LMFDB - Embedded newform 161.4.e.a.93.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,4,Mod(93,161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("161.93");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.49930751092$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.4
Character	$\chi$	$=$	161.93
Dual form			161.4.e.a.116.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.21363 + 3.83412i) q^{2} +(-4.64135 - 8.03905i) q^{3} +(-5.80032 - 10.0465i) q^{4} +(-8.69922 + 15.0675i) q^{5} +41.0969 q^{6} +(-7.29013 + 17.0251i) q^{7} +15.9410 q^{8} +(-29.5843 + 51.2414i) q^{9} +(-38.5137 - 66.7078i) q^{10} +(-5.80024 - 10.0463i) q^{11} +(-53.8426 + 93.2582i) q^{12} -43.4448 q^{13} +(-49.1386 - 65.6385i) q^{14} +161.505 q^{15} +(11.1151 - 19.2519i) q^{16} +(27.5840 + 47.7769i) q^{17} +(-130.977 - 226.859i) q^{18} +(40.3038 - 69.8082i) q^{19} +201.833 q^{20} +(170.702 - 20.4137i) q^{21} +51.3584 q^{22} +(11.5000 - 19.9186i) q^{23} +(-73.9877 - 128.150i) q^{24} +(-88.8530 - 153.898i) q^{25} +(96.1706 - 166.572i) q^{26} +298.611 q^{27} +(213.327 - 25.5112i) q^{28} -55.6132 q^{29} +(-357.512 + 619.228i) q^{30} +(-120.315 - 208.392i) q^{31} +(112.973 + 195.676i) q^{32} +(-53.8419 + 93.2570i) q^{33} -244.243 q^{34} +(-193.107 - 257.949i) q^{35} +686.393 q^{36} +(-121.911 + 211.155i) q^{37} +(178.435 + 309.059i) q^{38} +(201.642 + 349.255i) q^{39} +(-138.674 + 240.191i) q^{40} +257.654 q^{41} +(-299.602 + 699.680i) q^{42} +142.269 q^{43} +(-67.2866 + 116.544i) q^{44} +(-514.720 - 891.522i) q^{45} +(50.9135 + 88.1848i) q^{46} +(321.037 - 556.053i) q^{47} -206.357 q^{48} +(-236.708 - 248.230i) q^{49} +786.751 q^{50} +(256.054 - 443.499i) q^{51} +(251.994 + 436.466i) q^{52} +(241.864 + 418.920i) q^{53} +(-661.014 + 1144.91i) q^{54} +201.831 q^{55} +(-116.212 + 271.397i) q^{56} -748.256 q^{57} +(123.107 - 213.228i) q^{58} +(175.266 + 303.570i) q^{59} +(-936.779 - 1622.55i) q^{60} +(-172.105 + 298.095i) q^{61} +1065.33 q^{62} +(-656.718 - 877.232i) q^{63} -822.484 q^{64} +(377.936 - 654.604i) q^{65} +(-238.372 - 412.873i) q^{66} +(377.658 + 654.123i) q^{67} +(319.993 - 554.243i) q^{68} -213.502 q^{69} +(1416.48 - 169.392i) q^{70} -877.494 q^{71} +(-471.602 + 816.839i) q^{72} +(-612.837 - 1061.46i) q^{73} +(-539.730 - 934.839i) q^{74} +(-824.796 + 1428.59i) q^{75} -935.100 q^{76} +(213.324 - 25.5108i) q^{77} -1785.45 q^{78} +(-110.002 + 190.528i) q^{79} +(193.386 + 334.954i) q^{80} +(-587.182 - 1017.03i) q^{81} +(-570.350 + 987.875i) q^{82} +416.384 q^{83} +(-1195.21 - 1596.54i) q^{84} -959.839 q^{85} +(-314.930 + 545.475i) q^{86} +(258.120 + 447.077i) q^{87} +(-92.4616 - 160.148i) q^{88} +(770.627 - 1334.77i) q^{89} +4557.60 q^{90} +(316.718 - 739.651i) q^{91} -266.815 q^{92} +(-1116.85 + 1934.44i) q^{93} +(1421.32 + 2461.79i) q^{94} +(701.224 + 1214.55i) q^{95} +(1048.70 - 1816.40i) q^{96} +754.400 q^{97} +(1475.73 - 358.078i) q^{98} +686.384 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 6 q^{3} - 88 q^{4} - 20 q^{5} + 24 q^{6} - 12 q^{7} + 42 q^{8} - 238 q^{9} - 182 q^{10} + 28 q^{11} - 127 q^{12} + 440 q^{13} + 16 q^{14} + 40 q^{15} - 436 q^{16} - 294 q^{17} + 155 q^{18} - 252 q^{19}+ \cdots - 5764 q^{99}+O(q^{100}) $ 44 * q - 6 * q^3 - 88 * q^4 - 20 * q^5 + 24 * q^6 - 12 * q^7 + 42 * q^8 - 238 * q^9 - 182 * q^10 + 28 * q^11 - 127 * q^12 + 440 * q^13 + 16 * q^14 + 40 * q^15 - 436 * q^16 - 294 * q^17 + 155 * q^18 - 252 * q^19 + 708 * q^20 + 110 * q^21 + 28 * q^22 + 506 * q^23 - 458 * q^24 - 684 * q^25 - 396 * q^26 + 972 * q^27 - 354 * q^28 + 628 * q^29 + 905 * q^30 - 172 * q^31 + 127 * q^32 - 1524 * q^33 + 800 * q^34 - 1588 * q^35 + 2644 * q^36 + 710 * q^37 + 323 * q^38 + 136 * q^39 - 1808 * q^40 + 784 * q^41 - 2775 * q^42 + 504 * q^43 + 1106 * q^44 - 658 * q^45 - 448 * q^47 + 2730 * q^48 - 570 * q^49 + 738 * q^50 + 896 * q^51 - 1224 * q^52 - 308 * q^53 - 945 * q^54 + 4324 * q^55 - 481 * q^56 - 124 * q^57 + 1153 * q^58 + 282 * q^59 - 4442 * q^60 - 3076 * q^61 + 3500 * q^62 - 732 * q^63 - 4354 * q^64 + 1024 * q^65 + 549 * q^66 - 1056 * q^67 - 2478 * q^68 - 276 * q^69 + 2071 * q^70 - 96 * q^71 + 1922 * q^72 - 4430 * q^73 - 3322 * q^74 - 2540 * q^75 + 15026 * q^76 - 1116 * q^77 - 3990 * q^78 + 530 * q^79 - 296 * q^80 - 3446 * q^81 - 1570 * q^82 + 3572 * q^83 - 4571 * q^84 - 2624 * q^85 + 397 * q^86 + 1724 * q^87 - 5375 * q^88 - 658 * q^89 + 13620 * q^90 - 1098 * q^91 - 4048 * q^92 + 1722 * q^93 + 1944 * q^94 - 1742 * q^95 - 1142 * q^96 + 21364 * q^97 + 2001 * q^98 - 5764 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/161\mathbb{Z}\right)^\times$.

$n$	$24$	$120$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.21363	+	3.83412i	−0.782637	+	1.35557i	0.147764	+	0.989023i	$0.452792\pi$
$2$	−2.21363	+	3.83412i	−0.782637	+	1.35557i	−0.930401	+	0.366544i	$0.880541\pi$
$3$	−4.64135	−	8.03905i	−0.893228	−	1.54712i	−0.835982	−	0.548757i	$-0.815101\pi$
$3$	−4.64135	−	8.03905i	−0.893228	−	1.54712i	−0.0572461	−	0.998360i	$-0.518232\pi$
$4$	−5.80032	−	10.0465i	−0.725040	−	1.25581i
$5$	−8.69922	+	15.0675i	−0.778082	+	1.34768i	0.154963	+	0.987920i	$0.450474\pi$
$5$	−8.69922	+	15.0675i	−0.778082	+	1.34768i	−0.933046	+	0.359758i	$0.882859\pi$
$6$	41.0969			2.79629
$7$	−7.29013	+	17.0251i	−0.393630	+	0.919269i
$7$	−7.29013	+	17.0251i	−0.393630	+	0.919269i
$8$	15.9410			0.704499
$9$	−29.5843	+	51.2414i	−1.09571	+	1.89783i
$10$	−38.5137	−	66.7078i	−1.21791	−	2.10948i
$11$	−5.80024	−	10.0463i	−0.158985	−	0.275371i	0.775518	−	0.631326i	$-0.217489\pi$
$11$	−5.80024	−	10.0463i	−0.158985	−	0.275371i	−0.934503	+	0.355955i	$0.884156\pi$
$12$	−53.8426	+	93.2582i	−1.29525	+	2.24344i
$13$	−43.4448			−0.926877			−0.463439	−	0.886129i	$-0.653385\pi$
$13$	−43.4448			−0.926877			−0.463439	+	0.886129i	$0.653385\pi$
$14$	−49.1386	−	65.6385i	−0.938061	−	1.25304i
$15$	161.505			2.78002
$16$	11.1151	−	19.2519i	0.173674	−	0.300812i
$17$	27.5840	+	47.7769i	0.393536	+	0.681624i	0.992913	−	0.118843i	$-0.0379184\pi$
$17$	27.5840	+	47.7769i	0.393536	+	0.681624i	−0.599377	+	0.800467i	$0.704585\pi$
$18$	−130.977	−	226.859i	−1.71509	−	2.97062i
$19$	40.3038	−	69.8082i	0.486649	−	0.842900i	−0.513234	−	0.858249i	$-0.671553\pi$
$19$	40.3038	−	69.8082i	0.486649	−	0.842900i	0.999882	+	0.0153488i	$0.00488586\pi$
$20$	201.833			2.25656
$21$	170.702	−	20.4137i	1.77382	−	0.212126i
$22$	51.3584			0.497711
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$24$	−73.9877	−	128.150i	−0.629278	−	1.08994i
$25$	−88.8530	−	153.898i	−0.710824	−	1.23118i
$26$	96.1706	−	166.572i	0.725408	−	1.25644i
$27$	298.611			2.12843
$28$	213.327	−	25.5112i	1.43982	−	0.172184i
$29$	−55.6132			−0.356107			−0.178054	−	0.984021i	$-0.556980\pi$
$29$	−55.6132			−0.356107			−0.178054	+	0.984021i	$0.556980\pi$
$30$	−357.512	+	619.228i	−2.17575	+	3.76850i
$31$	−120.315	−	208.392i	−0.697072	−	1.20736i	−0.969477	−	0.245181i	$-0.921153\pi$
$31$	−120.315	−	208.392i	−0.697072	−	1.20736i	0.272405	−	0.962183i	$-0.412181\pi$
$32$	112.973	+	195.676i	0.624096	+	1.08097i
$33$	−53.8419	+	93.2570i	−0.284021	+	0.491938i
$34$	−244.243			−1.23198
$35$	−193.107	−	257.949i	−0.932602	−	1.24575i
$36$	686.393			3.17774
$37$	−121.911	+	211.155i	−0.541675	+	0.938208i	0.457133	+	0.889398i	$0.348876\pi$
$37$	−121.911	+	211.155i	−0.541675	+	0.938208i	−0.998808	+	0.0488101i	$0.984457\pi$
$38$	178.435	+	309.059i	0.761738	+	1.31937i
$39$	201.642	+	349.255i	0.827913	+	1.43399i
$40$	−138.674	+	240.191i	−0.548158	+	0.949437i
$41$	257.654			0.981433			0.490716	−	0.871319i	$-0.336735\pi$
$41$	257.654			0.981433			0.490716	+	0.871319i	$0.336735\pi$
$42$	−299.602	+	699.680i	−1.10070	+	2.57055i
$43$	142.269			0.504553			0.252276	−	0.967655i	$-0.418821\pi$
$43$	142.269			0.504553			0.252276	+	0.967655i	$0.418821\pi$
$44$	−67.2866	+	116.544i	−0.230542	+	0.399310i
$45$	−514.720	−	891.522i	−1.70511	−	2.95334i
$46$	50.9135	+	88.1848i	0.163191	+	0.282655i
$47$	321.037	−	556.053i	0.996342	−	1.72571i	0.424164	−	0.905585i	$-0.360568\pi$
$47$	321.037	−	556.053i	0.996342	−	1.72571i	0.572178	−	0.820129i	$-0.306099\pi$
$48$	−206.357			−0.620521
$49$	−236.708	−	248.230i	−0.690111	−	0.723703i
$50$	786.751			2.22527
$51$	256.054	−	443.499i	0.703035	−	1.21769i
$52$	251.994	+	436.466i	0.672023	+	1.16398i
$53$	241.864	+	418.920i	0.626840	+	1.08572i	0.988182	+	0.153285i	$0.0489853\pi$
$53$	241.864	+	418.920i	0.626840	+	1.08572i	−0.361342	+	0.932433i	$0.617681\pi$
$54$	−661.014	+	1144.91i	−1.66579	+	2.88523i
$55$	201.831			0.494815
$56$	−116.212	+	271.397i	−0.277312	+	0.647624i
$57$	−748.256			−1.73875
$58$	123.107	−	213.228i	0.278703	−	0.482727i
$59$	175.266	+	303.570i	0.386741	+	0.669855i	0.992009	−	0.126167i	$-0.0402675\pi$
