LMFDB - Embedded newform 63.4.i.a.5.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [63,4,Mod(5,63)] 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("63.5"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(63, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 5])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.i (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:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.5
Character	$\chi$	$=$	63.5
Dual form			63.4.i.a.38.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.72062i q^{2} +(3.26996 + 4.03824i) q^{3} -5.84303 q^{4} +(6.83336 + 11.8357i) q^{5} +(15.0248 - 12.1663i) q^{6} +(18.4941 - 0.984293i) q^{7} -8.02526i q^{8} +(-5.61469 + 26.4098i) q^{9} +(44.0363 - 25.4243i) q^{10} +(-21.3043 - 12.3000i) q^{11} +(-19.1065 - 23.5955i) q^{12} +(2.03747 + 1.17634i) q^{13} +(-3.66218 - 68.8095i) q^{14} +(-25.4506 + 66.2971i) q^{15} -76.6032 q^{16} +(-63.8439 - 110.581i) q^{17} +(98.2607 + 20.8902i) q^{18} +(87.2223 + 50.3578i) q^{19} +(-39.9275 - 69.1565i) q^{20} +(64.4498 + 71.4649i) q^{21} +(-45.7638 + 79.2652i) q^{22} +(42.0276 - 24.2647i) q^{23} +(32.4079 - 26.2423i) q^{24} +(-30.8895 + 53.5022i) q^{25} +(4.37670 - 7.58067i) q^{26} +(-125.009 + 63.6854i) q^{27} +(-108.062 + 5.75126i) q^{28} +(-171.644 + 99.0987i) q^{29} +(246.666 + 94.6921i) q^{30} +42.9953i q^{31} +220.810i q^{32} +(-19.9938 - 126.252i) q^{33} +(-411.430 + 237.539i) q^{34} +(138.026 + 212.165i) q^{35} +(32.8068 - 154.313i) q^{36} +(-42.0011 + 72.7481i) q^{37} +(187.363 - 324.521i) q^{38} +(1.91214 + 12.0744i) q^{39} +(94.9848 - 54.8395i) q^{40} +(92.8172 - 160.764i) q^{41} +(265.894 - 239.793i) q^{42} +(-185.452 - 321.213i) q^{43} +(124.482 + 71.8695i) q^{44} +(-350.946 + 114.013i) q^{45} +(-90.2797 - 156.369i) q^{46} -504.729 q^{47} +(-250.490 - 309.342i) q^{48} +(341.062 - 36.4072i) q^{49} +(199.062 + 114.928i) q^{50} +(237.785 - 619.412i) q^{51} +(-11.9050 - 6.87337i) q^{52} +(372.688 - 215.171i) q^{53} +(236.950 + 465.110i) q^{54} -336.202i q^{55} +(-7.89921 - 148.420i) q^{56} +(81.8569 + 516.893i) q^{57} +(368.709 + 638.622i) q^{58} -312.164 q^{59} +(148.709 - 387.376i) q^{60} +548.565i q^{61} +159.969 q^{62} +(-77.8437 + 493.951i) q^{63} +208.723 q^{64} +32.1533i q^{65} +(-469.737 + 74.3893i) q^{66} -651.533 q^{67} +(373.042 + 646.128i) q^{68} +(235.415 + 90.3730i) q^{69} +(789.385 - 513.545i) q^{70} +18.9019i q^{71} +(211.945 + 45.0594i) q^{72} +(525.319 - 303.293i) q^{73} +(270.668 + 156.270i) q^{74} +(-317.062 + 50.2111i) q^{75} +(-509.643 - 294.243i) q^{76} +(-406.110 - 206.508i) q^{77} +(44.9242 - 7.11436i) q^{78} +435.435 q^{79} +(-523.457 - 906.654i) q^{80} +(-665.950 - 296.565i) q^{81} +(-598.142 - 345.338i) q^{82} +(424.248 + 734.819i) q^{83} +(-376.582 - 417.572i) q^{84} +(872.537 - 1511.28i) q^{85} +(-1195.11 + 689.998i) q^{86} +(-961.453 - 369.090i) q^{87} +(-98.7110 + 170.972i) q^{88} +(-147.005 + 254.620i) q^{89} +(424.201 + 1305.74i) q^{90} +(38.8391 + 19.7498i) q^{91} +(-245.569 + 141.779i) q^{92} +(-173.625 + 140.593i) q^{93} +1877.91i q^{94} +1376.45i q^{95} +(-891.681 + 722.039i) q^{96} +(900.965 - 520.172i) q^{97} +(-135.457 - 1268.96i) q^{98} +(444.458 - 493.580i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 3 q^{3} - 162 q^{4} - 3 q^{5} + 24 q^{6} + 5 q^{7} - 45 q^{9} - 6 q^{10} + 9 q^{11} + 186 q^{12} - 36 q^{13} + 54 q^{14} - 141 q^{15} + 526 q^{16} - 72 q^{17} - 54 q^{18} - 6 q^{19} + 24 q^{20} - 81 q^{21}+ \cdots + 4335 q^{99}+O(q^{100}) $ 44 * q - 3 * q^3 - 162 * q^4 - 3 * q^5 + 24 * q^6 + 5 * q^7 - 45 * q^9 - 6 * q^10 + 9 * q^11 + 186 * q^12 - 36 * q^13 + 54 * q^14 - 141 * q^15 + 526 * q^16 - 72 * q^17 - 54 * q^18 - 6 * q^19 + 24 * q^20 - 81 * q^21 + 14 * q^22 - 285 * q^23 - 114 * q^24 - 349 * q^25 - 96 * q^26 + 432 * q^27 - 156 * q^28 - 132 * q^29 - 447 * q^30 - 3 * q^33 + 24 * q^34 + 765 * q^35 + 1122 * q^36 + 82 * q^37 - 873 * q^38 + 306 * q^39 + 420 * q^40 + 618 * q^41 - 282 * q^42 + 82 * q^43 + 603 * q^44 + 291 * q^45 + 266 * q^46 - 402 * q^47 - 1569 * q^48 - 79 * q^49 - 1845 * q^50 + 453 * q^51 + 189 * q^52 + 564 * q^53 - 2385 * q^54 + 66 * q^56 + 1170 * q^57 + 269 * q^58 + 1494 * q^59 + 2265 * q^60 - 2904 * q^62 - 636 * q^63 - 1144 * q^64 - 372 * q^66 - 590 * q^67 + 3504 * q^68 - 1005 * q^69 - 105 * q^70 + 1830 * q^72 - 6 * q^73 + 1515 * q^74 - 33 * q^75 - 144 * q^76 - 4443 * q^77 - 5985 * q^78 + 1102 * q^79 - 4239 * q^80 - 4017 * q^81 + 18 * q^82 + 1830 * q^83 + 3165 * q^84 - 237 * q^85 + 1209 * q^86 + 2013 * q^87 - 623 * q^88 + 4266 * q^89 + 9993 * q^90 - 1140 * q^91 + 7896 * q^92 - 729 * q^93 + 3975 * q^96 - 792 * q^97 + 5667 * q^98 + 4335 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	3.72062i		−	1.31544i	−0.753263	−	0.657719i	$-0.771521\pi$
$2$		−	3.72062i		−	1.31544i	0.753263	−	0.657719i	$-0.228479\pi$
$3$	3.26996	+	4.03824i	0.629305	+	0.777159i
$3$	3.26996	+	4.03824i	0.629305	+	0.777159i
$4$	−5.84303			−0.730379
$5$	6.83336	+	11.8357i	0.611194	+	1.05862i	0.991039	+	0.133569i	$0.0426438\pi$
$5$	6.83336	+	11.8357i	0.611194	+	1.05862i	−0.379845	+	0.925050i	$0.624023\pi$
$6$	15.0248	−	12.1663i	1.02230	−	0.827812i
$7$	18.4941	−	0.984293i	0.998587	−	0.0531468i
$7$	18.4941	−	0.984293i	0.998587	−	0.0531468i
$8$		−	8.02526i		−	0.354670i
$9$	−5.61469	+	26.4098i	−0.207952	+	0.978139i
$10$	44.0363	−	25.4243i	1.39255	−	0.803988i
$11$	−21.3043	−	12.3000i	−0.583953	−	0.337145i	0.178750	−	0.983895i	$-0.442795\pi$
$11$	−21.3043	−	12.3000i	−0.583953	−	0.337145i	−0.762703	+	0.646749i	$0.776128\pi$
$12$	−19.1065	−	23.5955i	−0.459631	−	0.567621i
$13$	2.03747	+	1.17634i	0.0434688	+	0.0250967i	0.521577	−	0.853204i	$-0.325344\pi$
$13$	2.03747	+	1.17634i	0.0434688	+	0.0250967i	−0.478108	+	0.878301i	$0.658677\pi$
$14$	−3.66218	−	68.8095i	−0.0699114	−	1.31358i
$15$	−25.4506	+	66.2971i	−0.438088	+	1.14119i
$16$	−76.6032			−1.19693
$17$	−63.8439	−	110.581i	−0.910848	−	1.57764i	−0.812868	−	0.582447i	$-0.802095\pi$
$17$	−63.8439	−	110.581i	−0.910848	−	1.57764i	−0.0979801	−	0.995188i	$-0.531238\pi$
$18$	98.2607	+	20.8902i	1.28668	+	0.273548i
$19$	87.2223	+	50.3578i	1.05317	+	0.608046i	0.923534	−	0.383516i	$-0.125287\pi$
$19$	87.2223	+	50.3578i	1.05317	+	0.608046i	0.129633	+	0.991562i	$0.458620\pi$
$20$	−39.9275	−	69.1565i	−0.446403	−	0.773193i
$21$	64.4498	+	71.4649i	0.669719	+	0.742615i
$22$	−45.7638	+	79.2652i	−0.443494	+	0.768154i
$23$	42.0276	−	24.2647i	0.381016	−	0.219980i	−0.297244	−	0.954801i	$-0.596068\pi$
$23$	42.0276	−	24.2647i	0.381016	−	0.219980i	0.678260	+	0.734822i	$0.262734\pi$
$24$	32.4079	−	26.2423i	0.275635	−	0.223195i
$25$	−30.8895	+	53.5022i	−0.247116	+	0.428018i
$26$	4.37670	−	7.58067i	0.0330132	−	0.0571805i
$27$	−125.009	+	63.6854i	−0.891034	+	0.453936i
$28$	−108.062	+	5.75126i	−0.729347	+	0.0388173i
$29$	−171.644	+	99.0987i	−1.09909	+	0.634557i	−0.935981	−	0.352051i	$-0.885484\pi$
$29$	−171.644	+	99.0987i	−1.09909	+	0.634557i	−0.163105	+	0.986609i	$0.552151\pi$
$30$	246.666	+	94.6921i	1.50116	+	0.576278i
$31$			42.9953i			0.249103i	0.992213	+	0.124551i	$0.0397492\pi$
$31$			42.9953i			0.249103i	−0.992213	+	0.124551i	$0.960251\pi$
$32$			220.810i			1.21981i
$33$	−19.9938	−	126.252i	−0.105469	−	0.665991i
$34$	−411.430	+	237.539i	−2.07528	+	1.19817i
$35$	138.026	+	212.165i	0.666592	+	1.02464i
$36$	32.8068	−	154.313i	0.151884	−	0.714412i
$37$	−42.0011	+	72.7481i	−0.186620	+	0.323235i	−0.944121	−	0.329598i	$-0.893087\pi$
$37$	−42.0011	+	72.7481i	−0.186620	+	0.323235i	0.757501	+	0.652834i	$0.226420\pi$
$38$	187.363	−	324.521i	0.799848	−	1.38538i
$39$	1.91214	+	12.0744i	0.00785097	+	0.0495756i
$40$	94.9848	−	54.8395i	0.375460	−	0.216772i
$41$	92.8172	−	160.764i	0.353551	−	0.612369i	−0.633318	−	0.773892i	$-0.718307\pi$
$41$	92.8172	−	160.764i	0.353551	−	0.612369i	0.986869	+	0.161523i	$0.0516406\pi$
$42$	265.894	−	239.793i	0.976864	−	0.880974i
$43$	−185.452	−	321.213i	−0.657702	−	1.13917i	−0.981209	−	0.192948i	$-0.938195\pi$
$43$	−185.452	−	321.213i	−0.657702	−	1.13917i	0.323507	−	0.946226i	$-0.395138\pi$
$44$	124.482	+	71.8695i	0.426507	+	0.246244i
$45$	−350.946	+	114.013i	−1.16258	+	0.377691i
$46$	−90.2797	−	156.369i	−0.289370	−	0.501203i
$47$	−504.729			−1.56643			−0.783215	−	0.621750i	$-0.786422\pi$
$47$	−504.729			−1.56643			−0.783215	+	0.621750i	$0.786422\pi$
$48$	−250.490	−	309.342i	−0.753231	−	0.930201i
$49$	341.062	−	36.4072i	0.994351	−	0.106143i
$50$	199.062	+	114.928i	0.563031	+	0.325066i
$51$	237.785	−	619.412i	0.652873	−	1.70069i
$52$	−11.9050	−	6.87337i	−0.0317487	−	0.0183301i
$53$	372.688	−	215.171i	0.965898	−	0.557661i	0.0679145	−	0.997691i	$-0.478365\pi$
$53$	372.688	−	215.171i	0.965898	−	0.557661i	0.897983	+	0.440030i	$0.145032\pi$
$54$	236.950	+	465.110i	0.597125	+	1.17210i
$55$		−	336.202i		−	0.824245i
$56$	−7.89921	−	148.420i	−0.0188496	−	0.354169i
$57$	81.8569	+	516.893i	0.190214	+	1.20112i
$58$	368.709	+	638.622i	0.834721	+	1.44578i
$59$	−312.164			−0.688819			−0.344410	−	0.938819i	$-0.611921\pi$
$59$	−312.164			−0.688819			−0.344410	+	0.938819i	$0.611921\pi$
