LMFDB - Embedded newform 405.3.h.k.269.4

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			269.4
Character	$\chi$	$=$	405.269
Dual form			405.3.h.k.134.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.74200 + 3.01723i) q^{2} +(-4.06913 - 7.04793i) q^{4} +(-1.26172 - 4.83819i) q^{5} +(11.0647 + 6.38818i) q^{7} +14.4177 q^{8} +(16.7958 + 4.62123i) q^{10} +(-12.2871 - 7.09395i) q^{11} +(-3.89787 + 2.25044i) q^{13} +(-38.5493 + 22.2564i) q^{14} +(-8.83907 + 15.3097i) q^{16} -9.20574 q^{17} -15.8342 q^{19} +(-28.9651 + 28.5797i) q^{20} +(42.8082 - 24.7153i) q^{22} +(2.12146 + 3.67447i) q^{23} +(-21.8161 + 12.2089i) q^{25} -15.6810i q^{26} -103.977i q^{28} +(-22.9719 - 13.2628i) q^{29} +(-15.7179 - 27.2242i) q^{31} +(-1.95998 - 3.39479i) q^{32} +(16.0364 - 27.7759i) q^{34} +(16.9468 - 61.5930i) q^{35} -14.6355i q^{37} +(27.5831 - 47.7753i) q^{38} +(-18.1910 - 69.7554i) q^{40} +(38.6673 - 22.3246i) q^{41} +(-56.6228 - 32.6912i) q^{43} +115.465i q^{44} -14.7823 q^{46} +(-28.2856 + 48.9921i) q^{47} +(57.1178 + 98.9309i) q^{49} +(1.16674 - 87.0922i) q^{50} +(31.7218 + 18.3146i) q^{52} -17.8840 q^{53} +(-18.8190 + 68.3978i) q^{55} +(159.527 + 92.1027i) q^{56} +(80.0340 - 46.2076i) q^{58} +(-41.8306 + 24.1509i) q^{59} +(45.7349 - 79.2151i) q^{61} +109.522 q^{62} -57.0554 q^{64} +(15.8060 + 16.0192i) q^{65} +(-43.8758 + 25.3317i) q^{67} +(37.4593 + 64.8815i) q^{68} +(156.319 + 158.427i) q^{70} -67.7587i q^{71} -52.6768i q^{73} +(44.1586 + 25.4950i) q^{74} +(64.4312 + 111.598i) q^{76} +(-90.6349 - 156.984i) q^{77} +(27.4481 - 47.5415i) q^{79} +(85.2237 + 23.4485i) q^{80} +155.558i q^{82} +(-1.27876 + 2.21487i) q^{83} +(11.6151 + 44.5391i) q^{85} +(197.274 - 113.896i) q^{86} +(-177.151 - 102.278i) q^{88} -82.7313i q^{89} -57.5048 q^{91} +(17.2650 - 29.9038i) q^{92} +(-98.5469 - 170.688i) q^{94} +(19.9782 + 76.6086i) q^{95} +(-55.3388 - 31.9499i) q^{97} -397.997 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.503195\pi$
$2$	−1.74200	+	3.01723i	−0.871000	+	1.50862i	−0.860964	+	0.508666i	$0.830139\pi$
$3$		0			0
$3$		0			0
$4$	−4.06913	−	7.04793i	−1.01728	−	1.76198i
$5$	−1.26172	−	4.83819i	−0.252344	−	0.967638i
$5$	−1.26172	−	4.83819i	−0.252344	−	0.967638i
$6$		0			0
$7$	11.0647	+	6.38818i	1.58067	+	0.912598i	0.994762	+	0.102217i	$0.0325936\pi$
$7$	11.0647	+	6.38818i	1.58067	+	0.912598i	0.585903	+	0.810381i	$0.300740\pi$
$8$	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	−0.642369	−	0.766395i	$-0.722048\pi$
$13$	−3.89787	+	2.25044i	−0.299836	+	0.173110i	0.342533	+	0.939506i	$0.388715\pi$
$14$	−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	$-0.587274\pi$
$17$	−9.20574			−0.541514			−0.270757	+	0.962648i	$0.587274\pi$
$18$		0			0
$19$	−15.8342			−0.833376			−0.416688	−	0.909049i	$-0.636809\pi$
$19$	−15.8342			−0.833376			−0.416688	+	0.909049i	$0.636809\pi$
$20$	−28.9651	+	28.5797i	−1.44826	+	1.42899i
$21$		0			0
$22$	42.8082	−	24.7153i	1.94583	−	1.12342i
$23$	2.12146	+	3.67447i	0.0922373	+	0.159760i	0.908452	−	0.417989i	$-0.137265\pi$
$23$	2.12146	+	3.67447i	0.0922373	+	0.159760i	−0.816215	+	0.577748i	$0.803932\pi$
$24$		0			0
$25$	−21.8161	+	12.2089i	−0.872645	+	0.488354i
$26$		−	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	$-0.936628\pi$
$37$		−	14.6355i		−	0.395553i	0.980247	−	0.197777i	$-0.0633720\pi$
$38$	27.5831	−	47.7753i	0.725871	−	1.25725i
$39$		0			0
$40$	−18.1910	−	69.7554i	−0.454776	−	1.74388i
$41$	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	−0.333596	−	0.942716i	$-0.608262\pi$
$43$	−56.6228	−	32.6912i	−1.31681	−	0.760261i	−0.983214	+	0.182455i	$0.941596\pi$
$44$			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	$0.372224\pi$
$47$	−28.2856	+	48.9921i	−0.601821	+	1.04238i	−0.992545	+	0.121876i	$0.961109\pi$
$48$		0			0
$49$	57.1178	+	98.9309i	1.16567	+	2.01900i
