LMFDB - Embedded newform 242.4.c.n.27.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [242,4,Mod(3,242)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(242, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("242.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 242 = 2 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	242.c (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$14.2784622214$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 71x^{6} - 141x^{5} + 2911x^{4} + 2710x^{3} + 75340x^{2} + 169400x + 5856400 $ x^8 - x^7 + 71x^6 - 141x^5 + 2911x^4 + 2710x^3 + 75340x^2 + 169400x + 5856400
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			27.1
Root			$5.60402 - 4.07156i$ of defining polynomial
Character	$\chi$	$=$	242.27
Dual form			242.4.c.n.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.618034 + 1.90211i) q^{2} +(-6.91304 - 5.02262i) q^{3} +(-3.23607 + 2.35114i) q^{4} +(3.93561 - 12.1126i) q^{5} +(5.28109 - 16.2535i) q^{6} +(18.9804 - 13.7901i) q^{7} +(-6.47214 - 4.70228i) q^{8} +(14.2200 + 43.7646i) q^{9} +O(q^{10})$	\(q+(0.618034 + 1.90211i) q^{2} +(-6.91304 - 5.02262i) q^{3} +(-3.23607 + 2.35114i) q^{4} +(3.93561 - 12.1126i) q^{5} +(5.28109 - 16.2535i) q^{6} +(18.9804 - 13.7901i) q^{7} +(-6.47214 - 4.70228i) q^{8} +(14.2200 + 43.7646i) q^{9} +25.4718 q^{10} +34.1799 q^{12} +(-3.54302 - 10.9043i) q^{13} +(37.9609 + 27.5802i) q^{14} +(-88.0439 + 63.9676i) q^{15} +(4.94427 - 15.2169i) q^{16} +(20.2413 - 62.2963i) q^{17} +(-74.4568 + 54.0960i) q^{18} +(-5.86548 - 4.26152i) q^{19} +(15.7425 + 48.4503i) q^{20} -200.475 q^{21} -104.072 q^{23} +(21.1244 + 65.0141i) q^{24} +(-30.0982 - 21.8676i) q^{25} +(18.5515 - 13.4784i) q^{26} +(50.2148 - 154.545i) q^{27} +(-28.9995 + 89.2514i) q^{28} +(-103.029 + 74.8551i) q^{29} +(-176.088 - 127.935i) q^{30} +(-89.2476 - 274.676i) q^{31} +32.0000 q^{32} +131.004 q^{34} +(-92.3339 - 284.174i) q^{35} +(-148.914 - 108.192i) q^{36} +(69.0919 - 50.1982i) q^{37} +(4.48082 - 13.7906i) q^{38} +(-30.2750 + 93.1770i) q^{39} +(-82.4285 + 59.8878i) q^{40} +(-109.576 - 79.6118i) q^{41} +(-123.900 - 381.326i) q^{42} -353.691 q^{43} +586.066 q^{45} +(-64.3203 - 197.957i) q^{46} +(108.897 + 79.1180i) q^{47} +(-110.609 + 80.3619i) q^{48} +(64.0975 - 197.272i) q^{49} +(22.9930 - 70.7651i) q^{50} +(-452.819 + 328.992i) q^{51} +(37.1030 + 26.9569i) q^{52} +(154.951 + 476.889i) q^{53} +324.997 q^{54} -187.689 q^{56} +(19.1443 + 58.9201i) q^{57} +(-206.058 - 149.710i) q^{58} +(-527.202 + 383.035i) q^{59} +(134.519 - 414.007i) q^{60} +(-113.034 + 347.884i) q^{61} +(467.306 - 339.518i) q^{62} +(873.419 + 634.576i) q^{63} +(19.7771 + 60.8676i) q^{64} -146.023 q^{65} -294.576 q^{67} +(80.9651 + 249.185i) q^{68} +(719.456 + 522.716i) q^{69} +(483.466 - 351.259i) q^{70} +(40.9282 - 125.964i) q^{71} +(113.760 - 350.117i) q^{72} +(379.825 - 275.959i) q^{73} +(138.184 + 100.396i) q^{74} +(98.2373 + 302.343i) q^{75} +29.0005 q^{76} -195.944 q^{78} +(-126.089 - 388.062i) q^{79} +(-164.857 - 119.776i) q^{80} +(-118.192 + 85.8712i) q^{81} +(83.7088 - 257.629i) q^{82} +(420.122 - 1293.00i) q^{83} +(648.751 - 471.345i) q^{84} +(-674.906 - 490.348i) q^{85} +(-218.593 - 672.760i) q^{86} +1088.21 q^{87} -260.255 q^{89} +(362.209 + 1114.76i) q^{90} +(-217.619 - 158.110i) q^{91} +(336.785 - 244.689i) q^{92} +(-762.620 + 2347.10i) q^{93} +(-83.1896 + 256.031i) q^{94} +(-74.7022 + 54.2743i) q^{95} +(-221.217 - 160.724i) q^{96} +(437.114 + 1345.30i) q^{97} +414.848 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 7 q^{3} - 8 q^{4} - 30 q^{5} + 6 q^{6} - 4 q^{7} - 16 q^{8} - 81 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 7 * q^3 - 8 * q^4 - 30 * q^5 + 6 * q^6 - 4 * q^7 - 16 * q^8 - 81 * q^9	\( 8 q - 4 q^{2} - 7 q^{3} - 8 q^{4} - 30 q^{5} + 6 q^{6} - 4 q^{7} - 16 q^{8} - 81 q^{9} + 100 q^{10} + 32 q^{12} + 48 q^{13} - 8 q^{14} - 279 q^{15} - 32 q^{16} + 109 q^{17} - 42 q^{18} - 288 q^{19} - 120 q^{20} + 50 q^{21} + 628 q^{23} + 24 q^{24} + 38 q^{25} - 14 q^{26} + 242 q^{27} + 4 q^{28} - 528 q^{29} - 558 q^{30} - 522 q^{31} + 256 q^{32} + 208 q^{34} + 17 q^{35} - 84 q^{36} - 406 q^{37} + 544 q^{38} + 1429 q^{39} + 40 q^{40} + 329 q^{41} - 1480 q^{42} - 1442 q^{43} + 2652 q^{45} - 1044 q^{46} + 666 q^{47} - 112 q^{48} - 114 q^{49} - 34 q^{50} - 1158 q^{51} - 28 q^{52} + 414 q^{53} + 1144 q^{54} + 48 q^{56} + 593 q^{57} - 1056 q^{58} - 888 q^{59} + 844 q^{60} + 302 q^{61} + 646 q^{62} + 2061 q^{63} - 128 q^{64} + 138 q^{65} + 578 q^{67} + 436 q^{68} + 1930 q^{69} + 1394 q^{70} + 1090 q^{71} - 648 q^{72} - 253 q^{73} - 812 q^{74} + 2763 q^{75} + 128 q^{76} - 4152 q^{78} + 674 q^{79} + 80 q^{80} - 230 q^{81} - 722 q^{82} + 428 q^{83} + 2860 q^{84} - 1046 q^{85} - 984 q^{86} - 2122 q^{87} - 2202 q^{89} - 1366 q^{90} - 2217 q^{91} + 832 q^{92} - 3721 q^{93} - 2138 q^{94} + 973 q^{95} - 224 q^{96} + 3012 q^{97} + 3292 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 7 * q^3 - 8 * q^4 - 30 * q^5 + 6 * q^6 - 4 * q^7 - 16 * q^8 - 81 * q^9 + 100 * q^10 + 32 * q^12 + 48 * q^13 - 8 * q^14 - 279 * q^15 - 32 * q^16 + 109 * q^17 - 42 * q^18 - 288 * q^19 - 120 * q^20 + 50 * q^21 + 628 * q^23 + 24 * q^24 + 38 * q^25 - 14 * q^26 + 242 * q^27 + 4 * q^28 - 528 * q^29 - 558 * q^30 - 522 * q^31 + 256 * q^32 + 208 * q^34 + 17 * q^35 - 84 * q^36 - 406 * q^37 + 544 * q^38 + 1429 * q^39 + 40 * q^40 + 329 * q^41 - 1480 * q^42 - 1442 * q^43 + 2652 * q^45 - 1044 * q^46 + 666 * q^47 - 112 * q^48 - 114 * q^49 - 34 * q^50 - 1158 * q^51 - 28 * q^52 + 414 * q^53 + 1144 * q^54 + 48 * q^56 + 593 * q^57 - 1056 * q^58 - 888 * q^59 + 844 * q^60 + 302 * q^61 + 646 * q^62 + 2061 * q^63 - 128 * q^64 + 138 * q^65 + 578 * q^67 + 436 * q^68 + 1930 * q^69 + 1394 * q^70 + 1090 * q^71 - 648 * q^72 - 253 * q^73 - 812 * q^74 + 2763 * q^75 + 128 * q^76 - 4152 * q^78 + 674 * q^79 + 80 * q^80 - 230 * q^81 - 722 * q^82 + 428 * q^83 + 2860 * q^84 - 1046 * q^85 - 984 * q^86 - 2122 * q^87 - 2202 * q^89 - 1366 * q^90 - 2217 * q^91 + 832 * q^92 - 3721 * q^93 - 2138 * q^94 + 973 * q^95 - 224 * q^96 + 3012 * q^97 + 3292 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/242\mathbb{Z}\right)^\times$.

$n$	$123$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	0.618034	+	1.90211i	0.218508	+	0.672499i
$2$	0.618034	+	1.90211i	0.218508	+	0.672499i
$3$	−6.91304	−	5.02262i	−1.33042	−	0.966603i	−0.999739	−	0.0228590i	$-0.992723\pi$
$3$	−6.91304	−	5.02262i	−1.33042	−	0.966603i	−0.330676	−	0.943744i	$-0.607277\pi$
$4$	−3.23607	+	2.35114i	−0.404508	+	0.293893i
$5$	3.93561	−	12.1126i	0.352012	−	1.08338i	−0.605710	−	0.795686i	$-0.707111\pi$
$5$	3.93561	−	12.1126i	0.352012	−	1.08338i	0.957722	−	0.287696i	$-0.0928892\pi$
$6$	5.28109	−	16.2535i	0.359333	−	1.10591i
$7$	18.9804	−	13.7901i	1.02485	−	0.744595i	0.0575766	−	0.998341i	$-0.481663\pi$
$7$	18.9804	−	13.7901i	1.02485	−	0.744595i	0.967271	+	0.253746i	$0.0816627\pi$
$8$	−6.47214	−	4.70228i	−0.286031	−	0.207813i
$9$	14.2200	+	43.7646i	0.526666	+	1.62091i
$10$	25.4718			0.805490
$11$		0			0
$11$		0			0
$12$	34.1799			0.822242
$13$	−3.54302	−	10.9043i	−0.0755889	−	0.232639i	0.906122	−	0.423016i	$-0.139029\pi$
$13$	−3.54302	−	10.9043i	−0.0755889	−	0.232639i	−0.981711	+	0.190378i	$0.939029\pi$
$14$	37.9609	+	27.5802i	0.724677	+	0.526508i
$15$	−88.0439	+	63.9676i	−1.51552	+	1.10109i
$16$	4.94427	−	15.2169i	0.0772542	−	0.237764i
$17$	20.2413	−	62.2963i	0.288778	−	0.888768i	−0.696462	−	0.717593i	$-0.745244\pi$
$17$	20.2413	−	62.2963i	0.288778	−	0.888768i	0.985241	−	0.171175i	$-0.0547564\pi$
$18$	−74.4568	+	54.0960i	−0.974979	+	0.708364i
$19$	−5.86548	−	4.26152i	−0.0708228	−	0.0514557i	0.551811	−	0.833970i	$-0.313937\pi$
$19$	−5.86548	−	4.26152i	−0.0708228	−	0.0514557i	−0.622633	+	0.782514i	$0.713937\pi$
$20$	15.7425	+	48.4503i	0.176006	+	0.541691i
$21$	−200.475			−2.08320
$22$		0			0
$23$	−104.072			−0.943504			−0.471752	−	0.881731i	$-0.656378\pi$
$23$	−104.072			−0.943504			−0.471752	+	0.881731i	$0.656378\pi$
$24$	21.1244	+	65.0141i	0.179666	+	0.552956i
$25$	−30.0982	−	21.8676i	−0.240785	−	0.174941i
$26$	18.5515	−	13.4784i	0.139932	−	0.101667i
$27$	50.2148	−	154.545i	0.357920	−	1.10156i
$28$	−28.9995	+	89.2514i	−0.195728	+	0.602390i
$29$	−103.029	+	74.8551i	−0.659725	+	0.479319i	−0.866570	−	0.499055i	$-0.833681\pi$
$29$	−103.029	+	74.8551i	−0.659725	+	0.479319i	0.206845	+	0.978374i	$0.433681\pi$
$30$	−176.088	−	127.935i	−1.07164	−	0.778589i
$31$	−89.2476	−	274.676i	−0.517076	−	1.59139i	−0.779474	−	0.626435i	$-0.784513\pi$
$31$	−89.2476	−	274.676i	−0.517076	−	1.59139i	0.262398	−	0.964960i	$-0.415487\pi$
$32$	32.0000			0.176777
$33$		0			0
$34$	131.004			0.660796
$35$	−92.3339	−	284.174i	−0.445922	−	1.37241i
$36$	−148.914	−	108.192i	−0.689414	−	0.500889i
$37$	69.0919	−	50.1982i	0.306990	−	0.223042i	−0.423614	−	0.905843i	$-0.639239\pi$
$37$	69.0919	−	50.1982i	0.306990	−	0.223042i	0.730604	+	0.682801i	$0.239239\pi$
$38$	4.48082	−	13.7906i	0.0191286	−	0.0588717i
$39$	−30.2750	+	93.1770i	−0.124305	+	0.382571i
$40$	−82.4285	+	59.8878i	−0.325827	+	0.236727i
$41$	−109.576	−	79.6118i	−0.417389	−	0.303251i	0.359198	−	0.933262i	$-0.383050\pi$
