LMFDB - Embedded newform 117.4.t.a.103.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,4,Mod(25,117)] 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("117.25"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	117.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.90322347067$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.1
Character	$\chi$	$=$	117.103
Dual form			117.4.t.a.25.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.76791 + 2.75276i) q^{2} +(2.56905 + 4.51663i) q^{3} +(11.1553 - 19.3216i) q^{4} +(-10.5269 - 6.07771i) q^{5} +(-24.6822 - 14.4629i) q^{6} +(15.9136 - 9.18770i) q^{7} +78.7874i q^{8} +(-13.7999 + 23.2069i) q^{9} +66.9218 q^{10} +(21.1425 - 12.2066i) q^{11} +(115.927 + 0.746343i) q^{12} +(34.1199 + 32.1377i) q^{13} +(-50.5830 + 87.6123i) q^{14} +(0.406627 - 63.1601i) q^{15} +(-127.640 - 221.079i) q^{16} +36.2127 q^{17} +(1.91393 - 148.636i) q^{18} +139.810i q^{19} +(-234.862 + 135.598i) q^{20} +(82.3803 + 48.2721i) q^{21} +(-67.2036 + 116.400i) q^{22} +(4.44194 - 7.69366i) q^{23} +(-355.854 + 202.409i) q^{24} +(11.3772 + 19.7059i) q^{25} +(-251.148 - 59.3057i) q^{26} +(-140.270 - 2.70949i) q^{27} -409.967i q^{28} +(107.290 + 185.832i) q^{29} +(171.926 + 302.261i) q^{30} +(-67.1586 - 38.7741i) q^{31} +(671.296 + 387.573i) q^{32} +(109.449 + 64.1333i) q^{33} +(-172.659 + 99.6846i) q^{34} -223.361 q^{35} +(294.452 + 525.518i) q^{36} -94.1274i q^{37} +(-384.863 - 666.603i) q^{38} +(-57.4981 + 236.671i) q^{39} +(478.847 - 829.388i) q^{40} +(26.0643 + 15.0482i) q^{41} +(-525.663 - 3.38424i) q^{42} +(132.587 + 229.647i) q^{43} -544.674i q^{44} +(286.316 - 160.425i) q^{45} +48.9103i q^{46} +(54.3039 - 31.3524i) q^{47} +(670.618 - 1144.47i) q^{48} +(-2.67228 + 4.62852i) q^{49} +(-108.491 - 62.6373i) q^{50} +(93.0322 + 163.559i) q^{51} +(1001.57 - 300.746i) q^{52} +555.540 q^{53} +(676.253 - 373.210i) q^{54} -296.753 q^{55} +(723.875 + 1253.79i) q^{56} +(-631.471 + 359.180i) q^{57} +(-1023.10 - 590.686i) q^{58} +(126.478 + 73.0223i) q^{59} +(-1215.82 - 712.428i) q^{60} +(386.697 + 669.779i) q^{61} +426.942 q^{62} +(-6.38802 + 496.095i) q^{63} -2225.34 q^{64} +(-163.854 - 545.681i) q^{65} +(-698.385 - 4.49623i) q^{66} +(-19.1771 - 11.0719i) q^{67} +(403.964 - 699.686i) q^{68} +(46.1610 + 0.297186i) q^{69} +(1064.96 - 614.858i) q^{70} +820.920i q^{71} +(-1828.41 - 1087.26i) q^{72} +267.020i q^{73} +(259.110 + 448.791i) q^{74} +(-59.7756 + 102.012i) q^{75} +(2701.35 + 1559.63i) q^{76} +(224.301 - 388.501i) q^{77} +(-377.350 - 1286.70i) q^{78} +(66.9431 + 115.949i) q^{79} +3103.03i q^{80} +(-348.123 - 640.509i) q^{81} -165.696 q^{82} +(-239.172 + 138.086i) q^{83} +(1851.67 - 1053.23i) q^{84} +(-381.208 - 220.090i) q^{85} +(-1264.33 - 729.959i) q^{86} +(-563.700 + 962.001i) q^{87} +(961.726 + 1665.76i) q^{88} -1186.58i q^{89} +(-923.518 + 1553.05i) q^{90} +(838.241 + 197.941i) q^{91} +(-99.1025 - 171.651i) q^{92} +(2.59416 - 402.943i) q^{93} +(-172.611 + 298.971i) q^{94} +(849.726 - 1471.77i) q^{95} +(-25.9304 + 4027.69i) q^{96} +(717.108 - 414.022i) q^{97} -29.4245i q^{98} +(-8.48699 + 659.102i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{3} + 150 q^{4} - 68 q^{9} - 40 q^{10} + 190 q^{12} - 13 q^{13} + 78 q^{14} - 530 q^{16} + 264 q^{17} - 34 q^{22} - 174 q^{23} + 798 q^{25} - 1032 q^{26} + 302 q^{27} + 642 q^{29} + 198 q^{30}+ \cdots + 2136 q^{95}+O(q^{100}) $ 80 * q - 4 * q^3 + 150 * q^4 - 68 * q^9 - 40 * q^10 + 190 * q^12 - 13 * q^13 + 78 * q^14 - 530 * q^16 + 264 * q^17 - 34 * q^22 - 174 * q^23 + 798 * q^25 - 1032 * q^26 + 302 * q^27 + 642 * q^29 + 198 * q^30 - 2136 * q^35 - 802 * q^36 - 708 * q^38 + 211 * q^39 + 88 * q^40 - 1212 * q^42 + 166 * q^43 + 4334 * q^48 + 1610 * q^49 + 150 * q^51 + 786 * q^52 + 1296 * q^53 - 508 * q^55 - 888 * q^56 + 838 * q^61 + 3540 * q^62 - 3652 * q^64 - 201 * q^65 - 2418 * q^66 + 612 * q^68 - 1890 * q^69 + 4458 * q^74 - 632 * q^75 - 2166 * q^77 - 2280 * q^78 + 514 * q^79 - 4076 * q^81 - 5188 * q^82 - 4458 * q^87 + 2338 * q^88 - 2226 * q^90 - 1086 * q^91 + 516 * q^92 + 488 * q^94 + 2136 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−4.76791	+	2.75276i	−1.68571	+	0.973246i	−0.727973	+	0.685606i	$0.759537\pi$
$2$	−4.76791	+	2.75276i	−1.68571	+	0.973246i	−0.957739	+	0.287640i	$0.907129\pi$
$3$	2.56905	+	4.51663i	0.494414	+	0.869226i
$3$	2.56905	+	4.51663i	0.494414	+	0.869226i
$4$	11.1553	−	19.3216i	1.39442	−	2.41520i
$5$	−10.5269	−	6.07771i	−0.941555	−	0.543607i	−0.0511078	−	0.998693i	$-0.516275\pi$
$5$	−10.5269	−	6.07771i	−0.941555	−	0.543607i	−0.890448	+	0.455086i	$0.849609\pi$
$6$	−24.6822	−	14.4629i	−1.67941	−	0.984078i
$7$	15.9136	−	9.18770i	0.859252	−	0.496089i	−0.00450986	−	0.999990i	$-0.501436\pi$
$7$	15.9136	−	9.18770i	0.859252	−	0.496089i	0.863762	+	0.503901i	$0.168102\pi$
$8$			78.7874i			3.48194i
$9$	−13.7999	+	23.2069i	−0.511109	+	0.859516i
$10$	66.9218			2.11625
$11$	21.1425	−	12.2066i	0.579517	−	0.334584i	−0.181424	−	0.983405i	$-0.558071\pi$
$11$	21.1425	−	12.2066i	0.579517	−	0.334584i	0.760941	+	0.648821i	$0.224737\pi$
$12$	115.927	+	0.746343i	2.78877	+	0.0179542i
$13$	34.1199	+	32.1377i	0.727936	+	0.685645i
$13$	34.1199	+	32.1377i	0.727936	+	0.685645i
$14$	−50.5830	+	87.6123i	−0.965634	+	1.67253i
$15$	0.406627	−	63.1601i	0.00699938	−	1.08719i
$16$	−127.640	−	221.079i	−1.99437	−	3.45436i
$17$	36.2127			0.516639			0.258320	−	0.966060i	$-0.416831\pi$
$17$	36.2127			0.516639			0.258320	+	0.966060i	$0.416831\pi$
$18$	1.91393	−	148.636i	0.0250621	−	1.94633i
$19$			139.810i			1.68814i	0.536233	+	0.844070i	$0.319847\pi$
$19$			139.810i			1.68814i	−0.536233	+	0.844070i	$0.680153\pi$
$20$	−234.862	+	135.598i	−2.62584	+	1.51603i
$21$	82.3803	+	48.2721i	0.856040	+	0.501611i
$22$	−67.2036	+	116.400i	−0.651266	+	1.12803i
$23$	4.44194	−	7.69366i	0.0402699	−	0.0697495i	−0.845188	−	0.534469i	$-0.820512\pi$
$23$	4.44194	−	7.69366i	0.0402699	−	0.0697495i	0.885458	+	0.464720i	$0.153845\pi$
$24$	−355.854	+	202.409i	−3.02660	+	1.72152i
$25$	11.3772	+	19.7059i	0.0910176	+	0.157647i
$26$	−251.148	−	59.3057i	−1.89439	−	0.447338i
$27$	−140.270	−	2.70949i	−0.999813	−	0.0193126i
$28$		−	409.967i		−	2.76702i
$29$	107.290	+	185.832i	0.687009	+	1.18993i	0.972801	+	0.231642i	$0.0744099\pi$
$29$	107.290	+	185.832i	0.687009	+	1.18993i	−0.285792	+	0.958292i	$0.592257\pi$
$30$	171.926	+	302.261i	1.04631	+	1.83950i
$31$	−67.1586	−	38.7741i	−0.389098	−	0.224646i	0.292671	−	0.956213i	$-0.405456\pi$
$31$	−67.1586	−	38.7741i	−0.389098	−	0.224646i	−0.681769	+	0.731567i	$0.738789\pi$
$32$	671.296	+	387.573i	3.70842	+	2.14106i
$33$	109.449	+	64.1333i	0.577351	+	0.338308i
$34$	−172.659	+	99.6846i	−0.870904	+	0.502817i
$35$	−223.361			−1.07871
$36$	294.452	+	525.518i	1.36320	+	2.43295i
$37$		−	94.1274i		−	0.418228i	−0.977891	−	0.209114i	$-0.932942\pi$
$37$		−	94.1274i		−	0.418228i	0.977891	−	0.209114i	$-0.0670580\pi$
$38$	−384.863	−	666.603i	−1.64297	−	2.84572i
$39$	−57.4981	+	236.671i	−0.236079	+	0.971734i
$40$	478.847	−	829.388i	1.89281	−	3.27844i
$41$	26.0643	+	15.0482i	0.0992820	+	0.0573205i	0.548819	−	0.835941i	$-0.315078\pi$
$41$	26.0643	+	15.0482i	0.0992820	+	0.0573205i	−0.449537	+	0.893262i	$0.648411\pi$
$42$	−525.663	−	3.38424i	−1.93123	−	0.0124333i
$43$	132.587	+	229.647i	0.470217	+	0.814440i	0.999420	−	0.0340557i	$-0.0108424\pi$
$43$	132.587	+	229.647i	0.470217	+	0.814440i	−0.529203	+	0.848495i	$0.677509\pi$
$44$		−	544.674i		−	1.86620i
$45$	286.316	−	160.425i	0.948476	−	0.531439i
$46$			48.9103i			0.156770i
$47$	54.3039	−	31.3524i	0.168533	−	0.0973024i	−0.413361	−	0.910567i	$-0.635645\pi$
$47$	54.3039	−	31.3524i	0.168533	−	0.0973024i	0.581894	+	0.813265i	$0.302312\pi$
$48$	670.618	−	1144.47i	2.01657	−	3.44144i
$49$	−2.67228	+	4.62852i	−0.00779089	+	0.0134942i
$50$	−108.491	−	62.6373i	−0.306859	−	0.177165i
$51$	93.0322	+	163.559i	0.255434	+	0.449076i
$52$	1001.57	−	300.746i	2.67101	−	0.802037i
$53$	555.540			1.43980			0.719898	−	0.694079i	$-0.244188\pi$
$53$	555.540			1.43980			0.719898	+	0.694079i	$0.244188\pi$
$54$	676.253	−	373.210i	1.70419	−	0.940509i
$55$	−296.753			−0.727530
$56$	723.875	+	1253.79i	1.72736	+	2.99187i
$57$	−631.471	+	359.180i	−1.46738	+	0.834640i
$58$	−1023.10	−	590.686i	−2.31620	−	1.33726i
$59$	126.478	+	73.0223i	0.279086	+	0.161130i	0.633010	−	0.774144i	$-0.281819\pi$
$59$	126.478	+	73.0223i	0.279086	+	0.161130i	−0.353923	+	0.935274i	$0.615153\pi$
$60$	−1215.82	−	712.428i	−2.61602	−	1.53290i
$61$	386.697	+	669.779i	0.811663	+	1.40584i	0.911699	+	0.410858i	$0.134771\pi$
$61$	386.697	+	669.779i	0.811663	+	1.40584i	−0.100036	+	0.994984i	$0.531896\pi$
$62$	426.942			0.874543
$63$	−6.38802	+	496.095i	−0.0127748	+	0.992096i
$64$	−2225.34			−4.34636
$65$	−163.854	−	545.681i	−0.312671	−	1.04128i
$66$	−698.385	−	4.49623i	−1.30250	−	0.00838557i
$67$	−19.1771	−	11.0719i	−0.0349680	−	0.0201888i	0.482414	−	0.875943i	$-0.339760\pi$
