LMFDB - Embedded newform 126.4.m.a.41.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,4,Mod(41,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("126.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	126.m (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.43424066072$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.19
Character	$\chi$	$=$	126.41
Dual form			126.4.m.a.83.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 - 1.00000i) q^{2} +(0.618827 + 5.15917i) q^{3} +(2.00000 - 3.46410i) q^{4} +(-4.67738 + 8.10146i) q^{5} +(6.23101 + 8.31712i) q^{6} +(-10.5029 + 15.2541i) q^{7} -8.00000i q^{8} +(-26.2341 + 6.38527i) q^{9} +O(q^{10})$	\(q+(1.73205 - 1.00000i) q^{2} +(0.618827 + 5.15917i) q^{3} +(2.00000 - 3.46410i) q^{4} +(-4.67738 + 8.10146i) q^{5} +(6.23101 + 8.31712i) q^{6} +(-10.5029 + 15.2541i) q^{7} -8.00000i q^{8} +(-26.2341 + 6.38527i) q^{9} +18.7095i q^{10} +(-12.5541 + 7.24812i) q^{11} +(19.1095 + 8.17466i) q^{12} +(-2.42151 - 1.39806i) q^{13} +(-2.93751 + 36.9239i) q^{14} +(-44.6913 - 19.1180i) q^{15} +(-8.00000 - 13.8564i) q^{16} +47.3777 q^{17} +(-39.0535 + 37.2937i) q^{18} +75.6711i q^{19} +(18.7095 + 32.4058i) q^{20} +(-85.1981 - 44.7468i) q^{21} +(-14.4962 + 25.1082i) q^{22} +(53.4375 + 30.8522i) q^{23} +(41.2734 - 4.95062i) q^{24} +(18.7442 + 32.4660i) q^{25} -5.59223 q^{26} +(-49.1771 - 131.395i) q^{27} +(31.8359 + 66.8915i) q^{28} +(15.3934 - 8.88741i) q^{29} +(-96.5256 + 11.5780i) q^{30} +(28.5640 + 16.4914i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(-45.1631 - 60.2835i) q^{33} +(82.0606 - 47.3777i) q^{34} +(-74.4544 - 156.439i) q^{35} +(-30.3490 + 103.648i) q^{36} +340.681 q^{37} +(75.6711 + 131.066i) q^{38} +(5.71432 - 13.3581i) q^{39} +(64.8117 + 37.4190i) q^{40} +(9.20200 - 15.9383i) q^{41} +(-192.314 + 7.69436i) q^{42} +(174.489 + 302.224i) q^{43} +57.9849i q^{44} +(70.9768 - 242.401i) q^{45} +123.409 q^{46} +(-49.7597 - 86.1864i) q^{47} +(66.5370 - 49.8481i) q^{48} +(-122.376 - 320.426i) q^{49} +(64.9319 + 37.4885i) q^{50} +(29.3186 + 244.430i) q^{51} +(-9.68602 + 5.59223i) q^{52} -615.865i q^{53} +(-216.572 - 178.405i) q^{54} -135.609i q^{55} +(122.033 + 84.0236i) q^{56} +(-390.400 + 46.8273i) q^{57} +(17.7748 - 30.7869i) q^{58} +(266.903 - 462.289i) q^{59} +(-155.609 + 116.579i) q^{60} +(-663.603 + 383.131i) q^{61} +65.9657 q^{62} +(178.134 - 467.242i) q^{63} -64.0000 q^{64} +(22.6526 - 13.0785i) q^{65} +(-138.508 - 59.2509i) q^{66} +(-348.599 + 603.791i) q^{67} +(94.7554 - 164.121i) q^{68} +(-126.103 + 294.786i) q^{69} +(-285.397 - 196.505i) q^{70} -597.683i q^{71} +(51.0822 + 209.873i) q^{72} -572.023i q^{73} +(590.077 - 340.681i) q^{74} +(-155.898 + 116.796i) q^{75} +(262.132 + 151.342i) q^{76} +(21.2914 - 267.628i) q^{77} +(-3.46062 - 28.8513i) q^{78} +(643.996 + 1115.43i) q^{79} +149.676 q^{80} +(647.457 - 335.024i) q^{81} -36.8080i q^{82} +(147.704 + 255.831i) q^{83} +(-325.404 + 205.641i) q^{84} +(-221.604 + 383.829i) q^{85} +(604.449 + 348.979i) q^{86} +(55.3775 + 73.9176i) q^{87} +(57.9849 + 100.433i) q^{88} +258.046 q^{89} +(-119.465 - 490.828i) q^{90} +(46.7591 - 22.2542i) q^{91} +(213.750 - 123.409i) q^{92} +(-67.4059 + 157.572i) q^{93} +(-172.373 - 99.5195i) q^{94} +(-613.046 - 353.942i) q^{95} +(65.3973 - 152.876i) q^{96} +(-583.718 + 337.010i) q^{97} +(-532.388 - 432.618i) q^{98} +(283.065 - 270.309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9}+O(q^{10}) $ 48 * q + 96 * q^4 - 12 * q^7 - 36 * q^9	$ 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9} + 24 q^{11} - 132 q^{14} - 120 q^{15} - 384 q^{16} + 120 q^{18} + 180 q^{21} + 348 q^{23} - 600 q^{25} - 96 q^{28} - 84 q^{29} + 192 q^{30} + 96 q^{36} - 672 q^{37} + 1368 q^{39} + 1128 q^{42} + 84 q^{43} - 1008 q^{46} - 42 q^{49} + 456 q^{50} + 2016 q^{51} - 528 q^{56} + 732 q^{57} + 504 q^{58} - 1008 q^{60} - 774 q^{63} - 3072 q^{64} - 6972 q^{65} + 1176 q^{67} + 216 q^{70} - 384 q^{72} + 2520 q^{74} + 1500 q^{77} + 2832 q^{78} + 348 q^{79} + 2268 q^{81} - 1080 q^{84} + 720 q^{85} + 1200 q^{86} + 180 q^{91} + 1392 q^{92} + 5232 q^{93} - 5892 q^{95} + 972 q^{99}+O(q^{100}) $ 48 * q + 96 * q^4 - 12 * q^7 - 36 * q^9 + 24 * q^11 - 132 * q^14 - 120 * q^15 - 384 * q^16 + 120 * q^18 + 180 * q^21 + 348 * q^23 - 600 * q^25 - 96 * q^28 - 84 * q^29 + 192 * q^30 + 96 * q^36 - 672 * q^37 + 1368 * q^39 + 1128 * q^42 + 84 * q^43 - 1008 * q^46 - 42 * q^49 + 456 * q^50 + 2016 * q^51 - 528 * q^56 + 732 * q^57 + 504 * q^58 - 1008 * q^60 - 774 * q^63 - 3072 * q^64 - 6972 * q^65 + 1176 * q^67 + 216 * q^70 - 384 * q^72 + 2520 * q^74 + 1500 * q^77 + 2832 * q^78 + 348 * q^79 + 2268 * q^81 - 1080 * q^84 + 720 * q^85 + 1200 * q^86 + 180 * q^91 + 1392 * q^92 + 5232 * q^93 - 5892 * q^95 + 972 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$	0.618827	+	5.15917i	0.119093	+	0.992883i
$3$	0.618827	+	5.15917i	0.119093	+	0.992883i
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$	−4.67738	+	8.10146i	−0.418358	+	0.724617i	−0.995774	−	0.0918329i	$-0.970727\pi$
$5$	−4.67738	+	8.10146i	−0.418358	+	0.724617i	0.577417	+	0.816450i	$0.304061\pi$
$6$	6.23101	+	8.31712i	0.423967	+	0.565908i
$7$	−10.5029	+	15.2541i	−0.567106	+	0.823645i
$7$	−10.5029	+	15.2541i	−0.567106	+	0.823645i
$8$		−	8.00000i		−	0.353553i
$9$	−26.2341	+	6.38527i	−0.971634	+	0.236492i
$10$			18.7095i			0.591647i
$11$	−12.5541	+	7.24812i	−0.344110	+	0.198672i	−0.662088	−	0.749426i	$-0.730329\pi$
$11$	−12.5541	+	7.24812i	−0.344110	+	0.198672i	0.317978	+	0.948098i	$0.396996\pi$
$12$	19.1095	+	8.17466i	0.459704	+	0.196652i
$13$	−2.42151	−	1.39806i	−0.0516619	−	0.0298270i	0.473947	−	0.880554i	$-0.342829\pi$
$13$	−2.42151	−	1.39806i	−0.0516619	−	0.0298270i	−0.525608	+	0.850727i	$0.676162\pi$
$14$	−2.93751	+	36.9239i	−0.0560774	+	0.704880i
$15$	−44.6913	−	19.1180i	−0.769283	−	0.329083i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	47.3777			0.675928			0.337964	−	0.941159i	$-0.390262\pi$
$17$	47.3777			0.675928			0.337964	+	0.941159i	$0.390262\pi$
$18$	−39.0535	+	37.2937i	−0.511389	+	0.488345i
$19$			75.6711i			0.913691i	0.889546	+	0.456846i	$0.151021\pi$
$19$			75.6711i			0.913691i	−0.889546	+	0.456846i	$0.848979\pi$
$20$	18.7095	+	32.4058i	0.209179	+	0.362308i
$21$	−85.1981	−	44.7468i	−0.885322	−	0.464979i
$22$	−14.4962	+	25.1082i	−0.140482	+	0.243322i
$23$	53.4375	+	30.8522i	0.484456	+	0.279701i	0.722272	−	0.691609i	$-0.243098\pi$
$23$	53.4375	+	30.8522i	0.484456	+	0.279701i	−0.237815	+	0.971310i	$0.576431\pi$
$24$	41.2734	−	4.95062i	0.351037	−	0.0421059i
$25$	18.7442	+	32.4660i	0.149954	+	0.259728i
$26$	−5.59223			−0.0421818
$27$	−49.1771	−	131.395i	−0.350524	−	0.936554i
$28$	31.8359	+	66.8915i	0.214872	+	0.451475i
$29$	15.3934	−	8.88741i	0.0985686	−	0.0569086i	−0.449905	−	0.893076i	$-0.648542\pi$
$29$	15.3934	−	8.88741i	0.0985686	−	0.0569086i	0.548474	+	0.836168i	$0.315209\pi$
$30$	−96.5256	+	11.5780i	−0.587436	+	0.0704612i
$31$	28.5640	+	16.4914i	0.165492	+	0.0955466i	0.580458	−	0.814290i	$-0.302873\pi$
$31$	28.5640	+	16.4914i	0.165492	+	0.0955466i	−0.414967	+	0.909837i	$0.636207\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$	−45.1631	−	60.2835i	−0.238239	−	0.318000i
$34$	82.0606	−	47.3777i	0.413920	−	0.238977i
$35$	−74.4544	−	156.439i	−0.359574	−	0.755512i
$36$	−30.3490	+	103.648i	−0.140505	+	0.479853i
$37$	340.681			1.51372			0.756859	−	0.653578i	$-0.226733\pi$
$37$	340.681			1.51372			0.756859	+	0.653578i	$0.226733\pi$
$38$	75.6711	+	131.066i	0.323039	+	0.559519i
$39$	5.71432	−	13.3581i	0.0234621	−	0.0548464i
$40$	64.8117	+	37.4190i	0.256191	+	0.147912i
$41$	9.20200	−	15.9383i	0.0350515	−	0.0607110i	−0.847967	−	0.530048i	$-0.822174\pi$
$41$	9.20200	−	15.9383i	0.0350515	−	0.0607110i	0.883019	+	0.469337i	$0.155507\pi$
$42$	−192.314	+	7.69436i	−0.706542	+	0.0282682i
$43$	174.489	+	302.224i	0.618822	+	1.07183i	0.989701	+	0.143150i	$0.0457233\pi$
$43$	174.489	+	302.224i	0.618822	+	1.07183i	−0.370879	+	0.928681i	$0.620943\pi$
$44$			57.9849i			0.198672i
$45$	70.9768	−	242.401i	0.235125	−	0.803000i
$46$	123.409			0.395557
$47$	−49.7597	−	86.1864i	−0.154430	−	0.267480i	0.778421	−	0.627742i	$-0.216021\pi$
$47$	−49.7597	−	86.1864i	−0.154430	−	0.267480i	−0.932851	+	0.360262i	$0.882687\pi$
$48$	66.5370	−	49.8481i	0.200079	−	0.149895i
$49$	−122.376	−	320.426i	−0.356782	−	0.934188i
$50$	64.9319	+	37.4885i	0.183655	+	0.106033i
$51$	29.3186	+	244.430i	0.0804986	+	0.671118i
$52$	−9.68602	+	5.59223i	−0.0258309	+	0.0149135i
$53$		−	615.865i		−	1.59614i	−0.602564	−	0.798071i	$-0.705854\pi$
$53$		−	615.865i		−	1.59614i	0.602564	−	0.798071i	$-0.294146\pi$
$54$	−216.572	−	178.405i	−0.545773	−	0.449591i
$55$		−	135.609i		−	0.332463i
$56$	122.033	+	84.0236i	0.291202	+	0.200502i
$57$	−390.400	+	46.8273i	−0.907189	+	0.108815i
$58$	17.7748	−	30.7869i	0.0402405	−	0.0696985i
$59$	266.903	−	462.289i	0.588946	−	1.02008i	−0.405425	−	0.914128i	$-0.632876\pi$
$59$	266.903	−	462.289i	0.588946	−	1.02008i	0.994371	−	0.105956i	$-0.0337902\pi$
$60$	−155.609	+	116.579i	−0.334818	+	0.250839i
$61$	−663.603	+	383.131i	−1.39288	+	0.804179i	−0.993633	−	0.112665i	$-0.964061\pi$
$61$	−663.603	+	383.131i	−1.39288	+	0.804179i	−0.399246	+	0.916844i	$0.630728\pi$
