
$29$	−22.9719	−	13.2628i	−0.792133	−	0.457338i	−0.840713	+	0.541481i	$0.817864\pi$
$30$		0			0
$31$	−15.7179	−	27.2242i	−0.507028	−	0.878199i	−0.999967	−	0.00813474i	$-0.997411\pi$
$31$	−15.7179	−	27.2242i	−0.507028	−	0.878199i	0.492939	−	0.870064i	$-0.335923\pi$
$32$	1.95998	+	3.39479i	0.0612494	+	0.106087i
$33$		0			0
$34$	16.0364	−	27.7759i	0.471659	−	0.816937i
$35$	−16.9468	−	61.5930i	−0.484193	−	1.75980i
$36$		0			0
$37$			14.6355i			0.395553i	0.980247	+	0.197777i	$0.0633720\pi$
$37$			14.6355i			0.395553i	−0.980247	+	0.197777i	$0.936628\pi$
$38$	−27.5831	+	47.7753i	−0.725871	+	1.25725i
$39$		0			0
$40$	−51.3144	−	50.6316i	−1.28286	−	1.26579i
$41$	38.6673	−	22.3246i	0.943104	−	0.544502i	0.0521722	−	0.998638i	$-0.483386\pi$
$41$	38.6673	−	22.3246i	0.943104	−	0.544502i	0.890932	+	0.454137i	$0.150052\pi$
$42$		0			0
$43$	56.6228	+	32.6912i	1.31681	+	0.760261i	0.983214	−	0.182455i	$-0.0584045\pi$
$43$	56.6228	+	32.6912i	1.31681	+	0.760261i	0.333596	+	0.942716i	$0.391738\pi$
$44$			115.465i			2.62420i
$45$		0			0
$46$	−14.7823			−0.321355
$47$	28.2856	−	48.9921i	0.601821	−	1.04238i	−0.390725	−	0.920508i	$-0.627776\pi$
$47$	28.2856	−	48.9921i	0.601821	−	1.04238i	0.992545	−	0.121876i	$-0.0388912\pi$
$48$		0			0
$49$	57.1178	+	98.9309i	1.16567	+	2.01900i
$50$	76.0074	+	42.5357i	1.52015	+	0.850713i
$51$		0			0
$52$	−31.7218	−	18.3146i	−0.610035	−	0.352204i
$53$	17.8840			0.337434			0.168717	−	0.985665i	$-0.446038\pi$
$53$	17.8840			0.337434			0.168717	+	0.985665i	$0.446038\pi$
$54$		0			0
$55$	−18.8190	−	68.3978i	−0.342164	−	1.24360i
$56$	159.527	+	92.1027i	2.84869	+	1.64469i
$57$		0			0
$58$	−80.0340	+	46.2076i	−1.37990	+	0.796683i
$59$	−41.8306	+	24.1509i	−0.708992	+	0.409337i	−0.810688	−	0.585479i	$-0.800907\pi$
$59$	−41.8306	+	24.1509i	−0.708992	+	0.409337i	0.101695	+	0.994816i	$0.467573\pi$
$60$		0			0
$61$	45.7349	−	79.2151i	0.749752	−	1.29861i	−0.198190	−	0.980164i	$-0.563506\pi$
$61$	45.7349	−	79.2151i	0.749752	−	1.29861i	0.947942	−	0.318444i	$-0.103160\pi$
$62$	−109.522			−1.76649
$63$		0			0
$64$	−57.0554			−0.891491
$65$	21.7761	+	5.67883i	0.335016	+	0.0873666i
$66$		0			0
$67$	43.8758	−	25.3317i	0.654862	−	0.378085i	−0.135454	−	0.990784i	$-0.543249\pi$
$67$	43.8758	−	25.3317i	0.654862	−	0.378085i	0.790317	+	0.612699i	$0.209916\pi$
$68$	−37.4593	−	64.8815i	−0.550873	−	0.954139i
$69$		0			0
$70$	−215.362	−	56.1627i	−3.07659	−	0.802324i
$71$		−	67.7587i		−	0.954348i	−0.878809	−	0.477174i	$-0.841661\pi$
$71$		−	67.7587i		−	0.954348i	0.878809	−	0.477174i	$-0.158339\pi$
$72$		0			0
$73$			52.6768i			0.721600i	0.932643	+	0.360800i	$0.117496\pi$
$73$			52.6768i			0.721600i	−0.932643	+	0.360800i	$0.882504\pi$
$74$	44.1586	+	25.4950i	0.596738	+	0.344527i
$75$		0			0
$76$	64.4312	+	111.598i	0.847778	+	1.46840i
$77$	90.6349	+	156.984i	1.17708	+	2.03876i
$78$		0			0
$79$	27.4481	−	47.5415i	0.347444	−	0.601791i	−0.638351	−	0.769746i	$-0.720383\pi$
$79$	27.4481	−	47.5415i	0.347444	−	0.601791i	0.985795	+	0.167955i	$0.0537163\pi$
$80$	−85.2237	+	23.4485i	−1.06530	+	0.293107i
$81$		0			0
$82$		−	155.558i		−	1.89704i
$83$	1.27876	−	2.21487i	0.0154067	−	0.0266852i	−0.858219	−	0.513283i	$-0.828429\pi$
$83$	1.27876	−	2.21487i	0.0154067	−	0.0266852i	0.873626	+	0.486598i	$0.161762\pi$
$84$		0			0
$85$	32.7645	+	32.3285i	0.385465	+	0.380335i
$86$	197.274	−	113.896i	2.29388	−	1.32437i
$87$		0			0
$88$	177.151	+	102.278i	2.01308	+	1.16225i
$89$		−	82.7313i		−	0.929565i	−0.885425	−	0.464783i	$-0.846132\pi$
$89$		−	82.7313i		−	0.929565i	0.885425	−	0.464783i	$-0.153868\pi$
$90$		0			0
$91$	−57.5048			−0.631921
$92$	−17.2650	+	29.9038i	−0.187663	+	0.325041i
$93$		0			0
$94$	−98.5469	−	170.688i	−1.04837	−	1.81583i
$95$	−56.3559	−	55.6060i	−0.593220	−	0.585326i
$96$		0			0
$97$	55.3388	+	31.9499i	0.570503	+	0.329380i	0.757350	−	0.653009i	$-0.226494\pi$
$97$	55.3388	+	31.9499i	0.570503	+	0.329380i	−0.186847	+	0.982389i	$0.559827\pi$
$98$	397.997			4.06119
$99$		0			0
$100$	174.820	−	104.079i	1.74820	−	1.04079i
$101$	−69.8180	−	40.3094i	−0.691267	−	0.399103i	0.112819	−	0.993616i	$-0.464012\pi$
$101$	−69.8180	−	40.3094i	−0.691267	−	0.399103i	−0.804087	+	0.594512i	$0.797345\pi$
$102$		0			0
$103$	31.1536	−	17.9866i	0.302462	−	0.174627i	−0.341086	−	0.940032i	$-0.610795\pi$
$103$	31.1536	−	17.9866i	0.302462	−	0.174627i	0.643549	+	0.765405i	$0.277461\pi$
$104$	−56.1982	+	32.4460i	−0.540367	+	0.311981i
$105$		0			0
$106$	31.1539	−	53.9602i	0.293905	−	0.509059i
$107$	−21.6725			−0.202546			−0.101273	−	0.994859i	$-0.532292\pi$
$107$	−21.6725			−0.202546			−0.101273	+	0.994859i	$0.532292\pi$
$108$		0			0
$109$	−1.09218			−0.0100200			−0.00501000	−	0.999987i	$-0.501595\pi$
$109$	−1.09218			−0.0100200			−0.00501000	+	0.999987i	$0.501595\pi$
$110$	−239.155	−	62.3675i	−2.17413	−	0.566978i
$111$		0			0
$112$	195.603	−	112.931i	1.74645	−	1.00831i
$113$	−76.1074	−	131.822i	−0.673517	−	1.16657i	−0.976900	−	0.213697i	$-0.931449\pi$
$113$	−76.1074	−	131.822i	−0.673517	−	1.16657i	0.303383	−	0.952869i	$-0.401884\pi$
$114$		0			0
$115$	5.35336	−	20.5280i	0.0465510	−	0.178505i
$116$			215.872i			1.86097i
$117$		0			0
$118$			168.283i			1.42613i
$119$	−101.858	−	58.8080i	−0.855953	−	0.494185i
$120$		0			0
$121$	40.1483	+	69.5389i	0.331804	+	0.574702i
$122$	−159.340	−	275.985i	−1.30607	−	2.26217i
$123$		0			0
$124$	−127.916	+	221.557i	−1.03158	+	1.78675i
$125$	−86.5946	+	90.1464i	−0.692757	+	0.721172i
$126$		0			0
$127$			114.497i			0.901549i	0.892638	+	0.450775i	$0.148852\pi$
$127$			114.497i			0.901549i	−0.892638	+	0.450775i	$0.851148\pi$
$128$	−107.230	+	185.729i	−0.837738	+	1.45100i
$129$		0			0
$130$	55.0682	−	55.8109i	0.423602	−	0.429315i
$131$	−148.182	+	85.5530i	−1.13116	+	0.653077i	−0.944227	−	0.329296i	$-0.893189\pi$
$131$	−148.182	+	85.5530i	−1.13116	+	0.653077i	−0.186935	+	0.982372i	$0.559855\pi$
$132$		0			0
$133$	175.200	+	101.151i	1.31729	+	0.760537i
$134$		−	176.511i		−	1.31725i
$135$		0			0
$136$	−132.725			−0.975922
$137$	18.2103	−	31.5412i	0.132922	−	0.230228i	−0.791880	−	0.610677i	$-0.790897\pi$
$137$	18.2103	−	31.5412i	0.132922	−	0.230228i	0.924802	+	0.380449i	$0.124231\pi$
$138$		0			0
$139$	−37.8921	−	65.6311i	−0.272605	−	0.472166i	0.696923	−	0.717146i	$-0.254552\pi$
$139$	−37.8921	−	65.6311i	−0.272605	−	0.472166i	−0.969528	+	0.244980i	$0.921219\pi$
$140$	−365.145	+	370.069i	−2.60818	+	2.64335i
$141$		0			0
$142$	−204.444	−	118.036i	−1.43974	−	0.831237i
$143$	−63.8579			−0.446559
$144$		0			0
$145$	−35.1840	−	127.876i	−0.242648	−	0.881905i
$146$	158.938	+	91.7629i	1.08862	+	0.628513i
$147$		0			0
$148$	103.150	−	59.5535i	0.696958	−	0.402389i