$41$	−109.576	−	79.6118i	−0.417389	−	0.303251i	−0.776586	+	0.630011i	$0.783050\pi$
$42$	−123.900	−	381.326i	−0.455196	−	1.40095i
$43$	−353.691			−1.25436			−0.627178	−	0.778876i	$-0.715790\pi$
$43$	−353.691			−1.25436			−0.627178	+	0.778876i	$0.715790\pi$
$44$		0			0
$45$	586.066			1.94146
$46$	−64.3203	−	197.957i	−0.206163	−	0.634505i
$47$	108.897	+	79.1180i	0.337962	+	0.245544i	0.743801	−	0.668401i	$-0.233021\pi$
$47$	108.897	+	79.1180i	0.337962	+	0.245544i	−0.405840	+	0.913944i	$0.633021\pi$
$48$	−110.609	+	80.3619i	−0.332604	+	0.241651i
$49$	64.0975	−	197.272i	0.186873	−	0.575137i
$50$	22.9930	−	70.7651i	0.0650339	−	0.200154i
$51$	−452.819	+	328.992i	−1.24328	+	0.903297i
$52$	37.1030	+	26.9569i	0.0989472	+	0.0718894i
$53$	154.951	+	476.889i	0.401587	+	1.23596i	0.923711	+	0.383089i	$0.125140\pi$
$53$	154.951	+	476.889i	0.401587	+	1.23596i	−0.522124	+	0.852869i	$0.674860\pi$
$54$	324.997			0.819008
$55$		0			0
$56$	−187.689			−0.447875
$57$	19.1443	+	58.9201i	0.0444864	+	0.136915i
$58$	−206.058	−	149.710i	−0.466496	−	0.338929i
$59$	−527.202	+	383.035i	−1.16332	+	0.845201i	−0.990194	−	0.139698i	$-0.955387\pi$
$59$	−527.202	+	383.035i	−1.16332	+	0.845201i	−0.173126	+	0.984900i	$0.555387\pi$
$60$	134.519	−	414.007i	0.289439	−	0.890801i
$61$	−113.034	+	347.884i	−0.237255	+	0.730197i	0.759559	+	0.650439i	$0.225415\pi$
$61$	−113.034	+	347.884i	−0.237255	+	0.730197i	−0.996814	+	0.0797584i	$0.974585\pi$
$62$	467.306	−	339.518i	0.957226	−	0.695465i
$63$	873.419	+	634.576i	1.74667	+	1.26903i
$64$	19.7771	+	60.8676i	0.0386271	+	0.118882i
$65$	−146.023			−0.278645
$66$		0			0
$67$	−294.576			−0.537136			−0.268568	−	0.963261i	$-0.586550\pi$
$67$	−294.576			−0.537136			−0.268568	+	0.963261i	$0.586550\pi$
$68$	80.9651	+	249.185i	0.144389	+	0.444384i
$69$	719.456	+	522.716i	1.25525	+	0.911994i
$70$	483.466	−	351.259i	0.825504	−	0.599764i
$71$	40.9282	−	125.964i	0.0684124	−	0.210552i	−0.911006	−	0.412394i	$-0.864693\pi$
$71$	40.9282	−	125.964i	0.0684124	−	0.210552i	0.979418	+	0.201842i	$0.0646928\pi$
$72$	113.760	−	350.117i	0.186204	−	0.573078i
$73$	379.825	−	275.959i	0.608974	−	0.442446i	−0.240079	−	0.970753i	$-0.577173\pi$
$73$	379.825	−	275.959i	0.608974	−	0.442446i	0.849053	+	0.528308i	$0.177173\pi$
$74$	138.184	+	100.396i	0.217075	+	0.157714i
$75$	98.2373	+	302.343i	0.151246	+	0.465488i
$76$	29.0005			0.0437709
$77$		0			0
$78$	−195.944			−0.284440
$79$	−126.089	−	388.062i	−0.179571	−	0.552663i	0.820241	−	0.572017i	$-0.193839\pi$
$79$	−126.089	−	388.062i	−0.179571	−	0.552663i	−0.999813	+	0.0193540i	$0.993839\pi$
$80$	−164.857	−	119.776i	−0.230395	−	0.167392i
$81$	−118.192	+	85.8712i	−0.162128	+	0.117793i
$82$	83.7088	−	257.629i	0.112733	−	0.346956i
$83$	420.122	−	1293.00i	0.555594	−	1.70994i	−0.138774	−	0.990324i	$-0.544316\pi$
$83$	420.122	−	1293.00i	0.555594	−	1.70994i	0.694368	−	0.719620i	$-0.255684\pi$
$84$	648.751	−	471.345i	0.842672	−	0.612237i
$85$	−674.906	−	490.348i	−0.861222	−	0.625714i
$86$	−218.593	−	672.760i	−0.274087	−	0.843553i
$87$	1088.21			1.34102
$88$		0			0
$89$	−260.255			−0.309966			−0.154983	−	0.987917i	$-0.549532\pi$
$89$	−260.255			−0.309966			−0.154983	+	0.987917i	$0.549532\pi$
$90$	362.209	+	1114.76i	0.424224	+	1.30563i
$91$	−217.619	−	158.110i	−0.250689	−	0.182136i
$92$	336.785	−	244.689i	0.381655	−	0.277289i
$93$	−762.620	+	2347.10i	−0.850322	+	2.61702i
$94$	−83.1896	+	256.031i	−0.0912804	+	0.280932i
$95$	−74.7022	+	54.2743i	−0.0806766	+	0.0586150i
$96$	−221.217	−	160.724i	−0.235186	−	0.170873i
$97$	437.114	+	1345.30i	0.457549	+	1.40819i	0.868117	+	0.496360i	$0.165330\pi$
$97$	437.114	+	1345.30i	0.457549	+	1.40819i	−0.410568	+	0.911830i	$0.634670\pi$
$98$	414.848			0.427612
$99$		0			0
$100$	148.814			0.148814
$101$	57.6678	+	177.483i	0.0568135	+	0.174854i	0.975436	−	0.220282i	$-0.0706976\pi$
$101$	57.6678	+	177.483i	0.0568135	+	0.174854i	−0.918623	+	0.395135i	$0.870698\pi$
$102$	−905.638	−	657.985i	−0.879133	−	0.638727i
$103$	948.908	−	689.422i	0.907754	−	0.659522i	−0.0326920	−	0.999465i	$-0.510408\pi$
$103$	948.908	−	689.422i	0.907754	−	0.659522i	0.940446	+	0.339944i	$0.110408\pi$
$104$	−28.3441	+	87.2343i	−0.0267247	+	0.0822503i
$105$	−788.992	+	2428.27i	−0.733311	+	2.25690i
$106$	−811.333	+	589.468i	−0.743430	+	0.540134i
$107$	−576.598	−	418.923i	−0.520951	−	0.378493i	0.296011	−	0.955185i	$-0.404344\pi$
$107$	−576.598	−	418.923i	−0.520951	−	0.378493i	−0.816962	+	0.576691i	$0.804344\pi$
$108$	200.859	+	618.181i	0.178960	+	0.550782i
$109$	−1247.22			−1.09598			−0.547989	−	0.836486i	$-0.684606\pi$
$109$	−1247.22			−1.09598			−0.547989	+	0.836486i	$0.684606\pi$
$110$		0			0
$111$	−729.762			−0.624017
$112$	−115.998	−	357.006i	−0.0978642	−	0.301195i
$113$	794.456	+	577.206i	0.661382	+	0.480522i	0.867129	−	0.498083i	$-0.165963\pi$
$113$	794.456	+	577.206i	0.661382	+	0.480522i	−0.205748	+	0.978605i	$0.565963\pi$
$114$	−100.241	+	72.8292i	−0.0823545	+	0.0598340i
$115$	−409.589	+	1260.58i	−0.332125	+	1.02217i
$116$	157.415	−	484.472i	0.125996	−	0.387777i
$117$	426.840	−	310.117i	0.337277	−	0.245046i
$118$	−1054.40	−	766.070i	−0.822591	−	0.597648i
$119$	−474.883	−	1461.54i	−0.365819	−	1.12588i
$120$	870.625			0.662307
$121$		0			0
$122$	−731.574			−0.542899
$123$	357.645	+	1100.72i	0.262177	+	0.806898i
$124$	934.613	+	679.036i	0.676861	+	0.491768i
$125$	904.618	−	657.244i	0.647292	−	0.470285i
$126$	−667.233	+	2053.53i	−0.471761	+	1.45193i
$127$	479.183	−	1474.77i	0.334808	−	1.03043i	−0.632009	−	0.774961i	$-0.717769\pi$
$127$	479.183	−	1474.77i	0.334808	−	1.03043i	0.966817	−	0.255471i	$-0.0822307\pi$
$128$	−103.554	+	75.2365i	−0.0715077	+	0.0519534i
$129$	2445.08	+	1776.45i	1.66881	+	1.21246i
$130$	−90.2471	−	277.752i	−0.0608861	−	0.187388i
$131$	−742.114			−0.494953			−0.247476	−	0.968894i	$-0.579601\pi$
$131$	−742.114			−0.494953			−0.247476	+	0.968894i	$0.579601\pi$
$132$		0			0
$133$	−170.096			−0.110896
$134$	−182.058	−	560.316i	−0.117369	−	0.361223i
$135$	−1674.31	−	1216.46i	−1.06742	−	0.775527i
$136$	−423.939	+	308.010i	−0.267298	+	0.194203i
$137$	159.353	−	490.439i	0.0993757	−	0.305847i	−0.888994	−	0.457920i	$-0.848595\pi$
$137$	159.353	−	490.439i	0.0993757	−	0.305847i	0.988369	+	0.152073i	$0.0485948\pi$
$138$	−549.616	+	1691.54i	−0.339032	+	1.04343i
$139$	1992.74	−	1447.81i	1.21599	−	0.883467i	0.220227	−	0.975449i	$-0.429320\pi$
$139$	1992.74	−	1447.81i	1.21599	−	0.883467i	0.995761	+	0.0919821i	$0.0293203\pi$
$140$	966.933	+	702.518i	0.583720	+	0.424097i
$141$	−355.427	−	1093.89i	−0.212286	−	0.653350i
$142$	264.893			0.156544
$143$		0			0
$144$	736.269			0.426082
$145$	501.204	+	1542.55i	0.287054	+	0.883460i
$146$	759.649	+	551.917i	0.430610	+	0.312856i
$147$	−1433.93	+	1041.81i	−0.804548	+	0.584538i
$148$	−105.563	+	324.890i	−0.0586300	+	0.180444i
$149$	134.347	−	413.479i	0.0738669	−	0.227339i	−0.907306	−	0.420471i	$-0.861865\pi$
$149$	134.347	−	413.479i	0.0738669	−	0.227339i	0.981173	+	0.193132i	$0.0618647\pi$
$150$	−514.377	+	373.717i	−0.279991	+	0.203426i
$151$	−631.836	−	459.056i	−0.340517	−	0.247400i	0.404363	−	0.914599i	$-0.367493\pi$
$151$	−631.836	−	459.056i	−0.340517	−	0.247400i	−0.744880	+	0.667198i	$0.767493\pi$
$152$	17.9233	+	55.1622i	0.00956429	+	0.0294358i
$153$	3014.20			1.59270
$154$		0			0
$155$	−3678.27			−1.90610
$156$	−121.100	−	372.708i	−0.0621524	−	0.191285i
$157$	−422.616	−	307.048i	−0.214831	−	0.156084i	0.475166	−	0.879896i	$-0.342388\pi$
$157$	−422.616	−	307.048i	−0.214831	−	0.156084i	−0.689997	+	0.723813i	$0.742388\pi$
$158$	660.211	−	479.671i	0.332428	−	0.241523i
$159$	1324.05	−	4075.01i	0.660404	−	2.03251i
$160$	125.940	−	387.602i	0.0622275	−	0.191517i
$161$	−1975.34	+	1435.17i	−0.966948	+	0.702529i
$162$	−236.383	−	171.742i	−0.114642	−	0.0832923i
$163$	785.918	+	2418.81i	0.377656	+	1.16230i	0.941669	+	0.336539i	$0.109257\pi$
$163$	785.918	+	2418.81i	0.377656	+	1.16230i	−0.564014	+	0.825765i	$0.690743\pi$
$164$	541.775			0.257960
$165$		0			0
$166$	2719.08			1.27134
$167$	−428.125	−	1317.63i	−0.198379	−	0.610548i	−0.999921	−	0.0126088i	$-0.995986\pi$
$167$	−428.125	−	1317.63i	−0.198379	−	0.610548i	0.801541	−	0.597939i	$-0.204014\pi$
$168$	1297.50	+	942.690i	0.595859	+	0.432917i
$169$	1671.06	−	1214.10i	0.760610	−	0.552615i
$170$	515.582	−	1586.80i	0.232608	−	0.715894i
$171$	103.097	−	317.299i	0.0461052	−	0.141897i
$172$	1144.57	−	831.577i	0.507398	−	0.368646i
$173$	−358.808	−	260.689i	−0.157686	−	0.114566i	0.506144	−	0.862449i	$-0.331070\pi$
$173$	−358.808	−	260.689i	−0.157686	−	0.114566i	−0.663830	+	0.747883i	$0.731070\pi$
$174$	672.553	+	2069.90i	0.293024	+	0.901834i
$175$	−872.833			−0.377029
$176$		0			0
$177$	5568.41			2.36467
$178$	−160.846	−	495.034i	−0.0677300	−	0.208452i
$179$	−304.707	−	221.383i	−0.127234	−	0.0924409i	0.522348	−	0.852732i	$-0.325056\pi$
$179$	−304.707	−	221.383i	−0.127234	−	0.0924409i	−0.649582	+	0.760291i	$0.725056\pi$
$180$	−1896.55	+	1377.92i	−0.785336	+	0.570580i
$181$	1017.83	−	3132.55i	0.417981	−	1.28641i	−0.491576	−	0.870834i	$-0.663579\pi$
$181$	1017.83	−	3132.55i	0.417981	−	1.28641i	0.909557	−	0.415578i	$-0.136421\pi$
