LMFDB - Embedded newform 375.3.k.a.7.2

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,-4,0,0,0,0,4,12] 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			7.2
Character	$\chi$	$=$	375.7
Dual form			375.3.k.a.268.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.73870 + 1.39544i) q^{2} +(-1.71073 + 0.270952i) q^{3} +(3.20210 - 4.40731i) q^{4} +(4.30707 - 3.12927i) q^{6} +(0.250082 + 0.250082i) q^{7} +(-0.696119 + 4.39513i) q^{8} +(2.85317 - 0.927051i) q^{9} +(-2.45351 + 7.55112i) q^{11} +(-4.28374 + 8.40731i) q^{12} +(10.5776 + 5.38954i) q^{13} +(-1.03387 - 0.335926i) q^{14} +(2.50710 + 7.71607i) q^{16} +(-24.0906 - 3.81558i) q^{17} +(-6.52034 + 6.52034i) q^{18} +(-15.4606 - 21.2797i) q^{19} +(-0.495582 - 0.360061i) q^{21} +(-3.81770 - 24.1040i) q^{22} +(5.83489 + 11.4516i) q^{23} -7.70747i q^{24} -36.4896 q^{26} +(-4.62981 + 2.35900i) q^{27} +(1.90297 - 0.301401i) q^{28} +(-27.7376 + 38.1776i) q^{29} +(27.8697 - 20.2485i) q^{31} +(-30.2198 - 30.2198i) q^{32} +(2.15129 - 13.5827i) q^{33} +(71.3015 - 23.1673i) q^{34} +(5.05032 - 15.5433i) q^{36} +(3.75426 - 7.36815i) q^{37} +(72.0364 + 36.7044i) q^{38} +(-19.5556 - 6.35401i) q^{39} +(-14.5062 - 44.6455i) q^{41} +(1.85969 + 0.294547i) q^{42} +(-1.08084 + 1.08084i) q^{43} +(25.4237 + 34.9928i) q^{44} +(-31.9601 - 23.2203i) q^{46} +(-6.73620 - 42.5307i) q^{47} +(-6.37966 - 12.5208i) q^{48} -48.8749i q^{49} +42.2463 q^{51} +(57.6237 - 29.3608i) q^{52} +(28.7572 - 4.55469i) q^{53} +(9.38781 - 12.9212i) q^{54} +(-1.27323 + 0.925055i) q^{56} +(32.2146 + 32.2146i) q^{57} +(22.6907 - 143.263i) q^{58} +(71.3918 - 23.1966i) q^{59} +(26.0031 - 80.0294i) q^{61} +(-48.0713 + 94.3452i) q^{62} +(0.945365 + 0.481688i) q^{63} +(94.0684 + 30.5647i) q^{64} +(13.0621 + 40.2009i) q^{66} +(41.9801 + 6.64899i) q^{67} +(-93.9570 + 93.9570i) q^{68} +(-13.0848 - 18.0096i) q^{69} +(49.0998 + 35.6731i) q^{71} +(2.08836 + 13.1854i) q^{72} +(-43.1099 - 84.6079i) q^{73} +25.4180i q^{74} -143.292 q^{76} +(-2.50198 + 1.27482i) q^{77} +(62.4237 - 9.88694i) q^{78} +(-62.3659 + 85.8393i) q^{79} +(7.28115 - 5.29007i) q^{81} +(102.028 + 102.028i) q^{82} +(15.0878 - 95.2606i) q^{83} +(-3.17380 + 1.03123i) q^{84} +(1.45185 - 4.46832i) q^{86} +(37.1072 - 72.8270i) q^{87} +(-31.4802 - 16.0400i) q^{88} +(-163.312 - 53.0634i) q^{89} +(1.29743 + 3.99309i) q^{91} +(69.1547 + 10.9530i) q^{92} +(-42.1911 + 42.1911i) q^{93} +(77.7974 + 107.079i) q^{94} +(59.8858 + 43.5096i) q^{96} +(-16.8062 - 106.110i) q^{97} +(68.2019 + 133.854i) q^{98} +23.8192i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{2} + 4 q^{7} + 12 q^{8} + 24 q^{12} - 32 q^{13} + 80 q^{16} + 100 q^{17} + 48 q^{18} - 100 q^{19} + 100 q^{22} + 96 q^{23} - 40 q^{26} - 196 q^{28} + 200 q^{29} - 636 q^{32} - 216 q^{33} + 100 q^{34}+ \cdots + 92 q^{98}+O(q^{100}) $ 80 * q - 4 * q^2 + 4 * q^7 + 12 * q^8 + 24 * q^12 - 32 * q^13 + 80 * q^16 + 100 * q^17 + 48 * q^18 - 100 * q^19 + 100 * q^22 + 96 * q^23 - 40 * q^26 - 196 * q^28 + 200 * q^29 - 636 * q^32 - 216 * q^33 + 100 * q^34 - 120 * q^36 + 184 * q^37 + 564 * q^38 + 160 * q^41 + 12 * q^42 + 472 * q^43 - 700 * q^44 + 288 * q^47 + 48 * q^48 - 620 * q^52 - 304 * q^53 - 72 * q^57 - 1272 * q^58 + 800 * q^59 - 240 * q^61 - 1212 * q^62 + 12 * q^63 + 100 * q^64 + 80 * q^67 - 104 * q^68 - 36 * q^72 + 116 * q^73 + 88 * q^77 + 120 * q^78 + 200 * q^79 + 180 * q^81 + 168 * q^82 + 1264 * q^83 - 1200 * q^84 + 876 * q^87 + 212 * q^88 - 1500 * q^89 + 1504 * q^92 + 648 * q^93 - 200 * q^94 + 60 * q^96 + 260 * q^97 + 92 * q^98

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$1$

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 $

$2$	−2.73870	+	1.39544i	−1.36935	+	0.697719i	−0.975200	−	0.221327i	$-0.928961\pi$
$2$	−2.73870	+	1.39544i	−1.36935	+	0.697719i	−0.394151	+	0.919046i	$0.628961\pi$
$3$	−1.71073	+	0.270952i	−0.570242	+	0.0903175i
$3$	−1.71073	+	0.270952i	−0.570242	+	0.0903175i
$4$	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	0.724744	−	0.689018i	$-0.241958\pi$
$7$	0.250082	+	0.250082i	0.0357260	+	0.0357260i	−0.689018	+	0.724744i	$0.741958\pi$
$8$	−0.696119	+	4.39513i	−0.0870149	+	0.549391i
$9$	2.85317	−	0.927051i	0.317019	−	0.103006i
$10$		0			0
$11$	−2.45351	+	7.55112i	−0.223046	+	0.686466i	0.775438	+	0.631424i	$0.217529\pi$
$11$	−2.45351	+	7.55112i	−0.223046	+	0.686466i	−0.998484	+	0.0550418i	$0.982471\pi$
$12$	−4.28374	+	8.40731i	−0.356978	+	0.700609i
$13$	10.5776	+	5.38954i	0.813659	+	0.414580i	0.810733	−	0.585416i	$-0.199069\pi$
$13$	10.5776	+	5.38954i	0.813659	+	0.414580i	0.00292573	+	0.999996i	$0.499069\pi$
$14$	−1.03387	−	0.335926i	−0.0738481	−	0.0239947i
$15$		0			0
$16$	2.50710	+	7.71607i	0.156694	+	0.482254i
$17$	−24.0906	−	3.81558i	−1.41710	−	0.224446i	−0.599563	−	0.800327i	$-0.704659\pi$
$17$	−24.0906	−	3.81558i	−1.41710	−	0.224446i	−0.817533	+	0.575881i	$0.804659\pi$
$18$	−6.52034	+	6.52034i	−0.362241	+	0.362241i
$19$	−15.4606	−	21.2797i	−0.813715	−	1.11998i	−0.990740	−	0.135776i	$-0.956647\pi$
$19$	−15.4606	−	21.2797i	−0.813715	−	1.11998i	0.177024	−	0.984206i	$-0.443353\pi$
$20$		0			0
$21$	−0.495582	−	0.360061i	−0.0235991	−	0.0171458i
$22$	−3.81770	−	24.1040i	−0.173532	−	1.09564i
$23$	5.83489	+	11.4516i	0.253691	+	0.497897i	0.982367	−	0.186962i	$-0.0598641\pi$
$23$	5.83489	+	11.4516i	0.253691	+	0.497897i	−0.728676	+	0.684858i	$0.759864\pi$
$24$		−	7.70747i		−	0.321145i
$25$		0			0
$26$	−36.4896			−1.40344
$27$	−4.62981	+	2.35900i	−0.171474	+	0.0873705i
$28$	1.90297	−	0.301401i	0.0679634	−	0.0107643i
$29$	−27.7376	+	38.1776i	−0.956470	+	1.31647i	−0.00787767	+	0.999969i	$0.502508\pi$
$29$	−27.7376	+	38.1776i	−0.956470	+	1.31647i	−0.948593	+	0.316500i	$0.897492\pi$
$30$		0			0
$31$	27.8697	−	20.2485i	0.899023	−	0.653179i	−0.0391915	−	0.999232i	$-0.512478\pi$
$31$	27.8697	−	20.2485i	0.899023	−	0.653179i	0.938215	+	0.346053i	$0.112478\pi$
$32$	−30.2198	−	30.2198i	−0.944367	−	0.944367i
$33$	2.15129	−	13.5827i	0.0651905	−	0.411597i
$34$	71.3015	−	23.1673i	2.09710	−	0.681390i
$35$		0			0
$36$	5.05032	−	15.5433i	0.140287	−	0.431758i
$37$	3.75426	−	7.36815i	0.101466	−	0.199139i	−0.834692	−	0.550716i	$-0.814355\pi$
$37$	3.75426	−	7.36815i	0.101466	−	0.199139i	0.936159	+	0.351577i	$0.114355\pi$
$38$	72.0364	+	36.7044i	1.89569	+	0.965905i
$39$	−19.5556	−	6.35401i	−0.501426	−	0.162923i
$40$		0			0
$41$	−14.5062	−	44.6455i	−0.353810	−	1.08892i	−0.956696	−	0.291088i	$-0.905983\pi$
$41$	−14.5062	−	44.6455i	−0.353810	−	1.08892i	0.602886	−	0.797827i	$-0.294017\pi$
$42$	1.85969	+	0.294547i	0.0442784	+	0.00701302i
$43$	−1.08084	+	1.08084i	−0.0251357	+	0.0251357i	−0.719563	−	0.694427i	$-0.755658\pi$
$43$	−1.08084	+	1.08084i	−0.0251357	+	0.0251357i	0.694427	+	0.719563i	$0.255658\pi$
$44$	25.4237	+	34.9928i	0.577812	+	0.795291i
$45$		0			0
$46$	−31.9601	−	23.2203i	−0.694784	−	0.504790i
$47$	−6.73620	−	42.5307i	−0.143323	−	0.904909i	−0.949621	−	0.313399i	$-0.898532\pi$
$47$	−6.73620	−	42.5307i	−0.143323	−	0.904909i	0.806298	−	0.591509i	$-0.201468\pi$
$48$	−6.37966	−	12.5208i	−0.132910	−	0.260850i
$49$		−	48.8749i		−	0.997447i
$50$		0			0
$51$	42.2463			0.828360
$52$	57.6237	−	29.3608i	1.10815	−	0.564630i
$53$	28.7572	−	4.55469i	0.542589	−	0.0859376i	0.120877	−	0.992668i	$-0.461429\pi$
$53$	28.7572	−	4.55469i	0.542589	−	0.0859376i	0.421712	+	0.906730i	$0.361429\pi$
$54$	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
$58$	22.6907	−	143.263i	0.391218	−	2.47005i
$59$	71.3918	−	23.1966i	1.21003	−	0.393163i	0.366588	−	0.930383i	$-0.380526\pi$
$59$	71.3918	−	23.1966i	1.21003	−	0.393163i	0.843442	+	0.537221i	$0.180526\pi$
$60$		0			0