$60$	148.709	−	387.376i	0.319970	−	0.833500i
$61$			548.565i			1.15142i	0.817655	+	0.575709i	$0.195274\pi$
$61$			548.565i			1.15142i	−0.817655	+	0.575709i	$0.804726\pi$
$62$	159.969			0.327679
$63$	−77.8437	+	493.951i	−0.155673	+	0.987809i
$64$	208.723			0.407663
$65$			32.1533i			0.0613558i
$66$	−469.737	+	74.3893i	−0.876071	+	0.138738i
$67$	−651.533			−1.18802			−0.594010	−	0.804457i	$-0.702456\pi$
$67$	−651.533			−1.18802			−0.594010	+	0.804457i	$0.702456\pi$
$68$	373.042	+	646.128i	0.665265	+	1.15227i
$69$	235.415	+	90.3730i	0.410734	+	0.157676i
$70$	789.385	−	513.545i	1.34785	−	0.876862i
$71$			18.9019i			0.0315950i	0.999875	+	0.0157975i	$0.00502871\pi$
$71$			18.9019i			0.0315950i	−0.999875	+	0.0157975i	$0.994971\pi$
$72$	211.945	+	45.0594i	0.346916	+	0.0737542i
$73$	525.319	−	303.293i	0.842245	−	0.486271i	−0.0157815	−	0.999875i	$-0.505024\pi$
$73$	525.319	−	303.293i	0.842245	−	0.486271i	0.858027	+	0.513605i	$0.171690\pi$
$74$	270.668	+	156.270i	0.425196	+	0.245487i
$75$	−317.062	+	50.2111i	−0.488149	+	0.0773050i
$76$	−509.643	−	294.243i	−0.769211	−	0.444104i
$77$	−406.110	−	206.508i	−0.601046	−	0.305634i
$78$	44.9242	−	7.11436i	0.0652137	−	0.0103275i
$79$	435.435			0.620130			0.310065	−	0.950715i	$-0.399649\pi$
$79$	435.435			0.620130			0.310065	+	0.950715i	$0.399649\pi$
$80$	−523.457	−	906.654i	−0.731554	−	1.26709i
$81$	−665.950	−	296.565i	−0.913512	−	0.406811i
$82$	−598.142	−	345.338i	−0.805534	−	0.465075i
$83$	424.248	+	734.819i	0.561051	+	0.971769i	0.997405	+	0.0719942i	$0.0229363\pi$
$83$	424.248	+	734.819i	0.561051	+	0.971769i	−0.436354	+	0.899775i	$0.643730\pi$
$84$	−376.582	−	417.572i	−0.489149	−	0.542390i
$85$	872.537	−	1511.28i	1.11341	−	1.92848i
$86$	−1195.11	+	689.998i	−1.49851	+	0.865167i
$87$	−961.453	−	369.090i	−1.18481	−	0.454834i
$88$	−98.7110	+	170.972i	−0.119575	+	0.207110i
$89$	−147.005	+	254.620i	−0.175084	+	0.303254i	−0.940190	−	0.340650i	$-0.889353\pi$
$89$	−147.005	+	254.620i	−0.175084	+	0.303254i	0.765106	+	0.643904i	$0.222686\pi$
$90$	424.201	+	1305.74i	0.496830	+	1.52930i
$91$	38.8391	+	19.7498i	0.0447411	+	0.0227510i
$92$	−245.569	+	141.779i	−0.278286	+	0.160669i
$93$	−173.625	+	140.593i	−0.193592	+	0.156761i
$94$			1877.91i			2.06054i
$95$			1376.45i			1.48654i
$96$	−891.681	+	722.039i	−0.947988	+	0.767633i
$97$	900.965	−	520.172i	0.943084	−	0.544490i	0.0521583	−	0.998639i	$-0.483390\pi$
$97$	900.965	−	520.172i	0.943084	−	0.544490i	0.890926	+	0.454149i	$0.150057\pi$
$98$	−135.457	−	1268.96i	−0.139625	−	1.30801i
$99$	444.458	−	493.580i	0.451209	−	0.501077i
$100$	180.489	−	312.615i	0.180489	−	0.312615i
$101$	124.628	−	215.862i	0.122782	−	0.212664i	−0.798082	−	0.602549i	$-0.794152\pi$
$101$	124.628	−	215.862i	0.122782	−	0.212664i	0.920864	+	0.389885i	$0.127485\pi$
$102$	−2304.60	−	884.707i	−2.23715	−	0.858814i
$103$	650.861	−	375.775i	0.622634	−	0.359478i	−0.155260	−	0.987874i	$-0.549622\pi$
$103$	650.861	−	375.775i	0.622634	−	0.359478i	0.777894	+	0.628396i	$0.216288\pi$
$104$	9.44041	−	16.3513i	0.00890104	−	0.0154171i
$105$	−405.430	+	1251.15i	−0.376818	+	1.16286i
$106$	−800.571	−	1386.63i	−0.733569	−	1.27058i
$107$	1406.36	+	811.965i	1.27064	+	0.733604i	0.975108	−	0.221729i	$-0.0711700\pi$
$107$	1406.36	+	811.965i	1.27064	+	0.733604i	0.295531	+	0.955333i	$0.404503\pi$
$108$	730.430	−	372.116i	0.650793	−	0.331545i
$109$	724.736	+	1255.28i	0.636854	+	1.10306i	0.986119	+	0.166040i	$0.0530981\pi$
$109$	724.736	+	1255.28i	0.636854	+	1.10306i	−0.349265	+	0.937024i	$0.613569\pi$
$110$	−1250.88			−1.08424
$111$	−431.116	+	68.2730i	−0.368646	+	0.0583801i
$112$	−1416.71	+	75.4000i	−1.19523	+	0.0636128i
$113$	227.719	+	131.473i	0.189575	+	0.109451i	0.591784	−	0.806097i	$-0.298424\pi$
$113$	227.719	+	131.473i	0.189575	+	0.109451i	−0.402209	+	0.915548i	$0.631757\pi$
$114$	1923.16	−	304.559i	1.58001	−	0.250215i
$115$	574.380	+	331.618i	0.465750	+	0.268901i
$116$	1002.92	−	579.037i	0.802749	−	0.463467i
$117$	−42.5066	+	47.2044i	−0.0335875	+	0.0372996i
$118$			1161.45i			0.906100i
$119$	−1289.58	−	1982.25i	−0.993408	−	1.52700i
$120$	532.051	+	204.248i	0.404745	+	0.155377i
$121$	−362.918	−	628.593i	−0.272666	−	0.472271i
$122$	2041.00			1.51462
$123$	952.712	−	150.875i	0.698399	−	0.110601i
$124$		−	251.223i		−	0.181939i
$125$	864.022			0.618244
$126$	1837.80	+	289.627i	1.29940	+	0.204778i
$127$	−368.812			−0.257691			−0.128846	−	0.991665i	$-0.541127\pi$
$127$	−368.812			−0.257691			−0.128846	+	0.991665i	$0.541127\pi$
$128$			989.896i			0.683557i
$129$	690.710	−	1799.25i	0.471424	−	1.22803i
$130$	119.630			0.0807098
$131$	551.575	+	955.356i	0.367873	+	0.637174i	0.989233	−	0.146351i	$-0.0467528\pi$
$131$	551.575	+	955.356i	0.367873	+	0.637174i	−0.621360	+	0.783525i	$0.713420\pi$
$132$	116.824	+	737.697i	0.0770322	+	0.486426i
$133$	1662.66	+	845.470i	1.08399	+	0.551215i
$134$			2424.11i			1.56277i
$135$	−1607.99	−	1044.38i	−1.02514	−	0.665823i
$136$	−887.441	+	512.364i	−0.559540	+	0.323050i
$137$	1078.05	+	622.413i	0.672293	+	0.388148i	0.796945	−	0.604052i	$-0.206448\pi$
$137$	1078.05	+	622.413i	0.672293	+	0.388148i	−0.124652	+	0.992201i	$0.539781\pi$
$138$	336.244	−	875.891i	0.207413	−	0.540296i
$139$	−1997.85	−	1153.46i	−1.21910	−	0.703848i	−0.254376	−	0.967106i	$-0.581870\pi$
$139$	−1997.85	−	1153.46i	−1.21910	−	0.703848i	−0.964726	+	0.263257i	$0.915203\pi$
$140$	−806.493	−	1239.69i	−0.486865	−	0.748376i
$141$	−1650.44	−	2038.21i	−0.985762	−	1.21737i
$142$	70.3270			0.0415613
$143$	−28.9380	−	50.1220i	−0.0169225	−	0.0293106i
$144$	430.104	−	2023.07i	0.248903	−	1.17076i
$145$	−2345.81	−	1354.35i	−1.34351	−	0.775675i
$146$	−1128.44	−	1954.51i	−0.639659	−	1.10792i
$147$	1262.28	+	1258.24i	0.708240	+	0.705972i
$148$	245.414	−	425.069i	0.136303	−	0.236084i
$149$	286.796	−	165.582i	0.157686	−	0.0910402i	−0.419080	−	0.907949i	$-0.637647\pi$
$149$	286.796	−	165.582i	0.157686	−	0.0910402i	0.576767	+	0.816909i	$0.304314\pi$
$150$	186.817	+	1179.67i	0.101690	+	0.642130i
$151$	−914.722	+	1584.35i	−0.492974	+	0.853856i	−0.999967	−	0.00809418i	$-0.997424\pi$
$151$	−914.722	+	1584.35i	−0.492974	+	0.853856i	0.506993	+	0.861950i	$0.330757\pi$
$152$	404.135	−	699.982i	0.215656	−	0.373527i
$153$	3278.88	−	1065.22i	1.73256	−	0.562865i
$154$	−768.339	+	1510.98i	−0.402042	+	0.790639i
$155$	−508.880	+	293.802i	−0.263705	+	0.152250i
$156$	−11.1727	−	70.5510i	−0.00573418	−	0.0362090i
$157$		−	43.4645i		−	0.0220946i	−0.999939	−	0.0110473i	$-0.996483\pi$
$157$		−	43.4645i		−	0.0220946i	0.999939	−	0.0110473i	$-0.00351653\pi$
$158$		−	1620.09i		−	0.815743i
$159$	2087.59	+	801.398i	1.04124	+	0.399717i
$160$	−2613.44	+	1508.87i	−1.29132	+	0.745542i
$161$	753.379	−	490.120i	0.368786	−	0.239919i
$162$	−1103.41	+	2477.75i	−0.535135	+	1.20167i
$163$	−1337.78	+	2317.11i	−0.642841	+	1.11343i	0.341954	+	0.939717i	$0.388911\pi$
$163$	−1337.78	+	2317.11i	−0.642841	+	1.11343i	−0.984796	+	0.173717i	$0.944422\pi$
$164$	−542.334	+	939.350i	−0.258227	+	0.447261i
$165$	1357.66	−	1099.37i	0.640569	−	0.518701i
$166$	2733.98	−	1578.47i	1.27830	−	0.738029i
$167$	1300.57	−	2252.66i	0.602644	−	1.04381i	−0.389775	−	0.920910i	$-0.627447\pi$
$167$	1300.57	−	2252.66i	0.602644	−	1.04381i	0.992419	−	0.122900i	$-0.0392193\pi$
$168$	573.524	−	517.226i	0.263383	−	0.237529i
$169$	−1095.73	−	1897.86i	−0.498740	−	0.863844i
$170$	−5622.89	−	3246.38i	−2.53680	−	1.46462i
$171$	−1819.67	+	2020.78i	−0.813762	+	0.903700i
$172$	1083.60	+	1876.86i	0.480372	+	0.832028i
$173$	1751.09			0.769552			0.384776	−	0.923010i	$-0.374279\pi$
$173$	1751.09			0.769552			0.384776	+	0.923010i	$0.374279\pi$
$174$	−1373.24	+	3577.20i	−0.598307	+	1.55855i
$175$	−518.612	+	1019.88i	−0.224019	+	0.440546i
$176$	1631.98	+	942.222i	0.698948	+	0.403538i
$177$	−1020.77	−	1260.59i	−0.433477	−	0.535322i
$178$	947.344	+	546.949i	0.398913	+	0.230312i
$179$	−3563.92	+	2057.63i	−1.48816	+	0.859187i	−0.999909	−	0.0135177i	$-0.995697\pi$
$179$	−3563.92	+	2057.63i	−1.48816	+	0.859187i	−0.488248	+	0.872705i	$0.662364\pi$
$180$	2050.59	−	666.184i	0.849121	−	0.275858i
$181$		−	2733.54i		−	1.12256i	−0.827628	−	0.561278i	$-0.810310\pi$
$181$		−	2733.54i		−	1.12256i	0.827628	−	0.561278i	$-0.189690\pi$
$182$	73.4815	−	144.506i	0.0299276	−	0.0588542i
$183$	−2215.23	+	1793.79i	−0.894835	+	0.724593i
$184$	−194.730	−	337.283i	−0.0780202	−	0.135135i
$185$	−1148.03			−0.456244
$186$	523.094	+	645.994i	0.206210	+	0.254659i
$187$			3141.13i			1.22835i
$188$	2949.15			1.14409
$189$	−2249.24	+	1300.85i	−0.865650	+	0.500650i
$190$	5121.26			1.95545
$191$		−	210.385i		−	0.0797012i	−0.999206	−	0.0398506i	$-0.987312\pi$
$191$		−	210.385i		−	0.0797012i	0.999206	−	0.0398506i	$-0.0126882\pi$
$192$	682.518	+	842.874i	0.256544	+	0.316819i
$193$	827.826			0.308747			0.154374	−	0.988013i	$-0.450664\pi$
$193$	827.826			0.308747			0.154374	+	0.988013i	$0.450664\pi$
$194$	−1935.37	−	3352.15i	−0.716243	−	1.24057i
$195$	−129.843	+	105.140i	−0.0476832	+	0.0386115i
$196$	−1992.84	+	212.728i	−0.726253	+	0.0775249i
$197$			4969.34i			1.79721i	0.438756	+	0.898606i	$0.355419\pi$
