LMFDB - Embedded newform 375.3.k.c.232.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [375,3,Mod(7,375)] 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("375.7"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(375, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 17])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	375.k (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [80,4,0,0,0,0,-4,-72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$10.2180099135$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			232.2
Character	$\chi$	$=$	375.232
Dual form			375.3.k.c.118.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39544 + 2.73870i) q^{2} +(0.270952 - 1.71073i) q^{3} +(-3.20210 - 4.40731i) q^{4} +(4.30707 + 3.12927i) q^{6} +(-0.250082 - 0.250082i) q^{7} +(4.39513 - 0.696119i) q^{8} +(-2.85317 - 0.927051i) q^{9} +(-2.45351 - 7.55112i) q^{11} +(-8.40731 + 4.28374i) q^{12} +(5.38954 + 10.5776i) q^{13} +(1.03387 - 0.335926i) q^{14} +(2.50710 - 7.71607i) q^{16} +(3.81558 + 24.0906i) q^{17} +(6.52034 - 6.52034i) q^{18} +(15.4606 - 21.2797i) q^{19} +(-0.495582 + 0.360061i) q^{21} +(24.1040 + 3.81770i) q^{22} +(11.4516 + 5.83489i) q^{23} -7.70747i q^{24} -36.4896 q^{26} +(-2.35900 + 4.62981i) q^{27} +(-0.301401 + 1.90297i) q^{28} +(27.7376 + 38.1776i) q^{29} +(27.8697 + 20.2485i) q^{31} +(30.2198 + 30.2198i) q^{32} +(-13.5827 + 2.15129i) q^{33} +(-71.3015 - 23.1673i) q^{34} +(5.05032 + 15.5433i) q^{36} +(7.36815 - 3.75426i) q^{37} +(36.7044 + 72.0364i) q^{38} +(19.5556 - 6.35401i) q^{39} +(-14.5062 + 44.6455i) q^{41} +(-0.294547 - 1.85969i) q^{42} +(1.08084 - 1.08084i) q^{43} +(-25.4237 + 34.9928i) q^{44} +(-31.9601 + 23.2203i) q^{46} +(42.5307 + 6.73620i) q^{47} +(-12.5208 - 6.37966i) q^{48} -48.8749i q^{49} +42.2463 q^{51} +(29.3608 - 57.6237i) q^{52} +(-4.55469 + 28.7572i) q^{53} +(-9.38781 - 12.9212i) q^{54} +(-1.27323 - 0.925055i) q^{56} +(-32.2146 - 32.2146i) q^{57} +(-143.263 + 22.6907i) q^{58} +(-71.3918 - 23.1966i) q^{59} +(26.0031 + 80.0294i) q^{61} +(-94.3452 + 48.0713i) q^{62} +(0.481688 + 0.945365i) q^{63} +(-94.0684 + 30.5647i) q^{64} +(13.0621 - 40.2009i) q^{66} +(-6.64899 - 41.9801i) q^{67} +(93.9570 - 93.9570i) q^{68} +(13.0848 - 18.0096i) q^{69} +(49.0998 - 35.6731i) q^{71} +(-13.1854 - 2.08836i) q^{72} +(-84.6079 - 43.1099i) q^{73} +25.4180i q^{74} -143.292 q^{76} +(-1.27482 + 2.50198i) q^{77} +(-9.88694 + 62.4237i) q^{78} +(62.3659 + 85.8393i) q^{79} +(7.28115 + 5.29007i) q^{81} +(-102.028 - 102.028i) q^{82} +(-95.2606 + 15.0878i) q^{83} +(3.17380 + 1.03123i) q^{84} +(1.45185 + 4.46832i) q^{86} +(72.8270 - 37.1072i) q^{87} +(-16.0400 - 31.4802i) q^{88} +(163.312 - 53.0634i) q^{89} +(1.29743 - 3.99309i) q^{91} +(-10.9530 - 69.1547i) q^{92} +(42.1911 - 42.1911i) q^{93} +(-77.7974 + 107.079i) q^{94} +(59.8858 - 43.5096i) q^{96} +(106.110 + 16.8062i) q^{97} +(133.854 + 68.2019i) q^{98} +23.8192i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{2} - 4 q^{7} - 72 q^{8} - 24 q^{12} + 32 q^{13} + 80 q^{16} + 40 q^{17} - 48 q^{18} + 100 q^{19} + 280 q^{22} + 264 q^{23} - 40 q^{26} - 44 q^{28} - 200 q^{29} + 636 q^{32} + 36 q^{33} - 100 q^{34}+ \cdots + 828 q^{98}+O(q^{100}) $ 80 * q + 4 * q^2 - 4 * q^7 - 72 * q^8 - 24 * q^12 + 32 * q^13 + 80 * q^16 + 40 * q^17 - 48 * q^18 + 100 * q^19 + 280 * q^22 + 264 * q^23 - 40 * q^26 - 44 * q^28 - 200 * q^29 + 636 * q^32 + 36 * q^33 - 100 * q^34 - 120 * q^36 - 124 * q^37 + 96 * q^38 + 160 * q^41 - 252 * q^42 - 472 * q^43 + 700 * q^44 - 128 * q^47 - 48 * q^48 - 620 * q^52 - 76 * q^53 + 72 * q^57 - 108 * q^58 - 800 * q^59 - 240 * q^61 - 328 * q^62 + 168 * q^63 - 100 * q^64 - 1240 * q^67 + 104 * q^68 + 216 * q^72 + 244 * q^73 - 648 * q^77 - 120 * q^78 - 200 * q^79 + 180 * q^81 - 168 * q^82 - 44 * q^83 + 1200 * q^84 + 84 * q^87 + 1008 * q^88 + 1500 * q^89 + 2236 * q^92 - 648 * q^93 + 200 * q^94 + 60 * q^96 + 200 * q^97 + 828 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.39544	+	2.73870i	−0.697719	+	1.36935i	0.221327	+	0.975200i	$0.428961\pi$
$2$	−1.39544	+	2.73870i	−0.697719	+	1.36935i	−0.919046	+	0.394151i	$0.871039\pi$
$3$	0.270952	−	1.71073i	0.0903175	−	0.570242i
$3$	0.270952	−	1.71073i	0.0903175	−	0.570242i
$4$	−3.20210	−	4.40731i	−0.800524	−	1.10183i
$5$		0			0
$5$		0			0
$6$	4.30707	+	3.12927i	0.717845	+	0.521545i
$7$	−0.250082	−	0.250082i	−0.0357260	−	0.0357260i	0.689018	−	0.724744i	$-0.258042\pi$
$7$	−0.250082	−	0.250082i	−0.0357260	−	0.0357260i	−0.724744	+	0.689018i	$0.758042\pi$
$8$	4.39513	−	0.696119i	0.549391	−	0.0870149i
$9$	−2.85317	−	0.927051i	−0.317019	−	0.103006i
$10$		0			0
$11$	−2.45351	−	7.55112i	−0.223046	−	0.686466i	−0.998484	−	0.0550418i	$-0.982471\pi$
$11$	−2.45351	−	7.55112i	−0.223046	−	0.686466i	0.775438	−	0.631424i	$-0.217529\pi$
$12$	−8.40731	+	4.28374i	−0.700609	+	0.356978i
$13$	5.38954	+	10.5776i	0.414580	+	0.813659i	0.999996	+	0.00292573i	$0.000931290\pi$
$13$	5.38954	+	10.5776i	0.414580	+	0.813659i	−0.585416	+	0.810733i	$0.699069\pi$
$14$	1.03387	−	0.335926i	0.0738481	−	0.0239947i
$15$		0			0
$16$	2.50710	−	7.71607i	0.156694	−	0.482254i
$17$	3.81558	+	24.0906i	0.224446	+	1.41710i	0.800327	+	0.599563i	$0.204659\pi$
$17$	3.81558	+	24.0906i	0.224446	+	1.41710i	−0.575881	+	0.817533i	$0.695341\pi$
$18$	6.52034	−	6.52034i	0.362241	−	0.362241i
$19$	15.4606	−	21.2797i	0.813715	−	1.11998i	−0.177024	−	0.984206i	$-0.556647\pi$
$19$	15.4606	−	21.2797i	0.813715	−	1.11998i	0.990740	−	0.135776i	$-0.0433529\pi$
$20$		0			0
$21$	−0.495582	+	0.360061i	−0.0235991	+	0.0171458i
$22$	24.1040	+	3.81770i	1.09564	+	0.173532i
$23$	11.4516	+	5.83489i	0.497897	+	0.253691i	0.684858	−	0.728676i	$-0.259864\pi$
$23$	11.4516	+	5.83489i	0.497897	+	0.253691i	−0.186962	+	0.982367i	$0.559864\pi$
$24$		−	7.70747i		−	0.321145i
$25$		0			0
$26$	−36.4896			−1.40344
$27$	−2.35900	+	4.62981i	−0.0873705	+	0.171474i
$28$	−0.301401	+	1.90297i	−0.0107643	+	0.0679634i
$29$	27.7376	+	38.1776i	0.956470	+	1.31647i	0.948593	+	0.316500i	$0.102508\pi$
$29$	27.7376	+	38.1776i	0.956470	+	1.31647i	0.00787767	+	0.999969i	$0.497492\pi$
$30$		0			0
$31$	27.8697	+	20.2485i	0.899023	+	0.653179i	0.938215	−	0.346053i	$-0.112478\pi$
$31$	27.8697	+	20.2485i	0.899023	+	0.653179i	−0.0391915	+	0.999232i	$0.512478\pi$
$32$	30.2198	+	30.2198i	0.944367	+	0.944367i
$33$	−13.5827	+	2.15129i	−0.411597	+	0.0651905i
$34$	−71.3015	−	23.1673i	−2.09710	−	0.681390i
$35$		0			0
$36$	5.05032	+	15.5433i	0.140287	+	0.431758i
$37$	7.36815	−	3.75426i	0.199139	−	0.101466i	−0.351577	−	0.936159i	$-0.614355\pi$
$37$	7.36815	−	3.75426i	0.199139	−	0.101466i	0.550716	+	0.834692i	$0.314355\pi$
$38$	36.7044	+	72.0364i	0.965905	+	1.89569i
$39$	19.5556	−	6.35401i	0.501426	−	0.162923i
$40$		0			0
$41$	−14.5062	+	44.6455i	−0.353810	+	1.08892i	0.602886	+	0.797827i	$0.294017\pi$
$41$	−14.5062	+	44.6455i	−0.353810	+	1.08892i	−0.956696	+	0.291088i	$0.905983\pi$
$42$	−0.294547	−	1.85969i	−0.00701302	−	0.0442784i
$43$	1.08084	−	1.08084i	0.0251357	−	0.0251357i	−0.694427	−	0.719563i	$-0.744342\pi$
$43$	1.08084	−	1.08084i	0.0251357	−	0.0251357i	0.719563	+	0.694427i	$0.244342\pi$
$44$	−25.4237	+	34.9928i	−0.577812	+	0.795291i
$45$		0			0
$46$	−31.9601	+	23.2203i	−0.694784	+	0.504790i
$47$	42.5307	+	6.73620i	0.904909	+	0.143323i	0.591509	−	0.806298i	$-0.298532\pi$
$47$	42.5307	+	6.73620i	0.904909	+	0.143323i	0.313399	+	0.949621i	$0.398532\pi$
$48$	−12.5208	−	6.37966i	−0.260850	−	0.132910i
$49$		−	48.8749i		−	0.997447i
$50$		0			0
$51$	42.2463			0.828360
$52$	29.3608	−	57.6237i	0.564630	−	1.10815i
$53$	−4.55469	+	28.7572i	−0.0859376	+	0.542589i	0.906730	+	0.421712i	$0.138571\pi$
$53$	−4.55469	+	28.7572i	−0.0859376	+	0.542589i	−0.992668	+	0.120877i	$0.961429\pi$
$54$	−9.38781	−	12.9212i	−0.173848	−	0.239282i
$55$		0			0
$56$	−1.27323	−	0.925055i	−0.0227362	−	0.0165188i
$57$	−32.2146	−	32.2146i	−0.565169	−	0.565169i
$58$	−143.263	+	22.6907i	−2.47005	+	0.391218i
$59$	−71.3918	−	23.1966i	−1.21003	−	0.393163i	−0.366588	−	0.930383i	$-0.619474\pi$
$59$	−71.3918	−	23.1966i	−1.21003	−	0.393163i	−0.843442	+	0.537221i	$0.819474\pi$
$60$		0			0
$61$	26.0031	+	80.0294i	0.426281	+	1.31196i	0.901762	+	0.432232i	$0.142274\pi$
$61$	26.0031	+	80.0294i	0.426281	+	1.31196i	−0.475481	+	0.879726i	$0.657726\pi$
$62$	−94.3452	+	48.0713i	−1.52170	+	0.775343i
$63$	0.481688	+	0.945365i	0.00764583	+	0.0150058i
$64$	−94.0684	+	30.5647i	−1.46982	+	0.477573i
$65$		0			0