$62$	65.9657			0.135123
$63$	178.134	−	467.242i	0.356234	−	0.934397i
$64$	−64.0000			−0.125000
$65$	22.6526	−	13.0785i	0.0432263	−	0.0249567i
$66$	−138.508	−	59.2509i	−0.258321	−	0.110504i
$67$	−348.599	+	603.791i	−0.635643	+	1.10097i	0.350735	+	0.936475i	$0.385932\pi$
$67$	−348.599	+	603.791i	−0.635643	+	1.10097i	−0.986378	+	0.164492i	$0.947402\pi$
$68$	94.7554	−	164.121i	0.168982	−	0.292686i
$69$	−126.103	+	294.786i	−0.220015	+	0.514319i
$70$	−285.397	−	196.505i	−0.487307	−	0.335526i
$71$		−	597.683i		−	0.999041i	−0.866302	−	0.499521i	$-0.833510\pi$
$71$		−	597.683i		−	0.999041i	0.866302	−	0.499521i	$-0.166490\pi$
$72$	51.0822	+	209.873i	0.0836124	+	0.343524i
$73$		−	572.023i		−	0.917126i	−0.888662	−	0.458563i	$-0.848364\pi$
$73$		−	572.023i		−	0.917126i	0.888662	−	0.458563i	$-0.151636\pi$
$74$	590.077	−	340.681i	0.926960	−	0.535180i
$75$	−155.898	+	116.796i	−0.240021	+	0.179818i
$76$	262.132	+	151.342i	0.395640	+	0.228423i
$77$	21.2914	−	267.628i	0.0315115	−	0.396092i
$78$	−3.46062	−	28.8513i	−0.00502357	−	0.0418816i
$79$	643.996	+	1115.43i	0.917154	+	1.58856i	0.803717	+	0.595012i	$0.202853\pi$
$79$	643.996	+	1115.43i	0.917154	+	1.58856i	0.113438	+	0.993545i	$0.463814\pi$
$80$	149.676			0.209179
$81$	647.457	−	335.024i	0.888143	−	0.459566i
$82$		−	36.8080i		−	0.0495703i
$83$	147.704	+	255.831i	0.195333	+	0.338327i	0.947010	−	0.321205i	$-0.104088\pi$
$83$	147.704	+	255.831i	0.195333	+	0.338327i	−0.751677	+	0.659532i	$0.770755\pi$
$84$	−325.404	+	205.641i	−0.422672	+	0.267111i
$85$	−221.604	+	383.829i	−0.282780	+	0.489789i
$86$	604.449	+	348.979i	0.757900	+	0.437574i
$87$	55.3775	+	73.9176i	0.0682425	+	0.0910897i
$88$	57.9849	+	100.433i	0.0702411	+	0.121661i
$89$	258.046			0.307335			0.153668	−	0.988123i	$-0.450891\pi$
$89$	258.046			0.307335			0.153668	+	0.988123i	$0.450891\pi$
$90$	−119.465	−	490.828i	−0.139920	−	0.574864i
$91$	46.7591	−	22.2542i	0.0538646	−	0.0256360i
$92$	213.750	−	123.409i	0.242228	−	0.139851i
$93$	−67.4059	+	157.572i	−0.0751577	+	0.175693i
$94$	−172.373	−	99.5195i	−0.189137	−	0.109198i
$95$	−613.046	−	353.942i	−0.662076	−	0.382250i
$96$	65.3973	−	152.876i	0.0695269	−	0.162530i
$97$	−583.718	+	337.010i	−0.611006	+	0.352765i	−0.773359	−	0.633968i	$-0.781425\pi$
$97$	−583.718	+	337.010i	−0.611006	+	0.352765i	0.162353	+	0.986733i	$0.448092\pi$
$98$	−532.388	−	432.618i	−0.548769	−	0.445929i
$99$	283.065	−	270.309i	0.287364	−	0.274415i
$100$	149.954			0.149954
$101$	765.672	+	1326.18i	0.754329	+	1.30654i	0.945707	+	0.325019i	$0.105371\pi$
$101$	765.672	+	1326.18i	0.754329	+	1.30654i	−0.191379	+	0.981516i	$0.561296\pi$
$102$	295.211	+	394.046i	0.286571	+	0.382513i
$103$	1306.46	+	754.283i	1.24980	+	0.721570i	0.971069	−	0.238800i	$-0.0767542\pi$
$103$	1306.46	+	754.283i	1.24980	+	0.721570i	0.278727	+	0.960370i	$0.410088\pi$
$104$	−11.1845	+	19.3720i	−0.0105454	+	0.0182652i
$105$	761.019	−	480.931i	0.707313	−	0.446991i
$106$	−615.865	−	1066.71i	−0.564321	−	0.977433i
$107$			959.454i			0.866859i	0.901188	+	0.433429i	$0.142697\pi$
$107$			959.454i			0.866859i	−0.901188	+	0.433429i	$0.857303\pi$
$108$	−553.519	−	92.4353i	−0.493171	−	0.0823573i
$109$	−20.1041			−0.0176662			−0.00883311	−	0.999961i	$-0.502812\pi$
$109$	−20.1041			−0.0176662			−0.00883311	+	0.999961i	$0.502812\pi$
$110$	−135.609	−	234.881i	−0.117544	−	0.203591i
$111$	210.823	+	1757.63i	0.180274	+	1.50295i
$112$	295.391	+	23.5001i	0.249213	+	0.0198263i
$113$	−1685.66	−	973.215i	−1.40330	−	0.810198i	−0.408574	−	0.912725i	$-0.633974\pi$
$113$	−1685.66	−	973.215i	−1.40330	−	0.810198i	−0.994730	+	0.102527i	$0.967307\pi$
$114$	−629.365	+	471.507i	−0.517065	+	0.387375i
$115$	−499.895	+	288.615i	−0.405352	+	0.234030i
$116$		−	71.0992i		−	0.0569086i
$117$	72.4530	+	21.2148i	0.0572503	+	0.0167633i
$118$		−	1067.61i		−	0.832895i
$119$	−497.605	+	722.705i	−0.383323	+	0.556725i
$120$	−152.944	+	357.531i	−0.116348	+	0.271983i
$121$	−560.430	+	970.693i	−0.421059	+	0.729296i
$122$	−766.263	+	1327.21i	−0.568641	+	0.984914i
$123$	87.9231	+	37.6116i	0.0644533	+	0.0275718i
$124$	114.256	−	65.9657i	0.0827458	−	0.0477733i
$125$	−1520.04			−1.08765
$126$	−158.706	−	987.421i	−0.112211	−	0.698147i
$127$	−323.855			−0.226280			−0.113140	−	0.993579i	$-0.536091\pi$
$127$	−323.855			−0.226280			−0.113140	+	0.993579i	$0.536091\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$	−1451.25	+	1087.24i	−0.990506	+	0.742066i
$130$	26.1570	−	45.3052i	0.0176471	−	0.0305656i
$131$	496.393	−	859.777i	0.331069	−	0.573428i	−0.651653	−	0.758517i	$-0.725924\pi$
$131$	496.393	−	859.777i	0.331069	−	0.573428i	0.982722	+	0.185089i	$0.0592574\pi$
$132$	−299.154	+	35.8827i	−0.197258	+	0.0236605i
$133$	−1154.30	−	794.769i	−0.752557	−	0.518159i
$134$			1394.39i			0.898936i
$135$	1294.51	+	216.177i	0.825287	+	0.137819i
$136$		−	379.022i		−	0.238977i
$137$	−1285.39	+	742.118i	−0.801590	+	0.462798i	−0.844027	−	0.536301i	$-0.819821\pi$
$137$	−1285.39	+	742.118i	−0.801590	+	0.462798i	0.0424366	+	0.999099i	$0.486488\pi$
$138$	76.3687	+	636.687i	0.0471082	+	0.392742i
$139$	1791.09	+	1034.09i	1.09294	+	0.631009i	0.934357	−	0.356337i	$-0.115975\pi$
$139$	1791.09	+	1034.09i	1.09294	+	0.631009i	0.158582	+	0.987346i	$0.449308\pi$
$140$	−690.828	−	54.9595i	−0.417040	−	0.0331780i
$141$	413.858	−	310.053i	0.247185	−	0.185186i
$142$	−597.683	−	1035.22i	−0.353214	−	0.611785i
$143$	40.5331			0.0237031
$144$	298.350	+	312.428i	0.172656	+	0.180803i
$145$			166.279i			0.0952326i
$146$	−572.023	−	990.773i	−0.324253	−	0.561623i
$147$	1577.40	−	829.649i	0.885049	−	0.465499i
$148$	681.362	−	1180.15i	0.378430	−	0.655460i
$149$	2888.58	+	1667.72i	1.58820	+	0.916948i	0.993604	+	0.112925i	$0.0360218\pi$
$149$	2888.58	+	1667.72i	1.58820	+	0.916948i	0.594597	+	0.804024i	$0.297312\pi$
$150$	−153.228	+	358.194i	−0.0834066	+	0.194976i
$151$	−938.899	−	1626.22i	−0.506003	−	0.876424i	−0.999976	−	0.00694599i	$-0.997789\pi$
$151$	−938.899	−	1626.22i	−0.506003	−	0.876424i	0.493973	−	0.869478i	$-0.335544\pi$
$152$	605.369			0.323039
$153$	−1242.91	+	302.520i	−0.656755	+	0.159851i
$154$	−230.751	−	484.837i	−0.120743	−	0.253697i
$155$	−267.209	+	154.273i	−0.138469	+	0.0799453i
$156$	−34.8452	−	46.5112i	−0.0178837	−	0.0238710i
$157$	−420.903	−	243.008i	−0.213960	−	0.123530i	0.389191	−	0.921157i	$-0.372755\pi$
$157$	−420.903	−	243.008i	−0.213960	−	0.123530i	−0.603150	+	0.797628i	$0.706088\pi$
$158$	2230.87	+	1287.99i	1.12328	+	0.648526i
$159$	3177.35	−	381.114i	1.58478	−	0.190090i
$160$	259.247	−	149.676i	0.128095	−	0.0739559i
$161$	−1031.87	+	491.104i	−0.505112	+	0.240400i
$162$	786.404	−	1227.73i	0.381393	−	0.595432i
$163$	2268.47			1.09007			0.545033	−	0.838415i	$-0.316517\pi$
$163$	2268.47			1.09007			0.545033	+	0.838415i	$0.316517\pi$
$164$	−36.8080	−	63.7533i	−0.0175257	−	0.0303555i
$165$	699.629	−	83.9184i	0.330097	−	0.0395942i
$166$	511.662	+	295.408i	0.239233	+	0.138121i
$167$	1783.26	−	3088.69i	0.826303	−	1.43120i	−0.0746169	−	0.997212i	$-0.523773\pi$
$167$	1783.26	−	3088.69i	0.826303	−	1.43120i	0.900920	−	0.433986i	$-0.142893\pi$
$168$	−357.975	+	681.585i	−0.164395	+	0.313009i
$169$	−1094.59	−	1895.89i	−0.498221	−	0.862944i
$170$			886.414i			0.399911i
$171$	−483.180	−	1985.16i	−0.216080	−	0.887773i
$172$	1395.91			0.618822
$173$	−2091.48	−	3622.55i	−0.919147	−	1.59201i	−0.800714	−	0.599047i	$-0.795546\pi$
$173$	−2091.48	−	3622.55i	−0.919147	−	1.59201i	−0.118433	−	0.992962i	$-0.537787\pi$
$174$	169.834	+	72.6515i	0.0739949	+	0.0316534i
$175$	−692.109	−	55.0614i	−0.298963	−	0.0237843i
$176$	200.866	+	115.970i	0.0860274	+	0.0496679i
$177$	2550.20	+	1090.92i	1.08296	+	0.463269i
$178$	446.949	−	258.046i	0.188204	−	0.108659i
$179$			3756.49i			1.56857i	0.620403	+	0.784283i	$0.286969\pi$
$179$			3756.49i			1.56857i	−0.620403	+	0.784283i	$0.713031\pi$
$180$	−697.748	−	730.673i	−0.288928	−	0.302562i
$181$		−	2645.35i		−	1.08634i	−0.839623	−	0.543169i	$-0.817224\pi$
$181$		−	2645.35i		−	1.08634i	0.839623	−	0.543169i	$-0.182776\pi$
$182$	58.7348	−	85.3045i	0.0239215	−	0.0347428i
$183$	−2387.30	−	3186.55i	−0.964339	−	1.28719i
$184$	246.817	−	427.500i	0.0988893	−	0.171281i
$185$	−1593.49	+	2760.01i	−0.633276	+	1.09687i
$186$	40.8214	+	340.328i	0.0160923	+	0.134162i
$187$	−594.785	+	343.399i	−0.232593	+	0.134288i
$188$	−398.078			−0.154430
$189$	2520.82	+	629.880i	0.970172	+	0.242418i
$190$	−1415.77			−0.540583
$191$	−2012.55	+	1161.95i	−0.762425	+	0.440186i	−0.830166	−	0.557517i	$-0.811754\pi$
$191$	−2012.55	+	1161.95i	−0.762425	+	0.440186i	0.0677410	+	0.997703i	$0.478421\pi$
$192$	−39.6050	−	330.187i	−0.0148867	−	0.124110i
$193$	−712.482	+	1234.06i	−0.265729	+	0.460255i	−0.967754	−	0.251896i	$-0.918946\pi$
$193$	−712.482	+	1234.06i	−0.265729	+	0.460255i	0.702026	+	0.712152i	$0.252279\pi$
$194$	−674.020	+	1167.44i	−0.249442	+	0.432047i
$195$	81.4922	+	108.775i	0.0299271	+	0.0399465i
$196$	−1354.74	−	216.929i	−0.493711	−	0.0790556i
$197$		−	1517.59i		−	0.548851i	−0.961608	−	0.274426i	$-0.911512\pi$
$197$		−	1517.59i		−	0.548851i	0.961608	−	0.274426i	$-0.0884877\pi$
$198$	219.973	−	751.254i	0.0789535	−	0.269643i
$199$		−	5305.53i		−	1.88995i	−0.327149	−	0.944973i	$-0.606088\pi$
