LMFDB - Embedded newform 168.4.i.c.125.77

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,4,Mod(125,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1, 1])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.125"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	168.i (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$9.91232088096$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			125.77
Character	$\chi$	$=$	168.125
Dual form			168.4.i.c.125.79

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.81762 - 0.246982i) q^{2} +(-3.70908 + 3.63906i) q^{3} +(7.87800 - 1.39180i) q^{4} -9.02015i q^{5} +(-9.55201 + 11.1696i) q^{6} +(5.01951 - 17.8271i) q^{7} +(21.8535 - 5.86730i) q^{8} +(0.514533 - 26.9951i) q^{9} +(-2.22781 - 25.4154i) q^{10} +8.71540 q^{11} +(-24.1553 + 33.8308i) q^{12} -52.4602 q^{13} +(9.74012 - 51.4697i) q^{14} +(32.8248 + 33.4564i) q^{15} +(60.1258 - 21.9293i) q^{16} +69.0503 q^{17} +(-5.21754 - 76.1891i) q^{18} +129.296 q^{19} +(-12.5543 - 71.0607i) q^{20} +(46.2560 + 84.3883i) q^{21} +(24.5567 - 2.15254i) q^{22} -177.747i q^{23} +(-59.7049 + 101.288i) q^{24} +43.6369 q^{25} +(-147.813 + 12.9567i) q^{26} +(96.3282 + 101.999i) q^{27} +(14.7319 - 147.428i) q^{28} -247.372 q^{29} +(100.751 + 86.1605i) q^{30} +52.1678i q^{31} +(163.996 - 76.6384i) q^{32} +(-32.3261 + 31.7158i) q^{33} +(194.558 - 17.0542i) q^{34} +(-160.803 - 45.2767i) q^{35} +(-33.5184 - 213.384i) q^{36} +299.492i q^{37} +(364.308 - 31.9338i) q^{38} +(194.579 - 190.905i) q^{39} +(-52.9239 - 197.122i) q^{40} -185.754 q^{41} +(151.174 + 226.350i) q^{42} +330.296i q^{43} +(68.6599 - 12.1301i) q^{44} +(-243.500 - 4.64117i) q^{45} +(-43.9002 - 500.824i) q^{46} -81.9844 q^{47} +(-143.209 + 300.138i) q^{48} +(-292.609 - 178.966i) q^{49} +(122.952 - 10.7775i) q^{50} +(-256.113 + 251.278i) q^{51} +(-413.281 + 73.0142i) q^{52} -238.316 q^{53} +(296.609 + 263.604i) q^{54} -78.6142i q^{55} +(5.09695 - 419.035i) q^{56} +(-479.570 + 470.517i) q^{57} +(-697.001 + 61.0964i) q^{58} -198.589i q^{59} +(305.159 + 217.884i) q^{60} +157.196 q^{61} +(12.8845 + 146.989i) q^{62} +(-478.661 - 144.675i) q^{63} +(443.150 - 256.442i) q^{64} +473.198i q^{65} +(-83.2495 + 97.3472i) q^{66} -527.615i q^{67} +(543.978 - 96.1044i) q^{68} +(646.831 + 659.277i) q^{69} +(-464.264 - 87.8573i) q^{70} +245.212i q^{71} +(-147.144 - 592.956i) q^{72} +745.090i q^{73} +(73.9691 + 843.855i) q^{74} +(-161.853 + 158.797i) q^{75} +(1018.60 - 179.955i) q^{76} +(43.7470 - 155.370i) q^{77} +(501.100 - 585.957i) q^{78} +598.112 q^{79} +(-197.805 - 542.343i) q^{80} +(-728.471 - 27.7798i) q^{81} +(-523.385 + 45.8779i) q^{82} -3.93633i q^{83} +(481.857 + 600.432i) q^{84} -622.844i q^{85} +(81.5772 + 930.651i) q^{86} +(917.522 - 900.200i) q^{87} +(190.462 - 51.1359i) q^{88} +1258.73 q^{89} +(-687.237 + 47.0630i) q^{90} +(-263.324 + 935.211i) q^{91} +(-247.389 - 1400.29i) q^{92} +(-189.841 - 193.494i) q^{93} +(-231.001 + 20.2487i) q^{94} -1166.27i q^{95} +(-329.381 + 881.047i) q^{96} +755.959i q^{97} +(-868.663 - 431.990i) q^{98} +(4.48436 - 235.273i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 28 q^{4} + 64 q^{7} + 104 q^{9} - 8 q^{15} - 892 q^{16} + 692 q^{18} + 128 q^{22} - 976 q^{25} + 612 q^{28} - 332 q^{30} + 1544 q^{36} + 568 q^{39} + 780 q^{42} + 208 q^{46} - 4048 q^{49} - 1448 q^{57}+ \cdots - 2072 q^{88}+O(q^{100}) $ 80 * q + 28 * q^4 + 64 * q^7 + 104 * q^9 - 8 * q^15 - 892 * q^16 + 692 * q^18 + 128 * q^22 - 976 * q^25 + 612 * q^28 - 332 * q^30 + 1544 * q^36 + 568 * q^39 + 780 * q^42 + 208 * q^46 - 4048 * q^49 - 1448 * q^57 - 1760 * q^58 + 4156 * q^60 - 2152 * q^63 + 2764 * q^64 + 1968 * q^70 - 2740 * q^72 - 3620 * q^78 + 4992 * q^79 + 1568 * q^81 + 2484 * q^84 - 2072 * q^88

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	2.81762	−	0.246982i	0.996180	−	0.0873213i
$2$	2.81762	−	0.246982i	0.996180	−	0.0873213i
$3$	−3.70908	+	3.63906i	−0.713813	+	0.700337i
$3$	−3.70908	+	3.63906i	−0.713813	+	0.700337i
$4$	7.87800	−	1.39180i	0.984750	−	0.173975i
$5$		−	9.02015i		−	0.806787i	−0.915027	−	0.403393i	$-0.867831\pi$
$5$		−	9.02015i		−	0.806787i	0.915027	−	0.403393i	$-0.132169\pi$
$6$	−9.55201	+	11.1696i	−0.649932	+	0.759993i
$7$	5.01951	−	17.8271i	0.271028	−	0.962571i
$7$	5.01951	−	17.8271i	0.271028	−	0.962571i
$8$	21.8535	−	5.86730i	0.965797	−	0.259301i
$9$	0.514533	−	26.9951i	0.0190568	−	0.999818i
$10$	−2.22781	−	25.4154i	−0.0704496	−	0.803705i
$11$	8.71540			0.238890			0.119445	−	0.992841i	$-0.461888\pi$
$11$	8.71540			0.238890			0.119445	+	0.992841i	$0.461888\pi$
$12$	−24.1553	+	33.8308i	−0.581086	+	0.813843i
$13$	−52.4602			−1.11922			−0.559609	−	0.828757i	$-0.689049\pi$
$13$	−52.4602			−1.11922			−0.559609	+	0.828757i	$0.689049\pi$
$14$	9.74012	−	51.4697i	0.185940	−	0.982561i
$15$	32.8248	+	33.4564i	0.565022	+	0.575895i
$16$	60.1258	−	21.9293i	0.939465	−	0.342645i
$17$	69.0503			0.985127			0.492563	−	0.870277i	$-0.336060\pi$
$17$	69.0503			0.985127			0.492563	+	0.870277i	$0.336060\pi$
$18$	−5.21754	−	76.1891i	−0.0683214	−	0.997663i
$19$	129.296			1.56119			0.780595	−	0.625037i	$-0.214916\pi$
$19$	129.296			1.56119			0.780595	+	0.625037i	$0.214916\pi$
$20$	−12.5543	−	71.0607i	−0.140361	−	0.794483i
$21$	46.2560	+	84.3883i	0.480661	+	0.876906i
$22$	24.5567	−	2.15254i	0.237978	−	0.0208602i
$23$		−	177.747i		−	1.61143i	−0.592307	−	0.805713i	$-0.701783\pi$
$23$		−	177.747i		−	1.61143i	0.592307	−	0.805713i	$-0.298217\pi$
$24$	−59.7049	+	101.288i	−0.507800	+	0.861475i
$25$	43.6369			0.349095
$26$	−147.813	+	12.9567i	−1.11494	+	0.0977315i
$27$	96.3282	+	101.999i	0.686607	+	0.727029i
$28$	14.7319	−	147.428i	0.0994310	−	0.995044i
$29$	−247.372			−1.58399			−0.791996	−	0.610526i	$-0.790958\pi$
$29$	−247.372			−1.58399			−0.791996	+	0.610526i	$0.790958\pi$
$30$	100.751	+	86.1605i	0.613152	+	0.524356i
$31$			52.1678i			0.302245i	0.988515	+	0.151123i	$0.0482888\pi$
$31$			52.1678i			0.302245i	−0.988515	+	0.151123i	$0.951711\pi$
$32$	163.996	−	76.6384i	0.905956	−	0.423371i
$33$	−32.3261	+	31.7158i	−0.170523	+	0.167304i
$34$	194.558	−	17.0542i	0.981364	−	0.0860225i
$35$	−160.803	−	45.2767i	−0.776590	−	0.218662i
$36$	−33.5184	−	213.384i	−0.155178	−	0.987887i
$37$			299.492i			1.33071i	0.746528	+	0.665354i	$0.231719\pi$
$37$			299.492i			1.33071i	−0.746528	+	0.665354i	$0.768281\pi$
$38$	364.308	−	31.9338i	1.55523	−	0.136325i
$39$	194.579	−	190.905i	0.798912	−	0.783829i
$40$	−52.9239	−	197.122i	−0.209200	−	0.779192i
$41$	−185.754			−0.707559			−0.353780	−	0.935329i	$-0.615104\pi$
$41$	−185.754			−0.707559			−0.353780	+	0.935329i	$0.615104\pi$
$42$	151.174	+	226.350i	0.555398	+	0.831585i
$43$			330.296i			1.17139i	0.810532	+	0.585695i	$0.199178\pi$
$43$			330.296i			1.17139i	−0.810532	+	0.585695i	$0.800822\pi$
$44$	68.6599	−	12.1301i	0.235247	−	0.0415610i
$45$	−243.500	−	4.64117i	−0.806640	−	0.0153748i
$46$	−43.9002	−	500.824i	−0.140712	−	1.60527i
$47$	−81.9844			−0.254440			−0.127220	−	0.991875i	$-0.540605\pi$
$47$	−81.9844			−0.254440			−0.127220	+	0.991875i	$0.540605\pi$
$48$	−143.209	+	300.138i	−0.430635	+	0.902526i
$49$	−292.609	−	178.966i	−0.853088	−	0.521768i
$50$	122.952	−	10.7775i	0.347762	−	0.0304834i
$51$	−256.113	+	251.278i	−0.703196	+	0.689920i
$52$	−413.281	+	73.0142i	−1.10215	+	0.194716i
$53$	−238.316			−0.617646			−0.308823	−	0.951120i	$-0.599935\pi$
$53$	−238.316			−0.617646			−0.308823	+	0.951120i	$0.599935\pi$
$54$	296.609	+	263.604i	0.747469	+	0.664297i
$55$		−	78.6142i		−	0.192733i
$56$	5.09695	−	419.035i	0.0121626	−	0.999926i
$57$	−479.570	+	470.517i	−1.11440	+	1.09336i
$58$	−697.001	+	61.0964i	−1.57794	+	0.138316i
$59$		−	198.589i		−	0.438204i	−0.975702	−	0.219102i	$-0.929687\pi$
$59$		−	198.589i		−	0.438204i	0.975702	−	0.219102i	$-0.0703128\pi$
$60$	305.159	+	217.884i	0.656597	+	0.468812i
$61$	157.196			0.329950			0.164975	−	0.986298i	$-0.447246\pi$
$61$	157.196			0.329950			0.164975	+	0.986298i	$0.447246\pi$
$62$	12.8845	+	146.989i	0.0263924	+	0.301091i
$63$	−478.661	−	144.675i	−0.957232	−	0.289322i
$64$	443.150	−	256.442i	0.865526	−	0.500863i
$65$			473.198i			0.902970i
$66$	−83.2495	+	97.3472i	−0.155262	+	0.181555i
$67$		−	527.615i		−	0.962066i	−0.876703	−	0.481033i	$-0.840262\pi$
$67$		−	527.615i		−	0.962066i	0.876703	−	0.481033i	$-0.159738\pi$
$68$	543.978	−	96.1044i	0.970103	−	0.171388i
$69$	646.831	+	659.277i	1.12854	+	1.15026i
$70$	−464.264	−	87.8573i	−0.792717	−	0.150014i
$71$			245.212i			0.409878i	0.978775	+	0.204939i	$0.0656996\pi$