$50$	1.16674	−	87.0922i	0.0233348	−	1.74184i
$51$		0			0
$52$	31.7218	+	18.3146i	0.610035	+	0.352204i
$53$	−17.8840			−0.337434			−0.168717	−	0.985665i	$-0.553962\pi$
$53$	−17.8840			−0.337434			−0.168717	+	0.985665i	$0.553962\pi$
$54$		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
$65$	15.8060	+	16.0192i	0.243170	+	0.246449i
$66$		0			0
$67$	−43.8758	+	25.3317i	−0.654862	+	0.378085i	−0.790317	−	0.612699i	$-0.790084\pi$
$67$	−43.8758	+	25.3317i	−0.654862	+	0.378085i	0.135454	+	0.990784i	$0.456751\pi$
$68$	37.4593	+	64.8815i	0.550873	+	0.954139i
$69$		0			0
$70$	156.319	+	158.427i	2.23313	+	2.26325i
$71$		−	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	$-0.882504\pi$
$73$		−	52.6768i		−	0.721600i	0.932643	−	0.360800i	$-0.117496\pi$
$74$	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	−0.873626	−	0.486598i	$-0.838238\pi$
$83$	−1.27876	+	2.21487i	−0.0154067	+	0.0266852i	0.858219	+	0.513283i	$0.171571\pi$
$84$		0			0
$85$	11.6151	+	44.5391i	0.136648	+	0.523990i
$86$	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
$95$	19.9782	+	76.6086i	0.210297	+	0.806406i
$96$		0			0
$97$	−55.3388	−	31.9499i	−0.570503	−	0.329380i	0.186847	−	0.982389i	$-0.440173\pi$
$97$	−55.3388	−	31.9499i	−0.570503	−	0.329380i	−0.757350	+	0.653009i	$0.773506\pi$
$98$	−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	−0.643549	−	0.765405i	$-0.722539\pi$
$103$	−31.1536	+	17.9866i	−0.302462	+	0.174627i	0.341086	+	0.940032i	$0.389205\pi$
$104$	−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	$-0.467708\pi$
$107$	21.6725			0.202546			0.101273	+	0.994859i	$0.467708\pi$
$108$		0			0
$109$	−1.09218			−0.0100200			−0.00501000	−	0.999987i	$-0.501595\pi$
$109$	−1.09218			−0.0100200			−0.00501000	+	0.999987i	$0.501595\pi$
$110$	−173.589	−	175.930i	−1.57808	−	1.59937i
$111$		0			0
$112$	−195.603	+	112.931i	−1.74645	+	1.00831i
$113$	76.1074	+	131.822i	0.673517	+	1.16657i	0.976900	+	0.213697i	$0.0685505\pi$
$113$	76.1074	+	131.822i	0.673517	+	1.16657i	−0.303383	+	0.952869i	$0.598116\pi$
$114$		0			0
$115$	15.1011	−	14.9002i	0.131314	−	0.129567i
$116$			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	$-0.851148\pi$
$127$		−	114.497i		−	0.901549i	0.892638	−	0.450775i	$-0.148852\pi$
$128$	107.230	−	185.729i	0.837738	−	1.45100i
$129$		0			0
$130$	−75.8678	+	19.7850i	−0.583598	+	0.152193i
$131$	−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	−0.924802	−	0.380449i	$-0.875769\pi$
$137$	−18.2103	+	31.5412i	−0.132922	+	0.230228i	0.791880	+	0.610677i	$0.209103\pi$
$138$		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	$0.921219\pi$
$140$	−503.062	+	131.190i	−3.59330	+	0.937072i
$141$		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
$155$	−111.884	+	110.395i	−0.721833	+	0.712228i
$156$		0			0
$157$	124.141	−	71.6729i	0.790707	−	0.456515i	−0.0495042	−	0.998774i	$-0.515764\pi$
$157$	124.141	−	71.6729i	0.790707	−	0.456515i	0.840212	+	0.542259i	$0.182431\pi$
$158$	95.6291	+	165.634i	0.605248	+	1.04832i
$159$		0			0
$160$	−13.9517	+	13.7660i	−0.0871979	+	0.0860376i
$161$			54.2090i			0.336702i
$162$		0			0
$163$			138.957i			0.852496i	0.904606	+	0.426248i	$0.140165\pi$
$163$			138.957i			0.852496i	−0.904606	+	0.426248i	$0.859835\pi$
$164$	−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	$-0.955617\pi$
$167$	−102.790	−	178.038i	−0.615510	−	1.06610i	0.374784	−	0.927112i	$-0.377717\pi$
$168$		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	−0.926508	−	0.376274i	$-0.877205\pi$
$173$	−23.7687	+	41.1687i	−0.137392	+	0.237969i	0.789117	+	0.614243i	$0.210539\pi$
$174$		0			0
$175$	−319.381	−	4.27863i	−1.82503	−	0.0244493i
$176$	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
$185$	−70.8091	+	18.4658i	−0.382752	+	0.0998153i
$186$		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	−0.999624	−	0.0274255i	$-0.991269\pi$
