LMFDB - Embedded newform 425.3.u.b.401.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,3,Mod(126,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 11])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.126"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.u (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,8,8,0,0,-8,-8,24,-16,0,-8,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5804112353$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			401.1
Root			$0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	425.401
Dual form			425.3.u.b.301.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.15851 - 2.79690i) q^{2} +(0.675577 + 0.451406i) q^{3} +(-3.65205 - 3.65205i) q^{4} +(2.04520 - 1.36656i) q^{6} +(7.70353 + 1.53233i) q^{7} +(-3.25778 + 1.34942i) q^{8} +(-3.19151 - 7.70500i) q^{9} +(4.48649 + 6.71450i) q^{11} +(-0.818684 - 4.11580i) q^{12} +(0.798835 - 0.798835i) q^{13} +(13.2104 - 19.7707i) q^{14} -9.98414i q^{16} +(6.50562 - 15.7060i) q^{17} -25.2475 q^{18} +(1.07647 - 2.59882i) q^{19} +(4.51262 + 4.51262i) q^{21} +(23.9774 - 4.76941i) q^{22} +(7.13426 - 4.76696i) q^{23} +(-2.81002 - 0.558947i) q^{24} +(-1.30880 - 3.15972i) q^{26} +(2.74858 - 13.8181i) q^{27} +(-22.5376 - 33.7298i) q^{28} +(-0.599020 - 3.01148i) q^{29} +(-7.13254 + 10.6746i) q^{31} +(-40.9557 - 16.9644i) q^{32} +6.56139i q^{33} +(-36.3911 - 36.3911i) q^{34} +(-16.4835 + 39.7946i) q^{36} +(-19.6817 - 13.1509i) q^{37} +(-6.02153 - 6.02153i) q^{38} +(0.900273 - 0.179075i) q^{39} +(21.4206 + 4.26082i) q^{41} +(17.8493 - 7.39341i) q^{42} +(8.89197 + 21.4671i) q^{43} +(8.13684 - 40.9066i) q^{44} +(-5.06757 - 25.4764i) q^{46} +(-55.6597 + 55.6597i) q^{47} +(4.50690 - 6.74505i) q^{48} +(11.7262 + 4.85715i) q^{49} +(11.4848 - 7.67390i) q^{51} -5.83478 q^{52} +(22.9922 - 55.5080i) q^{53} +(-35.4634 - 23.6959i) q^{54} +(-27.1642 + 5.40329i) q^{56} +(1.90036 - 1.26978i) q^{57} +(-9.11677 - 1.81344i) q^{58} +(-25.3733 + 10.5100i) q^{59} +(7.11302 - 35.7596i) q^{61} +(21.5926 + 32.3156i) q^{62} +(-12.7793 - 64.2461i) q^{63} +(-66.6561 + 66.6561i) q^{64} +(18.3515 + 7.60145i) q^{66} +117.219i q^{67} +(-81.1179 + 33.6001i) q^{68} +6.97157 q^{69} +(88.1108 + 58.8738i) q^{71} +(20.7945 + 20.7945i) q^{72} +(59.8620 - 11.9073i) q^{73} +(-59.5832 + 39.8122i) q^{74} +(-13.4223 + 5.55971i) q^{76} +(24.2730 + 58.6001i) q^{77} +(0.542122 - 2.72543i) q^{78} +(52.9382 + 79.2276i) q^{79} +(-44.9799 + 44.9799i) q^{81} +(36.7331 - 54.9749i) q^{82} +(109.791 + 45.4770i) q^{83} -32.9607i q^{84} +70.3428 q^{86} +(0.954715 - 2.30489i) q^{87} +(-23.6767 - 15.8202i) q^{88} +(-61.4534 - 61.4534i) q^{89} +(7.37792 - 4.92977i) q^{91} +(-43.4639 - 8.64551i) q^{92} +(-9.63715 + 3.99184i) q^{93} +(91.1920 + 220.157i) q^{94} +(-20.0109 - 29.9484i) q^{96} +(-4.79748 - 24.1185i) q^{97} +(27.1699 - 27.1699i) q^{98} +(37.4165 - 55.9978i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} - 8 q^{6} - 8 q^{7} + 24 q^{8} - 16 q^{9} - 8 q^{11} - 48 q^{12} - 16 q^{13} + 8 q^{14} - 56 q^{18} - 64 q^{21} + 104 q^{22} + 56 q^{23} - 80 q^{24} + 176 q^{26} - 40 q^{27} - 152 q^{28}+ \cdots - 224 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^3 - 8 * q^6 - 8 * q^7 + 24 * q^8 - 16 * q^9 - 8 * q^11 - 48 * q^12 - 16 * q^13 + 8 * q^14 - 56 * q^18 - 64 * q^21 + 104 * q^22 + 56 * q^23 - 80 * q^24 + 176 * q^26 - 40 * q^27 - 152 * q^28 + 48 * q^29 + 24 * q^31 - 88 * q^32 - 136 * q^34 - 128 * q^36 - 32 * q^37 + 120 * q^38 + 48 * q^39 + 48 * q^41 - 16 * q^42 + 232 * q^43 + 120 * q^44 - 88 * q^46 - 192 * q^47 - 136 * q^48 + 16 * q^49 + 136 * q^51 + 384 * q^52 + 32 * q^53 + 8 * q^54 - 120 * q^56 - 24 * q^57 - 240 * q^58 - 48 * q^59 - 160 * q^61 + 168 * q^62 - 56 * q^63 - 64 * q^64 - 8 * q^66 - 272 * q^68 + 240 * q^69 + 40 * q^71 - 40 * q^72 - 48 * q^73 - 160 * q^74 + 80 * q^76 + 48 * q^77 + 400 * q^78 - 136 * q^79 - 424 * q^81 + 64 * q^82 + 264 * q^83 + 832 * q^86 - 208 * q^87 - 264 * q^88 + 160 * q^89 + 320 * q^91 - 24 * q^92 + 64 * q^93 + 32 * q^94 - 56 * q^96 - 48 * q^97 + 120 * q^98 - 224 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{3}{16}\right)$

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 $

$2$	1.15851	−	2.79690i	0.579256	−	1.39845i	−0.314225	−	0.949348i	$-0.601745\pi$
$2$	1.15851	−	2.79690i	0.579256	−	1.39845i	0.893481	−	0.449100i	$-0.148255\pi$
$3$	0.675577	+	0.451406i	0.225192	+	0.150469i	0.663049	−	0.748576i	$-0.269262\pi$
$3$	0.675577	+	0.451406i	0.225192	+	0.150469i	−0.437857	+	0.899045i	$0.644262\pi$
$4$	−3.65205	−	3.65205i	−0.913014	−	0.913014i
$5$		0			0
$5$		0			0
$6$	2.04520	−	1.36656i	0.340867	−	0.227760i
$7$	7.70353	+	1.53233i	1.10050	+	0.218904i	0.711746	−	0.702436i	$-0.247904\pi$
$7$	7.70353	+	1.53233i	1.10050	+	0.218904i	0.388757	+	0.921340i	$0.372904\pi$
$8$	−3.25778	+	1.34942i	−0.407223	+	0.168677i
$9$	−3.19151	−	7.70500i	−0.354613	−	0.856111i
$10$		0			0
$11$	4.48649	+	6.71450i	0.407863	+	0.610410i	0.977360	−	0.211584i	$-0.0678621\pi$
$11$	4.48649	+	6.71450i	0.407863	+	0.610410i	−0.569497	+	0.821993i	$0.692862\pi$
$12$	−0.818684	−	4.11580i	−0.0682236	−	0.342983i
$13$	0.798835	−	0.798835i	0.0614489	−	0.0614489i	−0.675715	−	0.737163i	$-0.736165\pi$
$13$	0.798835	−	0.798835i	0.0614489	−	0.0614489i	0.737163	+	0.675715i	$0.236165\pi$
$14$	13.2104	−	19.7707i	0.943599	−	1.41220i
$15$		0			0
$16$		−	9.98414i		−	0.624009i
$17$	6.50562	−	15.7060i	0.382683	−	0.923880i
$17$	6.50562	−	15.7060i	0.382683	−	0.923880i
$18$	−25.2475			−1.40264
$19$	1.07647	−	2.59882i	0.0566561	−	0.136780i	−0.893017	−	0.450023i	$-0.851416\pi$
$19$	1.07647	−	2.59882i	0.0566561	−	0.136780i	0.949673	+	0.313244i	$0.101416\pi$
$20$		0			0
$21$	4.51262	+	4.51262i	0.214887	+	0.214887i
$22$	23.9774	−	4.76941i	1.08988	−	0.216791i
$23$	7.13426	−	4.76696i	0.310185	−	0.207259i	−0.390727	−	0.920507i	$-0.627776\pi$
$23$	7.13426	−	4.76696i	0.310185	−	0.207259i	0.700912	+	0.713247i	$0.252776\pi$
$24$	−2.81002	−	0.558947i	−0.117084	−	0.0232895i
$25$		0			0
$26$	−1.30880	−	3.15972i	−0.0503384	−	0.121528i
$27$	2.74858	−	13.8181i	0.101799	−	0.511780i
$28$	−22.5376	−	33.7298i	−0.804913	−	1.20464i
$29$	−0.599020	−	3.01148i	−0.0206559	−	0.103844i	0.969082	−	0.246739i	$-0.0793590\pi$
$29$	−0.599020	−	3.01148i	−0.0206559	−	0.103844i	−0.989738	+	0.142895i	$0.954359\pi$
$30$		0			0
$31$	−7.13254	+	10.6746i	−0.230082	+	0.344342i	−0.928490	−	0.371358i	$-0.878892\pi$
$31$	−7.13254	+	10.6746i	−0.230082	+	0.344342i	0.698408	+	0.715700i	$0.253892\pi$
$32$	−40.9557	−	16.9644i	−1.27987	−	0.530138i
$33$			6.56139i			0.198830i
$34$	−36.3911	−	36.3911i	−1.07033	−	1.07033i
$35$		0			0
$36$	−16.4835	+	39.7946i	−0.457875	+	1.10541i
$37$	−19.6817	−	13.1509i	−0.531938	−	0.355429i	0.260411	−	0.965498i	$-0.416142\pi$
$37$	−19.6817	−	13.1509i	−0.531938	−	0.355429i	−0.792349	+	0.610068i	$0.791142\pi$
$38$	−6.02153	−	6.02153i	−0.158461	−	0.158461i
$39$	0.900273	−	0.179075i	0.0230839	−	0.00459168i
$40$		0			0
$41$	21.4206	+	4.26082i	0.522453	+	0.103922i	0.449270	−	0.893396i	$-0.351684\pi$
$41$	21.4206	+	4.26082i	0.522453	+	0.103922i	0.0731833	+	0.997319i	$0.476684\pi$
$42$	17.8493	−	7.39341i	0.424982	−	0.176034i
$43$	8.89197	+	21.4671i	0.206790	+	0.499235i	0.992914	−	0.118833i	$-0.0379154\pi$
$43$	8.89197	+	21.4671i	0.206790	+	0.499235i	−0.786124	+	0.618069i	$0.787915\pi$
$44$	8.13684	−	40.9066i	0.184928	−	0.929696i
$45$		0			0
$46$	−5.06757	−	25.4764i	−0.110164	−	0.553834i
$47$	−55.6597	+	55.6597i	−1.18425	+	1.18425i	−0.205617	+	0.978632i	$0.565920\pi$
$47$	−55.6597	+	55.6597i	−1.18425	+	1.18425i	−0.978632	+	0.205617i	$0.934080\pi$
$48$	4.50690	−	6.74505i	0.0938937	−	0.140522i
$49$	11.7262	+	4.85715i	0.239310	+	0.0991254i
$50$		0			0
$51$	11.4848	−	7.67390i	0.225192	−	0.150469i
$52$	−5.83478			−0.112207
$53$	22.9922	−	55.5080i	0.433815	−	1.04732i	−0.544232	−	0.838935i	$-0.683179\pi$
$53$	22.9922	−	55.5080i	0.433815	−	1.04732i	0.978047	−	0.208386i	$-0.0668212\pi$
$54$	−35.4634	−	23.6959i	−0.656730	−	0.438813i
$55$		0			0
$56$	−27.1642	+	5.40329i	−0.485074	+	0.0964873i
$57$	1.90036	−	1.26978i	0.0333396	−	0.0222768i
$58$	−9.11677	−	1.81344i	−0.157186	−	0.0312662i
$59$	−25.3733	+	10.5100i	−0.430057	+	0.178135i	−0.587202	−	0.809440i	$-0.699771\pi$
$59$	−25.3733	+	10.5100i	−0.430057	+	0.178135i	0.157146	+	0.987575i	$0.449771\pi$
$60$		0			0
$61$	7.11302	−	35.7596i	0.116607	−	0.586223i	−0.877659	−	0.479286i	$-0.840896\pi$
$61$	7.11302	−	35.7596i	0.116607	−	0.586223i	0.994266	−	0.106937i	$-0.0341043\pi$
$62$	21.5926	+	32.3156i	0.348268	+	0.521220i