$66$	13.0621	−	40.2009i	0.197910	−	0.609105i
$67$	−6.64899	−	41.9801i	−0.0992386	−	0.626568i	−0.986306	−	0.164927i	$-0.947261\pi$
$67$	−6.64899	−	41.9801i	−0.0992386	−	0.626568i	0.887067	−	0.461641i	$-0.152739\pi$
$68$	93.9570	−	93.9570i	1.38172	−	1.38172i
$69$	13.0848	−	18.0096i	0.189634	−	0.261009i
$70$		0			0
$71$	49.0998	−	35.6731i	0.691546	−	0.502438i	−0.185622	−	0.982621i	$-0.559430\pi$
$71$	49.0998	−	35.6731i	0.691546	−	0.502438i	0.877168	+	0.480183i	$0.159430\pi$
$72$	−13.1854	−	2.08836i	−0.183130	−	0.0290050i
$73$	−84.6079	−	43.1099i	−1.15901	−	0.590547i	−0.234657	−	0.972078i	$-0.575397\pi$
$73$	−84.6079	−	43.1099i	−1.15901	−	0.590547i	−0.924356	+	0.381532i	$0.875397\pi$
$74$			25.4180i			0.343486i
$75$		0			0
$76$	−143.292			−1.88543
$77$	−1.27482	+	2.50198i	−0.0165561	+	0.0324932i
$78$	−9.88694	+	62.4237i	−0.126756	+	0.800303i
$79$	62.3659	+	85.8393i	0.789442	+	1.08657i	0.994177	+	0.107756i	$0.0343665\pi$
$79$	62.3659	+	85.8393i	0.789442	+	1.08657i	−0.204736	+	0.978817i	$0.565634\pi$
$80$		0			0
$81$	7.28115	+	5.29007i	0.0898908	+	0.0653095i
$82$	−102.028	−	102.028i	−1.24425	−	1.24425i
$83$	−95.2606	+	15.0878i	−1.14772	+	0.181781i	−0.701180	−	0.712984i	$-0.747343\pi$
$83$	−95.2606	+	15.0878i	−1.14772	+	0.181781i	−0.446538	+	0.894765i	$0.647343\pi$
$84$	3.17380	+	1.03123i	0.0377834	+	0.0122766i
$85$		0			0
$86$	1.45185	+	4.46832i	0.0168819	+	0.0519572i
$87$	72.8270	−	37.1072i	0.837092	−	0.426520i
$88$	−16.0400	−	31.4802i	−0.182272	−	0.357730i
$89$	163.312	−	53.0634i	1.83497	−	0.596218i	0.836107	−	0.548567i	$-0.184826\pi$
$89$	163.312	−	53.0634i	1.83497	−	0.596218i	0.998864	−	0.0476516i	$-0.0151737\pi$
$90$		0			0
$91$	1.29743	−	3.99309i	0.0142575	−	0.0438801i
$92$	−10.9530	−	69.1547i	−0.119055	−	0.751681i
$93$	42.1911	−	42.1911i	0.453668	−	0.453668i
$94$	−77.7974	+	107.079i	−0.827632	+	1.13914i
$95$		0			0
$96$	59.8858	−	43.5096i	0.623811	−	0.453225i
$97$	106.110	+	16.8062i	1.09392	+	0.173259i	0.677216	−	0.735784i	$-0.263186\pi$
$97$	106.110	+	16.8062i	1.09392	+	0.173259i	0.416701	+	0.909044i	$0.363186\pi$
$98$	133.854	+	68.2019i	1.36585	+	0.695938i
$99$			23.8192i			0.240598i
$100$		0			0
$101$	−107.110			−1.06049			−0.530247	−	0.847843i	$-0.677901\pi$
$101$	−107.110			−1.06049			−0.530247	+	0.847843i	$0.677901\pi$
$102$	−58.9522	+	115.700i	−0.577962	+	1.13431i
$103$	14.9281	−	94.2525i	0.144933	−	0.915073i	−0.802855	−	0.596174i	$-0.796687\pi$
$103$	14.9281	−	94.2525i	0.144933	−	0.915073i	0.947789	−	0.318899i	$-0.103313\pi$
$104$	31.0510	+	42.7380i	0.298567	+	0.410942i
$105$		0			0
$106$	−72.4016	−	52.6028i	−0.683034	−	0.496253i
$107$	128.543	+	128.543i	1.20134	+	1.20134i	0.973761	+	0.227575i	$0.0730796\pi$
$107$	128.543	+	128.543i	1.20134	+	1.20134i	0.227575	+	0.973761i	$0.426920\pi$
$108$	27.9587	−	4.42823i	0.258877	−	0.0410021i
$109$	89.3002	+	29.0154i	0.819268	+	0.266196i	0.688518	−	0.725219i	$-0.258262\pi$
$109$	89.3002	+	29.0154i	0.819268	+	0.266196i	0.130750	+	0.991415i	$0.458262\pi$
$110$		0			0
$111$	−4.42609	−	13.6221i	−0.0398747	−	0.122722i
$112$	−2.55663	+	1.30267i	−0.0228271	+	0.0116310i
$113$	6.69828	+	13.1461i	0.0592768	+	0.116337i	0.918744	−	0.394853i	$-0.129205\pi$
$113$	6.69828	+	13.1461i	0.0592768	+	0.116337i	−0.859467	+	0.511191i	$0.829205\pi$
$114$	133.180	−	43.2727i	1.16824	−	0.379585i
$115$		0			0
$116$	79.4417	−	244.497i	0.684843	−	2.10773i
$117$	−5.57133	−	35.1760i	−0.0476182	−	0.300649i
$118$	163.151	−	163.151i	1.38264	−	1.38264i
$119$	5.07043	−	6.97885i	0.0426086	−	0.0586458i
$120$		0			0
$121$	46.8913	−	34.0685i	0.387531	−	0.281558i
$122$	−255.462	−	40.4613i	−2.09395	−	0.331650i
$123$	72.4458	+	36.9130i	0.588990	+	0.300105i
$124$		−	187.668i		−	1.51345i
$125$		0			0
$126$	−3.26124			−0.0258828
$127$	−18.4466	+	36.2034i	−0.145249	+	0.285066i	−0.952157	−	0.305611i	$-0.901139\pi$
$127$	−18.4466	+	36.2034i	−0.145249	+	0.285066i	0.806908	+	0.590677i	$0.201139\pi$
$128$	20.8168	−	131.432i	0.162631	−	1.02681i
$129$	−1.55616	−	2.14187i	−0.0120632	−	0.0166036i
$130$		0			0
$131$	121.554	+	88.3139i	0.927890	+	0.674152i	0.945475	−	0.325694i	$-0.105598\pi$
$131$	121.554	+	88.3139i	0.927890	+	0.674152i	−0.0175852	+	0.999845i	$0.505598\pi$
$132$	52.9745	+	52.9745i	0.401322	+	0.401322i
$133$	−9.18808	+	1.45525i	−0.0690833	+	0.0109417i
$134$	124.249	+	40.3710i	0.927232	+	0.301276i
$135$		0			0
$136$	33.5399	+	103.225i	0.246617	+	0.759010i
$137$	14.4013	−	7.33780i	0.105119	−	0.0535606i	−0.400641	−	0.916235i	$-0.631212\pi$
$137$	14.4013	−	7.33780i	0.105119	−	0.0535606i	0.505759	+	0.862675i	$0.331212\pi$
$138$	31.0640	+	60.9665i	0.225101	+	0.441786i
$139$	−45.4296	+	14.7610i	−0.326832	+	0.106194i	−0.467837	−	0.883815i	$-0.654967\pi$
$139$	−45.4296	+	14.7610i	−0.326832	+	0.106194i	0.141005	+	0.990009i	$0.454967\pi$
$140$		0			0
$141$	23.0476	−	70.9332i	0.163458	−	0.503072i
$142$	29.1822	+	184.249i	0.205509	+	1.29753i
$143$	66.6492	−	66.6492i	0.466079	−	0.466079i
$144$	−14.3064	+	19.6910i	−0.0993499	+	0.136743i
$145$		0			0
$146$	236.130	−	171.559i	1.61733	−	1.17506i
$147$	−83.6116	−	13.2428i	−0.568786	−	0.0900869i
$148$	−40.1397	−	20.4522i	−0.271214	−	0.138190i
$149$		−	108.380i		−	0.727379i	−0.931520	−	0.363690i	$-0.881517\pi$
$149$		−	108.380i		−	0.727379i	0.931520	−	0.363690i	$-0.118483\pi$
$150$		0			0
$151$	−59.8487			−0.396349			−0.198175	−	0.980167i	$-0.563501\pi$
$151$	−59.8487			−0.396349			−0.198175	+	0.980167i	$0.563501\pi$
$152$	53.1380	−	104.289i	0.349592	−	0.686114i
$153$	11.4468	−	72.2719i	0.0748154	−	0.472366i
$154$	−5.07324	−	6.98271i	−0.0329431	−	0.0453423i
$155$		0			0
$156$	−90.6231	−	65.8415i	−0.580917	−	0.422061i
$157$	−87.1877	−	87.1877i	−0.555336	−	0.555336i	0.372640	−	0.927976i	$-0.378453\pi$
$157$	−87.1877	−	87.1877i	−0.555336	−	0.555336i	−0.927976	+	0.372640i	$0.878453\pi$
$158$	−322.116	+	51.0181i	−2.03871	+	0.322900i
$159$	47.9616	+	15.5837i	0.301645	+	0.0980105i
$160$		0			0
$161$	−1.40464	−	4.32305i	−0.00872449	−	0.0268512i
$162$	−24.6483	+	12.5589i	−0.152150	+	0.0775243i
$163$	−42.2593	−	82.9386i	−0.259260	−	0.508826i	0.724283	−	0.689503i	$-0.242171\pi$
$163$	−42.2593	−	82.9386i	−0.259260	−	0.508826i	−0.983542	+	0.180677i	$0.942171\pi$
$164$	243.217	−	79.0259i	1.48303	−	0.481865i
$165$		0			0
$166$	91.6093	−	281.944i	0.551863	−	1.69846i
$167$	−37.2062	−	234.911i	−0.222792	−	1.40665i	−0.804837	−	0.593495i	$-0.797748\pi$
$167$	−37.2062	−	234.911i	−0.222792	−	1.40665i	0.582046	−	0.813156i	$-0.302252\pi$
$168$	−1.92750	+	1.92750i	−0.0114732	+	0.0114732i
$169$	16.4979	−	22.7075i	0.0976209	−	0.134364i
$170$		0			0
$171$	−63.8390	+	46.3818i	−0.373328	+	0.271238i
$172$	−8.22451	−	1.30263i	−0.0478169	−	0.00757346i
$173$	−29.4657	−	15.0135i	−0.170322	−	0.0867833i	0.366751	−	0.930319i	$-0.380470\pi$
$173$	−29.4657	−	15.0135i	−0.170322	−	0.0867833i	−0.537073	+	0.843536i	$0.680470\pi$
$174$			251.232i			1.44386i
$175$		0			0
$176$	−64.4162			−0.366001
$177$	−59.0268	+	115.847i	−0.333485	+	0.654501i
$178$	−82.5675	+	521.311i	−0.463862	+	2.92871i
$179$	−157.338	−	216.558i	−0.878985	−	1.20982i	−0.976701	−	0.214605i	$-0.931153\pi$
$179$	−157.338	−	216.558i	−0.878985	−	1.20982i	0.0977154	−	0.995214i	$-0.468847\pi$
$180$		0			0
$181$	−32.1635	−	23.3682i	−0.177699	−	0.129106i	0.495380	−	0.868676i	$-0.335029\pi$
$181$	−32.1635	−	23.3682i	−0.177699	−	0.129106i	−0.673079	+	0.739570i	$0.735029\pi$
$182$	9.12538	+	9.12538i	0.0501395	+	0.0501395i
$183$	143.954	−	22.8001i	0.786634	−	0.124591i
$184$	54.3931	+	17.6734i	0.295615	+	0.0960510i
$185$		0			0
$186$	56.6737	+	174.424i	0.304697	+	0.937762i
$187$	172.550	−	87.9186i	0.922727	−	0.470153i
$188$	−106.499	−	209.016i	−0.566483	−	1.11179i
$189$	1.74778	−	0.567887i	0.00924749	−	0.00300469i
$190$		0			0
$191$	−40.9280	+	125.963i	−0.214283	+	0.659495i	0.784921	+	0.619596i	$0.212704\pi$
$191$	−40.9280	+	125.963i	−0.214283	+	0.659495i	−0.999204	+	0.0398988i	$0.987296\pi$
$192$	26.7997	+	169.207i	0.139582	+	0.881286i
$193$	−31.7199	+	31.7199i	−0.164352	+	0.164352i	−0.784491	−	0.620140i	$-0.787076\pi$
$193$	−31.7199	+	31.7199i	−0.164352	+	0.164352i	0.620140	+	0.784491i	$0.287076\pi$
$194$	−194.097	+	267.151i	−1.00050	+	1.37707i
$195$		0			0
$196$	−215.407	+	156.502i	−1.09901	+	0.798480i
$197$	−169.980	−	26.9222i	−0.862844	−	0.136661i	−0.290700	−	0.956814i	$-0.593888\pi$
$197$	−169.980	−	26.9222i	−0.862844	−	0.136661i	−0.572144	+	0.820153i	$0.693888\pi$
$198$	−65.2336	−	33.2382i	−0.329462	−	0.167870i
