LMFDB - Embedded newform 30.4.e.a.23.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [30,4,Mod(17,30)] 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("30.17"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	30.e (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.77005730017$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 1577x^{8} + 284056x^{4} + 810000 $ x^12 + 1577x^8 + 284056x^4 + 810000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.1
Root			$2.67233 + 2.67233i$ of defining polynomial
Character	$\chi$	$=$	30.23
Dual form			30.4.e.a.17.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41421 - 1.41421i) q^{2} +(-4.79094 + 2.01170i) q^{3} +4.00000i q^{4} +(-10.8454 + 2.71609i) q^{5} +(9.62038 + 3.93044i) q^{6} +(-16.1789 + 16.1789i) q^{7} +(5.65685 - 5.65685i) q^{8} +(18.9062 - 19.2758i) q^{9} +(19.1789 + 11.4966i) q^{10} -12.7562i q^{11} +(-8.04679 - 19.1637i) q^{12} +(-34.2057 - 34.2057i) q^{13} +45.7607 q^{14} +(46.4957 - 34.8303i) q^{15} -16.0000 q^{16} +(26.9917 + 26.9917i) q^{17} +(-53.9975 + 0.522794i) q^{18} +136.755i q^{19} +(-10.8644 - 43.3816i) q^{20} +(44.9649 - 110.059i) q^{21} +(-18.0400 + 18.0400i) q^{22} +(-72.2934 + 72.2934i) q^{23} +(-15.7218 + 38.4815i) q^{24} +(110.246 - 58.9143i) q^{25} +96.7483i q^{26} +(-51.8011 + 130.383i) q^{27} +(-64.7154 - 64.7154i) q^{28} -206.570 q^{29} +(-115.012 - 16.4974i) q^{30} +6.41137 q^{31} +(22.6274 + 22.6274i) q^{32} +(25.6616 + 61.1141i) q^{33} -76.3440i q^{34} +(131.523 - 219.410i) q^{35} +(77.1033 + 75.6246i) q^{36} +(148.178 - 148.178i) q^{37} +(193.401 - 193.401i) q^{38} +(232.689 + 95.0658i) q^{39} +(-45.9863 + 76.7154i) q^{40} +20.5652i q^{41} +(-219.237 + 92.0567i) q^{42} +(-162.284 - 162.284i) q^{43} +51.0248 q^{44} +(-152.690 + 260.405i) q^{45} +204.477 q^{46} +(191.575 + 191.575i) q^{47} +(76.6550 - 32.1871i) q^{48} -180.511i q^{49} +(-239.228 - 72.5935i) q^{50} +(-183.615 - 75.0164i) q^{51} +(136.823 - 136.823i) q^{52} +(12.0238 - 12.0238i) q^{53} +(257.647 - 111.131i) q^{54} +(34.6470 + 138.346i) q^{55} +183.043i q^{56} +(-275.110 - 655.187i) q^{57} +(292.134 + 292.134i) q^{58} -627.311 q^{59} +(139.321 + 185.983i) q^{60} -543.776 q^{61} +(-9.06704 - 9.06704i) q^{62} +(5.98086 + 617.741i) q^{63} -64.0000i q^{64} +(463.880 + 278.069i) q^{65} +(50.1375 - 122.719i) q^{66} +(-120.548 + 120.548i) q^{67} +(-107.967 + 107.967i) q^{68} +(200.921 - 491.786i) q^{69} +(-496.294 + 124.290i) q^{70} -149.269i q^{71} +(-2.09118 - 215.990i) q^{72} +(771.809 + 771.809i) q^{73} -419.112 q^{74} +(-409.662 + 504.035i) q^{75} -547.022 q^{76} +(206.381 + 206.381i) q^{77} +(-194.628 - 463.515i) q^{78} +97.9422i q^{79} +(173.526 - 43.4575i) q^{80} +(-14.1148 - 728.863i) q^{81} +(29.0836 - 29.0836i) q^{82} +(735.158 - 735.158i) q^{83} +(440.235 + 179.860i) q^{84} +(-366.048 - 219.424i) q^{85} +459.009i q^{86} +(989.662 - 415.556i) q^{87} +(-72.1599 - 72.1599i) q^{88} +492.823 q^{89} +(584.205 - 152.332i) q^{90} +1106.82 q^{91} +(-289.174 - 289.174i) q^{92} +(-30.7164 + 12.8977i) q^{93} -541.857i q^{94} +(-371.441 - 1483.17i) q^{95} +(-153.926 - 62.8870i) q^{96} +(-811.978 + 811.978i) q^{97} +(-255.281 + 255.281i) q^{98} +(-245.886 - 241.171i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{3} + 8 q^{6} + 12 q^{7} + 24 q^{10} - 32 q^{12} - 120 q^{13} - 172 q^{15} - 192 q^{16} - 16 q^{18} + 464 q^{21} + 312 q^{22} + 504 q^{25} - 688 q^{27} + 48 q^{28} + 168 q^{30} - 504 q^{31} + 788 q^{33}+ \cdots - 7596 q^{97}+O(q^{100}) $ 12 * q + 8 * q^3 + 8 * q^6 + 12 * q^7 + 24 * q^10 - 32 * q^12 - 120 * q^13 - 172 * q^15 - 192 * q^16 - 16 * q^18 + 464 * q^21 + 312 * q^22 + 504 * q^25 - 688 * q^27 + 48 * q^28 + 168 * q^30 - 504 * q^31 + 788 * q^33 + 368 * q^36 + 768 * q^37 - 192 * q^40 - 872 * q^42 - 1968 * q^43 - 1328 * q^45 - 1152 * q^46 - 128 * q^48 + 256 * q^51 + 480 * q^52 + 1572 * q^55 + 968 * q^57 + 2280 * q^58 + 896 * q^60 + 1848 * q^61 + 1268 * q^63 + 944 * q^66 - 1752 * q^67 - 2616 * q^70 + 64 * q^72 + 180 * q^73 - 1112 * q^75 - 1152 * q^76 - 4080 * q^78 - 4316 * q^81 + 2208 * q^82 - 1872 * q^85 + 3620 * q^87 + 1248 * q^88 + 5168 * q^90 + 4080 * q^91 + 584 * q^93 - 128 * q^96 - 7596 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−1.41421	−	1.41421i	−0.500000	−	0.500000i
$2$	−1.41421	−	1.41421i	−0.500000	−	0.500000i
$3$	−4.79094	+	2.01170i	−0.922016	+	0.387151i
$3$	−4.79094	+	2.01170i	−0.922016	+	0.387151i
$4$			4.00000i			0.500000i
$5$	−10.8454	+	2.71609i	−0.970043	+	0.242935i
$5$	−10.8454	+	2.71609i	−0.970043	+	0.242935i
$6$	9.62038	+	3.93044i	0.654584	+	0.267433i
$7$	−16.1789	+	16.1789i	−0.873576	+	0.873576i	−0.992860	−	0.119284i	$-0.961940\pi$
$7$	−16.1789	+	16.1789i	−0.873576	+	0.873576i	0.119284	+	0.992860i	$0.461940\pi$
$8$	5.65685	−	5.65685i	0.250000	−	0.250000i
$9$	18.9062	−	19.2758i	0.700228	−	0.713919i
$10$	19.1789	+	11.4966i	0.606489	+	0.363554i
$11$		−	12.7562i		−	0.349649i	−0.984600	−	0.174824i	$-0.944064\pi$
$11$		−	12.7562i		−	0.349649i	0.984600	−	0.174824i	$-0.0559358\pi$
$12$	−8.04679	−	19.1637i	−0.193576	−	0.461008i
$13$	−34.2057	−	34.2057i	−0.729765	−	0.729765i	0.240808	−	0.970573i	$-0.422588\pi$
$13$	−34.2057	−	34.2057i	−0.729765	−	0.729765i	−0.970573	+	0.240808i	$0.922588\pi$
$14$	45.7607			0.873576
$15$	46.4957	−	34.8303i	0.800343	−	0.599543i
$16$	−16.0000			−0.250000
$17$	26.9917	+	26.9917i	0.385085	+	0.385085i	0.872930	−	0.487845i	$-0.162217\pi$
$17$	26.9917	+	26.9917i	0.385085	+	0.385085i	−0.487845	+	0.872930i	$0.662217\pi$
$18$	−53.9975	+	0.522794i	−0.707074	+	0.00684577i
$19$			136.755i			1.65125i	0.564216	+	0.825627i	$0.309179\pi$
$19$			136.755i			1.65125i	−0.564216	+	0.825627i	$0.690821\pi$
$20$	−10.8644	−	43.3816i	−0.121467	−	0.485021i
$21$	44.9649	−	110.059i	0.467245	−	1.14366i
$22$	−18.0400	+	18.0400i	−0.174824	+	0.174824i
$23$	−72.2934	+	72.2934i	−0.655401	+	0.655401i	−0.954288	−	0.298887i	$-0.903384\pi$
$23$	−72.2934	+	72.2934i	−0.655401	+	0.655401i	0.298887	+	0.954288i	$0.403384\pi$
$24$	−15.7218	+	38.4815i	−0.133716	+	0.327292i
$25$	110.246	−	58.9143i	0.881965	−	0.471314i
$26$			96.7483i			0.729765i
$27$	−51.8011	+	130.383i	−0.369227	+	0.929339i
$28$	−64.7154	−	64.7154i	−0.436788	−	0.436788i
$29$	−206.570			−1.32272			−0.661362	−	0.750066i	$-0.730021\pi$
$29$	−206.570			−1.32272			−0.661362	+	0.750066i	$0.730021\pi$
$30$	−115.012	−	16.4974i	−0.699943	−	0.100400i
$31$	6.41137			0.0371457			0.0185728	−	0.999828i	$-0.494088\pi$
$31$	6.41137			0.0371457			0.0185728	+	0.999828i	$0.494088\pi$
$32$	22.6274	+	22.6274i	0.125000	+	0.125000i
$33$	25.6616	+	61.1141i	0.135367	+	0.322382i
$34$		−	76.3440i		−	0.385085i
$35$	131.523	−	219.410i	0.635184	−	1.05963i
$36$	77.1033	+	75.6246i	0.356960	+	0.350114i
$37$	148.178	−	148.178i	0.658388	−	0.658388i	−0.296610	−	0.954999i	$-0.595856\pi$
$37$	148.178	−	148.178i	0.658388	−	0.658388i	0.954999	+	0.296610i	$0.0958562\pi$
$38$	193.401	−	193.401i	0.825627	−	0.825627i
$39$	232.689	+	95.0658i	0.955385	+	0.390326i
$40$	−45.9863	+	76.7154i	−0.181777	+	0.303244i
$41$			20.5652i			0.0783354i	0.999233	+	0.0391677i	$0.0124706\pi$
$41$			20.5652i			0.0783354i	−0.999233	+	0.0391677i	$0.987529\pi$
$42$	−219.237	+	92.0567i	−0.805451	+	0.338206i
$43$	−162.284	−	162.284i	−0.575537	−	0.575537i	0.358133	−	0.933670i	$-0.383413\pi$
$43$	−162.284	−	162.284i	−0.575537	−	0.575537i	−0.933670	+	0.358133i	$0.883413\pi$
$44$	51.0248			0.174824
$45$	−152.690	+	260.405i	−0.505815	+	0.862642i
$46$	204.477			0.655401
$47$	191.575	+	191.575i	0.594556	+	0.594556i	0.938859	−	0.344303i	$-0.111885\pi$
$47$	191.575	+	191.575i	0.594556	+	0.594556i	−0.344303	+	0.938859i	$0.611885\pi$
$48$	76.6550	−	32.1871i	0.230504	−	0.0967878i
$49$		−	180.511i		−	0.526271i
$50$	−239.228	−	72.5935i	−0.676640	−	0.205326i
$51$	−183.615	−	75.0164i	−0.504141	−	0.205969i
$52$	136.823	−	136.823i	0.364883	−	0.364883i
$53$	12.0238	−	12.0238i	0.0311622	−	0.0311622i	−0.691354	−	0.722516i	$-0.742985\pi$
$53$	12.0238	−	12.0238i	0.0311622	−	0.0311622i	0.722516	+	0.691354i	$0.242985\pi$
$54$	257.647	−	111.131i	0.649283	−	0.280056i
$55$	34.6470	+	138.346i	0.0849419	+	0.339174i
$56$			183.043i			0.436788i
$57$	−275.110	−	655.187i	−0.639285	−	1.52248i
$58$	292.134	+	292.134i	0.661362	+	0.661362i
$59$	−627.311			−1.38422			−0.692110	−	0.721792i	$-0.743319\pi$
$59$	−627.311			−1.38422			−0.692110	+	0.721792i	$0.743319\pi$
$60$	139.321	+	185.983i	0.299772	+	0.400171i
$61$	−543.776			−1.14137			−0.570684	−	0.821170i	$-0.693322\pi$
$61$	−543.776			−1.14137			−0.570684	+	0.821170i	$0.693322\pi$
$62$	−9.06704	−	9.06704i	−0.0185728	−	0.0185728i
$63$	5.98086	+	617.741i	0.0119606	+	1.23537i
$64$		−	64.0000i		−	0.125000i
$65$	463.880	+	278.069i	0.885189	+	0.530618i
$66$	50.1375	−	122.719i	0.0935075	−	0.228874i