$63$	−12.7793	−	64.2461i	−0.202847	−	1.01978i
$64$	−66.6561	+	66.6561i	−1.04150	+	1.04150i
$65$		0			0
$66$	18.3515	+	7.60145i	0.278054	+	0.115174i
$67$			117.219i			1.74953i	0.484544	+	0.874767i	$0.338985\pi$
$67$			117.219i			1.74953i	−0.484544	+	0.874767i	$0.661015\pi$
$68$	−81.1179	+	33.6001i	−1.19291	+	0.494119i
$69$	6.97157			0.101037
$70$		0			0
$71$	88.1108	+	58.8738i	1.24100	+	0.829208i	0.990312	−	0.138861i	$-0.0443440\pi$
$71$	88.1108	+	58.8738i	1.24100	+	0.829208i	0.250685	+	0.968069i	$0.419344\pi$
$72$	20.7945	+	20.7945i	0.288813	+	0.288813i
$73$	59.8620	−	11.9073i	0.820028	−	0.163114i	0.232789	−	0.972527i	$-0.425215\pi$
$73$	59.8620	−	11.9073i	0.820028	−	0.163114i	0.587239	+	0.809414i	$0.300215\pi$
$74$	−59.5832	+	39.8122i	−0.805178	+	0.538003i
$75$		0			0
$76$	−13.4223	+	5.55971i	−0.176610	+	0.0731541i
$77$	24.2730	+	58.6001i	0.315233	+	0.761041i
$78$	0.542122	−	2.72543i	0.00695029	−	0.0349414i
$79$	52.9382	+	79.2276i	0.670103	+	1.00288i	0.998301	+	0.0582714i	$0.0185589\pi$
$79$	52.9382	+	79.2276i	0.670103	+	1.00288i	−0.328197	+	0.944609i	$0.606441\pi$
$80$		0			0
$81$	−44.9799	+	44.9799i	−0.555308	+	0.555308i
$82$	36.7331	−	54.9749i	0.447964	−	0.670426i
$83$	109.791	+	45.4770i	1.32279	+	0.547916i	0.928589	−	0.371110i	$-0.121023\pi$
$83$	109.791	+	45.4770i	1.32279	+	0.547916i	0.394197	+	0.919026i	$0.371023\pi$
$84$		−	32.9607i		−	0.392389i
$85$		0			0
$86$	70.3428			0.817939
$87$	0.954715	−	2.30489i	0.0109737	−	0.0264929i
$88$	−23.6767	−	15.8202i	−0.269053	−	0.179776i
$89$	−61.4534	−	61.4534i	−0.690488	−	0.690488i	0.271851	−	0.962339i	$-0.412364\pi$
$89$	−61.4534	−	61.4534i	−0.690488	−	0.690488i	−0.962339	+	0.271851i	$0.912364\pi$
$90$		0			0
$91$	7.37792	−	4.92977i	0.0810761	−	0.0541733i
$92$	−43.4639	−	8.64551i	−0.472434	−	0.0939729i
$93$	−9.63715	+	3.99184i	−0.103625	+	0.0429230i
$94$	91.1920	+	220.157i	0.970128	+	2.34210i
$95$		0			0
$96$	−20.0109	−	29.9484i	−0.208447	−	0.311963i
$97$	−4.79748	−	24.1185i	−0.0494585	−	0.248645i	0.948145	−	0.317839i	$-0.102957\pi$
$97$	−4.79748	−	24.1185i	−0.0494585	−	0.248645i	−0.997603	+	0.0691943i	$0.977957\pi$
$98$	27.1699	−	27.1699i	0.277244	−	0.277244i
$99$	37.4165	−	55.9978i	0.377945	−	0.565635i
$100$		0			0
$101$			7.70266i			0.0762640i	0.999273	+	0.0381320i	$0.0121407\pi$
$101$			7.70266i			0.0762640i	−0.999273	+	0.0381320i	$0.987859\pi$
$102$	−8.15782	−	41.0121i	−0.0799786	−	0.402080i
$103$	−41.5688			−0.403581			−0.201790	−	0.979429i	$-0.564676\pi$
$103$	−41.5688			−0.403581			−0.201790	+	0.979429i	$0.564676\pi$
$104$	−1.52447	+	3.68039i	−0.0146584	+	0.0353884i
$105$		0			0
$106$	−128.614	−	128.614i	−1.21333	−	1.21333i
$107$	−86.7136	+	17.2484i	−0.810407	+	0.161200i	−0.582866	−	0.812568i	$-0.698069\pi$
$107$	−86.7136	+	17.2484i	−0.810407	+	0.161200i	−0.227541	+	0.973768i	$0.573069\pi$
$108$	−60.5023	+	40.4263i	−0.560206	+	0.374318i
$109$	18.2754	+	3.63521i	0.167665	+	0.0333506i	0.278209	−	0.960521i	$-0.410259\pi$
$109$	18.2754	+	3.63521i	0.167665	+	0.0333506i	−0.110544	+	0.993871i	$0.535259\pi$
$110$		0			0
$111$	−7.36011	−	17.7689i	−0.0663073	−	0.160080i
$112$	15.2990	−	76.9131i	0.136598	−	0.686724i
$113$	33.6909	+	50.4220i	0.298150	+	0.446212i	0.950053	−	0.312090i	$-0.101029\pi$
$113$	33.6909	+	50.4220i	0.298150	+	0.446212i	−0.651903	+	0.758302i	$0.726029\pi$
$114$	−1.34985	−	6.78616i	−0.0118408	−	0.0595277i
$115$		0			0
$116$	−8.81043	+	13.1857i	−0.0759520	+	0.113670i
$117$	−8.70452	−	3.60553i	−0.0743976	−	0.0308165i
$118$			83.1426i			0.704598i
$119$	74.1828	−	111.022i	0.623385	−	0.932962i
$120$		0			0
$121$	21.3487	−	51.5403i	0.176436	−	0.425953i
$122$	−91.7753	−	61.3223i	−0.752257	−	0.502642i
$123$	12.5479	+	12.5479i	0.102015	+	0.102015i
$124$	65.0326	−	12.9358i	0.524456	−	0.104321i
$125$		0			0
$126$	−194.495	−	38.6874i	−1.54361	−	0.307043i
$127$	−110.168	+	45.6333i	−0.867468	+	0.359317i	−0.771624	−	0.636079i	$-0.780555\pi$
$127$	−110.168	+	45.6333i	−0.867468	+	0.359317i	−0.0958444	+	0.995396i	$0.530555\pi$
$128$	41.3506	+	99.8291i	0.323051	+	0.779915i
$129$	−3.68317	+	18.5166i	−0.0285517	+	0.143539i
$130$		0			0
$131$	33.4238	+	168.033i	0.255144	+	1.28269i	0.869605	+	0.493748i	$0.164373\pi$
$131$	33.4238	+	168.033i	0.255144	+	1.28269i	−0.614461	+	0.788947i	$0.710627\pi$
$132$	23.9626	−	23.9626i	0.181534	−	0.181534i
$133$	12.2748	−	18.3706i	0.0922919	−	0.138125i
$134$	327.849	+	135.799i	2.44663	+	1.01343i
$135$		0			0
$136$			59.9454i			0.440775i
$137$	173.113			1.26360			0.631799	−	0.775132i	$-0.282317\pi$
$137$	173.113			1.26360			0.631799	+	0.775132i	$0.282317\pi$
$138$	8.07666	−	19.4988i	0.0585265	−	0.141295i
$139$	−149.307	−	99.7637i	−1.07415	−	0.717724i	−0.112957	−	0.993600i	$-0.536032\pi$
$139$	−149.307	−	99.7637i	−1.07415	−	0.717724i	−0.961193	+	0.275876i	$0.911032\pi$
$140$		0			0
$141$	−62.7276	+	12.4773i	−0.444876	+	0.0884914i
$142$	266.741	−	178.231i	1.87846	−	1.25515i
$143$	8.94775	+	1.77982i	0.0625717	+	0.0124463i
$144$	−76.9278	+	31.8645i	−0.534221	+	0.221281i
$145$		0			0
$146$	36.0474	−	181.223i	0.246900	−	1.24125i
$147$	5.72939	+	8.57464i	0.0389755	+	0.0583309i
$148$	23.8509	+	119.906i	0.161154	+	0.810178i
$149$	31.6842	−	31.6842i	0.212646	−	0.212646i	−0.592745	−	0.805391i	$-0.701956\pi$
$149$	31.6842	−	31.6842i	0.212646	−	0.212646i	0.805391	+	0.592745i	$0.201956\pi$
$150$		0			0
$151$	−121.384	−	50.2789i	−0.803868	−	0.332973i	−0.0573634	−	0.998353i	$-0.518269\pi$
$151$	−121.384	−	50.2789i	−0.803868	−	0.332973i	−0.746504	+	0.665380i	$0.768269\pi$
$152$			9.91898i			0.0652565i
$153$	−141.777			−0.926648
$154$	192.019			1.24688
$155$		0			0
$156$	−3.94184	−	2.63385i	−0.0252682	−	0.0168837i
$157$	−25.4694	−	25.4694i	−0.162225	−	0.162225i	0.621327	−	0.783552i	$-0.286594\pi$
$157$	−25.4694	−	25.4694i	−0.162225	−	0.162225i	−0.783552	+	0.621327i	$0.786594\pi$
$158$	282.921	−	56.2765i	1.79064	−	0.356180i
$159$	40.5896	−	27.1211i	0.255281	−	0.170573i
$160$		0			0
$161$	62.2635	−	25.7904i	0.386730	−	0.160189i
$162$	73.6944	+	177.914i	0.454904	+	1.09823i
$163$	−31.1596	+	156.650i	−0.191163	+	0.961041i	0.759427	+	0.650592i	$0.225479\pi$
$163$	−31.1596	+	156.650i	−0.191163	+	0.961041i	−0.950590	+	0.310449i	$0.899521\pi$
$164$	−62.6684	−	93.7898i	−0.382124	−	0.571889i
$165$		0			0
$166$	254.389	−	254.389i	1.53246	−	1.53246i
$167$	61.5214	−	92.0734i	0.368392	−	0.551337i	−0.600246	−	0.799816i	$-0.704930\pi$
$167$	61.5214	−	92.0734i	0.368392	−	0.551337i	0.968637	+	0.248478i	$0.0799305\pi$
$168$	−20.7905	−	8.61173i	−0.123753	−	0.0512603i
$169$			167.724i			0.992448i
$170$		0			0
$171$	−23.4594			−0.137190
$172$	45.9251	−	110.873i	0.267006	−	0.644611i
$173$	148.047	+	98.9216i	0.855761	+	0.571801i	0.904241	−	0.427023i	$-0.140438\pi$
$173$	148.047	+	98.9216i	0.855761	+	0.571801i	−0.0484797	+	0.998824i	$0.515438\pi$
$174$	−5.34048	−	5.34048i	−0.0306924	−	0.0306924i
$175$		0			0
$176$	67.0386	−	44.7937i	0.380901	−	0.254510i
$177$	−21.8859	−	4.35338i	−0.123649	−	0.0245954i
$178$	−243.074	+	100.684i	−1.36558	+	0.565642i
$179$	96.5028	+	232.978i	0.539122	+	1.30155i	0.925337	+	0.379146i	$0.123782\pi$
$179$	96.5028	+	232.978i	0.539122	+	1.30155i	−0.386215	+	0.922409i	$0.626218\pi$
$180$		0			0
$181$	167.421	+	250.563i	0.924977	+	1.38433i	0.923197	+	0.384328i	$0.125567\pi$
$181$	167.421	+	250.563i	0.924977	+	1.38433i	0.00178027	+	0.999998i	$0.499433\pi$
$182$	−5.24064	−	26.3465i	−0.0287947	−	0.144761i
$183$	20.9475	−	20.9475i	0.114467	−	0.114467i
$184$	−16.8092	+	25.1568i	−0.0913546	+	0.136722i
$185$		0			0
$186$			31.5787i			0.169778i
$187$	134.645	−	26.7826i	0.720027	−	0.143222i
$188$	406.545			2.16247
$189$	42.3476	−	102.236i	0.224061	−	0.540931i
$190$		0			0
$191$	93.7287	+	93.7287i	0.490726	+	0.490726i	0.908535	−	0.417809i	$-0.137202\pi$
$191$	93.7287	+	93.7287i	0.490726	+	0.490726i	−0.417809	+	0.908535i	$0.637202\pi$
$192$	−75.1202	+	14.9423i	−0.391251	+	0.0778247i
$193$	−264.917	+	177.012i	−1.37263	+	0.917161i	−0.999942	−	0.0107958i	$-0.996564\pi$
$193$	−264.917	+	177.012i	−1.37263	+	0.917161i	−0.372687	+	0.927957i	$0.621564\pi$
$194$	−73.0150	−	14.5236i	−0.376366	−	0.0748639i
$195$		0			0
$196$	−25.0861	−	60.5632i	−0.127990	−	0.308996i
$197$	−22.5650	+	113.442i	−0.114543	+	0.575847i	0.880300	+	0.474418i	$0.157341\pi$
$197$	−22.5650	+	113.442i	−0.114543	+	0.575847i	−0.994843	+	0.101429i	$0.967659\pi$
$198$	−113.273	−	169.524i	−0.572084	−	0.856184i
$199$	−57.7166	−	290.161i	−0.290033	−	1.45809i	−0.801088	−	0.598547i	$-0.795745\pi$
$199$	−57.7166	−	290.161i	−0.290033	−	1.45809i	0.511055	−	0.859548i	$-0.329255\pi$
$200$		0			0