$199$		−	26.7052i		−	0.134197i	−0.997746	−	0.0670985i	$-0.978626\pi$
$199$		−	26.7052i		−	0.134197i	0.997746	−	0.0670985i	$-0.0213742\pi$
$200$		0			0
$201$	−73.6179			−0.366258
$202$	149.465	−	293.342i	0.739927	−	1.45219i
$203$	2.61084	−	16.4842i	0.0128613	−	0.0812030i
$204$	−135.277	−	186.193i	−0.663122	−	0.912709i
$205$		0			0
$206$	237.298	+	172.407i	1.15193	+	0.836928i
$207$	−27.2642	−	27.2642i	−0.131711	−	0.131711i
$208$	95.1294	−	15.0670i	0.457353	−	0.0724376i
$209$	−198.618	−	64.5350i	−0.950326	−	0.308780i
$210$		0			0
$211$	4.07202	+	12.5324i	0.0192987	+	0.0593952i	0.960242	−	0.279169i	$-0.0900589\pi$
$211$	4.07202	+	12.5324i	0.0192987	+	0.0593952i	−0.940943	+	0.338564i	$0.890059\pi$
$212$	141.326	−	72.0094i	0.666634	−	0.339667i
$213$	−47.7232	−	93.6620i	−0.224052	−	0.439728i
$214$	−531.414	+	172.667i	−2.48324	+	0.806855i
$215$		0			0
$216$	−7.14522	+	21.9907i	−0.0330797	+	0.101809i
$217$	−1.90592	−	12.0335i	−0.00878305	−	0.0554540i
$218$	−204.077	+	204.077i	−0.936134	+	0.936134i
$219$	−96.6740	+	133.060i	−0.441434	+	0.607581i
$220$		0			0
$221$	−234.256	+	170.197i	−1.05998	+	0.770123i
$222$	43.4832	+	6.88706i	0.195870	+	0.0310228i
$223$	195.116	+	99.4164i	0.874958	+	0.445814i	0.832979	−	0.553305i	$-0.186634\pi$
$223$	195.116	+	99.4164i	0.874958	+	0.445814i	0.0419796	+	0.999118i	$0.486634\pi$
$224$		−	15.1148i		−	0.0674769i
$225$		0			0
$226$	−45.3503			−0.200665
$227$	−68.2679	+	133.983i	−0.300740	+	0.590235i	−0.991083	−	0.133247i	$-0.957460\pi$
$227$	−68.2679	+	133.983i	−0.300740	+	0.590235i	0.690343	+	0.723482i	$0.257460\pi$
$228$	−38.8254	+	245.134i	−0.170287	+	1.07515i
$229$	218.119	+	300.215i	0.952483	+	1.31098i	0.950415	+	0.310983i	$0.100658\pi$
$229$	218.119	+	300.215i	0.952483	+	1.31098i	0.00206788	+	0.999998i	$0.499342\pi$
$230$		0			0
$231$	3.93478	+	2.85879i	0.0170337	+	0.0123757i
$232$	148.487	+	148.487i	0.640028	+	0.640028i
$233$	73.2641	−	11.6039i	0.314438	−	0.0498021i	0.00277928	−	0.999996i	$-0.499115\pi$
$233$	73.2641	−	11.6039i	0.314438	−	0.0498021i	0.311659	+	0.950194i	$0.399115\pi$
$234$	104.111	+	33.8277i	0.444918	+	0.144563i
$235$		0			0
$236$	126.369	+	388.923i	0.535461	+	1.64798i
$237$	163.746	−	83.4326i	0.690910	−	0.352036i
$238$	12.0375	+	23.6249i	0.0505777	+	0.0992644i
$239$	−216.055	+	70.2006i	−0.903996	+	0.293726i	−0.723885	−	0.689920i	$-0.757646\pi$
$239$	−216.055	+	70.2006i	−0.903996	+	0.293726i	−0.180111	+	0.983646i	$0.557646\pi$
$240$		0			0
$241$	−106.433	+	327.566i	−0.441629	+	1.35919i	0.444510	+	0.895774i	$0.353378\pi$
$241$	−106.433	+	327.566i	−0.441629	+	1.35919i	−0.886139	+	0.463420i	$0.846622\pi$
$242$	27.8696	+	175.962i	0.115164	+	0.727115i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$	269.450	−	370.866i	1.10430	−	1.51994i
$245$		0			0
$246$	−202.187	+	146.898i	−0.821899	+	0.597145i
$247$	308.413	+	48.8478i	1.24863	+	0.197764i
$248$	136.586	+	69.5942i	0.550751	+	0.280622i
$249$			167.053i			0.670895i
$250$		0			0
$251$	−210.120			−0.837130			−0.418565	−	0.908187i	$-0.637467\pi$
$251$	−210.120			−0.837130			−0.418565	+	0.908187i	$0.637467\pi$
$252$	2.62410	−	5.15009i	0.0104131	−	0.0204369i
$253$	15.9633	−	100.789i	0.0630962	−	0.398374i
$254$	−73.4094	−	101.039i	−0.289013	−	0.397793i
$255$		0			0
$256$	10.8275	+	7.86664i	0.0422949	+	0.0307290i
$257$	−181.816	−	181.816i	−0.707456	−	0.707456i	0.258544	−	0.966000i	$-0.416757\pi$
$257$	−181.816	−	181.816i	−0.707456	−	0.707456i	−0.966000	+	0.258544i	$0.916757\pi$
$258$	8.03746	−	1.27301i	0.0311529	−	0.00493414i
$259$	−2.78151	−	0.903768i	−0.0107394	−	0.00348945i
$260$		0			0
$261$	−43.7476	−	134.641i	−0.167615	−	0.515867i
$262$	−411.486	+	209.662i	−1.57056	+	0.800238i
$263$	−35.1550	−	68.9955i	−0.133669	−	0.262340i	0.814464	−	0.580214i	$-0.197031\pi$
$263$	−35.1550	−	68.9955i	−0.133669	−	0.262340i	−0.948133	+	0.317874i	$0.897031\pi$
$264$	−58.2001	+	18.9104i	−0.220455	+	0.0716301i
$265$		0			0
$266$	8.83590	−	27.1941i	0.0332177	−	0.102233i
$267$	−46.5271	−	293.761i	−0.174259	−	1.10023i
$268$	−163.728	+	163.728i	−0.610926	+	0.610926i
$269$	187.609	−	258.221i	0.697430	−	0.959931i	−0.302546	−	0.953135i	$-0.597837\pi$
$269$	187.609	−	258.221i	0.697430	−	0.959931i	0.999977	−	0.00679606i	$-0.00216327\pi$
$270$		0			0
$271$	286.845	−	208.405i	1.05847	−	0.769022i	0.0846638	−	0.996410i	$-0.473018\pi$
$271$	286.845	−	208.405i	1.05847	−	0.769022i	0.973804	+	0.227387i	$0.0730184\pi$
$272$	195.451	+	30.9564i	0.718571	+	0.113810i
$273$	−6.47953	−	3.30149i	−0.0237346	−	0.0120934i
$274$			49.6802i			0.181314i
$275$		0			0
$276$	−121.273			−0.439393
$277$	−150.469	+	295.312i	−0.543209	+	1.06611i	0.442360	+	0.896837i	$0.354141\pi$
$277$	−150.469	+	295.312i	−0.543209	+	1.06611i	−0.985570	+	0.169271i	$0.945859\pi$
$278$	22.9683	−	145.016i	0.0826198	−	0.521641i
$279$	−60.7456	−	83.6092i	−0.217726	−	0.299674i
$280$		0			0
$281$	−87.3274	−	63.4471i	−0.310774	−	0.225790i	0.421455	−	0.906849i	$-0.361520\pi$
$281$	−87.3274	−	63.4471i	−0.310774	−	0.225790i	−0.732228	+	0.681059i	$0.761520\pi$
$282$	162.103	+	162.103i	0.574835	+	0.574835i
$283$	132.020	−	20.9100i	0.466503	−	0.0738868i	0.0812417	−	0.996694i	$-0.474111\pi$
$283$	132.020	−	20.9100i	0.466503	−	0.0738868i	0.385261	+	0.922808i	$0.374111\pi$
$284$	−314.444	−	102.169i	−1.10720	−	0.359751i
$285$		0			0
$286$	89.5275	+	275.537i	0.313033	+	0.963417i
$287$	14.7928	−	7.53730i	0.0515428	−	0.0262624i
$288$	−58.2068	−	114.237i	−0.202107	−	0.396657i
$289$	−290.945	+	94.5339i	−1.00673	+	0.327107i
$290$		0			0
$291$	57.5015	−	176.971i	0.197600	−	0.608149i
$292$	80.9242	+	510.935i	0.277138	+	1.74978i
$293$	−255.208	+	255.208i	−0.871017	+	0.871017i	−0.992583	−	0.121566i	$-0.961208\pi$
$293$	−255.208	+	255.208i	−0.871017	+	0.871017i	0.121566	+	0.992583i	$0.461208\pi$
$294$	152.943	−	210.508i	0.520214	−	0.716013i
$295$		0			0
$296$	29.7705	−	21.6295i	0.100576	−	0.0730728i
$297$	40.7481	+	6.45386i	0.137199	+	0.0217302i
$298$	296.819	+	151.237i	0.996037	+	0.507506i
$299$			152.578i			0.510293i
$300$		0			0
$301$	−0.540595			−0.00179600
$302$	83.5152	−	163.908i	0.276540	−	0.542741i
$303$	−29.0217	+	183.236i	−0.0957811	+	0.604738i
$304$	−125.434	−	172.645i	−0.412612	−	0.567912i
$305$		0			0
$306$	181.958	+	132.200i	0.594634	+	0.432027i
$307$	−299.563	−	299.563i	−0.975775	−	0.975775i	0.0239382	−	0.999713i	$-0.492380\pi$
$307$	−299.563	−	299.563i	−0.975775	−	0.975775i	−0.999713	+	0.0239382i	$0.992380\pi$
$308$	15.1091	−	2.39304i	0.0490555	−	0.00776962i
$309$	−157.195	−	51.0759i	−0.508723	−	0.165294i
$310$		0			0
$311$	−11.4518	−	35.2451i	−0.0368226	−	0.113328i	0.930956	−	0.365132i	$-0.118976\pi$
$311$	−11.4518	−	35.2451i	−0.0368226	−	0.113328i	−0.967778	+	0.251804i	$0.918976\pi$
$312$	81.5263	−	41.5397i	0.261302	−	0.133140i
$313$	−190.953	−	374.766i	−0.610073	−	1.19734i	−0.964953	−	0.262424i	$-0.915478\pi$
$313$	−190.953	−	374.766i	−0.610073	−	1.19734i	0.354880	−	0.934912i	$-0.384522\pi$
$314$	360.446	−	117.116i	1.14792	−	0.372981i
$315$		0			0
$316$	178.618	−	549.731i	0.565248	−	1.73966i
$317$	25.6622	+	162.025i	0.0809533	+	0.511119i	0.994530	+	0.104452i	$0.0333090\pi$
$317$	25.6622	+	162.025i	0.0809533	+	0.511119i	−0.913577	+	0.406667i	$0.866691\pi$
$318$	−109.606	+	109.606i	−0.344674	+	0.344674i
$319$	220.229	−	303.119i	0.690373	−	0.950218i
$320$		0			0
$321$	254.731	−	185.073i	0.793554	−	0.576550i
$322$	13.7996	+	2.18565i	0.0428560	+	0.00678772i
$323$	571.632	+	291.261i	1.76976	+	0.901738i
$324$		−	49.0296i		−	0.151326i
$325$		0			0
$326$	286.114			0.877652
$327$	73.8335	−	144.906i	0.225790	−	0.443139i
$328$	−32.6780	+	206.321i	−0.0996280	+	0.629027i
$329$	−8.95156	−	12.3208i	−0.0272084	−	0.0374491i
$330$		0			0
$331$	265.305	+	192.756i	0.801527	+	0.582343i	0.911362	−	0.411607i	$-0.135032\pi$
$331$	265.305	+	192.756i	0.801527	+	0.582343i	−0.109835	+	0.993950i	$0.535032\pi$
$332$	371.530	+	371.530i	1.11907	+	1.11907i
$333$	−24.5030	+	3.88089i	−0.0735825	+	0.0116543i
$334$	695.269	+	225.907i	2.08164	+	0.676367i
$335$		0			0
$336$	1.53578	+	4.72666i	0.00457079	+	0.0140674i
$337$	−408.154	+	207.965i	−1.21114	+	0.617107i	−0.938590	−	0.345035i	$-0.887867\pi$
$337$	−408.154	+	207.965i	−1.21114	+	0.617107i	−0.272550	+	0.962142i	$0.587867\pi$
$338$	39.1671	+	76.8697i	0.115879	+	0.227425i
$339$	24.3043	−	7.89696i	0.0716942	−	0.0232949i
$340$		0			0
$341$	84.5206	−	260.128i	0.247861	−	0.762838i
$342$	−37.9424	−	239.559i	−0.110943	−	0.700465i
$343$	−24.4768	+	24.4768i	−0.0713608	+	0.0713608i