$59$	175.266	+	303.570i	0.386741	+	0.669855i	−0.605268	+	0.796022i	$0.706934\pi$
$60$	−936.779	−	1622.55i	−2.01563	−	3.49117i
$61$	−172.105	+	298.095i	−0.361243	+	0.625692i	−0.988166	−	0.153390i	$-0.950981\pi$
$61$	−172.105	+	298.095i	−0.361243	+	0.625692i	0.626922	+	0.779082i	$0.284314\pi$
$62$	1065.33			2.18222
$63$	−656.718	−	877.232i	−1.31331	−	1.75430i
$64$	−822.484			−1.60641
$65$	377.936	−	654.604i	0.721187	−	1.24913i
$66$	−238.372	−	412.873i	−0.444570	−	0.770017i
$67$	377.658	+	654.123i	0.688631	+	1.19274i	0.972281	+	0.233816i	$0.0751213\pi$
$67$	377.658	+	654.123i	0.688631	+	1.19274i	−0.283650	+	0.958928i	$0.591545\pi$
$68$	319.993	−	554.243i	0.570659	−	0.988410i
$69$	−213.502			−0.372502
$70$	1416.48	−	169.392i	2.41859	−	0.289232i
$71$	−877.494			−1.46675			−0.733376	−	0.679823i	$-0.762057\pi$
$71$	−877.494			−1.46675			−0.733376	+	0.679823i	$0.762057\pi$
$72$	−471.602	+	816.839i	−0.771929	+	1.33702i
$73$	−612.837	−	1061.46i	−0.982564	−	1.70185i	−0.652299	−	0.757962i	$-0.726195\pi$
$73$	−612.837	−	1061.46i	−0.982564	−	1.70185i	−0.330264	−	0.943888i	$-0.607138\pi$
$74$	−539.730	−	934.839i	−0.847869	−	1.46855i
$75$	−824.796	+	1428.59i	−1.26986	+	2.19946i
$76$	−935.100			−1.41136
$77$	213.324	−	25.5108i	0.315721	−	0.0377562i
$78$	−1785.45			−2.59182
$79$	−110.002	+	190.528i	−0.156660	+	0.271343i	−0.933662	−	0.358155i	$-0.883406\pi$
$79$	−110.002	+	190.528i	−0.156660	+	0.271343i	0.777002	+	0.629498i	$0.216739\pi$
$80$	193.386	+	334.954i	0.270265	+	0.468113i
$81$	−587.182	−	1017.03i	−0.805463	−	1.39510i
$82$	−570.350	+	987.875i	−0.768105	+	1.33040i
$83$	416.384			0.550652			0.275326	−	0.961351i	$-0.411214\pi$
$83$	416.384			0.550652			0.275326	+	0.961351i	$0.411214\pi$
$84$	−1195.21	−	1596.54i	−1.55248	−	2.07377i
$85$	−959.839			−1.22481
$86$	−314.930	+	545.475i	−0.394881	+	0.683955i
$87$	258.120	+	447.077i	0.318085	+	0.550939i
$88$	−92.4616	−	160.148i	−0.112005	−	0.193998i
$89$	770.627	−	1334.77i	0.917824	−	1.58972i	0.115111	−	0.993353i	$-0.463278\pi$
$89$	770.627	−	1334.77i	0.917824	−	1.58972i	0.802713	−	0.596365i	$-0.203389\pi$
$90$	4557.60			5.33793
$91$	316.718	−	739.651i	0.364847	−	0.852050i
$92$	−266.815			−0.302363
$93$	−1116.85	+	1934.44i	−1.24529	+	2.15690i
$94$	1421.32	+	2461.79i	1.55955	+	2.70122i
$95$	701.224	+	1214.55i	0.757305	+	1.31169i
$96$	1048.70	−	1816.40i	1.11492	−	1.93110i
$97$	754.400			0.789667			0.394834	−	0.918753i	$-0.370802\pi$
$97$	754.400			0.789667			0.394834	+	0.918753i	$0.370802\pi$
$98$	1475.73	−	358.078i	1.52113	−	0.369095i
$99$	686.384			0.696810
$100$	−1030.75	+	1785.32i	−1.03075	+	1.78532i
$101$	−123.357	−	213.661i	−0.121530	−	0.210496i	0.798841	−	0.601542i	$-0.205447\pi$
$101$	−123.357	−	213.661i	−0.121530	−	0.210496i	−0.920371	+	0.391046i	$0.872113\pi$
$102$	1133.62	+	1963.49i	1.10044	+	1.90602i
$103$	−181.256	+	313.945i	−0.173395	+	0.300329i	−0.939605	−	0.342261i	$-0.888807\pi$
$103$	−181.256	+	313.945i	−0.173395	+	0.300329i	0.766210	+	0.642591i	$0.222140\pi$
$104$	−692.552			−0.652984
$105$	−1177.39	+	2749.63i	−1.09430	+	2.55559i
$106$	−2141.59			−1.96235
$107$	−439.048	+	760.453i	−0.396676	+	0.687063i	−0.993314	−	0.115448i	$-0.963170\pi$
$107$	−439.048	+	760.453i	−0.396676	+	0.687063i	0.596637	+	0.802511i	$0.296503\pi$
$108$	−1732.04	−	2999.98i	−1.54320	−	2.67290i
$109$	−389.372	−	674.412i	−0.342156	−	0.592632i	0.642677	−	0.766138i	$-0.277824\pi$
$109$	−389.372	−	674.412i	−0.342156	−	0.592632i	−0.984833	+	0.173505i	$0.944491\pi$
$110$	−446.778	+	773.843i	−0.387260	+	0.670754i
$111$	2263.32			1.93536
$112$	246.736	+	329.585i	0.208164	+	0.278061i
$113$	577.027			0.480373			0.240186	−	0.970727i	$-0.422791\pi$
$113$	577.027			0.480373			0.240186	+	0.970727i	$0.422791\pi$
$114$	1656.36	−	2868.90i	1.36081	−	2.35700i
$115$	200.082	+	346.552i	0.162241	+	0.281010i
$116$	322.574	+	558.715i	0.258192	+	0.447202i
$117$	1285.28	−	2226.17i	1.01559	−	1.75906i
$118$	−1551.90			−1.21071
$119$	−1014.50	+	121.321i	−0.781504	+	0.0934578i
$120$	2574.54			1.95852
$121$	598.214	−	1036.14i	0.449447	−	0.778466i
$122$	−761.956	−	1319.75i	−0.565445	−	0.979379i
$123$	−1195.86	−	2071.29i	−0.876643	−	1.51839i
$124$	−1395.73	+	2417.48i	−1.01081	+	1.75077i
$125$	917.003			0.656154
$126$	4817.14	−	576.069i	3.40591	−	0.407304i
$127$	−651.406			−0.455141			−0.227570	−	0.973762i	$-0.573078\pi$
$127$	−651.406			−0.455141			−0.227570	+	0.973762i	$0.573078\pi$
$128$	916.889	−	1588.10i	0.633143	−	1.09664i
$129$	−660.319	−	1143.71i	−0.450681	−	0.780602i
$130$	1673.22	+	2898.10i	1.12885	+	1.95523i
$131$	−515.815	+	893.418i	−0.344023	+	0.595865i	−0.985176	−	0.171548i	$-0.945123\pi$
$131$	−515.815	+	893.418i	−0.344023	+	0.595865i	0.641153	+	0.767413i	$0.278456\pi$
$132$	1249.20			0.823705
$133$	894.672	+	1195.09i	0.583293	+	0.779152i
$134$	−3343.98			−2.15579
$135$	−2597.68	+	4499.32i	−1.65610	+	2.86844i
$136$	439.717	+	761.612i	0.277246	+	0.480203i
$137$	358.393	+	620.755i	0.223501	+	0.387115i	0.955869	−	0.293795i	$-0.0949182\pi$
$137$	358.393	+	620.755i	0.223501	+	0.387115i	−0.732368	+	0.680909i	$0.761585\pi$
$138$	472.615	−	818.593i	0.291534	−	0.504951i
$139$	146.968			0.0896807			0.0448404	−	0.998994i	$-0.485722\pi$
$139$	146.968			0.0896807			0.0448404	+	0.998994i	$0.485722\pi$
$140$	−1471.39	+	3436.23i	−0.888251	+	2.07439i
$141$	−5960.18			−3.55984
$142$	1942.45	−	3364.42i	1.14793	−	1.98828i
$143$	251.990	+	436.460i	0.147360	+	0.255235i
$144$	657.665	+	1139.11i	0.380593	+	0.659207i
$145$	483.792	−	837.952i	0.277081	−	0.479918i
$146$	5426.38			3.07596
$147$	−896.891	+	3055.03i	−0.503227	+	1.71411i
$148$	2828.48			1.57094
$149$	−293.128	+	507.712i	−0.161168	+	0.279150i	−0.935288	−	0.353888i	$-0.884859\pi$
$149$	−293.128	+	507.712i	−0.161168	+	0.279150i	0.774120	+	0.633039i	$0.218193\pi$
$150$	−3651.59	−	6324.73i	−1.98767	−	3.44275i
$151$	−893.112	−	1546.92i	−0.481327	−	0.833683i	0.518443	−	0.855112i	$-0.326512\pi$
$151$	−893.112	−	1546.92i	−0.481327	−	0.833683i	−0.999770	+	0.0214287i	$0.993179\pi$
$152$	642.482	−	1112.81i	0.342843	−	0.593822i
$153$	−3264.21			−1.72481
$154$	−374.409	+	874.382i	−0.195914	+	0.457531i
$155$	4186.59			2.16952
$156$	2339.18	−	4051.58i	1.20054	−	2.07940i
$157$	−422.666	−	732.078i	−0.214856	−	0.372141i	0.738372	−	0.674394i	$-0.235595\pi$
$157$	−422.666	−	732.078i	−0.214856	−	0.372141i	−0.953228	+	0.302252i	$0.902262\pi$
$158$	−487.005	−	843.518i	−0.245216	−	0.424726i
$159$	2245.15	−	3888.71i	1.11982	−	1.93959i
$160$	−3931.13			−1.94239
$161$	255.279	+	340.998i	0.124962	+	0.166922i
$162$	5199.22			2.52154
$163$	543.369	−	941.142i	0.261104	−	0.452245i	−0.705432	−	0.708778i	$-0.749247\pi$
$163$	543.369	−	941.142i	0.261104	−	0.452245i	0.966536	+	0.256533i	$0.0825802\pi$
$164$	−1494.47	−	2588.50i	−0.711578	−	1.23249i
$165$	−936.766	−	1622.53i	−0.441983	−	0.765536i
$166$	−921.721	+	1596.47i	−0.430960	+	0.746445i
$167$	−2254.75			−1.04478			−0.522388	−	0.852708i	$-0.674959\pi$
$167$	−2254.75			−1.04478			−0.522388	+	0.852708i	$0.674959\pi$
$168$	2721.15	−	325.415i	1.24965	−	0.149442i
$169$	−309.553			−0.140898
$170$	2124.73	−	3680.14i	0.958584	−	1.66032i
$171$	2384.72	+	4130.45i	1.06645	+	1.84715i
$172$	−825.204	−	1429.29i	−0.365821	−	0.633620i
$173$	212.191	−	367.526i	0.0932519	−	0.161517i	−0.815626	−	0.578580i	$-0.803607\pi$
$173$	212.191	−	367.526i	0.0932519	−	0.161517i	0.908878	+	0.417063i	$0.136940\pi$
$174$	−2285.53			−0.995780
$175$	3267.88	−	390.796i	1.41159	−	0.168808i
$176$	−257.882			−0.110446
$177$	1626.94	−	2817.95i	0.690896	−	1.19667i
$178$	3411.77	+	5909.36i	1.43665	+	2.48834i
$179$	−795.576	−	1377.98i	−0.332202	−	0.575390i	0.650742	−	0.759299i	$-0.274458\pi$
$179$	−795.576	−	1377.98i	−0.332202	−	0.575390i	−0.982943	+	0.183909i	$0.941125\pi$
$180$	−5971.09	+	10342.2i	−2.47255	+	4.28258i
$181$	3219.16			1.32198			0.660990	−	0.750395i	$-0.270137\pi$
$181$	3219.16			1.32198			0.660990	+	0.750395i	$0.270137\pi$
$182$	2134.82	+	2851.65i	0.869468	+	1.16142i
$183$	3195.21			1.29069
$184$	183.321	−	317.522i	0.0734491	−	0.127218i
$185$	−2121.05	−	3673.77i	−0.842935	−	1.46001i
$186$	−4944.58	−	8564.27i	−1.94922	−	3.37614i
$187$	319.988	−	554.236i	0.125133	−	0.216737i
$188$	−7448.47			−2.88955
$189$	−2176.91	+	5083.88i	−0.837814	+	1.95660i
$190$	−6209.00			−2.37078
$191$	2473.23	−	4283.76i	0.936945	−	1.62284i	0.165816	−	0.986157i	$-0.446974\pi$
$191$	2473.23	−	4283.76i	0.936945	−	1.62284i	0.771129	−	0.636679i	$-0.219692\pi$
$192$	3817.44	+	6612.00i	1.43489	+	2.48531i
$193$	761.952	+	1319.74i	0.284179	+	0.492212i	0.972410	−	0.233280i	$-0.0749458\pi$
$193$	761.952	+	1319.74i	0.284179	+	0.492212i	−0.688231	+	0.725492i	$0.741612\pi$
$194$	−1669.96	+	2892.46i	−0.618023	+	1.07045i