$182$	166.246	−	511.654i	0.0677088	−	0.208386i
$183$	2528.70	−	1837.21i	1.02146	−	0.742133i
$184$	673.571	+	489.378i	0.269871	+	0.196073i
$185$	−336.111	−	1034.44i	−0.133575	−	0.411101i
$186$	−4935.78			−1.94575
$187$		0			0
$188$	−538.415			−0.208872
$189$	−1178.09	−	3625.80i	−0.453406	−	1.39544i
$190$	−149.404	−	108.549i	−0.0570470	−	0.0414471i
$191$	−1852.86	+	1346.18i	−0.701928	+	0.509981i	−0.880560	−	0.473935i	$-0.842833\pi$
$191$	−1852.86	+	1346.18i	−0.701928	+	0.509981i	0.178631	+	0.983916i	$0.442833\pi$
$192$	168.995	−	520.113i	0.0635217	−	0.195500i
$193$	711.789	−	2190.66i	0.265470	−	0.817033i	−0.726115	−	0.687574i	$-0.758676\pi$
$193$	711.789	−	2190.66i	0.265470	−	0.817033i	0.991585	−	0.129459i	$-0.0413241\pi$
$194$	−2288.76	+	1662.88i	−0.847027	+	0.615401i
$195$	1009.46	+	733.417i	0.370713	+	0.269339i
$196$	256.390	+	789.088i	0.0934366	+	0.287568i
$197$	1041.86			0.376801			0.188400	−	0.982092i	$-0.439670\pi$
$197$	1041.86			0.376801			0.188400	+	0.982092i	$0.439670\pi$
$198$		0			0
$199$	3463.83			1.23389			0.616946	−	0.787005i	$-0.288370\pi$
$199$	3463.83			1.23389			0.616946	+	0.787005i	$0.288370\pi$
$200$	91.9719	+	283.060i	0.0325170	+	0.100077i
$201$	2036.41	+	1479.54i	0.714614	+	0.519198i
$202$	−301.952	+	219.381i	−0.105175	+	0.0764139i
$203$	−923.280	+	2841.57i	−0.319220	+	0.982457i
$204$	691.846	−	2129.28i	0.237446	−	0.730783i
$205$	−1395.55	+	1013.93i	−0.475462	+	0.345443i
$206$	1897.82	+	1378.84i	0.641879	+	0.466352i
$207$	−1479.91	−	4554.68i	−0.496911	−	1.52934i
$208$	−183.447			−0.0611527
$209$		0			0
$210$	−5106.46			−1.67800
$211$	−646.457	−	1989.59i	−0.210919	−	0.649142i	−0.999418	−	0.0341063i	$-0.989142\pi$
$211$	−646.457	−	1989.59i	−0.210919	−	0.649142i	0.788499	−	0.615036i	$-0.210858\pi$
$212$	−1622.67	−	1178.94i	−0.525684	−	0.381932i
$213$	−915.606	+	665.227i	−0.294537	+	0.213993i
$214$	440.481	−	1355.66i	0.140704	−	0.433043i
$215$	−1391.99	+	4284.10i	−0.441548	+	1.35895i
$216$	−1051.71	+	764.113i	−0.331296	+	0.240701i
$217$	−5481.77	−	3982.74i	−1.71487	−	1.24593i
$218$	−770.822	−	2372.34i	−0.239480	−	0.737043i
$219$	−4011.78			−1.23786
$220$		0			0
$221$	−751.012			−0.228591
$222$	−451.018	−	1388.09i	−0.136353	−	0.419651i
$223$	−2996.21	−	2176.88i	−0.899737	−	0.653697i	0.0386614	−	0.999252i	$-0.487691\pi$
$223$	−2996.21	−	2176.88i	−0.899737	−	0.653697i	−0.938398	+	0.345555i	$0.887691\pi$
$224$	607.374	−	441.283i	0.181169	−	0.131627i
$225$	529.031	−	1628.19i	0.156750	−	0.482427i
$226$	−606.910	+	1867.88i	−0.178633	+	0.549776i
$227$	−3926.56	+	2852.82i	−1.14808	+	0.834132i	−0.988225	−	0.153007i	$-0.951104\pi$
$227$	−3926.56	+	2852.82i	−1.14808	+	0.834132i	−0.159860	+	0.987140i	$0.551104\pi$
$228$	−200.482	−	145.658i	−0.0582334	−	0.0423091i
$229$	−413.108	−	1271.42i	−0.119209	−	0.366889i	0.873592	−	0.486658i	$-0.161784\pi$
$229$	−413.108	−	1271.42i	−0.119209	−	0.366889i	−0.992802	+	0.119770i	$0.961784\pi$
$230$	−2650.91			−0.759983
$231$		0			0
$232$	1018.81			0.288311
$233$	1824.41	+	5614.95i	0.512965	+	1.57874i	0.786954	+	0.617012i	$0.211657\pi$
$233$	1824.41	+	5614.95i	0.512965	+	1.57874i	−0.273989	+	0.961733i	$0.588343\pi$
$234$	853.680	+	620.235i	0.238491	+	0.173274i
$235$	1386.90	−	1007.64i	0.384984	−	0.279707i
$236$	805.493	−	2479.05i	0.222174	−	0.683782i
$237$	−1077.43	+	3315.99i	−0.295302	+	0.908846i
$238$	2486.52	−	1806.56i	0.677215	−	0.492026i
$239$	−2685.76	−	1951.32i	−0.726894	−	0.528119i	0.161686	−	0.986842i	$-0.448307\pi$
$239$	−2685.76	−	1951.32i	−0.726894	−	0.528119i	−0.888579	+	0.458723i	$0.848307\pi$
$240$	538.076	+	1656.03i	0.144719	+	0.445401i
$241$	5275.95			1.41018			0.705091	−	0.709116i	$-0.250906\pi$
$241$	5275.95			1.41018			0.705091	+	0.709116i	$0.250906\pi$
$242$		0			0
$243$	−3139.10			−0.828696
$244$	−452.138	−	1391.54i	−0.118628	−	0.365098i
$245$	−2137.21	−	1552.77i	−0.557311	−	0.404910i
$246$	−1872.66	+	1360.56i	−0.485350	+	0.352627i
$247$	−25.6873	+	79.0575i	−0.00661719	+	0.0203656i
$248$	−713.981	+	2197.41i	−0.182814	+	0.562643i
$249$	−9398.57	+	6828.46i	−2.39201	+	1.73790i
$250$	1809.24	+	1314.49i	0.457705	+	0.332542i
$251$	−606.245	−	1865.83i	−0.152454	−	0.469204i	0.845440	−	0.534070i	$-0.179338\pi$
$251$	−606.245	−	1865.83i	−0.152454	−	0.469204i	−0.997894	+	0.0648658i	$0.979338\pi$
$252$	−4318.42			−1.07950
$253$		0			0
$254$	3101.34			0.766123
$255$	2202.82	+	6779.59i	0.540965	+	1.66492i
$256$	−207.108	−	150.473i	−0.0505636	−	0.0367366i
$257$	−4807.15	+	3492.60i	−1.16678	+	0.847714i	−0.990620	−	0.136648i	$-0.956367\pi$
$257$	−4807.15	+	3492.60i	−1.16678	+	0.847714i	−0.176158	+	0.984362i	$0.556367\pi$
$258$	−1867.87	+	5748.72i	−0.450731	+	1.38721i
$259$	619.157	−	1905.57i	0.148543	−	0.457167i
$260$	472.540	−	343.320i	0.112714	−	0.0818916i
$261$	−4741.07	−	3444.59i	−1.12439	−	0.816915i
$262$	−458.652	−	1411.59i	−0.108151	−	0.332855i
$263$	1704.11			0.399544			0.199772	−	0.979842i	$-0.435980\pi$
$263$	1704.11			0.399544			0.199772	+	0.979842i	$0.435980\pi$
$264$		0			0
$265$	6386.18			1.48038
$266$	−105.125	−	323.542i	−0.0242317	−	0.0745775i
$267$	1799.15	+	1307.16i	0.412383	+	0.299614i
$268$	953.266	−	692.589i	0.217276	−	0.157860i
$269$	−1806.31	+	5559.24i	−0.409414	+	1.26005i	0.507738	+	0.861511i	$0.330482\pi$
$269$	−1806.31	+	5559.24i	−0.409414	+	1.26005i	−0.917153	+	0.398536i	$0.869518\pi$
$270$	1279.06	−	3936.55i	0.288301	−	0.887298i
$271$	4777.92	−	3471.36i	1.07099	−	0.778120i	0.0948997	−	0.995487i	$-0.469747\pi$
$271$	4777.92	−	3471.36i	1.07099	−	0.778120i	0.976090	+	0.217367i	$0.0697469\pi$
$272$	−847.878	−	616.019i	−0.189008	−	0.137322i
$273$	710.286	+	2186.04i	0.157467	+	0.484633i
$274$	1031.36			0.227396
$275$		0			0
$276$	−3557.19			−0.775788
$277$	−2744.81	−	8447.65i	−0.595377	−	1.83238i	−0.552839	−	0.833288i	$-0.686456\pi$
$277$	−2744.81	−	8447.65i	−0.595377	−	1.83238i	−0.0425380	−	0.999095i	$-0.513544\pi$
$278$	3985.49	+	2895.63i	0.859833	+	0.624705i
$279$	10752.0	−	7811.77i	2.30718	−	1.67627i
$280$	−738.671	+	2273.40i	−0.157657	+	0.485219i
$281$	2519.03	−	7752.79i	0.534779	−	1.64588i	−0.209346	−	0.977842i	$-0.567133\pi$
$281$	2519.03	−	7752.79i	0.534779	−	1.64588i	0.744125	−	0.668040i	$-0.232867\pi$
$282$	1861.04	−	1352.13i	0.392991	−	0.285524i
$283$	4744.04	+	3446.75i	0.996481	+	0.723986i	0.961331	−	0.275396i	$-0.0888091\pi$
$283$	4744.04	+	3446.75i	0.996481	+	0.723986i	0.0351500	+	0.999382i	$0.488809\pi$
$284$	163.713	+	503.856i	0.0342062	+	0.105276i
$285$	789.018			0.163991
$286$		0			0
$287$	−3177.66			−0.653559
$288$	455.039	+	1400.47i	0.0931022	+	0.286539i
$289$	503.585	+	365.876i	0.102501	+	0.0744710i
$290$	−2624.34	+	1906.70i	−0.531402	+	0.386086i
$291$	3735.13	−	11495.6i	0.752431	−	2.31574i
$292$	−580.320	+	1786.04i	−0.116304	+	0.357946i
$293$	6161.93	−	4476.91i	1.22861	−	0.892641i	0.231829	−	0.972757i	$-0.425529\pi$
$293$	6161.93	−	4476.91i	1.22861	−	0.892641i	0.996786	+	0.0801158i	$0.0255290\pi$
$294$	−2867.86	−	2083.62i	−0.568901	−	0.413331i
$295$	2564.67	+	7893.25i	0.506173	+	1.55784i
$296$	−683.219			−0.134160
$297$		0			0
$298$	869.515			0.169026
$299$	368.730	+	1134.84i	0.0713185	+	0.219496i
$300$	−1028.75	−	747.434i	−0.197984	−	0.143844i
$301$	−6713.20	+	4877.43i	−1.28552	+	0.933988i
$302$	482.680	−	1485.54i	0.0919705	−	0.283056i
$303$	492.771	−	1516.59i	0.0934288	−	0.287544i
$304$	−93.8476	+	68.1843i	−0.0177057	+	0.0128639i
$305$	3768.91	+	2738.28i	0.707565	+	0.514076i
$306$	1862.88	+	5733.35i	0.348019	+	1.07109i
$307$	−4100.68			−0.762339			−0.381170	−	0.924505i	$-0.624479\pi$
$307$	−4100.68			−0.762339			−0.381170	+	0.924505i	$0.624479\pi$
$308$		0			0
$309$	−10022.5			−1.84519
$310$	−2273.30	−	6996.49i	−0.416499	−	1.28185i
$311$	−1178.04	−	855.893i	−0.214792	−	0.156055i	0.475187	−	0.879885i	$-0.342380\pi$
$311$	−1178.04	−	855.893i	−0.214792	−	0.156055i	−0.689979	+	0.723829i	$0.742380\pi$
$312$	634.089	−	460.692i	0.115058	−	0.0835948i
$313$	−1069.72	+	3292.25i	−0.193176	+	0.594533i	0.806817	+	0.590801i	$0.201188\pi$
$313$	−1069.72	+	3292.25i	−0.193176	+	0.594533i	−0.999993	+	0.00373259i	$0.998812\pi$
$314$	322.850	−	993.630i	0.0580238	−	0.178579i
$315$	11123.8	−	8081.91i	1.98970	−	1.44560i
$316$	1320.42	+	959.342i	0.235062	+	0.170782i
$317$	1542.71	+	4747.97i	0.273335	+	0.841238i	0.989655	+	0.143467i	$0.0458249\pi$
$317$	1542.71	+	4747.97i	0.273335	+	0.841238i	−0.716320	+	0.697772i	$0.754175\pi$
$318$	8569.44			1.51117
$319$		0			0
$320$	815.098			0.142392
$321$	1881.95	+	5792.06i	0.327229	+	1.00711i
$322$	−3950.68	−	2870.34i	−0.683735	−	0.496763i
$323$	−384.201	+	279.139i	−0.0661843	+	0.0480857i
$324$	180.581	−	555.770i	0.0309637	−	0.0952966i
$325$	−131.812	+	405.677i	−0.0224973	+	0.0692397i
$326$	−4115.12	+	2989.81i	−0.699127	+	0.507946i
$327$	8622.05	+	6264.29i	1.45811	+	1.05938i
$328$	334.835	+	1030.52i	0.0563664	+	0.173478i
$329$	3157.95			0.529190
$330$		0			0
$331$	10199.3			1.69366			0.846832	−	0.531861i	$-0.178507\pi$
$331$	10199.3			1.69366			0.846832	+	0.531861i	$0.178507\pi$
$332$	1680.49	+	5172.01i	0.277797	+	0.854972i
$333$	3179.39	+	2309.96i	0.523212	+	0.380136i
$334$	2241.69	−	1628.68i	0.367245	−	0.266819i