$67$	−19.1771	−	11.0719i	−0.0349680	−	0.0201888i	−0.517382	+	0.855754i	$0.673093\pi$
$68$	403.964	−	699.686i	0.720409	−	1.24779i
$69$	46.1610	+	0.297186i	0.0805381	+	0.000518507i
$70$	1064.96	−	614.858i	1.81840	−	1.04985i
$71$			820.920i			1.37219i	0.727513	+	0.686094i	$0.240676\pi$
$71$			820.920i			1.37219i	−0.727513	+	0.686094i	$0.759324\pi$
$72$	−1828.41	−	1087.26i	−2.99279	−	1.77965i
$73$			267.020i			0.428114i	0.976821	+	0.214057i	$0.0686678\pi$
$73$			267.020i			0.428114i	−0.976821	+	0.214057i	$0.931332\pi$
$74$	259.110	+	448.791i	0.407039	+	0.705012i
$75$	−59.7756	+	102.012i	−0.0920306	+	0.157058i
$76$	2701.35	+	1559.63i	4.07719	+	2.35397i
$77$	224.301	−	388.501i	0.331967	−	0.574984i
$78$	−377.350	−	1286.70i	−0.547776	−	1.86783i
$79$	66.9431	+	115.949i	0.0953378	+	0.165130i	0.909750	−	0.415158i	$-0.136274\pi$
$79$	66.9431	+	115.949i	0.0953378	+	0.165130i	−0.814412	+	0.580287i	$0.802940\pi$
$80$			3103.03i			4.33662i
$81$	−348.123	−	640.509i	−0.477535	−	0.878613i
$82$	−165.696			−0.223148
$83$	−239.172	+	138.086i	−0.316295	+	0.182613i	−0.649740	−	0.760156i	$-0.725122\pi$
$83$	−239.172	+	138.086i	−0.316295	+	0.182613i	0.333445	+	0.942770i	$0.391789\pi$
$84$	1851.67	−	1053.23i	2.40516	−	1.36805i
$85$	−381.208	−	220.090i	−0.486444	−	0.280849i
$86$	−1264.33	−	729.959i	−1.58530	−	0.915273i
$87$	−563.700	+	962.001i	−0.694655	+	1.18549i
$88$	961.726	+	1665.76i	1.16500	+	2.01785i
$89$		−	1186.58i		−	1.41322i	−0.707601	−	0.706612i	$-0.750222\pi$
$89$		−	1186.58i		−	1.41322i	0.707601	−	0.706612i	$-0.249778\pi$
$90$	−923.518	+	1553.05i	−1.08164	+	1.81895i
$91$	838.241	+	197.941i	0.965622	+	0.228020i
$92$	−99.1025	−	171.651i	−0.112306	−	0.194520i
$93$	2.59416	−	402.943i	0.00289250	−	0.449283i
$94$	−172.611	+	298.971i	−0.189398	+	0.328047i
$95$	849.726	−	1471.77i	0.917685	−	1.58948i
$96$	−25.9304	+	4027.69i	−0.0275679	+	4.28203i
$97$	717.108	−	414.022i	0.750631	−	0.433377i	−0.0752906	−	0.997162i	$-0.523988\pi$
$97$	717.108	−	414.022i	0.750631	−	0.433377i	0.825922	+	0.563784i	$0.190655\pi$
$98$		−	29.4245i		−	0.0303298i
$99$	−8.48699	+	659.102i	−0.00861591	+	0.669113i
$100$	507.665			0.507665
$101$	−887.726	−	1537.59i	−0.874574	−	1.51481i	−0.857215	−	0.514958i	$-0.827807\pi$
$101$	−887.726	−	1537.59i	−0.874574	−	1.51481i	−0.0173591	−	0.999849i	$-0.505526\pi$
$102$	−893.808	−	523.742i	−0.867649	−	0.508413i
$103$	675.351	−	1169.74i	0.646061	−	1.11901i	−0.337994	−	0.941148i	$-0.609748\pi$
$103$	675.351	−	1169.74i	0.646061	−	1.11901i	0.984055	−	0.177862i	$-0.0569182\pi$
$104$	−2532.04	+	2688.22i	−2.38738	+	2.53463i
$105$	−573.826	−	1008.84i	−0.533330	−	0.937644i
$106$	−2648.76	+	1529.26i	−2.42708	+	1.40128i
$107$	−1089.33			−0.984203			−0.492101	−	0.870538i	$-0.663771\pi$
$107$	−1089.33			−0.984203			−0.492101	+	0.870538i	$0.663771\pi$
$108$	−1617.11	+	2680.01i	−1.44080	+	2.38782i
$109$		−	167.053i		−	0.146796i	−0.997303	−	0.0733979i	$-0.976616\pi$
$109$		−	167.053i		−	0.146796i	0.997303	−	0.0733979i	$-0.0233843\pi$
$110$	1414.89	−	816.888i	1.22641	−	0.708066i
$111$	425.139	−	241.818i	0.363535	−	0.206778i
$112$	−4062.41	−	2345.43i	−3.42734	−	1.97877i
$113$	27.0541	−	46.8591i	0.0225224	−	0.0390100i	−0.854545	−	0.519378i	$-0.826164\pi$
$113$	27.0541	−	46.8591i	0.0225224	−	0.0390100i	0.877067	+	0.480368i	$0.159497\pi$
$114$	2022.07	−	3450.82i	1.66126	−	2.83508i
$115$	−93.5197	+	53.9936i	−0.0758327	+	0.0437820i
$116$	4787.42			3.83190
$117$	−1216.67	+	348.321i	−0.961377	+	0.275233i
$118$	−804.050			−0.627278
$119$	576.273	−	332.711i	0.443923	−	0.256299i
$120$	4976.22	+	32.0371i	3.78554	+	0.0243715i
$121$	−367.498	+	636.525i	−0.276107	+	0.478231i
$122$	−3687.47	−	2128.96i	−2.73646	−	1.57990i
$123$	−1.00680	+	156.383i	−0.000738047	+	0.114639i
$124$	−1498.35	+	865.074i	−1.08513	+	0.626500i
$125$			1242.84i			0.889303i
$126$	−1335.17	−	2382.92i	−0.944019	−	1.68482i
$127$	26.9682			0.0188429			0.00942143	−	0.999956i	$-0.497001\pi$
$127$	26.9682			0.0188429			0.00942143	+	0.999956i	$0.497001\pi$
$128$	5239.84	−	3025.22i	3.61829	−	2.08902i
$129$	−696.610	+	1188.82i	−0.475450	+	0.811395i
$130$	2283.37	+	2150.71i	1.54050	+	1.45100i
$131$	832.028	−	1441.12i	0.554921	−	0.961152i	−0.442989	−	0.896527i	$-0.646082\pi$
$131$	832.028	−	1441.12i	0.554921	−	0.961152i	0.997910	−	0.0646243i	$-0.0205849\pi$
$132$	2460.09	−	1399.30i	1.62215	−	0.922675i
$133$	1284.53	+	2224.88i	0.837468	+	1.45054i
$134$	121.913			0.0785947
$135$	1460.14	+	881.043i	0.930881	+	0.561690i
$136$			2853.10i			1.79891i
$137$	−797.686	+	460.544i	−0.497452	+	0.287204i	−0.727661	−	0.685937i	$-0.759392\pi$
$137$	−797.686	+	460.544i	−0.497452	+	0.287204i	0.230209	+	0.973141i	$0.426059\pi$
$138$	−220.910	+	125.653i	−0.136269	+	0.0775094i
$139$	943.317	−	1633.87i	0.575619	−	0.997002i	−0.420355	−	0.907360i	$-0.638094\pi$
$139$	943.317	−	1633.87i	0.575619	−	0.997002i	0.995974	−	0.0896421i	$-0.0285723\pi$
$140$	−2491.66	+	4315.69i	−1.50417	+	2.60530i
$141$	281.117	+	164.725i	0.167903	+	0.0983853i
$142$	−2259.79	−	3914.08i	−1.33548	−	2.31311i
$143$	1113.67	+	262.980i	0.651258	+	0.153787i
$144$	6891.98	+	88.7453i	3.98842	+	0.0513573i
$145$		−	2608.31i		−	1.49385i
$146$	−735.040	−	1273.13i	−0.416660	−	0.721677i
$147$	−27.7705	−	0.178788i	−0.0155815	−	0.000100314i
$148$	−1818.69	−	1050.02i	−1.01010	−	0.583184i
$149$	1293.63	+	746.879i	0.711265	+	0.410649i	0.811529	−	0.584312i	$-0.198635\pi$
$149$	1293.63	+	746.879i	0.711265	+	0.410649i	−0.100264	+	0.994961i	$0.531969\pi$
$150$	4.19072	−	650.932i	0.00228114	−	0.354323i
$151$	389.704	−	224.995i	0.210024	−	0.121257i	−0.391299	−	0.920264i	$-0.627974\pi$
$151$	389.704	−	224.995i	0.210024	−	0.121257i	0.601323	+	0.799006i	$0.294641\pi$
$152$	−11015.3			−5.87801
$153$	−499.733	+	840.385i	−0.264059	+	0.444059i
$154$			2469.79i			1.29234i
$155$	471.315	+	816.342i	0.244238	+	0.423033i
$156$	3931.44	+	3751.09i	2.01774	+	1.92518i
$157$	41.8059	−	72.4099i	0.0212514	−	0.0368085i	−0.855204	−	0.518291i	$-0.826568\pi$
$157$	41.8059	−	72.4099i	0.0212514	−	0.0368085i	0.876456	+	0.481483i	$0.159902\pi$
$158$	−638.357	−	368.556i	−0.321424	−	0.185574i
$159$	1427.21	+	2509.17i	0.711856	+	1.25151i
$160$	−4711.11	−	8159.89i	−2.32779	−	4.03185i
$161$		−	163.245i		−	0.0799099i
$162$	3422.98	+	2095.59i	1.66009	+	1.01633i
$163$		−	2384.83i		−	1.14598i	−0.819563	−	0.572989i	$-0.805784\pi$
$163$		−	2384.83i		−	1.14598i	0.819563	−	0.572989i	$-0.194216\pi$
$164$	581.511	−	335.736i	0.276881	−	0.159857i
$165$	−762.373	−	1340.32i	−0.359701	−	0.632388i
$166$	760.234	−	1316.76i	0.355455	−	0.615667i
$167$	975.239	+	563.055i	0.451894	+	0.260901i	0.708630	−	0.705581i	$-0.249314\pi$
$167$	975.239	+	563.055i	0.451894	+	0.260901i	−0.256736	+	0.966482i	$0.582647\pi$
$168$	−3803.23	+	6490.53i	−1.74658	+	2.98068i
$169$	131.342	+	2193.07i	0.0597824	+	0.998211i
$170$	2423.42			1.09334
$171$	−3244.56	−	1929.37i	−1.45098	−	0.862823i
$172$	5916.20			2.62271
$173$	−768.662	−	1331.36i	−0.337805	−	0.585096i	0.646214	−	0.763156i	$-0.276351\pi$
$173$	−768.662	−	1331.36i	−0.337805	−	0.585096i	−0.984020	+	0.178060i	$0.943018\pi$
$174$	39.5196	−	6138.46i	0.0172183	−	2.67446i
$175$	362.104	+	209.061i	0.156414	+	0.0903057i
$176$	−5397.24	−	3116.10i	−2.31155	−	1.33457i
$177$	−4.88553	+	758.855i	−0.00207468	+	0.322254i
$178$	3266.36	+	5657.50i	1.37542	+	2.38229i
$179$	−2140.61			−0.893835			−0.446918	−	0.894575i	$-0.647478\pi$
$179$	−2140.61			−0.893835			−0.446918	+	0.894575i	$0.647478\pi$
$180$	94.2783	−	7321.67i	0.0390394	−	3.03181i
$181$	−1043.98			−0.428722			−0.214361	−	0.976755i	$-0.568767\pi$
$181$	−1043.98			−0.428722			−0.214361	+	0.976755i	$0.568767\pi$
$182$	−4541.54	+	1363.71i	−1.84968	+	0.555411i
$183$	−2031.70	+	3467.26i	−0.820697	+	1.40059i
$184$	606.163	+	349.969i	0.242864	+	0.140218i
$185$	−572.079	+	990.870i	−0.227352	+	0.393785i
$186$	1096.84	+	1928.34i	0.432387	+	0.760176i
$187$	765.625	−	442.034i	0.299401	−	0.172859i
$188$		−	1398.98i		−	0.542720i
$189$	−2257.09	+	1245.64i	−0.868672	+	0.479402i
$190$			9356.35i			3.57253i
$191$	961.404	+	1665.20i	0.364214	+	0.630836i	0.988650	−	0.150240i	$-0.0480045\pi$
$191$	961.404	+	1665.20i	0.364214	+	0.630836i	−0.624436	+	0.781076i	$0.714671\pi$
$192$	−5717.00	−	10051.0i	−2.14890	−	3.77797i
$193$	−2700.75	−	1559.28i	−1.00727	−	0.581550i	−0.0968820	−	0.995296i	$-0.530887\pi$
$193$	−2700.75	−	1559.28i	−1.00727	−	0.581550i	−0.910392	+	0.413746i	$0.864220\pi$
$194$	−2279.40	+	3948.04i	−0.843565	+	1.46110i
$195$	2043.69	−	2141.95i	0.750523	−	0.786607i
$196$	59.6202	+	103.265i	0.0217275	+	0.0376331i
$197$		−	3703.94i		−	1.33957i	−0.742557	−	0.669783i	$-0.766387\pi$
$197$		−	3703.94i		−	1.33957i	0.742557	−	0.669783i	$-0.233613\pi$
$198$	−1773.88	−	3165.90i	−0.636688	−	1.13632i
$199$	−5250.10			−1.87020			−0.935099	−	0.354386i	$-0.884690\pi$
$199$	−5250.10			−1.87020			−0.935099	+	0.354386i	$0.884690\pi$