$71$			245.212i			0.409878i	−0.978775	+	0.204939i	$0.934300\pi$
$72$	−147.144	−	592.956i	−0.240848	−	0.970563i
$73$			745.090i			1.19461i	0.802016	+	0.597303i	$0.203761\pi$
$73$			745.090i			1.19461i	−0.802016	+	0.597303i	$0.796239\pi$
$74$	73.9691	+	843.855i	0.116199	+	1.32562i
$75$	−161.853	+	158.797i	−0.249188	+	0.244484i
$76$	1018.60	−	179.955i	1.53738	−	0.271609i
$77$	43.7470	−	155.370i	0.0647459	−	0.229949i
$78$	501.100	−	585.957i	0.727415	−	0.850597i
$79$	598.112			0.851808			0.425904	−	0.904768i	$-0.359956\pi$
$79$	598.112			0.851808			0.425904	+	0.904768i	$0.359956\pi$
$80$	−197.805	−	542.343i	−0.276441	−	0.757948i
$81$	−728.471	−	27.7798i	−0.999274	−	0.0381067i
$82$	−523.385	+	45.8779i	−0.704857	+	0.0617850i
$83$		−	3.93633i		−	0.00520564i	−0.999997	−	0.00260282i	$-0.999171\pi$
$83$		−	3.93633i		−	0.00520564i	0.999997	−	0.00260282i	$-0.000828505\pi$
$84$	481.857	+	600.432i	0.625891	+	0.779910i
$85$		−	622.844i		−	0.794787i
$86$	81.5772	+	930.651i	0.102287	+	1.16691i
$87$	917.522	−	900.200i	1.13067	−	1.10933i
$88$	190.462	−	51.1359i	0.230719	−	0.0619443i
$89$	1258.73			1.49916			0.749579	−	0.661915i	$-0.230256\pi$
$89$	1258.73			1.49916			0.749579	+	0.661915i	$0.230256\pi$
$90$	−687.237	+	47.0630i	−0.804902	+	0.0551208i
$91$	−263.324	+	935.211i	−0.303339	+	1.07733i
$92$	−247.389	−	1400.29i	−0.280348	−	1.58685i
$93$	−189.841	−	193.494i	−0.211674	−	0.215747i
$94$	−231.001	+	20.2487i	−0.253468	+	0.0222180i
$95$		−	1166.27i		−	1.25955i
$96$	−329.381	+	881.047i	−0.350181	+	0.936682i
$97$			755.959i			0.791300i	0.918401	+	0.395650i	$0.129481\pi$
$97$			755.959i			0.791300i	−0.918401	+	0.395650i	$0.870519\pi$
$98$	−868.663	−	431.990i	−0.895390	−	0.445282i
$99$	4.48436	−	235.273i	0.00455248	−	0.238847i
$100$	343.771	−	60.7340i	0.343771	−	0.0607340i
$101$		−	1045.75i		−	1.03026i	−0.857113	−	0.515128i	$-0.827744\pi$
$101$		−	1045.75i		−	1.03026i	0.857113	−	0.515128i	$-0.172256\pi$
$102$	−659.569	+	771.262i	−0.640265	+	0.748689i
$103$			1520.53i			1.45458i	0.686328	+	0.727292i	$0.259221\pi$
$103$			1520.53i			1.45458i	−0.686328	+	0.727292i	$0.740779\pi$
$104$	−1146.44	+	307.800i	−1.08094	+	0.290214i
$105$	761.195	−	417.236i	0.707477	−	0.387791i
$106$	−671.485	+	58.8597i	−0.615287	+	0.0539336i
$107$	283.267			0.255930			0.127965	−	0.991779i	$-0.459156\pi$
$107$	283.267			0.255930			0.127965	+	0.991779i	$0.459156\pi$
$108$	900.837	+	669.481i	0.802621	+	0.596489i
$109$			1180.64i			1.03747i	0.854935	+	0.518736i	$0.173597\pi$
$109$			1180.64i			1.03747i	−0.854935	+	0.518736i	$0.826403\pi$
$110$	−19.4163	−	221.505i	−0.0168297	−	0.191997i
$111$	−1089.87	−	1110.84i	−0.931943	−	0.949876i
$112$	−89.1327	−	1181.94i	−0.0751986	−	0.997169i
$113$			1867.56i			1.55473i	0.629047	+	0.777367i	$0.283445\pi$
$113$			1867.56i			1.55473i	−0.629047	+	0.777367i	$0.716555\pi$
$114$	−1235.04	+	1444.18i	−1.01467	+	1.18649i
$115$	−1603.30			−1.30008
$116$	−1948.80	+	344.293i	−1.55984	+	0.275576i
$117$	−26.9925	+	1416.17i	−0.0213287	+	1.11901i
$118$	−49.0478	−	559.548i	−0.0382645	−	0.436530i
$119$	346.598	−	1230.96i	0.266997	−	0.948255i
$120$	913.636	+	538.547i	0.695027	+	0.409686i
$121$	−1255.04			−0.942932
$122$	442.920	−	38.8247i	0.328690	−	0.0288116i
$123$	688.977	−	675.970i	0.505065	−	0.495530i
$124$	72.6073	+	410.978i	0.0525833	+	0.297636i
$125$		−	1521.13i		−	1.08843i
$126$	−1384.42	−	289.418i	−0.978839	−	0.204630i
$127$	960.566			0.671153			0.335577	−	0.942013i	$-0.391069\pi$
$127$	960.566			0.671153			0.335577	+	0.942013i	$0.391069\pi$
$128$	1185.29	−	832.007i	0.818484	−	0.574529i
$129$	−1201.97	−	1225.10i	−0.820367	−	0.836152i
$130$	116.871	+	1333.29i	0.0788485	+	0.899521i
$131$			1477.86i			0.985659i	0.870126	+	0.492829i	$0.164037\pi$
$131$			1477.86i			0.985659i	−0.870126	+	0.492829i	$0.835963\pi$
$132$	−210.523	+	294.849i	−0.138816	+	0.194419i
$133$	649.004	−	2304.97i	0.423126	−	1.50276i
$134$	−130.311	−	1486.62i	−0.0840088	−	0.958391i
$135$	920.050	−	868.895i	0.586557	−	0.553945i
$136$	1508.99	−	405.139i	0.951432	−	0.255444i
$137$		−	344.829i		−	0.215042i	−0.994203	−	0.107521i	$-0.965709\pi$
$137$		−	344.829i		−	0.215042i	0.994203	−	0.107521i	$-0.0342913\pi$
$138$	1985.36	+	1697.84i	1.22467	+	1.04732i
$139$	1156.15			0.705489			0.352745	−	0.935720i	$-0.385248\pi$
$139$	1156.15			0.705489			0.352745	+	0.935720i	$0.385248\pi$
$140$	−1329.82	−	132.884i	−0.802789	−	0.0802196i
$141$	304.087	−	298.346i	0.181622	−	0.178193i
$142$	60.5629	+	690.915i	0.0357911	+	0.408312i
$143$	−457.211			−0.267370
$144$	−561.046	−	1634.38i	−0.324679	−	0.945824i
$145$			2231.33i			1.27794i
$146$	184.024	+	2099.38i	0.104315	+	1.19004i
$147$	1736.58	−	401.021i	0.974358	−	0.225004i
$148$	416.834	+	2359.40i	0.231510	+	1.31041i
$149$	1849.45			1.01687			0.508433	−	0.861102i	$-0.330225\pi$
$149$	1849.45			1.01687			0.508433	+	0.861102i	$0.330225\pi$
$150$	−416.820	+	487.405i	−0.226888	+	0.265310i
$151$	2628.03			1.41633			0.708167	−	0.706045i	$-0.249523\pi$
$151$	2628.03			1.41633			0.708167	+	0.706045i	$0.249523\pi$
$152$	2825.57	−	758.620i	1.50779	−	0.404817i
$153$	35.5287	−	1864.02i	0.0187734	−	0.984948i
$154$	84.8890	−	448.579i	0.0444192	−	0.234724i
$155$	470.561			0.243848
$156$	1267.19	−	1774.77i	0.650361	−	0.910867i
$157$	−1909.32			−0.970577			−0.485288	−	0.874354i	$-0.661285\pi$
$157$	−1909.32			−0.970577			−0.485288	+	0.874354i	$0.661285\pi$
$158$	1685.25	−	147.723i	0.848554	−	0.0743809i
$159$	883.933	−	867.246i	0.440883	−	0.432560i
$160$	−691.289	−	1479.27i	−0.341570	−	0.730914i
$161$	−3168.71	−	892.202i	−1.55111	−	0.436741i
$162$	−2059.42	+	101.646i	−0.998784	+	0.0492967i
$163$		−	3458.92i		−	1.66211i	−0.556191	−	0.831054i	$-0.687738\pi$
$163$		−	3458.92i		−	1.66211i	0.556191	−	0.831054i	$-0.312262\pi$
$164$	−1463.37	+	258.533i	−0.696769	+	0.123098i
$165$	286.081	+	291.586i	0.134978	+	0.137575i
$166$	−0.972202	−	11.0911i	−0.000454563	−	0.00518576i
$167$	−2306.06			−1.06855			−0.534277	−	0.845310i	$-0.679416\pi$
$167$	−2306.06			−1.06855			−0.534277	+	0.845310i	$0.679416\pi$
$168$	1505.99	+	1572.78i	0.691603	+	0.722278i
$169$	555.068			0.252648
$170$	−153.831	−	1754.94i	−0.0694018	−	0.791751i
$171$	66.5273	−	3490.37i	0.0297513	−	1.56091i
$172$	459.708	+	2602.08i	0.203793	+	1.15353i
$173$			18.1258i			0.00796576i	0.999992	+	0.00398288i	$0.00126779\pi$
$173$			18.1258i			0.00796576i	−0.999992	+	0.00398288i	$0.998732\pi$
$174$	2362.90	−	2763.04i	1.02949	−	1.20382i
$175$	219.036	−	777.918i	0.0946146	−	0.336029i
$176$	524.020	−	191.122i	0.224429	−	0.0818544i
$177$	722.675	+	736.581i	0.306890	+	0.312796i
$178$	3546.63	−	310.883i	1.49343	−	0.130908i
$179$	2596.01			1.08400			0.541998	−	0.840380i	$-0.317668\pi$
$179$	2596.01			1.08400			0.541998	+	0.840380i	$0.317668\pi$
$180$	−1924.75	+	302.341i	−0.797014	+	0.125195i
$181$	−1200.67			−0.493069			−0.246534	−	0.969134i	$-0.579292\pi$
$181$	−1200.67			−0.493069			−0.246534	+	0.969134i	$0.579292\pi$
$182$	−510.968	+	2700.11i	−0.208107	+	1.09970i
$183$	−583.054	+	572.047i	−0.235522	+	0.231076i
$184$	−1042.89	−	3884.39i	−0.417843	−	1.55631i
$185$	2701.46			1.07360
$186$	−582.691	−	498.307i	−0.229704	−	0.196439i
$187$	601.801			0.235337
$188$	−645.873	+	114.106i	−0.250559	+	0.0442662i
$189$	2301.87	−	1205.26i	0.885907	−	0.463863i
$190$	−288.048	−	3286.11i	−0.109985	−	1.25474i
$191$			1778.65i			0.673816i	0.941538	+	0.336908i	$0.109381\pi$
$191$			1778.65i			0.673816i	−0.941538	+	0.336908i	$0.890619\pi$
$192$	−710.470	+	2563.81i	−0.267051	+	0.963682i
$193$	151.059			0.0563393			0.0281697	−	0.999603i	$-0.491032\pi$
$193$	151.059			0.0563393			0.0281697	+	0.999603i	$0.491032\pi$
$194$	186.708	+	2130.01i	0.0690973	+	0.788277i
$195$	−1722.00	−	1755.13i	−0.632383	−	0.644551i
$196$	−2554.26	−	1002.64i	−0.930853	−	0.365394i
$197$	346.401			0.125280			0.0626398	−	0.998036i	$-0.480048\pi$
$197$	346.401			0.125280			0.0626398	+	0.998036i	$0.480048\pi$
$198$	−45.4729	−	664.018i	−0.0163213	−	0.238332i
$199$			3780.44i			1.34668i	0.739335	+	0.673338i	$0.235140\pi$
$199$			3780.44i			1.34668i	−0.739335	+	0.673338i	$0.764860\pi$
$200$	953.618	−	256.031i	0.337155	−	0.0905206i
$201$	1920.02	+	1956.97i	0.673770	+	0.686735i
$202$	−258.281	−	2946.53i	−0.0899633	−	1.02632i
$203$	−1241.69	+	4409.92i	−0.429306	+	1.52471i
$204$	−1667.93	+	2336.03i	−0.572443	+	0.801738i
$205$			1675.53i			0.570850i
$206$	375.543	+	4284.28i	0.127016	+	1.44903i
$207$	−4798.29	−	91.4567i	−1.61113	−	0.0307086i