$201$	−52.9132	+	79.1902i	−0.263250	+	0.393981i
$202$	21.5436	+	8.92363i	0.106651	+	0.0441764i
$203$		−	24.1169i		−	0.118802i
$204$	−69.9686	−	13.9176i	−0.342983	−	0.0682236i
$205$		0			0
$206$	−48.1580	+	116.264i	−0.233777	+	0.564387i
$207$	−59.4985	−	39.7556i	−0.287432	−	0.192056i
$208$	−7.97568	−	7.97568i	−0.0383446	−	0.0383446i
$209$	22.2793	−	4.43163i	0.106600	−	0.0212040i
$210$		0			0
$211$	−225.325	−	44.8199i	−1.06789	−	0.212417i	−0.370300	−	0.928912i	$-0.620745\pi$
$211$	−225.325	−	44.8199i	−1.06789	−	0.212417i	−0.697592	+	0.716495i	$0.745745\pi$
$212$	−286.687	+	118.750i	−1.35230	+	0.560140i
$213$	32.9496	+	79.5475i	0.154693	+	0.373462i
$214$	−52.2168	+	262.511i	−0.244004	+	1.22669i
$215$		0			0
$216$	9.69205	+	48.7252i	0.0448706	+	0.225580i
$217$	−71.3026	+	71.3026i	−0.328584	+	0.328584i
$218$	31.3396	−	46.9031i	0.143760	−	0.215152i
$219$	45.8164	+	18.9778i	0.209207	+	0.0866565i
$220$		0			0
$221$	−7.34955	−	17.7434i	−0.0332559	−	0.0802868i
$222$	−58.2245			−0.262272
$223$	139.061	−	335.723i	0.623593	−	1.50549i	−0.223863	−	0.974621i	$-0.571867\pi$
$223$	139.061	−	335.723i	0.623593	−	1.50549i	0.847456	−	0.530865i	$-0.178133\pi$
$224$	−289.509	−	193.443i	−1.29245	−	0.863587i
$225$		0			0
$226$	180.056	−	35.8155i	0.796710	−	0.158475i
$227$	80.5890	−	53.8478i	0.355017	−	0.237215i	−0.365253	−	0.930908i	$-0.619018\pi$
$227$	80.5890	−	53.8478i	0.355017	−	0.237215i	0.720271	+	0.693693i	$0.244018\pi$
$228$	−11.5775	−	2.30291i	−0.0507785	−	0.0101005i
$229$	−334.120	+	138.397i	−1.45904	+	0.604353i	−0.964329	−	0.264706i	$-0.914725\pi$
$229$	−334.120	+	138.397i	−1.45904	+	0.604353i	−0.494708	+	0.869059i	$0.664725\pi$
$230$		0			0
$231$	−10.0542	+	50.5458i	−0.0435246	+	0.218813i
$232$	6.01522	+	9.00241i	0.0259277	+	0.0388035i
$233$	−54.6542	−	274.765i	−0.234567	−	1.17925i	−0.901045	−	0.433725i	$-0.857199\pi$
$233$	−54.6542	−	274.765i	−0.234567	−	1.17925i	0.666478	−	0.745525i	$-0.267801\pi$
$234$	−20.1686	+	20.1686i	−0.0861905	+	0.0861905i
$235$		0			0
$236$	131.048	+	54.2818i	0.555288	+	0.230008i
$237$			77.4209i			0.326670i
$238$	−224.577	−	336.103i	−0.943599	−	1.41220i
$239$	328.551			1.37469			0.687345	−	0.726331i	$-0.258776\pi$
$239$	328.551			1.37469			0.687345	+	0.726331i	$0.258776\pi$
$240$		0			0
$241$	−201.560	−	134.678i	−0.836349	−	0.558831i	0.0620186	−	0.998075i	$-0.480246\pi$
$241$	−201.560	−	134.678i	−0.836349	−	0.558831i	−0.898368	+	0.439244i	$0.855246\pi$
$242$	−119.420	−	119.420i	−0.493472	−	0.493472i
$243$	−175.054	+	34.8204i	−0.720387	+	0.143294i
$244$	−156.573	+	104.619i	−0.641693	+	0.428765i
$245$		0			0
$246$	49.6320	−	20.5583i	0.201756	−	0.0835701i
$247$	−1.21611	−	2.93595i	−0.00492352	−	0.0118864i
$248$	8.83176	−	44.4003i	0.0356119	−	0.179033i
$249$	53.6438	+	80.2836i	0.215437	+	0.322424i
$250$		0			0
$251$	−155.463	+	155.463i	−0.619375	+	0.619375i	−0.945371	−	0.325996i	$-0.894300\pi$
$251$	−155.463	+	155.463i	−0.619375	+	0.619375i	0.325996	+	0.945371i	$0.394300\pi$
$252$	−187.959	+	281.301i	−0.745870	+	1.11627i
$253$	64.0155	+	26.5161i	0.253026	+	0.104807i
$254$			360.996i			1.42125i
$255$		0			0
$256$	−49.9468			−0.195105
$257$	−124.463	+	300.480i	−0.484292	+	1.16918i	0.473260	+	0.880923i	$0.343077\pi$
$257$	−124.463	+	300.480i	−0.484292	+	1.16918i	−0.957552	+	0.288261i	$0.906923\pi$
$258$	47.5219	+	31.7531i	0.184194	+	0.123074i
$259$	−131.467	−	131.467i	−0.507595	−	0.507595i
$260$		0			0
$261$	−21.2917	+	14.2266i	−0.0815772	+	0.0545082i
$262$	508.693	+	101.185i	1.94158	+	0.386203i
$263$	−128.172	+	53.0907i	−0.487347	+	0.201866i	−0.612806	−	0.790233i	$-0.709959\pi$
$263$	−128.172	+	53.0907i	−0.487347	+	0.201866i	0.125460	+	0.992099i	$0.459959\pi$
$264$	−8.85405	−	21.3756i	−0.0335381	−	0.0809681i
$265$		0			0
$266$	−37.1600	−	55.6139i	−0.139699	−	0.209075i
$267$	−13.7761	−	69.2570i	−0.0515957	−	0.259389i
$268$	428.089	−	428.089i	1.59735	−	1.59735i
$269$	−180.493	+	270.126i	−0.670976	+	1.00419i	0.327267	+	0.944932i	$0.393872\pi$
$269$	−180.493	+	270.126i	−0.670976	+	1.00419i	−0.998243	+	0.0592547i	$0.981128\pi$
$270$		0			0
$271$			19.1867i			0.0707996i	0.999373	+	0.0353998i	$0.0112705\pi$
$271$			19.1867i			0.0707996i	−0.999373	+	0.0353998i	$0.988730\pi$
$272$	−156.810	−	64.9530i	−0.576509	−	0.238798i
$273$	7.20968			0.0264091
$274$	200.554	−	484.179i	0.731947	−	1.76708i
$275$		0			0
$276$	−25.4606	−	25.4606i	−0.0922484	−	0.0922484i
$277$	−302.084	+	60.0883i	−1.09056	+	0.216925i	−0.707439	−	0.706774i	$-0.750150\pi$
$277$	−302.084	+	60.0883i	−1.09056	+	0.216925i	−0.383118	+	0.923700i	$0.625150\pi$
$278$	−452.003	+	302.018i	−1.62591	+	1.08640i
$279$	105.011	+	20.8880i	0.376385	+	0.0748676i
$280$		0			0
$281$	−33.1106	−	79.9361i	−0.117831	−	0.284470i	0.853949	−	0.520356i	$-0.174201\pi$
$281$	−33.1106	−	79.9361i	−0.117831	−	0.284470i	−0.971781	+	0.235886i	$0.924201\pi$
$282$	−37.7730	+	189.898i	−0.133947	+	0.673396i
$283$	−4.15656	−	6.22073i	−0.0146875	−	0.0219814i	0.824053	−	0.566512i	$-0.191708\pi$
$283$	−4.15656	−	6.22073i	−0.0146875	−	0.0219814i	−0.838741	+	0.544531i	$0.816708\pi$
$284$	−106.775	−	536.796i	−0.375969	−	1.89013i
$285$		0			0
$286$	15.3440	−	22.9640i	0.0536505	−	0.0802937i
$287$	158.485	+	65.6466i	0.552213	+	0.228734i
$288$			369.706i			1.28370i
$289$	−204.354	−	204.354i	−0.707107	−	0.707107i
$290$		0			0
$291$	7.64619	−	18.4595i	0.0262756	−	0.0634348i
$292$	−262.105	−	175.133i	−0.897621	−	0.599771i
$293$	−54.4583	−	54.4583i	−0.185864	−	0.185864i	0.608041	−	0.793906i	$-0.291956\pi$
$293$	−54.4583	−	54.4583i	−0.185864	−	0.185864i	−0.793906	+	0.608041i	$0.791956\pi$
$294$	30.6200	−	6.09069i	0.104150	−	0.0207166i
$295$		0			0
$296$	81.8647	+	16.2839i	0.276570	+	0.0550132i
$297$	105.113	−	43.5392i	0.353915	−	0.146597i
$298$	−51.9110	−	125.324i	−0.174198	−	0.420551i
$299$	1.89108	−	9.50711i	0.00632469	−	0.0317964i
$300$		0			0
$301$	35.6049	+	178.998i	0.118289	+	0.594677i
$302$	−281.250	+	281.250i	−0.931291	+	0.931291i
$303$	−3.47703	+	5.20374i	−0.0114753	+	0.0171741i
$304$	−25.9470	−	10.7476i	−0.0853519	−	0.0353539i
$305$		0			0
$306$	−164.251	+	396.536i	−0.536767	+	1.29587i
$307$	159.680			0.520132			0.260066	−	0.965591i	$-0.416256\pi$
$307$	159.680			0.520132			0.260066	+	0.965591i	$0.416256\pi$
$308$	125.365	−	302.657i	0.407028	−	0.982653i
$309$	−28.0829	−	18.7644i	−0.0908832	−	0.0607262i
$310$		0			0
$311$	−326.615	+	64.9678i	−1.05021	+	0.208900i	−0.689879	−	0.723925i	$-0.742336\pi$
$311$	−326.615	+	64.9678i	−1.05021	+	0.208900i	−0.360331	+	0.932825i	$0.617336\pi$
$312$	−2.69125	+	1.79823i	−0.00862579	+	0.00576357i
$313$	−386.986	−	76.9763i	−1.23638	−	0.245931i	−0.466729	−	0.884400i	$-0.654568\pi$
$313$	−386.986	−	76.9763i	−1.23638	−	0.245931i	−0.769647	+	0.638470i	$0.779568\pi$
$314$	−100.742	+	41.7286i	−0.320834	+	0.132894i
$315$		0			0
$316$	96.0103	−	482.676i	0.303830	−	1.52746i
$317$	77.2775	+	115.654i	0.243778	+	0.364839i	0.933101	−	0.359615i	$-0.117092\pi$
$317$	77.2775	+	115.654i	0.243778	+	0.364839i	−0.689323	+	0.724454i	$0.742092\pi$
$318$	−28.8314	−	144.945i	−0.0906647	−	0.455802i
$319$	17.5331	−	17.5331i	0.0549627	−	0.0549627i
$320$		0			0
$321$	−66.3677	−	27.4904i	−0.206753	−	0.0856399i
$322$		−	204.023i		−	0.633612i
$323$	−33.8138	−	33.8138i	−0.104687	−	0.104687i
$324$	328.538			1.01401
$325$		0			0
$326$	402.034	+	268.631i	1.23323	+	0.824021i
$327$	10.7055	+	10.7055i	0.0327385	+	0.0327385i
$328$	−75.5332	+	15.0245i	−0.230284	+	0.0458064i
$329$	−514.065	+	343.487i	−1.56251	+	1.04403i
$330$		0			0
$331$	146.717	−	60.7720i	0.443252	−	0.183601i	−0.149883	−	0.988704i	$-0.547890\pi$
$331$	146.717	−	60.7720i	0.443252	−	0.183601i	0.593136	+	0.805103i	$0.297890\pi$
$332$	−234.879	−	567.048i	−0.707467	−	1.70798i
$333$	−38.5132	+	193.619i	−0.115655	+	0.581438i
$334$	−186.246	−	278.737i	−0.557624	−	0.834543i
$335$		0			0
$336$	45.0546	−	45.0546i	0.134091	−	0.134091i
$337$	267.981	−	401.062i	0.795195	−	1.19009i	−0.183144	−	0.983086i	$-0.558628\pi$
$337$	267.981	−	401.062i	0.795195	−	1.19009i	0.978339	−	0.207008i	$-0.0663725\pi$
$338$	469.106	+	194.310i	1.38789	+	0.574882i
$339$			49.2722i			0.145346i
$340$		0			0
$341$	−103.675			−0.304031
$342$	−27.1781	+	65.6136i	−0.0794680	+	0.191853i
$343$	−237.116	−	158.436i	−0.691299	−	0.461912i
$344$	−57.9362	−	57.9362i	−0.168419	−	0.168419i
$345$		0			0
$346$	448.188	−	299.469i	1.29534	−	0.865518i
$347$	19.4096	+	3.86080i	0.0559353	+	0.0111262i	0.222979	−	0.974823i	$-0.428422\pi$
$347$	19.4096	+	3.86080i	0.0559353	+	0.0111262i	−0.167043	+	0.985950i	$0.553422\pi$
$348$	−11.9042	+	4.93090i	−0.0342076	+	0.0141692i
