LMFDB - Embedded newform 168.4.i.c.125.1

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			125.1
Character	$\chi$	$=$	168.125
Dual form			168.4.i.c.125.3

$q$-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} +(11.3496 - 9.33741i) 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} +(-34.2850 + 23.5062i) 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} +(-8.11706 + 75.9349i) q^{18} +129.296 q^{19} +(12.5543 - 71.0607i) q^{20} +(-83.4915 - 47.8557i) q^{21} +(24.5567 + 2.15254i) q^{22} -177.747i q^{23} +(102.408 - 57.7638i) 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} +(-84.2249 - 102.375i) 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} +(41.6254 - 211.951i) 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} +(223.428 + 155.460i) 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} +(-302.813 + 137.464i) 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} +(-246.225 - 311.187i) 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} +(212.029 + 309.256i) q^{60} +157.196 q^{61} +(-12.8845 + 146.989i) q^{62} +(483.826 - 126.329i) q^{63} +(443.150 + 256.442i) q^{64} +473.198i q^{65} +(-98.9160 + 81.3793i) 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} +(-169.633 + 586.918i) 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} +(-595.400 + 489.842i) 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} +(-591.140 - 493.211i) 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} +(684.944 + 73.2171i) 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} +(887.164 - 312.532i) 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	$-0.132169\pi$
$6$	11.3496	−	9.33741i	0.772240	−	0.635331i
$7$	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	$-0.538112\pi$
$11$	−8.71540			−0.238890			−0.119445	+	0.992841i	$0.538112\pi$
$12$	−34.2850	+	23.5062i	−0.824768	+	0.565471i
$13$	−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	$-0.663940\pi$
$17$	−69.0503			−0.985127			−0.492563	+	0.870277i	$0.663940\pi$
$18$	−8.11706	+	75.9349i	−0.106289	+	0.994335i
$19$	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
$21$	−83.4915	−	47.8557i	−0.867587	−	0.497285i
$22$	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	$-0.298217\pi$
$24$	102.408	−	57.7638i	0.870996	−	0.491291i
$25$	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	$-0.209042\pi$
$29$	247.372			1.58399			0.791996	+	0.610526i	$0.209042\pi$
$30$	−84.2249	−	102.375i	−0.512576	−	0.623033i
$31$		−	52.1678i		−	0.302245i	−0.988515	−	0.151123i	$-0.951711\pi$
$31$		−	52.1678i		−	0.302245i	0.988515	−	0.151123i	$-0.0482888\pi$
$32$	−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
$36$	41.6254	−	211.951i	0.192710	−	0.981256i
$37$		−	299.492i		−	1.33071i	−0.746528	−	0.665354i	$-0.768281\pi$
$37$		−	299.492i		−	1.33071i	0.746528	−	0.665354i	$-0.231719\pi$
$38$	−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	$-0.384896\pi$
$41$	185.754			0.707559			0.353780	+	0.935329i	$0.384896\pi$
$42$	223.428	+	155.460i	0.820850	+	0.571144i
$43$		−	330.296i		−	1.17139i	−0.810532	−	0.585695i	$-0.800822\pi$
$43$		−	330.296i		−	1.17139i	0.810532	−	0.585695i	$-0.199178\pi$
$44$	−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	$-0.459395\pi$
$47$	81.9844			0.254440			0.127220	+	0.991875i	$0.459395\pi$
$48$	−302.813	+	137.464i	−0.910569	+	0.413358i
$49$	−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	$-0.400065\pi$
$53$	238.316			0.617646			0.308823	+	0.951120i	$0.400065\pi$
$54$	−246.225	−	311.187i	−0.620499	−	0.784207i
$55$			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	$-0.0703128\pi$
$60$	212.029	+	309.256i	0.456214	+	0.665412i
$61$	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
$63$	483.826	−	126.329i	0.967562	−	0.252635i
$64$	443.150	+	256.442i	0.865526	+	0.500863i
$65$			473.198i			0.902970i
$66$	−98.9160	+	81.3793i	−0.184481	+	0.151774i
$67$			527.615i			0.962066i	0.876703	+	0.481033i	$0.159738\pi$
$67$			527.615i			0.962066i	−0.876703	+	0.481033i	$0.840262\pi$
$68$	−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	$0.934300\pi$
$72$	−169.633	+	586.918i	−0.277658	+	0.960680i
$73$		−	745.090i		−	1.19461i	−0.802016	−	0.597303i	$-0.796239\pi$