$61$	26.0031	−	80.0294i	0.426281	−	1.31196i	−0.475481	−	0.879726i	$-0.657726\pi$
$61$	26.0031	−	80.0294i	0.426281	−	1.31196i	0.901762	−	0.432232i	$-0.142274\pi$
$62$	−48.0713	+	94.3452i	−0.775343	+	1.52170i
$63$	0.945365	+	0.481688i	0.0150058	+	0.00764583i
$64$	94.0684	+	30.5647i	1.46982	+	0.477573i
$65$		0			0
$66$	13.0621	+	40.2009i	0.197910	+	0.609105i
$67$	41.9801	+	6.64899i	0.626568	+	0.0992386i	0.461641	−	0.887067i	$-0.347261\pi$
$67$	41.9801	+	6.64899i	0.626568	+	0.0992386i	0.164927	+	0.986306i	$0.447261\pi$
$68$	−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	0.877168	−	0.480183i	$-0.159430\pi$
$71$	49.0998	+	35.6731i	0.691546	+	0.502438i	−0.185622	+	0.982621i	$0.559430\pi$
$72$	2.08836	+	13.1854i	0.0290050	+	0.183130i
$73$	−43.1099	−	84.6079i	−0.590547	−	1.15901i	−0.972078	−	0.234657i	$-0.924603\pi$
$73$	−43.1099	−	84.6079i	−0.590547	−	1.15901i	0.381532	−	0.924356i	$-0.375397\pi$
$74$			25.4180i			0.343486i
$75$		0			0
$76$	−143.292			−1.88543
$77$	−2.50198	+	1.27482i	−0.0324932	+	0.0165561i
$78$	62.4237	−	9.88694i	0.800303	−	0.126756i
$79$	−62.3659	+	85.8393i	−0.789442	+	1.08657i	0.204736	+	0.978817i	$0.434366\pi$
$79$	−62.3659	+	85.8393i	−0.789442	+	1.08657i	−0.994177	+	0.107756i	$0.965634\pi$
$80$		0			0
$81$	7.28115	−	5.29007i	0.0898908	−	0.0653095i
$82$	102.028	+	102.028i	1.24425	+	1.24425i
$83$	15.0878	−	95.2606i	0.181781	−	1.14772i	−0.712984	−	0.701180i	$-0.752657\pi$
$83$	15.0878	−	95.2606i	0.181781	−	1.14772i	0.894765	−	0.446538i	$-0.147343\pi$
$84$	−3.17380	+	1.03123i	−0.0377834	+	0.0122766i
$85$		0			0
$86$	1.45185	−	4.46832i	0.0168819	−	0.0519572i
$87$	37.1072	−	72.8270i	0.426520	−	0.837092i
$88$	−31.4802	−	16.0400i	−0.357730	−	0.182272i
$89$	−163.312	−	53.0634i	−1.83497	−	0.596218i	−0.998864	−	0.0476516i	$-0.984826\pi$
$89$	−163.312	−	53.0634i	−1.83497	−	0.596218i	−0.836107	−	0.548567i	$-0.815174\pi$
$90$		0			0
$91$	1.29743	+	3.99309i	0.0142575	+	0.0438801i
$92$	69.1547	+	10.9530i	0.751681	+	0.119055i
$93$	−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
$97$	−16.8062	−	106.110i	−0.173259	−	1.09392i	−0.909044	−	0.416701i	$-0.863186\pi$
$97$	−16.8062	−	106.110i	−0.173259	−	1.09392i	0.735784	−	0.677216i	$-0.236814\pi$
$98$	68.2019	+	133.854i	0.695938	+	1.36585i
$99$			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	$0.677901\pi$
$102$	−115.700	+	58.9522i	−1.13431	+	0.577962i
$103$	−94.2525	+	14.9281i	−0.915073	+	0.144933i	−0.596174	−	0.802855i	$-0.703313\pi$
$103$	−94.2525	+	14.9281i	−0.915073	+	0.144933i	−0.318899	+	0.947789i	$0.603313\pi$
$104$	−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	$-0.926920\pi$
$107$	−128.543	−	128.543i	−1.20134	−	1.20134i	−0.227575	−	0.973761i	$-0.573080\pi$
$108$	−4.42823	+	27.9587i	−0.0410021	+	0.258877i
$109$	−89.3002	+	29.0154i	−0.819268	+	0.266196i	−0.688518	−	0.725219i	$-0.741738\pi$
$109$	−89.3002	+	29.0154i	−0.819268	+	0.266196i	−0.130750	+	0.991415i	$0.541738\pi$
$110$		0			0
$111$	−4.42609	+	13.6221i	−0.0398747	+	0.122722i
$112$	−1.30267	+	2.55663i	−0.0116310	+	0.0228271i
$113$	13.1461	+	6.69828i	0.116337	+	0.0592768i	0.511191	−	0.859467i	$-0.329205\pi$
$113$	13.1461	+	6.69828i	0.116337	+	0.0592768i	−0.394853	+	0.918744i	$0.629205\pi$
$114$	−133.180	−	43.2727i	−1.16824	−	0.379585i
$115$		0			0
$116$	79.4417	+	244.497i	0.684843	+	2.10773i
$117$	35.1760	+	5.57133i	0.300649	+	0.0476182i
$118$	−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
$122$	40.4613	+	255.462i	0.331650	+	2.09395i
$123$	36.9130	+	72.4458i	0.300105	+	0.588990i
$124$		−	187.668i		−	1.51345i
$125$		0			0
$126$	−3.26124			−0.0258828
$127$	−36.2034	+	18.4466i	−0.285066	+	0.145249i	−0.590677	−	0.806908i	$-0.701139\pi$
$127$	−36.2034	+	18.4466i	−0.285066	+	0.145249i	0.305611	+	0.952157i	$0.401139\pi$
$128$	−131.432	+	20.8168i	−1.02681	+	0.162631i
$129$	1.55616	−	2.14187i	0.0120632	−	0.0166036i
$130$		0			0
$131$	121.554	−	88.3139i	0.927890	−	0.674152i	−0.0175852	−	0.999845i	$-0.505598\pi$
$131$	121.554	−	88.3139i	0.927890	−	0.674152i	0.945475	+	0.325694i	$0.105598\pi$
$132$	−52.9745	−	52.9745i	−0.401322	−	0.401322i
$133$	1.45525	−	9.18808i	0.0109417	−	0.0690833i
$134$	−124.249	+	40.3710i	−0.927232	+	0.301276i
$135$		0			0
$136$	33.5399	−	103.225i	0.246617	−	0.759010i
$137$	7.33780	−	14.4013i	0.0535606	−	0.105119i	−0.862675	−	0.505759i	$-0.831212\pi$
$137$	7.33780	−	14.4013i	0.0535606	−	0.105119i	0.916235	+	0.400641i	$0.131212\pi$
$138$	60.9665	+	31.0640i	0.441786	+	0.225101i
$139$	45.4296	+	14.7610i	0.326832	+	0.106194i	0.467837	−	0.883815i	$-0.345033\pi$
$139$	45.4296	+	14.7610i	0.326832	+	0.106194i	−0.141005	+	0.990009i	$0.545033\pi$
$140$		0			0
$141$	23.0476	+	70.9332i	0.163458	+	0.503072i
$142$	−184.249	−	29.1822i	−1.29753	−	0.205509i
$143$	−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
$147$	13.2428	+	83.6116i	0.0900869	+	0.568786i
$148$	−20.4522	−	40.1397i	−0.138190	−	0.271214i
$149$		−	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	$0.563501\pi$
$152$	104.289	−	53.1380i	0.686114	−	0.349592i
$153$	−72.2719	+	11.4468i	−0.472366	+	0.0748154i
$154$	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	0.927976	−	0.372640i	$-0.121547\pi$
$157$	87.1877	+	87.1877i	0.555336	+	0.555336i	−0.372640	+	0.927976i	$0.621547\pi$
$158$	51.0181	−	322.116i	0.322900	−	2.03871i
$159$	−47.9616	+	15.5837i	−0.301645	+	0.0980105i
$160$		0			0
$161$	−1.40464	+	4.32305i	−0.00872449	+	0.0268512i
$162$	−12.5589	+	24.6483i	−0.0775243	+	0.152150i
$163$	−82.9386	−	42.2593i	−0.508826	−	0.259260i	0.180677	−	0.983542i	$-0.442171\pi$
$163$	−82.9386	−	42.2593i	−0.508826	−	0.259260i	−0.689503	+	0.724283i	$0.742171\pi$
$164$	−243.217	−	79.0259i	−1.48303	−	0.481865i
$165$		0			0
$166$	91.6093	+	281.944i	0.551863	+	1.69846i
$167$	234.911	+	37.2062i	1.40665	+	0.222792i	0.813156	−	0.582046i	$-0.197748\pi$
$167$	234.911	+	37.2062i	1.40665	+	0.222792i	0.593495	+	0.804837i	$0.297748\pi$
$168$	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
$172$	1.30263	+	8.22451i	0.00757346	+	0.0478169i
$173$	−15.0135	−	29.4657i	−0.0867833	−	0.170322i	0.843536	−	0.537073i	$-0.180470\pi$
$173$	−15.0135	−	29.4657i	−0.0867833	−	0.170322i	−0.930319	+	0.366751i	$0.880470\pi$
$174$			251.232i			1.44386i
$175$		0			0
$176$	−64.4162			−0.366001
$177$	−115.847	+	59.0268i	−0.654501	+	0.333485i
$178$	521.311	−	82.5675i	2.92871	−	0.463862i
$179$	157.338	−	216.558i	0.878985	−	1.20982i	−0.0977154	−	0.995214i	$-0.531153\pi$
$179$	157.338	−	216.558i	0.878985	−	1.20982i	0.976701	−	0.214605i	$-0.0688465\pi$
$180$		0			0
$181$	−32.1635	+	23.3682i	−0.177699	+	0.129106i	−0.673079	−	0.739570i	$-0.735029\pi$
$181$	−32.1635	+	23.3682i	−0.177699	+	0.129106i	0.495380	+	0.868676i	$0.335029\pi$
$182$	−9.12538	−	9.12538i	−0.0501395	−	0.0501395i
$183$	−22.8001	+	143.954i	−0.124591	+	0.786634i
$184$	−54.3931	+	17.6734i	−0.295615	+	0.0960510i
$185$		0			0
$186$	56.6737	−	174.424i	0.304697	−	0.937762i
$187$	87.9186	−	172.550i	0.470153	−	0.922727i
$188$	−209.016	−	106.499i	−1.11179	−	0.566483i
$189$	−1.74778	−	0.567887i	−0.00924749	−	0.00300469i
$190$		0			0
$191$	−40.9280	−	125.963i	−0.214283	−	0.659495i	−0.999204	−	0.0398988i	$-0.987296\pi$
$191$	−40.9280	−	125.963i	−0.214283	−	0.659495i	0.784921	−	0.619596i	$-0.212704\pi$
$192$	−169.207	−	26.7997i	−0.881286	−	0.139582i
$193$	31.7199	−	31.7199i	0.164352	−	0.164352i	−0.620140	−	0.784491i	$-0.712924\pi$
$193$	31.7199	−	31.7199i	0.164352	−	0.164352i	0.784491	+	0.620140i	$0.212924\pi$
$194$	194.097	+	267.151i	1.00050	+	1.37707i
$195$		0			0
$196$	−215.407	−	156.502i	−1.09901	−	0.798480i