$349$	−149.801	−	361.651i	−0.429229	−	1.03625i	−0.979533	−	0.201286i	$-0.935488\pi$
$349$	−149.801	−	361.651i	−0.429229	−	1.03625i	0.550304	−	0.834965i	$-0.314512\pi$
$350$		0			0
$351$	−8.84268	−	13.2340i	−0.0251928	−	0.0377037i
$352$	−69.8398	−	351.108i	−0.198408	−	0.997466i
$353$	−138.024	+	138.024i	−0.391003	+	0.391003i	−0.875045	−	0.484042i	$-0.839168\pi$
$353$	−138.024	+	138.024i	−0.391003	+	0.391003i	0.484042	+	0.875045i	$0.339168\pi$
$354$	−37.5311	+	56.1692i	−0.106020	+	0.158670i
$355$		0			0
$356$			448.863i			1.26085i
$357$	100.232	−	41.5176i	0.280763	−	0.116296i
$358$	763.416			2.13245
$359$	136.163	−	328.726i	0.379284	−	0.915672i	−0.612817	−	0.790225i	$-0.709964\pi$
$359$	136.163	−	328.726i	0.379284	−	0.915672i	0.992100	−	0.125447i	$-0.0400364\pi$
$360$		0			0
$361$	249.670	+	249.670i	0.691608	+	0.691608i
$362$	894.758	−	177.978i	2.47171	−	0.491653i
$363$	37.6883	−	25.1825i	0.103824	−	0.0693733i
$364$	−44.9484	−	8.94078i	−0.123485	−	0.0245626i
$365$		0			0
$366$	−34.3200	−	82.8558i	−0.0937705	−	0.226382i
$367$	15.9442	−	80.1568i	0.0434446	−	0.218411i	−0.952964	−	0.303083i	$-0.901984\pi$
$367$	15.9442	−	80.1568i	0.0434446	−	0.218411i	0.996409	+	0.0846717i	$0.0269842\pi$
$368$	−47.5940	−	71.2294i	−0.129331	−	0.193558i
$369$	−35.5345	−	178.644i	−0.0962994	−	0.484130i
$370$		0			0
$371$	262.177	−	392.376i	0.706677	−	1.05762i
$372$	49.7738	+	20.6170i	0.133801	+	0.0554220i
$373$		−	76.8209i		−	0.205954i	−0.994684	−	0.102977i	$-0.967163\pi$
$373$		−	76.8209i		−	0.205954i	0.994684	−	0.102977i	$-0.0328368\pi$
$374$	81.0799	−	407.616i	0.216791	−	1.08988i
$375$		0			0
$376$	106.219	−	256.436i	0.282498	−	0.682009i
$377$	−2.88419	−	1.92716i	−0.00765038	−	0.00511182i
$378$	−236.883	−	236.883i	−0.626676	−	0.626676i
$379$	577.940	−	114.959i	1.52491	−	0.303323i	0.639739	−	0.768592i	$-0.279043\pi$
$379$	577.940	−	114.959i	1.52491	−	0.303323i	0.885169	+	0.465269i	$0.154043\pi$
$380$		0			0
$381$	−95.0264	−	18.9019i	−0.249413	−	0.0496113i
$382$	370.735	−	153.564i	0.970511	−	0.401999i
$383$	89.4016	+	215.834i	0.233424	+	0.563537i	0.996576	−	0.0826832i	$-0.0263490\pi$
$383$	89.4016	+	215.834i	0.233424	+	0.563537i	−0.763151	+	0.646220i	$0.776349\pi$
$384$	−17.1280	+	86.1081i	−0.0446041	+	0.224240i
$385$		0			0
$386$	188.175	+	946.017i	0.487499	+	2.45082i
$387$	137.025	−	137.025i	0.354070	−	0.354070i
$388$	−70.5616	+	105.603i	−0.181860	+	0.272172i
$389$	372.916	+	154.467i	0.958653	+	0.397087i	0.806477	−	0.591266i	$-0.201372\pi$
$389$	372.916	+	154.467i	0.958653	+	0.397087i	0.152177	+	0.988353i	$0.451372\pi$
$390$		0			0
$391$	−28.4569	−	143.062i	−0.0727797	−	0.365888i
$392$	−44.7557			−0.114173
$393$	−53.2707	+	128.607i	−0.135549	+	0.327244i
$394$	291.143	+	194.536i	0.738943	+	0.493746i
$395$		0			0
$396$	−341.154	+	67.8598i	−0.861501	+	0.171363i
$397$	−219.332	+	146.553i	−0.552474	+	0.369151i	−0.800251	−	0.599666i	$-0.795300\pi$
$397$	−219.332	+	146.553i	−0.552474	+	0.369151i	0.247776	+	0.968817i	$0.420300\pi$
$398$	−878.415	−	174.728i	−2.20707	−	0.439014i
$399$	16.5852	−	6.86980i	0.0415668	−	0.0172175i
$400$		0			0
$401$	46.6830	−	234.691i	0.116416	−	0.585265i	−0.877904	−	0.478837i	$-0.841059\pi$
$401$	46.6830	−	234.691i	0.116416	−	0.585265i	0.994320	−	0.106428i	$-0.0339414\pi$
$402$	160.186	+	239.736i	0.398473	+	0.596358i
$403$	2.82952	+	14.2250i	0.00702114	+	0.0352977i
$404$	28.1305	−	28.1305i	0.0696300	−	0.0696300i
$405$		0			0
$406$	−67.4525	−	27.9397i	−0.166139	−	0.0688171i
$407$		−	191.154i		−	0.469666i
$408$	−27.0597	+	40.4977i	−0.0663228	+	0.0992590i
$409$	259.903			0.635461			0.317730	−	0.948181i	$-0.397079\pi$
$409$	259.903			0.635461			0.317730	+	0.948181i	$0.397079\pi$
$410$		0			0
$411$	116.951	+	78.1442i	0.284552	+	0.190132i
$412$	151.812	+	151.812i	0.368475	+	0.368475i
$413$	−211.569	+	42.0837i	−0.512274	+	0.101898i
$414$	−180.122	+	120.354i	−0.435078	+	0.290710i
$415$		0			0
$416$	−46.2687	+	19.1651i	−0.111223	+	0.0460700i
$417$	−55.8343	−	134.796i	−0.133895	−	0.323252i
$418$	13.4161	−	67.4471i	0.0320958	−	0.161357i
$419$	−95.3087	−	142.640i	−0.227467	−	0.340429i	0.700127	−	0.714018i	$-0.253127\pi$
$419$	−95.3087	−	142.640i	−0.227467	−	0.340429i	−0.927594	+	0.373590i	$0.878127\pi$
$420$		0			0
$421$	443.214	−	443.214i	1.05276	−	1.05276i	0.0542356	−	0.998528i	$-0.482728\pi$
$421$	443.214	−	443.214i	1.05276	−	1.05276i	0.998528	−	0.0542356i	$-0.0172722\pi$
$422$	−386.399	+	578.287i	−0.915637	+	1.37035i
$423$	606.497	+	251.219i	1.43380	+	0.593899i
$424$			211.859i			0.499668i
$425$		0			0
$426$	260.659			0.611875
$427$	109.591	−	264.575i	0.256653	−	0.619614i
$428$	379.675	+	253.691i	0.887090	+	0.592735i
$429$	5.24147	+	5.24147i	0.0122179	+	0.0122179i
$430$		0			0
$431$	−633.734	+	423.447i	−1.47038	+	0.982477i	−0.475684	+	0.879616i	$0.657799\pi$
$431$	−633.734	+	423.447i	−1.47038	+	0.982477i	−0.994696	+	0.102860i	$0.967201\pi$
$432$	−137.961	−	27.4422i	−0.319355	−	0.0635237i
$433$	−87.4681	+	36.2305i	−0.202005	+	0.0836732i	−0.481392	−	0.876505i	$-0.659869\pi$
$433$	−87.4681	+	36.2305i	−0.202005	+	0.0836732i	0.279387	+	0.960179i	$0.409869\pi$
$434$	116.821	+	282.031i	0.269173	+	0.649841i
$435$		0			0
$436$	−53.4669	−	80.0189i	−0.122630	−	0.183530i
$437$	−4.70868	−	23.6721i	−0.0107750	−	0.0541696i
$438$	106.158	−	106.158i	0.242369	−	0.242369i
$439$	−20.5441	+	30.7465i	−0.0467976	+	0.0700375i	−0.854131	−	0.520059i	$-0.825910\pi$
$439$	−20.5441	+	30.7465i	−0.0467976	+	0.0700375i	0.807333	+	0.590096i	$0.200910\pi$
$440$		0			0
$441$		−	105.852i		−	0.240027i
$442$	−58.1410			−0.131541
$443$	634.146			1.43148			0.715740	−	0.698367i	$-0.246089\pi$
$443$	634.146			1.43148			0.715740	+	0.698367i	$0.246089\pi$
$444$	−38.0134	+	91.7724i	−0.0856157	+	0.206695i
$445$		0			0
$446$	−777.880	−	777.880i	−1.74412	−	1.74412i
$447$	35.7076	−	7.10268i	0.0798828	−	0.0158897i
$448$	−615.626	+	411.348i	−1.37416	+	0.918187i
$449$	433.336	+	86.1959i	0.965114	+	0.191973i	0.652400	−	0.757874i	$-0.273762\pi$
$449$	433.336	+	86.1959i	0.965114	+	0.191973i	0.312713	+	0.949848i	$0.398762\pi$
$450$		0			0
$451$	67.4939	+	162.945i	0.149654	+	0.361296i
$452$	61.1029	−	307.185i	0.135183	−	0.679613i
$453$	−59.3080	−	88.7607i	−0.130923	−	0.195940i
$454$	−57.2435	−	287.782i	−0.126087	−	0.633882i
$455$		0			0
$456$	−4.47749	+	6.70103i	−0.00981905	+	0.0146953i
$457$	−246.501	−	102.104i	−0.539390	−	0.223423i	0.0963202	−	0.995350i	$-0.469293\pi$
$457$	−246.501	−	102.104i	−0.539390	−	0.223423i	−0.635710	+	0.771928i	$0.719293\pi$
$458$			1094.83i			2.39046i
$459$	−199.145	−	133.064i	−0.433866	−	0.289900i
$460$		0			0
$461$	172.768	−	417.100i	0.374769	−	0.904772i	−0.618159	−	0.786053i	$-0.712121\pi$
$461$	172.768	−	417.100i	0.374769	−	0.904772i	0.992928	−	0.118719i	$-0.0378787\pi$
$462$	129.724	+	86.6785i	0.280787	+	0.187616i
$463$	57.1171	+	57.1171i	0.123363	+	0.123363i	0.766093	−	0.642730i	$-0.222198\pi$
$463$	57.1171	+	57.1171i	0.123363	+	0.123363i	−0.642730	+	0.766093i	$0.722198\pi$
$464$	−30.0670	+	5.98070i	−0.0647996	+	0.0128894i
$465$		0			0
$466$	−831.808	−	165.457i	−1.78499	−	0.355058i
$467$	−76.1879	+	31.5580i	−0.163143	+	0.0675761i	−0.462760	−	0.886483i	$-0.653141\pi$
$467$	−76.1879	+	31.5580i	−0.163143	+	0.0675761i	0.299617	+	0.954059i	$0.403141\pi$
$468$	18.6218	+	44.9569i	0.0397901	+	0.0960619i
$469$	−179.617	+	902.998i	−0.382979	+	1.92537i
$470$		0			0
$471$	−5.70949	−	28.7035i	−0.0121221	−	0.0609417i
$472$	68.4785	−	68.4785i	0.145082	−	0.145082i
$473$	−104.247	+	156.017i	−0.220396	+	0.329846i
$474$	216.538	+	89.6931i	0.456832	+	0.189226i
$475$		0			0
$476$	−676.380	+	134.540i	−1.42097	+	0.282648i
$477$	−501.069			−1.05046
$478$	380.630	−	918.923i	0.796298	−	1.92243i
$479$	382.794	+	255.775i	0.799153	+	0.533977i	0.886788	−	0.462176i	$-0.152931\pi$
$479$	382.794	+	255.775i	0.799153	+	0.533977i	−0.0876357	+	0.996153i	$0.527931\pi$
$480$		0			0
$481$	−26.2278	+	5.21704i	−0.0545277	+	0.0108462i
$482$	−610.191	+	407.717i	−1.26596	+	0.845885i
$483$	53.7057	+	10.6827i	0.111192	+	0.0221174i
$484$	−266.195	+	110.261i	−0.549989	+	0.227813i
$485$		0			0
$486$	−105.413	+	529.948i	−0.216900	+	1.09043i
$487$	−290.646	−	434.982i	−0.596809	−	0.893187i	0.402948	−	0.915223i	$-0.367985\pi$
$487$	−290.646	−	434.982i	−0.596809	−	0.893187i	−0.999757	+	0.0220352i	$0.992985\pi$
$488$	25.0819	+	126.095i	0.0513974	+	0.258392i
$489$	−91.7633	+	91.7633i	−0.187655	+	0.187655i
$490$		0			0
$491$	−451.862	−	187.167i	−0.920289	−	0.381196i	−0.128303	−	0.991735i	$-0.540953\pi$
