LMFDB - Embedded newform 30.4.e.a.17.5

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			17.5
Root			$-2.67233 + 2.67233i$ of defining polynomial
Character	$\chi$	$=$	30.17
Dual form			30.4.e.a.23.5

$q$-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} +(2.01170 + 4.79094i) 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} +(19.1637 - 8.04679i) q^{12} +(-34.2057 + 34.2057i) q^{13} -45.7607 q^{14} +(8.80503 + 57.4236i) q^{15} -16.0000 q^{16} +(-26.9917 + 26.9917i) q^{17} +(0.522794 + 53.9975i) 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} +(-130.383 - 51.8011i) q^{27} +(-64.7154 + 64.7154i) q^{28} +206.570 q^{29} +(93.6615 + 68.7571i) q^{30} +6.41137 q^{31} +(-22.6274 + 22.6274i) q^{32} +(61.1141 - 25.6616i) 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} +(-92.0567 - 219.237i) q^{42} +(-162.284 + 162.284i) q^{43} -51.0248 q^{44} +(-257.400 + 157.703i) q^{45} +204.477 q^{46} +(-191.575 + 191.575i) q^{47} +(-32.1871 - 76.6550i) 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} +(655.187 - 275.110i) q^{57} +(292.134 - 292.134i) q^{58} +627.311 q^{59} +(229.694 - 35.2201i) q^{60} -543.776 q^{61} +(9.06704 - 9.06704i) q^{62} +(617.741 - 5.98086i) 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} +(215.990 - 2.09118i) q^{72} +(771.809 - 771.809i) q^{73} +419.112 q^{74} +(-60.4737 + 646.698i) q^{75} -547.022 q^{76} +(-206.381 + 206.381i) q^{77} +(-463.515 + 194.628i) 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} +(415.556 + 989.662i) q^{87} +(-72.1599 + 72.1599i) q^{88} -492.823 q^{89} +(-140.992 + 587.044i) q^{90} +1106.82 q^{91} +(289.174 - 289.174i) q^{92} +(12.8977 + 30.7164i) 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 $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

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

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
$3$	2.01170	+	4.79094i	0.387151	+	0.922016i
$3$	2.01170	+	4.79094i	0.387151	+	0.922016i
$4$		−	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	0.119284	−	0.992860i	$-0.461940\pi$
$7$	−16.1789	−	16.1789i	−0.873576	−	0.873576i	−0.992860	+	0.119284i	$0.961940\pi$
$8$	−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	$-0.0559358\pi$
$12$	19.1637	−	8.04679i	0.461008	−	0.193576i
$13$	−34.2057	+	34.2057i	−0.729765	+	0.729765i	−0.970573	−	0.240808i	$-0.922588\pi$
$13$	−34.2057	+	34.2057i	−0.729765	+	0.729765i	0.240808	+	0.970573i	$0.422588\pi$
$14$	−45.7607			−0.873576
$15$	8.80503	+	57.4236i	0.151563	+	0.988448i
$16$	−16.0000			−0.250000
$17$	−26.9917	+	26.9917i	−0.385085	+	0.385085i	−0.872930	−	0.487845i	$-0.837783\pi$
$17$	−26.9917	+	26.9917i	−0.385085	+	0.385085i	0.487845	+	0.872930i	$0.337783\pi$
$18$	0.522794	+	53.9975i	0.00684577	+	0.707074i
$19$		−	136.755i		−	1.65125i	−0.564216	−	0.825627i	$-0.690821\pi$
$19$		−	136.755i		−	1.65125i	0.564216	−	0.825627i	$-0.309179\pi$
$20$	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	$-0.0966155\pi$
$23$	72.2934	+	72.2934i	0.655401	+	0.655401i	−0.298887	+	0.954288i	$0.596616\pi$
$24$	15.7218	−	38.4815i	0.133716	−	0.327292i
$25$	110.246	+	58.9143i	0.881965	+	0.471314i
$26$			96.7483i			0.729765i
$27$	−130.383	−	51.8011i	−0.929339	−	0.369227i
$28$	−64.7154	+	64.7154i	−0.436788	+	0.436788i
$29$	206.570			1.32272			0.661362	−	0.750066i	$-0.269979\pi$
$29$	206.570			1.32272			0.661362	+	0.750066i	$0.269979\pi$
$30$	93.6615	+	68.7571i	0.570005	+	0.418442i
$31$	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
$33$	61.1141	−	25.6616i	0.322382	−	0.135367i
$34$			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	0.954999	−	0.296610i	$-0.0958562\pi$
$37$	148.178	+	148.178i	0.658388	+	0.658388i	−0.296610	+	0.954999i	$0.595856\pi$
$38$	−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	$0.987529\pi$
$42$	−92.0567	−	219.237i	−0.338206	−	0.805451i
$43$	−162.284	+	162.284i	−0.575537	+	0.575537i	−0.933670	−	0.358133i	$-0.883413\pi$
$43$	−162.284	+	162.284i	−0.575537	+	0.575537i	0.358133	+	0.933670i	$0.383413\pi$
$44$	−51.0248			−0.174824
$45$	−257.400	+	157.703i	−0.852687	+	0.522423i
$46$	204.477			0.655401
$47$	−191.575	+	191.575i	−0.594556	+	0.594556i	−0.938859	−	0.344303i	$-0.888115\pi$
$47$	−191.575	+	191.575i	−0.594556	+	0.594556i	0.344303	+	0.938859i	$0.388115\pi$
$48$	−32.1871	−	76.6550i	−0.0967878	−	0.230504i
$49$			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	$-0.257015\pi$
$53$	−12.0238	−	12.0238i	−0.0311622	−	0.0311622i	−0.722516	+	0.691354i	$0.757015\pi$
$54$	−257.647	+	111.131i	−0.649283	+	0.280056i
$55$	34.6470	−	138.346i	0.0849419	−	0.339174i
$56$			183.043i			0.436788i
$57$	655.187	−	275.110i	1.52248	−	0.639285i
$58$	292.134	−	292.134i	0.661362	−	0.661362i
$59$	627.311			1.38422			0.692110	−	0.721792i	$-0.256681\pi$
$59$	627.311			1.38422			0.692110	+	0.721792i	$0.256681\pi$
$60$	229.694	−	35.2201i	0.494224	−	0.0757817i
$61$	−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
$63$	617.741	−	5.98086i	1.23537	−	0.0119606i
$64$			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	0.588608	−	0.808419i	$-0.299676\pi$
$67$	−120.548	−	120.548i	−0.219810	−	0.219810i	−0.808419	+	0.588608i	$0.799676\pi$
$68$	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	$-0.0398140\pi$
$72$	215.990	−	2.09118i	0.353537	−	0.00342288i
$73$	771.809	−	771.809i	1.23744	−	1.23744i	0.276402	−	0.961042i	$-0.410858\pi$
$73$	771.809	−	771.809i	1.23744	−	1.23744i	0.961042	−	0.276402i	$-0.0891422\pi$
$74$	419.112			0.658388
$75$	−60.4737	+	646.698i	−0.0931054	+	0.995656i
$76$	−547.022			−0.825627
$77$	−206.381	+	206.381i	−0.305445	+	0.305445i
$78$	−463.515	+	194.628i	−0.672855	+	0.282530i
$79$		−	97.9422i		−	0.139486i	−0.997565	−	0.0697428i	$-0.977782\pi$
$79$		−	97.9422i		−	0.139486i	0.997565	−	0.0697428i	$-0.0222178\pi$
$80$	−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	$-0.491275\pi$