$197$	26.9222	+	169.980i	0.136661	+	0.862844i	0.956814	+	0.290700i	$0.0938881\pi$
$197$	26.9222	+	169.980i	0.136661	+	0.862844i	−0.820153	+	0.572144i	$0.806112\pi$
$198$	−33.2382	−	65.2336i	−0.167870	−	0.329462i
$199$		−	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
$202$	293.342	−	149.465i	1.45219	−	0.739927i
$203$	−16.4842	+	2.61084i	−0.0812030	+	0.0128613i
$204$	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
$208$	−15.0670	+	95.1294i	−0.0724376	+	0.457353i
$209$	198.618	−	64.5350i	0.950326	−	0.308780i
$210$		0			0
$211$	4.07202	−	12.5324i	0.0192987	−	0.0593952i	−0.940943	−	0.338564i	$-0.890059\pi$
$211$	4.07202	−	12.5324i	0.0192987	−	0.0593952i	0.960242	+	0.279169i	$0.0900589\pi$
$212$	72.0094	−	141.326i	0.339667	−	0.666634i
$213$	−93.6620	−	47.7232i	−0.439728	−	0.224052i
$214$	531.414	+	172.667i	2.48324	+	0.806855i
$215$		0			0
$216$	−7.14522	−	21.9907i	−0.0330797	−	0.101809i
$217$	12.0335	+	1.90592i	0.0554540	+	0.00878305i
$218$	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
$222$	−6.88706	−	43.4832i	−0.0310228	−	0.195870i
$223$	99.4164	+	195.116i	0.445814	+	0.874958i	0.999118	+	0.0419796i	$0.0133665\pi$
$223$	99.4164	+	195.116i	0.445814	+	0.874958i	−0.553305	+	0.832979i	$0.686634\pi$
$224$		−	15.1148i		−	0.0674769i
$225$		0			0
$226$	−45.3503			−0.200665
$227$	−133.983	+	68.2679i	−0.590235	+	0.300740i	−0.723482	−	0.690343i	$-0.757460\pi$
$227$	−133.983	+	68.2679i	−0.590235	+	0.300740i	0.133247	+	0.991083i	$0.457460\pi$
$228$	245.134	−	38.8254i	1.07515	−	0.170287i
$229$	−218.119	+	300.215i	−0.952483	+	1.31098i	−0.00206788	+	0.999998i	$0.500658\pi$
$229$	−218.119	+	300.215i	−0.952483	+	1.31098i	−0.950415	+	0.310983i	$0.899342\pi$
$230$		0			0
$231$	3.93478	−	2.85879i	0.0170337	−	0.0123757i
$232$	−148.487	−	148.487i	−0.640028	−	0.640028i
$233$	−11.6039	+	73.2641i	−0.0498021	+	0.314438i	0.950194	+	0.311659i	$0.100885\pi$
$233$	−11.6039	+	73.2641i	−0.0498021	+	0.314438i	−0.999996	+	0.00277928i	$0.999115\pi$
$234$	−104.111	+	33.8277i	−0.444918	+	0.144563i
$235$		0			0
$236$	126.369	−	388.923i	0.535461	−	1.64798i
$237$	83.4326	−	163.746i	0.352036	−	0.690910i
$238$	23.6249	+	12.0375i	0.0992644	+	0.0505777i
$239$	216.055	+	70.2006i	0.903996	+	0.293726i	0.723885	−	0.689920i	$-0.242354\pi$
$239$	216.055	+	70.2006i	0.903996	+	0.293726i	0.180111	+	0.983646i	$0.442354\pi$
$240$		0			0
$241$	−106.433	−	327.566i	−0.441629	−	1.35919i	−0.886139	−	0.463420i	$-0.846622\pi$
$241$	−106.433	−	327.566i	−0.441629	−	1.35919i	0.444510	−	0.895774i	$-0.353378\pi$
$242$	−175.962	−	27.8696i	−0.727115	−	0.115164i
$243$	−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
$247$	−48.8478	−	308.413i	−0.197764	−	1.24863i
$248$	69.5942	+	136.586i	0.280622	+	0.550751i
$249$			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	$0.637467\pi$
$252$	5.15009	−	2.62410i	0.0204369	−	0.0104131i
$253$	−100.789	+	15.9633i	−0.398374	+	0.0630962i
$254$	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	0.966000	−	0.258544i	$-0.0832426\pi$
$257$	181.816	+	181.816i	0.707456	+	0.707456i	−0.258544	+	0.966000i	$0.583243\pi$
$258$	−1.27301	+	8.03746i	−0.00493414	+	0.0311529i
$259$	2.78151	−	0.903768i	0.0107394	−	0.00348945i
$260$		0			0
$261$	−43.7476	+	134.641i	−0.167615	+	0.515867i
$262$	−209.662	+	411.486i	−0.800238	+	1.57056i
$263$	−68.9955	−	35.1550i	−0.262340	−	0.133669i	0.317874	−	0.948133i	$-0.397031\pi$
$263$	−68.9955	−	35.1550i	−0.262340	−	0.133669i	−0.580214	+	0.814464i	$0.697031\pi$
$264$	58.2001	+	18.9104i	0.220455	+	0.0716301i
$265$		0			0
$266$	8.83590	+	27.1941i	0.0332177	+	0.102233i
$267$	293.761	+	46.5271i	1.10023	+	0.174259i
$268$	163.728	−	163.728i	0.610926	−	0.610926i
$269$	−187.609	−	258.221i	−0.697430	−	0.959931i	−0.999977	−	0.00679606i	$-0.997837\pi$
$269$	−187.609	−	258.221i	−0.697430	−	0.959931i	0.302546	−	0.953135i	$-0.402163\pi$
$270$		0			0
$271$	286.845	+	208.405i	1.05847	+	0.769022i	0.973804	−	0.227387i	$-0.0730184\pi$
$271$	286.845	+	208.405i	1.05847	+	0.769022i	0.0846638	+	0.996410i	$0.473018\pi$
$272$	−30.9564	−	195.451i	−0.113810	−	0.718571i
$273$	−3.30149	−	6.47953i	−0.0120934	−	0.0237346i
$274$			49.6802i			0.181314i
$275$		0			0
$276$	−121.273			−0.439393
$277$	−295.312	+	150.469i	−1.06611	+	0.543209i	−0.896837	−	0.442360i	$-0.854141\pi$
$277$	−295.312	+	150.469i	−1.06611	+	0.543209i	−0.169271	+	0.985570i	$0.554141\pi$
$278$	−145.016	+	22.9683i	−0.521641	+	0.0826198i
$279$	60.7456	−	83.6092i	0.217726	−	0.299674i
$280$		0			0
$281$	−87.3274	+	63.4471i	−0.310774	+	0.225790i	−0.732228	−	0.681059i	$-0.761520\pi$
$281$	−87.3274	+	63.4471i	−0.310774	+	0.225790i	0.421455	+	0.906849i	$0.361520\pi$
$282$	−162.103	−	162.103i	−0.574835	−	0.574835i
$283$	−20.9100	+	132.020i	−0.0738868	+	0.466503i	0.922808	+	0.385261i	$0.125889\pi$
$283$	−20.9100	+	132.020i	−0.0738868	+	0.466503i	−0.996694	+	0.0812417i	$0.974111\pi$
$284$	314.444	−	102.169i	1.10720	−	0.359751i
$285$		0			0
$286$	89.5275	−	275.537i	0.313033	−	0.963417i
$287$	7.53730	−	14.7928i	0.0262624	−	0.0515428i
$288$	−114.237	−	58.2068i	−0.396657	−	0.202107i
$289$	290.945	+	94.5339i	1.00673	+	0.327107i
$290$		0			0
$291$	57.5015	+	176.971i	0.197600	+	0.608149i
$292$	−510.935	−	80.9242i	−1.74978	−	0.277138i
$293$	255.208	−	255.208i	0.871017	−	0.871017i	−0.121566	−	0.992583i	$-0.538792\pi$
$293$	255.208	−	255.208i	0.871017	−	0.871017i	0.992583	+	0.121566i	$0.0387917\pi$
$294$	−152.943	−	210.508i	−0.520214	−	0.716013i
$295$		0			0
$296$	29.7705	+	21.6295i	0.100576	+	0.0730728i
$297$	−6.45386	−	40.7481i	−0.0217302	−	0.137199i
$298$	151.237	+	296.819i	0.507506	+	0.996037i
$299$			152.578i			0.510293i
$300$		0			0
$301$	−0.540595			−0.00179600
$302$	163.908	−	83.5152i	0.542741	−	0.276540i
$303$	183.236	−	29.0217i	0.604738	−	0.0957811i
$304$	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	0.999713	−	0.0239382i	$-0.00762048\pi$
$307$	299.563	+	299.563i	0.975775	+	0.975775i	−0.0239382	+	0.999713i	$0.507620\pi$
$308$	−2.39304	+	15.1091i	−0.00776962	+	0.0490555i
$309$	157.195	−	51.0759i	0.508723	−	0.165294i
$310$		0			0
$311$	−11.4518	+	35.2451i	−0.0368226	+	0.113328i	−0.967778	−	0.251804i	$-0.918976\pi$
$311$	−11.4518	+	35.2451i	−0.0368226	+	0.113328i	0.930956	+	0.365132i	$0.118976\pi$
$312$	41.5397	−	81.5263i	0.133140	−	0.261302i
$313$	−374.766	−	190.953i	−1.19734	−	0.610073i	−0.262424	−	0.964953i	$-0.584522\pi$
$313$	−374.766	−	190.953i	−1.19734	−	0.610073i	−0.934912	+	0.354880i	$0.884522\pi$
$314$	−360.446	−	117.116i	−1.14792	−	0.372981i
$315$		0			0
$316$	178.618	+	549.731i	0.565248	+	1.73966i
$317$	−162.025	−	25.6622i	−0.511119	−	0.0809533i	−0.104452	−	0.994530i	$-0.533309\pi$
$317$	−162.025	−	25.6622i	−0.511119	−	0.0809533i	−0.406667	+	0.913577i	$0.633309\pi$
$318$	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
$322$	−2.18565	−	13.7996i	−0.00678772	−	0.0428560i
$323$	291.261	+	571.632i	0.901738	+	1.76976i
$324$		−	49.0296i		−	0.151326i
$325$		0			0
$326$	286.114			0.877652
$327$	144.906	−	73.8335i	0.443139	−	0.225790i
$328$	206.321	−	32.6780i	0.629027	−	0.0996280i
$329$	8.95156	−	12.3208i	0.0272084	−	0.0374491i
$330$		0			0
$331$	265.305	−	192.756i	0.801527	−	0.582343i	−0.109835	−	0.993950i	$-0.535032\pi$
$331$	265.305	−	192.756i	0.801527	−	0.582343i	0.911362	+	0.411607i	$0.135032\pi$
$332$	−371.530	−	371.530i	−1.11907	−	1.11907i
$333$	3.88089	−	24.5030i	0.0116543	−	0.0735825i
$334$	−695.269	+	225.907i	−2.08164	+	0.676367i
$335$		0			0
$336$	1.53578	−	4.72666i	0.00457079	−	0.0140674i
$337$	−207.965	+	408.154i	−0.617107	+	1.21114i	0.345035	+	0.938590i	$0.387867\pi$
$337$	−207.965	+	408.154i	−0.617107	+	1.21114i	−0.962142	+	0.272550i	$0.912133\pi$