$197$			4969.34i			1.79721i	−0.438756	+	0.898606i	$0.644581\pi$
$198$	−1836.42	−	1653.66i	−0.659137	−	0.593538i
$199$	1994.86	−	1151.74i	0.710614	−	0.410273i	−0.100674	−	0.994919i	$-0.532100\pi$
$199$	1994.86	−	1151.74i	0.710614	−	0.410273i	0.811288	+	0.584646i	$0.198767\pi$
$200$	429.369	+	247.897i	0.151805	+	0.0876447i
$201$	−2130.49	−	2631.04i	−0.747627	−	0.923281i
$202$	−803.142	−	463.694i	−0.279747	−	0.161512i
$203$	−3076.86	+	2001.69i	−1.06381	+	0.692074i
$204$	−1389.38	+	3619.25i	−0.476844	+	1.24215i
$205$	2537.01			0.864354
$206$	−1398.12	−	2421.61i	−0.472871	−	0.819036i
$207$	404.852	+	1246.18i	0.135938	+	0.418432i
$208$	−156.077	−	90.1112i	−0.0520289	−	0.0300389i
$209$	−1238.81	−	2145.68i	−0.410000	−	0.710141i
$210$	4655.07	+	1508.45i	1.52967	+	0.495681i
$211$	−1406.66	+	2436.40i	−0.458949	+	0.794923i	−0.998906	−	0.0467701i	$-0.985107\pi$
$211$	−1406.66	+	2436.40i	−0.458949	+	0.794923i	0.539957	+	0.841693i	$0.318441\pi$
$212$	−2177.63	+	1257.25i	−0.705471	+	0.407304i
$213$	−76.3305	+	61.8086i	−0.0245544	+	0.0198829i
$214$	3021.02	−	5232.55i	0.965011	−	1.67145i
$215$	2534.52	−	4389.92i	0.803967	−	1.39251i
$216$	511.092	+	1003.23i	0.160997	+	0.316023i
$217$	42.3200	+	795.159i	0.0132390	+	0.248751i
$218$	4670.42	−	2696.47i	1.45101	−	0.837743i
$219$	2942.54	+	1129.60i	0.907938	+	0.348546i
$220$			1964.44i			0.602011i
$221$		−	300.408i		−	0.0914372i
$222$	254.018	+	1604.02i	0.0767954	+	0.484931i
$223$	−3655.84	+	2110.70i	−1.09782	+	0.633825i	−0.935647	−	0.352938i	$-0.885183\pi$
$223$	−3655.84	+	2110.70i	−1.09782	+	0.633825i	−0.162170	+	0.986763i	$0.551849\pi$
$224$	217.341	+	4083.67i	0.0648292	+	1.21809i
$225$	−1239.55	−	1116.18i	−0.367273	−	0.330721i
$226$	489.163	−	847.256i	0.143976	−	0.249374i
$227$	−622.021	+	1077.37i	−0.181872	+	0.315012i	−0.942518	−	0.334155i	$-0.891549\pi$
$227$	−622.021	+	1077.37i	−0.181872	+	0.315012i	0.760646	+	0.649167i	$0.224882\pi$
$228$	−478.293	−	3020.22i	−0.138929	−	0.877276i
$229$	4050.44	−	2338.52i	1.16882	−	0.674820i	0.215420	−	0.976522i	$-0.430888\pi$
$229$	4050.44	−	2338.52i	1.16882	−	0.674820i	0.953402	+	0.301702i	$0.0975546\pi$
$230$	1233.83	−	2137.05i	0.353722	−	0.612665i
$231$	−494.036	−	2315.24i	−0.140715	−	0.659445i
$232$	795.293	+	1377.49i	0.225058	+	0.389812i
$233$	−651.597	−	376.200i	−0.183208	−	0.105775i	0.405591	−	0.914055i	$-0.367066\pi$
$233$	−651.597	−	376.200i	−0.183208	−	0.105775i	−0.588799	+	0.808279i	$0.700399\pi$
$234$	175.630	+	158.151i	0.0490653	+	0.0441822i
$235$	−3448.99	−	5973.83i	−0.957393	−	1.65825i
$236$	1823.99			0.503099
$237$	1423.86	+	1758.39i	0.390251	+	0.481939i
$238$	−7375.21	+	4798.04i	−2.00867	+	1.30677i
$239$	−1800.76	−	1039.67i	−0.487370	−	0.281383i	0.236113	−	0.971726i	$-0.424126\pi$
$239$	−1800.76	−	1039.67i	−0.487370	−	0.281383i	−0.723483	+	0.690343i	$0.757460\pi$
$240$	1949.60	−	5078.57i	0.524359	−	1.36592i
$241$	−3383.00	−	1953.17i	−0.904224	−	0.522054i	−0.0256558	−	0.999671i	$-0.508167\pi$
$241$	−3383.00	−	1953.17i	−0.904224	−	0.522054i	−0.878568	+	0.477617i	$0.841501\pi$
$242$	−2338.76	+	1350.28i	−0.621244	+	0.358675i
$243$	−980.032	−	3659.02i	−0.258720	−	0.965952i
$244$		−	3205.28i		−	0.840972i
$245$	2761.51	+	3787.94i	0.720107	+	0.987765i
$246$	−561.348	−	3544.68i	−0.145489	−	0.918702i
$247$	118.476	+	205.206i	0.0305199	+	0.0528620i
$248$	345.048			0.0883492
$249$	−1580.10	+	4116.04i	−0.402147	+	1.04756i
$250$		−	3214.70i		−	0.813262i
$251$	1877.00			0.472012			0.236006	−	0.971752i	$-0.424162\pi$
$251$	1877.00			0.472012			0.236006	+	0.971752i	$0.424162\pi$
$252$	454.843	−	2886.17i	0.113700	−	0.721475i
$253$	−1193.83			−0.296661
$254$			1372.21i			0.338977i
$255$	8956.06	−	1418.31i	2.19941	−	0.348307i
$256$	5352.82			1.30684
$257$	2650.88	+	4591.46i	0.643414	+	1.11443i	0.984665	+	0.174454i	$0.0558159\pi$
$257$	2650.88	+	4591.46i	0.643414	+	1.11443i	−0.341251	+	0.939972i	$0.610851\pi$
$258$	−6694.34	−	2569.87i	−1.61539	−	0.620129i
$259$	−705.167	+	1386.75i	−0.169177	+	0.332697i
$260$		−	187.873i		−	0.0448130i
$261$	−1653.44	−	5089.48i	−0.392129	−	1.20702i
$262$	3554.52	−	2052.20i	0.838164	−	0.483914i
$263$	−1436.08	−	829.124i	−0.336703	−	0.194395i	0.322110	−	0.946702i	$-0.395608\pi$
$263$	−1436.08	−	829.124i	−0.336703	−	0.194395i	−0.658813	+	0.752307i	$0.728941\pi$
$264$	−1013.21	+	160.455i	−0.236207	+	0.0374066i
$265$	5093.41	+	2940.68i	1.18070	+	0.681678i
$266$	3145.67	−	6186.15i	0.725089	−	1.42593i
$267$	−1508.91	+	238.957i	−0.345858	+	0.0547713i
$268$	3806.93			0.867706
$269$	1903.76	+	3297.40i	0.431502	+	0.747383i	0.997003	−	0.0773642i	$-0.0246504\pi$
$269$	1903.76	+	3297.40i	0.431502	+	0.747383i	−0.565501	+	0.824748i	$0.691317\pi$
$270$	−3885.75	+	5982.73i	−0.875849	+	1.34851i
$271$	2510.98	+	1449.71i	0.562845	+	0.324959i	0.754287	−	0.656545i	$-0.227983\pi$
$271$	2510.98	+	1449.71i	0.562845	+	0.324959i	−0.191442	+	0.981504i	$0.561316\pi$
$272$	4890.65	+	8470.85i	1.09022	+	1.88831i
$273$	47.2480	+	221.422i	0.0104747	+	0.0490883i
$274$	2315.76	−	4011.02i	0.510585	−	0.884360i
$275$	1316.16	−	759.885i	0.288609	−	0.166628i
$276$	−1375.54	−	528.052i	−0.299992	−	0.115163i
$277$	2187.01	−	3788.01i	0.474385	−	0.821659i	−0.525185	−	0.850988i	$-0.676004\pi$
$277$	2187.01	−	3788.01i	0.474385	−	0.821659i	0.999570	+	0.0293295i	$0.00933721\pi$
$278$	−4291.58	+	7433.23i	−0.925870	+	1.60365i
$279$	−1135.50	−	241.405i	−0.243657	−	0.0518013i
$280$	1702.68	−	1107.70i	0.363409	−	0.236420i
$281$	1910.31	−	1102.92i	0.405550	−	0.234144i	−0.283326	−	0.959024i	$-0.591438\pi$
$281$	1910.31	−	1102.92i	0.405550	−	0.234144i	0.688876	+	0.724879i	$0.258104\pi$
$282$	−7583.42	+	6140.68i	−1.60137	+	1.29671i
$283$			5547.66i			1.16528i	0.812730	+	0.582640i	$0.197980\pi$
$283$			5547.66i			1.16528i	−0.812730	+	0.582640i	$0.802020\pi$
$284$		−	110.445i		−	0.0230763i
$285$	−5558.44	+	4500.95i	−1.15528	+	0.935485i
$286$	−186.485	+	107.667i	−0.0385563	+	0.0222605i
$287$	1558.33	−	3064.54i	0.320506	−	0.630294i
$288$	−5831.53	−	1239.78i	−1.19315	−	0.253662i
$289$	−5695.59	+	9865.05i	−1.15929	+	2.00795i
$290$	−5039.04	+	8727.87i	−1.02035	+	1.76730i
$291$	5046.70	+	1937.37i	1.01664	+	0.390276i
$292$	−3069.45	+	1772.15i	−0.615158	+	0.355162i
$293$	332.172	−	575.338i	0.0662310	−	0.114715i	−0.831008	−	0.556260i	$-0.812236\pi$
$293$	332.172	−	575.338i	0.0662310	−	0.114715i	0.897239	+	0.441544i	$0.145569\pi$
$294$	4681.44	−	4696.47i	0.928663	−	0.931646i
$295$	−2133.13	−	3694.69i	−0.421002	−	0.729197i
$296$	583.822	+	337.070i	0.114642	+	0.0661885i
$297$	3446.55	+	180.838i	0.673365	+	0.0353309i
$298$	−616.068	−	1067.06i	−0.119758	−	0.207427i
$299$	114.174			0.0220831
$300$	1852.61	−	293.385i	0.356534	−	0.0564620i
$301$	−3745.94	−	5757.99i	−0.717316	−	1.10261i
$302$	5894.75	+	3403.34i	1.12319	+	0.648477i
$303$	1279.23	−	202.584i	0.242541	−	0.0384097i
$304$	−6681.51	−	3857.57i	−1.26056	−	0.727786i
$305$	−6492.66	+	3748.54i	−1.21891	+	0.703740i
$306$	−3963.30	−	12199.5i	−0.740414	−	2.27908i
$307$		−	3371.17i		−	0.626720i	−0.949634	−	0.313360i	$-0.898545\pi$
$307$		−	3371.17i		−	0.626720i	0.949634	−	0.313360i	$-0.101455\pi$
$308$	2372.91	+	1206.63i	0.438991	+	0.223228i
$309$	3645.76	+	1399.56i	0.671197	+	0.257664i
$310$	1093.13	+	1893.35i	0.200276	+	0.346888i
$311$	−4957.37			−0.903881			−0.451940	−	0.892048i	$-0.649268\pi$
$311$	−4957.37			−0.903881			−0.451940	+	0.892048i	$0.649268\pi$
$312$	96.9000	−	15.3454i	0.0175830	−	0.00278450i
$313$			7901.00i			1.42681i	0.700753	+	0.713404i	$0.252847\pi$
$313$			7901.00i			1.42681i	−0.700753	+	0.713404i	$0.747153\pi$
$314$	−161.715			−0.0290641
$315$	−6378.20	+	2454.01i	−1.14086	+	0.438945i
$316$	−2544.26			−0.452930
$317$		−	6001.53i		−	1.06334i	−0.846951	−	0.531671i	$-0.821564\pi$
$317$		−	6001.53i		−	1.06334i	0.846951	−	0.531671i	$-0.178436\pi$
$318$	2981.70	−	7767.12i	0.525803	−	1.36968i
$319$	4875.67			0.855753
$320$	1426.28	+	2470.39i	0.249161	+	0.431560i
$321$	1319.85	+	8334.33i	0.229492	+	1.44915i
$322$	−1823.55	−	2803.04i	−0.315598	−	0.485116i
$323$		−	12860.2i		−	2.21535i
$324$	3891.17	+	1732.84i	0.667210	+	0.297126i
$325$	−125.873	+	72.6730i	−0.0214837	+	0.0124036i
$326$	8621.08	+	4977.38i	1.46465	+	0.845618i
$327$	−2699.26	+	7031.37i	−0.456481	+	1.18910i
$328$	−1290.17	−	744.882i	−0.217189	−	0.125394i
$329$	−9334.50	+	496.801i	−1.56422	+	0.0832508i
$330$	−4090.33	−	5051.35i	−0.682320	−	0.842630i
$331$	6753.39			1.12145			0.560725	−	0.828002i	$-0.310522\pi$
$331$	6753.39			1.12145			0.560725	+	0.828002i	$0.310522\pi$
$332$	−2478.89	−	4293.57i	−0.409780	−	0.709760i
$333$	−1685.44	−	1517.70i	−0.277361	−	0.249758i
$334$	−8381.30	−	4838.95i	−1.37307	−	0.792741i
$335$	−4452.16	−	7711.36i	−0.726111	−	1.25766i
$336$	−4937.06	−	5474.44i	−0.801603	−	0.888855i
$337$	−622.587	+	1078.35i	−0.100636	+	0.174307i	−0.911947	−	0.410308i	$-0.865421\pi$
$337$	−622.587	+	1078.35i	−0.100636	+	0.174307i	0.811311	+	0.584615i	$0.198755\pi$
$338$	−7061.24	+	4076.81i	−1.13633	+	0.656062i
$339$	213.711	+	1349.50i	0.0342395	+	0.216208i
$340$	−5098.26	+	8830.44i	−0.813212	+	1.40852i
$341$	528.844	−	915.984i	0.0839838	−	0.145464i