$199$		−	5305.53i		−	1.88995i	0.327149	−	0.944973i	$-0.393912\pi$
$200$	259.728	−	149.954i	0.0918276	−	0.0530167i
$201$	−3330.78	−	1424.84i	−1.16883	−	0.500002i
$202$	2652.36	+	1531.34i	0.923860	+	0.533391i
$203$	−26.1069	+	328.157i	−0.00902632	+	0.113459i
$204$	905.367	+	387.297i	0.310727	+	0.132923i
$205$	86.0825	+	149.099i	0.0293281	+	0.0507978i
$206$	3017.13			1.02045
$207$	−1598.89	−	468.166i	−0.536861	−	0.157197i
$208$			44.7378i			0.0149135i
$209$	−548.473	−	949.983i	−0.181525	−	0.314410i
$210$	837.192	−	1594.02i	0.275103	−	0.523798i
$211$	1124.40	−	1947.51i	0.366856	−	0.635413i	−0.622216	−	0.782845i	$-0.713768\pi$
$211$	1124.40	−	1947.51i	0.366856	−	0.635413i	0.989072	+	0.147433i	$0.0471009\pi$
$212$	−2133.42	−	1231.73i	−0.691150	−	0.399035i
$213$	3083.55	−	369.863i	0.991931	−	0.118979i
$214$	959.454	+	1661.82i	0.306481	+	0.530840i
$215$	−3264.61			−1.03556
$216$	−1051.16	+	393.417i	−0.331122	+	0.123929i
$217$	−551.568	+	262.510i	−0.172548	+	0.0821213i
$218$	−34.8212	+	20.1041i	−0.0108183	+	0.00624596i
$219$	2951.17	−	353.984i	0.910599	−	0.109224i
$220$	−469.763	−	271.218i	−0.143961	−	0.0831159i
$221$	−114.725	−	66.2367i	−0.0349197	−	0.0201609i
$222$	2122.79	+	2833.48i	0.641766	+	0.856626i
$223$	2301.40	−	1328.72i	0.691092	−	0.399002i	−0.112929	−	0.993603i	$-0.536023\pi$
$223$	2301.40	−	1328.72i	0.691092	−	0.399002i	0.804021	+	0.594601i	$0.202690\pi$
$224$	535.132	−	254.687i	0.159621	−	0.0759688i
$225$	−699.042	−	732.028i	−0.207124	−	0.216897i
$226$	−3892.86			−1.14579
$227$	1800.17	+	3117.98i	0.526349	+	0.911664i	0.999529	+	0.0306975i	$0.00977285\pi$
$227$	1800.17	+	3117.98i	0.526349	+	0.911664i	−0.473180	+	0.880966i	$0.656894\pi$
$228$	−618.585	+	1446.04i	−0.179679	+	0.420028i
$229$	960.785	+	554.710i	0.277251	+	0.160071i	0.632178	−	0.774823i	$-0.282161\pi$
$229$	960.785	+	554.710i	0.277251	+	0.160071i	−0.354927	+	0.934894i	$0.615494\pi$
$230$	−577.230	+	999.791i	−0.165484	+	0.286627i
$231$	1393.92	−	55.7696i	0.397026	−	0.0158847i
$232$	−71.0992	−	123.148i	−0.0201202	−	0.0348493i
$233$		−	3630.24i		−	1.02071i	−0.859964	−	0.510354i	$-0.829514\pi$
$233$		−	3630.24i		−	1.02071i	0.859964	−	0.510354i	$-0.170486\pi$
$234$	146.707	−	35.7079i	0.0409852	−	0.00997563i
$235$	930.981			0.258428
$236$	−1067.61	−	1849.16i	−0.294473	−	0.510042i
$237$	−5356.19	+	4012.74i	−1.46802	+	1.09981i
$238$	−139.173	+	1749.37i	−0.0379043	+	0.476448i
$239$	445.368	+	257.133i	0.120537	+	0.0695923i	0.559056	−	0.829130i	$-0.311163\pi$
$239$	445.368	+	257.133i	0.120537	+	0.0695923i	−0.438519	+	0.898722i	$0.644497\pi$
$240$	92.6237	+	772.205i	0.0249118	+	0.207690i
$241$	−1147.98	+	662.785i	−0.306837	+	0.177152i	−0.645510	−	0.763752i	$-0.723355\pi$
$241$	−1147.98	+	662.785i	−0.306837	+	0.177152i	0.338673	+	0.940904i	$0.390022\pi$
$242$			2241.72i			0.595467i
$243$	2129.11	+	3133.02i	0.562068	+	0.827091i
$244$			3065.05i			0.804179i
$245$	3168.32	+	507.329i	0.826190	+	0.132294i
$246$	189.899	−	22.7778i	0.0492175	−	0.00590350i
$247$	105.792	−	183.238i	0.0272527	−	0.0472030i
$248$	131.931	−	228.512i	0.0337808	−	0.0585101i
$249$	−1228.47	+	920.346i	−0.312656	+	0.234235i
$250$	−2632.79	+	1520.04i	−0.666048	+	0.384543i
$251$	425.270			0.106943			0.0534717	−	0.998569i	$-0.482971\pi$
$251$	425.270			0.106943			0.0534717	+	0.998569i	$0.482971\pi$
$252$	−1262.31	−	1551.56i	−0.315547	−	0.387853i
$253$	−894.481			−0.222275
$254$	−560.934	+	323.855i	−0.138567	+	0.0800019i
$255$	−2117.37	−	905.767i	−0.519980	−	0.222437i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−1984.12	+	3436.59i	−0.481579	+	0.834120i	−0.999776	−	0.0211414i	$-0.993270\pi$
$257$	−1984.12	+	3436.59i	−0.481579	+	0.834120i	0.518197	+	0.855261i	$0.326603\pi$
$258$	−1426.39	+	3334.41i	−0.344198	+	0.804618i
$259$	−3578.15	+	5196.79i	−0.858439	+	1.24677i
$260$		−	104.628i		−	0.0249567i
$261$	−347.085	+	331.444i	−0.0823142	+	0.0786050i
$262$		−	1985.57i		−	0.468202i
$263$	−1276.22	+	736.824i	−0.299220	+	0.172755i	−0.642093	−	0.766627i	$-0.721933\pi$
$263$	−1276.22	+	736.824i	−0.299220	+	0.172755i	0.342872	+	0.939382i	$0.388600\pi$
$264$	−482.268	+	361.305i	−0.112430	+	0.0842302i
$265$	4989.40	+	2880.63i	1.15659	+	0.667758i
$266$	−2794.07	−	222.285i	−0.644042	−	0.0512374i
$267$	159.686	+	1331.31i	0.0366016	+	0.305148i
$268$	1394.39	+	2415.16i	0.317822	+	0.550483i
$269$	5746.34			1.30246			0.651228	−	0.758883i	$-0.274254\pi$
$269$	5746.34			1.30246			0.651228	+	0.758883i	$0.274254\pi$
$270$	2458.34	−	920.080i	0.554109	−	0.207386i
$271$			4099.23i			0.918858i	0.888215	+	0.459429i	$0.151946\pi$
$271$			4099.23i			0.918858i	−0.888215	+	0.459429i	$0.848054\pi$
$272$	−379.022	−	656.485i	−0.0844910	−	0.146343i
$273$	143.749	+	227.466i	0.0318685	+	0.0504282i
$274$	−1484.24	+	2570.77i	−0.327248	+	0.566810i
$275$	−470.634	−	271.721i	−0.103201	−	0.0595832i
$276$	768.961	+	1026.41i	0.167703	+	0.223849i
$277$	−3511.99	−	6082.94i	−0.761787	−	1.31945i	−0.941929	−	0.335813i	$-0.890989\pi$
$277$	−3511.99	−	6082.94i	−0.761787	−	1.31945i	0.180142	−	0.983641i	$-0.442344\pi$
$278$	4136.35			0.892381
$279$	−854.652	−	250.249i	−0.183393	−	0.0536989i
$280$	−1251.51	+	595.635i	−0.267114	+	0.127129i
$281$	2922.16	−	1687.11i	0.620360	−	0.358165i	−0.156649	−	0.987654i	$-0.550069\pi$
$281$	2922.16	−	1687.11i	0.620360	−	0.358165i	0.777009	+	0.629489i	$0.216736\pi$
$282$	406.769	−	950.886i	0.0858962	−	0.200796i
$283$	−2480.01	−	1431.83i	−0.520923	−	0.300755i	0.216389	−	0.976307i	$-0.430572\pi$
$283$	−2480.01	−	1431.83i	−0.520923	−	0.300755i	−0.737312	+	0.675552i	$0.763905\pi$
$284$	−2070.43	−	1195.37i	−0.432598	−	0.249760i
$285$	1446.68	−	3381.84i	0.300680	−	0.702887i
$286$	70.2054	−	40.5331i	0.0145152	−	0.00838033i
$287$	146.477	+	307.768i	0.0301264	+	0.0632995i
$288$	829.185	+	242.792i	0.169654	+	0.0496758i
$289$	−2668.35			−0.543121
$290$	166.279	+	288.004i	0.0336698	+	0.0583178i
$291$	−2099.91	−	2802.95i	−0.423021	−	0.564646i
$292$	−1981.55	−	1144.05i	−0.397127	−	0.229282i
$293$	4332.12	−	7503.45i	0.863772	−	1.49610i	−0.00448978	−	0.999990i	$-0.501429\pi$
$293$	4332.12	−	7503.45i	0.863772	−	1.49610i	0.868262	−	0.496107i	$-0.165238\pi$
$294$	1902.50	−	3014.40i	0.377401	−	0.597970i
$295$	2496.81	+	4324.61i	0.492780	+	0.853520i
$296$		−	2725.45i		−	0.535180i
$297$	1569.74	+	1293.10i	0.306685	+	0.252638i
$298$	6670.90			1.29676
$299$	−86.2662	−	149.417i	−0.0166853	−	0.0288998i
$300$	92.7955	+	773.637i	0.0178585	+	0.148887i
$301$	−6442.82	−	512.564i	−1.23375	−	0.0981519i
$302$	−3252.44	−	1877.80i	−0.619725	−	0.357798i
$303$	−6368.18	+	4770.91i	−1.20740	+	0.904560i
$304$	1048.53	−	605.369i	0.197820	−	0.114211i
$305$		−	7168.20i		−	1.34574i
$306$	−1850.27	+	1766.89i	−0.345662	+	0.330086i
$307$			3338.33i			0.620614i	0.950636	+	0.310307i	$0.100432\pi$
$307$			3338.33i			0.620614i	−0.950636	+	0.310307i	$0.899568\pi$
$308$	−884.509	−	609.013i	−0.163635	−	0.112668i
$309$	−3083.00	+	7207.00i	−0.567592	+	1.32684i
$310$	−308.546	+	534.418i	−0.0565299	+	0.0979126i
$311$	−2086.47	+	3613.88i	−0.380428	+	0.658920i	−0.991123	−	0.132945i	$-0.957557\pi$
$311$	−2086.47	+	3613.88i	−0.380428	+	0.658920i	0.610696	+	0.791865i	$0.290890\pi$
$312$	−106.865	−	45.7146i	−0.0193911	−	0.00829512i
$313$	2682.93	−	1548.99i	0.484499	−	0.279725i	−0.237791	−	0.971316i	$-0.576423\pi$
$313$	2682.93	−	1548.99i	0.484499	−	0.279725i	0.722289	+	0.691591i	$0.243090\pi$
$314$	−972.033			−0.174697
$315$	2952.15	+	3628.61i	0.528046	+	0.649045i
$316$	5151.97			0.917154
$317$	5234.81	−	3022.32i	0.927496	−	0.535490i	0.0414775	−	0.999139i	$-0.486794\pi$
$317$	5234.81	−	3022.32i	0.927496	−	0.535490i	0.886019	+	0.463649i	$0.153460\pi$
$318$	5122.22	−	3837.46i	0.903270	−	0.676711i
$319$	−128.834	+	223.147i	−0.0226123	+	0.0391656i
$320$	299.352	−	518.493i	0.0522947	−	0.0905771i
$321$	−4949.99	+	593.736i	−0.860689	+	0.103237i
$322$	−1296.16	+	1882.49i	−0.224323	+	0.325799i
$323$			3585.12i			0.617590i
$324$	134.356	−	2912.90i	0.0230378	−	0.499469i
$325$		−	104.822i		−	0.0178907i
$326$	3929.11	−	2268.47i	0.667526	−	0.385396i
$327$	−12.4409	−	103.720i	−0.00210393	−	0.0175405i
$328$	−127.507	−	73.6160i	−0.0214646	−	0.0123926i
$329$	1837.32	+	146.170i	0.307887	+	0.0244942i
$330$	1127.87	−	844.980i	0.188144	−	0.140953i
$331$	879.236	+	1522.88i	0.146004	+	0.252886i	0.929747	−	0.368199i	$-0.120026\pi$
$331$	879.236	+	1522.88i	0.146004	+	0.252886i	−0.783743	+	0.621085i	$0.786692\pi$
$332$	1181.63			0.195333
$333$	−8937.46	+	2175.34i	−1.47078	+	0.357982i
$334$		−	7133.03i		−	1.16857i
$335$	−3261.06	−	5648.32i	−0.531853	−	0.921196i
$336$	61.5549	+	1538.51i	0.00999433	+	0.249800i
$337$	−616.678	+	1068.12i	−0.0996813	+	0.172653i	−0.911553	−	0.411183i	$-0.865116\pi$
$337$	−616.678	+	1068.12i	−0.0996813	+	0.172653i	0.811871	+	0.583836i	$0.198449\pi$
$338$	−3791.77	−	2189.18i	−0.610193	−	0.352295i
$339$	3977.85	−	9298.85i	0.637308	−	1.48981i
$340$	886.414	+	1535.31i	0.141390	+	0.244894i
$341$	−478.127			−0.0759297
$342$	−2822.06	−	2955.22i	−0.446197	−	0.467252i
$343$	6173.13	+	1498.68i	0.971772	+	0.235921i
$344$	2417.79	−	1395.91i	0.378950	−	0.218787i
$345$	−1798.36	−	2400.44i	−0.280639	−	0.374596i
$346$	−7245.11	−	4182.96i	−1.12572	−	0.649935i