$67$	−120.548	+	120.548i	−0.219810	+	0.219810i	−0.808419	−	0.588608i	$-0.799676\pi$
$67$	−120.548	+	120.548i	−0.219810	+	0.219810i	0.588608	+	0.808419i	$0.299676\pi$
$68$	−107.967	+	107.967i	−0.192543	+	0.192543i
$69$	200.921	−	491.786i	0.350551	−	0.858029i
$70$	−496.294	+	124.290i	−0.847406	+	0.212222i
$71$		−	149.269i		−	0.249507i	−0.992188	−	0.124753i	$-0.960186\pi$
$71$		−	149.269i		−	0.249507i	0.992188	−	0.124753i	$-0.0398140\pi$
$72$	−2.09118	−	215.990i	−0.00342288	−	0.353537i
$73$	771.809	+	771.809i	1.23744	+	1.23744i	0.961042	+	0.276402i	$0.0891422\pi$
$73$	771.809	+	771.809i	1.23744	+	1.23744i	0.276402	+	0.961042i	$0.410858\pi$
$74$	−419.112			−0.658388
$75$	−409.662	+	504.035i	−0.630717	+	0.776013i
$76$	−547.022			−0.825627
$77$	206.381	+	206.381i	0.305445	+	0.305445i
$78$	−194.628	−	463.515i	−0.282530	−	0.672855i
$79$			97.9422i			0.139486i	0.997565	+	0.0697428i	$0.0222178\pi$
$79$			97.9422i			0.139486i	−0.997565	+	0.0697428i	$0.977782\pi$
$80$	173.526	−	43.4575i	0.242511	−	0.0607337i
$81$	−14.1148	−	728.863i	−0.0193619	−	0.999813i
$82$	29.0836	−	29.0836i	0.0391677	−	0.0391677i
$83$	735.158	−	735.158i	0.972218	−	0.972218i	−0.0274067	−	0.999624i	$-0.508725\pi$
$83$	735.158	−	735.158i	0.972218	−	0.972218i	0.999624	+	0.0274067i	$0.00872490\pi$
$84$	440.235	+	179.860i	0.571829	+	0.233623i
$85$	−366.048	−	219.424i	−0.467100	−	0.279998i
$86$			459.009i			0.575537i
$87$	989.662	−	415.556i	1.21957	−	0.512095i
$88$	−72.1599	−	72.1599i	−0.0874122	−	0.0874122i
$89$	492.823			0.586956			0.293478	−	0.955966i	$-0.405187\pi$
$89$	492.823			0.586956			0.293478	+	0.955966i	$0.405187\pi$
$90$	584.205	−	152.332i	0.684228	−	0.178413i
$91$	1106.82			1.27501
$92$	−289.174	−	289.174i	−0.327700	−	0.327700i
$93$	−30.7164	+	12.8977i	−0.0342489	+	0.0143810i
$94$		−	541.857i		−	0.594556i
$95$	−371.441	−	1483.17i	−0.401147	−	1.60179i
$96$	−153.926	−	62.8870i	−0.163646	−	0.0668581i
$97$	−811.978	+	811.978i	−0.849937	+	0.849937i	−0.990125	−	0.140188i	$-0.955229\pi$
$97$	−811.978	+	811.978i	−0.849937	+	0.849937i	0.140188	+	0.990125i	$0.455229\pi$
$98$	−255.281	+	255.281i	−0.263135	+	0.263135i
$99$	−245.886	−	241.171i	−0.249621	−	0.244834i
$100$	235.657	+	440.983i	0.235657	+	0.440983i
$101$			1221.28i			1.20319i	0.798801	+	0.601596i	$0.205468\pi$
$101$			1221.28i			1.20319i	−0.798801	+	0.601596i	$0.794532\pi$
$102$	153.581	+	365.760i	0.149086	+	0.355055i
$103$	−1013.81	−	1013.81i	−0.969841	−	0.969841i	0.0297171	−	0.999558i	$-0.490539\pi$
$103$	−1013.81	−	1013.81i	−0.969841	−	0.969841i	−0.999558	+	0.0297171i	$0.990539\pi$
$104$	−386.993			−0.364883
$105$	−188.733	+	1315.76i	−0.175414	+	1.22291i
$106$	−34.0085			−0.0311622
$107$	104.272	+	104.272i	0.0942090	+	0.0942090i	0.752641	−	0.658432i	$-0.228780\pi$
$107$	104.272	+	104.272i	0.0942090	+	0.0942090i	−0.658432	+	0.752641i	$0.728780\pi$
$108$	−521.531	−	207.204i	−0.464670	−	0.184613i
$109$			728.726i			0.640360i	0.947357	+	0.320180i	$0.103743\pi$
$109$			728.726i			0.640360i	−0.947357	+	0.320180i	$0.896257\pi$
$110$	146.653	−	244.649i	0.127116	−	0.212058i
$111$	−411.823	+	1008.00i	−0.352149	+	0.861941i
$112$	258.862	−	258.862i	0.218394	−	0.218394i
$113$	−124.657	+	124.657i	−0.103777	+	0.103777i	−0.757089	−	0.653312i	$-0.773379\pi$
$113$	−124.657	+	124.657i	−0.103777	+	0.103777i	0.653312	+	0.757089i	$0.273379\pi$
$114$	−537.509	+	1315.64i	−0.441599	+	1.08088i
$115$	587.696	−	980.407i	0.476547	−	0.794986i
$116$		−	826.279i		−	0.661362i
$117$	−1306.04	+	12.6449i	−1.03200	+	0.00999161i
$118$	887.152	+	887.152i	0.692110	+	0.692110i
$119$	−873.390			−0.672802
$120$	65.9895	−	460.049i	0.0501999	−	0.349971i
$121$	1168.28			0.877746
$122$	769.015	+	769.015i	0.570684	+	0.570684i
$123$	−41.3710	−	98.5267i	−0.0303276	−	0.0722265i
$124$			25.6455i			0.0185728i
$125$	−1035.64	+	938.387i	−0.741045	+	0.671455i
$126$	865.159	−	882.076i	0.611702	−	0.623663i
$127$	292.476	−	292.476i	0.204355	−	0.204355i	−0.597508	−	0.801863i	$-0.703842\pi$
$127$	292.476	−	292.476i	0.204355	−	0.204355i	0.801863	+	0.597508i	$0.203842\pi$
$128$	−90.5097	+	90.5097i	−0.0625000	+	0.0625000i
$129$	1103.96	+	451.026i	0.753474	+	0.307835i
$130$	−262.777	−	1049.27i	−0.177285	−	0.707903i
$131$			464.976i			0.310115i	0.987905	+	0.155058i	$0.0495563\pi$
$131$			464.976i			0.310115i	−0.987905	+	0.155058i	$0.950444\pi$
$132$	−244.457	+	102.646i	−0.161191	+	0.0676835i
$133$	−2212.55	−	2212.55i	−1.44250	−	1.44250i
$134$	340.962			0.219810
$135$	207.672	−	1554.75i	0.132397	−	0.991197i
$136$	305.376			0.192543
$137$	−102.116	−	102.116i	−0.0636815	−	0.0636815i	0.674549	−	0.738230i	$-0.264338\pi$
$137$	−102.116	−	102.116i	−0.0636815	−	0.0636815i	−0.738230	+	0.674549i	$0.764338\pi$
$138$	−979.635	+	411.345i	−0.604290	+	0.253739i
$139$			336.335i			0.205234i	0.994721	+	0.102617i	$0.0327216\pi$
$139$			336.335i			0.205234i	−0.994721	+	0.102617i	$0.967278\pi$
$140$	877.638	+	526.092i	0.529814	+	0.317592i
$141$	−1303.22	−	532.434i	−0.778373	−	0.318007i
$142$	−211.098	+	211.098i	−0.124753	+	0.124753i
$143$	−436.334	+	436.334i	−0.255162	+	0.255162i
$144$	−302.498	+	308.413i	−0.175057	+	0.178480i
$145$	2240.33	−	561.063i	1.28310	−	0.321336i
$146$		−	2183.01i		−	1.23744i
$147$	363.133	+	864.816i	0.203746	+	0.485230i
$148$	592.713	+	592.713i	0.329194	+	0.329194i
$149$	3241.32			1.78214			0.891071	−	0.453864i	$-0.149955\pi$
$149$	3241.32			1.78214			0.891071	+	0.453864i	$0.149955\pi$
$150$	1292.16	−	133.464i	0.703365	−	0.0726484i
$151$	−224.154			−0.120804			−0.0604019	−	0.998174i	$-0.519238\pi$
$151$	−224.154			−0.120804			−0.0604019	+	0.998174i	$0.519238\pi$
$152$	773.605	+	773.605i	0.412814	+	0.412814i
$153$	1030.60	−	9.97806i	0.544567	−	0.00527241i
$154$		−	583.733i		−	0.305445i
$155$	−69.5339	+	17.4139i	−0.0360329	+	0.00902397i
$156$	−380.263	+	930.755i	−0.195163	+	0.477693i
$157$	−1006.73	+	1006.73i	−0.511759	+	0.511759i	−0.915065	−	0.403306i	$-0.867861\pi$
$157$	−1006.73	+	1006.73i	−0.511759	+	0.511759i	0.403306	+	0.915065i	$0.367861\pi$
$158$	138.511	−	138.511i	0.0697428	−	0.0697428i
$159$	−33.4171	+	81.7936i	−0.0166676	+	0.0407966i
$160$	−306.862	−	183.945i	−0.151622	−	0.0908885i
$161$		−	2339.25i		−	1.14509i
$162$	−1010.81	+	1050.73i	−0.490225	+	0.509587i
$163$	694.457	+	694.457i	0.333706	+	0.333706i	0.853992	−	0.520286i	$-0.174175\pi$
$163$	694.457	+	694.457i	0.333706	+	0.333706i	−0.520286	+	0.853992i	$0.674175\pi$
$164$	−82.2609			−0.0391677
$165$	−444.302	−	593.108i	−0.209630	−	0.279839i
$166$	−2079.34			−0.972218
$167$	−1875.50	−	1875.50i	−0.869044	−	0.869044i	0.123322	−	0.992367i	$-0.460645\pi$
$167$	−1875.50	−	1875.50i	−0.869044	−	0.869044i	−0.992367	+	0.123322i	$0.960645\pi$
$168$	−368.227	−	876.947i	−0.169103	−	0.402726i
$169$			143.057i			0.0651149i
$170$	207.358	+	827.982i	0.0935506	+	0.373549i
$171$	2636.07	+	2585.52i	1.17886	+	1.15625i
$172$	649.136	−	649.136i	0.287768	−	0.287768i
$173$	−2100.72	+	2100.72i	−0.923208	+	0.923208i	−0.997255	−	0.0740463i	$-0.976409\pi$
$173$	−2100.72	+	2100.72i	−0.923208	+	0.923208i	0.0740463	+	0.997255i	$0.476409\pi$
$174$	−1987.28	−	811.910i	−0.865834	−	0.353740i
$175$	−830.483	+	2736.81i	−0.358735	+	1.18219i
$176$			204.099i			0.0874122i
$177$	3005.41	−	1261.96i	1.27627	−	0.535902i
$178$	−696.957	−	696.957i	−0.293478	−	0.293478i
$179$	−1272.12			−0.531190			−0.265595	−	0.964085i	$-0.585568\pi$
$179$	−1272.12			−0.531190			−0.265595	+	0.964085i	$0.585568\pi$
$180$	−1041.62	−	610.760i	−0.431321	−	0.252908i
$181$	62.7280			0.0257599			0.0128799	−	0.999917i	$-0.495900\pi$
$181$	62.7280			0.0257599			0.0128799	+	0.999917i	$0.495900\pi$
$182$	−1565.28	−	1565.28i	−0.637506	−	0.637506i
$183$	2605.20	−	1093.91i	1.05236	−	0.441882i
$184$			817.907i			0.327700i
$185$	−1204.59	+	2009.52i	−0.478719	+	0.798610i
$186$	61.6798	+	25.1995i	0.0243149	+	0.00993396i
$187$	344.311	−	344.311i	0.134645	−	0.134645i
$188$	−766.301	+	766.301i	−0.297278	+	0.297278i
$189$	−1271.36	−	2947.53i	−0.489301	−	1.13440i
$190$	−1572.22	+	2622.81i	−0.600320	+	1.00147i
$191$			2039.90i			0.772785i	0.922335	+	0.386392i	$0.126279\pi$
$191$			2039.90i			0.772785i	−0.922335	+	0.386392i	$0.873721\pi$
$192$	128.749	+	306.620i	0.0483939	+	0.115252i
$193$	1274.49	+	1274.49i	0.475335	+	0.475335i	0.903636	−	0.428301i	$-0.140888\pi$
$193$	1274.49	+	1274.49i	0.475335	+	0.475335i	−0.428301	+	0.903636i	$0.640888\pi$
$194$	2296.62			0.849937
$195$	−2781.81	−	399.023i	−1.02159	−	0.146537i
$196$	722.043			0.263135
$197$	−1983.65	−	1983.65i	−0.717407	−	0.717407i	0.250667	−	0.968073i	$-0.419350\pi$
$197$	−1983.65	−	1983.65i	−0.717407	−	0.717407i	−0.968073	+	0.250667i	$0.919350\pi$
$198$	6.66887	+	688.802i	0.00239362	+	0.247228i
$199$			1815.35i			0.646666i	0.946285	+	0.323333i	$0.104803\pi$
$199$			1815.35i			0.646666i	−0.946285	+	0.323333i	$0.895197\pi$