$344$	3.99802	−	5.50280i	0.0116221	−	0.0159965i
$345$		0			0
$346$	82.2351	−	59.7473i	0.237674	−	0.172680i
$347$	383.531	+	60.7454i	1.10528	+	0.175059i	0.682293	−	0.731078i	$-0.260983\pi$
$347$	383.531	+	60.7454i	1.10528	+	0.175059i	0.422984	+	0.906137i	$0.360983\pi$
$348$	−396.742	−	202.150i	−1.14006	−	0.580891i
$349$		−	160.925i		−	0.461103i	−0.973060	−	0.230552i	$-0.925947\pi$
$349$		−	160.925i		−	0.461103i	0.973060	−	0.230552i	$-0.0740530\pi$
$350$		0			0
$351$	−61.6860			−0.175744
$352$	154.049	−	302.338i	0.437638	−	0.858913i
$353$	−11.1745	+	70.5532i	−0.0316559	+	0.199868i	−0.998448	−	0.0556979i	$-0.982262\pi$
$353$	−11.1745	+	70.5532i	−0.0316559	+	0.199868i	0.966792	+	0.255565i	$0.0822616\pi$
$354$	−234.901	−	323.313i	−0.663562	−	0.913315i
$355$		0			0
$356$	−756.809	−	549.854i	−2.12587	−	1.54453i
$357$	−10.5650	−	10.5650i	−0.0295940	−	0.0295940i
$358$	812.643	−	128.710i	2.26995	−	0.359525i
$359$	−96.8130	−	31.4565i	−0.269674	−	0.0876225i	0.171058	−	0.985261i	$-0.445281\pi$
$359$	−96.8130	−	31.4565i	−0.269674	−	0.0876225i	−0.440733	+	0.897638i	$0.645281\pi$
$360$		0			0
$361$	−102.240	−	314.661i	−0.283212	−	0.871638i
$362$	108.881	−	55.4774i	0.300775	−	0.153253i
$363$	−45.5766	−	89.4491i	−0.125555	−	0.246416i
$364$	−21.7533	+	7.06806i	−0.0597617	+	0.0194177i
$365$		0			0
$366$	−138.436	+	426.063i	−0.378241	+	1.16411i
$367$	65.6306	+	414.375i	0.178830	+	1.12909i	0.899858	+	0.436183i	$0.143670\pi$
$367$	65.6306	+	414.375i	0.178830	+	1.12909i	−0.721028	+	0.692906i	$0.756330\pi$
$368$	73.7328	−	73.7328i	0.200361	−	0.200361i
$369$	82.7774	−	113.933i	0.224329	−	0.308762i
$370$		0			0
$371$	8.33070	−	6.05261i	0.0224547	−	0.0163143i
$372$	−321.049	−	50.8492i	−0.863035	−	0.136691i
$373$	−352.748	−	179.734i	−0.945705	−	0.481861i	−0.0880667	−	0.996115i	$-0.528069\pi$
$373$	−352.748	−	179.734i	−0.945705	−	0.481861i	−0.857638	+	0.514254i	$0.828069\pi$
$374$			595.248i			1.59157i
$375$		0			0
$376$	191.617			0.509620
$377$	−254.333	+	499.156i	−0.674623	+	1.32402i
$378$	−0.883640	+	5.57908i	−0.00233767	+	0.0147595i
$379$	364.178	+	501.248i	0.960892	+	1.32255i	0.946516	+	0.322657i	$0.104576\pi$
$379$	364.178	+	501.248i	0.960892	+	1.32255i	0.0143757	+	0.999897i	$0.495424\pi$
$380$		0			0
$381$	56.9360	+	41.3665i	0.149438	+	0.108573i
$382$	−287.864	−	287.864i	−0.753570	−	0.753570i
$383$	242.068	−	38.3398i	0.632031	−	0.100104i	0.167804	−	0.985820i	$-0.446332\pi$
$383$	242.068	−	38.3398i	0.632031	−	0.100104i	0.464227	+	0.885716i	$0.346332\pi$
$384$	−219.204	−	71.2237i	−0.570844	−	0.185478i
$385$		0			0
$386$	−42.6081	−	131.134i	−0.110384	−	0.339726i
$387$	−4.08580	+	2.08182i	−0.0105576	+	0.00537937i
$388$	−265.704	−	521.474i	−0.684805	−	1.34401i
$389$	−21.1457	+	6.87066i	−0.0543591	+	0.0176624i	−0.336070	−	0.941837i	$-0.609098\pi$
$389$	−21.1457	+	6.87066i	−0.0543591	+	0.0176624i	0.281711	+	0.959499i	$0.409098\pi$
$390$		0			0
$391$	−96.8717	+	298.141i	−0.247754	+	0.762508i
$392$	−34.0228	−	214.811i	−0.0867928	−	0.547988i
$393$	184.016	−	184.016i	0.468234	−	0.468234i
$394$	310.929	−	427.957i	0.789159	−	1.08618i
$395$		0			0
$396$	104.978	−	76.2712i	0.265097	−	0.192604i
$397$	−172.591	−	27.3358i	−0.434739	−	0.0688559i	−0.0647705	−	0.997900i	$-0.520632\pi$
$397$	−172.591	−	27.3358i	−0.434739	−	0.0688559i	−0.369968	+	0.929044i	$0.620632\pi$
$398$	73.1375	+	37.2654i	0.183763	+	0.0936317i
$399$			16.1126i			0.0403824i
$400$		0			0
$401$	−352.160			−0.878204			−0.439102	−	0.898437i	$-0.644703\pi$
$401$	−352.160			−0.878204			−0.439102	+	0.898437i	$0.644703\pi$
$402$	102.729	−	201.618i	0.255545	−	0.501536i
$403$	−63.9753	+	403.924i	−0.158748	+	1.00229i
$404$	342.976	+	472.066i	0.848951	+	1.16848i
$405$		0			0
$406$	41.5021	+	30.1530i	0.102222	+	0.0742685i
$407$	−46.4267	−	46.4267i	−0.114070	−	0.114070i
$408$	185.678	−	29.4085i	0.455093	−	0.0720797i
$409$	454.282	+	147.605i	1.11071	+	0.360893i	0.806217	−	0.591620i	$-0.201511\pi$
$409$	454.282	+	147.605i	1.11071	+	0.360893i	0.304498	+	0.952513i	$0.401511\pi$
$410$		0			0
$411$	−8.65092	−	26.6248i	−0.0210485	−	0.0647805i
$412$	−463.201	+	236.013i	−1.12427	+	0.572846i
$413$	12.0527	+	23.6548i	0.0291834	+	0.0572756i
$414$	112.714	−	36.6230i	0.272256	−	0.0884613i
$415$		0			0
$416$	−156.781	+	482.522i	−0.376877	+	1.15991i
$417$	12.9427	+	81.7172i	0.0310377	+	0.195965i
$418$	453.901	−	453.901i	1.08589	−	1.08589i
$419$	−362.429	+	498.840i	−0.864985	+	1.19055i	0.115373	+	0.993322i	$0.463194\pi$
$419$	−362.429	+	498.840i	−0.864985	+	1.19055i	−0.980358	+	0.197227i	$0.936806\pi$
$420$		0			0
$421$	374.959	−	272.424i	0.890639	−	0.647087i	−0.0454057	−	0.998969i	$-0.514458\pi$
$421$	374.959	−	272.424i	0.890639	−	0.647087i	0.936044	+	0.351882i	$0.114458\pi$
$422$	−40.0047	−	6.33613i	−0.0947980	−	0.0150145i
$423$	−115.103	−	58.6477i	−0.272110	−	0.138647i
$424$			129.562i			0.305571i
$425$		0			0
$426$	323.107			0.758467
$427$	13.5110	−	26.5168i	0.0316417	−	0.0621003i
$428$	154.921	−	978.134i	0.361966	−	2.28536i
$429$	−95.9598	−	132.077i	−0.223683	−	0.307873i
$430$		0			0
$431$	−19.0751	−	13.8589i	−0.0442578	−	0.0321552i	0.565436	−	0.824792i	$-0.308708\pi$
$431$	−19.0751	−	13.8589i	−0.0442578	−	0.0321552i	−0.609694	+	0.792637i	$0.708708\pi$
$432$	29.8096	+	29.8096i	0.0690038	+	0.0690038i
$433$	−110.943	+	17.5716i	−0.256218	+	0.0405810i	−0.283222	−	0.959054i	$-0.591403\pi$
$433$	−110.943	+	17.5716i	−0.256218	+	0.0405810i	0.0270038	+	0.999635i	$0.491403\pi$
$434$	35.6158	+	11.5723i	0.0820640	+	0.0266642i
$435$		0			0
$436$	−158.068	−	486.483i	−0.362541	−	1.11579i
$437$	301.213	−	153.476i	0.689276	−	0.351203i
$438$	−229.510	−	450.439i	−0.523995	−	1.02840i
$439$	−519.678	+	168.854i	−1.18378	+	0.384632i	−0.833768	−	0.552114i	$-0.813821\pi$
$439$	−519.678	+	168.854i	−1.18378	+	0.384632i	−0.350008	+	0.936747i	$0.613821\pi$
$440$		0			0
$441$	−45.3095	+	139.448i	−0.102743	+	0.316210i
$442$	−139.229	−	879.057i	−0.314998	−	1.98882i
$443$	−165.809	+	165.809i	−0.374287	+	0.374287i	−0.869036	−	0.494749i	$-0.835260\pi$
$443$	−165.809	+	165.809i	−0.374287	+	0.374287i	0.494749	+	0.869036i	$0.335260\pi$
$444$	−45.8640	+	63.1264i	−0.103297	+	0.142177i
$445$		0			0
$446$	−544.544	+	395.634i	−1.22095	+	0.887072i
$447$	−185.408	−	29.3657i	−0.414782	−	0.0656951i
$448$	31.1685	+	15.8811i	0.0695725	+	0.0354490i
$449$		−	201.205i		−	0.448119i	−0.974576	−	0.224059i	$-0.928069\pi$
$449$		−	201.205i		−	0.448119i	0.974576	−	0.224059i	$-0.0719309\pi$
$450$		0			0
$451$	372.715			0.826419
$452$	36.4904	−	71.6165i	0.0807311	−	0.158444i
$453$	−16.2162	+	102.385i	−0.0357973	+	0.226015i
$454$	−271.677	−	373.931i	−0.598407	−	0.823636i
$455$		0			0
$456$	−164.013	−	119.162i	−0.359677	−	0.261320i
$457$	449.591	+	449.591i	0.983788	+	0.983788i	0.999871	−	0.0160822i	$-0.00511934\pi$
$457$	449.591	+	449.591i	0.983788	+	0.983788i	−0.0160822	+	0.999871i	$0.505119\pi$
$458$	−1126.57	+	178.431i	−2.45976	+	0.389587i
$459$	−120.536	−	39.1645i	−0.262606	−	0.0853258i
$460$		0			0
$461$	−130.749	−	402.403i	−0.283620	−	0.872892i	−0.986809	−	0.161889i	$-0.948241\pi$
$461$	−130.749	−	402.403i	−0.283620	−	0.872892i	0.703189	−	0.711003i	$-0.251759\pi$
$462$	−13.3201	+	6.78694i	−0.0288314	+	0.0146903i
$463$	298.580	+	585.996i	0.644881	+	1.26565i	0.949676	+	0.313233i	$0.101412\pi$
$463$	298.580	+	585.996i	0.644881	+	1.26565i	−0.304795	+	0.952418i	$0.598588\pi$
$464$	364.122	−	118.310i	0.784746	−	0.254979i
$465$		0			0
$466$	−70.4559	+	216.841i	−0.151193	+	0.465324i
$467$	−102.897	−	649.664i	−0.220335	−	1.39114i	−0.811387	−	0.584509i	$-0.801287\pi$
$467$	−102.897	−	649.664i	−0.220335	−	1.39114i	0.591052	−	0.806634i	$-0.298713\pi$
$468$	−137.191	+	137.191i	−0.293144	+	0.293144i
$469$	−8.83566	+	12.1612i	−0.0188394	+	0.0259302i
$470$		0			0
$471$	−172.778	+	125.531i	−0.366832	+	0.266519i
$472$	−329.923	−	52.2547i	−0.698990	−	0.110709i
$473$	−10.8134	−	5.50968i	−0.0228612	−	0.0116484i
$474$			564.875i			1.19172i
$475$		0			0
$476$	−46.9939			−0.0987267
$477$	39.6547	−	77.8267i	0.0831336	−	0.163159i
$478$	109.233	−	689.671i	0.228521	−	1.44283i
$479$	394.709	+	543.270i	0.824026	+	1.13418i	0.989006	+	0.147878i	$0.0472443\pi$
$479$	394.709	+	543.270i	0.824026	+	1.13418i	−0.164979	+	0.986297i	$0.552756\pi$
$480$		0			0
$481$	79.4218	+	57.7033i	0.165118	+	0.119965i
$482$	−748.584	−	748.584i	−1.55308	−	1.55308i
$483$	−7.77614	+	1.23162i	−0.0160997	+	0.00254994i
$484$	−300.301	−	97.5736i	−0.620456	−	0.201598i