$208$	−3154.21	+	1150.41i	−1.05147	+	0.383494i
$209$	1126.87			0.372953
$210$	2041.71	−	1363.61i	0.670912	−	0.448087i
$211$			2168.92i			0.707652i	0.935311	+	0.353826i	$0.115119\pi$
$211$			2168.92i			0.707652i	−0.935311	+	0.353826i	$0.884881\pi$
$212$	−1877.45	+	331.689i	−0.608227	+	0.107455i
$213$	−892.341	−	909.511i	−0.287053	−	0.292576i
$214$	798.140	−	69.9618i	0.254952	−	0.0223481i
$215$	2979.32			0.945061
$216$	2703.57	+	1663.85i	0.851641	+	0.524125i
$217$	929.998	+	261.857i	0.290933	+	0.0819169i
$218$	291.596	+	3326.59i	0.0905933	+	1.03351i
$219$	−2711.43	−	2763.60i	−0.836626	−	0.852725i
$220$	−109.416	−	619.323i	−0.0335309	−	0.189794i
$221$	−3622.39			−1.10257
$222$	−3345.19	−	2860.75i	−1.01133	−	0.864869i
$223$		−	3892.25i		−	1.16881i	−0.811462	−	0.584405i	$-0.801328\pi$
$223$		−	3892.25i		−	1.16881i	0.811462	−	0.584405i	$-0.198672\pi$
$224$	−543.060	−	3308.25i	−0.161985	−	0.986793i
$225$	22.4526	−	1177.98i	0.00665263	−	0.349032i
$226$	461.253	+	5262.07i	0.135761	+	1.54880i
$227$			2544.85i			0.744085i	0.928216	+	0.372043i	$0.121342\pi$
$227$			2544.85i			0.744085i	−0.928216	+	0.372043i	$0.878658\pi$
$228$	−3123.19	+	4374.20i	−0.907185	+	1.27056i
$229$	775.951			0.223914			0.111957	−	0.993713i	$-0.464288\pi$
$229$	775.951			0.223914			0.111957	+	0.993713i	$0.464288\pi$
$230$	−4517.50	+	395.987i	−1.29511	+	0.113524i
$231$	403.139	+	735.477i	0.114825	+	0.209484i
$232$	−5405.94	+	1451.40i	−1.52982	+	0.410730i
$233$			475.828i			0.133788i	0.997760	+	0.0668938i	$0.0213089\pi$
$233$			475.828i			0.133788i	−0.997760	+	0.0668938i	$0.978691\pi$
$234$	273.713	+	3996.89i	0.0764665	+	1.11660i
$235$			739.512i			0.205278i
$236$	−276.396	−	1564.48i	−0.0762367	−	0.431521i
$237$	−2218.44	+	2176.56i	−0.608031	+	0.596552i
$238$	672.558	−	3554.00i	0.183174	−	0.967947i
$239$			295.661i			0.0800196i	0.999199	+	0.0400098i	$0.0127389\pi$
$239$			295.661i			0.0800196i	−0.999199	+	0.0400098i	$0.987261\pi$
$240$	2707.29	+	1291.77i	0.728146	+	0.347431i
$241$		−	3284.88i		−	0.877998i	−0.898488	−	0.438999i	$-0.855333\pi$
$241$		−	3284.88i		−	0.877998i	0.898488	−	0.438999i	$-0.144667\pi$
$242$	−3536.23	+	309.973i	−0.939330	+	0.0823380i
$243$	2803.05	−	2547.91i	0.739982	−	0.672627i
$244$	1238.39	−	218.787i	0.324918	−	0.0574032i
$245$	−1614.30	+	2639.38i	−0.420955	+	0.688260i
$246$	1774.33	−	2074.79i	0.459865	−	0.537740i
$247$	−6782.90			−1.74731
$248$	306.084	+	1140.05i	0.0783724	+	0.291908i
$249$	14.3245	+	14.6002i	0.00364570	+	0.00371585i
$250$	−375.692	−	4285.97i	−0.0950433	−	1.08427i
$251$		−	1029.64i		−	0.258926i	−0.991584	−	0.129463i	$-0.958675\pi$
$251$		−	1029.64i		−	0.258926i	0.991584	−	0.129463i	$-0.0413253\pi$
$252$	−3972.25	−	473.546i	−0.992969	−	0.118375i
$253$		−	1549.13i		−	0.384953i
$254$	2706.51	−	237.242i	0.668589	−	0.0586059i
$255$	2266.56	+	2310.18i	0.556619	+	0.567329i
$256$	3134.22	−	2637.03i	0.765189	−	0.643805i
$257$	−2451.85			−0.595106			−0.297553	−	0.954705i	$-0.596170\pi$
$257$	−2451.85			−0.595106			−0.297553	+	0.954705i	$0.596170\pi$
$258$	−3689.27	−	3154.99i	−0.890247	−	0.761323i
$259$	5339.06	+	1503.30i	1.28090	+	0.360659i
$260$	658.599	+	3727.86i	0.157095	+	0.889200i
$261$	−127.281	+	6677.83i	−0.0301858	+	1.58371i
$262$	365.005	+	4164.05i	0.0860690	+	0.981894i
$263$			4396.49i			1.03080i	0.856951	+	0.515398i	$0.172356\pi$
$263$			4396.49i			1.03080i	−0.856951	+	0.515398i	$0.827644\pi$
$264$	−520.351	+	882.768i	−0.121308	+	0.205798i
$265$			2149.65i			0.498308i
$266$	1259.36	−	6654.84i	0.290287	−	1.53396i
$267$	−4668.73	+	4580.59i	−1.07012	+	1.04992i
$268$	−734.336	−	4156.55i	−0.167376	−	0.947394i
$269$		−	3402.69i		−	0.771248i	−0.922656	−	0.385624i	$-0.873986\pi$
$269$		−	3402.69i		−	0.771248i	0.922656	−	0.385624i	$-0.126014\pi$
$270$	2377.75	−	2675.45i	0.535946	−	0.603048i
$271$			4179.66i			0.936887i	0.883493	+	0.468444i	$0.155185\pi$
$271$			4179.66i			0.936887i	−0.883493	+	0.468444i	$0.844815\pi$
$272$	4151.70	−	1514.22i	0.925492	−	0.337548i
$273$	−2426.60	−	4427.02i	−0.537964	−	0.981449i
$274$	−85.1666	−	971.600i	−0.0187778	−	0.214221i
$275$	380.313			0.0833954
$276$	6013.32	+	4293.52i	1.31145	+	0.936376i
$277$			2605.51i			0.565163i	0.959243	+	0.282581i	$0.0911907\pi$
$277$			2605.51i			0.565163i	−0.959243	+	0.282581i	$0.908809\pi$
$278$	3257.58	−	285.547i	0.702794	−	0.0616042i
$279$	1408.27	+	26.8421i	0.302190	+	0.00575983i
$280$	−3779.76	−	45.9752i	−0.806727	−	0.00981266i
$281$		−	7988.99i		−	1.69603i	−0.529976	−	0.848013i	$-0.677799\pi$
$281$		−	7988.99i		−	1.69603i	0.529976	−	0.848013i	$-0.322201\pi$
$282$	783.116	−	915.730i	0.165368	−	0.193372i
$283$	−3622.36			−0.760873			−0.380437	−	0.924807i	$-0.624226\pi$
$283$	−3622.36			−0.760873			−0.380437	+	0.924807i	$0.624226\pi$
$284$	341.287	+	1931.78i	0.0713087	+	0.403627i
$285$	4244.13	+	4325.79i	0.882107	+	0.899081i
$286$	−1288.25	+	112.923i	−0.266349	+	0.0233471i
$287$	−932.395	+	3311.45i	−0.191768	+	0.681077i
$288$	−1984.48	−	4466.51i	−0.406030	−	0.913860i
$289$	−145.058			−0.0295254
$290$	551.098	+	6287.05i	0.111592	+	1.27306i
$291$	−2750.98	−	2803.91i	−0.554176	−	0.564840i
$292$	1037.02	+	5869.82i	0.207832	+	1.17639i
$293$		−	8260.81i		−	1.64710i	−0.567241	−	0.823552i	$-0.691989\pi$
$293$		−	8260.81i		−	1.64710i	0.567241	−	0.823552i	$-0.308011\pi$
$294$	4793.98	−	1558.83i	0.950988	−	0.309227i
$295$	−1791.30			−0.353537
$296$	1757.21	+	6544.94i	0.345053	+	1.28519i
$297$	839.539	+	888.965i	0.164024	+	0.173680i
$298$	5211.06	−	456.781i	1.01298	−	0.0887940i
$299$			9324.63i			1.80354i
$300$	−1054.06	+	1476.27i	−0.202854	+	0.284108i
$301$	5888.22	+	1657.93i	1.12755	+	0.317479i
$302$	7404.81	−	649.076i	1.41092	−	0.123676i
$303$	3805.54	+	3878.77i	0.721527	+	0.735410i
$304$	7774.04	−	2835.37i	1.46668	−	0.534933i
$305$		−	1417.94i		−	0.266199i
$306$	−360.272	−	5260.88i	−0.0673052	−	0.982825i
$307$	−6375.65			−1.18527			−0.592635	−	0.805471i	$-0.701912\pi$
$307$	−6375.65			−1.18527			−0.592635	+	0.805471i	$0.701912\pi$
$308$	128.394	−	1284.89i	0.0237531	−	0.237706i
$309$	−5533.29	−	5639.76i	−1.01870	−	1.03830i
$310$	1325.86	−	116.220i	0.242916	−	0.0212931i
$311$	3566.99			0.650371			0.325186	−	0.945650i	$-0.394573\pi$
$311$	3566.99			0.650371			0.325186	+	0.945650i	$0.394573\pi$
$312$	3132.13	−	5313.60i	0.568339	−	0.964178i
$313$		−	2364.18i		−	0.426936i	−0.976950	−	0.213468i	$-0.931524\pi$
$313$		−	2364.18i		−	0.426936i	0.976950	−	0.213468i	$-0.0684760\pi$
$314$	−5379.75	+	471.568i	−0.966870	+	0.0847520i
$315$	−1304.99	+	4317.59i	−0.233421	+	0.772282i
$316$	4711.92	−	832.454i	0.838818	−	0.148194i
$317$	−5296.44			−0.938415			−0.469207	−	0.883088i	$-0.655460\pi$
$317$	−5296.44			−0.938415			−0.469207	+	0.883088i	$0.655460\pi$
$318$	2276.40	−	2661.89i	0.401428	−	0.469406i
$319$	−2155.94			−0.378400
$320$	−2313.14	−	3997.28i	−0.404090	−	0.698295i
$321$	−1050.66	+	1030.83i	−0.182686	+	0.179237i
$322$	−9148.58	−	1731.28i	−1.58332	−	0.299628i
$323$	8927.95			1.53797
$324$	−5777.55	+	795.039i	−0.990664	+	0.136324i
$325$	−2289.20			−0.390713
$326$	−854.291	−	9745.94i	−0.145137	−	1.65576i
$327$	−4296.40	−	4379.07i	−0.726579	−	0.740560i
$328$	−4059.38	+	1089.88i	−0.683359	+	0.183471i
$329$	−411.522	+	1461.54i	−0.0689602	+	0.244916i
$330$	878.086	+	750.923i	0.146476	+	0.125264i
$331$			664.908i			0.110413i	0.998475	+	0.0552064i	$0.0175817\pi$
$331$			664.908i			0.110413i	−0.998475	+	0.0552064i	$0.982418\pi$
$332$	−5.47860	−	31.0104i	−0.000905654	−	0.00512626i
$333$	8084.81	+	154.099i	1.33047	+	0.0253590i
$334$	−6497.61	+	569.555i	−1.06447	+	0.0933074i
$335$	−4759.17			−0.776182
$336$	4631.75	+	4059.55i	0.752032	+	0.659127i
$337$	8618.15			1.39306			0.696529	−	0.717529i	$-0.254727\pi$
$337$	8618.15			1.39306			0.696529	+	0.717529i	$0.254727\pi$
$338$	1563.97	−	137.092i	0.251683	−	0.0220615i
$339$	−6796.15	−	6926.92i	−1.08884	−	1.10979i
$340$	−866.876	−	4906.76i	−0.138273	−	0.782667i
$341$			454.663i			0.0722034i
$342$	−674.608	−	9850.97i	−0.106663	−	1.55754i
$343$	−4659.20	+	4318.04i	−0.733449	+	0.679744i
$344$	1937.95	+	7218.13i	0.303742	+	1.13132i
$345$	5946.78	−	5834.51i	0.928011	−	0.910491i
$346$	4.47673	+	51.0716i	0.000695580	+	0.00793533i
$347$	−11525.2			−1.78301			−0.891507	−	0.453006i	$-0.850352\pi$
$347$	−11525.2			−1.78301			−0.891507	+	0.453006i	$0.850352\pi$
$348$	5975.33	−	8368.79i	0.920435	−	1.28912i
$349$	−232.968			−0.0357320			−0.0178660	−	0.999840i	$-0.505687\pi$
$349$	−232.968			−0.0357320			−0.0178660	+	0.999840i	$0.505687\pi$