$149$	165.772	−	95.7083i	1.11256	−	0.642338i	0.173070	−	0.984910i	$-0.444631\pi$
$149$	165.772	−	95.7083i	1.11256	−	0.642338i	0.939492	+	0.342572i	$0.111298\pi$
$150$		0			0
$151$	−119.619	+	207.186i	−0.792178	+	1.37209i	0.132438	+	0.991191i	$0.457719\pi$
$151$	−119.619	+	207.186i	−0.792178	+	1.37209i	−0.924616	+	0.380901i	$0.875614\pi$
$152$	228.292			1.50192
$153$		0			0
$154$	631.544			4.10094
$155$	39.6631	−	152.092i	0.255891	−	0.981239i
$156$		0			0
$157$	−124.141	+	71.6729i	−0.790707	+	0.456515i	−0.840212	−	0.542259i	$-0.817569\pi$
$157$	−124.141	+	71.6729i	−0.790707	+	0.456515i	0.0495042	+	0.998774i	$0.484236\pi$
$158$	−95.6291	−	165.634i	−0.605248	−	1.04832i
$159$		0			0
$160$	−4.94588	+	18.9655i	−0.0309118	+	0.118534i
$161$			54.2090i			0.336702i
$162$		0			0
$163$		−	138.957i		−	0.852496i	−0.904606	−	0.426248i	$-0.859835\pi$
$163$		−	138.957i		−	0.852496i	0.904606	−	0.426248i	$-0.140165\pi$
$164$	−314.684	−	181.683i	−1.91881	−	1.10782i
$165$		0			0
$166$	−4.45519	−	7.71661i	−0.0268385	−	0.0464856i
$167$	102.790	+	178.038i	0.615510	+	1.06610i	0.990295	+	0.138983i	$0.0443834\pi$
$167$	102.790	+	178.038i	0.615510	+	1.06610i	−0.374784	+	0.927112i	$0.622283\pi$
$168$		0			0
$169$	−74.3711	+	128.814i	−0.440066	+	0.762216i
$170$	154.618	−	42.5418i	0.909519	−	0.250246i
$171$		0			0
$172$		−	532.099i		−	3.09360i
$173$	23.7687	−	41.1687i	0.137392	−	0.237969i	−0.789117	−	0.614243i	$-0.789461\pi$
$173$	23.7687	−	41.1687i	0.137392	−	0.237969i	0.926508	+	0.376274i	$0.122795\pi$
$174$		0			0
$175$	155.985	−	278.731i	0.891342	−	1.59275i
$176$	217.213	−	125.408i	1.23416	−	0.712545i
$177$		0			0
$178$	−249.620	−	144.118i	−1.40236	−	0.809651i
$179$		−	124.298i		−	0.694402i	−0.937791	−	0.347201i	$-0.887132\pi$
$179$		−	124.298i		−	0.694402i	0.937791	−	0.347201i	$-0.112868\pi$
$180$		0			0
$181$	−12.0770			−0.0667237			−0.0333618	−	0.999443i	$-0.510621\pi$
$181$	−12.0770			−0.0667237			−0.0333618	+	0.999443i	$0.510621\pi$
$182$	−100.173	+	173.505i	−0.550403	+	0.953326i
$183$		0			0
$184$	30.5865	+	52.9773i	0.166231	+	0.287920i
$185$	−51.3964	+	52.0896i	−0.277819	+	0.281565i
$186$		0			0
$187$	−113.112	−	65.3051i	−0.604876	−	0.349225i
$188$	−460.390			−2.44888
$189$		0			0
$190$	−265.948	+	73.1732i	−1.39973	+	0.385122i
$191$	247.436	+	142.857i	1.29548	+	0.747945i	0.979620	−	0.200862i	$-0.0643742\pi$
$191$	247.436	+	142.857i	1.29548	+	0.747945i	0.315859	+	0.948806i	$0.397708\pi$
$192$		0			0
$193$	284.807	−	164.433i	1.47568	−	0.851987i	0.476061	−	0.879412i	$-0.342064\pi$
$193$	284.807	−	164.433i	1.47568	−	0.851987i	0.999624	+	0.0274255i	$0.00873089\pi$
$194$	192.800	−	111.313i	0.993816	−	0.573780i
$195$		0			0
$196$	464.839	−	805.125i	2.37163	−	4.10778i
$197$	−90.3147			−0.458450			−0.229225	−	0.973373i	$-0.573619\pi$
$197$	−90.3147			−0.458450			−0.229225	+	0.973373i	$0.573619\pi$
$198$		0			0
$199$	0.315816			0.00158702			0.000793508	−	1.00000i	$-0.499747\pi$
$199$	0.315816			0.00158702			0.000793508		1.00000i	$0.499747\pi$
$200$	−4.82827	−	360.409i	−0.0241414	−	1.80205i
$201$		0			0
$202$	−243.246	+	140.438i	−1.20419	+	0.695238i
$203$	169.451	+	293.497i	0.834732	+	1.44580i
$204$		0			0
$205$	216.021	+	56.3346i	1.05376	+	0.274803i
$206$		−	125.330i		−	0.608399i
$207$		0			0
$208$			79.5670i			0.382534i
$209$	194.556	+	112.327i	0.930888	+	0.537448i
$210$		0			0
$211$	164.187	+	284.380i	0.778137	+	1.34777i	0.933014	+	0.359839i	$0.117168\pi$
$211$	164.187	+	284.380i	0.778137	+	1.34777i	−0.154878	+	0.987934i	$0.549498\pi$
$212$	−72.7723	−	126.045i	−0.343266	−	0.594553i
$213$		0			0
$214$	−37.7534	+	65.3909i	−0.176418	+	0.305565i
$215$	86.7242	+	315.199i	0.403368	+	1.46604i
$216$		0			0
$217$			401.635i			1.85085i
$218$	−1.90258	+	3.29536i	−0.00872741	+	0.0151163i
$219$		0			0
$220$	−405.486	+	410.955i	−1.84312	+	1.86798i
$221$	35.8828	−	20.7169i	0.162366	−	0.0937418i
$222$		0			0
$223$	−43.7853	−	25.2795i	−0.196347	−	0.113361i	0.398604	−	0.917123i	$-0.369495\pi$
$223$	−43.7853	−	25.2795i	−0.196347	−	0.113361i	−0.594950	+	0.803763i	$0.702828\pi$
$224$		−	50.0829i		−	0.223584i
$225$		0			0
$226$	−530.316			−2.34653
$227$	150.507	−	260.685i	0.663024	−	1.14839i	−0.316793	−	0.948495i	$-0.602606\pi$
$227$	150.507	−	260.685i	0.663024	−	1.14839i	0.979817	−	0.199897i	$-0.0640607\pi$
$228$		0			0
$229$	−139.713	−	241.989i	−0.610099	−	1.05672i	−0.991223	−	0.132198i	$-0.957796\pi$
$229$	−139.713	−	241.989i	−0.610099	−	1.05672i	0.381124	−	0.924524i	$-0.375537\pi$
$230$	−52.6123	−	51.9121i	−0.228749	−	0.225705i
$231$		0			0
$232$	331.201	+	191.219i	1.42759	+	0.824219i
$233$	27.3269			0.117283			0.0586415	−	0.998279i	$-0.481323\pi$
$233$	27.3269			0.117283			0.0586415	+	0.998279i	$0.481323\pi$
$234$		0			0
$235$	272.721	−	75.0368i	1.16052	−	0.319305i
$236$	340.428	+	196.546i	1.44249	+	0.832822i
$237$		0			0
$238$	−354.875	+	204.887i	−1.49107	+	0.860870i
$239$	15.3488	−	8.86165i	0.0642210	−	0.0370780i	−0.467546	−	0.883969i	$-0.654862\pi$
$239$	15.3488	−	8.86165i	0.0642210	−	0.0370780i	0.531767	+	0.846891i	$0.321528\pi$
$240$		0			0
$241$	−101.946	+	176.576i	−0.423014	+	0.732682i	−0.996233	−	0.0867204i	$-0.972361\pi$
$241$	−101.946	+	176.576i	−0.423014	+	0.732682i	0.573218	+	0.819403i	$0.305695\pi$
$242$	279.753			1.15601
$243$		0			0
$244$	−744.404			−3.05083
$245$	−144.133	+	552.693i	−0.588298	+	2.25589i
$246$		0			0
$247$	−61.7194	+	35.6337i	−0.249876	+	0.144266i
$248$	226.615	+	392.509i	0.913771	+	1.58270i
$249$		0			0
$250$	121.145	+	418.311i	0.484580	+	1.67324i
$251$			117.194i			0.466908i	0.972368	+	0.233454i	$0.0750029\pi$
$251$			117.194i			0.466908i	−0.972368	+	0.233454i	$0.924997\pi$
$252$		0			0
$253$			60.1981i			0.237937i
$254$	345.463	+	199.453i	1.36009	+	0.785249i
$255$		0			0
$256$	259.480	+	449.433i	1.01359	+	1.75560i
$257$	−76.6823	−	132.818i	−0.298375	−	0.516800i	0.677390	−	0.735624i	$-0.263111\pi$
$257$	−76.6823	−	132.818i	−0.298375	−	0.516800i	−0.975764	+	0.218824i	$0.929778\pi$
$258$		0			0
$259$	93.4940	−	161.936i	0.360981	−	0.625237i
$260$	−48.5855	−	176.584i	−0.186867	−	0.679170i
$261$		0			0
$262$			596.133i			2.27532i
$263$	−131.747	+	228.193i	−0.500941	+	0.867655i	0.499059	+	0.866568i	$0.333679\pi$
$263$	−131.747	+	228.193i	−0.500941	+	0.867655i	−0.999999	+	0.00108680i	$0.999654\pi$
$264$		0			0
$265$	63.6516	+	62.8046i	0.240195	+	0.236999i
$266$	610.395	−	352.412i	2.29472	−	1.32486i
$267$		0			0
$268$	−357.072	−	206.156i	−1.33236	−	0.769238i
$269$		−	10.4219i		−	0.0387431i	−0.999812	−	0.0193715i	$-0.993833\pi$
$269$		−	10.4219i		−	0.0387431i	0.999812	−	0.0193715i	$-0.00616654\pi$
$270$		0			0