$342$	7518.55	+	6770.29i	1.18876	+	1.07045i
$343$	6271.80	−	1009.02i	0.987304	−	0.158840i
$344$	−2577.81	+	1488.30i	−0.404030	+	0.233267i
$345$	539.047	+	3403.86i	0.0841198	+	0.531182i
$346$		−	6515.13i		−	1.01230i
$347$		−	9502.44i		−	1.47008i	−0.678024	−	0.735040i	$-0.737163\pi$
$347$		−	9502.44i		−	1.47008i	0.678024	−	0.735040i	$-0.262837\pi$
$348$	5617.80	+	2156.60i	0.865362	+	0.332201i
$349$	3593.91	−	2074.94i	0.551225	−	0.318250i	−0.198391	−	0.980123i	$-0.563572\pi$
$349$	3593.91	−	2074.94i	0.551225	−	0.318250i	0.749616	+	0.661873i	$0.230238\pi$
$350$	3794.59	+	1929.56i	0.579512	+	0.294684i
$351$	−329.618	−	17.2948i	−0.0501244	−	0.00262999i
$352$	2715.97	−	4704.19i	0.411254	−	0.712313i
$353$	433.888	−	751.517i	0.0654208	−	0.113312i	−0.831460	−	0.555585i	$-0.812494\pi$
$353$	433.888	−	751.517i	0.0654208	−	0.113312i	0.896881	+	0.442273i	$0.145828\pi$
$354$	−4690.19	+	3797.88i	−0.704183	+	0.570213i
$355$	−223.718	+	129.164i	−0.0334471	+	0.0193107i
$356$	858.954	−	1487.75i	0.127878	−	0.221491i
$357$	3787.92	−	11689.5i	0.561564	−	1.73298i
$358$	7655.67	+	13260.0i	1.13021	+	1.95758i
$359$	1830.91	+	1057.08i	0.269170	+	0.155405i	0.628510	−	0.777801i	$-0.283665\pi$
$359$	1830.91	+	1057.08i	0.269170	+	0.155405i	−0.359341	+	0.933206i	$0.616998\pi$
$360$	914.987	+	2816.43i	0.133956	+	0.412330i
$361$	1642.32	+	2844.59i	0.239441	+	0.414724i
$362$	−10170.5			−1.47665
$363$	1351.68	−	3521.03i	0.195440	−	0.509107i
$364$	−226.938	−	115.399i	−0.0326780	−	0.0166169i
$365$	7179.38	+	4145.02i	1.02955	+	0.594411i
$366$	6674.00	+	8242.05i	0.953157	+	1.17710i
$367$	−271.211	−	156.584i	−0.0385753	−	0.0222714i	0.480588	−	0.876946i	$-0.340423\pi$
$367$	−271.211	−	156.584i	−0.0385753	−	0.0222714i	−0.519164	+	0.854675i	$0.673756\pi$
$368$	−3219.45	+	1858.75i	−0.456048	+	0.263299i
$369$	3724.60	+	3353.92i	0.525460	+	0.473166i
$370$			4271.40i			0.600161i
$371$	6680.72	−	4346.23i	0.934895	−	0.608208i
$372$	1014.50	−	821.490i	0.141396	−	0.114495i
$373$	−2703.78	−	4683.09i	−0.375326	−	0.650083i	0.615050	−	0.788488i	$-0.289136\pi$
$373$	−2703.78	−	4683.09i	−0.375326	−	0.650083i	−0.990376	+	0.138405i	$0.955802\pi$
$374$	11687.0			1.61582
$375$	2825.32	+	3489.13i	0.389064	+	0.480474i
$376$			4050.58i			0.555566i
$377$	−466.294			−0.0637012
$378$	4839.97	+	8368.56i	0.658574	+	1.13871i
$379$	793.227			0.107508			0.0537538	−	0.998554i	$-0.482881\pi$
$379$	793.227			0.107508			0.0537538	+	0.998554i	$0.482881\pi$
$380$		−	8042.66i		−	1.08574i
$381$	−1206.00	−	1489.35i	−0.162166	−	0.200267i
$382$	−782.763			−0.104842
$383$	−5099.84	−	8833.18i	−0.680391	−	1.17847i	−0.974862	−	0.222811i	$-0.928477\pi$
$383$	−5099.84	−	8833.18i	−0.680391	−	1.17847i	0.294471	−	0.955660i	$-0.404857\pi$
$384$	−3997.43	+	3236.92i	−0.531232	+	0.430165i
$385$	−330.921	−	6217.75i	−0.0438060	−	0.823080i
$386$		−	3080.03i		−	0.406138i
$387$	9524.40	−	3094.24i	1.25104	−	0.406431i
$388$	−5264.37	+	3039.38i	−0.688809	+	0.397684i
$389$	−8551.58	−	4937.26i	−1.11461	−	0.643519i	−0.174589	−	0.984641i	$-0.555860\pi$
$389$	−8551.58	−	4937.26i	−1.11461	−	0.643519i	−0.940019	+	0.341122i	$0.889193\pi$
$390$	391.187	+	483.096i	0.0507910	+	0.0627243i
$391$	−5366.42	−	3098.30i	−0.694096	−	0.400736i
$392$	−292.177	−	2737.11i	−0.0376459	−	0.352666i
$393$	−2054.32	+	5351.37i	−0.263682	+	0.686872i
$394$	18489.0			2.36412
$395$	2975.48	+	5153.69i	0.379020	+	0.656481i
$396$	−2596.98	+	2884.00i	−0.329554	+	0.365976i
$397$	9104.46	+	5256.46i	1.15098	+	0.664520i	0.949126	−	0.314896i	$-0.101970\pi$
$397$	9104.46	+	5256.46i	1.15098	+	0.664520i	0.201856	+	0.979415i	$0.435303\pi$
$398$	−4285.17	−	7422.14i	−0.539689	−	0.934769i
$399$	2022.64	+	9478.88i	0.253781	+	1.18932i
$400$	2366.24	−	4098.44i	0.295780	−	0.512306i
$401$	−383.072	+	221.167i	−0.0477050	+	0.0275425i	−0.523663	−	0.851926i	$-0.675435\pi$
$401$	−383.072	+	221.167i	−0.0477050	+	0.0275425i	0.475958	+	0.879468i	$0.342101\pi$
$402$	−9789.12	+	7926.74i	−1.21452	+	0.983457i
$403$	−50.5769	+	87.6018i	−0.00625166	+	0.0108282i
$404$	−728.206	+	1261.29i	−0.0896773	+	0.155326i
$405$	−1040.61	−	9908.54i	−0.127675	−	1.21570i
$406$	7447.52	+	11447.8i	0.910380	+	1.39937i
$407$	1789.61	−	1033.23i	0.217955	−	0.125836i
$408$	−4970.94	−	1908.28i	−0.603182	−	0.231554i
$409$		−	8194.64i		−	0.990706i	−0.868692	−	0.495353i	$-0.835039\pi$
$409$		−	8194.64i		−	0.990706i	0.868692	−	0.495353i	$-0.164961\pi$
$410$		−	9439.26i		−	1.13700i
$411$	1011.74	+	6388.69i	0.121424	+	0.766742i
$412$	−3803.00	+	2195.66i	−0.454759	+	0.262555i
$413$	−5773.20	+	307.261i	−0.687846	+	0.0366086i
$414$	4636.56	−	1506.30i	0.550422	−	0.178818i
$415$	−5798.07	+	10042.6i	−0.685822	+	1.18788i
$416$	−259.746	+	449.894i	−0.0306133	+	0.0530237i
$417$	−1874.95	−	11839.5i	−0.220184	−	1.39037i
$418$	−7983.25	+	4609.13i	−0.934147	+	0.539330i
$419$	−7956.71	+	13781.4i	−0.927711	+	1.60684i	−0.140569	+	0.990071i	$0.544893\pi$
$419$	−7956.71	+	13781.4i	−0.927711	+	1.60684i	−0.787142	+	0.616772i	$0.788440\pi$
$420$	2368.94	−	7310.54i	0.275220	−	0.849328i
$421$	−6044.72	−	10469.8i	−0.699766	−	1.21203i	−0.968547	−	0.248829i	$-0.919954\pi$
$421$	−6044.72	−	10469.8i	−0.699766	−	1.21203i	0.268781	−	0.963201i	$-0.413379\pi$
$422$	9064.92	+	5233.64i	1.04567	+	0.603719i
$423$	2833.90	−	13329.8i	0.325742	−	1.53219i
$424$	−1726.81	−	2990.92i	−0.197786	−	0.342575i
$425$	7888.43			0.900342
$426$	229.967	+	283.997i	0.0261547	+	0.0322997i
$427$	539.948	+	10145.2i	0.0611942	+	1.14979i
$428$	−8217.44	−	4744.34i	−0.928049	−	0.535809i
$429$	107.778	−	280.755i	0.0121296	−	0.0315967i
$430$	−16333.2	−	9430.00i	−1.83176	−	1.05757i
$431$	7013.76	−	4049.40i	0.783854	−	0.452558i	−0.0539405	−	0.998544i	$-0.517178\pi$
$431$	7013.76	−	4049.40i	0.783854	−	0.452558i	0.837794	+	0.545986i	$0.183845\pi$
$432$	9576.07	−	4878.51i	1.06650	−	0.543327i
$433$			760.926i			0.0844522i	0.999108	+	0.0422261i	$0.0134450\pi$
$433$			760.926i			0.0844522i	−0.999108	+	0.0422261i	$0.986555\pi$
$434$	2958.49	−	157.457i	0.327216	−	0.0174151i
$435$	−2201.51	−	13901.6i	−0.242653	−	1.53226i
$436$	−4234.66	−	7334.64i	−0.465145	−	0.805655i
$437$	4887.67			0.535032
$438$	4202.83	−	10948.1i	0.458491	−	1.19434i
$439$		−	2640.98i		−	0.287123i	−0.989641	−	0.143561i	$-0.954145\pi$
$439$		−	2640.98i		−	0.287123i	0.989641	−	0.143561i	$-0.0458555\pi$
$440$	−2698.11			−0.292335
$441$	−953.455	+	9211.79i	−0.102954	+	0.994686i
$442$	−1117.70			−0.120280
$443$			6531.03i			0.700449i	0.936666	+	0.350224i	$0.113895\pi$
$443$			6531.03i			0.700449i	−0.936666	+	0.350224i	$0.886105\pi$
$444$	2519.02	−	398.922i	0.269251	−	0.0426396i
$445$	−4018.15			−0.428041
$446$	7853.12	+	13602.0i	0.833758	+	1.44411i
$447$	1606.47	+	616.704i	0.169985	+	0.0652553i
$448$	3860.15	−	205.445i	0.407087	−	0.0216660i
$449$			6932.75i			0.728678i	0.931266	+	0.364339i	$0.118705\pi$
$449$			6932.75i			0.728678i	−0.931266	+	0.364339i	$0.881295\pi$
$450$	−4152.90	+	4611.88i	−0.435043	+	0.483125i
$451$	−3954.81	+	2283.31i	−0.412915	+	0.238396i
$452$	−1330.57	−	768.204i	−0.138462	−	0.0799409i
$453$	−9389.07	+	1486.89i	−0.973812	+	0.154216i
$454$	4008.49	+	2314.31i	0.414379	+	0.239242i
$455$	31.6483	+	594.646i	0.00326087	+	0.0612691i
$456$	4148.20	−	656.923i	0.426003	−	0.0674633i
$457$	−14591.5			−1.49357			−0.746784	−	0.665066i	$-0.768403\pi$
$457$	−14591.5			−1.49357			−0.746784	+	0.665066i	$0.768403\pi$
$458$	−8700.75	−	15070.1i	−0.887684	−	1.53751i
$459$	15023.4	+	9757.64i	1.52774	+	0.992261i
$460$	−3356.12	−	1937.66i	−0.340174	−	0.196399i
$461$	−5053.02	−	8752.08i	−0.510504	−	0.884219i	−0.999926	−	0.0121719i	$-0.996125\pi$
$461$	−5053.02	−	8752.08i	−0.510504	−	0.884219i	0.489422	−	0.872047i	$-0.337208\pi$
$462$	−8614.14	+	1838.12i	−0.867459	+	0.185102i
$463$	−8356.28	+	14473.5i	−0.838768	+	1.45279i	0.0521577	+	0.998639i	$0.483390\pi$
$463$	−8356.28	+	14473.5i	−0.838768	+	1.45279i	−0.890925	+	0.454150i	$0.849943\pi$
$464$	13148.5	−	7591.28i	1.31552	−	0.759518i
$465$	−2850.46	−	1094.26i	−0.284273	−	0.109129i
$466$	−1399.70	+	2424.35i	−0.139141	+	0.240999i
$467$	1460.16	−	2529.07i	0.144685	−	0.250602i	−0.784570	−	0.620040i	$-0.787116\pi$
$467$	1460.16	−	2529.07i	0.144685	−	0.250602i	0.929256	+	0.369438i	$0.120450\pi$
$468$	248.367	−	275.817i	0.0245316	−	0.0272428i
$469$	−12049.5	+	641.299i	−1.18634	+	0.0631395i
$470$	−22226.4	+	12832.4i	−2.18133	+	1.25939i
$471$	175.520	−	142.127i	0.0171710	−	0.0139042i
$472$			2505.20i			0.244303i
$473$			9124.27i			0.886965i
$474$	6542.30	−	5297.63i	0.633962	−	0.513351i
$475$	−5388.51	+	3111.06i	−0.520509	+	0.300516i
$476$	7535.05	+	11582.4i	0.725564	+	1.11529i
$477$	3590.09	+	11050.7i	0.344610	+	1.06075i
$478$	−3868.21	+	6699.94i	−0.370142	+	0.641105i
$479$	−3147.51	+	5451.65i	−0.300237	+	0.520026i	−0.976189	−	0.216920i	$-0.930399\pi$
$479$	−3147.51	+	5451.65i	−0.300237	+	0.520026i	0.675953	+	0.736945i	$0.263732\pi$
$480$	−14639.0	−	5619.74i	−1.39204	−	0.534385i
$481$	−171.152	+	98.8149i	−0.0162243	+	0.00936709i
$482$	−7267.02	+	12586.9i	−0.686730	+	1.18945i
$483$	4442.74	+	1439.65i	0.418534	+	0.135624i
$484$	2120.54	+	3672.89i	0.199149	+	0.344937i