$485$		0			0
$486$	14.8064	+	45.5694i	0.0304658	+	0.0937642i
$487$	93.9218	−	47.8556i	0.192858	−	0.0982660i	−0.354895	−	0.934906i	$-0.615483\pi$
$487$	93.9218	−	47.8556i	0.192858	−	0.0982660i	0.547753	+	0.836640i	$0.315483\pi$
$488$	169.997	+	333.638i	0.348355	+	0.683685i
$489$	−153.336	+	49.8218i	−0.313570	+	0.101885i
$490$		0			0
$491$	52.5414	−	161.706i	0.107009	−	0.329340i	−0.883188	−	0.469020i	$-0.844607\pi$
$491$	52.5414	−	161.706i	0.107009	−	0.329340i	0.990197	+	0.139680i	$0.0446073\pi$
$492$	−69.2916	−	437.490i	−0.140836	−	0.889207i
$493$	−813.888	+	813.888i	−1.65089	+	1.65089i
$494$	−564.150	+	776.486i	−1.14200	+	1.57183i
$495$		0			0
$496$	226.111	−	164.280i	0.455870	−	0.331209i
$497$	−21.2002	−	3.35778i	−0.0426563	−	0.00675609i
$498$	−457.508	−	233.112i	−0.918690	−	0.468096i
$499$		−	290.197i		−	0.581557i	−0.956790	−	0.290779i	$-0.906086\pi$
$499$		−	290.197i		−	0.581557i	0.956790	−	0.290779i	$-0.0939143\pi$
$500$		0			0
$501$	−411.949			−0.822254
$502$	293.209	−	575.455i	0.584081	−	1.14632i
$503$	20.4555	−	129.151i	0.0406671	−	0.256762i	−0.958976	−	0.283488i	$-0.908508\pi$
$503$	20.4555	−	129.151i	0.0406671	−	0.256762i	0.999643	+	0.0267264i	$0.00850830\pi$
$504$	2.77516	+	3.81969i	0.00550628	+	0.00757874i
$505$		0			0
$506$	253.754	+	184.363i	0.501490	+	0.364354i
$507$	−34.3761	−	34.3761i	−0.0678029	−	0.0678029i
$508$	218.627	−	34.6272i	0.430369	−	0.0681637i
$509$	88.4961	+	28.7541i	0.173863	+	0.0564914i	0.394655	−	0.918830i	$-0.370864\pi$
$509$	88.4961	+	28.7541i	0.173863	+	0.0564914i	−0.220792	+	0.975321i	$0.570864\pi$
$510$		0			0
$511$	10.3779	+	31.9399i	0.0203090	+	0.0625048i
$512$	437.613	−	222.975i	0.854713	−	0.435498i
$513$	62.0492	+	121.778i	0.120954	+	0.237385i
$514$	751.653	−	244.227i	1.46236	−	0.475150i
$515$		0			0
$516$	−4.45690	+	13.7169i	−0.00863741	+	0.0265832i
$517$	−53.4836	−	337.682i	−0.103450	−	0.653157i
$518$	6.35658	−	6.35658i	0.0122714	−	0.0122714i
$519$	−33.6678	+	46.3398i	−0.0648706	+	0.0892867i
$520$		0			0
$521$	−55.2207	+	40.1202i	−0.105990	+	0.0770062i	−0.639518	−	0.768776i	$-0.720866\pi$
$521$	−55.2207	+	40.1202i	−0.105990	+	0.0770062i	0.533528	+	0.845782i	$0.320866\pi$
$522$	429.789	+	68.0720i	0.823351	+	0.130406i
$523$	−766.544	−	390.574i	−1.46567	−	0.746795i	−0.474605	−	0.880199i	$-0.657409\pi$
$523$	−766.544	−	390.574i	−1.46567	−	0.746795i	−0.991062	+	0.133404i	$0.957409\pi$
$524$		−	818.513i		−	1.56205i
$525$		0			0
$526$	238.015			0.452499
$527$	−381.461	+	748.660i	−0.723835	+	1.42061i
$528$	−17.4537	+	110.199i	−0.0330563	+	0.208709i
$529$	−213.845	−	294.332i	−0.404243	−	0.556393i
$530$		0			0
$531$	182.188	+	132.368i	0.343104	+	0.249280i
$532$	35.8348	+	35.8348i	0.0673587	+	0.0673587i
$533$	−550.423	+	87.1784i	−1.03269	+	0.163562i
$534$	869.448	+	282.501i	1.62818	+	0.529028i
$535$		0			0
$536$	−58.4463	−	179.879i	−0.109042	−	0.335595i
$537$	−413.102	+	210.486i	−0.769278	+	0.391967i
$538$	445.395	+	874.136i	0.827871	+	1.62479i
$539$	−369.061	+	119.915i	−0.684713	+	0.222477i
$540$		0			0
$541$	−6.85938	+	21.1110i	−0.0126791	+	0.0390222i	−0.957196	−	0.289441i	$-0.906531\pi$
$541$	−6.85938	+	21.1110i	−0.0126791	+	0.0390222i	0.944517	+	0.328463i	$0.106531\pi$
$542$	170.485	+	1076.40i	0.314548	+	1.98598i
$543$	−48.6913	+	48.6913i	−0.0896710	+	0.0896710i
$544$	−612.707	+	843.319i	−1.12630	+	1.55022i
$545$		0			0
$546$	18.0836	−	13.1385i	0.0331201	−	0.0240632i
$547$	428.590	+	67.8821i	0.783529	+	0.124099i	0.535367	−	0.844620i	$-0.320173\pi$
$547$	428.590	+	67.8821i	0.783529	+	0.124099i	0.248162	+	0.968718i	$0.420173\pi$
$548$	−78.4541	−	39.9744i	−0.143164	−	0.0729459i
$549$		−	252.444i		−	0.459825i
$550$		0			0
$551$	1241.25			2.25272
$552$	44.9723	−	88.2631i	0.0814715	−	0.159897i
$553$	5.87027	−	37.0634i	0.0106153	−	0.0670225i
$554$	−598.801	−	824.179i	−1.08087	−	1.48769i
$555$		0			0
$556$	210.526	+	152.956i	0.378644	+	0.275101i
$557$	−161.067	−	161.067i	−0.289169	−	0.289169i	0.547583	−	0.836752i	$-0.315548\pi$
$557$	−161.067	−	161.067i	−0.289169	−	0.289169i	−0.836752	+	0.547583i	$0.815548\pi$
$558$	313.747	−	49.6927i	0.562271	−	0.0890550i
$559$	17.2578	+	5.60740i	0.0308727	+	0.0100311i
$560$		0			0
$561$	−103.652	−	319.007i	−0.184763	−	0.568641i
$562$	295.623	−	150.627i	0.526019	−	0.268020i
$563$	86.4014	+	169.572i	0.153466	+	0.301194i	0.954920	−	0.296862i	$-0.0959401\pi$
$563$	86.4014	+	169.572i	0.153466	+	0.301194i	−0.801454	+	0.598056i	$0.795940\pi$
$564$	−386.425	+	125.557i	−0.685151	+	0.222619i
$565$		0			0
$566$	−126.960	+	390.743i	−0.224311	+	0.690358i
$567$	−0.497935	−	3.14384i	−0.000878192	−	0.00554468i
$568$	190.967	−	190.967i	0.336210	−	0.336210i
$569$	249.297	−	343.128i	0.438132	−	0.603036i	−0.531664	−	0.846955i	$-0.678433\pi$
$569$	249.297	−	343.128i	0.438132	−	0.603036i	0.969796	+	0.243919i	$0.0784331\pi$
$570$		0			0
$571$	−148.638	+	107.992i	−0.260312	+	0.189128i	−0.710285	−	0.703914i	$-0.751434\pi$
$571$	−148.638	+	107.992i	−0.260312	+	0.189128i	0.449972	+	0.893042i	$0.351434\pi$
$572$	−507.161	−	80.3264i	−0.886645	−	0.140431i
$573$	204.400	+	104.147i	0.356718	+	0.181757i
$574$			51.0308i			0.0889039i
$575$		0			0
$576$	296.728			0.515153
$577$	−344.292	+	675.710i	−0.596693	+	1.17108i	0.373248	+	0.927732i	$0.378244\pi$
$577$	−344.292	+	675.710i	−0.596693	+	1.17108i	−0.969940	+	0.243343i	$0.921756\pi$
$578$	147.096	−	928.728i	0.254492	−	1.60680i
$579$	45.6694	+	62.8586i	0.0788764	+	0.108564i
$580$		0			0
$581$	27.5961	+	20.0498i	0.0474977	+	0.0345091i
$582$	404.432	+	404.432i	0.694900	+	0.694900i
$583$	228.324	−	36.1630i	0.391637	−	0.0620292i
$584$	−401.872	−	130.576i	−0.688137	−	0.223589i
$585$		0			0
$586$	−342.811	−	1055.07i	−0.585002	−	1.80045i
$587$	243.176	−	123.904i	0.414269	−	0.211081i	−0.234418	−	0.972136i	$-0.575318\pi$
$587$	243.176	−	123.904i	0.414269	−	0.211081i	0.648687	+	0.761055i	$0.275318\pi$
$588$	209.367	+	410.907i	0.356067	+	0.698821i
$589$	861.765	−	280.004i	1.46310	−	0.475389i
$590$		0			0
$591$	−92.1131	+	283.495i	−0.155860	+	0.479687i
$592$	−10.4954	−	66.2655i	−0.0177287	−	0.111935i
$593$	367.718	−	367.718i	0.620098	−	0.620098i	−0.325458	−	0.945556i	$-0.605519\pi$
$593$	367.718	−	367.718i	0.620098	−	0.620098i	0.945556	+	0.325458i	$0.105519\pi$
$594$	−74.5366	+	102.591i	−0.125482	+	0.172712i
$595$		0			0
$596$	−477.662	+	347.042i	−0.801446	+	0.582284i
$597$	−45.6853	−	7.23584i	−0.0765247	−	0.0121203i
$598$	−417.865	−	212.913i	−0.698770	−	0.356041i
$599$		−	654.311i		−	1.09234i	−0.837675	−	0.546170i	$-0.816085\pi$
$599$		−	654.311i		−	1.09234i	0.837675	−	0.546170i	$-0.183915\pi$
$600$		0			0
$601$	−233.449			−0.388434			−0.194217	−	0.980959i	$-0.562217\pi$
$601$	−233.449			−0.388434			−0.194217	+	0.980959i	$0.562217\pi$
$602$	0.754367	−	1.48053i	0.00125310	−	0.00245935i
$603$	−19.9470	+	125.940i	−0.0330795	+	0.208856i
$604$	191.641	+	263.772i	0.317287	+	0.436708i
$605$		0			0
$606$	−461.330	−	335.176i	−0.761270	−	0.553095i
$607$	581.645	+	581.645i	0.958229	+	0.958229i	0.999162	−	0.0409329i	$-0.0130330\pi$
$607$	581.645	+	581.645i	0.958229	+	0.958229i	−0.0409329	+	0.999162i	$0.513033\pi$
$608$	1110.28	−	175.851i	1.82612	−	0.289229i
$609$	−27.4926	−	8.93287i	−0.0451438	−	0.0146681i
$610$		0			0
$611$	157.968	+	486.176i	0.258541	+	0.795706i
$612$	−355.178	+	180.972i	−0.580357	+	0.295706i
$613$	324.087	+	636.056i	0.528689	+	1.03761i	0.988729	+	0.149713i	$0.0478350\pi$
$613$	324.087	+	636.056i	0.528689	+	1.03761i	−0.460040	+	0.887898i	$0.652165\pi$
$614$	1238.44	−	402.392i	2.01700	−	0.655361i
$615$		0			0
$616$	−3.86133	+	11.8839i	−0.00626838	+	0.0192921i
$617$	−41.3960	−	261.364i	−0.0670924	−	0.423605i	−0.998258	−	0.0590070i	$-0.981207\pi$
$617$	−41.3960	−	261.364i	−0.0670924	−	0.423605i	0.931165	−	0.364598i	$-0.118793\pi$
$618$	359.238	−	359.238i	0.581291	−	0.581291i
$619$	159.169	−	219.077i	0.257138	−	0.353921i	−0.660857	−	0.750512i	$-0.729807\pi$
$619$	159.169	−	219.077i	0.257138	−	0.353921i	0.917995	+	0.396591i	$0.129807\pi$
$620$		0			0
$621$	−54.0288	+	39.2543i	−0.0870030	+	0.0632114i
$622$	112.506	+	17.8192i	0.180878	+	0.0286482i
$623$	−54.1117	−	27.5713i	−0.0868566	−	0.0442557i
$624$		−	166.823i		−	0.267344i
$625$		0			0
$626$	1292.84			2.06523
$627$	−164.218	+	322.295i	−0.261910	+	0.514028i
$628$	−105.080	+	663.446i	−0.167324	+	1.05644i
$629$	118.556	+	163.179i	0.188484	+	0.259426i
$630$		0			0
$631$	−777.204	−	564.672i	−1.23170	−	0.894884i	−0.234686	−	0.972071i	$-0.575406\pi$