$335$	−1159.34	+	3568.07i	−0.189078	+	0.581923i
$336$	−991.203	+	3050.61i	−0.160936	+	0.495310i
$337$	−1359.74	+	987.912i	−0.219792	+	0.159688i	−0.692233	−	0.721674i	$-0.743373\pi$
$337$	−1359.74	+	987.912i	−0.219792	+	0.159688i	0.472441	+	0.881362i	$0.343373\pi$
$338$	3342.12	+	2428.19i	0.537832	+	0.390758i
$339$	−2593.02	−	7980.50i	−0.415438	−	1.27859i
$340$	3336.92			0.532264
$341$		0			0
$342$	667.255			0.105500
$343$	982.910	+	3025.09i	0.154729	+	0.476208i
$344$	2289.13	+	1663.15i	0.358784	+	0.260672i
$345$	9162.93	−	6657.26i	1.42990	−	1.03888i
$346$	274.105	−	843.608i	0.0425895	−	0.131077i
$347$	−3252.80	+	10011.1i	−0.503225	+	1.54877i	0.300508	+	0.953779i	$0.402844\pi$
$347$	−3252.80	+	10011.1i	−0.503225	+	1.54877i	−0.803734	+	0.594989i	$0.797156\pi$
$348$	−3521.53	+	2558.54i	−0.542454	+	0.394116i
$349$	−4288.08	−	3115.47i	−0.657696	−	0.477844i	0.208188	−	0.978089i	$-0.433243\pi$
$349$	−4288.08	−	3115.47i	−0.657696	−	0.477844i	−0.865884	+	0.500245i	$0.833243\pi$
$350$	−539.441	−	1660.23i	−0.0823838	−	0.253551i
$351$	−1863.12			−0.283321
$352$		0			0
$353$	−7438.40			−1.12155			−0.560773	−	0.827969i	$-0.689496\pi$
$353$	−7438.40			−1.12155			−0.560773	+	0.827969i	$0.689496\pi$
$354$	3441.46	+	10591.7i	0.516700	+	1.59024i
$355$	−1364.67	−	991.490i	−0.204026	−	0.148233i
$356$	842.202	−	611.896i	0.125384	−	0.0910966i
$357$	−4057.87	+	12488.8i	−0.601583	+	1.85148i
$358$	232.776	−	716.410i	0.0343647	−	0.105764i
$359$	8212.58	−	5966.79i	1.20736	−	0.877201i	0.212374	−	0.977188i	$-0.431880\pi$
$359$	8212.58	−	5966.79i	1.20736	−	0.877201i	0.994989	+	0.0999877i	$0.0318803\pi$
$360$	−3793.10	−	2755.85i	−0.555316	−	0.403461i
$361$	−2103.30	−	6473.30i	−0.306649	−	0.943768i
$362$	6587.52			0.956443
$363$		0			0
$364$	1075.97			0.154934
$365$	−1847.73	−	5686.72i	−0.264971	−	0.815497i
$366$	5057.40	+	3674.42i	0.722280	+	0.524767i
$367$	−385.742	+	280.258i	−0.0548652	+	0.0398619i	−0.614880	−	0.788621i	$-0.710796\pi$
$367$	−385.742	+	280.258i	−0.0548652	+	0.0398619i	0.560015	+	0.828483i	$0.310796\pi$
$368$	−514.562	+	1583.66i	−0.0728897	+	0.224331i
$369$	1926.01	−	5927.64i	0.271718	−	0.836261i
$370$	1759.90	−	1278.64i	0.247278	−	0.179658i
$371$	9517.38	+	6914.78i	1.33185	+	0.967649i
$372$	−3050.48	−	9388.41i	−0.425161	−	1.30851i
$373$	12738.5			1.76829			0.884146	−	0.467210i	$-0.154741\pi$
$373$	12738.5			1.76829			0.884146	+	0.467210i	$0.154741\pi$
$374$		0			0
$375$	−9554.74			−1.31575
$376$	−332.759	−	1024.13i	−0.0456402	−	0.140466i
$377$	1181.28	+	858.247i	0.161376	+	0.117247i
$378$	6168.58	−	4481.74i	0.839359	−	0.609830i
$379$	−401.317	+	1235.13i	−0.0543912	+	0.167399i	−0.974562	−	0.224119i	$-0.928050\pi$
$379$	−401.317	+	1235.13i	−0.0543912	+	0.167399i	0.920171	+	0.391517i	$0.128050\pi$
$380$	114.135	−	351.271i	0.0154079	−	0.0474205i
$381$	−10719.8	+	7788.41i	−1.44145	+	1.04728i
$382$	−3705.72	−	2692.37i	−0.496338	−	0.360611i
$383$	−207.217	−	637.748i	−0.0276456	−	0.0850846i	0.936282	−	0.351250i	$-0.114243\pi$
$383$	−207.217	−	637.748i	−0.0276456	−	0.0850846i	−0.963927	+	0.266165i	$0.914243\pi$
$384$	1093.76			0.145353
$385$		0			0
$386$	4606.80			0.607461
$387$	−5029.47	−	15479.1i	−0.660626	−	2.03320i
$388$	−4577.52	−	3325.76i	−0.598939	−	0.435155i
$389$	−4235.93	+	3077.59i	−0.552109	+	0.401131i	−0.828562	−	0.559897i	$-0.810841\pi$
$389$	−4235.93	+	3077.59i	−0.552109	+	0.401131i	0.276453	+	0.961027i	$0.410841\pi$
$390$	−771.160	+	2373.39i	−0.100126	+	0.308157i
$391$	−2106.56	+	6483.32i	−0.272464	+	0.838557i
$392$	−1342.48	+	975.366i	−0.172973	+	0.125672i
$393$	5130.27	+	3727.36i	0.658493	+	0.478423i
$394$	643.908	+	1981.74i	0.0823340	+	0.253398i
$395$	−5196.67			−0.661956
$396$		0			0
$397$	1751.64			0.221442			0.110721	−	0.993852i	$-0.464684\pi$
$397$	1751.64			0.221442			0.110721	+	0.993852i	$0.464684\pi$
$398$	2140.77	+	6588.60i	0.269615	+	0.829791i
$399$	1175.88	+	854.327i	0.147538	+	0.107193i
$400$	−481.571	+	349.882i	−0.0601964	+	0.0437352i
$401$	1116.41	−	3435.95i	0.139029	−	0.427889i	−0.857166	−	0.515041i	$-0.827777\pi$
$401$	1116.41	−	3435.95i	0.139029	−	0.427889i	0.996195	+	0.0871524i	$0.0277767\pi$
$402$	−1555.68	+	4787.89i	−0.193011	+	0.594026i
$403$	−2678.94	+	1946.36i	−0.331135	+	0.240584i
$404$	−603.905	−	438.763i	−0.0743698	−	0.0540328i
$405$	574.964	+	1769.56i	0.0705437	+	0.217111i
$406$	−5975.60			−0.730453
$407$		0			0
$408$	4477.72			0.543334
$409$	3490.34	+	10742.2i	0.421971	+	1.29869i	0.905865	+	0.423567i	$0.139222\pi$
$409$	3490.34	+	10742.2i	0.421971	+	1.29869i	−0.483894	+	0.875127i	$0.660778\pi$
$410$	−2791.11	−	2027.86i	−0.336202	−	0.244265i
$411$	−3564.90	+	2590.05i	−0.427843	+	0.310846i
$412$	−1449.80	+	4462.03i	−0.173366	+	0.533564i
$413$	−4724.44	+	14540.3i	−0.562893	+	1.73241i
$414$	7748.89	−	5629.90i	0.919897	−	0.668344i
$415$	−14008.1	−	10177.5i	−1.65695	−	1.20384i
$416$	−113.377	−	348.937i	−0.0133624	−	0.0411251i
$417$	−21047.7			−2.47173
$418$		0			0
$419$	−3680.45			−0.429121			−0.214560	−	0.976711i	$-0.568832\pi$
$419$	−3680.45			−0.429121			−0.214560	+	0.976711i	$0.568832\pi$
$420$	−3155.97	−	9713.07i	−0.366656	−	1.12845i
$421$	−7488.40	−	5440.64i	−0.866894	−	0.629835i	0.0628578	−	0.998022i	$-0.479979\pi$
$421$	−7488.40	−	5440.64i	−0.866894	−	0.629835i	−0.929752	+	0.368187i	$0.879979\pi$
$422$	3384.89	−	2459.27i	0.390460	−	0.283686i
$423$	−1914.06	+	5890.87i	−0.220011	+	0.677125i
$424$	1239.61	−	3815.11i	0.141983	−	0.436977i
$425$	−1971.50	+	1432.38i	−0.225016	+	0.163483i
$426$	−1831.21	−	1330.45i	−0.208269	−	0.151316i
$427$	2651.91	+	8161.75i	0.300551	+	0.925000i
$428$	2850.85			0.321966
$429$		0			0
$430$	−9009.14			−1.01037
$431$	−1107.53	−	3408.62i	−0.123777	−	0.380946i	0.869899	−	0.493229i	$-0.164184\pi$
$431$	−1107.53	−	3408.62i	−0.123777	−	0.380946i	−0.993676	+	0.112283i	$0.964184\pi$
$432$	−2103.42	−	1528.23i	−0.234262	−	0.170201i
$433$	6720.35	−	4882.62i	0.745864	−	0.541902i	−0.148678	−	0.988886i	$-0.547502\pi$
$433$	6720.35	−	4882.62i	0.745864	−	0.541902i	0.894542	+	0.446984i	$0.147502\pi$
$434$	4187.70	−	12888.4i	0.463170	−	1.42549i
$435$	4282.79	−	13181.1i	0.472055	−	1.45284i
$436$	4036.07	−	2932.38i	0.443332	−	0.322100i
$437$	610.434	+	443.506i	0.0668215	+	0.0485487i
$438$	−2479.41	−	7630.85i	−0.270482	−	0.832457i
$439$	−11932.4			−1.29727			−0.648634	−	0.761101i	$-0.724659\pi$
$439$	−11932.4			−1.29727			−0.648634	+	0.761101i	$0.724659\pi$
$440$		0			0
$441$	9544.99			1.03067
$442$	−464.151	−	1428.51i	−0.0499489	−	0.153727i
$443$	−872.785	−	634.115i	−0.0936055	−	0.0680084i	0.539998	−	0.841666i	$-0.318425\pi$
$443$	−872.785	−	634.115i	−0.0936055	−	0.0680084i	−0.633604	+	0.773658i	$0.718425\pi$
$444$	2361.56	−	1715.77i	0.252420	−	0.183394i
$445$	−1024.26	+	3152.35i	−0.109112	+	0.335811i
$446$	2288.90	−	7044.52i	0.243011	−	0.747910i
$447$	−3005.49	+	2183.62i	−0.318020	+	0.231055i
$448$	1214.75	+	882.566i	0.128106	+	0.0930744i
$449$	3944.89	+	12141.1i	0.414635	+	1.27611i	0.912577	+	0.408904i	$0.134089\pi$
$449$	3944.89	+	12141.1i	0.414635	+	1.27611i	−0.497943	+	0.867210i	$0.665911\pi$
$450$	3423.96			0.358683
$451$		0			0
$452$	−3928.01			−0.408756
$453$	2062.25	+	6346.94i	0.213891	+	0.658290i
$454$	−7853.13	−	5705.63i	−0.811819	−	0.589821i
$455$	−2771.58	+	2013.67i	−0.285568	+	0.207478i
$456$	153.154	−	471.361i	0.0157283	−	0.0484068i
$457$	3469.28	−	10677.3i	0.355112	−	1.09292i	−0.600833	−	0.799375i	$-0.705164\pi$
$457$	3469.28	−	10677.3i	0.355112	−	1.09292i	0.955945	−	0.293547i	$-0.0948357\pi$
$458$	2163.06	−	1571.56i	0.220684	−	0.160336i
$459$	−8611.17	−	6256.38i	−0.875676	−	0.636216i
$460$	−1638.35	−	5042.34i	−0.166062	−	0.511087i
$461$	2160.58			0.218283			0.109141	−	0.994026i	$-0.465190\pi$
$461$	2160.58			0.218283			0.109141	+	0.994026i	$0.465190\pi$
$462$		0			0
$463$	11469.5			1.15125			0.575627	−	0.817712i	$-0.304758\pi$
$463$	11469.5			1.15125			0.575627	+	0.817712i	$0.304758\pi$
$464$	629.658	+	1937.89i	0.0629982	+	0.193888i
$465$	25428.1	+	18474.6i	2.53591	+	1.84245i
$466$	−9552.72	+	6940.46i	−0.949616	+	0.689937i
$467$	623.717	−	1919.60i	0.0618034	−	0.190211i	−0.915388	−	0.402574i	$-0.868116\pi$
$467$	623.717	−	1919.60i	0.0618034	−	0.190211i	0.977191	+	0.212362i	$0.0681157\pi$
$468$	−652.153	+	2007.12i	−0.0644141	+	0.198246i
$469$	−5591.17	+	4062.23i	−0.550483	+	0.399949i
$470$	2773.80	+	2015.28i	0.272225	+	0.197783i
$471$	1379.37	+	4245.28i	0.134943	+	0.415312i
$472$	5213.26			0.508389
$473$		0			0
$474$	−6973.27			−0.675723
$475$	83.3510	+	256.528i	0.00805138	+	0.0247796i
$476$	4973.04	+	3613.13i	0.478863	+	0.347915i
$477$	−18667.5	+	13562.7i	−1.79188	+	1.30187i
$478$	2051.74	−	6314.61i	0.196327	−	0.604233i
$479$	2264.17	−	6968.40i	0.215976	−	0.664706i	−0.783107	−	0.621887i	$-0.786366\pi$
$479$	2264.17	−	6968.40i	0.215976	−	0.664706i	0.999083	−	0.0428187i	$-0.0136338\pi$
$480$	−2817.40	+	2046.96i	−0.267909	+	0.194647i
$481$	−792.170	−	575.545i	−0.0750932	−	0.0545584i
$482$	3260.72	+	10035.5i	0.308136	+	0.948346i
$483$	20863.9			1.96551
$484$		0			0
$485$	18015.3			1.68667
$486$	−1940.07	−	5970.91i	−0.181077	−	0.557297i
$487$	5007.65	+	3638.27i	0.465952	+	0.338534i	0.795861	−	0.605479i	$-0.207018\pi$