$200$	−1552.58	+	896.380i	−0.548918	+	0.316918i
$201$	0.740763	−	115.060i	0.000259947	−	0.0403768i
$202$	8465.20	+	4887.38i	2.94856	+	1.70235i
$203$	3414.73	+	1971.50i	1.18063	+	0.681635i
$204$	4198.03	+	27.0271i	1.44079	+	0.00927585i
$205$	−182.918	−	316.823i	−0.0623196	−	0.107941i
$206$			7436.30i			2.51511i
$207$	117.248	+	209.256i	0.0393685	+	0.0702622i
$208$	2749.89	−	11645.2i	0.916684	−	3.88198i
$209$	1706.61	+	2955.93i	0.564825	+	0.978306i
$210$	5513.04	+	3230.45i	1.81160	+	1.06154i
$211$	1256.94	−	2177.08i	0.410101	−	0.710315i	−0.584800	−	0.811178i	$-0.698827\pi$
$211$	1256.94	−	2177.08i	0.410101	−	0.710315i	0.994900	+	0.100863i	$0.0321602\pi$
$212$	6197.22	−	10733.9i	2.00767	−	3.47739i
$213$	−3707.80	+	2108.99i	−1.19274	+	0.678429i
$214$	5193.84	−	2998.66i	1.65908	−	0.957871i
$215$		−	3223.30i		−	1.02245i
$216$	213.474	−	11051.5i	0.0672455	−	3.48129i
$217$	−1424.98			−0.445778
$218$	459.855	+	796.493i	0.142868	+	0.247456i
$219$	−1206.03	+	685.988i	−0.372128	+	0.211666i
$220$	−3310.37	+	5733.74i	−1.01448	+	1.75713i
$221$	1235.57	+	1163.79i	0.376080	+	0.354231i
$222$	−1361.36	+	2323.27i	−0.411569	+	0.702377i
$223$	3991.07	−	2304.24i	1.19848	−	0.691944i	0.238266	−	0.971200i	$-0.423421\pi$
$223$	3991.07	−	2304.24i	1.19848	−	0.691944i	0.960217	+	0.279256i	$0.0900878\pi$
$224$	14243.6			4.24862
$225$	−614.318	−	7.91033i	−0.182020	−	0.00234380i
$226$			297.893i			0.0876794i
$227$	877.599	−	506.682i	0.256600	−	0.148148i	−0.366182	−	0.930543i	$-0.619335\pi$
$227$	877.599	−	506.682i	0.256600	−	0.148148i	0.622783	+	0.782395i	$0.286002\pi$
$228$	−104.346	+	16207.8i	−0.0303092	+	4.70784i
$229$	−2248.36	−	1298.09i	−0.648801	−	0.374586i	0.139195	−	0.990265i	$-0.455548\pi$
$229$	−2248.36	−	1298.09i	−0.648801	−	0.374586i	−0.787997	+	0.615679i	$0.788882\pi$
$230$	297.263	−	514.874i	0.0852213	−	0.147608i
$231$	2330.96	+	15.0068i	0.663921	+	0.00427435i
$232$	−14641.2	+	8453.10i	−4.14328	+	2.39213i
$233$	2738.84			0.770074			0.385037	−	0.922901i	$-0.374189\pi$
$233$	2738.84			0.770074			0.385037	+	0.922901i	$0.374189\pi$
$234$	4842.13	−	5009.96i	1.35274	−	1.39962i
$235$	−762.203			−0.211577
$236$	2821.81	−	1629.18i	0.778324	−	0.449366i
$237$	−351.718	+	600.236i	−0.0963989	+	0.164513i
$238$	−1831.75	+	3172.68i	−0.498884	+	0.864093i
$239$	1318.93	+	761.483i	0.356964	+	0.206093i	0.667748	−	0.744387i	$-0.267258\pi$
$239$	1318.93	+	761.483i	0.356964	+	0.206093i	−0.310784	+	0.950480i	$0.600592\pi$
$240$	−14015.3	+	7971.85i	−3.76951	+	2.14409i
$241$	−2038.96	+	1177.19i	−0.544983	+	0.314646i	−0.747096	−	0.664716i	$-0.768553\pi$
$241$	−2038.96	+	1177.19i	−0.544983	+	0.314646i	0.202113	+	0.979362i	$0.435219\pi$
$242$		−	4046.53i		−	1.07488i
$243$	1998.60	−	3217.84i	0.527613	−	0.849485i
$244$	17254.9			4.52718
$245$	56.2616	−	32.4827i	0.0146711	−	0.00847037i
$246$	−425.683	−	748.390i	−0.110327	−	0.193966i
$247$	−4493.17	+	4770.32i	−1.15746	+	1.22886i
$248$	3054.91	−	5291.25i	0.782205	−	1.35482i
$249$	−1238.13	−	725.502i	−0.315113	−	0.184646i
$250$	−3421.23	−	5925.75i	−0.865511	−	1.49911i
$251$	−3649.97			−0.917864			−0.458932	−	0.888471i	$-0.651768\pi$
$251$	−3649.97			−0.917864			−0.458932	+	0.888471i	$0.651768\pi$
$252$	9514.08	+	5657.52i	2.37830	+	1.41425i
$253$		−	216.884i		−	0.0538947i
$254$	−128.582	+	74.2369i	−0.0317636	+	0.0183387i
$255$	14.7251	−	2287.20i	0.00361615	−	0.561686i
$256$	−7754.05	+	13430.4i	−1.89308	+	3.27891i
$257$	−2354.85	+	4078.72i	−0.571562	+	0.989975i	0.424843	+	0.905267i	$0.360329\pi$
$257$	−2354.85	+	4078.72i	−0.571562	+	0.989975i	−0.996406	+	0.0847082i	$0.973004\pi$
$258$	48.8377	−	7585.80i	0.0117849	−	1.83051i
$259$	−864.814	−	1497.90i	−0.207479	−	0.359363i
$260$	−12371.3	−	2921.33i	−2.95090	−	0.696820i
$261$	−5793.18	−	74.5965i	−1.37390	−	0.0176912i
$262$			9161.48i			2.16030i
$263$	−631.265	−	1093.38i	−0.148006	−	0.256353i	0.782485	−	0.622670i	$-0.213952\pi$
$263$	−631.265	−	1093.38i	−0.148006	−	0.256353i	−0.930490	+	0.366317i	$0.880619\pi$
$264$	−5052.90	+	8623.19i	−1.17797	+	2.01030i
$265$	−5848.11	−	3376.41i	−1.35565	−	0.782684i
$266$	−12249.1	−	7072.02i	−2.82346	−	1.63012i
$267$	5359.34	−	3048.38i	1.22841	−	0.698718i
$268$	−427.854	+	247.022i	−0.0975199	+	0.0563031i
$269$	4003.66			0.907463			0.453731	−	0.891139i	$-0.350093\pi$
$269$	4003.66			0.907463			0.453731	+	0.891139i	$0.350093\pi$
$270$	−9387.12	−	181.324i	−2.11586	−	0.0408705i
$271$			3943.15i			0.883872i	0.897047	+	0.441936i	$0.145708\pi$
$271$			3943.15i			0.883872i	−0.897047	+	0.441936i	$0.854292\pi$
$272$	−4622.18	−	8005.85i	−1.03037	−	1.78465i
$273$	1259.46	+	4294.55i	0.279216	+	0.952080i
$274$	2535.53	−	4391.67i	0.559040	−	0.968286i
$275$	481.084	+	277.754i	0.105492	+	0.0609061i
$276$	520.683	−	888.589i	0.113556	−	0.193793i
$277$	2041.85	+	3536.59i	0.442899	+	0.767123i	0.997903	−	0.0647241i	$-0.0206167\pi$
$277$	2041.85	+	3536.59i	0.442899	+	0.767123i	−0.555004	+	0.831847i	$0.687283\pi$
$278$			10386.9i			2.24088i
$279$	1826.61	−	1023.47i	0.391958	−	0.219618i
$280$		−	17598.0i		−	3.75601i
$281$	−1082.81	+	625.162i	−0.229876	+	0.132719i	−0.610515	−	0.792005i	$-0.709037\pi$
$281$	−1082.81	+	625.162i	−0.229876	+	0.132719i	0.380639	+	0.924724i	$0.375704\pi$
$282$	−1793.79	−	11.5485i	−0.378789	−	0.00243866i
$283$	569.429	−	986.281i	0.119608	−	0.207167i	−0.800004	−	0.599994i	$-0.795170\pi$
$283$	569.429	−	986.281i	0.119608	−	0.207167i	0.919612	+	0.392827i	$0.128503\pi$
$284$	15861.5	+	9157.63i	3.31410	+	1.91340i
$285$	8830.43	+	56.8506i	1.83533	+	0.0118159i
$286$	−6033.81	+	1811.80i	−1.24750	+	0.374594i
$287$	553.035			0.113744
$288$	−18258.2	+	10230.2i	−3.73568	+	2.09313i
$289$	−3601.64			−0.733084
$290$	7180.04	+	12436.2i	1.45388	+	2.51820i
$291$	3712.27	+	2175.27i	0.747826	+	0.438201i
$292$	5159.25	+	2978.69i	1.03398	+	0.596969i
$293$	−248.156	−	143.273i	−0.0494792	−	0.0285668i	0.475056	−	0.879955i	$-0.342428\pi$
$293$	−248.156	−	143.273i	−0.0494792	−	0.0285668i	−0.524536	+	0.851389i	$0.675761\pi$
$294$	132.900	−	75.5930i	0.0263635	−	0.0149955i
$295$	−887.618	−	1537.40i	−0.175183	−	0.303426i
$296$	7416.05			1.45625
$297$	−2998.72	+	1654.93i	−0.585871	+	0.323330i
$298$	−8223.90			−1.59865
$299$	398.815	−	119.754i	0.0771373	−	0.0231624i
$300$	1304.22	+	2292.94i	0.250997	+	0.441276i
$301$	4219.86	+	2436.34i	0.808069	+	0.466539i
$302$	−1238.71	+	2145.52i	−0.236027	+	0.408810i
$303$	4664.10	−	7959.67i	0.884309	−	1.50915i
$304$	30909.1	−	17845.3i	5.83143	−	3.36678i
$305$		−	9400.93i		−	1.76490i
$306$	69.3086	−	5382.52i	0.0129481	−	1.00555i
$307$		−	4281.13i		−	0.795887i	−0.917410	−	0.397943i	$-0.869724\pi$
$307$		−	4281.13i		−	0.795887i	0.917410	−	0.397943i	$-0.130276\pi$
$308$	−5004.30	−	8667.71i	−0.925801	−	1.60353i
$309$	7018.31	+	45.1841i	1.29210	+	0.00831856i
$310$	−4494.38	−	2594.83i	−0.823431	−	0.475408i
$311$	−424.312	+	734.929i	−0.0773650	+	0.134000i	−0.902112	−	0.431501i	$-0.857984\pi$
$311$	−424.312	+	734.929i	−0.0773650	+	0.134000i	0.824747	+	0.565501i	$0.191317\pi$
$312$	−18646.7	−	4530.12i	−3.38352	−	0.822012i
$313$	−3212.09	−	5563.51i	−0.580058	−	1.00469i	−0.995472	−	0.0950575i	$-0.969697\pi$
$313$	−3212.09	−	5563.51i	−0.580058	−	1.00469i	0.415414	−	0.909633i	$-0.363637\pi$
$314$			460.325i			0.0827314i
$315$	3082.37	−	5183.52i	0.551339	−	0.927169i
$316$	2987.09			0.531762
$317$	−7665.78	+	4425.84i	−1.35821	+	0.784164i	−0.989383	−	0.145333i	$-0.953575\pi$
$317$	−7665.78	+	4425.84i	−1.35821	+	0.784164i	−0.368829	+	0.929497i	$0.620241\pi$
$318$	−13711.9	−	8034.73i	−2.41801	−	1.41687i
$319$	4536.75	+	2619.29i	0.796267	+	0.459725i
$320$	23425.9	+	13525.0i	4.09234	+	2.36271i
$321$	−2798.55	−	4920.11i	−0.486604	−	0.855495i
$322$	449.373	+	778.337i	0.0777720	+	0.134705i
$323$			5062.90i			0.872159i
$324$	−16259.1	−	418.793i	−2.78791	−	0.0718094i
$325$	−245.112	+	1038.00i	−0.0418349	+	0.177163i
$326$	6564.86	+	11370.7i	1.11532	+	1.93179i
$327$	754.516	−	429.167i	0.127599	−	0.0725780i
$328$	−1185.61	+	2053.54i	−0.199587	+	0.345694i
$329$	576.112	−	997.856i	0.0965413	−	0.167214i
$330$	7324.51	+	4291.92i	1.22182	+	0.715946i
$331$	5211.72	−	3008.99i	0.865444	−	0.499664i	−0.000387841	−	1.00000i	$-0.500123\pi$
$331$	5211.72	−	3008.99i	0.865444	−	0.499664i	0.865831	+	0.500336i	$0.166790\pi$
$332$			6161.57i			1.01855i
$333$	2184.41	+	1298.95i	0.359474	+	0.213760i
$334$	−6199.81			−1.01568
$335$	134.584	+	233.106i	0.0219496	+	0.0380177i
$336$	156.920	−	24374.0i	0.0254783	−	3.95747i
$337$	4352.53	−	7538.79i	0.703552	−	1.21859i	−0.263659	−	0.964616i	$-0.584929\pi$
$337$	4352.53	−	7538.79i	0.703552	−	1.21859i	0.967211	−	0.253973i	$-0.0817373\pi$
$338$	−6663.21	−	10094.8i	−1.07228	−	1.62451i
$339$	281.148	+	1.81004i	0.0450439	+	0.000289994i
$340$	−8504.99	+	4910.36i	−1.35661	+	0.783240i
$341$	−1893.20			−0.300652
$342$	20780.9	+	267.587i	3.28568	+	0.0423084i
$343$			6400.97i			1.00764i
$344$	−18093.3	+	10446.2i	−2.83583	+	1.63727i