$73$		−	745.090i		−	1.19461i	0.802016	−	0.597303i	$-0.203761\pi$
$74$	−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
$78$	−595.400	+	489.842i	−0.864305	+	0.711073i
$79$	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	$-0.000828505\pi$
$84$	−591.140	−	493.211i	−0.767841	−	0.640640i
$85$			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	$-0.769744\pi$
$89$	−1258.73			−1.49916			−0.749579	+	0.661915i	$0.769744\pi$
$90$	684.944	+	73.2171i	0.802216	+	0.0857529i
$91$	−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
$96$	887.164	−	312.532i	0.943185	−	0.332267i
$97$		−	755.959i		−	0.791300i	−0.918401	−	0.395650i	$-0.870519\pi$
$97$		−	755.959i		−	0.791300i	0.918401	−	0.395650i	$-0.129481\pi$
$98$	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	$-0.172256\pi$
$102$	−783.691	+	644.751i	−0.760754	+	0.625881i
$103$		−	1520.53i		−	1.45458i	−0.686328	−	0.727292i	$-0.740779\pi$
$103$		−	1520.53i		−	1.45458i	0.686328	−	0.727292i	$-0.259221\pi$
$104$	1146.44	+	307.800i	1.08094	+	0.290214i
$105$	−431.666	+	753.106i	−0.401203	+	0.699958i
$106$	−671.485	−	58.8597i	−0.615287	−	0.0539336i
$107$	−283.267			−0.255930			−0.127965	−	0.991779i	$-0.540844\pi$
$107$	−283.267			−0.255930			−0.127965	+	0.991779i	$0.540844\pi$
$108$	616.911	+	937.621i	0.549651	+	0.835395i
$109$		−	1180.64i		−	1.03747i	−0.854935	−	0.518736i	$-0.826403\pi$
$109$		−	1180.64i		−	1.03747i	0.854935	−	0.518736i	$-0.173597\pi$
$110$	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	$0.716555\pi$
$114$	1467.46	−	1207.29i	1.20561	−	0.991872i
$115$	−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
$120$	−521.038	−	923.733i	−0.396367	−	0.702708i
$121$	−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
$126$	−1394.44	+	236.453i	−0.985926	+	0.167182i
$127$	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	$0.835963\pi$
$132$	298.807	−	204.866i	0.197029	−	0.135085i
$133$	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	$-0.0342913\pi$
$138$	−1659.70	−	2017.35i	−1.02379	−	1.24441i
$139$	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
$144$	622.919	−	1611.82i	0.360486	−	0.932765i
$145$		−	2231.33i		−	1.27794i
$146$	−184.024	+	2099.38i	−0.104315	+	1.19004i
$147$	434.042	−	1728.62i	0.243532	−	0.969893i
$148$	416.834	−	2359.40i	0.231510	−	1.31041i
$149$	−1849.45			−1.01687			−0.508433	−	0.861102i	$-0.669775\pi$
$149$	−1849.45			−1.01687			−0.508433	+	0.861102i	$0.669775\pi$
$150$	495.260	−	407.456i	0.269585	−	0.221791i
$151$	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
$156$	1798.60	−	1233.14i	0.923095	−	0.632885i
$157$	−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
$162$	2045.69	+	258.192i	0.992129	+	0.125219i
$163$			3458.92i			1.66211i	0.556191	+	0.831054i	$0.312262\pi$
$163$			3458.92i			1.66211i	−0.556191	+	0.831054i	$0.687738\pi$
$164$	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	$-0.320584\pi$
$167$	2306.06			1.06855			0.534277	+	0.845310i	$0.320584\pi$
$168$	1543.80	+	1535.68i	0.708967	+	0.705242i
$169$	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	$0.998732\pi$
$174$	2807.56	−	2309.81i	1.22322	−	1.00636i
$175$	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	$-0.682332\pi$
$179$	−2596.01			−1.08400			−0.541998	+	0.840380i	$0.682332\pi$
$180$	−1911.83	−	375.467i	−0.791664	−	0.155476i
$181$	−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
$186$	−487.112	−	592.081i	−0.192026	−	0.233406i
$187$	601.801			0.235337
$188$	645.873	+	114.106i	0.250559	+	0.0442662i
$189$	−1334.83	+	2229.24i	−0.513728	+	0.857953i
$190$	−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	$0.890619\pi$
$192$	−2576.88	+	661.483i	−0.968597	+	0.248638i
$193$	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	$-0.519952\pi$
$197$	−346.401			−0.125280			−0.0626398	+	0.998036i	$0.519952\pi$
$198$	70.7434	−	661.803i	0.0253915	−	0.237537i
$199$		−	3780.44i		−	1.34668i	−0.739335	−	0.673338i	$-0.764860\pi$
$199$		−	3780.44i		−	1.34668i	0.739335	−	0.673338i	$-0.235140\pi$
$200$	−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
$204$	2367.39	−	1623.11i	0.812501	−	0.557060i
$205$		−	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
$210$	1402.28	−	2015.35i	0.460791	−	0.662251i