$350$	425.029	−	2245.98i	0.0649107	−	0.343007i
$351$	−5053.39	−	5350.90i	−0.768462	−	0.813704i
$352$	1429.29	−	667.934i	0.216424	−	0.101139i
$353$	−10995.6			−1.65789			−0.828944	−	0.559331i	$-0.811058\pi$
$353$	−10995.6			−1.65789			−0.828944	+	0.559331i	$0.811058\pi$
$354$	2218.15	+	1896.92i	0.333032	+	0.284803i
$355$	2211.85			0.330684
$356$	9916.27	−	1751.90i	1.47630	−	0.260817i
$357$	3193.99	+	5827.04i	0.473512	+	0.863864i
$358$	7314.59	−	641.168i	1.07986	−	0.0946559i
$359$		−	3732.36i		−	0.548709i	−0.961629	−	0.274354i	$-0.911536\pi$
$359$		−	3732.36i		−	0.548709i	0.961629	−	0.274354i	$-0.0884642\pi$
$360$	−5348.55	+	1327.26i	−0.783037	+	0.194313i
$361$	9858.53			1.43731
$362$	−3383.05	+	296.545i	−0.491185	+	0.0430554i
$363$	4655.05	−	4567.17i	0.673076	−	0.660370i
$364$	−772.838	+	7734.09i	−0.111285	+	1.11367i
$365$	6720.83			0.963792
$366$	−1501.54	+	1755.82i	−0.214445	+	0.250759i
$367$		−	1187.53i		−	0.168907i	−0.996427	−	0.0844534i	$-0.973086\pi$
$367$		−	1187.53i		−	0.168907i	0.996427	−	0.0844534i	$-0.0269144\pi$
$368$	−3897.86	−	10687.2i	−0.552146	−	1.51388i
$369$	−95.5768	+	5014.45i	−0.0134838	+	0.707431i
$370$	7611.70	−	667.212i	1.06950	−	0.0937479i
$371$	−1196.23	+	4248.48i	−0.167399	+	0.594528i
$372$	−1764.88	−	1260.13i	−0.245980	−	0.175630i
$373$			4872.40i			0.676362i	0.941081	+	0.338181i	$0.109812\pi$
$373$			4872.40i			0.676362i	−0.941081	+	0.338181i	$0.890188\pi$
$374$	1695.65	−	148.634i	0.234438	−	0.0205499i
$375$	5535.48	+	5641.99i	0.762269	+	0.776937i
$376$	−1791.65	+	481.027i	−0.245737	+	0.0659763i
$377$	12977.2			1.77283
$378$	6188.13	−	3964.50i	0.842018	−	0.539449i
$379$			3969.71i			0.538022i	0.963137	+	0.269011i	$0.0866967\pi$
$379$			3969.71i			0.538022i	−0.963137	+	0.269011i	$0.913303\pi$
$380$	−1623.22	−	9187.89i	−0.219130	−	1.24034i
$381$	−3562.82	+	3495.55i	−0.479078	+	0.470033i
$382$	439.295	+	5011.58i	0.0588385	+	0.671242i
$383$	−2981.45			−0.397768			−0.198884	−	0.980023i	$-0.563732\pi$
$383$	−2981.45			−0.397768			−0.198884	+	0.980023i	$0.563732\pi$
$384$	−1368.62	+	7399.32i	−0.181881	+	0.983321i
$385$	−1401.46	−	394.605i	−0.185520	−	0.0522361i
$386$	425.628	−	37.3089i	0.0561241	−	0.00491962i
$387$	8916.38	+	169.949i	1.17118	+	0.0223229i
$388$	1052.15	+	5955.45i	0.137667	+	0.779232i
$389$	−477.774			−0.0622728			−0.0311364	−	0.999515i	$-0.509913\pi$
$389$	−477.774			−0.0622728			−0.0311364	+	0.999515i	$0.509913\pi$
$390$	−5285.42	−	4519.99i	−0.686251	−	0.586869i
$391$		−	12273.5i		−	1.58746i
$392$	−7444.58	−	2194.21i	−0.959204	−	0.282715i
$393$	−5378.02	−	5481.50i	−0.690293	−	0.703576i
$394$	976.029	−	85.5549i	0.124801	−	0.0109396i
$395$		−	5395.06i		−	0.687227i
$396$	−292.126	−	1859.72i	−0.0370704	−	0.235996i
$397$	6740.60			0.852143			0.426072	−	0.904689i	$-0.359897\pi$
$397$	6740.60			0.852143			0.426072	+	0.904689i	$0.359897\pi$
$398$	933.701	+	10651.9i	0.117593	+	1.34153i
$399$	5980.73	+	10911.1i	0.750403	+	1.36902i
$400$	2623.70	−	956.925i	0.327963	−	0.119616i
$401$		−	10739.9i		−	1.33746i	−0.743504	−	0.668732i	$-0.766837\pi$
$401$		−	10739.9i		−	1.33746i	0.743504	−	0.668732i	$-0.233163\pi$
$402$	5893.23	+	5039.78i	0.731163	+	0.625277i
$403$		−	2736.73i		−	0.338278i
$404$	−1455.48	−	8238.41i	−0.179239	−	1.01455i
$405$	−250.578	+	6570.91i	−0.0307440	+	0.806201i
$406$	−2409.43	+	12732.2i	−0.294527	+	1.55637i
$407$			2610.19i			0.317893i
$408$	−4122.64	+	6993.99i	−0.500247	+	0.848662i
$409$		−	15374.7i		−	1.85875i	−0.369139	−	0.929374i	$-0.620347\pi$
$409$		−	15374.7i		−	1.85875i	0.369139	−	0.929374i	$-0.379653\pi$
$410$	413.826	+	4721.02i	0.0498473	+	0.568669i
$411$	1254.85	+	1279.00i	0.150602	+	0.153500i
$412$	2116.28	+	11978.7i	0.253062	+	1.43240i
$413$	−3540.25	−	996.817i	−0.421803	−	0.118766i
$414$	−13542.4	+	927.401i	−1.60766	+	0.110095i
$415$	−35.5063			−0.00419984
$416$	−8603.24	+	4020.46i	−1.01396	+	0.473844i
$417$	−4288.23	+	4207.28i	−0.503587	+	0.494080i
$418$	3175.09	−	278.316i	0.371528	−	0.0325667i
$419$			1812.00i			0.211269i	0.994405	+	0.105635i	$0.0336874\pi$
$419$			1812.00i			0.211269i	−0.994405	+	0.105635i	$0.966313\pi$
$420$	5415.98	−	4346.42i	0.629221	−	0.504961i
$421$		−	1588.18i		−	0.183855i	−0.995766	−	0.0919276i	$-0.970697\pi$
$421$		−	1588.18i		−	0.183855i	0.995766	−	0.0919276i	$-0.0293028\pi$
$422$	535.684	+	6111.20i	0.0617931	+	0.704949i
$423$	−42.1837	+	2213.18i	−0.00484880	+	0.254393i
$424$	−5208.04	+	1398.27i	−0.596520	+	0.160156i
$425$	3013.14			0.343903
$426$	−2738.91	−	2342.27i	−0.311504	−	0.266393i
$427$	789.049	−	2802.35i	0.0894257	−	0.317600i
$428$	2231.58	−	394.252i	0.252027	−	0.0445255i
$429$	1695.83	−	1663.82i	0.190852	−	0.187249i
$430$	8394.61	−	735.839i	0.941451	−	0.0825240i
$431$		−	2266.42i		−	0.253294i	−0.991948	−	0.126647i	$-0.959578\pi$
$431$		−	2266.42i		−	0.253294i	0.991948	−	0.126647i	$-0.0404216\pi$
$432$	8028.58	+	4020.38i	0.894156	+	0.447756i
$433$			12900.1i			1.43173i	0.698238	+	0.715865i	$0.253968\pi$
$433$			12900.1i			1.43173i	−0.698238	+	0.715865i	$0.746032\pi$
$434$	2685.06	+	508.120i	0.296975	+	0.0561994i
$435$	−8119.94	−	8276.18i	−0.894992	−	0.912213i
$436$	1643.21	+	9301.05i	0.180495	+	1.02165i
$437$		−	22982.0i		−	2.51574i
$438$	−8322.34	−	7117.11i	−0.907892	−	0.776412i
$439$		−	3778.78i		−	0.410823i	−0.978676	−	0.205412i	$-0.934147\pi$
$439$		−	3778.78i		−	0.410823i	0.978676	−	0.205412i	$-0.0658533\pi$
$440$	−461.253	−	1717.99i	−0.0499759	−	0.186141i
$441$	−4981.77	+	7806.93i	−0.537930	+	0.842990i
$442$	−10206.5	+	894.664i	−1.09836	+	0.0962779i
$443$	372.016			0.0398985			0.0199492	−	0.999801i	$-0.493650\pi$
$443$	372.016			0.0398985			0.0199492	+	0.999801i	$0.493650\pi$
$444$	−10132.1	−	7234.31i	−1.08299	−	0.773255i
$445$		−	11353.9i		−	1.20950i
$446$	−961.316	−	10966.9i	−0.102062	−	1.16434i
$447$	−6859.76	+	6730.26i	−0.725852	+	0.712149i
$448$	−2347.22	−	9187.27i	−0.247535	−	0.968879i
$449$			12340.3i			1.29705i	0.761192	+	0.648526i	$0.224614\pi$
$449$			12340.3i			1.29705i	−0.761192	+	0.648526i	$0.775386\pi$
$450$	−227.677	−	3324.65i	−0.0238507	−	0.348279i
$451$	−1618.92			−0.169029
$452$	2599.27	+	14712.6i	0.270486	+	1.53102i
$453$	−9747.58	+	9563.56i	−1.01100	+	0.991910i
$454$	628.531	+	7170.42i	0.0649745	+	0.741243i
$455$	8435.74	+	2375.22i	0.869173	+	0.244730i
$456$	−7719.62	+	13096.2i	−0.792772	+	1.34493i
$457$	−13249.9			−1.35625			−0.678124	−	0.734947i	$-0.737207\pi$
$457$	−13249.9			−1.35625			−0.678124	+	0.734947i	$0.737207\pi$
$458$	2186.34	−	191.646i	0.223058	−	0.0195524i
$459$	6651.49	+	7043.08i	0.676394	+	0.716216i
$460$	−12630.8	+	2231.48i	−1.28025	+	0.226181i
$461$			3328.58i			0.336285i	0.985763	+	0.168143i	$0.0537769\pi$
$461$			3328.58i			0.336285i	−0.985763	+	0.168143i	$0.946223\pi$
$462$	1317.54	+	1972.73i	0.132679	+	0.198657i
$463$	4155.03			0.417064			0.208532	−	0.978016i	$-0.433131\pi$
$463$	4155.03			0.417064			0.208532	+	0.978016i	$0.433131\pi$
$464$	−14873.4	+	5424.68i	−1.48811	+	0.542747i
$465$	−1745.35	+	1712.40i	−0.174061	+	0.170775i
$466$	117.521	+	1340.70i	0.0116825	+	0.133277i
$467$		−	497.911i		−	0.0493374i	−0.999696	−	0.0246687i	$-0.992147\pi$
$467$		−	497.911i		−	0.0493374i	0.999696	−	0.0246687i	$-0.00785309\pi$
$468$	1758.38	+	11194.1i	0.173678	+	1.10566i
$469$	−9405.83	−	2648.37i	−0.926057	−	0.260747i
$470$	182.646	+	2083.67i	0.0179252	+	0.204494i
$471$	7081.83	−	6948.14i	0.692810	−	0.679731i
$472$	−1165.18	−	4339.85i	−0.113627	−	0.423216i
$473$			2878.66i			0.279833i
$474$	−5713.16	+	6680.65i	−0.553617	+	0.647368i
$475$	5642.09			0.545004
$476$	1017.24	−	10179.9i	0.0979521	−	0.980245i
$477$	−122.622	+	6433.36i	−0.0117703	+	0.617534i
$478$	73.0228	+	833.060i	0.00698742	+	0.0797140i
$479$	20052.8			1.91281			0.956406	−	0.292041i	$-0.0943345\pi$
$479$	20052.8			1.91281			0.956406	+	0.292041i	$0.0943345\pi$
$480$	7947.18	+	2971.07i	0.755703	+	0.282521i
$481$		−	15711.4i		−	1.48935i
$482$	−811.305	−	9255.54i	−0.0766679	−	0.874644i
$483$	14999.8	−	8221.85i	1.41307	−	0.774549i
$484$	−9887.22	+	1746.77i	−0.928552	+	0.164047i
$485$	6818.87			0.638410
$486$	7268.64	−	7871.35i	0.678420	−	0.734674i
$487$	−5918.14			−0.550670			−0.275335	−	0.961348i	$-0.588789\pi$
$487$	−5918.14			−0.550670			−0.275335	+	0.961348i	$0.588789\pi$
$488$	3435.29	−	922.319i	0.318664	−	0.0855562i
$489$	12587.2	+	12829.4i	1.16404	+	1.18643i
$490$	−3896.62	+	7835.48i	−0.359248	+	0.722389i
$491$	2586.64			0.237746			0.118873	−	0.992909i	$-0.462072\pi$
$491$	2586.64			0.237746			0.118873	+	0.992909i	$0.462072\pi$