$195$	−7016.53			−2.57674
$196$	−1120.85	+	3817.89i	−0.408473	+	1.39136i
$197$	175.543			0.0634869			0.0317434	−	0.999496i	$-0.489894\pi$
$197$	175.543			0.0634869			0.0317434	+	0.999496i	$0.489894\pi$
$198$	−1519.40	+	2631.68i	−0.545349	+	0.944572i
$199$	−1426.73	−	2471.17i	−0.508233	−	0.880285i	−0.999955	−	0.00953286i	$-0.996966\pi$
$199$	−1426.73	−	2471.17i	−0.508233	−	0.880285i	0.491722	−	0.870752i	$-0.336368\pi$
$200$	−1416.40	−	2453.28i	−0.500775	−	0.867367i
$201$	3505.69	−	6072.03i	1.23021	−	2.13078i
$202$	1092.27			0.380455
$203$	405.427	−	946.820i	0.140174	−	0.327358i
$204$	−5940.79			−2.03891
$205$	−2241.39	+	3882.20i	−0.763635	+	1.32266i
$206$	−802.469	−	1389.92i	−0.271411	−	0.470097i
$207$	680.438	+	1178.55i	0.228472	+	0.395725i
$208$	−482.894	+	836.396i	−0.160974	+	0.278816i
$209$	−935.087			−0.309480
$210$	−7936.12	−	10600.9i	−2.60783	−	3.48349i
$211$	5844.66			1.90693			0.953466	−	0.301500i	$-0.0974875\pi$
$211$	5844.66			1.90693			0.953466	+	0.301500i	$0.0974875\pi$
$212$	2805.77	−	4859.74i	0.908968	−	1.57438i
$213$	4072.76	+	7054.23i	1.31014	+	2.26924i
$214$	−1943.78	−	3366.72i	−0.620906	−	1.07544i
$215$	−1237.63	+	2143.63i	−0.392583	+	0.679975i
$216$	4760.15			1.49948
$217$	4425.00	−	529.174i	1.38428	−	0.165542i
$218$	3447.70			1.07114
$219$	−5688.78	+	9853.26i	−1.75531	+	3.04028i
$220$	−1170.68	−	2027.68i	−0.358761	−	0.621392i
$221$	−1198.38	−	2075.66i	−0.364760	−	0.631782i
$222$	−5010.15	+	8677.83i	−1.51468	+	2.62350i
$223$	922.882			0.277134			0.138567	−	0.990353i	$-0.455750\pi$
$223$	922.882			0.277134			0.138567	+	0.990353i	$0.455750\pi$
$224$	−4154.99	+	496.884i	−1.23936	+	0.148212i
$225$	10514.6			3.11544
$226$	−1277.32	+	2212.39i	−0.375957	+	0.651177i
$227$	−3295.73	−	5708.36i	−0.963634	−	1.66906i	−0.713240	−	0.700919i	$-0.752773\pi$
$227$	−3295.73	−	5708.36i	−0.963634	−	1.66906i	−0.250394	−	0.968144i	$-0.580560\pi$
$228$	4340.13	+	7517.32i	1.26067	+	2.18354i
$229$	−230.270	+	398.839i	−0.0664483	+	0.115092i	−0.897336	−	0.441349i	$-0.854500\pi$
$229$	−230.270	+	398.839i	−0.0664483	+	0.115092i	0.830887	+	0.556441i	$0.187833\pi$
$230$	−1771.63			−0.507904
$231$	−1195.19	−	1596.52i	−0.340424	−	0.454733i
$232$	−886.529			−0.250877
$233$	220.359	−	381.672i	0.0619578	−	0.107314i	−0.833383	−	0.552696i	$-0.813599\pi$
$233$	220.359	−	381.672i	0.0619578	−	0.107314i	0.895340	+	0.445382i	$0.146932\pi$
$234$	5690.27	+	9855.85i	1.58968	+	2.75340i
$235$	5585.55	+	9674.45i	1.55047	+	2.68550i
$236$	2033.20	−	3521.60i	0.560805	−	0.971343i
$237$	2042.22			0.559732
$238$	1780.57	−	4158.27i	0.484945	−	1.13252i
$239$	737.812			0.199687			0.0998433	−	0.995003i	$-0.468166\pi$
$239$	737.812			0.199687			0.0998433	+	0.995003i	$0.468166\pi$
$240$	1795.14	−	3109.28i	0.482817	−	0.836263i
$241$	−3051.65	−	5285.62i	−0.815661	−	1.41277i	−0.908853	−	0.417118i	$-0.863040\pi$
$241$	−3051.65	−	5285.62i	−0.815661	−	1.41277i	0.0931918	−	0.995648i	$-0.470293\pi$
$242$	2648.45	+	4587.25i	0.703508	+	1.21851i
$243$	−1419.39	+	2458.46i	−0.374708	+	0.649013i
$244$	3993.07			1.04766
$245$	5799.39	−	1407.19i	1.51228	−	0.366947i
$246$	10588.8			2.74437
$247$	−1750.99	+	3032.80i	−0.451064	+	0.781265i
$248$	−1917.94	−	3321.97i	−0.491086	−	0.850586i
$249$	−1932.59	−	3347.34i	−0.491858	−	0.851923i
$250$	−2029.91	+	3515.90i	−0.513530	+	0.889461i
$251$	2763.36			0.694908			0.347454	−	0.937697i	$-0.387046\pi$
$251$	2763.36			0.694908			0.347454	+	0.937697i	$0.387046\pi$
$252$	−5003.89	+	11685.9i	−1.25085	+	2.92120i
$253$	−266.811			−0.0663015
$254$	1441.97	−	2497.57i	0.356210	−	0.616974i
$255$	4454.95	+	7716.20i	1.09404	+	1.89493i
$256$	769.368	+	1332.58i	0.187834	+	0.325338i
$257$	554.609	−	960.611i	0.134613	−	0.233157i	−0.790837	−	0.612027i	$-0.790354\pi$
$257$	554.609	−	960.611i	0.134613	−	0.233157i	0.925450	+	0.378871i	$0.123688\pi$
$258$	5846.81			1.41088
$259$	−2706.20	−	3614.89i	−0.649247	−	0.867252i
$260$	−8768.59			−2.09156
$261$	1645.27	−	2849.70i	0.390191	−	0.675831i
$262$	−2283.65	−	3955.39i	−0.538489	−	0.932691i
$263$	1409.77	+	2441.80i	0.330533	+	0.572500i	0.982617	−	0.185647i	$-0.0594381\pi$
$263$	1409.77	+	2441.80i	0.330533	+	0.572500i	−0.652083	+	0.758147i	$0.726105\pi$
$264$	−858.293	+	1486.61i	−0.200092	+	0.346570i
$265$	−8416.10			−1.95093
$266$	−6562.58	+	784.801i	−1.51270	+	0.180899i
$267$	−14307.0			−3.27931
$268$	4381.08	−	7588.25i	0.998570	−	1.72957i
$269$	174.023	+	301.417i	0.0394439	+	0.0683188i	0.885073	−	0.465452i	$-0.154108\pi$
$269$	174.023	+	301.417i	0.0394439	+	0.0683188i	−0.845630	+	0.533770i	$0.820775\pi$
$270$	−11500.6	−	19919.7i	−2.59224	−	4.48990i
$271$	−1126.63	+	1951.38i	−0.252538	+	0.437409i	−0.964224	−	0.265089i	$-0.914599\pi$
$271$	−1126.63	+	1951.38i	−0.252538	+	0.437409i	0.711686	+	0.702498i	$0.247932\pi$
$272$	1226.40			0.273387
$273$	−7416.09	+	886.870i	−1.64411	+	0.196615i
$274$	−3173.40			−0.699679
$275$	−1030.74	+	1785.29i	−0.226021	+	0.391480i
$276$	1238.38	+	2144.94i	0.270079	+	0.467790i
$277$	−328.581	−	569.119i	−0.0712726	−	0.123448i	0.828187	−	0.560452i	$-0.189373\pi$
$277$	−328.581	−	569.119i	−0.0712726	−	0.123448i	−0.899459	+	0.437005i	$0.856039\pi$
$278$	−325.332	+	563.491i	−0.0701874	+	0.121568i
$279$	14237.7			3.05516
$280$	−3078.32	−	4111.96i	−0.657017	−	0.877631i
$281$	−5507.00			−1.16911			−0.584555	−	0.811354i	$-0.698731\pi$
$281$	−5507.00			−1.16911			−0.584555	+	0.811354i	$0.698731\pi$
$282$	13193.6	−	22852.1i	2.78606	−	4.82560i
$283$	−1403.28	−	2430.55i	−0.294757	−	0.510535i	0.680171	−	0.733053i	$-0.261905\pi$
$283$	−1403.28	−	2430.55i	−0.294757	−	0.510535i	−0.974928	+	0.222519i	$0.928572\pi$
$284$	5089.75	+	8815.71i	1.06345	+	1.84196i
$285$	6509.25	−	11274.3i	1.35289	−	2.34328i
$286$	−2231.25			−0.461317
$287$	−1878.33	+	4386.58i	−0.386321	+	0.902201i
$288$	−13368.9			−2.73532
$289$	934.742	−	1619.02i	0.190259	−	0.329538i
$290$	2141.87	+	3709.83i	0.433707	+	0.751203i
$291$	−3501.44	−	6064.66i	−0.705353	−	1.22171i
$292$	−7109.30	+	12313.7i	−1.42480	+	2.46782i
$293$	247.712			0.0493908			0.0246954	−	0.999695i	$-0.492138\pi$
$293$	247.712			0.0493908			0.0246954	+	0.999695i	$0.492138\pi$
$294$	−9727.98	−	10201.5i	−1.92975	−	2.02369i
$295$	−6098.72			−1.20366
$296$	−1943.37	+	3366.02i	−0.381609	+	0.660966i
$297$	−1732.02	−	2999.94i	−0.338390	−	0.586108i
$298$	−1297.75	−	2247.78i	−0.252271	−	0.436947i
$299$	−499.615	+	865.358i	−0.0966337	+	0.167374i
$300$	19136.3			3.68279
$301$	−1037.16	+	2422.14i	−0.198607	+	0.463820i
$302$	7908.08			1.50682
$303$	−1145.09	+	1983.35i	−0.217108	+	0.376042i
$304$	−895.963	−	1551.85i	−0.169036	−	0.292779i
$305$	−2994.37	−	5186.40i	−0.562154	−	0.973680i
$306$	7225.76	−	12515.4i	1.34990	−	2.33810i
$307$	−10391.6			−1.93186			−0.965930	−	0.258804i	$-0.916672\pi$
$307$	−10391.6			−1.93186			−0.965930	+	0.258804i	$0.916672\pi$
$308$	−1493.64	−	1995.18i	−0.276325	−	0.369110i
$309$	3365.09			0.619526
$310$	−9267.57	+	16051.9i	−1.69794	+	2.94092i
$311$	3573.25	+	6189.04i	0.651512	+	1.12845i	0.982756	+	0.184907i	$0.0591983\pi$
$311$	3573.25	+	6189.04i	0.651512	+	1.12845i	−0.331244	+	0.943545i	$0.607468\pi$
$312$	3214.38	+	5567.46i	0.583264	+	1.01024i
$313$	−298.006	+	516.162i	−0.0538157	+	0.0932116i	−0.891678	−	0.452670i	$-0.850472\pi$
$313$	−298.006	+	516.162i	−0.0538157	+	0.0932116i	0.837863	+	0.545881i	$0.183805\pi$
$314$	3742.50			0.672617
$315$	18930.6	−	2263.86i	3.38609	−	0.404934i
$316$	2552.18			0.454339
$317$	−296.046	+	512.767i	−0.0524531	+	0.0908513i	−0.891060	−	0.453886i	$-0.850037\pi$
$317$	−296.046	+	512.767i	−0.0524531	+	0.0908513i	0.838607	+	0.544737i	$0.183371\pi$
$318$	9939.85	+	17216.3i	1.75283	+	3.03599i
$319$	322.570	+	558.708i	0.0566158	+	0.0980615i
$320$	7154.98	−	12392.8i	1.24992	−	2.16493i
$321$	8151.10			1.41729
$322$	−1872.52	+	223.930i	−0.324073	+	0.0387550i
$323$	4446.96			0.766055
$324$	−6811.69	+	11798.2i	−1.16799	+	2.02301i
$325$	3860.20	+	6686.06i	0.658847	+	1.14116i
$326$	2405.64	+	4166.68i	0.408699	+	0.707887i
$327$	−3614.42	+	6260.36i	−0.611248	+	1.05871i
$328$	4107.25			0.691418
$329$	7126.45	+	9519.38i	1.19421	+	1.59520i
$330$	8294.62			1.38365
$331$	5512.67	−	9548.22i	0.915419	−	1.58555i	0.109133	−	0.994027i	$-0.465193\pi$
$331$	5512.67	−	9548.22i	0.915419	−	1.58555i	0.806286	−	0.591525i	$-0.201474\pi$
$332$	−2415.16	−	4183.18i	−0.399245	−	0.691512i
$333$	−7213.27	−	12493.7i	−1.18704	−	2.05601i
$334$	4991.18	−	8644.98i	0.817680	−	1.41626i
$335$	−13141.3			−2.14325
$336$	1504.37	−	3513.24i	0.244256	−	0.570426i
$337$	−6670.16			−1.07818			−0.539090	−	0.842248i	$-0.681232\pi$
$337$	−6670.16			−1.07818			−0.539090	+	0.842248i	$0.681232\pi$
$338$	685.237	−	1186.87i	0.110272	−	0.190997i