$271$	501.590			1.85089			0.925443	−	0.378886i	$-0.123693\pi$
$271$	501.590			1.85089			0.925443	+	0.378886i	$0.123693\pi$
$272$	−81.3702	+	140.937i	−0.299155	+	0.518152i
$273$		0			0
$274$	−63.4448	−	109.890i	−0.231550	−	0.401057i
$275$	173.218	−	309.525i	0.629884	−	1.12555i
$276$		0			0
$277$	304.210	+	175.636i	1.09823	+	0.634065i	0.935756	−	0.352648i	$-0.114719\pi$
$277$	304.210	+	175.636i	1.09823	+	0.634065i	0.162476	+	0.986713i	$0.448052\pi$
$278$	−264.032			−0.949756
$279$		0			0
$280$	244.333	+	888.027i	0.872617	+	3.17153i
$281$	252.986	+	146.061i	0.900304	+	0.519791i	0.877299	−	0.479944i	$-0.159343\pi$
$281$	252.986	+	146.061i	0.900304	+	0.519791i	0.0230054	+	0.999735i	$0.492677\pi$
$282$		0			0
$283$	−162.862	+	94.0285i	−0.575485	+	0.332256i	−0.759337	−	0.650698i	$-0.774477\pi$
$283$	−162.862	+	94.0285i	−0.575485	+	0.332256i	0.183852	+	0.982954i	$0.441143\pi$
$284$	−477.559	+	275.719i	−1.68155	+	0.970840i
$285$		0			0
$286$	−111.241	+	192.674i	−0.388953	+	0.673686i
$287$	−570.454			−1.98764
$288$		0			0
$289$	−204.254			−0.706762
$290$	−447.123	−	116.602i	−1.54180	−	0.402076i
$291$		0			0
$292$	371.262	−	214.348i	1.27145	−	0.734070i
$293$	−154.985	−	268.442i	−0.528958	−	0.916183i	−0.999430	−	0.0337676i	$-0.989249\pi$
$293$	−154.985	−	268.442i	−0.528958	−	0.916183i	0.470471	−	0.882415i	$-0.344084\pi$
$294$		0			0
$295$	−233.693	−	60.9432i	−0.792180	−	0.206587i
$296$		−	211.009i		−	0.712869i
$297$		0			0
$298$		−	666.895i		−	2.23790i
$299$	−16.5383	−	9.54841i	−0.0553121	−	0.0319345i
$300$		0			0
$301$	−417.675	−	723.434i	−1.38762	−	2.40344i
$302$	416.752	+	721.836i	1.37997	+	2.39018i
$303$		0			0
$304$	139.959	−	242.416i	0.460392	−	0.797422i
$305$	440.962	−	121.327i	1.44578	−	0.397793i
$306$		0			0
$307$			143.887i			0.468687i	0.972154	+	0.234344i	$0.0752941\pi$
$307$			143.887i			0.468687i	−0.972154	+	0.234344i	$0.924706\pi$
$308$	737.610	−	1277.58i	2.39484	−	4.14798i
$309$		0			0
$310$	−389.804	−	384.617i	−1.25743	−	1.24070i
$311$	24.1305	−	13.9318i	0.0775901	−	0.0447966i	−0.460703	−	0.887554i	$-0.652403\pi$
$311$	24.1305	−	13.9318i	0.0775901	−	0.0447966i	0.538293	+	0.842758i	$0.319069\pi$
$312$		0			0
$313$	−361.967	−	208.982i	−1.15644	−	0.667673i	−0.205995	−	0.978553i	$-0.566043\pi$
$313$	−361.967	−	208.982i	−1.15644	−	0.667673i	−0.950449	+	0.310880i	$0.899376\pi$
$314$			499.416i			1.59050i
$315$		0			0
$316$	−446.759			−1.41379
$317$	33.5344	−	58.0833i	0.105787	−	0.183228i	−0.808273	−	0.588808i	$-0.799597\pi$
$317$	33.5344	−	58.0833i	0.105787	−	0.183228i	0.914059	+	0.405580i	$0.132931\pi$
$318$		0			0
$319$	188.172	+	325.923i	0.589880	+	1.02170i
$320$	−203.068	−	200.366i	−0.634587	−	0.626143i
$321$		0			0
$322$	163.561	+	94.4321i	0.507954	+	0.293268i
$323$	−145.765			−0.451285
$324$		0			0
$325$	57.5612	+	96.6843i	0.177111	+	0.297490i
$326$	−419.265	−	242.063i	−1.28609	−	0.742524i
$327$		0			0
$328$	−557.492	+	321.868i	−1.69967	+	0.981305i
$329$	−625.940	+	361.387i	−1.90255	+	1.09844i
$330$		0			0
$331$	53.2428	−	92.2192i	0.160854	−	0.278608i	−0.774321	−	0.632793i	$-0.781908\pi$
$331$	53.2428	−	92.2192i	0.160854	−	0.278608i	0.935175	+	0.354185i	$0.115242\pi$
$332$	−20.8137			−0.0626918
$333$		0			0
$334$	716.242			2.14444
$335$	245.119	+	63.9229i	0.731698	+	0.190815i
$336$		0			0
$337$	−461.486	+	266.439i	−1.36940	+	0.790621i	−0.990851	−	0.134962i	$-0.956909\pi$
$337$	−461.486	+	266.439i	−1.36940	+	0.790621i	−0.378545	+	0.925583i	$0.623576\pi$
$338$	259.109	+	448.790i	0.766594	+	1.32778i
$339$		0			0
$340$	94.5262	−	362.471i	0.278018	−	1.06609i
$341$			446.008i			1.30794i
$342$		0			0
$343$		−	833.474i		−	2.42995i
$344$	−816.369	−	471.331i	−2.37317	−	1.37015i
$345$		0			0
$346$	−82.8103	−	143.432i	−0.239336	−	0.414542i
$347$	−1.35563	−	2.34802i	−0.00390672	−	0.00676664i	0.864065	−	0.503380i	$-0.167910\pi$
$347$	−1.35563	−	2.34802i	−0.00390672	−	0.00676664i	−0.867972	+	0.496613i	$0.834577\pi$
$348$		0			0
$349$	99.4267	−	172.212i	0.284890	−	0.493444i	−0.687692	−	0.726002i	$-0.741376\pi$
$349$	99.4267	−	172.212i	0.284890	−	0.493444i	0.972583	+	0.232558i	$0.0747095\pi$
$350$	−569.270	−	956.192i	−1.62649	−	2.73198i
$351$		0			0
$352$		−	55.6160i		−	0.158000i
$353$	125.575	−	217.503i	0.355737	−	0.616155i	−0.631506	−	0.775371i	$-0.717563\pi$
$353$	125.575	−	217.503i	0.355737	−	0.616155i	0.987244	+	0.159215i	$0.0508964\pi$
$354$		0			0
$355$	237.953	−	241.162i	0.670291	−	0.679331i
$356$	−583.085	+	336.644i	−1.63788	+	0.945630i
$357$		0			0
$358$	−375.036	−	216.527i	−1.04759	−	0.604824i
$359$			314.839i			0.876989i	0.898734	+	0.438495i	$0.144488\pi$
$359$			314.839i			0.876989i	−0.898734	+	0.438495i	$0.855512\pi$
$360$		0			0
$361$	−110.280			−0.305484
$362$	−21.0381	+	36.4391i	−0.0581163	+	0.100660i
$363$		0			0
$364$	233.994	+	405.290i	0.642841	+	1.11343i
$365$	−184.989	+	187.484i	−0.506819	+	0.513654i
$366$		0			0
$367$	−195.196	−	112.696i	−0.531868	−	0.307074i	0.209909	−	0.977721i	$-0.432683\pi$
$367$	−195.196	−	112.696i	−0.531868	−	0.307074i	−0.741777	+	0.670647i	$0.766017\pi$
$368$	75.0069			0.203823
$369$		0			0
$370$	67.6338	+	245.815i	0.182794	+	0.664365i
$371$	−197.880	−	114.246i	−0.533371	−	0.307942i
$372$		0			0
$373$	434.035	−	250.590i	1.16363	−	0.671824i	0.211461	−	0.977386i	$-0.432178\pi$
$373$	434.035	−	250.590i	1.16363	−	0.671824i	0.952172	+	0.305563i	$0.0988445\pi$
$374$	−394.081	+	227.523i	−1.05369	+	0.608350i
$375$		0			0
$376$	−407.812	+	706.351i	−1.08461	+	1.87859i
$377$	−119.388			−0.316680
$378$		0			0
$379$	3.37369			0.00890156			0.00445078	−	0.999990i	$-0.498583\pi$
$379$	3.37369			0.00890156			0.00445078	+	0.999990i	$0.498583\pi$
$380$	−162.588	+	623.460i	−0.427863	+	1.64068i
$381$		0			0
$382$	862.068	−	497.715i	2.25672	−	1.30292i
$383$	207.530	+	359.452i	0.541853	+	0.938516i	0.998798	+	0.0490215i	$0.0156103\pi$
$383$	207.530	+	359.452i	0.541853	+	0.938516i	−0.456945	+	0.889495i	$0.651056\pi$
$384$		0			0
$385$	−228.711	+	877.018i	−0.594056	+	2.27797i
$386$		−	1145.77i		−	2.96832i
$387$		0			0
$388$		−	520.032i		−	1.34029i
$389$	−639.742	−	369.355i	−1.64458	−	0.949499i	−0.979175	−	0.203018i	$-0.934925\pi$
$389$	−639.742	−	369.355i	−1.64458	−	0.949499i	−0.665406	−	0.746482i	$-0.731742\pi$
$390$		0			0
$391$	−19.5296	−	33.8263i	−0.0499478	−	0.0865122i
$392$	−823.505	−	1426.35i	−2.10078	−	3.63866i
$393$		0			0
$394$	−157.328	+	272.500i	−0.399310	+	0.691625i
$395$	264.646	−	72.8151i	0.669991	−	0.184342i
$396$		0			0
$397$			258.122i			0.650183i	0.945683	+	0.325091i	$0.105395\pi$
$397$			258.122i			0.650183i	−0.945683	+	0.325091i	$0.894605\pi$
$398$	0.550152	−	0.952891i	0.00138229	−	0.00239420i