$193$	−284.807	+	164.433i	−1.47568	+	0.851987i	−0.476061	+	0.879412i	$0.657936\pi$
$194$	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	$-0.426381\pi$
$197$	90.3147			0.458450			0.229225	+	0.973373i	$0.426381\pi$
$198$		0			0
$199$	0.315816			0.00158702			0.000793508	−	1.00000i	$-0.499747\pi$
$199$	0.315816			0.00158702			0.000793508		1.00000i	$0.499747\pi$
$200$	−314.538	+	176.023i	−1.57269	+	0.880116i
$201$		0			0
$202$	243.246	−	140.438i	1.20419	−	0.695238i
$203$	−169.451	−	293.497i	−0.834732	−	1.44580i
$204$		0			0
$205$	−156.798	−	158.912i	−0.764867	−	0.775182i
$206$		−	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
$220$	558.640	−	145.684i	2.53927	−	0.662200i
$221$	35.8828	−	20.7169i	0.162366	−	0.0937418i
$222$		0			0
$223$	43.7853	+	25.2795i	0.196347	+	0.113361i	0.594950	−	0.803763i	$-0.297172\pi$
$223$	43.7853	+	25.2795i	0.196347	+	0.113361i	−0.398604	+	0.917123i	$0.630505\pi$
$224$		−	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	$0.397394\pi$
$227$	−150.507	+	260.685i	−0.663024	+	1.14839i	−0.979817	+	0.199897i	$0.935939\pi$
$228$		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	$-0.375537\pi$
$230$	18.6511	+	71.5196i	0.0810918	+	0.310955i
$231$		0			0
$232$	−331.201	−	191.219i	−1.42759	−	0.824219i
$233$	−27.3269			−0.117283			−0.0586415	−	0.998279i	$-0.518677\pi$
$233$	−27.3269			−0.117283			−0.0586415	+	0.998279i	$0.518677\pi$
$234$		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
$245$	406.580	−	401.170i	1.65951	−	1.63743i
$246$		0			0
$247$	61.7194	−	35.6337i	0.249876	−	0.144266i
$248$	−226.615	−	392.509i	−0.913771	−	1.58270i
$249$		0			0
$250$	−422.840	+	104.241i	−1.69136	+	0.416963i
$251$			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	0.975764	−	0.218824i	$-0.0702222\pi$
$257$	76.6823	+	132.818i	0.298375	+	0.516800i	−0.677390	+	0.735624i	$0.736889\pi$
$258$		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	$-0.666321\pi$
$263$	131.747	−	228.193i	0.500941	−	0.867655i	0.999999	−	0.00108680i	$-0.000345938\pi$
$264$		0			0
$265$	22.5646	+	86.5262i	0.0851494	+	0.326514i
$266$	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
$275$	354.666	+	4.75133i	1.28969	+	0.0172776i
$276$		0			0
$277$	−304.210	−	175.636i	−1.09823	−	0.634065i	−0.162476	−	0.986713i	$-0.551948\pi$
$277$	−304.210	−	175.636i	−1.09823	−	0.634065i	−0.935756	+	0.352648i	$0.885281\pi$
$278$	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	−0.183852	−	0.982954i	$-0.558857\pi$
$283$	162.862	−	94.0285i	0.575485	−	0.332256i	0.759337	+	0.650698i	$0.225523\pi$
$284$	−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
$290$	−324.542	−	328.918i	−1.11911	−	1.13420i
$291$		0			0
$292$	−371.262	+	214.348i	−1.27145	+	0.734070i
$293$	154.985	+	268.442i	0.528958	+	0.916183i	0.999430	+	0.0337676i	$0.0107506\pi$
$293$	154.985	+	268.442i	0.528958	+	0.916183i	−0.470471	+	0.882415i	$0.655916\pi$
$294$		0			0
$295$	169.625	+	171.913i	0.575000	+	0.582754i
$296$		−	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	$-0.924706\pi$
$307$		−	143.887i		−	0.468687i	0.972154	−	0.234344i	$-0.0752941\pi$
$308$	−737.610	+	1277.58i	−2.39484	+	4.14798i
$309$		0			0
$310$	−138.186	−	529.889i	−0.445762	−	1.70932i
$311$	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	0.950449	−	0.310880i	$-0.100624\pi$
$313$	361.967	+	208.982i	1.15644	+	0.667673i	0.205995	+	0.978553i	$0.433957\pi$
$314$			499.416i			1.59050i
$315$		0			0
$316$	−446.759			−1.41379
$317$	−33.5344	+	58.0833i	−0.105787	+	0.183228i	−0.914059	−	0.405580i	$-0.867069\pi$
$317$	−33.5344	+	58.0833i	−0.105787	+	0.183228i	0.808273	+	0.588808i	$0.200403\pi$
$318$		0			0
$319$	188.172	+	325.923i	0.589880	+	1.02170i
$320$	71.9879	+	276.045i	0.224962	+	0.862640i
$321$		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
$335$	177.918	+	180.318i	0.531100	+	0.538262i
$336$		0			0