$347$	180.579	+	104.258i	0.0279366	+	0.0161292i	0.513903	−	0.857848i	$-0.328199\pi$
$347$	180.579	+	104.258i	0.0279366	+	0.0161292i	−0.485967	+	0.873977i	$0.661532\pi$
$348$	366.813	−	43.9982i	0.0565036	−	0.00677744i
$349$	9319.18	−	5380.43i	1.42935	−	0.825238i	0.432284	−	0.901737i	$-0.357708\pi$
$349$	9319.18	−	5380.43i	1.42935	−	0.825238i	0.997070	+	0.0764996i	$0.0243744\pi$
$350$	−1253.83	+	596.740i	−0.191486	+	0.0911345i
$351$	−64.6149	+	386.926i	−0.00982589	+	0.0588392i
$352$	463.880			0.0702411
$353$	6252.53	+	10829.7i	0.942744	+	1.63288i	0.760206	+	0.649683i	$0.225098\pi$
$353$	6252.53	+	10829.7i	0.942744	+	1.63288i	0.182539	+	0.983199i	$0.441568\pi$
$354$	5507.99	−	660.667i	0.826968	−	0.0991923i
$355$	4842.11	+	2795.59i	0.723922	+	0.417956i
$356$	516.093	−	893.899i	0.0768339	−	0.133080i
$357$	−4036.49	−	2120.00i	−0.598414	−	0.314292i
$358$	3756.49	+	6506.43i	0.554572	+	0.960546i
$359$		−	4120.90i		−	0.605830i	−0.953018	−	0.302915i	$-0.902040\pi$
$359$		−	4120.90i		−	0.605830i	0.953018	−	0.302915i	$-0.0979597\pi$
$360$	−1939.21	−	567.815i	−0.283903	−	0.0831291i
$361$	1132.89			0.165168
$362$	−2645.35	−	4581.88i	−0.384079	−	0.665244i
$363$	−5354.78	−	2290.66i	−0.774251	−	0.331208i
$364$	16.4272	−	206.487i	0.00236544	−	0.0297331i
$365$	4634.22	+	2675.57i	0.664565	+	0.383687i
$366$	−7321.47	−	3131.97i	−1.04563	−	0.447297i
$367$	−8479.20	+	4895.47i	−1.20602	+	0.696298i	−0.961888	−	0.273443i	$-0.911837\pi$
$367$	−8479.20	+	4895.47i	−1.20602	+	0.696298i	−0.244135	+	0.969741i	$0.578504\pi$
$368$		−	987.270i		−	0.139851i
$369$	−139.636	+	476.885i	−0.0196996	+	0.0672782i
$370$			6373.98i			0.895587i
$371$	9394.47	+	6468.39i	1.31465	+	0.905181i
$372$	411.033	+	548.644i	0.0572878	+	0.0764674i
$373$	3590.86	−	6219.55i	0.498465	−	0.863367i	−0.501533	−	0.865139i	$-0.667230\pi$
$373$	3590.86	−	6219.55i	0.498465	−	0.863367i	0.999998	+	0.00177107i	$0.000563750\pi$
$374$	−686.798	+	1189.57i	−0.0949559	+	0.164468i
$375$	−940.643	−	7842.15i	−0.129532	−	1.07991i
$376$	−689.491	+	398.078i	−0.0945686	+	0.0545992i
$377$	−49.7004			−0.00678966
$378$	4996.06	−	1429.83i	0.679814	−	0.194557i
$379$	1782.32			0.241561			0.120780	−	0.992679i	$-0.461460\pi$
$379$	1782.32			0.241561			0.120780	+	0.992679i	$0.461460\pi$
$380$	−2452.18	+	1415.77i	−0.331038	+	0.191125i
$381$	−200.410	−	1670.82i	−0.0269484	−	0.224669i
$382$	−2323.89	+	4025.10i	−0.311259	+	0.539116i
$383$	−391.275	+	677.709i	−0.0522017	+	0.0904160i	−0.890945	−	0.454110i	$-0.849957\pi$
$383$	−391.275	+	677.709i	−0.0522017	+	0.0904160i	0.838744	+	0.544526i	$0.183291\pi$
$384$	−398.785	−	532.296i	−0.0529958	−	0.0707385i
$385$	2068.59	+	1424.29i	0.273832	+	0.188542i
$386$			2849.93i			0.375797i
$387$	−6507.35	−	6814.42i	−0.854748	−	0.895081i
$388$			2696.08i			0.352765i
$389$	3549.72	−	2049.43i	0.462668	−	0.267121i	−0.250498	−	0.968117i	$-0.580594\pi$
$389$	3549.72	−	2049.43i	0.462668	−	0.267121i	0.713165	+	0.700996i	$0.247261\pi$
$390$	249.924	+	106.912i	0.0324497	+	0.0138813i
$391$	2531.75	+	1461.71i	0.327458	+	0.189058i
$392$	−2563.41	+	979.011i	−0.330285	+	0.126142i
$393$	4742.92	+	2028.92i	0.608775	+	0.260421i
$394$	−1517.59	−	2628.54i	−0.194048	−	0.336101i
$395$	−12048.9			−1.53479
$396$	−370.250	−	1521.18i	−0.0469842	−	0.193036i
$397$			629.373i			0.0795650i	0.999208	+	0.0397825i	$0.0126665\pi$
$397$			629.373i			0.0795650i	−0.999208	+	0.0397825i	$0.987333\pi$
$398$	−5305.53	−	9189.45i	−0.668197	−	1.15735i
$399$	3386.04	−	6447.03i	0.424847	−	0.808911i
$400$	299.908	−	519.455i	0.0374885	−	0.0649319i
$401$	6643.12	+	3835.41i	0.827286	+	0.477634i	0.852922	−	0.522038i	$-0.174828\pi$
$401$	6643.12	+	3835.41i	0.827286	+	0.477634i	−0.0256365	+	0.999671i	$0.508161\pi$
$402$	−7193.92	+	862.890i	−0.892538	+	0.107057i
$403$	−46.1119	−	79.8681i	−0.00569974	−	0.00987224i
$404$	6125.37			0.754329
$405$	−314.218	+	6812.38i	−0.0385521	+	0.835827i
$406$	282.939	+	594.492i	0.0345863	+	0.0726703i
$407$	−4276.94	+	2469.30i	−0.520885	+	0.300733i
$408$	1955.44	−	234.549i	0.237276	−	0.0284606i
$409$	−381.519	−	220.270i	−0.0461244	−	0.0266299i	0.476760	−	0.879033i	$-0.341811\pi$
$409$	−381.519	−	220.270i	−0.0461244	−	0.0266299i	−0.522885	+	0.852403i	$0.675144\pi$
$410$	298.199	+	172.165i	0.0359195	+	0.0207381i
$411$	−4624.14	−	6172.28i	−0.554969	−	0.740769i
$412$	5225.82	−	3017.13i	0.624898	−	0.360785i
$413$	4248.55	+	8926.77i	0.506193	+	1.06358i
$414$	−3237.52	+	787.999i	−0.384337	+	0.0935459i
$415$	−2763.47			−0.326876
$416$	44.7378	+	77.4882i	0.00527272	+	0.00913262i
$417$	−4226.66	+	9880.48i	−0.496356	+	1.16031i
$418$	−1899.97	−	1096.95i	−0.222321	−	0.128357i
$419$	5359.76	−	9283.38i	0.624920	−	1.08239i	−0.363636	−	0.931541i	$-0.618465\pi$
$419$	5359.76	−	9283.38i	0.624920	−	1.08239i	0.988556	−	0.150852i	$-0.0482017\pi$
$420$	−143.958	−	3598.11i	−0.0167248	−	0.418023i
$421$	1548.99	+	2682.94i	0.179319	+	0.310590i	0.941648	−	0.336600i	$-0.109277\pi$
$421$	1548.99	+	2682.94i	0.179319	+	0.310590i	−0.762328	+	0.647190i	$0.775944\pi$
$422$		−	4497.58i		−	0.518812i
$423$	1855.73	+	1943.29i	0.213306	+	0.223371i
$424$	−4926.92			−0.564321
$425$	888.058	+	1538.16i	0.101358	+	0.175557i
$426$	4971.00	−	3724.17i	0.565366	−	0.423560i
$427$	1125.45	−	14146.7i	0.127551	−	1.60329i
$428$	3323.65	+	1918.91i	0.375361	+	0.216715i
$429$	25.0830	+	209.117i	0.00282289	+	0.0235344i
$430$	−5654.47	+	3264.61i	−0.634146	+	0.366124i
$431$		−	8313.05i		−	0.929062i	−0.885557	−	0.464531i	$-0.846223\pi$
$431$		−	8313.05i		−	0.929062i	0.885557	−	0.464531i	$-0.153777\pi$
$432$	−1427.24	+	1732.58i	−0.158954	+	0.192960i
$433$			5702.37i			0.632883i	0.948612	+	0.316442i	$0.102488\pi$
$433$			5702.37i			0.632883i	−0.948612	+	0.316442i	$0.897512\pi$
$434$	−692.834	+	1006.25i	−0.0766292	+	0.111294i
$435$	−857.863	+	102.898i	−0.0945548	+	0.0113416i
$436$	−40.2081	+	69.6425i	−0.00441656	+	0.00764970i
$437$	−2334.62	+	4043.68i	−0.255560	+	0.442644i
$438$	4757.58	−	3564.28i	0.519010	−	0.388831i
$439$	8656.61	−	4997.90i	0.941133	−	0.543364i	0.0508180	−	0.998708i	$-0.483817\pi$
$439$	8656.61	−	4997.90i	0.941133	−	0.543364i	0.890315	+	0.455344i	$0.150484\pi$
$440$	−1084.87			−0.117544
$441$	5256.44	+	7624.69i	0.567589	+	0.823312i
$442$	−264.947			−0.0285118
$443$	−13681.2	+	7898.83i	−1.46730	+	0.847144i	−0.999330	−	0.0366030i	$-0.988346\pi$
$443$	−13681.2	+	7898.83i	−1.46730	+	0.847144i	−0.467966	+	0.883747i	$0.655013\pi$
$444$	6510.26	+	2784.95i	0.695863	+	0.297676i
$445$	−1206.98	+	2090.55i	−0.128576	+	0.222700i
$446$	2657.43	−	4602.81i	0.282137	−	0.488676i
$447$	−6816.54	+	15934.7i	−0.721278	+	1.68610i
$448$	672.188	−	976.264i	0.0708882	−	0.102956i
$449$			7652.96i			0.804378i	0.915557	+	0.402189i	$0.131750\pi$
$449$			7652.96i			0.804378i	−0.915557	+	0.402189i	$0.868250\pi$
$450$	−1942.80	−	568.868i	−0.203522	−	0.0595927i
$451$			266.789i			0.0278550i
$452$	−6742.63	+	3892.86i	−0.701652	+	0.405099i
$453$	7808.93	−	5850.29i	0.809924	−	0.606778i
$454$	6235.96	+	3600.33i	0.644643	+	0.372185i
$455$	−38.4182	+	482.908i	−0.00395840	+	0.0497562i
$456$	374.619	+	3123.20i	0.0384718	+	0.320740i
$457$	−3591.88	−	6221.31i	−0.367660	−	0.636807i	0.621539	−	0.783383i	$-0.286508\pi$
$457$	−3591.88	−	6221.31i	−0.367660	−	0.636807i	−0.989199	+	0.146577i	$0.953174\pi$
$458$	2218.84			0.226375
$459$	−2329.90	−	6225.19i	−0.236929	−	0.633043i
$460$			2308.92i			0.234030i
$461$	−61.7406	−	106.938i	−0.00623762	−	0.0108039i	0.862890	−	0.505392i	$-0.168652\pi$
$461$	−61.7406	−	106.938i	−0.00623762	−	0.0108039i	−0.869127	+	0.494588i	$0.835319\pi$
$462$	2358.56	−	1490.51i	0.237512	−	0.150097i
$463$	1121.84	−	1943.09i	0.112606	−	0.195039i	−0.804215	−	0.594339i	$-0.797414\pi$
$463$	1121.84	−	1943.09i	0.112606	−	0.195039i	0.916820	+	0.399301i	$0.130747\pi$
$464$	−246.295	−	142.198i	−0.0246422	−	0.0142272i
$465$	−961.278	−	1283.11i	−0.0958671	−	0.127963i
$466$	−3630.24	−	6287.76i	−0.360875	−	0.625054i
$467$	−13027.4			−1.29087			−0.645436	−	0.763814i	$-0.723324\pi$
$467$	−13027.4			−1.29087			−0.645436	+	0.763814i	$0.723324\pi$
$468$	218.396	−	208.555i	0.0215713	−	0.0205993i
$469$	−5548.98	−	11659.1i	−0.546329	−	1.14791i
$470$	1612.51	−	930.981i	0.158254	−	0.0913680i
$471$	993.255	−	2321.89i	0.0971694	−	0.227149i
$472$	−3698.32	−	2135.22i	−0.360654	−	0.208224i
$473$	−4381.11	−	2529.44i	−0.425885	−	0.245885i
$474$	−5264.45	+	12306.5i	−0.510135	+	1.19252i
$475$	−2456.73	+	1418.40i	−0.237311	+	0.137011i
$476$	1508.31	+	3169.17i	0.145238	+	0.305165i
$477$	3932.46	+	16156.7i	0.377474	+	1.55086i
$478$	1028.53			0.0984184
$479$	−2759.70	−	4779.94i	−0.263244	−	0.455952i	0.703858	−	0.710341i	$-0.251459\pi$
$479$	−2759.70	−	4779.94i	−0.263244	−	0.455952i	−0.967102	+	0.254389i	$0.918126\pi$
$480$	932.634	+	1244.87i	0.0886848	+	0.118376i
$481$	−824.961	−	476.291i	−0.0782016	−	0.0451497i
$482$	−1325.57	+	2295.96i	−0.125266	+	0.216967i
$483$	−3172.24	−	5019.71i	−0.298845	−	0.472888i
$484$	2241.72	+	3882.77i	0.210530	+	0.364648i
$485$		−	6305.30i		−	0.590327i
$486$	6820.74	+	3297.44i	0.636616	+	0.307767i
$487$	−3692.50			−0.343579			−0.171790	−	0.985134i	$-0.554955\pi$
$487$	−3692.50			−0.343579			−0.171790	+	0.985134i	$0.554955\pi$