$83$	−735.158	−	735.158i	−0.972218	−	0.972218i	−0.999624	+	0.0274067i	$0.991275\pi$
$84$	−440.235	−	179.860i	−0.571829	−	0.233623i
$85$	−366.048	+	219.424i	−0.467100	+	0.279998i
$86$			459.009i			0.575537i
$87$	415.556	+	989.662i	0.512095	+	1.21957i
$88$	−72.1599	+	72.1599i	−0.0874122	+	0.0874122i
$89$	−492.823			−0.586956			−0.293478	−	0.955966i	$-0.594813\pi$
$89$	−492.823			−0.586956			−0.293478	+	0.955966i	$0.594813\pi$
$90$	−140.992	+	587.044i	−0.165132	+	0.687555i
$91$	1106.82			1.27501
$92$	289.174	−	289.174i	0.327700	−	0.327700i
$93$	12.8977	+	30.7164i	0.0143810	+	0.0342489i
$94$			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	0.140188	−	0.990125i	$-0.455229\pi$
$97$	−811.978	−	811.978i	−0.849937	−	0.849937i	−0.990125	+	0.140188i	$0.955229\pi$
$98$	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	$0.794532\pi$
$102$	−365.760	+	153.581i	−0.355055	+	0.149086i
$103$	−1013.81	+	1013.81i	−0.969841	+	0.969841i	−0.999558	−	0.0297171i	$-0.990539\pi$
$103$	−1013.81	+	1013.81i	−0.969841	+	0.969841i	0.0297171	+	0.999558i	$0.490539\pi$
$104$	386.993			0.364883
$105$	786.593	−	1071.50i	0.731082	−	0.995886i
$106$	−34.0085			−0.0311622
$107$	−104.272	+	104.272i	−0.0942090	+	0.0942090i	−0.752641	−	0.658432i	$-0.771220\pi$
$107$	−104.272	+	104.272i	−0.0942090	+	0.0942090i	0.658432	+	0.752641i	$0.271220\pi$
$108$	−207.204	+	521.531i	−0.184613	+	0.464670i
$109$		−	728.726i		−	0.640360i	−0.947357	−	0.320180i	$-0.896257\pi$
$109$		−	728.726i		−	0.640360i	0.947357	−	0.320180i	$-0.103743\pi$
$110$	−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	$-0.226621\pi$
$113$	124.657	+	124.657i	0.103777	+	0.103777i	−0.653312	+	0.757089i	$0.726621\pi$
$114$	537.509	−	1315.64i	0.441599	−	1.08088i
$115$	587.696	+	980.407i	0.476547	+	0.794986i
$116$		−	826.279i		−	0.661362i
$117$	−12.6449	−	1306.04i	−0.00999161	−	1.03200i
$118$	887.152	−	887.152i	0.692110	−	0.692110i
$119$	873.390			0.672802
$120$	275.028	−	374.646i	0.209221	−	0.285003i
$121$	1168.28			0.877746
$122$	−769.015	+	769.015i	−0.570684	+	0.570684i
$123$	−98.5267	+	41.3710i	−0.0722265	+	0.0303276i
$124$		−	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	0.801863	−	0.597508i	$-0.203842\pi$
$127$	292.476	+	292.476i	0.204355	+	0.204355i	−0.597508	+	0.801863i	$0.703842\pi$
$128$	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	$0.950444\pi$
$132$	−102.646	−	244.457i	−0.0676835	−	0.161191i
$133$	−2212.55	+	2212.55i	−1.44250	+	1.44250i
$134$	−340.962			−0.219810
$135$	−1273.36	−	915.935i	−0.811801	−	0.583935i
$136$	305.376			0.192543
$137$	102.116	−	102.116i	0.0636815	−	0.0636815i	−0.674549	−	0.738230i	$-0.735662\pi$
$137$	102.116	−	102.116i	0.0636815	−	0.0636815i	0.738230	+	0.674549i	$0.235662\pi$
$138$	411.345	+	979.635i	0.253739	+	0.604290i
$139$		−	336.335i		−	0.205234i	−0.994721	−	0.102617i	$-0.967278\pi$
$139$		−	336.335i		−	0.205234i	0.994721	−	0.102617i	$-0.0327216\pi$
$140$	−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
$147$	−864.816	+	363.133i	−0.485230	+	0.203746i
$148$	592.713	−	592.713i	0.329194	−	0.329194i
$149$	−3241.32			−1.78214			−0.891071	−	0.453864i	$-0.850045\pi$
$149$	−3241.32			−1.78214			−0.891071	+	0.453864i	$0.850045\pi$
$150$	829.046	+	1000.09i	0.451275	+	0.544381i
$151$	−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
$153$	−9.97806	−	1030.60i	−0.00527241	−	0.544567i
$154$			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	0.403306	−	0.915065i	$-0.367861\pi$
$157$	−1006.73	−	1006.73i	−0.511759	−	0.511759i	−0.915065	+	0.403306i	$0.867861\pi$
$158$	−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
$162$	−1050.73	−	1010.81i	−0.509587	−	0.490225i
$163$	694.457	−	694.457i	0.333706	−	0.333706i	−0.520286	−	0.853992i	$-0.674175\pi$
$163$	694.457	−	694.457i	0.333706	−	0.333706i	0.853992	+	0.520286i	$0.174175\pi$
$164$	82.2609			0.0391677
$165$	732.507	−	112.319i	0.345610	−	0.0529940i
$166$	−2079.34			−0.972218
$167$	1875.50	−	1875.50i	0.869044	−	0.869044i	−0.123322	−	0.992367i	$-0.539355\pi$
$167$	1875.50	−	1875.50i	0.869044	−	0.869044i	0.992367	+	0.123322i	$0.0393550\pi$
$168$	−876.947	+	368.227i	−0.402726	+	0.169103i
$169$		−	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	$-0.0235913\pi$
$173$	2100.72	+	2100.72i	0.923208	+	0.923208i	−0.0740463	+	0.997255i	$0.523591\pi$
$174$	1987.28	+	811.910i	0.865834	+	0.353740i
$175$	−830.483	−	2736.81i	−0.358735	−	1.18219i
$176$			204.099i			0.0874122i
$177$	1261.96	+	3005.41i	0.535902	+	1.27627i
$178$	−696.957	+	696.957i	−0.293478	+	0.293478i
$179$	1272.12			0.531190			0.265595	−	0.964085i	$-0.414432\pi$
$179$	1272.12			0.531190			0.265595	+	0.964085i	$0.414432\pi$
$180$	630.813	+	1029.60i	0.261211	+	0.426343i
$181$	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
$183$	−1093.91	−	2605.20i	−0.441882	−	1.05236i
$184$		−	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	$0.873721\pi$
$192$	−306.620	+	128.749i	−0.115252	+	0.0483939i
$193$	1274.49	−	1274.49i	0.475335	−	0.475335i	−0.428301	−	0.903636i	$-0.640888\pi$
$193$	1274.49	−	1274.49i	0.475335	−	0.475335i	0.903636	+	0.428301i	$0.140888\pi$
$194$	−2296.62			−0.849937
$195$	−2265.40	−	1663.03i	−0.831940	−	0.610729i
$196$	722.043			0.263135
$197$	1983.65	−	1983.65i	0.717407	−	0.717407i	−0.250667	−	0.968073i	$-0.580650\pi$
$197$	1983.65	−	1983.65i	0.717407	−	0.717407i	0.968073	+	0.250667i	$0.0806499\pi$
$198$	688.802	−	6.66887i	0.247228	−	0.00239362i
$199$		−	1815.35i		−	0.646666i	−0.946285	−	0.323333i	$-0.895197\pi$
$199$		−	1815.35i		−	0.646666i	0.946285	−	0.323333i	$-0.104803\pi$
$200$	−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
$207$	−2760.31	+	26.7248i	−0.926833	+	0.00897345i
$208$	547.291	−	547.291i	0.182441	−	0.182441i
$209$	−1744.48			−0.577360
$210$	−402.925	−	2627.75i	−0.132402	−	0.863484i