$492$	4486.94	−	6284.21i	0.411153	−	0.575842i
$493$	−17081.1			−1.56043
$494$	−19111.7	+	1675.25i	−1.74064	+	0.152577i
$495$	−2122.20	−	40.4496i	−0.192698	−	0.00367288i
$496$	1144.00	+	3136.63i	0.103563	+	0.283949i
$497$	4371.41	+	1230.84i	0.394537	+	0.111088i
$498$	43.9671	+	37.5998i	0.00395625	+	0.00338331i
$499$		−	18254.1i		−	1.63761i	−0.574072	−	0.818805i	$-0.694637\pi$
$499$		−	18254.1i		−	1.63761i	0.574072	−	0.818805i	$-0.305363\pi$
$500$	−2117.11	−	11983.5i	−0.189360	−	1.07183i
$501$	8553.37	−	8391.89i	0.762747	−	0.748347i
$502$	−254.302	−	2901.14i	−0.0226097	−	0.257937i
$503$	−10858.4			−0.962531			−0.481265	−	0.876575i	$-0.659823\pi$
$503$	−10858.4			−0.962531			−0.481265	+	0.876575i	$0.659823\pi$
$504$	−11309.3	−	353.200i	−0.999513	−	0.0312158i
$505$	−9432.81			−0.831197
$506$	−382.608	−	4364.88i	−0.0336146	−	0.383483i
$507$	−2058.79	+	2019.92i	−0.180343	+	0.176939i
$508$	7567.34	−	1336.92i	0.660918	−	0.116764i
$509$		−	5017.32i		−	0.436913i	−0.975847	−	0.218456i	$-0.929898\pi$
$509$		−	5017.32i		−	0.436913i	0.975847	−	0.218456i	$-0.0701022\pi$
$510$	6956.90	+	5949.41i	0.604032	+	0.516557i
$511$	13282.8	+	3739.99i	1.14989	+	0.323772i
$512$	8179.74	−	8204.24i	0.706049	−	0.708163i
$513$	12454.9	+	13188.1i	1.07192	+	1.13503i
$514$	−6908.39	+	605.562i	−0.592832	+	0.0519654i
$515$	13715.4			1.17354
$516$	−11174.2	−	7978.40i	−0.953326	−	0.680677i
$517$	−714.527			−0.0607831
$518$	15414.8	+	2917.09i	1.30750	+	0.247431i
$519$	−65.9607	−	67.2299i	−0.00557871	−	0.00568606i
$520$	2776.40	+	10341.0i	0.234141	+	0.872085i
$521$	−13237.4			−1.11313			−0.556564	−	0.830805i	$-0.687881\pi$
$521$	−13237.4			−1.11313			−0.556564	+	0.830805i	$0.687881\pi$
$522$	1290.67	+	18847.0i	0.108221	+	1.58029i
$523$	17806.0			1.48872			0.744361	−	0.667777i	$-0.232754\pi$
$523$	17806.0			1.48872			0.744361	+	0.667777i	$0.232754\pi$
$524$	2056.89	+	11642.6i	0.171480	+	0.970627i
$525$	2018.47	+	3682.44i	0.167796	+	0.306124i
$526$	1085.85	+	12387.7i	0.0900104	+	1.02686i
$527$			3602.20i			0.297750i
$528$	−1248.13	+	2615.83i	−0.102875	+	0.215605i
$529$	−19426.9			−1.59669
$530$	530.924	+	6056.89i	0.0435129	+	0.496405i
$531$	−5360.92	−	102.180i	−0.438124	−	0.00835076i
$532$	1904.78	−	19061.9i	0.155231	−	1.55345i
$533$	9744.70			0.791913
$534$	−12023.4	+	14059.5i	−0.974351	+	1.13935i
$535$		−	2555.11i		−	0.206481i
$536$	−3095.68	−	11530.2i	−0.249464	−	0.929160i
$537$	−9628.82	+	9447.04i	−0.773770	+	0.759162i
$538$	−840.403	−	9587.50i	−0.0673464	−	0.768302i
$539$	−2550.20	−	1559.76i	−0.203794	−	0.124645i
$540$	6038.82	−	8125.68i	0.481240	−	0.647544i
$541$		−	7729.85i		−	0.614292i	−0.951662	−	0.307146i	$-0.900626\pi$
$541$		−	7729.85i		−	0.614292i	0.951662	−	0.307146i	$-0.0993740\pi$
$542$	1032.30	+	11776.7i	0.0818102	+	0.933309i
$543$	4453.40	−	4369.32i	0.351959	−	0.345314i
$544$	11323.9	−	5291.90i	0.892482	−	0.417074i
$545$	10649.5			0.837018
$546$	−7930.63	−	11874.4i	−0.621611	−	0.930725i
$547$		−	9563.57i		−	0.747548i	−0.927520	−	0.373774i	$-0.878064\pi$
$547$		−	9563.57i		−	0.747548i	0.927520	−	0.373774i	$-0.121936\pi$
$548$	−479.935	−	2716.57i	−0.0374121	−	0.211763i
$549$	80.8828	−	4243.53i	0.00628779	−	0.329890i
$550$	1071.58	−	93.9304i	0.0830768	−	0.00728219i
$551$	−31984.3			−2.47291
$552$	18003.7	+	10612.4i	1.38820	+	0.818282i
$553$	3002.23	−	10662.6i	0.230864	−	0.819926i
$554$	643.514	+	7341.35i	0.0493507	+	0.563004i
$555$	−10019.9	+	9830.77i	−0.766347	+	0.751880i
$556$	9108.11	−	1609.13i	0.694730	−	0.122738i
$557$	−16797.4			−1.27779			−0.638894	−	0.769295i	$-0.720608\pi$
$557$	−16797.4			−1.27779			−0.638894	+	0.769295i	$0.720608\pi$
$558$	3974.61	−	272.187i	0.301539	−	0.0206498i
$559$		−	17327.4i		−	1.31104i
$560$	−10661.3	+	803.990i	−0.804502	+	0.0606693i
$561$	−2232.13	+	2189.99i	−0.167986	+	0.164815i
$562$	−1973.14	−	22510.0i	−0.148099	−	1.68955i
$563$		−	15342.1i		−	1.14848i	−0.818688	−	0.574239i	$-0.805298\pi$
$563$		−	15342.1i		−	1.14848i	0.818688	−	0.574239i	$-0.194702\pi$
$564$	1980.36	−	2773.60i	0.147851	−	0.207074i
$565$	16845.6			1.25434
$566$	−10206.5	+	894.658i	−0.757967	+	0.0664404i
$567$	−4151.80	+	12847.1i	−0.307512	+	0.951544i
$568$	1438.73	+	5358.74i	0.106282	+	0.395859i
$569$			23658.3i			1.74307i	0.490329	+	0.871537i	$0.336877\pi$
$569$			23658.3i			1.74307i	−0.490329	+	0.871537i	$0.663123\pi$
$570$	13026.8	+	11140.2i	0.957247	+	0.818620i
$571$			20556.7i			1.50661i	0.657673	+	0.753304i	$0.271541\pi$
$571$			20556.7i			1.50661i	−0.657673	+	0.753304i	$0.728459\pi$
$572$	−3601.91	+	636.348i	−0.263293	+	0.0465158i
$573$	−6472.62	−	6597.17i	−0.471898	−	0.480978i
$574$	−1809.27	+	9560.71i	−0.131563	+	0.695220i
$575$		−	7756.32i		−	0.562541i
$576$	−6694.66	−	12094.8i	−0.484278	−	0.874914i
$577$		−	1404.98i		−	0.101369i	−0.998715	−	0.0506847i	$-0.983860\pi$
$577$		−	1404.98i		−	0.101369i	0.998715	−	0.0506847i	$-0.0161404\pi$
$578$	−408.720	+	35.8268i	−0.0294127	+	0.00257820i
$579$	−560.291	+	549.713i	−0.0402157	+	0.0394565i
$580$	3105.57	+	17578.4i	0.222331	+	1.25846i
$581$	−70.1732	−	19.7584i	−0.00501080	−	0.00141087i
$582$	−8443.74	−	7220.93i	−0.601382	−	0.514291i
$583$	−2077.02			−0.147549
$584$	4371.67	+	16282.8i	0.309762	+	1.15375i
$585$	12774.0	+	243.476i	0.902806	+	0.0172077i
$586$	−2040.27	−	23275.8i	−0.143827	−	1.64081i
$587$			14366.9i			1.01020i	0.863062	+	0.505098i	$0.168544\pi$
$587$			14366.9i			1.01020i	−0.863062	+	0.505098i	$0.831456\pi$
$588$	13122.6	−	5576.22i	0.920354	−	0.391087i
$589$			6745.10i			0.471862i
$590$	−5047.21	+	442.418i	−0.352187	+	0.0308713i
$591$	−1284.83	+	1260.57i	−0.0894262	+	0.0877379i
$592$	6567.64	+	18007.2i	0.455960	+	1.25015i
$593$	5376.81			0.372343			0.186171	−	0.982517i	$-0.440392\pi$
$593$	5376.81			0.372343			0.186171	+	0.982517i	$0.440392\pi$
$594$	2585.06	+	2297.42i	0.178563	+	0.158694i
$595$	−11103.5	−	3126.37i	−0.765039	−	0.215410i
$596$	14570.0	−	2574.07i	1.00136	−	0.176910i
$597$	−13757.2	−	14022.0i	−0.943127	−	0.961274i
$598$	2303.01	+	26273.3i	0.157487	+	1.79665i
$599$		−	15516.0i		−	1.05837i	−0.848505	−	0.529187i	$-0.822497\pi$
$599$		−	15516.0i		−	1.05837i	0.848505	−	0.529187i	$-0.177503\pi$
$600$	−2605.33	+	4419.91i	−0.177271	+	0.300737i
$601$			28358.0i			1.92470i	0.271811	+	0.962351i	$0.412378\pi$
$601$			28358.0i			1.92470i	−0.271811	+	0.962351i	$0.587622\pi$
$602$	17000.3	+	3217.13i	1.15096	+	0.217808i
$603$	−14243.0	−	271.476i	−0.961891	−	0.0183339i
$604$	20703.6	−	3657.71i	1.39473	−	0.246407i
$605$			11320.7i			0.760745i
$606$	11680.6	+	9989.00i	0.782988	+	0.669596i
$607$		−	16509.3i		−	1.10394i	−0.833865	−	0.551969i	$-0.813877\pi$
$607$		−	16509.3i		−	1.10394i	0.833865	−	0.551969i	$-0.186123\pi$
$608$	21204.0	−	9909.05i	1.41437	−	0.660963i
$609$	−11442.4	−	20875.3i	−0.761364	−	1.38901i
$610$	−350.204	−	3995.21i	−0.0232449	−	0.265182i
$611$	4300.92			0.284773
$612$	−2314.45	−	14734.2i	−0.152870	−	0.973193i
$613$			8227.79i			0.542117i	0.962563	+	0.271058i	$0.0873736\pi$
$613$			8227.79i			0.542117i	−0.962563	+	0.271058i	$0.912626\pi$
$614$	−17964.2	+	1574.67i	−1.18074	+	0.103499i
$615$	−6097.35	−	6214.68i	−0.399787	−	0.407480i
$616$	44.4219	−	3652.05i	0.00290554	−	0.238872i
$617$			2275.68i			0.148485i	0.997240	+	0.0742425i	$0.0236539\pi$
$617$			2275.68i			0.148485i	−0.997240	+	0.0742425i	$0.976346\pi$
$618$	−16983.6	−	14524.1i	−1.10547	−	0.945380i
$619$	−19550.8			−1.26949			−0.634743	−	0.772723i	$-0.718894\pi$
$619$	−19550.8			−1.26949			−0.634743	+	0.772723i	$0.718894\pi$
$620$	3707.08	−	654.928i	0.240129	−	0.0424235i
$621$	18130.1	−	17122.0i	1.17155	−	1.10642i
$622$	10050.4	−	880.982i	0.647887	−	0.0567913i
$623$	6318.21	−	22439.5i	0.406314	−	1.44305i
$624$	7512.79	−	15745.3i	0.481975	−	1.01012i
$625$	−8266.21			−0.529037
$626$	−583.908	−	6661.35i	−0.0372806	−	0.425306i
$627$	−4179.64	+	4100.74i	−0.266218	+	0.261192i
$628$	−15041.6	+	2657.40i	−0.955776	+	0.168857i
$629$			20680.0i			1.31092i
$630$	−2610.60	+	12487.7i	−0.165093	+	0.789715i
$631$	25354.7			1.59961			0.799807	−	0.600257i	$-0.204935\pi$
$631$	25354.7			1.59961			0.799807	+	0.600257i	$0.204935\pi$
$632$	13070.8	−	3509.30i	0.822673	−	0.220874i
$633$	−7892.82	−	8044.69i	−0.495595	−	0.505131i
$634$	−14923.4	+	1308.12i	−0.934830	+	0.0819436i
$635$		−	8664.45i		−	0.541477i
$636$	5756.59	−	8062.42i	0.358905	−	0.502666i
$637$	15350.3	+	9388.60i	0.954791	+	0.583972i
$638$	−6074.64	+	532.479i	−0.376955	+	0.0330424i
$639$	6619.53	+	126.170i	0.409803	+	0.00781096i