$339$	−2678.19	−	4638.75i	−0.429083	−	0.743193i
$340$	5567.37	+	9642.97i	0.888039	+	1.53813i
$341$	−1395.71	+	2417.45i	−0.221648	+	0.383906i
$342$	−21115.5			−3.33859
$343$	5951.78	−	2220.35i	0.936926	−	0.349527i
$344$	2267.90			0.355457
$345$	1857.30	−	3216.94i	0.289837	−	0.502013i
$346$	939.425	+	1627.13i	0.145965	+	0.252818i
$347$	−2393.43	−	4145.54i	−0.370276	−	0.641338i	0.619332	−	0.785130i	$-0.287404\pi$
$347$	−2393.43	−	4145.54i	−0.370276	−	0.641338i	−0.989608	+	0.143792i	$0.954070\pi$
$348$	2994.36	−	5186.38i	0.461249	−	0.798906i
$349$	6758.51			1.03660			0.518302	−	0.855198i	$-0.326564\pi$
$349$	6758.51			1.03660			0.518302	+	0.855198i	$0.326564\pi$
$350$	−5735.51	+	13394.5i	−0.875932	+	2.04562i
$351$	−12973.1			−1.97280
$352$	1310.55	−	2269.93i	0.198444	−	0.343716i
$353$	1975.13	+	3421.02i	0.297806	+	0.515815i	0.975634	−	0.219406i	$-0.0704119\pi$
$353$	1975.13	+	3421.02i	0.297806	+	0.515815i	−0.677828	+	0.735221i	$0.737079\pi$
$354$	7202.90	+	12475.8i	1.08144	+	1.87311i
$355$	7633.52	−	13221.6i	1.14125	−	1.97671i
$356$	−17879.5			−2.66184
$357$	5683.95	+	7592.51i	0.842651	+	1.12560i
$358$	7044.44			1.03997
$359$	−843.170	+	1460.41i	−0.123958	+	0.214701i	−0.921325	−	0.388793i	$-0.872892\pi$
$359$	−843.170	+	1460.41i	−0.123958	+	0.214701i	0.797367	+	0.603494i	$0.206225\pi$
$360$	−8205.15	−	14211.7i	−1.20125	−	2.08062i
$361$	180.708	+	312.996i	0.0263462	+	0.0456329i
$362$	−7126.03	+	12342.6i	−1.03463	+	1.79203i
$363$	−11106.1			−1.60584
$364$	−9267.93	+	1108.33i	−1.33454	+	0.159594i
$365$	21324.8			3.05806
$366$	−7073.01	+	12250.8i	−1.01014	+	1.74962i
$367$	−5436.54	−	9416.36i	−0.773256	−	1.33932i	−0.935769	−	0.352613i	$-0.885293\pi$
$367$	−5436.54	−	9416.36i	−0.773256	−	1.33932i	0.162513	−	0.986706i	$-0.448040\pi$
$368$	−255.648	−	442.795i	−0.0362135	−	0.0627236i
$369$	−7622.49	+	13202.5i	−1.07537	+	1.86259i
$370$	18780.9			2.63885
$371$	−8895.37	+	1063.77i	−1.24481	+	0.148863i
$372$	25912.3			3.61154
$373$	−4079.22	+	7065.42i	−0.566258	+	0.980787i	0.430674	+	0.902508i	$0.358276\pi$
$373$	−4079.22	+	7065.42i	−0.566258	+	0.980787i	−0.996931	+	0.0782793i	$0.975057\pi$
$374$	1416.67	+	2453.75i	0.195867	+	0.339252i
$375$	−4256.13	−	7371.84i	−0.586096	−	1.01515i
$376$	5117.65	−	8864.02i	0.701922	−	1.21576i
$377$	2416.10			0.330068
$378$	−14673.3	−	19600.4i	−1.99660	−	2.66702i
$379$	4579.71			0.620697			0.310348	−	0.950623i	$-0.399554\pi$
$379$	4579.71			0.620697			0.310348	+	0.950623i	$0.399554\pi$
$380$	8134.64	−	14089.6i	1.09815	−	1.90206i
$381$	3023.40	+	5236.69i	0.406545	+	0.704156i
$382$	10949.6	+	18965.3i	1.46657	+	2.54018i
$383$	−3153.52	+	5462.06i	−0.420724	+	0.728716i	−0.996010	−	0.0892362i	$-0.971557\pi$
$383$	−3153.52	+	5462.06i	−0.420724	+	0.728716i	0.575286	+	0.817952i	$0.304891\pi$
$384$	−17022.4			−2.26216
$385$	−1471.37	+	3436.19i	−0.194774	+	0.454868i
$386$	−6746.72			−0.889634
$387$	−4208.91	+	7290.05i	−0.552845	+	0.957556i
$388$	−4375.76	−	7579.04i	−0.572540	−	0.991669i
$389$	−2827.37	−	4897.14i	−0.368517	−	0.638290i	0.620817	−	0.783956i	$-0.286801\pi$
$389$	−2827.37	−	4897.14i	−0.368517	−	0.638290i	−0.989334	+	0.145665i	$0.953468\pi$
$390$	15532.0	−	26902.2i	2.01665	−	3.49294i
$391$	1268.87			0.164116
$392$	−3773.36	−	3957.03i	−0.486182	−	0.509848i
$393$	9576.31			1.22916
$394$	−388.587	+	673.052i	−0.0496871	+	0.0860606i
$395$	−1913.86	−	3314.90i	−0.243789	−	0.422254i
$396$	−3981.25	−	6895.72i	−0.505215	−	0.875058i
$397$	−104.426	+	180.872i	−0.0132015	+	0.0228657i	−0.872551	−	0.488524i	$-0.837536\pi$
$397$	−104.426	+	180.872i	−0.0132015	+	0.0228657i	0.859349	+	0.511389i	$0.170869\pi$
$398$	12633.0			1.59105
$399$	5454.88	−	12739.1i	0.684425	−	1.59838i
$400$	−3950.45			−0.493806
$401$	−4079.10	+	7065.21i	−0.507981	+	0.879849i	0.491976	+	0.870609i	$0.336275\pi$
$401$	−4079.10	+	7065.21i	−0.507981	+	0.879849i	−0.999957	+	0.00924054i	$0.997059\pi$
$402$	15520.6	+	26882.5i	1.92561	+	3.33526i
$403$	5227.06	+	9053.53i	0.646100	+	1.11908i
$404$	−1431.02	+	2478.61i	−0.176228	+	0.305236i
$405$	20432.1			2.50686
$406$	2732.76	+	3650.37i	0.334050	+	0.446218i
$407$	2828.44			0.344474
$408$	4081.76	−	7069.81i	0.495287	−	0.857862i
$409$	−3651.09	−	6323.87i	−0.441405	−	0.764536i	0.556389	−	0.830922i	$-0.312186\pi$
$409$	−3651.09	−	6323.87i	−0.441405	−	0.764536i	−0.997794	+	0.0663862i	$0.978853\pi$
$410$	−9923.21	−	17187.5i	−1.19530	−	2.07032i
$411$	3326.86	−	5762.28i	0.399274	−	0.691563i
$412$	4205.38			0.502874
$413$	−6446.02	+	770.861i	−0.768009	+	0.0918441i
$414$	−6024.95			−0.715242
$415$	−3622.22	+	6273.87i	−0.428453	+	0.742102i
$416$	−4908.10	−	8501.09i	−0.578461	−	1.00192i
$417$	−682.128	−	1181.48i	−0.0801054	−	0.138747i
$418$	2069.94	−	3585.24i	0.242210	−	0.419521i
$419$	−10705.0			−1.24815			−0.624075	−	0.781364i	$-0.714524\pi$
$419$	−10705.0			−1.24815			−0.624075	+	0.781364i	$0.714524\pi$
$420$	34453.3	−	4120.17i	4.00273	−	0.478676i
$421$	820.006			0.0949279			0.0474640	−	0.998873i	$-0.484886\pi$
$421$	820.006			0.0949279			0.0474640	+	0.998873i	$0.484886\pi$
$422$	−12937.9	+	22409.1i	−1.49243	+	2.58497i
$423$	18995.3	+	32900.8i	2.18341	+	3.78178i
$424$	3855.54	+	6678.00i	0.441608	+	0.764887i
$425$	4901.85	−	8490.25i	0.559470	−	0.969030i
$426$	−36062.3			−4.10147
$427$	−3820.43	−	5103.27i	−0.432983	−	0.578371i
$428$	10186.5			1.15042
$429$	2339.15	−	4051.53i	0.263252	−	0.455966i
$430$	−5479.30	−	9490.42i	−0.614500	−	1.06435i
$431$	2121.39	+	3674.35i	0.237085	+	0.410643i	0.959877	−	0.280423i	$-0.0904747\pi$
$431$	2121.39	+	3674.35i	0.237085	+	0.410643i	−0.722792	+	0.691066i	$0.757141\pi$
$432$	3319.09	−	5748.84i	0.369653	−	0.640257i
$433$	9352.65			1.03801			0.519007	−	0.854770i	$-0.326302\pi$
$433$	9352.65			1.03801			0.519007	+	0.854770i	$0.326302\pi$
$434$	−7766.41	+	18137.4i	−0.858985	+	2.00604i
$435$	−8981.78			−0.989985
$436$	−4516.96	+	7823.61i	−0.496154	+	0.859364i
$437$	−926.987	−	1605.59i	−0.101473	−	0.175757i
$438$	−25185.7	−	43623.0i	−2.74754	−	4.75887i
$439$	3139.61	−	5437.96i	0.341333	−	0.591207i	−0.643347	−	0.765574i	$-0.722455\pi$
$439$	3139.61	−	5437.96i	0.341333	−	0.591207i	0.984681	+	0.174368i	$0.0557882\pi$
$440$	3217.38			0.348596
$441$	19722.5	−	4785.56i	2.12963	−	0.516743i
$442$	10611.1			1.14190
$443$	4222.97	−	7314.40i	0.452910	−	0.784464i	−0.545655	−	0.838010i	$-0.683719\pi$
$443$	4222.97	−	7314.40i	0.452910	−	0.784464i	0.998565	+	0.0535460i	$0.0170524\pi$
$444$	−13128.0	−	22738.3i	−1.40321	−	2.43043i
$445$	13407.7	+	23222.9i	1.42829	+	2.47386i
$446$	−2042.92	+	3538.44i	−0.216895	+	0.375673i
$447$	5442.04			0.575838
$448$	5996.01	−	14002.9i	0.632333	−	1.47673i
$449$	−6259.59			−0.657925			−0.328962	−	0.944343i	$-0.606699\pi$
$449$	−6259.59			−0.657925			−0.328962	+	0.944343i	$0.606699\pi$
$450$	−23275.5	+	40314.3i	−2.43826	+	4.22318i
$451$	−1494.45	−	2588.47i	−0.156033	−	0.270258i
$452$	−3346.94	−	5797.07i	−0.348290	−	0.603255i
$453$	−8290.49	+	14359.6i	−0.859870	+	1.48934i
$454$	29182.1			3.01670
$455$	8389.50	+	11206.5i	0.864408	+	1.15466i
$456$	−11927.9			−1.22495
$457$	3740.46	−	6478.66i	0.382869	−	0.663149i	−0.608602	−	0.793476i	$-0.708269\pi$
$457$	3740.46	−	6478.66i	0.382869	−	0.663149i	0.991471	+	0.130327i	$0.0416027\pi$
$458$	−1019.47	−	1765.77i	−0.104010	−	0.180150i
$459$	8236.89	+	14266.7i	0.837615	+	1.45079i
$460$	2321.08	−	4020.23i	0.235263	−	0.407488i
$461$	−5358.20			−0.541336			−0.270668	−	0.962673i	$-0.587245\pi$
$461$	−5358.20			−0.541336			−0.270668	+	0.962673i	$0.587245\pi$
$462$	8766.97	−	1048.42i	0.882849	−	0.105577i
$463$	−7221.15			−0.724828			−0.362414	−	0.932017i	$-0.618047\pi$
$463$	−7221.15			−0.724828			−0.362414	+	0.932017i	$0.618047\pi$
$464$	−618.147	+	1070.66i	−0.0618465	+	0.107121i
$465$	−19431.4	−	33656.2i	−1.93787	−	3.35650i
$466$	975.585	+	1689.76i	0.0969809	+	0.167976i
$467$	−9157.43	+	15861.1i	−0.907399	+	1.57166i	−0.0897344	+	0.995966i	$0.528602\pi$
$467$	−9157.43	+	15861.1i	−0.907399	+	1.57166i	−0.817664	+	0.575695i	$0.804732\pi$
$468$	−29820.2			−2.94538
$469$	−13889.7	+	1661.03i	−1.36752	+	0.163538i
$470$	−49457.4			−4.85382
$471$	−3923.48	+	6795.66i	−0.383831	+	0.664814i
$472$	2793.91	+	4839.20i	0.272458	+	0.471912i
$473$	−825.193	−	1429.28i	−0.0802165	−	0.138939i
$474$	−4520.73	+	7830.13i	−0.438067	+	0.758755i
$475$	−14324.5			−1.38369
$476$	7103.26	+	9488.41i	0.683986	+	0.913656i
$477$	−28621.4			−2.74735
$478$	−1633.24	+	2828.86i	−0.156282	+	0.270688i
$479$	5037.24	+	8724.76i	0.480496	+	0.832243i	0.999750	−	0.0223770i	$-0.00712343\pi$
$479$	5037.24	+	8724.76i	0.480496	+	0.832243i	−0.519254	+	0.854620i	$0.673790\pi$
$480$	18245.7	+	31602.5i	1.73500	+	3.00511i
$481$	5296.37	−	9173.59i	0.502066	−	0.869604i
$482$	27020.9			2.55346
