LMFDB - Embedded newform 38.3.f.a.33.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [38,3,Mod(3,38)] 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("38.3"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(38, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([13])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	38.f (of order $18$, degree $6$, 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:	$1.03542500457$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			33.2
Character	$\chi$	$=$	38.33
Dual form			38.3.f.a.15.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.483690 - 1.32893i) q^{2} +(3.64826 + 0.643286i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(0.297798 + 0.249882i) q^{5} +(-0.909744 - 5.15941i) q^{6} +(-2.96431 - 5.13434i) q^{7} +(2.44949 + 1.41421i) q^{8} +(4.43872 + 1.61556i) q^{9} +(0.188033 - 0.516617i) q^{10} +(-8.13043 + 14.0823i) q^{11} +(-6.41645 + 3.70454i) q^{12} +(1.76528 - 0.311267i) q^{13} +(-5.38935 + 6.42278i) q^{14} +(0.925699 + 1.10320i) q^{15} +(0.694593 - 3.93923i) q^{16} +(-24.3446 + 8.86071i) q^{17} -6.68017i q^{18} +(18.6700 + 3.52570i) q^{19} -0.777496 q^{20} +(-7.51173 - 20.6383i) q^{21} +(22.6470 + 3.99327i) q^{22} +(32.3354 - 27.1326i) q^{23} +(8.02662 + 6.73514i) q^{24} +(-4.31496 - 24.4714i) q^{25} +(-1.26750 - 2.19538i) q^{26} +(-13.7197 - 7.92106i) q^{27} +(11.1422 + 4.05542i) q^{28} +(-9.40038 + 25.8273i) q^{29} +(1.01833 - 1.76379i) q^{30} +(17.4291 - 10.0627i) q^{31} +(-5.57091 + 0.982302i) q^{32} +(-38.7208 + 46.1457i) q^{33} +(23.5505 + 28.0663i) q^{34} +(0.400214 - 2.26973i) q^{35} +(-8.87745 + 3.23113i) q^{36} -19.4424i q^{37} +(-4.34510 - 26.5164i) q^{38} +6.64044 q^{39} +(0.376067 + 1.03323i) q^{40} +(-18.6213 - 3.28344i) q^{41} +(-23.7934 + 19.9651i) q^{42} +(37.5820 + 31.5350i) q^{43} +(-5.64734 - 32.0276i) q^{44} +(0.918143 + 1.59027i) q^{45} +(-51.6975 - 29.8476i) q^{46} +(52.0500 + 18.9446i) q^{47} +(5.06810 - 13.9245i) q^{48} +(6.92569 - 11.9956i) q^{49} +(-30.4335 + 17.5708i) q^{50} +(-94.5153 + 16.6656i) q^{51} +(-2.30441 + 2.74629i) q^{52} +(-9.03932 - 10.7726i) q^{53} +(-3.89044 + 22.0638i) q^{54} +(-5.94015 + 2.16204i) q^{55} -16.7687i q^{56} +(65.8450 + 24.8728i) q^{57} +38.8695 q^{58} +(7.58069 + 20.8278i) q^{59} +(-2.83651 - 0.500152i) q^{60} +(-10.9255 + 9.16757i) q^{61} +(-21.8028 - 18.2948i) q^{62} +(-4.86291 - 27.5790i) q^{63} +(4.00000 + 6.92820i) q^{64} +(0.603479 + 0.348419i) q^{65} +(80.0531 + 29.1369i) q^{66} +(12.7327 - 34.9828i) q^{67} +(25.9070 - 44.8722i) q^{68} +(135.422 - 78.1858i) q^{69} +(-3.20988 + 0.565989i) q^{70} +(-20.3418 + 24.2424i) q^{71} +(8.58785 + 10.2346i) q^{72} +(-12.9628 + 73.5160i) q^{73} +(-25.8376 + 9.40410i) q^{74} -92.0536i q^{75} +(-33.1367 + 18.6000i) q^{76} +96.4045 q^{77} +(-3.21191 - 8.82466i) q^{78} +(-147.140 - 25.9447i) q^{79} +(1.19119 - 0.999530i) q^{80} +(-77.5237 - 65.0501i) q^{81} +(4.64349 + 26.3345i) q^{82} +(29.0689 + 50.3489i) q^{83} +(38.0407 + 21.9628i) q^{84} +(-9.46392 - 3.44458i) q^{85} +(23.7297 - 65.1969i) q^{86} +(-50.9094 + 88.1776i) q^{87} +(-39.8308 + 22.9963i) q^{88} +(-91.8814 + 16.2012i) q^{89} +(1.66926 - 1.98934i) q^{90} +(-6.83101 - 8.14088i) q^{91} +(-14.6597 + 83.1391i) q^{92} +(70.0590 - 25.4994i) q^{93} -78.3339i q^{94} +(4.67889 + 5.71526i) q^{95} -20.9560 q^{96} +(41.6935 + 114.552i) q^{97} +(-19.2912 - 3.40156i) q^{98} +(-58.8396 + 49.3723i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} + 12 q^{6} - 18 q^{7} + 6 q^{9} + 30 q^{11} - 36 q^{12} - 90 q^{13} - 48 q^{14} - 114 q^{15} + 18 q^{17} - 12 q^{19} + 24 q^{20} + 90 q^{21} + 84 q^{22} + 120 q^{23} - 24 q^{24} + 252 q^{25}+ \cdots - 204 q^{99}+O(q^{100}) $ 24 * q - 6 * q^3 + 12 * q^6 - 18 * q^7 + 6 * q^9 + 30 * q^11 - 36 * q^12 - 90 * q^13 - 48 * q^14 - 114 * q^15 + 18 * q^17 - 12 * q^19 + 24 * q^20 + 90 * q^21 + 84 * q^22 + 120 * q^23 - 24 * q^24 + 252 * q^25 + 48 * q^26 + 126 * q^27 + 72 * q^28 - 210 * q^29 - 108 * q^31 - 132 * q^33 - 24 * q^34 - 66 * q^35 - 12 * q^36 + 84 * q^38 + 120 * q^39 + 54 * q^41 + 72 * q^42 + 90 * q^43 - 48 * q^44 - 144 * q^45 - 360 * q^46 - 246 * q^47 - 48 * q^48 + 54 * q^49 - 432 * q^50 - 342 * q^51 + 36 * q^52 - 174 * q^53 - 42 * q^55 - 12 * q^57 + 48 * q^58 + 228 * q^59 + 132 * q^60 + 12 * q^61 + 204 * q^62 + 174 * q^63 + 96 * q^64 + 630 * q^65 + 696 * q^66 + 72 * q^67 - 48 * q^68 + 702 * q^69 + 528 * q^70 + 432 * q^71 + 96 * q^72 - 144 * q^74 + 72 * q^76 - 144 * q^77 - 708 * q^78 - 246 * q^79 - 642 * q^81 - 384 * q^82 - 126 * q^83 - 540 * q^84 - 684 * q^85 - 12 * q^86 - 324 * q^87 - 12 * q^89 - 336 * q^90 + 372 * q^91 - 132 * q^92 - 168 * q^93 - 570 * q^95 + 72 * q^97 + 384 * q^98 - 204 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{7}{18}\right)$

Coefficient data

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

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

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

$2$	−0.483690	−	1.32893i	−0.241845	−	0.664463i
$2$	−0.483690	−	1.32893i	−0.241845	−	0.664463i
$3$	3.64826	+	0.643286i	1.21609	+	0.214429i	0.744640	−	0.667466i	$-0.232621\pi$
$3$	3.64826	+	0.643286i	1.21609	+	0.214429i	0.471446	+	0.881895i	$0.343732\pi$
$4$	−1.53209	+	1.28558i	−0.383022	+	0.321394i
$5$	0.297798	+	0.249882i	0.0595597	+	0.0499765i	0.672082	−	0.740477i	$-0.265400\pi$
$5$	0.297798	+	0.249882i	0.0595597	+	0.0499765i	−0.612522	+	0.790454i	$0.709845\pi$
$6$	−0.909744	−	5.15941i	−0.151624	−	0.859902i
$7$	−2.96431	−	5.13434i	−0.423473	−	0.733477i	0.572803	−	0.819693i	$-0.305856\pi$
$7$	−2.96431	−	5.13434i	−0.423473	−	0.733477i	−0.996277	+	0.0862156i	$0.972523\pi$
$8$	2.44949	+	1.41421i	0.306186	+	0.176777i
$9$	4.43872	+	1.61556i	0.493191	+	0.179507i
$10$	0.188033	−	0.516617i	0.0188033	−	0.0516617i
$11$	−8.13043	+	14.0823i	−0.739130	+	1.28021i	0.213758	+	0.976887i	$0.431430\pi$
$11$	−8.13043	+	14.0823i	−0.739130	+	1.28021i	−0.952888	+	0.303324i	$0.901904\pi$
$12$	−6.41645	+	3.70454i	−0.534704	+	0.308711i
$13$	1.76528	−	0.311267i	0.135791	−	0.0239436i	−0.105339	−	0.994436i	$-0.533593\pi$
$13$	1.76528	−	0.311267i	0.135791	−	0.0239436i	0.241131	+	0.970493i	$0.422482\pi$
$14$	−5.38935	+	6.42278i	−0.384954	+	0.458770i
$15$	0.925699	+	1.10320i	0.0617132	+	0.0735470i
$16$	0.694593	−	3.93923i	0.0434120	−	0.246202i
$17$	−24.3446	+	8.86071i	−1.43204	+	0.521218i	−0.937514	−	0.347947i	$-0.886879\pi$
$17$	−24.3446	+	8.86071i	−1.43204	+	0.521218i	−0.494521	+	0.869166i	$0.664657\pi$
$18$		−	6.68017i		−	0.371120i
$19$	18.6700	+	3.52570i	0.982632	+	0.185563i
$19$	18.6700	+	3.52570i	0.982632	+	0.185563i
$20$	−0.777496			−0.0388748
$21$	−7.51173	−	20.6383i	−0.357701	−	0.982776i
$22$	22.6470	+	3.99327i	1.02941	+	0.181512i
$23$	32.3354	−	27.1326i	1.40589	−	1.17968i	0.447471	−	0.894299i	$-0.352325\pi$
$23$	32.3354	−	27.1326i	1.40589	−	1.17968i	0.958415	−	0.285379i	$-0.0921196\pi$
$24$	8.02662	+	6.73514i	0.334443	+	0.280631i
$25$	−4.31496	−	24.4714i	−0.172598	−	0.978855i
$26$	−1.26750	−	2.19538i	−0.0487500	−	0.0844375i
$27$	−13.7197	−	7.92106i	−0.508136	−	0.293373i
$28$	11.1422	+	4.05542i	0.397935	+	0.144836i
$29$	−9.40038	+	25.8273i	−0.324151	+	0.890598i	0.665409	+	0.746479i	$0.268257\pi$
$29$	−9.40038	+	25.8273i	−0.324151	+	0.890598i	−0.989560	+	0.144119i	$0.953965\pi$
$30$	1.01833	−	1.76379i	0.0339442	−	0.0587931i
$31$	17.4291	−	10.0627i	0.562229	−	0.324603i	−0.191811	−	0.981432i	$-0.561436\pi$
$31$	17.4291	−	10.0627i	0.562229	−	0.324603i	0.754040	+	0.656829i	$0.228103\pi$
$32$	−5.57091	+	0.982302i	−0.174091	+	0.0306970i
$33$	−38.7208	+	46.1457i	−1.17336	+	1.39835i
$34$	23.5505	+	28.0663i	0.692660	+	0.825481i
$35$	0.400214	−	2.26973i	0.0114347	−	0.0648494i
$36$	−8.87745	+	3.23113i	−0.246596	+	0.0897535i
$37$		−	19.4424i		−	0.525471i	−0.964868	−	0.262736i	$-0.915375\pi$
$37$		−	19.4424i		−	0.525471i	0.964868	−	0.262736i	$-0.0846247\pi$
$38$	−4.34510	−	26.5164i	−0.114345	−	0.697800i
$39$	6.64044			0.170268
$40$	0.376067	+	1.03323i	0.00940167	+	0.0258309i
$41$	−18.6213	−	3.28344i	−0.454179	−	0.0800839i	−0.0581209	−	0.998310i	$-0.518511\pi$
$41$	−18.6213	−	3.28344i	−0.454179	−	0.0800839i	−0.396058	+	0.918226i	$0.629622\pi$
$42$	−23.7934	+	19.9651i	−0.566510	+	0.475358i
$43$	37.5820	+	31.5350i	0.874000	+	0.733373i	0.964936	−	0.262484i	$-0.0845416\pi$
$43$	37.5820	+	31.5350i	0.874000	+	0.733373i	−0.0909364	+	0.995857i	$0.528986\pi$
$44$	−5.64734	−	32.0276i	−0.128349	−	0.727901i
$45$	0.918143	+	1.59027i	0.0204032	+	0.0353394i
$46$	−51.6975	−	29.8476i	−1.12386	−	0.648860i
$47$	52.0500	+	18.9446i	1.10745	+	0.403077i	0.830056	−	0.557680i	$-0.188308\pi$
$47$	52.0500	+	18.9446i	1.10745	+	0.403077i	0.277390	+	0.960757i	$0.410531\pi$
$48$	5.06810	−	13.9245i	0.105586	−	0.290094i
$49$	6.92569	−	11.9956i	0.141341	−	0.244809i
$50$	−30.4335	+	17.5708i	−0.608671	+	0.351416i
$51$	−94.5153	+	16.6656i	−1.85324	+	0.326776i
$52$	−2.30441	+	2.74629i	−0.0443157	+	0.0528134i
$53$	−9.03932	−	10.7726i	−0.170553	−	0.203257i	0.673997	−	0.738734i	$-0.264576\pi$
$53$	−9.03932	−	10.7726i	−0.170553	−	0.203257i	−0.844550	+	0.535477i	$0.820132\pi$
$54$	−3.89044	+	22.0638i	−0.0720451	+	0.408588i
$55$	−5.94015	+	2.16204i	−0.108003	+	0.0393098i
$56$		−	16.7687i		−	0.299441i
$57$	65.8450	+	24.8728i	1.15517	+	0.436365i
$58$	38.8695			0.670163
$59$	7.58069	+	20.8278i	0.128486	+	0.353013i	0.987210	−	0.159426i	$-0.0509643\pi$
$59$	7.58069	+	20.8278i	0.128486	+	0.353013i	−0.858724	+	0.512439i	$0.828742\pi$
$60$	−2.83651	−	0.500152i	−0.0472751	−	0.00833587i