$211$		−	2168.92i		−	0.707652i	−0.935311	−	0.353826i	$-0.884881\pi$
$211$		−	2168.92i		−	0.707652i	0.935311	−	0.353826i	$-0.115119\pi$
$212$	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
$216$	−1506.65	−	2794.23i	−0.474603	−	0.880200i
$217$	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
$222$	−2796.48	−	3399.10i	−0.845439	−	1.02763i
$223$			3892.25i			1.16881i	0.811462	+	0.584405i	$0.198672\pi$
$223$			3892.25i			1.16881i	−0.811462	+	0.584405i	$0.801328\pi$
$224$	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	$0.878658\pi$
$228$	−4432.92	+	3039.26i	−1.28762	+	0.882807i
$229$	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
$231$	727.661	+	417.082i	0.207258	+	0.118796i
$232$	−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	$0.978691\pi$
$234$	425.822	−	3983.56i	0.118961	−	1.11288i
$235$		−	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	$0.987261\pi$
$240$	1239.94	+	2731.42i	0.333492	+	0.734635i
$241$			3284.88i			0.877998i	0.898488	+	0.438999i	$0.144667\pi$
$241$			3284.88i			0.877998i	−0.898488	+	0.438999i	$0.855333\pi$
$242$	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
$246$	2108.23	−	1734.46i	0.546406	−	0.449534i
$247$	−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	$-0.0413253\pi$
$252$	3987.41	−	321.833i	0.996759	−	0.0804506i
$253$			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	$-0.403830\pi$
$257$	2451.85			0.595106			0.297553	+	0.954705i	$0.403830\pi$
$258$	−3084.11	−	3748.72i	−0.744219	−	0.904594i
$259$	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	$0.827644\pi$
$264$	−892.524	+	503.434i	−0.208072	+	0.117365i
$265$		−	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	$-0.126014\pi$
$270$	−2806.95	+	2220.98i	−0.632688	+	0.500610i
$271$		−	4179.66i		−	0.936887i	−0.883493	−	0.468444i	$-0.844815\pi$
$271$		−	4179.66i		−	0.936887i	0.883493	−	0.468444i	$-0.155185\pi$
$272$	−4151.70	−	1514.22i	−0.925492	−	0.337548i
$273$	4379.98	+	2510.52i	0.971019	+	0.556570i
$274$	−85.1666	+	971.600i	−0.0187778	+	0.214221i
$275$	−380.313			−0.0833954
$276$	4178.15	+	6094.05i	0.911214	+	1.32905i
$277$		−	2605.51i		−	0.565163i	−0.959243	−	0.282581i	$-0.908809\pi$
$277$		−	2605.51i		−	0.565163i	0.959243	−	0.282581i	$-0.0911907\pi$
$278$	−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	$-0.322201\pi$
$282$	930.488	−	765.523i	0.196488	−	0.161653i
$283$	−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
$288$	−2153.24	+	4387.64i	−0.440559	+	0.897724i
$289$	−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	$-0.308011\pi$
$294$	−1649.90	+	4763.40i	−0.327294	+	0.944923i
$295$	−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
$300$	−1496.09	+	1025.74i	−0.287923	+	0.197403i
$301$	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
$306$	560.485	−	5243.33i	0.104709	−	0.979546i
$307$	−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	$-0.605427\pi$
$311$	−3566.99			−0.650371			−0.325186	+	0.945650i	$0.605427\pi$
$312$	−5372.33	+	3030.30i	−0.974834	+	0.549861i
$313$			2364.18i			0.426936i	0.976950	+	0.213468i	$0.0684760\pi$
$313$			2364.18i			0.426936i	−0.976950	+	0.213468i	$0.931524\pi$
$314$	5379.75	+	471.568i	0.966870	+	0.0847520i
$315$	−1139.51	−	4364.19i	−0.203823	−	0.780616i
$316$	4711.92	+	832.454i	0.838818	+	0.148194i
$317$	5296.44			0.938415			0.469207	−	0.883088i	$-0.344540\pi$
$317$	5296.44			0.938415			0.469207	+	0.883088i	$0.344540\pi$
$318$	2704.78	−	2225.26i	0.476971	−	0.392409i
$319$	−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
$324$	−5700.23	−	1232.74i	−0.977405	−	0.211375i
$325$	−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
$330$	734.053	+	892.237i	0.122449	+	0.148836i
$331$		−	664.908i		−	0.110413i	−0.998475	−	0.0552064i	$-0.982418\pi$
$331$		−	664.908i		−	0.110413i	0.998475	−	0.0552064i	$-0.0175817\pi$
$332$	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
$336$	−3970.55	−	4708.27i	−0.644676	−	0.764456i
$337$	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
$342$	−1049.51	+	9818.10i	−0.165938	+	1.55235i
$343$	−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	$-0.149648\pi$
$347$	11525.2			1.78301			0.891507	+	0.453006i	$0.149648\pi$
$348$	−8481.14	+	5814.77i	−1.30643	+	0.895702i