$338$	76.8697	+	39.1671i	0.227425	+	0.115879i
$339$	−24.3043	−	7.89696i	−0.0716942	−	0.0232949i
$340$		0			0
$341$	84.5206	+	260.128i	0.247861	+	0.762838i
$342$	239.559	+	37.9424i	0.700465	+	0.110943i
$343$	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
$347$	−60.7454	−	383.531i	−0.175059	−	1.10528i	−0.906137	−	0.422984i	$-0.860983\pi$
$347$	−60.7454	−	383.531i	−0.175059	−	1.10528i	0.731078	−	0.682293i	$-0.239017\pi$
$348$	−202.150	−	396.742i	−0.580891	−	1.14006i
$349$		−	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
$352$	302.338	−	154.049i	0.858913	−	0.437638i
$353$	70.5532	−	11.1745i	0.199868	−	0.0316559i	−0.0556979	−	0.998448i	$-0.517738\pi$
$353$	70.5532	−	11.1745i	0.199868	−	0.0316559i	0.255565	+	0.966792i	$0.417738\pi$
$354$	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
$358$	−128.710	+	812.643i	−0.359525	+	2.26995i
$359$	96.8130	−	31.4565i	0.269674	−	0.0876225i	−0.171058	−	0.985261i	$-0.554719\pi$
$359$	96.8130	−	31.4565i	0.269674	−	0.0876225i	0.440733	+	0.897638i	$0.354719\pi$
$360$		0			0
$361$	−102.240	+	314.661i	−0.283212	+	0.871638i
$362$	55.4774	−	108.881i	0.153253	−	0.300775i
$363$	−89.4491	−	45.5766i	−0.246416	−	0.125555i
$364$	21.7533	+	7.06806i	0.0597617	+	0.0194177i
$365$		0			0
$366$	−138.436	−	426.063i	−0.378241	−	1.16411i
$367$	−414.375	−	65.6306i	−1.12909	−	0.178830i	−0.436183	−	0.899858i	$-0.643670\pi$
$367$	−414.375	−	65.6306i	−1.12909	−	0.178830i	−0.692906	+	0.721028i	$0.743670\pi$
$368$	−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
$372$	50.8492	+	321.049i	0.136691	+	0.863035i
$373$	−179.734	−	352.748i	−0.481861	−	0.945705i	−0.996115	−	0.0880667i	$-0.971931\pi$
$373$	−179.734	−	352.748i	−0.481861	−	0.945705i	0.514254	−	0.857638i	$-0.328069\pi$
$374$			595.248i			1.59157i
$375$		0			0
$376$	191.617			0.509620
$377$	−499.156	+	254.333i	−1.32402	+	0.674623i
$378$	5.57908	−	0.883640i	0.0147595	−	0.00233767i
$379$	−364.178	+	501.248i	−0.960892	+	1.32255i	−0.0143757	+	0.999897i	$0.504576\pi$
$379$	−364.178	+	501.248i	−0.960892	+	1.32255i	−0.946516	+	0.322657i	$0.895424\pi$
$380$		0			0
$381$	56.9360	−	41.3665i	0.149438	−	0.108573i
$382$	287.864	+	287.864i	0.753570	+	0.753570i
$383$	−38.3398	+	242.068i	−0.100104	+	0.632031i	0.885716	+	0.464227i	$0.153668\pi$
$383$	−38.3398	+	242.068i	−0.100104	+	0.632031i	−0.985820	+	0.167804i	$0.946332\pi$
$384$	219.204	−	71.2237i	0.570844	−	0.185478i
$385$		0			0
$386$	−42.6081	+	131.134i	−0.110384	+	0.339726i
$387$	−2.08182	+	4.08580i	−0.00537937	+	0.0105576i
$388$	−521.474	−	265.704i	−1.34401	−	0.684805i
$389$	21.1457	+	6.87066i	0.0543591	+	0.0176624i	0.336070	−	0.941837i	$-0.390902\pi$
$389$	21.1457	+	6.87066i	0.0543591	+	0.0176624i	−0.281711	+	0.959499i	$0.590902\pi$
$390$		0			0
$391$	−96.8717	−	298.141i	−0.247754	−	0.762508i
$392$	214.811	+	34.0228i	0.547988	+	0.0867928i
$393$	−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
$397$	27.3358	+	172.591i	0.0688559	+	0.434739i	0.997900	+	0.0647705i	$0.0206315\pi$
$397$	27.3358	+	172.591i	0.0688559	+	0.434739i	−0.929044	+	0.369968i	$0.879368\pi$
$398$	37.2654	+	73.1375i	0.0936317	+	0.183763i
$399$			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	$0.644703\pi$
$402$	201.618	−	102.729i	0.501536	−	0.255545i
$403$	403.924	−	63.9753i	1.00229	−	0.158748i
$404$	−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
$408$	−29.4085	+	185.678i	−0.0720797	+	0.455093i
$409$	−454.282	+	147.605i	−1.11071	+	0.360893i	−0.806217	−	0.591620i	$-0.798489\pi$
$409$	−454.282	+	147.605i	−1.11071	+	0.360893i	−0.304498	+	0.952513i	$0.598489\pi$
$410$		0			0
$411$	−8.65092	+	26.6248i	−0.0210485	+	0.0647805i
$412$	−236.013	+	463.201i	−0.572846	+	1.12427i
$413$	23.6548	+	12.0527i	0.0572756	+	0.0291834i
$414$	−112.714	−	36.6230i	−0.272256	−	0.0884613i
$415$		0			0
$416$	−156.781	−	482.522i	−0.376877	−	1.15991i
$417$	−81.7172	−	12.9427i	−0.195965	−	0.0310377i
$418$	−453.901	+	453.901i	−1.08589	+	1.08589i
$419$	362.429	+	498.840i	0.864985	+	1.19055i	0.980358	+	0.197227i	$0.0631937\pi$
$419$	362.429	+	498.840i	0.864985	+	1.19055i	−0.115373	+	0.993322i	$0.536806\pi$
$420$		0			0
$421$	374.959	+	272.424i	0.890639	+	0.647087i	0.936044	−	0.351882i	$-0.114458\pi$
$421$	374.959	+	272.424i	0.890639	+	0.647087i	−0.0454057	+	0.998969i	$0.514458\pi$
$422$	6.33613	+	40.0047i	0.0150145	+	0.0947980i
$423$	−58.6477	−	115.103i	−0.138647	−	0.272110i
$424$			129.562i			0.305571i
$425$		0			0
$426$	323.107			0.758467
$427$	26.5168	−	13.5110i	0.0621003	−	0.0316417i
$428$	−978.134	+	154.921i	−2.28536	+	0.361966i
$429$	95.9598	−	132.077i	0.223683	−	0.307873i
$430$		0			0
$431$	−19.0751	+	13.8589i	−0.0442578	+	0.0321552i	−0.609694	−	0.792637i	$-0.708708\pi$
$431$	−19.0751	+	13.8589i	−0.0442578	+	0.0321552i	0.565436	+	0.824792i	$0.308708\pi$
$432$	−29.8096	−	29.8096i	−0.0690038	−	0.0690038i
$433$	17.5716	−	110.943i	0.0405810	−	0.256218i	−0.959054	−	0.283222i	$-0.908597\pi$
$433$	17.5716	−	110.943i	0.0405810	−	0.256218i	0.999635	+	0.0270038i	$0.00859661\pi$
$434$	−35.6158	+	11.5723i	−0.0820640	+	0.0266642i
$435$		0			0
$436$	−158.068	+	486.483i	−0.362541	+	1.11579i
$437$	153.476	−	301.213i	0.351203	−	0.689276i
$438$	−450.439	−	229.510i	−1.02840	−	0.523995i
$439$	519.678	+	168.854i	1.18378	+	0.384632i	0.833768	−	0.552114i	$-0.186179\pi$
$439$	519.678	+	168.854i	1.18378	+	0.384632i	0.350008	+	0.936747i	$0.386179\pi$
$440$		0			0
$441$	−45.3095	−	139.448i	−0.102743	−	0.316210i
$442$	879.057	+	139.229i	1.98882	+	0.314998i
$443$	165.809	−	165.809i	0.374287	−	0.374287i	−0.494749	−	0.869036i	$-0.664740\pi$
$443$	165.809	−	165.809i	0.374287	−	0.374287i	0.869036	+	0.494749i	$0.164740\pi$
$444$	45.8640	+	63.1264i	0.103297	+	0.142177i
$445$		0			0
$446$	−544.544	−	395.634i	−1.22095	−	0.887072i
$447$	29.3657	+	185.408i	0.0656951	+	0.414782i
$448$	15.8811	+	31.1685i	0.0354490	+	0.0695725i
$449$		−	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
$452$	71.6165	−	36.4904i	0.158444	−	0.0807311i
$453$	102.385	−	16.2162i	0.226015	−	0.0357973i
$454$	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	0.0160822	−	0.999871i	$-0.494881\pi$
$457$	−449.591	−	449.591i	−0.983788	−	0.983788i	−0.999871	+	0.0160822i	$0.994881\pi$
$458$	178.431	−	1126.57i	0.389587	−	2.45976i
$459$	120.536	−	39.1645i	0.262606	−	0.0853258i
$460$		0			0
$461$	−130.749	+	402.403i	−0.283620	+	0.872892i	0.703189	+	0.711003i	$0.251759\pi$
$461$	−130.749	+	402.403i	−0.283620	+	0.872892i	−0.986809	+	0.161889i	$0.948241\pi$
$462$	−6.78694	+	13.3201i	−0.0146903	+	0.0288314i
$463$	585.996	+	298.580i	1.26565	+	0.644881i	0.952418	−	0.304795i	$-0.0985880\pi$
$463$	585.996	+	298.580i	1.26565	+	0.644881i	0.313233	+	0.949676i	$0.398588\pi$
$464$	−364.122	−	118.310i	−0.784746	−	0.254979i
$465$		0			0
$466$	−70.4559	−	216.841i	−0.151193	−	0.465324i
$467$	649.664	+	102.897i	1.39114	+	0.220335i	0.806634	−	0.591052i	$-0.201287\pi$
$467$	649.664	+	102.897i	1.39114	+	0.220335i	0.584509	+	0.811387i	$0.301287\pi$
$468$	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
$472$	52.2547	+	329.923i	0.110709	+	0.698990i
$473$	−5.50968	−	10.8134i	−0.0116484	−	0.0228612i
$474$			564.875i			1.19172i
$475$		0			0
$476$	−46.9939			−0.0987267
$477$	77.8267	−	39.6547i	0.163159	−	0.0831336i
$478$	−689.671	+	109.233i	−1.44283	+	0.228521i
$479$	−394.709	+	543.270i	−0.824026	+	1.13418i	0.164979	+	0.986297i	$0.447244\pi$
$479$	−394.709	+	543.270i	−0.824026	+	1.13418i	−0.989006	+	0.147878i	$0.952756\pi$
$480$		0			0
$481$	79.4218	−	57.7033i	0.165118	−	0.119965i
$482$	748.584	+	748.584i	1.55308	+	1.55308i