$399$		0			0
$400$	−385.669	−	215.830i	−0.964172	−	0.539575i
$401$	259.533	−	149.841i	0.647214	−	0.373669i	−0.140174	−	0.990127i	$-0.544766\pi$
$401$	259.533	−	149.841i	0.647214	−	0.373669i	0.787388	+	0.616458i	$0.211433\pi$
$402$		0			0
$403$	−122.532	−	70.7441i	−0.304051	−	0.175544i
$404$			656.097i			1.62400i
$405$		0			0
$406$	1180.73			2.90821
$407$	103.823	−	179.827i	0.255094	−	0.441836i
$408$		0			0
$409$	274.690	+	475.777i	0.671614	+	1.16327i	0.977446	+	0.211184i	$0.0677320\pi$
$409$	274.690	+	475.777i	0.671614	+	1.16327i	−0.305832	+	0.952085i	$0.598935\pi$
$410$	546.283	−	553.650i	1.33240	−	1.35037i
$411$		0			0
$412$	−253.536	−	146.379i	−0.615379	−	0.355289i
$413$	617.121			1.49424
$414$		0			0
$415$	12.3294	−	3.39232i	0.0297094	−	0.00817427i
$416$	15.2795	+	8.82162i	0.0367295	+	0.0212058i
$417$		0			0
$418$	677.832	−	391.346i	1.62161	−	0.936235i
$419$	214.767	−	123.996i	0.512571	−	0.295933i	−0.221319	−	0.975202i	$-0.571036\pi$
$419$	214.767	−	123.996i	0.512571	−	0.295933i	0.733890	+	0.679268i	$0.237703\pi$
$420$		0			0
$421$	163.175	−	282.627i	0.387588	−	0.671322i	−0.604537	−	0.796577i	$-0.706642\pi$
$421$	163.175	−	282.627i	0.387588	−	0.671322i	0.992125	+	0.125255i	$0.0399750\pi$
$422$	1144.05			2.71103
$423$		0			0
$424$	−257.846			−0.608127
$425$	3.08287	+	230.123i	0.00725382	+	0.541466i
$426$		0			0
$427$	−1012.08	+	584.325i	−2.37021	+	1.36844i
$428$	88.1880	+	152.746i	0.206047	+	0.356884i
$429$		0			0
$430$	1102.10	+	287.410i	2.56303	+	0.668395i
$431$			96.3692i			0.223594i	0.993731	+	0.111797i	$0.0356607\pi$
$431$			96.3692i			0.223594i	−0.993731	+	0.111797i	$0.964339\pi$
$432$		0			0
$433$			672.095i			1.55218i	0.630620	+	0.776091i	$0.282800\pi$
$433$			672.095i			1.55218i	−0.630620	+	0.776091i	$0.717200\pi$
$434$	1211.83	+	699.648i	2.79222	+	1.61209i
$435$		0			0
$436$	4.44422	+	7.69761i	0.0101932	+	0.0176551i
$437$	33.5915	+	58.1822i	0.0768684	+	0.133140i
$438$		0			0
$439$	−51.8764	+	89.8526i	−0.118170	+	0.204676i	−0.919042	−	0.394159i	$-0.871036\pi$
$439$	−51.8764	+	89.8526i	−0.118170	+	0.204676i	0.800873	+	0.598835i	$0.204369\pi$
$440$	271.327	+	986.137i	0.616652	+	2.24122i
$441$		0			0
$442$		−	144.356i		−	0.326596i
$443$	−113.879	+	197.244i	−0.257063	+	0.445247i	−0.965454	−	0.260574i	$-0.916088\pi$
$443$	−113.879	+	197.244i	−0.257063	+	0.445247i	0.708391	+	0.705821i	$0.249422\pi$
$444$		0			0
$445$	290.534	−	294.452i	0.652885	−	0.661690i
$446$	−152.548	+	88.0736i	−0.342036	+	0.197474i
$447$		0			0
$448$	631.299	+	364.481i	1.40915	+	0.813573i
$449$		−	504.100i		−	1.12272i	−0.827573	−	0.561359i	$-0.810279\pi$
$449$		−	504.100i		−	1.12272i	0.827573	−	0.561359i	$-0.189721\pi$
$450$		0			0
$451$	−633.478			−1.40461
$452$	−619.381	+	1072.80i	−1.37031	+	2.37345i
$453$		0			0
$454$	−524.365	−	908.226i	−1.15499	−	2.00050i
$455$	−204.667	−	201.944i	−0.449818	−	0.443833i
$456$		0			0
$457$	155.873	+	89.9933i	0.341079	+	0.196922i	0.660749	−	0.750607i	$-0.270239\pi$
$457$	155.873	+	89.9933i	0.341079	+	0.196922i	−0.319670	+	0.947529i	$0.603572\pi$
$458$	−973.518			−2.12558
$459$		0			0
$460$	−166.464	+	45.8010i	−0.361877	+	0.0995673i
$461$	−505.060	−	291.597i	−1.09558	−	0.632531i	−0.160520	−	0.987033i	$-0.551317\pi$
$461$	−505.060	−	291.597i	−1.09558	−	0.632531i	−0.935055	+	0.354502i	$0.884650\pi$
$462$		0			0
$463$	−13.6629	+	7.88827i	−0.0295095	+	0.0170373i	−0.514682	−	0.857381i	$-0.672090\pi$
$463$	−13.6629	+	7.88827i	−0.0295095	+	0.0170373i	0.485173	+	0.874418i	$0.338757\pi$
$464$	406.100	−	234.462i	0.875215	−	0.505306i
$465$		0			0
$466$	47.6035	−	82.4517i	0.102154	−	0.176935i
$467$	−400.171			−0.856896			−0.428448	−	0.903566i	$-0.640940\pi$
$467$	−400.171			−0.856896			−0.428448	+	0.903566i	$0.640940\pi$
$468$		0			0
$469$	−647.294			−1.38016
$470$	248.677	−	953.577i	0.529100	−	2.02889i
$471$		0			0
$472$	603.099	−	348.199i	1.27775	−	0.737711i
$473$	−463.820	−	803.360i	−0.980592	−	1.69843i
$474$		0			0
$475$	−5.30263	−	395.818i	−0.0111634	−	0.833302i
$476$			957.189i			2.01090i
$477$		0			0
$478$		−	61.7480i		−	0.129180i
$479$	140.425	+	81.0741i	0.293162	+	0.169257i	0.639367	−	0.768902i	$-0.279197\pi$
$479$	140.425	+	81.0741i	0.293162	+	0.169257i	−0.346205	+	0.938159i	$0.612530\pi$
$480$		0			0
$481$	32.9362	+	57.0471i	0.0684744	+	0.118601i
$482$	355.181	+	615.192i	0.736891	+	1.27633i
$483$		0			0
$484$	326.737	−	565.925i	0.675077	−	1.16927i
$485$	84.7576	+	308.051i	0.174758	+	0.635157i
$486$		0			0
$487$		−	328.071i		−	0.673658i	−0.941566	−	0.336829i	$-0.890646\pi$
$487$		−	328.071i		−	0.673658i	0.941566	−	0.336829i	$-0.109354\pi$
$488$	−659.390	+	1142.10i	−1.35121	+	2.34036i
$489$		0			0
$490$	1416.52	+	1397.67i	2.89087	+	2.85240i
$491$	34.1647	−	19.7250i	0.0695819	−	0.0401731i	−0.464805	−	0.885413i	$-0.653876\pi$
$491$	34.1647	−	19.7250i	0.0695819	−	0.0401731i	0.534387	+	0.845240i	$0.320542\pi$
$492$		0			0
$493$	−211.473	−	122.094i	−0.428952	−	0.247655i
$494$			248.296i			0.502623i
$495$		0			0
$496$	555.726			1.12041
$497$	−432.855	+	749.727i	−0.870936	+	1.50850i
$498$		0			0
$499$	37.8512	+	65.5602i	0.0758541	+	0.131383i	0.901457	−	0.432868i	$-0.142498\pi$
$499$	37.8512	+	65.5602i	0.0758541	+	0.131383i	−0.825603	+	0.564251i	$0.809165\pi$
$500$	987.710	+	243.496i	1.97542	+	0.486991i
$501$		0			0
$502$	353.602	+	204.152i	0.704385	+	0.406677i
$503$	−139.725			−0.277784			−0.138892	−	0.990308i	$-0.544354\pi$
$503$	−139.725			−0.277784			−0.138892	+	0.990308i	$0.544354\pi$
$504$		0			0
$505$	−106.934	−	388.652i	−0.211751	−	0.769607i
$506$	181.632	+	104.865i	0.358956	+	0.207243i
$507$		0			0
$508$	806.966	−	465.902i	1.58851	−	0.917129i
$509$	694.059	−	400.715i	1.36357	−	0.787259i	0.373475	−	0.927640i	$-0.378166\pi$
$509$	694.059	−	400.715i	1.36357	−	0.787259i	0.990098	+	0.140381i	$0.0448327\pi$
$510$		0			0
$511$	336.509	−	582.851i	0.658530	−	1.14061i
$512$	950.213			1.85588
$513$		0			0
$514$	−534.322			−1.03954
$515$	174.045	+	45.3879i	0.337951	+	0.0881319i
$516$		0			0
$517$	−695.095	+	401.313i	−1.34448	+	0.776234i
$518$	−325.733	−	564.186i	−0.628828	−	1.08916i
$519$		0			0
$520$	−313.960	−	81.8755i	−0.603769	−	0.157453i
$521$		−	472.323i		−	0.906570i	−0.891366	−	0.453285i	$-0.850252\pi$
$521$		−	472.323i		−	0.906570i	0.891366	−	0.453285i	$-0.149748\pi$
$522$		0			0
$523$		−	843.303i		−	1.61243i	−0.591620	−	0.806217i	$-0.701511\pi$
$523$		−	843.303i		−	1.61243i	0.591620	−	0.806217i	$-0.298489\pi$
$524$	1205.94	+	696.252i	2.30142	+	1.32873i
$525$		0			0
$526$	459.008	+	795.025i	0.872639	+	1.51145i
$527$	−144.695	−	250.619i	−0.274563	−	0.475557i
$528$		0			0
$529$	255.499	−	442.537i	0.482985	−	0.836554i