$200$	290.374	−	956.913i	0.102663	−	0.338320i
$201$	335.032	−	820.045i	0.117569	−	0.287769i
$202$	1727.16	−	1727.16i	0.601596	−	0.601596i
$203$	3342.06	−	3342.06i	1.15550	−	1.15550i
$204$	300.066	−	734.459i	0.102984	−	0.252070i
$205$	−55.8571	−	223.038i	−0.0190304	−	0.0759886i
$206$			2867.49i			0.969841i
$207$	26.7248	+	2760.31i	0.00897345	+	0.926833i
$208$	547.291	+	547.291i	0.182441	+	0.182441i
$209$	1744.48			0.577360
$210$	2127.68	−	1593.86i	0.699160	−	0.523746i
$211$	−3581.87			−1.16865			−0.584327	−	0.811518i	$-0.698642\pi$
$211$	−3581.87			−1.16865			−0.584327	+	0.811518i	$0.698642\pi$
$212$	48.0952	+	48.0952i	0.0155811	+	0.0155811i
$213$	300.284	+	715.139i	0.0965969	+	0.230049i
$214$		−	294.926i		−	0.0942090i
$215$	2200.82	+	1319.26i	0.698113	+	0.418477i
$216$	444.525	+	1030.59i	0.140028	+	0.324642i
$217$	−103.729	+	103.729i	−0.0324496	+	0.0324496i
$218$	1030.57	−	1030.57i	0.320180	−	0.320180i
$219$	−5250.34	−	2145.04i	−1.62002	−	0.661866i
$220$	−553.385	+	138.588i	−0.169587	+	0.0424709i
$221$		−	1846.54i		−	0.562044i
$222$	2007.94	−	843.126i	0.607045	−	0.254896i
$223$	−285.691	−	285.691i	−0.0857906	−	0.0857906i	0.662909	−	0.748700i	$-0.269322\pi$
$223$	−285.691	−	285.691i	−0.0857906	−	0.0857906i	−0.748700	+	0.662909i	$0.769322\pi$
$224$	−732.171			−0.218394
$225$	948.700	−	3238.92i	0.281096	−	0.959680i
$226$	352.584			0.103777
$227$	4779.51	+	4779.51i	1.39748	+	1.39748i	0.807206	+	0.590270i	$0.200979\pi$
$227$	4779.51	+	4779.51i	1.39748	+	1.39748i	0.590270	+	0.807206i	$0.299021\pi$
$228$	2620.75	−	1100.44i	0.761242	−	0.319643i
$229$		−	5062.03i		−	1.46074i	−0.683054	−	0.730368i	$-0.739349\pi$
$229$		−	5062.03i		−	1.46074i	0.683054	−	0.730368i	$-0.260651\pi$
$230$	−2217.63	+	555.378i	−0.635767	+	0.159220i
$231$	−1403.93	−	573.582i	−0.399879	−	0.163372i
$232$	−1168.53	+	1168.53i	−0.330681	+	0.330681i
$233$	−1012.79	+	1012.79i	−0.284765	+	0.284765i	−0.835006	−	0.550241i	$-0.814536\pi$
$233$	−1012.79	+	1012.79i	−0.284765	+	0.284765i	0.550241	+	0.835006i	$0.314536\pi$
$234$	1864.90	+	1829.14i	0.520994	+	0.511002i
$235$	−2598.05	−	1557.38i	−0.721183	−	0.432306i
$236$		−	2509.25i		−	0.692110i
$237$	−197.030	−	469.235i	−0.0540020	−	0.128608i
$238$	1235.16	+	1235.16i	0.336401	+	0.336401i
$239$	−1140.60			−0.308701			−0.154350	−	0.988016i	$-0.549328\pi$
$239$	−1140.60			−0.308701			−0.154350	+	0.988016i	$0.549328\pi$
$240$	−743.931	+	557.285i	−0.200086	+	0.149886i
$241$	894.509			0.239089			0.119544	−	0.992829i	$-0.461857\pi$
$241$	894.509			0.239089			0.119544	+	0.992829i	$0.461857\pi$
$242$	−1652.20	−	1652.20i	−0.438873	−	0.438873i
$243$	1533.88	+	3463.54i	0.404931	+	0.914347i
$244$		−	2175.10i		−	0.570684i
$245$	490.284	+	1957.71i	0.127849	+	0.510505i
$246$	−80.8304	+	197.845i	−0.0209494	+	0.0512771i
$247$	4677.81	−	4677.81i	1.20503	−	1.20503i
$248$	36.2682	−	36.2682i	0.00928641	−	0.00928641i
$249$	−2043.18	+	5001.01i	−0.520005	+	1.27280i
$250$	2791.70	+	137.540i	0.706250	+	0.0347952i
$251$		−	4198.52i		−	1.05581i	−0.849304	−	0.527905i	$-0.822978\pi$
$251$		−	4198.52i		−	1.05581i	0.849304	−	0.527905i	$-0.177022\pi$
$252$	−2470.96	+	23.9235i	−0.617683	+	0.00598030i
$253$	922.189	+	922.189i	0.229160	+	0.229160i
$254$	−827.246			−0.204355
$255$	2195.13	+	314.869i	0.539075	+	0.0773249i
$256$	256.000			0.0625000
$257$	−3004.70	−	3004.70i	−0.729291	−	0.729291i	0.241188	−	0.970479i	$-0.422463\pi$
$257$	−3004.70	−	3004.70i	−0.729291	−	0.729291i	−0.970479	+	0.241188i	$0.922463\pi$
$258$	−923.386	−	2199.08i	−0.222820	−	0.530654i
$259$			4794.71i			1.15030i
$260$	−1112.27	+	1855.52i	−0.265309	+	0.442594i
$261$	−3905.44	+	3981.80i	−0.926209	+	0.944319i
$262$	657.575	−	657.575i	0.155058	−	0.155058i
$263$	−3594.55	+	3594.55i	−0.842773	+	0.842773i	−0.989219	−	0.146446i	$-0.953217\pi$
$263$	−3594.55	+	3594.55i	−0.842773	+	0.842773i	0.146446	+	0.989219i	$0.453217\pi$
$264$	490.878	+	200.550i	0.114437	+	0.0467537i
$265$	−97.7453	+	163.061i	−0.0226583	+	0.0377991i
$266$			6258.03i			1.44250i
$267$	−2361.08	+	991.410i	−0.541183	+	0.227241i
$268$	−482.193	−	482.193i	−0.109905	−	0.109905i
$269$	2096.25			0.475132			0.237566	−	0.971371i	$-0.423650\pi$
$269$	2096.25			0.475132			0.237566	+	0.971371i	$0.423650\pi$
$270$	−2492.44	+	1905.06i	−0.561797	+	0.429400i
$271$	−588.893			−0.132002			−0.0660012	−	0.997820i	$-0.521024\pi$
$271$	−588.893			−0.132002			−0.0660012	+	0.997820i	$0.521024\pi$
$272$	−431.867	−	431.867i	−0.0962713	−	0.0962713i
$273$	−5302.69	+	2226.58i	−1.17558	+	0.493622i
$274$			288.828i			0.0636815i
$275$	−751.522	−	1406.32i	−0.164795	−	0.308378i
$276$	1967.14	+	803.683i	0.429015	+	0.175276i
$277$	−1492.04	+	1492.04i	−0.323639	+	0.323639i	−0.850161	−	0.526522i	$-0.823496\pi$
$277$	−1492.04	+	1492.04i	−0.323639	+	0.323639i	0.526522	+	0.850161i	$0.323496\pi$
$278$	475.649	−	475.649i	0.102617	−	0.102617i
$279$	121.214	−	123.584i	0.0260104	−	0.0265190i
$280$	−497.162	−	1985.17i	−0.106111	−	0.423703i
$281$		−	5169.08i		−	1.09737i	−0.836028	−	0.548686i	$-0.815128\pi$
$281$		−	5169.08i		−	1.09737i	0.836028	−	0.548686i	$-0.184872\pi$
$282$	1090.05	+	2596.00i	0.230183	+	0.548190i
$283$	−892.521	−	892.521i	−0.187473	−	0.187473i	0.607130	−	0.794603i	$-0.292321\pi$
$283$	−892.521	−	892.521i	−0.187473	−	0.187473i	−0.794603	+	0.607130i	$0.792321\pi$
$284$	597.077			0.124753
$285$	4763.23	+	6358.54i	0.989998	+	1.32157i
$286$	1234.14			0.255162
$287$	−332.722	−	332.722i	−0.0684319	−	0.0684319i
$288$	863.960	−	8.36471i	0.176768	−	0.00171144i
$289$		−	3455.90i		−	0.703419i
$290$	−3961.77	−	2374.85i	−0.802218	−	0.480882i
$291$	2256.68	−	5523.59i	0.454602	−	1.11271i
$292$	−3087.24	+	3087.24i	−0.618722	+	0.618722i
$293$	3323.48	−	3323.48i	0.662661	−	0.662661i	−0.293346	−	0.956006i	$-0.594769\pi$
$293$	3323.48	−	3323.48i	0.662661	−	0.662661i	0.956006	+	0.293346i	$0.0947687\pi$
$294$	709.487	−	1736.58i	0.140742	−	0.344488i
$295$	6803.45	−	1703.84i	1.34275	−	0.336275i
$296$		−	1676.45i		−	0.329194i
$297$	1663.19	+	660.785i	0.324943	+	0.129100i
$298$	−4583.92	−	4583.92i	−0.891071	−	0.891071i
$299$	4945.69			0.956578
$300$	−2016.14	−	1638.65i	−0.388007	−	0.315358i
$301$	5251.14			1.00555
$302$	317.001	+	317.001i	0.0604019	+	0.0604019i
$303$	−2456.85	−	5851.09i	−0.465817	−	1.10936i
$304$		−	2188.09i		−	0.412814i
$305$	5897.47	−	1476.95i	1.10717	−	0.277278i
$306$	−1471.59	−	1443.37i	−0.274920	−	0.269647i
$307$	−2558.00	+	2558.00i	−0.475547	+	0.475547i	−0.903704	−	0.428157i	$-0.859163\pi$
$307$	−2558.00	+	2558.00i	−0.475547	+	0.475547i	0.428157	+	0.903704i	$0.359163\pi$
$308$	−825.523	+	825.523i	−0.152722	+	0.152722i
$309$	6896.58	+	2817.62i	1.26968	+	0.518734i
$310$	122.963	+	73.7088i	0.0225284	+	0.0135044i
$311$			8102.38i			1.47731i	0.674083	+	0.738655i	$0.264539\pi$
$311$			8102.38i			1.47731i	−0.674083	+	0.738655i	$0.735461\pi$
$312$	1854.06	−	778.513i	0.336428	−	0.141265i
$313$	106.246	+	106.246i	0.0191865	+	0.0191865i	0.716635	−	0.697448i	$-0.245681\pi$
$313$	106.246	+	106.246i	0.0191865	+	0.0191865i	−0.697448	+	0.716635i	$0.745681\pi$
$314$	2847.47			0.511759
$315$	−1742.71	−	6683.40i	−0.311716	−	1.19545i
$316$	−391.769			−0.0697428
$317$	1174.48	+	1174.48i	0.208093	+	0.208093i	0.803456	−	0.595364i	$-0.202992\pi$
$317$	1174.48	+	1174.48i	0.208093	+	0.208093i	−0.595364	+	0.803456i	$0.702992\pi$
$318$	162.932	−	68.4147i	0.0287321	−	0.0120645i
$319$			2635.04i			0.462489i
$320$	173.830	+	694.106i	0.0303669	+	0.121255i
$321$	−709.325	−	289.797i	−0.123335	−	0.0503891i
$322$	−3308.20	+	3308.20i	−0.572543	+	0.572543i
$323$	−3691.26	+	3691.26i	−0.635874	+	0.635874i
$324$	2915.45	−	56.4592i	0.499906	−	0.00968093i
$325$	−5786.23	−	1755.83i	−0.987577	−	0.299679i
$326$		−	1964.22i		−	0.333706i
$327$	−1465.98	−	3491.28i	−0.247916	−	0.590423i
$328$	116.335	+	116.335i	0.0195838	+	0.0195838i
$329$	−6198.94			−1.03878
$330$	−210.444	+	1467.12i	−0.0351047	+	0.244734i
$331$	2832.47			0.470352			0.235176	−	0.971953i	$-0.424433\pi$
$331$	2832.47			0.470352			0.235176	+	0.971953i	$0.424433\pi$
$332$	2940.63	+	2940.63i	0.486109	+	0.486109i
$333$	−54.7773	−	5657.74i	−0.00901435	−	0.931058i
$334$			5304.71i			0.869044i
$335$	979.974	−	1634.81i	0.159826	−	0.266625i
$336$	−719.439	+	1760.94i	−0.116811	+	0.285914i
$337$	−4789.86	+	4789.86i	−0.774244	+	0.774244i	−0.978845	−	0.204601i	$-0.934410\pi$
$337$	−4789.86	+	4789.86i	−0.774244	+	0.774244i	0.204601	+	0.978845i	$0.434410\pi$
$338$	202.314	−	202.314i	0.0325575	−	0.0325575i
$339$	346.453	−	847.998i	0.0555066	−	0.135861i
$340$	877.696	−	1464.19i	0.139999	−	0.233550i
$341$		−	81.7846i		−	0.0129879i
$342$	−71.4950	−	7384.45i	−0.0113041	−	1.16756i
$343$	−2628.89	−	2628.89i	−0.413839	−	0.413839i
$344$	−1836.03			−0.287768
$345$	−843.332	+	5879.33i	−0.131604	+	0.917486i