$61$	−10.9255	+	9.16757i	−0.179106	+	0.150288i	−0.727933	−	0.685648i	$-0.759519\pi$
$61$	−10.9255	+	9.16757i	−0.179106	+	0.150288i	0.548827	+	0.835936i	$0.315075\pi$
$62$	−21.8028	−	18.2948i	−0.351659	−	0.295077i
$63$	−4.86291	−	27.5790i	−0.0771891	−	0.437761i
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	0.603479	+	0.348419i	0.00928429	+	0.00536029i
$66$	80.0531	+	29.1369i	1.21293	+	0.441469i
$67$	12.7327	−	34.9828i	0.190040	−	0.522131i	−0.807680	−	0.589621i	$-0.799277\pi$
$67$	12.7327	−	34.9828i	0.190040	−	0.522131i	0.997720	+	0.0674903i	$0.0214992\pi$
$68$	25.9070	−	44.8722i	0.380985	−	0.659885i
$69$	135.422	−	78.1858i	1.96263	−	1.13313i
$70$	−3.20988	+	0.565989i	−0.0458554	+	0.00808555i
$71$	−20.3418	+	24.2424i	−0.286505	+	0.341443i	−0.890031	−	0.455900i	$-0.849317\pi$
$71$	−20.3418	+	24.2424i	−0.286505	+	0.341443i	0.603526	+	0.797343i	$0.293762\pi$
$72$	8.58785	+	10.2346i	0.119276	+	0.142147i
$73$	−12.9628	+	73.5160i	−0.177573	+	1.00707i	0.757558	+	0.652767i	$0.226392\pi$
$73$	−12.9628	+	73.5160i	−0.177573	+	1.00707i	−0.935132	+	0.354301i	$0.884719\pi$
$74$	−25.8376	+	9.40410i	−0.349156	+	0.127082i
$75$		−	92.0536i		−	1.22738i
$76$	−33.1367	+	18.6000i	−0.436009	+	0.244737i
$77$	96.4045			1.25201
$78$	−3.21191	−	8.82466i	−0.0411784	−	0.113137i
$79$	−147.140	−	25.9447i	−1.86253	−	0.328414i	−0.874785	−	0.484512i	$-0.838997\pi$
$79$	−147.140	−	25.9447i	−1.86253	−	0.328414i	−0.987741	+	0.156099i	$0.950108\pi$
$80$	1.19119	−	0.999530i	0.0148899	−	0.0124941i
$81$	−77.5237	−	65.0501i	−0.957083	−	0.803088i
$82$	4.64349	+	26.3345i	0.0566279	+	0.321153i
$83$	29.0689	+	50.3489i	0.350228	+	0.606613i	0.986289	−	0.165026i	$-0.0527707\pi$
$83$	29.0689	+	50.3489i	0.350228	+	0.606613i	−0.636061	+	0.771639i	$0.719437\pi$
$84$	38.0407	+	21.9628i	0.452866	+	0.261462i
$85$	−9.46392	−	3.44458i	−0.111340	−	0.0405245i
$86$	23.7297	−	65.1969i	0.275927	−	0.758103i
$87$	−50.9094	+	88.1776i	−0.585165	+	1.01354i
$88$	−39.8308	+	22.9963i	−0.452623	+	0.261322i
$89$	−91.8814	+	16.2012i	−1.03238	+	0.182036i	−0.664071	−	0.747670i	$-0.731173\pi$
$89$	−91.8814	+	16.2012i	−1.03238	+	0.182036i	−0.368304	+	0.929705i	$0.620062\pi$
$90$	1.66926	−	1.98934i	0.0185473	−	0.0221038i
$91$	−6.83101	−	8.14088i	−0.0750660	−	0.0894602i
$92$	−14.6597	+	83.1391i	−0.159344	+	0.903686i
$93$	70.0590	−	25.4994i	0.753322	−	0.274187i
$94$		−	78.3339i		−	0.833339i
$95$	4.67889	+	5.71526i	0.0492515	+	0.0601606i
$96$	−20.9560			−0.218292
$97$	41.6935	+	114.552i	0.429830	+	1.18095i	0.945916	+	0.324411i	$0.105166\pi$
$97$	41.6935	+	114.552i	0.429830	+	1.18095i	−0.516086	+	0.856537i	$0.672612\pi$
$98$	−19.2912	−	3.40156i	−0.196849	−	0.0347098i
$99$	−58.8396	+	49.3723i	−0.594339	+	0.498710i
$100$	38.0707	+	31.9451i	0.380707	+	0.319451i
$101$	−23.4332	−	132.896i	−0.232012	−	1.31580i	−0.848816	−	0.528688i	$-0.822684\pi$
$101$	−23.4332	−	132.896i	−0.232012	−	1.31580i	0.616805	−	0.787116i	$-0.288427\pi$
$102$	67.8634	+	117.543i	0.665328	+	1.15238i
$103$	−92.3597	−	53.3239i	−0.896697	−	0.517708i	−0.0205696	−	0.999788i	$-0.506548\pi$
$103$	−92.3597	−	53.3239i	−0.896697	−	0.517708i	−0.876127	+	0.482080i	$0.839881\pi$
$104$	4.76424	+	1.73404i	0.0458100	+	0.0166735i
$105$	2.92017	−	8.02310i	0.0278111	−	0.0764105i
$106$	−9.94382	+	17.2232i	−0.0938096	+	0.162483i
$107$	6.51505	−	3.76147i	0.0608883	−	0.0351539i	−0.469247	−	0.883067i	$-0.655475\pi$
$107$	6.51505	−	3.76147i	0.0608883	−	0.0351539i	0.530135	+	0.847913i	$0.322141\pi$
$108$	31.2029	−	5.50191i	0.288916	−	0.0509436i
$109$	−9.26982	+	11.0473i	−0.0850442	+	0.101352i	−0.806889	−	0.590704i	$-0.798850\pi$
$109$	−9.26982	+	11.0473i	−0.0850442	+	0.101352i	0.721844	+	0.692055i	$0.243295\pi$
$110$	5.74638	+	6.84827i	0.0522398	+	0.0622570i
$111$	12.5070	−	70.9310i	0.112676	−	0.639018i
$112$	−22.2843	+	8.11084i	−0.198967	+	0.0724182i
$113$			141.490i			1.25212i	0.779774	+	0.626061i	$0.215334\pi$
$113$			141.490i			1.25212i	−0.779774	+	0.626061i	$0.784666\pi$
$114$	1.20560	−	99.5338i	0.0105754	−	0.873104i
$115$	16.4094			0.142690
$116$	−18.8008	−	51.6547i	−0.162076	−	0.445299i
$117$	8.33848	+	1.47030i	0.0712690	+	0.0125667i
$118$	24.0119	−	20.1483i	0.203490	−	0.170749i
$119$	117.659	+	98.7276i	0.988731	+	0.829643i
$120$	0.707322	+	4.01142i	0.00589435	+	0.0334285i
$121$	−71.7077	−	124.201i	−0.592626	−	1.02646i
$122$	17.4676	+	10.0849i	0.143177	+	0.0826631i
$123$	−65.8232	−	23.9577i	−0.535148	−	0.194778i
$124$	−13.7666	+	37.8233i	−0.111021	+	0.305027i
$125$	9.68933	−	16.7824i	0.0775146	−	0.134259i
$126$	−34.2983	+	19.8021i	−0.272208	+	0.157160i
$127$	92.1323	−	16.2454i	0.725451	−	0.127917i	0.201285	−	0.979533i	$-0.435488\pi$
$127$	92.1323	−	16.2454i	0.725451	−	0.127917i	0.524166	+	0.851616i	$0.324377\pi$
$128$	7.27231	−	8.66680i	0.0568149	−	0.0677094i
$129$	116.823	+	139.224i	0.905602	+	1.07926i
$130$	0.171126	−	0.970505i	0.00131636	−	0.00746542i
$131$	155.637	−	56.6473i	1.18807	−	0.432422i	0.329025	−	0.944321i	$-0.393280\pi$
$131$	155.637	−	56.6473i	1.18807	−	0.432422i	0.859046	+	0.511899i	$0.171058\pi$
$132$		−	120.478i		−	0.912711i
$133$	−37.2416	−	106.310i	−0.280012	−	0.799320i
$134$	−52.6482			−0.392897
$135$	−2.10636	−	5.78718i	−0.0156027	−	0.0428680i
$136$	−72.1628	−	12.7242i	−0.530609	−	0.0935606i
$137$	100.767	−	84.5537i	0.735526	−	0.617180i	−0.196106	−	0.980583i	$-0.562830\pi$
$137$	100.767	−	84.5537i	0.735526	−	0.617180i	0.931632	+	0.363403i	$0.118385\pi$
$138$	−169.405	−	142.148i	−1.22757	−	1.03006i
$139$	−20.5435	−	116.508i	−0.147795	−	0.838188i	−0.965080	−	0.261955i	$-0.915633\pi$
$139$	−20.5435	−	116.508i	−0.147795	−	0.838188i	0.817285	−	0.576234i	$-0.195478\pi$
$140$	2.30474	+	3.99193i	0.0164624	+	0.0285138i
$141$	177.705	+	102.598i	1.26032	+	0.727645i
$142$	42.0555	+	15.3070i	0.296166	+	0.107796i
$143$	−9.96915	+	27.3900i	−0.0697143	+	0.191539i
$144$	9.44718	−	16.3630i	0.0656054	−	0.113632i
$145$	−9.25321	+	5.34235i	−0.0638153	+	0.0368438i
$146$	103.967	−	18.3322i	0.712105	−	0.125563i
$147$	32.9833	−	39.3080i	0.224376	−	0.267401i
$148$	24.9947	+	29.7875i	0.168883	+	0.201267i
$149$	−22.4518	+	127.331i	−0.150683	+	0.854568i	0.811943	+	0.583736i	$0.198410\pi$
$149$	−22.4518	+	127.331i	−0.150683	+	0.854568i	−0.962627	+	0.270832i	$0.912701\pi$
$150$	−122.332	+	44.5253i	−0.815549	+	0.296836i
$151$			288.719i			1.91204i	0.293294	+	0.956022i	$0.405249\pi$
$151$			288.719i			1.91204i	−0.293294	+	0.956022i	$0.594751\pi$
$152$	40.7459	+	35.0395i	0.268065	+	0.230523i
$153$	−122.374			−0.799830
$154$	−46.6299	−	128.115i	−0.302791	−	0.831912i
$155$	7.70484	+	1.35857i	0.0497087	+	0.00876498i
$156$	−10.1737	+	8.53679i	−0.0652163	+	0.0547230i
$157$	89.0151	+	74.6926i	0.566975	+	0.475749i	0.880641	−	0.473785i	$-0.157113\pi$
$157$	89.0151	+	74.6926i	0.566975	+	0.475749i	−0.313665	+	0.949534i	$0.601557\pi$
$158$	36.6913	+	208.087i	0.232223	+	1.31700i
$159$	−26.0479	−	45.1162i	−0.163823	−	0.283750i
$160$	−1.90447	−	1.09955i	−0.0119029	−	0.00687216i
$161$	−235.160	−	85.5913i	−1.46062	−	0.531623i
$162$	−48.9494	+	134.487i	−0.302157	+	0.830169i
$163$	−90.4066	+	156.589i	−0.554642	+	0.960668i	0.443289	+	0.896379i	$0.353811\pi$
$163$	−90.4066	+	156.589i	−0.554642	+	0.960668i	−0.997931	+	0.0642894i	$0.979522\pi$
$164$	32.7506	−	18.9086i	0.199699	−	0.115296i
$165$	−23.0620	+	4.06645i	−0.139770	+	0.0246452i
$166$	52.8496	−	62.9837i	0.318371	−	0.379420i
$167$	−134.977	−	160.860i	−0.808247	−	0.963232i	0.191586	−	0.981476i	$-0.438637\pi$
$167$	−134.977	−	160.860i	−0.808247	−	0.963232i	−0.999834	+	0.0182441i	$0.994192\pi$
$168$	10.7871	−	61.1765i	0.0642087	−	0.364146i
$169$	−155.789	+	56.7025i	−0.921827	+	0.335517i
$170$			14.2430i			0.0837821i
$171$	77.1750	+	45.8122i	0.451316	+	0.267907i
$172$	−98.1196			−0.570463
$173$	−82.3903	−	226.365i	−0.476244	−	1.30847i	−0.912658	−	0.408725i	$-0.865974\pi$
$173$	−82.3903	−	226.365i	−0.476244	−	1.30847i	0.436413	−	0.899746i	$-0.356249\pi$
$174$	141.806	+	25.0042i	0.814976	+	0.143702i
$175$	−112.853	+	94.6953i	−0.644877	+	0.541116i
$176$	49.8262	+	41.8091i	0.283103	+	0.237552i
$177$	14.2581	+	80.8616i	0.0805541	+	0.456845i
$178$	65.9722	+	114.267i	0.370630	+	0.641951i
$179$	7.69927	+	4.44517i	0.0430127	+	0.0248334i	0.521352	−	0.853342i	$-0.325428\pi$
$179$	7.69927	+	4.44517i	0.0430127	+	0.0248334i	−0.478339	+	0.878175i	$0.658761\pi$
$180$	−3.45109	−	1.25609i	−0.0191727	−	0.00697830i
$181$	46.2352	−	127.030i	0.255443	−	0.701824i	−0.743991	−	0.668190i	$-0.767069\pi$
$181$	46.2352	−	127.030i	0.255443	−	0.701824i	0.999434	−	0.0336348i	$-0.0107083\pi$
$182$	−7.51454	+	13.0156i	−0.0412887	+	0.0715141i
$183$	−45.7563	+	26.4174i	−0.250035	+	0.144357i
$184$	117.576	−	20.7319i	0.639002	−	0.112673i
$185$	4.85832	−	5.78992i	0.0262612	−	0.0312969i
$186$	−67.7736	−	80.7694i	−0.364374	−	0.434244i
$187$	73.1527	−	414.870i	0.391191	−	2.21855i
$188$	−104.100	+	37.8893i	−0.553723	+	0.201539i
$189$			93.9220i			0.496942i
$190$	5.33202	−	8.98231i	0.0280633	−	0.0472753i
$191$	−109.638			−0.574020			−0.287010	−	0.957928i	$-0.592661\pi$
$191$	−109.638			−0.574020			−0.287010	+	0.957928i	$0.592661\pi$
$192$	10.1362	+	27.8490i	0.0527928	+	0.145047i
$193$	311.671	+	54.9559i	1.61487	+	0.284746i	0.906853	−	0.421446i	$-0.138477\pi$
$193$	311.671	+	54.9559i	1.61487	+	0.284746i	0.708020	+	0.706192i	$0.249589\pi$
$194$	132.064	−	110.815i	0.680744	−	0.571212i
$195$	1.97751	+	1.65933i	0.0101411	+	0.00850938i
$196$	4.81053	+	27.2819i	0.0245435	+	0.139193i