$485$	12313.2	+	7109.05i	1.15281	+	0.665578i
$486$	−13613.8	+	3646.33i	−1.27065	+	0.340331i
$487$	2731.42	+	4730.96i	0.254153	+	0.440206i	0.964665	−	0.263479i	$-0.0848700\pi$
$487$	2731.42	+	4730.96i	0.254153	+	0.440206i	−0.710512	+	0.703685i	$0.751537\pi$
$488$	4402.37			0.408373
$489$	−13731.5	+	2174.57i	−1.26986	+	0.201099i
$490$	14093.5	−	10274.5i	1.29934	−	0.947256i
$491$	3732.70	+	2155.07i	0.343084	+	0.198080i	0.661635	−	0.749826i	$-0.269863\pi$
$491$	3732.70	+	2155.07i	0.343084	+	0.198080i	−0.318551	+	0.947906i	$0.603196\pi$
$492$	−5566.73	+	881.566i	−0.510096	+	0.0807806i
$493$	21916.8	+	12653.7i	2.00220	+	1.15597i
$494$	763.493	−	440.803i	0.0695368	−	0.0401471i
$495$	8879.02	+	1887.67i	0.806226	+	0.171403i
$496$		−	3293.58i		−	0.298157i
$497$	18.6050	+	349.574i	0.00167918	+	0.0315504i
$498$	15314.2	+	5878.95i	1.37801	+	0.529000i
$499$	−9015.59	−	15615.5i	−0.808804	−	1.40089i	−0.913693	−	0.406405i	$-0.866782\pi$
$499$	−9015.59	−	15615.5i	−0.808804	−	1.40089i	0.104889	−	0.994484i	$-0.466551\pi$
$500$	−5048.51			−0.451553
$501$	13349.6	−	2114.09i	1.19045	−	0.188524i
$502$		−	6983.59i		−	0.620902i
$503$	8764.80			0.776945			0.388472	−	0.921460i	$-0.373003\pi$
$503$	8764.80			0.776945			0.388472	+	0.921460i	$0.373003\pi$
$504$	3964.08	+	624.716i	0.350346	+	0.0552124i
$505$	3406.51			0.300174
$506$			4441.77i			0.390239i
$507$	4081.02	−	10630.8i	0.357484	−	0.931221i
$508$	2154.98			0.188212
$509$	−758.058	−	1313.00i	−0.0660125	−	0.114337i	0.831130	−	0.556078i	$-0.187694\pi$
$509$	−758.058	−	1313.00i	−0.0660125	−	0.114337i	−0.897143	+	0.441741i	$0.854361\pi$
$510$	−5277.01	−	33322.1i	−0.458176	−	2.89319i
$511$	9416.76	−	6126.19i	0.815211	−	0.530346i
$512$		−	11996.6i		−	1.03551i
$513$	−14110.6	−	740.372i	−1.21442	−	0.0637198i
$514$	17083.1	−	9862.93i	1.46596	−	0.846372i
$515$	8895.13	+	5135.61i	0.761100	+	0.439421i
$516$	−4035.84	+	10513.1i	−0.344318	+	0.896924i
$517$	10752.9	+	6208.18i	0.914722	+	0.528115i
$518$	5159.57	+	2623.66i	0.437642	+	0.222542i
$519$	5725.98	+	7071.30i	0.484283	+	0.598064i
$520$	258.039			0.0217611
$521$	−2984.80	−	5169.82i	−0.250991	−	0.434729i	0.712808	−	0.701359i	$-0.247423\pi$
$521$	−2984.80	−	5169.82i	−0.250991	−	0.434729i	−0.963799	+	0.266630i	$0.914090\pi$
$522$	−18936.1	+	6151.84i	−1.58776	+	0.515821i
$523$	−10006.2	−	5777.11i	−0.836601	−	0.483012i	0.0195064	−	0.999810i	$-0.493791\pi$
$523$	−10006.2	−	5777.11i	−0.836601	−	0.483012i	−0.856107	+	0.516798i	$0.827124\pi$
$524$	−3222.87	−	5582.18i	−0.268687	−	0.465379i
$525$	−5814.35	+	1240.69i	−0.483351	+	0.103139i
$526$	−3084.86	+	5343.13i	−0.255715	+	0.442912i
$527$	4754.46	−	2744.99i	0.392993	−	0.226895i
$528$	1531.59	+	9671.34i	0.126238	+	0.797142i
$529$	−4905.95	+	8497.36i	−0.403218	+	0.698394i
$530$	10941.2	−	18950.7i	0.896706	−	1.55314i
$531$	1752.71	−	8244.19i	0.143241	−	0.673761i
$532$	−9715.00	−	4940.11i	−0.791727	−	0.402596i
$533$	378.225	−	218.368i	0.0307369	−	0.0177459i
$534$	889.069	+	5614.10i	0.0720483	+	0.454955i
$535$			22193.8i			1.79350i
$536$			5228.72i			0.421355i
$537$	−19963.1	−	7663.58i	−1.60423	−	0.615843i
$538$	12268.4	−	7083.16i	0.983137	−	0.567615i
$539$	−7713.90	−	3419.45i	−0.616440	−	0.273258i
$540$	9395.55	+	6102.36i	0.748741	+	0.486303i
$541$	11902.5	−	20615.7i	0.945891	−	1.63833i	0.191935	−	0.981408i	$-0.438524\pi$
$541$	11902.5	−	20615.7i	0.945891	−	1.63833i	0.753957	−	0.656924i	$-0.228143\pi$
$542$	5393.84	−	9342.40i	0.427463	−	0.740388i
$543$	11038.7	−	8938.58i	0.872404	−	0.706429i
$544$	24417.3	−	14097.4i	1.92442	−	1.11106i
$545$	−9904.76	+	17155.5i	−0.778483	+	1.34837i
$546$	823.830	−	175.792i	0.0645726	−	0.0137788i
$547$	−6766.49	−	11719.9i	−0.528911	−	0.916100i	−0.999432	−	0.0337115i	$-0.989267\pi$
$547$	−6766.49	−	11719.9i	−0.528911	−	0.916100i	0.470521	−	0.882389i	$-0.344066\pi$
$548$	−6299.09	−	3636.78i	−0.491029	−	0.283495i
$549$	−14487.5	−	3080.02i	−1.12625	−	0.239439i
$550$	−2827.24	−	4896.93i	−0.219189	−	0.379647i
$551$	−19961.6			−1.54336
$552$	725.267	−	1889.27i	0.0559228	−	0.145675i
$553$	8052.97	−	428.596i	0.619254	−	0.0329579i
$554$	−14093.8	−	8137.03i	−1.08084	−	0.624024i
$555$	−3754.03	−	4636.03i	−0.287117	−	0.354574i
$556$	11673.5	+	6739.69i	0.890406	+	0.514076i
$557$	−11739.1	+	6777.54i	−0.892997	+	0.515572i	−0.874922	−	0.484264i	$-0.839087\pi$
$557$	−11739.1	+	6777.54i	−0.892997	+	0.515572i	−0.0180757	+	0.999837i	$0.505754\pi$
$558$	−898.179	+	4224.75i	−0.0681415	+	0.320516i
$559$		−	872.617i		−	0.0660246i
$560$	−10573.3	−	16252.5i	−0.797862	−	1.22642i
$561$	−12684.6	+	10271.4i	−0.954626	+	0.773009i
$562$	−4103.54	−	7107.54i	−0.308003	−	0.533476i
$563$	9865.16			0.738484			0.369242	−	0.929333i	$-0.379617\pi$
$563$	9865.16			0.738484			0.369242	+	0.929333i	$0.379617\pi$
$564$	9643.60	+	11909.3i	0.719980	+	0.889138i
$565$			3593.62i			0.267584i
$566$	20640.7			1.53285
$567$	−12608.1	−	4829.22i	−0.933842	−	0.357686i
$568$	151.693			0.0112058
$569$			6262.01i			0.461366i	0.973029	+	0.230683i	$0.0740960\pi$
$569$			6262.01i			0.461366i	−0.973029	+	0.230683i	$0.925904\pi$
$570$	16746.3	+	20680.9i	1.23057	+	1.51969i
$571$	−10100.3			−0.740255			−0.370128	−	0.928981i	$-0.620686\pi$
$571$	−10100.3			−0.740255			−0.370128	+	0.928981i	$0.620686\pi$
$572$	169.085	+	292.865i	0.0123598	+	0.0214078i
$573$	849.584	−	687.951i	0.0619405	−	0.0501563i
$574$	−11402.0	−	5797.96i	−0.829113	−	0.421606i
$575$			2998.10i			0.217442i
$576$	−1171.92	+	5512.34i	−0.0847742	+	0.398751i
$577$	15135.0	−	8738.22i	1.09199	−	0.630462i	0.157886	−	0.987457i	$-0.449532\pi$
$577$	15135.0	−	8738.22i	1.09199	−	0.630462i	0.934106	+	0.356995i	$0.116199\pi$
$578$	36704.1	+	21191.1i	2.64133	+	1.52497i
$579$	2706.96	+	3342.96i	0.194296	+	0.239946i
$580$	13706.6	+	7913.53i	0.981271	+	0.566537i
$581$	8569.35	+	13172.2i	0.611905	+	0.940578i
$582$	7208.20	−	18776.9i	0.513384	−	1.33733i
$583$	−10586.5			−0.752052
$584$	−2434.00	−	4215.82i	−0.172465	−	0.298719i
$585$	−849.161	−	180.531i	−0.0600145	−	0.0127590i
$586$	−2140.62	−	1235.89i	−0.150901	−	0.0871228i
$587$	3676.64	+	6368.12i	0.258520	+	0.447769i	0.965846	−	0.259118i	$-0.0834320\pi$
$587$	3676.64	+	6368.12i	0.258520	+	0.447769i	−0.707326	+	0.706888i	$0.750099\pi$
$588$	−7375.55	−	7351.94i	−0.517284	−	0.515627i
$589$	−2165.15	+	3750.15i	−0.151466	+	0.262347i
$590$	−13746.6	+	7936.58i	−0.959215	+	0.553803i
$591$	−20067.4	+	16249.6i	−1.39672	+	1.13099i
$592$	3217.42	−	5572.74i	0.223370	−	0.386889i
$593$	4475.21	−	7751.29i	0.309907	−	0.536775i	−0.668435	−	0.743771i	$-0.733035\pi$
$593$	4475.21	−	7751.29i	0.309907	−	0.536775i	0.978342	+	0.206996i	$0.0663687\pi$
$594$	672.829	−	12823.3i	0.0464756	−	0.885770i
$595$	14649.2	−	28808.5i	1.00934	−	1.98493i
$596$	−1675.76	+	967.500i	−0.115171	+	0.0664939i
$597$	11174.1	+	4289.60i	0.766040	+	0.294073i
$598$		−	424.797i		−	0.0290489i
$599$		−	12548.8i		−	0.855978i	−0.903784	−	0.427989i	$-0.859222\pi$
$599$		−	12548.8i		−	0.855978i	0.903784	−	0.427989i	$-0.140778\pi$
$600$	402.957	+	2544.51i	0.0274178	+	0.173132i
$601$	8672.73	−	5007.20i	0.588632	−	0.339847i	−0.175924	−	0.984404i	$-0.556291\pi$
$601$	8672.73	−	5007.20i	0.588632	−	0.339847i	0.764556	+	0.644557i	$0.222958\pi$
$602$	−21423.3	+	13937.2i	−1.45041	+	0.943585i
$603$	3658.16	−	17206.8i	0.247051	−	1.16205i
$604$	5344.75	−	9257.38i	0.360058	−	0.623638i
$605$	4959.90	−	8590.80i	0.333304	−	0.577299i
$606$	−753.737	−	4759.54i	−0.0505256	−	0.319048i
$607$	−769.474	+	444.256i	−0.0514530	+	0.0297064i	−0.525506	−	0.850790i	$-0.676124\pi$
$607$	−769.474	+	444.256i	−0.0514530	+	0.0297064i	0.474053	+	0.880496i	$0.342791\pi$
$608$	−11119.5	+	19259.5i	−0.741702	+	1.28467i
$609$	−18144.5	−	5879.63i	−1.20731	−	0.391223i
$610$	13946.9	+	24156.7i	0.925727	+	1.60341i
$611$	−1028.37	−	593.731i	−0.0680908	−	0.0393122i
$612$	−19158.6	+	6224.14i	−1.26543	+	0.411105i
$613$	−6545.70	−	11337.5i	−0.431286	−	0.747009i	0.565698	−	0.824612i	$-0.308607\pi$
$613$	−6545.70	−	11337.5i	−0.431286	−	0.747009i	−0.996984	+	0.0776029i	$0.975273\pi$
$614$	−12542.9			−0.824411
$615$	8295.93	+	10245.0i	0.543942	+	0.671740i
$616$	−1657.28	+	3259.14i	−0.108399	+	0.213173i
$617$	−7968.85	−	4600.82i	−0.519957	−	0.300198i	0.216960	−	0.976181i	$-0.430386\pi$
$617$	−7968.85	−	4600.82i	−0.519957	−	0.300198i	−0.736917	+	0.675983i	$0.763719\pi$
$618$	5207.24	−	13564.5i	0.338942	−	0.882919i
$619$	1455.41	+	840.280i	0.0945037	+	0.0545617i	0.546507	−	0.837455i	$-0.315957\pi$
$619$	1455.41	+	840.280i	0.0945037	+	0.0545617i	−0.452003	+	0.892016i	$0.649291\pi$
$620$	2973.40	−	1716.70i	0.192605	−	0.111200i
$621$	−3708.51	+	5709.84i	−0.239642	+	0.368966i
$622$			18444.5i			1.18900i
$623$	−2468.10	+	4853.66i	−0.158720	+	0.312131i
$624$	−146.476	−	924.936i	−0.00939702	−	0.0593383i
$625$	9765.37	+	16914.1i	0.624983	+	1.08250i
$626$	29396.6			1.87688
$627$	4613.89	−	12018.9i	0.293877	−	0.765530i
$628$			253.965i			0.0161374i
$629$	10726.1			0.679930
$630$	9130.43	+	23730.9i	0.577405	+	1.50073i
$631$	−341.784			−0.0215629			−0.0107815	−	0.999942i	$-0.503432\pi$
$631$	−341.784			−0.0215629			−0.0107815	+	0.999942i	$0.503432\pi$