$488$	3065.05	+	5308.82i	0.284320	+	0.492457i
$489$	1403.79	+	11703.4i	0.129820	+	1.08231i
$490$	5995.02	−	2289.60i	0.552709	−	0.211089i
$491$	3554.05	+	2051.93i	0.326664	+	0.188600i	0.654359	−	0.756184i	$-0.272938\pi$
$491$	3554.05	+	2051.93i	0.326664	+	0.188600i	−0.327695	+	0.944784i	$0.606272\pi$
$492$	306.137	−	229.351i	0.0280522	−	0.0210162i
$493$	729.306	−	421.065i	0.0666253	−	0.0384661i
$494$		−	423.170i		−	0.0385411i
$495$	865.899	+	3557.58i	0.0786248	+	0.323033i
$496$		−	527.725i		−	0.0477733i
$497$	9117.13	+	6277.43i	0.822855	+	0.566562i
$498$	−1207.43	+	2822.56i	−0.108647	+	0.253980i
$499$	5776.11	−	10004.5i	0.518185	−	0.897522i	−0.481592	−	0.876396i	$-0.659941\pi$
$499$	5776.11	−	10004.5i	0.518185	−	0.897522i	0.999777	−	0.0211268i	$-0.00672538\pi$
$500$	−3040.08	+	5265.58i	−0.271913	+	0.470967i
$501$	17038.6	+	7288.76i	1.51942	+	0.649976i
$502$	736.589	−	425.270i	0.0654892	−	0.0378102i
$503$	−10569.4			−0.936911			−0.468455	−	0.883487i	$-0.655189\pi$
$503$	−10569.4			−0.936911			−0.468455	+	0.883487i	$0.655189\pi$
$504$	−3737.94	−	1425.07i	−0.330359	−	0.125948i
$505$	−14325.4			−1.26232
$506$	−1549.29	+	894.481i	−0.136115	+	0.0785860i
$507$	9103.84	−	6820.41i	0.797467	−	0.597446i
$508$	−647.710	+	1121.87i	−0.0565699	+	0.0979819i
$509$	4556.05	−	7891.31i	0.396745	−	0.687183i	−0.596577	−	0.802556i	$-0.703473\pi$
$509$	4556.05	−	7891.31i	0.396745	−	0.687183i	0.993322	+	0.115373i	$0.0368063\pi$
$510$	−4573.16	+	548.537i	−0.397065	+	0.0476268i
$511$	8725.71	+	6007.93i	0.755387	+	0.520108i
$512$			512.000i			0.0441942i
$513$	9942.79	−	3721.28i	0.855721	−	0.320270i
$514$			7936.47i			0.681056i
$515$	−12221.6	+	7056.14i	−1.04572	+	0.603749i
$516$	863.830	+	7201.76i	0.0736977	+	0.614418i
$517$	1249.38	+	721.329i	0.106282	+	0.0613617i
$518$	−1000.75	+	12579.3i	−0.0848854	+	1.06699i
$519$	17395.1	−	13032.1i	1.47121	−	1.10220i
$520$	−104.628	−	181.221i	−0.00882353	−	0.0152828i
$521$	−1275.38			−0.107247			−0.0536233	−	0.998561i	$-0.517077\pi$
$521$	−1275.38			−0.107247			−0.0536233	+	0.998561i	$0.517077\pi$
$522$	−269.724	+	921.163i	−0.0226159	+	0.0772380i
$523$			19531.7i			1.63300i	0.577344	+	0.816501i	$0.304089\pi$
$523$			19531.7i			1.63300i	−0.577344	+	0.816501i	$0.695911\pi$
$524$	−1985.57	−	3439.11i	−0.165534	−	0.286714i
$525$	−144.225	−	3604.78i	−0.0119895	−	0.299668i
$526$	−1473.65	+	2552.43i	−0.122156	+	0.211581i
$527$	1353.30	+	781.325i	0.111860	+	0.0645827i
$528$	−474.007	+	1108.07i	−0.0390692	+	0.0913303i
$529$	−4179.79	−	7239.60i	−0.343535	−	0.595019i
$530$	11522.5			0.944352
$531$	−4050.12	+	13832.0i	−0.330998	+	1.13043i
$532$	−5061.75	+	2409.06i	−0.412509	+	0.196327i
$533$	−44.5654	+	25.7298i	−0.00362165	+	0.00209096i
$534$	1607.89	+	2146.20i	0.130300	+	0.173924i
$535$	−7772.98	−	4487.73i	−0.628140	−	0.362657i
$536$	4830.33	+	2788.79i	0.389251	+	0.224734i
$537$	−19380.4	+	2324.62i	−1.55740	+	0.186806i
$538$	9952.95	−	5746.34i	0.797588	−	0.460487i
$539$	3858.81	+	3135.67i	0.308369	+	0.250580i
$540$	3337.88	−	4051.96i	0.265999	−	0.322905i
$541$	−18559.0			−1.47488			−0.737442	−	0.675411i	$-0.763966\pi$
$541$	−18559.0			−1.47488			−0.737442	+	0.675411i	$0.763966\pi$
$542$	4099.23	+	7100.07i	0.324865	+	0.562683i
$543$	13647.8	−	1637.02i	1.07861	−	0.129376i
$544$	−1312.97	−	758.043i	−0.103480	−	0.0597442i
$545$	94.0343	−	162.872i	0.00739080	−	0.0128012i
$546$	476.447	+	250.234i	0.0373444	+	0.0196136i
$547$	−4368.54	−	7566.54i	−0.341472	−	0.591448i	0.643234	−	0.765670i	$-0.277592\pi$
$547$	−4368.54	−	7566.54i	−0.341472	−	0.591448i	−0.984706	+	0.174222i	$0.944259\pi$
$548$			5936.94i			0.462798i
$549$	14962.6	−	14288.4i	1.16319	−	1.11077i
$550$	−1086.88			−0.0842633
$551$	672.520	+	1164.84i	0.0519969	+	0.0900613i
$552$	2358.29	+	1008.82i	0.181839	+	0.0777870i
$553$	−23778.8	−	1891.75i	−1.82853	−	0.145471i
$554$	−12165.9	−	7023.98i	−0.932994	−	0.538665i
$555$	−15225.5	−	6513.14i	−1.16448	−	0.498139i
$556$	7164.37	−	4136.35i	0.546469	−	0.315504i
$557$		−	2891.17i		−	0.219933i	−0.993935	−	0.109966i	$-0.964926\pi$
$557$		−	2891.17i		−	0.219933i	0.993935	−	0.109966i	$-0.0350743\pi$
$558$	−1730.55	+	421.209i	−0.131290	+	0.0319555i
$559$		−	975.783i		−	0.0738305i
$560$	−1572.04	+	2283.18i	−0.118626	+	0.172289i
$561$	−2139.72	−	2856.09i	−0.161033	−	0.214945i
$562$	3374.22	−	5844.31i	0.253261	−	0.438661i
$563$	6228.23	−	10787.6i	0.466232	−	0.807537i	−0.533024	−	0.846100i	$-0.678945\pi$
$563$	6228.23	−	10787.6i	0.466232	−	0.807537i	0.999256	+	0.0385627i	$0.0122779\pi$
$564$	−246.341	−	2053.75i	−0.0183916	−	0.153331i
$565$	15768.9	−	9104.19i	1.17417	−	0.677905i
$566$	−5727.34			−0.425332
$567$	−1689.71	+	13395.1i	−0.125152	+	0.992138i
$568$	−4781.46			−0.353214
$569$	−6404.53	+	3697.66i	−0.471866	+	0.272432i	−0.717021	−	0.697052i	$-0.754495\pi$
$569$	−6404.53	+	3697.66i	−0.471866	+	0.272432i	0.245154	+	0.969484i	$0.421161\pi$
$570$	−876.117	−	7304.20i	−0.0643798	−	0.536735i
$571$	−9691.32	+	16785.9i	−0.710279	+	1.23024i	0.254474	+	0.967080i	$0.418098\pi$
$571$	−9691.32	+	16785.9i	−0.710279	+	1.23024i	−0.964752	+	0.263159i	$0.915236\pi$
$572$	81.0662	−	140.411i	0.00592579	−	0.0102638i
$573$	−7240.11	−	9664.05i	−0.527853	−	0.704575i
$574$	561.474	+	386.592i	0.0408283	+	0.0281116i
$575$			2313.20i			0.167769i
$576$	1678.98	−	408.658i	0.121454	−	0.0295615i
$577$			7829.00i			0.564862i	0.959288	+	0.282431i	$0.0911409\pi$
$577$			7829.00i			0.564862i	−0.959288	+	0.282431i	$0.908859\pi$
$578$	−4621.72	+	2668.35i	−0.332592	+	0.192022i
$579$	−6807.61	−	2912.15i	−0.488626	−	0.209024i
$580$	576.008	+	332.558i	0.0412369	+	0.0238082i
$581$	−5453.81	−	433.883i	−0.389436	−	0.0309819i
$582$	−6440.11	−	2754.94i	−0.458679	−	0.196213i
$583$	4463.86	+	7731.63i	0.317108	+	0.549248i
$584$	−4576.18			−0.324253
$585$	−510.761	+	487.745i	−0.0360981	+	0.0344714i
$586$		−	17328.5i		−	1.22156i
$587$	−9532.03	−	16510.0i	−0.670236	−	1.16088i	−0.977837	−	0.209368i	$-0.932859\pi$
$587$	−9532.03	−	16510.0i	−0.670236	−	1.16088i	0.307600	−	0.951516i	$-0.400474\pi$
$588$	280.820	−	7123.59i	0.0196953	−	0.499612i
$589$	−1247.92	+	2161.47i	−0.0873001	+	0.151208i
$590$	8649.21	+	4993.63i	0.603530	+	0.348448i
$591$	7829.50	−	939.125i	0.544945	−	0.0653645i
$592$	−2725.45	−	4720.61i	−0.189215	−	0.327730i
$593$	−9765.03			−0.676226			−0.338113	−	0.941106i	$-0.609789\pi$
$593$	−9765.03			−0.676226			−0.338113	+	0.941106i	$0.609789\pi$
$594$	4011.97	+	669.982i	0.277127	+	0.0462789i
$595$	−3527.48	−	7411.70i	−0.243046	−	0.510672i
$596$	11554.3	−	6670.90i	0.794100	−	0.458474i
$597$	27372.1	−	3283.21i	1.87649	−	0.225080i
$598$	−298.835	−	172.532i	−0.0204352	−	0.0117983i
$599$	9337.62	+	5391.08i	0.636936	+	0.367735i	0.783433	−	0.621476i	$-0.213467\pi$
$599$	9337.62	+	5391.08i	0.636936	+	0.367735i	−0.146497	+	0.989211i	$0.546800\pi$
$600$	934.364	+	1247.18i	0.0635754	+	0.0848601i
$601$	8669.41	−	5005.28i	0.588407	−	0.339717i	−0.176061	−	0.984379i	$-0.556335\pi$
$601$	8669.41	−	5005.28i	0.588407	−	0.339717i	0.764467	+	0.644663i	$0.223002\pi$
$602$	−11671.8	+	5555.03i	−0.790214	+	0.376090i
$603$	5289.81	−	18065.8i	0.357243	−	1.22006i
$604$	−7511.19			−0.506003
$605$	−5242.68	−	9080.60i	−0.352307	−	0.610213i
$606$	−6259.11	+	14631.6i	−0.419569	+	0.980808i
$607$	−5635.98	−	3253.93i	−0.376865	−	0.217583i	0.299588	−	0.954069i	$-0.403151\pi$
$607$	−5635.98	−	3253.93i	−0.376865	−	0.217583i	−0.676454	+	0.736485i	$0.736484\pi$
$608$	1210.74	−	2097.06i	0.0807597	−	0.139880i
$609$	−1709.18	+	68.3829i	−0.113726	+	0.00455011i
$610$	−7168.20	−	12415.7i	−0.475790	−	0.824093i
$611$			278.268i			0.0184247i
$612$	−1437.86	+	4910.61i	−0.0949710	+	0.324346i
$613$	19139.8			1.26109			0.630545	−	0.776153i	$-0.282832\pi$
$613$	19139.8			1.26109			0.630545	+	0.776153i	$0.282832\pi$
$614$	3338.33	+	5782.16i	0.219420	+	0.380047i
$615$	−715.959	+	536.381i	−0.0469435	+	0.0351691i
$616$	−2141.03	−	170.331i	−0.140040	−	0.0111410i
$617$	−14556.6	−	8404.28i	−0.949802	−	0.548369i	−0.0567827	−	0.998387i	$-0.518084\pi$
$617$	−14556.6	−	8404.28i	−0.949802	−	0.548369i	−0.893019	+	0.450018i	$0.851418\pi$
$618$	1867.08	+	15565.9i	0.121529	+	1.01319i
$619$	3483.23	−	2011.04i	0.226176	−	0.130582i	−0.382631	−	0.923901i	$-0.624982\pi$
$619$	3483.23	−	2011.04i	0.226176	−	0.130582i	0.608806	+	0.793319i	$0.291649\pi$
$620$			1234.19i			0.0799453i
$621$	1425.91	−	8538.64i	0.0921417	−	0.551761i
$622$			8345.89i			0.538006i
$623$	−2710.25	+	3936.27i	−0.174292	+	0.253135i
$624$	−230.810	+	27.6850i	−0.0148074	+	0.00177610i
$625$	4766.78	−	8256.30i	0.305074	−	0.528403i
$626$	3097.98	−	5365.86i	0.197796	−	0.342592i
$627$	4561.71	−	3417.54i	0.290554	−	0.217677i
$628$	−1683.61	+	972.033i	−0.106980	+	0.0617649i
$629$	16140.7			1.02317
$630$	8741.88	+	3332.79i	0.552833	+	0.210765i
$631$	20915.1			1.31952			0.659761	−	0.751475i	$-0.270657\pi$
$631$	20915.1			1.31952			0.659761	+	0.751475i	$0.270657\pi$
$632$	8923.47	−	5151.97i	0.561640	−	0.324263i
$633$	10743.3	+	4595.78i	0.674581	+	0.288571i
$634$	6044.64	−	10469.6i	0.378649	−	0.655839i
$635$	1514.79	−	2623.70i	0.0946658	−	0.163966i
$636$	5034.48	−	11768.9i	0.313884	−	0.733753i
$637$	−151.639	+	947.003i	−0.00943197	+	0.0589037i
$638$			515.336i			0.0319786i