$197$	−92.7151	−	160.587i	−0.470635	−	0.815164i	0.528801	−	0.848746i	$-0.322642\pi$
$197$	−92.7151	−	160.587i	−0.470635	−	0.815164i	−0.999436	+	0.0335821i	$0.989308\pi$
$198$	94.0722	+	54.3126i	0.475112	+	0.274306i
$199$	44.3698	+	16.1493i	0.222964	+	0.0811521i	0.451087	−	0.892480i	$-0.351037\pi$
$199$	44.3698	+	16.1493i	0.222964	+	0.0811521i	−0.228123	+	0.973632i	$0.573259\pi$
$200$	24.0383	−	66.0446i	0.120191	−	0.330223i
$201$	68.9561	−	119.435i	0.343065	−	0.594206i
$202$	−165.275	+	95.4215i	−0.818192	+	0.472384i
$203$	160.472	−	28.2955i	0.790503	−	0.139387i
$204$	123.381	−	147.040i	0.604809	−	0.720783i
$205$	−4.72492	−	5.63094i	−0.0230484	−	0.0274680i
$206$	−26.1901	+	148.531i	−0.127136	+	0.721027i
$207$	187.362	−	68.1942i	0.905131	−	0.329441i
$208$		−	7.17007i		−	0.0344715i
$209$	−201.445	+	234.252i	−0.963853	+	1.12082i
$210$	−12.0746			−0.0574979
$211$	83.5213	+	229.473i	0.395835	+	1.08755i	0.964293	+	0.264837i	$0.0853180\pi$
$211$	83.5213	+	229.473i	0.395835	+	1.08755i	−0.568458	+	0.822712i	$0.692460\pi$
$212$	27.6981	+	4.88392i	0.130651	+	0.0230374i
$213$	−89.8070	+	75.3570i	−0.421629	+	0.353789i
$214$	−8.14997	−	6.83864i	−0.0380840	−	0.0319563i
$215$	3.31180	+	18.7822i	0.0154037	+	0.0873589i
$216$	−22.4041	−	38.8051i	−0.103723	−	0.179653i
$217$	−103.331	−	59.6579i	−0.476178	−	0.274921i
$218$	19.1648	+	6.97542i	0.0879120	+	0.0319973i
$219$	−94.5836	+	259.866i	−0.431889	+	1.18660i
$220$	6.32138	−	10.9489i	0.0287335	−	0.0497679i
$221$	−40.2171	+	23.2193i	−0.181978	+	0.105065i
$222$	−100.312	+	17.6876i	−0.451854	+	0.0796740i
$223$	161.214	−	192.127i	0.722933	−	0.861558i	−0.271979	−	0.962303i	$-0.587678\pi$
$223$	161.214	−	192.127i	0.722933	−	0.861558i	0.994912	+	0.100745i	$0.0321227\pi$
$224$	21.5574	+	25.6911i	0.0962384	+	0.114693i
$225$	20.3821	−	115.593i	0.0905872	−	0.513745i
$226$	188.030	−	68.4372i	0.831989	−	0.302819i
$227$		−	0.891777i		−	0.00392853i	−0.999998	−	0.00196427i	$-0.999375\pi$
$227$		−	0.891777i		−	0.00392853i	0.999998	−	0.00196427i	$-0.000625246\pi$
$228$	−132.856	+	46.5413i	−0.582703	+	0.204129i
$229$	289.709			1.26510			0.632552	−	0.774518i	$-0.282007\pi$
$229$	289.709			1.26510			0.632552	+	0.774518i	$0.282007\pi$
$230$	−7.93704	−	21.8068i	−0.0345089	−	0.0948124i
$231$	351.708	+	62.0157i	1.52255	+	0.268466i
$232$	−59.5515	+	49.9696i	−0.256687	+	0.215386i
$233$	−192.719	−	161.710i	−0.827118	−	0.694034i	0.127509	−	0.991837i	$-0.459302\pi$
$233$	−192.719	−	161.710i	−0.827118	−	0.694034i	−0.954627	+	0.297803i	$0.903746\pi$
$234$	−2.07932	−	11.7924i	−0.00888597	−	0.0503948i
$235$	10.7665	+	18.6480i	0.0458147	+	0.0793534i
$236$	−38.3900	−	22.1645i	−0.162669	−	0.0939172i
$237$	−520.113	−	189.306i	−2.19457	−	0.798758i
$238$	74.2912	−	204.114i	0.312148	−	0.857620i
$239$	104.580	−	181.137i	0.437572	−	0.757897i	−0.559929	−	0.828540i	$-0.689172\pi$
$239$	104.580	−	181.137i	0.437572	−	0.757897i	0.997502	+	0.0706430i	$0.0225051\pi$
$240$	4.98876	−	2.88026i	0.0207865	−	0.0120011i
$241$	−49.6606	+	8.75651i	−0.206061	+	0.0363341i	−0.275726	−	0.961236i	$-0.588918\pi$
$241$	−49.6606	+	8.75651i	−0.206061	+	0.0363341i	0.0696649	+	0.997570i	$0.477807\pi$
$242$	−130.370	+	155.369i	−0.538720	+	0.642021i
$243$	−149.332	−	177.967i	−0.614537	−	0.732377i
$244$	4.95321	−	28.0911i	0.0203000	−	0.115127i
$245$	5.05996	−	1.84167i	0.0206529	−	0.00751704i
$246$			99.0622i			0.402692i
$247$	34.0553	+	0.412493i	0.137876	+	0.00167001i
$248$	56.9232			0.229529
$249$	73.6622	+	202.385i	0.295832	+	0.812792i
$250$	−26.9892	−	4.75892i	−0.107957	−	0.0190357i
$251$	35.2847	−	29.6073i	0.140576	−	0.117958i	−0.569788	−	0.821792i	$-0.692975\pi$
$251$	35.2847	−	29.6073i	0.140576	−	0.117958i	0.710364	+	0.703834i	$0.248530\pi$
$252$	42.9052	+	36.0018i	0.170259	+	0.142864i
$253$	119.189	+	675.956i	0.471104	+	2.67176i
$254$	−66.1523	−	114.579i	−0.260442	−	0.451099i
$255$	−32.3109	−	18.6547i	−0.126710	−	0.0731558i
$256$	−15.0351	−	5.47232i	−0.0587308	−	0.0213763i
$257$	−29.1491	+	80.0866i	−0.113421	+	0.311621i	−0.983396	−	0.181475i	$-0.941913\pi$
$257$	−29.1491	+	80.0866i	−0.113421	+	0.311621i	0.869975	+	0.493096i	$0.164135\pi$
$258$	128.512	−	222.590i	0.498110	−	0.862752i
$259$	−99.8241	+	57.6335i	−0.385421	+	0.222523i
$260$	−1.37250	+	0.242009i	−0.00527885	+	0.000930804i
$261$	−83.4514	+	99.4535i	−0.319737	+	0.381048i
$262$	−150.560	−	179.431i	−0.574657	−	0.684850i
$263$	−13.4824	+	76.4625i	−0.0512639	+	0.290732i	−0.999652	−	0.0263800i	$-0.991602\pi$
$263$	−13.4824	+	76.4625i	−0.0512639	+	0.290732i	0.948388	+	0.317112i	$0.102713\pi$
$264$	−160.106	+	58.2739i	−0.606463	+	0.220734i
$265$		−	5.46684i		−	0.0206296i
$266$	−123.264	+	100.912i	−0.463399	+	0.379369i
$267$	−345.629			−1.29449
$268$	25.4654	+	69.9656i	0.0950201	+	0.261066i
$269$	−313.463	−	55.2719i	−1.16529	−	0.205472i	−0.442648	−	0.896695i	$-0.645961\pi$
$269$	−313.463	−	55.2719i	−1.16529	−	0.205472i	−0.722641	+	0.691224i	$0.757072\pi$
$270$	−6.67191	+	5.59840i	−0.0247108	+	0.0207348i
$271$	85.7299	+	71.9360i	0.316347	+	0.265446i	0.787109	−	0.616814i	$-0.211577\pi$
$271$	85.7299	+	71.9360i	0.316347	+	0.265446i	−0.470763	+	0.882260i	$0.656021\pi$
$272$	17.9948	+	102.054i	0.0661574	+	0.375197i
$273$	−19.6844	−	34.0943i	−0.0721039	−	0.124888i
$274$	−161.106	−	93.0143i	−0.587977	−	0.339468i
$275$	379.696	+	138.198i	1.38071	+	0.502538i
$276$	−106.964	+	293.882i	−0.387552	+	1.06479i
$277$	86.2411	−	149.374i	0.311340	−	0.539256i	−0.667313	−	0.744777i	$-0.732556\pi$
$277$	86.2411	−	149.374i	0.311340	−	0.539256i	0.978653	+	0.205521i	$0.0658890\pi$
$278$	−144.894	+	83.6546i	−0.521202	+	0.300916i
$279$	93.6198	−	16.5077i	0.335555	−	0.0591674i
$280$	4.19020	−	4.99369i	0.0149650	−	0.0178346i
$281$	−5.93324	−	7.07097i	−0.0211147	−	0.0251636i	0.755384	−	0.655283i	$-0.227450\pi$
$281$	−5.93324	−	7.07097i	−0.0211147	−	0.0251636i	−0.776498	+	0.630119i	$0.783006\pi$
$282$	50.3911	−	285.782i	0.178692	−	1.01341i
$283$	133.243	−	48.4965i	0.470824	−	0.171366i	−0.0957017	−	0.995410i	$-0.530510\pi$
$283$	133.243	−	48.4965i	0.470824	−	0.171366i	0.566525	+	0.824044i	$0.308287\pi$
$284$		−	63.2925i		−	0.222861i
$285$	13.3932	+	23.8606i	0.0469938	+	0.0837213i
$286$	41.2213			0.144130
$287$	38.3411	+	105.341i	0.133593	+	0.367043i
$288$	−26.3147	−	4.63999i	−0.0913705	−	0.0161111i
$289$	292.760	−	245.655i	1.01301	−	0.850018i
$290$	11.5753	+	9.71280i	0.0399147	+	0.0334924i
$291$	78.4189	+	444.736i	0.269481	+	1.52830i
$292$	−74.6501	−	129.298i	−0.255651	−	0.442800i
$293$	362.249	+	209.145i	1.23634	+	0.713804i	0.968345	−	0.249615i	$-0.0803041\pi$
$293$	362.249	+	209.145i	1.23634	+	0.713804i	0.268000	+	0.963419i	$0.413637\pi$
$294$	−68.1911	−	24.8195i	−0.231943	−	0.0844202i
$295$	−2.94698	+	8.09676i	−0.00998976	+	0.0274466i
$296$	27.4958	−	47.6240i	0.0928911	−	0.160892i
$297$	223.094	−	128.803i	0.751157	−	0.433681i
$298$	180.073	−	31.7517i	0.604271	−	0.106549i
$299$	48.6356	−	57.9617i	0.162661	−	0.193852i
$300$	118.342	+	141.034i	0.394473	+	0.470114i
$301$	50.5069	−	286.439i	0.167797	−	0.951623i
$302$	383.686	−	139.650i	1.27048	−	0.462418i
$303$		−	499.914i		−	1.64988i
$304$	26.8566	−	71.0966i	0.0883440	−	0.233870i
$305$	−5.54440			−0.0181784
$306$	59.1910	+	162.626i	0.193435	+	0.531457i
$307$	−396.123	−	69.8472i	−1.29030	−	0.227515i	−0.513954	−	0.857818i	$-0.671820\pi$
$307$	−396.123	−	69.8472i	−1.29030	−	0.227515i	−0.776350	+	0.630302i	$0.782931\pi$
$308$	−147.700	+	123.935i	−0.479547	+	0.402387i
$309$	−302.649	−	253.953i	−0.979448	−	0.821855i
$310$	−1.92131	−	10.8963i	−0.00619778	−	0.0351493i
$311$	1.92896	+	3.34106i	0.00620244	+	0.0107429i	0.869110	−	0.494619i	$-0.164692\pi$
$311$	1.92896	+	3.34106i	0.00620244	+	0.0107429i	−0.862908	+	0.505362i	$0.831359\pi$
$312$	16.2657	+	9.39100i	0.0521336	+	0.0300994i
$313$	317.780	+	115.663i	1.01527	+	0.369529i	0.795455	−	0.606012i	$-0.207232\pi$
$313$	317.780	+	115.663i	1.01527	+	0.369529i	0.219817	+	0.975541i	$0.429454\pi$
$314$	56.2052	−	154.423i	0.178997	−	0.491792i
$315$	5.44333	−	9.42812i	0.0172804	−	0.0299305i
$316$	258.785	−	149.409i	0.818939	−	0.472815i
$317$	10.5173	−	1.85448i	0.0331775	−	0.00585009i	−0.157035	−	0.987593i	$-0.550193\pi$
$317$	10.5173	−	1.85448i	0.0331775	−	0.00585009i	0.190212	+	0.981743i	$0.439082\pi$
$318$	−47.3570	+	56.4379i	−0.148922	+	0.177478i
$319$	−287.279	−	342.366i	−0.900563	−	1.07325i
$320$	−0.540043	+	3.06274i	−0.00168763	+	0.00957105i
$321$	26.1883	−	9.53175i	0.0815834	−	0.0296939i
$322$			353.910i			1.09910i
$323$	−485.754	+	79.5979i	−1.50388	+	0.246433i
$324$	202.400			0.624691
$325$	−15.2343	−	41.8558i	−0.0468747	−	0.128787i
$326$	251.824	+	44.4033i	0.772466	+	0.136207i
$327$	−40.9253	+	34.3404i	−0.125154	+	0.105016i
$328$	−40.9693	−	34.3773i	−0.124906	−	0.104809i
$329$	−57.0242	−	323.400i	−0.173326	−	0.982979i
$330$	16.5589	+	28.6808i	0.0501784	+	0.0869115i
$331$	−148.405	−	85.6815i	−0.448353	−	0.258857i	0.258782	−	0.965936i	$-0.416679\pi$
$331$	−148.405	−	85.6815i	−0.448353	−	0.258857i	−0.707134	+	0.707079i	$0.750012\pi$
$332$	−109.263	−	39.7686i	−0.329107	−	0.119785i
$333$	31.4105	−	86.2996i	0.0943258	−	0.259158i
$334$	−148.484	+	257.181i	−0.444561	+	0.770003i
$335$	12.5334	−	7.23614i	0.0374130	−	0.0216004i
$336$	−86.5166	+	15.2552i	−0.257490	+	0.0454024i
$337$	−3.21424	+	3.83059i	−0.00953782	+	0.0113667i	−0.770792	−	0.637087i	$-0.780139\pi$
$337$	−3.21424	+	3.83059i	−0.00953782	+	0.0113667i	0.761254	+	0.648453i	$0.224584\pi$
$338$	150.707	+	179.605i	0.445878	+	0.531377i
$339$	−91.0185	+	516.191i	−0.268491	+	1.52269i