$632$		−	3494.48i		−	0.219941i
$633$	−14438.5	+	2286.53i	−0.906600	+	0.143572i
$634$	−22329.4			−1.39876
$635$	−2520.23	−	4365.16i	−0.157499	−	0.272797i
$636$	−12197.8	−	4682.60i	−0.760496	−	0.291945i
$637$	737.733	+	327.025i	0.0458870	+	0.0203410i
$638$		−	18140.5i		−	1.12569i
$639$	−499.195	−	106.129i	−0.0309043	−	0.00657024i
$640$	−11716.1	+	6764.31i	−0.723626	+	0.417786i
$641$	−3851.53	−	2223.68i	−0.237326	−	0.137020i	0.376621	−	0.926367i	$-0.377086\pi$
$641$	−3851.53	−	2223.68i	−0.237326	−	0.137020i	−0.613947	+	0.789347i	$0.710419\pi$
$642$	31008.9	−	4910.68i	1.90627	−	0.301883i
$643$	3417.70	+	1973.21i	0.209612	+	0.121020i	0.601131	−	0.799150i	$-0.294717\pi$
$643$	3417.70	+	1973.21i	0.209612	+	0.121020i	−0.391519	+	0.920170i	$0.628050\pi$
$644$	−4402.02	+	2863.79i	−0.269354	+	0.175232i
$645$	26015.3	−	4119.88i	1.58814	−	0.251504i
$646$	−47847.8			−2.91416
$647$	−815.600	−	1412.66i	−0.0495588	−	0.0858384i	0.840182	−	0.542305i	$-0.182448\pi$
$647$	−815.600	−	1412.66i	−0.0495588	−	0.0858384i	−0.889741	+	0.456466i	$0.849115\pi$
$648$	−2380.01	+	5344.43i	−0.144284	+	0.323995i
$649$	6650.44	+	3839.63i	0.402238	+	0.232232i
$650$	270.389	+	468.327i	0.0163162	+	0.0282605i
$651$	−3072.65	+	2771.04i	−0.184987	+	0.166829i
$652$	7816.70	−	13538.9i	0.469518	−	0.813229i
$653$	−9217.89	+	5321.95i	−0.552410	+	0.318934i	−0.750094	−	0.661332i	$-0.769992\pi$
$653$	−9217.89	+	5321.95i	−0.552410	+	0.318934i	0.197683	+	0.980266i	$0.436658\pi$
$654$	26161.1	+	10042.9i	1.56419	+	0.600472i
$655$	−7538.22	+	13056.6i	−0.449683	+	0.778874i
$656$	−7110.10	+	12315.0i	−0.423175	+	0.732960i
$657$	5060.39	+	15576.4i	0.300494	+	0.924954i
$658$	1848.41	+	34730.1i	0.109511	+	2.05763i
$659$	23.4141	−	13.5182i	0.00138404	−	0.000799079i	−0.499308	−	0.866425i	$-0.666412\pi$
$659$	23.4141	−	13.5182i	0.00138404	−	0.000799079i	0.500692	+	0.865626i	$0.333079\pi$
$660$	−7932.87	+	6423.64i	−0.467858	+	0.378848i
$661$		−	7757.38i		−	0.456471i	−0.973606	−	0.228235i	$-0.926704\pi$
$661$		−	7757.38i		−	0.456471i	0.973606	−	0.228235i	$-0.0732955\pi$
$662$		−	25126.8i		−	1.47520i
$663$	1213.12	−	982.322i	0.0710612	−	0.0575418i
$664$	5897.11	−	3404.70i	0.344657	−	0.198988i
$665$	1354.83	+	25456.2i	0.0790047	+	1.48444i
$666$	−5646.78	+	6270.87i	−0.328541	+	0.364852i
$667$	−4809.19	+	8329.77i	−0.279180	+	0.483553i
$668$	−7599.30	+	13162.4i	−0.440158	+	0.762377i
$669$	−20478.0	−	7861.23i	−1.18344	−	0.454309i
$670$	−28691.1	+	16564.8i	−1.65438	+	0.955155i
$671$	6747.36	−	11686.8i	0.388195	−	0.672374i
$672$	−15780.1	+	14231.1i	−0.905851	+	0.816931i
$673$	−16598.3	−	28749.0i	−0.950693	−	1.64665i	−0.743931	−	0.668257i	$-0.767041\pi$
$673$	−16598.3	−	28749.0i	−0.950693	−	1.64665i	−0.206762	−	0.978391i	$-0.566293\pi$
$674$	4012.14	+	2316.41i	0.229291	+	0.132381i
$675$	454.145	−	8655.46i	0.0258964	−	0.493554i
$676$	6402.40	+	11089.3i	0.364270	+	0.630933i
$677$	10932.0			0.620605			0.310303	−	0.950638i	$-0.399570\pi$
$677$	10932.0			0.620605			0.310303	+	0.950638i	$0.399570\pi$
$678$	5020.96	−	795.137i	0.284408	−	0.0450399i
$679$	16150.5	−	10506.9i	0.912813	−	0.593842i
$680$	−12128.4	−	7002.33i	−0.683975	−	0.394893i
$681$	−6384.67	+	1011.10i	−0.359267	+	0.0568948i
$682$	−3408.03	−	1967.63i	−0.191349	−	0.110476i
$683$	12991.1	−	7500.40i	0.727804	−	0.420198i	−0.0898144	−	0.995959i	$-0.528627\pi$
$683$	12991.1	−	7500.40i	0.727804	−	0.420198i	0.817618	+	0.575761i	$0.195294\pi$
$684$	10632.4	−	11807.5i	0.594355	−	0.660043i
$685$			17012.7i			0.948936i
$686$	−3754.19	−	23335.0i	−0.208944	−	1.29874i
$687$	22688.3	+	8709.74i	1.25999	+	0.483693i
$688$	14206.2	+	24605.9i	0.787220	+	1.36351i
$689$	1012.46			0.0559818
$690$	12664.5	−	2005.59i	0.698737	−	0.110654i
$691$			1059.56i			0.0583325i	0.999575	+	0.0291662i	$0.00928522\pi$
$691$			1059.56i			0.0583325i	−0.999575	+	0.0291662i	$0.990715\pi$
$692$	−10231.6			−0.562065
$693$	7734.02	−	9565.79i	0.423941	−	0.524350i
$694$	−35355.0			−1.93380
$695$		−	31527.9i		−	1.72075i
$696$	−2962.04	+	7715.91i	−0.161316	+	0.420217i
$697$	−23703.2			−1.28813
$698$	−7720.08	−	13371.6i	−0.418638	−	0.725102i
$699$	−611.514	−	3861.46i	−0.0330896	−	0.208947i
$700$	3030.27	−	5959.19i	0.163619	−	0.321766i
$701$			21617.3i			1.16473i	0.812928	+	0.582365i	$0.197872\pi$
$701$			21617.3i			1.16473i	−0.812928	+	0.582365i	$0.802128\pi$
$702$	−64.3473	+	1226.38i	−0.00345959	+	0.0659356i
$703$	−7326.87	+	4230.17i	−0.393084	+	0.226947i
$704$	−4446.70	−	2567.31i	−0.238056	−	0.137442i
$705$	12845.7	−	33462.0i	0.686235	−	1.78759i
$706$	−2796.11	−	1614.34i	−0.149055	−	0.0860571i
$707$	2092.41	−	4114.85i	0.111306	−	0.218889i
$708$	5964.37	+	7365.69i	0.316603	+	0.390988i
$709$	−25066.6			−1.32778			−0.663889	−	0.747831i	$-0.731095\pi$
$709$	−25066.6			−1.32778			−0.663889	+	0.747831i	$0.731095\pi$
$710$	480.569	+	832.370i	0.0254020	+	0.0439976i
$711$	−2444.83	+	11499.7i	−0.128957	+	0.606573i
$712$	2043.39	+	1179.75i	0.107555	+	0.0620970i
$713$	1043.27	+	1806.99i	0.0547975	+	0.0949121i
$714$	−43492.3	−	14093.4i	−2.27963	−	0.738703i
$715$	395.487	−	685.003i	0.0206858	−	0.0358289i
$716$	20824.1	−	12022.8i	1.08692	−	0.627533i
$717$	−1689.99	−	10671.6i	−0.0880246	−	0.555839i
$718$	3932.99	−	6812.14i	0.204426	−	0.354076i
$719$	−1208.60	+	2093.36i	−0.0626888	+	0.108580i	−0.895666	−	0.444726i	$-0.853301\pi$
$719$	−1208.60	+	2093.36i	−0.0626888	+	0.108580i	0.832978	+	0.553307i	$0.186634\pi$
$720$	26883.6	−	8733.79i	1.39152	−	0.452068i
$721$	11667.2	−	7590.25i	0.602648	−	0.392061i
$722$	10583.6	−	6110.47i	0.545544	−	0.314970i
$723$	−3174.89	−	20048.1i	−0.163313	−	1.03126i
$724$			15972.2i			0.819891i
$725$		−	12244.4i		−	0.627238i
$726$	−13100.4	−	5029.08i	−0.669699	−	0.257089i
$727$	−3918.13	+	2262.13i	−0.199884	+	0.115403i	−0.596601	−	0.802538i	$-0.703483\pi$
$727$	−3918.13	+	2262.13i	−0.199884	+	0.115403i	0.396718	+	0.917941i	$0.370149\pi$
$728$	158.497	−	311.694i	0.00806909	−	0.0158683i
$729$	11571.3	−	15922.5i	0.587884	−	0.808945i
$730$	15422.0	−	26711.8i	0.781912	−	1.35431i
$731$	−23680.0	+	41014.9i	−1.19813	+	2.07523i
$732$	12943.7	−	10481.1i	0.653569	−	0.529227i
$733$	25576.2	−	14766.4i	1.28878	−	0.744080i	0.310346	−	0.950624i	$-0.399555\pi$
$733$	25576.2	−	14766.4i	1.28878	−	0.744080i	0.978437	+	0.206544i	$0.0662216\pi$
$734$	−582.590	+	1009.08i	−0.0292967	+	0.0507434i
$735$	−6266.55	+	23538.0i	−0.314483	+	1.18124i
$736$	5357.87	+	9280.11i	0.268334	+	0.464768i
$737$	13880.4	+	8013.87i	0.693748	+	0.400536i
$738$	12478.7	−	13857.8i	0.622420	−	0.691211i
$739$	11492.3	+	19905.2i	0.572057	+	0.990832i	0.996355	+	0.0853088i	$0.0271877\pi$
$739$	11492.3	+	19905.2i	0.572057	+	0.990832i	−0.424298	+	0.905523i	$0.639479\pi$
$740$	6708.00			0.333231
$741$	−441.258	+	1149.45i	−0.0218759	+	0.0569851i
$742$	−16170.7	−	24856.5i	−0.800060	−	1.22980i
$743$	12127.5	+	7001.83i	0.598810	+	0.345723i	0.768573	−	0.639762i	$-0.220967\pi$
$743$	12127.5	+	7001.83i	0.598810	+	0.345723i	−0.169763	+	0.985485i	$0.554300\pi$
$744$	1128.30	+	1393.39i	0.0555986	+	0.0686614i
$745$	3919.56	+	2262.96i	0.192754	+	0.111286i
$746$	−17424.0	+	10059.8i	−0.855145	+	0.493718i
$747$	−21788.4	+	7078.50i	−1.06720	+	0.346705i
$748$		−	18353.7i		−	0.897164i
$749$	26808.6	+	13632.3i	1.30783	+	0.665037i
$750$	12981.7	−	10512.0i	0.632034	−	0.511790i
$751$	−13995.6	−	24241.1i	−0.680036	−	1.17786i	−0.974969	−	0.222339i	$-0.928631\pi$
$751$	−13995.6	−	24241.1i	−0.680036	−	1.17786i	0.294933	−	0.955518i	$-0.404703\pi$
$752$	38663.9			1.87490
$753$	6137.70	+	7579.75i	0.297039	+	0.366828i
$754$			1734.90i			0.0837950i
$755$	−25002.5			−1.20521
$756$	13142.4	−	7600.90i	0.632253	−	0.365664i
$757$	32553.0			1.56296			0.781479	−	0.623932i	$-0.214466\pi$
$757$	32553.0			1.56296			0.781479	+	0.623932i	$0.214466\pi$
$758$		−	2951.30i		−	0.141420i
$759$	−3903.76	−	4820.95i	−0.186690	−	0.230552i
$760$	11046.4			0.527230
$761$	7445.71	+	12896.3i	0.354674	+	0.614313i	0.987062	−	0.160339i	$-0.0512587\pi$
$761$	7445.71	+	12896.3i	0.354674	+	0.614313i	−0.632388	+	0.774651i	$0.717925\pi$
$762$	−5541.31	+	4487.08i	−0.263439	+	0.213320i
$763$	14638.9	+	22501.9i	0.694579	+	1.06766i
$764$			1229.29i			0.0582121i
$765$	35013.4	+	31528.8i	1.65479	+	1.49010i
$766$	−32864.9	+	18974.6i	−1.55021	+	0.895012i
$767$	−636.027	−	367.210i	−0.0299421	−	0.0172871i
$768$	17503.5	+	21615.9i	0.822400	+	1.01562i
$769$	−6873.39	−	3968.36i	−0.322316	−	0.186089i	0.330108	−	0.943943i	$-0.392915\pi$
$769$	−6873.39	−	3968.36i	−0.322316	−	0.186089i	−0.652424	+	0.757854i	$0.726248\pi$
$770$	−23133.9	+	1231.23i	−1.08271	+	0.0576241i
$771$	−9873.12	+	25718.8i	−0.461182	+	1.20135i
$772$	−4837.02			−0.225503
$773$	−8421.63	−	14586.7i	−0.391856	−	0.678715i	0.600838	−	0.799371i	$-0.294834\pi$
$773$	−8421.63	−	14586.7i	−0.391856	−	0.678715i	−0.992694	+	0.120656i	$0.961500\pi$
$774$	−11512.5	−	35436.7i	−0.534635	−	1.64567i
$775$	−2300.34	−	1328.10i	−0.106620	−	0.0615573i
$776$	−4174.52	−	7230.48i	−0.193114	−	0.334483i
$777$	−7905.89	+	1686.99i	−0.365022	+	0.0778899i
$778$	−18369.7	+	31817.2i	−0.846510	+	1.46620i