$346$	5941.74			0.923208
$347$	2124.17	+	2124.17i	0.328621	+	0.328621i	0.852062	−	0.523441i	$-0.175352\pi$
$347$	2124.17	+	2124.17i	0.328621	+	0.328621i	−0.523441	+	0.852062i	$0.675352\pi$
$348$	1662.22	+	3958.65i	0.256047	+	0.609787i
$349$			9235.10i			1.41646i	0.705983	+	0.708229i	$0.250505\pi$
$349$			9235.10i			1.41646i	−0.705983	+	0.708229i	$0.749495\pi$
$350$	5044.92	−	2695.96i	0.770464	−	0.411729i
$351$	6231.72	−	2687.94i	0.947649	−	0.408751i
$352$	288.640	−	288.640i	0.0437061	−	0.0437061i
$353$	−986.773	+	986.773i	−0.148784	+	0.148784i	−0.777574	−	0.628791i	$-0.783550\pi$
$353$	−986.773	+	986.773i	−0.148784	+	0.148784i	0.628791	+	0.777574i	$0.283550\pi$
$354$	−6034.97	−	2465.61i	−0.906088	−	0.370185i
$355$	405.429	+	1618.88i	0.0606139	+	0.242032i
$356$			1971.29i			0.293478i
$357$	4184.35	−	1757.00i	0.620335	−	0.260476i
$358$	1799.06	+	1799.06i	0.265595	+	0.265595i
$359$	−10701.5			−1.57327			−0.786635	−	0.617419i	$-0.788178\pi$
$359$	−10701.5			−1.57327			−0.786635	+	0.617419i	$0.788178\pi$
$360$	609.328	+	2336.82i	0.0892067	+	0.342114i
$361$	−11843.0			−1.72664
$362$	−88.7108	−	88.7108i	−0.0128799	−	0.0128799i
$363$	−5597.15	+	2350.22i	−0.809296	+	0.339820i
$364$			4427.27i			0.637506i
$365$	−10466.9	−	6274.28i	−1.50099	−	0.899755i
$366$	−5231.33	−	2137.28i	−0.747120	−	0.305239i
$367$	1004.85	−	1004.85i	0.142923	−	0.142923i	−0.632025	−	0.774948i	$-0.717776\pi$
$367$	1004.85	−	1004.85i	0.142923	−	0.142923i	0.774948	+	0.632025i	$0.217776\pi$
$368$	1156.69	−	1156.69i	0.163850	−	0.163850i
$369$	396.412	+	388.809i	0.0559251	+	0.0548526i
$370$	4545.44	−	1138.35i	0.638665	−	0.159945i
$371$			389.063i			0.0544451i
$372$	−51.5909	−	122.866i	−0.00719049	−	0.0171244i
$373$	8677.69	+	8677.69i	1.20460	+	1.20460i	0.972754	+	0.231842i	$0.0744751\pi$
$373$	8677.69	+	8677.69i	1.20460	+	1.20460i	0.231842	+	0.972754i	$0.425525\pi$
$374$	−973.860			−0.134645
$375$	3073.95	−	6579.15i	0.423301	−	0.905989i
$376$	2167.43			0.297278
$377$	7065.86	+	7065.86i	0.965279	+	0.965279i
$378$	−2370.45	+	5966.41i	−0.322548	+	0.811849i
$379$		−	14693.0i		−	1.99137i	−0.0927715	−	0.995687i	$-0.529573\pi$
$379$		−	14693.0i		−	1.99137i	0.0927715	−	0.995687i	$-0.470427\pi$
$380$	5932.67	−	1485.76i	0.800894	−	0.200574i
$381$	−812.860	+	1989.61i	−0.109302	+	0.267534i
$382$	2884.85	−	2884.85i	0.386392	−	0.386392i
$383$	1850.91	−	1850.91i	0.246937	−	0.246937i	−0.572775	−	0.819713i	$-0.694133\pi$
$383$	1850.91	−	1850.91i	0.246937	−	0.246937i	0.819713	+	0.572775i	$0.194133\pi$
$384$	251.548	−	615.704i	0.0334291	−	0.0818230i
$385$	−2798.83	−	1677.73i	−0.370498	−	0.222091i
$386$		−	3604.80i		−	0.475335i
$387$	−6196.33	+	59.9918i	−0.813894	+	0.00787999i
$388$	−3247.91	−	3247.91i	−0.424969	−	0.424969i
$389$	−9296.60			−1.21171			−0.605856	−	0.795574i	$-0.707169\pi$
$389$	−9296.60			−1.21171			−0.605856	+	0.795574i	$0.707169\pi$
$390$	3369.77	+	4498.38i	0.437526	+	0.584062i
$391$	−3902.64			−0.504770
$392$	−1021.12	−	1021.12i	−0.131568	−	0.131568i
$393$	−935.390	−	2227.67i	−0.120062	−	0.285931i
$394$			5610.60i			0.717407i
$395$	−266.020	−	1062.22i	−0.0338859	−	0.135307i
$396$	964.682	−	983.545i	0.122417	−	0.124811i
$397$	848.145	−	848.145i	0.107222	−	0.107222i	−0.651460	−	0.758683i	$-0.725843\pi$
$397$	848.145	−	848.145i	0.107222	−	0.107222i	0.758683	+	0.651460i	$0.225843\pi$
$398$	2567.29	−	2567.29i	0.323333	−	0.323333i
$399$	15051.1	+	6149.20i	1.88847	+	0.771541i
$400$	−1763.93	+	942.628i	−0.220491	+	0.117829i
$401$			8527.15i			1.06191i	0.847400	+	0.530954i	$0.178166\pi$
$401$			8527.15i			1.06191i	−0.847400	+	0.530954i	$0.821834\pi$
$402$	−1633.53	+	685.911i	−0.202669	+	0.0850999i
$403$	−219.305	−	219.305i	−0.0271076	−	0.0271076i
$404$	−4885.14			−0.601596
$405$	2132.74	+	7866.48i	0.261671	+	0.965157i
$406$	−9452.78			−1.15550
$407$	−1890.19	−	1890.19i	−0.230205	−	0.230205i
$408$	−1463.04	+	614.324i	−0.177527	+	0.0745431i
$409$		−	7604.85i		−	0.919403i	−0.888073	−	0.459702i	$-0.847956\pi$
$409$		−	7604.85i		−	0.919403i	0.888073	−	0.459702i	$-0.152044\pi$
$410$	−236.430	+	394.418i	−0.0284791	+	0.0475095i
$411$	694.658	+	283.805i	0.0833697	+	0.0340610i
$412$	4055.24	−	4055.24i	0.484921	−	0.484921i
$413$	10149.2	−	10149.2i	1.20922	−	1.20922i
$414$	3865.87	−	3941.46i	0.458930	−	0.467903i
$415$	−5976.33	+	9969.84i	−0.706907	+	1.17928i
$416$		−	1547.97i		−	0.182441i
$417$	−676.603	−	1611.36i	−0.0794566	−	0.189229i
$418$	−2467.07	−	2467.07i	−0.288680	−	0.288680i
$419$	13904.7			1.62122			0.810609	−	0.585588i	$-0.199136\pi$
$419$	13904.7			1.62122			0.810609	+	0.585588i	$0.199136\pi$
$420$	−5263.05	−	754.931i	−0.611453	−	0.0877068i
$421$	15613.5			1.80749			0.903745	−	0.428071i	$-0.140807\pi$
$421$	15613.5			1.80749			0.903745	+	0.428071i	$0.140807\pi$
$422$	5065.53	+	5065.53i	0.584327	+	0.584327i
$423$	7314.73	−	70.8200i	0.840790	−	0.00814039i
$424$		−	136.034i		−	0.0155811i
$425$	4565.91	+	1385.52i	0.521128	+	0.158136i
$426$	586.693	−	1436.03i	0.0667263	−	0.163323i
$427$	8797.68	−	8797.68i	0.997071	−	0.997071i
$428$	−417.088	+	417.088i	−0.0471045	+	0.0471045i
$429$	1212.68	−	2968.22i	0.136477	−	0.334049i
$430$	−1246.71	−	4978.14i	−0.139818	−	0.558295i
$431$			1687.62i			0.188607i	0.995544	+	0.0943034i	$0.0300624\pi$
$431$			1687.62i			0.188607i	−0.995544	+	0.0943034i	$0.969938\pi$
$432$	828.817	−	2086.12i	0.0923067	−	0.232335i
$433$	3605.54	+	3605.54i	0.400164	+	0.400164i	0.878291	−	0.478127i	$-0.158684\pi$
$433$	3605.54	+	3605.54i	0.400164	+	0.400164i	−0.478127	+	0.878291i	$0.658684\pi$
$434$	293.389			0.0324496
$435$	−9604.60	+	7194.88i	−1.05863	+	0.793031i
$436$	−2914.90			−0.320180
$437$	−9886.52	−	9886.52i	−1.08223	−	1.08223i
$438$	4391.55	+	10458.6i	0.479078	+	1.14094i
$439$		−	8014.92i		−	0.871369i	−0.900099	−	0.435685i	$-0.856506\pi$
$439$		−	8014.92i		−	0.871369i	0.900099	−	0.435685i	$-0.143494\pi$
$440$	978.597	+	586.611i	0.106029	+	0.0635581i
$441$	−3479.50	−	3412.77i	−0.375715	−	0.368509i
$442$	−2611.40	+	2611.40i	−0.281022	+	0.281022i
$443$	4788.70	−	4788.70i	0.513584	−	0.513584i	−0.402039	−	0.915623i	$-0.631698\pi$
$443$	4788.70	−	4788.70i	0.513584	−	0.513584i	0.915623	+	0.402039i	$0.131698\pi$
$444$	−4032.01	−	1647.29i	−0.430970	−	0.176074i
$445$	−5344.86	+	1338.55i	−0.569373	+	0.142592i
$446$			808.057i			0.0857906i
$447$	−15528.9	+	6520.55i	−1.64316	+	0.689958i
$448$	1035.45	+	1035.45i	0.109197	+	0.109197i
$449$	−6437.16			−0.676588			−0.338294	−	0.941040i	$-0.609850\pi$
$449$	−6437.16			−0.676588			−0.338294	+	0.941040i	$0.609850\pi$
$450$	−5922.19	+	3238.86i	−0.620388	+	0.339292i
$451$	262.334			0.0273899
$452$	−498.629	−	498.629i	−0.0518884	−	0.0518884i
$453$	1073.91	−	450.929i	0.111383	−	0.0467693i
$454$		−	13518.5i		−	1.39748i
$455$	−12003.9	+	3006.22i	−1.23682	+	0.309745i
$456$	−5262.55	−	2150.04i	−0.540442	−	0.220800i
$457$	7433.15	−	7433.15i	0.760850	−	0.760850i	−0.215626	−	0.976476i	$-0.569179\pi$
$457$	7433.15	−	7433.15i	0.760850	−	0.760850i	0.976476	+	0.215626i	$0.0691793\pi$
$458$	−7158.79	+	7158.79i	−0.730368	+	0.730368i
$459$	−4917.45	+	2121.05i	−0.500059	+	0.215691i
$460$	3921.63	+	2350.78i	0.397493	+	0.238274i
$461$			15742.8i			1.59049i	0.606291	+	0.795243i	$0.292657\pi$
$461$			15742.8i			1.59049i	−0.606291	+	0.795243i	$0.707343\pi$
$462$	1174.29	+	2796.63i	0.118253	+	0.281625i
$463$	4385.12	+	4385.12i	0.440160	+	0.440160i	0.892066	−	0.451906i	$-0.149256\pi$
$463$	4385.12	+	4385.12i	0.440160	+	0.440160i	−0.451906	+	0.892066i	$0.649256\pi$
$464$	3305.11			0.330681
$465$	298.101	−	223.310i	0.0297292	−	0.0222704i
$466$	2864.61			0.284765
$467$	405.352	+	405.352i	0.0401659	+	0.0401659i	0.726904	−	0.686739i	$-0.240958\pi$
$467$	405.352	+	405.352i	0.0401659	+	0.0401659i	−0.686739	+	0.726904i	$0.740958\pi$
$468$	−50.5795	−	5224.16i	−0.00499581	−	0.515998i
$469$		−	3900.66i		−	0.384042i
$470$	1471.73	+	5876.66i	0.144438	+	0.576745i
$471$	2797.96	−	6848.44i	0.273722	−	0.669978i
$472$	−3548.61	+	3548.61i	−0.346055	+	0.346055i
$473$	−2070.13	+	2070.13i	−0.201236	+	0.201236i
$474$	−384.956	+	942.241i	−0.0373030	+	0.0913049i
$475$	8056.85	+	15076.7i	0.778260	+	1.45635i
$476$		−	3493.56i		−	0.336401i
$477$	−4.44486	−	459.093i	−0.000426659	−	0.0440680i
$478$	1613.06	+	1613.06i	0.154350	+	0.154350i
$479$	834.821			0.0796324			0.0398162	−	0.999207i	$-0.487323\pi$
$479$	834.821			0.0796324			0.0398162	+	0.999207i	$0.487323\pi$
$480$	1840.20	+	263.958i	0.174986	+	0.0250999i
$481$	−10137.1			−0.960938
$482$	−1265.03	−	1265.03i	−0.119544	−	0.119544i
$483$	4705.86	+	11207.2i	0.443321	+	1.05579i
$484$			4673.12i			0.438873i
$485$	6600.83	−	11011.6i	0.617996	−	1.03095i
$486$	2728.96	−	7067.42i	0.254708	−	0.659639i
$487$	1123.69	−	1123.69i	0.104557	−	0.104557i	−0.652893	−	0.757450i	$-0.726445\pi$