$211$	−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
$213$	715.139	−	300.284i	0.230049	−	0.0965969i
$214$			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
$222$	843.126	+	2007.94i	0.254896	+	0.607045i
$223$	−285.691	+	285.691i	−0.0857906	+	0.0857906i	−0.748700	−	0.662909i	$-0.769322\pi$
$223$	−285.691	+	285.691i	−0.0857906	+	0.0857906i	0.662909	+	0.748700i	$0.269322\pi$
$224$	732.171			0.218394
$225$	−3219.94	+	1011.23i	−0.954057	+	0.299625i
$226$	352.584			0.103777
$227$	−4779.51	+	4779.51i	−1.39748	+	1.39748i	−0.590270	+	0.807206i	$0.700979\pi$
$227$	−4779.51	+	4779.51i	−1.39748	+	1.39748i	−0.807206	+	0.590270i	$0.799021\pi$
$228$	−1100.44	−	2620.75i	−0.319643	−	0.761242i
$229$			5062.03i			1.46074i	0.683054	+	0.730368i	$0.260651\pi$
$229$			5062.03i			1.46074i	−0.683054	+	0.730368i	$0.739349\pi$
$230$	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	$-0.185464\pi$
$233$	1012.79	+	1012.79i	0.284765	+	0.284765i	−0.550241	+	0.835006i	$0.685464\pi$
$234$	−1864.90	−	1829.14i	−0.520994	−	0.511002i
$235$	−2598.05	+	1557.38i	−0.721183	+	0.432306i
$236$		−	2509.25i		−	0.692110i
$237$	469.235	−	197.030i	0.128608	−	0.0540020i
$238$	1235.16	−	1235.16i	0.336401	−	0.336401i
$239$	1140.60			0.308701			0.154350	−	0.988016i	$-0.450672\pi$
$239$	1140.60			0.308701			0.154350	+	0.988016i	$0.450672\pi$
$240$	−140.881	−	918.778i	−0.0378908	−	0.247112i
$241$	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
$243$	3463.54	−	1533.88i	0.914347	−	0.404931i
$244$			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	$-0.177022\pi$
$252$	−23.9235	−	2470.96i	−0.00598030	−	0.617683i
$253$	922.189	−	922.189i	0.229160	−	0.229160i
$254$	827.246			0.204355
$255$	−1787.62	−	1312.30i	−0.439001	−	0.322272i
$256$	256.000			0.0625000
$257$	3004.70	−	3004.70i	0.729291	−	0.729291i	−0.241188	−	0.970479i	$-0.577537\pi$
$257$	3004.70	−	3004.70i	0.729291	−	0.729291i	0.970479	+	0.241188i	$0.0775369\pi$
$258$	−2199.08	+	923.386i	−0.530654	+	0.222820i
$259$		−	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	$-0.0467834\pi$
$263$	3594.55	+	3594.55i	0.842773	+	0.842773i	−0.146446	+	0.989219i	$0.546783\pi$
$264$	−490.878	−	200.550i	−0.114437	−	0.0467537i
$265$	−97.7453	−	163.061i	−0.0226583	−	0.0377991i
$266$			6258.03i			1.44250i
$267$	−991.410	−	2361.08i	−0.227241	−	0.541183i
$268$	−482.193	+	482.193i	−0.109905	+	0.109905i
$269$	−2096.25			−0.475132			−0.237566	−	0.971371i	$-0.576350\pi$
$269$	−2096.25			−0.475132			−0.237566	+	0.971371i	$0.576350\pi$
$270$	−3096.13	+	505.470i	−0.697868	+	0.113933i
$271$	−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
$273$	2226.58	+	5302.69i	0.493622	+	1.17558i
$274$		−	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	0.526522	−	0.850161i	$-0.323496\pi$
$277$	−1492.04	−	1492.04i	−0.323639	−	0.323639i	−0.850161	+	0.526522i	$0.823496\pi$
$278$	−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	$-0.184872\pi$
$282$	−2596.00	+	1090.05i	−0.548190	+	0.230183i
$283$	−892.521	+	892.521i	−0.187473	+	0.187473i	−0.794603	−	0.607130i	$-0.792321\pi$
$283$	−892.521	+	892.521i	−0.187473	+	0.187473i	0.607130	+	0.794603i	$0.292321\pi$
$284$	−597.077			−0.124753
$285$	7852.99	−	1204.14i	1.63218	−	0.250270i
$286$	1234.14			0.255162
$287$	332.722	−	332.722i	0.0684319	−	0.0684319i
$288$	−8.36471	−	863.960i	−0.00171144	−	0.176768i
$289$			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	$-0.405231\pi$
$293$	−3323.48	−	3323.48i	−0.662661	−	0.662661i	−0.956006	+	0.293346i	$0.905231\pi$
$294$	−709.487	+	1736.58i	−0.140742	+	0.344488i
$295$	6803.45	+	1703.84i	1.34275	+	0.336275i
$296$		−	1676.45i		−	0.329194i
$297$	−660.785	+	1663.19i	−0.129100	+	0.324943i
$298$	−4583.92	+	4583.92i	−0.891071	+	0.891071i
$299$	−4945.69			−0.956578
$300$	2586.79	+	241.895i	0.497828	+	0.0465527i
$301$	5251.14			1.00555
$302$	−317.001	+	317.001i	−0.0604019	+	0.0604019i
$303$	−5851.09	+	2456.85i	−1.10936	+	0.465817i
$304$			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	0.428157	−	0.903704i	$-0.359163\pi$
$307$	−2558.00	−	2558.00i	−0.475547	−	0.475547i	−0.903704	+	0.428157i	$0.859163\pi$
$308$	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	$0.735461\pi$
$312$	778.513	+	1854.06i	0.141265	+	0.336428i
$313$	106.246	−	106.246i	0.0191865	−	0.0191865i	−0.697448	−	0.716635i	$-0.745681\pi$
$313$	106.246	−	106.246i	0.0191865	−	0.0191865i	0.716635	+	0.697448i	$0.245681\pi$
$314$	−2847.47			−0.511759
$315$	6715.89	+	1612.98i	1.20126	+	0.288511i
$316$	−391.769			−0.0697428
$317$	−1174.48	+	1174.48i	−0.208093	+	0.208093i	−0.803456	−	0.595364i	$-0.797008\pi$
$317$	−1174.48	+	1174.48i	−0.208093	+	0.208093i	0.595364	+	0.803456i	$0.297008\pi$
$318$	−68.4147	−	162.932i	−0.0120645	−	0.0287321i
$319$		−	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
$327$	3491.28	−	1465.98i	0.590423	−	0.247916i
$328$	116.335	−	116.335i	0.0195838	−	0.0195838i
$329$	6198.94			1.03878
$330$	877.079	−	1194.76i	0.146308	−	0.199302i
$331$	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
$333$	−5657.74	+	54.7773i	−0.931058	+	0.00901435i
$334$		−	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	0.204601	−	0.978845i	$-0.434410\pi$
$337$	−4789.86	−	4789.86i	−0.774244	−	0.774244i	−0.978845	+	0.204601i	$0.934410\pi$
$338$	−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
$342$	7384.45	−	71.4950i	1.16756	−	0.0113041i
$343$	−2628.89	+	2628.89i	−0.413839	+	0.413839i
$344$	1836.03			0.287768
$345$	−3514.80	+	4787.90i	−0.548495	+	0.747164i
$346$	5941.74			0.923208
$347$	−2124.17	+	2124.17i	−0.328621	+	0.328621i	−0.852062	−	0.523441i	$-0.824648\pi$
$347$	−2124.17	+	2124.17i	−0.328621	+	0.328621i	0.523441	+	0.852062i	$0.324648\pi$
$348$	3958.65	−	1662.22i	0.609787	−	0.256047i
$349$		−	9235.10i		−	1.41646i	−0.705983	−	0.708229i	$-0.749495\pi$