$340$	18.9278	−	6.88917i	0.0556701	−	0.0202623i
$341$			327.256i			0.959695i
$342$	23.5522	−	124.719i	0.0688662	−	0.364675i
$343$	−372.622			−1.08636
$344$	47.4594	+	130.394i	0.137963	+	0.379052i
$345$	59.8656	+	10.5559i	0.173523	+	0.0305969i
$346$	−260.972	+	218.981i	−0.754253	+	0.632894i
$347$	32.3482	+	27.1434i	0.0932226	+	0.0782231i	0.688208	−	0.725514i	$-0.258398\pi$
$347$	32.3482	+	27.1434i	0.0932226	+	0.0782231i	−0.594985	+	0.803737i	$0.702842\pi$
$348$	−35.3613	−	200.544i	−0.101613	−	0.576275i
$349$	68.5275	+	118.693i	0.196354	+	0.340095i	0.947344	−	0.320219i	$-0.103757\pi$
$349$	68.5275	+	118.693i	0.196354	+	0.340095i	−0.750990	+	0.660314i	$0.770423\pi$
$350$	180.429	+	104.171i	0.515512	+	0.297631i
$351$	−26.6847	−	9.71243i	−0.0760248	−	0.0276707i
$352$	31.4608	−	86.4379i	0.0893773	−	0.245562i
$353$	179.947	−	311.677i	0.509765	−	0.882938i	−0.490171	−	0.871626i	$-0.663066\pi$
$353$	179.947	−	311.677i	0.509765	−	0.882938i	0.999936	−	0.0113122i	$-0.00360086\pi$
$354$	100.563	−	58.0598i	0.284075	−	0.164011i
$355$	−12.1155	+	2.13629i	−0.0341282	+	0.00601773i
$356$	119.943	−	142.942i	0.336918	−	0.401523i
$357$	365.740	+	435.872i	1.02448	+	1.22093i
$358$	2.18325	−	12.3818i	0.00609847	−	0.0345861i
$359$	−322.462	+	117.367i	−0.898224	+	0.326927i	−0.749541	−	0.661958i	$-0.769726\pi$
$359$	−322.462	+	117.367i	−0.898224	+	0.326927i	−0.148683	+	0.988885i	$0.547503\pi$
$360$			5.19380i			0.0144272i
$361$	336.139	+	131.650i	0.931133	+	0.364680i
$362$	−191.177			−0.528114
$363$	−181.711	−	499.247i	−0.500581	−	1.37534i
$364$	20.9314	+	3.69077i	0.0575039	+	0.0101395i
$365$	−22.2307	+	18.6537i	−0.0609059	+	0.0511061i
$366$	57.2386	+	48.0289i	0.156390	+	0.131227i
$367$	−31.2479	−	177.216i	−0.0851441	−	0.482876i	−0.997325	−	0.0730895i	$-0.976714\pi$
$367$	−31.2479	−	177.216i	−0.0851441	−	0.482876i	0.912181	−	0.409787i	$-0.134397\pi$
$368$	−84.4216	−	146.223i	−0.229407	−	0.397344i
$369$	−77.3503	−	44.6582i	−0.209621	−	0.121025i
$370$	−10.0443	−	3.65583i	−0.0271468	−	0.00988061i
$371$	−28.5150	+	78.3444i	−0.0768600	+	0.211171i
$372$	−74.5552	+	129.133i	−0.200417	+	0.347133i
$373$	−614.242	+	354.633i	−1.64676	+	0.950757i	−0.668412	+	0.743791i	$0.733026\pi$
$373$	−614.242	+	354.633i	−1.64676	+	0.950757i	−0.978348	+	0.206966i	$0.933641\pi$
$374$	−586.714	+	103.454i	−1.56875	+	0.276614i
$375$	46.1450	−	54.9935i	0.123053	−	0.146649i
$376$	100.704	+	120.014i	0.267830	+	0.319187i
$377$	−8.55514	+	48.5186i	−0.0226927	+	0.128697i
$378$	124.815	−	45.4291i	0.330199	−	0.120183i
$379$		−	36.9284i		−	0.0974365i	−0.998813	−	0.0487183i	$-0.984486\pi$
$379$		−	36.9284i		−	0.0974365i	0.998813	−	0.0487183i	$-0.0155136\pi$
$380$	−14.5159	−	2.74122i	−0.0381996	−	0.00721373i
$381$	346.572			0.909639
$382$	53.0307	+	145.701i	0.138824	+	0.381415i
$383$	289.583	+	51.0612i	0.756090	+	0.133319i	0.538389	−	0.842696i	$-0.319033\pi$
$383$	289.583	+	51.0612i	0.756090	+	0.133319i	0.217701	+	0.976015i	$0.430144\pi$
$384$	32.1065	−	26.9405i	0.0836106	−	0.0701577i
$385$	28.7091	+	24.0898i	0.0745691	+	0.0625709i
$386$	−77.7194	−	440.769i	−0.201346	−	1.14189i
$387$	115.869	+	200.691i	0.299404	+	0.518582i
$388$	−211.143	−	121.904i	−0.544184	−	0.314185i
$389$	−29.3487	−	10.6820i	−0.0754464	−	0.0274602i	0.304021	−	0.952665i	$-0.401671\pi$
$389$	−29.3487	−	10.6820i	−0.0754464	−	0.0274602i	−0.379468	+	0.925205i	$0.623893\pi$
$390$	1.24862	−	3.43057i	0.00320160	−	0.00879633i
$391$	−546.777	+	947.046i	−1.39841	+	2.42211i
$392$	33.9288	−	19.5888i	0.0865531	−	0.0499715i
$393$	604.245	−	106.545i	1.53752	−	0.271106i
$394$	−168.563	+	200.886i	−0.427826	+	0.509863i
$395$	−37.3348	−	44.4939i	−0.0945185	−	0.112643i
$396$	26.6757	−	151.285i	0.0673629	−	0.382034i
$397$	−383.480	+	139.575i	−0.965945	+	0.351575i	−0.776361	−	0.630289i	$-0.782936\pi$
$397$	−383.480	+	139.575i	−0.965945	+	0.351575i	−0.189585	+	0.981864i	$0.560714\pi$
$398$		−	66.7754i		−	0.167777i
$399$	−67.4796	−	411.801i	−0.169122	−	1.03208i
$400$	−99.3955			−0.248489
$401$	−85.5142	−	234.948i	−0.213252	−	0.585906i	0.786235	−	0.617928i	$-0.212028\pi$
$401$	−85.5142	−	234.948i	−0.213252	−	0.585906i	−0.999487	+	0.0320219i	$0.989805\pi$
$402$	−192.074	−	33.8679i	−0.477796	−	0.0842484i
$403$	27.6351	−	23.1886i	0.0685735	−	0.0575400i
$404$	206.750	+	173.484i	0.511757	+	0.429415i
$405$	−6.83155	−	38.7436i	−0.0168680	−	0.0956633i
$406$	−115.221	−	199.569i	−0.283796	−	0.491550i
$407$	273.794	+	158.075i	0.672714	+	0.388391i
$408$	−255.083	−	92.8426i	−0.625203	−	0.227555i
$409$	226.429	−	622.110i	0.553617	−	1.52105i	−0.275118	−	0.961410i	$-0.588717\pi$
$409$	226.429	−	622.110i	0.553617	−	1.52105i	0.828735	−	0.559641i	$-0.189061\pi$
$410$	−5.19771	+	9.00270i	−0.0126773	+	0.0219578i
$411$	422.016	−	243.651i	1.02680	−	0.592826i
$412$	210.055	−	37.0384i	0.509843	−	0.0898991i
$413$	84.4654	−	100.662i	0.204517	−	0.243733i
$414$	−181.250	−	216.006i	−0.437802	−	0.521753i
$415$	−3.92462	+	22.2576i	−0.00945691	+	0.0536328i
$416$	−9.52849	+	3.46809i	−0.0229050	+	0.00833674i
$417$		−	438.267i		−	1.05100i
$418$	408.740	+	154.401i	0.977847	+	0.369380i
$419$	587.978			1.40329			0.701645	−	0.712527i	$-0.252449\pi$
$419$	587.978			1.40329			0.701645	+	0.712527i	$0.252449\pi$
$420$	5.84034	+	16.0462i	0.0139056	+	0.0382052i
$421$	−641.015	−	113.028i	−1.52260	−	0.268476i	−0.651147	−	0.758952i	$-0.725712\pi$
$421$	−641.015	−	113.028i	−1.52260	−	0.268476i	−0.871455	+	0.490476i	$0.836823\pi$
$422$	264.554	−	221.987i	0.626905	−	0.526036i
$423$	200.429	+	168.180i	0.473828	+	0.397589i
$424$	−6.90690	−	39.1710i	−0.0162899	−	0.0923844i
$425$	321.880	+	557.512i	0.757364	+	1.31179i
$426$	143.583	+	82.8975i	0.337048	+	0.194595i
$427$	79.4560	+	28.9196i	0.186080	+	0.0677274i
$428$	−5.14599	+	14.1385i	−0.0120233	+	0.0330338i
$429$	−53.9896	+	93.5128i	−0.125850	+	0.217979i
$430$	23.3582	−	13.4859i	0.0543215	−	0.0313625i
$431$	−216.189	+	38.1199i	−0.501599	+	0.0884453i	−0.418722	−	0.908114i	$-0.637522\pi$
$431$	−216.189	+	38.1199i	−0.501599	+	0.0884453i	−0.0828765	+	0.996560i	$0.526411\pi$
$432$	−40.7325	+	48.5431i	−0.0942881	+	0.112368i
$433$	178.919	+	213.227i	0.413207	+	0.492441i	0.932000	−	0.362459i	$-0.118063\pi$
$433$	178.919	+	213.227i	0.413207	+	0.492441i	−0.518793	+	0.854900i	$0.673618\pi$
$434$	−29.3011	+	166.175i	−0.0675140	+	0.382891i
$435$	−37.1947	+	13.5378i	−0.0855052	+	0.0311213i
$436$		−	28.8425i		−	0.0661526i
$437$	699.363	−	392.561i	1.60037	−	0.898309i
$438$	391.092			0.892904
$439$	−126.632	−	347.918i	−0.288455	−	0.792525i	−0.996283	−	0.0861396i	$-0.972547\pi$
$439$	−126.632	−	347.918i	−0.288455	−	0.792525i	0.707828	−	0.706385i	$-0.249675\pi$
$440$	−17.6079	−	3.10475i	−0.0400180	−	0.00705625i
$441$	50.1209	−	42.0565i	0.113653	−	0.0953661i
$442$	50.3094	+	42.2146i	0.113822	+	0.0955081i
$443$	−97.2235	−	551.382i	−0.219466	−	1.24465i	−0.872986	−	0.487745i	$-0.837820\pi$
$443$	−97.2235	−	551.382i	−0.219466	−	1.24465i	0.653520	−	0.756909i	$-0.273292\pi$
$444$	72.0252	+	124.751i	0.162219	+	0.280971i
$445$	−31.4105	−	18.1349i	−0.0705854	−	0.0407525i
$446$	−333.301	−	121.312i	−0.747311	−	0.271999i
$447$	−163.820	+	450.092i	−0.366488	+	1.00692i
$448$	23.7145	−	41.0747i	0.0529342	−	0.0916847i
$449$	−127.703	+	73.7296i	−0.284417	+	0.164208i	−0.635422	−	0.772165i	$-0.719174\pi$
$449$	−127.703	+	73.7296i	−0.284417	+	0.164208i	0.351004	+	0.936374i	$0.385840\pi$
$450$	−163.473	+	28.8247i	−0.363273	+	0.0640548i
$451$	197.638	−	235.536i	0.438221	−	0.522252i
$452$	−181.896	−	216.775i	−0.402425	−	0.479591i
$453$	−185.729	+	1053.32i	−0.409997	+	2.32521i
$454$	−1.18511	+	0.431343i	−0.00261037	+	0.000950095i
$455$		−	4.13129i		−	0.00907975i
$456$	126.111	+	154.045i	0.276559	+	0.337817i
$457$	−448.874			−0.982219			−0.491110	−	0.871098i	$-0.663409\pi$
$457$	−448.874			−0.982219			−0.491110	+	0.871098i	$0.663409\pi$
$458$	−140.129	−	385.002i	−0.305959	−	0.840615i
$459$	404.186	+	71.2689i	0.880580	+	0.155270i
$460$	−25.1406	+	21.0955i	−0.0546535	+	0.0458597i
$461$	−93.2749	−	78.2670i	−0.202332	−	0.169776i	0.535992	−	0.844223i	$-0.319938\pi$
$461$	−93.2749	−	78.2670i	−0.202332	−	0.169776i	−0.738324	+	0.674447i	$0.764382\pi$
$462$	−87.7034	−	497.391i	−0.189834	−	1.07660i
$463$	309.579	+	536.206i	0.668636	+	1.15811i	0.978286	+	0.207261i	$0.0664551\pi$
$463$	309.579	+	536.206i	0.668636	+	1.15811i	−0.309649	+	0.950851i	$0.600212\pi$
$464$	95.2104	+	54.9697i	0.205195	+	0.118469i
$465$	27.2353	+	9.91284i	0.0585705	+	0.0213179i
$466$	−121.685	+	334.326i	−0.261126	+	0.717438i
$467$	161.988	−	280.572i	0.346870	−	0.600796i	−0.638822	−	0.769355i	$-0.720578\pi$
$467$	161.988	−	280.572i	0.346870	−	0.600796i	0.985692	+	0.168558i	$0.0539112\pi$
$468$	−14.6655	+	8.46711i	−0.0313365	+	0.0180921i
$469$	−217.357	+	38.3259i	−0.463448	+	0.0817184i
$470$	19.5743	−	23.3277i	0.0416474	−	0.0496334i
$471$	276.701	+	329.760i	0.587476	+	0.700127i
$472$	−10.8861	+	61.7381i	−0.0230638	+	0.130801i
$473$	−749.644	+	272.848i	−1.58487	+	0.576846i
$474$			782.757i			1.65139i
$475$	5.71821	−	472.094i	0.0120383	−	0.993882i
$476$	−307.186			−0.645348
$477$	−22.7192	−	62.4204i	−0.0476292	−	0.130860i
$478$	−291.302	−	51.3645i	−0.609419	−	0.107457i
$479$	56.2520	−	47.2011i	0.117436	−	0.0985408i	−0.582178	−	0.813061i	$-0.697799\pi$
$479$	56.2520	−	47.2011i	0.117436	−	0.0985408i	0.699615	+	0.714520i	$0.253355\pi$
$480$	−6.24067	−	5.23654i	−0.0130014	−	0.0109095i
$481$	−6.05179	−	34.3214i	−0.0125817	−	0.0713543i
$482$	35.6571	+	61.7599i	0.0739774	+	0.128133i