$487$	1123.69	−	1123.69i	0.104557	−	0.104557i	0.757450	+	0.652893i	$0.226445\pi$
$488$	−3076.06	+	3076.06i	−0.285342	+	0.285342i
$489$	−4724.14	−	1930.06i	−0.436877	−	0.178488i
$490$	2075.26	−	3461.99i	0.191328	−	0.319177i
$491$			2933.72i			0.269647i	0.990870	+	0.134824i	$0.0430468\pi$
$491$			2933.72i			0.269647i	−0.990870	+	0.134824i	$0.956953\pi$
$492$	394.107	−	165.484i	0.0361132	−	0.0151638i
$493$	−5575.67	−	5575.67i	−0.509362	−	0.509362i
$494$	−13230.9			−1.20503
$495$	3321.78	+	1947.74i	0.301622	+	0.176858i
$496$	−102.582			−0.00928641
$497$	2415.00	+	2415.00i	0.217963	+	0.217963i
$498$	9961.99	−	4183.00i	0.896401	−	0.376395i
$499$			19512.5i			1.75050i	0.483668	+	0.875252i	$0.339304\pi$
$499$			19512.5i			1.75050i	−0.483668	+	0.875252i	$0.660696\pi$
$500$	−3753.55	−	4142.57i	−0.335727	−	0.370523i
$501$	12758.3	+	5212.46i	1.13772	+	0.464821i
$502$	−5937.60	+	5937.60i	−0.527905	+	0.527905i
$503$	−8770.75	+	8770.75i	−0.777472	+	0.777472i	−0.979400	−	0.201928i	$-0.935279\pi$
$503$	−8770.75	+	8770.75i	−0.777472	+	0.777472i	0.201928	+	0.979400i	$0.435279\pi$
$504$	3528.30	+	3460.64i	0.311831	+	0.305851i
$505$	−3317.12	−	13245.3i	−0.292297	−	1.16715i
$506$		−	2608.34i		−	0.229160i
$507$	−287.788	−	685.379i	−0.0252093	−	0.0600370i
$508$	1169.90	+	1169.90i	0.102177	+	0.102177i
$509$	16213.8			1.41192			0.705959	−	0.708253i	$-0.250516\pi$
$509$	16213.8			1.41192			0.705959	+	0.708253i	$0.250516\pi$
$510$	−2659.09	−	3549.67i	−0.230875	−	0.308200i
$511$	−24974.0			−2.16200
$512$	−362.039	−	362.039i	−0.0312500	−	0.0312500i
$513$	−17830.5	−	7084.08i	−1.53458	−	0.609687i
$514$			8498.56i			0.729291i
$515$	13748.8	+	8241.58i	1.17640	+	0.705179i
$516$	−1804.11	+	4415.84i	−0.153917	+	0.376737i
$517$	2443.77	−	2443.77i	0.207886	−	0.207886i
$518$	6780.75	−	6780.75i	0.575152	−	0.575152i
$519$	5838.42	−	14290.5i	0.493792	−	1.20863i
$520$	4197.10	−	1051.11i	0.353952	−	0.0886427i
$521$		−	17031.0i		−	1.43213i	−0.698032	−	0.716067i	$-0.745941\pi$
$521$		−	17031.0i		−	1.43213i	0.698032	−	0.716067i	$-0.254059\pi$
$522$	11154.2	−	107.993i	0.935264	−	0.00905507i
$523$	−6159.97	−	6159.97i	−0.515023	−	0.515023i	0.401039	−	0.916061i	$-0.368649\pi$
$523$	−6159.97	−	6159.97i	−0.515023	−	0.515023i	−0.916061	+	0.401039i	$0.868649\pi$
$524$	−1859.90			−0.155058
$525$	−1526.85	−	14782.6i	−0.126928	−	1.22889i
$526$	10166.9			0.842773
$527$	173.054	+	173.054i	0.0143042	+	0.0143042i
$528$	−410.586	−	977.826i	−0.0338418	−	0.0805955i
$529$			1714.32i			0.140899i
$530$	368.836	−	92.3702i	0.0302287	−	0.00757039i
$531$	−11860.0	+	12091.9i	−0.969269	+	0.988221i
$532$	8850.19	−	8850.19i	0.721248	−	0.721248i
$533$	703.448	−	703.448i	0.0571664	−	0.0571664i
$534$	4741.14	+	1937.01i	0.384212	+	0.156971i
$535$	−1414.09	−	847.660i	−0.114273	−	0.0685001i
$536$			1363.85i			0.109905i
$537$	6094.67	−	2559.13i	0.489766	−	0.205651i
$538$	−2964.54	−	2964.54i	−0.237566	−	0.237566i
$539$	−2302.63			−0.184010
$540$	6219.00	+	830.688i	0.495598	+	0.0661984i
$541$	17947.7			1.42630			0.713152	−	0.701010i	$-0.247267\pi$
$541$	17947.7			1.42630			0.713152	+	0.701010i	$0.247267\pi$
$542$	832.820	+	832.820i	0.0660012	+	0.0660012i
$543$	−300.526	+	126.190i	−0.0237510	+	0.00997297i
$544$			1221.50i			0.0962713i
$545$	−1979.29	−	7903.33i	−0.155566	−	0.621177i
$546$	10648.0	+	4350.28i	0.834602	+	0.340979i
$547$	−6743.17	+	6743.17i	−0.527088	+	0.527088i	−0.919703	−	0.392615i	$-0.871571\pi$
$547$	−6743.17	+	6743.17i	−0.527088	+	0.527088i	0.392615	+	0.919703i	$0.371571\pi$
$548$	408.464	−	408.464i	0.0318407	−	0.0318407i
$549$	−10280.7	+	10481.7i	−0.799217	+	0.814844i
$550$	−926.018	+	3051.64i	−0.0717919	+	0.236586i
$551$		−	28249.5i		−	2.18416i
$552$	−1645.38	−	3918.54i	−0.126870	−	0.302145i
$553$	−1584.59	−	1584.59i	−0.121851	−	0.121851i
$554$	4220.13			0.323639
$555$	1728.56	−	12050.8i	0.132204	−	0.921668i
$556$	−1345.34			−0.102617
$557$	14440.2	+	14440.2i	1.09847	+	1.09847i	0.994589	+	0.103884i	$0.0331270\pi$
$557$	14440.2	+	14440.2i	1.09847	+	1.09847i	0.103884	+	0.994589i	$0.466873\pi$
$558$	−346.198	+	3.35183i	−0.0262647	+	0.000254291i
$559$			11102.1i			0.840014i
$560$	−2104.37	+	3510.55i	−0.158796	+	0.264907i
$561$	−956.924	+	2342.22i	−0.0720167	+	0.176272i
$562$	−7310.19	+	7310.19i	−0.548686	+	0.548686i
$563$	13865.7	−	13865.7i	1.03796	−	1.03796i	0.0387094	−	0.999251i	$-0.487675\pi$
$563$	13865.7	−	13865.7i	1.03796	−	1.03796i	0.999251	−	0.0387094i	$-0.0123247\pi$
$564$	2129.74	−	5212.87i	0.159004	−	0.389187i
$565$	1013.38	−	1690.54i	0.0754569	−	0.125879i
$566$			2524.43i			0.187473i
$567$	12020.5	+	11563.8i	0.890326	+	0.856498i
$568$	−844.394	−	844.394i	−0.0623767	−	0.0623767i
$569$	−18660.0			−1.37481			−0.687405	−	0.726274i	$-0.741250\pi$
$569$	−18660.0			−1.37481			−0.687405	+	0.726274i	$0.741250\pi$
$570$	2256.10	−	15728.6i	0.165786	−	1.15578i
$571$	6653.04			0.487602			0.243801	−	0.969825i	$-0.421606\pi$
$571$	6653.04			0.487602			0.243801	+	0.969825i	$0.421606\pi$
$572$	−1745.34	−	1745.34i	−0.127581	−	0.127581i
$573$	−4103.66	−	9773.03i	−0.299185	−	0.712520i
$574$			941.080i			0.0684319i
$575$	−3710.92	+	12229.2i	−0.269141	+	0.886941i
$576$	−1233.65	−	1209.99i	−0.0892399	−	0.0875285i
$577$	−18037.4	+	18037.4i	−1.30140	+	1.30140i	−0.373944	+	0.927451i	$0.621995\pi$
$577$	−18037.4	+	18037.4i	−1.30140	+	1.30140i	−0.927451	+	0.373944i	$0.878005\pi$
$578$	−4887.38	+	4887.38i	−0.351709	+	0.351709i
$579$	−8669.87	−	3542.11i	−0.622293	−	0.254240i
$580$	2244.25	+	8961.33i	0.160668	+	0.641550i
$581$			23788.0i			1.69861i
$582$	−11003.0	+	4620.11i	−0.783656	+	0.329054i
$583$	−153.378	−	153.378i	−0.0108958	−	0.0108958i
$584$	8732.02			0.618722
$585$	14130.2	−	3684.47i	0.998652	−	0.260400i
$586$	−9400.21			−0.662661
$587$	−14567.2	−	14567.2i	−1.02428	−	1.02428i	−0.999698	−	0.0245838i	$-0.992174\pi$
$587$	−14567.2	−	14567.2i	−1.02428	−	1.02428i	−0.0245838	−	0.999698i	$-0.507826\pi$
$588$	−3459.26	+	1452.53i	−0.242615	+	0.101873i
$589$			876.789i			0.0613369i
$590$	−12031.1	−	7211.94i	−0.839514	−	0.503239i
$591$	13494.0	+	5513.04i	0.939205	+	0.383716i
$592$	−2370.85	+	2370.85i	−0.164597	+	0.164597i
$593$	−20017.5	+	20017.5i	−1.38621	+	1.38621i	−0.553080	+	0.833128i	$0.686547\pi$
$593$	−20017.5	+	20017.5i	−1.38621	+	1.38621i	−0.833128	+	0.553080i	$0.813453\pi$
$594$	−1417.61	−	3286.59i	−0.0979214	−	0.227021i
$595$	9472.27	−	2372.21i	0.652647	−	0.163447i
$596$			12965.3i			0.891071i
$597$	−3651.93	−	8697.21i	−0.250357	−	0.596236i
$598$	−6994.26	−	6994.26i	−0.478289	−	0.478289i
$599$	19821.1			1.35203			0.676017	−	0.736886i	$-0.263705\pi$
$599$	19821.1			1.35203			0.676017	+	0.736886i	$0.263705\pi$
$600$	533.855	+	5168.66i	0.0363242	+	0.351682i
$601$	9850.79			0.668589			0.334294	−	0.942469i	$-0.391502\pi$
$601$	9850.79			0.668589			0.334294	+	0.942469i	$0.391502\pi$
$602$	−7426.24	−	7426.24i	−0.502775	−	0.502775i
$603$	44.5632	+	4602.77i	0.00300954	+	0.310844i
$604$		−	896.614i		−	0.0604019i
$605$	−12670.5	+	3173.16i	−0.851451	+	0.213235i
$606$	−4800.18	+	11749.2i	−0.321772	+	0.787589i
$607$	403.095	−	403.095i	0.0269540	−	0.0269540i	−0.693501	−	0.720455i	$-0.743933\pi$
$607$	403.095	−	403.095i	0.0269540	−	0.0269540i	0.720455	+	0.693501i	$0.243933\pi$
$608$	−3094.42	+	3094.42i	−0.206407	+	0.206407i
$609$	−9288.39	+	22734.8i	−0.618037	+	1.51274i
$610$	−10429.0	−	6251.57i	−0.692226	−	0.414948i
$611$		−	13105.9i		−	0.867773i
$612$	39.9122	+	4122.39i	0.00263620	+	0.272284i
$613$	4616.26	+	4616.26i	0.304158	+	0.304158i	0.842638	−	0.538480i	$-0.181001\pi$
$613$	4616.26	+	4616.26i	0.304158	+	0.304158i	−0.538480	+	0.842638i	$0.681001\pi$
$614$	7235.13			0.475547
$615$	716.293	+	956.195i	0.0469654	+	0.0626951i
$616$	2334.93			0.152722
$617$	14556.9	+	14556.9i	0.949818	+	0.949818i	0.998800	−	0.0489818i	$-0.0155976\pi$
$617$	14556.9	+	14556.9i	0.949818	+	0.949818i	−0.0489818	+	0.998800i	$0.515598\pi$
$618$	−5768.51	−	13738.0i	−0.375475	−	0.894209i
$619$		−	12601.3i		−	0.818236i	−0.912482	−	0.409118i	$-0.865837\pi$
$619$		−	12601.3i		−	0.818236i	0.912482	−	0.409118i	$-0.134163\pi$
$620$	−69.6555	−	278.135i	−0.00451199	−	0.0180164i
$621$	−5680.93	−	13170.7i	−0.367098	−	0.851081i
$622$	11458.5	−	11458.5i	0.738655	−	0.738655i
$623$	−7973.31	+	7973.31i	−0.512751	+	0.512751i
$624$	−3723.02	−	1521.05i	−0.238846	−	0.0975815i
$625$	8683.22	−	12990.1i	0.555726	−	0.831366i
$626$		−	300.509i		−	0.0191865i
$627$	−8357.69	+	3509.36i	−0.532335	+	0.223525i
$628$	−4026.94	−	4026.94i	−0.255879	−	0.255879i
$629$	7999.17			0.507071
$630$	−6987.20	+	11916.3i	−0.441868	+	0.753583i
$631$	20754.9			1.30942			0.654708	−	0.755882i	$-0.272792\pi$
$631$	20754.9			1.30942			0.654708	+	0.755882i	$0.272792\pi$
$632$	554.045	+	554.045i	0.0348714	+	0.0348714i
$633$	17160.5	−	7205.64i	1.07752	−	0.452446i
$634$		−	3321.93i		−	0.208093i