$349$		−	9235.10i		−	1.41646i	0.705983	−	0.708229i	$-0.250505\pi$
$350$	−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	$-0.216450\pi$
$353$	986.773	+	986.773i	0.148784	+	0.148784i	−0.628791	+	0.777574i	$0.716450\pi$
$354$	6034.97	+	2465.61i	0.906088	+	0.370185i
$355$	405.429	−	1618.88i	0.0606139	−	0.242032i
$356$			1971.29i			0.293478i
$357$	1757.00	+	4184.35i	0.260476	+	0.620335i
$358$	1799.06	−	1799.06i	0.265595	−	0.265595i
$359$	10701.5			1.57327			0.786635	−	0.617419i	$-0.211822\pi$
$359$	10701.5			1.57327			0.786635	+	0.617419i	$0.211822\pi$
$360$	2348.18	+	563.969i	0.343777	+	0.0825661i
$361$	−11843.0			−1.72664
$362$	88.7108	−	88.7108i	0.0128799	−	0.0128799i
$363$	2350.22	+	5597.15i	0.339820	+	0.809296i
$364$		−	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	0.774948	−	0.632025i	$-0.217776\pi$
$367$	1004.85	+	1004.85i	0.142923	+	0.142923i	−0.632025	+	0.774948i	$0.717776\pi$
$368$	−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
$372$	122.866	−	51.5909i	0.0171244	−	0.00719049i
$373$	8677.69	−	8677.69i	1.20460	−	1.20460i	0.231842	−	0.972754i	$-0.425525\pi$
$373$	8677.69	−	8677.69i	1.20460	−	1.20460i	0.972754	−	0.231842i	$-0.0744751\pi$
$374$	973.860			0.134645
$375$	−2412.35	+	6849.45i	−0.332196	+	0.943210i
$376$	2167.43			0.297278
$377$	−7065.86	+	7065.86i	−0.965279	+	0.965279i
$378$	5966.41	+	2370.45i	0.811849	+	0.322548i
$379$			14693.0i			1.99137i	0.0927715	+	0.995687i	$0.470427\pi$
$379$			14693.0i			1.99137i	−0.0927715	+	0.995687i	$0.529573\pi$
$380$	−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	$-0.305867\pi$
$383$	−1850.91	−	1850.91i	−0.246937	−	0.246937i	−0.819713	+	0.572775i	$0.805867\pi$
$384$	−251.548	+	615.704i	−0.0334291	+	0.0818230i
$385$	−2798.83	+	1677.73i	−0.370498	+	0.222091i
$386$		−	3604.80i		−	0.475335i
$387$	−59.9918	−	6196.33i	−0.00787999	−	0.813894i
$388$	−3247.91	+	3247.91i	−0.424969	+	0.424969i
$389$	9296.60			1.21171			0.605856	−	0.795574i	$-0.292831\pi$
$389$	9296.60			1.21171			0.605856	+	0.795574i	$0.292831\pi$
$390$	−5555.64	+	851.872i	−0.721335	+	0.110606i
$391$	−3902.64			−0.504770
$392$	1021.12	−	1021.12i	0.131568	−	0.131568i
$393$	−2227.67	+	935.390i	−0.285931	+	0.120062i
$394$		−	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	0.758683	−	0.651460i	$-0.225843\pi$
$397$	848.145	+	848.145i	0.107222	+	0.107222i	−0.651460	+	0.758683i	$0.725843\pi$
$398$	−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	$0.821834\pi$
$402$	−685.911	−	1633.53i	−0.0850999	−	0.202669i
$403$	−219.305	+	219.305i	−0.0271076	+	0.0271076i
$404$	4885.14			0.601596
$405$	1826.58	−	7943.16i	0.224107	−	0.974564i
$406$	−9452.78			−1.15550
$407$	1890.19	−	1890.19i	0.230205	−	0.230205i
$408$	614.324	+	1463.04i	0.0745431	+	0.177527i
$409$			7604.85i			0.919403i	0.888073	+	0.459702i	$0.152044\pi$
$409$			7604.85i			0.919403i	−0.888073	+	0.459702i	$0.847956\pi$
$410$	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
$417$	1611.36	−	676.603i	0.189229	−	0.0794566i
$418$	−2467.07	+	2467.07i	−0.288680	+	0.288680i
$419$	−13904.7			−1.62122			−0.810609	−	0.585588i	$-0.800864\pi$
$419$	−13904.7			−1.62122			−0.810609	+	0.585588i	$0.800864\pi$
$420$	−4286.02	−	3146.37i	−0.497943	−	0.365541i
$421$	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
$423$	−70.8200	−	7314.73i	−0.00814039	−	0.840790i
$424$			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	$0.969938\pi$
$432$	2086.12	+	828.817i	0.232335	+	0.0923067i
$433$	3605.54	−	3605.54i	0.400164	−	0.400164i	−0.478127	−	0.878291i	$-0.658684\pi$
$433$	3605.54	−	3605.54i	0.400164	−	0.400164i	0.878291	+	0.478127i	$0.158684\pi$
$434$	−293.389			−0.0324496
$435$	1818.85	+	11862.0i	0.200477	+	1.30744i
$436$	−2914.90			−0.320180
$437$	9886.52	−	9886.52i	1.08223	−	1.08223i
$438$	10458.6	−	4391.55i	1.14094	−	0.479078i
$439$			8014.92i			0.871369i	0.900099	+	0.435685i	$0.143494\pi$
$439$			8014.92i			0.871369i	−0.900099	+	0.435685i	$0.856506\pi$
$440$	−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	$-0.368302\pi$
$443$	−4788.70	−	4788.70i	−0.513584	−	0.513584i	−0.915623	+	0.402039i	$0.868302\pi$
$444$	4032.01	+	1647.29i	0.430970	+	0.176074i
$445$	−5344.86	−	1338.55i	−0.569373	−	0.142592i
$446$			808.057i			0.0857906i
$447$	−6520.55	−	15528.9i	−0.689958	−	1.64316i
$448$	1035.45	−	1035.45i	0.109197	−	0.109197i
$449$	6437.16			0.676588			0.338294	−	0.941040i	$-0.390150\pi$
$449$	6437.16			0.676588			0.338294	+	0.941040i	$0.390150\pi$
$450$	−3123.59	+	5983.79i	−0.327216	+	0.626841i
$451$	262.334			0.0273899
$452$	498.629	−	498.629i	0.0518884	−	0.0518884i
$453$	−450.929	−	1073.91i	−0.0467693	−	0.111383i
$454$			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	0.976476	−	0.215626i	$-0.0691793\pi$
$457$	7433.15	+	7433.15i	0.760850	+	0.760850i	−0.215626	+	0.976476i	$0.569179\pi$
$458$	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	$0.707343\pi$
$462$	−2796.63	+	1174.29i	−0.281625	+	0.118253i
$463$	4385.12	−	4385.12i	0.440160	−	0.440160i	−0.451906	−	0.892066i	$-0.649256\pi$
$463$	4385.12	−	4385.12i	0.440160	−	0.440160i	0.892066	+	0.451906i	$0.149256\pi$
$464$	−3305.11			−0.330681
$465$	56.4523	+	368.164i	0.00562992	+	0.0367165i
$466$	2864.61			0.284765
$467$	−405.352	+	405.352i	−0.0401659	+	0.0401659i	−0.726904	−	0.686739i	$-0.759042\pi$
$467$	−405.352	+	405.352i	−0.0401659	+	0.0401659i	0.686739	+	0.726904i	$0.259042\pi$
$468$	−5224.16	+	50.5795i	−0.515998	+	0.00499581i
$469$			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
$477$	459.093	−	4.44486i	0.0440680	−	0.000426659i
$478$	1613.06	−	1613.06i	0.154350	−	0.154350i
$479$	−834.821			−0.0796324			−0.0398162	−	0.999207i	$-0.512677\pi$
$479$	−834.821			−0.0796324			−0.0398162	+	0.999207i	$0.512677\pi$
$480$	−1498.58	−	1100.11i	−0.142501	−	0.104611i
$481$	−10137.1			−0.960938
$482$	1265.03	−	1265.03i	0.119544	−	0.119544i