$349$	−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	$-0.188942\pi$
$353$	10995.6			1.65789			0.828944	+	0.559331i	$0.188942\pi$
$354$	−1854.30	−	2253.90i	−0.278404	−	0.338399i
$355$	2211.85			0.330684
$356$	−9916.27	−	1751.90i	−1.47630	−	0.260817i
$357$	5765.11	+	3304.45i	0.854683	+	0.489888i
$358$	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	$-0.0884642\pi$
$360$	5294.09	+	1530.11i	0.775064	+	0.224011i
$361$	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
$366$	1784.11	−	1467.81i	0.254801	−	0.209627i
$367$			1187.53i			0.168907i	0.996427	+	0.0844534i	$0.0269144\pi$
$367$			1187.53i			0.168907i	−0.996427	+	0.0844534i	$0.973086\pi$
$368$	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
$372$	1226.26	+	1788.57i	0.170911	+	0.249282i
$373$		−	4872.40i		−	0.676362i	−0.941081	−	0.338181i	$-0.890188\pi$
$373$		−	4872.40i		−	0.676362i	0.941081	−	0.338181i	$-0.109812\pi$
$374$	−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
$378$	4311.63	−	5951.47i	0.586683	−	0.809817i
$379$		−	3969.71i		−	0.538022i	−0.963137	−	0.269011i	$-0.913303\pi$
$379$		−	3969.71i		−	0.538022i	0.963137	−	0.269011i	$-0.0866967\pi$
$380$	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	$-0.436268\pi$
$383$	2981.45			0.397768			0.198884	+	0.980023i	$0.436268\pi$
$384$	7424.06	−	1227.37i	0.986608	−	0.163109i
$385$	−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	$-0.490087\pi$
$389$	477.774			0.0622728			0.0311364	+	0.999515i	$0.490087\pi$
$390$	4418.45	+	5370.60i	0.573684	+	0.697310i
$391$			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
$396$	−362.782	+	1847.24i	−0.0460365	+	0.234412i
$397$	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
$399$	−10795.1	−	6187.57i	−1.35447	−	0.776356i
$400$	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	$-0.233163\pi$
$402$	4926.56	+	5988.20i	0.611230	+	0.742946i
$403$			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
$408$	−7071.28	+	3988.61i	−0.858041	+	0.483984i
$409$			15374.7i			1.85875i	0.369139	+	0.929374i	$0.379653\pi$
$409$			15374.7i			1.85875i	−0.369139	+	0.929374i	$0.620347\pi$
$410$	−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
$414$	13497.2	+	1442.78i	1.60230	+	0.171277i
$415$	−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	$0.966313\pi$
$420$	−4448.84	+	5332.17i	−0.516860	+	0.619484i
$421$			1588.18i			0.183855i	0.995766	+	0.0919276i	$0.0293028\pi$
$421$			1588.18i			0.183855i	−0.995766	+	0.0919276i	$0.970697\pi$
$422$	−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
$426$	2289.65	+	2783.05i	0.260408	+	0.316524i
$427$	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	$-0.0404216\pi$
$432$	3555.04	+	8245.20i	0.395930	+	0.918281i
$433$		−	12900.1i		−	1.43173i	−0.698238	−	0.715865i	$-0.746032\pi$
$433$		−	12900.1i		−	1.43173i	0.698238	−	0.715865i	$-0.253968\pi$
$434$	−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
$438$	−6957.22	−	8456.45i	−0.758970	−	0.922523i
$439$			3778.78i			0.410823i	0.978676	+	0.205412i	$0.0658533\pi$
$439$			3778.78i			0.410823i	−0.978676	+	0.205412i	$0.934147\pi$
$440$	461.253	−	1717.99i	0.0499759	−	0.186141i
$441$	4680.66	+	7991.09i	0.505416	+	0.862876i
$442$	−10206.5	−	894.664i	−1.09836	−	0.0962779i
$443$	−372.016			−0.0398985			−0.0199492	−	0.999801i	$-0.506350\pi$
$443$	−372.016			−0.0398985			−0.0199492	+	0.999801i	$0.506350\pi$
$444$	7039.91	+	10268.1i	0.752476	+	1.09753i
$445$			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	$0.775386\pi$
$450$	−354.203	+	3313.56i	−0.0371051	+	0.347118i
$451$	−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
$456$	13240.9	−	7468.64i	1.35979	−	0.766998i
$457$	−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	$0.946223\pi$
$462$	−1947.26	−	1354.90i	−0.196093	−	0.136441i
$463$	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	$-0.00785309\pi$
$468$	−2183.67	+	11119.0i	−0.215684	+	1.09824i
$469$	−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
$474$	6788.31	−	5584.82i	0.657800	−	0.541179i
$475$	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	$-0.905666\pi$
$479$	−20052.8			−1.91281			−0.956406	+	0.292041i	$0.905666\pi$
$480$	−2819.08	−	8002.35i	−0.268069	−	0.760949i