$337$	461.486	−	266.439i	1.36940	−	0.790621i	0.378545	−	0.925583i	$-0.376424\pi$
$337$	461.486	−	266.439i	1.36940	−	0.790621i	0.990851	+	0.134962i	$0.0430911\pi$
$338$	−259.109	−	448.790i	−0.766594	−	1.32778i
$339$		0			0
$340$	266.646	−	263.097i	0.784252	−	0.773816i
$341$			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	0.867972	−	0.496613i	$-0.165423\pi$
$347$	1.35563	+	2.34802i	0.00390672	+	0.00676664i	−0.864065	+	0.503380i	$0.832090\pi$
$348$		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	−0.987244	−	0.159215i	$-0.949104\pi$
$353$	−125.575	+	217.503i	−0.355737	+	0.616155i	0.631506	+	0.775371i	$0.282437\pi$
$354$		0			0
$355$	−327.829	+	85.4924i	−0.923463	+	0.240824i
$356$	−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
$365$	−254.860	+	66.4632i	−0.698247	+	0.182091i
$366$		0			0
$367$	195.196	+	112.696i	0.531868	+	0.307074i	0.741777	−	0.670647i	$-0.233983\pi$
$367$	195.196	+	112.696i	0.531868	+	0.307074i	−0.209909	+	0.977721i	$0.567317\pi$
$368$	−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	−0.952172	−	0.305563i	$-0.901156\pi$
$373$	−434.035	+	250.590i	−1.16363	+	0.671824i	−0.211461	+	0.977386i	$0.567822\pi$
$374$	−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	$0.498583\pi$
$380$	458.638	−	452.535i	1.20694	−	1.19088i
$381$		0			0
$382$	−862.068	+	497.715i	−2.25672	+	1.30292i
$383$	−207.530	−	359.452i	−0.541853	−	0.938516i	−0.998798	−	0.0490215i	$-0.984390\pi$
$383$	−207.530	−	359.452i	−0.541853	−	0.938516i	0.456945	−	0.889495i	$-0.348944\pi$
$384$		0			0
$385$	−645.164	+	636.579i	−1.67575	+	1.65345i
$386$		−	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	$-0.894605\pi$
$397$		−	258.122i		−	0.650183i	0.945683	−	0.325091i	$-0.105395\pi$
$398$	−0.550152	+	0.952891i	−0.00138229	+	0.00239420i
$399$		0			0
$400$	5.92016	−	441.914i	0.0148004	−	1.10478i
$401$	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	$0.598935\pi$
$410$	752.617	−	196.270i	1.83565	−	0.478707i
$411$		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
$425$	200.834	−	112.392i	0.472550	−	0.264451i
$426$		0			0
$427$	1012.08	−	584.325i	2.37021	−	1.36844i
$428$	−88.1880	−	152.746i	−0.206047	−	0.356884i
$429$		0			0
$430$	−799.955	−	810.744i	−1.86036	−	1.88545i
$431$			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	$-0.717200\pi$
$433$		−	672.095i		−	1.55218i	0.630620	−	0.776091i	$-0.282800\pi$
$434$	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	−0.708391	−	0.705821i	$-0.750578\pi$
$443$	113.879	−	197.244i	0.257063	−	0.445247i	0.965454	+	0.260574i	$0.0839118\pi$
$444$		0			0
$445$	−400.270	+	104.384i	−0.899482	+	0.234570i
$446$	−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
$455$	72.5548	+	278.219i	0.159461	+	0.611470i
$456$		0			0
$457$	−155.873	−	89.9933i	−0.341079	−	0.196922i	0.319670	−	0.947529i	$-0.396428\pi$
$457$	−155.873	−	89.9933i	−0.341079	−	0.196922i	−0.660749	+	0.750607i	$0.729761\pi$
$458$	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	−0.485173	−	0.874418i	$-0.661243\pi$
$463$	13.6629	−	7.88827i	0.0295095	−	0.0170373i	0.514682	+	0.857381i	$0.327910\pi$
$464$	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	$-0.359060\pi$
$467$	400.171			0.856896			0.428448	+	0.903566i	$0.359060\pi$
$468$		0			0
$469$	−647.294			−1.38016
$470$	−701.484	+	692.149i	−1.49252	+	1.47266i
$471$		0			0
$472$	−603.099	+	348.199i	−1.27775	+	0.737711i
$473$	463.820	+	803.360i	0.980592	+	1.69843i
$474$		0			0
$475$	345.440	−	193.317i	0.727242	−	0.406983i
$476$			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	$0.109354\pi$
$487$			328.071i			0.673658i	−0.941566	+	0.336829i	$0.890646\pi$
$488$	659.390	−	1142.10i	1.35121	−	2.34036i
$489$		0			0
$490$	502.160	+	1925.58i	1.02482	+	3.92976i
$491$	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	$0.809165\pi$