$530$	300.377	−	82.6461i	0.566749	−	0.155936i
$531$		0			0
$532$		−	1646.39i		−	3.09472i
$533$	100.480	−	174.036i	0.188518	−	0.326522i
$534$		0			0
$535$	−77.1353	−	76.1088i	−0.144178	−	0.142259i
$536$	−632.586	+	365.224i	−1.18020	+	0.681388i
$537$		0			0
$538$	−31.4452	−	18.1549i	−0.0584484	−	0.0337452i
$539$		−	1620.76i		−	3.00698i
$540$		0			0
$541$	797.318			1.47379			0.736893	−	0.676010i	$-0.236292\pi$
$541$	797.318			1.47379			0.736893	+	0.676010i	$0.236292\pi$
$542$	873.770	−	1513.41i	1.61212	−	2.79228i
$543$		0			0
$544$	18.0431	+	31.2515i	0.0331674	+	0.0574477i
$545$	−3.88721	−	3.83549i	−0.00713250	−	0.00703759i
$546$		0			0
$547$	−764.052	−	441.126i	−1.39680	−	0.806446i	−0.402748	−	0.915311i	$-0.631945\pi$
$547$	−764.052	−	441.126i	−1.39680	−	0.806446i	−0.994057	+	0.108865i	$0.965278\pi$
$548$	−296.401			−0.540877
$549$		0			0
$550$	−632.164	−	1061.83i	−1.14939	−	1.93060i
$551$	363.740	+	210.005i	0.660145	+	0.381135i
$552$		0			0
$553$	−607.407	+	350.687i	−1.09839	+	0.634153i
$554$	1059.87	−	611.915i	1.91312	−	1.10454i
$555$		0			0
$556$	−308.376	+	534.122i	−0.554632	+	0.960652i
$557$	589.979			1.05921			0.529604	−	0.848245i	$-0.322341\pi$
$557$	589.979			1.05921			0.529604	+	0.848245i	$0.322341\pi$
$558$		0			0
$559$	294.278			0.526436
$560$	1092.77	+	284.975i	1.95137	+	0.508883i
$561$		0			0
$562$	881.401	−	508.877i	1.56833	−	0.905476i
$563$	393.077	+	680.830i	0.698183	+	1.20929i	0.969096	+	0.246685i	$0.0793414\pi$
$563$	393.077	+	680.830i	0.698183	+	1.20929i	−0.270912	+	0.962604i	$0.587325\pi$
$564$		0			0
$565$	192.052	−	736.444i	0.339915	−	1.30344i
$566$			655.191i			1.15758i
$567$		0			0
$568$			976.922i			1.71993i
$569$	−944.299	−	545.191i	−1.65958	−	0.958157i	−0.972910	−	0.231185i	$-0.925740\pi$
$569$	−944.299	−	545.191i	−1.65958	−	0.958157i	−0.686667	−	0.726972i	$-0.740927\pi$
$570$		0			0
$571$	1.34031	+	2.32148i	0.00234730	+	0.00406565i	0.867197	−	0.497966i	$-0.165919\pi$
$571$	1.34031	+	2.32148i	0.00234730	+	0.00406565i	−0.864849	+	0.502031i	$0.832586\pi$
$572$	259.846	+	450.066i	0.454276	+	0.786829i
$573$		0			0
$574$	−993.730	+	1721.19i	−1.73124	+	2.99859i
$575$	91.1431	−	54.2622i	0.158510	−	0.0943691i
$576$		0			0
$577$			802.089i			1.39010i	0.718960	+	0.695051i	$0.244618\pi$
$577$			802.089i			1.39010i	−0.718960	+	0.695051i	$0.755382\pi$
$578$	−355.811	+	616.282i	−0.615590	+	1.06623i
$579$		0			0
$580$	−758.095	+	768.319i	−1.30706	+	1.32469i
$581$	−28.2980	+	16.3379i	−0.0487057	+	0.0281202i
$582$		0			0
$583$	−219.742	−	126.868i	−0.376917	−	0.217613i
$584$		−	759.476i		−	1.30047i
$585$		0			0
$586$	−1079.93			−1.84289
$587$	554.555	−	960.517i	0.944727	−	1.63632i	0.188431	−	0.982086i	$-0.439660\pi$
$587$	554.555	−	960.517i	0.944727	−	1.63632i	0.756296	−	0.654230i	$-0.227007\pi$
$588$		0			0
$589$	248.879	+	431.072i	0.422545	+	0.731870i
$590$	−590.973	+	598.943i	−1.00165	+	1.01516i
$591$		0			0
$592$	−224.065	−	129.364i	−0.378488	−	0.218520i
$593$	633.417			1.06816			0.534078	−	0.845435i	$-0.320659\pi$
$593$	633.417			1.06816			0.534078	+	0.845435i	$0.320659\pi$
$594$		0			0
$595$	−156.008	−	567.009i	−0.262198	−	0.952957i
$596$	−1349.09	−	778.898i	−2.26358	−	1.30688i
$597$		0			0
$598$	−57.6195	+	33.2666i	−0.0963537	+	0.0556298i
$599$	454.283	−	262.281i	0.758403	−	0.437864i	−0.0703190	−	0.997525i	$-0.522402\pi$
$599$	454.283	−	262.281i	0.758403	−	0.437864i	0.828722	+	0.559660i	$0.189068\pi$
$600$		0			0
$601$	−347.002	+	601.024i	−0.577374	+	1.00004i	0.418406	+	0.908260i	$0.362589\pi$
$601$	−347.002	+	601.024i	−0.577374	+	1.00004i	−0.995779	+	0.0917802i	$0.970744\pi$
$602$	−2910.36			−4.83448
$603$		0			0
$604$	1946.98			3.22347
$605$	−101.312	+	388.490i	−0.167457	+	0.642133i
$606$		0			0
$607$	779.225	−	449.886i	1.28373	−	0.741163i	0.306203	−	0.951966i	$-0.400941\pi$
$607$	779.225	−	449.886i	1.28373	−	0.741163i	0.977528	+	0.210804i	$0.0676081\pi$
$608$	−31.0346	−	53.7536i	−0.0510438	−	0.0884104i
$609$		0			0
$610$	402.085	−	1541.84i	0.659155	−	2.52760i
$611$		−	254.619i		−	0.416726i
$612$		0			0
$613$			966.059i			1.57595i	0.615706	+	0.787976i	$0.288871\pi$
$613$			966.059i			1.57595i	−0.615706	+	0.787976i	$0.711129\pi$
$614$	434.140	+	250.651i	0.707069	+	0.408226i
$615$		0			0
$616$	−1306.74	−	2263.35i	−2.12134	−	3.67427i
$617$	139.629	+	241.844i	0.226302	+	0.391967i	0.956709	−	0.291045i	$-0.0940029\pi$
$617$	139.629	+	241.844i	0.226302	+	0.391967i	−0.730407	+	0.683012i	$0.760670\pi$
$618$		0			0
$619$	419.292	−	726.234i	0.677369	−	1.17324i	−0.298401	−	0.954441i	$-0.596453\pi$
$619$	419.292	−	726.234i	0.677369	−	1.17324i	0.975770	−	0.218797i	$-0.0702134\pi$
$620$	−1233.33	+	339.339i	−1.98924	+	0.547322i
$621$		0			0
$622$		−	97.0765i		−	0.156071i
$623$	−528.503	+	915.394i	−0.848319	+	1.46933i
$624$		0			0
$625$	−624.776	+	16.7428i	−0.999641	+	0.0267885i
$626$	−1261.09	+	728.092i	−2.01453	+	1.16309i
$627$		0			0
$628$	1010.29	+	583.292i	1.60874	+	0.928809i
$629$			134.730i			0.214198i
$630$		0			0
$631$	−544.887			−0.863529			−0.431764	−	0.901986i	$-0.642109\pi$
$631$	−544.887			−0.863529			−0.431764	+	0.901986i	$0.642109\pi$
$632$	−395.737	+	685.437i	−0.626167	+	1.08455i
$633$		0			0
$634$	−116.834	−	202.362i	−0.184280	−	0.319183i
$635$	−402.087	+	407.509i	−0.633207	+	0.641747i
$636$		0			0
$637$	445.275	+	257.080i	0.699019	+	0.403579i
$638$	1311.18			2.05514
$639$		0			0
$640$	−1033.88	+	284.464i	−1.61544	+	0.444475i
$641$	−0.254013	−	0.146655i	−0.000396276	−	0.000228790i	0.499802	−	0.866140i	$-0.333406\pi$
$641$	−0.254013	−	0.146655i	−0.000396276	−	0.000228790i	−0.500198	+	0.865911i	$0.666739\pi$
$642$		0			0
$643$	−134.596	+	77.7089i	−0.209325	+	0.120854i	−0.600997	−	0.799251i	$-0.705230\pi$
$643$	−134.596	+	77.7089i	−0.209325	+	0.120854i	0.391673	+	0.920105i	$0.371897\pi$
$644$	382.062	−	220.583i	0.593264	−	0.342521i
$645$		0			0
$646$	−253.923	+	439.807i	−0.393069	+	0.680816i
$647$	657.668			1.01649			0.508244	−	0.861213i	$-0.330295\pi$
$647$	657.668			1.01649			0.508244	+	0.861213i	$0.330295\pi$
$648$		0			0
$649$	685.301			1.05593
$650$	391.991	−	5.25136i	0.603063	−	0.00807901i
$651$		0			0
$652$	−979.358	+	565.433i	−1.50208	+	0.867228i
$653$	−503.101	−	871.396i	−0.770446	−	1.33445i	−0.937319	−	0.348473i	$-0.886700\pi$
$653$	−503.101	−	871.396i	−0.770446	−	1.33445i	0.166873	−	0.985978i	$-0.446633\pi$
$654$		0			0
$655$	−827.843	−	215.888i	−1.26388	−	0.329599i
$656$			789.314i			1.20322i
$657$		0			0
$658$			2518.14i			3.82697i
$659$	−1083.60	−	625.615i	−1.64431	−	0.949340i	−0.979278	−	0.202522i	$-0.935086\pi$
$659$	−1083.60	−	625.615i	−1.64431	−	0.949340i	−0.665028	−	0.746818i	$-0.731581\pi$