$481$			15711.4i			1.48935i
$482$	811.305	−	9255.54i	0.0766679	−	0.874644i
$483$	−8506.21	+	14840.3i	−0.801337	+	1.39805i
$484$	−9887.22	−	1746.77i	−0.928552	−	0.164047i
$485$	−6818.87			−0.638410
$486$	−8527.22	+	6486.74i	−0.795890	+	0.605442i
$487$	−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	$-0.537928\pi$
$491$	−2586.64			−0.237746			−0.118873	+	0.992909i	$0.537928\pi$
$492$	−6368.58	+	4366.37i	−0.583573	+	0.400104i
$493$	−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
$498$	−36.7551	−	44.6756i	−0.00330730	−	0.00402001i
$499$			18254.1i			1.63761i	0.574072	+	0.818805i	$0.305363\pi$
$499$			18254.1i			1.63761i	−0.574072	+	0.818805i	$0.694637\pi$
$500$	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	$-0.340177\pi$
$503$	10858.4			0.962531			0.481265	+	0.876575i	$0.340177\pi$
$504$	−11314.5	−	78.0147i	−0.999976	−	0.00689494i
$505$	−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	$-0.0701022\pi$
$510$	5815.75	+	7069.01i	0.504953	+	0.613767i
$511$	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
$516$	7764.01	+	11324.2i	0.662386	+	0.966125i
$517$	−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	$-0.312119\pi$
$521$	13237.4			1.11313			0.556564	+	0.830805i	$0.312119\pi$
$522$	−2007.93	+	18784.2i	−0.168362	+	1.57502i
$523$	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
$525$	−3643.31	−	2088.28i	−0.302871	−	0.173600i
$526$	1085.85	−	12387.7i	0.0900104	−	1.02686i
$527$			3602.20i			0.297750i
$528$	2639.14	−	1198.05i	0.217526	−	0.0987471i
$529$	−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
$534$	−14286.0	+	11753.3i	−1.15771	+	0.952461i
$535$			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
$540$	8457.48	−	5564.63i	0.673985	−	0.443451i
$541$			7729.85i			0.614292i	0.951662	+	0.307146i	$0.0993740\pi$
$541$			7729.85i			0.614292i	−0.951662	+	0.307146i	$0.900626\pi$
$542$	−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
$546$	−11721.1	−	8155.47i	−0.918710	−	0.639234i
$547$			9563.57i			0.747548i	0.927520	+	0.373774i	$0.121936\pi$
$547$			9563.57i			0.747548i	−0.927520	+	0.373774i	$0.878064\pi$
$548$	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
$552$	−10267.3	−	18202.7i	−0.791679	−	1.40354i
$553$	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	$-0.279392\pi$
$557$	16797.4			1.27779			0.638894	+	0.769295i	$0.279392\pi$
$558$	3961.35	+	423.449i	0.300533	+	0.0321255i
$559$			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	$-0.194702\pi$
$564$	−2810.83	+	1927.14i	−0.209854	+	0.143878i
$565$	16845.6			1.25434
$566$	10206.5	+	894.658i	0.757967	+	0.0664404i
$567$	−3161.33	−	13125.9i	−0.234151	−	0.972200i
$568$	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	$0.663123\pi$
$570$	−10890.0	−	13236.7i	−0.800229	−	0.972673i
$571$		−	20556.7i		−	1.50661i	−0.657673	−	0.753304i	$-0.728459\pi$
$571$		−	20556.7i		−	1.50661i	0.657673	−	0.753304i	$-0.271541\pi$
$572$	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
$576$	7150.69	−	11830.9i	0.517266	−	0.855824i
$577$			1404.98i			0.101369i	0.998715	+	0.0506847i	$0.0161404\pi$
$577$			1404.98i			0.101369i	−0.998715	+	0.0506847i	$0.983860\pi$
$578$	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
$582$	−7058.71	−	8579.81i	−0.502737	−	0.611073i
$583$	−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	$0.831456\pi$
$588$	5825.28	−	13014.0i	0.408555	−	0.912734i
$589$		−	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	$-0.559608\pi$
$593$	−5376.81			−0.372343			−0.186171	+	0.982517i	$0.559608\pi$
$594$	2145.95	+	2712.12i	0.148231	+	0.187339i
$595$	−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	$-0.177503\pi$
$600$	4468.76	−	2520.63i	0.304060	−	0.171507i
$601$		−	28358.0i		−	1.92470i	−0.271811	−	0.962351i	$-0.587622\pi$
$601$		−	28358.0i		−	1.92470i	0.271811	−	0.962351i	$-0.412378\pi$
$602$	−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
$606$	−9764.59	−	11868.8i	−0.654554	−	0.795606i
$607$			16509.3i			1.10394i	0.833865	+	0.551969i	$0.186123\pi$
$607$			16509.3i			1.10394i	−0.833865	+	0.551969i	$0.813877\pi$
$608$	−21204.0	−	9909.05i	−1.41437	−	0.660963i
$609$	−20653.4	−	11838.2i	−1.37425	−	0.787696i
$610$	−350.204	+	3995.21i	−0.0232449	+	0.265182i