$491$	−451.862	−	187.167i	−0.920289	−	0.381196i	−0.791986	+	0.610539i	$0.790953\pi$
$492$		−	91.6511i		−	0.186283i
$493$	−51.1951	−	10.1833i	−0.103844	−	0.0206559i
$494$	−9.62041			−0.0194745
$495$		0			0
$496$	106.577	+	71.2122i	0.214872	+	0.143573i
$497$	588.550	+	588.550i	1.18421	+	1.18421i
$498$	286.692	−	57.0266i	0.575687	−	0.114511i
$499$	−421.610	+	281.711i	−0.844910	+	0.564551i	−0.900972	−	0.433876i	$-0.857145\pi$
$499$	−421.610	+	281.711i	−0.844910	+	0.564551i	0.0560623	+	0.998427i	$0.482145\pi$
$500$		0			0
$501$	83.1249	−	34.4315i	0.165918	−	0.0687255i
$502$	254.709	+	614.921i	0.507388	+	1.22494i
$503$	131.577	−	661.484i	0.261585	−	1.31508i	−0.596932	−	0.802292i	$-0.703614\pi$
$503$	131.577	−	661.484i	0.261585	−	1.31508i	0.858517	−	0.512785i	$-0.171386\pi$
$504$	128.327	+	192.055i	0.254617	+	0.381062i
$505$		0			0
$506$	148.326	−	148.326i	0.293134	−	0.293134i
$507$	−75.7115	+	113.310i	−0.149332	+	0.223492i
$508$	568.996	+	235.686i	1.12007	+	0.463949i
$509$		−	349.504i		−	0.686648i	−0.939217	−	0.343324i	$-0.888447\pi$
$509$		−	349.504i		−	0.686648i	0.939217	−	0.343324i	$-0.111553\pi$
$510$		0			0
$511$	479.395			0.938150
$512$	−223.266	+	539.012i	−0.436067	+	1.05276i
$513$	−32.9519	−	22.0177i	−0.0642337	−	0.0429196i
$514$	696.221	+	696.221i	1.35451	+	1.35451i
$515$		0			0
$516$	81.0747	−	54.1724i	0.157121	−	0.104985i
$517$	−623.444	−	124.011i	−1.20589	−	0.239866i
$518$	−520.006	+	215.393i	−1.00387	+	0.415818i
$519$	55.3631	+	133.658i	0.106673	+	0.257530i
$520$		0			0
$521$	−175.223	−	262.240i	−0.336320	−	0.503339i	0.624307	−	0.781179i	$-0.285381\pi$
$521$	−175.223	−	262.240i	−0.336320	−	0.503339i	−0.960627	+	0.277840i	$0.910381\pi$
$522$	15.1238	+	76.0323i	0.0289727	+	0.145656i
$523$	145.221	−	145.221i	0.277669	−	0.277669i	−0.554509	−	0.832178i	$-0.687094\pi$
$523$	145.221	−	145.221i	0.277669	−	0.277669i	0.832178	+	0.554509i	$0.187094\pi$
$524$	491.600	−	735.731i	0.938168	−	1.40407i
$525$		0			0
$526$			419.991i			0.798461i
$527$	121.253	+	181.468i	0.230082	+	0.344342i
$528$	65.5098			0.124072
$529$	−174.266	+	420.715i	−0.329425	+	0.795302i
$530$		0			0
$531$	161.959	+	161.959i	0.305007	+	0.305007i
$532$	−111.919	+	22.2620i	−0.210373	+	0.0418459i
$533$	20.5152	−	13.7078i	0.0384901	−	0.0257182i
$534$	−209.664	−	41.7048i	−0.392630	−	0.0780989i
$535$		0			0
$536$	−158.177	−	381.873i	−0.295106	−	0.712450i
$537$	−39.9728	+	200.957i	−0.0744372	+	0.374221i
$538$	546.412	+	817.764i	1.01564	+	1.52001i
$539$	19.9961	+	100.527i	0.0370985	+	0.186507i
$540$		0			0
$541$	439.282	−	657.431i	0.811981	−	1.21522i	−0.161596	−	0.986857i	$-0.551664\pi$
$541$	439.282	−	657.431i	0.811981	−	1.21522i	0.973577	−	0.228358i	$-0.0733358\pi$
$542$	53.6632	+	22.2280i	0.0990096	+	0.0410111i
$543$			244.849i			0.450919i
$544$	−532.885	+	532.885i	−0.979568	+	0.979568i
$545$		0			0
$546$	8.35251	−	20.1647i	0.0152976	−	0.0369317i
$547$	783.860	+	523.758i	1.43302	+	0.957511i	0.998380	+	0.0569051i	$0.0181232\pi$
$547$	783.860	+	523.758i	1.43302	+	0.957511i	0.434637	+	0.900606i	$0.356877\pi$
$548$	−632.218	−	632.218i	−1.15368	−	1.15368i
$549$	−298.229	+	59.3214i	−0.543222	+	0.108054i
$550$		0			0
$551$	−8.47111	−	1.68501i	−0.0153741	−	0.00305809i
$552$	−22.7119	+	9.40756i	−0.0411447	+	0.0170427i
$553$	286.408	+	691.450i	0.517917	+	1.25036i
$554$	−181.908	+	914.512i	−0.328353	+	1.65074i
$555$		0			0
$556$	180.934	+	909.619i	0.325422	+	1.63601i
$557$	303.284	−	303.284i	0.544495	−	0.544495i	−0.380348	−	0.924843i	$-0.624196\pi$
$557$	303.284	−	303.284i	0.544495	−	0.544495i	0.924843	+	0.380348i	$0.124196\pi$
$558$	180.079	−	269.507i	0.322722	−	0.482987i
$559$	24.2519	+	10.0455i	0.0433844	+	0.0179704i
$560$		0			0
$561$	103.053	+	42.6859i	0.183695	+	0.0760889i
$562$	−261.932			−0.466071
$563$	264.879	−	639.473i	0.470477	−	1.13583i	−0.493476	−	0.869759i	$-0.664274\pi$
$563$	264.879	−	639.473i	0.470477	−	1.13583i	0.963953	−	0.266072i	$-0.0857260\pi$
$564$	274.652	+	183.517i	0.486972	+	0.325384i
$565$		0			0
$566$	−22.2142	+	4.41867i	−0.0392476	+	0.00780684i
$567$	−415.428	+	277.580i	−0.732677	+	0.489559i
$568$	−366.491	−	72.8996i	−0.645231	−	0.128344i
$569$	−370.173	+	153.331i	−0.650567	+	0.269474i	−0.683463	−	0.729985i	$-0.739527\pi$
$569$	−370.173	+	153.331i	−0.650567	+	0.269474i	0.0328958	+	0.999459i	$0.489527\pi$
$570$		0			0
$571$	127.142	−	639.187i	0.222666	−	1.11942i	−0.694065	−	0.719912i	$-0.744182\pi$
$571$	127.142	−	639.187i	0.222666	−	1.11942i	0.916731	−	0.399505i	$-0.130818\pi$
$572$	−26.1777	−	39.1776i	−0.0457651	−	0.0684924i
$573$	21.0112	+	105.631i	0.0366688	+	0.184347i
$574$	367.214	−	367.214i	0.639745	−	0.639745i
$575$		0			0
$576$	726.319	+	300.851i	1.26097	+	0.522311i
$577$		−	684.109i		−	1.18563i	−0.805339	−	0.592815i	$-0.798017\pi$
$577$		−	684.109i		−	1.18563i	0.805339	−	0.592815i	$-0.201983\pi$
$578$	−808.303	+	334.810i	−1.39845	+	0.579256i
$579$	−258.876			−0.447109
$580$		0			0
$581$	776.094	+	518.569i	1.33579	+	0.892546i
$582$	−42.7712	−	42.7712i	−0.0734900	−	0.0734900i
$583$	475.863	−	94.6550i	0.816232	−	0.162359i
$584$	−178.950	+	119.570i	−0.306420	+	0.204744i
$585$		0			0
$586$	−215.405	+	89.2236i	−0.367585	+	0.152259i
$587$	141.750	+	342.216i	0.241483	+	0.582991i	0.997430	−	0.0716408i	$-0.0228235\pi$
$587$	141.750	+	342.216i	0.241483	+	0.582991i	−0.755948	+	0.654632i	$0.772824\pi$
$588$	10.3910	−	52.2391i	0.0176718	−	0.0888420i
$589$	20.0634	+	30.0270i	0.0340635	+	0.0509796i
$590$		0			0
$591$	−66.4527	+	66.4527i	−0.112441	+	0.112441i
$592$	−131.300	+	196.505i	−0.221791	+	0.331934i
$593$	−585.245	−	242.416i	−0.986922	−	0.408797i	−0.169937	−	0.985455i	$-0.554356\pi$
$593$	−585.245	−	242.416i	−0.986922	−	0.408797i	−0.816985	+	0.576658i	$0.804356\pi$
$594$		−	344.431i		−	0.579850i
$595$		0			0
$596$	−231.425			−0.388297
$597$	91.9883	−	222.080i	0.154084	−	0.371992i
$598$	−24.3996	−	16.3033i	−0.0408020	−	0.0272630i
$599$	315.855	+	315.855i	0.527304	+	0.527304i	0.919768	−	0.392463i	$-0.128377\pi$
$599$	315.855	+	315.855i	0.527304	+	0.527304i	−0.392463	+	0.919768i	$0.628377\pi$
$600$		0			0
$601$	362.279	−	242.067i	0.602794	−	0.402774i	−0.216388	−	0.976307i	$-0.569428\pi$
$601$	362.279	−	242.067i	0.602794	−	0.402774i	0.819182	+	0.573533i	$0.194428\pi$
$602$	541.887	+	107.788i	0.900145	+	0.179050i
$603$	903.170	−	374.105i	1.49779	−	0.620407i
$604$	259.680	+	626.922i	0.429933	+	1.03795i
$605$		0			0
$606$	10.5261	+	15.7535i	0.0173699	+	0.0259958i
$607$	−123.803	−	622.400i	−0.203959	−	1.02537i	−0.938098	−	0.346371i	$-0.887414\pi$
$607$	−123.803	−	622.400i	−0.203959	−	1.02537i	0.734139	−	0.679000i	$-0.237586\pi$
$608$	−88.1749	+	88.1749i	−0.145025	+	0.145025i
$609$	10.8865	−	16.2928i	0.0178760	−	0.0267534i
$610$		0			0
$611$			88.9259i			0.145542i
$612$	517.778	+	517.778i	0.846042	+	0.846042i
$613$	692.422			1.12956			0.564782	−	0.825240i	$-0.308960\pi$
$613$	692.422			1.12956			0.564782	+	0.825240i	$0.308960\pi$
$614$	184.992	−	446.610i	0.301290	−	0.727377i
$615$		0			0
$616$	−158.152	−	158.152i	−0.256740	−	0.256740i
$617$	263.077	−	52.3292i	0.426381	−	0.0848124i	0.0227645	−	0.999741i	$-0.492753\pi$
$617$	263.077	−	52.3292i	0.426381	−	0.0848124i	0.403616	+	0.914928i	$0.367753\pi$
$618$	−85.0165	+	56.8062i	−0.137567	+	0.0919195i
$619$	−153.549	−	30.5428i	−0.248060	−	0.0493422i	0.0694940	−	0.997582i	$-0.477862\pi$
$619$	−153.549	−	30.5428i	−0.248060	−	0.0493422i	−0.317554	+	0.948240i	$0.602862\pi$
$620$		0			0
$621$	−46.2610	−	111.684i	−0.0744944	−	0.179845i
$622$	−196.680	+	988.775i	−0.316205	+	1.58967i
$623$	−379.241	−	567.575i	−0.608734	−	0.911035i
$624$	−1.78791	−	8.98845i	−0.00286525	−	0.0144046i
$625$		0			0
$626$	−663.623	+	993.182i	−1.06010	+	1.58655i
$627$	17.0519	+	7.06311i	0.0271959	+	0.0112649i
$628$			186.031i			0.296228i
$629$	−334.589	+	223.565i	−0.531938	+	0.355429i
$630$		0			0
$631$	−119.803	+	289.230i	−0.189862	+	0.458368i	−0.989933	−	0.141538i	$-0.954795\pi$
$631$	−119.803	+	289.230i	−0.189862	+	0.458368i	0.800071	+	0.599906i	$0.204795\pi$
$632$	−279.372	−	186.670i	−0.442044	−	0.295365i
$633$	−131.992	−	131.992i	−0.208519	−	0.208519i
$634$	412.999	−	82.1506i	0.651418	−	0.129575i
$635$		0			0
$636$	−247.283	−	49.1877i	−0.388810	−	0.0773392i
$637$	13.2473	−	5.48723i	0.0207965	−	0.00861418i
$638$	−28.7259	−	69.3506i	−0.0450250	−	0.108700i
$639$	172.415	−	866.790i	0.269820	−	1.35648i
$640$		0			0
$641$	−72.2074	−	363.011i	−0.112648	−	0.566320i	−0.995345	−	0.0963771i	$-0.969275\pi$
$641$	−72.2074	−	363.011i	−0.112648	−	0.566320i	0.882697	−	0.469943i	$-0.155725\pi$
$642$	−153.776	+	153.776i	−0.239526	+	0.239526i