$635$	−2377.63	+	3966.41i	−0.148588	+	0.247877i
$636$	−327.174	−	133.668i	−0.0203983	−	0.00833379i
$637$	−6174.50	+	6174.50i	−0.384054	+	0.384054i
$638$	3726.51	−	3726.51i	0.231245	−	0.231245i
$639$	−2877.29	−	2822.11i	−0.178128	−	0.174712i
$640$	735.781	−	1227.45i	0.0454442	−	0.0758111i
$641$		−	28695.5i		−	1.76818i	−0.467313	−	0.884092i	$-0.654778\pi$
$641$		−	28695.5i		−	1.76818i	0.467313	−	0.884092i	$-0.345222\pi$
$642$	593.301	+	1412.97i	0.0364731	+	0.0868622i
$643$	−7444.99	−	7444.99i	−0.456612	−	0.456612i	0.440930	−	0.897542i	$-0.354649\pi$
$643$	−7444.99	−	7444.99i	−0.456612	−	0.456612i	−0.897542	+	0.440930i	$0.854649\pi$
$644$	9357.00			0.572543
$645$	−13197.9	−	1893.11i	−0.805686	−	0.115568i
$646$	10440.5			0.635874
$647$	−15997.5	−	15997.5i	−0.972065	−	0.972065i	0.0275552	−	0.999620i	$-0.491228\pi$
$647$	−15997.5	−	15997.5i	−0.972065	−	0.972065i	−0.999620	+	0.0275552i	$0.991228\pi$
$648$	−4202.92	−	4043.23i	−0.254794	−	0.245113i
$649$			8002.11i			0.483991i
$650$	5699.86	+	10666.1i	0.343949	+	0.643628i
$651$	288.287	−	705.627i	0.0173561	−	0.0424819i
$652$	−2777.83	+	2777.83i	−0.166853	+	0.166853i
$653$	4592.90	−	4592.90i	0.275243	−	0.275243i	−0.555963	−	0.831207i	$-0.687651\pi$
$653$	4592.90	−	4592.90i	0.275243	−	0.275243i	0.831207	+	0.555963i	$0.187651\pi$
$654$	−2864.21	+	7010.62i	−0.171253	+	0.419170i
$655$	−1262.92	−	5042.85i	−0.0753378	−	0.300825i
$656$		−	329.044i		−	0.0195838i
$657$	29469.2	−	285.316i	1.74993	−	0.0169425i
$658$	8766.63	+	8766.63i	0.519390	+	0.519390i
$659$	12460.6			0.736565			0.368282	−	0.929714i	$-0.379946\pi$
$659$	12460.6			0.736565			0.368282	+	0.929714i	$0.379946\pi$
$660$	2372.43	−	1777.21i	0.139919	−	0.104815i
$661$	−21945.5			−1.29135			−0.645675	−	0.763612i	$-0.723424\pi$
$661$	−21945.5			−1.29135			−0.645675	+	0.763612i	$0.723424\pi$
$662$	−4005.71	−	4005.71i	−0.235176	−	0.235176i
$663$	3714.68	+	8846.65i	0.217596	+	0.518213i
$664$		−	8317.36i		−	0.486109i
$665$	30005.4	+	17986.5i	1.74972	+	1.04885i
$666$	−7923.79	+	8078.72i	−0.461022	+	0.470036i
$667$	14933.6	−	14933.6i	0.866915	−	0.866915i
$668$	7501.99	−	7501.99i	0.434522	−	0.434522i
$669$	1943.45	+	794.005i	0.112314	+	0.0458864i
$670$	−3697.87	+	926.084i	−0.213225	+	0.0533996i
$671$			6936.51i			0.399078i
$672$	3507.79	−	1472.91i	0.201363	−	0.0845515i
$673$	5271.96	+	5271.96i	0.301960	+	0.301960i	0.841780	−	0.539820i	$-0.181508\pi$
$673$	5271.96	+	5271.96i	0.301960	+	0.301960i	−0.539820	+	0.841780i	$0.681508\pi$
$674$	13547.8			0.774244
$675$	1970.56	+	17426.0i	0.112366	+	0.993667i
$676$	−572.230			−0.0325575
$677$	−6270.55	−	6270.55i	−0.355977	−	0.355977i	0.506350	−	0.862328i	$-0.330994\pi$
$677$	−6270.55	−	6270.55i	−0.355977	−	0.355977i	−0.862328	+	0.506350i	$0.830994\pi$
$678$	−1689.21	+	709.293i	−0.0956839	+	0.0401773i
$679$		−	26273.8i		−	1.48497i
$680$	−3311.93	+	829.430i	−0.186775	+	0.0467753i
$681$	−32513.2	−	13283.4i	−1.82953	−	0.747461i
$682$	−115.661	+	115.661i	−0.00649397	+	0.00649397i
$683$	−16616.6	+	16616.6i	−0.930917	+	0.930917i	−0.997763	−	0.0668461i	$-0.978706\pi$
$683$	−16616.6	+	16616.6i	−0.930917	+	0.930917i	0.0668461	+	0.997763i	$0.478706\pi$
$684$	−10342.1	+	10544.3i	−0.578127	+	0.589431i
$685$	1384.85	+	830.133i	0.0772442	+	0.0463033i
$686$			7435.62i			0.413839i
$687$	10183.3	+	24251.9i	0.565526	+	1.34682i
$688$	2596.55	+	2596.55i	0.143884	+	0.143884i
$689$	−822.565			−0.0454822
$690$	9507.29	−	7121.98i	0.524545	−	0.392941i
$691$	−35477.3			−1.95314			−0.976571	−	0.215197i	$-0.930961\pi$
$691$	−35477.3			−1.95314			−0.976571	+	0.215197i	$0.930961\pi$
$692$	−8402.89	−	8402.89i	−0.461604	−	0.461604i
$693$	7880.02	−	76.2931i	0.431944	−	0.00418201i
$694$		−	6008.07i		−	0.328621i
$695$	−913.516	−	3647.68i	−0.0498585	−	0.199086i
$696$	3247.64	−	7949.11i	0.176870	−	0.432917i
$697$	−555.091	+	555.091i	−0.0301658	+	0.0301658i
$698$	13060.4	−	13060.4i	0.708229	−	0.708229i
$699$	2814.79	−	6889.65i	0.152311	−	0.372805i
$700$	−10947.3	−	3321.93i	−0.591096	−	0.179368i
$701$			6316.02i			0.340304i	0.985418	+	0.170152i	$0.0544258\pi$
$701$			6316.02i			0.340304i	−0.985418	+	0.170152i	$0.945574\pi$
$702$	−12614.3	−	5011.66i	−0.678200	−	0.269449i
$703$	20264.2	+	20264.2i	1.08717	+	1.08717i
$704$	−816.397			−0.0437061
$705$	15580.1	+	2234.80i	0.832310	+	0.119387i
$706$	2791.01			0.148784
$707$	−19759.0	−	19759.0i	−1.05108	−	1.05108i
$708$	5047.84	+	12021.6i	0.267951	+	0.638137i
$709$		−	4327.74i		−	0.229241i	−0.993409	−	0.114620i	$-0.963435\pi$
$709$		−	4327.74i		−	0.229241i	0.993409	−	0.114620i	$-0.0365652\pi$
$710$	1716.09	−	2862.81i	0.0907092	−	0.151323i
$711$	1887.92	+	1851.71i	0.0995814	+	0.0976716i
$712$	2787.83	−	2787.83i	0.146739	−	0.146739i
$713$	−463.500	+	463.500i	−0.0243453	+	0.0243453i
$714$	−8402.34	−	3432.80i	−0.440406	−	0.179929i
$715$	3547.10	−	5917.35i	0.185530	−	0.309505i
$716$		−	5088.50i		−	0.265595i
$717$	5464.55	−	2294.55i	0.284627	−	0.119514i
$718$	15134.2	+	15134.2i	0.786635	+	0.786635i
$719$	−26854.1			−1.39289			−0.696447	−	0.717609i	$-0.745237\pi$
$719$	−26854.1			−1.39289			−0.696447	+	0.717609i	$0.745237\pi$
$720$	2443.04	−	4166.48i	0.126454	−	0.215660i
$721$	32804.6			1.69446
$722$	16748.6	+	16748.6i	0.863321	+	0.863321i
$723$	−4285.53	+	1799.48i	−0.220444	+	0.0925635i
$724$			250.912i			0.0128799i
$725$	−22773.4	+	12169.9i	−1.16660	+	0.623419i
$726$	11239.3	+	4591.85i	0.574558	+	0.234738i
$727$	15761.3	−	15761.3i	0.804065	−	0.804065i	−0.179663	−	0.983728i	$-0.557501\pi$
$727$	15761.3	−	15761.3i	0.804065	−	0.804065i	0.983728	+	0.179663i	$0.0575007\pi$
$728$	6261.11	−	6261.11i	0.318753	−	0.318753i
$729$	−14316.3	−	13507.9i	−0.727343	−	0.686274i
$730$	5929.25	+	23675.6i	0.300618	+	1.20037i
$731$		−	8760.65i		−	0.443262i
$732$	4375.65	+	10420.8i	0.220941	+	0.526179i
$733$	−16481.2	−	16481.2i	−0.830487	−	0.830487i	0.157096	−	0.987583i	$-0.449787\pi$
$733$	−16481.2	−	16481.2i	−0.830487	−	0.830487i	−0.987583	+	0.157096i	$0.949787\pi$
$734$	−2842.14			−0.142923
$735$	−6287.25	−	8392.98i	−0.315522	−	0.421197i
$736$	−3271.63			−0.163850
$737$	1537.74	+	1537.74i	0.0768565	+	0.0768565i
$738$	−10.7514	−	1110.47i	−0.000536266	−	0.0553889i
$739$			18693.3i			0.930505i	0.885178	+	0.465253i	$0.154037\pi$
$739$			18693.3i			0.930505i	−0.885178	+	0.465253i	$0.845963\pi$
$740$	−8038.08	−	4818.35i	−0.399305	−	0.239360i
$741$	−13000.8	+	31821.4i	−0.644528	+	1.57758i
$742$	550.218	−	550.218i	0.0272226	−	0.0272226i
$743$	2518.82	−	2518.82i	0.124369	−	0.124369i	−0.642182	−	0.766552i	$-0.721971\pi$
$743$	2518.82	−	2518.82i	0.124369	−	0.124369i	0.766552	+	0.642182i	$0.221971\pi$
$744$	−100.798	+	246.719i	−0.00496698	+	0.0121575i
$745$	−35153.4	+	8803.72i	−1.72875	+	0.432944i
$746$		−	24544.2i		−	1.20460i
$747$	−271.767	−	28069.8i	−0.0133112	−	1.37486i
$748$	1377.25	+	1377.25i	0.0673223	+	0.0673223i
$749$	−3374.01			−0.164597
$750$	−13651.5	+	4957.11i	−0.664645	+	0.241344i
$751$	−2523.97			−0.122638			−0.0613190	−	0.998118i	$-0.519531\pi$
$751$	−2523.97			−0.122638			−0.0613190	+	0.998118i	$0.519531\pi$
$752$	−3065.21	−	3065.21i	−0.148639	−	0.148639i
$753$	8446.15	+	20114.8i	0.408758	+	0.973474i
$754$		−	19985.3i		−	0.965279i
$755$	2431.04	−	608.822i	0.117185	−	0.0293474i
$756$	11790.1	−	5085.44i	0.567198	−	0.244651i
$757$	−23079.0	+	23079.0i	−1.10809	+	1.10809i	−0.114684	+	0.993402i	$0.536585\pi$
$757$	−23079.0	+	23079.0i	−1.10809	+	1.10809i	−0.993402	+	0.114684i	$0.963415\pi$
$758$	−20779.1	+	20779.1i	−0.995687	+	0.995687i
$759$	−6273.31	−	2562.99i	−0.300009	−	0.122570i
$760$	−10491.3	−	6288.88i	−0.500734	−	0.300160i
$761$			30848.4i			1.46945i	0.678364	+	0.734726i	$0.262689\pi$
$761$			30848.4i			1.46945i	−0.678364	+	0.734726i	$0.737311\pi$
$762$	3963.28	−	1664.17i	0.188418	−	0.0791161i
$763$	−11790.0	−	11790.0i	−0.559404	−	0.559404i
$764$	−8159.59			−0.386392
$765$	−11150.1	+	2907.41i	−0.526973	+	0.137409i
$766$	−5235.16			−0.246937
$767$	21457.6	+	21457.6i	1.01016	+	1.01016i
$768$	−1226.48	+	514.994i	−0.0576260	+	0.0241970i
$769$			24831.0i			1.16441i	0.813043	+	0.582204i	$0.197809\pi$
$769$			24831.0i			1.16441i	−0.813043	+	0.582204i	$0.802191\pi$
$770$	1585.47	+	6330.82i	0.0742032	+	0.296295i
$771$	20439.8	+	8350.77i	0.954764	+	0.390072i
$772$	−5097.95	+	5097.95i	−0.237667	+	0.237667i
$773$	17900.7	−	17900.7i	0.832913	−	0.832913i	−0.155001	−	0.987914i	$-0.549538\pi$
$773$	17900.7	−	17900.7i	0.832913	−	0.832913i	0.987914	+	0.155001i	$0.0495380\pi$
$774$	8847.77	+	8678.09i	0.410887	+	0.403007i
$775$	706.825	−	377.721i	0.0327612	−	0.0175073i
$776$			9186.49i			0.424969i
$777$	−9645.51	−	22971.2i	−0.445342	−	1.06060i
$778$	13147.4	+	13147.4i	0.605856	+	0.605856i
$779$	−2812.41			−0.129352
$780$	1596.09	−	11127.2i	0.0732683	−	0.510794i
$781$	−1904.11			−0.0872398