$500$	282.982	−	977.130i	0.565964	−	1.95426i
$501$		0			0
$502$	−353.602	−	204.152i	−0.704385	−	0.406677i
$503$	139.725			0.277784			0.138892	−	0.990308i	$-0.455646\pi$
$503$	139.725			0.277784			0.138892	+	0.990308i	$0.455646\pi$
$504$		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
$515$	126.329	+	128.033i	0.245300	+	0.248608i
$516$		0			0
$517$	695.095	−	401.313i	1.34448	−	0.776234i
$518$	325.733	+	564.186i	0.628828	+	1.08916i
$519$		0			0
$520$	227.886	+	230.960i	0.438243	+	0.444153i
$521$		−	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	$0.298489\pi$
$523$			843.303i			1.61243i	−0.591620	+	0.806217i	$0.701511\pi$
$524$	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
$535$	−27.3445	−	104.856i	−0.0511113	−	0.195992i
$536$	−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
$545$	1.37802	+	5.28417i	0.00252848	+	0.00969572i
$546$		0			0
$547$	764.052	+	441.126i	1.39680	+	0.806446i	0.994057	−	0.108865i	$-0.0347216\pi$
$547$	764.052	+	441.126i	1.39680	+	0.806446i	0.402748	+	0.915311i	$0.368055\pi$
$548$	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	$-0.677659\pi$
$557$	−589.979			−1.05921			−0.529604	+	0.848245i	$0.677659\pi$
$558$		0			0
$559$	294.278			0.526436
$560$	793.178	+	803.875i	1.41639	+	1.43549i
$561$		0			0
$562$	−881.401	+	508.877i	−1.56833	+	0.905476i
$563$	−393.077	−	680.830i	−0.698183	−	1.20929i	−0.969096	−	0.246685i	$-0.920659\pi$
$563$	−393.077	−	680.830i	−0.698183	−	1.20929i	0.270912	−	0.962604i	$-0.412675\pi$
$564$		0			0
$565$	541.753	−	534.544i	0.958855	−	0.946096i
$566$			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	$-0.755382\pi$
$577$		−	802.089i		−	1.39010i	0.718960	−	0.695051i	$-0.244618\pi$
$578$	355.811	−	616.282i	0.615590	−	1.06623i
$579$		0			0
$580$	1044.43	−	272.370i	1.80074	−	0.469603i
$581$	−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	$0.560340\pi$
$587$	−554.555	+	960.517i	−0.944727	+	1.63632i	−0.756296	+	0.654230i	$0.772993\pi$
$588$		0			0
$589$	248.879	+	431.072i	0.422545	+	0.731870i
$590$	−814.186	+	212.326i	−1.37998	+	0.359875i
$591$		0			0
$592$	224.065	+	129.364i	0.378488	+	0.218520i
$593$	−633.417			−1.06816			−0.534078	−	0.845435i	$-0.679341\pi$
$593$	−633.417			−1.06816			−0.534078	+	0.845435i	$0.679341\pi$
$594$		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
$605$	285.787	−	281.984i	0.472375	−	0.466089i
$606$		0			0
$607$	−779.225	+	449.886i	−1.28373	+	0.741163i	−0.977528	−	0.210804i	$-0.932392\pi$
$607$	−779.225	+	449.886i	−1.28373	+	0.741163i	−0.306203	+	0.951966i	$0.599059\pi$
$608$	31.0346	+	53.7536i	0.0510438	+	0.0884104i
$609$		0			0
$610$	1134.23	−	1119.13i	1.85939	−	1.83465i
$611$		−	254.619i		−	0.416726i
$612$		0			0
$613$		−	966.059i		−	1.57595i	−0.615706	−	0.787976i	$-0.711129\pi$
$613$		−	966.059i		−	1.57595i	0.615706	−	0.787976i	$-0.288871\pi$
$614$	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	0.730407	−	0.683012i	$-0.239330\pi$
$617$	−139.629	−	241.844i	−0.226302	−	0.391967i	−0.956709	+	0.291045i	$0.905997\pi$
$618$		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
$625$	326.888	−	532.700i	0.523020	−	0.852320i
$626$	−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
$635$	−553.957	+	144.463i	−0.872373	+	0.227500i
$636$		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	−0.391673	−	0.920105i	$-0.628103\pi$
$643$	134.596	−	77.7089i	0.209325	−	0.120854i	0.600997	+	0.799251i	$0.294770\pi$
$644$	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	$-0.669705\pi$
$647$	−657.668			−1.01649			−0.508244	+	0.861213i	$0.669705\pi$
$648$		0			0
$649$	685.301			1.05593
$650$	191.448	+	342.100i	0.294535	+	0.526307i
$651$		0			0
$652$	979.358	−	565.433i	1.50208	−	0.867228i
$653$	503.101	+	871.396i	0.770446	+	1.33445i	0.937319	+	0.348473i	$0.113300\pi$
$653$	503.101	+	871.396i	0.770446	+	1.33445i	−0.166873	+	0.985978i	$0.553367\pi$