$643$	122.220	−	182.915i	0.190077	−	0.284471i	−0.724175	−	0.689616i	$-0.757779\pi$
$643$	122.220	−	182.915i	0.190077	−	0.284471i	0.914252	+	0.405146i	$0.132779\pi$
$644$	−321.577	−	133.202i	−0.499344	−	0.206835i
$645$		0			0
$646$	−133.748	+	55.4001i	−0.207040	+	0.0857586i
$647$	−769.098			−1.18871			−0.594357	−	0.804201i	$-0.702593\pi$
$647$	−769.098			−1.18871			−0.594357	+	0.804201i	$0.702593\pi$
$648$	85.8381	−	207.231i	0.132466	−	0.319802i
$649$	−184.407	−	123.217i	−0.284140	−	0.189856i
$650$		0			0
$651$	−80.3568	+	15.9840i	−0.123436	+	0.0245529i
$652$	685.889	−	458.297i	1.05198	−	0.702909i
$653$	41.6201	+	8.27876i	0.0637368	+	0.0126780i	0.226856	−	0.973928i	$-0.427155\pi$
$653$	41.6201	+	8.27876i	0.0637368	+	0.0126780i	−0.163119	+	0.986606i	$0.552155\pi$
$654$	42.3446	−	17.5397i	0.0647472	−	0.0268192i
$655$		0			0
$656$	42.5406	−	213.866i	0.0648485	−	0.326015i
$657$	−282.796	−	423.234i	−0.430436	−	0.644192i
$658$	365.148	+	1835.72i	0.554936	+	2.78985i
$659$	472.719	−	472.719i	0.717328	−	0.717328i	−0.250729	−	0.968057i	$-0.580670\pi$
$659$	472.719	−	472.719i	0.717328	−	0.717328i	0.968057	+	0.250729i	$0.0806703\pi$
$660$		0			0
$661$	−380.158	−	157.467i	−0.575126	−	0.238225i	0.0761113	−	0.997099i	$-0.475750\pi$
$661$	−380.158	−	157.467i	−0.575126	−	0.238225i	−0.651237	+	0.758874i	$0.725750\pi$
$662$		−	480.756i		−	0.726218i
$663$	3.04428	−	15.3046i	0.00459168	−	0.0230839i
$664$	−419.043			−0.631089
$665$		0			0
$666$	496.914	+	332.027i	0.746116	+	0.498539i
$667$	−18.6292	−	18.6292i	−0.0279298	−	0.0279298i
$668$	−560.937	+	111.577i	−0.839725	+	0.167032i
$669$	245.494	−	164.034i	0.366957	−	0.245193i
$670$		0			0
$671$	272.020	−	112.675i	0.405395	−	0.167920i
$672$	−108.264	−	261.372i	−0.161107	−	0.388946i
$673$	−3.16371	+	15.9051i	−0.00470091	+	0.0236331i	−0.983065	−	0.183260i	$-0.941335\pi$
$673$	−3.16371	+	15.9051i	−0.00470091	+	0.0236331i	0.978364	+	0.206893i	$0.0663351\pi$
$674$	−811.269	−	1214.15i	−1.20366	−	1.80141i
$675$		0			0
$676$	612.536	−	612.536i	0.906119	−	0.906119i
$677$	571.240	−	854.921i	0.843782	−	1.26281i	−0.119099	−	0.992882i	$-0.538001\pi$
$677$	571.240	−	854.921i	0.843782	−	1.26281i	0.962881	−	0.269926i	$-0.0869993\pi$
$678$	137.809	+	57.0825i	0.203258	+	0.0841924i
$679$		−	193.149i		−	0.284461i
$680$		0			0
$681$	78.7512			0.115641
$682$	−120.108	+	289.967i	−0.176112	+	0.425172i
$683$	−188.201	−	125.752i	−0.275551	−	0.184117i	0.410114	−	0.912034i	$-0.365489\pi$
$683$	−188.201	−	125.752i	−0.275551	−	0.184117i	−0.685666	+	0.727917i	$0.740489\pi$
$684$	85.6752	+	85.6752i	0.125256	+	0.125256i
$685$		0			0
$686$	−717.830	+	479.639i	−1.04640	+	0.699181i
$687$	−288.197	−	57.3259i	−0.419500	−	0.0834438i
$688$	214.331	−	88.7787i	0.311527	−	0.129039i
$689$	−25.9748	−	62.7087i	−0.0376993	−	0.0910141i
$690$		0			0
$691$	−21.7058	−	32.4851i	−0.0314122	−	0.0470117i	0.815431	−	0.578854i	$-0.196500\pi$
$691$	−21.7058	−	32.4851i	−0.0314122	−	0.0470117i	−0.846843	+	0.531842i	$0.821500\pi$
$692$	−179.407	−	901.942i	−0.259259	−	1.30338i
$693$	374.046	−	374.046i	0.539749	−	0.539749i
$694$	33.2845	−	49.8138i	0.0479604	−	0.0717778i
$695$		0			0
$696$			8.79713i			0.0126395i
$697$	206.274	−	308.711i	0.295946	−	0.442914i
$698$	−1185.05			−1.69778
$699$	87.1075	−	210.296i	0.124617	−	0.300853i
$700$		0			0
$701$	−401.261	−	401.261i	−0.572412	−	0.572412i	0.360390	−	0.932802i	$-0.382644\pi$
$701$	−401.261	−	401.261i	−0.572412	−	0.572412i	−0.932802	+	0.360390i	$0.882644\pi$
$702$	−47.2585	+	9.40031i	−0.0673198	+	0.0133908i
$703$	−55.3634	+	36.9927i	−0.0787531	+	0.0526212i
$704$	−746.614	−	148.511i	−1.06053	−	0.210953i
$705$		0			0
$706$	226.136	+	545.941i	0.320306	+	0.773288i
$707$	−11.8030	+	59.3377i	−0.0166945	+	0.0839288i
$708$	64.0298	+	95.8273i	0.0904375	+	0.135349i
$709$	55.6759	+	279.901i	0.0785273	+	0.394783i	0.999980	+	0.00629329i	$0.00200323\pi$
$709$	55.6759	+	279.901i	0.0785273	+	0.394783i	−0.921453	+	0.388490i	$0.872997\pi$
$710$		0			0
$711$	441.495	−	660.744i	0.620950	−	0.929317i
$712$	283.128	+	117.276i	0.397652	+	0.164713i
$713$			110.156i			0.154496i
$714$		−	328.438i		−	0.459998i
$715$		0			0
$716$	498.416	−	1203.28i	0.696112	−	1.68056i
$717$	221.961	+	148.310i	0.309569	+	0.206848i
$718$	−761.667	−	761.667i	−1.06082	−	1.06082i
$719$	601.644	−	119.674i	0.836779	−	0.166446i	0.241941	−	0.970291i	$-0.422216\pi$
$719$	601.644	−	119.674i	0.836779	−	0.166446i	0.594838	+	0.803845i	$0.297216\pi$
$720$		0			0
$721$	−320.226	−	63.6970i	−0.444142	−	0.0883453i
$722$	987.549	−	409.056i	1.36780	−	0.566560i
$723$	−75.3748	−	181.971i	−0.104253	−	0.251689i
$724$	303.640	−	1526.50i	0.419392	−	2.10842i
$725$		0			0
$726$	−26.7705	−	134.585i	−0.0368740	−	0.185378i
$727$	−244.413	+	244.413i	−0.336194	+	0.336194i	−0.854933	−	0.518739i	$-0.826402\pi$
$727$	−244.413	+	244.413i	−0.336194	+	0.336194i	0.518739	+	0.854933i	$0.326402\pi$
$728$	−17.3833	+	26.0160i	−0.0238782	+	0.0357363i
$729$	394.941	+	163.590i	0.541758	+	0.224403i
$730$		0			0
$731$	395.009			0.540368
$732$	−153.003			−0.209020
$733$	−516.266	+	1246.38i	−0.704319	+	1.70038i	0.00941053	+	0.999956i	$0.497004\pi$
$733$	−516.266	+	1246.38i	−0.704319	+	1.70038i	−0.713730	+	0.700421i	$0.752996\pi$
$734$	−205.719	−	137.457i	−0.280271	−	0.187271i
$735$		0			0
$736$	−373.058	+	74.2058i	−0.506872	+	0.100823i
$737$	−787.066	+	525.901i	−1.06793	+	0.713569i
$738$	−540.816	−	107.575i	−0.732813	−	0.145766i
$739$	602.925	−	249.740i	0.815866	−	0.337943i	0.0645741	−	0.997913i	$-0.479431\pi$
$739$	602.925	−	249.740i	0.815866	−	0.337943i	0.751292	+	0.659970i	$0.229431\pi$
$740$		0			0
$741$	0.503729	−	2.53241i	0.000679796	−	0.00341756i
$742$	−793.700	−	1187.86i	−1.06968	−	1.60088i
$743$	43.5044	+	218.711i	0.0585523	+	0.294362i	0.998955	−	0.0456999i	$-0.0145518\pi$
$743$	43.5044	+	218.711i	0.0585523	+	0.294362i	−0.940403	+	0.340062i	$0.889552\pi$
$744$	26.0091	−	26.0091i	0.0349584	−	0.0349584i
$745$		0			0
$746$	−214.860	−	88.9980i	−0.288016	−	0.119300i
$747$		−	991.082i		−	1.32675i
$748$	−589.542	−	393.920i	−0.788158	−	0.526631i
$749$	−694.430			−0.927143
$750$		0			0
$751$	−373.353	−	249.467i	−0.497142	−	0.332180i	0.281592	−	0.959534i	$-0.409138\pi$
$751$	−373.353	−	249.467i	−0.497142	−	0.332180i	−0.778734	+	0.627355i	$0.784138\pi$
$752$	555.715	+	555.715i	0.738982	+	0.738982i
$753$	−175.204	+	34.8503i	−0.232675	+	0.0462820i
$754$	−8.73143	+	5.83416i	−0.0115802	+	0.00773761i
$755$		0			0
$756$	−528.027	+	218.716i	−0.698449	+	0.289307i
$757$	17.6369	+	42.5792i	0.0232984	+	0.0562473i	0.935101	−	0.354382i	$-0.115309\pi$
$757$	17.6369	+	42.5792i	0.0232984	+	0.0562473i	−0.911802	+	0.410630i	$0.865309\pi$
$758$	348.021	−	1749.62i	0.459131	−	2.30821i
$759$	31.2779	+	46.8107i	0.0412093	+	0.0616741i
$760$		0			0
$761$	−552.081	+	552.081i	−0.725467	+	0.725467i	−0.969713	−	0.244246i	$-0.921460\pi$
$761$	−552.081	+	552.081i	−0.725467	+	0.725467i	0.244246	+	0.969713i	$0.421460\pi$
$762$	−162.956	+	243.881i	−0.213853	+	0.320054i
$763$	135.215	+	56.0079i	0.177215	+	0.0734048i
$764$		−	684.604i		−	0.896079i
$765$		0			0
$766$	707.240			0.923289
$767$	−11.8734	+	28.6649i	−0.0154803	+	0.0373727i
$768$	−33.7429	−	22.5463i	−0.0439360	−	0.0293571i
$769$	−625.504	−	625.504i	−0.813400	−	0.813400i	0.171742	−	0.985142i	$-0.445060\pi$
$769$	−625.504	−	625.504i	−0.813400	−	0.813400i	−0.985142	+	0.171742i	$0.945060\pi$
$770$		0			0
$771$	−219.723	+	146.814i	−0.284984	+	0.190420i
$772$	1613.95	+	321.035i	2.09061	+	0.415848i
$773$	−1123.75	+	465.474i	−1.45376	+	0.602166i	−0.963090	−	0.269181i	$-0.913247\pi$
$773$	−1123.75	+	465.474i	−1.45376	+	0.602166i	−0.490667	+	0.871347i	$0.663247\pi$
$774$	−224.500	−	541.991i	−0.290052	−	0.700247i
$775$		0			0
$776$	48.1751	+	72.0992i	0.0620813	+	0.0929113i
$777$	−29.4711	−	148.161i	−0.0379293	−	0.190683i
$778$	864.056	−	864.056i	1.11061	−	1.11061i
$779$	34.1316	−	51.0816i	0.0438146	−	0.0655733i
$780$		0			0
$781$			855.757i			1.09572i
$782$	−433.098	−	86.1486i	−0.553834	−	0.110164i
$783$	−43.2592			−0.0552481
$784$	48.4944	−	117.076i	0.0618551	−	0.149331i
$785$		0			0
$786$	297.985	+	297.985i	0.379116	+	0.379116i
$787$	190.336	−	37.8601i	0.241850	−	0.0481069i	−0.0726771	−	0.997356i	$-0.523154\pi$
$787$	190.336	−	37.8601i	0.241850	−	0.0481069i	0.314527	+	0.949249i	$0.398154\pi$
$788$	496.704	−	331.887i	0.630336	−	0.421177i
$789$	−110.556	−	21.9909i	−0.140121	−	0.0278718i
$790$		0			0
$791$	182.276	+	440.053i	0.230437	+	0.556324i
$792$	−46.3305	+	232.919i	−0.0584981	+	0.294090i
$793$	−22.8839	−	34.2481i	−0.0288573	−	0.0431881i