$640$	−7504.82	−	10691.5i	−0.463522	−	0.660342i
$641$		−	1867.33i		−	0.115063i	−0.998344	−	0.0575313i	$-0.981677\pi$
$641$		−	1867.33i		−	0.115063i	0.998344	−	0.0575313i	$-0.0183229\pi$
$642$	−2705.77	+	3163.97i	−0.166337	+	0.194505i
$643$	5536.73			0.339576			0.169788	−	0.985481i	$-0.445692\pi$
$643$	5536.73			0.339576			0.169788	+	0.985481i	$0.445692\pi$
$644$	−26204.8	−	2618.55i	−1.60344	−	0.160226i
$645$	−11050.5	+	10841.9i	−0.674597	+	0.661861i
$646$	25155.6	−	2205.04i	1.53209	−	0.134297i
$647$	7249.89			0.440529			0.220265	−	0.975440i	$-0.429308\pi$
$647$	7249.89			0.440529			0.220265	+	0.975440i	$0.429308\pi$
$648$	−16082.6	+	3667.07i	−0.974976	+	0.222309i
$649$		−	1730.78i		−	0.104683i
$650$	−6450.10	+	565.390i	−0.389221	+	0.0341176i
$651$	−4402.35	+	2413.07i	−0.265041	+	0.145278i
$652$	−4814.14	−	27249.4i	−0.289166	−	1.63676i
$653$	5007.60			0.300096			0.150048	−	0.988679i	$-0.452057\pi$
$653$	5007.60			0.300096			0.150048	+	0.988679i	$0.452057\pi$
$654$	−13187.2	−	11277.4i	−0.788471	−	0.674286i
$655$	13330.5			0.795216
$656$	−11168.6	+	4073.45i	−0.664727	+	0.242441i
$657$	20113.8	+	383.374i	1.19439	+	0.0227654i
$658$	−798.538	+	4219.71i	−0.0473104	+	0.250002i
$659$	20066.4			1.18616			0.593078	−	0.805145i	$-0.297912\pi$
$659$	20066.4			1.18616			0.593078	+	0.805145i	$0.297912\pi$
$660$	2659.58	+	1898.95i	0.156855	+	0.111995i
$661$	24092.4			1.41768			0.708840	−	0.705369i	$-0.249219\pi$
$661$	24092.4			1.41768			0.708840	+	0.705369i	$0.249219\pi$
$662$	164.220	+	1873.46i	0.00964139	+	0.109991i
$663$	13435.7	−	13182.1i	0.787029	−	0.772171i
$664$	−23.0956	−	86.0225i	−0.00134983	−	0.00502759i
$665$	−20791.2	−	5854.11i	−1.21240	−	0.341373i
$666$	22818.0	−	1562.61i	1.32760	−	0.0909158i
$667$			43969.6i			2.55249i
$668$	−18167.2	+	3209.59i	−1.05226	+	0.185902i
$669$	14164.1	+	14436.7i	0.818560	+	0.834311i
$670$	−13409.5	+	1175.43i	−0.773217	+	0.0677772i
$671$	1370.03			0.0788217
$672$	14053.2	+	10294.3i	0.806715	+	0.590941i
$673$	−17.0224			−0.000974985			−0.000487493	−	1.00000i	$-0.500155\pi$
$673$	−17.0224			−0.000974985			−0.000487493		1.00000i	$0.500155\pi$
$674$	24282.7	−	2128.53i	1.38774	−	0.121644i
$675$	4203.46	+	4450.94i	0.239691	+	0.253802i
$676$	4372.82	−	772.545i	0.248795	−	0.0439546i
$677$			25059.2i			1.42261i	0.702885	+	0.711304i	$0.251895\pi$
$677$			25059.2i			1.42261i	−0.702885	+	0.711304i	$0.748105\pi$
$678$	−20859.8	−	17838.9i	−1.18159	−	1.01047i
$679$	13476.5	+	3794.55i	0.761682	+	0.214464i
$680$	−3654.41	−	13611.3i	−0.206089	−	0.767603i
$681$	−9260.84	−	9439.04i	−0.521110	−	0.531137i
$682$	112.293	+	1281.07i	0.00630489	+	0.0719276i
$683$	−22610.8			−1.26673			−0.633367	−	0.773851i	$-0.718328\pi$
$683$	−22610.8			−1.26673			−0.633367	+	0.773851i	$0.718328\pi$
$684$	−4333.80	−	27589.7i	−0.242262	−	1.54228i
$685$	−3110.41			−0.173493
$686$	−12061.4	+	13317.3i	−0.671292	+	0.741193i
$687$	−2878.06	+	2823.73i	−0.159832	+	0.156815i
$688$	7243.16	+	19859.3i	0.401370	+	1.10048i
$689$	12502.1			0.691280
$690$	15314.8	−	17908.2i	0.844961	−	0.988049i
$691$	−22189.8			−1.22162			−0.610810	−	0.791777i	$-0.709156\pi$
$691$	−22189.8			−1.22162			−0.610810	+	0.791777i	$0.709156\pi$
$692$	25.2275	+	142.795i	0.00138585	+	0.00784428i
$693$	−4171.72	−	1260.90i	−0.228673	−	0.0691162i
$694$	−32473.7	+	2846.52i	−1.77620	+	0.155695i
$695$		−	10428.6i		−	0.569179i
$696$	14769.3	−	25055.9i	0.804352	−	1.36457i
$697$	−12826.4			−0.697036
$698$	−656.416	+	57.5388i	−0.0355955	+	0.00312017i
$699$	−1731.57	−	1764.88i	−0.0936964	−	0.0954993i
$700$	642.855	−	6433.29i	0.0347109	−	0.347365i
$701$	−9475.27			−0.510522			−0.255261	−	0.966872i	$-0.582161\pi$
$701$	−9475.27			−0.510522			−0.255261	+	0.966872i	$0.582161\pi$
$702$	−15560.1	−	13828.7i	−0.836580	−	0.743493i
$703$			38723.2i			2.07749i
$704$	3862.22	−	2234.99i	0.206766	−	0.119651i
$705$	−2691.13	−	2742.91i	−0.143764	−	0.146530i
$706$	−30981.3	+	2715.70i	−1.65156	+	0.144769i
$707$	−18642.6	−	5249.15i	−0.991696	−	0.279228i
$708$	6718.41	+	4796.96i	0.356629	+	0.254634i
$709$		−	27170.6i		−	1.43923i	−0.694374	−	0.719614i	$-0.744319\pi$
$709$		−	27170.6i		−	1.43923i	0.694374	−	0.719614i	$-0.255681\pi$
$710$	6232.16	−	546.287i	0.329421	−	0.0288757i
$711$	307.748	−	16146.1i	0.0162327	−	0.851653i
$712$	27507.6	−	7385.35i	1.44788	−	0.388733i
$713$	9272.65			0.487046
$714$	10438.6	+	15629.5i	0.547137	+	0.819217i
$715$			4124.11i			0.215711i
$716$	20451.4	−	3613.14i	1.06746	−	0.188589i
$717$	−1075.93	−	1096.63i	−0.0560407	−	0.0571190i
$718$	−921.826	−	10516.4i	−0.0479140	−	0.546613i
$719$	387.852			0.0201174			0.0100587	−	0.999949i	$-0.496798\pi$
$719$	387.852			0.0201174			0.0100587	+	0.999949i	$0.496798\pi$
$720$	−14742.4	+	5060.72i	−0.763078	+	0.261947i
$721$	27106.6	+	7632.31i	1.40014	+	0.394233i
$722$	27777.6	−	2434.88i	1.43182	−	0.125508i
$723$	11953.8	+	12183.9i	0.614894	+	0.626726i
$724$	−9458.92	+	1671.10i	−0.485550	+	0.0857819i
$725$	−10794.5			−0.552964
$726$	11988.2	−	14018.3i	0.612841	−	0.716621i
$727$		−	1084.95i		−	0.0553488i	−0.999617	−	0.0276744i	$-0.991190\pi$
$727$		−	1084.95i		−	0.0553488i	0.999617	−	0.0276744i	$-0.00881016\pi$
$728$	−267.387	+	21982.6i	−0.0136127	+	1.11913i
$729$	−1124.74	+	19650.8i	−0.0571427	+	0.998366i
$730$	18936.8	−	1659.92i	0.960111	−	0.0841596i
$731$			22807.1i			1.15397i
$732$	−3797.12	+	5318.08i	−0.191729	+	0.268527i
$733$	−35437.5			−1.78570			−0.892848	−	0.450358i	$-0.851296\pi$
$733$	−35437.5			−1.78570			−0.892848	+	0.450358i	$0.851296\pi$
$734$	−293.299	−	3346.02i	−0.0147491	−	0.168262i
$735$	−3617.27	−	15664.2i	−0.181531	−	0.786099i
$736$	−13622.2	−	29149.7i	−0.682231	−	1.45988i
$737$		−	4598.37i		−	0.229828i
$738$	969.180	+	14152.4i	0.0483415	+	0.705906i
$739$		−	34674.6i		−	1.72601i	−0.505192	−	0.863007i	$-0.668578\pi$
$739$		−	34674.6i		−	1.72601i	0.505192	−	0.863007i	$-0.331422\pi$
$740$	21282.1	−	3759.90i	1.05722	−	0.186780i
$741$	25158.3	−	24683.4i	1.24725	−	1.22371i
$742$	−2321.23	+	12266.1i	−0.114845	+	0.606875i
$743$			22561.8i			1.11401i	0.830508	+	0.557007i	$0.188050\pi$
$743$			22561.8i			1.11401i	−0.830508	+	0.557007i	$0.811950\pi$
$744$	−5283.99	−	3114.67i	−0.260377	−	0.153480i
$745$		−	16682.3i		−	0.820394i
$746$	1203.39	+	13728.6i	0.0590608	+	0.673779i
$747$	−106.262	−	2.02537i	−0.00520470	−	9.92029e-5i
$748$	4740.98	−	837.588i	0.231748	−	0.0409429i
$749$	1421.86	−	5049.82i	0.0693641	−	0.246351i
$750$	16990.4	+	14529.8i	0.827200	+	0.707406i
$751$	−28928.9			−1.40563			−0.702816	−	0.711372i	$-0.748074\pi$
$751$	−28928.9			−1.40563			−0.702816	+	0.711372i	$0.748074\pi$
$752$	−4929.38	+	1797.86i	−0.239037	+	0.0871823i
$753$	3746.92	+	3819.02i	0.181335	+	0.184824i
$754$	36564.8	−	3205.12i	1.76606	−	0.154806i
$755$		−	23705.3i		−	1.14268i
$756$	16456.6	−	12698.8i	0.791696	−	0.610915i
$757$			19462.5i			0.934449i	0.884139	+	0.467224i	$0.154746\pi$
$757$			19462.5i			0.934449i	−0.884139	+	0.467224i	$0.845254\pi$
$758$	980.446	+	11185.1i	0.0469807	+	0.535966i
$759$	5637.39	+	5745.86i	0.269597	+	0.274785i
$760$	−6842.87	−	25487.1i	−0.326601	−	1.21647i
$761$	−5992.80			−0.285465			−0.142732	−	0.989761i	$-0.545589\pi$
$761$	−5992.80			−0.285465			−0.142732	+	0.989761i	$0.545589\pi$
$762$	−9175.33	+	10729.1i	−0.436204	+	0.510071i
$763$	21047.3	+	5926.21i	0.998640	+	0.281184i
$764$	2475.54	+	14012.2i	0.117227	+	0.663540i
$765$	−16813.7	−	320.474i	−0.794643	−	0.0151461i
$766$	−8400.62	+	736.365i	−0.396249	+	0.0347336i
$767$			10418.0i			0.490446i
$768$	−2028.76	+	21186.5i	−0.0953212	+	0.995447i
$769$			15433.8i			0.723742i	0.932228	+	0.361871i	$0.117862\pi$
$769$			15433.8i			0.723742i	−0.932228	+	0.361871i	$0.882138\pi$
$770$	−4046.25	−	765.712i	−0.189372	−	0.0358368i
$771$	9094.10	−	8922.42i	0.424794	−	0.416774i
$772$	1190.05	−	210.245i	0.0554801	−	0.00980166i
$773$			17828.8i			0.829569i	0.909920	+	0.414785i	$0.136143\pi$
$773$			17828.8i			0.829569i	−0.909920	+	0.414785i	$0.863857\pi$
$774$	25165.0	−	1723.33i	1.16865	−	0.0800310i
$775$			2276.44i			0.105512i
$776$	4435.44	+	16520.3i	0.205184	+	0.764234i
$777$	−25273.6	+	13853.3i	−1.16691	+	0.639619i
$778$	−1346.19	+	118.002i	−0.0620349	+	0.00543774i
$779$	−24017.3			−1.10463
$780$	−16008.7	−	11430.2i	−0.734875	−	0.524703i
$781$			2137.12i			0.0979157i
$782$	−3031.32	−	34582.0i	−0.138619	−	1.58139i
$783$	−23828.9	−	25231.8i	−1.08758	−	1.15161i
$784$	−21517.9	−	4343.79i	−0.980227	−	0.197877i
$785$			17222.4i			0.783049i