$487$	5007.65	+	3638.27i	0.465952	+	0.338534i	−0.329910	+	0.944012i	$0.607018\pi$
$488$	2367.42	−	1720.03i	0.219607	−	0.159554i
$489$	6715.66	−	20668.7i	0.621049	−	1.91139i
$490$	1632.68	−	5024.87i	0.150524	−	0.463267i
$491$	−8188.00	+	5948.93i	−0.752585	+	0.546785i	−0.896627	−	0.442786i	$-0.853990\pi$
$491$	−8188.00	+	5948.93i	−0.752585	+	0.546785i	0.144042	+	0.989572i	$0.453990\pi$
$492$	−3745.31	−	2721.13i	−0.343194	−	0.249345i
$493$	2577.75	+	7933.50i	0.235489	+	0.724760i
$494$	−166.252			−0.0151418
$495$		0			0
$496$	−4620.98			−0.418323
$497$	−960.220	−	2955.25i	−0.0866635	−	0.266723i
$498$	−18797.1	−	13656.9i	−1.69141	−	1.22888i
$499$	−2073.36	+	1506.38i	−0.186004	+	0.135140i	−0.676891	−	0.736083i	$-0.736673\pi$
$499$	−2073.36	+	1506.38i	−0.186004	+	0.135140i	0.490886	+	0.871224i	$0.336673\pi$
$500$	−1382.13	+	4253.77i	−0.123622	+	0.380469i
$501$	−3658.32	+	11259.2i	−0.326231	+	1.00404i
$502$	3174.34	−	2306.29i	0.282227	−	0.205050i
$503$	6958.77	+	5055.84i	0.616851	+	0.448169i	0.851820	−	0.523834i	$-0.175499\pi$
$503$	6958.77	+	5055.84i	0.616851	+	0.448169i	−0.234969	+	0.972003i	$0.575499\pi$
$504$	−2668.93	−	8214.13i	−0.235880	−	0.725965i
$505$	2376.74			0.209432
$506$		0			0
$507$	−17650.0			−1.54609
$508$	1916.73	+	5899.09i	0.167404	+	0.515216i
$509$	11281.8	+	8196.72i	0.982431	+	0.713778i	0.958251	−	0.285930i	$-0.0923023\pi$
$509$	11281.8	+	8196.72i	0.982431	+	0.713778i	0.0241805	+	0.999708i	$0.492302\pi$
$510$	−11534.1	+	8380.03i	−1.00145	+	0.727596i
$511$	3403.74	−	10475.6i	0.294663	−	0.906878i
$512$	158.217	−	486.941i	0.0136568	−	0.0420312i
$513$	−953.130	+	692.490i	−0.0820307	+	0.0595988i
$514$	−9614.30	−	6985.20i	−0.825037	−	0.599424i
$515$	−4616.14	−	14207.0i	−0.394973	−	1.21560i
$516$	−12089.1			−1.03138
$517$		0			0
$518$	4007.27			0.339902
$519$	1171.11	+	3604.31i	0.0990483	+	0.304839i
$520$	945.080	+	686.641i	0.0797010	+	0.0579061i
$521$	9783.30	−	7107.98i	0.822676	−	0.597709i	−0.0948019	−	0.995496i	$-0.530222\pi$
$521$	9783.30	−	7107.98i	0.822676	−	0.597709i	0.917478	+	0.397787i	$0.130222\pi$
$522$	3621.86	−	11146.9i	0.303687	−	0.934651i
$523$	5158.06	−	15874.9i	0.431254	−	1.32726i	−0.465622	−	0.884984i	$-0.654169\pi$
$523$	5158.06	−	15874.9i	0.431254	−	1.32726i	0.896876	−	0.442281i	$-0.145831\pi$
$524$	2401.53	−	1744.82i	0.200213	−	0.145463i
$525$	6033.93	+	4383.91i	0.501604	+	0.364437i
$526$	1053.20	+	3241.41i	0.0873035	+	0.268693i
$527$	−18917.8			−1.56370
$528$		0			0
$529$	−1335.94			−0.109800
$530$	3946.88	+	12147.2i	0.323474	+	0.995552i
$531$	−24260.2	−	17626.0i	−1.98268	−	1.44050i
$532$	550.442	−	399.920i	0.0448585	−	0.0325916i
$533$	−479.879	+	1476.92i	−0.0389979	+	0.120023i
$534$	−1374.43	+	4230.06i	−0.111381	+	0.342795i
$535$	−7343.49	+	5335.36i	−0.593434	+	0.431155i
$536$	1906.53	+	1385.18i	0.153637	+	0.111624i
$537$	994.532	+	3060.86i	0.0799204	+	0.245970i
$538$	−11690.7			−0.936840
$539$		0			0
$540$	8278.26			0.659703
$541$	−6388.40	−	19661.5i	−0.507688	−	1.56250i	−0.796205	−	0.605027i	$-0.793162\pi$
$541$	−6388.40	−	19661.5i	−0.507688	−	1.56250i	0.288517	−	0.957475i	$-0.406838\pi$
$542$	9555.85	+	6942.73i	0.757304	+	0.550214i
$543$	−22769.9	+	16543.3i	−1.79954	+	1.30744i
$544$	647.721	−	1993.48i	0.0510493	−	0.157114i
$545$	−4908.56	+	15107.0i	−0.385797	+	1.18736i
$546$	−3719.11	+	2702.09i	−0.291507	+	0.211793i
$547$	7418.52	+	5389.87i	0.579878	+	0.421306i	0.838680	−	0.544625i	$-0.183328\pi$
$547$	7418.52	+	5389.87i	0.579878	+	0.421306i	−0.258802	+	0.965930i	$0.583328\pi$
$548$	637.413	+	1961.76i	0.0496878	+	0.152923i
$549$	−16832.4			−1.30854
$550$		0			0
$551$	923.311			0.0713873
$552$	−2198.46	−	6766.17i	−0.169516	−	0.521717i
$553$	−7744.64	−	5626.81i	−0.595544	−	0.432688i
$554$	14372.0	−	10441.9i	1.10218	−	0.800781i
$555$	−2872.06	+	8839.29i	−0.219662	+	0.676049i
$556$	−3044.64	+	9370.44i	−0.232233	+	0.714739i
$557$	16431.8	−	11938.4i	1.24998	−	0.908161i	0.251756	−	0.967791i	$-0.418992\pi$
$557$	16431.8	−	11938.4i	1.24998	−	0.908161i	0.998221	+	0.0596296i	$0.0189919\pi$
$558$	21504.0	+	15623.5i	1.63142	+	1.18530i
$559$	1253.13	+	3856.74i	0.0948155	+	0.291812i
$560$	−4780.78			−0.360759
$561$		0			0
$562$	16303.5			1.22371
$563$	−1719.11	−	5290.87i	−0.128689	−	0.396063i	0.865866	−	0.500275i	$-0.166768\pi$
$563$	−1719.11	−	5290.87i	−0.128689	−	0.396063i	−0.994555	+	0.104212i	$0.966768\pi$
$564$	3722.08	+	2704.25i	0.277886	+	0.201896i
$565$	10118.1	−	7351.24i	0.753403	−	0.547379i
$566$	−3624.13	+	11153.9i	−0.269140	+	0.828328i
$567$	−1059.16	+	3259.74i	−0.0784486	+	0.241440i
$568$	−857.210	+	622.800i	−0.0633235	+	0.0460072i
$569$	−18433.8	−	13393.0i	−1.35815	−	0.986752i	−0.998560	−	0.0536407i	$-0.982917\pi$
$569$	−18433.8	−	13393.0i	−1.35815	−	0.986752i	−0.359587	−	0.933111i	$-0.617083\pi$
$570$	487.640	+	1500.80i	0.0358333	+	0.110284i
$571$	11157.6			0.817743			0.408871	−	0.912592i	$-0.365922\pi$
$571$	11157.6			0.817743			0.408871	+	0.912592i	$0.365922\pi$
$572$		0			0
$573$	19570.3			1.42681
$574$	−1963.90	−	6044.27i	−0.142808	−	0.439517i
$575$	3132.39	+	2275.81i	0.227182	+	0.165057i
$576$	−2382.62	+	1731.07i	−0.172354	+	0.125222i
$577$	3840.80	−	11820.8i	0.277114	−	0.852869i	−0.711538	−	0.702647i	$-0.752001\pi$
$577$	3840.80	−	11820.8i	0.277114	−	0.852869i	0.988652	−	0.150222i	$-0.0479987\pi$
$578$	−384.705	+	1184.00i	−0.0276844	+	0.0852039i
$579$	−15923.5	+	11569.1i	−1.14293	+	0.830389i
$580$	−5248.68	−	3813.39i	−0.375758	−	0.273004i
$581$	−9856.52	−	30335.3i	−0.703817	−	2.16612i
$582$	24174.3			1.72175
$583$		0			0
$584$	−3755.91			−0.266131
$585$	−2076.44	−	6390.63i	−0.146753	−	0.451658i
$586$	12323.9	+	8953.82i	0.868762	+	0.631192i
$587$	−4947.09	+	3594.27i	−0.347851	+	0.252728i	−0.747967	−	0.663736i	$-0.768970\pi$
$587$	−4947.09	+	3594.27i	−0.347851	+	0.252728i	0.400116	+	0.916464i	$0.368970\pi$
$588$	2190.85	−	6742.74i	0.153655	−	0.472902i
$589$	−647.056	+	1991.43i	−0.0452657	+	0.139313i
$590$	−13428.8	+	9756.59i	−0.937042	+	0.680801i
$591$	−7202.45	−	5232.89i	−0.501302	−	0.364217i
$592$	−422.252	−	1299.56i	−0.0293150	−	0.0902222i
$593$	−7188.32			−0.497789			−0.248894	−	0.968531i	$-0.580067\pi$
$593$	−7188.32			−0.497789			−0.248894	+	0.968531i	$0.580067\pi$
$594$		0			0
$595$	−19572.0			−1.34852
$596$	537.390	+	1653.92i	0.0369334	+	0.113669i
$597$	−23945.6	−	17397.5i	−1.64159	−	1.19268i
$598$	−1930.70	+	1402.73i	−0.132027	+	0.0959231i
$599$	−312.782	+	962.644i	−0.0213354	+	0.0656637i	−0.961157	−	0.276001i	$-0.910991\pi$
$599$	−312.782	+	962.644i	−0.0213354	+	0.0656637i	0.939822	+	0.341665i	$0.110991\pi$
$600$	785.898	−	2418.75i	0.0534736	−	0.164575i
$601$	10825.4	−	7865.10i	0.734736	−	0.533817i	−0.156322	−	0.987706i	$-0.549964\pi$
$601$	10825.4	−	7865.10i	0.734736	−	0.533817i	0.891058	+	0.453889i	$0.149964\pi$
$602$	−13426.4	−	9754.86i	−0.909003	−	0.660429i
$603$	−4188.86	−	12892.0i	−0.282891	−	0.870650i
$604$	3123.97			0.210451
$605$		0			0
$606$	3189.28			0.213788
$607$	−169.017	−	520.181i	−0.0113018	−	0.0347834i	0.945247	−	0.326357i	$-0.105821\pi$
$607$	−169.017	−	520.181i	−0.0113018	−	0.0347834i	−0.956548	+	0.291574i	$0.905821\pi$
$608$	−187.695	−	136.369i	−0.0125198	−	0.00909618i
$609$	20654.8	−	15006.6i	1.37434	−	0.998517i
$610$	−2879.19	+	8861.25i	−0.191107	+	0.588166i
$611$	476.903	−	1467.76i	0.0315768	−	0.0971835i
$612$	−9754.16	+	7086.81i	−0.644262	+	0.468084i
$613$	11120.4	+	8079.46i	0.732708	+	0.532343i	0.890419	−	0.455142i	$-0.150412\pi$
$613$	11120.4	+	8079.46i	0.732708	+	0.532343i	−0.157711	+	0.987485i	$0.550412\pi$
$614$	−2534.36	−	7799.96i	−0.166577	−	0.512672i
$615$	14740.1			0.966468
$616$		0			0
$617$	−3323.39			−0.216847			−0.108423	−	0.994105i	$-0.534580\pi$
$617$	−3323.39			−0.216847			−0.108423	+	0.994105i	$0.534580\pi$
$618$	−6194.27	−	19064.0i	−0.403188	−	1.24088i
$619$	17538.7	+	12742.6i	1.13884	+	0.827415i	0.986957	−	0.160983i	$-0.0514665\pi$
$619$	17538.7	+	12742.6i	1.13884	+	0.827415i	0.151882	+	0.988399i	$0.451467\pi$
$620$	11903.1	−	8648.14i	0.771035	−	0.560190i
$621$	−5225.97	+	16083.9i	−0.337699	+	1.03933i
$622$	899.939	−	2769.73i	0.0580133	−	0.178547i
$623$	−4939.75	+	3588.94i	−0.317668	+	0.230799i
$624$	1268.18	+	921.385i	0.0813585	+	0.0591104i
$625$	−5837.74	−	17966.7i	−0.373616	−	1.14987i
$626$	−6923.35			−0.442033
$627$		0			0
$628$	2089.53			0.132773
$629$	−1728.65	−	5320.25i	−0.109580	−	0.337253i
$630$	22247.6	+	16163.8i	1.40693	+	1.02219i
$631$	24180.5	−	17568.2i	1.52553	−	1.10836i	0.566874	−	0.823804i	$-0.308153\pi$
$631$	24180.5	−	17568.2i	1.52553	−	1.10836i	0.958658	−	0.284560i	$-0.0918475\pi$
$632$	−1008.71	+	3104.50i	−0.0634880	+	0.195396i
$633$	−5523.97	+	17001.0i	−0.346853	+	1.06750i
$634$	−8077.73	+	5868.81i	−0.506006	+	0.367635i
$635$	−15977.4	−	11608.3i	−0.998495	−	0.725449i
$636$	5296.21	+	16300.1i	0.330202	+	1.01626i
$637$	−2378.21			−0.147925
$638$		0			0
$639$	6094.75			0.377316
$640$	503.758	+	1550.41i	0.0311137	+	0.0957583i
$641$	−21987.4	−	15974.8i	−1.35484	−	0.984348i	−0.998755	−	0.0498934i	$-0.984112\pi$
$641$	−21987.4	−	15974.8i	−1.35484	−	0.984348i	−0.356084	−	0.934454i	$-0.615888\pi$