$483$	11207.2	−	4705.86i	1.05579	−	0.443321i
$484$		−	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	0.757450	−	0.652893i	$-0.226445\pi$
$487$	1123.69	+	1123.69i	0.104557	+	0.104557i	−0.652893	+	0.757450i	$0.726445\pi$
$488$	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	$0.956953\pi$
$492$	165.484	+	394.107i	0.0151638	+	0.0361132i
$493$	−5575.67	+	5575.67i	−0.509362	+	0.509362i
$494$	13230.9			1.20503
$495$	2011.69	+	3283.44i	0.182664	+	0.298141i
$496$	−102.582			−0.00928641
$497$	−2415.00	+	2415.00i	−0.217963	+	0.217963i
$498$	−4183.00	−	9961.99i	−0.376395	−	0.896401i
$499$		−	19512.5i		−	1.75050i	−0.483668	−	0.875252i	$-0.660696\pi$
$499$		−	19512.5i		−	1.75050i	0.483668	−	0.875252i	$-0.339304\pi$
$500$	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	$-0.0647208\pi$
$503$	8770.75	+	8770.75i	0.777472	+	0.777472i	−0.201928	+	0.979400i	$0.564721\pi$
$504$	−3528.30	−	3460.64i	−0.311831	−	0.305851i
$505$	−3317.12	+	13245.3i	−0.292297	+	1.16715i
$506$		−	2608.34i		−	0.229160i
$507$	685.379	−	287.788i	0.0600370	−	0.0252093i
$508$	1169.90	−	1169.90i	0.102177	−	0.102177i
$509$	−16213.8			−1.41192			−0.705959	−	0.708253i	$-0.749484\pi$
$509$	−16213.8			−1.41192			−0.705959	+	0.708253i	$0.749484\pi$
$510$	−4383.95	+	672.212i	−0.380637	+	0.0583648i
$511$	−24974.0			−2.16200
$512$	362.039	−	362.039i	0.0312500	−	0.0312500i
$513$	−7084.08	+	17830.5i	−0.609687	+	1.53458i
$514$		−	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	$-0.254059\pi$
$522$	107.993	+	11154.2i	0.00905507	+	0.935264i
$523$	−6159.97	+	6159.97i	−0.515023	+	0.515023i	−0.916061	−	0.401039i	$-0.868649\pi$
$523$	−6159.97	+	6159.97i	−0.515023	+	0.515023i	0.401039	+	0.916061i	$0.368649\pi$
$524$	1859.90			0.155058
$525$	11441.2	−	9484.43i	0.951116	−	0.788447i
$526$	10166.9			0.842773
$527$	−173.054	+	173.054i	−0.0143042	+	0.0143042i
$528$	−977.826	+	410.586i	−0.0805955	+	0.0338418i
$529$		−	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
$537$	2559.13	+	6094.67i	0.205651	+	0.489766i
$538$	−2964.54	+	2964.54i	−0.237566	+	0.237566i
$539$	2302.63			0.184010
$540$	−3663.74	+	5093.43i	−0.291967	+	0.405900i
$541$	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
$543$	126.190	+	300.526i	0.00997297	+	0.0237510i
$544$		−	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	0.392615	−	0.919703i	$-0.371571\pi$
$547$	−6743.17	−	6743.17i	−0.527088	−	0.527088i	−0.919703	+	0.392615i	$0.871571\pi$
$548$	−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
$552$	3918.54	−	1645.38i	0.302145	−	0.126870i
$553$	−1584.59	+	1584.59i	−0.121851	+	0.121851i
$554$	−4220.13			−0.323639
$555$	−7204.22	+	9813.65i	−0.550995	+	0.750570i
$556$	−1345.34			−0.102617
$557$	−14440.2	+	14440.2i	−1.09847	+	1.09847i	−0.103884	+	0.994589i	$0.533127\pi$
$557$	−14440.2	+	14440.2i	−1.09847	+	1.09847i	−0.994589	+	0.103884i	$0.966873\pi$
$558$	3.35183	+	346.198i	0.000254291	+	0.0262647i
$559$		−	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	−0.999251	−	0.0387094i	$-0.987675\pi$
$563$	−13865.7	−	13865.7i	−1.03796	−	1.03796i	−0.0387094	−	0.999251i	$-0.512325\pi$
$564$	−2129.74	+	5212.87i	−0.159004	+	0.389187i
$565$	1013.38	+	1690.54i	0.0754569	+	0.125879i
$566$			2524.43i			0.187473i
$567$	−11563.8	+	12020.5i	−0.856498	+	0.890326i
$568$	−844.394	+	844.394i	−0.0623767	+	0.0623767i
$569$	18660.0			1.37481			0.687405	−	0.726274i	$-0.258750\pi$
$569$	18660.0			1.37481			0.687405	+	0.726274i	$0.258750\pi$
$570$	9402.90	−	12808.7i	0.690955	−	0.941224i
$571$	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
$573$	−9773.03	+	4103.66i	−0.712520	+	0.299185i
$574$		−	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	−0.927451	−	0.373944i	$-0.878005\pi$
$577$	−18037.4	−	18037.4i	−1.30140	−	1.30140i	−0.373944	−	0.927451i	$-0.621995\pi$
$578$	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
$582$	−4620.11	−	11003.0i	−0.329054	−	0.783656i
$583$	−153.378	+	153.378i	−0.0108958	+	0.0108958i
$584$	−8732.02			−0.618722
$585$	3410.19	−	14198.9i	0.241015	−	1.00351i
$586$	−9400.21			−0.662661
$587$	14567.2	−	14567.2i	1.02428	−	1.02428i	0.0245838	−	0.999698i	$-0.492174\pi$
$587$	14567.2	−	14567.2i	1.02428	−	1.02428i	0.999698	−	0.0245838i	$-0.00782605\pi$
$588$	1452.53	+	3459.26i	0.101873	+	0.242615i
$589$		−	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	0.833128	+	0.553080i	$0.186547\pi$
$593$	20017.5	+	20017.5i	1.38621	+	1.38621i	0.553080	+	0.833128i	$0.313453\pi$
$594$	1417.61	+	3286.59i	0.0979214	+	0.227021i
$595$	9472.27	+	2372.21i	0.652647	+	0.163447i
$596$			12965.3i			0.891071i
$597$	8697.21	−	3651.93i	0.596236	−	0.250357i
$598$	−6994.26	+	6994.26i	−0.478289	+	0.478289i
$599$	−19821.1			−1.35203			−0.676017	−	0.736886i	$-0.736295\pi$
$599$	−19821.1			−1.35203			−0.676017	+	0.736886i	$0.736295\pi$
$600$	4000.37	−	3316.18i	0.272190	−	0.225638i
$601$	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
$603$	4602.77	−	44.5632i	0.310844	−	0.00300954i
$604$			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	0.720455	−	0.693501i	$-0.243933\pi$
$607$	403.095	+	403.095i	0.0269540	+	0.0269540i	−0.693501	+	0.720455i	$0.743933\pi$
$608$	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
$612$	−4122.39	+	39.9122i	−0.272284	+	0.00263620i
$613$	4616.26	−	4616.26i	0.304158	−	0.304158i	−0.538480	−	0.842638i	$-0.681001\pi$
$613$	4616.26	−	4616.26i	0.304158	−	0.304158i	0.842638	+	0.538480i	$0.181001\pi$
$614$	−7235.13			−0.475547
$615$	−1180.93	+	181.078i	−0.0774304	+	0.0118728i
$616$	2334.93			0.152722
$617$	−14556.9	+	14556.9i	−0.949818	+	0.949818i	−0.998800	−	0.0489818i	$-0.984402\pi$
$617$	−14556.9	+	14556.9i	−0.949818	+	0.949818i	0.0489818	+	0.998800i	$0.484402\pi$
$618$	−13738.0	+	5768.51i	−0.894209	+	0.375475i
$619$			12601.3i			0.818236i	0.912482	+	0.409118i	$0.134163\pi$