$654$		0			0
$655$	600.886	+	608.990i	0.917383	+	0.929755i
$656$			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
$670$	−853.994	+	222.707i	−1.27462	+	0.332399i
$671$	−1123.90	+	648.882i	−1.67496	+	0.967037i
$672$		0			0
$673$	−1083.26	−	625.421i	−1.60960	−	0.929303i	−0.989459	−	0.144812i	$-0.953742\pi$
$673$	−1083.26	−	625.421i	−1.60960	−	0.929303i	−0.620141	−	0.784491i	$-0.712925\pi$
$674$			1856.55i			2.75452i
$675$		0			0
$676$	1210.50			1.79068
$677$	−302.147	+	523.335i	−0.446303	+	0.773020i	−0.998142	−	0.0609308i	$-0.980593\pi$
$677$	−302.147	+	523.335i	−0.446303	+	0.773020i	0.551839	+	0.833951i	$0.313926\pi$
$678$		0			0
$679$	−408.203	−	707.029i	−0.601183	−	1.04128i
$680$	167.462	+	642.150i	0.246268	+	0.944339i
$681$		0			0
$682$	−1345.71	−	776.945i	−1.97318	−	1.13922i
$683$	−707.854			−1.03639			−0.518195	−	0.855263i	$-0.673396\pi$
$683$	−707.854			−1.03639			−0.518195	+	0.855263i	$0.673396\pi$
$684$		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
$695$	−269.726	+	266.137i	−0.388095	+	0.382931i
$696$		0			0
$697$	−355.961	+	205.514i	−0.510705	+	0.294855i
$698$	346.403	+	599.987i	0.496279	+	0.859580i
$699$		0			0
$700$	1269.44	+	2268.38i	1.81349	+	3.24055i
$701$		−	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
$715$	−80.5707	−	308.957i	−0.112686	−	0.432107i
$716$	−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
$725$	663.081	+	8.88306i	0.914595	+	0.0122525i
$726$		0			0
$727$	692.899	+	400.045i	0.953093	+	0.550269i	0.894040	−	0.447986i	$-0.147859\pi$
$727$	692.899	+	400.045i	0.953093	+	0.550269i	0.0590528	+	0.998255i	$0.481192\pi$
$728$	−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	−0.505711	−	0.862703i	$-0.668770\pi$
$733$	−8.38843	+	4.84307i	−0.0114440	+	0.00660718i	0.494267	+	0.869310i	$0.335436\pi$
$734$	−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	$0.769749\pi$
$740$	418.277	+	423.918i	0.565239	+	0.572862i
$741$		0			0
$742$	689.416	−	398.034i	0.929131	−	0.536434i
$743$	390.228	+	675.894i	0.525206	+	0.909683i	0.999569	+	0.0293537i	$0.00934491\pi$
$743$	390.228	+	675.894i	0.525206	+	0.909683i	−0.474364	+	0.880329i	$0.657322\pi$
$744$		0			0
$745$	−672.212	−	681.278i	−0.902298	−	0.914467i
$746$		−	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	$-0.979907\pi$
$757$		−	95.5082i		−	0.126167i	0.998008	−	0.0630834i	$-0.0200934\pi$
$758$	−5.87697	+	10.1792i	−0.00775325	+	0.0134290i
$759$		0			0
$760$	288.040	+	1104.52i	0.378999	+	1.45331i
$761$	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	$0.827114\pi$
$770$	−796.831	−	3055.53i	−1.03485	−	3.96822i
$771$		0			0
$772$	2317.83	+	1338.20i	3.00237	+	1.73342i
$773$	1290.89			1.66998			0.834988	−	0.550269i	$-0.185475\pi$
$773$	1290.89			1.66998			0.834988	+	0.550269i	$0.185475\pi$
$774$		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
$785$	−503.398	−	510.187i	−0.641271	−	0.649920i
$786$		0			0
$787$	74.1557	−	42.8138i	0.0942258	−	0.0544013i	−0.452147	−	0.891944i	$-0.649342\pi$
$787$	74.1557	−	42.8138i	0.0942258	−	0.0544013i	0.546372	+	0.837542i	$0.316008\pi$
$788$	−367.502	−	636.532i	−0.466373	−	0.807781i
$789$		0			0
$790$	680.714	−	671.656i	0.861663	−	0.850197i
$791$			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	0.999600	−	0.0282806i	$-0.00900321\pi$
$797$	378.821	+	656.137i	0.475308	+	0.823258i	−0.524292	+	0.851539i	$0.675670\pi$
$798$		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
$805$	262.274	−	68.3965i	0.325806	−	0.0849646i
$806$	−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
$815$	672.299	−	175.324i	0.824907	−	0.215122i
$816$		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	−0.629030	−	0.777381i	$-0.716548\pi$
$823$	−222.467	+	128.441i	−0.270312	+	0.156065i	0.358717	+	0.933446i	$0.383214\pi$
$824$	−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	$-0.497466\pi$