$642$	−9854.04	+	7159.38i	−0.605775	+	0.440122i
$643$	5060.00	−	15573.1i	0.310337	−	0.955120i	−0.667294	−	0.744794i	$-0.732548\pi$
$643$	5060.00	−	15573.1i	0.310337	−	0.955120i	0.977631	−	0.210326i	$-0.0674524\pi$
$644$	3018.05	−	9288.60i	0.184671	−	0.568358i
$645$	31140.3	−	22624.7i	1.90100	−	1.38116i
$646$	−768.403	−	558.277i	−0.0467994	−	0.0340017i
$647$	706.928	+	2175.70i	0.0429555	+	0.132203i	0.970234	−	0.242168i	$-0.0778585\pi$
$647$	706.928	+	2175.70i	0.0429555	+	0.132203i	−0.927279	+	0.374371i	$0.877859\pi$
$648$	1168.74			0.0708526
$649$		0			0
$650$	−853.107			−0.0514794
$651$	17891.9	+	55065.6i	1.07717	+	3.31520i
$652$	−8230.25	−	5979.62i	−0.494358	−	0.359172i
$653$	927.881	−	674.145i	0.0556061	−	0.0404002i	−0.559635	−	0.828739i	$-0.689059\pi$
$653$	927.881	−	674.145i	0.0556061	−	0.0404002i	0.615241	+	0.788339i	$0.289059\pi$
$654$	−6586.66	+	20271.7i	−0.393821	+	1.21206i
$655$	−2920.67	+	8988.91i	−0.174229	+	0.536223i
$656$	−1753.22	+	1273.79i	−0.104347	+	0.0758126i
$657$	17478.3	+	12698.7i	1.03789	+	0.754071i
$658$	1951.72	+	6006.78i	0.115632	+	0.355880i
$659$	377.923			0.0223396			0.0111698	−	0.999938i	$-0.496444\pi$
$659$	377.923			0.0223396			0.0111698	+	0.999938i	$0.496444\pi$
$660$		0			0
$661$	−17500.4			−1.02978			−0.514892	−	0.857255i	$-0.672168\pi$
$661$	−17500.4			−1.02978			−0.514892	+	0.857255i	$0.672168\pi$
$662$	6303.50	+	19400.2i	0.370079	+	1.13899i
$663$	5191.77	+	3772.04i	0.304120	+	0.220956i
$664$	−8799.14	+	6392.95i	−0.514266	+	0.373636i
$665$	−669.432	+	2060.30i	−0.0390368	+	0.120143i
$666$	−2428.84	+	7475.20i	−0.141315	+	0.434922i
$667$	10722.5	−	7790.35i	0.622454	−	0.452239i
$668$	4483.38	+	3257.37i	0.259682	+	0.188670i
$669$	9779.33	+	30097.7i	0.565158	+	1.73938i
$670$	−7503.38			−0.432658
$671$		0			0
$672$	−6415.20			−0.368261
$673$	4484.00	+	13800.3i	0.256828	+	0.790437i	0.993464	+	0.114147i	$0.0364134\pi$
$673$	4484.00	+	13800.3i	0.256828	+	0.790437i	−0.736635	+	0.676290i	$0.763587\pi$
$674$	−2719.49	−	1975.82i	−0.155417	−	0.112917i
$675$	−4890.91	+	3553.45i	−0.278890	+	0.202626i
$676$	−2553.15	+	7857.79i	−0.145264	+	0.447075i
$677$	−144.963	+	446.150i	−0.00822950	+	0.0253278i	−0.955087	−	0.296326i	$-0.904239\pi$
$677$	−144.963	+	446.150i	−0.00822950	+	0.0253278i	0.946857	+	0.321654i	$0.104239\pi$
$678$	13577.2	−	9864.44i	0.769072	−	0.558763i
$679$	26848.4	+	19506.5i	1.51745	+	1.10249i
$680$	2062.33	+	6347.20i	0.116304	+	0.357947i
$681$	41473.1			2.33370
$682$		0			0
$683$	−15892.3			−0.890342			−0.445171	−	0.895446i	$-0.646857\pi$
$683$	−15892.3			−0.890342			−0.445171	+	0.895446i	$0.646857\pi$
$684$	412.386	+	1269.20i	0.0230526	+	0.0709487i
$685$	−5313.32	−	3860.35i	−0.296367	−	0.215323i
$686$	−5146.59	+	3739.21i	−0.286440	+	0.208111i
$687$	−3530.00	+	10864.2i	−0.196038	+	0.603342i
$688$	−1748.74	+	5382.08i	−0.0969043	+	0.298241i
$689$	4651.15	−	3379.25i	0.257176	−	0.186850i
$690$	18325.9	+	13314.5i	1.01109	+	0.734602i
$691$	−1917.65	−	5901.91i	−0.105573	−	0.324920i	0.884292	−	0.466935i	$-0.154642\pi$
$691$	−1917.65	−	5901.91i	−0.105573	−	0.324920i	−0.989864	+	0.142015i	$0.954642\pi$
$692$	1774.04			0.0974553
$693$		0			0
$694$	−21052.5			−1.15150
$695$	−9694.07	−	29835.3i	−0.529089	−	1.62837i
$696$	−7043.06	−	5117.09i	−0.383573	−	0.278682i
$697$	−7177.48	+	5214.75i	−0.390052	+	0.283390i
$698$	3275.80	−	10081.9i	0.177638	−	0.546712i
$699$	15589.5	−	47979.7i	0.843563	−	2.59622i
$700$	2824.55	−	2052.15i	0.152511	−	0.110806i
$701$	1514.91	+	1100.65i	0.0816228	+	0.0593024i	0.627848	−	0.778336i	$-0.283936\pi$
$701$	1514.91	+	1100.65i	0.0816228	+	0.0593024i	−0.546226	+	0.837638i	$0.683936\pi$
$702$	−1151.47	−	3543.86i	−0.0619080	−	0.190533i
$703$	−619.178			−0.0332187
$704$		0			0
$705$	−14648.7			−0.782554
$706$	−4597.18	−	14148.7i	−0.245067	−	0.754239i
$707$	3542.07	+	2573.47i	0.188420	+	0.136895i
$708$	−18019.7	+	13092.1i	−0.956530	+	0.694960i
$709$	1618.02	−	4979.74i	0.0857065	−	0.263777i	−0.899014	−	0.437920i	$-0.855715\pi$
$709$	1618.02	−	4979.74i	0.0857065	−	0.263777i	0.984720	+	0.174142i	$0.0557153\pi$
$710$	1042.51	−	3208.53i	0.0551055	−	0.169597i
$711$	15190.4	−	11036.5i	0.801244	−	0.582138i
$712$	1684.40	+	1223.79i	0.0886597	+	0.0644151i
$713$	9288.21	+	28586.2i	0.487863	+	1.50149i
$714$	−26263.1			−1.37657
$715$		0			0
$716$	1506.56			0.0786349
$717$	8766.05	+	26979.1i	0.456589	+	1.40524i
$718$	16425.2	+	11933.6i	0.853735	+	0.620275i
$719$	13975.6	−	10153.9i	0.724898	−	0.526669i	−0.163047	−	0.986618i	$-0.552132\pi$
$719$	13975.6	−	10153.9i	0.724898	−	0.526669i	0.887945	+	0.459949i	$0.152132\pi$
$720$	2897.67	−	8918.11i	0.149986	−	0.461609i
$721$	8503.49	−	26171.1i	0.439232	−	1.35182i
$722$	11013.0	−	8001.45i	0.567677	−	0.412442i
$723$	−36472.9	−	26499.1i	−1.87613	−	1.36309i
$724$	4071.31	+	12530.2i	0.208990	+	0.643206i
$725$	4737.89			0.242705
$726$		0			0
$727$	17292.7			0.882190			0.441095	−	0.897461i	$-0.354590\pi$
$727$	17292.7			0.882190			0.441095	+	0.897461i	$0.354590\pi$
$728$	664.985	+	2046.61i	0.0338544	+	0.104193i
$729$	24891.9	+	18085.0i	1.26464	+	0.918813i
$730$	9674.82	−	7029.17i	0.490522	−	0.356385i
$731$	−7159.15	+	22033.6i	−0.362231	+	1.11483i
$732$	−3863.51	+	11890.7i	−0.195081	+	0.600398i
$733$	−11230.2	+	8159.25i	−0.565891	+	0.411144i	−0.833610	−	0.552353i	$-0.813730\pi$
$733$	−11230.2	+	8159.25i	−0.565891	+	0.411144i	0.267719	+	0.963497i	$0.413730\pi$
$734$	−771.483	−	560.515i	−0.0387956	−	0.0281866i
$735$	6975.62	+	21468.7i	0.350067	+	1.07740i
$736$	−3330.32			−0.166790
$737$		0			0
$738$	12465.4			0.621757
$739$	−1971.30	−	6067.04i	−0.0981265	−	0.302002i	0.889929	−	0.456098i	$-0.150753\pi$
$739$	−1971.30	−	6067.04i	−0.0981265	−	0.302002i	−0.988056	+	0.154096i	$0.950753\pi$
$740$	3519.79	+	2557.28i	0.174852	+	0.127037i
$741$	574.653	−	417.510i	0.0284891	−	0.0206985i
$742$	−7270.63	+	22376.7i	−0.359722	+	1.10711i
$743$	−7120.59	+	21914.9i	−0.351587	+	1.08207i	0.606375	+	0.795179i	$0.292623\pi$
$743$	−7120.59	+	21914.9i	−0.351587	+	1.08207i	−0.957962	+	0.286895i	$0.907377\pi$
$744$	15972.5	−	11604.7i	0.787071	−	0.571840i
$745$	−4479.55	−	3254.58i	−0.220293	−	0.160052i
$746$	7872.81	+	24230.0i	0.386386	+	1.18917i
$747$	62561.8			3.06428
$748$		0			0
$749$	−16721.1			−0.815720
$750$	−5905.16	−	18174.2i	−0.287501	−	0.884838i
$751$	16832.5	+	12229.5i	0.817878	+	0.594223i	0.916104	−	0.400941i	$-0.131317\pi$
$751$	16832.5	+	12229.5i	0.817878	+	0.594223i	−0.0982261	+	0.995164i	$0.531317\pi$
$752$	1742.35	−	1265.89i	0.0844905	−	0.0613859i
$753$	−5180.36	+	15943.5i	−0.250707	+	0.771598i
$754$	−902.414	+	2777.35i	−0.0435862	+	0.134145i
$755$	−8047.01	+	5846.49i	−0.387895	+	0.281822i
$756$	12337.2	+	8963.47i	0.593516	+	0.431215i
$757$	−6748.23	−	20768.9i	−0.324001	−	0.997173i	−0.971890	−	0.235437i	$-0.924348\pi$
$757$	−6748.23	−	20768.9i	−0.324001	−	0.997173i	0.647888	−	0.761735i	$-0.275652\pi$
$758$	−2597.38			−0.124460
$759$		0			0
$760$	738.696			0.0352570
$761$	2206.21	+	6790.03i	0.105092	+	0.323441i	0.989752	−	0.142796i	$-0.0456094\pi$
$761$	2206.21	+	6790.03i	0.105092	+	0.323441i	−0.884660	+	0.466237i	$0.845609\pi$
$762$	−21439.7	−	15576.8i	−1.01926	−	0.740537i
$763$	−23672.7	+	17199.2i	−1.12321	+	0.816060i
$764$	2830.92	−	8712.68i	0.134056	−	0.412583i
$765$	11862.7	−	36509.7i	0.560651	−	1.72551i
$766$	1085.00	−	788.299i	0.0511784	−	0.0371833i
$767$	6044.61	+	4391.67i	0.284561	+	0.206746i
$768$	675.980	+	2080.45i	0.0317608	+	0.0977498i
$769$	−15473.8			−0.725618			−0.362809	−	0.931864i	$-0.618182\pi$
$769$	−15473.8			−0.725618			−0.362809	+	0.931864i	$0.618182\pi$
$770$		0			0
$771$	50774.0			2.37170
$772$	2847.16	+	8762.65i	0.132735	+	0.408516i
$773$	−12330.1	−	8958.37i	−0.573718	−	0.416831i	0.262736	−	0.964868i	$-0.415375\pi$
$773$	−12330.1	−	8958.37i	−0.573718	−	0.416831i	−0.836454	+	0.548037i	$0.815375\pi$
$774$	26334.7	−	19133.2i	1.22297	−	0.888541i
$775$	−3320.31	+	10218.9i	−0.153896	+	0.473642i
$776$	3496.91	−	10762.4i	0.161768	−	0.497870i
$777$	−13851.2	+	10063.5i	−0.639523	+	0.464640i
$778$	−8471.87	−	6155.17i	−0.390400	−	0.283642i
$779$	303.450	+	933.922i	0.0139566	+	0.0429541i
$780$	−4991.05			−0.229113
$781$		0			0
$782$	−13633.9			−0.623464
$783$	6394.90	+	19681.5i	0.291871	+	0.898287i
$784$	−2684.95	−	1950.73i	−0.122310	−	0.0888635i
$785$	−5382.40	+	3910.54i	−0.244721	+	0.177800i
$786$	−3919.18	+	12062.0i	−0.177853	+	0.547375i
$787$	−11149.8	+	34315.5i	−0.505015	+	1.55428i	0.295731	+	0.955271i	$0.404437\pi$
$787$	−11149.8	+	34315.5i	−0.505015	+	1.55428i	−0.800746	+	0.599004i	$0.795563\pi$
$788$	−3371.54	+	2449.57i	−0.152419	+	0.110739i
$789$	−11780.6	−	8559.10i	−0.531559	−	0.386200i
$790$	−3211.72	−	9884.65i	−0.144643	−	0.445165i
$791$	23038.9			1.03561
$792$		0			0
$793$	4193.91			0.187806
$794$	1082.58	+	3331.83i	0.0483869	+	0.148919i
$795$	−44147.9	−	32075.3i	−1.96952	−	1.43094i
$796$	−11209.2	+	8143.96i	−0.499120	+	0.362632i
$797$	1045.55	−	3217.89i	0.0464686	−	0.143016i	−0.925130	−	0.379650i	$-0.876044\pi$
$797$	1045.55	−	3217.89i	0.0464686	−	0.143016i	0.971599	+	0.236635i	$0.0760444\pi$
$798$	−898.293	+	2764.66i	−0.0398487	+	0.122642i