$619$			12601.3i			0.818236i	−0.912482	+	0.409118i	$0.865837\pi$
$620$	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
$627$	−3509.36	−	8357.69i	−0.223525	−	0.532335i
$628$	−4026.94	+	4026.94i	−0.255879	+	0.255879i
$629$	−7999.17			−0.507071
$630$	11778.8	−	7216.61i	0.744887	−	0.456376i
$631$	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
$633$	−7205.64	−	17160.5i	−0.452446	−	1.07752i
$634$			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	$-0.345222\pi$
$642$	−1412.97	+	593.301i	−0.0868622	+	0.0364731i
$643$	−7444.99	+	7444.99i	−0.456612	+	0.456612i	−0.897542	−	0.440930i	$-0.854649\pi$
$643$	−7444.99	+	7444.99i	−0.456612	+	0.456612i	0.440930	+	0.897542i	$0.354649\pi$
$644$	−9357.00			−0.572543
$645$	−10747.9	−	7890.02i	−0.656118	−	0.481658i
$646$	10440.5			0.635874
$647$	15997.5	−	15997.5i	0.972065	−	0.972065i	−0.0275552	−	0.999620i	$-0.508772\pi$
$647$	15997.5	−	15997.5i	0.972065	−	0.972065i	0.999620	+	0.0275552i	$0.00877220\pi$
$648$	−4043.23	+	4202.92i	−0.245113	+	0.254794i
$649$		−	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	$-0.312349\pi$
$653$	−4592.90	−	4592.90i	−0.275243	−	0.275243i	−0.831207	+	0.555963i	$0.812349\pi$
$654$	2864.21	−	7010.62i	0.171253	−	0.419170i
$655$	−1262.92	+	5042.85i	−0.0753378	+	0.300825i
$656$		−	329.044i		−	0.0195838i
$657$	285.316	+	29469.2i	0.0169425	+	1.74993i
$658$	8766.63	−	8766.63i	0.519390	−	0.519390i
$659$	−12460.6			−0.736565			−0.368282	−	0.929714i	$-0.620054\pi$
$659$	−12460.6			−0.736565			−0.368282	+	0.929714i	$0.620054\pi$
$660$	−449.275	−	2930.03i	−0.0264970	−	0.172805i
$661$	−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
$663$	8846.65	−	3714.68i	0.518213	−	0.217596i
$664$			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
$672$	1472.91	+	3507.79i	0.0845515	+	0.201363i
$673$	5271.96	−	5271.96i	0.301960	−	0.301960i	−0.539820	−	0.841780i	$-0.681508\pi$
$673$	5271.96	−	5271.96i	0.301960	−	0.301960i	0.841780	+	0.539820i	$0.181508\pi$
$674$	−13547.8			−0.774244
$675$	−11322.3	−	13392.2i	−0.645623	−	0.763656i
$676$	−572.230			−0.0325575
$677$	6270.55	−	6270.55i	0.355977	−	0.355977i	−0.506350	−	0.862328i	$-0.669006\pi$
$677$	6270.55	−	6270.55i	0.355977	−	0.355977i	0.862328	+	0.506350i	$0.169006\pi$
$678$	709.293	+	1689.21i	0.0401773	+	0.0956839i
$679$			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	$-0.0212936\pi$
$683$	16616.6	+	16616.6i	0.930917	+	0.930917i	−0.0668461	+	0.997763i	$0.521294\pi$
$684$	10342.1	−	10544.3i	0.578127	−	0.589431i
$685$	1384.85	−	830.133i	0.0772442	−	0.0463033i
$686$			7435.62i			0.413839i
$687$	−24251.9	+	10183.3i	−1.34682	+	0.565526i
$688$	2596.55	−	2596.55i	0.143884	−	0.143884i
$689$	822.565			0.0454822
$690$	1800.42	+	11741.8i	0.0993347	+	0.647829i
$691$	−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
$693$	−76.2931	−	7880.02i	−0.00418201	−	0.431944i
$694$			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	$0.945574\pi$
$702$	5011.66	−	12614.3i	0.269449	−	0.678200i
$703$	20264.2	−	20264.2i	1.08717	−	1.08717i
$704$	816.397			0.0437061
$705$	−12687.8	−	9314.12i	−0.677800	−	0.497575i
$706$	2791.01			0.148784
$707$	19759.0	−	19759.0i	1.05108	−	1.05108i
$708$	12021.6	−	5047.84i	0.638137	−	0.267951i
$709$			4327.74i			0.229241i	0.993409	+	0.114620i	$0.0365652\pi$
$709$			4327.74i			0.229241i	−0.993409	+	0.114620i	$0.963435\pi$
$710$	−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
$717$	2294.55	+	5464.55i	0.119514	+	0.284627i
$718$	15134.2	−	15134.2i	0.786635	−	0.786635i
$719$	26854.1			1.39289			0.696447	−	0.717609i	$-0.254763\pi$
$719$	26854.1			1.39289			0.696447	+	0.717609i	$0.254763\pi$
$720$	4118.40	−	2523.25i	0.213172	−	0.130606i
$721$	32804.6			1.69446
$722$	−16748.6	+	16748.6i	−0.863321	+	0.863321i
$723$	1799.48	+	4285.53i	0.0925635	+	0.220444i
$724$		−	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	0.983728	−	0.179663i	$-0.0575007\pi$
$727$	15761.3	+	15761.3i	0.804065	+	0.804065i	−0.179663	+	0.983728i	$0.557501\pi$
$728$	−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
$732$	−10420.8	+	4375.65i	−0.526179	+	0.220941i
$733$	−16481.2	+	16481.2i	−0.830487	+	0.830487i	−0.987583	−	0.157096i	$-0.949787\pi$
$733$	−16481.2	+	16481.2i	−0.830487	+	0.830487i	0.157096	+	0.987583i	$0.449787\pi$
$734$	2842.14			0.142923
$735$	−10365.6	+	1589.40i	−0.520191	+	0.0797633i
$736$	−3271.63			−0.163850
$737$	−1537.74	+	1537.74i	−0.0768565	+	0.0768565i
$738$	−1110.47	+	10.7514i	−0.0553889	+	0.000536266i
$739$		−	18693.3i		−	0.930505i	−0.885178	−	0.465253i	$-0.845963\pi$
$739$		−	18693.3i		−	0.930505i	0.885178	−	0.465253i	$-0.154037\pi$
$740$	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	$-0.278029\pi$
$743$	−2518.82	−	2518.82i	−0.124369	−	0.124369i	−0.766552	+	0.642182i	$0.778029\pi$
$744$	100.798	−	246.719i	0.00496698	−	0.0121575i
$745$	−35153.4	−	8803.72i	−1.72875	−	0.432944i
$746$		−	24544.2i		−	1.20460i
$747$	28069.8	−	271.767i	1.37486	−	0.0133112i
$748$	1377.25	−	1377.25i	0.0673223	−	0.0673223i
$749$	3374.01			0.164597
$750$	6275.00	+	13098.2i	0.305507	+	0.637703i
$751$	−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
$753$	20114.8	−	8446.15i	0.973474	−	0.408758i
$754$			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	−0.993402	−	0.114684i	$-0.963415\pi$
$757$	−23079.0	−	23079.0i	−1.10809	−	1.10809i	−0.114684	−	0.993402i	$-0.536585\pi$
$758$	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	$0.737311\pi$
$762$	1664.17	+	3963.28i	0.0791161	+	0.188418i
$763$	−11790.0	+	11790.0i	−0.559404	+	0.559404i
$764$	8159.59			0.386392
$765$	2690.98	−	11204.3i	0.127180	−	0.529534i
$766$	−5235.16			−0.246937
$767$	−21457.6	+	21457.6i	−1.01016	+	1.01016i
$768$	514.994	+	1226.48i	0.0241970	+	0.0576260i
$769$		−	24831.0i		−	1.16441i	−0.813043	−	0.582204i	$-0.802191\pi$
$769$		−	24831.0i		−	1.16441i	0.813043	−	0.582204i	$-0.197809\pi$