$827$	13.1651			0.0159191			0.00795957	+	0.999968i	$0.497466\pi$
$828$		0			0
$829$	−1494.14			−1.80234			−0.901171	−	0.433464i	$-0.857291\pi$
$829$	−1494.14			−1.80234			−0.901171	+	0.433464i	$0.857291\pi$
$830$	−31.7132	+	31.2912i	−0.0382087	+	0.0377003i
$831$		0			0
$832$	222.395	−	128.400i	0.267301	−	0.154326i
$833$	−525.812	−	910.733i	−0.631227	−	1.09332i
$834$		0			0
$835$	−731.689	+	721.952i	−0.876274	+	0.864613i
$836$		−	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
$850$	−10.7407	+	801.748i	−0.0126362	+	0.943233i
$851$	53.7776	−	31.0485i	0.0631934	−	0.0364847i
$852$		0			0
$853$	−54.0966	−	31.2327i	−0.0634192	−	0.0366151i	0.467955	−	0.883752i	$-0.344991\pi$
$853$	−54.0966	−	31.2327i	−0.0634192	−	0.0366151i	−0.531374	+	0.847137i	$0.678324\pi$
$854$			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	$-0.483178\pi$
$857$	763.782	−	1322.91i	0.891228	−	1.54365i	0.838405	−	0.545048i	$-0.183489\pi$
$858$		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	$0.665538\pi$
$860$	2574.39	−	671.359i	2.99348	−	0.780649i
$861$		0			0
$862$	−290.768	−	167.875i	−0.337318	−	0.194751i
$863$	593.430			0.687636			0.343818	−	0.939036i	$-0.388280\pi$
$863$	593.430			0.687636			0.343818	+	0.939036i	$0.388280\pi$
$864$		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
$875$	382.267	+	1550.62i	0.436877	+	1.77214i
$876$		0			0
$877$	−69.3714	+	40.0516i	−0.0791008	+	0.0456689i	−0.539029	−	0.842287i	$-0.681209\pi$
$877$	−69.3714	+	40.0516i	−0.0791008	+	0.0456689i	0.459928	+	0.887956i	$0.347875\pi$
$878$	−180.738	−	313.047i	−0.205851	−	0.356545i
$879$		0			0
$880$	−880.808	−	892.687i	−1.00092	−	1.01442i
$881$			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	$-0.784394\pi$
$883$		−	1106.80i		−	1.25345i	0.779239	−	0.626727i	$-0.215606\pi$
$884$	−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	0.578008	−	0.816031i	$-0.303830\pi$
$887$	−370.500	−	641.725i	−0.417700	−	0.723477i	−0.995708	+	0.0925538i	$0.970497\pi$
$888$		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
$895$	−601.377	+	156.829i	−0.671930	+	0.175228i
$896$	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
$905$	15.2377	+	58.4307i	0.0168373	+	0.0645643i
$906$		0			0
$907$	−256.204	−	147.920i	−0.282475	−	0.163087i	0.352069	−	0.935974i	$-0.385478\pi$
$907$	−256.204	−	147.920i	−0.282475	−	0.163087i	−0.634543	+	0.772887i	$0.718812\pi$
$908$	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	$0.489586\pi$
$920$	217.723	−	214.826i	0.236655	−	0.233506i
$921$		0			0
$922$	1759.63	−	1015.92i	1.90849	−	1.10187i
$923$	152.487	+	264.115i	0.165208	+	0.286148i
$924$		0			0
$925$	178.682	+	319.289i	0.193170	+	0.345178i
$926$			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	$0.0296566\pi$
$937$			174.346i			0.186068i	−0.995663	+	0.0930341i	$0.970343\pi$
$938$	1127.59	−	1953.04i	1.20212	−	2.08213i
$939$		0			0
$940$	−580.883	−	2227.45i	−0.617960	−	2.36963i
$941$	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	−0.547557	−	0.836769i	$-0.684442\pi$
$947$	426.988	−	739.564i	0.450884	−	0.780955i	0.998441	+	0.0558137i	$0.0177753\pi$
$948$		0			0
$949$	118.546	+	205.327i	0.124916	+	0.216362i
$950$	−18.4744	+	1379.03i	−0.0194467	+	1.45161i
$951$		0			0
$952$	−1468.56	−	847.874i	−1.54261	−	0.890624i
$953$	−1103.28			−1.15769			−0.578843	−	0.815439i	$-0.696496\pi$
$953$	−1103.28			−1.15769			−0.578843	+	0.815439i	$0.696496\pi$
$954$		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
$965$	1154.91	+	1170.48i	1.19679	+	1.21293i
$966$		0			0
$967$	−886.133	+	511.609i	−0.916373	+	0.529068i	−0.882476	−	0.470357i	$-0.844125\pi$
$967$	−886.133	+	511.609i	−0.916373	+	0.529068i	−0.0338972	+	0.999425i	$0.510792\pi$
$968$	578.845	+	1002.59i	0.597981	+	1.03573i
$969$		0			0
$970$	−781.815	−	792.359i	−0.805995	−	0.816864i