$631$	−777.204	−	564.672i	−1.23170	−	0.894884i	−0.997017	+	0.0771869i	$0.975406\pi$
$632$	333.860	+	333.860i	0.528260	+	0.528260i
$633$	22.5428	−	3.57043i	0.0356127	−	0.00564049i
$634$	−479.547	−	155.814i	−0.756384	−	0.245764i
$635$		0			0
$636$	−84.8956	−	261.282i	−0.133484	−	0.410821i
$637$	516.978	−	263.413i	0.811582	−	0.413522i
$638$	522.837	+	1026.13i	0.819494	+	1.60835i
$639$	−173.161	+	56.2634i	−0.270987	+	0.0880491i
$640$		0			0
$641$	252.698	−	777.724i	0.394224	−	1.21330i	−0.535340	−	0.844637i	$-0.679816\pi$
$641$	252.698	−	777.724i	0.394224	−	1.21330i	0.929564	−	0.368661i	$-0.120184\pi$
$642$	151.398	+	955.889i	0.235822	+	1.48892i
$643$	865.400	−	865.400i	1.34588	−	1.34588i	0.455794	−	0.890085i	$-0.349356\pi$
$643$	865.400	−	865.400i	1.34588	−	1.34588i	0.890085	−	0.455794i	$-0.150644\pi$
$644$	−14.5552	+	20.0335i	−0.0226012	+	0.0311079i
$645$		0			0
$646$	−1595.35	+	1159.09i	−2.46959	+	1.79426i
$647$	168.866	+	26.7458i	0.260999	+	0.0413381i	0.285562	−	0.958360i	$-0.407820\pi$
$647$	168.866	+	26.7458i	0.260999	+	0.0413381i	−0.0245637	+	0.999698i	$0.507820\pi$
$648$	35.6841	+	18.1820i	0.0550681	+	0.0280586i
$649$			596.001i			0.918338i
$650$		0			0
$651$	−21.1025			−0.0324155
$652$	−230.218	+	451.827i	−0.353094	+	0.692987i
$653$	122.734	−	774.910i	0.187954	−	1.18669i	−0.695623	−	0.718407i	$-0.744872\pi$
$653$	122.734	−	774.910i	0.187954	−	1.18669i	0.883577	−	0.468286i	$-0.155128\pi$
$654$	293.825	+	404.416i	0.449274	+	0.618373i
$655$		0			0
$656$	308.119	+	223.862i	0.469694	+	0.341253i
$657$	201.436	+	201.436i	0.306599	+	0.306599i
$658$	46.2342	−	7.32278i	0.0702648	−	0.0111289i
$659$	−259.236	−	84.2308i	−0.393377	−	0.127816i	0.105648	−	0.994404i	$-0.466308\pi$
$659$	−259.236	−	84.2308i	−0.393377	−	0.127816i	−0.499025	+	0.866588i	$0.666308\pi$
$660$		0			0
$661$	212.501	+	654.010i	0.321484	+	0.989426i	0.973003	+	0.230793i	$0.0741321\pi$
$661$	212.501	+	654.010i	0.321484	+	0.989426i	−0.651519	+	0.758632i	$0.725868\pi$
$662$	−898.117	+	457.613i	−1.35667	+	0.691259i
$663$	227.688	+	446.864i	0.343421	+	0.674002i
$664$	−408.179	+	132.625i	−0.614728	+	0.199737i
$665$		0			0
$666$	23.5638	−	72.5218i	0.0353810	−	0.108892i
$667$	94.8788	+	599.041i	0.142247	+	0.898113i
$668$	−916.186	+	916.186i	−1.37154	+	1.37154i
$669$	222.941	−	306.853i	0.333246	−	0.458673i
$670$		0			0
$671$	540.513	−	392.706i	0.805534	−	0.585255i
$672$	−25.8573	−	4.09540i	−0.0384782	−	0.00609435i
$673$	−67.4786	−	34.3821i	−0.100265	−	0.0510878i	0.403139	−	0.915139i	$-0.367919\pi$
$673$	−67.4786	−	34.3821i	−0.100265	−	0.0510878i	−0.503404	+	0.864051i	$0.667919\pi$
$674$		−	1408.01i		−	2.08904i
$675$		0			0
$676$	−152.907			−0.226193
$677$	384.015	−	753.672i	0.567230	−	1.11325i	−0.412129	−	0.911125i	$-0.635215\pi$
$677$	384.015	−	753.672i	0.567230	−	1.11325i	0.979359	−	0.202127i	$-0.0647853\pi$
$678$	−12.2878	+	77.5820i	−0.0181236	+	0.114428i
$679$	−22.3333	−	30.7391i	−0.0328914	−	0.0452711i
$680$		0			0
$681$	210.712	+	153.091i	0.309415	+	0.224803i
$682$	594.469	+	594.469i	0.871655	+	0.871655i
$683$	−1104.20	+	174.888i	−1.61669	+	0.256059i	−0.898236	−	0.439513i	$-0.855151\pi$
$683$	−1104.20	+	174.888i	−1.61669	+	0.256059i	−0.718457	+	0.695572i	$0.755151\pi$
$684$	408.837	+	132.839i	0.597715	+	0.194209i
$685$		0			0
$686$	−32.8787	−	101.190i	−0.0479282	−	0.147508i
$687$	572.685	−	291.798i	0.833602	−	0.424742i
$688$	−5.63004	−	11.0496i	−0.00818319	−	0.0160604i
$689$	−328.729	+	106.811i	−0.477110	+	0.155022i
$690$		0			0
$691$	−326.956	+	1006.27i	−0.473163	+	1.45625i	0.375257	+	0.926921i	$0.377555\pi$
$691$	−326.956	+	1006.27i	−0.473163	+	1.45625i	−0.848419	+	0.529325i	$0.822445\pi$
$692$	28.1828	+	177.939i	0.0407266	+	0.257137i
$693$	5.95674	−	5.95674i	0.00859559	−	0.00859559i
$694$	−701.558	+	965.611i	−1.01089	+	1.39137i
$695$		0			0
$696$	294.253	−	213.787i	0.422777	−	0.307165i
$697$	−1130.89	−	179.115i	−1.62251	−	0.256980i
$698$	440.725	+	224.561i	0.631412	+	0.321720i
$699$		−	128.479i		−	0.183804i
$700$		0			0
$701$	−406.455			−0.579822			−0.289911	−	0.957054i	$-0.593626\pi$
$701$	−406.455			−0.579822			−0.289911	+	0.957054i	$0.593626\pi$
$702$	86.0790	−	168.940i	0.122620	−	0.240655i
$703$	34.0265	−	214.835i	0.0484018	−	0.305597i
$704$	461.595	+	635.331i	0.655675	+	0.902459i
$705$		0			0
$706$	−177.631	−	129.056i	−0.251602	−	0.182799i
$707$	26.7863	+	26.7863i	0.0378872	+	0.0378872i
$708$	699.581	−	110.803i	0.988109	−	0.156501i
$709$	−767.230	−	249.288i	−1.08213	−	0.351605i	−0.286929	−	0.957952i	$-0.592635\pi$
$709$	−767.230	−	249.288i	−1.08213	−	0.351605i	−0.795201	+	0.606346i	$0.792635\pi$
$710$		0			0
$711$	−98.3631	−	302.730i	−0.138345	−	0.425781i
$712$	680.840	−	346.905i	0.956236	−	0.487227i
$713$	201.006	+	394.496i	0.281915	+	0.553290i
$714$	43.6774	−	14.1916i	0.0611728	−	0.0198762i
$715$		0			0
$716$	−450.624	+	1386.88i	−0.629363	+	1.93698i
$717$	61.5533	+	388.632i	0.0858484	+	0.542025i
$718$	221.246	−	221.246i	0.308143	−	0.308143i
$719$	−189.988	+	261.496i	−0.264239	+	0.363694i	−0.920434	−	0.390897i	$-0.872165\pi$
$719$	−189.988	+	261.496i	−0.264239	+	0.363694i	0.656195	+	0.754591i	$0.272165\pi$
$720$		0			0
$721$	−27.3041	+	19.8376i	−0.0378698	+	0.0275140i
$722$	1004.43	+	159.086i	1.39118	+	0.220341i
$723$	531.537	+	270.832i	0.735182	+	0.374594i
$724$			216.582i			0.299146i
$725$		0			0
$726$	308.574			0.425033
$727$	−303.885	+	596.408i	−0.417999	+	0.820369i	0.581975	+	0.813206i	$0.302280\pi$
$727$	−303.885	+	596.408i	−0.417999	+	0.820369i	−0.999974	+	0.00716266i	$0.997720\pi$
$728$	2.92271	−	18.4533i	0.00401471	−	0.0253479i
$729$	−15.8702	−	21.8435i	−0.0217698	−	0.0299636i
$730$		0			0
$731$	30.1620	+	21.9140i	0.0412613	+	0.0299781i
$732$	−561.442	−	561.442i	−0.766997	−	0.766997i
$733$	−799.081	+	126.562i	−1.09015	+	0.172663i	−0.675531	−	0.737332i	$-0.736086\pi$
$733$	−799.081	+	126.562i	−1.09015	+	0.172663i	−0.414620	+	0.909995i	$0.636086\pi$
$734$	−1226.43	−	398.492i	−1.67089	−	0.542905i
$735$		0			0
$736$	169.736	+	522.394i	0.230620	+	0.709775i
$737$	−300.683	+	153.206i	−0.407983	+	0.207878i
$738$	196.518	+	385.689i	0.266285	+	0.522614i
$739$	−225.122	+	73.1467i	−0.304631	+	0.0989806i	−0.457344	−	0.889290i	$-0.651199\pi$
$739$	−225.122	+	73.1467i	−0.304631	+	0.0989806i	0.152713	+	0.988271i	$0.451199\pi$
$740$		0			0
$741$	167.130	−	514.374i	0.225547	−	0.694162i
$742$	4.95131	+	31.2614i	0.00667293	+	0.0421312i
$743$	820.748	−	820.748i	1.10464	−	1.10464i	0.110797	−	0.993843i	$-0.464660\pi$
$743$	820.748	−	820.748i	1.10464	−	1.10464i	0.993843	−	0.110797i	$-0.0353404\pi$
$744$	156.065	−	214.805i	0.209765	−	0.288717i
$745$		0			0
$746$	984.475	−	715.263i	1.31967	−	0.958798i
$747$	285.782	+	45.2634i	0.382573	+	0.0605935i
$748$	−940.005	−	478.957i	−1.25669	−	0.640316i
$749$		−	64.2925i		−	0.0858378i
$750$		0			0
$751$	622.914			0.829446			0.414723	−	0.909948i	$-0.363878\pi$
$751$	622.914			0.829446			0.414723	+	0.909948i	$0.363878\pi$
$752$	158.606	−	311.282i	0.210912	−	0.413938i
$753$	−56.9324	+	359.457i	−0.0756075	+	0.477367i
$754$	−1012.13	−	1393.08i	−1.34235	−	1.84759i
$755$		0			0
$756$	−8.09939	−	5.88455i	−0.0107135	−	0.00778380i
$757$	−588.326	−	588.326i	−0.777180	−	0.777180i	0.202170	−	0.979350i	$-0.435201\pi$
$757$	−588.326	−	588.326i	−0.777180	−	0.777180i	−0.979350	+	0.202170i	$0.935201\pi$
$758$	−1880.96	+	297.914i	−2.48147	+	0.393027i
$759$	−168.096	−	54.6178i	−0.221471	−	0.0719602i
$760$		0			0
$761$	−383.044	−	1178.89i	−0.503343	−	1.54913i	−0.803538	−	0.595254i	$-0.797052\pi$
$761$	−383.044	−	1178.89i	−0.503343	−	1.54913i	0.300194	−	0.953878i	$-0.402948\pi$
$762$	−192.741	+	98.2065i	−0.252941	+	0.128880i
$763$	−15.0761	−	29.5886i	−0.0197590	−	0.0387793i
$764$	686.215	−	222.965i	0.898187	−	0.291839i
$765$		0			0
$766$	−232.789	+	716.452i	−0.303903	+	0.935316i
$767$	−139.405	−	880.170i	−0.181754	−	1.14755i
$768$	16.3914	−	16.3914i	0.0213430	−	0.0213430i
$769$	−48.2171	+	66.3651i	−0.0627010	+	0.0863006i	−0.839216	−	0.543798i	$-0.816986\pi$
$769$	−48.2171	+	66.3651i	−0.0627010	+	0.0863006i	0.776515	+	0.630099i	$0.216986\pi$
$770$		0			0
$771$	−360.301	+	261.774i	−0.467317	+	0.339525i
$772$	241.369	+	38.2291i	0.312654	+	0.0495196i
$773$	−668.593	−	340.665i	−0.864933	−	0.440705i	−0.0355381	−	0.999368i	$-0.511314\pi$
$773$	−668.593	−	340.665i	−0.864933	−	0.440705i	−0.829395	+	0.558663i	$0.811314\pi$
$774$		−	14.0948i		−	0.0182104i
$775$		0			0
$776$	478.066			0.616064