$639$	3816.37	+	15679.7i	0.236265	+	0.970702i
$640$		−	1197.41i		−	0.0739559i
$641$	14099.6	−	8140.41i	0.868800	−	0.501602i	0.00185053	−	0.999998i	$-0.499411\pi$
$641$	14099.6	−	8140.41i	0.868800	−	0.501602i	0.866949	+	0.498397i	$0.166078\pi$
$642$	−7979.89	+	5978.37i	−0.490563	+	0.367519i
$643$	−8807.03	−	5084.74i	−0.540148	−	0.311855i	0.204991	−	0.978764i	$-0.434284\pi$
$643$	−8807.03	−	5084.74i	−0.540148	−	0.311855i	−0.745139	+	0.666909i	$0.767617\pi$
$644$	−362.515	+	4556.73i	−0.0221818	+	0.278820i
$645$	−2020.23	−	16842.7i	−0.123328	−	1.02819i
$646$	3585.12	+	6209.61i	0.218351	+	0.378195i
$647$	−1501.59			−0.0912417			−0.0456209	−	0.998959i	$-0.514527\pi$
$647$	−1501.59			−0.0912417			−0.0456209	+	0.998959i	$0.514527\pi$
$648$	−2680.19	−	5179.65i	−0.162481	−	0.314006i
$649$			7738.18i			0.468028i
$650$	−104.822	−	181.557i	−0.00632532	−	0.0109558i
$651$	−1695.66	−	2683.18i	−0.102086	−	0.161540i
$652$	4536.95	−	7858.23i	0.272516	−	0.472012i
$653$	506.929	+	292.675i	0.0303793	+	0.0175395i	0.515113	−	0.857122i	$-0.327750\pi$
$653$	506.929	+	292.675i	0.0303793	+	0.0175395i	−0.484733	+	0.874662i	$0.661083\pi$
$654$	−125.269	−	167.208i	−0.00748989	−	0.00999747i
$655$	4643.63	+	8043.01i	0.277010	+	0.479796i
$656$	−294.464			−0.0175257
$657$	3652.52	+	15006.5i	0.216893	+	0.891111i
$658$	3328.50	−	1584.15i	0.197201	−	0.0938549i
$659$	2453.48	−	1416.52i	0.145029	−	0.0837325i	−0.425730	−	0.904850i	$-0.639983\pi$
$659$	2453.48	−	1416.52i	0.145029	−	0.0837325i	0.570759	+	0.821118i	$0.306649\pi$
$660$	1108.56	−	2591.42i	0.0653795	−	0.152835i
$661$	−4862.22	−	2807.20i	−0.286109	−	0.165185i	0.350077	−	0.936721i	$-0.386156\pi$
$661$	−4862.22	−	2807.20i	−0.286109	−	0.165185i	−0.636186	+	0.771536i	$0.719489\pi$
$662$	3045.76	+	1758.47i	0.178817	+	0.103240i
$663$	270.731	−	632.877i	0.0158587	−	0.0370723i
$664$	2046.65	−	1181.63i	0.119617	−	0.0690606i
$665$	11837.9	−	5634.04i	0.690305	−	0.328540i
$666$	−13304.8	+	12705.3i	−0.774099	+	0.739217i
$667$	1096.78			0.0636696
$668$	−7133.03	−	12354.8i	−0.413151	−	0.715599i
$669$	8279.25	+	11051.1i	0.478467	+	0.638655i
$670$	−11296.6	−	6522.12i	−0.651384	−	0.376077i
$671$	5553.96	−	9619.74i	0.319535	−	0.553452i
$672$	1645.13	+	2603.23i	0.0944379	+	0.149437i
$673$	−5310.16	−	9197.46i	−0.304148	−	0.526800i	0.672923	−	0.739712i	$-0.265038\pi$
$673$	−5310.16	−	9197.46i	−0.304148	−	0.526800i	−0.977071	+	0.212913i	$0.931705\pi$
$674$			2466.71i			0.140971i
$675$	3344.07	−	4059.48i	0.190687	−	0.231480i
$676$	−8756.73			−0.498221
$677$	2425.01	+	4200.23i	0.137667	+	0.238446i	0.926613	−	0.376016i	$-0.122706\pi$
$677$	2425.01	+	4200.23i	0.137667	+	0.238446i	−0.788946	+	0.614462i	$0.789373\pi$
$678$	−2409.01	−	20083.9i	−0.136456	−	1.13764i
$679$	989.971	−	12443.7i	0.0559523	−	0.703307i
$680$	3070.63	+	1772.83i	0.173167	+	0.0999777i
$681$	−14972.2	+	11216.9i	−0.842491	+	0.631176i
$682$	−828.140	+	478.127i	−0.0464972	+	0.0268452i
$683$			29798.7i			1.66942i	0.550688	+	0.834711i	$0.314365\pi$
$683$			29798.7i			1.66942i	−0.550688	+	0.834711i	$0.685635\pi$
$684$	−7843.17	−	2296.54i	−0.438437	−	0.128378i
$685$		−	13884.7i		−	0.774461i
$686$	12190.9	−	3577.35i	0.678497	−	0.199102i
$687$	−2267.28	+	5300.13i	−0.125913	+	0.294341i
$688$	2791.83	−	4835.59i	0.154706	−	0.267958i
$689$	−861.013	+	1491.32i	−0.0476081	+	0.0824597i
$690$	−5515.30	−	2359.33i	−0.304295	−	0.130171i
$691$	355.449	−	205.218i	0.0195686	−	0.0112979i	−0.490184	−	0.871619i	$-0.663070\pi$
$691$	355.449	−	205.218i	0.0195686	−	0.0112979i	0.509752	+	0.860321i	$0.329737\pi$
$692$	−16731.9			−0.919147
$693$	1150.32	+	7156.94i	0.0630548	+	0.392309i
$694$	417.030			0.0228102
$695$	−16755.2	+	9673.64i	−0.914479	+	0.527974i
$696$	591.341	−	443.020i	0.0322051	−	0.0241274i
$697$	435.970	−	755.122i	0.0236923	−	0.0410363i
$698$	10760.9	−	18638.4i	0.583531	−	1.01071i
$699$	18729.0	−	2246.49i	1.01344	−	0.121560i
$700$	−1574.96	+	2287.41i	−0.0850397	+	0.123509i
$701$		−	7839.76i		−	0.422402i	−0.977443	−	0.211201i	$-0.932263\pi$
$701$		−	7839.76i		−	0.422402i	0.977443	−	0.211201i	$-0.0677374\pi$
$702$	275.010	+	734.790i	0.0147857	+	0.0395055i
$703$			25779.7i			1.38307i
$704$	803.463	−	463.880i	0.0430137	−	0.0248340i
$705$	576.116	+	4803.09i	0.0307770	+	0.256588i
$706$	21659.4	+	12505.1i	1.15462	+	0.666621i
$707$	−28271.5	−	2249.17i	−1.50391	−	0.119645i
$708$	8879.46	−	6652.30i	0.471342	−	0.353120i
$709$	16355.4	+	28328.4i	0.866346	+	1.50056i	0.865704	+	0.500556i	$0.166871\pi$
$709$	16355.4	+	28328.4i	0.866346	+	1.50056i	0.000642168		1.00000i	$0.499796\pi$
$710$	11182.4			0.591080
$711$	−24017.0	−	25150.3i	−1.26682	−	1.32660i
$712$		−	2064.37i		−	0.108659i
$713$	1017.59	+	1762.52i	0.0534490	+	0.0925764i
$714$	−9111.41	+	364.541i	−0.477571	+	0.0191073i
$715$	−189.589	+	328.377i	−0.00991639	+	0.0171757i
$716$	13012.9	+	7512.98i	0.679209	+	0.392141i
$717$	−1050.99	+	2456.85i	−0.0547418	+	0.127968i
$718$	−4120.90	−	7137.61i	−0.214193	−	0.370993i
$719$	−7172.48			−0.372028			−0.186014	−	0.982547i	$-0.559557\pi$
$719$	−7172.48			−0.372028			−0.186014	+	0.982547i	$0.559557\pi$
$720$	−3926.62	+	955.723i	−0.203245	+	0.0494690i
$721$	−25227.6	+	12006.6i	−1.30308	+	0.620182i
$722$	1962.22	−	1132.89i	0.101145	−	0.0583958i
$723$	−4129.82	−	5512.46i	−0.212434	−	0.283556i
$724$	−9163.76	−	5290.70i	−0.470398	−	0.271585i
$725$	577.076	+	333.175i	0.0295615	+	0.0170673i
$726$	−11565.4	+	1387.24i	−0.591230	+	0.0709162i
$727$	−7554.79	+	4361.76i	−0.385408	+	0.222515i	−0.680169	−	0.733056i	$-0.738093\pi$
$727$	−7554.79	+	4361.76i	−0.385408	+	0.222515i	0.294761	+	0.955571i	$0.404760\pi$
$728$	−178.034	−	374.072i	−0.00906369	−	0.0190440i
$729$	−14846.2	+	12923.2i	−0.754266	+	0.656569i
$730$	10702.3			0.542615
$731$	8266.90	+	14318.7i	0.418280	+	0.724482i
$732$	−15813.1	+	1896.74i	−0.798456	+	0.0957724i
$733$	29416.8	+	16983.8i	1.48231	+	0.855813i	0.999798	−	0.0200761i	$-0.00639085\pi$
$733$	29416.8	+	16983.8i	1.48231	+	0.855813i	0.482513	+	0.875889i	$0.339724\pi$
$734$	−9790.93	+	16958.4i	−0.492357	+	0.852787i
$735$	−656.752	+	16659.9i	−0.0329587	+	0.836066i
$736$	−987.270	−	1710.00i	−0.0494446	−	0.0856406i
$737$		−	10106.7i		−	0.505138i
$738$	235.029	+	965.625i	0.0117230	+	0.0481642i
$739$	30437.8			1.51512			0.757559	−	0.652767i	$-0.226392\pi$
$739$	30437.8			1.51512			0.757559	+	0.652767i	$0.226392\pi$
$740$	6373.98	+	11040.1i	0.316638	+	0.548433i
$741$	1010.82	+	432.409i	0.0501127	+	0.0214372i
$742$	22740.1	+	1809.11i	1.12509	+	0.0895074i
$743$	−10738.4	−	6199.79i	−0.530218	−	0.306122i	0.210887	−	0.977510i	$-0.432365\pi$
$743$	−10738.4	−	6199.79i	−0.530218	−	0.306122i	−0.741105	+	0.671389i	$0.765698\pi$
$744$	1260.57	+	539.247i	0.0621168	+	0.0265723i
$745$	−27022.0	+	15601.2i	−1.32887	+	0.767225i
$746$		−	14363.4i		−	0.704937i
$747$	−5508.44	−	5768.37i	−0.269804	−	0.282535i
$748$			2747.19i			0.134288i
$749$	−14635.6	−	10077.1i	−0.713984	−	0.491601i
$750$	−9471.39	−	12642.4i	−0.461128	−	0.615512i
$751$	−16999.8	+	29444.5i	−0.826007	+	1.43069i	0.0751404	+	0.997173i	$0.476060\pi$
$751$	−16999.8	+	29444.5i	−0.826007	+	1.43069i	−0.901147	+	0.433513i	$0.857274\pi$
$752$	−796.156	+	1378.98i	−0.0386075	+	0.0668701i
$753$	263.169	+	2194.04i	0.0127363	+	0.106182i
$754$	−86.0836	+	49.7004i	−0.00415780	+	0.00240051i
$755$	17566.3			0.846761
$756$	7223.60	−	7472.61i	0.347513	−	0.359492i
$757$	−1248.42			−0.0599402			−0.0299701	−	0.999551i	$-0.509541\pi$
$757$	−1248.42			−0.0599402			−0.0299701	+	0.999551i	$0.509541\pi$
$758$	3087.07	−	1782.32i	0.147925	−	0.0854046i
$759$	−553.529	−	4614.78i	−0.0264715	−	0.220693i
$760$	−2831.54	+	4904.37i	−0.135146	+	0.234079i
$761$	−19976.0	+	34599.4i	−0.951549	+	1.64813i	−0.209473	+	0.977814i	$0.567175\pi$
$761$	−19976.0	+	34599.4i	−0.951549	+	1.64813i	−0.742075	+	0.670316i	$0.766158\pi$
$762$	−2017.95	−	2693.54i	−0.0959350	−	0.128053i
$763$	211.152	−	306.670i	0.0100186	−	0.0145507i
$764$			9295.58i			0.440186i
$765$	3362.72	−	11484.4i	0.158927	−	0.542770i
$766$			1565.10i			0.0738243i
$767$	−1292.61	+	746.291i	−0.0608521	+	0.0351330i
$768$	−1223.01	−	523.178i	−0.0574630	−	0.0245815i
$769$	3471.68	+	2004.38i	0.162798	+	0.0939917i	0.579186	−	0.815196i	$-0.303371\pi$
$769$	3471.68	+	2004.38i	0.162798	+	0.0939917i	−0.416387	+	0.909187i	$0.636704\pi$
$770$	5007.20	+	398.353i	0.234347	+	0.0186437i
$771$	−18957.8	−	8109.75i	−0.885536	−	0.378814i
$772$	2849.93	+	4936.22i	0.132864	+	0.230128i
$773$	−9738.44			−0.453127			−0.226564	−	0.973996i	$-0.572749\pi$
$773$	−9738.44			−0.453127			−0.226564	+	0.973996i	$0.572749\pi$
$774$	−18085.5	−	5295.57i	−0.839883	−	0.245924i
$775$			1236.48i			0.0573103i
$776$	2696.08	+	4669.75i	0.124721	+	0.216023i
$777$	−29025.4	−	15244.4i	−1.34013	−	0.703847i
$778$	4098.86	−	7099.43i	0.188883	−	0.327155i
$779$	1206.07	+	696.325i	0.0554711	+	0.0320262i
$780$	539.793	−	64.7466i	0.0247791	−	0.00297218i
$781$	4332.08	+	7503.38i	0.198481	+	0.343780i
$782$	5846.82			0.267368
$783$	−1924.76	−	1585.56i	−0.0878486	−	0.0723670i
$784$	−3460.95	+	4259.11i	−0.157660	+	0.194019i
$785$	3937.44	−	2273.28i	0.179023	−	0.103359i
$786$	10243.9	−	1228.73i	0.464870	−	0.0557598i
$787$	27354.1	+	15792.9i	1.23897	+	0.715319i	0.968884	−	0.247517i	$-0.0796146\pi$