$779$	16191.5	−	9348.14i	0.744697	−	0.429951i
$780$	758.675	−	614.337i	0.0348268	−	0.0282010i
$781$	232.494	−	402.692i	0.0106521	−	0.0184500i
$782$	−11527.6	+	19966.4i	−0.527144	+	0.913041i
$783$	15145.8	−	23319.4i	0.691275	−	1.06433i
$784$	−26126.5	+	2788.91i	−1.19016	+	0.127046i
$785$	514.434	−	297.009i	0.0233897	−	0.0135041i
$786$	19910.4	+	7643.36i	0.903539	+	0.346857i
$787$		−	33935.6i		−	1.53707i	−0.639807	−	0.768536i	$-0.720986\pi$
$787$		−	33935.6i		−	1.53707i	0.639807	−	0.768536i	$-0.279014\pi$
$788$		−	29036.0i		−	1.31265i
$789$	−1347.74	−	8510.45i	−0.0608124	−	0.384005i
$790$	19174.9	−	11070.6i	0.863561	−	0.498577i
$791$	4340.86	+	2207.34i	0.195124	+	0.0992212i
$792$	−3961.11	−	3566.89i	−0.177717	−	0.160030i
$793$	−645.297	+	1117.69i	−0.0288968	+	0.0500507i
$794$	19557.3	−	33874.3i	0.874135	−	1.51405i
$795$	4780.10	+	30184.3i	0.213249	+	1.34658i
$796$	−11656.1	+	6729.63i	−0.519018	+	0.299655i
$797$	12449.1	−	21562.5i	0.553288	−	0.958324i	−0.444746	−	0.895657i	$-0.646706\pi$
$797$	12449.1	−	21562.5i	0.553288	−	0.958324i	0.998034	−	0.0626670i	$-0.0199606\pi$
$798$	35267.4	−	7525.49i	1.56447	−	0.333834i
$799$	32223.9	+	55813.4i	1.42678	+	2.47126i
$800$	−11813.8	−	6820.71i	−0.522102	−	0.301435i
$801$	−5899.06	−	5311.97i	−0.260216	−	0.234319i
$802$	822.878	+	1425.27i	0.0362305	+	0.0627530i
$803$	−14922.1			−0.655776
$804$	12448.5	+	15373.3i	0.546051	+	0.674345i
$805$	10949.0	+	5567.62i	0.479382	+	0.243767i
$806$	325.933	+	188.178i	0.0142438	+	0.00822367i
$807$	−7090.48	+	18470.2i	−0.309289	+	0.805677i
$808$	−1732.35	−	1000.17i	−0.0754256	−	0.0435470i
$809$	−5709.11	+	3296.16i	−0.248111	+	0.143247i	−0.618899	−	0.785471i	$-0.712421\pi$
$809$	−5709.11	+	3296.16i	−0.248111	+	0.143247i	0.370788	+	0.928718i	$0.379088\pi$
$810$	−36865.9	+	3871.72i	−1.59918	+	0.167949i
$811$			184.817i			0.00800222i	0.999992	+	0.00400111i	$0.00127360\pi$
$811$			184.817i			0.00800222i	−0.999992	+	0.00400111i	$0.998726\pi$
$812$	17978.2	−	11695.9i	0.776983	−	0.505476i
$813$	2356.52	+	14880.4i	0.101656	+	0.641918i
$814$	−3844.26	−	6658.45i	−0.165530	−	0.286706i
$815$	−36566.2			−1.57160
$816$	−18215.1	+	47449.0i	−0.781440	+	2.03560i
$817$		−	37355.9i		−	1.59965i
$818$	−30489.2			−1.30321
$819$	−739.657	+	914.842i	−0.0315576	+	0.0390319i
$820$	−14823.8			−0.631306
$821$			6921.45i			0.294227i	0.989120	+	0.147113i	$0.0469982\pi$
$821$			6921.45i			0.294227i	−0.989120	+	0.147113i	$0.953002\pi$
$822$	23769.9	−	3764.29i	1.00860	−	0.159726i
$823$	8628.73			0.365466			0.182733	−	0.983163i	$-0.441506\pi$
$823$	8628.73			0.365466			0.182733	+	0.983163i	$0.441506\pi$
$824$	−3015.69	−	5223.33i	−0.127496	−	0.220829i
$825$	7372.38	+	2830.17i	0.311119	+	0.119435i
$826$	1143.20	+	21479.9i	0.0481563	+	0.904819i
$827$		−	36959.2i		−	1.55405i	−0.629472	−	0.777023i	$-0.716729\pi$
$827$		−	36959.2i		−	1.55405i	0.629472	−	0.777023i	$-0.283271\pi$
$828$	−2365.56	−	7281.46i	−0.0992862	−	0.305614i
$829$	−12723.8	+	7346.11i	−0.533073	+	0.307770i	−0.742267	−	0.670104i	$-0.766249\pi$
$829$	−12723.8	+	7346.11i	−0.533073	+	0.307770i	0.209194	+	0.977874i	$0.432916\pi$
$830$	37364.6	+	21572.4i	1.56258	+	0.902157i
$831$	22448.3	−	3554.99i	0.937092	−	0.148401i
$832$	425.269	+	245.529i	0.0177206	+	0.0102310i
$833$	−25800.7	−	35390.6i	−1.07316	−	1.47204i
$834$	−44050.4	+	6975.98i	−1.82895	+	0.289638i
$835$	35549.2			1.47333
$836$	7238.39	+	12537.3i	0.299456	+	0.518672i
$837$	−2738.17	−	5374.78i	−0.113077	−	0.221959i
$838$	51275.5	+	29603.9i	2.11370	+	1.22035i
$839$	3876.68	+	6714.61i	0.159521	+	0.276298i	0.934696	−	0.355448i	$-0.115672\pi$
$839$	3876.68	+	6714.61i	0.159521	+	0.276298i	−0.775175	+	0.631746i	$0.782338\pi$
$840$	10040.8	+	3253.68i	0.412431	+	0.133646i
$841$	7446.60	−	12897.9i	0.305326	−	0.528841i
$842$	−38954.0	+	22490.1i	−1.59435	+	0.920499i
$843$	10700.5	+	4107.78i	0.437182	+	0.167829i
$844$	8219.14	−	14236.0i	0.335207	−	0.580595i
$845$	14975.1	−	25937.6i	0.609654	−	1.05595i
$846$	−49595.0	−	10543.9i	−2.01550	−	0.428493i
$847$	−7330.56	−	11268.0i	−0.297380	−	0.457112i
$848$	−28549.1	+	16482.8i	−1.15611	+	0.667479i
$849$	−22402.8	+	18140.6i	−0.905607	+	0.733316i
$850$		−	29349.9i		−	1.18434i
$851$			4076.57i			0.164210i
$852$	446.001	−	361.150i	0.0179340	−	0.0145220i
$853$	8892.58	−	5134.13i	0.356947	−	0.206084i	−0.310794	−	0.950477i	$-0.600595\pi$
$853$	8892.58	−	5134.13i	0.356947	−	0.206084i	0.667741	+	0.744394i	$0.267261\pi$
$854$	37746.5	−	2008.94i	1.51248	−	0.0804972i
$855$	−36351.8	−	7728.36i	−1.45404	−	0.309128i
$856$	6516.23	−	11286.4i	0.260187	−	0.450657i
$857$	−13906.9	+	24087.5i	−0.554320	+	0.960110i	0.443637	+	0.896207i	$0.353688\pi$
$857$	−13906.9	+	24087.5i	−0.554320	+	0.960110i	−0.997956	+	0.0639028i	$0.979645\pi$
$858$	−1044.58	−	401.003i	−0.0415636	−	0.0159557i
$859$	497.469	−	287.214i	0.0197595	−	0.0114082i	−0.490088	−	0.871673i	$-0.663035\pi$
$859$	497.469	−	287.214i	0.0197595	−	0.0114082i	0.509847	+	0.860265i	$0.329702\pi$
$860$	−14809.3	+	25650.4i	−0.587201	+	1.01706i
$861$	17471.0	−	3728.04i	0.691534	−	0.147562i
$862$	−15066.3	−	26095.6i	−0.595313	−	1.03111i
$863$	−26652.7	−	15388.0i	−1.05130	−	0.606967i	−0.128285	−	0.991737i	$-0.540947\pi$
$863$	−26652.7	−	15388.0i	−1.05130	−	0.606967i	−0.923012	+	0.384771i	$0.874280\pi$
$864$	−14062.4	−	27603.1i	−0.553717	−	1.08689i
$865$	11965.8	+	20725.4i	0.470346	+	0.814663i
$866$	2831.12			0.111092
$867$	−58461.8	+	9258.21i	−2.29004	+	0.362659i
$868$	−247.277	−	4646.14i	−0.00966950	−	0.181682i
$869$	−9276.63	−	5355.87i	−0.362127	−	0.209074i
$870$	−51722.7	+	8190.98i	−2.01559	+	0.319196i
$871$	−1327.48	−	766.422i	−0.0516418	−	0.0298154i
$872$	10073.9	−	5816.20i	0.391223	−	0.225873i
$873$	8678.98	+	26714.9i	0.336471	+	1.03569i
$874$		−	18185.2i		−	0.703801i
$875$	15979.3	−	850.451i	0.617370	−	0.0328577i
$876$	−17193.4	−	6600.32i	−0.663139	−	0.254571i
$877$	18861.3	+	32668.7i	0.726227	+	1.25786i	0.958467	+	0.285204i	$0.0920612\pi$
$877$	18861.3	+	32668.7i	0.726227	+	1.25786i	−0.232240	+	0.972659i	$0.574605\pi$
$878$	−9826.08			−0.377693
$879$	3409.54	−	539.947i	0.130832	−	0.0207189i
$880$			25754.2i			0.986560i
$881$	−30628.9			−1.17130			−0.585650	−	0.810564i	$-0.699161\pi$
$881$	−30628.9			−1.17130			−0.585650	+	0.810564i	$0.699161\pi$
$882$	34273.6	+	3547.45i	1.30845	+	0.135429i
$883$	−26121.2			−0.995524			−0.497762	−	0.867314i	$-0.665845\pi$
$883$	−26121.2			−0.995524			−0.497762	+	0.867314i	$0.665845\pi$
$884$			1755.29i			0.0667838i
$885$	7944.78	−	20695.6i	0.301764	−	0.786073i
$886$	24299.5			0.921397
$887$	14137.3	+	24486.6i	0.535158	+	0.926921i	0.999156	+	0.0410848i	$0.0130814\pi$
$887$	14137.3	+	24486.6i	0.535158	+	0.926921i	−0.463997	+	0.885837i	$0.653585\pi$
$888$	547.909	+	3459.82i	0.0207056	+	0.130748i
$889$	−6820.84	+	363.019i	−0.257327	+	0.0136955i
$890$			14950.0i			0.563062i
$891$	10539.8	+	14509.3i	0.396294	+	0.545545i
$892$	21361.2	−	12332.9i	0.801823	−	0.462933i
$893$	−44023.6	−	25417.0i	−1.64971	−	0.952463i
$894$	2294.52	−	5977.07i	0.0858393	−	0.223605i
$895$	−48707.1	−	28121.1i	−1.81910	−	1.05026i
$896$	974.348	+	18307.2i	0.0363289	+	0.682591i
$897$	373.344	+	461.060i	0.0138970	+	0.0171620i
$898$	25794.1			0.958532
$899$	−4260.78	−	7379.88i	−0.158070	−	0.273785i
$900$	7242.71	+	6521.90i	0.268248	+	0.241552i
$901$	−47587.7	−	27474.8i	−1.75957	−	1.01589i
$902$	8495.33	+	14714.3i	0.313596	+	0.543164i
$903$	11003.1	−	33955.4i	0.405492	−	1.25135i
$904$	1055.11	−	1827.50i	0.0388190	−	0.0672365i
$905$	32353.4	−	18679.3i	1.18836	−	0.686099i
$906$	5532.14	+	34933.2i	0.202862	+	1.28099i
$907$	13072.0	−	22641.3i	0.478553	−	0.828878i	−0.521144	−	0.853469i	$-0.674495\pi$
$907$	13072.0	−	22641.3i	0.478553	−	0.828878i	0.999698	+	0.0245901i	$0.00782805\pi$
$908$	3634.49	−	6295.12i	0.132836	−	0.230078i
$909$	5001.12	+	4503.40i	0.182483	+	0.164322i
$910$	2212.45	−	117.751i	0.0805957	−	0.00428947i
$911$	29605.2	−	17092.5i	1.07669	−	0.621626i	0.146687	−	0.989183i	$-0.453139\pi$
$911$	29605.2	−	17092.5i	1.07669	−	0.621626i	0.930001	+	0.367557i	$0.119806\pi$
$912$	−6270.51	−	39595.6i	−0.227672	−	1.43766i
$913$		−	20873.1i		−	0.756624i
$914$			54289.4i			1.96470i
$915$	−36368.2	−	13961.3i	−1.31399	−	0.504422i
$916$	−23666.8	+	13664.0i	−0.853683	+	0.492874i
$917$	11141.2	+	17125.5i	0.401217	+	0.616723i
$918$	36304.5	−	55896.5i	1.30526	−	2.00965i
$919$	−6975.24	+	12081.5i	−0.250372	+	0.433657i	−0.963628	−	0.267246i	$-0.913886\pi$
$919$	−6975.24	+	12081.5i	−0.250372	+	0.433657i	0.713256	+	0.700903i	$0.247220\pi$
$920$	2661.32	−	4609.55i	0.0953709	−	0.165187i
$921$	13613.6	−	11023.6i	0.487061	−	0.394398i
$922$	−32563.2	+	18800.4i	−1.16314	+	0.671537i
$923$	−22.2350	+	38.5122i	−0.000792931	+	0.00137340i
$924$	2886.67	+	13528.0i	0.102775	+	0.481645i
$925$	−2594.79	−	4494.31i	−0.0922337	−	0.159753i
$926$	53850.5	+	31090.6i	1.91105	+	1.10335i
$927$	6269.74	+	19298.9i	0.222141	+	0.683776i
$928$	−21881.9	−	37900.6i	−0.774041	−	1.34068i
$929$	31483.5			1.11188			0.555942	−	0.831221i	$-0.312357\pi$
$929$	31483.5			1.11188			0.555942	+	0.831221i	$0.312357\pi$