$483$	1556.46	−	3634.90i	0.146628	−	0.342430i
$484$	−13879.3			−1.30347
$485$	−6562.70	+	11366.9i	−0.614426	+	1.06422i
$486$	−6284.01	−	10884.2i	−0.586520	−	1.01588i
$487$	−3049.48	−	5281.86i	−0.283748	−	0.491466i	0.688557	−	0.725182i	$-0.258245\pi$
$487$	−3049.48	−	5281.86i	−0.283748	−	0.491466i	−0.972305	+	0.233717i	$0.924911\pi$
$488$	−2743.53	+	4751.93i	−0.254495	+	0.440799i
$489$	−10087.9			−0.932901
$490$	−7442.37	+	25350.5i	−0.686147	+	2.33719i
$491$	8250.70			0.758348			0.379174	−	0.925325i	$-0.376208\pi$
$491$	8250.70			0.758348			0.379174	+	0.925325i	$0.376208\pi$
$492$	−13872.8	+	24028.3i	−1.27120	+	2.20179i
$493$	−1534.04	−	2657.03i	−0.140141	−	0.242731i
$494$	−7752.08	−	13427.0i	−0.706038	−	1.22289i
$495$	−5971.01	+	10342.1i	−0.542175	+	0.939075i
$496$	−5349.27			−0.484252
$497$	6397.04	−	14939.4i	0.577357	−	1.34834i
$498$	17112.1			1.53978
$499$	4125.55	−	7145.66i	0.370110	−	0.641050i	−0.619472	−	0.785019i	$-0.712653\pi$
$499$	4125.55	−	7145.66i	0.370110	−	0.641050i	0.989582	+	0.143969i	$0.0459866\pi$
$500$	−5318.91	−	9212.63i	−0.475738	−	0.824003i
$501$	10465.1	+	18126.0i	0.933224	+	1.61639i
$502$	−6117.06	+	10595.1i	−0.543860	+	0.941993i
$503$	13561.4			1.20213			0.601067	−	0.799199i	$-0.294742\pi$
$503$	13561.4			1.20213			0.601067	+	0.799199i	$0.294742\pi$
$504$	−10468.7	−	13983.9i	−0.925227	−	1.23590i
$505$	4292.45			0.378241
$506$	590.622	−	1022.99i	0.0518900	−	0.0898761i
$507$	1436.75	+	2488.52i	0.125854	+	0.217986i
$508$	3778.36	+	6544.31i	0.329995	+	0.571569i
$509$	6470.26	−	11206.8i	0.563436	−	0.975900i	−0.433757	−	0.901030i	$-0.642812\pi$
$509$	6470.26	−	11206.8i	0.563436	−	0.975900i	0.997193	−	0.0748703i	$-0.0238543\pi$
$510$	−39446.4			−3.42494
$511$	22539.2	−	2695.40i	1.95122	−	0.233341i
$512$	7857.83			0.678262
$513$	12035.1	−	20845.5i	1.03580	−	1.79406i
$514$	2455.40	+	4252.87i	0.210706	+	0.364954i
$515$	−3153.58	−	5462.16i	−0.269832	−	0.467362i
$516$	−7660.12	+	13267.7i	−0.653523	+	1.13194i
$517$	−7448.37			−0.633615
$518$	19850.4	−	2373.86i	1.68374	−	0.201354i
$519$	−3939.41			−0.333181
$520$	6024.67	−	10435.0i	0.508075	−	0.880012i
$521$	839.520	+	1454.09i	0.0705951	+	0.122274i	0.899162	−	0.437615i	$-0.144177\pi$
$521$	839.520	+	1454.09i	0.0705951	+	0.122274i	−0.828567	+	0.559890i	$0.810844\pi$
$522$	7284.06	+	12616.4i	0.610756	+	1.05786i
$523$	864.413	−	1497.21i	0.0722718	−	0.125178i	−0.827625	−	0.561282i	$-0.810308\pi$
$523$	864.413	−	1497.21i	0.0722718	−	0.125178i	0.899897	+	0.436103i	$0.143642\pi$
$524$	11967.6			0.997721
$525$	−18309.0	−	24456.8i	−1.52204	−	2.03311i
$526$	−12482.9			−1.03475
$527$	6637.55	−	11496.6i	0.548646	−	0.950282i
$528$	1196.92	+	2073.12i	0.0986538	+	0.170873i
$529$	−264.500	−	458.127i	−0.0217391	−	0.0376533i
$530$	18630.1	−	32268.3i	1.52687	−	2.64462i
$531$	−20740.5			−1.69503
$532$	6816.99	−	15920.2i	0.555553	−	1.29742i
$533$	−11193.7			−0.909668
$534$	31670.4	−	54854.8i	2.56650	−	4.44532i
$535$	−7638.75	−	13230.7i	−0.617293	−	1.06918i
$536$	6020.24	+	10427.4i	0.485140	+	0.840286i
$537$	−7385.09	+	12791.4i	−0.593464	+	1.02791i
$538$	−1540.89			−0.123481
$539$	−1120.83	+	3817.84i	−0.0895691	+	0.305095i
$540$	60269.6			4.80294
$541$	3811.84	−	6602.30i	0.302928	−	0.524686i	−0.673870	−	0.738850i	$-0.735369\pi$
$541$	3811.84	−	6602.30i	0.302928	−	0.524686i	0.976798	+	0.214164i	$0.0687026\pi$
$542$	−4987.88	−	8639.27i	−0.395291	−	0.684665i
$543$	−14941.2	−	25879.0i	−1.18083	−	2.04526i
$544$	−6232.53	+	10795.1i	−0.491209	+	0.850798i
$545$	13548.9			1.06490
$546$	13016.1	−	30397.4i	1.02022	−	2.38258i
$547$	−219.112			−0.0171272			−0.00856359	−	0.999963i	$-0.502726\pi$
$547$	−219.112			−0.0171272			−0.00856359	+	0.999963i	$0.502726\pi$
$548$	4157.59	−	7201.16i	0.324094	−	0.561347i
$549$	−10183.2	−	17637.9i	−0.791638	−	1.37116i
$550$	−4563.35	−	7903.95i	−0.353785	−	0.612774i
$551$	−2241.42	+	3882.26i	−0.173299	+	0.300163i
$552$	−3403.43			−0.262427
$553$	−2441.84	−	3261.76i	−0.187771	−	0.250821i
$554$	2909.43			0.223122
$555$	−19689.1	+	34102.5i	−1.50587	+	2.60824i
$556$	−852.459	−	1476.50i	−0.0650221	−	0.112622i
$557$	5519.14	+	9559.43i	0.419844	+	0.727192i	0.995923	−	0.0902021i	$-0.0287513\pi$
$557$	5519.14	+	9559.43i	0.419844	+	0.727192i	−0.576079	+	0.817394i	$0.695418\pi$
$558$	−31517.1	+	54589.2i	−2.39108	+	4.14148i
$559$	−6180.83			−0.467658
$560$	−7112.43	+	850.556i	−0.536706	+	0.0641831i
$561$	−5940.71			−0.447089
$562$	12190.5	−	21114.5i	0.914988	−	1.58481i
$563$	5695.31	+	9864.56i	0.426338	+	0.738440i	0.996544	−	0.0830620i	$-0.0264700\pi$
$563$	5695.31	+	9864.56i	0.426338	+	0.738440i	−0.570206	+	0.821502i	$0.693137\pi$
$564$	34571.0	+	59878.7i	2.58103	+	4.47047i
$565$	−5019.69	+	8694.36i	−0.373770	+	0.647388i
$566$	12425.4			0.922752
$567$	21595.7	−	2582.56i	1.59953	−	0.191283i
$568$	−13988.1			−1.03333
$569$	−185.277	+	320.909i	−0.0136506	+	0.0236436i	−0.872770	−	0.488132i	$-0.837679\pi$
$569$	−185.277	+	320.909i	−0.0136506	+	0.0236436i	0.859119	+	0.511775i	$0.171012\pi$
$570$	28818.1	+	49914.5i	2.11765	+	3.66787i
$571$	−466.586	−	808.150i	−0.0341962	−	0.0592295i	0.848421	−	0.529322i	$-0.177554\pi$
$571$	−466.586	−	808.150i	−0.0341962	−	0.0592295i	−0.882617	+	0.470093i	$0.844220\pi$
$572$	2923.25	−	5063.21i	0.213684	−	0.370111i
$573$	−45916.5			−3.34762
$574$	−12660.8	−	16912.0i	−0.920644	−	1.22978i
$575$	−4087.24			−0.296434
$576$	24332.6	−	42145.3i	1.76017	−	3.04870i
$577$	−8734.43	−	15128.5i	−0.630189	−	1.09152i	−0.987513	−	0.157539i	$-0.949644\pi$
$577$	−8734.43	−	15128.5i	−0.630189	−	1.09152i	0.357324	−	0.933981i	$-0.383689\pi$
$578$	4138.35	+	7167.83i	0.297807	+	0.515817i
$579$	7072.97	−	12250.7i	0.507673	−	0.879315i
$580$	−11224.6			−0.803579
$581$	−3035.49	+	7088.98i	−0.216753	+	0.506197i
$582$	31003.5			2.20814
$583$	2805.73	−	4859.68i	0.199317	−	0.345227i
$584$	−9769.22	−	16920.8i	−0.692215	−	1.19895i
$585$	22361.9	+	38731.9i	1.58043	+	2.73738i
$586$	−548.343	+	949.758i	−0.0386550	+	0.0669525i
$587$	21809.1			1.53349			0.766745	−	0.641952i	$-0.221875\pi$
$587$	21809.1			1.53349			0.766745	+	0.641952i	$0.221875\pi$
$588$	35894.5	−	8709.60i	2.51746	−	0.610847i
$589$	−19396.6			−1.35692
$590$	13500.3	−	23383.2i	0.942032	−	1.63165i
$591$	−814.756	−	1411.20i	−0.0567083	−	0.0982216i
$592$	2710.10	+	4694.03i	0.188149	+	0.325884i
$593$	90.5412	−	156.822i	0.00626995	−	0.0108599i	−0.862873	−	0.505420i	$-0.831338\pi$
$593$	90.5412	−	156.822i	0.00626995	−	0.0108599i	0.869143	+	0.494560i	$0.164671\pi$
$594$	15336.2			1.05934
$595$	6997.35	−	16341.4i	0.482123	−	1.12593i
$596$	6800.94			0.467412
$597$	−13243.9	+	22939.2i	−0.907936	+	1.57259i
$598$	−2211.92	−	3831.17i	−0.151258	−	0.261987i
$599$	1222.08	+	2116.71i	0.0833605	+	0.144385i	0.904691	−	0.426067i	$-0.140101\pi$
$599$	1222.08	+	2116.71i	0.0833605	+	0.144385i	−0.821331	+	0.570452i	$0.806768\pi$
$600$	−13148.1	+	22773.1i	−0.894612	+	1.54951i
$601$	11195.9			0.759882			0.379941	−	0.925011i	$-0.375944\pi$
$601$	11195.9			0.759882			0.379941	+	0.925011i	$0.375944\pi$
$602$	−6990.89	−	9338.30i	−0.473301	−	0.632227i
$603$	−44690.9			−3.01817
$604$	−10360.7	+	17945.2i	−0.697963	+	1.20891i
$605$	10408.0	+	18027.2i	0.699414	+	1.21142i
$606$	−5069.61	−	8780.82i	−0.339833	−	0.588608i
$607$	5847.39	−	10128.0i	0.391002	−	0.677236i	−0.601580	−	0.798813i	$-0.705462\pi$
$607$	5847.39	−	10128.0i	0.391002	−	0.677236i	0.992582	+	0.121577i	$0.0387951\pi$
$608$	18213.0			1.21486
$609$	−9493.27	+	1135.27i	−0.631669	+	0.0755396i
$610$	26513.7			1.75985
$611$	−13947.4	+	24157.6i	−0.923487	+	1.59953i
$612$	18933.5	+	32793.8i	1.25056	+	2.16603i
$613$	5812.54	+	10067.6i	0.382979	+	0.663339i	0.991487	−	0.130209i	$-0.0415648\pi$
$613$	5812.54	+	10067.6i	0.382979	+	0.663339i	−0.608507	+	0.793548i	$0.708231\pi$
$614$	23003.2	−	39842.7i	1.51194	−	2.61876i
$615$	41612.2			2.72840
$616$	3400.60	−	406.668i	0.222425	−	0.0265992i
$617$	9680.73			0.631655			0.315828	−	0.948817i	$-0.397718\pi$
$617$	9680.73			0.631655			0.315828	+	0.948817i	$0.397718\pi$
$618$	−7449.08	+	12902.2i	−0.484864	+	0.839809i
$619$	9772.93	+	16927.2i	0.634583	+	1.09913i	0.986603	+	0.163138i	$0.0521617\pi$
$619$	9772.93	+	16927.2i	0.634583	+	1.09913i	−0.352020	+	0.935993i	$0.614505\pi$
$620$	−24283.6	−	42060.4i	−1.57299	−	2.72449i
$621$	3434.02	−	5947.90i	0.221904	−	0.384350i
$622$	−31639.4			−2.03959
$623$	17106.6	+	22850.6i	1.10010	+	1.46949i
$624$	8965.11			0.575147
$625$	3129.41	−	5420.29i	0.200282	−	0.346899i
$626$	−1319.35	−	2285.19i	−0.0842363	−	0.145902i
$627$	4340.07	+	7517.22i	0.276436	+	0.478802i
$628$	−4903.19	+	8492.58i	−0.311558	+	0.539635i
$629$	−13451.1			−0.852674
$630$	−33225.5	+	77593.6i	−2.10117	+	4.90699i