$786$	−16507.1	−	14116.5i	−0.749093	−	0.640611i
$787$	30953.0			1.40197			0.700987	−	0.713174i	$-0.252743\pi$
$787$	30953.0			1.40197			0.700987	+	0.713174i	$0.252743\pi$
$788$	2728.95	−	482.123i	0.123369	−	0.0217956i
$789$	−15999.1	−	16306.9i	−0.721904	−	0.735795i
$790$	−1332.48	−	15201.2i	−0.0600095	−	0.684602i
$791$	33293.1	+	9374.22i	1.49654	+	0.421377i
$792$	−1282.42	−	5167.85i	−0.0575363	−	0.231858i
$793$	−8246.55			−0.369286
$794$	18992.5	−	1664.81i	0.848888	−	0.0744102i
$795$	−7822.69	−	7973.21i	−0.348984	−	0.355699i
$796$	5261.63	+	29782.3i	0.234289	+	1.32614i
$797$			7162.07i			0.318310i	0.987254	+	0.159155i	$0.0508770\pi$
$797$			7162.07i			0.318310i	−0.987254	+	0.159155i	$0.949123\pi$
$798$	19546.3	+	29266.2i	0.867081	+	1.29826i
$799$	−5661.05			−0.250655
$800$	7156.26	−	3344.26i	0.316265	−	0.147797i
$801$	647.659	−	33979.5i	0.0285692	−	1.49889i
$802$	−2652.55	−	30260.9i	−0.116789	−	1.33236i
$803$			6493.76i			0.285380i
$804$	17849.6	+	12744.7i	0.782970	+	0.559043i
$805$	−8047.79	+	28582.2i	−0.352357	+	1.25142i
$806$	−675.922	−	7711.07i	−0.0295389	−	0.336986i
$807$	12382.6	+	12620.9i	0.540134	+	0.550527i
$808$	−6135.73	−	22853.3i	−0.267146	−	0.995019i
$809$		−	21655.6i		−	0.941125i	−0.882367	−	0.470562i	$-0.844051\pi$
$809$		−	21655.6i		−	0.941125i	0.882367	−	0.470562i	$-0.155949\pi$
$810$	916.863	+	18576.2i	0.0397720	+	0.805806i
$811$	−2523.86			−0.109278			−0.0546392	−	0.998506i	$-0.517401\pi$
$811$	−2523.86			−0.109278			−0.0546392	+	0.998506i	$0.517401\pi$
$812$	−3644.26	+	36469.5i	−0.157498	+	1.57614i
$813$	−15210.0	−	15502.7i	−0.656137	−	0.668762i
$814$	644.670	+	7354.53i	0.0277588	+	0.316678i
$815$	−31200.0			−1.34097
$816$	−9888.65	+	20724.6i	−0.424230	+	0.889102i
$817$			42706.1i			1.82876i
$818$	−3797.26	−	43320.0i	−0.162308	−	1.85165i
$819$	25110.6	+	7589.66i	1.07135	+	0.323815i
$820$	2332.01	+	13199.8i	0.0993138	+	0.562144i
$821$	24747.6			1.05200			0.526002	−	0.850483i	$-0.323690\pi$
$821$	24747.6			1.05200			0.526002	+	0.850483i	$0.323690\pi$
$822$	3851.60	+	3293.81i	0.163430	+	0.139763i
$823$	−35614.1			−1.50842			−0.754210	−	0.656634i	$-0.771980\pi$
$823$	−35614.1			−1.50842			−0.754210	+	0.656634i	$0.771980\pi$
$824$	8921.40	+	33228.8i	0.377174	+	1.40483i
$825$	−1410.61	+	1383.98i	−0.0595287	+	0.0584048i
$826$	−10221.3	−	1934.28i	−0.430562	−	0.0814795i
$827$	−29256.6			−1.23017			−0.615085	−	0.788461i	$-0.710878\pi$
$827$	−29256.6			−1.23017			−0.615085	+	0.788461i	$0.710878\pi$
$828$	−37928.2	+	5957.79i	−1.59191	+	0.250057i
$829$	14291.2			0.598740			0.299370	−	0.954137i	$-0.403224\pi$
$829$	14291.2			0.598740			0.299370	+	0.954137i	$0.403224\pi$
$830$	−100.043	+	8.76941i	−0.00418380	+	0.000366736i
$831$	−9481.61	−	9664.05i	−0.395804	−	0.403420i
$832$	−23247.7	+	13453.0i	−0.968712	+	0.560575i
$833$	−20204.7	−	12357.7i	−0.840399	−	0.514007i
$834$	−11043.5	+	12913.6i	−0.458520	+	0.536167i
$835$			20801.0i			0.862095i
$836$	8877.47	−	1568.38i	0.367265	−	0.0648846i
$837$	−5321.08	+	5025.23i	−0.219741	+	0.207524i
$838$	447.531	+	5105.53i	0.0184483	+	0.210462i
$839$	−43247.8			−1.77959			−0.889796	−	0.456358i	$-0.849154\pi$
$839$	−43247.8			−1.77959			−0.889796	+	0.456358i	$0.849154\pi$
$840$	14186.7	−	13584.2i	0.582724	−	0.557976i
$841$	36803.8			1.50903
$842$	−392.251	−	4474.89i	−0.0160545	−	0.183153i
$843$	29072.4	+	29631.8i	1.18779	+	1.21064i
$844$	3018.71	+	17086.7i	0.123114	+	0.696860i
$845$		−	5006.79i		−	0.203833i
$846$	427.757	+	6246.32i	0.0173837	+	0.253845i
$847$	−6299.69	+	22373.7i	−0.255561	+	0.907639i
$848$	−14328.9	+	5226.09i	−0.580257	+	0.211633i
$849$	13435.6	−	13182.0i	0.543121	−	0.532868i
$850$	8489.89	−	744.191i	0.342589	−	0.0300300i
$851$	53233.7			2.14434
$852$	−8295.72	−	5923.17i	−0.333576	−	0.238174i
$853$	−27143.0			−1.08952			−0.544758	−	0.838593i	$-0.683378\pi$
$853$	−27143.0			−1.08952			−0.544758	+	0.838593i	$0.683378\pi$
$854$	1531.11	−	8090.85i	0.0613508	−	0.324196i
$855$	−31483.6	−	600.086i	−1.25932	−	0.0240029i
$856$	6190.37	−	1662.01i	0.247176	−	0.0663627i
$857$	−41131.4			−1.63947			−0.819733	−	0.572746i	$-0.805878\pi$
$857$	−41131.4			−1.63947			−0.819733	+	0.572746i	$0.805878\pi$
$858$	4367.28	−	5106.85i	0.173772	−	0.203199i
$859$	−3353.69			−0.133209			−0.0666045	−	0.997779i	$-0.521217\pi$
$859$	−3353.69			−0.133209			−0.0666045	+	0.997779i	$0.521217\pi$
$860$	23471.1	−	4146.63i	0.930649	−	0.164417i
$861$	−8592.24	−	15675.5i	−0.340096	−	0.620463i
$862$	−559.765	−	6385.93i	−0.0221180	−	0.252327i
$863$			32515.9i			1.28257i	0.767304	+	0.641283i	$0.221598\pi$
$863$			32515.9i			1.28257i	−0.767304	+	0.641283i	$0.778402\pi$
$864$	23614.5	+	9345.01i	0.929839	+	0.367967i
$865$	163.497			0.00642667
$866$	3186.09	+	36347.6i	0.125021	+	1.42626i
$867$	538.033	−	527.876i	0.0210756	−	0.0206777i
$868$	7690.98	+	768.530i	0.300748	+	0.0300526i
$869$	5212.78			0.203488
$870$	−24923.0	−	21313.7i	−0.971228	−	0.830577i
$871$			27678.8i			1.07676i
$872$	6927.14	+	25801.0i	0.269017	+	1.00199i
$873$	20407.2	+	388.966i	0.791156	+	0.0150796i
$874$	−5676.14	−	64754.6i	−0.219678	−	2.50613i
$875$	−27117.3	−	7635.33i	−1.04769	−	0.294996i
$876$	−25207.0	−	17997.9i	−0.972221	−	0.694168i
$877$		−	11908.4i		−	0.458517i	−0.973366	−	0.229259i	$-0.926370\pi$
$877$		−	11908.4i		−	0.458517i	0.973366	−	0.229259i	$-0.0736301\pi$
$878$	−933.290	−	10647.2i	−0.0358736	−	0.409254i
$879$	30061.5	+	30640.0i	1.15353	+	1.17572i
$880$	−1723.95	−	4726.74i	−0.0660390	−	0.181066i
$881$	36671.3			1.40237			0.701184	−	0.712980i	$-0.252655\pi$
$881$	36671.3			1.40237			0.701184	+	0.712980i	$0.252655\pi$
$882$	−12108.6	+	23227.4i	−0.462264	+	0.886742i
$883$		−	37102.7i		−	1.41405i	−0.707190	−	0.707024i	$-0.750037\pi$
$883$		−	37102.7i		−	1.41405i	0.707190	−	0.707024i	$-0.249963\pi$
$884$	−28537.2	+	5041.65i	−1.08576	+	0.191820i
$885$	6644.07	−	6518.64i	0.252359	−	0.247595i
$886$	1048.20	−	91.8812i	0.0397461	−	0.00348399i
$887$	48774.0			1.84630			0.923152	−	0.384435i	$-0.125604\pi$
$887$	48774.0			1.84630			0.923152	+	0.384435i	$0.125604\pi$
$888$	−30335.0	−	17881.1i	−1.14637	−	0.675733i
$889$	4821.57	−	17124.1i	0.181901	−	0.646033i
$890$	−2804.22	−	31991.1i	−0.105615	−	1.20488i
$891$	−6348.91	−	242.112i	−0.238717	−	0.00910330i
$892$	−5417.25	−	30663.2i	−0.203344	−	1.15098i
$893$	−10600.3			−0.397228
$894$	−17666.0	+	20657.6i	−0.660893	+	0.772811i
$895$		−	23416.4i		−	0.874553i
$896$	−8882.66	−	25306.6i	−0.331193	−	0.943563i
$897$	−33932.8	−	34585.8i	−1.26308	−	1.28739i
$898$	3047.84	+	34770.4i	0.113260	+	1.29210i
$899$		−	12904.8i		−	0.478754i
$900$	−1462.64	−	9311.39i	−0.0541718	−	0.344866i
$901$	−16455.8			−0.608459
$902$	−4561.51	+	399.844i	−0.168383	+	0.0147598i
$903$	−27873.2	+	15278.2i	−1.02720	+	0.563041i
$904$	10957.5	+	40812.6i	0.403143	+	1.50156i
$905$			10830.3i			0.397801i
$906$	−25103.0	+	29354.0i	−0.920520	+	1.07640i
$907$		−	1891.26i		−	0.0692372i	−0.999401	−	0.0346186i	$-0.988978\pi$
$907$		−	1891.26i		−	0.0692372i	0.999401	−	0.0346186i	$-0.0110216\pi$
$908$	3541.93	+	20048.3i	0.129453	+	0.732738i
$909$	−28230.1	−	538.073i	−1.03007	−	0.0196334i
$910$	24355.4	+	4609.01i	0.887223	+	0.167898i
$911$			674.242i			0.0245210i	0.999925	+	0.0122605i	$0.00390274\pi$
$911$			674.242i			0.0245210i	−0.999925	+	0.0122605i	$0.996097\pi$
$912$	−18516.4	+	38806.8i	−0.672303	+	1.40901i
$913$		−	34.3067i		−	0.00124358i
$914$	−37333.3	+	3272.49i	−1.35107	+	0.118429i
$915$	5159.95	+	5259.23i	0.186429	+	0.190016i
$916$	6112.94	−	1079.97i	0.220499	−	0.0389555i
$917$	26345.9	+	7418.13i	0.948767	+	0.267141i
$918$	20480.9	+	18202.0i	0.736352	+	0.654416i
$919$	−246.949			−0.00886408			−0.00443204	−	0.999990i	$-0.501411\pi$
$919$	−246.949			−0.00886408			−0.00443204	+	0.999990i	$0.501411\pi$
$920$	−35037.8	+	9407.06i	−1.25561	+	0.337111i
$921$	23647.8	−	23201.4i	0.846060	−	0.830088i
$922$	822.099	+	9378.69i	0.0293648	+	0.335001i
$923$		−	12863.9i		−	0.458742i
$924$	4199.57	+	5233.00i	0.149519	+	0.186313i
$925$			13068.9i			0.464543i
$926$	11707.3	−	1026.22i	0.415471	−	0.0364185i
$927$	41046.8	+	782.363i	1.45432	+	0.0277197i
$928$	−40567.9	+	18958.2i	−1.43503	+	0.670617i
$929$	26737.6			0.944275			0.472138	−	0.881525i	$-0.343483\pi$
$929$	26737.6			0.944275			0.472138	+	0.881525i	$0.343483\pi$
$930$	−4494.80	+	5255.96i	−0.158484	+	0.185322i
$931$	−37833.3	−	23139.7i	−1.33183	−	0.814578i
$932$	662.259	+	3748.57i	0.0232758	+	0.131747i
$933$	−13230.3	+	12980.5i	−0.464243	+	0.455479i
$934$	−122.975	−	1402.93i	−0.00430821	−	0.0491490i