$930$	−4071.32	+	10605.5i	−0.143552	+	0.373944i
$931$	31581.6	+	13999.6i	1.11176	+	0.492825i
$932$	3807.30	+	2198.15i	0.133811	+	0.0772561i
$933$	−16210.4	−	20019.0i	−0.568816	−	0.702459i
$934$	−9409.71	−	5432.70i	−0.329652	−	0.190325i
$935$	−37177.5	+	21464.5i	−1.30036	+	0.750762i
$936$	378.828	+	341.126i	0.0132290	+	0.0119125i
$937$			40165.8i			1.40038i	0.713955	+	0.700192i	$0.246902\pi$
$937$			40165.8i			1.40038i	−0.713955	+	0.700192i	$0.753098\pi$
$938$	2386.03	+	44831.6i	0.0830562	+	1.56056i
$939$	−31906.1	+	25836.0i	−1.10886	+	0.897896i
$940$	20152.6	+	34905.3i	0.699260	+	1.21115i
$941$	1053.93			0.0365114			0.0182557	−	0.999833i	$-0.494189\pi$
$941$	1053.93			0.0365114			0.0182557	+	0.999833i	$0.494189\pi$
$942$	−528.802	−	653.044i	−0.0182901	−	0.0225874i
$943$		−	9008.71i		−	0.311097i
$944$	23912.8			0.824466
$945$	−30766.3	−	17732.2i	−1.05908	−	0.610399i
$946$	33948.0			1.16675
$947$			42313.5i			1.45196i	0.687716	+	0.725980i	$0.258613\pi$
$947$			42313.5i			1.45196i	−0.687716	+	0.725980i	$0.741387\pi$
$948$	−8319.64	−	10274.3i	−0.285031	−	0.351998i
$949$	1427.10			0.0488151
$950$	11575.1	+	20048.6i	0.395311	+	0.684698i
$951$	24235.6	−	19624.8i	0.826386	−	0.669166i
$952$	−15908.1	+	10349.2i	−0.541580	+	0.352332i
$953$			20155.3i			0.685095i	0.939501	+	0.342547i	$0.111290\pi$
$953$			20155.3i			0.685095i	−0.939501	+	0.342547i	$0.888710\pi$
$954$	41115.5	−	13357.4i	1.39535	−	0.453314i
$955$	2490.06	−	1437.64i	0.0843732	−	0.0487129i
$956$	10521.9	+	6074.81i	0.355965	+	0.205516i
$957$	15943.3	+	19689.1i	0.538529	+	0.665056i
$958$	20283.5	+	11710.7i	0.684062	+	0.394943i
$959$	20550.2	+	10449.8i	0.691971	+	0.351870i
$960$	−5312.14	+	13837.8i	−0.178592	+	0.465220i
$961$	27942.4			0.937948
$962$	367.653	+	636.794i	0.0123218	+	0.0213420i
$963$	−29340.1	+	32582.8i	−0.981798	+	1.09031i
$964$	19767.0	+	11412.5i	0.660426	+	0.381297i
$965$	5656.83	+	9797.92i	0.188705	+	0.326846i
$966$	5356.39	−	16529.8i	0.178405	−	0.550556i
$967$	−2887.13	+	5000.66i	−0.0960123	+	0.166298i	−0.910031	−	0.414541i	$-0.863942\pi$
$967$	−2887.13	+	5000.66i	−0.0960123	+	0.166298i	0.814018	+	0.580839i	$0.197275\pi$
$968$	−5044.62	+	2912.51i	−0.167500	+	0.0967064i
$969$	51932.4	−	42052.3i	1.72168	−	1.39413i
$970$	26450.1	−	45812.9i	0.875527	−	1.51646i
$971$	−5434.98	+	9413.66i	−0.179626	+	0.311121i	−0.941752	−	0.336307i	$-0.890822\pi$
$971$	−5434.98	+	9413.66i	−0.179626	+	0.311121i	0.762126	+	0.647428i	$0.224155\pi$
$972$	5726.36	+	21379.8i	0.188964	+	0.705511i
$973$	−38083.7	−	19365.7i	−1.25479	−	0.638062i
$974$	17602.1	−	10162.6i	0.579064	−	0.334323i
$975$	−705.072	−	270.668i	−0.0231593	−	0.00889058i
$976$		−	42021.8i		−	1.37816i
$977$		−	32409.0i		−	1.06127i	−0.847602	−	0.530633i	$-0.821954\pi$
$977$		−	32409.0i		−	1.06127i	0.847602	−	0.530633i	$-0.178046\pi$
$978$	8090.76	+	51089.8i	0.264534	+	1.67042i
$979$	6263.66	−	3616.33i	0.204482	−	0.118058i
$980$	−16135.6	−	22133.0i	−0.525951	−	0.721443i
$981$	−37220.8	+	12092.1i	−1.21139	+	0.393548i
$982$	8018.22	−	13888.0i	0.260562	−	0.451306i
$983$	−14236.2	+	24657.9i	−0.461918	+	0.800065i	−0.999057	−	0.0434287i	$-0.986172\pi$
$983$	−14236.2	+	24657.9i	−0.461918	+	0.800065i	0.537139	+	0.843494i	$0.319505\pi$
$984$	−1210.81	−	7645.76i	−0.0392268	−	0.247701i
$985$	−58815.7	+	33957.3i	−1.90256	+	1.09845i
$986$	47079.6	−	81544.3i	1.52061	−	2.63377i
$987$	−32529.6	−	36070.4i	−1.04907	−	1.16325i
$988$	−692.257	−	1199.02i	−0.0222911	−	0.0386093i
$989$	−15588.2	−	8999.87i	−0.501190	−	0.289362i
$990$	7023.31	−	33035.5i	0.225470	−	1.06054i
$991$	9926.08	+	17192.5i	0.318176	+	0.551097i	0.980107	−	0.198468i	$-0.0635964\pi$
$991$	9926.08	+	17192.5i	0.318176	+	0.551097i	−0.661932	+	0.749564i	$0.730263\pi$
$992$	−9493.78			−0.303859
$993$	22083.3	+	27271.8i	0.705734	+	0.871545i
$994$	1300.63	−	69.2223i	0.0415026	−	0.00220885i
$995$	27263.2	+	15740.4i	0.868646	+	0.501513i
$996$	9232.56	−	24050.2i	0.293720	−	0.765119i
$997$	8045.34	+	4644.98i	0.255565	+	0.147551i	0.622310	−	0.782771i	$-0.286194\pi$
$997$	8045.34	+	4644.98i	0.255565	+	0.147551i	−0.366745	+	0.930322i	$0.619528\pi$
$998$	−58099.2	+	33543.6i	−1.84278	+	1.06393i
$999$	617.510	−	11769.0i	0.0195567	−	0.372727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.i.a.5.5	✓	44
3.2	odd	2		189.4.i.a.152.18		44
7.3	odd	6		63.4.s.a.59.18	yes	44
9.2	odd	6		63.4.s.a.47.18	yes	44
9.7	even	3		189.4.s.a.89.5		44
21.17	even	6		189.4.s.a.17.5		44
63.38	even	6	inner	63.4.i.a.38.18	yes	44
63.52	odd	6		189.4.i.a.143.5		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.5	✓	44	1.1	even	1	trivial
63.4.i.a.38.18	yes	44	63.38	even	6	inner
63.4.s.a.47.18	yes	44	9.2	odd	6
63.4.s.a.59.18	yes	44	7.3	odd	6
189.4.i.a.143.5		44	63.52	odd	6
189.4.i.a.152.18		44	3.2	odd	2
189.4.s.a.17.5		44	21.17	even	6
189.4.s.a.89.5		44	9.7	even	3

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-3.72062i q^{2} +(3.26996 + 4.03824i) q^{3} -5.84303 q^{4} +(6.83336 + 11.8357i) q^{5} +(15.0248 - 12.1663i) q^{6} +(18.4941 - 0.984293i) q^{7} -8.02526i q^{8} +(-5.61469 + 26.4098i) q^{9} +(44.0363 - 25.4243i) q^{10} +(-21.3043 - 12.3000i) q^{11} +(-19.1065 - 23.5955i) q^{12} +(2.03747 + 1.17634i) q^{13} +(-3.66218 - 68.8095i) q^{14} +(-25.4506 + 66.2971i) q^{15} -76.6032 q^{16} +(-63.8439 - 110.581i) q^{17} +(98.2607 + 20.8902i) q^{18} +(87.2223 + 50.3578i) q^{19} +(-39.9275 - 69.1565i) q^{20} +(64.4498 + 71.4649i) q^{21} +(-45.7638 + 79.2652i) q^{22} +(42.0276 - 24.2647i) q^{23} +(32.4079 - 26.2423i) q^{24} +(-30.8895 + 53.5022i) q^{25} +(4.37670 - 7.58067i) q^{26} +(-125.009 + 63.6854i) q^{27} +(-108.062 + 5.75126i) q^{28} +(-171.644 + 99.0987i) q^{29} +(246.666 + 94.6921i) q^{30} +42.9953i q^{31} +220.810i q^{32} +(-19.9938 - 126.252i) q^{33} +(-411.430 + 237.539i) q^{34} +(138.026 + 212.165i) q^{35} +(32.8068 - 154.313i) q^{36} +(-42.0011 + 72.7481i) q^{37} +(187.363 - 324.521i) q^{38} +(1.91214 + 12.0744i) q^{39} +(94.9848 - 54.8395i) q^{40} +(92.8172 - 160.764i) q^{41} +(265.894 - 239.793i) q^{42} +(-185.452 - 321.213i) q^{43} +(124.482 + 71.8695i) q^{44} +(-350.946 + 114.013i) q^{45} +(-90.2797 - 156.369i) q^{46} -504.729 q^{47} +(-250.490 - 309.342i) q^{48} +(341.062 - 36.4072i) q^{49} +(199.062 + 114.928i) q^{50} +(237.785 - 619.412i) q^{51} +(-11.9050 - 6.87337i) q^{52} +(372.688 - 215.171i) q^{53} +(236.950 + 465.110i) q^{54} -336.202i q^{55} +(-7.89921 - 148.420i) q^{56} +(81.8569 + 516.893i) q^{57} +(368.709 + 638.622i) q^{58} -312.164 q^{59} +(148.709 - 387.376i) q^{60} +548.565i q^{61} +159.969 q^{62} +(-77.8437 + 493.951i) q^{63} +208.723 q^{64} +32.1533i q^{65} +(-469.737 + 74.3893i) q^{66} -651.533 q^{67} +(373.042 + 646.128i) q^{68} +(235.415 + 90.3730i) q^{69} +(789.385 - 513.545i) q^{70} +18.9019i q^{71} +(211.945 + 45.0594i) q^{72} +(525.319 - 303.293i) q^{73} +(270.668 + 156.270i) q^{74} +(-317.062 + 50.2111i) q^{75} +(-509.643 - 294.243i) q^{76} +(-406.110 - 206.508i) q^{77} +(44.9242 - 7.11436i) q^{78} +435.435 q^{79} +(-523.457 - 906.654i) q^{80} +(-665.950 - 296.565i) q^{81} +(-598.142 - 345.338i) q^{82} +(424.248 + 734.819i) q^{83} +(-376.582 - 417.572i) q^{84} +(872.537 - 1511.28i) q^{85} +(-1195.11 + 689.998i) q^{86} +(-961.453 - 369.090i) q^{87} +(-98.7110 + 170.972i) q^{88} +(-147.005 + 254.620i) q^{89} +(424.201 + 1305.74i) q^{90} +(38.8391 + 19.7498i) q^{91} +(-245.569 + 141.779i) q^{92} +(-173.625 + 140.593i) q^{93} +1877.91i q^{94} +1376.45i q^{95} +(-891.681 + 722.039i) q^{96} +(900.965 - 520.172i) q^{97} +(-135.457 - 1268.96i) q^{98} +(444.458 - 493.580i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 3 q^{3} - 162 q^{4} - 3 q^{5} + 24 q^{6} + 5 q^{7} - 45 q^{9} - 6 q^{10} + 9 q^{11} + 186 q^{12} - 36 q^{13} + 54 q^{14} - 141 q^{15} + 526 q^{16} - 72 q^{17} - 54 q^{18} - 6 q^{19} + 24 q^{20} - 81 q^{21}+ \cdots + 4335 q^{99}+O(q^{100}) \) 44 * q - 3 * q^3 - 162 * q^4 - 3 * q^5 + 24 * q^6 + 5 * q^7 - 45 * q^9 - 6 * q^10 + 9 * q^11 + 186 * q^12 - 36 * q^13 + 54 * q^14 - 141 * q^15 + 526 * q^16 - 72 * q^17 - 54 * q^18 - 6 * q^19 + 24 * q^20 - 81 * q^21 + 14 * q^22 - 285 * q^23 - 114 * q^24 - 349 * q^25 - 96 * q^26 + 432 * q^27 - 156 * q^28 - 132 * q^29 - 447 * q^30 - 3 * q^33 + 24 * q^34 + 765 * q^35 + 1122 * q^36 + 82 * q^37 - 873 * q^38 + 306 * q^39 + 420 * q^40 + 618 * q^41 - 282 * q^42 + 82 * q^43 + 603 * q^44 + 291 * q^45 + 266 * q^46 - 402 * q^47 - 1569 * q^48 - 79 * q^49 - 1845 * q^50 + 453 * q^51 + 189 * q^52 + 564 * q^53 - 2385 * q^54 + 66 * q^56 + 1170 * q^57 + 269 * q^58 + 1494 * q^59 + 2265 * q^60 - 2904 * q^62 - 636 * q^63 - 1144 * q^64 - 372 * q^66 - 590 * q^67 + 3504 * q^68 - 1005 * q^69 - 105 * q^70 + 1830 * q^72 - 6 * q^73 + 1515 * q^74 - 33 * q^75 - 144 * q^76 - 4443 * q^77 - 5985 * q^78 + 1102 * q^79 - 4239 * q^80 - 4017 * q^81 + 18 * q^82 + 1830 * q^83 + 3165 * q^84 - 237 * q^85 + 1209 * q^86 + 2013 * q^87 - 623 * q^88 + 4266 * q^89 + 9993 * q^90 - 1140 * q^91 + 7896 * q^92 - 729 * q^93 + 3975 * q^96 - 792 * q^97 + 5667 * q^98 + 4335 * q^99

Introduction

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