$483$	1.23162	−	7.77614i	0.00254994	−	0.0160997i
$484$	300.301	−	97.5736i	0.620456	−	0.201598i
$485$		0			0
$486$	14.8064	−	45.5694i	0.0304658	−	0.0937642i
$487$	47.8556	−	93.9218i	0.0982660	−	0.192858i	−0.836640	−	0.547753i	$-0.815483\pi$
$487$	47.8556	−	93.9218i	0.0982660	−	0.192858i	0.934906	+	0.354895i	$0.115483\pi$
$488$	333.638	+	169.997i	0.683685	+	0.348355i
$489$	153.336	+	49.8218i	0.313570	+	0.101885i
$490$		0			0
$491$	52.5414	+	161.706i	0.107009	+	0.329340i	0.990197	−	0.139680i	$-0.0446073\pi$
$491$	52.5414	+	161.706i	0.107009	+	0.329340i	−0.883188	+	0.469020i	$0.844607\pi$
$492$	437.490	+	69.2916i	0.889207	+	0.140836i
$493$	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
$497$	3.35778	+	21.2002i	0.00675609	+	0.0426563i
$498$	−233.112	−	457.508i	−0.468096	−	0.918690i
$499$		−	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
$502$	575.455	−	293.209i	1.14632	−	0.584081i
$503$	−129.151	+	20.4555i	−0.256762	+	0.0406671i	−0.283488	−	0.958976i	$-0.591492\pi$
$503$	−129.151	+	20.4555i	−0.256762	+	0.0406671i	0.0267264	+	0.999643i	$0.491492\pi$
$504$	−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
$508$	−34.6272	+	218.627i	−0.0681637	+	0.430369i
$509$	−88.4961	+	28.7541i	−0.173863	+	0.0564914i	−0.394655	−	0.918830i	$-0.629136\pi$
$509$	−88.4961	+	28.7541i	−0.173863	+	0.0564914i	0.220792	+	0.975321i	$0.429136\pi$
$510$		0			0
$511$	10.3779	−	31.9399i	0.0203090	−	0.0625048i
$512$	222.975	−	437.613i	0.435498	−	0.854713i
$513$	121.778	+	62.0492i	0.237385	+	0.120954i
$514$	−751.653	−	244.227i	−1.46236	−	0.475150i
$515$		0			0
$516$	−4.45690	−	13.7169i	−0.00863741	−	0.0265832i
$517$	337.682	+	53.4836i	0.653157	+	0.103450i
$518$	−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	0.533528	−	0.845782i	$-0.320866\pi$
$521$	−55.2207	−	40.1202i	−0.105990	−	0.0770062i	−0.639518	+	0.768776i	$0.720866\pi$
$522$	−68.0720	−	429.789i	−0.130406	−	0.823351i
$523$	−390.574	−	766.544i	−0.746795	−	1.46567i	−0.880199	−	0.474605i	$-0.842591\pi$
$523$	−390.574	−	766.544i	−0.746795	−	1.46567i	0.133404	−	0.991062i	$-0.457409\pi$
$524$		−	818.513i		−	1.56205i
$525$		0			0
$526$	238.015			0.452499
$527$	−748.660	+	381.461i	−1.42061	+	0.723835i
$528$	110.199	−	17.4537i	0.208709	−	0.0330563i
$529$	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
$533$	87.1784	−	550.423i	0.163562	−	1.03269i
$534$	−869.448	+	282.501i	−1.62818	+	0.529028i
$535$		0			0
$536$	−58.4463	+	179.879i	−0.109042	+	0.335595i
$537$	−210.486	+	413.102i	−0.391967	+	0.769278i
$538$	874.136	+	445.395i	1.62479	+	0.827871i
$539$	369.061	+	119.915i	0.684713	+	0.222477i
$540$		0			0
$541$	−6.85938	−	21.1110i	−0.0126791	−	0.0390222i	0.944517	−	0.328463i	$-0.106531\pi$
$541$	−6.85938	−	21.1110i	−0.0126791	−	0.0390222i	−0.957196	+	0.289441i	$0.906531\pi$
$542$	−1076.40	−	170.485i	−1.98598	−	0.314548i
$543$	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
$547$	−67.8821	−	428.590i	−0.124099	−	0.783529i	−0.968718	−	0.248162i	$-0.920173\pi$
$547$	−67.8821	−	428.590i	−0.124099	−	0.783529i	0.844620	−	0.535367i	$-0.179827\pi$
$548$	−39.9744	−	78.4541i	−0.0729459	−	0.143164i
$549$		−	252.444i		−	0.459825i
$550$		0			0
$551$	1241.25			2.25272
$552$	88.2631	−	44.9723i	0.159897	−	0.0814715i
$553$	−37.0634	+	5.87027i	−0.0670225	+	0.0106153i
$554$	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	0.836752	−	0.547583i	$-0.184452\pi$
$557$	161.067	+	161.067i	0.289169	+	0.289169i	−0.547583	+	0.836752i	$0.684452\pi$
$558$	−49.6927	+	313.747i	−0.0890550	+	0.562271i
$559$	−17.2578	+	5.60740i	−0.0308727	+	0.0100311i
$560$		0			0
$561$	−103.652	+	319.007i	−0.184763	+	0.568641i
$562$	150.627	−	295.623i	0.268020	−	0.526019i
$563$	169.572	+	86.4014i	0.301194	+	0.153466i	0.598056	−	0.801454i	$-0.295940\pi$
$563$	169.572	+	86.4014i	0.301194	+	0.153466i	−0.296862	+	0.954920i	$0.595940\pi$
$564$	386.425	+	125.557i	0.685151	+	0.222619i
$565$		0			0
$566$	−126.960	−	390.743i	−0.224311	−	0.690358i
$567$	3.14384	+	0.497935i	0.00554468	+	0.000878192i
$568$	−190.967	+	190.967i	−0.336210	+	0.336210i
$569$	−249.297	−	343.128i	−0.438132	−	0.603036i	0.531664	−	0.846955i	$-0.321567\pi$
$569$	−249.297	−	343.128i	−0.438132	−	0.603036i	−0.969796	+	0.243919i	$0.921567\pi$
$570$		0			0
$571$	−148.638	−	107.992i	−0.260312	−	0.189128i	0.449972	−	0.893042i	$-0.351434\pi$
$571$	−148.638	−	107.992i	−0.260312	−	0.189128i	−0.710285	+	0.703914i	$0.751434\pi$
$572$	80.3264	+	507.161i	0.140431	+	0.886645i
$573$	104.147	+	204.400i	0.181757	+	0.356718i
$574$			51.0308i			0.0889039i
$575$		0			0
$576$	296.728			0.515153
$577$	−675.710	+	344.292i	−1.17108	+	0.596693i	−0.927732	−	0.373248i	$-0.878244\pi$
$577$	−675.710	+	344.292i	−1.17108	+	0.596693i	−0.243343	+	0.969940i	$0.578244\pi$
$578$	−928.728	+	147.096i	−1.60680	+	0.254492i
$579$	−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
$583$	−36.1630	+	228.324i	−0.0620292	+	0.391637i
$584$	401.872	−	130.576i	0.688137	−	0.223589i
$585$		0			0
$586$	−342.811	+	1055.07i	−0.585002	+	1.80045i
$587$	123.904	−	243.176i	0.211081	−	0.414269i	−0.761055	−	0.648687i	$-0.775318\pi$
$587$	123.904	−	243.176i	0.211081	−	0.414269i	0.972136	+	0.234418i	$0.0753184\pi$
$588$	410.907	+	209.367i	0.698821	+	0.356067i
$589$	−861.765	−	280.004i	−1.46310	−	0.475389i
$590$		0			0
$591$	−92.1131	−	283.495i	−0.155860	−	0.479687i
$592$	66.2655	+	10.4954i	0.111935	+	0.0177287i
$593$	−367.718	+	367.718i	−0.620098	+	0.620098i	−0.945556	−	0.325458i	$-0.894481\pi$
$593$	−367.718	+	367.718i	−0.620098	+	0.620098i	0.325458	+	0.945556i	$0.394481\pi$
$594$	74.5366	+	102.591i	0.125482	+	0.172712i
$595$		0			0
$596$	−477.662	−	347.042i	−0.801446	−	0.582284i
$597$	7.23584	+	45.6853i	0.0121203	+	0.0765247i
$598$	−212.913	−	417.865i	−0.356041	−	0.698770i
$599$		−	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	$0.562217\pi$
$602$	1.48053	−	0.754367i	0.00245935	−	0.00125310i
$603$	125.940	−	19.9470i	0.208856	−	0.0330795i
$604$	−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	0.0409329	−	0.999162i	$-0.486967\pi$
$607$	−581.645	−	581.645i	−0.958229	−	0.958229i	−0.999162	+	0.0409329i	$0.986967\pi$
$608$	−175.851	+	1110.28i	−0.289229	+	1.82612i
$609$	27.4926	−	8.93287i	0.0451438	−	0.0146681i
$610$		0			0
$611$	157.968	−	486.176i	0.258541	−	0.795706i
$612$	−180.972	+	355.178i	−0.295706	+	0.580357i
$613$	636.056	+	324.087i	1.03761	+	0.528689i	0.887898	−	0.460040i	$-0.152165\pi$
$613$	636.056	+	324.087i	1.03761	+	0.528689i	0.149713	+	0.988729i	$0.452165\pi$
$614$	−1238.44	−	402.392i	−2.01700	−	0.655361i
$615$		0			0
$616$	−3.86133	−	11.8839i	−0.00626838	−	0.0192921i
$617$	261.364	+	41.3960i	0.423605	+	0.0670924i	0.364598	−	0.931165i	$-0.381207\pi$
$617$	261.364	+	41.3960i	0.423605	+	0.0670924i	0.0590070	+	0.998258i	$0.481207\pi$
$618$	−359.238	+	359.238i	−0.581291	+	0.581291i
$619$	−159.169	−	219.077i	−0.257138	−	0.353921i	0.660857	−	0.750512i	$-0.270193\pi$
$619$	−159.169	−	219.077i	−0.257138	−	0.353921i	−0.917995	+	0.396591i	$0.870193\pi$
$620$		0			0
$621$	−54.0288	−	39.2543i	−0.0870030	−	0.0632114i
$622$	−17.8192	−	112.506i	−0.0286482	−	0.180878i
$623$	−27.5713	−	54.1117i	−0.0442557	−	0.0868566i
$624$		−	166.823i		−	0.267344i
$625$		0			0
$626$	1292.84			2.06523
$627$	−322.295	+	164.218i	−0.514028	+	0.261910i
$628$	663.446	−	105.080i	1.05644	−	0.167324i
$629$	−118.556	+	163.179i	−0.188484	+	0.259426i
$630$		0			0
$631$	−777.204	+	564.672i	−1.23170	+	0.894884i	−0.997017	−	0.0771869i	$-0.975406\pi$
$631$	−777.204	+	564.672i	−1.23170	+	0.894884i	−0.234686	+	0.972071i	$0.575406\pi$
$632$	−333.860	−	333.860i	−0.528260	−	0.528260i
$633$	−3.57043	+	22.5428i	−0.00564049	+	0.0356127i