$787$	27354.1	+	15792.9i	1.23897	+	0.715319i	0.270086	+	0.962836i	$0.412948\pi$
$788$	−5257.08	−	3035.18i	−0.237660	−	0.137213i
$789$	−4591.16	−	6128.25i	−0.207160	−	0.276517i
$790$	−20869.2	+	12048.9i	−0.939865	+	0.542631i
$791$	32549.9	−	15491.6i	1.46314	−	0.696357i
$792$	−2162.47	−	2264.52i	−0.0970204	−	0.101599i
$793$	2142.56			0.0959450
$794$	629.373	+	1090.11i	0.0281305	+	0.0487234i
$795$	−11774.1	+	27523.8i	−0.525263	+	1.22788i
$796$	−18378.9	−	10611.1i	−0.818370	−	0.472486i
$797$	−5967.55	+	10336.1i	−0.265221	+	0.459377i	−0.967622	−	0.252405i	$-0.918778\pi$
$797$	−5967.55	+	10336.1i	−0.265221	+	0.459377i	0.702400	+	0.711782i	$0.252112\pi$
$798$	−582.240	−	14552.6i	−0.0258284	−	0.645561i
$799$	−2357.50	−	4083.31i	−0.104384	−	0.180798i
$800$		−	1199.63i		−	0.0530167i
$801$	−6769.61	+	1647.70i	−0.298617	+	0.0726823i
$802$	15341.6			0.675476
$803$	4146.09	+	7181.24i	0.182207	+	0.315592i
$804$	−11597.4	+	8688.49i	−0.508715	+	0.381119i
$805$	847.810	−	10656.8i	0.0371197	−	0.466586i
$806$	−159.736	−	92.2237i	−0.00698073	−	0.00403033i
$807$	3555.99	+	29646.3i	0.155114	+	1.29319i
$808$	10609.5	−	6125.37i	0.461930	−	0.266695i
$809$			3597.19i			0.156329i	0.996940	+	0.0781647i	$0.0249060\pi$
$809$			3597.19i			0.156329i	−0.996940	+	0.0781647i	$0.975094\pi$
$810$	6268.14	+	12113.6i	0.271901	+	0.525467i
$811$		−	3545.83i		−	0.153528i	−0.997049	−	0.0767639i	$-0.975541\pi$
$811$		−	3545.83i		−	0.153528i	0.997049	−	0.0767639i	$-0.0244588\pi$
$812$	1084.56	+	746.751i	0.0468725	+	0.0322732i
$813$	−21148.6	+	2536.72i	−0.912318	+	0.109430i
$814$	−4938.59	+	8553.89i	−0.212651	+	0.368321i
$815$	−10610.5	+	18378.0i	−0.456037	+	0.789879i
$816$	3152.37	−	2361.69i	0.135239	−	0.101318i
$817$	−22869.6	+	13203.8i	−0.979323	+	0.565413i
$818$	−881.080			−0.0376604
$819$	−1084.58	+	882.389i	−0.0462740	+	0.0376473i
$820$	688.660			0.0293281
$821$	35969.3	−	20766.9i	1.52903	−	0.882787i	0.529630	−	0.848229i	$-0.322331\pi$
$821$	35969.3	−	20766.9i	1.52903	−	0.882787i	0.999403	−	0.0345582i	$-0.0110024\pi$
$822$	−14181.5	−	6066.56i	−0.601749	−	0.257416i
$823$	−7717.65	+	13367.4i	−0.326878	+	0.566169i	−0.981891	−	0.189449i	$-0.939330\pi$
$823$	−7717.65	+	13367.4i	−0.326878	+	0.566169i	0.655013	+	0.755618i	$0.272663\pi$
$824$	6034.26	−	10451.6i	0.255113	−	0.441870i
$825$	1110.61	−	2596.23i	0.0468686	−	0.109563i
$826$	16285.5	+	11213.1i	0.686010	+	0.472340i
$827$		−	22203.6i		−	0.933609i	−0.884361	−	0.466804i	$-0.845405\pi$
$827$		−	22203.6i		−	0.933609i	0.884361	−	0.466804i	$-0.154595\pi$
$828$	−4819.55	+	4602.37i	−0.202284	+	0.193168i
$829$		−	15099.5i		−	0.632603i	−0.948659	−	0.316302i	$-0.897559\pi$
$829$		−	15099.5i		−	0.632603i	0.948659	−	0.316302i	$-0.102441\pi$
$830$	−4786.48	+	2763.47i	−0.200170	+	0.115568i
$831$	29209.6	−	21883.2i	1.21934	−	0.913503i
$832$	154.976	+	89.4756i	0.00645774	+	0.00372838i
$833$	−5797.91	−	15181.1i	−0.241159	−	0.631444i
$834$	2559.69	+	21340.1i	0.106277	+	0.886030i
$835$	16681.9	+	28894.0i	0.691380	+	1.19751i
$836$	−4387.78			−0.181525
$837$	762.194	−	4564.16i	0.0314758	−	0.188483i
$838$		−	21439.0i		−	0.883770i
$839$	6950.00	+	12037.8i	0.285984	+	0.495339i	0.972847	−	0.231448i	$-0.0743462\pi$
$839$	6950.00	+	12037.8i	0.285984	+	0.495339i	−0.686863	+	0.726787i	$0.741013\pi$
$840$	−3847.45	−	6088.15i	−0.158035	−	0.250073i
$841$	−12036.5	+	20847.9i	−0.493523	+	0.854807i
$842$	5365.88	+	3097.99i	0.219620	+	0.126798i
$843$	10512.4	+	14031.9i	0.429497	+	0.573290i
$844$	−4497.58	−	7790.04i	−0.183428	−	0.317706i
$845$	20479.3			0.833738
$846$	5157.50	+	1510.16i	0.209597	+	0.0613715i
$847$	−8920.90	−	18744.0i	−0.361896	−	0.760391i
$848$	−8533.67	+	4926.92i	−0.345575	+	0.199518i
$849$	5852.38	−	13680.8i	0.236576	−	0.553034i
$850$	3076.32	+	1776.12i	0.124138	+	0.0716710i
$851$	18205.2	+	10510.8i	0.733331	+	0.423389i
$852$	4885.86	−	11421.5i	0.196463	−	0.459264i
$853$	−28287.4	+	16331.7i	−1.13545	+	0.655554i	−0.945300	−	0.326201i	$-0.894231\pi$
$853$	−28287.4	+	16331.7i	−1.13545	+	0.655554i	−0.190152	+	0.981755i	$0.560898\pi$
$854$	−12197.3	−	25628.2i	−0.488741	−	1.02691i
$855$	18342.7	+	5370.89i	0.733694	+	0.214831i
$856$	7675.63			0.306481
$857$	−19265.4	−	33368.6i	−0.767903	−	1.33005i	−0.938698	−	0.344741i	$-0.887967\pi$
$857$	−19265.4	−	33368.6i	−0.767903	−	1.33005i	0.170795	−	0.985307i	$-0.445366\pi$
$858$	252.562	+	337.119i	0.0100493	+	0.0134138i
$859$	12974.3	+	7490.70i	0.515339	+	0.297531i	0.735026	−	0.678039i	$-0.237170\pi$
$859$	12974.3	+	7490.70i	0.515339	+	0.297531i	−0.219686	+	0.975571i	$0.570503\pi$
$860$	−6529.22	+	11308.9i	−0.258889	+	0.448409i
$861$	−1497.18	+	946.156i	−0.0592612	+	0.0374505i
$862$	−8313.05	−	14398.6i	−0.328473	−	0.568932i
$863$		−	18321.2i		−	0.722667i	−0.932437	−	0.361333i	$-0.882322\pi$
$863$		−	18321.2i		−	0.722667i	0.932437	−	0.361333i	$-0.117678\pi$
$864$	−739.482	+	4428.16i	−0.0291177	+	0.174362i
$865$	39130.6			1.53813
$866$	5702.37	+	9876.80i	0.223758	+	0.387560i
$867$	−1651.25	−	13766.5i	−0.0646821	−	0.539256i
$868$	−193.775	+	2435.71i	−0.00757736	+	0.0952457i
$869$	−16169.6	−	9335.51i	−0.631203	−	0.364425i
$870$	−1382.96	+	1036.09i	−0.0538929	+	0.0403755i
$871$	1688.27	−	974.722i	0.0656771	−	0.0379187i
$872$			160.832i			0.00624596i
$873$	13161.4	−	12568.4i	0.510248	−	0.487256i
$874$			9338.47i			0.361417i
$875$	15964.9	−	23186.9i	0.616814	−	0.895840i
$876$	4676.10	−	10931.1i	0.180355	−	0.421607i
$877$	9914.41	−	17172.3i	0.381740	−	0.661193i	−0.609571	−	0.792731i	$-0.708658\pi$
$877$	9914.41	−	17172.3i	0.381740	−	0.661193i	0.991311	+	0.131538i	$0.0419917\pi$
$878$	9995.80	−	17313.2i	0.384216	−	0.665482i
$879$	41392.4	+	17706.8i	1.58832	+	0.679449i
$880$	−1879.05	+	1084.87i	−0.0719804	+	0.0415579i
$881$	29202.8			1.11676			0.558381	−	0.829585i	$-0.311423\pi$
$881$	29202.8			1.11676			0.558381	+	0.829585i	$0.311423\pi$
$882$	16729.1	+	7949.91i	0.638661	+	0.303500i
$883$	30048.5			1.14520			0.572601	−	0.819834i	$-0.305934\pi$
$883$	30048.5			1.14520			0.572601	+	0.819834i	$0.305934\pi$
$884$	−458.901	+	264.947i	−0.0174599	+	0.0100805i
$885$	−20766.3	+	15557.7i	−0.788759	+	0.590921i
$886$	−15797.7	+	27362.3i	−0.599021	+	1.03753i
$887$	11313.3	−	19595.2i	0.428257	−	0.741763i	−0.568461	−	0.822710i	$-0.692461\pi$
$887$	11313.3	−	19595.2i	0.428257	−	0.741763i	0.996718	+	0.0809471i	$0.0257945\pi$
$888$	14061.1	−	1686.58i	0.531372	−	0.0637365i
$889$	3401.43	−	4940.13i	0.128324	−	0.186374i
$890$			4827.92i			0.181834i
$891$	−5699.95	+	8898.77i	−0.214316	+	0.334590i
$892$		−	10629.7i		−	0.399002i
$893$	6521.82	−	3765.37i	0.244394	−	0.141101i
$894$	4128.13	+	34416.3i	0.154436	+	1.28753i
$895$	−30433.1	−	17570.5i	−1.13661	−	0.656221i
$896$	188.001	−	2363.13i	0.00700967	−	0.0881100i
$897$	717.486	−	537.526i	0.0267070	−	0.0200083i
$898$	7652.96	+	13255.3i	0.284390	+	0.492579i
$899$	586.264			0.0217497
$900$	−3933.90	+	957.496i	−0.145700	+	0.0354628i
$901$		−	29178.2i		−	1.07888i
$902$	266.789	+	462.092i	0.00984822	+	0.0170576i
$903$	−1342.58	−	33556.8i	−0.0494777	−	1.23666i
$904$	−7785.72	+	13485.3i	−0.286448	+	0.496143i
$905$	21431.2	+	12373.3i	0.787179	+	0.454478i
$906$	7675.18	−	17941.9i	0.281447	−	0.657926i
$907$	−19974.6	−	34597.1i	−0.731253	−	1.26657i	−0.956348	−	0.292231i	$-0.905602\pi$
$907$	−19974.6	−	34597.1i	−0.731253	−	1.26657i	0.225094	−	0.974337i	$-0.427731\pi$
$908$	14401.3			0.526349
$909$	−28554.7	−	29902.2i	−1.04192	−	1.09108i
$910$	416.366	+	874.840i	0.0151675	+	0.0318688i
$911$	24232.2	−	13990.5i	0.881283	−	0.508809i	0.0102019	−	0.999948i	$-0.496753\pi$
$911$	24232.2	−	13990.5i	0.881283	−	0.508809i	0.871081	+	0.491139i	$0.163419\pi$
$912$	3772.06	+	5034.92i	0.136958	+	0.182810i
$913$	−3708.59	−	2141.15i	−0.134432	−	0.0776143i
$914$	−12442.6	−	7183.75i	−0.450290	−	0.259975i
$915$	36982.0	−	4435.88i	1.33616	−	0.160268i
$916$	3843.14	−	2218.84i	0.138626	−	0.0800355i
$917$	7901.56	+	16602.2i	0.284550	+	0.597878i
$918$	−10260.7	−	8452.44i	−0.368903	−	0.303891i
$919$	−30431.5			−1.09232			−0.546159	−	0.837681i	$-0.683911\pi$
$919$	−30431.5			−1.09232			−0.546159	+	0.837681i	$0.683911\pi$
$920$	2308.92	+	3999.16i	0.0827422	+	0.143314i
$921$	−17223.0	+	2065.85i	−0.616197	+	0.0739111i
$922$	−213.876	−	123.481i	−0.00763950	−	0.00441067i
$923$	−835.595	+	1447.29i	−0.0297984	+	0.0516124i
$924$	2594.64	−	4940.21i	0.0923782	−	0.175888i
$925$	6385.80	+	11060.5i	0.226988	+	0.393155i
$926$		−	4487.36i		−	0.159248i
$927$	−39090.0	−	11445.9i	−1.38499	−	0.405535i
$928$	−568.794			−0.0201202
$929$	−21793.0	−	37746.6i	−0.769651	−	1.33307i	−0.937752	−	0.347304i	$-0.887097\pi$
$929$	−21793.0	−	37746.6i	−0.769651	−	1.33307i	0.168102	−	0.985770i	$-0.446236\pi$
$930$	−2948.09	−	1261.13i	−0.103948	−	0.0444668i
$931$	24247.0	−	9260.35i	0.853559	−	0.325989i
$932$	−12575.5	−	7260.48i	−0.441980	−	0.255177i
$933$	−19935.8	−	8528.11i	−0.699537	−	0.299247i
$934$	−22564.2	+	13027.4i	−0.790495	+	0.456392i
$935$		−	6424.83i		−	0.224721i
$936$	169.718	−	579.624i	0.00592673	−	0.0202410i
$937$		−	20889.0i		−	0.728295i	−0.931341	−	0.364147i	$-0.881360\pi$
$937$		−	20889.0i		−	0.728295i	0.931341	−	0.364147i	$-0.118640\pi$