$971$			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	0.604587	−	0.796539i	$-0.293338\pi$
$977$	−378.616	−	655.783i	−0.387530	−	0.671221i	−0.992117	+	0.125318i	$0.960005\pi$
$978$		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	$0.419826\pi$
$983$	−701.951	+	1215.82i	−0.714091	+	1.23684i	−0.963309	+	0.268394i	$0.913507\pi$
$984$		0			0
$985$	−113.952	−	436.959i	−0.115687	−	0.443614i
$986$	−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
$995$	−0.398471	−	1.52798i	−0.000400473	−	0.00153566i
$996$		0			0
$997$	−1207.19	−	696.970i	−1.21082	−	0.699067i	−0.247882	−	0.968790i	$-0.579735\pi$
$997$	−1207.19	−	696.970i	−1.21082	−	0.699067i	−0.962938	+	0.269723i	$0.913068\pi$
$998$	−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.269.4		48
3.2	odd	2	inner	405.3.h.k.269.21		48
5.4	even	2	inner	405.3.h.k.269.22		48
9.2	odd	6		405.3.d.b.404.3	✓	24
9.4	even	3	inner	405.3.h.k.134.3		48
9.5	odd	6	inner	405.3.h.k.134.22		48
9.7	even	3		405.3.d.b.404.22	yes	24
15.14	odd	2	inner	405.3.h.k.269.3		48
45.4	even	6	inner	405.3.h.k.134.21		48
45.14	odd	6	inner	405.3.h.k.134.4		48
45.29	odd	6		405.3.d.b.404.21	yes	24
45.34	even	6		405.3.d.b.404.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.3.d.b.404.3	✓	24	9.2	odd	6
405.3.d.b.404.4	yes	24	45.34	even	6
405.3.d.b.404.21	yes	24	45.29	odd	6
405.3.d.b.404.22	yes	24	9.7	even	3
405.3.h.k.134.3		48	9.4	even	3	inner
405.3.h.k.134.4		48	45.14	odd	6	inner
405.3.h.k.134.21		48	45.4	even	6	inner
405.3.h.k.134.22		48	9.5	odd	6	inner
405.3.h.k.269.3		48	15.14	odd	2	inner
405.3.h.k.269.4		48	1.1	even	1	trivial
405.3.h.k.269.21		48	3.2	odd	2	inner
405.3.h.k.269.22		48	5.4	even	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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.74200 + 3.01723i) q^{2} +(-4.06913 - 7.04793i) q^{4} +(-1.26172 - 4.83819i) q^{5} +(11.0647 + 6.38818i) q^{7} +14.4177 q^{8} +(16.7958 + 4.62123i) q^{10} +(-12.2871 - 7.09395i) q^{11} +(-3.89787 + 2.25044i) q^{13} +(-38.5493 + 22.2564i) q^{14} +(-8.83907 + 15.3097i) q^{16} -9.20574 q^{17} -15.8342 q^{19} +(-28.9651 + 28.5797i) q^{20} +(42.8082 - 24.7153i) q^{22} +(2.12146 + 3.67447i) q^{23} +(-21.8161 + 12.2089i) q^{25} -15.6810i q^{26} -103.977i q^{28} +(-22.9719 - 13.2628i) q^{29} +(-15.7179 - 27.2242i) q^{31} +(-1.95998 - 3.39479i) q^{32} +(16.0364 - 27.7759i) q^{34} +(16.9468 - 61.5930i) q^{35} -14.6355i q^{37} +(27.5831 - 47.7753i) q^{38} +(-18.1910 - 69.7554i) q^{40} +(38.6673 - 22.3246i) q^{41} +(-56.6228 - 32.6912i) q^{43} +115.465i q^{44} -14.7823 q^{46} +(-28.2856 + 48.9921i) q^{47} +(57.1178 + 98.9309i) q^{49} +(1.16674 - 87.0922i) q^{50} +(31.7218 + 18.3146i) q^{52} -17.8840 q^{53} +(-18.8190 + 68.3978i) q^{55} +(159.527 + 92.1027i) q^{56} +(80.0340 - 46.2076i) q^{58} +(-41.8306 + 24.1509i) q^{59} +(45.7349 - 79.2151i) q^{61} +109.522 q^{62} -57.0554 q^{64} +(15.8060 + 16.0192i) q^{65} +(-43.8758 + 25.3317i) q^{67} +(37.4593 + 64.8815i) q^{68} +(156.319 + 158.427i) q^{70} -67.7587i q^{71} -52.6768i q^{73} +(44.1586 + 25.4950i) q^{74} +(64.4312 + 111.598i) q^{76} +(-90.6349 - 156.984i) q^{77} +(27.4481 - 47.5415i) q^{79} +(85.2237 + 23.4485i) q^{80} +155.558i q^{82} +(-1.27876 + 2.21487i) q^{83} +(11.6151 + 44.5391i) q^{85} +(197.274 - 113.896i) q^{86} +(-177.151 - 102.278i) q^{88} -82.7313i q^{89} -57.5048 q^{91} +(17.2650 - 29.9038i) q^{92} +(-98.5469 - 170.688i) q^{94} +(19.9782 + 76.6086i) q^{95} +(-55.3388 - 31.9499i) q^{97} -397.997 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} + 24 q^{10} - 96 q^{16} - 48 q^{25} - 144 q^{34} - 72 q^{40} - 336 q^{46} + 288 q^{49} - 264 q^{55} + 360 q^{61} - 144 q^{64} + 156 q^{70} - 48 q^{76} + 480 q^{79} + 456 q^{85} - 96 q^{91}+ \cdots - 384 q^{94}+O(q^{100}) \) 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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