$634$	479.547	−	155.814i	0.756384	−	0.245764i
$635$		0			0
$636$	−84.8956	+	261.282i	−0.133484	+	0.410821i
$637$	263.413	−	516.978i	0.413522	−	0.811582i
$638$	1026.13	+	522.837i	1.60835	+	0.819494i
$639$	173.161	+	56.2634i	0.270987	+	0.0880491i
$640$		0			0
$641$	252.698	+	777.724i	0.394224	+	1.21330i	0.929564	+	0.368661i	$0.120184\pi$
$641$	252.698	+	777.724i	0.394224	+	1.21330i	−0.535340	+	0.844637i	$0.679816\pi$
$642$	−955.889	−	151.398i	−1.48892	−	0.235822i
$643$	−865.400	+	865.400i	−1.34588	+	1.34588i	−0.455794	+	0.890085i	$0.650644\pi$
$643$	−865.400	+	865.400i	−1.34588	+	1.34588i	−0.890085	+	0.455794i	$0.849356\pi$
$644$	14.5552	+	20.0335i	0.0226012	+	0.0311079i
$645$		0			0
$646$	−1595.35	−	1159.09i	−2.46959	−	1.79426i
$647$	−26.7458	−	168.866i	−0.0413381	−	0.260999i	0.958360	−	0.285562i	$-0.0921803\pi$
$647$	−26.7458	−	168.866i	−0.0413381	−	0.260999i	−0.999698	+	0.0245637i	$0.992180\pi$
$648$	18.1820	+	35.6841i	0.0280586	+	0.0550681i
$649$			596.001i			0.918338i
$650$		0			0
$651$	−21.1025			−0.0324155
$652$	−451.827	+	230.218i	−0.692987	+	0.353094i
$653$	−774.910	+	122.734i	−1.18669	+	0.187954i	−0.718407	−	0.695623i	$-0.755128\pi$
$653$	−774.910	+	122.734i	−1.18669	+	0.187954i	−0.468286	+	0.883577i	$0.655128\pi$
$654$	−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
$658$	−7.32278	+	46.2342i	−0.0111289	+	0.0702648i
$659$	259.236	−	84.2308i	0.393377	−	0.127816i	−0.105648	−	0.994404i	$-0.533692\pi$
$659$	259.236	−	84.2308i	0.393377	−	0.127816i	0.499025	+	0.866588i	$0.333692\pi$
$660$		0			0
$661$	212.501	−	654.010i	0.321484	−	0.989426i	−0.651519	−	0.758632i	$-0.725868\pi$
$661$	212.501	−	654.010i	0.321484	−	0.989426i	0.973003	−	0.230793i	$-0.0741321\pi$
$662$	−457.613	+	898.117i	−0.691259	+	1.35667i
$663$	446.864	+	227.688i	0.674002	+	0.343421i
$664$	408.179	+	132.625i	0.614728	+	0.199737i
$665$		0			0
$666$	23.5638	+	72.5218i	0.0353810	+	0.108892i
$667$	−599.041	−	94.8788i	−0.898113	−	0.142247i
$668$	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
$672$	4.09540	+	25.8573i	0.00609435	+	0.0384782i
$673$	−34.3821	−	67.4786i	−0.0510878	−	0.100265i	0.864051	−	0.503404i	$-0.167919\pi$
$673$	−34.3821	−	67.4786i	−0.0510878	−	0.100265i	−0.915139	+	0.403139i	$0.867919\pi$
$674$		−	1408.01i		−	2.08904i
$675$		0			0
$676$	−152.907			−0.226193
$677$	753.672	−	384.015i	1.11325	−	0.567230i	0.202127	−	0.979359i	$-0.435215\pi$
$677$	753.672	−	384.015i	1.11325	−	0.567230i	0.911125	+	0.412129i	$0.135215\pi$
$678$	77.5820	−	12.2878i	0.114428	−	0.0181236i
$679$	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
$683$	174.888	−	1104.20i	0.256059	−	1.61669i	−0.439513	−	0.898236i	$-0.644849\pi$
$683$	174.888	−	1104.20i	0.256059	−	1.61669i	0.695572	−	0.718457i	$-0.255151\pi$
$684$	−408.837	+	132.839i	−0.597715	+	0.194209i
$685$		0			0
$686$	−32.8787	+	101.190i	−0.0479282	+	0.147508i
$687$	291.798	−	572.685i	0.424742	−	0.833602i
$688$	−11.0496	−	5.63004i	−0.0160604	−	0.00818319i
$689$	328.729	+	106.811i	0.477110	+	0.155022i
$690$		0			0
$691$	−326.956	−	1006.27i	−0.473163	−	1.45625i	−0.848419	−	0.529325i	$-0.822445\pi$
$691$	−326.956	−	1006.27i	−0.473163	−	1.45625i	0.375257	−	0.926921i	$-0.377555\pi$
$692$	−177.939	−	28.1828i	−0.257137	−	0.0407266i
$693$	−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
$697$	179.115	+	1130.89i	0.256980	+	1.62251i
$698$	224.561	+	440.725i	0.321720	+	0.631412i
$699$		−	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	$0.593626\pi$
$702$	168.940	−	86.0790i	0.240655	−	0.122620i
$703$	−214.835	+	34.0265i	−0.305597	+	0.0484018i
$704$	−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
$708$	−110.803	+	699.581i	−0.156501	+	0.988109i
$709$	767.230	−	249.288i	1.08213	−	0.351605i	0.286929	−	0.957952i	$-0.407365\pi$
$709$	767.230	−	249.288i	1.08213	−	0.351605i	0.795201	+	0.606346i	$0.207365\pi$
$710$		0			0
$711$	−98.3631	+	302.730i	−0.138345	+	0.425781i
$712$	346.905	−	680.840i	0.487227	−	0.956236i
$713$	394.496	+	201.006i	0.553290	+	0.281915i
$714$	−43.6774	−	14.1916i	−0.0611728	−	0.0198762i
$715$		0			0
$716$	−450.624	−	1386.88i	−0.629363	−	1.93698i
$717$	−388.632	−	61.5533i	−0.542025	−	0.0858484i
$718$	−221.246	+	221.246i	−0.308143	+	0.308143i
$719$	189.988	+	261.496i	0.264239	+	0.363694i	0.920434	−	0.390897i	$-0.127835\pi$
$719$	189.988	+	261.496i	0.264239	+	0.363694i	−0.656195	+	0.754591i	$0.727835\pi$
$720$		0			0
$721$	−27.3041	−	19.8376i	−0.0378698	−	0.0275140i
$722$	−159.086	−	1004.43i	−0.220341	−	1.39118i
$723$	270.832	+	531.537i	0.374594	+	0.735182i
$724$			216.582i			0.299146i
$725$		0			0
$726$	308.574			0.425033
$727$	−596.408	+	303.885i	−0.820369	+	0.417999i	−0.813206	−	0.581975i	$-0.802280\pi$
$727$	−596.408	+	303.885i	−0.820369	+	0.417999i	−0.00716266	+	0.999974i	$0.502280\pi$
$728$	−18.4533	+	2.92271i	−0.0253479	+	0.00401471i
$729$	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
$733$	126.562	−	799.081i	0.172663	−	1.09015i	−0.737332	−	0.675531i	$-0.763914\pi$
$733$	126.562	−	799.081i	0.172663	−	1.09015i	0.909995	−	0.414620i	$-0.136086\pi$
$734$	1226.43	−	398.492i	1.67089	−	0.542905i
$735$		0			0
$736$	169.736	−	522.394i	0.230620	−	0.709775i
$737$	−153.206	+	300.683i	−0.207878	+	0.407983i
$738$	385.689	+	196.518i	0.522614	+	0.266285i
$739$	225.122	+	73.1467i	0.304631	+	0.0989806i	0.457344	−	0.889290i	$-0.348801\pi$
$739$	225.122	+	73.1467i	0.304631	+	0.0989806i	−0.152713	+	0.988271i	$0.548801\pi$
$740$		0			0
$741$	167.130	+	514.374i	0.225547	+	0.694162i
$742$	−31.2614	−	4.95131i	−0.0421312	−	0.00667293i
$743$	−820.748	+	820.748i	−1.10464	+	1.10464i	−0.110797	+	0.993843i	$0.535340\pi$
$743$	−820.748	+	820.748i	−1.10464	+	1.10464i	−0.993843	+	0.110797i	$0.964660\pi$
$744$	−156.065	−	214.805i	−0.209765	−	0.288717i
$745$		0			0
$746$	984.475	+	715.263i	1.31967	+	0.958798i
$747$	−45.2634	−	285.782i	−0.0605935	−	0.382573i
$748$	−478.957	−	940.005i	−0.640316	−	1.25669i
$749$		−	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	$0.363878\pi$
$752$	311.282	−	158.606i	0.413938	−	0.210912i
$753$	359.457	−	56.9324i	0.477367	−	0.0756075i
$754$	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	0.979350	−	0.202170i	$-0.0647994\pi$
$757$	588.326	+	588.326i	0.777180	+	0.777180i	−0.202170	+	0.979350i	$0.564799\pi$
$758$	297.914	−	1880.96i	0.393027	−	2.48147i
$759$	168.096	−	54.6178i	0.221471	−	0.0719602i
$760$		0			0
$761$	−383.044	+	1178.89i	−0.503343	+	1.54913i	0.300194	+	0.953878i	$0.402948\pi$
$761$	−383.044	+	1178.89i	−0.503343	+	1.54913i	−0.803538	+	0.595254i	$0.797052\pi$
$762$	−98.2065	+	192.741i	−0.128880	+	0.252941i
$763$	−29.5886	−	15.0761i	−0.0387793	−	0.0197590i
$764$	−686.215	−	222.965i	−0.898187	−	0.291839i
$765$		0			0
$766$	−232.789	−	716.452i	−0.303903	−	0.935316i
$767$	880.170	+	139.405i	1.14755	+	0.181754i
$768$	−16.3914	+	16.3914i	−0.0213430	+	0.0213430i
$769$	48.2171	+	66.3651i	0.0627010	+	0.0863006i	0.839216	−	0.543798i	$-0.183014\pi$
$769$	48.2171	+	66.3651i	0.0627010	+	0.0863006i	−0.776515	+	0.630099i	$0.783014\pi$
$770$		0			0
$771$	−360.301	−	261.774i	−0.467317	−	0.339525i
$772$	−38.2291	−	241.369i	−0.0495196	−	0.312654i
$773$	−340.665	−	668.593i	−0.440705	−	0.864933i	−0.999368	−	0.0355381i	$-0.988686\pi$
$773$	−340.665	−	668.593i	−0.440705	−	0.864933i	0.558663	−	0.829395i	$-0.311314\pi$
$774$		−	14.0948i		−	0.0182104i
$775$		0			0
$776$	478.066			0.616064
$777$	−4.51353	+	2.29976i	−0.00580892	+	0.00295979i
$778$	−67.4993	+	10.6908i	−0.0867601	+	0.0137414i
$779$	−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
$783$	38.3588	−	242.188i	0.0489895	−	0.309308i