$799$	7132.97	−	5182.40i	0.315828	−	0.229462i
$800$	−963.142	−	699.764i	−0.0425653	−	0.0309255i
$801$	−3700.82	−	11389.9i	−0.163248	−	0.502427i
$802$	7225.55			0.318134
$803$		0			0
$804$	−10068.6			−0.441656
$805$	9609.40	+	29574.7i	0.420729	+	1.29487i
$806$	−5357.88	−	3892.73i	−0.234148	−	0.170118i
$807$	40409.0	−	29358.9i	1.76266	−	1.28065i
$808$	461.342	−	1419.87i	0.0200866	−	0.0618202i
$809$	−4165.63	+	12820.5i	−0.181033	+	0.557162i	−0.999857	−	0.0168817i	$-0.994626\pi$
$809$	−4165.63	+	12820.5i	−0.181033	+	0.557162i	0.818825	+	0.574044i	$0.194626\pi$
$810$	−3010.55	+	2187.29i	−0.130593	+	0.0948811i
$811$	−17331.6	−	12592.2i	−0.750427	−	0.545217i	0.145532	−	0.989354i	$-0.453511\pi$
$811$	−17331.6	−	12592.2i	−0.750427	−	0.545217i	−0.895959	+	0.444136i	$0.853511\pi$
$812$	−3693.12	−	11366.3i	−0.159610	−	0.491229i
$813$	−50465.3			−2.17699
$814$		0			0
$815$	32391.1			1.39216
$816$	2767.38	+	8517.13i	0.118723	+	0.365391i
$817$	2074.56	+	1507.26i	0.0888370	+	0.0645438i
$818$	−18275.7	+	13278.0i	−0.781165	+	0.567550i
$819$	3825.06	−	11772.3i	0.163197	−	0.502269i
$820$	2132.22	−	6562.28i	0.0908051	−	0.279469i
$821$	8628.01	−	6268.62i	0.366772	−	0.266475i	−0.389099	−	0.921196i	$-0.627214\pi$
$821$	8628.01	−	6268.62i	0.366772	−	0.266475i	0.755871	+	0.654720i	$0.227214\pi$
$822$	−7129.80	−	5180.11i	−0.302531	−	0.219802i
$823$	−3707.24	−	11409.7i	−0.157019	−	0.483254i	0.841341	−	0.540504i	$-0.181767\pi$
$823$	−3707.24	−	11409.7i	−0.157019	−	0.483254i	−0.998360	+	0.0572506i	$0.981767\pi$
$824$	−9383.31			−0.396703
$825$		0			0
$826$	−30577.2			−1.28804
$827$	−12632.8	−	38879.9i	−0.531181	−	1.63481i	−0.751759	−	0.659438i	$-0.770794\pi$
$827$	−12632.8	−	38879.9i	−0.531181	−	1.63481i	0.220578	−	0.975369i	$-0.429206\pi$
$828$	15497.8	+	11259.8i	0.650465	+	0.472591i
$829$	26889.3	−	19536.2i	1.12654	−	0.818480i	0.141354	−	0.989959i	$-0.454855\pi$
$829$	26889.3	−	19536.2i	1.12654	−	0.818480i	0.985188	+	0.171479i	$0.0548545\pi$
$830$	10701.3	−	32935.1i	0.447526	−	1.37734i
$831$	−23454.3	+	72185.1i	−0.979088	+	3.01332i
$832$	593.647	−	431.310i	0.0247368	−	0.0179723i
$833$	−10991.9	−	7986.07i	−0.457199	−	0.332174i
$834$	−13008.2	−	40035.1i	−0.540093	−	1.66223i
$835$	−17644.9			−0.731288
$836$		0			0
$837$	−46931.4			−1.93809
$838$	−2274.64	−	7000.63i	−0.0937663	−	0.288583i
$839$	5152.28	+	3743.35i	0.212010	+	0.154034i	0.688723	−	0.725025i	$-0.258172\pi$
$839$	5152.28	+	3743.35i	0.212010	+	0.154034i	−0.476713	+	0.879059i	$0.658172\pi$
$840$	16524.9	−	12006.0i	0.678764	−	0.493151i
$841$	−2524.89	+	7770.80i	−0.103526	+	0.318619i
$842$	5720.63	−	17606.3i	0.234140	−	0.720609i
$843$	−56353.5	+	40943.2i	−2.30239	+	1.67279i
$844$	6769.78	+	4918.54i	0.276097	+	0.200596i
$845$	−8129.18	−	25019.0i	−0.330949	−	1.01856i
$846$	−12388.1			−0.503440
$847$		0			0
$848$	8022.90			0.324891
$849$	−15484.1	−	47655.0i	−0.625926	−	1.92640i
$850$	−3942.99	−	2864.75i	−0.159110	−	0.115600i
$851$	−7190.56	+	5224.25i	−0.289647	+	0.210441i
$852$	1398.92	−	4305.44i	0.0562515	−	0.173124i
$853$	−938.303	+	2887.80i	−0.0376634	+	0.115916i	−0.968121	−	0.250485i	$-0.919410\pi$
$853$	−938.303	+	2887.80i	−0.0376634	+	0.115916i	0.930457	+	0.366401i	$0.119410\pi$
$854$	−13885.6	+	10088.5i	−0.556388	+	0.404240i
$855$	−3437.56	−	2497.53i	−0.137499	−	0.0998991i
$856$	1761.93	+	5422.65i	0.0703521	+	0.216521i
$857$	10184.8			0.405959			0.202979	−	0.979183i	$-0.434938\pi$
$857$	10184.8			0.405959			0.202979	+	0.979183i	$0.434938\pi$
$858$		0			0
$859$	−34929.8			−1.38742			−0.693708	−	0.720256i	$-0.744024\pi$
$859$	−34929.8			−1.38742			−0.693708	+	0.720256i	$0.744024\pi$
$860$	−5567.96	−	17136.4i	−0.220774	−	0.679473i
$861$	21967.3	+	15960.2i	0.869504	+	0.631732i
$862$	5799.10	−	4213.29i	0.229139	−	0.166479i
$863$	−3795.73	+	11682.1i	−0.149720	+	0.460791i	−0.997588	−	0.0694172i	$-0.977886\pi$
$863$	−3795.73	+	11682.1i	−0.149720	+	0.460791i	0.847868	+	0.530208i	$0.177886\pi$
$864$	1606.87	−	4945.44i	0.0632719	−	0.194731i
$865$	−4569.75	+	3320.11i	−0.179625	+	0.130506i
$866$	13440.7	+	9765.23i	0.527406	+	0.383183i
$867$	−1643.65	−	5058.63i	−0.0643843	−	0.198155i
$868$	27103.3			1.05985
$869$		0			0
$870$	27718.8			1.08018
$871$	1043.69	+	3212.14i	0.0406016	+	0.124959i
$872$	8072.15	+	5864.76i	0.313483	+	0.227759i
$873$	−52660.7	+	38260.2i	−2.04157	+	1.48329i
$874$	−466.330	+	1435.22i	−0.0180479	+	0.0555457i
$875$	8106.60	−	24949.5i	0.313204	−	0.963941i
$876$	12982.4	−	9432.25i	0.500724	−	0.363797i
$877$	15482.9	+	11249.0i	0.596146	+	0.433125i	0.844509	−	0.535542i	$-0.179893\pi$
$877$	15482.9	+	11249.0i	0.596146	+	0.433125i	−0.248363	+	0.968667i	$0.579893\pi$
$878$	−7374.60	−	22696.7i	−0.283463	−	0.872410i
$879$	−65083.5			−2.49740
$880$		0			0
$881$	−16737.0			−0.640049			−0.320024	−	0.947409i	$-0.603691\pi$
$881$	−16737.0			−0.640049			−0.320024	+	0.947409i	$0.603691\pi$
$882$	5899.13	+	18155.6i	0.225209	+	0.693121i
$883$	15051.1	+	10935.3i	0.573625	+	0.416763i	0.836420	−	0.548089i	$-0.184644\pi$
$883$	15051.1	+	10935.3i	0.573625	+	0.416763i	−0.262795	+	0.964852i	$0.584644\pi$
$884$	2430.32	−	1765.73i	0.0924668	−	0.0671811i
$885$	21915.1	−	67447.7i	0.832393	−	2.56184i
$886$	666.748	−	2052.04i	0.0252820	−	0.0778100i
$887$	12873.7	−	9353.32i	0.487326	−	0.354063i	−0.316829	−	0.948483i	$-0.602618\pi$
$887$	12873.7	−	9353.32i	0.487326	−	0.354063i	0.804155	+	0.594420i	$0.202618\pi$
$888$	4723.12	+	3431.55i	0.178488	+	0.129679i
$889$	−11242.2	−	34599.8i	−0.424128	−	1.30533i
$890$	−6629.16			−0.249674
$891$		0			0
$892$	14814.1			0.556068
$893$	−301.568	−	928.130i	−0.0113008	−	0.0347802i
$894$	−6010.99	−	4367.24i	−0.224874	−	0.163381i
$895$	−3880.72	+	2819.51i	−0.144937	+	0.105303i
$896$	−927.985	+	2856.04i	−0.0346002	+	0.106489i
$897$	3150.80	−	9697.15i	0.117282	−	0.360957i
$898$	−20655.7	+	15007.3i	−0.767584	+	0.557682i
$899$	29756.0	+	21619.0i	1.10391	+	0.802040i
$900$	2116.13	+	6512.77i	0.0783750	+	0.241214i
$901$	32844.8			1.21445
$902$		0			0
$903$	70906.1			2.61308
$904$	−2427.64	−	7471.51i	−0.0893165	−	0.274888i
$905$	−33937.5	−	24657.0i	−1.24654	−	0.905665i
$906$	−10798.1	+	7845.25i	−0.395962	+	0.287683i
$907$	−6969.97	+	21451.4i	−0.255164	+	0.785315i	0.738633	+	0.674108i	$0.235472\pi$
$907$	−6969.97	+	21451.4i	−0.255164	+	0.785315i	−0.993797	+	0.111207i	$0.964528\pi$
$908$	5999.26	−	18463.8i	0.219265	−	0.674827i
$909$	−6947.44	+	5047.61i	−0.253501	+	0.184179i
$910$	−5543.16	−	4027.34i	−0.201927	−	0.146709i
$911$	14943.9	+	45992.7i	0.543485	+	1.67268i	0.724564	+	0.689207i	$0.242041\pi$
$911$	14943.9	+	45992.7i	0.543485	+	1.67268i	−0.181079	+	0.983469i	$0.557959\pi$
$912$	991.236			0.0359902
$913$		0			0
$914$	22453.6			0.812583
$915$	−12301.3	−	37859.6i	−0.444448	−	1.36787i
$916$	4326.12	+	3143.11i	0.156047	+	0.113375i
$917$	−14085.7	+	10233.8i	−0.507251	+	0.368540i
$918$	6578.35	−	20246.1i	0.236512	−	0.727909i
$919$	−6493.77	+	19985.8i	−0.233090	+	0.717378i	0.764279	+	0.644886i	$0.223095\pi$
$919$	−6493.77	+	19985.8i	−0.233090	+	0.717378i	−0.997369	+	0.0724918i	$0.976905\pi$
$920$	8578.53	−	6232.67i	0.307419	−	0.223353i
$921$	28348.2	+	20596.1i	1.01423	+	0.736880i
$922$	1335.31	+	4109.67i	0.0476966	+	0.146795i
$923$	−1518.56			−0.0541537
$924$		0			0
$925$	−3177.26			−0.112938
$926$	7088.51	+	21816.2i	0.251558	+	0.774217i
$927$	43665.7	+	31725.0i	1.54711	+	1.12404i
$928$	−3296.93	+	2395.36i	−0.116624	+	0.0847324i
$929$	1520.26	−	4678.88i	0.0536901	−	0.165241i	−0.920616	−	0.390469i	$-0.872313\pi$
$929$	1520.26	−	4678.88i	0.0536901	−	0.165241i	0.974306	+	0.225228i	$0.0723127\pi$
$930$	−19425.3	+	59785.0i	−0.684926	+	2.10798i
$931$	−1216.64	+	883.941i	−0.0428290	+	0.0311171i
$932$	−19105.4	−	13880.9i	−0.671480	−	0.487859i
$933$	3844.98	+	11833.6i	0.134919	+	0.415237i
$934$	4036.78			0.141421
$935$		0			0
$936$	−4220.83			−0.147395
$937$	5309.00	+	16339.4i	0.185099	+	0.569675i	0.999950	−	0.00999505i	$-0.00318158\pi$
$937$	5309.00	+	16339.4i	0.185099	+	0.569675i	−0.814852	+	0.579670i	$0.803182\pi$
$938$	−11182.3	−	8124.45i	−0.389250	−	0.282807i
$939$	23930.7	−	17386.7i	0.831682	−	0.604252i
$940$	−2118.99	+	6521.58i	−0.0735254	+	0.226288i
$941$	15910.3	−	48966.9i	0.551181	−	1.69636i	−0.154639	−	0.987971i	$-0.549421\pi$
$941$	15910.3	−	48966.9i	0.551181	−	1.69636i	0.705820	−	0.708391i	$-0.250579\pi$
$942$	−7222.49	+	5247.45i	−0.249811	+	0.181498i
$943$	11403.9	+	8285.39i	0.393808	+	0.286118i
$944$	3221.97	+	9916.21i	0.111087	+	0.341891i
$945$	−48554.3			−1.67140
$946$		0			0
$947$	45107.8			1.54784			0.773920	−	0.633283i	$-0.218293\pi$
$947$	45107.8			1.54784			0.773920	+	0.633283i	$0.218293\pi$
$948$	−4309.72	−	13263.9i	−0.147651	−	0.454423i
$949$	−4354.86	−	3163.99i	−0.148962	−	0.108227i
$950$	−436.431	+	317.086i	−0.0149049	+	0.0108291i
$951$	13182.4	−	40571.3i	0.449495	−	1.38340i
$952$	−3799.07	+	11692.3i	−0.129337	+	0.398057i
$953$	20537.5	−	14921.4i	0.698085	−	0.507189i	−0.181223	−	0.983442i	$-0.558006\pi$
$953$	20537.5	−	14921.4i	0.698085	−	0.507189i	0.879308	+	0.476253i	$0.158006\pi$
$954$	−37334.9	−	27125.4i	−1.26705	−	0.920564i
$955$	9013.59	+	27741.0i	0.305417	+	0.939975i
$956$	13279.1			0.449245