$483$	−802.865	−	463.534i	−1.66225	−	0.959698i
$484$	269.533	+	98.1019i	0.556886	+	0.202690i
$485$	−16.2083	+	44.5319i	−0.0334191	+	0.0918183i
$486$	−164.275	+	284.533i	−0.338015	+	0.585458i
$487$	−16.2303	+	9.37057i	−0.0333271	+	0.0192414i	−0.516571	−	0.856244i	$-0.672792\pi$
$487$	−16.2303	+	9.37057i	−0.0333271	+	0.0192414i	0.483244	+	0.875486i	$0.339458\pi$
$488$	−39.7267	+	7.00490i	−0.0814073	+	0.0143543i
$489$	−430.558	+	513.119i	−0.880487	+	1.04932i
$490$	−4.89490	−	5.83351i	−0.00998959	−	0.0119051i
$491$	−58.4551	+	331.515i	−0.119053	+	0.675184i	0.865610	+	0.500718i	$0.166931\pi$
$491$	−58.4551	+	331.515i	−0.119053	+	0.675184i	−0.984663	+	0.174465i	$0.944180\pi$
$492$	131.646	−	47.9153i	0.267574	−	0.0973889i
$493$		−	712.050i		−	1.44432i
$494$	−15.9240	−	45.4565i	−0.0322349	−	0.0920172i
$495$	−29.8596			−0.0603224
$496$	−27.5331	−	75.6467i	−0.0555104	−	0.152513i
$497$	184.769	+	32.5797i	0.371768	+	0.0655527i
$498$	233.325	−	195.783i	0.468525	−	0.393139i
$499$	234.470	+	196.743i	0.469879	+	0.394275i	0.846750	−	0.531990i	$-0.178556\pi$
$499$	234.470	+	196.743i	0.469879	+	0.394275i	−0.376872	+	0.926266i	$0.623000\pi$
$500$	6.73014	+	38.1685i	0.0134603	+	0.0763370i
$501$	−388.953	−	673.686i	−0.776353	−	1.34468i
$502$	−56.4128	−	32.5699i	−0.112376	−	0.0648804i
$503$	466.415	+	169.761i	0.927267	+	0.337498i	0.761126	−	0.648604i	$-0.224647\pi$
$503$	466.415	+	169.761i	0.927267	+	0.337498i	0.166141	+	0.986102i	$0.446869\pi$
$504$	27.0909	−	74.4316i	0.0537517	−	0.147682i
$505$	26.2301	−	45.4318i	0.0519407	−	0.0899640i
$506$	840.645	−	485.347i	1.66135	−	0.959183i
$507$	−604.833	+	106.648i	−1.19296	+	0.210352i
$508$	−120.270	+	143.332i	−0.236752	+	0.282150i
$509$	277.084	+	330.215i	0.544369	+	0.648753i	0.966161	−	0.257939i	$-0.0830434\pi$
$509$	277.084	+	330.215i	0.544369	+	0.648753i	−0.421793	+	0.906692i	$0.638599\pi$
$510$	−9.16229	+	51.9619i	−0.0179653	+	0.101886i
$511$	415.882	−	151.369i	0.813859	−	0.296221i
$512$			22.6274i			0.0441942i
$513$	−228.219	−	196.258i	−0.444872	−	0.382569i
$514$	120.528			0.234491
$515$	−14.1799	−	38.9589i	−0.0275337	−	0.0756483i
$516$	−357.966	−	63.1190i	−0.693732	−	0.122324i
$517$	−689.973	+	578.956i	−1.33457	+	1.11984i
$518$	124.875	+	104.782i	0.241070	+	0.202282i
$519$	−154.963	−	878.840i	−0.298580	−	1.69333i
$520$	0.985477	+	1.70690i	0.00189515	+	0.00328249i
$521$	15.6249	+	9.02106i	0.0299903	+	0.0173149i	0.514920	−	0.857238i	$-0.327822\pi$
$521$	15.6249	+	9.02106i	0.0299903	+	0.0173149i	−0.484930	+	0.874553i	$0.661155\pi$
$522$	172.531	+	62.7961i	0.330519	+	0.120299i
$523$	43.7031	−	120.073i	0.0835624	−	0.229586i	−0.890874	−	0.454251i	$-0.849907\pi$
$523$	43.7031	−	120.073i	0.0835624	−	0.229586i	0.974436	+	0.224666i	$0.0721290\pi$
$524$	−165.626	+	286.872i	−0.316080	+	0.547466i
$525$	−472.634	+	272.876i	−0.900256	+	0.519763i
$526$	108.134	−	19.0670i	0.205579	−	0.0362490i
$527$	−335.142	+	399.406i	−0.635942	+	0.757887i
$528$	154.883	+	184.583i	0.293340	+	0.349589i
$529$	217.538	−	1233.72i	0.411226	−	2.33218i
$530$	−7.26503	+	2.64425i	−0.0137076	+	0.00498916i
$531$			104.696i			0.197167i
$532$	193.726	+	114.999i	0.364147	+	0.216163i
$533$	−33.8939			−0.0635909
$534$	167.177	+	459.315i	0.313066	+	0.860141i
$535$	2.88010	+	0.507838i	0.00538336	+	0.000949231i
$536$	80.6617	−	67.6832i	0.150488	−	0.126275i
$537$	25.2294	+	21.1700i	0.0469821	+	0.0394226i
$538$	78.1663	+	443.303i	0.145291	+	0.823984i
$539$	112.618	+	195.059i	0.208938	+	0.361891i
$540$	10.6670	+	6.15859i	0.0197537	+	0.0114048i
$541$	640.195	+	233.012i	1.18335	+	0.430706i	0.857386	−	0.514675i	$-0.172087\pi$
$541$	640.195	+	233.012i	1.18335	+	0.430706i	0.325969	+	0.945380i	$0.394309\pi$
$542$	54.1309	−	148.723i	0.0998725	−	0.274397i
$543$	250.395	−	433.696i	0.461132	−	0.798704i
$544$	126.918	−	73.2760i	0.233305	−	0.134699i
$545$	−5.52107	+	0.973514i	−0.0101304	+	0.00178626i
$546$	−35.7877	+	42.6501i	−0.0655452	+	0.0781137i
$547$	181.686	+	216.525i	0.332151	+	0.395842i	0.906110	−	0.423042i	$-0.139038\pi$
$547$	181.686	+	216.525i	0.332151	+	0.395842i	−0.573959	+	0.818884i	$0.694593\pi$
$548$	−45.6841	+	259.087i	−0.0833652	+	0.472787i
$549$	−63.3060	+	23.0415i	−0.115311	+	0.0419699i
$550$		−	571.433i		−	1.03897i
$551$	−266.565	+	449.054i	−0.483783	+	0.814980i
$552$	442.285			0.801242
$553$	302.959	+	832.373i	0.547846	+	1.50520i
$554$	−240.221	−	42.3574i	−0.433611	−	0.0764574i
$555$	21.4490	−	17.9978i	0.0386468	−	0.0324285i
$556$	181.255	+	152.091i	0.325997	+	0.273544i
$557$	−23.2813	−	132.035i	−0.0417977	−	0.237047i	0.956751	−	0.290909i	$-0.0939578\pi$
$557$	−23.2813	−	132.035i	−0.0417977	−	0.237047i	−0.998548	+	0.0538627i	$0.982847\pi$
$558$	−67.2204	−	116.429i	−0.120467	−	0.208655i
$559$	76.1587	+	43.9703i	0.136241	+	0.0786588i
$560$	−8.66300	−	3.15307i	−0.0154696	−	0.00563049i
$561$	533.760	−	1466.49i	0.951443	−	2.61407i
$562$	−6.52694	+	11.3050i	−0.0116138	+	0.0201157i
$563$	−65.0895	+	37.5795i	−0.115612	+	0.0667486i	−0.556691	−	0.830720i	$-0.687929\pi$
$563$	−65.0895	+	37.5795i	−0.115612	+	0.0667486i	0.441079	+	0.897468i	$0.354596\pi$
$564$	−404.157	+	71.2637i	−0.716590	+	0.126354i
$565$	−35.3558	+	42.1354i	−0.0625767	+	0.0745760i
$566$	−128.897	−	153.613i	−0.227733	−	0.271401i
$567$	−104.185	+	590.862i	−0.183748	+	1.04208i
$568$	−84.1111	+	30.6139i	−0.148083	+	0.0538978i
$569$			184.239i			0.323794i	0.986808	+	0.161897i	$0.0517612\pi$
$569$			184.239i			0.323794i	−0.986808	+	0.161897i	$0.948239\pi$
$570$	25.2308	−	29.3397i	0.0442645	−	0.0514732i
$571$	90.1138			0.157818			0.0789088	−	0.996882i	$-0.474856\pi$
$571$	90.1138			0.157818			0.0789088	+	0.996882i	$0.474856\pi$
$572$	−19.9383	−	54.7800i	−0.0348572	−	0.0957693i
$573$	−399.987	−	70.5285i	−0.698058	−	0.123086i
$574$	121.446	−	101.905i	0.211578	−	0.177535i
$575$	−803.497	−	674.214i	−1.39739	−	1.17255i
$576$	6.56194	+	37.2146i	0.0113923	+	0.0646087i
$577$	162.882	+	282.120i	0.282291	+	0.488943i	0.971949	−	0.235193i	$-0.0755722\pi$
$577$	162.882	+	282.120i	0.282291	+	0.488943i	−0.689657	+	0.724136i	$0.742239\pi$
$578$	−468.063	−	270.236i	−0.809797	−	0.467537i
$579$	1101.70	+	400.987i	1.90277	+	0.692550i
$580$	7.30876	−	20.0806i	0.0126013	−	0.0346218i
$581$	172.339	−	298.500i	0.296625	−	0.513769i
$582$	553.091	−	319.327i	0.950327	−	0.548672i
$583$	225.197	−	39.7083i	0.386273	−	0.0681104i
$584$	−135.720	+	161.744i	−0.232397	+	0.276960i
$585$	2.11578	+	2.52149i	0.00361672	+	0.00431024i
$586$	102.722	−	582.563i	0.175293	−	0.994135i
$587$	835.717	−	304.176i	1.42371	−	0.518188i	0.488587	−	0.872515i	$-0.337512\pi$
$587$	835.717	−	304.176i	1.42371	−	0.518188i	0.935121	+	0.354327i	$0.115290\pi$
$588$			102.626i			0.174534i
$589$	360.879	−	126.421i	0.612699	−	0.214637i
$590$	12.1854			0.0206532
$591$	−234.945	−	645.506i	−0.397538	−	1.09223i
$592$	−76.5882	−	13.5046i	−0.129372	−	0.0228118i
$593$	−267.026	+	224.062i	−0.450297	+	0.377844i	−0.839546	−	0.543288i	$-0.817179\pi$
$593$	−267.026	+	224.062i	−0.450297	+	0.377844i	0.389249	+	0.921133i	$0.372735\pi$
$594$	−279.078	−	234.174i	−0.469828	−	0.394233i
$595$	10.3683	+	58.8018i	0.0174258	+	0.0988266i
$596$	−129.295	−	223.945i	−0.216938	−	0.375747i
$597$	151.484	+	87.4592i	0.253742	+	0.146498i
$598$	−100.551	−	36.5977i	−0.168146	−	0.0612001i
$599$	−392.697	+	1078.93i	−0.655588	+	1.80121i	−0.0595953	+	0.998223i	$0.518981\pi$
$599$	−392.697	+	1078.93i	−0.655588	+	1.80121i	−0.595993	+	0.802990i	$0.703241\pi$
$600$	130.183	−	225.484i	0.216972	−	0.375807i
$601$	197.455	−	114.000i	0.328543	−	0.189685i	−0.326651	−	0.945145i	$-0.605920\pi$
$601$	197.455	−	114.000i	0.328543	−	0.189685i	0.655194	+	0.755460i	$0.272587\pi$
$602$	−405.085	+	71.4275i	−0.672899	+	0.118650i
$603$	113.034	−	134.708i	0.187452	−	0.223397i
$604$	−371.170	−	442.343i	−0.614519	−	0.732356i
$605$	9.68131	−	54.9055i	0.0160022	−	0.0907528i
$606$	−664.348	+	241.803i	−1.09628	+	0.399015i
$607$		−	1077.82i		−	1.77566i	−0.460174	−	0.887829i	$-0.652213\pi$
$607$		−	1077.82i		−	1.77566i	0.460174	−	0.887829i	$-0.347787\pi$
$608$	−107.472	−	1.30175i	−0.176764	−	0.00214104i
$609$	603.645			0.991207
$610$	2.68177	+	7.36810i	0.00439634	+	0.0120789i
$611$	97.7798	+	17.2412i	0.160032	+	0.0282180i
$612$	187.488	−	157.321i	0.306353	−	0.257060i
$613$	664.095	+	557.242i	1.08335	+	0.909041i	0.996195	−	0.0871532i	$-0.0277770\pi$
$613$	664.095	+	557.242i	1.08335	+	0.909041i	0.0871583	+	0.996194i	$0.472221\pi$
$614$	98.7789	+	560.203i	0.160878	+	0.912383i
$615$	−13.6154	−	23.5826i	−0.0221389	−	0.0383457i
$616$	236.142	+	136.337i	0.383347	+	0.221326i
$617$	−572.032	−	208.203i	−0.927119	−	0.337444i	−0.166052	−	0.986117i	$-0.553102\pi$
$617$	−572.032	−	208.203i	−0.927119	−	0.337444i	−0.761067	+	0.648673i	$0.775324\pi$
$618$	−191.096	+	525.033i	−0.309218	+	0.849568i
$619$	91.1210	−	157.826i	0.147207	−	0.254970i	−0.782987	−	0.622038i	$-0.786305\pi$
$619$	91.1210	−	157.826i	0.147207	−	0.254970i	0.930194	+	0.367068i	$0.119638\pi$
$620$	−13.5511	+	7.82370i	−0.0218565	+	0.0126189i
$621$	−658.549	+	116.120i	−1.06047	+	0.186989i
$622$	3.50700	−	4.17948i	0.00563826	−	0.00671942i
$623$	355.548	+	423.725i	0.570702	+	0.680137i
$624$	4.61240	−	26.1582i	0.00739167	−	0.0419202i
$625$	−576.679	+	209.894i	−0.922686	+	0.335830i
$626$		−	478.251i		−	0.763979i
$627$	−885.614	+	725.023i	−1.41246	+	1.15634i
$628$	−232.402			−0.370067
$629$	172.274	+	473.318i	0.273885	+	0.752493i
$630$	−15.1622	−	2.67350i	−0.0240669	−	0.00424365i
$631$	205.728	−	172.626i	0.326035	−	0.273576i	−0.465047	−	0.885286i	$-0.653963\pi$