$794$	155.795	+	783.233i	0.196215	+	0.986440i
$795$		0			0
$796$	−848.899	+	1270.47i	−1.06646	+	1.59606i
$797$	−118.577	−	49.1164i	−0.148780	−	0.0616266i	0.307051	−	0.951693i	$-0.400658\pi$
$797$	−118.577	−	49.1164i	−0.148780	−	0.0616266i	−0.455831	+	0.890066i	$0.650658\pi$
$798$		−	54.3457i		−	0.0681024i
$799$	512.088	+	1236.29i	0.640911	+	1.54730i
$800$		0			0
$801$	−277.369	+	669.628i	−0.346278	+	0.835990i
$802$	−602.324	−	402.460i	−0.751028	−	0.501821i
$803$	348.522	+	348.522i	0.434025	+	0.434025i
$804$	482.449	−	95.9651i	0.600061	−	0.119360i
$805$		0			0
$806$	43.0638	+	8.56592i	0.0534290	+	0.0106277i
$807$	−243.873	+	101.016i	−0.302197	+	0.125174i
$808$	−10.3941	−	25.0936i	−0.0128640	−	0.0310564i
$809$	68.1098	−	342.411i	0.0841902	−	0.423253i	−0.915587	−	0.402121i	$-0.868273\pi$
$809$	68.1098	−	342.411i	0.0841902	−	0.423253i	0.999777	−	0.0211316i	$-0.00672688\pi$
$810$		0			0
$811$	36.2150	+	182.065i	0.0446547	+	0.224494i	0.996668	−	0.0815613i	$-0.0259906\pi$
$811$	36.2150	+	182.065i	0.0446547	+	0.224494i	−0.952014	+	0.306056i	$0.900991\pi$
$812$	−88.0762	+	88.0762i	−0.108468	+	0.108468i
$813$	−8.66099	+	12.9621i	−0.0106531	+	0.0159435i
$814$	−534.639	−	221.455i	−0.656804	−	0.272057i
$815$		0			0
$816$	−76.6173	−	114.666i	−0.0938937	−	0.140522i
$817$	65.3610			0.0800013
$818$	301.101	−	726.923i	0.368095	−	0.888659i
$819$	−61.5306	−	41.1134i	−0.0751290	−	0.0501996i
$820$		0			0
$821$	1545.78	−	307.474i	1.88280	−	0.374512i	0.886669	−	0.462404i	$-0.153013\pi$
$821$	1545.78	−	307.474i	1.88280	−	0.374512i	0.996130	+	0.0878920i	$0.0280130\pi$
$822$	354.051	−	236.569i	0.430718	−	0.287797i
$823$	−986.291	−	196.185i	−1.19841	−	0.238378i	−0.444757	−	0.895651i	$-0.646710\pi$
$823$	−986.291	−	196.185i	−1.19841	−	0.238378i	−0.753653	+	0.657273i	$0.771710\pi$
$824$	135.422	−	56.0937i	0.164347	−	0.0680749i
$825$		0			0
$826$	−127.402	+	640.491i	−0.154239	+	0.775413i
$827$	883.014	+	1321.52i	1.06773	+	1.59797i	0.764001	+	0.645216i	$0.223232\pi$
$827$	883.014	+	1321.52i	1.06773	+	1.59797i	0.303731	+	0.952758i	$0.401768\pi$
$828$	72.1020	+	362.481i	0.0870798	+	0.437780i
$829$	−269.747	+	269.747i	−0.325388	+	0.325388i	−0.850830	−	0.525442i	$-0.823900\pi$
$829$	−269.747	+	269.747i	−0.325388	+	0.325388i	0.525442	+	0.850830i	$0.323900\pi$
$830$		0			0
$831$	−231.205	−	95.7684i	−0.278225	−	0.115245i
$832$			106.494i			0.127998i
$833$	152.572	−	152.572i	0.183160	−	0.183160i
$834$	−441.695			−0.529611
$835$		0			0
$836$	−97.5499	−	65.1807i	−0.116686	−	0.0779674i
$837$	127.898	+	127.898i	0.152805	+	0.152805i
$838$	−509.365	+	101.319i	−0.607834	+	0.120906i
$839$	−30.7798	+	20.5664i	−0.0366862	+	0.0245130i	−0.573778	−	0.819011i	$-0.694523\pi$
$839$	−30.7798	+	20.5664i	−0.0366862	+	0.0245130i	0.537092	+	0.843524i	$0.319523\pi$
$840$		0			0
$841$	768.273	−	318.229i	0.913523	−	0.378393i
$842$	−726.154	−	1753.09i	−0.862416	−	2.08206i
$843$	13.7149	−	68.9493i	0.0162691	−	0.0817904i
$844$	659.215	+	986.584i	0.781060	+	1.16894i
$845$		0			0
$846$	1405.27	−	1405.27i	1.66107	−	1.66107i
$847$	243.437	−	364.329i	0.287411	−	0.430141i
$848$	−554.200	−	229.557i	−0.653538	−	0.270704i
$849$		−	6.07887i		−	0.00716004i
$850$		0			0
$851$	−203.104			−0.238665
$852$	170.178	−	410.846i	0.199739	−	0.482213i
$853$	65.5718	+	43.8137i	0.0768720	+	0.0513642i	0.593412	−	0.804899i	$-0.297780\pi$
$853$	65.5718	+	43.8137i	0.0768720	+	0.0513642i	−0.516540	+	0.856263i	$0.672780\pi$
$854$	−613.028	−	613.028i	−0.717831	−	0.717831i
$855$		0			0
$856$	259.219	−	173.204i	0.302825	−	0.202342i
$857$	653.288	+	129.947i	0.762297	+	0.151630i	0.560905	−	0.827880i	$-0.310453\pi$
$857$	653.288	+	129.947i	0.762297	+	0.151630i	0.201392	+	0.979511i	$0.435453\pi$
$858$	20.7322	−	8.58754i	0.0241634	−	0.0100088i
$859$	−530.649	−	1281.10i	−0.617752	−	1.49138i	−0.854308	−	0.519767i	$-0.826019\pi$
$859$	−530.649	−	1281.10i	−0.617752	−	1.49138i	0.236556	−	0.971618i	$-0.423981\pi$
$860$		0			0
$861$	77.4355	+	115.890i	0.0899367	+	0.134600i
$862$	450.150	+	2263.06i	0.522216	+	2.62536i
$863$	375.548	−	375.548i	0.435166	−	0.435166i	−0.455215	−	0.890381i	$-0.650438\pi$
$863$	375.548	−	375.548i	0.435166	−	0.435166i	0.890381	+	0.455215i	$0.150438\pi$
$864$	−346.986	+	519.301i	−0.401604	+	0.601042i
$865$		0			0
$866$			286.613i			0.330962i
$867$	−45.8102	−	230.303i	−0.0528376	−	0.265632i
$868$	520.802			0.600002
$869$	−294.467	+	710.907i	−0.338858	+	0.818075i
$870$		0			0
$871$	93.6384	+	93.6384i	0.107507	+	0.107507i
$872$	−64.4428	+	12.8185i	−0.0739023	+	0.0147001i
$873$	−170.522	+	113.939i	−0.195329	+	0.130515i
$874$	−71.6635	−	14.2548i	−0.0819949	−	0.0163098i
$875$		0			0
$876$	−98.0161	−	236.632i	−0.111891	−	0.270128i
$877$	48.4908	−	243.780i	0.0552917	−	0.277970i	−0.943242	−	0.332107i	$-0.892241\pi$
$877$	48.4908	−	243.780i	0.0552917	−	0.277970i	0.998534	+	0.0541366i	$0.0172406\pi$
$878$	62.1940	+	93.0800i	0.0708360	+	0.106014i
$879$	−12.2080	−	61.3735i	−0.0138885	−	0.0698220i
$880$		0			0
$881$	−81.3688	+	121.777i	−0.0923595	+	0.138226i	−0.874772	−	0.484535i	$-0.838989\pi$
$881$	−81.3688	+	121.777i	−0.0923595	+	0.138226i	0.782412	+	0.622761i	$0.213989\pi$
$882$	−296.057	−	122.631i	−0.335665	−	0.139037i
$883$		−	322.505i		−	0.365237i	−0.983184	−	0.182619i	$-0.941543\pi$
$883$		−	322.505i		−	0.365237i	0.983184	−	0.182619i	$-0.0584574\pi$
$884$	−37.9588	+	91.6407i	−0.0429399	+	0.103666i
$885$		0			0
$886$	734.666	−	1773.64i	0.829194	−	2.00185i
$887$	52.2618	+	34.9202i	0.0589197	+	0.0393689i	0.584681	−	0.811263i	$-0.301220\pi$
$887$	52.2618	+	34.9202i	0.0589197	+	0.0393689i	−0.525762	+	0.850632i	$0.676220\pi$
$888$	47.9552	+	47.9552i	0.0540037	+	0.0540037i
$889$	−918.610	+	182.723i	−1.03331	+	0.205538i
$890$		0			0
$891$	−503.820	−	100.216i	−0.565454	−	0.112476i
$892$	−1733.94	+	718.221i	−1.94388	+	0.805180i
$893$	84.7337	+	204.565i	0.0948866	+	0.229077i
$894$	21.5022	−	108.099i	0.0240517	−	0.120916i
$895$		0			0
$896$	165.574	+	832.399i	0.184793	+	0.929016i
$897$	5.56914	−	5.56914i	0.00620863	−	0.00620863i
$898$	743.106	−	1112.14i	0.827513	−	1.23846i
$899$	36.4189	+	15.0852i	0.0405104	+	0.0167800i
$900$		0			0
$901$	−722.228	−	722.228i	−0.801585	−	0.801585i
$902$	533.932			0.591942
$903$	−56.7469	+	136.999i	−0.0628426	+	0.151715i
$904$	−177.798	−	118.801i	−0.196679	−	0.131417i
$905$		0			0
$906$	−316.964	+	63.0480i	−0.349850	+	0.0695894i
$907$	182.765	−	122.120i	0.201505	−	0.134641i	−0.450724	−	0.892663i	$-0.648834\pi$
$907$	182.765	−	122.120i	0.201505	−	0.134641i	0.652229	+	0.758022i	$0.273834\pi$
$908$	−490.970	−	97.6601i	−0.540716	−	0.107555i
$909$	59.3490	−	24.5832i	0.0652904	−	0.0270442i
$910$		0			0
$911$	98.5913	−	495.652i	0.108223	−	0.544074i	−0.888192	−	0.459473i	$-0.848038\pi$
$911$	98.5913	−	495.652i	0.108223	−	0.544074i	0.996415	−	0.0846014i	$-0.0269617\pi$
$912$	−12.6776	−	18.9734i	−0.0139009	−	0.0208042i
$913$	187.221	+	941.226i	0.205062	+	1.03092i
$914$	−571.150	+	571.150i	−0.624890	+	0.624890i
$915$		0			0
$916$	1725.66	+	714.790i	1.88390	+	0.780338i
$917$			1345.66i			1.46746i
$918$	−602.878	+	402.830i	−0.656730	+	0.438813i
$919$	−930.196			−1.01218			−0.506091	−	0.862480i	$-0.668910\pi$
$919$	−930.196			−1.01218			−0.506091	+	0.862480i	$0.668910\pi$
$920$		0			0
$921$	107.876	+	72.0807i	0.117130	+	0.0782635i
$922$	−966.431	−	966.431i	−1.04819	−	1.04819i
$923$	117.416	−	23.3556i	0.127212	−	0.0253040i
$924$	221.315	−	147.878i	0.239518	−	0.160041i
$925$		0			0
$926$	225.922	−	93.5798i	0.243976	−	0.101058i
$927$	132.667	+	320.288i	0.143115	+	0.345510i
$928$	−26.5547	+	133.499i	−0.0286150	+	0.143857i
$929$	637.592	+	954.224i	0.686321	+	1.02715i	0.997058	+	0.0766557i	$0.0244242\pi$
$929$	637.592	+	954.224i	0.686321	+	1.02715i	−0.310737	+	0.950496i	$0.600576\pi$
$930$		0			0
$931$	25.2457	−	25.2457i	0.0271167	−	0.0271167i
$932$	−803.857	+	1203.06i	−0.862508	+	1.29083i
$933$	−249.980	−	103.545i	−0.267932	−	0.110981i
$934$			249.650i			0.267291i
$935$		0			0
$936$	33.2228			0.0354944
$937$	−517.380	+	1249.07i	−0.552166	+	1.33305i	0.363682	+	0.931523i	$0.381519\pi$
$937$	−517.380	+	1249.07i	−0.552166	+	1.33305i	−0.915848	+	0.401524i	$0.868481\pi$
$938$	2317.50	+	1548.51i	2.47068	+	1.65086i
$939$	−226.691	−	226.691i	−0.241418	−	0.241418i
$940$		0			0
$941$	−1529.70	+	1022.11i	−1.62561	+	1.08620i	−0.695743	+	0.718291i	$0.744925\pi$
$941$	−1529.70	+	1022.11i	−1.62561	+	1.08620i	−0.929864	+	0.367905i	$0.880075\pi$
$942$	−86.8953	−	17.2846i	−0.0922455	−	0.0183488i
$943$	173.131	−	71.7133i	0.183596	−	0.0760480i
$944$	104.933	+	253.331i	0.111158	+	0.268359i