$784$	377.122	−	122.534i	0.481023	−	0.156294i
$785$		0			0
$786$	247.182	−	760.748i	0.314481	−	0.967873i
$787$	229.977	−	451.355i	0.292219	−	0.573513i	−0.697492	−	0.716593i	$-0.745701\pi$
$787$	229.977	−	451.355i	0.292219	−	0.573513i	0.989711	+	0.143080i	$0.0457006\pi$
$788$	835.363	+	425.638i	1.06010	+	0.540150i
$789$	127.558	+	41.4460i	0.161670	+	0.0525298i
$790$		0			0
$791$	1.61249	+	4.96273i	0.00203854	+	0.00627399i
$792$	−104.688	−	16.5810i	−0.132182	−	0.0209356i
$793$	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
$797$	171.689	+	1084.00i	0.215419	+	1.36010i	0.823990	+	0.566605i	$0.191743\pi$
$797$	171.689	+	1084.00i	0.215419	+	1.36010i	−0.608570	+	0.793500i	$0.708257\pi$
$798$	−22.4841	−	44.1276i	−0.0281756	−	0.0552977i
$799$			1050.29i			1.31451i
$800$		0			0
$801$	−515.150			−0.643134
$802$	964.461	−	491.417i	1.20257	−	0.612740i
$803$	744.656	−	117.942i	0.927342	−	0.146877i
$804$	−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
$808$	74.5613	−	470.761i	0.0922788	−	0.582626i
$809$	−67.5579	+	21.9509i	−0.0835079	+	0.0271334i	−0.350473	−	0.936573i	$-0.613979\pi$
$809$	−67.5579	+	21.9509i	−0.0835079	+	0.0271334i	0.266965	+	0.963706i	$0.413979\pi$
$810$		0			0
$811$	−19.2331	+	59.1935i	−0.0237153	+	0.0729882i	−0.962214	−	0.272295i	$-0.912217\pi$
$811$	−19.2331	+	59.1935i	−0.0237153	+	0.0729882i	0.938498	+	0.345284i	$0.112217\pi$
$812$	−41.2772	+	81.0111i	−0.0508340	+	0.0997674i
$813$	−547.181	−	278.803i	−0.673039	−	0.342931i
$814$	−191.934	−	62.3633i	−0.235792	−	0.0766133i
$815$		0			0
$816$	105.916	+	325.976i	0.129799	+	0.399480i
$817$	39.7102	+	6.28947i	0.0486049	+	0.00769825i
$818$	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	0.395099	−	0.918639i	$-0.370710\pi$
$821$	−292.676	−	212.641i	−0.356487	−	0.259003i	−0.751585	+	0.659636i	$0.770710\pi$
$822$	−13.4610	−	84.9892i	−0.0163759	−	0.103393i
$823$	5.03504	+	9.88181i	0.00611791	+	0.0120071i	0.894045	−	0.447977i	$-0.147855\pi$
$823$	5.03504	+	9.88181i	0.00611791	+	0.0120071i	−0.887927	+	0.459984i	$0.847855\pi$
$824$		−	424.643i		−	0.515344i
$825$		0			0
$826$	−81.6024			−0.0987923
$827$	1390.02	−	708.250i	1.68080	−	0.856408i	0.689571	−	0.724218i	$-0.257799\pi$
$827$	1390.02	−	708.250i	1.68080	−	0.856408i	0.991224	−	0.132191i	$-0.0422011\pi$
$828$	207.464	−	32.8591i	0.250560	−	0.0396849i
$829$	−5.75207	+	7.91705i	−0.00693857	+	0.00955012i	−0.812472	−	0.583000i	$-0.801879\pi$
$829$	−5.75207	+	7.91705i	−0.00693857	+	0.00955012i	0.805534	+	0.592550i	$0.201879\pi$
$830$		0			0
$831$	464.428	−	337.427i	0.558878	−	0.406049i
$832$	830.285	+	830.285i	0.997939	+	0.997939i
$833$	−186.486	+	1177.43i	−0.223873	+	1.41348i
$834$	241.860	−	78.5850i	0.290000	−	0.0942266i
$835$		0			0
$836$	351.569	−	1082.02i	0.420537	−	1.29428i
$837$	−81.2650	+	159.492i	−0.0970908	+	0.190552i
$838$	−1688.68	−	860.428i	−2.01514	−	1.02676i
$839$	576.373	+	187.275i	0.686976	+	0.223212i	0.631647	−	0.775256i	$-0.282379\pi$
$839$	576.373	+	187.275i	0.686976	+	0.223212i	0.0553292	+	0.998468i	$0.482379\pi$
$840$		0			0
$841$	−428.268	−	1318.07i	−0.509237	−	1.56727i
$842$	−1407.05	−	222.855i	−1.67108	−	0.264673i
$843$	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
$847$	3.20674	+	20.2466i	0.00378600	+	0.0239039i
$848$	107.242	+	210.474i	0.126464	+	0.248200i
$849$		−	231.516i		−	0.272693i
$850$		0			0
$851$	106.283			0.124892
$852$	−510.245	+	259.983i	−0.598880	+	0.305144i
$853$	−555.263	+	87.9451i	−0.650953	+	0.103101i	−0.473173	−	0.880969i	$-0.656892\pi$
$853$	−555.263	+	87.9451i	−0.650953	+	0.103101i	−0.177780	+	0.984070i	$0.556892\pi$
$854$	−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	$-0.938527\pi$
$857$	−1005.55	−	1005.55i	−1.17333	−	1.17333i	−0.191924	−	0.981410i	$-0.561473\pi$
$858$	−78.4995	+	495.626i	−0.0914913	+	0.577653i
$859$	1176.31	−	382.208i	1.36940	−	0.444945i	0.470229	−	0.882544i	$-0.344171\pi$
$859$	1176.31	−	382.208i	1.36940	−	0.444945i	0.899170	+	0.437600i	$0.144171\pi$
$860$		0			0
$861$	−8.88612	+	27.3487i	−0.0103207	+	0.0317638i
$862$	32.9018	−	64.5735i	0.0381692	−	0.0749112i
$863$	−728.140	−	371.006i	−0.843731	−	0.429902i	−0.0219863	−	0.999758i	$-0.506999\pi$
$863$	−728.140	−	371.006i	−0.843731	−	0.429902i	−0.821745	+	0.569856i	$0.806999\pi$
$864$	211.200	+	68.6231i	0.244445	+	0.0794249i
$865$		0			0
$866$	106.690	+	328.359i	0.123199	+	0.379167i
$867$	−523.342	−	82.8892i	−0.603624	−	0.0956047i
$868$	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
$872$	−65.3627	−	412.684i	−0.0749572	−	0.473261i
$873$	−146.320	−	287.170i	−0.167606	−	0.328946i
$874$			1039.10i			1.18890i
$875$		0			0
$876$	895.997			1.02283
$877$	760.694	−	387.593i	0.867382	−	0.441953i	0.0371096	−	0.999311i	$-0.488185\pi$
$877$	760.694	−	387.593i	0.867382	−	0.441953i	0.830272	+	0.557358i	$0.188185\pi$
$878$	−1658.87	+	262.739i	−1.88937	+	0.299247i
$879$	−367.442	+	505.740i	−0.418022	+	0.575359i
$880$		0			0
$881$	425.461	−	309.115i	0.482929	−	0.350869i	−0.319529	−	0.947576i	$-0.603525\pi$
$881$	425.461	−	309.115i	0.482929	−	0.350869i	0.802459	+	0.596708i	$0.203525\pi$
$882$	318.681	+	318.681i	0.361316	+	0.361316i
$883$	−155.162	+	979.657i	−0.175722	+	1.10946i	0.729330	+	0.684163i	$0.239832\pi$
$883$	−155.162	+	979.657i	−0.175722	+	1.10946i	−0.905051	+	0.425302i	$0.860168\pi$
$884$	−1500.22	+	487.451i	−1.69708	+	0.551416i
$885$		0			0
$886$	−222.725	+	685.477i	−0.251383	+	0.773676i
$887$	−356.099	+	698.883i	−0.401464	+	0.787918i	−0.999912	−	0.0132438i	$-0.995784\pi$
$887$	−356.099	+	698.883i	−0.401464	+	0.787918i	0.598448	+	0.801162i	$0.295784\pi$
$888$	−56.7898	−	28.9358i	−0.0639525	−	0.0325854i
$889$	−13.6670	−	4.44067i	−0.0153734	−	0.00499513i
$890$		0			0
$891$	22.0816	+	67.9601i	0.0247829	+	0.0762740i
$892$	1178.28	+	186.621i	1.32094	+	0.209216i
$893$	−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
$897$	−41.3413	−	261.019i	−0.0460884	−	0.290991i
$898$	280.769	+	551.041i	0.312661	+	0.613631i
$899$			1625.65i			1.80828i
$900$		0			0
$901$	−710.158			−0.788189
$902$	−1020.76	+	520.101i	−1.13166	+	0.576608i
$903$	0.924810	−	0.146475i	0.00102415	−	0.000162210i
$904$	−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	0.555747	−	0.831352i	$-0.312432\pi$
$907$	−249.974	−	249.974i	−0.275605	−	0.275605i	−0.831352	+	0.555747i	$0.812432\pi$
$908$	−128.150	+	809.106i	−0.141134	+	0.891086i
$909$	−305.603	+	99.2963i	−0.336197	+	0.109237i
$910$		0			0
$911$	232.883	−	716.740i	0.255634	−	0.786761i	−0.738070	−	0.674724i	$-0.764262\pi$
$911$	232.883	−	716.740i	0.255634	−	0.786761i	0.993704	−	0.112037i	$-0.0357375\pi$
$912$	−167.805	+	329.336i	−0.183997	+	0.361114i
$913$	682.306	+	347.652i	0.747324	+	0.380780i
$914$	1858.67	+	603.919i	2.03356	+	0.660743i
$915$		0			0
$916$	624.701	+	1922.63i	0.681988	+	2.09894i
$917$	52.4841	+	8.31266i	0.0572345	+	0.00906506i
$918$	−275.460	+	275.460i	−0.300066	+	0.300066i
$919$	−548.369	−	754.765i	−0.596701	−	0.821289i	0.398700	−	0.917081i	$-0.369462\pi$
$919$	−548.369	−	754.765i	−0.596701	−	0.821289i	−0.995401	+	0.0957924i	$0.969462\pi$
$920$		0			0
$921$	−593.638	−	431.303i	−0.644558	−	0.468299i
$922$	−203.447	−	1284.51i	−0.220658	−	1.39318i
$923$	327.095	+	641.960i	0.354382	+	0.695514i
$924$		−	26.4959i		−	0.0286752i
$925$		0			0
$926$	−2021.52			−2.18306
$927$	−255.079	+	129.969i	−0.275166	+	0.140204i
$928$	1991.94	−	315.493i	2.14649	−	0.339970i
$929$	−702.940	+	967.513i	−0.756663	+	1.04146i	0.240822	+	0.970569i	$0.422583\pi$
$929$	−702.940	+	967.513i	−0.756663	+	1.04146i	−0.997484	+	0.0708875i	$0.977417\pi$
$930$		0			0
$931$	−1040.04	+	755.635i	−1.11712	+	0.811638i