$631$	205.728	−	172.626i	0.326035	−	0.273576i	0.791082	+	0.611710i	$0.209518\pi$
$632$	−323.726	−	271.638i	−0.512224	−	0.429807i
$633$	157.090	+	890.904i	0.248168	+	1.40743i
$634$	−7.55156	−	13.0797i	−0.0119110	−	0.0206304i
$635$	31.4963	+	18.1844i	0.0496004	+	0.0286368i
$636$	97.9079	+	35.6356i	0.153943	+	0.0560308i
$637$	8.49196	−	23.3315i	0.0133312	−	0.0366271i
$638$	−316.025	+	547.372i	−0.495338	+	0.857950i
$639$	−129.457	+	74.7420i	−0.202593	+	0.116967i
$640$	4.33136	−	0.763736i	0.00676776	−	0.00119334i
$641$	−786.917	+	937.811i	−1.22764	+	1.46304i	−0.386443	+	0.922313i	$0.626296\pi$
$641$	−786.917	+	937.811i	−1.22764	+	1.46304i	−0.841196	+	0.540730i	$0.818148\pi$
$642$	−25.3340	−	30.1919i	−0.0394610	−	0.0470278i
$643$	−73.9991	+	419.670i	−0.115084	+	0.652675i	0.871624	+	0.490174i	$0.163067\pi$
$643$	−73.9991	+	419.670i	−0.115084	+	0.652675i	−0.986709	+	0.162500i	$0.948044\pi$
$644$	470.320	−	171.183i	0.730311	−	0.265811i
$645$			70.6526i			0.109539i
$646$	340.734	+	607.031i	0.527452	+	0.939676i
$647$	546.821			0.845163			0.422582	−	0.906325i	$-0.361124\pi$
$647$	546.821			0.845163			0.422582	+	0.906325i	$0.361124\pi$
$648$	−97.8988	−	268.975i	−0.151078	−	0.415084i
$649$	−354.937	−	62.5850i	−0.546899	−	0.0964330i
$650$	−48.2546	+	40.4904i	−0.0742379	+	0.0622930i
$651$	−338.599	−	284.119i	−0.520122	−	0.436434i
$652$	−62.7958	−	356.133i	−0.0963126	−	0.546216i
$653$	−485.458	−	840.838i	−0.743428	−	1.28765i	−0.950926	−	0.309419i	$-0.899865\pi$
$653$	−485.458	−	840.838i	−0.743428	−	1.28765i	0.207498	−	0.978235i	$-0.433468\pi$
$654$	65.4309	+	37.7766i	0.100047	+	0.0577623i
$655$	60.5037	+	22.0215i	0.0923720	+	0.0336207i
$656$	−25.8685	+	71.0730i	−0.0394336	+	0.108343i
$657$	−176.308	+	305.375i	−0.268353	+	0.464802i
$658$	−402.193	+	232.206i	−0.611235	+	0.352897i
$659$	57.2312	−	10.0914i	0.0868456	−	0.0153132i	−0.130056	−	0.991507i	$-0.541516\pi$
$659$	57.2312	−	10.0914i	0.0868456	−	0.0153132i	0.216902	+	0.976193i	$0.430405\pi$
$660$	30.1053	−	35.8781i	0.0456141	−	0.0543608i
$661$	−675.405	−	804.917i	−1.02179	−	1.21773i	−0.975773	−	0.218786i	$-0.929790\pi$
$661$	−675.405	−	804.917i	−1.02179	−	1.21773i	−0.0460205	−	0.998940i	$-0.514654\pi$
$662$	−42.0826	+	238.662i	−0.0635689	+	0.360517i
$663$	−161.659	+	58.8390i	−0.243829	+	0.0887466i
$664$			164.439i			0.247649i
$665$	15.4744	−	40.9648i	0.0232697	−	0.0616012i
$666$	−129.879			−0.195013
$667$	396.798	+	1090.19i	0.594899	+	1.63447i
$668$	413.594	+	72.9279i	0.619153	+	0.109173i
$669$	711.743	−	597.223i	1.06389	−	0.892710i
$670$	−15.6785	−	13.1559i	−0.0234008	−	0.0196356i
$671$	−40.2717	−	228.392i	−0.0600175	−	0.340376i
$672$	62.1202	+	107.595i	0.0924408	+	0.160112i
$673$	−561.669	−	324.280i	−0.834576	−	0.481842i	0.0208412	−	0.999783i	$-0.493366\pi$
$673$	−561.669	−	324.280i	−0.834576	−	0.481842i	−0.855417	+	0.517940i	$0.826699\pi$
$674$	6.64526	+	2.41868i	0.00985944	+	0.00358854i
$675$	−134.639	+	369.918i	−0.199466	+	0.548027i
$676$	165.787	−	287.151i	0.245247	−	0.424780i
$677$	−291.669	+	168.395i	−0.430826	+	0.248737i	−0.699698	−	0.714438i	$-0.746682\pi$
$677$	−291.669	+	168.395i	−0.430826	+	0.248737i	0.268873	+	0.963176i	$0.413349\pi$
$678$	730.005	−	128.720i	1.07670	−	0.189852i
$679$	464.556	−	553.637i	0.684177	−	0.815371i
$680$	−18.3104	−	21.8215i	−0.0269270	−	0.0320904i
$681$	0.573668	−	3.25343i	0.000842390	−	0.00477743i
$682$	434.899	−	158.290i	0.637682	−	0.232097i
$683$		−	914.053i		−	1.33829i	−0.743131	−	0.669146i	$-0.766660\pi$
$683$		−	914.053i		−	1.33829i	0.743131	−	0.669146i	$-0.233340\pi$
$684$	−177.134	+	29.0260i	−0.258968	+	0.0424357i
$685$	51.1368			0.0746522
$686$	180.234	+	495.188i	0.262731	+	0.721848i
$687$	1056.93	+	186.366i	1.53847	+	0.271275i
$688$	150.328	−	126.140i	0.218500	−	0.183343i
$689$	−19.3101	−	16.2031i	−0.0280263	−	0.0235169i
$690$	−14.9283	−	84.6627i	−0.0216353	−	0.122700i
$691$	−112.767	−	195.319i	−0.163195	−	0.282661i	0.772818	−	0.634628i	$-0.218846\pi$
$691$	−112.767	−	195.319i	−0.163195	−	0.282661i	−0.936013	+	0.351966i	$0.885513\pi$
$692$	417.239	+	240.893i	0.602947	+	0.348111i
$693$	427.913	+	155.748i	0.617479	+	0.224744i
$694$	20.4251	−	56.1174i	0.0294309	−	0.0808608i
$695$	22.9955	−	39.8294i	0.0330871	−	0.0573085i
$696$	−249.404	+	143.993i	−0.358339	+	0.206887i
$697$	482.422	−	85.0641i	0.692141	−	0.122043i
$698$	124.588	−	148.479i	0.178493	−	0.212720i
$699$	−599.061	−	713.933i	−0.857025	−	1.02136i
$700$	51.1636	−	290.163i	0.0730909	−	0.414519i
$701$	597.024	−	217.299i	0.851674	−	0.309984i	0.120951	−	0.992658i	$-0.461405\pi$
$701$	597.024	−	217.299i	0.851674	−	0.309984i	0.730723	+	0.682674i	$0.239183\pi$
$702$			40.1598i			0.0572077i
$703$	68.5481	−	362.991i	0.0975080	−	0.516345i
$704$	−130.087			−0.184782
$705$	27.2828	+	74.9588i	0.0386990	+	0.106325i
$706$	−501.234	−	88.3811i	−0.709964	−	0.125186i
$707$	−612.871	+	514.260i	−0.866862	+	0.727383i
$708$	−125.798	−	105.557i	−0.177681	−	0.149092i
$709$	119.189	+	675.954i	0.168108	+	0.953390i	0.945801	+	0.324746i	$0.105279\pi$
$709$	119.189	+	675.954i	0.168108	+	0.953390i	−0.777693	+	0.628644i	$0.783610\pi$
$710$	8.69913	+	15.0673i	0.0122523	+	0.0212216i
$711$	−611.196	−	352.874i	−0.859629	−	0.496307i
$712$	−247.974	−	90.2553i	−0.348279	−	0.126763i
$713$	290.549	−	798.277i	0.407502	−	1.11960i
$714$	402.337	−	696.868i	0.563497	−	0.976005i
$715$	−9.81308	+	5.66558i	−0.0137246	+	0.00792389i
$716$	−17.5106	+	3.08758i	−0.0244561	+	0.00431227i
$717$	498.057	−	593.561i	0.694640	−	0.827840i
$718$	311.943	+	371.760i	0.434462	+	0.517771i
$719$	146.800	−	832.545i	0.204173	−	1.15792i	−0.694564	−	0.719431i	$-0.744402\pi$
$719$	146.800	−	832.545i	0.204173	−	1.15792i	0.898736	−	0.438490i	$-0.144486\pi$
$720$	6.90218	−	2.51219i	0.00958636	−	0.00348915i
$721$			632.275i			0.876942i
$722$	12.3657	−	510.381i	0.0171271	−	0.706899i
$723$	−186.808			−0.258379
$724$	92.4704	+	254.060i	0.127722	+	0.350912i
$725$	672.592	+	118.596i	0.927713	+	0.163581i
$726$	−575.571	+	482.961i	−0.792797	+	0.665236i
$727$	697.047	+	584.892i	0.958799	+	0.804528i	0.980757	−	0.195231i	$-0.0625457\pi$
$727$	697.047	+	584.892i	0.958799	+	0.804528i	−0.0219584	+	0.999759i	$0.506990\pi$
$728$	−5.21954	−	29.6015i	−0.00716970	−	0.0406614i
$729$	25.0810	+	43.4415i	0.0344046	+	0.0595905i
$730$	35.5422	+	20.5203i	0.0486879	+	0.0281100i
$731$	−1194.34	−	434.705i	−1.63385	−	0.594671i
$732$	36.1412	−	99.2970i	0.0493732	−	0.135652i
$733$	99.4128	−	172.188i	0.135625	−	0.234909i	−0.790211	−	0.612834i	$-0.790029\pi$
$733$	99.4128	−	172.188i	0.135625	−	0.234909i	0.925836	+	0.377926i	$0.123363\pi$
$734$	−220.392	+	127.244i	−0.300262	+	0.173356i
$735$	19.6448	−	3.46390i	0.0267276	−	0.00471279i
$736$	−153.485	+	182.916i	−0.208540	+	0.248528i
$737$	389.116	+	463.731i	0.527973	+	0.629214i
$738$	−21.9339	+	124.394i	−0.0297208	+	0.168555i
$739$	−570.980	+	207.820i	−0.772639	+	0.281218i	−0.698100	−	0.716000i	$-0.745971\pi$
$739$	−570.980	+	207.820i	−0.772639	+	0.281218i	−0.0745393	+	0.997218i	$0.523749\pi$
$740$			15.1164i			0.0204276i
$741$	123.977	+	23.4122i	0.167311	+	0.0315954i
$742$	117.906			0.158903
$743$	−470.492	−	1292.66i	−0.633232	−	1.73979i	−0.672008	−	0.740543i	$-0.734568\pi$
$743$	−470.492	−	1292.66i	−0.633232	−	1.73979i	0.0387762	−	0.999248i	$-0.487654\pi$
$744$	207.670	+	36.6179i	0.279127	+	0.0492176i
$745$	−38.5038	+	32.3085i	−0.0516829	+	0.0433671i
$746$	768.383	+	644.750i	1.03000	+	0.864275i
$747$	47.6872	+	270.447i	0.0638382	+	0.362045i
$748$	421.270	+	729.660i	0.563195	+	0.975482i
$749$	−38.6253	−	22.3003i	−0.0515692	−	0.0297735i
$750$	−95.4022	−	34.7236i	−0.127203	−	0.0462981i
$751$	−198.529	+	545.453i	−0.264352	+	0.726302i	0.734509	+	0.678599i	$0.237412\pi$
$751$	−198.529	+	545.453i	−0.264352	+	0.726302i	−0.998862	+	0.0477032i	$0.984810\pi$
$752$	110.781	−	191.878i	0.147315	−	0.255157i
$753$	147.773	−	85.3171i	0.196246	−	0.113303i
$754$	68.6157	−	12.0988i	0.0910022	−	0.0160461i
$755$	−72.1457	+	85.9799i	−0.0955573	+	0.113881i
$756$	−120.744	−	143.897i	−0.159714	−	0.190340i
$757$	160.240	−	908.768i	0.211678	−	1.20049i	−0.674901	−	0.737909i	$-0.735813\pi$
$757$	160.240	−	908.768i	0.211678	−	1.20049i	0.886579	−	0.462578i	$-0.153075\pi$
$758$	−49.0752	+	17.8619i	−0.0647430	+	0.0235645i
$759$			2542.73i			3.35011i
$760$	3.37830	+	20.6164i	0.00444513	+	0.0271269i
$761$	−514.855			−0.676550			−0.338275	−	0.941047i	$-0.609843\pi$
$761$	−514.855			−0.676550			−0.338275	+	0.941047i	$0.609843\pi$
$762$	−167.633	−	460.569i	−0.219991	−	0.604422i
$763$	84.1994	+	14.8466i	0.110353	+	0.0194582i
$764$	167.975	−	140.948i	0.219863	−	0.184487i
$765$	−36.4428	−	30.5791i	−0.0476376	−	0.0399727i
$766$	−72.2115	−	409.532i	−0.0942709	−	0.534637i
$767$	19.8651	+	34.4073i	0.0258997	+	0.0448596i
$768$	−51.3316	−	29.6363i	−0.0668380	−	0.0385889i
$769$	−728.967	−	265.322i	−0.947941	−	0.345022i	−0.178644	−	0.983914i	$-0.557171\pi$
$769$	−728.967	−	265.322i	−0.947941	−	0.345022i	−0.769297	+	0.638891i	$0.779393\pi$
$770$	18.1273	−	49.8043i	0.0235419	−	0.0646809i
$771$	−157.862	+	273.425i	−0.204750	+	0.354637i
$772$	−548.157	+	316.479i	−0.710048	+	0.409946i
$773$	1143.59	−	201.645i	1.47941	−	0.260860i	0.625069	−	0.780570i	$-0.285071\pi$
$773$	1143.59	−	201.645i	1.47941	−	0.260860i	0.854343	+	0.519710i	$0.173960\pi$
$774$	210.659	−	251.054i	0.272170	−	0.324359i
$775$	−321.454	−	383.094i	−0.414779	−	0.494314i
$776$	−59.8731	+	339.557i	−0.0771561	+	0.437574i
$777$	−401.259	+	146.046i	−0.516421	+	0.187962i
$778$			44.1690i			0.0567725i