$345$	−484.126	−	283.682i	−0.0755492	−	0.0442693i
$346$	7329.82	+	4231.88i	1.13888	+	0.657535i
$347$	−5226.20	+	9052.04i	−0.808522	+	1.40040i	0.105366	+	0.994434i	$0.466399\pi$
$347$	−5226.20	+	9052.04i	−0.808522	+	1.40040i	−0.913888	+	0.405967i	$0.866935\pi$
$348$	12299.1	+	21623.0i	1.89455	+	3.33079i
$349$	−11083.5	+	6399.07i	−1.69996	+	0.981474i	−0.754184	+	0.656663i	$0.771967\pi$
$349$	−11083.5	+	6399.07i	−1.69996	+	0.981474i	−0.945779	+	0.324811i	$0.894699\pi$
$350$	−2301.97			−0.351559
$351$	−4698.93	−	4600.40i	−0.714559	−	0.699575i
$352$	18923.8			2.86546
$353$	7560.34	−	4364.97i	1.13993	−	0.658141i	0.193519	−	0.981096i	$-0.438010\pi$
$353$	7560.34	−	4364.97i	1.13993	−	0.658141i	0.946414	+	0.322956i	$0.104676\pi$
$354$	−2065.65	−	3631.60i	−0.310135	−	0.545247i
$355$	4989.32	−	8641.75i	0.745931	−	1.29199i
$356$	−22926.6	−	13236.7i	−3.41322	−	1.97062i
$357$	2983.21	+	1748.06i	0.442264	+	0.259152i
$358$	10206.2	−	5892.57i	1.50675	−	0.869922i
$359$			7671.87i			1.12787i	0.825819	+	0.563936i	$0.190713\pi$
$359$			7671.87i			1.12787i	−0.825819	+	0.563936i	$0.809287\pi$
$360$	12639.5	+	22558.1i	1.85044	+	3.30254i
$361$	−12687.9			−1.84981
$362$	4977.62	−	2873.83i	0.722701	−	0.417252i
$363$	−3819.07	−	24.5873i	−0.552202	−	0.00355509i
$364$	13175.4	−	13988.1i	1.89719	−	2.01421i
$365$	1622.87	−	2810.89i	0.232726	−	0.403093i
$366$	142.438	−	22124.4i	0.0203424	−	3.15973i
$367$	575.272	+	996.401i	0.0818228	+	0.141721i	0.904033	−	0.427463i	$-0.140593\pi$
$367$	575.272	+	996.401i	0.0818228	+	0.141721i	−0.822210	+	0.569184i	$0.807259\pi$
$368$	−2267.87			−0.321253
$369$	−708.909	+	397.208i	−0.100012	+	0.0560374i
$370$		−	6299.18i		−	0.885077i
$371$	8840.62	−	5104.13i	1.23715	−	0.714268i
$372$	−7756.57	−	4545.09i	−1.08107	−	0.633473i
$373$	3659.22	−	6337.96i	0.507955	−	0.879805i	−0.492002	−	0.870594i	$-0.663735\pi$
$373$	3659.22	−	6337.96i	0.507955	−	0.879805i	0.999958	−	0.00921063i	$-0.00293188\pi$
$374$	−2433.62	+	4215.16i	−0.336469	+	0.582782i
$375$	−5613.45	+	3192.92i	−0.773006	+	0.439684i
$376$	2470.17	+	4278.46i	0.338801	+	0.586821i
$377$	−2311.47	+	9788.62i	−0.315773	+	1.33724i
$378$	7332.66	−	12152.3i	0.997755	−	1.65357i
$379$		−	1388.52i		−	0.188189i	−0.995563	−	0.0940944i	$-0.970004\pi$
$379$		−	1388.52i		−	0.188189i	0.995563	−	0.0940944i	$-0.0299956\pi$
$380$	−18957.9	−	32836.1i	−2.55927	−	4.43278i
$381$	69.2828	+	121.806i	0.00931618	+	0.0163787i
$382$	−9167.78	−	5293.02i	−1.22792	−	0.708939i
$383$	6518.48	+	3763.45i	0.869657	+	0.502097i	0.867234	−	0.497900i	$-0.165895\pi$
$383$	6518.48	+	3763.45i	0.869657	+	0.502097i	0.00242307	+	0.999997i	$0.499229\pi$
$384$	27125.2	+	15894.5i	3.60476	+	2.11227i
$385$	−4722.40	+	2726.48i	−0.625131	+	0.360920i
$386$	17169.2			2.26397
$387$	−7159.10	−	92.1850i	−0.940356	−	0.0121086i
$388$		−	18474.2i		−	2.41723i
$389$	−3038.04	−	5262.04i	−0.395976	−	0.685851i	0.597249	−	0.802056i	$-0.296260\pi$
$389$	−3038.04	−	5262.04i	−0.395976	−	0.685851i	−0.993225	+	0.116205i	$0.962927\pi$
$390$	−3847.88	+	15838.4i	−0.499602	+	2.05644i
$391$	160.854	−	278.608i	0.0208050	−	0.0360353i
$392$	−364.669	−	210.542i	−0.0469861	−	0.0271275i
$393$	8646.51	+	55.6666i	1.10982	+	0.00714506i
$394$	10196.0	+	17660.0i	1.30373	+	2.25812i
$395$		−	1627.44i		−	0.207305i
$396$	12640.2	+	7516.47i	1.60403	+	0.953831i
$397$			1036.75i			0.131065i	0.997850	+	0.0655327i	$0.0208747\pi$
$397$			1036.75i			0.131065i	−0.997850	+	0.0655327i	$0.979125\pi$
$398$	25032.0	−	14452.2i	3.15262	−	1.82016i
$399$	−6748.92	+	11517.6i	−0.846789	+	1.44512i
$400$	2904.37	−	5030.51i	0.363046	−	0.628814i
$401$	−5613.74	−	3241.10i	−0.699094	−	0.403622i	0.107916	−	0.994160i	$-0.465582\pi$
$401$	−5613.74	−	3241.10i	−0.699094	−	0.403622i	−0.807010	+	0.590538i	$0.798916\pi$
$402$	313.201	+	550.637i	0.0388583	+	0.0683166i
$403$	−1045.34	−	3481.29i	−0.129211	−	0.430311i
$404$	−39611.5			−4.87808
$405$	−228.169	+	8858.37i	−0.0279946	+	1.08685i
$406$	−21708.2			−2.65359
$407$	−1148.98	−	1990.08i	−0.139933	−	0.242370i
$408$	−12886.4	+	7329.77i	−1.56366	+	0.889406i
$409$	−13676.2	−	7895.98i	−1.65341	−	0.954599i	−0.975654	−	0.219317i	$-0.929617\pi$
$409$	−13676.2	−	7895.98i	−1.65341	−	0.954599i	−0.677761	−	0.735282i	$-0.737050\pi$
$410$	1744.27	+	1007.06i	0.210106	+	0.121305i
$411$	−4129.41	−	2419.69i	−0.495593	−	0.290401i
$412$	−15067.5	−	26097.7i	−1.80175	−	3.12073i
$413$	2683.63			0.319740
$414$	−1135.06	−	674.959i	−0.134746	−	0.0801266i
$415$	3356.99			0.397080
$416$	10448.9	+	34797.9i	1.23149	+	4.10121i
$417$	9803.03	+	63.1123i	1.15121	+	0.00741156i
$418$	−16273.9	−	9395.74i	−1.90426	−	1.09943i
$419$	281.645	−	487.823i	0.0328383	−	0.0568776i	−0.849139	−	0.528169i	$-0.822879\pi$
$419$	281.645	−	487.823i	0.0328383	−	0.0568776i	0.881977	+	0.471292i	$0.156212\pi$
$420$	−25893.6	−	166.704i	−3.00828	−	0.0193674i
$421$	9141.28	−	5277.72i	1.05824	−	0.610975i	0.133295	−	0.991076i	$-0.457444\pi$
$421$	9141.28	−	5277.72i	1.05824	−	0.610975i	0.924945	+	0.380102i	$0.124111\pi$
$422$			13840.2i			1.59652i
$423$	−21.7986	+	1692.89i	−0.00250564	+	0.194589i
$424$			43769.5i			5.01329i
$425$	411.999	+	713.603i	0.0470232	+	0.0814466i
$426$	11872.9	−	20262.1i	1.35034	−	2.30447i
$427$	12307.5	+	7105.71i	1.39485	+	0.805315i
$428$	−12151.9	+	21047.6i	−1.37239	+	2.37705i
$429$	1673.29	+	5705.65i	0.188315	+	0.642125i
$430$	8872.96	+	15368.4i	0.995098	+	1.72356i
$431$			2075.83i			0.231993i	0.993250	+	0.115997i	$0.0370062\pi$
$431$			2075.83i			0.231993i	−0.993250	+	0.115997i	$0.962994\pi$
$432$	17305.0	+	31356.5i	1.92729	+	3.49223i
$433$	−469.788			−0.0521399			−0.0260700	−	0.999660i	$-0.508299\pi$
$433$	−469.788			−0.0521399			−0.0260700	+	0.999660i	$0.508299\pi$
$434$	6794.17	−	3922.62i	0.751453	−	0.433851i
$435$	11780.8	−	6700.89i	1.29849	−	0.738581i
$436$	−3227.72	−	1863.53i	−0.354541	−	0.204694i
$437$	1075.65	+	621.028i	0.117747	+	0.0679812i
$438$	3861.89	−	6590.64i	0.421298	−	0.718979i
$439$	4160.94	+	7206.96i	0.452371	+	0.783530i	0.998533	−	0.0541499i	$-0.0172449\pi$
$439$	4160.94	+	7206.96i	0.452371	+	0.783530i	−0.546162	+	0.837680i	$0.683912\pi$
$440$		−	23380.4i		−	2.53322i
$441$	−70.5364	−	125.889i	−0.00761650	−	0.0135934i
$442$	−9094.74	−	2147.62i	−0.978717	−	0.231112i
$443$	7302.46	+	12648.2i	0.783183	+	1.35651i	0.930078	+	0.367361i	$0.119739\pi$
$443$	7302.46	+	12648.2i	0.783183	+	1.35651i	−0.146895	+	0.989152i	$0.546928\pi$
$444$	70.2513	−	10911.9i	0.00750896	−	1.16634i
$445$	−7211.68	+	12491.0i	−0.768239	+	1.33063i
$446$	−12686.0	+	21972.9i	−1.34686	+	2.33284i
$447$	−49.9697	+	7761.63i	−0.00528744	+	0.821281i
$448$	−35413.0	+	20445.7i	−3.73462	+	2.15618i
$449$		−	6918.64i		−	0.727196i	−0.931556	−	0.363598i	$-0.881548\pi$
$449$		−	6918.64i		−	0.727196i	0.931556	−	0.363598i	$-0.118452\pi$
$450$	2950.79	−	1653.35i	0.309114	−	0.173199i
$451$	734.751			0.0767141
$452$	−603.594	−	1045.46i	−0.0628112	−	0.108792i
$453$	2017.39	+	1182.12i	0.209239	+	0.122607i
$454$	−2789.54	+	4831.63i	−0.288369	+	0.499470i
$455$	−7621.06	−	7178.29i	−0.785233	−	0.739612i
$456$	−28298.8	−	49752.0i	−2.90617	−	5.10932i
$457$	1914.91	−	1105.57i	0.196008	−	0.113165i	−0.398784	−	0.917045i	$-0.630568\pi$
$457$	1914.91	−	1105.57i	0.196008	−	0.113165i	0.594792	+	0.803880i	$0.297234\pi$
$458$	14293.3			1.45826
$459$	−5079.55	−	98.1178i	−0.516543	−	0.00997767i
$460$			2409.27i			0.244201i
$461$	3043.80	−	1757.34i	0.307514	−	0.177543i	−0.338299	−	0.941038i	$-0.609852\pi$
$461$	3043.80	−	1757.34i	0.307514	−	0.177543i	0.645814	+	0.763495i	$0.276518\pi$
$462$	−11155.1	+	6345.01i	−1.12334	+	0.638953i
$463$	−6350.25	−	3666.32i	−0.637410	−	0.368009i	0.146206	−	0.989254i	$-0.453294\pi$
$463$	−6350.25	−	3666.32i	−0.637410	−	0.368009i	−0.783616	+	0.621245i	$0.786627\pi$
$464$	27389.0	−	47439.1i	2.74030	−	4.74634i
$465$	−2476.28	+	4225.98i	−0.246957	+	0.421452i
$466$	−13058.5	+	7539.35i	−1.29812	+	0.749471i
$467$	4666.40			0.462388			0.231194	−	0.972908i	$-0.425737\pi$
$467$	4666.40			0.462388			0.231194	+	0.972908i	$0.425737\pi$
$468$	−6842.22	+	27393.6i	−0.675816	+	2.70571i
$469$	−406.902			−0.0400618
$470$	3634.11	−	2098.16i	0.356658	−	0.205917i
$471$	434.450	+	2.79701i	0.0425019	+	0.000273629i
$472$	−5753.24	+	9964.90i	−0.561047	+	0.971762i
$473$	5606.43	+	3236.87i	0.544998	+	0.314654i
$474$	24.6581	−	3830.06i	0.00238942	−	0.371141i
$475$	−2755.08	+	1590.65i	−0.266130	+	0.153650i
$476$		−	14846.0i		−	1.42955i
$477$	−7666.42	+	12892.4i	−0.735893	+	1.23753i
$478$	−8384.70			−0.802317
$479$	−10674.6	+	6162.97i	−1.01823	+	0.587877i	−0.913592	−	0.406633i	$-0.866703\pi$
$479$	−10674.6	+	6162.97i	−1.01823	+	0.587877i	−0.104642	+	0.994510i	$0.533370\pi$
$480$	24752.1	−	42241.6i	2.35370	−	4.01678i
$481$	3025.03	−	3211.62i	0.286756	−	0.304444i
$482$	6481.05	−	11225.5i	0.612456	−	1.06081i
$483$	737.317	−	419.384i	0.0694598	−	0.0395086i
$484$	8199.11	+	14201.3i	0.770014	+	1.33370i
$485$	−10065.2			−0.942348