$777$	−2.29976	+	4.51353i	−0.00295979	+	0.00580892i
$778$	10.6908	−	67.4993i	0.0137414	−	0.0867601i
$779$	725.768	+	998.934i	0.931666	+	1.28233i
$780$		0			0
$781$	−389.839	−	283.234i	−0.499153	−	0.362656i
$782$	−681.339	−	681.339i	−0.871278	−	0.871278i
$783$	−242.188	+	38.3588i	−0.309308	+	0.0489895i
$784$	−377.122	−	122.534i	−0.481023	−	0.156294i
$785$		0			0
$786$	247.182	+	760.748i	0.314481	+	0.967873i
$787$	451.355	−	229.977i	0.573513	−	0.292219i	−0.143080	−	0.989711i	$-0.545701\pi$
$787$	451.355	−	229.977i	0.573513	−	0.292219i	0.716593	+	0.697492i	$0.245701\pi$
$788$	425.638	+	835.363i	0.540150	+	1.06010i
$789$	−127.558	+	41.4460i	−0.161670	+	0.0525298i
$790$		0			0
$791$	1.61249	−	4.96273i	0.00203854	−	0.00627399i
$792$	16.5810	+	104.688i	0.0209356	+	0.132182i
$793$	−706.372	+	706.372i	−0.890759	+	0.890759i
$794$	315.705	−	434.531i	0.397613	−	0.547268i
$795$		0			0
$796$	−117.698	+	85.5126i	−0.147862	+	0.107428i
$797$	−1084.00	−	171.689i	−1.36010	−	0.215419i	−0.566605	−	0.823990i	$-0.691743\pi$
$797$	−1084.00	−	171.689i	−1.36010	−	0.215419i	−0.793500	+	0.608570i	$0.791743\pi$
$798$	−44.1276	−	22.4841i	−0.0552977	−	0.0281756i
$799$			1050.29i			1.31451i
$800$		0			0
$801$	−515.150			−0.643134
$802$	491.417	−	964.461i	0.612740	−	1.20257i
$803$	−117.942	+	744.656i	−0.146877	+	0.927342i
$804$	235.732	+	324.457i	0.293199	+	0.403553i
$805$		0			0
$806$	−1016.95	−	738.860i	−1.26173	−	0.916700i
$807$	−390.913	−	390.913i	−0.484403	−	0.484403i
$808$	−470.761	+	74.5613i	−0.582626	+	0.0922788i
$809$	67.5579	+	21.9509i	0.0835079	+	0.0271334i	0.350473	−	0.936573i	$-0.386021\pi$
$809$	67.5579	+	21.9509i	0.0835079	+	0.0271334i	−0.266965	+	0.963706i	$0.586021\pi$
$810$		0			0
$811$	−19.2331	−	59.1935i	−0.0237153	−	0.0729882i	0.938498	−	0.345284i	$-0.112217\pi$
$811$	−19.2331	−	59.1935i	−0.0237153	−	0.0729882i	−0.962214	+	0.272295i	$0.912217\pi$
$812$	−81.0111	+	41.2772i	−0.0997674	+	0.0508340i
$813$	−278.803	−	547.181i	−0.342931	−	0.673039i
$814$	191.934	−	62.3633i	0.235792	−	0.0766133i
$815$		0			0
$816$	105.916	−	325.976i	0.129799	−	0.399480i
$817$	−6.28947	−	39.7102i	−0.00769825	−	0.0486049i
$818$	−1038.17	+	1038.17i	−1.26916	+	1.26916i
$819$	−7.40359	+	10.1902i	−0.00903979	+	0.0124422i
$820$		0			0
$821$	−292.676	+	212.641i	−0.356487	+	0.259003i	−0.751585	−	0.659636i	$-0.770710\pi$
$821$	−292.676	+	212.641i	−0.356487	+	0.259003i	0.395099	+	0.918639i	$0.370710\pi$
$822$	84.9892	+	13.4610i	0.103393	+	0.0163759i
$823$	9.88181	+	5.03504i	0.0120071	+	0.00611791i	0.459984	−	0.887927i	$-0.347855\pi$
$823$	9.88181	+	5.03504i	0.0120071	+	0.00611791i	−0.447977	+	0.894045i	$0.647855\pi$
$824$		−	424.643i		−	0.515344i
$825$		0			0
$826$	−81.6024			−0.0987923
$827$	708.250	−	1390.02i	0.856408	−	1.68080i	0.132191	−	0.991224i	$-0.457799\pi$
$827$	708.250	−	1390.02i	0.856408	−	1.68080i	0.724218	−	0.689571i	$-0.242201\pi$
$828$	−32.8591	+	207.464i	−0.0396849	+	0.250560i
$829$	5.75207	+	7.91705i	0.00693857	+	0.00955012i	0.812472	−	0.583000i	$-0.198121\pi$
$829$	5.75207	+	7.91705i	0.00693857	+	0.00955012i	−0.805534	+	0.592550i	$0.798121\pi$
$830$		0			0
$831$	464.428	+	337.427i	0.558878	+	0.406049i
$832$	−830.285	−	830.285i	−0.997939	−	0.997939i
$833$	1177.43	−	186.486i	1.41348	−	0.223873i
$834$	−241.860	−	78.5850i	−0.290000	−	0.0942266i
$835$		0			0
$836$	351.569	+	1082.02i	0.420537	+	1.29428i
$837$	−159.492	+	81.2650i	−0.190552	+	0.0970908i
$838$	−860.428	−	1688.68i	−1.02676	−	2.01514i
$839$	−576.373	+	187.275i	−0.686976	+	0.223212i	−0.631647	−	0.775256i	$-0.717621\pi$
$839$	−576.373	+	187.275i	−0.686976	+	0.223212i	−0.0553292	+	0.998468i	$0.517621\pi$
$840$		0			0
$841$	−428.268	+	1318.07i	−0.509237	+	1.56727i
$842$	222.855	+	1407.05i	0.264673	+	1.67108i
$843$	−132.202	+	132.202i	−0.156823	+	0.156823i
$844$	42.1951	−	58.0766i	0.0499942	−	0.0688111i
$845$		0			0
$846$	321.237	−	233.392i	0.379713	−	0.275877i
$847$	−20.2466	−	3.20674i	−0.0239039	−	0.00378600i
$848$	210.474	+	107.242i	0.248200	+	0.126464i
$849$		−	231.516i		−	0.272693i
$850$		0			0
$851$	106.283			0.124892
$852$	−259.983	+	510.245i	−0.305144	+	0.598880i
$853$	87.9451	−	555.263i	0.103101	−	0.650953i	−0.880969	−	0.473173i	$-0.843108\pi$
$853$	87.9451	−	555.263i	0.103101	−	0.650953i	0.984070	−	0.177780i	$-0.0568916\pi$
$854$	53.7679	+	74.0052i	0.0629601	+	0.0866571i
$855$		0			0
$856$	654.443	+	475.481i	0.764537	+	0.555468i
$857$	1005.55	+	1005.55i	1.17333	+	1.17333i	0.981410	+	0.191924i	$0.0614726\pi$
$857$	1005.55	+	1005.55i	1.17333	+	1.17333i	0.191924	+	0.981410i	$0.438527\pi$
$858$	495.626	−	78.4995i	0.577653	−	0.0914913i
$859$	−1176.31	−	382.208i	−1.36940	−	0.444945i	−0.470229	−	0.882544i	$-0.655829\pi$
$859$	−1176.31	−	382.208i	−1.36940	−	0.444945i	−0.899170	+	0.437600i	$0.855829\pi$
$860$		0			0
$861$	−8.88612	−	27.3487i	−0.0103207	−	0.0317638i
$862$	64.5735	−	32.9018i	0.0749112	−	0.0381692i
$863$	−371.006	−	728.140i	−0.429902	−	0.843731i	−0.999758	−	0.0219863i	$-0.993001\pi$
$863$	−371.006	−	728.140i	−0.429902	−	0.843731i	0.569856	−	0.821745i	$-0.306999\pi$
$864$	−211.200	+	68.6231i	−0.244445	+	0.0794249i
$865$		0			0
$866$	106.690	−	328.359i	0.123199	−	0.379167i
$867$	82.8892	+	523.342i	0.0956047	+	0.603624i
$868$	−46.9324	+	46.9324i	−0.0540696	+	0.0540696i
$869$	495.168	−	681.540i	0.569813	−	0.784281i
$870$		0			0
$871$	408.212	−	296.583i	0.468670	−	0.340509i
$872$	412.684	+	65.3627i	0.473261	+	0.0749572i
$873$	−287.170	−	146.320i	−0.328946	−	0.167606i
$874$			1039.10i			1.18890i
$875$		0			0
$876$	895.997			1.02283
$877$	387.593	−	760.694i	0.441953	−	0.867382i	−0.557358	−	0.830272i	$-0.688185\pi$
$877$	387.593	−	760.694i	0.441953	−	0.867382i	0.999311	−	0.0371096i	$-0.0118151\pi$
$878$	262.739	−	1658.87i	0.299247	−	1.88937i
$879$	367.442	+	505.740i	0.418022	+	0.575359i
$880$		0			0
$881$	425.461	+	309.115i	0.482929	+	0.350869i	0.802459	−	0.596708i	$-0.203525\pi$
$881$	425.461	+	309.115i	0.482929	+	0.350869i	−0.319529	+	0.947576i	$0.603525\pi$
$882$	−318.681	−	318.681i	−0.361316	−	0.361316i
$883$	979.657	−	155.162i	1.10946	−	0.175722i	0.425302	−	0.905051i	$-0.360168\pi$
$883$	979.657	−	155.162i	1.10946	−	0.175722i	0.684163	+	0.729330i	$0.260168\pi$
$884$	1500.22	+	487.451i	1.69708	+	0.551416i
$885$		0			0
$886$	−222.725	−	685.477i	−0.251383	−	0.773676i
$887$	−698.883	+	356.099i	−0.787918	+	0.401464i	−0.801162	−	0.598448i	$-0.795784\pi$
$887$	−698.883	+	356.099i	−0.787918	+	0.401464i	0.0132438	+	0.999912i	$0.495784\pi$
$888$	−28.9358	−	56.7898i	−0.0325854	−	0.0639525i
$889$	13.6670	−	4.44067i	0.0153734	−	0.00499513i
$890$		0			0
$891$	22.0816	−	67.9601i	0.0247829	−	0.0762740i
$892$	−186.621	−	1178.28i	−0.209216	−	1.32094i
$893$	800.894	−	800.894i	0.896858	−	0.896858i
$894$	339.149	−	466.798i	0.379361	−	0.522146i
$895$		0			0
$896$	−38.0747	+	27.6629i	−0.0424941	+	0.0308738i
$897$	261.019	+	41.3413i	0.290991	+	0.0460884i
$898$	551.041	+	280.769i	0.613631	+	0.312661i
$899$			1625.65i			1.80828i
$900$		0			0
$901$	−710.158			−0.788189
$902$	−520.101	+	1020.76i	−0.576608	+	1.13166i
$903$	−0.146475	+	0.924810i	−0.000162210	+	0.00102415i
$904$	38.5911	+	53.1160i	0.0426892	+	0.0587567i
$905$		0			0
$906$	−257.773	−	187.283i	−0.284517	−	0.206714i
$907$	249.974	+	249.974i	0.275605	+	0.275605i	0.831352	−	0.555747i	$-0.187568\pi$
$907$	249.974	+	249.974i	0.275605	+	0.275605i	−0.555747	+	0.831352i	$0.687568\pi$
$908$	809.106	−	128.150i	0.891086	−	0.141134i
$909$	305.603	+	99.2963i	0.336197	+	0.109237i
$910$		0			0
$911$	232.883	+	716.740i	0.255634	+	0.786761i	0.993704	+	0.112037i	$0.0357375\pi$
$911$	232.883	+	716.740i	0.255634	+	0.786761i	−0.738070	+	0.674724i	$0.764262\pi$
$912$	−329.336	+	167.805i	−0.361114	+	0.183997i
$913$	347.652	+	682.306i	0.380780	+	0.747324i
$914$	−1858.67	+	603.919i	−2.03356	+	0.660743i
$915$		0			0
$916$	624.701	−	1922.63i	0.681988	−	2.09894i
$917$	−8.31266	−	52.4841i	−0.00906506	−	0.0572345i
$918$	275.460	−	275.460i	0.300066	−	0.300066i
$919$	548.369	−	754.765i	0.596701	−	0.821289i	−0.398700	−	0.917081i	$-0.630538\pi$
$919$	548.369	−	754.765i	0.596701	−	0.821289i	0.995401	+	0.0957924i	$0.0305385\pi$
$920$		0			0
$921$	−593.638	+	431.303i	−0.644558	+	0.468299i
$922$	1284.51	+	203.447i	1.39318	+	0.220658i
$923$	641.960	+	327.095i	0.695514	+	0.354382i
$924$		−	26.4959i		−	0.0286752i
$925$		0			0
$926$	−2021.52			−2.18306
$927$	−129.969	+	255.079i	−0.140204	+	0.275166i
$928$	−315.493	+	1991.94i	−0.339970	+	2.14649i