$770$	−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	$-0.450462\pi$
$773$	−17900.7	−	17900.7i	−0.832913	−	0.832913i	−0.987914	+	0.155001i	$0.950462\pi$
$774$	−8847.77	−	8678.09i	−0.410887	−	0.403007i
$775$	706.825	+	377.721i	0.0327612	+	0.0175073i
$776$			9186.49i			0.424969i
$777$	22971.2	−	9645.51i	1.06060	−	0.445342i
$778$	13147.4	−	13147.4i	0.605856	−	0.605856i
$779$	2812.41			0.129352
$780$	−6652.13	+	9061.58i	−0.305365	+	0.415970i
$781$	−1904.11			−0.0872398
$782$	−5519.17	+	5519.17i	−0.252385	+	0.252385i
$783$	−26933.1	−	10700.5i	−1.22926	−	0.488385i
$784$		−	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	0.612515	−	0.790459i	$-0.290158\pi$
$787$	−3928.66	−	3928.66i	−0.177944	−	0.177944i	−0.790459	+	0.612515i	$0.790158\pi$
$788$	−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
$792$	−26.6755	−	2755.21i	−0.00119681	−	0.123614i
$793$	18600.2	−	18600.2i	0.832930	−	0.832930i
$794$	2398.92			0.107222
$795$	584.581	−	796.321i	0.0260792	−	0.0355253i
$796$	−7261.38			−0.323333
$797$	10942.0	−	10942.0i	0.486307	−	0.486307i	−0.420832	−	0.907139i	$-0.638262\pi$
$797$	10942.0	−	10942.0i	0.486307	−	0.486307i	0.907139	+	0.420832i	$0.138262\pi$
$798$	−29981.8	+	12589.3i	−1.33001	+	0.558464i
$799$		−	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
$807$	−4217.02	−	10043.0i	−0.183948	−	0.438080i
$808$	6908.63	−	6908.63i	0.300798	−	0.300798i
$809$	−15310.9			−0.665395			−0.332697	−	0.943034i	$-0.607959\pi$
$809$	−15310.9			−0.665395			−0.332697	+	0.943034i	$0.607959\pi$
$810$	−8650.14	−	13816.5i	−0.375228	−	0.599336i
$811$	−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
$813$	−1184.67	−	2821.35i	−0.0511049	−	0.121708i
$814$		−	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	$0.951586\pi$
$822$	1383.76	−	581.034i	0.0587153	−	0.0246544i
$823$	−17408.3	+	17408.3i	−0.737321	+	0.737321i	−0.972059	−	0.234738i	$-0.924577\pi$
$823$	−17408.3	+	17408.3i	−0.737321	+	0.737321i	0.234738	+	0.972059i	$0.424577\pi$
$824$	11469.9			0.484921
$825$	8249.40	+	771.415i	0.348130	+	0.0325542i
$826$	−28706.2			−1.20922
$827$	−25331.1	+	25331.1i	−1.06511	+	1.06511i	−0.0673858	+	0.997727i	$0.521466\pi$
$827$	−25331.1	+	25331.1i	−1.06511	+	1.06511i	−0.997727	+	0.0673858i	$0.978534\pi$
$828$	106.899	+	11041.2i	0.00448672	+	0.463417i
$829$			37685.9i			1.57887i	0.613832	+	0.789437i	$0.289627\pi$
$829$			37685.9i			1.57887i	−0.613832	+	0.789437i	$0.710373\pi$
$830$	−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
$837$	−835.931	−	332.116i	−0.0345209	−	0.0137152i
$838$	−19664.2	+	19664.2i	−0.810609	+	0.810609i
$839$	−10906.1			−0.448774			−0.224387	−	0.974500i	$-0.572038\pi$
$839$	−10906.1			−0.448774			−0.224387	+	0.974500i	$0.572038\pi$
$840$	−10511.0	+	1611.70i	−0.431742	+	0.0662011i
$841$	18282.0			0.749601
$842$	22080.8	−	22080.8i	0.903745	−	0.903745i
$843$	24764.7	−	10398.6i	1.01180	−	0.424849i
$844$			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
$852$	−1201.14	−	2860.56i	−0.0482984	−	0.115025i
$853$	−14701.8	+	14701.8i	−0.590131	+	0.590131i	−0.937667	−	0.347536i	$-0.887018\pi$
$853$	−14701.8	+	14701.8i	−0.590131	+	0.590131i	0.347536	+	0.937667i	$0.387018\pi$
$854$	24883.6			0.997071
$855$	21566.8	+	35200.8i	0.862653	+	1.40800i
$856$	1179.70			0.0471045
$857$	14745.6	−	14745.6i	0.587749	−	0.587749i	−0.349272	−	0.937021i	$-0.613571\pi$
$857$	14745.6	−	14745.6i	0.587749	−	0.587749i	0.937021	+	0.349272i	$0.113571\pi$
$858$	2482.72	+	5912.69i	0.0987862	+	0.235263i
$859$		−	45884.6i		−	1.82254i	−0.411808	−	0.911271i	$-0.635103\pi$
$859$		−	45884.6i		−	1.82254i	0.411808	−	0.911271i	$-0.364897\pi$
$860$	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	$-0.348666\pi$
$863$	−10936.4	−	10936.4i	−0.431376	−	0.431376i	−0.889096	+	0.457720i	$0.848666\pi$
$864$	4122.35	−	1778.10i	0.162321	−	0.0700141i
$865$	17077.4	+	28489.0i	0.671272	+	1.11983i
$866$		−	10198.0i		−	0.400164i
$867$	−16557.0	+	6952.22i	−0.648564	+	0.272329i
$868$	−414.914	+	414.914i	−0.0162248	+	0.0162248i
$869$	−1249.37			−0.0487710
$870$	19347.6	+	14203.1i	0.753960	+	0.553484i
$871$	8246.86			0.320820
$872$	−4122.30	+	4122.30i	−0.160090	+	0.160090i
$873$	31002.9	−	300.165i	1.20194	−	0.0116370i
$874$		−	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	0.604567	−	0.796554i	$-0.293346\pi$
$877$	−4986.22	−	4986.22i	−0.191987	−	0.191987i	−0.796554	+	0.604567i	$0.793346\pi$
$878$	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	$-0.280936\pi$
$882$	−9747.13	+	94.3701i	−0.372112	+	0.00360273i
$883$	−16473.1	+	16473.1i	−0.627819	+	0.627819i	−0.947519	−	0.319700i	$-0.896418\pi$
$883$	−16473.1	+	16473.1i	−0.627819	+	0.627819i	0.319700	+	0.947519i	$0.396418\pi$
$884$	−7386.16			−0.281022
$885$	5523.50	+	36022.5i	0.209797	+	1.36823i
$886$	−13544.5			−0.513584
$887$	−8236.06	+	8236.06i	−0.311770	+	0.311770i	−0.845595	−	0.533825i	$-0.820754\pi$
$887$	−8236.06	+	8236.06i	−0.311770	+	0.311770i	0.533825	+	0.845595i	$0.320754\pi$
$888$	8031.75	−	3372.50i	0.303522	−	0.127448i
$889$		−	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
$897$	−9949.23	−	23694.5i	−0.370340	−	0.881980i
$898$	9103.51	−	9103.51i	0.338294	−	0.338294i
$899$	1324.39			0.0491335
$900$	4044.94	+	12879.8i	0.149812	+	0.477029i
$901$	649.086			0.0240002
$902$	370.997	−	370.997i	0.0136949	−	0.0136949i
$903$	10563.7	+	25157.9i	0.389300	+	0.927134i
$904$		−	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	0.600033	−	0.799975i	$-0.295154\pi$
$907$	−5461.54	−	5461.54i	−0.199942	−	0.199942i	−0.799975	+	0.600033i	$0.795154\pi$
$908$	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	$0.989040\pi$
$912$	−10483.0	+	4401.77i	−0.380621	+	0.159821i
$913$	−9377.82	+	9377.82i	−0.339935	+	0.339935i
$914$	21024.1			0.760850
$915$	−4787.97	−	31225.6i	−0.172989	−	1.12818i
$916$	20248.1			0.730368