$660$		0			0
$661$	398.585	+	690.369i	0.603002	+	1.04443i	0.992364	+	0.123346i	$0.0393624\pi$
$661$	398.585	+	690.369i	0.603002	+	1.04443i	−0.389361	+	0.921085i	$0.627304\pi$
$662$	−185.498	−	321.292i	−0.280208	−	0.485335i
$663$		0			0
$664$	−18.4367	+	31.9333i	−0.0277661	+	0.0480923i
$665$	268.338	+	975.273i	0.403515	+	1.46658i
$666$		0			0
$667$			112.546i			0.168735i
$668$	836.533	−	1448.92i	1.25229	−	2.16904i
$669$		0			0
$670$	619.867	−	628.227i	0.925175	−	0.937653i
$671$	−1123.90	+	648.882i	−1.67496	+	0.967037i
$672$		0			0
$673$	1083.26	+	625.421i	1.60960	+	0.929303i	0.989459	+	0.144812i	$0.0462579\pi$
$673$	1083.26	+	625.421i	1.60960	+	0.929303i	0.620141	+	0.784491i	$0.287075\pi$
$674$			1856.55i			2.75452i
$675$		0			0
$676$	1210.50			1.79068
$677$	302.147	−	523.335i	0.446303	−	0.773020i	−0.551839	−	0.833951i	$-0.686074\pi$
$677$	302.147	−	523.335i	0.446303	−	0.773020i	0.998142	+	0.0609308i	$0.0194069\pi$
$678$		0			0
$679$	−408.203	−	707.029i	−0.601183	−	1.04128i
$680$	−472.388	−	466.102i	−0.694688	−	0.685443i
$681$		0			0
$682$	1345.71	+	776.945i	1.97318	+	1.13922i
$683$	707.854			1.03639			0.518195	−	0.855263i	$-0.326604\pi$
$683$	707.854			1.03639			0.518195	+	0.855263i	$0.326604\pi$
$684$		0			0
$685$	175.579	−	48.3089i	0.256319	−	0.0705240i
$686$	−2514.78	−	1451.91i	−3.66587	−	2.11649i
$687$		0			0
$688$	−1000.99	+	577.920i	−1.45492	+	0.840000i
$689$	69.7095	−	40.2468i	0.101175	−	0.0584134i
$690$		0			0
$691$	−243.104	+	421.069i	−0.351815	+	0.609362i	−0.986568	−	0.163354i	$-0.947769\pi$
$691$	−243.104	+	421.069i	−0.351815	+	0.609362i	0.634752	+	0.772716i	$0.281102\pi$
$692$	−386.872			−0.559063
$693$		0			0
$694$	−9.44604			−0.0136110
$695$	95.6183	−	366.658i	0.137580	−	0.527566i
$696$		0			0
$697$	355.961	−	205.514i	0.510705	−	0.294855i
$698$	−346.403	−	599.987i	−0.496279	−	0.859580i
$699$		0			0
$700$	−2599.20	+	34.8205i	−3.71314	+	0.0497436i
$701$		−	646.017i		−	0.921564i	−0.887513	−	0.460782i	$-0.847569\pi$
$701$		−	646.017i		−	0.921564i	0.887513	−	0.460782i	$-0.152431\pi$
$702$		0			0
$703$		−	231.740i		−	0.329645i
$704$	701.045	+	404.748i	0.995802	+	0.574927i
$705$		0			0
$706$	−437.504	−	757.780i	−0.619695	−	1.07334i
$707$	515.008	+	892.020i	0.728441	+	1.26170i
$708$		0			0
$709$	−319.634	+	553.622i	−0.450823	+	0.780849i	−0.998437	−	0.0558820i	$-0.982203\pi$
$709$	−319.634	+	553.622i	−0.450823	+	0.780849i	0.547614	+	0.836731i	$0.315536\pi$
$710$	−313.128	−	1138.06i	−0.441026	−	1.60291i
$711$		0			0
$712$			1192.79i			1.67527i
$713$	−66.6896	+	115.510i	−0.0935338	+	0.162005i
$714$		0			0
$715$	−227.279	−	224.255i	−0.317873	−	0.313643i
$716$	−876.044	+	505.784i	−1.22352	+	0.706402i
$717$		0			0
$718$	949.943	+	548.450i	1.32304	+	0.763858i
$719$		−	1060.47i		−	1.47493i	−0.675386	−	0.737465i	$-0.736023\pi$
$719$		−	1060.47i		−	1.47493i	0.675386	−	0.737465i	$-0.263977\pi$
$720$		0			0
$721$	−459.606			−0.637456
$722$	−192.107	+	332.739i	−0.266076	+	0.460858i
$723$		0			0
$724$	49.1428	+	85.1178i	0.0678768	+	0.117566i
$725$	323.848	−	578.687i	0.446686	−	0.798189i
$726$		0			0
$727$	−692.899	−	400.045i	−0.953093	−	0.550269i	−0.0590528	−	0.998255i	$-0.518808\pi$
$727$	−692.899	−	400.045i	−0.953093	−	0.550269i	−0.894040	+	0.447986i	$0.852141\pi$
$728$	829.085			1.13885
$729$		0			0
$730$	243.431	+	884.751i	0.333468	+	1.21199i
$731$	521.255	+	300.947i	0.713072	+	0.411692i
$732$		0			0
$733$	8.38843	−	4.84307i	0.0114440	−	0.00660718i	−0.494267	−	0.869310i	$-0.664564\pi$
$733$	8.38843	−	4.84307i	0.0114440	−	0.00660718i	0.505711	+	0.862703i	$0.331230\pi$
$734$	−680.061	+	392.633i	−0.926514	+	0.534923i
$735$		0			0
$736$	8.31603	−	14.4038i	0.0112990	−	0.0195704i
$737$	−718.807			−0.975315
$738$		0			0
$739$	−1107.89			−1.49918			−0.749590	−	0.661902i	$-0.769749\pi$
$739$	−1107.89			−1.49918			−0.749590	+	0.661902i	$0.769749\pi$
$740$	576.263	+	150.280i	0.778733	+	0.203080i
$741$		0			0
$742$	−689.416	+	398.034i	−0.929131	+	0.536434i
$743$	−390.228	−	675.894i	−0.525206	−	0.909683i	−0.999569	−	0.0293537i	$-0.990655\pi$
$743$	−390.228	−	675.894i	−0.525206	−	0.909683i	0.474364	−	0.880329i	$-0.342678\pi$
$744$		0			0
$745$	926.110	+	241.514i	1.24310	+	0.324180i
$746$		−	1746.11i		−	2.34063i
$747$		0			0
$748$			1062.94i			1.42104i
$749$	239.799	+	138.448i	0.320158	+	0.184843i
$750$		0			0
$751$	36.6548	+	63.4880i	0.0488080	+	0.0845379i	0.889397	−	0.457135i	$-0.151124\pi$
$751$	36.6548	+	63.4880i	0.0488080	+	0.0845379i	−0.840589	+	0.541673i	$0.817791\pi$
$752$	500.036	+	866.088i	0.664942	+	1.15171i
$753$		0			0
$754$	−207.975	+	360.223i	−0.275828	+	0.477749i
$755$	−1153.33	+	317.328i	−1.52759	+	0.420302i
$756$		0			0
$757$			95.5082i			0.126167i	0.998008	+	0.0630834i	$0.0200934\pi$
$757$			95.5082i			0.126167i	−0.998008	+	0.0630834i	$0.979907\pi$
$758$	5.87697	−	10.1792i	0.00775325	−	0.0134290i
$759$		0			0
$760$	812.521	+	801.708i	1.06911	+	1.05488i
$761$	683.596	−	394.674i	0.898286	−	0.518626i	0.0216424	−	0.999766i	$-0.493110\pi$
$761$	683.596	−	394.674i	0.898286	−	0.518626i	0.876644	+	0.481140i	$0.159777\pi$
$762$		0			0
$763$	12.0846	+	6.97704i	0.0158383	+	0.00914422i
$764$		−	2325.22i		−	3.04348i
$765$		0			0
$766$	1446.07			1.88781
$767$	−108.700	+	188.274i	−0.141721	+	0.245468i
$768$		0			0
$769$	15.0251	+	26.0242i	0.0195385	+	0.0338416i	0.875629	−	0.482984i	$-0.160447\pi$
$769$	15.0251	+	26.0242i	0.0195385	+	0.0338416i	−0.856091	+	0.516825i	$0.827114\pi$
$770$	2247.75	+	2217.84i	2.91916	+	2.88031i
$771$		0			0
$772$	−2317.83	−	1338.20i	−3.00237	−	1.73342i
$773$	−1290.89			−1.66998			−0.834988	−	0.550269i	$-0.814525\pi$
$773$	−1290.89			−1.66998			−0.834988	+	0.550269i	$0.814525\pi$
$774$		0			0
$775$	675.279	−	402.029i	0.871328	−	0.518747i
$776$	−797.857	−	460.643i	−1.02817	−	0.593612i
$777$		0			0
$778$	−2228.86	+	1286.83i	−2.86486	+	1.65403i
$779$	−612.264	+	353.491i	−0.785961	+	0.453775i
$780$		0			0
$781$	−480.677	+	832.557i	−0.615463	+	1.06601i
$782$	−136.082			−0.174018
$783$		0			0
$784$	−2019.47			−2.57586
$785$	−693.534	−	180.862i	−0.883482	−	0.230397i
$786$		0			0
$787$	−74.1557	+	42.8138i	−0.0942258	+	0.0544013i	−0.546372	−	0.837542i	$-0.683992\pi$
$787$	−74.1557	+	42.8138i	−0.0942258	+	0.0544013i	0.452147	+	0.891944i	$0.350658\pi$
$788$	367.502	+	636.532i	0.466373	+	0.807781i
$789$		0			0
$790$	241.314	−	925.343i	0.305461	−	1.17132i
$791$			1944.75i			2.45860i
$792$		0			0
$793$		−	411.693i		−	0.519159i
$794$	778.815	+	449.649i	0.980876	+	0.566309i
$795$		0			0
$796$	−1.28510	−	2.22585i	−0.00161444	−	0.00279630i
$797$	−378.821	−	656.137i	−0.475308	−	0.823258i	0.524292	−	0.851539i	$-0.324330\pi$