$782$	5519.17	+	5519.17i	0.252385	+	0.252385i
$783$	10700.5	−	26933.1i	0.488385	−	1.22926i
$784$			2888.17i			0.131568i
$785$	8184.06	−	13652.8i	0.372104	−	0.620752i
$786$	−1827.56	+	4473.24i	−0.0829349	+	0.202996i
$787$	−3928.66	+	3928.66i	−0.177944	+	0.177944i	−0.790459	−	0.612515i	$-0.790158\pi$
$787$	−3928.66	+	3928.66i	−0.177944	+	0.177944i	0.612515	+	0.790459i	$0.290158\pi$
$788$	7934.59	−	7934.59i	0.358703	−	0.358703i
$789$	9990.11	−	24452.4i	0.450770	−	1.10333i
$790$	−1126.00	+	1878.42i	−0.0507105	+	0.0845964i
$791$		−	4033.63i		−	0.181314i
$792$	−2755.21	+	26.6755i	−0.123614	+	0.00119681i
$793$	18600.2	+	18600.2i	0.832930	+	0.832930i
$794$	−2398.92			−0.107222
$795$	140.263	−	977.849i	0.00625736	−	0.0436235i
$796$	−7261.38			−0.323333
$797$	−10942.0	−	10942.0i	−0.486307	−	0.486307i	0.420832	−	0.907139i	$-0.361738\pi$
$797$	−10942.0	−	10942.0i	−0.486307	−	0.486307i	−0.907139	+	0.420832i	$0.861738\pi$
$798$	−12589.3	−	29981.8i	−0.558464	−	1.33001i
$799$			10341.9i			0.457909i
$800$	3827.65	+	1161.50i	0.169160	+	0.0513314i
$801$	9317.38	−	9499.56i	0.411003	−	0.419039i
$802$	12059.2	−	12059.2i	0.530954	−	0.530954i
$803$	9845.35	−	9845.35i	0.432671	−	0.432671i
$804$	3280.18	+	1340.13i	0.143884	+	0.0587845i
$805$	6353.62	+	25370.1i	0.278181	+	1.11078i
$806$			620.289i			0.0271076i
$807$	−10043.0	+	4217.02i	−0.438080	+	0.183948i
$808$	6908.63	+	6908.63i	0.300798	+	0.300798i
$809$	15310.9			0.665395			0.332697	−	0.943034i	$-0.392041\pi$
$809$	15310.9			0.665395			0.332697	+	0.943034i	$0.392041\pi$
$810$	8108.73	−	14141.0i	0.351743	−	0.613414i
$811$	−3667.20			−0.158783			−0.0793915	−	0.996844i	$-0.525298\pi$
$811$	−3667.20			−0.158783			−0.0793915	+	0.996844i	$0.525298\pi$
$812$	13368.2	+	13368.2i	0.577751	+	0.577751i
$813$	2821.35	−	1184.67i	0.121708	−	0.0511049i
$814$			5346.27i			0.230205i
$815$	−9417.88	−	5645.46i	−0.404778	−	0.242640i
$816$	2937.83	+	1200.26i	0.126035	+	0.0514921i
$817$	22193.2	−	22193.2i	0.950358	−	0.950358i
$818$	−10754.9	+	10754.9i	−0.459702	+	0.459702i
$819$	20925.7	−	21334.8i	0.892798	−	0.910255i
$820$	892.153	−	223.428i	0.0379943	−	0.00951519i
$821$			7128.41i			0.303025i	0.988455	+	0.151512i	$0.0484143\pi$
$821$			7128.41i			0.303025i	−0.988455	+	0.151512i	$0.951586\pi$
$822$	−581.034	−	1383.76i	−0.0246544	−	0.0587153i
$823$	−17408.3	−	17408.3i	−0.737321	−	0.737321i	0.234738	−	0.972059i	$-0.424577\pi$
$823$	−17408.3	−	17408.3i	−0.737321	−	0.737321i	−0.972059	+	0.234738i	$0.924577\pi$
$824$	−11469.9			−0.484921
$825$	6429.58	+	5225.73i	0.271332	+	0.220529i
$826$	−28706.2			−1.20922
$827$	25331.1	+	25331.1i	1.06511	+	1.06511i	0.997727	+	0.0673858i	$0.0214658\pi$
$827$	25331.1	+	25331.1i	1.06511	+	1.06511i	0.0673858	+	0.997727i	$0.478534\pi$
$828$	−11041.2	+	106.899i	−0.463417	+	0.00448672i
$829$		−	37685.9i		−	1.57887i	−0.613832	−	0.789437i	$-0.710373\pi$
$829$		−	37685.9i		−	1.57887i	0.613832	−	0.789437i	$-0.289627\pi$
$830$	22551.3	−	5647.68i	0.943093	−	0.236186i
$831$	4146.74	−	10149.8i	0.173103	−	0.423698i
$832$	−2189.16	+	2189.16i	−0.0912207	+	0.0912207i
$833$	4872.29	−	4872.29i	0.202659	−	0.202659i
$834$	−1321.94	+	3235.67i	−0.0548862	+	0.134343i
$835$	25434.6	+	15246.5i	1.05413	+	0.631889i
$836$			6977.92i			0.288680i
$837$	−332.116	+	835.931i	−0.0137152	+	0.0345209i
$838$	−19664.2	−	19664.2i	−0.810609	−	0.810609i
$839$	10906.1			0.448774			0.224387	−	0.974500i	$-0.427962\pi$
$839$	10906.1			0.448774			0.224387	+	0.974500i	$0.427962\pi$
$840$	6375.44	+	8510.71i	0.261873	+	0.349580i
$841$	18282.0			0.749601
$842$	−22080.8	−	22080.8i	−0.903745	−	0.903745i
$843$	10398.6	+	24764.7i	0.424849	+	1.01180i
$844$		−	14327.5i		−	0.584327i
$845$	−388.557	−	1551.52i	−0.0158187	−	0.0631642i
$846$	−10444.7	−	10244.4i	−0.424465	−	0.416325i
$847$	−18901.4	+	18901.4i	−0.766778	+	0.766778i
$848$	−192.381	+	192.381i	−0.00779055	+	0.00779055i
$849$	6071.49	+	2480.53i	0.245434	+	0.100273i
$850$	−4497.75	−	8416.60i	−0.181496	−	0.339632i
$851$			21424.6i			0.863017i
$852$	−2860.56	+	1201.14i	−0.115025	+	0.0482984i
$853$	−14701.8	−	14701.8i	−0.590131	−	0.590131i	0.347536	−	0.937667i	$-0.387018\pi$
$853$	−14701.8	−	14701.8i	−0.590131	−	0.590131i	−0.937667	+	0.347536i	$0.887018\pi$
$854$	−24883.6			−0.997071
$855$	−35611.8	−	20881.2i	−1.42444	−	0.835230i
$856$	1179.70			0.0471045
$857$	−14745.6	−	14745.6i	−0.587749	−	0.587749i	0.349272	−	0.937021i	$-0.386429\pi$
$857$	−14745.6	−	14745.6i	−0.587749	−	0.587749i	−0.937021	+	0.349272i	$0.886429\pi$
$858$	−5912.69	+	2482.72i	−0.235263	+	0.0987862i
$859$			45884.6i			1.82254i	0.411808	+	0.911271i	$0.364897\pi$
$859$			45884.6i			1.82254i	−0.411808	+	0.911271i	$0.635103\pi$
$860$	−5277.03	+	8803.26i	−0.209239	+	0.349057i
$861$	2263.39	+	924.714i	0.0895888	+	0.0366018i
$862$	2386.65	−	2386.65i	0.0943034	−	0.0943034i
$863$	10936.4	−	10936.4i	0.431376	−	0.431376i	−0.457720	−	0.889096i	$-0.651334\pi$
$863$	10936.4	−	10936.4i	0.431376	−	0.431376i	0.889096	+	0.457720i	$0.151334\pi$
$864$	−4122.35	+	1778.10i	−0.162321	+	0.0700141i
$865$	17077.4	−	28489.0i	0.671272	−	1.11983i
$866$		−	10198.0i		−	0.400164i
$867$	6952.22	+	16557.0i	0.272329	+	0.648564i
$868$	−414.914	−	414.914i	−0.0162248	−	0.0162248i
$869$	1249.37			0.0487710
$870$	23758.1	+	3407.86i	0.925832	+	0.132801i
$871$	8246.86			0.320820
$872$	4122.30	+	4122.30i	0.160090	+	0.160090i
$873$	300.165	+	31002.9i	0.0116370	+	1.20194i
$874$			27963.3i			1.08223i
$875$	1573.48	−	31937.5i	0.0607925	−	1.23393i
$876$	8580.17	−	21001.3i	0.330933	−	0.810011i
$877$	−4986.22	+	4986.22i	−0.191987	+	0.191987i	−0.796554	−	0.604567i	$-0.793346\pi$
$877$	−4986.22	+	4986.22i	−0.191987	+	0.191987i	0.604567	+	0.796554i	$0.293346\pi$
$878$	−11334.8	+	11334.8i	−0.435685	+	0.435685i
$879$	−9236.74	+	22608.4i	−0.354434	+	0.867534i
$880$	−554.352	−	2213.54i	−0.0212355	−	0.0847936i
$881$		−	40395.0i		−	1.54477i	−0.635155	−	0.772385i	$-0.719064\pi$
$881$		−	40395.0i		−	1.54477i	0.635155	−	0.772385i	$-0.280936\pi$
$882$	94.3701	+	9747.13i	0.00360273	+	0.372112i
$883$	−16473.1	−	16473.1i	−0.627819	−	0.627819i	0.319700	−	0.947519i	$-0.396418\pi$
$883$	−16473.1	−	16473.1i	−0.627819	−	0.627819i	−0.947519	+	0.319700i	$0.896418\pi$
$884$	7386.16			0.281022
$885$	−29167.3	+	21849.4i	−1.10785	+	0.829899i
$886$	−13544.5			−0.513584
$887$	8236.06	+	8236.06i	0.311770	+	0.311770i	0.845595	−	0.533825i	$-0.179246\pi$
$887$	8236.06	+	8236.06i	0.311770	+	0.311770i	−0.533825	+	0.845595i	$0.679246\pi$
$888$	3372.50	+	8031.75i	0.127448	+	0.303522i
$889$			9463.85i			0.357038i
$890$	9451.78	+	5665.78i	0.355982	+	0.213390i
$891$	−9297.52	+	180.051i	−0.349583	+	0.00676985i
$892$	1142.77	−	1142.77i	0.0428953	−	0.0428953i
$893$	−26199.0	+	26199.0i	−0.981764	+	0.981764i
$894$	31182.7	+	12739.8i	1.16656	+	0.476603i
$895$	13796.7	−	3455.21i	0.515277	−	0.129045i
$896$		−	2928.69i		−	0.109197i
$897$	−23694.5	+	9949.23i	−0.881980	+	0.370340i
$898$	9103.51	+	9103.51i	0.338294	+	0.338294i
$899$	−1324.39			−0.0491335
$900$	12955.7	+	3794.80i	0.479840	+	0.140548i
$901$	649.086			0.0240002
$902$	−370.997	−	370.997i	−0.0136949	−	0.0136949i
$903$	−25157.9	+	10563.7i	−0.927134	+	0.389300i
$904$			1410.34i			0.0518884i
$905$	−680.311	+	170.375i	−0.0249882	+	0.00625797i
$906$	−2156.44	−	881.022i	−0.0790761	−	0.0323068i
$907$	−5461.54	+	5461.54i	−0.199942	+	0.199942i	−0.799975	−	0.600033i	$-0.795154\pi$
$907$	−5461.54	+	5461.54i	−0.199942	+	0.199942i	0.600033	+	0.799975i	$0.295154\pi$
$908$	−19118.0	+	19118.0i	−0.698738	+	0.698738i
$909$	23541.3	+	23089.8i	0.858982	+	0.842508i
$910$	21227.5	+	12724.6i	0.773280	+	0.463535i
$911$			1893.10i			0.0688486i	0.999407	+	0.0344243i	$0.0109598\pi$
$911$			1893.10i			0.0688486i	−0.999407	+	0.0344243i	$0.989040\pi$
$912$	4401.77	+	10483.0i	0.159821	+	0.380621i
$913$	−9377.82	−	9377.82i	−0.339935	−	0.339935i
$914$	−21024.1			−0.760850
$915$	−25283.2	+	18939.9i	−0.913485	+	0.684299i
$916$	20248.1			0.730368
$917$	−7522.77	−	7522.77i	−0.270909	−	0.270909i
$918$	9953.94	+	3954.70i	0.357875	+	0.142184i
$919$			6455.86i			0.231729i	0.993265	+	0.115865i	$0.0369638\pi$
$919$			6455.86i			0.231729i	−0.993265	+	0.115865i	$0.963036\pi$
$920$	−2221.51	−	8870.53i	−0.0796098	−	0.317883i
$921$	7109.31	−	17401.2i	0.254354	−	0.622571i
$922$	22263.6	−	22263.6i	0.795243	−	0.795243i
$923$	−5105.85	+	5105.85i	−0.182081	+	0.182081i
$924$	2294.33	−	5615.73i	0.0816859	−	0.199939i
$925$	7606.20	−	25065.8i	0.270368	−	0.890984i
$926$		−	12403.0i		−	0.440160i
$927$	−38709.3	+	374.777i	−1.37150	+	0.0132786i
$928$	−4674.14	−	4674.14i	−0.165341	−	0.165341i
$929$	−14798.5			−0.522628			−0.261314	−	0.965254i	$-0.584156\pi$
$929$	−14798.5			−0.522628			−0.261314	+	0.965254i	$0.584156\pi$
$930$	−737.386	−	105.771i	−0.0259998	−	0.00372941i
$931$	24685.8			0.869007