$486$	−671.196	+	20844.0i	−0.0626462	+	1.94548i
$487$		−	13962.2i		−	1.29915i	−0.760297	−	0.649575i	$-0.774947\pi$
$487$		−	13962.2i		−	1.29915i	0.760297	−	0.649575i	$-0.225053\pi$
$488$	−52770.1	+	30466.8i	−4.89506	+	2.82617i
$489$	10771.4	−	6126.76i	0.996115	−	0.566588i
$490$	−178.834	+	309.749i	−0.0164875	+	0.0285572i
$491$	6364.63	−	11023.9i	0.584994	−	1.01324i	−0.409883	−	0.912138i	$-0.634430\pi$
$491$	6364.63	−	11023.9i	0.584994	−	1.01324i	0.994876	−	0.101100i	$-0.0322363\pi$
$492$	3010.33	+	1763.95i	0.275846	+	0.161636i
$493$	3885.26	+	6729.46i	0.354935	+	0.614766i
$494$	8291.53	−	35113.0i	0.755169	−	3.19800i
$495$	4095.17	−	6886.72i	0.371847	−	0.625324i
$496$			19796.5i			1.79211i
$497$	7542.37	+	13063.8i	0.680727	+	1.17905i
$498$	7900.42	+	50.8632i	0.710896	+	0.00457677i
$499$	12709.1	+	7337.60i	1.14016	+	0.658269i	0.946469	−	0.322794i	$-0.104622\pi$
$499$	12709.1	+	7337.60i	1.14016	+	0.658269i	0.193686	+	0.981063i	$0.437956\pi$
$500$	24013.6	+	13864.3i	2.14784	+	1.24006i
$501$	−37.6710	+	5851.31i	−0.00335931	+	0.521791i
$502$	17402.7	−	10047.5i	1.54725	−	0.893307i
$503$	3551.67			0.314833			0.157417	−	0.987532i	$-0.449683\pi$
$503$	3551.67			0.314833			0.157417	+	0.987532i	$0.449683\pi$
$504$	−39086.0	−	503.295i	−3.45442	−	0.0444813i
$505$			21581.4i			1.90170i
$506$	597.028	+	1034.08i	0.0524528	+	0.0908510i
$507$	−9567.87	+	6227.34i	−0.838114	+	0.545494i
$508$	300.839	−	521.069i	0.0262748	−	0.0455092i
$509$	8721.36	+	5035.28i	0.759465	+	0.438477i	0.829104	−	0.559095i	$-0.188851\pi$
$509$	8721.36	+	5035.28i	0.759465	+	0.438477i	−0.0696387	+	0.997572i	$0.522185\pi$
$510$	6225.89	+	10945.7i	0.540563	+	0.950360i
$511$	2453.30	+	4249.24i	0.212383	+	0.367858i
$512$		−	36976.4i		−	3.19168i
$513$	378.814	−	19611.2i	0.0326024	−	1.68782i
$514$		−	25929.3i		−	2.22508i
$515$	−14218.7	+	8209.18i	−1.21660	+	0.702407i
$516$	15199.0	+	26721.3i	1.29671	+	2.27973i
$517$	765.411	−	1325.73i	0.0651117	−	0.112777i
$518$	8246.72	+	4761.24i	0.699498	+	0.403855i
$519$	4038.54	−	6892.10i	0.341565	−	0.582909i
$520$	42992.8	−	12909.6i	3.62569	−	1.08870i
$521$	−14507.3			−1.21992			−0.609958	−	0.792434i	$-0.708814\pi$
$521$	−14507.3			−1.21992			−0.609958	+	0.792434i	$0.708814\pi$
$522$	27826.7	−	15591.5i	2.33322	−	1.30732i
$523$	19405.2			1.62243			0.811214	−	0.584749i	$-0.198807\pi$
$523$	19405.2			1.62243			0.811214	+	0.584749i	$0.198807\pi$
$524$	−18563.1	−	32152.2i	−1.54758	−	2.68049i
$525$	−13.9871	+	2172.58i	−0.00116276	+	0.180608i
$526$	6019.63	+	3475.44i	0.498989	+	0.288092i
$527$	−2431.99	−	1404.11i	−0.201023	−	0.116061i
$528$	208.481	−	32382.8i	0.0171837	−	2.66909i
$529$	6044.04	+	10468.6i	0.496757	+	0.860408i
$530$	37177.7			3.04698
$531$	−3440.02	+	1927.47i	−0.281138	+	0.157524i
$532$	57317.6			4.67111
$533$	405.698	+	1351.09i	0.0329695	+	0.109798i
$534$	−17161.4	+	29287.3i	−1.39072	+	2.37338i
$535$	11467.3	+	6620.65i	0.926681	+	0.535020i
$536$	872.327	−	1510.92i	0.0702963	−	0.121757i
$537$	−5499.33	−	9668.34i	−0.441925	−	0.776945i
$538$	−19089.1	+	11021.1i	−1.52972	+	0.883184i
$539$			130.478i			0.0104268i
$540$	33311.5	−	18383.9i	2.65463	−	1.46503i
$541$		−	3031.27i		−	0.240895i	−0.992720	−	0.120448i	$-0.961567\pi$
$541$		−	3031.27i		−	0.240895i	0.992720	−	0.120448i	$-0.0384330\pi$
$542$	−10854.5	−	18800.6i	−0.860225	−	1.48995i
$543$	−2682.05	−	4715.29i	−0.211966	−	0.372656i
$544$	24309.4	+	14035.1i	1.91592	+	1.10615i
$545$	−1015.30	+	1758.55i	−0.0797993	+	0.138216i
$546$	−17826.8	−	17009.0i	−1.39729	−	1.33319i
$547$	−1158.89	−	2007.26i	−0.0905861	−	0.156900i	0.817172	−	0.576394i	$-0.195541\pi$
$547$	−1158.89	−	2007.26i	−0.0905861	−	0.156900i	−0.907758	+	0.419494i	$0.862207\pi$
$548$			20550.1i			1.60193i
$549$	−20879.9	−	268.862i	−1.62319	−	0.0209012i
$550$	−3058.35			−0.237107
$551$	−25981.2	+	15000.2i	−2.00877	+	1.15977i
$552$	−23.4145	+	3636.91i	−0.00180541	+	0.280429i
$553$	2130.61	+	1230.11i	0.163838	+	0.0945921i
$554$	−19470.7	−	11241.4i	−1.49320	−	0.862099i
$555$	−5945.10	−	38.2748i	−0.454694	−	0.00292734i
$556$	−21046.0	−	36452.8i	−1.60530	−	2.78047i
$557$		−	6082.67i		−	0.462713i	−0.972869	−	0.231356i	$-0.925684\pi$
$557$		−	6082.67i		−	0.462713i	0.972869	−	0.231356i	$-0.0743163\pi$
$558$	−5891.78	+	9908.01i	−0.446987	+	0.751684i
$559$	−2856.47	+	12096.6i	−0.216128	+	0.915262i
$560$	28509.8	+	49380.3i	2.15135	+	3.72625i
$561$	3963.43	+	2322.44i	0.298282	+	0.174783i
$562$	3441.84	−	5961.44i	0.258337	−	0.447452i
$563$	2068.20	−	3582.22i	0.154821	−	0.268157i	−0.778173	−	0.628050i	$-0.783853\pi$
$563$	2068.20	−	3582.22i	0.154821	−	0.268157i	0.932994	+	0.359893i	$0.117187\pi$
$564$	6318.69	−	3594.06i	0.471746	−	0.268328i
$565$	−569.592	+	328.854i	−0.0424122	+	0.0244867i
$566$			6270.00i			0.465632i
$567$	−11424.7	−	6994.33i	−0.846193	−	0.518050i
$568$	−64678.2			−4.77788
$569$	−6568.46	−	11376.9i	−0.483944	−	0.838216i	0.515886	−	0.856657i	$-0.327463\pi$
$569$	−6568.46	−	11376.9i	−0.483944	−	0.838216i	−0.999830	+	0.0184413i	$0.994130\pi$
$570$	−42259.2	+	24037.0i	−3.10534	+	1.76631i
$571$	−12921.9	+	22381.3i	−0.947045	+	1.64033i	−0.195441	+	0.980715i	$0.562614\pi$
$571$	−12921.9	+	22381.3i	−0.947045	+	1.64033i	−0.751604	+	0.659615i	$0.770720\pi$
$572$	17504.6	−	18584.3i	1.27955	−	1.35847i
$573$	−5051.21	+	8620.30i	−0.368267	+	0.628478i
$574$	−2636.82	+	1522.37i	−0.191740	+	0.110701i
$575$	202.147			0.0146611
$576$	30709.5	−	51643.2i	2.22146	−	3.73577i
$577$		−	18949.9i		−	1.36724i	−0.729840	−	0.683618i	$-0.760406\pi$
$577$		−	18949.9i		−	1.36724i	0.729840	−	0.683618i	$-0.239594\pi$
$578$	17172.3	−	9914.44i	1.23577	−	0.713471i
$579$	104.323	−	16204.1i	0.00748793	−	1.16308i
$580$	−50396.7	−	29096.5i	−3.60795	−	2.08305i
$581$	−2537.38	+	4394.88i	−0.181185	+	0.313822i
$582$	−23687.8	−	152.503i	−1.68710	−	0.0108616i
$583$	11745.5	−	6781.25i	0.834387	−	0.481734i
$584$	−21037.8			−1.49067
$585$	14924.8	+	3727.82i	1.05481	+	0.263464i
$586$	1577.58			0.111210
$587$	1252.24	−	722.981i	0.0880503	−	0.0508358i	−0.455328	−	0.890324i	$-0.650478\pi$
$587$	1252.24	−	722.981i	0.0880503	−	0.0508358i	0.543379	+	0.839488i	$0.317145\pi$
$588$	−313.244	+	534.576i	−0.0219693	+	0.0374924i
$589$	5421.01	−	9389.46i	0.379234	−	0.656852i
$590$	8464.16	+	4886.79i	0.590617	+	0.340993i
$591$	16729.3	−	9515.61i	1.16439	−	0.662301i
$592$	−20809.6	+	12014.4i	−1.44471	+	0.834103i
$593$		−	19607.0i		−	1.35778i	−0.734239	−	0.678891i	$-0.762461\pi$
$593$		−	19607.0i		−	1.35778i	0.734239	−	0.678891i	$-0.237539\pi$
$594$	9742.02	−	16145.3i	0.672929	−	1.11524i
$595$	−8088.49			−0.557304
$596$	28861.8	−	16663.4i	1.98360	−	1.14523i
$597$	−13487.8	−	23712.8i	−0.924653	−	1.62563i
$598$	−1571.86	+	1668.82i	−0.107489	+	0.114119i
$599$	9376.78	−	16241.1i	0.639608	−	1.10783i	−0.345911	−	0.938267i	$-0.612430\pi$
$599$	9376.78	−	16241.1i	0.639608	−	1.10783i	0.985519	−	0.169566i	$-0.0542365\pi$
$600$	−8037.26	−	4709.57i	−0.546867	−	0.320445i
$601$	−2497.06	−	4325.04i	−0.169480	−	0.293548i	0.768757	−	0.639541i	$-0.220875\pi$
$601$	−2497.06	−	4325.04i	−0.169480	−	0.293548i	−0.938237	+	0.345993i	$0.887542\pi$
$602$	−26826.6			−1.81623
$603$	521.588	−	292.250i	0.0352251	−	0.0197369i
$604$		−	10039.6i		−	0.676333i
$605$	7737.23	−	4467.09i	0.519939	−	0.300187i
$606$	−326.989	+	50790.1i	−0.0219192	+	3.40463i
$607$	−7380.40	+	12783.2i	−0.493511	+	0.854787i	−0.999972	−	0.00747634i	$-0.997620\pi$
$607$	−7380.40	+	12783.2i	−0.493511	+	0.854787i	0.506461	+	0.862263i	$0.330954\pi$
$608$	−54186.6	+	93854.0i	−3.61441	+	6.26033i
$609$	−131.902	+	20488.0i	−0.00877660	+	1.36324i
$610$	25878.5	+	44822.8i	1.71769	+	2.97512i
$611$	2860.44	+	675.458i	0.189396	+	0.0447236i
$612$	10662.9	+	19030.4i	0.704284	+	1.25696i
$613$			4082.29i			0.268976i	0.990915	+	0.134488i	$0.0429390\pi$
$613$			4082.29i			0.268976i	−0.990915	+	0.134488i	$0.957061\pi$
$614$	11784.9	+	20412.1i	0.774593	+	1.34164i
$615$	961.047	−	1640.11i	0.0630133	−	0.107537i
$616$	30609.0	+	17672.1i	2.00206	+	1.15589i
$617$	−12685.7	−	7324.11i	−0.827729	−	0.477889i	0.0253456	−	0.999679i	$-0.491931\pi$
$617$	−12685.7	−	7324.11i	−0.827729	−	0.477889i	−0.853074	+	0.521789i	$0.825265\pi$
$618$	−33587.0	+	19104.2i	−2.18620	+	1.24350i
$619$	972.893	−	561.700i	0.0631727	−	0.0364728i	−0.468081	−	0.883686i	$-0.655054\pi$
$619$	972.893	−	561.700i	0.0631727	−	0.0364728i	0.531254	+	0.847213i	$0.321721\pi$
$620$	21030.7			1.36228
$621$	−643.916	+	1067.15i	−0.0416094	+	0.0689588i
$622$		−	4672.10i		−	0.301181i
$623$	−10901.9	−	18882.7i	−0.701086	−	1.21432i
$624$	59661.9	−	17497.0i	3.82754	−	1.12250i
$625$	8975.77	−	15546.5i	0.574449	−	0.994975i
$626$	30629.9	+	17684.2i	1.95562	+	1.12908i
$627$	−8966.49	+	15302.1i	−0.571112	+	0.974649i
$628$	−932.716	−	1615.51i	−0.0592666	−	0.102653i
$629$		−	3408.60i		−	0.216073i
$630$	−427.498	+	33199.6i	−0.0270348	+	2.09953i
$631$			28564.2i			1.80210i	0.433719	+	0.901048i	$0.357201\pi$