$611$	−4300.92			−0.284773
$612$	−2874.24	+	14635.3i	−0.189844	+	0.966661i
$613$		−	8227.79i		−	0.542117i	−0.962563	−	0.271058i	$-0.912626\pi$
$613$		−	8227.79i		−	0.542117i	0.962563	−	0.271058i	$-0.0873736\pi$
$614$	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	$0.976346\pi$
$618$	−14197.8	−	17257.3i	−0.924142	−	1.12329i
$619$	−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
$624$	15885.6	−	7211.37i	1.01912	−	0.462637i
$625$	−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
$630$	2132.84	+	12578.1i	0.134880	+	0.795432i
$631$	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
$636$	−8170.66	+	5601.90i	−0.509415	+	0.349261i
$637$	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	$-0.0183229\pi$
$642$	−3214.96	+	2644.98i	−0.197639	+	0.162600i
$643$	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	$-0.570692\pi$
$647$	−7249.89			−0.440529			−0.220265	+	0.975440i	$0.570692\pi$
$648$	15756.6	+	4881.24i	0.955214	+	0.295915i
$649$			1730.78i			0.104683i
$650$	6450.10	+	565.390i	0.389221	+	0.0341176i
$651$	−2496.53	+	4355.56i	−0.150302	+	0.262224i
$652$	−4814.14	+	27249.4i	−0.289166	+	1.63676i
$653$	−5007.60			−0.300096			−0.150048	−	0.988679i	$-0.547943\pi$
$653$	−5007.60			−0.300096			−0.150048	+	0.988679i	$0.547943\pi$
$654$	−11024.1	−	13399.7i	−0.659137	−	0.801177i
$655$	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	$-0.702088\pi$
$659$	−20066.4			−1.18616			−0.593078	+	0.805145i	$0.702088\pi$
$660$	−1847.92	−	2695.29i	−0.108985	−	0.158960i
$661$	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
$666$	22741.9	+	2430.99i	1.32317	+	0.141440i
$667$		−	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
$672$	10024.7	+	14246.8i	0.575460	+	0.817830i
$673$	−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	$0.748105\pi$
$678$	17438.2	+	21196.0i	0.987770	+	1.20063i
$679$	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	$-0.281672\pi$
$683$	22610.8			1.26673			0.633367	+	0.773851i	$0.281672\pi$
$684$	5382.01	−	27404.5i	0.300857	−	1.53193i
$685$	−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
$690$	−18196.8	+	14970.7i	−1.00397	+	0.825978i
$691$	−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
$693$	−4216.74	+	1101.01i	−0.231141	+	0.0603521i
$694$	−32473.7	−	2846.52i	−1.77620	−	0.155695i
$695$		−	10428.6i		−	0.569179i
$696$	25332.8	−	14289.1i	1.37965	−	0.778201i
$697$	−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	$-0.417839\pi$
$701$	9475.27			0.510522			0.255261	+	0.966872i	$0.417839\pi$
$702$	12917.0	+	16324.9i	0.694473	+	0.877699i
$703$		−	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
$708$	4668.06	+	6808.61i	0.247792	+	0.361417i
$709$			27170.6i			1.43923i	0.694374	+	0.719614i	$0.255681\pi$
$709$			27170.6i			1.43923i	−0.694374	+	0.719614i	$0.744319\pi$
$710$	−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
$714$	−15427.8	−	10734.6i	−0.808641	−	0.562649i
$715$		−	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	$-0.503202\pi$
$719$	−387.852			−0.0201174			−0.0100587	+	0.999949i	$0.503202\pi$
$720$	−14538.8	−	5618.82i	−0.752542	−	0.290835i
$721$	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
$726$	−14244.2	+	11718.8i	−0.728170	+	0.599073i
$727$			1084.95i			0.0553488i	0.999617	+	0.0276744i	$0.00881016\pi$
$727$			1084.95i			0.0553488i	−0.999617	+	0.0276744i	$0.991190\pi$
$728$	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
$732$	−5389.48	+	3695.09i	−0.272132	+	0.186577i
$733$	−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
$735$	−15592.4	−	3915.12i	−0.782497	−	0.196478i
$736$	−13622.2	+	29149.7i	−0.682231	+	1.45988i
$737$		−	4598.37i		−	0.229828i
$738$	−1507.78	+	14105.2i	−0.0752061	+	0.703551i
$739$			34674.6i			1.72601i	0.505192	+	0.863007i	$0.331422\pi$
$739$			34674.6i			1.72601i	−0.505192	+	0.863007i	$0.668578\pi$
$740$	−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	$0.811950\pi$
$744$	−3013.41	−	5342.38i	−0.148490	−	0.263254i
$745$			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
$750$	−14203.4	−	17264.2i	−0.691514	−	0.840531i
$751$	−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
$756$	−13618.4	+	15704.1i	−0.655156	+	0.755493i