$797$	−378.821	−	656.137i	−0.475308	−	0.823258i	−0.999600	+	0.0282806i	$0.990997\pi$
$798$		0			0
$799$	260.390	−	451.008i	0.325895	−	0.564466i
$800$	−84.2057	+	50.1320i	−0.105257	+	0.0626650i
$801$		0			0
$802$		−	1044.09i		−	1.30186i
$803$	373.687	−	647.244i	0.465363	−	0.806032i
$804$		0			0
$805$	−190.370	+	192.937i	−0.236484	+	0.239674i
$806$	−426.903	+	246.473i	−0.529656	+	0.305797i
$807$		0			0
$808$	1006.61	+	581.168i	1.24581	+	0.719267i
$809$			624.032i			0.771362i	0.922632	+	0.385681i	$0.126033\pi$
$809$			624.032i			0.771362i	−0.922632	+	0.385681i	$0.873967\pi$
$810$		0			0
$811$	972.993			1.19974			0.599872	−	0.800096i	$-0.295218\pi$
$811$	972.993			1.19974			0.599872	+	0.800096i	$0.295218\pi$
$812$	1379.03	−	2388.55i	1.69832	−	2.94157i
$813$		0			0
$814$	−361.720	−	626.518i	−0.444374	−	0.769678i
$815$	487.985	−	494.566i	0.598754	−	0.606829i
$816$		0			0
$817$	−896.575	−	517.638i	−1.09740	−	0.633583i
$818$	1914.04			2.33990
$819$		0			0
$820$	−481.974	−	1751.73i	−0.587773	−	2.13626i
$821$	810.895	+	468.170i	0.987692	+	0.570244i	0.904584	−	0.426296i	$-0.140182\pi$
$821$	810.895	+	468.170i	0.987692	+	0.570244i	0.0831083	+	0.996541i	$0.473515\pi$
$822$		0			0
$823$	222.467	−	128.441i	0.270312	−	0.156065i	−0.358717	−	0.933446i	$-0.616786\pi$
$823$	222.467	−	128.441i	0.270312	−	0.156065i	0.629030	+	0.777381i	$0.283452\pi$
$824$	−449.163	+	259.324i	−0.545100	+	0.314714i
$825$		0			0
$826$	1075.02	−	1862.00i	1.30148	−	2.25423i
$827$	−13.1651			−0.0159191			−0.00795957	−	0.999968i	$-0.502534\pi$
$827$	−13.1651			−0.0159191			−0.00795957	+	0.999968i	$0.502534\pi$
$828$		0			0
$829$	−1494.14			−1.80234			−0.901171	−	0.433464i	$-0.857291\pi$
$829$	−1494.14			−1.80234			−0.901171	+	0.433464i	$0.857291\pi$
$830$	11.2424	−	43.1101i	0.0135450	−	0.0519398i
$831$		0			0
$832$	−222.395	+	128.400i	−0.267301	+	0.154326i
$833$	525.812	+	910.733i	0.631227	+	1.09332i
$834$		0			0
$835$	−259.385	+	994.637i	−0.310640	+	1.19118i
$836$		−	1828.29i		−	2.18695i
$837$		0			0
$838$		−	864.004i		−	1.03103i
$839$	97.3526	+	56.2066i	0.116034	+	0.0669923i	0.556894	−	0.830584i	$-0.311993\pi$
$839$	97.3526	+	56.2066i	0.116034	+	0.0669923i	−0.440860	+	0.897576i	$0.645326\pi$
$840$		0			0
$841$	−68.6954	−	118.984i	−0.0816830	−	0.141479i
$842$	−568.500	−	984.671i	−0.675178	−	1.16944i
$843$		0			0
$844$	1336.19	−	2314.36i	1.58317	−	2.74213i
$845$	−717.064	+	197.294i	−0.848597	+	0.233484i
$846$		0			0
$847$		−	1025.90i		−	1.21122i
$848$	−158.078	+	273.799i	−0.186413	+	0.322876i
$849$		0			0
$850$	699.705	+	391.572i	0.823182	+	0.460673i
$851$	53.7776	−	31.0485i	0.0631934	−	0.0364847i
$852$		0			0
$853$	54.0966	+	31.2327i	0.0634192	+	0.0366151i	0.531374	−	0.847137i	$-0.321676\pi$
$853$	54.0966	+	31.2327i	0.0634192	+	0.0366151i	−0.467955	+	0.883752i	$0.655009\pi$
$854$			4071.58i			4.76766i
$855$		0			0
$856$	312.467			0.365031
$857$	−763.782	+	1322.91i	−0.891228	+	1.54365i	−0.0528232	+	0.998604i	$0.516822\pi$
$857$	−763.782	+	1322.91i	−0.891228	+	1.54365i	−0.838405	+	0.545048i	$0.816511\pi$
$858$		0			0
$859$	432.136	+	748.481i	0.503068	+	0.871340i	0.999994	+	0.00354649i	$0.00112888\pi$
$859$	432.136	+	748.481i	0.503068	+	0.871340i	−0.496926	+	0.867793i	$0.665538\pi$
$860$	1868.61	−	1893.81i	2.17280	−	2.20211i
$861$		0			0
$862$	290.768	+	167.875i	0.337318	+	0.194751i
$863$	−593.430			−0.687636			−0.343818	−	0.939036i	$-0.611720\pi$
$863$	−593.430			−0.687636			−0.343818	+	0.939036i	$0.611720\pi$
$864$		0			0
$865$	229.171	−	63.0544i	0.264938	−	0.0728952i
$866$	2027.87	+	1170.79i	2.34165	+	1.35195i
$867$		0			0
$868$	2830.70	−	1634.30i	3.26117	−	1.88284i
$869$	−674.514	+	389.431i	−0.776196	+	0.448137i
$870$		0			0
$871$	114.015	−	197.479i	0.130901	−	0.226727i
$872$	15.7467			0.0180581
$873$		0			0
$874$	234.065			0.267809
$875$	1534.01	−	444.258i	1.75316	−	0.507723i
$876$		0			0
$877$	69.3714	−	40.0516i	0.0791008	−	0.0456689i	−0.459928	−	0.887956i	$-0.652125\pi$
$877$	69.3714	−	40.0516i	0.0791008	−	0.0456689i	0.539029	+	0.842287i	$0.318791\pi$
$878$	180.738	+	313.047i	0.205851	+	0.356545i
$879$		0			0
$880$	1213.49	+	316.459i	1.37897	+	0.359612i
$881$			612.391i			0.695109i	0.937660	+	0.347555i	$0.112988\pi$
$881$			612.391i			0.695109i	−0.937660	+	0.347555i	$0.887012\pi$
$882$		0			0
$883$			1106.80i			1.25345i	0.779239	+	0.626727i	$0.215606\pi$
$883$			1106.80i			1.25345i	−0.779239	+	0.626727i	$0.784394\pi$
$884$	−292.023	−	168.600i	−0.330343	−	0.190724i
$885$		0			0
$886$	396.755	+	687.199i	0.447804	+	0.775620i
$887$	370.500	+	641.725i	0.417700	+	0.723477i	0.995708	−	0.0925538i	$-0.0295030\pi$
$887$	370.500	+	641.725i	0.417700	+	0.723477i	−0.578008	+	0.816031i	$0.696170\pi$
$888$		0			0
$889$	731.426	−	1266.87i	0.822752	−	1.42505i
$890$	−382.320	−	1389.54i	−0.429573	−	1.56128i
$891$		0			0
$892$			411.461i			0.461279i
$893$	−447.878	+	775.748i	−0.501543	+	0.868698i
$894$		0			0
$895$	436.506	−	442.393i	0.487717	−	0.494294i
$896$	2372.94	−	1370.02i	2.64837	−	1.52904i
$897$		0			0
$898$	−1520.99	−	878.142i	−1.69375	−	0.977887i
$899$			833.853i			0.927534i
$900$		0			0
$901$	164.636			0.182725
$902$	−1103.52	+	1911.35i	−1.22341	+	2.11901i
$903$		0			0
$904$	1097.29	+	1900.56i	1.21382	+	2.10239i
$905$	−42.9836	−	42.4116i	−0.0474957	−	0.0468637i
$906$		0			0
$907$	256.204	+	147.920i	0.282475	+	0.163087i	0.634543	−	0.772887i	$-0.281188\pi$
$907$	256.204	+	147.920i	0.282475	+	0.163087i	−0.352069	+	0.935974i	$0.614522\pi$
$908$	−2449.72			−2.69793
$909$		0			0
$910$	−965.842	+	265.743i	−1.06136	+	0.292025i
$911$	−602.338	−	347.760i	−0.661183	−	0.381734i	0.131544	−	0.991310i	$-0.458006\pi$
$911$	−602.338	−	347.760i	−0.661183	−	0.381734i	−0.792728	+	0.609576i	$0.791340\pi$
$912$		0			0
$913$	−31.4244	+	18.1429i	−0.0344188	+	0.0198717i
$914$	543.061	−	313.537i	0.594159	−	0.343038i
$915$		0			0
$916$	−1137.02	+	1969.37i	−1.24128	+	2.14997i
$917$	2186.11			2.38399
$918$		0			0
$919$	60.1197			0.0654186			0.0327093	−	0.999465i	$-0.489586\pi$
$919$	60.1197			0.0654186			0.0327093	+	0.999465i	$0.489586\pi$
$920$	−77.1830	+	295.966i	−0.0838946	+	0.321702i
$921$		0			0
$922$	−1759.63	+	1015.92i	−1.90849	+	1.10187i
$923$	−152.487	−	264.115i	−0.165208	−	0.286148i
$924$		0			0
$925$	−365.854	+	4.90121i	−0.395518	+	0.00529861i
$926$			54.9654i			0.0593579i
$927$		0			0
$928$		−	103.979i		−	0.112047i
$929$	1236.02	+	713.617i	1.33049	+	0.768156i	0.985374	−	0.170405i	$-0.0545077\pi$
$929$	1236.02	+	713.617i	1.33049	+	0.768156i	0.345112	+	0.938562i	$0.387841\pi$
$930$		0			0
$931$	−904.412	−	1566.49i	−0.971441	−	1.68259i