$932$	285.741	+	285.741i	0.306589	+	0.306589i
$933$	10.0412	−	63.3975i	0.0107623	−	0.0679502i
$934$	−1922.82	+	624.762i	−2.05869	+	0.668910i
$935$		0			0
$936$	−48.9734	+	150.724i	−0.0523220	+	0.161030i
$937$	478.587	−	939.280i	0.510766	−	1.00243i	−0.481282	−	0.876566i	$-0.659829\pi$
$937$	478.587	−	939.280i	0.510766	−	1.00243i	0.992047	−	0.125868i	$-0.0401715\pi$
$938$	−41.1685	−	20.9764i	−0.0438897	−	0.0223629i
$939$	692.861	+	225.124i	0.737872	+	0.239749i
$940$		0			0
$941$	179.429	+	552.226i	0.190679	+	0.586850i	1.00000		0.000517053i	$-0.000164583\pi$
$941$	179.429	+	552.226i	0.190679	+	0.586850i	−0.809321	+	0.587367i	$0.800165\pi$
$942$	648.358	+	102.690i	0.688278	+	0.109012i
$943$	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
$947$	94.5461	+	596.940i	0.0998375	+	0.630349i	0.985971	+	0.166918i	$0.0533816\pi$
$947$	94.5461	+	596.940i	0.0998375	+	0.630349i	−0.886133	+	0.463431i	$0.846618\pi$
$948$	−454.518	−	892.042i	−0.479450	−	0.940973i
$949$		−	1127.29i		−	1.18787i
$950$		0			0
$951$	284.133			0.298773
$952$	34.2025	−	17.4271i	0.0359270	−	0.0183057i
$953$	48.1641	−	7.62845i	0.0505395	−	0.00800467i	−0.131114	−	0.991367i	$-0.541855\pi$
$953$	48.1641	−	7.62845i	0.0505395	−	0.00800467i	0.181653	+	0.983363i	$0.441855\pi$
$954$	−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
$958$	322.890	−	2038.65i	0.337046	−	2.12802i
$959$	5.43655	−	1.76644i	0.00566897	−	0.00184196i
$960$		0			0
$961$	69.7529	−	214.677i	0.0725837	−	0.223390i
$962$	−136.991	+	268.860i	−0.142403	+	0.279481i
$963$	−485.920	−	247.589i	−0.504590	−	0.257102i
$964$	−1784.49	−	579.816i	−1.85113	−	0.601468i
$965$		0			0
$966$	7.47808	+	23.0152i	0.00774129	+	0.0238252i
$967$	1446.65	+	229.127i	1.49602	+	0.236946i	0.850166	−	0.526514i	$-0.176501\pi$
$967$	1446.65	+	229.127i	1.49602	+	0.236946i	0.645854	+	0.763461i	$0.276501\pi$
$968$	−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	0.182145	−	0.983272i	$-0.441696\pi$
$971$	−676.512	−	491.514i	−0.696716	−	0.506194i	−0.878861	+	0.477078i	$0.841696\pi$
$972$	13.2847	+	83.8762i	0.0136674	+	0.0862924i
$973$	7.66968	+	15.0526i	0.00788250	+	0.0154703i
$974$			324.003i			0.332652i
$975$		0			0
$976$	682.705			0.699493
$977$	468.100	−	238.509i	0.479120	−	0.244124i	−0.197714	−	0.980260i	$-0.563352\pi$
$977$	468.100	−	238.509i	0.479120	−	0.244124i	0.676834	+	0.736136i	$0.263352\pi$
$978$	−489.463	+	77.5234i	−0.500474	+	0.0792673i
$979$	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
$983$	−222.203	+	1402.94i	−0.226046	+	1.42720i	0.569842	+	0.821754i	$0.307004\pi$
$983$	−222.203	+	1402.94i	−0.226046	+	1.42720i	−0.795888	+	0.605443i	$0.792996\pi$
$984$	−344.104	+	111.806i	−0.349699	+	0.113624i
$985$		0			0
$986$	−1093.27	+	3364.72i	−1.10879	+	3.41250i
$987$	−11.9753	+	23.5029i	−0.0121331	+	0.0238125i
$988$	−1515.68	−	772.280i	−1.53409	−	0.781660i
$989$	−18.6839	−	6.07076i	−0.0188917	−	0.00613828i
$990$		0			0
$991$	451.716	+	1390.24i	0.455819	+	1.40287i	0.870171	+	0.492750i	$0.164008\pi$
$991$	451.716	+	1390.24i	0.455819	+	1.40287i	−0.414352	+	0.910117i	$0.635992\pi$
$992$	−1454.12	−	230.310i	−1.46585	−	0.232168i
$993$	−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
$997$	290.899	+	1836.66i	0.291774	+	1.84219i	0.502414	+	0.864627i	$0.332445\pi$
$997$	290.899	+	1836.66i	0.291774	+	1.84219i	−0.210639	+	0.977564i	$0.567555\pi$
$998$	404.952	+	794.763i	0.405763	+	0.796355i
$999$			42.9694i			0.0430124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.3.k.a.7.2		80
5.2	odd	4		375.3.k.c.118.2		80
5.3	odd	4		375.3.k.b.118.9		80
5.4	even	2		75.3.k.a.22.9	✓	80
15.14	odd	2		225.3.r.b.172.2		80
25.6	even	5		375.3.k.b.232.9		80
25.8	odd	20	inner	375.3.k.a.268.2		80
25.17	odd	20		75.3.k.a.58.9	yes	80
25.19	even	10		375.3.k.c.232.2		80
75.17	even	20		225.3.r.b.208.2		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.22.9	✓	80	5.4	even	2
75.3.k.a.58.9	yes	80	25.17	odd	20
225.3.r.b.172.2		80	15.14	odd	2
225.3.r.b.208.2		80	75.17	even	20
375.3.k.a.7.2		80	1.1	even	1	trivial
375.3.k.a.268.2		80	25.8	odd	20	inner
375.3.k.b.118.9		80	5.3	odd	4
375.3.k.b.232.9		80	25.6	even	5
375.3.k.c.118.2		80	5.2	odd	4
375.3.k.c.232.2		80	25.19	even	10

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+(-2.73870 + 1.39544i) q^{2} +(-1.71073 + 0.270952i) q^{3} +(3.20210 - 4.40731i) q^{4} +(4.30707 - 3.12927i) q^{6} +(0.250082 + 0.250082i) q^{7} +(-0.696119 + 4.39513i) q^{8} +(2.85317 - 0.927051i) q^{9} +(-2.45351 + 7.55112i) q^{11} +(-4.28374 + 8.40731i) q^{12} +(10.5776 + 5.38954i) q^{13} +(-1.03387 - 0.335926i) q^{14} +(2.50710 + 7.71607i) q^{16} +(-24.0906 - 3.81558i) q^{17} +(-6.52034 + 6.52034i) q^{18} +(-15.4606 - 21.2797i) q^{19} +(-0.495582 - 0.360061i) q^{21} +(-3.81770 - 24.1040i) q^{22} +(5.83489 + 11.4516i) q^{23} -7.70747i q^{24} -36.4896 q^{26} +(-4.62981 + 2.35900i) q^{27} +(1.90297 - 0.301401i) q^{28} +(-27.7376 + 38.1776i) q^{29} +(27.8697 - 20.2485i) q^{31} +(-30.2198 - 30.2198i) q^{32} +(2.15129 - 13.5827i) q^{33} +(71.3015 - 23.1673i) q^{34} +(5.05032 - 15.5433i) q^{36} +(3.75426 - 7.36815i) q^{37} +(72.0364 + 36.7044i) q^{38} +(-19.5556 - 6.35401i) q^{39} +(-14.5062 - 44.6455i) q^{41} +(1.85969 + 0.294547i) q^{42} +(-1.08084 + 1.08084i) q^{43} +(25.4237 + 34.9928i) q^{44} +(-31.9601 - 23.2203i) q^{46} +(-6.73620 - 42.5307i) q^{47} +(-6.37966 - 12.5208i) q^{48} -48.8749i q^{49} +42.2463 q^{51} +(57.6237 - 29.3608i) q^{52} +(28.7572 - 4.55469i) q^{53} +(9.38781 - 12.9212i) q^{54} +(-1.27323 + 0.925055i) q^{56} +(32.2146 + 32.2146i) q^{57} +(22.6907 - 143.263i) q^{58} +(71.3918 - 23.1966i) q^{59} +(26.0031 - 80.0294i) q^{61} +(-48.0713 + 94.3452i) q^{62} +(0.945365 + 0.481688i) q^{63} +(94.0684 + 30.5647i) q^{64} +(13.0621 + 40.2009i) q^{66} +(41.9801 + 6.64899i) q^{67} +(-93.9570 + 93.9570i) q^{68} +(-13.0848 - 18.0096i) q^{69} +(49.0998 + 35.6731i) q^{71} +(2.08836 + 13.1854i) q^{72} +(-43.1099 - 84.6079i) q^{73} +25.4180i q^{74} -143.292 q^{76} +(-2.50198 + 1.27482i) q^{77} +(62.4237 - 9.88694i) q^{78} +(-62.3659 + 85.8393i) q^{79} +(7.28115 - 5.29007i) q^{81} +(102.028 + 102.028i) q^{82} +(15.0878 - 95.2606i) q^{83} +(-3.17380 + 1.03123i) q^{84} +(1.45185 - 4.46832i) q^{86} +(37.1072 - 72.8270i) q^{87} +(-31.4802 - 16.0400i) q^{88} +(-163.312 - 53.0634i) q^{89} +(1.29743 + 3.99309i) q^{91} +(69.1547 + 10.9530i) q^{92} +(-42.1911 + 42.1911i) q^{93} +(77.7974 + 107.079i) q^{94} +(59.8858 + 43.5096i) q^{96} +(-16.8062 - 106.110i) q^{97} +(68.2019 + 133.854i) q^{98} +23.8192i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{2} + 4 q^{7} + 12 q^{8} + 24 q^{12} - 32 q^{13} + 80 q^{16} + 100 q^{17} + 48 q^{18} - 100 q^{19} + 100 q^{22} + 96 q^{23} - 40 q^{26} - 196 q^{28} + 200 q^{29} - 636 q^{32} - 216 q^{33} + 100 q^{34}+ \cdots + 92 q^{98}+O(q^{100}) \) 80 * q - 4 * q^2 + 4 * q^7 + 12 * q^8 + 24 * q^12 - 32 * q^13 + 80 * q^16 + 100 * q^17 + 48 * q^18 - 100 * q^19 + 100 * q^22 + 96 * q^23 - 40 * q^26 - 196 * q^28 + 200 * q^29 - 636 * q^32 - 216 * q^33 + 100 * q^34 - 120 * q^36 + 184 * q^37 + 564 * q^38 + 160 * q^41 + 12 * q^42 + 472 * q^43 - 700 * q^44 + 288 * q^47 + 48 * q^48 - 620 * q^52 - 304 * q^53 - 72 * q^57 - 1272 * q^58 + 800 * q^59 - 240 * q^61 - 1212 * q^62 + 12 * q^63 + 100 * q^64 + 80 * q^67 - 104 * q^68 - 36 * q^72 + 116 * q^73 + 88 * q^77 + 120 * q^78 + 200 * q^79 + 180 * q^81 + 168 * q^82 + 1264 * q^83 - 1200 * q^84 + 876 * q^87 + 212 * q^88 - 1500 * q^89 + 1504 * q^92 + 648 * q^93 - 200 * q^94 + 60 * q^96 + 260 * q^97 + 92 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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