$631$	5773.39			0.364239			0.182120	−	0.983276i	$-0.441704\pi$
$631$	5773.39			0.364239			0.182120	+	0.983276i	$0.441704\pi$
$632$	−1753.53	+	3037.21i	−0.110367	+	0.191161i
$633$	−27127.1	−	46985.5i	−1.70333	−	2.95025i
$634$	−1310.67	−	2270.15i	−0.0821034	−	0.142207i
$635$	5666.72	−	9815.05i	0.354137	−	0.613384i
$636$	−52090.3			−3.24766
$637$	10283.7	+	10784.3i	0.639649	+	0.670784i
$638$	−2856.20			−0.177239
$639$	25960.0	−	44964.1i	1.60714	−	2.78365i
$640$	15952.4	+	27630.4i	0.985274	+	1.70655i
$641$	−8943.48	−	15490.6i	−0.551086	−	0.954509i	−0.998197	−	0.0600303i	$-0.980880\pi$
$641$	−8943.48	−	15490.6i	−0.551086	−	0.954509i	0.447111	−	0.894479i	$-0.352453\pi$
$642$	−18043.5	+	31252.3i	−1.10922	+	1.92123i
$643$	10365.3			0.635719			0.317860	−	0.948138i	$-0.397036\pi$
$643$	10365.3			0.635719			0.317860	+	0.948138i	$0.397036\pi$
$644$	1945.11	−	4542.55i	0.119019	−	0.277953i
$645$	22977.0			1.40267
$646$	−9843.94	+	17050.2i	−0.599543	+	1.03844i
$647$	15549.3	+	26932.1i	0.944830	+	1.63649i	0.756091	+	0.654466i	$0.227107\pi$
$647$	15549.3	+	26932.1i	0.944830	+	1.63649i	0.188739	+	0.982027i	$0.439560\pi$
$648$	−9360.26	−	16212.4i	−0.567447	−	0.982847i
$649$	2033.17	−	3521.56i	0.122972	−	0.212994i
$650$	−34180.2			−2.06255
$651$	−24792.1	−	33116.8i	−1.49259	−	1.99378i
$652$	−12606.9			−0.757243
$653$	4432.86	−	7677.94i	0.265653	−	0.460124i	−0.702082	−	0.712096i	$-0.747746\pi$
$653$	4432.86	−	7677.94i	0.265653	−	0.460124i	0.967734	+	0.251972i	$0.0810792\pi$
$654$	−16002.0	−	27716.3i	−0.956769	−	1.65717i
$655$	−8974.38	−	15544.1i	−0.535356	−	0.927263i
$656$	2863.85	−	4960.33i	0.170449	−	0.295226i
$657$	72521.3			4.30643
$658$	−52273.8	+	6251.28i	−3.09703	+	0.370365i
$659$	−5338.72			−0.315579			−0.157790	−	0.987473i	$-0.550437\pi$
$659$	−5338.72			−0.315579			−0.157790	+	0.987473i	$0.550437\pi$
$660$	−10867.1	+	18822.3i	−0.640910	+	1.11009i
$661$	−8310.83	−	14394.8i	−0.489037	−	0.847038i	0.510883	−	0.859650i	$-0.329319\pi$
$661$	−8310.83	−	14394.8i	−0.489037	−	0.847038i	−0.999920	+	0.0126125i	$0.995985\pi$
$662$	24406.0	+	42272.5i	1.43288	+	2.48182i
$663$	−11124.2	+	19267.7i	−0.651627	+	1.12865i
$664$	6637.57			0.387934
$665$	−25789.9	+	3084.15i	−1.50390	+	0.179847i
$666$	63870.0			3.71609
$667$	−639.552	+	1107.74i	−0.0371267	+	0.0643054i
$668$	13078.3	+	22652.2i	0.757505	+	1.31204i
$669$	−4283.42	−	7419.10i	−0.247543	−	0.428758i
$670$	29090.0	−	50385.4i	1.67738	−	2.90531i
$671$	3993.02			0.229730
$672$	23279.2	+	31096.0i	1.33633	+	1.78505i
$673$	140.606			0.00805344			0.00402672	−	0.999992i	$-0.498718\pi$
$673$	140.606			0.00805344			0.00402672	+	0.999992i	$0.498718\pi$
$674$	14765.3	−	25574.2i	0.843823	−	1.46155i
$675$	−26532.5	−	45955.6i	−1.51294	−	2.62049i
$676$	1795.51	+	3109.91i	0.102157	+	0.176941i
$677$	3760.65	−	6513.63i	0.213491	−	0.369777i	−0.739314	−	0.673361i	$-0.764850\pi$
$677$	3760.65	−	6513.63i	0.213491	−	0.369777i	0.952805	+	0.303584i	$0.0981832\pi$
$678$	23714.1			1.34326
$679$	−5499.67	+	12843.7i	−0.310837	+	0.725917i
$680$	−15300.8			−0.862879
$681$	−30593.2	+	52989.0i	−1.72149	+	2.98171i
$682$	−6179.19	−	10702.7i	−0.346940	−	0.600918i
$683$	−1294.60	−	2242.31i	−0.0725276	−	0.125622i	0.827481	−	0.561494i	$-0.189773\pi$
$683$	−1294.60	−	2242.31i	−0.0725276	−	0.125622i	−0.900008	+	0.435872i	$0.856440\pi$
$684$	27664.2	−	47915.9i	1.54645	−	2.67852i
$685$	−12471.0			−0.695608
$686$	−4661.94	+	27734.9i	−0.259466	+	1.54362i
$687$	4275.05			0.237414
$688$	1581.33	−	2738.95i	0.0876275	−	0.151775i
$689$	−10507.7	−	18199.9i	−0.581004	−	1.00633i
$690$	8222.76	+	14242.2i	0.453674	+	0.785787i
$691$	9126.57	−	15807.7i	0.502447	−	0.870264i	−0.497549	−	0.867436i	$-0.665766\pi$
$691$	9126.57	−	15807.7i	0.502447	−	0.870264i	0.999996	−	0.00282806i	$-0.000900201\pi$
$692$	−4923.10			−0.270446
$693$	−5003.82	+	11685.8i	−0.274285	+	0.640556i
$694$	21192.7			1.15917
$695$	−1278.50	+	2214.43i	−0.0697790	+	0.120861i
$696$	4114.69	+	7126.85i	0.224090	+	0.388136i
$697$	7107.13	+	12309.9i	0.386229	+	0.668968i
$698$	−14960.8	+	25912.9i	−0.811284	+	1.40518i
$699$	−4091.05			−0.221370
$700$	−22880.9	−	30563.8i	−1.23545	−	1.65029i
$701$	−2274.84			−0.122567			−0.0612836	−	0.998120i	$-0.519519\pi$
$701$	−2274.84			−0.122567			−0.0612836	+	0.998120i	$0.519519\pi$
$702$	28717.6	−	49740.3i	1.54398	−	2.67426i
$703$	9826.91	+	17020.7i	0.527211	+	0.913156i
$704$	4770.61	+	8262.94i	0.255396	+	0.442360i
$705$	51849.0	−	89805.0i	2.76985	−	4.79752i
$706$	−17488.8			−0.932294
$707$	4536.89	−	542.555i	0.241340	−	0.0288612i
$708$	−37747.2			−2.00371
$709$	2057.26	−	3563.28i	0.108973	−	0.188747i	−0.806381	−	0.591396i	$-0.798577\pi$
$709$	2057.26	−	3563.28i	0.108973	−	0.188747i	0.915355	+	0.402649i	$0.131910\pi$
$710$	33795.6	+	58535.7i	1.78637	+	3.09409i
$711$	−6508.63	−	11273.3i	−0.343309	−	0.594628i
$712$	12284.6	−	21277.5i	0.646606	−	1.11995i
$713$	−5534.49			−0.290699
$714$	−41692.8	+	4985.92i	−2.18531	+	0.261335i
$715$	−8768.48			−0.458633
$716$	−9229.19	+	15985.4i	−0.481719	+	0.834362i
$717$	−3424.44	−	5931.31i	−0.178366	−	0.308938i
$718$	−3732.93	−	6465.63i	−0.194028	−	0.336066i
$719$	−9267.93	+	16052.5i	−0.480717	+	0.832626i	−0.999755	−	0.0221251i	$-0.992957\pi$
$719$	−9267.93	+	16052.5i	−0.480717	+	0.832626i	0.519038	+	0.854751i	$0.326290\pi$
$720$	−22884.7			−1.18453
$721$	−4023.57	−	5374.60i	−0.207830	−	0.277615i
$722$	−1600.09			−0.0824779
$723$	−28327.6	+	49064.8i	−1.45714	+	2.52384i
$724$	−18672.2	−	32341.1i	−0.958488	−	1.66015i
$725$	4941.40	+	8558.75i	0.253130	+	0.438433i
$726$	24584.8	−	42582.1i	1.25679	−	2.17682i
$727$	−7186.10			−0.366600			−0.183300	−	0.983057i	$-0.558678\pi$
$727$	−7186.10			−0.366600			−0.183300	+	0.983057i	$0.558678\pi$
$728$	5048.79	−	11790.8i	0.257034	−	0.600268i
$729$	−5356.29			−0.272127
$730$	−47205.3	+	81762.0i	−2.39335	+	4.14541i
$731$	3924.34	+	6797.16i	0.198560	+	0.343915i
$732$	−18533.2	−	32100.5i	−0.935803	−	1.62086i
$733$	−11385.7	+	19720.6i	−0.573725	+	0.993720i	0.422454	+	0.906384i	$0.361169\pi$
$733$	−11385.7	+	19720.6i	−0.573725	+	0.993720i	−0.996179	+	0.0873360i	$0.972165\pi$
$734$	48138.0			2.42072
$735$	−38229.5	−	40090.3i	−1.91852	−	2.01191i
$736$	5196.78			0.260266
$737$	4381.02	−	7588.15i	0.218965	−	0.379258i
$738$	−33746.8	−	58451.1i	−1.68325	−	2.91547i
$739$	−6868.74	−	11897.0i	−0.341909	−	0.592204i	0.642878	−	0.765968i	$-0.277740\pi$
$739$	−6868.74	−	11897.0i	−0.341909	−	0.592204i	−0.984787	+	0.173765i	$0.944407\pi$
$740$	−24605.6	+	42618.1i	−1.22232	+	2.11713i
$741$	32507.8			1.61161
$742$	15612.4	−	36460.7i	0.772440	−	1.80393i
$743$	1666.06			0.0822634			0.0411317	−	0.999154i	$-0.486904\pi$
$743$	1666.06			0.0822634			0.0411317	+	0.999154i	$0.486904\pi$
$744$	−17803.7	+	30836.9i	−0.877304	+	1.51954i
$745$	−5099.97	−	8833.41i	−0.250803	−	0.434404i
$746$	−18059.8	−	31280.5i	−0.886348	−	1.53520i
$747$	−12318.4	+	21336.1i	−0.603357	+	1.04504i
$748$	−7424.14			−0.362906
$749$	−9746.07	−	13018.6i	−0.475452	−	0.635100i
$750$	37686.0			1.83480
$751$	834.219	−	1444.91i	0.0405340	−	0.0702070i	−0.845047	−	0.534693i	$-0.820427\pi$
$751$	834.219	−	1444.91i	0.0405340	−	0.0702070i	0.885581	+	0.464486i	$0.153761\pi$
$752$	−7136.73	−	12361.2i	−0.346077	−	0.599423i
$753$	−12825.7	−	22214.8i	−0.620711	−	1.07510i
$754$	−5348.35	+	9263.62i	−0.258323	+	0.447429i
$755$	31077.5			1.49805
$756$	63701.7	−	7617.91i	3.06456	−	0.366482i
$757$	−11899.9			−0.571347			−0.285674	−	0.958327i	$-0.592217\pi$
$757$	−11899.9			−0.571347			−0.285674	+	0.958327i	$0.592217\pi$
$758$	−10137.8	+	17559.2i	−0.485780	+	0.841396i
$759$	1238.36	+	2144.91i	0.0592224	+	0.102576i
$760$	11178.2	+	19361.2i	0.533521	+	0.924085i
$761$	466.711	−	808.367i	0.0222316	−	0.0385063i	−0.854696	−	0.519130i	$-0.826256\pi$
$761$	466.711	−	808.367i	0.0222316	−	0.0385063i	0.876927	+	0.480623i	$0.159590\pi$
$762$	−26770.8			−1.27271
$763$	14320.5	−	1712.55i	0.679471	−	0.0812561i
$764$	−57382.1			−2.71729
$765$	28396.1	−	49183.5i	1.34204	−	2.32449i
$766$	−13961.5	−	24182.0i	−0.658549	−	1.14064i
$767$	−7614.39	−	13188.5i	−0.358461	−	0.620873i
$768$	7141.81	−	12370.0i	0.335557	−	0.581202i
$769$	−12619.8			−0.591783			−0.295892	−	0.955221i	$-0.595617\pi$
$769$	−12619.8			−0.591783			−0.295892	+	0.955221i	$0.595617\pi$
$770$	−9917.68	−	13247.9i	−0.464167	−	0.620025i
$771$	−10296.5			−0.480961
$772$	8839.13	−	15309.8i	0.412082	−	0.713747i
$773$	−12901.8	−	22346.6i	−0.600317	−	1.03978i	−0.992773	−	0.120009i	$-0.961708\pi$
$773$	−12901.8	−	22346.6i	−0.600317	−	1.03978i	0.392456	−	0.919771i	$-0.371626\pi$
$774$	−18634.0	−	32275.0i	−0.865354	−	1.49884i
$775$	−21380.7	+	37032.5i	−0.990991	+	1.71645i
$776$	12025.9			0.556320
$777$	−16499.9	+	38533.2i	−0.761814	+	1.77911i