$779$	−336.084	−	126.955i	−0.431430	−	0.162972i
$780$	−5.16292			−0.00661913
$781$	−176.002	−	483.561i	−0.225355	−	0.619157i
$782$	1523.02	+	268.550i	1.94760	+	0.343415i
$783$	333.550	−	279.882i	0.425990	−	0.357448i
$784$	−42.4431	−	35.6140i	−0.0541366	−	0.0454260i
$785$	7.84420	+	44.4866i	0.00999261	+	0.0566709i
$786$	−433.857	−	751.462i	−0.551981	−	0.956059i
$787$	1036.38	+	598.354i	1.31687	+	0.760297i	0.983224	−	0.182401i	$-0.0583868\pi$
$787$	1036.38	+	598.354i	1.31687	+	0.760297i	0.333649	+	0.942698i	$0.391720\pi$
$788$	348.495	+	126.842i	0.442252	+	0.160967i
$789$	−98.3745	+	270.282i	−0.124683	+	0.342562i
$790$	−41.0706	+	71.1364i	−0.0519881	+	0.0900461i
$791$	726.457	−	419.420i	0.918404	−	0.530241i
$792$	−213.950	+	37.7251i	−0.270139	+	0.0476327i
$793$	−16.4330	+	19.5841i	−0.0207226	+	0.0246962i
$794$	370.971	+	442.106i	0.467218	+	0.556808i
$795$	3.51674	−	19.9444i	0.00442358	−	0.0250873i
$796$	−88.7395	+	32.2986i	−0.111482	+	0.0405761i
$797$			461.365i			0.578877i	0.957197	+	0.289438i	$0.0934685\pi$
$797$			461.365i			0.578877i	−0.957197	+	0.289438i	$0.906532\pi$
$798$	−514.614	+	288.859i	−0.644880	+	0.361979i
$799$	−1435.00			−1.79599
$800$	48.0766	+	132.089i	0.0600957	+	0.165112i
$801$	−434.010	−	76.5277i	−0.541835	−	0.0955402i
$802$	−270.867	+	227.284i	−0.337739	+	0.283396i
$803$	−929.881	−	780.263i	−1.15801	−	0.971685i
$804$	47.8964	+	271.634i	0.0595726	+	0.337853i
$805$	−48.6425	−	84.2513i	−0.0604255	−	0.104660i
$806$	−44.1828	−	25.5089i	−0.0548173	−	0.0316488i
$807$	−1108.04	−	403.292i	−1.37303	−	0.499743i
$808$	130.544	−	358.667i	0.161565	−	0.443895i
$809$	105.585	−	182.878i	0.130513	−	0.226055i	−0.793362	−	0.608751i	$-0.791671\pi$
$809$	105.585	−	182.878i	0.130513	−	0.226055i	0.923874	+	0.382696i	$0.125004\pi$
$810$	−48.1831	+	27.8185i	−0.0594853	+	0.0343438i
$811$	−112.676	+	19.8677i	−0.138934	+	0.0244978i	−0.242683	−	0.970106i	$-0.578027\pi$
$811$	−112.676	+	19.8677i	−0.138934	+	0.0244978i	0.103749	+	0.994604i	$0.466916\pi$
$812$	−209.481	+	249.650i	−0.257982	+	0.307451i
$813$	266.489	+	317.590i	0.327785	+	0.390639i
$814$	77.6389	−	440.312i	0.0953795	−	0.540924i
$815$	−66.0518	+	24.0409i	−0.0810451	+	0.0294980i
$816$			383.893i			0.470458i
$817$	590.474	+	721.263i	0.722734	+	0.882818i
$818$	−936.260			−1.14457
$819$	−17.1688	−	47.1710i	−0.0209632	−	0.0575959i
$820$	14.4780	+	2.55286i	0.0176561	+	0.00311325i
$821$	579.086	−	485.910i	0.705342	−	0.591852i	−0.217946	−	0.975961i	$-0.569936\pi$
$821$	579.086	−	485.910i	0.705342	−	0.591852i	0.923288	+	0.384109i	$0.125491\pi$
$822$	−527.920	−	442.977i	−0.642238	−	0.538902i
$823$	80.5969	+	457.088i	0.0979307	+	0.555392i	0.993810	+	0.111095i	$0.0354357\pi$
$823$	80.5969	+	457.088i	0.0979307	+	0.555392i	−0.895879	+	0.444298i	$0.853453\pi$
$824$	−150.823	−	261.233i	−0.183037	−	0.317030i
$825$	1296.33	+	748.435i	1.57131	+	0.907194i
$826$	−174.627	−	63.5591i	−0.211413	−	0.0769481i
$827$	−451.994	+	1241.84i	−0.546546	+	1.50162i	0.291797	+	0.956480i	$0.405747\pi$
$827$	−451.994	+	1241.84i	−0.546546	+	1.50162i	−0.838343	+	0.545143i	$0.816475\pi$
$828$	−199.387	+	345.348i	−0.240805	+	0.417087i
$829$	−882.290	+	509.390i	−1.06428	+	0.614464i	−0.926614	−	0.376015i	$-0.877294\pi$
$829$	−882.290	+	509.390i	−1.06428	+	0.614464i	−0.137669	+	0.990478i	$0.543961\pi$
$830$	31.4770	−	5.55025i	0.0379241	−	0.00668705i
$831$	410.720	−	489.477i	0.494247	−	0.589021i
$832$	9.21766	+	10.9852i	0.0110789	+	0.0132033i
$833$	−62.3132	+	353.396i	−0.0748058	+	0.424245i
$834$	−582.424	+	211.985i	−0.698351	+	0.254179i
$835$		−	81.6322i		−	0.0977631i
$836$	7.48388	−	617.867i	0.00895201	−	0.739076i
$837$	−318.829			−0.380918
$838$	−284.399	−	781.379i	−0.339378	−	0.932434i
$839$	−495.619	−	87.3910i	−0.590726	−	0.104161i	−0.129709	−	0.991552i	$-0.541404\pi$
$839$	−495.619	−	87.3910i	−0.590726	−	0.104161i	−0.461017	+	0.887391i	$0.652515\pi$
$840$	18.4993	−	15.5228i	0.0220230	−	0.0184795i
$841$	65.5595	+	55.0110i	0.0779543	+	0.0654114i
$842$	159.846	+	906.533i	0.189841	+	1.07664i
$843$	−17.0973	−	29.6135i	−0.0202815	−	0.0351287i
$844$	−422.967	−	244.200i	−0.501145	−	0.289336i
$845$	−60.5626	−	22.0430i	−0.0716717	−	0.0260864i
$846$	126.553	−	347.702i	0.149590	−	0.410996i
$847$	−425.128	+	736.344i	−0.501922	+	0.869355i
$848$	−48.7146	+	28.1254i	−0.0574464	+	0.0331667i
$849$	517.302	−	91.2143i	0.609308	−	0.107437i
$850$	585.202	−	697.417i	0.688473	−	0.820491i
$851$	−527.524	−	628.678i	−0.619887	−	0.738752i
$852$	40.7152	−	230.907i	0.0477878	−	0.271018i
$853$	805.856	−	293.307i	0.944731	−	0.343854i	0.176699	−	0.984265i	$-0.443458\pi$
$853$	805.856	−	293.307i	0.944731	−	0.343854i	0.768032	+	0.640411i	$0.221236\pi$
$854$		−	119.579i		−	0.140022i
$855$	11.5349	+	32.9275i	0.0134912	+	0.0385117i
$856$	21.2781			0.0248576
$857$	−166.727	−	458.079i	−0.194547	−	0.534514i	0.803612	−	0.595153i	$-0.202909\pi$
$857$	−166.727	−	458.079i	−0.194547	−	0.534514i	−0.998160	+	0.0606385i	$0.980686\pi$
$858$	150.386	+	26.5171i	0.175275	+	0.0309057i
$859$	−29.8375	+	25.0366i	−0.0347351	+	0.0291462i	−0.659990	−	0.751274i	$-0.729439\pi$
$859$	−29.8375	+	25.0366i	−0.0347351	+	0.0291462i	0.625255	+	0.780421i	$0.284995\pi$
$860$	−29.2199	−	24.5184i	−0.0339766	−	0.0285097i
$861$	72.1136	+	408.977i	0.0837557	+	0.475002i
$862$	155.227	+	268.861i	0.180078	+	0.311904i
$863$	107.887	+	62.2886i	0.125014	+	0.0721768i	0.561203	−	0.827678i	$-0.310339\pi$
$863$	107.887	+	62.2886i	0.125014	+	0.0721768i	−0.436189	+	0.899855i	$0.643672\pi$
$864$	84.2120	+	30.6507i	0.0974676	+	0.0354753i
$865$	32.0291	−	87.9991i	0.0370278	−	0.101733i
$866$	196.822	−	340.905i	0.227277	−	0.393655i
$867$	1226.09	−	707.884i	1.41418	−	0.816476i
$868$	235.006	−	41.4380i	0.270745	−	0.0477396i
$869$	1561.67	−	1861.12i	1.79709	−	2.14168i
$870$	35.9814	+	42.8810i	0.0413580	+	0.0492885i
$871$	11.5878	−	65.7178i	0.0133040	−	0.0754510i
$872$	−38.3296	+	13.9508i	−0.0439560	+	0.0159987i
$873$			575.823i			0.659591i
$874$	−859.959	−	739.524i	−0.983935	−	0.846137i
$875$	−114.889			−0.131302
$876$	−189.167	−	519.733i	−0.215944	−	0.593302i
$877$	−90.8962	−	16.0275i	−0.103644	−	0.0182753i	0.121585	−	0.992581i	$-0.461202\pi$
$877$	−90.8962	−	16.0275i	−0.103644	−	0.0182753i	−0.225230	+	0.974306i	$0.572313\pi$
$878$	−401.107	+	336.569i	−0.456842	+	0.383336i
$879$	1187.04	+	996.043i	1.35044	+	1.13315i
$880$	4.39078	+	24.9014i	0.00498952	+	0.0282970i
$881$	749.201	+	1297.65i	0.850398	+	1.47293i	0.880850	+	0.473396i	$0.156972\pi$
$881$	749.201	+	1297.65i	0.850398	+	1.47293i	−0.0304516	+	0.999536i	$0.509695\pi$
$882$	−80.1329	−	46.2648i	−0.0908536	−	0.0524544i
$883$	277.285	+	100.923i	0.314026	+	0.114296i	0.494225	−	0.869334i	$-0.335452\pi$
$883$	277.285	+	100.923i	0.314026	+	0.114296i	−0.180199	+	0.983630i	$0.557674\pi$
$884$	31.7659	−	87.2762i	0.0359343	−	0.0987287i
$885$	−15.9599	+	27.6433i	−0.0180337	+	0.0312354i
$886$	−685.720	+	395.900i	−0.773950	+	0.446840i
$887$	42.6298	−	7.51679i	0.0480607	−	0.00847439i	−0.149566	−	0.988752i	$-0.547788\pi$
$887$	42.6298	−	7.51679i	0.0480607	−	0.00847439i	0.197627	+	0.980277i	$0.436677\pi$
$888$	130.947	−	156.057i	0.147463	−	0.175740i
$889$	−356.518	−	424.882i	−0.401033	−	0.477933i
$890$	−8.90696	+	50.5139i	−0.0100078	+	0.0567572i
$891$	1546.36	−	562.828i	1.73553	−	0.631681i
$892$			501.609i			0.562342i
$893$	904.980	+	537.209i	1.01342	+	0.601578i
$894$	677.377			0.757692
$895$	1.18206	+	3.24768i	0.00132073	+	0.00362869i
$896$	−66.0557	−	11.6474i	−0.0737229	−	0.0129993i
$897$	214.721	−	180.172i	0.239377	−	0.200861i
$898$	159.750	+	134.046i	0.177895	+	0.149272i
$899$	96.0524	+	544.740i	0.106844	+	0.605940i
$900$	117.376	+	203.301i	0.130418	+	0.225890i
$901$	315.512	+	182.161i	0.350180	+	0.202176i
$902$	−408.605	−	148.720i	−0.452998	−	0.164878i
$903$	368.524	−	1012.51i	0.408111	−	1.12127i
$904$	−200.097	+	346.578i	−0.221346	+	0.383383i
$905$	45.5114	−	26.2760i	0.0502888	−	0.0290343i
$906$	1489.62	−	262.660i	1.64417	−	0.289912i
$907$	−480.494	+	572.630i	−0.529762	+	0.631346i	−0.962860	−	0.270001i	$-0.912976\pi$
$907$	−480.494	+	572.630i	−0.529762	+	0.631346i	0.433098	+	0.901347i	$0.357420\pi$
$908$	1.14645	+	1.36628i	0.00126261	+	0.00150472i
$909$	110.689	−	627.747i	0.121770	−	0.690591i
$910$	−5.49018	+	1.99826i	−0.00603316	+	0.00219589i
$911$			384.631i			0.422207i	0.977464	+	0.211104i	$0.0677058\pi$
$911$			384.631i			0.422207i	−0.977464	+	0.211104i	$0.932294\pi$
$912$	143.715	−	242.102i	0.157582	−	0.265463i
$913$	−945.371			−1.03546
$914$	217.116	+	596.521i	0.237545	+	0.652648i
$915$	−20.2274	−	3.56664i	−0.0221065	−	0.00389796i
$916$	−443.860	+	372.443i	−0.484563	+	0.406597i
$917$	−752.204	−	631.174i	−0.820288	−	0.688304i
$918$	−100.789	−	571.606i	−0.109792	−	0.622664i
$919$	−438.220	−	759.020i	−0.476845	−	0.825920i	0.522803	−	0.852453i	$-0.324886\pi$
$919$	−438.220	−	759.020i	−0.476845	−	0.825920i	−0.999648	+	0.0265340i	$0.991553\pi$
$920$	40.1946	+	23.2064i	0.0436898	+	0.0252243i
$921$	−1400.23	−	509.641i	−1.52033	−	0.553356i
$922$	−58.8949	+	161.812i	−0.0638773	+	0.175501i
$923$	−28.3632	+	49.1265i	−0.0307294	+	0.0532249i
$924$	−618.575	+	357.134i	−0.669453	+	0.386509i
$925$	−475.783	+	83.8934i	−0.514360	+	0.0906955i
$926$	562.838	−	670.764i	0.607817	−	0.724368i
$927$	−323.811	−	385.903i	−0.349311	−	0.416292i
$928$	26.9985	−	153.116i	0.0290932	−	0.164996i
$929$	−851.650	+	309.975i	−0.916739	+	0.333666i	−0.756940	−	0.653484i	$-0.773307\pi$
$929$	−851.650	+	309.975i	−0.916739	+	0.333666i	−0.159798	+	0.987150i	$0.551084\pi$