$957$		0			0
$958$	14654.0			0.494206
$959$	−3738.61	−	11506.2i	−0.125887	−	0.387441i
$960$	−5634.81	−	4093.93i	−0.189440	−	0.137636i
$961$	−43380.3	+	31517.6i	−1.45615	+	1.05796i
$962$	605.164	−	1862.50i	0.0202820	−	0.0624215i
$963$	10134.8	−	31191.6i	0.339136	−	1.04375i
$964$	−17073.3	+	12404.5i	−0.570431	+	0.414442i
$965$	−23733.2	−	17243.2i	−0.791709	−	0.575211i
$966$	12894.6	+	39685.5i	0.429479	+	1.32180i
$967$	−26837.3			−0.892482			−0.446241	−	0.894913i	$-0.647238\pi$
$967$	−26837.3			−0.892482			−0.446241	+	0.894913i	$0.647238\pi$
$968$		0			0
$969$	4058.01			0.134532
$970$	11134.1	+	34267.2i	0.368551	+	1.13428i
$971$	4410.63	+	3204.51i	0.145771	+	0.105909i	0.658281	−	0.752773i	$-0.271284\pi$
$971$	4410.63	+	3204.51i	0.145771	+	0.105909i	−0.512509	+	0.858682i	$0.671284\pi$
$972$	10158.3	−	7380.46i	0.335214	−	0.243548i
$973$	17857.7	−	54960.2i	0.588377	−	1.81084i
$974$	−3825.51	+	11773.7i	−0.125849	+	0.387324i
$975$	2948.78	−	2142.42i	0.0968581	−	0.0703715i
$976$	4734.85	+	3440.07i	0.155286	+	0.112822i
$977$	−1115.01	−	3431.64i	−0.0365120	−	0.112372i	0.931139	−	0.364663i	$-0.118816\pi$
$977$	−1115.01	−	3431.64i	−0.0365120	−	0.112372i	−0.967651	+	0.252291i	$0.918816\pi$
$978$	43464.7			1.42111
$979$		0			0
$980$	10566.9			0.344437
$981$	−17735.4	−	54583.9i	−0.577214	−	1.77648i
$982$	−16376.0	−	11897.9i	−0.532158	−	0.386635i
$983$	−46959.8	+	34118.3i	−1.52369	+	1.10702i	−0.564067	+	0.825729i	$0.690764\pi$
$983$	−46959.8	+	34118.3i	−1.52369	+	1.10702i	−0.959621	+	0.281295i	$0.909236\pi$
$984$	2861.16	−	8805.75i	0.0926936	−	0.285282i
$985$	4100.37	−	12619.7i	0.132638	−	0.408219i
$986$	−13497.3	+	9806.34i	−0.435944	+	0.316732i
$987$	−21831.0	−	15861.2i	−0.704042	−	0.511517i
$988$	−102.749	−	316.230i	−0.00330859	−	0.0101828i
$989$	36809.4			1.18349
$990$		0			0
$991$	−18977.5			−0.608315			−0.304157	−	0.952622i	$-0.598375\pi$
$991$	−18977.5			−0.608315			−0.304157	+	0.952622i	$0.598375\pi$
$992$	−2855.92	−	8789.63i	−0.0914069	−	0.281322i
$993$	−70508.0	−	51227.0i	−2.25328	−	1.63710i
$994$	5027.78	−	3652.89i	0.160434	−	0.116562i
$995$	13632.3	−	41955.9i	0.434345	−	1.33678i
$996$	14359.7	−	44194.7i	0.456833	−	1.40599i
$997$	−19626.9	+	14259.8i	−0.623462	+	0.452971i	−0.854129	−	0.520061i	$-0.825909\pi$
$997$	−19626.9	+	14259.8i	−0.623462	+	0.452971i	0.230667	+	0.973033i	$0.425909\pi$
$998$	−4146.72	−	3012.77i	−0.131525	−	0.0955585i
$999$	−4288.46	−	13198.5i	−0.135817	−	0.418001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.4.c.n.27.1		8
11.2	odd	10		242.4.c.r.9.1		8
11.3	even	5		242.4.a.o.1.4		4
11.4	even	5		242.4.c.q.3.2		8
11.5	even	5		242.4.c.q.81.2		8
11.6	odd	10		22.4.c.b.15.2	yes	8
11.7	odd	10		22.4.c.b.3.2	✓	8
11.8	odd	10		242.4.a.n.1.4		4
11.9	even	5	inner	242.4.c.n.9.1		8
11.10	odd	2		242.4.c.r.27.1		8
33.8	even	10		2178.4.a.by.1.2		4
33.14	odd	10		2178.4.a.bt.1.2		4
33.17	even	10		198.4.f.d.37.2		8
33.29	even	10		198.4.f.d.91.2		8
44.3	odd	10		1936.4.a.bm.1.1		4
44.7	even	10		176.4.m.b.113.1		8
44.19	even	10		1936.4.a.bn.1.1		4
44.39	even	10		176.4.m.b.81.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.4.c.b.3.2	✓	8	11.7	odd	10
22.4.c.b.15.2	yes	8	11.6	odd	10
176.4.m.b.81.1		8	44.39	even	10
176.4.m.b.113.1		8	44.7	even	10
198.4.f.d.37.2		8	33.17	even	10
198.4.f.d.91.2		8	33.29	even	10
242.4.a.n.1.4		4	11.8	odd	10
242.4.a.o.1.4		4	11.3	even	5
242.4.c.n.9.1		8	11.9	even	5	inner
242.4.c.n.27.1		8	1.1	even	1	trivial
242.4.c.q.3.2		8	11.4	even	5
242.4.c.q.81.2		8	11.5	even	5
242.4.c.r.9.1		8	11.2	odd	10
242.4.c.r.27.1		8	11.10	odd	2
1936.4.a.bm.1.1		4	44.3	odd	10
1936.4.a.bn.1.1		4	44.19	even	10
2178.4.a.bt.1.2		4	33.14	odd	10
2178.4.a.by.1.2		4	33.8	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	242.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.618034 + 1.90211i) q^{2} +(-6.91304 - 5.02262i) q^{3} +(-3.23607 + 2.35114i) q^{4} +(3.93561 - 12.1126i) q^{5} +(5.28109 - 16.2535i) q^{6} +(18.9804 - 13.7901i) q^{7} +(-6.47214 - 4.70228i) q^{8} +(14.2200 + 43.7646i) q^{9} +O(q^{10})\)	\(q+(0.618034 + 1.90211i) q^{2} +(-6.91304 - 5.02262i) q^{3} +(-3.23607 + 2.35114i) q^{4} +(3.93561 - 12.1126i) q^{5} +(5.28109 - 16.2535i) q^{6} +(18.9804 - 13.7901i) q^{7} +(-6.47214 - 4.70228i) q^{8} +(14.2200 + 43.7646i) q^{9} +25.4718 q^{10} +34.1799 q^{12} +(-3.54302 - 10.9043i) q^{13} +(37.9609 + 27.5802i) q^{14} +(-88.0439 + 63.9676i) q^{15} +(4.94427 - 15.2169i) q^{16} +(20.2413 - 62.2963i) q^{17} +(-74.4568 + 54.0960i) q^{18} +(-5.86548 - 4.26152i) q^{19} +(15.7425 + 48.4503i) q^{20} -200.475 q^{21} -104.072 q^{23} +(21.1244 + 65.0141i) q^{24} +(-30.0982 - 21.8676i) q^{25} +(18.5515 - 13.4784i) q^{26} +(50.2148 - 154.545i) q^{27} +(-28.9995 + 89.2514i) q^{28} +(-103.029 + 74.8551i) q^{29} +(-176.088 - 127.935i) q^{30} +(-89.2476 - 274.676i) q^{31} +32.0000 q^{32} +131.004 q^{34} +(-92.3339 - 284.174i) q^{35} +(-148.914 - 108.192i) q^{36} +(69.0919 - 50.1982i) q^{37} +(4.48082 - 13.7906i) q^{38} +(-30.2750 + 93.1770i) q^{39} +(-82.4285 + 59.8878i) q^{40} +(-109.576 - 79.6118i) q^{41} +(-123.900 - 381.326i) q^{42} -353.691 q^{43} +586.066 q^{45} +(-64.3203 - 197.957i) q^{46} +(108.897 + 79.1180i) q^{47} +(-110.609 + 80.3619i) q^{48} +(64.0975 - 197.272i) q^{49} +(22.9930 - 70.7651i) q^{50} +(-452.819 + 328.992i) q^{51} +(37.1030 + 26.9569i) q^{52} +(154.951 + 476.889i) q^{53} +324.997 q^{54} -187.689 q^{56} +(19.1443 + 58.9201i) q^{57} +(-206.058 - 149.710i) q^{58} +(-527.202 + 383.035i) q^{59} +(134.519 - 414.007i) q^{60} +(-113.034 + 347.884i) q^{61} +(467.306 - 339.518i) q^{62} +(873.419 + 634.576i) q^{63} +(19.7771 + 60.8676i) q^{64} -146.023 q^{65} -294.576 q^{67} +(80.9651 + 249.185i) q^{68} +(719.456 + 522.716i) q^{69} +(483.466 - 351.259i) q^{70} +(40.9282 - 125.964i) q^{71} +(113.760 - 350.117i) q^{72} +(379.825 - 275.959i) q^{73} +(138.184 + 100.396i) q^{74} +(98.2373 + 302.343i) q^{75} +29.0005 q^{76} -195.944 q^{78} +(-126.089 - 388.062i) q^{79} +(-164.857 - 119.776i) q^{80} +(-118.192 + 85.8712i) q^{81} +(83.7088 - 257.629i) q^{82} +(420.122 - 1293.00i) q^{83} +(648.751 - 471.345i) q^{84} +(-674.906 - 490.348i) q^{85} +(-218.593 - 672.760i) q^{86} +1088.21 q^{87} -260.255 q^{89} +(362.209 + 1114.76i) q^{90} +(-217.619 - 158.110i) q^{91} +(336.785 - 244.689i) q^{92} +(-762.620 + 2347.10i) q^{93} +(-83.1896 + 256.031i) q^{94} +(-74.7022 + 54.2743i) q^{95} +(-221.217 - 160.724i) q^{96} +(437.114 + 1345.30i) q^{97} +414.848 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 7 q^{3} - 8 q^{4} - 30 q^{5} + 6 q^{6} - 4 q^{7} - 16 q^{8} - 81 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 7 * q^3 - 8 * q^4 - 30 * q^5 + 6 * q^6 - 4 * q^7 - 16 * q^8 - 81 * q^9	\( 8 q - 4 q^{2} - 7 q^{3} - 8 q^{4} - 30 q^{5} + 6 q^{6} - 4 q^{7} - 16 q^{8} - 81 q^{9} + 100 q^{10} + 32 q^{12} + 48 q^{13} - 8 q^{14} - 279 q^{15} - 32 q^{16} + 109 q^{17} - 42 q^{18} - 288 q^{19} - 120 q^{20} + 50 q^{21} + 628 q^{23} + 24 q^{24} + 38 q^{25} - 14 q^{26} + 242 q^{27} + 4 q^{28} - 528 q^{29} - 558 q^{30} - 522 q^{31} + 256 q^{32} + 208 q^{34} + 17 q^{35} - 84 q^{36} - 406 q^{37} + 544 q^{38} + 1429 q^{39} + 40 q^{40} + 329 q^{41} - 1480 q^{42} - 1442 q^{43} + 2652 q^{45} - 1044 q^{46} + 666 q^{47} - 112 q^{48} - 114 q^{49} - 34 q^{50} - 1158 q^{51} - 28 q^{52} + 414 q^{53} + 1144 q^{54} + 48 q^{56} + 593 q^{57} - 1056 q^{58} - 888 q^{59} + 844 q^{60} + 302 q^{61} + 646 q^{62} + 2061 q^{63} - 128 q^{64} + 138 q^{65} + 578 q^{67} + 436 q^{68} + 1930 q^{69} + 1394 q^{70} + 1090 q^{71} - 648 q^{72} - 253 q^{73} - 812 q^{74} + 2763 q^{75} + 128 q^{76} - 4152 q^{78} + 674 q^{79} + 80 q^{80} - 230 q^{81} - 722 q^{82} + 428 q^{83} + 2860 q^{84} - 1046 q^{85} - 984 q^{86} - 2122 q^{87} - 2202 q^{89} - 1366 q^{90} - 2217 q^{91} + 832 q^{92} - 3721 q^{93} - 2138 q^{94} + 973 q^{95} - 224 q^{96} + 3012 q^{97} + 3292 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 7 * q^3 - 8 * q^4 - 30 * q^5 + 6 * q^6 - 4 * q^7 - 16 * q^8 - 81 * q^9 + 100 * q^10 + 32 * q^12 + 48 * q^13 - 8 * q^14 - 279 * q^15 - 32 * q^16 + 109 * q^17 - 42 * q^18 - 288 * q^19 - 120 * q^20 + 50 * q^21 + 628 * q^23 + 24 * q^24 + 38 * q^25 - 14 * q^26 + 242 * q^27 + 4 * q^28 - 528 * q^29 - 558 * q^30 - 522 * q^31 + 256 * q^32 + 208 * q^34 + 17 * q^35 - 84 * q^36 - 406 * q^37 + 544 * q^38 + 1429 * q^39 + 40 * q^40 + 329 * q^41 - 1480 * q^42 - 1442 * q^43 + 2652 * q^45 - 1044 * q^46 + 666 * q^47 - 112 * q^48 - 114 * q^49 - 34 * q^50 - 1158 * q^51 - 28 * q^52 + 414 * q^53 + 1144 * q^54 + 48 * q^56 + 593 * q^57 - 1056 * q^58 - 888 * q^59 + 844 * q^60 + 302 * q^61 + 646 * q^62 + 2061 * q^63 - 128 * q^64 + 138 * q^65 + 578 * q^67 + 436 * q^68 + 1930 * q^69 + 1394 * q^70 + 1090 * q^71 - 648 * q^72 - 253 * q^73 - 812 * q^74 + 2763 * q^75 + 128 * q^76 - 4152 * q^78 + 674 * q^79 + 80 * q^80 - 230 * q^81 - 722 * q^82 + 428 * q^83 + 2860 * q^84 - 1046 * q^85 - 984 * q^86 - 2122 * q^87 - 2202 * q^89 - 1366 * q^90 - 2217 * q^91 + 832 * q^92 - 3721 * q^93 - 2138 * q^94 + 973 * q^95 - 224 * q^96 + 3012 * q^97 + 3292 * q^98

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