$757$		−	19462.5i		−	0.934449i	−0.884139	−	0.467224i	$-0.845254\pi$
$757$		−	19462.5i		−	0.934449i	0.884139	−	0.467224i	$-0.154746\pi$
$758$	−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	$-0.454411\pi$
$761$	5992.80			0.285465			0.142732	+	0.989761i	$0.454411\pi$
$762$	10902.0	−	8969.20i	0.518291	−	0.426404i
$763$	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
$768$	−21221.3	+	1624.65i	−0.997082	+	0.0763338i
$769$		−	15433.8i		−	0.723742i	−0.932228	−	0.361871i	$-0.882138\pi$
$769$		−	15433.8i		−	0.723742i	0.932228	−	0.361871i	$-0.117862\pi$
$770$	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	$0.863857\pi$
$774$	25081.0	+	2681.04i	1.16475	+	0.124506i
$775$		−	2276.44i		−	0.105512i
$776$	−4435.44	+	16520.3i	−0.205184	+	0.764234i
$777$	−14332.4	+	25005.0i	−0.661740	+	1.15450i
$778$	−1346.19	−	118.002i	−0.0620349	−	0.00543774i
$779$	24017.3			1.10463
$780$	−11123.1	−	16223.6i	−0.510603	−	0.744741i
$781$		−	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
$786$	13799.4	+	16773.1i	0.626219	+	0.761165i
$787$	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
$792$	1478.42	−	5115.22i	0.0663298	−	0.229497i
$793$	−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	$0.949123\pi$
$798$	28888.4	+	20100.4i	1.28150	+	0.891664i
$799$	−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
$804$	−12402.2	−	18089.3i	−0.544020	−	0.793481i
$805$	−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	$-0.155949\pi$
$810$	2328.93	−	18452.5i	0.101025	−	0.800437i
$811$	−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
$816$	20909.3	−	9491.91i	0.897025	−	0.407210i
$817$		−	42706.1i		−	1.82876i
$818$	3797.26	−	43320.0i	0.162308	−	1.85165i
$819$	−25381.6	+	6627.26i	−1.08291	+	0.282754i
$820$	2332.01	−	13199.8i	0.0993138	−	0.562144i
$821$	−24747.6			−1.05200			−0.526002	−	0.850483i	$-0.676310\pi$
$821$	−24747.6			−1.05200			−0.526002	+	0.850483i	$0.676310\pi$
$822$	−3219.82	−	3913.67i	−0.136623	−	0.166064i
$823$	−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	$-0.289122\pi$
$827$	29256.6			1.23017			0.615085	+	0.788461i	$0.289122\pi$
$828$	−37673.7	−	7398.78i	−1.58122	−	0.310538i
$829$	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
$834$	13121.8	−	10795.4i	0.544807	−	0.448219i
$835$		−	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	$-0.150846\pi$
$839$	43247.8			1.77959			0.889796	+	0.456358i	$0.150846\pi$
$840$	13852.1	−	13925.3i	0.568980	−	0.571985i
$841$	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
$846$	−665.473	+	6225.48i	−0.0270442	+	0.252998i
$847$	−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
$852$	−5764.00	−	8407.09i	−0.231774	−	0.338054i
$853$	−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	$-0.194122\pi$
$857$	41131.4			1.63947			0.819733	+	0.572746i	$0.194122\pi$
$858$	5189.15	−	4269.17i	0.206474	−	0.169868i
$859$	−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
$861$	−15508.9	−	8889.41i	−0.613870	−	0.351859i
$862$	−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	$0.778402\pi$
$864$	−7980.35	−	24109.9i	−0.314233	−	0.949346i
$865$	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
$870$	−20834.9	−	25324.6i	−0.811917	−	0.986880i
$871$		−	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
$876$	17514.2	+	25545.4i	0.675515	+	0.985273i
$877$			11908.4i			0.458517i	0.973366	+	0.229259i	$0.0736301\pi$
$877$			11908.4i			0.458517i	−0.973366	+	0.229259i	$0.926370\pi$
$878$	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	$-0.747345\pi$
$881$	−36671.3			−1.40237			−0.701184	+	0.712980i	$0.747345\pi$
$882$	−11214.7	−	23671.9i	−0.428138	−	0.903713i
$883$			37102.7i			1.41405i	0.707190	+	0.707024i	$0.249963\pi$
$883$			37102.7i			1.41405i	−0.707190	+	0.707024i	$0.750037\pi$
$884$	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	$-0.874396\pi$
$887$	−48774.0			−1.84630			−0.923152	+	0.384435i	$0.874396\pi$
$888$	−17299.8	−	30670.3i	−0.653764	−	1.15904i
$889$	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
$894$	−20990.5	+	17269.1i	−0.785265	+	0.646046i
$895$			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
$900$	1816.40	−	9248.89i	0.0672741	−	0.342552i
$901$	−16455.8			−0.608459
$902$	4561.51	+	399.844i	0.168383	+	0.0147598i