$930$		−	40.9884i		−	0.0440736i
$931$	171.596	−	199.541i	0.184313	−	0.214330i
$932$	503.152			0.539863
$933$	4.88808	+	13.4299i	0.00523910	+	0.0143943i
$934$	−451.211	−	79.5607i	−0.483096	−	0.0851828i
$935$	125.453	−	105.268i	0.134175	−	0.112586i
$936$	18.3457	+	15.3939i	0.0196001	+	0.0164464i
$937$	−144.397	−	818.914i	−0.154105	−	0.873974i	−0.959599	−	0.281370i	$-0.909211\pi$
$937$	−144.397	−	818.914i	−0.154105	−	0.873974i	0.805494	−	0.592604i	$-0.201900\pi$
$938$	156.066	+	270.314i	0.166381	+	0.288181i
$939$	1084.94	+	626.390i	1.15542	+	0.667082i
$940$	−40.4686	−	14.7294i	−0.0430517	−	0.0156696i
$941$	−474.163	+	1302.75i	−0.503892	+	1.38443i	0.383553	+	0.923519i	$0.374700\pi$
$941$	−474.163	+	1302.75i	−0.503892	+	1.38443i	−0.887445	+	0.460913i	$0.847522\pi$
$942$	304.389	−	527.217i	0.323130	−	0.559678i
$943$	−691.215	+	399.073i	−0.732996	+	0.423196i
$944$	87.3109	−	15.3953i	0.0924904	−	0.0163085i
$945$	−23.4695	+	27.9698i	−0.0248354	+	0.0295977i
$946$	725.190	+	864.248i	0.766586	+	0.913581i
$947$	2.34633	−	13.3067i	0.00247764	−	0.0140514i	−0.983544	−	0.180669i	$-0.942174\pi$
$947$	2.34633	−	13.3067i	0.00247764	−	0.0140514i	0.986022	+	0.166618i	$0.0532847\pi$
$948$	1040.23	−	378.611i	1.09728	−	0.399379i
$949$			133.811i			0.141003i
$950$	−630.144	+	220.748i	−0.663309	+	0.232366i
$951$	39.5627			0.0416011
$952$	148.582	+	408.227i	0.156074	+	0.428810i
$953$	−555.176	−	97.8925i	−0.582556	−	0.102720i	−0.125399	−	0.992106i	$-0.540021\pi$
$953$	−555.176	−	97.8925i	−0.582556	−	0.102720i	−0.457157	+	0.889386i	$0.651132\pi$
$954$	−71.9630	+	60.3841i	−0.0754329	+	0.0632957i
$955$	−32.6500	−	27.3966i	−0.0341885	−	0.0286875i
$956$	72.6403	+	411.964i	0.0759836	+	0.430925i
$957$	−827.830	−	1433.84i	−0.865026	−	1.49827i
$958$	−89.9352	−	51.9241i	−0.0938781	−	0.0542006i
$959$	−732.833	−	266.729i	−0.764163	−	0.278133i
$960$	−3.94043	+	10.8262i	−0.00410462	+	0.0112773i
$961$	−277.984	+	481.483i	−0.289266	+	0.501023i
$962$	−42.6834	+	24.6433i	−0.0443695	+	0.0256167i
$963$	34.9954	−	6.17063i	0.0363400	−	0.00640772i
$964$	64.8274	−	77.2582i	0.0672483	−	0.0801434i
$965$	79.0824	+	94.2468i	0.0819507	+	0.0976651i
$966$	−227.665	+	1291.15i	−0.235678	+	1.33660i
$967$	603.875	−	219.792i	0.624482	−	0.227293i	−0.0103456	−	0.999946i	$-0.503293\pi$
$967$	603.875	−	219.792i	0.624482	−	0.227293i	0.634828	+	0.772653i	$0.281071\pi$
$968$		−	405.640i		−	0.419050i
$969$	−1823.36	−	22.0853i	−1.88169	−	0.0227919i
$970$	67.0193			0.0690921
$971$	593.190	+	1629.78i	0.610906	+	1.67845i	0.728210	+	0.685354i	$0.240353\pi$
$971$	593.190	+	1629.78i	0.610906	+	1.67845i	−0.117304	+	0.993096i	$0.537425\pi$
$972$	457.581	+	80.6839i	0.470763	+	0.0830081i
$973$	−537.295	+	450.844i	−0.552205	+	0.463355i
$974$	20.3032	+	17.0364i	0.0208452	+	0.0174912i
$975$	−28.6533	−	162.501i	−0.0293880	−	0.166667i
$976$	28.5244	+	49.4057i	0.0292258	+	0.0506206i
$977$	−718.452	−	414.798i	−0.735365	−	0.424563i	0.0850166	−	0.996380i	$-0.472906\pi$
$977$	−718.452	−	414.798i	−0.735365	−	0.424563i	−0.820382	+	0.571816i	$0.806239\pi$
$978$	890.154	+	323.989i	0.910178	+	0.331278i
$979$	518.885	−	1425.63i	0.530015	−	1.45621i
$980$	−5.38470	+	9.32657i	−0.00549459	+	0.00951691i
$981$	−58.9938	+	34.0601i	−0.0601364	+	0.0347198i
$982$	468.833	−	82.6679i	0.477427	−	0.0841832i
$983$	−123.720	+	147.444i	−0.125860	+	0.149994i	−0.825294	−	0.564703i	$-0.808991\pi$
$983$	−123.720	+	147.444i	−0.125860	+	0.149994i	0.699435	+	0.714697i	$0.253435\pi$
$984$	−127.352	−	151.772i	−0.129423	−	0.154240i
$985$	12.5175	−	70.9905i	0.0127082	−	0.0720716i
$986$	−946.262	+	344.411i	−0.959698	+	0.349301i
$987$		−	1216.53i		−	1.23255i
$988$	−52.7061	+	43.1487i	−0.0533462	+	0.0436728i
$989$	2070.86			2.09389
$990$	14.4428	+	39.6812i	0.0145887	+	0.0400820i
$991$	1012.91	+	178.603i	1.02211	+	0.180225i	0.659491	−	0.751712i	$-0.270772\pi$
$991$	1012.91	+	178.603i	1.02211	+	0.180225i	0.362618	+	0.931938i	$0.381883\pi$
$992$	−87.2114	+	73.1790i	−0.0879147	+	0.0737692i
$993$	−486.301	−	408.055i	−0.489729	−	0.410931i
$994$	−46.0746	−	261.302i	−0.0463527	−	0.262879i
$995$	9.17782	+	15.8965i	0.00922394	+	0.0159763i
$996$	−373.038	−	215.374i	−0.374537	−	0.216239i
$997$	−1235.15	−	449.559i	−1.23887	−	0.450912i	−0.362244	−	0.932083i	$-0.617989\pi$
$997$	−1235.15	−	449.559i	−1.23887	−	0.450912i	−0.876627	+	0.481171i	$0.840211\pi$
$998$	148.047	−	406.755i	0.148344	−	0.407570i
$999$	−154.005	+	266.744i	−0.154159	+	0.267011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.3.f.a.33.2	yes	24
3.2	odd	2		342.3.z.b.109.3		24
4.3	odd	2		304.3.z.c.33.2		24
19.2	odd	18		722.3.b.f.721.4		24
19.15	odd	18	inner	38.3.f.a.15.2	✓	24
19.17	even	9		722.3.b.f.721.21		24
57.53	even	18		342.3.z.b.91.3		24
76.15	even	18		304.3.z.c.129.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.3.f.a.15.2	✓	24	19.15	odd	18	inner
38.3.f.a.33.2	yes	24	1.1	even	1	trivial
304.3.z.c.33.2		24	4.3	odd	2
304.3.z.c.129.2		24	76.15	even	18
342.3.z.b.91.3		24	57.53	even	18
342.3.z.b.109.3		24	3.2	odd	2
722.3.b.f.721.4		24	19.2	odd	18
722.3.b.f.721.21		24	19.17	even	9

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	38.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.483690 - 1.32893i) q^{2} +(3.64826 + 0.643286i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(0.297798 + 0.249882i) q^{5} +(-0.909744 - 5.15941i) q^{6} +(-2.96431 - 5.13434i) q^{7} +(2.44949 + 1.41421i) q^{8} +(4.43872 + 1.61556i) q^{9} +(0.188033 - 0.516617i) q^{10} +(-8.13043 + 14.0823i) q^{11} +(-6.41645 + 3.70454i) q^{12} +(1.76528 - 0.311267i) q^{13} +(-5.38935 + 6.42278i) q^{14} +(0.925699 + 1.10320i) q^{15} +(0.694593 - 3.93923i) q^{16} +(-24.3446 + 8.86071i) q^{17} -6.68017i q^{18} +(18.6700 + 3.52570i) q^{19} -0.777496 q^{20} +(-7.51173 - 20.6383i) q^{21} +(22.6470 + 3.99327i) q^{22} +(32.3354 - 27.1326i) q^{23} +(8.02662 + 6.73514i) q^{24} +(-4.31496 - 24.4714i) q^{25} +(-1.26750 - 2.19538i) q^{26} +(-13.7197 - 7.92106i) q^{27} +(11.1422 + 4.05542i) q^{28} +(-9.40038 + 25.8273i) q^{29} +(1.01833 - 1.76379i) q^{30} +(17.4291 - 10.0627i) q^{31} +(-5.57091 + 0.982302i) q^{32} +(-38.7208 + 46.1457i) q^{33} +(23.5505 + 28.0663i) q^{34} +(0.400214 - 2.26973i) q^{35} +(-8.87745 + 3.23113i) q^{36} -19.4424i q^{37} +(-4.34510 - 26.5164i) q^{38} +6.64044 q^{39} +(0.376067 + 1.03323i) q^{40} +(-18.6213 - 3.28344i) q^{41} +(-23.7934 + 19.9651i) q^{42} +(37.5820 + 31.5350i) q^{43} +(-5.64734 - 32.0276i) q^{44} +(0.918143 + 1.59027i) q^{45} +(-51.6975 - 29.8476i) q^{46} +(52.0500 + 18.9446i) q^{47} +(5.06810 - 13.9245i) q^{48} +(6.92569 - 11.9956i) q^{49} +(-30.4335 + 17.5708i) q^{50} +(-94.5153 + 16.6656i) q^{51} +(-2.30441 + 2.74629i) q^{52} +(-9.03932 - 10.7726i) q^{53} +(-3.89044 + 22.0638i) q^{54} +(-5.94015 + 2.16204i) q^{55} -16.7687i q^{56} +(65.8450 + 24.8728i) q^{57} +38.8695 q^{58} +(7.58069 + 20.8278i) q^{59} +(-2.83651 - 0.500152i) q^{60} +(-10.9255 + 9.16757i) q^{61} +(-21.8028 - 18.2948i) q^{62} +(-4.86291 - 27.5790i) q^{63} +(4.00000 + 6.92820i) q^{64} +(0.603479 + 0.348419i) q^{65} +(80.0531 + 29.1369i) q^{66} +(12.7327 - 34.9828i) q^{67} +(25.9070 - 44.8722i) q^{68} +(135.422 - 78.1858i) q^{69} +(-3.20988 + 0.565989i) q^{70} +(-20.3418 + 24.2424i) q^{71} +(8.58785 + 10.2346i) q^{72} +(-12.9628 + 73.5160i) q^{73} +(-25.8376 + 9.40410i) q^{74} -92.0536i q^{75} +(-33.1367 + 18.6000i) q^{76} +96.4045 q^{77} +(-3.21191 - 8.82466i) q^{78} +(-147.140 - 25.9447i) q^{79} +(1.19119 - 0.999530i) q^{80} +(-77.5237 - 65.0501i) q^{81} +(4.64349 + 26.3345i) q^{82} +(29.0689 + 50.3489i) q^{83} +(38.0407 + 21.9628i) q^{84} +(-9.46392 - 3.44458i) q^{85} +(23.7297 - 65.1969i) q^{86} +(-50.9094 + 88.1776i) q^{87} +(-39.8308 + 22.9963i) q^{88} +(-91.8814 + 16.2012i) q^{89} +(1.66926 - 1.98934i) q^{90} +(-6.83101 - 8.14088i) q^{91} +(-14.6597 + 83.1391i) q^{92} +(70.0590 - 25.4994i) q^{93} -78.3339i q^{94} +(4.67889 + 5.71526i) q^{95} -20.9560 q^{96} +(41.6935 + 114.552i) q^{97} +(-19.2912 - 3.40156i) q^{98} +(-58.8396 + 49.3723i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} + 12 q^{6} - 18 q^{7} + 6 q^{9} + 30 q^{11} - 36 q^{12} - 90 q^{13} - 48 q^{14} - 114 q^{15} + 18 q^{17} - 12 q^{19} + 24 q^{20} + 90 q^{21} + 84 q^{22} + 120 q^{23} - 24 q^{24} + 252 q^{25}+ \cdots - 204 q^{99}+O(q^{100}) \) 24 * q - 6 * q^3 + 12 * q^6 - 18 * q^7 + 6 * q^9 + 30 * q^11 - 36 * q^12 - 90 * q^13 - 48 * q^14 - 114 * q^15 + 18 * q^17 - 12 * q^19 + 24 * q^20 + 90 * q^21 + 84 * q^22 + 120 * q^23 - 24 * q^24 + 252 * q^25 + 48 * q^26 + 126 * q^27 + 72 * q^28 - 210 * q^29 - 108 * q^31 - 132 * q^33 - 24 * q^34 - 66 * q^35 - 12 * q^36 + 84 * q^38 + 120 * q^39 + 54 * q^41 + 72 * q^42 + 90 * q^43 - 48 * q^44 - 144 * q^45 - 360 * q^46 - 246 * q^47 - 48 * q^48 + 54 * q^49 - 432 * q^50 - 342 * q^51 + 36 * q^52 - 174 * q^53 - 42 * q^55 - 12 * q^57 + 48 * q^58 + 228 * q^59 + 132 * q^60 + 12 * q^61 + 204 * q^62 + 174 * q^63 + 96 * q^64 + 630 * q^65 + 696 * q^66 + 72 * q^67 - 48 * q^68 + 702 * q^69 + 528 * q^70 + 432 * q^71 + 96 * q^72 - 144 * q^74 + 72 * q^76 - 144 * q^77 - 708 * q^78 - 246 * q^79 - 642 * q^81 - 384 * q^82 - 126 * q^83 - 540 * q^84 - 684 * q^85 - 12 * q^86 - 324 * q^87 - 12 * q^89 - 336 * q^90 + 372 * q^91 - 132 * q^92 - 168 * q^93 - 570 * q^95 + 72 * q^97 + 384 * q^98 - 204 * q^99

Introduction

L-functions

Modular forms

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Database

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