$778$	25035.0			1.15366
$779$	10384.4	−	17986.3i	0.477613	−	0.827250i
$780$	40698.1	+	70491.2i	1.86824	+	3.23588i
$781$	5089.68	+	8815.59i	0.233192	+	0.403901i
$782$	−2808.80	+	4864.98i	−0.128443	+	0.222470i
$783$	−16606.7			−0.757950
$784$	−7409.96	+	1797.98i	−0.337553	+	0.0819053i
$785$	14707.5			0.668702
$786$	−21198.4	+	36716.7i	−0.961988	+	1.66621i
$787$	3317.13	+	5745.44i	0.150245	+	0.260232i	0.931318	−	0.364208i	$-0.118660\pi$
$787$	3317.13	+	5745.44i	0.150245	+	0.260232i	−0.781072	+	0.624441i	$0.785327\pi$
$788$	−1018.20	−	1763.58i	−0.0460305	−	0.0797272i
$789$	13086.5	−	22666.5i	0.590483	−	1.02275i
$790$	16946.3			0.763192
$791$	−4206.60	+	9823.95i	−0.189089	+	0.441592i
$792$	10941.6			0.490902
$793$	7477.08	−	12950.7i	0.334828	−	0.579940i
$794$	−462.322	−	800.766i	−0.0206640	−	0.0357911i
$795$	39062.1	+	67657.5i	1.74263	+	3.01832i
$796$	−16551.0	+	28667.2i	−0.736979	+	1.27648i
$797$	−13915.7			−0.618467			−0.309234	−	0.950986i	$-0.600072\pi$
$797$	−13915.7			−0.618467			−0.309234	+	0.950986i	$0.600072\pi$
$798$	36768.3	+	49114.4i	1.63106	+	2.17874i
$799$	35422.0			1.56839
$800$	20076.1	−	34772.8i	0.887245	−	1.53675i
$801$	45596.9	+	78976.1i	2.01134	+	3.48375i
$802$	−18059.2	−	31279.5i	−0.795129	−	1.37720i
$803$	−7109.21	+	12313.5i	−0.312427	+	0.541139i
$804$	−81336.4			−3.56780
$805$	−7358.72	+	880.008i	−0.322187	+	0.0385295i
$806$	−46283.1			−2.02265
$807$	1615.41	−	2797.97i	0.0704647	−	0.122048i
$808$	−1966.44	−	3405.97i	−0.0856176	−	0.148294i
$809$	17959.4	+	31106.6i	0.780494	+	1.35185i	0.931655	+	0.363345i	$0.118365\pi$
$809$	17959.4	+	31106.6i	0.780494	+	1.35185i	−0.151161	+	0.988509i	$0.548301\pi$
$810$	−45229.2	+	78339.2i	−1.96196	+	3.39822i
$811$	−16053.2			−0.695074			−0.347537	−	0.937666i	$-0.612982\pi$
$811$	−16053.2			−0.695074			−0.347537	+	0.937666i	$0.612982\pi$
$812$	−11863.8	+	1418.76i	−0.512731	+	0.0613160i
$813$	20916.3			0.902297
$814$	−6261.13	+	10844.6i	−0.269598	+	0.466957i
$815$	9453.77	+	16374.4i	0.406321	+	0.703768i
$816$	−5692.15	−	9859.09i	−0.244197	−	0.422962i
$817$	5733.97	−	9931.52i	0.245540	−	0.425288i
$818$	32328.6			1.38184
$819$	28530.9	+	38111.1i	1.21728	+	1.62602i
$820$	52003.1			2.21467
$821$	−3305.71	+	5725.66i	−0.140524	+	0.243394i	−0.927694	−	0.373341i	$-0.878212\pi$
$821$	−3305.71	+	5725.66i	−0.140524	+	0.243394i	0.787170	+	0.616736i	$0.211545\pi$
$822$	14728.9	+	25511.1i	0.624973	+	1.08249i
$823$	−13194.9	−	22854.3i	−0.558865	−	0.967982i	−0.997592	−	0.0693618i	$-0.977904\pi$
$823$	−13194.9	−	22854.3i	−0.558865	−	0.967982i	0.438727	−	0.898621i	$-0.355430\pi$
$824$	−2889.40	+	5004.59i	−0.122157	+	0.211582i
$825$	19136.1			0.807555
$826$	11313.5	−	26421.2i	0.476571	−	1.11297i
$827$	−31541.1			−1.32623			−0.663114	−	0.748518i	$-0.730766\pi$
$827$	−31541.1			−1.32623			−0.663114	+	0.748518i	$0.730766\pi$
$828$	7893.52	−	13672.0i	0.331303	−	0.573833i
$829$	22720.6	+	39353.3i	0.951895	+	1.64873i	0.741320	+	0.671152i	$0.234200\pi$
$829$	22720.6	+	39353.3i	0.951895	+	1.64873i	0.210575	+	0.977578i	$0.432466\pi$
$830$	−16036.5	−	27776.1i	−0.670645	−	1.16159i
$831$	−3050.12	+	5282.96i	−0.127325	+	0.220534i
$832$	35732.6			1.48895
$833$	5330.32	−	18156.4i	0.221710	−	0.755200i
$834$	6039.92			0.250774
$835$	19614.6	−	33973.4i	0.812922	−	1.40802i
$836$	5423.81	+	9394.31i	0.224386	+	0.388647i
$837$	−35927.4	−	62228.0i	−1.48367	−	2.56979i
$838$	23697.0	−	41044.4i	0.976848	−	1.69195i
$839$	11788.0			0.485061			0.242531	−	0.970144i	$-0.422023\pi$
$839$	11788.0			0.485061			0.242531	+	0.970144i	$0.422023\pi$
$840$	−18768.7	+	43831.8i	−0.770932	+	1.80041i
$841$	−21296.2			−0.873188
$842$	−1815.19	+	3144.00i	−0.0742941	+	0.128681i
$843$	25559.9	+	44271.0i	1.04428	+	1.80875i
$844$	−33900.9	−	58718.0i	−1.38260	−	2.39474i
$845$	2692.88	−	4664.20i	0.109630	−	0.189886i
$846$	−168194.			−6.83527
$847$	13279.3	+	17738.2i	0.538703	+	0.719590i
$848$	10753.4			0.435462
$849$	−13026.2	+	22562.1i	−0.526571	+	0.912048i
$850$	21701.8	+	37588.6i	0.875723	+	1.51680i
$851$	2803.94	+	4856.57i	0.112947	+	0.195630i
$852$	47246.6	−	81833.5i	1.89982	−	3.29058i
$853$	−2595.56			−0.104186			−0.0520928	−	0.998642i	$-0.516589\pi$
$853$	−2595.56			−0.104186			−0.0520928	+	0.998642i	$0.516589\pi$
$854$	28023.6	−	3351.26i	1.12289	−	0.134283i
$855$	−82980.7			−3.31916
$856$	−6998.85	+	12122.4i	−0.279458	+	0.484035i
$857$	−22300.6	−	38625.9i	−0.888886	−	1.53960i	−0.841193	−	0.540734i	$-0.818146\pi$
$857$	−22300.6	−	38625.9i	−0.888886	−	1.53960i	−0.0476931	−	0.998862i	$-0.515187\pi$
$858$	10356.0	+	17937.2i	0.412062	+	0.713712i
$859$	8184.03	−	14175.2i	0.325071	−	0.563039i	−0.656456	−	0.754364i	$-0.727945\pi$
$859$	8184.03	−	14175.2i	0.325071	−	0.563039i	0.981527	+	0.191325i	$0.0612786\pi$
$860$	28714.5			1.13856
$861$	43981.9	−	5259.68i	1.74088	−	0.208187i
$862$	−18783.9			−0.742205
$863$	17416.3	−	30165.8i	0.686971	−	1.18987i	−0.285842	−	0.958277i	$-0.592273\pi$
$863$	17416.3	−	30165.8i	0.686971	−	1.18987i	0.972813	−	0.231592i	$-0.0743936\pi$
$864$	33735.1	+	58430.9i	1.32835	+	2.30076i
$865$	3691.79	+	6394.38i	0.145115	+	0.251347i
$866$	−20703.3	+	35859.2i	−0.812387	+	1.40710i
$867$	−17353.9			−0.679779
$868$	−30982.8	−	41386.2i	−1.21155	−	1.61836i
$869$	2552.14			0.0996266
$870$	19882.4	−	34437.2i	0.774799	−	1.34199i
$871$	−16407.3	−	28418.2i	−0.638276	−	1.10553i
$872$	−6206.97	−	10750.8i	−0.241049	−	0.417509i
$873$	−22318.4	+	38656.6i	−0.865249	+	1.49866i
$874$	8208.03			0.317667
$875$	−6685.07	+	15612.1i	−0.258282	+	0.603182i
$876$	131987.			5.09067
$877$	−18937.5	+	32800.7i	−0.729160	+	1.26294i	0.228078	+	0.973643i	$0.426756\pi$
$877$	−18937.5	+	32800.7i	−0.729160	+	1.26294i	−0.957239	+	0.289300i	$0.906578\pi$
$878$	13899.9	+	24075.3i	0.534280	+	0.925400i
$879$	−1149.72	−	1991.37i	−0.0441172	−	0.0764133i
$880$	2243.37	−	3885.63i	0.0859364	−	0.148846i
$881$	6036.75			0.230855			0.115428	−	0.993316i	$-0.463176\pi$
$881$	6036.75			0.230855			0.115428	+	0.993316i	$0.463176\pi$
$882$	−25309.9	+	86212.0i	−0.966247	+	3.29128i
$883$	35121.3			1.33853			0.669267	−	0.743022i	$-0.266608\pi$
$883$	35121.3			1.33853			0.669267	+	0.743022i	$0.266608\pi$
$884$	−13902.0	+	24079.0i	−0.528931	+	0.916135i
$885$	28306.3	+	49027.9i	1.07515	+	1.86221i
$886$	18696.2	+	32382.7i	0.708929	+	1.22790i
$887$	19777.1	−	34255.0i	0.748649	−	1.29670i	−0.199821	−	0.979832i	$-0.564036\pi$
$887$	19777.1	−	34255.0i	0.748649	−	1.29670i	0.948470	−	0.316866i	$-0.102630\pi$
$888$	36079.5			1.36346
$889$	4748.83	−	11090.2i	0.179157	−	0.418397i
$890$	−118719.			−4.47131
$891$	−6811.60	+	11798.0i	−0.256114	+	0.443602i
$892$	−5353.01	−	9271.69i	−0.200933	−	0.348026i
$893$	−25878.0	−	44822.1i	−0.969737	−	1.67963i
$894$	−12046.7	+	20865.4i	−0.450672	+	0.780586i
$895$	27683.6			1.03392
$896$	20353.3	+	27187.6i	0.758879	+	1.01370i
$897$	9275.55			0.345264
$898$	13856.4	−	24000.0i	0.514916	−	0.891861i
$899$	6691.10	+	11589.3i	0.248232	+	0.429951i
$900$	−60988.1	−	105634.i	−2.25882	−	3.91239i
$901$	−13343.1	+	23111.0i	−0.493368	+	0.854538i
$902$	13232.7			0.488470
$903$	24285.5	−	2904.24i	0.894984	−	0.107029i
$904$	9198.38			0.338422
$905$	−28004.2	+	48504.7i	−1.02861	+	1.78160i
$906$	−36704.2	−	63573.5i	−1.34593	−	2.33122i
$907$	−20294.2	−	35150.5i	−0.742951	−	1.28683i	−0.951146	−	0.308742i	$-0.900092\pi$
$907$	−20294.2	−	35150.5i	−0.742951	−	1.28683i	0.208194	−	0.978087i	$-0.433241\pi$
$908$	−38232.5	+	66220.7i	−1.39735	+	2.42028i
$909$	14597.7			0.532648
$910$	−61538.5	+	7359.21i	−2.24174	+	0.268083i
$911$	5779.45			0.210189			0.105094	−	0.994462i	$-0.466486\pi$
$911$	5779.45			0.210189			0.105094	+	0.994462i	$0.466486\pi$
$912$	−8316.95	+	14405.4i	−0.301976	+	0.523037i
$913$	−2415.13	−	4183.13i	−0.0875456	−	0.151633i
$914$	16560.0	+	28682.7i	0.599295	+	1.03801i
$915$	−27795.8	+	48143.8i	−1.00426	+	1.73944i
$916$	5342.56			0.192711
$917$	−11450.2	−	15294.9i	−0.412342	−	0.550799i
$918$	−72933.7			−2.62219
$919$	7049.47	−	12210.0i	0.253037	−	0.438272i	−0.711324	−	0.702864i	$-0.751904\pi$
$919$	7049.47	−	12210.0i	0.253037	−	0.438272i	0.964360	+	0.264592i	$0.0852374\pi$
$920$	3189.51	+	5524.39i	0.114299	+	0.197971i
$921$	48231.1	+	83538.8i	1.72559	+	2.98881i
$922$	11861.1	−	20544.0i	0.423670	−	0.733817i
$923$	38122.5			1.35950
$924$	−9106.84	+	21267.8i	−0.324235	+	0.757207i
$925$	43328.5			1.54014
$926$	15985.0	−	27686.8i	0.567277	−	0.982552i
$927$	−10724.7	−	18575.7i	−0.379983	−	0.658150i
$928$	−6282.81	−	10882.2i	−0.222245	−	0.384940i
$929$	12082.0	−	20926.6i	0.426692	−	0.739053i	−0.569885	−	0.821725i	$-0.693012\pi$
$929$	12082.0	−	20926.6i	0.426692	−	0.739053i	0.996577	+	0.0826721i	$0.0263454\pi$
$930$	172056.			6.06660