$938$	−21270.3	−	14645.3i	−0.740404	−	0.509791i
$939$	9651.77	+	12883.1i	0.335435	+	0.447737i
$940$	1861.96	−	3225.01i	0.0646069	−	0.111902i
$941$	4693.48	−	8129.34i	0.162596	−	0.281625i	−0.773203	−	0.634159i	$-0.781347\pi$
$941$	4693.48	−	8129.34i	0.162596	−	0.281625i	0.935799	+	0.352534i	$0.114680\pi$
$942$	−601.521	−	5014.89i	−0.0208053	−	0.173454i
$943$	983.465	−	567.804i	0.0339619	−	0.0196079i
$944$	−8540.89			−0.294473
$945$	−16893.8	+	17476.1i	−0.581539	+	0.601585i
$946$	−10117.7			−0.347734
$947$	−42737.3	+	24674.4i	−1.46650	+	0.846684i	−0.999298	−	0.0374664i	$-0.988071\pi$
$947$	−42737.3	+	24674.4i	−1.46650	+	0.846684i	−0.467202	+	0.884151i	$0.654738\pi$
$948$	3188.18	+	26579.9i	0.109227	+	0.910627i
$949$	−799.721	+	1385.16i	−0.0273551	+	0.0473805i
$950$	−2836.79	+	4913.47i	−0.0968818	+	0.167804i
$951$	18832.1	+	25137.0i	0.642138	+	0.857122i
$952$	5781.64	+	3980.84i	0.196832	+	0.135525i
$953$			20299.3i			0.689990i	0.938605	+	0.344995i	$0.112119\pi$
$953$			20299.3i			0.689990i	−0.938605	+	0.344995i	$0.887881\pi$
$954$	22967.9	+	24051.7i	0.779468	+	0.816249i
$955$		−	21739.5i		−	0.736621i
$956$	1781.47	−	1028.53i	0.0602687	−	0.0347962i
$957$	−1230.98	−	526.587i	−0.0415798	−	0.0177870i
$958$	−9559.87	−	5519.40i	−0.322407	−	0.186142i
$959$	2179.98	−	27401.8i	0.0734048	−	0.922682i
$960$	2860.24	+	1223.55i	0.0961604	+	0.0411354i
$961$	−14351.6	−	24857.6i	−0.481742	−	0.834401i
$962$	−1905.16			−0.0638513
$963$	−6126.37	−	25170.4i	−0.205005	−	0.842269i
$964$			5302.28i			0.177152i
$965$	−6665.10	−	11544.3i	−0.222339	−	0.385103i
$966$	−10514.2	−	5522.15i	−0.350195	−	0.183926i
$967$	−13578.3	+	23518.2i	−0.451548	+	0.782105i	−0.998482	−	0.0550710i	$-0.982461\pi$
$967$	−13578.3	+	23518.2i	−0.451548	+	0.782105i	0.546934	+	0.837176i	$0.315795\pi$
$968$	7765.54	+	4483.44i	0.257845	+	0.148867i
$969$	−18496.3	+	2218.57i	−0.613194	+	0.0735509i
$970$	−6305.30	−	10921.1i	−0.208712	−	0.361500i
$971$	−50554.8			−1.67084			−0.835418	−	0.549615i	$-0.814775\pi$
$971$	−50554.8			−1.67084			−0.835418	+	0.549615i	$0.814775\pi$
$972$	15111.3	−	1109.42i	0.498658	−	0.0366096i
$973$	−34585.8	+	16460.6i	−1.13954	+	0.542345i
$974$	−6395.59	+	3692.50i	−0.210398	+	0.121474i
$975$	540.794	−	64.8667i	0.0177634	−	0.00213066i
$976$	10617.6	+	6130.10i	0.348220	+	0.201045i
$977$	−23163.7	−	13373.5i	−0.758517	−	0.437930i	0.0702459	−	0.997530i	$-0.477622\pi$
$977$	−23163.7	−	13373.5i	−0.758517	−	0.437930i	−0.828763	+	0.559600i	$0.810955\pi$
$978$	14134.9	+	18867.2i	0.462151	+	0.616877i
$979$	−3239.54	+	1870.35i	−0.105757	+	0.0610589i
$980$	8094.08	−	9960.73i	0.263833	−	0.324677i
$981$	527.412	−	128.370i	0.0171651	−	0.00417792i
$982$	8207.74			0.266720
$983$	7032.89	+	12181.3i	0.228193	+	0.395243i	0.957273	−	0.289187i	$-0.0933848\pi$
$983$	7032.89	+	12181.3i	0.228193	+	0.395243i	−0.729079	+	0.684429i	$0.760051\pi$
$984$	300.893	−	703.385i	0.00974809	−	0.0227877i
$985$	12294.7	+	7098.34i	0.397707	+	0.229616i
$986$	842.130	−	1458.61i	0.0271997	−	0.0471112i
$987$	382.869	+	9569.51i	0.0123474	+	0.308613i
$988$	−423.170	−	732.951i	−0.0136263	−	0.0236015i
$989$			21533.5i			0.692341i
$990$	5057.36	+	5296.00i	0.162357	+	0.170018i
$991$	−25572.4			−0.819712			−0.409856	−	0.912150i	$-0.634421\pi$
$991$	−25572.4			−0.819712			−0.409856	+	0.912150i	$0.634421\pi$
$992$	−527.725	−	914.047i	−0.0168904	−	0.0292551i
$993$	−7312.71	+	5478.53i	−0.233698	+	0.175081i
$994$	22068.8	+	1755.70i	0.704204	+	0.0560236i
$995$	42982.5	+	24816.0i	1.36949	+	0.790673i
$996$	731.227	+	6096.25i	0.0232629	+	0.193943i
$997$	27641.8	−	15959.0i	0.878058	−	0.506947i	0.00804051	−	0.999968i	$-0.497441\pi$
$997$	27641.8	−	15959.0i	0.878058	−	0.506947i	0.870018	+	0.493021i	$0.164107\pi$
$998$		−	23104.4i		−	0.732824i
$999$	−16753.7	−	44763.7i	−0.530594	−	1.41768i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.4.m.a.41.19	yes	48
3.2	odd	2		378.4.m.a.125.8		48
7.6	odd	2	inner	126.4.m.a.41.18	✓	48
9.2	odd	6	inner	126.4.m.a.83.18	yes	48
9.4	even	3		1134.4.d.b.1133.26		48
9.5	odd	6		1134.4.d.b.1133.23		48
9.7	even	3		378.4.m.a.251.7		48
21.20	even	2		378.4.m.a.125.7		48
63.13	odd	6		1134.4.d.b.1133.24		48
63.20	even	6	inner	126.4.m.a.83.19	yes	48
63.34	odd	6		378.4.m.a.251.8		48
63.41	even	6		1134.4.d.b.1133.25		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.m.a.41.18	✓	48	7.6	odd	2	inner
126.4.m.a.41.19	yes	48	1.1	even	1	trivial
126.4.m.a.83.18	yes	48	9.2	odd	6	inner
126.4.m.a.83.19	yes	48	63.20	even	6	inner
378.4.m.a.125.7		48	21.20	even	2
378.4.m.a.125.8		48	3.2	odd	2
378.4.m.a.251.7		48	9.7	even	3
378.4.m.a.251.8		48	63.34	odd	6
1134.4.d.b.1133.23		48	9.5	odd	6
1134.4.d.b.1133.24		48	63.13	odd	6
1134.4.d.b.1133.25		48	63.41	even	6
1134.4.d.b.1133.26		48	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	126.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(0.618827 + 5.15917i) q^{3} +(2.00000 - 3.46410i) q^{4} +(-4.67738 + 8.10146i) q^{5} +(6.23101 + 8.31712i) q^{6} +(-10.5029 + 15.2541i) q^{7} -8.00000i q^{8} +(-26.2341 + 6.38527i) q^{9} +O(q^{10})\)	\(q+(1.73205 - 1.00000i) q^{2} +(0.618827 + 5.15917i) q^{3} +(2.00000 - 3.46410i) q^{4} +(-4.67738 + 8.10146i) q^{5} +(6.23101 + 8.31712i) q^{6} +(-10.5029 + 15.2541i) q^{7} -8.00000i q^{8} +(-26.2341 + 6.38527i) q^{9} +18.7095i q^{10} +(-12.5541 + 7.24812i) q^{11} +(19.1095 + 8.17466i) q^{12} +(-2.42151 - 1.39806i) q^{13} +(-2.93751 + 36.9239i) q^{14} +(-44.6913 - 19.1180i) q^{15} +(-8.00000 - 13.8564i) q^{16} +47.3777 q^{17} +(-39.0535 + 37.2937i) q^{18} +75.6711i q^{19} +(18.7095 + 32.4058i) q^{20} +(-85.1981 - 44.7468i) q^{21} +(-14.4962 + 25.1082i) q^{22} +(53.4375 + 30.8522i) q^{23} +(41.2734 - 4.95062i) q^{24} +(18.7442 + 32.4660i) q^{25} -5.59223 q^{26} +(-49.1771 - 131.395i) q^{27} +(31.8359 + 66.8915i) q^{28} +(15.3934 - 8.88741i) q^{29} +(-96.5256 + 11.5780i) q^{30} +(28.5640 + 16.4914i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(-45.1631 - 60.2835i) q^{33} +(82.0606 - 47.3777i) q^{34} +(-74.4544 - 156.439i) q^{35} +(-30.3490 + 103.648i) q^{36} +340.681 q^{37} +(75.6711 + 131.066i) q^{38} +(5.71432 - 13.3581i) q^{39} +(64.8117 + 37.4190i) q^{40} +(9.20200 - 15.9383i) q^{41} +(-192.314 + 7.69436i) q^{42} +(174.489 + 302.224i) q^{43} +57.9849i q^{44} +(70.9768 - 242.401i) q^{45} +123.409 q^{46} +(-49.7597 - 86.1864i) q^{47} +(66.5370 - 49.8481i) q^{48} +(-122.376 - 320.426i) q^{49} +(64.9319 + 37.4885i) q^{50} +(29.3186 + 244.430i) q^{51} +(-9.68602 + 5.59223i) q^{52} -615.865i q^{53} +(-216.572 - 178.405i) q^{54} -135.609i q^{55} +(122.033 + 84.0236i) q^{56} +(-390.400 + 46.8273i) q^{57} +(17.7748 - 30.7869i) q^{58} +(266.903 - 462.289i) q^{59} +(-155.609 + 116.579i) q^{60} +(-663.603 + 383.131i) q^{61} +65.9657 q^{62} +(178.134 - 467.242i) q^{63} -64.0000 q^{64} +(22.6526 - 13.0785i) q^{65} +(-138.508 - 59.2509i) q^{66} +(-348.599 + 603.791i) q^{67} +(94.7554 - 164.121i) q^{68} +(-126.103 + 294.786i) q^{69} +(-285.397 - 196.505i) q^{70} -597.683i q^{71} +(51.0822 + 209.873i) q^{72} -572.023i q^{73} +(590.077 - 340.681i) q^{74} +(-155.898 + 116.796i) q^{75} +(262.132 + 151.342i) q^{76} +(21.2914 - 267.628i) q^{77} +(-3.46062 - 28.8513i) q^{78} +(643.996 + 1115.43i) q^{79} +149.676 q^{80} +(647.457 - 335.024i) q^{81} -36.8080i q^{82} +(147.704 + 255.831i) q^{83} +(-325.404 + 205.641i) q^{84} +(-221.604 + 383.829i) q^{85} +(604.449 + 348.979i) q^{86} +(55.3775 + 73.9176i) q^{87} +(57.9849 + 100.433i) q^{88} +258.046 q^{89} +(-119.465 - 490.828i) q^{90} +(46.7591 - 22.2542i) q^{91} +(213.750 - 123.409i) q^{92} +(-67.4059 + 157.572i) q^{93} +(-172.373 - 99.5195i) q^{94} +(-613.046 - 353.942i) q^{95} +(65.3973 - 152.876i) q^{96} +(-583.718 + 337.010i) q^{97} +(-532.388 - 432.618i) q^{98} +(283.065 - 270.309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9}+O(q^{10}) \) 48 * q + 96 * q^4 - 12 * q^7 - 36 * q^9	\( 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9} + 24 q^{11} - 132 q^{14} - 120 q^{15} - 384 q^{16} + 120 q^{18} + 180 q^{21} + 348 q^{23} - 600 q^{25} - 96 q^{28} - 84 q^{29} + 192 q^{30} + 96 q^{36} - 672 q^{37} + 1368 q^{39} + 1128 q^{42} + 84 q^{43} - 1008 q^{46} - 42 q^{49} + 456 q^{50} + 2016 q^{51} - 528 q^{56} + 732 q^{57} + 504 q^{58} - 1008 q^{60} - 774 q^{63} - 3072 q^{64} - 6972 q^{65} + 1176 q^{67} + 216 q^{70} - 384 q^{72} + 2520 q^{74} + 1500 q^{77} + 2832 q^{78} + 348 q^{79} + 2268 q^{81} - 1080 q^{84} + 720 q^{85} + 1200 q^{86} + 180 q^{91} + 1392 q^{92} + 5232 q^{93} - 5892 q^{95} + 972 q^{99}+O(q^{100}) \) 48 * q + 96 * q^4 - 12 * q^7 - 36 * q^9 + 24 * q^11 - 132 * q^14 - 120 * q^15 - 384 * q^16 + 120 * q^18 + 180 * q^21 + 348 * q^23 - 600 * q^25 - 96 * q^28 - 84 * q^29 + 192 * q^30 + 96 * q^36 - 672 * q^37 + 1368 * q^39 + 1128 * q^42 + 84 * q^43 - 1008 * q^46 - 42 * q^49 + 456 * q^50 + 2016 * q^51 - 528 * q^56 + 732 * q^57 + 504 * q^58 - 1008 * q^60 - 774 * q^63 - 3072 * q^64 - 6972 * q^65 + 1176 * q^67 + 216 * q^70 - 384 * q^72 + 2520 * q^74 + 1500 * q^77 + 2832 * q^78 + 348 * q^79 + 2268 * q^81 - 1080 * q^84 + 720 * q^85 + 1200 * q^86 + 180 * q^91 + 1392 * q^92 + 5232 * q^93 - 5892 * q^95 + 972 * q^99

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