$945$		0			0
$946$	315.592	+	472.317i	0.333607	+	0.499278i
$947$	7.67691	+	38.5945i	0.00810656	+	0.0407544i	0.984627	−	0.174671i	$-0.0558862\pi$
$947$	7.67691	+	38.5945i	0.00810656	+	0.0407544i	−0.976520	+	0.215425i	$0.930886\pi$
$948$	282.745	−	282.745i	0.298255	−	0.298255i
$949$	38.3079	−	57.3319i	0.0403666	−	0.0604129i
$950$		0			0
$951$			113.017i			0.118840i
$952$	−91.8559	+	461.791i	−0.0964873	+	0.485074i
$953$	−183.445			−0.192492			−0.0962458	−	0.995358i	$-0.530683\pi$
$953$	−183.445			−0.192492			−0.0962458	+	0.995358i	$0.530683\pi$
$954$	−580.495	+	1401.44i	−0.608485	+	1.46901i
$955$		0			0
$956$	−1199.89	−	1199.89i	−1.25511	−	1.25511i
$957$	19.7595	−	3.93041i	0.0206473	−	0.00410701i
$958$	1158.85	−	774.317i	1.20965	−	0.808264i
$959$	1333.58	+	265.266i	1.39059	+	0.276606i
$960$		0			0
$961$	304.685	+	735.574i	0.317050	+	0.765426i
$962$	−15.7937	+	79.4005i	−0.0164176	+	0.0825369i
$963$	409.646	+	613.079i	0.425386	+	0.636635i
$964$	244.257	+	1227.96i	0.253378	+	1.27382i
$965$		0			0
$966$	92.0972	−	137.833i	0.0953387	−	0.142684i
$967$	−1181.69	−	489.471i	−1.22201	−	0.506175i	−0.323965	−	0.946069i	$-0.605016\pi$
$967$	−1181.69	−	489.471i	−1.22201	−	0.506175i	−0.898050	+	0.439894i	$0.855016\pi$
$968$			196.715i			0.203218i
$969$	−7.58007	−	38.1076i	−0.00782257	−	0.0393267i
$970$		0			0
$971$	−349.777	+	844.437i	−0.360224	+	0.869657i	0.635043	+	0.772477i	$0.280982\pi$
$971$	−349.777	+	844.437i	−0.360224	+	0.869657i	−0.995267	+	0.0971803i	$0.969018\pi$
$972$	766.473	+	512.141i	0.788553	+	0.526894i
$973$	−997.319	−	997.319i	−1.02499	−	1.02499i
$974$	−1553.32	+	308.974i	−1.59478	+	0.317222i
$975$		0			0
$976$	−357.029	−	71.0174i	−0.365808	−	0.0727637i
$977$	408.510	−	169.210i	0.418126	−	0.173194i	−0.163694	−	0.986511i	$-0.552341\pi$
$977$	408.510	−	169.210i	0.418126	−	0.173194i	0.581820	+	0.813318i	$0.302341\pi$
$978$	150.343	+	362.961i	0.153725	+	0.371126i
$979$	136.919	−	688.340i	0.139856	−	0.703105i
$980$		0			0
$981$	−30.3170	−	152.414i	−0.0309042	−	0.155366i
$982$	−1046.98	+	1046.98i	−1.06617	+	1.06617i
$983$	−369.695	+	553.287i	−0.376088	+	0.562856i	−0.970438	−	0.241351i	$-0.922410\pi$
$983$	−369.695	+	553.287i	−0.376088	+	0.562856i	0.594350	+	0.804207i	$0.297410\pi$
$984$	−57.8106	−	23.9459i	−0.0587506	−	0.0243353i
$985$		0			0
$986$	−87.7920	+	131.390i	−0.0890385	+	0.133256i
$987$	−502.343			−0.508959
$988$	−6.28094	+	15.1635i	−0.00635723	+	0.0153477i
$989$	165.770	+	110.764i	0.167614	+	0.111996i
$990$		0			0
$991$	−1534.80	+	305.291i	−1.54874	+	0.308063i	−0.894096	−	0.447876i	$-0.852181\pi$
$991$	−1534.80	+	305.291i	−1.54874	+	0.308063i	−0.654642	+	0.755939i	$0.727181\pi$
$992$	473.207	−	316.187i	0.477023	−	0.318736i
$993$	126.551	+	25.1726i	0.127443	+	0.0253500i
$994$	2327.96	−	964.271i	2.34201	−	0.970092i
$995$		0			0
$996$	97.2901	−	489.110i	0.0976808	−	0.491075i
$997$	855.639	+	1280.55i	0.858213	+	1.28441i	0.957232	+	0.289321i	$0.0934296\pi$
$997$	855.639	+	1280.55i	0.858213	+	1.28441i	−0.0990189	+	0.995086i	$0.531570\pi$
$998$	299.476	+	1505.57i	0.300076	+	1.50858i
$999$	−235.817	+	235.817i	−0.236053	+	0.236053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.3.u.b.401.1		8
5.2	odd	4		425.3.t.c.299.1		8
5.3	odd	4		425.3.t.a.299.1		8
5.4	even	2		17.3.e.a.10.1	✓	8
15.14	odd	2		153.3.p.b.10.1		8
17.12	odd	16	inner	425.3.u.b.301.1		8
20.19	odd	2		272.3.bh.c.129.1		8
85.4	even	4		289.3.e.i.75.1		8
85.9	even	8		289.3.e.k.249.1		8
85.12	even	16		425.3.t.a.199.1		8
85.14	odd	16		289.3.e.m.158.1		8
85.19	even	8		289.3.e.d.40.1		8
85.24	odd	16		289.3.e.k.65.1		8
85.29	odd	16		17.3.e.a.12.1	yes	8
85.39	odd	16		289.3.e.c.131.1		8
85.44	odd	16		289.3.e.l.65.1		8
85.49	even	8		289.3.e.b.40.1		8
85.54	odd	16		289.3.e.i.158.1		8
85.59	even	8		289.3.e.l.249.1		8
85.63	even	16		425.3.t.c.199.1		8
85.64	even	4		289.3.e.m.75.1		8
85.74	odd	16		289.3.e.d.224.1		8
85.79	odd	16		289.3.e.b.224.1		8
85.84	even	2		289.3.e.c.214.1		8
255.29	even	16		153.3.p.b.46.1		8
340.199	even	16		272.3.bh.c.97.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.a.10.1	✓	8	5.4	even	2
17.3.e.a.12.1	yes	8	85.29	odd	16
153.3.p.b.10.1		8	15.14	odd	2
153.3.p.b.46.1		8	255.29	even	16
272.3.bh.c.97.1		8	340.199	even	16
272.3.bh.c.129.1		8	20.19	odd	2
289.3.e.b.40.1		8	85.49	even	8
289.3.e.b.224.1		8	85.79	odd	16
289.3.e.c.131.1		8	85.39	odd	16
289.3.e.c.214.1		8	85.84	even	2
289.3.e.d.40.1		8	85.19	even	8
289.3.e.d.224.1		8	85.74	odd	16
289.3.e.i.75.1		8	85.4	even	4
289.3.e.i.158.1		8	85.54	odd	16
289.3.e.k.65.1		8	85.24	odd	16
289.3.e.k.249.1		8	85.9	even	8
289.3.e.l.65.1		8	85.44	odd	16
289.3.e.l.249.1		8	85.59	even	8
289.3.e.m.75.1		8	85.64	even	4
289.3.e.m.158.1		8	85.14	odd	16
425.3.t.a.199.1		8	85.12	even	16
425.3.t.a.299.1		8	5.3	odd	4
425.3.t.c.199.1		8	85.63	even	16
425.3.t.c.299.1		8	5.2	odd	4
425.3.u.b.301.1		8	17.12	odd	16	inner
425.3.u.b.401.1		8	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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	425.u (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15851 - 2.79690i) q^{2} +(0.675577 + 0.451406i) q^{3} +(-3.65205 - 3.65205i) q^{4} +(2.04520 - 1.36656i) q^{6} +(7.70353 + 1.53233i) q^{7} +(-3.25778 + 1.34942i) q^{8} +(-3.19151 - 7.70500i) q^{9} +(4.48649 + 6.71450i) q^{11} +(-0.818684 - 4.11580i) q^{12} +(0.798835 - 0.798835i) q^{13} +(13.2104 - 19.7707i) q^{14} -9.98414i q^{16} +(6.50562 - 15.7060i) q^{17} -25.2475 q^{18} +(1.07647 - 2.59882i) q^{19} +(4.51262 + 4.51262i) q^{21} +(23.9774 - 4.76941i) q^{22} +(7.13426 - 4.76696i) q^{23} +(-2.81002 - 0.558947i) q^{24} +(-1.30880 - 3.15972i) q^{26} +(2.74858 - 13.8181i) q^{27} +(-22.5376 - 33.7298i) q^{28} +(-0.599020 - 3.01148i) q^{29} +(-7.13254 + 10.6746i) q^{31} +(-40.9557 - 16.9644i) q^{32} +6.56139i q^{33} +(-36.3911 - 36.3911i) q^{34} +(-16.4835 + 39.7946i) q^{36} +(-19.6817 - 13.1509i) q^{37} +(-6.02153 - 6.02153i) q^{38} +(0.900273 - 0.179075i) q^{39} +(21.4206 + 4.26082i) q^{41} +(17.8493 - 7.39341i) q^{42} +(8.89197 + 21.4671i) q^{43} +(8.13684 - 40.9066i) q^{44} +(-5.06757 - 25.4764i) q^{46} +(-55.6597 + 55.6597i) q^{47} +(4.50690 - 6.74505i) q^{48} +(11.7262 + 4.85715i) q^{49} +(11.4848 - 7.67390i) q^{51} -5.83478 q^{52} +(22.9922 - 55.5080i) q^{53} +(-35.4634 - 23.6959i) q^{54} +(-27.1642 + 5.40329i) q^{56} +(1.90036 - 1.26978i) q^{57} +(-9.11677 - 1.81344i) q^{58} +(-25.3733 + 10.5100i) q^{59} +(7.11302 - 35.7596i) q^{61} +(21.5926 + 32.3156i) q^{62} +(-12.7793 - 64.2461i) q^{63} +(-66.6561 + 66.6561i) q^{64} +(18.3515 + 7.60145i) q^{66} +117.219i q^{67} +(-81.1179 + 33.6001i) q^{68} +6.97157 q^{69} +(88.1108 + 58.8738i) q^{71} +(20.7945 + 20.7945i) q^{72} +(59.8620 - 11.9073i) q^{73} +(-59.5832 + 39.8122i) q^{74} +(-13.4223 + 5.55971i) q^{76} +(24.2730 + 58.6001i) q^{77} +(0.542122 - 2.72543i) q^{78} +(52.9382 + 79.2276i) q^{79} +(-44.9799 + 44.9799i) q^{81} +(36.7331 - 54.9749i) q^{82} +(109.791 + 45.4770i) q^{83} -32.9607i q^{84} +70.3428 q^{86} +(0.954715 - 2.30489i) q^{87} +(-23.6767 - 15.8202i) q^{88} +(-61.4534 - 61.4534i) q^{89} +(7.37792 - 4.92977i) q^{91} +(-43.4639 - 8.64551i) q^{92} +(-9.63715 + 3.99184i) q^{93} +(91.1920 + 220.157i) q^{94} +(-20.0109 - 29.9484i) q^{96} +(-4.79748 - 24.1185i) q^{97} +(27.1699 - 27.1699i) q^{98} +(37.4165 - 55.9978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} - 8 q^{6} - 8 q^{7} + 24 q^{8} - 16 q^{9} - 8 q^{11} - 48 q^{12} - 16 q^{13} + 8 q^{14} - 56 q^{18} - 64 q^{21} + 104 q^{22} + 56 q^{23} - 80 q^{24} + 176 q^{26} - 40 q^{27} - 152 q^{28}+ \cdots - 224 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 - 8 * q^6 - 8 * q^7 + 24 * q^8 - 16 * q^9 - 8 * q^11 - 48 * q^12 - 16 * q^13 + 8 * q^14 - 56 * q^18 - 64 * q^21 + 104 * q^22 + 56 * q^23 - 80 * q^24 + 176 * q^26 - 40 * q^27 - 152 * q^28 + 48 * q^29 + 24 * q^31 - 88 * q^32 - 136 * q^34 - 128 * q^36 - 32 * q^37 + 120 * q^38 + 48 * q^39 + 48 * q^41 - 16 * q^42 + 232 * q^43 + 120 * q^44 - 88 * q^46 - 192 * q^47 - 136 * q^48 + 16 * q^49 + 136 * q^51 + 384 * q^52 + 32 * q^53 + 8 * q^54 - 120 * q^56 - 24 * q^57 - 240 * q^58 - 48 * q^59 - 160 * q^61 + 168 * q^62 - 56 * q^63 - 64 * q^64 - 8 * q^66 - 272 * q^68 + 240 * q^69 + 40 * q^71 - 40 * q^72 - 48 * q^73 - 160 * q^74 + 80 * q^76 + 48 * q^77 + 400 * q^78 - 136 * q^79 - 424 * q^81 + 64 * q^82 + 264 * q^83 + 832 * q^86 - 208 * q^87 - 264 * q^88 + 160 * q^89 + 320 * q^91 - 24 * q^92 + 64 * q^93 + 32 * q^94 - 56 * q^96 - 48 * q^97 + 120 * q^98 - 224 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more