$631$			28564.2i			1.80210i	−0.433719	+	0.901048i	$0.642799\pi$
$632$	−9135.30	+	5274.27i	−0.574973	+	0.331961i
$633$	13062.2	+	84.0950i	0.820184	+	0.00528038i
$634$	24366.5	−	42204.0i	1.52637	−	2.64375i
$635$	−283.892	−	163.905i	−0.0177416	−	0.0102431i
$636$	64402.1	+	414.623i	4.01527	+	0.0258504i
$637$	−239.928	+	72.0441i	−0.0149235	+	0.00448115i
$638$	−28841.1			−1.78970
$639$	−19051.0	−	11328.7i	−1.17942	−	0.701337i
$640$	−73545.7			−4.54242
$641$	7133.28	+	12355.2i	0.439544	+	0.761312i	0.997654	−	0.0684546i	$-0.0218068\pi$
$641$	7133.28	+	12355.2i	0.439544	+	0.761312i	−0.558111	+	0.829767i	$0.688473\pi$
$642$	26887.1	+	15754.9i	1.65288	+	0.968533i
$643$	2559.75	+	1477.87i	0.156993	+	0.0906400i	0.576438	−	0.817141i	$-0.304442\pi$
$643$	2559.75	+	1477.87i	0.156993	+	0.0906400i	−0.419445	+	0.907781i	$0.637775\pi$
$644$	−3154.15	−	1821.05i	−0.192998	−	0.111428i
$645$	14558.5	−	8280.83i	0.888743	−	0.505515i
$646$	−13936.9	−	24139.5i	−0.848825	−	1.47021i
$647$	11951.3			0.726206			0.363103	−	0.931749i	$-0.381717\pi$
$647$	11951.3			0.726206			0.363103	+	0.931749i	$0.381717\pi$
$648$	50464.0	−	27427.7i	3.05928	−	1.66275i
$649$	3565.42			0.215647
$650$	−1688.69	−	5623.83i	−0.101901	−	0.339361i
$651$	−3660.84	−	6436.10i	−0.220399	−	0.387482i
$652$	−46078.8	−	26603.6i	−2.76777	−	1.59797i
$653$	8724.18	−	15110.7i	0.522823	−	0.905556i	−0.476824	−	0.878999i	$-0.658212\pi$
$653$	8724.18	−	15110.7i	0.522823	−	0.905556i	0.999647	−	0.0265576i	$-0.00845455\pi$
$654$	−2416.07	+	4123.23i	−0.144459	+	0.246531i
$655$	−17517.4	+	10113.7i	−1.04498	+	0.603318i
$656$		−	7683.02i		−	0.457274i
$657$	−6196.71	−	3684.86i	−0.367971	−	0.218813i
$658$			6343.58i			0.375834i
$659$	−1298.92	−	2249.80i	−0.0767813	−	0.132989i	0.825078	−	0.565019i	$-0.191131\pi$
$659$	−1298.92	−	2249.80i	−0.0767813	−	0.132989i	−0.901859	+	0.432029i	$0.857798\pi$
$660$	−34401.7	−	221.479i	−2.02892	−	0.0130622i
$661$	−16052.8	−	9268.10i	−0.944602	−	0.545366i	−0.0532024	−	0.998584i	$-0.516943\pi$
$661$	−16052.8	−	9268.10i	−0.944602	−	0.545366i	−0.891400	+	0.453217i	$0.850276\pi$
$662$	−16566.0	+	28693.2i	−0.972592	+	1.68458i
$663$	−2082.16	+	8570.48i	−0.121967	+	0.502036i
$664$	−10879.4	−	18843.7i	−0.635849	−	1.10132i
$665$		−	31228.1i		−	1.82101i
$666$	−13990.8	−	180.154i	−0.814011	−	0.0104817i
$667$	1906.30			0.110663
$668$	21758.2	−	12562.1i	1.26026	−	0.727609i
$669$	20660.7	+	12106.5i	1.19400	+	0.699645i
$670$	−1283.37	−	740.953i	−0.0740012	−	0.0427246i
$671$	16351.4	+	9440.51i	0.940745	+	0.543140i
$672$	36592.6	+	64333.2i	2.10058	+	3.69302i
$673$	13688.1	+	23708.5i	0.784008	+	1.35794i	0.929590	+	0.368596i	$0.120161\pi$
$673$	13688.1	+	23708.5i	0.784008	+	1.35794i	−0.145581	+	0.989346i	$0.546505\pi$
$674$			47925.7i			2.73892i
$675$	−1542.49	−	2794.97i	−0.0879560	−	0.159375i
$676$	43838.8	+	21926.7i	2.49424	+	1.24753i
$677$	−15630.7	−	27073.1i	−0.887349	−	1.53693i	−0.842997	−	0.537918i	$-0.819211\pi$
$677$	−15630.7	−	27073.1i	−0.887349	−	1.53693i	−0.0443519	−	0.999016i	$-0.514122\pi$
$678$	−1345.47	+	765.303i	−0.0762133	+	0.0433500i
$679$	7607.83	−	13177.1i	0.429988	−	0.744760i
$680$	17340.3	−	30034.4i	0.977900	−	1.69377i
$681$	4543.09	+	2662.10i	0.255641	+	0.149797i
$682$	9026.60	−	5211.51i	0.506813	−	0.292609i
$683$		−	12238.4i		−	0.685633i	−0.939402	−	0.342817i	$-0.888619\pi$
$683$		−	12238.4i		−	0.685633i	0.939402	−	0.342817i	$-0.111381\pi$
$684$	−73472.7	+	41167.4i	−4.10716	+	2.30128i
$685$	11196.2			0.624505
$686$	−17620.3	−	30519.3i	−0.980680	−	1.69859i
$687$	86.8482	−	13489.9i	0.00482309	−	0.749156i
$688$	33846.8	−	58624.3i	1.87558	−	3.24859i
$689$	18955.0	+	17853.7i	1.04808	+	0.987189i
$690$	3089.18	+	19.8882i	0.170439	+	0.00109729i
$691$	11967.8	−	6909.61i	0.658866	−	0.380396i	−0.132979	−	0.991119i	$-0.542454\pi$
$691$	11967.8	−	6909.61i	0.658866	−	0.380396i	0.791845	+	0.610723i	$0.209121\pi$
$692$	−34298.7			−1.88416
$693$	5920.57	+	10566.6i	0.324537	+	0.579211i
$694$		−	57545.8i		−	3.14756i
$695$	−19860.4	+	11466.4i	−1.08395	+	0.625822i
$696$	−75793.5	−	44412.5i	−4.12780	−	2.41875i
$697$	943.858	+	544.937i	0.0512929	+	0.0296140i
$698$	35230.2	−	61020.4i	1.91043	−	3.30896i
$699$	7036.21	+	12370.3i	0.380735	+	0.669368i
$700$	8078.76	−	4664.28i	0.436212	−	0.251847i
$701$	8644.24			0.465747			0.232873	−	0.972507i	$-0.425187\pi$
$701$	8644.24			0.465747			0.232873	+	0.972507i	$0.425187\pi$
$702$	35067.8	+	8999.28i	1.88540	+	0.483841i
$703$	13160.0			0.706028
$704$	−47049.1	+	27163.8i	−2.51879	+	1.45422i
$705$	−1958.14	−	3442.59i	−0.104607	−	0.183908i
$706$	−24031.4	+	41623.6i	−1.28107	+	2.21887i
$707$	−28253.8	−	16312.3i	−1.50296	−	0.867734i
$708$	14607.8	+	8559.66i	0.775415	+	0.454367i
$709$	5711.74	−	3297.68i	0.302551	−	0.174678i	−0.341037	−	0.940050i	$-0.610778\pi$
$709$	5711.74	−	3297.68i	0.302551	−	0.174678i	0.643588	+	0.765372i	$0.277445\pi$
$710$			54937.5i			2.90390i
$711$	−3614.63	−	46.5441i	−0.190660	−	0.00245505i
$712$	93487.4			4.92077
$713$	−596.629	+	344.464i	−0.0313379	+	0.0180929i
$714$	−19035.7	−	122.552i	−0.997748	−	0.00642354i
$715$	−10125.2	−	9536.94i	−0.529595	−	0.498827i
$716$	−23879.2	+	41359.9i	−1.24638	+	2.15879i
$717$	−50.9467	+	7913.40i	−0.00265361	+	0.412177i
$718$	−21118.8	−	36578.8i	−1.09770	−	1.90127i
$719$	8242.11			0.427509			0.213754	−	0.976887i	$-0.431431\pi$
$719$	8242.11			0.427509			0.213754	+	0.976887i	$0.431431\pi$
$720$	−72011.9	−	42821.7i	−3.72740	−	2.21649i
$721$		−	24819.7i		−	1.28202i
$722$	60494.7	−	34926.6i	3.11825	−	1.80032i
$723$	−10555.1	−	6184.96i	−0.542946	−	0.318148i
$724$	−11646.0	+	20171.4i	−0.597816	+	1.03545i
$725$	−2441.32	+	4228.49i	−0.125060	+	0.216610i
$726$	18276.7	−	10395.7i	0.934313	−	0.531435i
$727$	−13252.4	−	22953.8i	−0.676070	−	1.17099i	−0.976155	−	0.217075i	$-0.930348\pi$
$727$	−13252.4	−	22953.8i	−0.676070	−	1.17099i	0.300085	−	0.953913i	$-0.402985\pi$
$728$	−15595.2	+	66042.9i	−0.793954	+	3.36224i
$729$	19668.3	+	760.120i	0.999254	+	0.0386181i
$730$			17869.5i			0.905998i
$731$	4801.33	+	8316.15i	0.242932	+	0.420771i
$732$	44328.8	+	77934.1i	2.23830	+	3.93515i
$733$	−21498.4	−	12412.1i	−1.08330	−	0.625446i	−0.151518	−	0.988455i	$-0.548416\pi$
$733$	−21498.4	−	12412.1i	−1.08330	−	0.625446i	−0.931786	+	0.363009i	$0.881749\pi$
$734$	−5485.69	−	3167.17i	−0.275859	−	0.159267i
$735$	291.251	+	170.663i	0.0146163	+	0.00856465i
$736$	5963.71	−	3443.15i	0.298676	−	0.172440i
$737$	−540.602			−0.0270194
$738$	2286.60	−	3845.30i	0.114053	−	0.191799i
$739$		−	19016.1i		−	0.946576i	−0.880908	−	0.473288i	$-0.843067\pi$
$739$		−	19016.1i		−	0.946576i	0.880908	−	0.473288i	$-0.156933\pi$
$740$	12763.5	+	22107.0i	0.634046	+	1.09820i
$741$	−33089.0	−	8038.82i	−1.64042	−	0.398533i
$742$	−28100.9	+	48672.1i	−1.39032	+	2.40810i
$743$	−31011.8	−	17904.7i	−1.53124	−	0.884064i	−0.999305	−	0.0372808i	$-0.988130\pi$
$743$	−31011.8	−	17904.7i	−1.53124	−	0.884064i	−0.531939	−	0.846783i	$-0.678536\pi$
$744$	31746.9	+	204.388i	1.56438	+	0.0100715i
$745$	−9078.63	−	15724.7i	−0.446464	−	0.773298i
$746$			40291.8i			1.97746i
$747$	96.0083	−	7456.02i	0.00470249	−	0.365196i
$748$		−	19724.1i		−	0.964151i
$749$	−17335.2	+	10008.5i	−0.845678	+	0.488252i
$750$	17975.1	−	30676.0i	0.875144	−	1.49351i
$751$	−9216.14	+	15962.8i	−0.447805	+	0.775621i	−0.998243	−	0.0592551i	$-0.981127\pi$
$751$	−9216.14	+	15962.8i	−0.447805	+	0.775621i	0.550438	+	0.834876i	$0.314461\pi$
$752$	−13862.7	−	8003.62i	−0.672234	−	0.388114i
$753$	−9376.95	−	16485.6i	−0.453805	−	0.797832i
$754$	−15924.8	−	53034.2i	−0.769160	−	2.56153i
$755$	−5469.83			−0.263666
$756$	−1110.80	+	57506.1i	−0.0534384	+	2.76650i
$757$	27280.6			1.30982			0.654908	−	0.755708i	$-0.272707\pi$
$757$	27280.6			1.30982			0.654908	+	0.755708i	$0.272707\pi$
$758$	3822.26	+	6620.35i	0.183154	+	0.317232i
$759$	979.584	−	557.186i	0.0468467	−	0.0266463i
$760$	115957.	+	66947.7i	5.53447	+	3.19533i
$761$	1835.59	+	1059.78i	0.0874375	+	0.0504820i	0.543081	−	0.839680i	$-0.317258\pi$
$761$	1835.59	+	1059.78i	0.0874375	+	0.0504820i	−0.455644	+	0.890162i	$0.650591\pi$
$762$	−665.635	−	390.040i	−0.0316449	−	0.0185429i
$763$	−1534.83	−	2658.40i	−0.0728239	−	0.126135i
$764$	42899.1			2.03146
$765$	10368.3	−	5809.42i	0.490020	−	0.274562i
$766$	−41439.4			−1.95466
$767$	1968.67	+	6556.24i	0.0926787	+	0.308647i
$768$	−80580.8	−	518.782i	−3.78608	−	0.0243749i
$769$	24041.9	+	13880.6i	1.12740	+	0.650906i	0.943280	−	0.331998i	$-0.107723\pi$
$769$	24041.9	+	13880.6i	1.12740	+	0.650906i	0.184122	+	0.982903i	$0.441056\pi$
$770$	15010.6	−	25999.2i	0.702527	−	1.21681i
$771$	−24471.8	−	157.550i	−1.14310	−	0.00735933i
$772$	−60255.4	+	34788.5i	−2.80912	+	1.62184i
$773$			21268.9i			0.989635i	0.868997	+	0.494818i	$0.164765\pi$
$773$			21268.9i			0.989635i	−0.868997	+	0.494818i	$0.835235\pi$
$774$	34387.7	−	19267.7i	1.59695	−	0.894786i
$775$		−	1764.56i		−	0.0817869i
$776$	32619.7	+	56499.1i	1.50900	+	2.61366i