$932$	−4051.17	−	4051.17i	−0.142382	−	0.142382i
$933$	−16299.5	−	38818.0i	−0.571943	−	1.36210i
$934$		−	1146.51i		−	0.0401659i
$935$	−2799.02	+	4669.38i	−0.0979012	+	0.163321i
$936$	−7316.55	+	7459.61i	−0.255501	+	0.260497i
$937$	5568.25	−	5568.25i	0.194137	−	0.194137i	−0.603344	−	0.797481i	$-0.706165\pi$
$937$	5568.25	−	5568.25i	0.194137	−	0.194137i	0.797481	+	0.603344i	$0.206165\pi$
$938$	−5516.37	+	5516.37i	−0.192021	+	0.192021i
$939$	−722.754	−	295.284i	−0.0251184	−	0.0102622i
$940$	6229.50	−	10392.2i	0.216153	−	0.360592i
$941$			26799.4i			0.928413i	0.885727	+	0.464207i	$0.153660\pi$
$941$			26799.4i			0.928413i	−0.885727	+	0.464207i	$0.846340\pi$
$942$	−13642.1	+	5728.25i	−0.471850	+	0.198128i
$943$	−1486.73	−	1486.73i	−0.0513411	−	0.0513411i
$944$	10037.0			0.346055
$945$	21794.2	+	28514.0i	0.750227	+	0.981545i
$946$	5855.21			0.201236
$947$	20065.7	+	20065.7i	0.688540	+	0.688540i	0.961909	−	0.273369i	$-0.0881379\pi$
$947$	20065.7	+	20065.7i	0.688540	+	0.688540i	−0.273369	+	0.961909i	$0.588138\pi$
$948$	1876.94	−	788.120i	0.0643039	−	0.0270010i
$949$		−	52800.5i		−	1.80609i
$950$	9927.56	−	32715.8i	0.339045	−	1.11730i
$951$	−7989.56	−	3264.16i	−0.272428	−	0.111302i
$952$	−4940.64	+	4940.64i	−0.168201	+	0.168201i
$953$	22947.3	−	22947.3i	0.779996	−	0.779996i	−0.199834	−	0.979830i	$-0.564040\pi$
$953$	22947.3	−	22947.3i	0.779996	−	0.779996i	0.979830	+	0.199834i	$0.0640402\pi$
$954$	−642.969	+	655.541i	−0.0218207	+	0.0222473i
$955$	−5540.56	−	22123.5i	−0.187736	−	0.749634i
$956$		−	4562.41i		−	0.154350i
$957$	−5300.91	−	12624.3i	−0.179053	−	0.426423i
$958$	−1180.61	−	1180.61i	−0.0398162	−	0.0398162i
$959$	3304.24			0.111261
$960$	−2229.14	−	2975.72i	−0.0749429	−	0.100043i
$961$	−29749.9			−0.998620
$962$	14336.0	+	14336.0i	0.480469	+	0.480469i
$963$	3981.31	−	38.5464i	0.133225	−	0.00128987i
$964$			3578.03i			0.119544i
$965$	−17284.0	−	10360.7i	−0.576571	−	0.345620i
$966$	9194.28	−	22504.5i	0.306233	−	0.749554i
$967$	−15372.5	+	15372.5i	−0.511218	+	0.511218i	−0.914899	−	0.403682i	$-0.867730\pi$
$967$	−15372.5	+	15372.5i	−0.511218	+	0.511218i	0.403682	+	0.914899i	$0.367730\pi$
$968$	6608.79	−	6608.79i	0.219436	−	0.219436i
$969$	10258.9	−	25110.3i	0.340107	−	0.832465i
$970$	−24907.8	+	6237.84i	−0.824475	+	0.206479i
$971$			50515.3i			1.66953i	0.550607	+	0.834765i	$0.314396\pi$
$971$			50515.3i			1.66953i	−0.550607	+	0.834765i	$0.685604\pi$
$972$	−13854.2	+	6135.50i	−0.457174	+	0.202465i
$973$	−5441.51	−	5441.51i	−0.179288	−	0.179288i
$974$	−3178.29			−0.104557
$975$	31253.7	−	3228.09i	1.02658	−	0.106033i
$976$	8700.42			0.285342
$977$	9640.67	+	9640.67i	0.315693	+	0.315693i	0.847110	−	0.531417i	$-0.178340\pi$
$977$	9640.67	+	9640.67i	0.315693	+	0.315693i	−0.531417	+	0.847110i	$0.678340\pi$
$978$	3951.42	+	9410.46i	0.129195	+	0.307682i
$979$		−	6286.54i		−	0.205229i
$980$	−7830.85	+	1961.14i	−0.255252	+	0.0639247i
$981$	14046.8	+	13777.4i	0.457166	+	0.448398i
$982$	4148.90	−	4148.90i	0.134824	−	0.134824i
$983$	30440.0	−	30440.0i	0.987677	−	0.987677i	−0.0122482	−	0.999925i	$-0.503899\pi$
$983$	30440.0	−	30440.0i	0.987677	−	0.987677i	0.999925	+	0.0122482i	$0.00389882\pi$
$984$	−791.381	−	323.322i	−0.0256385	−	0.0104747i
$985$	26901.2	+	16125.7i	0.870198	+	0.521632i
$986$			15770.4i			0.509362i
$987$	29698.7	−	12470.4i	0.957772	−	0.402165i
$988$	18711.2	+	18711.2i	0.602514	+	0.602514i
$989$	23464.1			0.754415
$990$	−1943.18	−	7452.23i	−0.0623821	−	0.239240i
$991$	−6167.34			−0.197691			−0.0988455	−	0.995103i	$-0.531515\pi$
$991$	−6167.34			−0.197691			−0.0988455	+	0.995103i	$0.531515\pi$
$992$	145.073	+	145.073i	0.00464321	+	0.00464321i
$993$	−13570.2	+	5698.07i	−0.433672	+	0.182097i
$994$		−	6830.66i		−	0.217963i
$995$	−4930.65	−	19688.2i	−0.157098	−	0.627293i
$996$	−20004.0	−	8172.72i	−0.636398	−	0.260003i
$997$	6952.37	−	6952.37i	0.220846	−	0.220846i	−0.588008	−	0.808855i	$-0.700088\pi$
$997$	6952.37	−	6952.37i	0.220846	−	0.220846i	0.808855	+	0.588008i	$0.200088\pi$
$998$	27594.9	−	27594.9i	0.875252	−	0.875252i
$999$	11644.1	+	26995.7i	0.368772	+	0.854961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.4.e.a.23.1	yes	12
3.2	odd	2	inner	30.4.e.a.23.5	yes	12
4.3	odd	2		240.4.v.d.113.6		12
5.2	odd	4	inner	30.4.e.a.17.5	yes	12
5.3	odd	4		150.4.e.c.107.2		12
5.4	even	2		150.4.e.c.143.6		12
12.11	even	2		240.4.v.d.113.4		12
15.2	even	4	inner	30.4.e.a.17.1	✓	12
15.8	even	4		150.4.e.c.107.6		12
15.14	odd	2		150.4.e.c.143.2		12
20.7	even	4		240.4.v.d.17.4		12
60.47	odd	4		240.4.v.d.17.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.4.e.a.17.1	✓	12	15.2	even	4	inner
30.4.e.a.17.5	yes	12	5.2	odd	4	inner
30.4.e.a.23.1	yes	12	1.1	even	1	trivial
30.4.e.a.23.5	yes	12	3.2	odd	2	inner
150.4.e.c.107.2		12	5.3	odd	4
150.4.e.c.107.6		12	15.8	even	4
150.4.e.c.143.2		12	15.14	odd	2
150.4.e.c.143.6		12	5.4	even	2
240.4.v.d.17.4		12	20.7	even	4
240.4.v.d.17.6		12	60.47	odd	4
240.4.v.d.113.4		12	12.11	even	2
240.4.v.d.113.6		12	4.3	odd	2

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:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	30.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 - 1.41421i) q^{2} +(-4.79094 + 2.01170i) q^{3} +4.00000i q^{4} +(-10.8454 + 2.71609i) q^{5} +(9.62038 + 3.93044i) q^{6} +(-16.1789 + 16.1789i) q^{7} +(5.65685 - 5.65685i) q^{8} +(18.9062 - 19.2758i) q^{9} +(19.1789 + 11.4966i) q^{10} -12.7562i q^{11} +(-8.04679 - 19.1637i) q^{12} +(-34.2057 - 34.2057i) q^{13} +45.7607 q^{14} +(46.4957 - 34.8303i) q^{15} -16.0000 q^{16} +(26.9917 + 26.9917i) q^{17} +(-53.9975 + 0.522794i) q^{18} +136.755i q^{19} +(-10.8644 - 43.3816i) q^{20} +(44.9649 - 110.059i) q^{21} +(-18.0400 + 18.0400i) q^{22} +(-72.2934 + 72.2934i) q^{23} +(-15.7218 + 38.4815i) q^{24} +(110.246 - 58.9143i) q^{25} +96.7483i q^{26} +(-51.8011 + 130.383i) q^{27} +(-64.7154 - 64.7154i) q^{28} -206.570 q^{29} +(-115.012 - 16.4974i) q^{30} +6.41137 q^{31} +(22.6274 + 22.6274i) q^{32} +(25.6616 + 61.1141i) q^{33} -76.3440i q^{34} +(131.523 - 219.410i) q^{35} +(77.1033 + 75.6246i) q^{36} +(148.178 - 148.178i) q^{37} +(193.401 - 193.401i) q^{38} +(232.689 + 95.0658i) q^{39} +(-45.9863 + 76.7154i) q^{40} +20.5652i q^{41} +(-219.237 + 92.0567i) q^{42} +(-162.284 - 162.284i) q^{43} +51.0248 q^{44} +(-152.690 + 260.405i) q^{45} +204.477 q^{46} +(191.575 + 191.575i) q^{47} +(76.6550 - 32.1871i) q^{48} -180.511i q^{49} +(-239.228 - 72.5935i) q^{50} +(-183.615 - 75.0164i) q^{51} +(136.823 - 136.823i) q^{52} +(12.0238 - 12.0238i) q^{53} +(257.647 - 111.131i) q^{54} +(34.6470 + 138.346i) q^{55} +183.043i q^{56} +(-275.110 - 655.187i) q^{57} +(292.134 + 292.134i) q^{58} -627.311 q^{59} +(139.321 + 185.983i) q^{60} -543.776 q^{61} +(-9.06704 - 9.06704i) q^{62} +(5.98086 + 617.741i) q^{63} -64.0000i q^{64} +(463.880 + 278.069i) q^{65} +(50.1375 - 122.719i) q^{66} +(-120.548 + 120.548i) q^{67} +(-107.967 + 107.967i) q^{68} +(200.921 - 491.786i) q^{69} +(-496.294 + 124.290i) q^{70} -149.269i q^{71} +(-2.09118 - 215.990i) q^{72} +(771.809 + 771.809i) q^{73} -419.112 q^{74} +(-409.662 + 504.035i) q^{75} -547.022 q^{76} +(206.381 + 206.381i) q^{77} +(-194.628 - 463.515i) q^{78} +97.9422i q^{79} +(173.526 - 43.4575i) q^{80} +(-14.1148 - 728.863i) q^{81} +(29.0836 - 29.0836i) q^{82} +(735.158 - 735.158i) q^{83} +(440.235 + 179.860i) q^{84} +(-366.048 - 219.424i) q^{85} +459.009i q^{86} +(989.662 - 415.556i) q^{87} +(-72.1599 - 72.1599i) q^{88} +492.823 q^{89} +(584.205 - 152.332i) q^{90} +1106.82 q^{91} +(-289.174 - 289.174i) q^{92} +(-30.7164 + 12.8977i) q^{93} -541.857i q^{94} +(-371.441 - 1483.17i) q^{95} +(-153.926 - 62.8870i) q^{96} +(-811.978 + 811.978i) q^{97} +(-255.281 + 255.281i) q^{98} +(-245.886 - 241.171i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{3} + 8 q^{6} + 12 q^{7} + 24 q^{10} - 32 q^{12} - 120 q^{13} - 172 q^{15} - 192 q^{16} - 16 q^{18} + 464 q^{21} + 312 q^{22} + 504 q^{25} - 688 q^{27} + 48 q^{28} + 168 q^{30} - 504 q^{31} + 788 q^{33}+ \cdots - 7596 q^{97}+O(q^{100}) \) 12 * q + 8 * q^3 + 8 * q^6 + 12 * q^7 + 24 * q^10 - 32 * q^12 - 120 * q^13 - 172 * q^15 - 192 * q^16 - 16 * q^18 + 464 * q^21 + 312 * q^22 + 504 * q^25 - 688 * q^27 + 48 * q^28 + 168 * q^30 - 504 * q^31 + 788 * q^33 + 368 * q^36 + 768 * q^37 - 192 * q^40 - 872 * q^42 - 1968 * q^43 - 1328 * q^45 - 1152 * q^46 - 128 * q^48 + 256 * q^51 + 480 * q^52 + 1572 * q^55 + 968 * q^57 + 2280 * q^58 + 896 * q^60 + 1848 * q^61 + 1268 * q^63 + 944 * q^66 - 1752 * q^67 - 2616 * q^70 + 64 * q^72 + 180 * q^73 - 1112 * q^75 - 1152 * q^76 - 4080 * q^78 - 4316 * q^81 + 2208 * q^82 - 1872 * q^85 + 3620 * q^87 + 1248 * q^88 + 5168 * q^90 + 4080 * q^91 + 584 * q^93 - 128 * q^96 - 7596 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more