$932$	−111.197	−	192.598i	−0.119310	−	0.206651i
$933$		0			0
$934$	−697.097	+	1207.41i	−0.746356	+	1.29273i
$935$	−173.243	−	629.653i	−0.185287	−	0.673425i
$936$		0			0
$937$		−	174.346i		−	0.186068i	−0.995663	−	0.0930341i	$-0.970343\pi$
$937$		−	174.346i		−	0.186068i	0.995663	−	0.0930341i	$-0.0296566\pi$
$938$	−1127.59	+	1953.04i	−1.20212	+	2.08213i
$939$		0			0
$940$	−1638.59	−	1616.79i	−1.74318	−	1.71999i
$941$	397.871	−	229.711i	0.422818	−	0.244114i	−0.273464	−	0.961882i	$-0.588170\pi$
$941$	397.871	−	229.711i	0.422818	−	0.244114i	0.696282	+	0.717768i	$0.254836\pi$
$942$		0			0
$943$	−164.062	−	94.7212i	−0.173979	−	0.100447i
$944$		−	853.885i		−	0.904540i
$945$		0			0
$946$	−3231.90			−3.41638
$947$	−426.988	+	739.564i	−0.450884	+	0.780955i	−0.998441	−	0.0558137i	$-0.982225\pi$
$947$	−426.988	+	739.564i	−0.450884	+	0.780955i	0.547557	+	0.836769i	$0.315558\pi$
$948$		0			0
$949$	118.546	+	205.327i	0.124916	+	0.216362i
$950$	−1203.51	−	673.516i	−1.26686	−	0.708964i
$951$		0			0
$952$	1468.56	+	847.874i	1.54261	+	0.890624i
$953$	1103.28			1.15769			0.578843	−	0.815439i	$-0.303504\pi$
$953$	1103.28			1.15769			0.578843	+	0.815439i	$0.303504\pi$
$954$		0			0
$955$	378.976	+	1377.39i	0.396834	+	1.44229i
$956$	−124.913	−	72.1183i	−0.130662	−	0.0754376i
$957$		0			0
$958$	489.239	−	282.462i	0.510688	−	0.294846i
$959$	−402.982	+	232.662i	−0.420211	+	0.242609i
$960$		0			0
$961$	−13.6034	+	23.5618i	−0.0141555	+	0.0245180i
$962$	229.499			0.238565
$963$		0			0
$964$	1659.33			1.72130
$965$	1591.12	+	414.937i	1.64883	+	0.429987i
$966$		0			0
$967$	886.133	−	511.609i	0.916373	−	0.529068i	0.0338972	−	0.999425i	$-0.489208\pi$
$967$	886.133	−	511.609i	0.916373	−	0.529068i	0.882476	+	0.470357i	$0.155875\pi$
$968$	−578.845	−	1002.59i	−0.597981	−	1.03573i
$969$		0			0
$970$	1077.11	+	280.892i	1.11042	+	0.289580i
$971$			589.306i			0.606906i	0.952846	+	0.303453i	$0.0981395\pi$
$971$			589.306i			0.606906i	−0.952846	+	0.303453i	$0.901860\pi$
$972$		0			0
$973$			968.247i			0.995115i
$974$	−989.868	−	571.500i	−1.01629	−	0.586756i
$975$		0			0
$976$	808.507	+	1400.38i	0.828389	+	1.43481i
$977$	378.616	+	655.783i	0.387530	+	0.671221i	0.992117	−	0.125318i	$-0.0399952\pi$
$977$	378.616	+	655.783i	0.387530	+	0.671221i	−0.604587	+	0.796539i	$0.706662\pi$
$978$		0			0
$979$	−586.892	+	1016.53i	−0.599481	+	1.03833i
$980$	4481.84	−	1233.14i	4.57331	−	1.25830i
$981$		0			0
$982$		−	137.444i		−	0.139963i
$983$	701.951	−	1215.82i	0.714091	−	1.23684i	−0.249218	−	0.968447i	$-0.580174\pi$
$983$	701.951	−	1215.82i	0.714091	−	1.23684i	0.963309	−	0.268394i	$-0.0864930\pi$
$984$		0			0
$985$	−321.442	−	317.165i	−0.326337	−	0.321995i
$986$	−736.772	+	425.376i	−0.747234	+	0.431416i
$987$		0			0
$988$	502.288	+	289.996i	0.508389	+	0.293519i
$989$		−	277.412i		−	0.280498i
$990$		0			0
$991$	1778.87			1.79502			0.897512	−	0.440990i	$-0.145373\pi$
$991$	1778.87			1.79502			0.897512	+	0.440990i	$0.145373\pi$
$992$	61.6135	−	106.718i	0.0621104	−	0.107578i
$993$		0			0
$994$	1508.07	+	2612.05i	1.51717	+	2.62782i
$995$	1.12403	+	1.10908i	0.00112968	+	0.00111465i
$996$		0			0
$997$	1207.19	+	696.970i	1.21082	+	0.699067i	0.962938	−	0.269723i	$-0.0869321\pi$
$997$	1207.19	+	696.970i	1.21082	+	0.699067i	0.247882	+	0.968790i	$0.420265\pi$
$998$	263.747			0.264276
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.h.k.269.22		48
3.2	odd	2	inner	405.3.h.k.269.3		48
5.4	even	2	inner	405.3.h.k.269.4		48
9.2	odd	6		405.3.d.b.404.21	yes	24
9.4	even	3	inner	405.3.h.k.134.21		48
9.5	odd	6	inner	405.3.h.k.134.4		48
9.7	even	3		405.3.d.b.404.4	yes	24
15.14	odd	2	inner	405.3.h.k.269.21		48
45.4	even	6	inner	405.3.h.k.134.3		48
45.14	odd	6	inner	405.3.h.k.134.22		48
45.29	odd	6		405.3.d.b.404.3	✓	24
45.34	even	6		405.3.d.b.404.22	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.3.d.b.404.3	✓	24	45.29	odd	6
405.3.d.b.404.4	yes	24	9.7	even	3
405.3.d.b.404.21	yes	24	9.2	odd	6
405.3.d.b.404.22	yes	24	45.34	even	6
405.3.h.k.134.3		48	45.4	even	6	inner
405.3.h.k.134.4		48	9.5	odd	6	inner
405.3.h.k.134.21		48	9.4	even	3	inner
405.3.h.k.134.22		48	45.14	odd	6	inner
405.3.h.k.269.3		48	3.2	odd	2	inner
405.3.h.k.269.4		48	5.4	even	2	inner
405.3.h.k.269.21		48	15.14	odd	2	inner
405.3.h.k.269.22		48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.74200 - 3.01723i) q^{2} +(-4.06913 - 7.04793i) q^{4} +(3.55914 + 3.51177i) q^{5} +(-11.0647 - 6.38818i) q^{7} -14.4177 q^{8} +(16.7958 - 4.62123i) q^{10} +(-12.2871 - 7.09395i) q^{11} +(3.89787 - 2.25044i) q^{13} +(-38.5493 + 22.2564i) q^{14} +(-8.83907 + 15.3097i) q^{16} +9.20574 q^{17} -15.8342 q^{19} +(10.2682 - 39.3744i) q^{20} +(-42.8082 + 24.7153i) q^{22} +(-2.12146 - 3.67447i) q^{23} +(0.334886 + 24.9978i) q^{25} -15.6810i q^{26} +103.977i q^{28} +(-22.9719 - 13.2628i) q^{29} +(-15.7179 - 27.2242i) q^{31} +(1.95998 + 3.39479i) q^{32} +(16.0364 - 27.7759i) q^{34} +(-16.9468 - 61.5930i) q^{35} +14.6355i q^{37} +(-27.5831 + 47.7753i) q^{38} +(-51.3144 - 50.6316i) q^{40} +(38.6673 - 22.3246i) q^{41} +(56.6228 + 32.6912i) q^{43} +115.465i q^{44} -14.7823 q^{46} +(28.2856 - 48.9921i) q^{47} +(57.1178 + 98.9309i) q^{49} +(76.0074 + 42.5357i) q^{50} +(-31.7218 - 18.3146i) q^{52} +17.8840 q^{53} +(-18.8190 - 68.3978i) q^{55} +(159.527 + 92.1027i) q^{56} +(-80.0340 + 46.2076i) q^{58} +(-41.8306 + 24.1509i) q^{59} +(45.7349 - 79.2151i) q^{61} -109.522 q^{62} -57.0554 q^{64} +(21.7761 + 5.67883i) q^{65} +(43.8758 - 25.3317i) q^{67} +(-37.4593 - 64.8815i) q^{68} +(-215.362 - 56.1627i) q^{70} -67.7587i q^{71} +52.6768i q^{73} +(44.1586 + 25.4950i) q^{74} +(64.4312 + 111.598i) q^{76} +(90.6349 + 156.984i) q^{77} +(27.4481 - 47.5415i) q^{79} +(-85.2237 + 23.4485i) q^{80} -155.558i q^{82} +(1.27876 - 2.21487i) q^{83} +(32.7645 + 32.3285i) q^{85} +(197.274 - 113.896i) q^{86} +(177.151 + 102.278i) q^{88} -82.7313i q^{89} -57.5048 q^{91} +(-17.2650 + 29.9038i) q^{92} +(-98.5469 - 170.688i) q^{94} +(-56.3559 - 55.6060i) q^{95} +(55.3388 + 31.9499i) q^{97} +397.997 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} + 24 q^{10} - 96 q^{16} - 48 q^{25} - 144 q^{34} - 72 q^{40} - 336 q^{46} + 288 q^{49} - 264 q^{55} + 360 q^{61} - 144 q^{64} + 156 q^{70} - 48 q^{76} + 480 q^{79} + 456 q^{85} - 96 q^{91}+ \cdots - 384 q^{94}+O(q^{100}) \) 48 * q - 48 * q^4 + 24 * q^10 - 96 * q^16 - 48 * q^25 - 144 * q^34 - 72 * q^40 - 336 * q^46 + 288 * q^49 - 264 * q^55 + 360 * q^61 - 144 * q^64 + 156 * q^70 - 48 * q^76 + 480 * q^79 + 456 * q^85 - 96 * q^91 - 384 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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