$931$	−26868.7	+	6519.55i	−0.945851	+	0.229506i
$932$	−5112.60			−0.179688
$933$	33169.4	−	57451.0i	1.16390	−	2.01593i
$934$	−40542.3	−	70221.4i	−1.42033	−	2.46008i
$935$	5567.30	+	9642.85i	0.194727	+	0.337278i
$936$	20488.6	−	35487.4i	0.715483	−	1.23925i
$937$	50837.1			1.77244			0.886219	−	0.463266i	$-0.153323\pi$
$937$	50837.1			1.77244			0.886219	+	0.463266i	$0.153323\pi$
$938$	24378.0	−	56931.6i	0.848584	−	1.98175i
$939$	5532.61			0.192279
$940$	64795.9	−	112230.i	2.24831	−	3.89419i
$941$	15172.3	+	26279.1i	0.525613	+	0.910388i	0.999555	+	0.0298320i	$0.00949723\pi$
$941$	15172.3	+	26279.1i	0.525613	+	0.910388i	−0.473942	+	0.880556i	$0.657169\pi$
$942$	−17370.3	−	30086.2i	−0.600800	−	1.04062i
$943$	2963.02	−	5132.10i	0.102321	−	0.177226i
$944$	7792.41			0.268667
$945$	−57663.9	−	77026.4i	−1.98498	−	2.65150i
$946$	7306.69			0.251122
$947$	−3971.77	+	6879.31i	−0.136289	+	0.236059i	−0.926089	−	0.377305i	$-0.876851\pi$
$947$	−3971.77	+	6879.31i	−0.136289	+	0.236059i	0.789800	+	0.613364i	$0.210184\pi$
$948$	−11845.5	−	20517.1i	−0.405829	−	0.702916i
$949$	26624.6	+	46115.1i	0.910716	+	1.57741i
$950$	31709.1	−	54921.7i	1.08292	−	1.87568i
$951$	5496.22			0.187410
$952$	−16172.1	+	1933.98i	−0.550568	+	0.0658409i
$953$	−36314.2			−1.23435			−0.617173	−	0.786827i	$-0.711722\pi$
$953$	−36314.2			−1.23435			−0.617173	+	0.786827i	$0.711722\pi$
$954$	63357.2	−	109738.i	2.15017	−	3.72421i
$955$	43030.3	+	74530.7i	1.45804	+	2.52540i
$956$	−4279.55	−	7412.39i	−0.144781	−	0.250768i
$957$	2994.32	−	5186.32i	0.101142	−	0.175183i
$958$	−44602.4			−1.50421
$959$	−13181.1	+	1576.30i	−0.443839	+	0.0530775i
$960$	−132835.			−4.46587
$961$	−14055.9	+	24345.6i	−0.471818	+	0.817213i
$962$	23448.4	+	40613.9i	0.785871	+	1.36117i
$963$	−25977.8	−	44994.9i	−0.869287	−	1.50565i
$964$	−35401.1	+	61316.6i	−1.18277	+	2.04862i
$965$	−26513.6			−0.884457
$966$	10491.2	+	14014.0i	0.349430	+	0.466762i
$967$	22788.9			0.757850			0.378925	−	0.925427i	$-0.376294\pi$
$967$	22788.9			0.757850			0.378925	+	0.925427i	$0.376294\pi$
$968$	9536.13	−	16517.1i	0.316635	−	0.548428i
$969$	−20639.9	−	35749.4i	−0.684262	−	1.18518i
$970$	−29054.8	−	50324.3i	−0.961745	−	1.66579i
$971$	−9883.33	+	17118.4i	−0.326644	+	0.565764i	−0.981844	−	0.189692i	$-0.939251\pi$
$971$	−9883.33	+	17118.4i	−0.326644	+	0.565764i	0.655200	+	0.755456i	$0.272584\pi$
$972$	32931.7			1.08671
$973$	−1071.41	+	2502.14i	−0.0353010	+	0.0824407i
$974$	27001.7			0.888286
$975$	35833.1	−	62064.7i	1.17700	−	2.03863i
$976$	3825.95	+	6626.73i	0.125477	+	0.217332i
$977$	−18697.0	−	32384.1i	−0.612251	−	1.06045i	−0.990860	−	0.134893i	$-0.956931\pi$
$977$	−18697.0	−	32384.1i	−0.612251	−	1.06045i	0.378609	−	0.925557i	$-0.376402\pi$
$978$	22330.8	−	38678.1i	0.730123	−	1.26461i
$979$	−17879.3			−0.583683
$980$	−47775.6	−	50101.1i	−1.55728	−	1.63308i
$981$	46077.1			1.49962
$982$	−18264.0	+	31634.2i	−0.593511	+	1.02799i
$983$	−19138.5	−	33148.8i	−0.620979	−	1.07557i	−0.989304	−	0.145870i	$-0.953402\pi$
$983$	−19138.5	−	33148.8i	−0.620979	−	1.07557i	0.368325	−	0.929697i	$-0.379931\pi$
$984$	−19063.2	−	33018.4i	−0.617594	−	1.06970i
$985$	−1527.09	+	2644.99i	−0.0493980	+	0.0855598i
$986$	13583.2			0.438718
$987$	43450.5	−	101473.i	1.40126	−	3.27245i
$988$	40625.2			1.30816
$989$	1636.09	−	2833.79i	0.0526032	−	0.0911115i
$990$	−26435.2	−	45787.1i	−0.848653	−	1.46991i
$991$	23102.9	+	40015.4i	0.740552	+	1.28267i	0.952244	+	0.305338i	$0.0987693\pi$
$991$	23102.9	+	40015.4i	0.740552	+	1.28267i	−0.211692	+	0.977336i	$0.567897\pi$
$992$	27184.8	−	47085.5i	0.870080	−	1.50702i
$993$	−102345.			−3.27071
$994$	43118.9	+	57597.4i	1.37590	+	1.83791i
$995$	49645.9			1.58179
$996$	−22419.2	+	38831.2i	−0.713233	+	1.23536i
$997$	−19405.6	−	33611.4i	−0.616430	−	1.06769i	−0.990132	−	0.140139i	$-0.955245\pi$
$997$	−19405.6	−	33611.4i	−0.616430	−	1.06769i	0.373702	−	0.927549i	$-0.378088\pi$
$998$	18264.9	+	31635.7i	0.579323	+	1.00342i
$999$	−36403.8	+	63053.2i	−1.15292	+	1.99691i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.e.a.93.4	✓	44
7.2	even	3		1127.4.a.l.1.19		22
7.4	even	3	inner	161.4.e.a.116.4	yes	44
7.5	odd	6		1127.4.a.k.1.19		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.e.a.93.4	✓	44	1.1	even	1	trivial
161.4.e.a.116.4	yes	44	7.4	even	3	inner
1127.4.a.k.1.19		22	7.5	odd	6
1127.4.a.l.1.19		22	7.2	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:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.21363 + 3.83412i) q^{2} +(-4.64135 - 8.03905i) q^{3} +(-5.80032 - 10.0465i) q^{4} +(-8.69922 + 15.0675i) q^{5} +41.0969 q^{6} +(-7.29013 + 17.0251i) q^{7} +15.9410 q^{8} +(-29.5843 + 51.2414i) q^{9} +(-38.5137 - 66.7078i) q^{10} +(-5.80024 - 10.0463i) q^{11} +(-53.8426 + 93.2582i) q^{12} -43.4448 q^{13} +(-49.1386 - 65.6385i) q^{14} +161.505 q^{15} +(11.1151 - 19.2519i) q^{16} +(27.5840 + 47.7769i) q^{17} +(-130.977 - 226.859i) q^{18} +(40.3038 - 69.8082i) q^{19} +201.833 q^{20} +(170.702 - 20.4137i) q^{21} +51.3584 q^{22} +(11.5000 - 19.9186i) q^{23} +(-73.9877 - 128.150i) q^{24} +(-88.8530 - 153.898i) q^{25} +(96.1706 - 166.572i) q^{26} +298.611 q^{27} +(213.327 - 25.5112i) q^{28} -55.6132 q^{29} +(-357.512 + 619.228i) q^{30} +(-120.315 - 208.392i) q^{31} +(112.973 + 195.676i) q^{32} +(-53.8419 + 93.2570i) q^{33} -244.243 q^{34} +(-193.107 - 257.949i) q^{35} +686.393 q^{36} +(-121.911 + 211.155i) q^{37} +(178.435 + 309.059i) q^{38} +(201.642 + 349.255i) q^{39} +(-138.674 + 240.191i) q^{40} +257.654 q^{41} +(-299.602 + 699.680i) q^{42} +142.269 q^{43} +(-67.2866 + 116.544i) q^{44} +(-514.720 - 891.522i) q^{45} +(50.9135 + 88.1848i) q^{46} +(321.037 - 556.053i) q^{47} -206.357 q^{48} +(-236.708 - 248.230i) q^{49} +786.751 q^{50} +(256.054 - 443.499i) q^{51} +(251.994 + 436.466i) q^{52} +(241.864 + 418.920i) q^{53} +(-661.014 + 1144.91i) q^{54} +201.831 q^{55} +(-116.212 + 271.397i) q^{56} -748.256 q^{57} +(123.107 - 213.228i) q^{58} +(175.266 + 303.570i) q^{59} +(-936.779 - 1622.55i) q^{60} +(-172.105 + 298.095i) q^{61} +1065.33 q^{62} +(-656.718 - 877.232i) q^{63} -822.484 q^{64} +(377.936 - 654.604i) q^{65} +(-238.372 - 412.873i) q^{66} +(377.658 + 654.123i) q^{67} +(319.993 - 554.243i) q^{68} -213.502 q^{69} +(1416.48 - 169.392i) q^{70} -877.494 q^{71} +(-471.602 + 816.839i) q^{72} +(-612.837 - 1061.46i) q^{73} +(-539.730 - 934.839i) q^{74} +(-824.796 + 1428.59i) q^{75} -935.100 q^{76} +(213.324 - 25.5108i) q^{77} -1785.45 q^{78} +(-110.002 + 190.528i) q^{79} +(193.386 + 334.954i) q^{80} +(-587.182 - 1017.03i) q^{81} +(-570.350 + 987.875i) q^{82} +416.384 q^{83} +(-1195.21 - 1596.54i) q^{84} -959.839 q^{85} +(-314.930 + 545.475i) q^{86} +(258.120 + 447.077i) q^{87} +(-92.4616 - 160.148i) q^{88} +(770.627 - 1334.77i) q^{89} +4557.60 q^{90} +(316.718 - 739.651i) q^{91} -266.815 q^{92} +(-1116.85 + 1934.44i) q^{93} +(1421.32 + 2461.79i) q^{94} +(701.224 + 1214.55i) q^{95} +(1048.70 - 1816.40i) q^{96} +754.400 q^{97} +(1475.73 - 358.078i) q^{98} +686.384 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 6 q^{3} - 88 q^{4} - 20 q^{5} + 24 q^{6} - 12 q^{7} + 42 q^{8} - 238 q^{9} - 182 q^{10} + 28 q^{11} - 127 q^{12} + 440 q^{13} + 16 q^{14} + 40 q^{15} - 436 q^{16} - 294 q^{17} + 155 q^{18} - 252 q^{19}+ \cdots - 5764 q^{99}+O(q^{100}) \) 44 * q - 6 * q^3 - 88 * q^4 - 20 * q^5 + 24 * q^6 - 12 * q^7 + 42 * q^8 - 238 * q^9 - 182 * q^10 + 28 * q^11 - 127 * q^12 + 440 * q^13 + 16 * q^14 + 40 * q^15 - 436 * q^16 - 294 * q^17 + 155 * q^18 - 252 * q^19 + 708 * q^20 + 110 * q^21 + 28 * q^22 + 506 * q^23 - 458 * q^24 - 684 * q^25 - 396 * q^26 + 972 * q^27 - 354 * q^28 + 628 * q^29 + 905 * q^30 - 172 * q^31 + 127 * q^32 - 1524 * q^33 + 800 * q^34 - 1588 * q^35 + 2644 * q^36 + 710 * q^37 + 323 * q^38 + 136 * q^39 - 1808 * q^40 + 784 * q^41 - 2775 * q^42 + 504 * q^43 + 1106 * q^44 - 658 * q^45 - 448 * q^47 + 2730 * q^48 - 570 * q^49 + 738 * q^50 + 896 * q^51 - 1224 * q^52 - 308 * q^53 - 945 * q^54 + 4324 * q^55 - 481 * q^56 - 124 * q^57 + 1153 * q^58 + 282 * q^59 - 4442 * q^60 - 3076 * q^61 + 3500 * q^62 - 732 * q^63 - 4354 * q^64 + 1024 * q^65 + 549 * q^66 - 1056 * q^67 - 2478 * q^68 - 276 * q^69 + 2071 * q^70 - 96 * q^71 + 1922 * q^72 - 4430 * q^73 - 3322 * q^74 - 2540 * q^75 + 15026 * q^76 - 1116 * q^77 - 3990 * q^78 + 530 * q^79 - 296 * q^80 - 3446 * q^81 - 1570 * q^82 + 3572 * q^83 - 4571 * q^84 - 2624 * q^85 + 397 * q^86 + 1724 * q^87 - 5375 * q^88 - 658 * q^89 + 13620 * q^90 - 1098 * q^91 - 4048 * q^92 + 1722 * q^93 + 1944 * q^94 - 1742 * q^95 - 1142 * q^96 + 21364 * q^97 + 2001 * q^98 - 5764 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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