$929$	702.940	+	967.513i	0.756663	+	1.04146i	0.997484	+	0.0708875i	$0.0225831\pi$
$929$	702.940	+	967.513i	0.756663	+	1.04146i	−0.240822	+	0.970569i	$0.577417\pi$
$930$		0			0
$931$	−1040.04	−	755.635i	−1.11712	−	0.811638i
$932$	−285.741	−	285.741i	−0.306589	−	0.306589i
$933$	−63.3975	+	10.0412i	−0.0679502	+	0.0107623i
$934$	1922.82	+	624.762i	2.05869	+	0.668910i
$935$		0			0
$936$	−48.9734	−	150.724i	−0.0523220	−	0.161030i
$937$	939.280	−	478.587i	1.00243	−	0.510766i	0.125868	−	0.992047i	$-0.459829\pi$
$937$	939.280	−	478.587i	1.00243	−	0.510766i	0.876566	+	0.481282i	$0.159829\pi$
$938$	−20.9764	−	41.1685i	−0.0223629	−	0.0438897i
$939$	−692.861	+	225.124i	−0.737872	+	0.239749i
$940$		0			0
$941$	179.429	−	552.226i	0.190679	−	0.586850i	−0.809321	−	0.587367i	$-0.800165\pi$
$941$	179.429	−	552.226i	0.190679	−	0.586850i	1.00000		0.000517053i	$0.000164583\pi$
$942$	−102.690	−	648.358i	−0.109012	−	0.688278i
$943$	−426.622	+	426.622i	−0.452409	+	0.452409i
$944$	−357.973	+	492.708i	−0.379209	+	0.521936i
$945$		0			0
$946$	30.1787	−	21.9261i	0.0319014	−	0.0231777i
$947$	−596.940	−	94.5461i	−0.630349	−	0.0998375i	−0.166918	−	0.985971i	$-0.553382\pi$
$947$	−596.940	−	94.5461i	−0.630349	−	0.0998375i	−0.463431	+	0.886133i	$0.653382\pi$
$948$	−892.042	−	454.518i	−0.940973	−	0.479450i
$949$		−	1127.29i		−	1.18787i
$950$		0			0
$951$	284.133			0.298773
$952$	17.4271	−	34.2025i	0.0183057	−	0.0359270i
$953$	−7.62845	+	48.1641i	−0.00800467	+	0.0505395i	−0.991367	−	0.131114i	$-0.958145\pi$
$953$	−7.62845	+	48.1641i	−0.00800467	+	0.0505395i	0.983363	+	0.181653i	$0.0581448\pi$
$954$	157.808	+	217.205i	0.165418	+	0.227678i
$955$		0			0
$956$	1001.22	+	727.432i	1.04731	+	0.760912i
$957$	−458.883	−	458.883i	−0.479501	−	0.479501i
$958$	−2038.65	+	322.890i	−2.12802	+	0.337046i
$959$	−5.43655	−	1.76644i	−0.00566897	−	0.00184196i
$960$		0			0
$961$	69.7529	+	214.677i	0.0725837	+	0.223390i
$962$	−268.860	+	136.991i	−0.279481	+	0.142403i
$963$	−247.589	−	485.920i	−0.257102	−	0.504590i
$964$	1784.49	−	579.816i	1.85113	−	0.601468i
$965$		0			0
$966$	7.47808	−	23.0152i	0.00774129	−	0.0238252i
$967$	−229.127	−	1446.65i	−0.236946	−	1.49602i	−0.763461	−	0.645854i	$-0.776501\pi$
$967$	−229.127	−	1446.65i	−0.236946	−	1.49602i	0.526514	−	0.850166i	$-0.323499\pi$
$968$	182.377	−	182.377i	0.188406	−	0.188406i
$969$	653.153	−	898.989i	0.674049	−	0.927749i
$970$		0			0
$971$	−676.512	+	491.514i	−0.696716	+	0.506194i	−0.878861	−	0.477078i	$-0.841696\pi$
$971$	−676.512	+	491.514i	−0.696716	+	0.506194i	0.182145	+	0.983272i	$0.441696\pi$
$972$	−83.8762	−	13.2847i	−0.0862924	−	0.0136674i
$973$	15.0526	+	7.66968i	0.0154703	+	0.00788250i
$974$			324.003i			0.332652i
$975$		0			0
$976$	682.705			0.699493
$977$	238.509	−	468.100i	0.244124	−	0.479120i	−0.736136	−	0.676834i	$-0.763352\pi$
$977$	238.509	−	468.100i	0.244124	−	0.479120i	0.980260	+	0.197714i	$0.0633517\pi$
$978$	77.5234	−	489.463i	0.0792673	−	0.500474i
$979$	−801.377	−	1103.00i	−0.818567	−	1.12666i
$980$		0			0
$981$	−227.890	−	165.572i	−0.232304	−	0.168778i
$982$	369.546	+	369.546i	0.376320	+	0.376320i
$983$	1402.94	−	222.203i	1.42720	−	0.226046i	0.605443	−	0.795888i	$-0.292996\pi$
$983$	1402.94	−	222.203i	1.42720	−	0.226046i	0.821754	+	0.569842i	$0.192996\pi$
$984$	344.104	+	111.806i	0.349699	+	0.113624i
$985$		0			0
$986$	−1093.27	−	3364.72i	−1.10879	−	3.41250i
$987$	−23.5029	+	11.9753i	−0.0238125	+	0.0121331i
$988$	−772.280	−	1515.68i	−0.781660	−	1.53409i
$989$	18.6839	−	6.07076i	0.0188917	−	0.00613828i
$990$		0			0
$991$	451.716	−	1390.24i	0.455819	−	1.40287i	−0.414352	−	0.910117i	$-0.635992\pi$
$991$	451.716	−	1390.24i	0.455819	−	1.40287i	0.870171	−	0.492750i	$-0.164008\pi$
$992$	230.310	+	1454.12i	0.232168	+	1.46585i
$993$	401.637	−	401.637i	0.404468	−	0.404468i
$994$	38.7795	−	53.3753i	0.0390135	−	0.0536975i
$995$		0			0
$996$	736.253	−	534.919i	0.739210	−	0.537067i
$997$	−1836.66	−	290.899i	−1.84219	−	0.291774i	−0.864627	−	0.502414i	$-0.832445\pi$
$997$	−1836.66	−	290.899i	−1.84219	−	0.291774i	−0.977564	+	0.210639i	$0.932445\pi$
$998$	794.763	+	404.952i	0.796355	+	0.405763i
$999$			42.9694i			0.0430124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.3.k.c.232.2		80
5.2	odd	4		375.3.k.a.268.2		80
5.3	odd	4		75.3.k.a.58.9	yes	80
5.4	even	2		375.3.k.b.232.9		80
15.8	even	4		225.3.r.b.208.2		80
25.3	odd	20	inner	375.3.k.c.118.2		80
25.4	even	10		375.3.k.a.7.2		80
25.21	even	5		75.3.k.a.22.9	✓	80
25.22	odd	20		375.3.k.b.118.9		80
75.71	odd	10		225.3.r.b.172.2		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.22.9	✓	80	25.21	even	5
75.3.k.a.58.9	yes	80	5.3	odd	4
225.3.r.b.172.2		80	75.71	odd	10
225.3.r.b.208.2		80	15.8	even	4
375.3.k.a.7.2		80	25.4	even	10
375.3.k.a.268.2		80	5.2	odd	4
375.3.k.b.118.9		80	25.22	odd	20
375.3.k.b.232.9		80	5.4	even	2
375.3.k.c.118.2		80	25.3	odd	20	inner
375.3.k.c.232.2		80	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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	375.k (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.39544 + 2.73870i) q^{2} +(0.270952 - 1.71073i) q^{3} +(-3.20210 - 4.40731i) q^{4} +(4.30707 + 3.12927i) q^{6} +(-0.250082 - 0.250082i) q^{7} +(4.39513 - 0.696119i) q^{8} +(-2.85317 - 0.927051i) q^{9} +(-2.45351 - 7.55112i) q^{11} +(-8.40731 + 4.28374i) q^{12} +(5.38954 + 10.5776i) q^{13} +(1.03387 - 0.335926i) q^{14} +(2.50710 - 7.71607i) q^{16} +(3.81558 + 24.0906i) q^{17} +(6.52034 - 6.52034i) q^{18} +(15.4606 - 21.2797i) q^{19} +(-0.495582 + 0.360061i) q^{21} +(24.1040 + 3.81770i) q^{22} +(11.4516 + 5.83489i) q^{23} -7.70747i q^{24} -36.4896 q^{26} +(-2.35900 + 4.62981i) q^{27} +(-0.301401 + 1.90297i) q^{28} +(27.7376 + 38.1776i) q^{29} +(27.8697 + 20.2485i) q^{31} +(30.2198 + 30.2198i) q^{32} +(-13.5827 + 2.15129i) q^{33} +(-71.3015 - 23.1673i) q^{34} +(5.05032 + 15.5433i) q^{36} +(7.36815 - 3.75426i) q^{37} +(36.7044 + 72.0364i) q^{38} +(19.5556 - 6.35401i) q^{39} +(-14.5062 + 44.6455i) q^{41} +(-0.294547 - 1.85969i) q^{42} +(1.08084 - 1.08084i) q^{43} +(-25.4237 + 34.9928i) q^{44} +(-31.9601 + 23.2203i) q^{46} +(42.5307 + 6.73620i) q^{47} +(-12.5208 - 6.37966i) q^{48} -48.8749i q^{49} +42.2463 q^{51} +(29.3608 - 57.6237i) q^{52} +(-4.55469 + 28.7572i) q^{53} +(-9.38781 - 12.9212i) q^{54} +(-1.27323 - 0.925055i) q^{56} +(-32.2146 - 32.2146i) q^{57} +(-143.263 + 22.6907i) q^{58} +(-71.3918 - 23.1966i) q^{59} +(26.0031 + 80.0294i) q^{61} +(-94.3452 + 48.0713i) q^{62} +(0.481688 + 0.945365i) q^{63} +(-94.0684 + 30.5647i) q^{64} +(13.0621 - 40.2009i) q^{66} +(-6.64899 - 41.9801i) q^{67} +(93.9570 - 93.9570i) q^{68} +(13.0848 - 18.0096i) q^{69} +(49.0998 - 35.6731i) q^{71} +(-13.1854 - 2.08836i) q^{72} +(-84.6079 - 43.1099i) q^{73} +25.4180i q^{74} -143.292 q^{76} +(-1.27482 + 2.50198i) q^{77} +(-9.88694 + 62.4237i) q^{78} +(62.3659 + 85.8393i) q^{79} +(7.28115 + 5.29007i) q^{81} +(-102.028 - 102.028i) q^{82} +(-95.2606 + 15.0878i) q^{83} +(3.17380 + 1.03123i) q^{84} +(1.45185 + 4.46832i) q^{86} +(72.8270 - 37.1072i) q^{87} +(-16.0400 - 31.4802i) q^{88} +(163.312 - 53.0634i) q^{89} +(1.29743 - 3.99309i) q^{91} +(-10.9530 - 69.1547i) q^{92} +(42.1911 - 42.1911i) q^{93} +(-77.7974 + 107.079i) q^{94} +(59.8858 - 43.5096i) q^{96} +(106.110 + 16.8062i) q^{97} +(133.854 + 68.2019i) q^{98} +23.8192i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{2} - 4 q^{7} - 72 q^{8} - 24 q^{12} + 32 q^{13} + 80 q^{16} + 40 q^{17} - 48 q^{18} + 100 q^{19} + 280 q^{22} + 264 q^{23} - 40 q^{26} - 44 q^{28} - 200 q^{29} + 636 q^{32} + 36 q^{33} - 100 q^{34}+ \cdots + 828 q^{98}+O(q^{100}) \) 80 * q + 4 * q^2 - 4 * q^7 - 72 * q^8 - 24 * q^12 + 32 * q^13 + 80 * q^16 + 40 * q^17 - 48 * q^18 + 100 * q^19 + 280 * q^22 + 264 * q^23 - 40 * q^26 - 44 * q^28 - 200 * q^29 + 636 * q^32 + 36 * q^33 - 100 * q^34 - 120 * q^36 - 124 * q^37 + 96 * q^38 + 160 * q^41 - 252 * q^42 - 472 * q^43 + 700 * q^44 - 128 * q^47 - 48 * q^48 - 620 * q^52 - 76 * q^53 + 72 * q^57 - 108 * q^58 - 800 * q^59 - 240 * q^61 - 328 * q^62 + 168 * q^63 - 100 * q^64 - 1240 * q^67 + 104 * q^68 + 216 * q^72 + 244 * q^73 - 648 * q^77 - 120 * q^78 - 200 * q^79 + 180 * q^81 - 168 * q^82 - 44 * q^83 + 1200 * q^84 + 84 * q^87 + 1008 * q^88 + 1500 * q^89 + 2236 * q^92 - 648 * q^93 + 200 * q^94 + 60 * q^96 + 200 * q^97 + 828 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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