$777$	4543.72	−	7754.24i	0.209788	−	0.358020i
$778$	28970.2	+	16726.0i	1.33500	+	0.770765i
$779$	−2103.90	+	3644.05i	−0.0967650	+	0.167602i
$780$	−18587.9	−	63381.6i	−0.853272	−	2.90952i
$781$	10020.6	+	17356.3i	0.459112	+	0.795206i
$782$			1771.17i			0.0809935i
$783$	−14546.1	−	26357.3i	−0.663900	−	1.20298i
$784$	1364.36			0.0621518
$785$	−880.173	+	508.168i	−0.0400188	+	0.0231048i
$786$	−41379.1	+	23536.3i	−1.87779	+	1.06808i
$787$	16286.8	+	9403.21i	0.737692	+	0.425906i	0.821229	−	0.570598i	$-0.193289\pi$
$787$	16286.8	+	9403.21i	0.737692	+	0.425906i	−0.0835378	+	0.996505i	$0.526622\pi$
$788$	−71565.9	−	41318.6i	−3.23532	−	1.86791i
$789$	3316.66	−	5660.15i	0.149653	−	0.255395i
$790$	4479.95	+	7759.51i	0.201759	+	0.349457i
$791$		−	994.260i		−	0.0446925i
$792$	−51928.9	−	668.668i	−2.32982	−	0.0300001i
$793$	−8331.04	+	35280.3i	−0.373069	+	1.57988i
$794$	−2853.92	−	4943.13i	−0.127559	−	0.220939i
$795$	225.898	−	35088.0i	0.0100777	−	1.56534i
$796$	−58566.5	+	101440.i	−2.60783	+	4.51690i
$797$	7658.43	−	13264.8i	0.340371	−	0.589539i	−0.644131	−	0.764915i	$-0.722781\pi$
$797$	7658.43	−	13264.8i	0.340371	−	0.589539i	0.984502	+	0.175376i	$0.0561141\pi$
$798$	473.151	−	73493.0i	0.0209892	−	3.26018i
$799$	1966.49	−	1135.35i	0.0870705	−	0.0502702i
$800$			17638.0i			0.779496i
$801$	27536.8	+	16374.7i	1.21469	+	0.722312i
$802$	35687.8			1.57130
$803$	3259.41	+	5645.46i	0.143240	+	0.248099i
$804$	−2214.88	−	1297.85i	−0.0971554	−	0.0569298i
$805$	−992.155	+	1718.46i	−0.0434396	+	0.0752396i
$806$	14567.2	+	13720.9i	0.636612	+	0.599626i
$807$	10285.6	+	18083.1i	0.448663	+	0.788791i
$808$	121142.	−	69941.6i	5.27448	−	3.04522i
$809$	−40852.9			−1.77541			−0.887707	−	0.460409i	$-0.847703\pi$
$809$	−40852.9			−1.77541			−0.887707	+	0.460409i	$0.847703\pi$
$810$	−23297.0	−	42864.0i	−1.01059	−	1.85937i
$811$		−	3588.52i		−	0.155376i	−0.996978	−	0.0776880i	$-0.975246\pi$
$811$		−	3588.52i		−	0.155376i	0.996978	−	0.0776880i	$-0.0247538\pi$
$812$	76184.9	−	43985.4i	3.29257	−	1.90096i
$813$	−17809.8	+	10130.2i	−0.768285	+	0.436999i
$814$	10956.4	+	6325.70i	0.471772	+	0.272378i
$815$	−14494.3	+	25104.9i	−0.622962	+	1.07900i
$816$	24284.9	−	41444.1i	1.04184	−	1.77798i
$817$	−32107.0	+	18537.0i	−1.37489	+	0.793792i
$818$	86942.8			3.71624
$819$	−16161.3	+	16721.4i	−0.689525	+	0.713424i
$820$	−8162.02			−0.347598
$821$	20768.0	−	11990.4i	0.882837	−	0.509706i	0.0112440	−	0.999937i	$-0.496421\pi$
$821$	20768.0	−	11990.4i	0.882837	−	0.509706i	0.871593	+	0.490231i	$0.163088\pi$
$822$	26349.5	+	169.639i	1.11806	+	0.00719810i
$823$	15566.4	−	26961.9i	0.659310	−	1.14196i	−0.321485	−	0.946915i	$-0.604182\pi$
$823$	15566.4	−	26961.9i	0.659310	−	1.14196i	0.980795	−	0.195043i	$-0.0624847\pi$
$824$	92160.9	+	53209.1i	3.89633	+	2.24955i
$825$	−18.5830	+	2886.44i	−0.000784215	+	0.121810i
$826$	−12795.3	+	7387.37i	−0.538990	+	0.311186i
$827$			18442.4i			0.775458i	0.921773	+	0.387729i	$0.126740\pi$
$827$			18442.4i			0.775458i	−0.921773	+	0.387729i	$0.873260\pi$
$828$	5351.09	+	68.9039i	0.224593	+	0.00289200i
$829$	−12496.8			−0.523559			−0.261780	−	0.965128i	$-0.584309\pi$
$829$	−12496.8			−0.523559			−0.261780	+	0.965128i	$0.584309\pi$
$830$	−16005.8	+	9240.96i	−0.669361	+	0.386456i
$831$	−10727.9	+	18308.0i	−0.447828	+	0.764256i
$832$	−75928.4	−	71517.1i	−3.16387	−	2.98006i
$833$	−96.7703	+	167.611i	−0.00402508	+	0.00697164i
$834$	−46913.7	+	26684.4i	−1.94783	+	1.10792i
$835$	−6844.17	−	11854.5i	−0.283655	−	0.491306i
$836$	76151.0			3.15040
$837$	9315.28	+	5620.80i	0.384687	+	0.232119i
$838$			3101.19i			0.127839i
$839$	−8488.21	+	4900.67i	−0.349279	+	0.201657i	−0.664368	−	0.747406i	$-0.731299\pi$
$839$	−8488.21	+	4900.67i	−0.349279	+	0.201657i	0.315088	+	0.949062i	$0.397966\pi$
$840$	79483.8	−	45210.2i	3.26482	−	1.85703i
$841$	−10827.8	+	18754.3i	−0.443962	+	0.768964i
$842$	−29056.5	+	50327.4i	−1.18926	+	2.05985i
$843$	−5605.43	−	3284.59i	−0.229017	−	0.134196i
$844$	−28043.1	−	48572.1i	−1.14370	−	1.98095i
$845$	11946.2	−	23884.5i	0.486346	−	0.972369i
$846$	−4556.17	−	8131.54i	−0.185159	−	0.330459i
$847$			13505.8i			0.547894i
$848$	−70909.0	−	122818.i	−2.87149	−	4.97357i
$849$	5917.56	+	38.0975i	0.239211	+	0.00154005i
$850$	−3928.75	−	2268.26i	−0.158535	−	0.0915303i
$851$	−724.184	−	418.108i	−0.0291712	−	0.0168420i
$852$	−612.688	+	95166.9i	−0.0246366	+	3.82672i
$853$	−7706.18	+	4449.16i	−0.309325	+	0.178589i	−0.646625	−	0.762808i	$-0.723820\pi$
$853$	−7706.18	+	4449.16i	−0.309325	+	0.178589i	0.337299	+	0.941398i	$0.390487\pi$
$854$	−78241.1			−3.13508
$855$	22429.1	+	40029.9i	0.897143	+	1.60116i
$856$		−	85825.7i		−	3.42694i
$857$	−13045.1	−	22594.8i	−0.519968	−	0.900612i	−0.999731	−	0.0232130i	$-0.992610\pi$
$857$	−13045.1	−	22594.8i	−0.519968	−	0.900612i	0.479762	−	0.877399i	$-0.340723\pi$
$858$	−23684.4	−	22597.9i	−0.942391	−	0.899160i
$859$	−8380.65	+	14515.7i	−0.332880	+	0.576565i	−0.983075	−	0.183202i	$-0.941354\pi$
$859$	−8380.65	+	14515.7i	−0.332880	+	0.576565i	0.650195	+	0.759767i	$0.274687\pi$
$860$	−62279.3	−	35957.0i	−2.46943	−	1.42572i
$861$	1420.77	+	2497.85i	0.0562368	+	0.0988695i
$862$	−5714.24	−	9897.36i	−0.225786	−	0.391074i
$863$			21385.2i			0.843524i	0.906707	+	0.421762i	$0.138588\pi$
$863$			21385.2i			0.843524i	−0.906707	+	0.421762i	$0.861412\pi$
$864$	−93112.5	−	56183.7i	−3.66638	−	2.21228i
$865$			18686.8i			0.734533i
$866$	2239.91	−	1293.21i	0.0878928	−	0.0507450i
$867$	−9252.80	−	16267.3i	−0.362447	−	0.637216i
$868$	−15896.1	+	27532.8i	−0.621599	+	1.07664i
$869$	2830.68	+	1634.29i	0.110500	+	0.0637971i
$870$	−37723.8	+	64378.8i	−1.47007	+	2.50879i
$871$	−298.497	−	994.081i	−0.0116122	−	0.0386718i
$872$	13161.7			0.511135
$873$	−287.861	+	22355.4i	−0.0111599	+	0.866683i
$874$	−6838.15			−0.264650
$875$	11418.8	+	19778.0i	0.441174	+	0.764135i
$876$	−199.288	+	30954.8i	−0.00768645	+	1.19391i
$877$	20640.5	+	11916.8i	0.794732	+	0.458839i	0.841626	−	0.540061i	$-0.181599\pi$
$877$	20640.5	+	11916.8i	0.794732	+	0.458839i	−0.0468938	+	0.998900i	$0.514932\pi$
$878$	−39678.0	−	22908.1i	−1.52513	−	0.880537i
$879$	9.58562	−	1488.90i	0.000367821	−	0.0571325i
$880$	37877.5	+	65605.7i	1.45097	+	2.51315i
$881$	−5515.41			−0.210918			−0.105459	−	0.994424i	$-0.533631\pi$
$881$	−5515.41			−0.210918			−0.105459	+	0.994424i	$0.533631\pi$
$882$	682.852	+	406.056i	0.0260690	+	0.0155018i
$883$	21375.9			0.814673			0.407336	−	0.913278i	$-0.366458\pi$
$883$	21375.9			0.814673			0.407336	+	0.913278i	$0.366458\pi$
$884$	36269.5	−	10890.8i	1.37995	−	0.414364i
$885$	4663.53	−	7958.70i	0.177133	−	0.302292i
$886$	−69635.0	−	40203.8i	−2.64044	−	1.52446i
$887$	2037.44	−	3528.96i	0.0771259	−	0.133586i	−0.824883	−	0.565304i	$-0.808759\pi$
$887$	2037.44	−	3528.96i	0.0771259	−	0.133586i	0.902009	+	0.431718i	$0.142092\pi$
$888$	19052.2	+	33495.6i	0.719990	+	1.26581i
$889$	429.161	−	247.776i	0.0161908	−	0.00934774i
$890$		−	79408.0i		−	2.99074i
$891$	−15178.6	−	9292.53i	−0.570710	−	0.349395i
$892$		−	102818.i		−	3.85943i
$893$	4383.38	+	7592.23i	0.164260	+	0.284507i
$894$	−21127.6	−	37144.3i	−0.790396	−	1.38959i
$895$	22534.0	+	13010.0i	0.841595	+	0.485895i
$896$	55589.7	−	96284.2i	2.07268	−	3.58999i
$897$	1565.46	+	1493.65i	0.0582711	+	0.0555980i
$898$	19045.3	+	32987.5i	0.707740	+	1.22584i
$899$		−	16640.3i		−	0.617335i
$900$	−7005.75	+	11781.3i	−0.259472	+	0.436346i
$901$	20117.6			0.743855
$902$	−3503.23	+	2022.59i	−0.129318	+	0.0746617i
$903$	−163.002	+	25318.7i	−0.00600707	+	0.933059i
$904$	3691.90	+	2131.52i	0.135831	+	0.0784218i
$905$	10989.9	+	6345.03i	0.403665	+	0.233056i
$906$	−12872.8	−	82.8758i	−0.472043	−	0.00303903i
$907$	−527.818	−	914.207i	−0.0193229	−	0.0334683i	0.856202	−	0.516641i	$-0.172818\pi$
$907$	−527.818	−	914.207i	−0.0193229	−	0.0334683i	−0.875525	+	0.483172i	$0.839484\pi$
$908$		−	22608.8i		−	0.826321i
$909$	47933.2	+	617.217i	1.74900	+	0.0225212i
$910$	56096.6	+	13246.6i	2.04350	+	0.482549i
$911$	10817.6	+	18736.7i	0.393418	+	0.681420i	0.992898	−	0.118970i	$-0.0379592\pi$
$911$	10817.6	+	18736.7i	0.393418	+	0.681420i	−0.599480	+	0.800390i	$0.704626\pi$
$912$	160008.	+	93759.2i	5.80964	+	3.40425i
$913$	−3371.12	+	5838.95i	−0.122199	+	0.211655i
$914$	−6086.74	+	10542.5i	−0.220275	+	0.381528i
$915$	42460.5	−	24151.5i	1.53410	−	0.872594i
$916$	−50162.3	+	28961.2i	−1.80940	+	1.04466i
$917$		−	30577.7i		−	1.10116i
$918$	24488.9	−	13514.9i	0.880453	−	0.485904i
$919$	−627.382			−0.0225195			−0.0112598	−	0.999937i	$-0.503584\pi$
$919$	−627.382			−0.0225195			−0.0112598	+	0.999937i	$0.503584\pi$
$920$	−4254.02	−	7368.18i	−0.152447	−	0.264045i
$921$	19336.3	−	10998.5i	0.691806	−	0.393498i
$922$	−9675.05	+	16757.7i	−0.345587	+	0.598574i
$923$	−26382.5	+	28009.8i	−0.940833	+	0.998865i
$924$	26292.5	−	44870.4i	0.936105	−	1.59754i
$925$	1854.86	−	1070.91i	0.0659325	−	0.0380661i
$926$	40369.9			1.43265
$927$	17826.3	+	31815.2i	0.631600	+	1.12724i