$917$	7522.77	−	7522.77i	0.270909	−	0.270909i
$918$	3954.70	−	9953.94i	0.142184	−	0.357875i
$919$		−	6455.86i		−	0.231729i	−0.993265	−	0.115865i	$-0.963036\pi$
$919$		−	6455.86i		−	0.231729i	0.993265	−	0.115865i	$-0.0369638\pi$
$920$	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
$927$	−374.777	−	38709.3i	−0.0132786	−	1.37150i
$928$	−4674.14	+	4674.14i	−0.165341	+	0.165341i
$929$	14798.5			0.522628			0.261314	−	0.965254i	$-0.415844\pi$
$929$	14798.5			0.522628			0.261314	+	0.965254i	$0.415844\pi$
$930$	600.498	+	440.827i	0.0211732	+	0.0155433i
$931$	24685.8			0.869007
$932$	4051.17	−	4051.17i	0.142382	−	0.142382i
$933$	−38818.0	+	16299.5i	−1.36210	+	0.571943i
$934$			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	0.797481	−	0.603344i	$-0.206165\pi$
$937$	5568.25	+	5568.25i	0.194137	+	0.194137i	−0.603344	+	0.797481i	$0.706165\pi$
$938$	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	$0.846340\pi$
$942$	−5728.25	−	13642.1i	−0.198128	−	0.471850i
$943$	−1486.73	+	1486.73i	−0.0513411	+	0.0513411i
$944$	−10037.0			−0.346055
$945$	5782.67	+	35420.2i	0.199059	+	1.21928i
$946$	5855.21			0.201236
$947$	−20065.7	+	20065.7i	−0.688540	+	0.688540i	−0.961909	−	0.273369i	$-0.911862\pi$
$947$	−20065.7	+	20065.7i	−0.688540	+	0.688540i	0.273369	+	0.961909i	$0.411862\pi$
$948$	−788.120	−	1876.94i	−0.0270010	−	0.0643039i
$949$			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	$-0.435960\pi$
$953$	−22947.3	−	22947.3i	−0.779996	−	0.779996i	−0.979830	+	0.199834i	$0.935960\pi$
$954$	642.969	−	655.541i	0.0218207	−	0.0222473i
$955$	−5540.56	+	22123.5i	−0.187736	+	0.749634i
$956$		−	4562.41i		−	0.154350i
$957$	12624.3	−	5300.91i	0.426423	−	0.179053i
$958$	−1180.61	+	1180.61i	−0.0398162	+	0.0398162i
$959$	−3304.24			−0.111261
$960$	−3675.11	+	563.522i	−0.123556	+	0.0189454i
$961$	−29749.9			−0.998620
$962$	−14336.0	+	14336.0i	−0.480469	+	0.480469i
$963$	−38.5464	−	3981.31i	−0.00128987	−	0.133225i
$964$		−	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	0.403682	−	0.914899i	$-0.367730\pi$
$967$	−15372.5	−	15372.5i	−0.511218	−	0.511218i	−0.914899	+	0.403682i	$0.867730\pi$
$968$	−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	$0.685604\pi$
$972$	−6135.50	−	13854.2i	−0.202465	−	0.457174i
$973$	−5441.51	+	5441.51i	−0.179288	+	0.179288i
$974$	3178.29			0.104557
$975$	−20052.2	−	24189.3i	−0.658650	−	0.794541i
$976$	8700.42			0.285342
$977$	−9640.67	+	9640.67i	−0.315693	+	0.315693i	−0.847110	−	0.531417i	$-0.821660\pi$
$977$	−9640.67	+	9640.67i	−0.315693	+	0.315693i	0.531417	+	0.847110i	$0.321660\pi$
$978$	9410.46	−	3951.42i	0.307682	−	0.129195i
$979$			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	$-0.496101\pi$
$983$	−30440.0	−	30440.0i	−0.987677	−	0.987677i	−0.999925	+	0.0122482i	$0.996101\pi$
$984$	791.381	+	323.322i	0.0256385	+	0.0104747i
$985$	26901.2	−	16125.7i	0.870198	−	0.521632i
$986$			15770.4i			0.509362i
$987$	12470.4	+	29698.7i	0.402165	+	0.957772i
$988$	18711.2	−	18711.2i	0.602514	−	0.602514i
$989$	−23464.1			−0.754415
$990$	7488.45	+	1798.53i	0.240403	+	0.0577383i
$991$	−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
$993$	5698.07	+	13570.2i	0.182097	+	0.433672i
$994$			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	0.808855	−	0.588008i	$-0.200088\pi$
$997$	6952.37	+	6952.37i	0.220846	+	0.220846i	−0.588008	+	0.808855i	$0.700088\pi$
$998$	−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.17.5	yes	12
3.2	odd	2	inner	30.4.e.a.17.1	✓	12
4.3	odd	2		240.4.v.d.17.4		12
5.2	odd	4		150.4.e.c.143.6		12
5.3	odd	4	inner	30.4.e.a.23.1	yes	12
5.4	even	2		150.4.e.c.107.2		12
12.11	even	2		240.4.v.d.17.6		12
15.2	even	4		150.4.e.c.143.2		12
15.8	even	4	inner	30.4.e.a.23.5	yes	12
15.14	odd	2		150.4.e.c.107.6		12
20.3	even	4		240.4.v.d.113.6		12
60.23	odd	4		240.4.v.d.113.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.4.e.a.17.1	✓	12	3.2	odd	2	inner
30.4.e.a.17.5	yes	12	1.1	even	1	trivial
30.4.e.a.23.1	yes	12	5.3	odd	4	inner
30.4.e.a.23.5	yes	12	15.8	even	4	inner
150.4.e.c.107.2		12	5.4	even	2
150.4.e.c.107.6		12	15.14	odd	2
150.4.e.c.143.2		12	15.2	even	4
150.4.e.c.143.6		12	5.2	odd	4
240.4.v.d.17.4		12	4.3	odd	2
240.4.v.d.17.6		12	12.11	even	2
240.4.v.d.113.4		12	60.23	odd	4
240.4.v.d.113.6		12	20.3	even	4

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} +(2.01170 + 4.79094i) 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} +(19.1637 - 8.04679i) q^{12} +(-34.2057 + 34.2057i) q^{13} -45.7607 q^{14} +(8.80503 + 57.4236i) q^{15} -16.0000 q^{16} +(-26.9917 + 26.9917i) q^{17} +(0.522794 + 53.9975i) 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} +(-130.383 - 51.8011i) q^{27} +(-64.7154 + 64.7154i) q^{28} +206.570 q^{29} +(93.6615 + 68.7571i) q^{30} +6.41137 q^{31} +(-22.6274 + 22.6274i) q^{32} +(61.1141 - 25.6616i) 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} +(-92.0567 - 219.237i) q^{42} +(-162.284 + 162.284i) q^{43} -51.0248 q^{44} +(-257.400 + 157.703i) q^{45} +204.477 q^{46} +(-191.575 + 191.575i) q^{47} +(-32.1871 - 76.6550i) 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} +(655.187 - 275.110i) q^{57} +(292.134 - 292.134i) q^{58} +627.311 q^{59} +(229.694 - 35.2201i) q^{60} -543.776 q^{61} +(9.06704 - 9.06704i) q^{62} +(617.741 - 5.98086i) 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} +(215.990 - 2.09118i) q^{72} +(771.809 - 771.809i) q^{73} +419.112 q^{74} +(-60.4737 + 646.698i) q^{75} -547.022 q^{76} +(-206.381 + 206.381i) q^{77} +(-463.515 + 194.628i) 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} +(415.556 + 989.662i) q^{87} +(-72.1599 + 72.1599i) q^{88} -492.823 q^{89} +(-140.992 + 587.044i) q^{90} +1106.82 q^{91} +(289.174 - 289.174i) q^{92} +(12.8977 + 30.7164i) 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

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