$935$		−	5428.33i		−	0.189867i
$936$	7719.20	+	31106.6i	0.269562	+	1.08627i
$937$		−	12780.7i		−	0.445602i	−0.974864	−	0.222801i	$-0.928480\pi$
$937$		−	12780.7i		−	0.445602i	0.974864	−	0.222801i	$-0.0715200\pi$
$938$	−27156.2	−	5139.03i	−0.945289	−	0.178886i
$939$	8603.37	+	8768.91i	0.298999	+	0.304753i
$940$	1029.26	+	5825.87i	0.0357134	+	0.202148i
$941$			43874.1i			1.51993i	0.649963	+	0.759966i	$0.274784\pi$
$941$			43874.1i			1.51993i	−0.649963	+	0.759966i	$0.725216\pi$
$942$	18237.9	−	21326.3i	0.630809	−	0.737631i
$943$			33017.2i			1.14018i
$944$	−4354.90	−	11940.3i	−0.150148	−	0.411677i
$945$	−10871.7	−	20763.2i	−0.374238	−	0.714738i
$946$	710.978	+	8110.99i	0.0244354	+	0.278764i
$947$	−2594.12			−0.0890153			−0.0445077	−	0.999009i	$-0.514172\pi$
$947$	−2594.12			−0.0890153			−0.0445077	+	0.999009i	$0.514172\pi$
$948$	−14447.5	+	20234.6i	−0.494973	+	0.693237i
$949$		−	39087.6i		−	1.33702i
$950$	15897.3	−	1393.49i	0.542922	−	0.0475904i
$951$	19644.9	−	19274.0i	0.669852	−	0.657206i
$952$	351.946	−	28934.5i	0.0119818	−	0.985054i
$953$		−	35759.6i		−	1.21550i	−0.794130	−	0.607748i	$-0.792073\pi$
$953$		−	35759.6i		−	1.21550i	0.794130	−	0.607748i	$-0.207927\pi$
$954$	1243.42	+	18157.1i	0.0421984	+	0.616203i
$955$	16043.7			0.543626
$956$	411.501	+	2329.21i	0.0139215	+	0.0787993i
$957$	7996.56	−	7845.60i	0.270107	−	0.265008i
$958$	56501.3	−	4952.68i	1.90550	−	0.167029i
$959$	−6147.30	−	1730.87i	−0.206993	−	0.0582824i
$960$	23125.9	+	6408.55i	0.777486	+	0.215453i
$961$	27069.5			0.908648
$962$	−3880.43	−	44268.8i	−0.130052	−	1.48366i
$963$	145.750	−	7646.82i	0.00487720	−	0.255883i
$964$	−4571.90	−	25878.2i	−0.152750	−	0.864608i
$965$		−	1362.58i		−	0.0454538i
$966$	40233.0	−	26870.8i	1.34004	−	0.894982i
$967$	950.541			0.0316105			0.0158052	−	0.999875i	$-0.494969\pi$
$967$	950.541			0.0316105			0.0158052	+	0.999875i	$0.494969\pi$
$968$	−27427.0	+	7363.71i	−0.910680	+	0.244503i
$969$	−33114.5	+	32489.3i	−1.09782	+	1.07710i
$970$	19213.0	−	1684.14i	0.635971	−	0.0557468i
$971$		−	59078.8i		−	1.95255i	−0.216531	−	0.976276i	$-0.569474\pi$
$971$		−	59078.8i		−	1.95255i	0.216531	−	0.976276i	$-0.430526\pi$
$972$	18536.2	−	23973.7i	0.611676	−	0.791108i
$973$	5803.28	−	20610.7i	0.191207	−	0.679084i
$974$	−16675.1	+	1461.67i	−0.548567	+	0.0480852i
$975$	8490.82	−	8330.52i	0.278896	−	0.273631i
$976$	9451.56	−	3447.20i	0.309976	−	0.113056i
$977$			14531.7i			0.475854i	0.971283	+	0.237927i	$0.0764678\pi$
$977$			14531.7i			0.475854i	−0.971283	+	0.237927i	$0.923532\pi$
$978$	38634.7	+	33039.6i	1.26319	+	1.08026i
$979$	10970.3			0.358134
$980$	−9043.98	+	23039.8i	−0.294795	+	0.751000i
$981$	31871.4	+	607.477i	1.03728	+	0.0197709i
$982$	7288.18	−	638.853i	0.236838	−	0.0207603i
$983$	58495.3			1.89798			0.948989	−	0.315310i	$-0.102109\pi$
$983$	58495.3			1.89798			0.948989	+	0.315310i	$0.102109\pi$
$984$	11090.4	−	18814.7i	0.359299	−	0.609545i
$985$		−	3124.59i		−	0.101074i
$986$	−48128.1	+	4218.72i	−1.55447	+	0.136259i
$987$	−3792.27	−	6918.53i	−0.122299	−	0.223120i
$988$	−53435.7	+	9440.47i	−1.72066	+	0.303989i
$989$	58709.2			1.88761
$990$	−5989.54	+	410.172i	−0.192283	+	0.0131678i
$991$	−29846.4			−0.956714			−0.478357	−	0.878166i	$-0.658767\pi$
$991$	−29846.4			−0.956714			−0.478357	+	0.878166i	$0.658767\pi$
$992$	3998.05	+	8555.28i	0.127962	+	0.273821i
$993$	−2419.64	−	2466.20i	−0.0773262	−	0.0788141i
$994$	12621.0	+	2388.40i	0.402730	+	0.0762126i
$995$	34100.2			1.08648
$996$	133.169	+	95.0831i	0.00423657	+	0.00302492i
$997$	14935.8			0.474444			0.237222	−	0.971455i	$-0.423763\pi$
$997$	14935.8			0.474444			0.237222	+	0.971455i	$0.423763\pi$
$998$	−4508.44	−	51433.3i	−0.142998	−	1.63135i
$999$	−30548.0	+	28849.5i	−0.967463	+	0.913672i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.i.c.125.77	yes	80
3.2	odd	2	inner	168.4.i.c.125.3	yes	80
4.3	odd	2		672.4.i.c.209.58		80
7.6	odd	2	inner	168.4.i.c.125.78	yes	80
8.3	odd	2		672.4.i.c.209.23		80
8.5	even	2	inner	168.4.i.c.125.2	yes	80
12.11	even	2		672.4.i.c.209.59		80
21.20	even	2	inner	168.4.i.c.125.4	yes	80
24.5	odd	2	inner	168.4.i.c.125.80	yes	80
24.11	even	2		672.4.i.c.209.22		80
28.27	even	2		672.4.i.c.209.24		80
56.13	odd	2	inner	168.4.i.c.125.1	✓	80
56.27	even	2		672.4.i.c.209.57		80
84.83	odd	2		672.4.i.c.209.21		80
168.83	odd	2		672.4.i.c.209.60		80
168.125	even	2	inner	168.4.i.c.125.79	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.i.c.125.1	✓	80	56.13	odd	2	inner
168.4.i.c.125.2	yes	80	8.5	even	2	inner
168.4.i.c.125.3	yes	80	3.2	odd	2	inner
168.4.i.c.125.4	yes	80	21.20	even	2	inner
168.4.i.c.125.77	yes	80	1.1	even	1	trivial
168.4.i.c.125.78	yes	80	7.6	odd	2	inner
168.4.i.c.125.79	yes	80	168.125	even	2	inner
168.4.i.c.125.80	yes	80	24.5	odd	2	inner
672.4.i.c.209.21		80	84.83	odd	2
672.4.i.c.209.22		80	24.11	even	2
672.4.i.c.209.23		80	8.3	odd	2
672.4.i.c.209.24		80	28.27	even	2
672.4.i.c.209.57		80	56.27	even	2
672.4.i.c.209.58		80	4.3	odd	2
672.4.i.c.209.59		80	12.11	even	2
672.4.i.c.209.60		80	168.83	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	168.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.81762 - 0.246982i) q^{2} +(-3.70908 + 3.63906i) q^{3} +(7.87800 - 1.39180i) q^{4} -9.02015i q^{5} +(-9.55201 + 11.1696i) q^{6} +(5.01951 - 17.8271i) q^{7} +(21.8535 - 5.86730i) q^{8} +(0.514533 - 26.9951i) q^{9} +(-2.22781 - 25.4154i) q^{10} +8.71540 q^{11} +(-24.1553 + 33.8308i) q^{12} -52.4602 q^{13} +(9.74012 - 51.4697i) q^{14} +(32.8248 + 33.4564i) q^{15} +(60.1258 - 21.9293i) q^{16} +69.0503 q^{17} +(-5.21754 - 76.1891i) q^{18} +129.296 q^{19} +(-12.5543 - 71.0607i) q^{20} +(46.2560 + 84.3883i) q^{21} +(24.5567 - 2.15254i) q^{22} -177.747i q^{23} +(-59.7049 + 101.288i) q^{24} +43.6369 q^{25} +(-147.813 + 12.9567i) q^{26} +(96.3282 + 101.999i) q^{27} +(14.7319 - 147.428i) q^{28} -247.372 q^{29} +(100.751 + 86.1605i) q^{30} +52.1678i q^{31} +(163.996 - 76.6384i) q^{32} +(-32.3261 + 31.7158i) q^{33} +(194.558 - 17.0542i) q^{34} +(-160.803 - 45.2767i) q^{35} +(-33.5184 - 213.384i) q^{36} +299.492i q^{37} +(364.308 - 31.9338i) q^{38} +(194.579 - 190.905i) q^{39} +(-52.9239 - 197.122i) q^{40} -185.754 q^{41} +(151.174 + 226.350i) q^{42} +330.296i q^{43} +(68.6599 - 12.1301i) q^{44} +(-243.500 - 4.64117i) q^{45} +(-43.9002 - 500.824i) q^{46} -81.9844 q^{47} +(-143.209 + 300.138i) q^{48} +(-292.609 - 178.966i) q^{49} +(122.952 - 10.7775i) q^{50} +(-256.113 + 251.278i) q^{51} +(-413.281 + 73.0142i) q^{52} -238.316 q^{53} +(296.609 + 263.604i) q^{54} -78.6142i q^{55} +(5.09695 - 419.035i) q^{56} +(-479.570 + 470.517i) q^{57} +(-697.001 + 61.0964i) q^{58} -198.589i q^{59} +(305.159 + 217.884i) q^{60} +157.196 q^{61} +(12.8845 + 146.989i) q^{62} +(-478.661 - 144.675i) q^{63} +(443.150 - 256.442i) q^{64} +473.198i q^{65} +(-83.2495 + 97.3472i) q^{66} -527.615i q^{67} +(543.978 - 96.1044i) q^{68} +(646.831 + 659.277i) q^{69} +(-464.264 - 87.8573i) q^{70} +245.212i q^{71} +(-147.144 - 592.956i) q^{72} +745.090i q^{73} +(73.9691 + 843.855i) q^{74} +(-161.853 + 158.797i) q^{75} +(1018.60 - 179.955i) q^{76} +(43.7470 - 155.370i) q^{77} +(501.100 - 585.957i) q^{78} +598.112 q^{79} +(-197.805 - 542.343i) q^{80} +(-728.471 - 27.7798i) q^{81} +(-523.385 + 45.8779i) q^{82} -3.93633i q^{83} +(481.857 + 600.432i) q^{84} -622.844i q^{85} +(81.5772 + 930.651i) q^{86} +(917.522 - 900.200i) q^{87} +(190.462 - 51.1359i) q^{88} +1258.73 q^{89} +(-687.237 + 47.0630i) q^{90} +(-263.324 + 935.211i) q^{91} +(-247.389 - 1400.29i) q^{92} +(-189.841 - 193.494i) q^{93} +(-231.001 + 20.2487i) q^{94} -1166.27i q^{95} +(-329.381 + 881.047i) q^{96} +755.959i q^{97} +(-868.663 - 431.990i) q^{98} +(4.48436 - 235.273i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 28 q^{4} + 64 q^{7} + 104 q^{9} - 8 q^{15} - 892 q^{16} + 692 q^{18} + 128 q^{22} - 976 q^{25} + 612 q^{28} - 332 q^{30} + 1544 q^{36} + 568 q^{39} + 780 q^{42} + 208 q^{46} - 4048 q^{49} - 1448 q^{57}+ \cdots - 2072 q^{88}+O(q^{100}) \) 80 * q + 28 * q^4 + 64 * q^7 + 104 * q^9 - 8 * q^15 - 892 * q^16 + 692 * q^18 + 128 * q^22 - 976 * q^25 + 612 * q^28 - 332 * q^30 + 1544 * q^36 + 568 * q^39 + 780 * q^42 + 208 * q^46 - 4048 * q^49 - 1448 * q^57 - 1760 * q^58 + 4156 * q^60 - 2152 * q^63 + 2764 * q^64 + 1968 * q^70 - 2740 * q^72 - 3620 * q^78 + 4992 * q^79 + 1568 * q^81 + 2484 * q^84 - 2072 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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