$928$			166331.i			5.88370i
$929$	−4430.88	+	2558.17i	−0.156483	+	0.0903453i	−0.576197	−	0.817311i	$-0.695464\pi$
$929$	−4430.88	+	2558.17i	−0.156483	+	0.0903453i	0.419714	+	0.907656i	$0.362130\pi$
$930$	173.606	−	26965.7i	0.00612126	−	0.950796i
$931$	−647.114	−	373.611i	−0.0227801	−	0.0131521i
$932$	30552.6	−	52918.7i	1.07380	−	1.85988i
$933$	−4409.48	−	28.3884i	−0.154727	−	0.000996136i
$934$	−22249.0	+	12845.5i	−0.779453	+	0.450017i
$935$	−10746.2			−0.375870
$936$	−27443.3	−	95858.3i	−0.958348	−	3.34746i
$937$	−43233.8			−1.50735			−0.753675	−	0.657247i	$-0.771721\pi$
$937$	−43233.8			−1.50735			−0.753675	+	0.657247i	$0.771721\pi$
$938$	1940.07	−	1120.10i	0.0675326	−	0.0389900i
$939$	16876.3	−	28800.8i	0.586514	−	1.00093i
$940$	−8502.62	+	14727.0i	−0.295026	+	0.511001i
$941$	28472.6	+	16438.7i	0.986376	+	0.569484i	0.904189	−	0.427133i	$-0.140476\pi$
$941$	28472.6	+	16438.7i	0.986376	+	0.569484i	0.0821869	+	0.996617i	$0.473810\pi$
$942$	−2079.12	+	1182.60i	−0.0719123	+	0.0409036i
$943$	231.552	−	133.687i	0.00799615	−	0.00461658i
$944$		−	37282.2i		−	1.28542i
$945$	31330.8	+	605.194i	1.07851	+	0.0208328i
$946$	−35641.3			−1.22494
$947$	865.992	−	499.981i	0.0297159	−	0.0171565i	−0.485068	−	0.874476i	$-0.661205\pi$
$947$	865.992	−	499.981i	0.0297159	−	0.0171565i	0.514784	+	0.857320i	$0.327872\pi$
$948$	7673.98	+	13491.6i	0.262911	+	0.462221i
$949$	−8581.39	+	9110.71i	−0.293534	+	0.311640i
$950$	8757.33	−	15168.1i	0.299079	−	0.518020i
$951$	−39683.7	−	23253.3i	−1.35314	−	0.792892i
$952$	26213.5	+	45403.0i	0.892419	+	1.54572i
$953$	43322.6			1.47257			0.736284	−	0.676673i	$-0.236579\pi$
$953$	43322.6			1.47257			0.736284	+	0.676673i	$0.236579\pi$
$954$	1063.27	−	82573.4i	0.0360844	−	2.80232i
$955$		−	23372.6i		−	0.791956i
$956$	29426.1	−	16989.2i	0.995511	−	0.574758i
$957$	−175.243	+	27219.9i	−0.00591933	+	0.919430i
$958$	33930.3	−	58769.0i	1.14430	−	1.98198i
$959$	−8462.69	+	14657.8i	−0.284958	+	0.493561i
$960$	−904.882	+	140553.i	−0.0304218	+	4.72533i
$961$	−11888.6	−	20591.7i	−0.399068	−	0.691207i
$962$	−5582.29	+	23639.9i	−0.187090	+	0.792288i
$963$	15032.7	−	25280.1i	0.503035	−	0.845938i
$964$			52527.9i			1.75499i
$965$	18953.7	+	32828.7i	0.632270	+	1.09512i
$966$	−2361.00	+	4029.24i	−0.0786376	+	0.134201i
$967$	−17344.4	−	10013.8i	−0.576793	−	0.333012i	0.183065	−	0.983101i	$-0.441398\pi$
$967$	−17344.4	−	10013.8i	−0.576793	−	0.333012i	−0.759858	+	0.650089i	$0.774732\pi$
$968$	−50150.1	−	28954.2i	−1.66517	−	0.961388i
$969$	−22867.3	+	13006.9i	−0.758103	+	0.431208i
$970$	47990.2	−	27707.1i	1.58853	−	0.917136i
$971$	−26355.0			−0.871032			−0.435516	−	0.900181i	$-0.643434\pi$
$971$	−26355.0			−0.871032			−0.435516	+	0.900181i	$0.643434\pi$
$972$	−39878.9	−	74512.1i	−1.31596	−	2.45883i
$973$		−	34667.7i		−	1.14223i
$974$	38434.4	+	66570.4i	1.26439	+	2.18999i
$975$	−5317.97	+	1559.60i	−0.174678	+	0.0512278i
$976$	98715.9	−	170981.i	3.23752	−	5.60755i
$977$	35206.4	+	20326.4i	1.15287	+	0.665608i	0.949584	−	0.313512i	$-0.101506\pi$
$977$	35206.4	+	20326.4i	1.15287	+	0.665608i	0.203283	+	0.979120i	$0.434839\pi$
$978$	−34491.7	+	58862.9i	−1.12773	+	1.92457i
$979$	−14484.1	−	25087.2i	−0.472843	−	0.818988i
$980$		−	1449.42i		−	0.0472449i
$981$	3876.78	+	2305.32i	0.126173	+	0.0750287i
$982$			70081.1i			2.27737i
$983$	8699.41	−	5022.61i	0.282267	−	0.162967i	−0.352182	−	0.935931i	$-0.614560\pi$
$983$	8699.41	−	5022.61i	0.282267	−	0.162967i	0.634449	+	0.772965i	$0.281227\pi$
$984$	−12321.0	−	79.3229i	−0.399165	−	0.00256984i
$985$	−22511.5	+	38991.0i	−0.728198	+	1.26128i
$986$	−37049.1	−	21390.3i	−1.19664	−	0.690879i
$987$	5987.01	+	38.5446i	0.193079	+	0.00124305i
$988$	42047.3	+	140030.i	1.35395	+	4.50904i
$989$	2355.77			0.0757424
$990$	−567.965	+	44108.3i	−0.0182335	+	1.41601i
$991$	−38058.2			−1.21994			−0.609970	−	0.792425i	$-0.708818\pi$
$991$	−38058.2			−1.21994			−0.609970	+	0.792425i	$0.708818\pi$
$992$	−30055.6	−	52057.7i	−0.961960	−	1.66616i
$993$	26979.7	+	15809.2i	0.862209	+	0.505225i
$994$	−71922.7	−	41524.6i	−2.29502	−	1.32503i
$995$	55267.3	+	31908.6i	1.76090	+	1.01665i
$996$	−27829.6	+	15829.4i	−0.885355	+	0.503588i
$997$	10762.6	+	18641.4i	0.341881	+	0.592155i	0.984782	−	0.173794i	$-0.0556028\pi$
$997$	10762.6	+	18641.4i	0.341881	+	0.592155i	−0.642901	+	0.765949i	$0.722269\pi$
$998$	−80794.5			−2.56263
$999$	−255.037	+	13203.2i	−0.00807709	+	0.418150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.t.a.103.1	yes	80
3.2	odd	2		351.4.t.a.64.40		80
9.2	odd	6		351.4.t.a.181.1		80
9.7	even	3	inner	117.4.t.a.25.40	yes	80
13.12	even	2	inner	117.4.t.a.103.40	yes	80
39.38	odd	2		351.4.t.a.64.1		80
117.25	even	6	inner	117.4.t.a.25.1	✓	80
117.38	odd	6		351.4.t.a.181.40		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.4.t.a.25.1	✓	80	117.25	even	6	inner
117.4.t.a.25.40	yes	80	9.7	even	3	inner
117.4.t.a.103.1	yes	80	1.1	even	1	trivial
117.4.t.a.103.40	yes	80	13.12	even	2	inner
351.4.t.a.64.1		80	39.38	odd	2
351.4.t.a.64.40		80	3.2	odd	2
351.4.t.a.181.1		80	9.2	odd	6
351.4.t.a.181.40		80	117.38	odd	6

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	117.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.76791 + 2.75276i) q^{2} +(2.56905 + 4.51663i) q^{3} +(11.1553 - 19.3216i) q^{4} +(-10.5269 - 6.07771i) q^{5} +(-24.6822 - 14.4629i) q^{6} +(15.9136 - 9.18770i) q^{7} +78.7874i q^{8} +(-13.7999 + 23.2069i) q^{9} +66.9218 q^{10} +(21.1425 - 12.2066i) q^{11} +(115.927 + 0.746343i) q^{12} +(34.1199 + 32.1377i) q^{13} +(-50.5830 + 87.6123i) q^{14} +(0.406627 - 63.1601i) q^{15} +(-127.640 - 221.079i) q^{16} +36.2127 q^{17} +(1.91393 - 148.636i) q^{18} +139.810i q^{19} +(-234.862 + 135.598i) q^{20} +(82.3803 + 48.2721i) q^{21} +(-67.2036 + 116.400i) q^{22} +(4.44194 - 7.69366i) q^{23} +(-355.854 + 202.409i) q^{24} +(11.3772 + 19.7059i) q^{25} +(-251.148 - 59.3057i) q^{26} +(-140.270 - 2.70949i) q^{27} -409.967i q^{28} +(107.290 + 185.832i) q^{29} +(171.926 + 302.261i) q^{30} +(-67.1586 - 38.7741i) q^{31} +(671.296 + 387.573i) q^{32} +(109.449 + 64.1333i) q^{33} +(-172.659 + 99.6846i) q^{34} -223.361 q^{35} +(294.452 + 525.518i) q^{36} -94.1274i q^{37} +(-384.863 - 666.603i) q^{38} +(-57.4981 + 236.671i) q^{39} +(478.847 - 829.388i) q^{40} +(26.0643 + 15.0482i) q^{41} +(-525.663 - 3.38424i) q^{42} +(132.587 + 229.647i) q^{43} -544.674i q^{44} +(286.316 - 160.425i) q^{45} +48.9103i q^{46} +(54.3039 - 31.3524i) q^{47} +(670.618 - 1144.47i) q^{48} +(-2.67228 + 4.62852i) q^{49} +(-108.491 - 62.6373i) q^{50} +(93.0322 + 163.559i) q^{51} +(1001.57 - 300.746i) q^{52} +555.540 q^{53} +(676.253 - 373.210i) q^{54} -296.753 q^{55} +(723.875 + 1253.79i) q^{56} +(-631.471 + 359.180i) q^{57} +(-1023.10 - 590.686i) q^{58} +(126.478 + 73.0223i) q^{59} +(-1215.82 - 712.428i) q^{60} +(386.697 + 669.779i) q^{61} +426.942 q^{62} +(-6.38802 + 496.095i) q^{63} -2225.34 q^{64} +(-163.854 - 545.681i) q^{65} +(-698.385 - 4.49623i) q^{66} +(-19.1771 - 11.0719i) q^{67} +(403.964 - 699.686i) q^{68} +(46.1610 + 0.297186i) q^{69} +(1064.96 - 614.858i) q^{70} +820.920i q^{71} +(-1828.41 - 1087.26i) q^{72} +267.020i q^{73} +(259.110 + 448.791i) q^{74} +(-59.7756 + 102.012i) q^{75} +(2701.35 + 1559.63i) q^{76} +(224.301 - 388.501i) q^{77} +(-377.350 - 1286.70i) q^{78} +(66.9431 + 115.949i) q^{79} +3103.03i q^{80} +(-348.123 - 640.509i) q^{81} -165.696 q^{82} +(-239.172 + 138.086i) q^{83} +(1851.67 - 1053.23i) q^{84} +(-381.208 - 220.090i) q^{85} +(-1264.33 - 729.959i) q^{86} +(-563.700 + 962.001i) q^{87} +(961.726 + 1665.76i) q^{88} -1186.58i q^{89} +(-923.518 + 1553.05i) q^{90} +(838.241 + 197.941i) q^{91} +(-99.1025 - 171.651i) q^{92} +(2.59416 - 402.943i) q^{93} +(-172.611 + 298.971i) q^{94} +(849.726 - 1471.77i) q^{95} +(-25.9304 + 4027.69i) q^{96} +(717.108 - 414.022i) q^{97} -29.4245i q^{98} +(-8.48699 + 659.102i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{3} + 150 q^{4} - 68 q^{9} - 40 q^{10} + 190 q^{12} - 13 q^{13} + 78 q^{14} - 530 q^{16} + 264 q^{17} - 34 q^{22} - 174 q^{23} + 798 q^{25} - 1032 q^{26} + 302 q^{27} + 642 q^{29} + 198 q^{30}+ \cdots + 2136 q^{95}+O(q^{100}) \) 80 * q - 4 * q^3 + 150 * q^4 - 68 * q^9 - 40 * q^10 + 190 * q^12 - 13 * q^13 + 78 * q^14 - 530 * q^16 + 264 * q^17 - 34 * q^22 - 174 * q^23 + 798 * q^25 - 1032 * q^26 + 302 * q^27 + 642 * q^29 + 198 * q^30 - 2136 * q^35 - 802 * q^36 - 708 * q^38 + 211 * q^39 + 88 * q^40 - 1212 * q^42 + 166 * q^43 + 4334 * q^48 + 1610 * q^49 + 150 * q^51 + 786 * q^52 + 1296 * q^53 - 508 * q^55 - 888 * q^56 + 838 * q^61 + 3540 * q^62 - 3652 * q^64 - 201 * q^65 - 2418 * q^66 + 612 * q^68 - 1890 * q^69 + 4458 * q^74 - 632 * q^75 - 2166 * q^77 - 2280 * q^78 + 514 * q^79 - 4076 * q^81 - 5188 * q^82 - 4458 * q^87 + 2338 * q^88 - 2226 * q^90 - 1086 * q^91 + 516 * q^92 + 488 * q^94 + 2136 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more