$903$	−15806.6	+	27576.9i	−0.582514	+	1.01628i
$904$	10957.5	−	40812.6i	0.403143	−	1.50156i
$905$			10830.3i			0.397801i
$906$	29827.0	−	24539.0i	1.09375	−	0.899840i
$907$			1891.26i			0.0692372i	0.999401	+	0.0346186i	$0.0110216\pi$
$907$			1891.26i			0.0692372i	−0.999401	+	0.0346186i	$0.988978\pi$
$908$	−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	$0.996097\pi$
$912$	−39152.6	+	17773.5i	−1.42157	+	0.645330i
$913$			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
$918$	17001.9	+	21487.6i	0.611270	+	0.772544i
$919$	−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
$924$	5152.02	+	4298.53i	0.183430	+	0.153043i
$925$		−	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	$-0.656517\pi$
$929$	−26737.6			−0.944275			−0.472138	+	0.881525i	$0.656517\pi$
$930$	−5340.66	+	4393.82i	−0.188309	+	0.154924i
$931$	−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
$936$	8898.96	−	30789.8i	0.310760	−	1.07521i
$937$			12780.7i			0.445602i	0.974864	+	0.222801i	$0.0715200\pi$
$937$			12780.7i			0.445602i	−0.974864	+	0.222801i	$0.928480\pi$
$938$	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	$0.725216\pi$
$942$	−21670.0	+	17828.1i	−0.749519	+	0.616637i
$943$		−	33017.2i		−	1.14018i
$944$	4354.90	−	11940.3i	0.150148	−	0.411677i
$945$	20108.1	+	12040.4i	0.692185	+	0.414469i
$946$	710.978	−	8110.99i	0.0244354	−	0.278764i
$947$	2594.12			0.0890153			0.0445077	−	0.999009i	$-0.485828\pi$
$947$	2594.12			0.0890153			0.0445077	+	0.999009i	$0.485828\pi$
$948$	−20506.2	+	14059.3i	−0.702544	+	0.481672i
$949$			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	$-0.207927\pi$
$954$	−1934.43	+	18096.5i	−0.0656492	+	0.614147i
$955$	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
$960$	5966.68	+	23243.9i	0.200598	+	0.781451i
$961$	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
$966$	27632.6	−	39713.6i	0.920356	−	1.32274i
$967$	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	$-0.430526\pi$
$972$	25628.6	−	16171.1i	0.845717	−	0.533631i
$973$	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	$0.923532\pi$
$978$	32297.4	+	39257.3i	1.05599	+	1.28355i
$979$	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	$-0.897891\pi$
$983$	−58495.3			−1.89798			−0.948989	+	0.315310i	$0.897891\pi$
$984$	19022.7	−	10729.9i	0.616281	−	0.347618i
$985$			3124.59i			0.101074i
$986$	48128.1	+	4218.72i	1.55447	+	0.136259i
$987$	−6845.00	−	3923.43i	−0.220749	−	0.126529i
$988$	−53435.7	−	9440.47i	−1.72066	−	0.303989i
$989$	−58709.2			−1.88761
$990$	−5969.56	−	638.116i	−0.191642	−	0.0204855i
$991$	−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
$996$	92.5281	+	134.957i	0.00294364	+	0.00429345i
$997$	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.125.1	✓	80
3.2	odd	2	inner	168.4.i.c.125.79	yes	80
4.3	odd	2		672.4.i.c.209.57		80
7.6	odd	2	inner	168.4.i.c.125.2	yes	80
8.3	odd	2		672.4.i.c.209.24		80
8.5	even	2	inner	168.4.i.c.125.78	yes	80
12.11	even	2		672.4.i.c.209.60		80
21.20	even	2	inner	168.4.i.c.125.80	yes	80
24.5	odd	2	inner	168.4.i.c.125.4	yes	80
24.11	even	2		672.4.i.c.209.21		80
28.27	even	2		672.4.i.c.209.23		80
56.13	odd	2	inner	168.4.i.c.125.77	yes	80
56.27	even	2		672.4.i.c.209.58		80
84.83	odd	2		672.4.i.c.209.22		80
168.83	odd	2		672.4.i.c.209.59		80
168.125	even	2	inner	168.4.i.c.125.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.i.c.125.1	✓	80	1.1	even	1	trivial
168.4.i.c.125.2	yes	80	7.6	odd	2	inner
168.4.i.c.125.3	yes	80	168.125	even	2	inner
168.4.i.c.125.4	yes	80	24.5	odd	2	inner
168.4.i.c.125.77	yes	80	56.13	odd	2	inner
168.4.i.c.125.78	yes	80	8.5	even	2	inner
168.4.i.c.125.79	yes	80	3.2	odd	2	inner
168.4.i.c.125.80	yes	80	21.20	even	2	inner
672.4.i.c.209.21		80	24.11	even	2
672.4.i.c.209.22		80	84.83	odd	2
672.4.i.c.209.23		80	28.27	even	2
672.4.i.c.209.24		80	8.3	odd	2
672.4.i.c.209.57		80	4.3	odd	2
672.4.i.c.209.58		80	56.27	even	2
672.4.i.c.209.59		80	168.83	odd	2
672.4.i.c.209.60		80	12.11	even	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} +(11.3496 - 9.33741i) 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} +(-34.2850 + 23.5062i) 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} +(-8.11706 + 75.9349i) q^{18} +129.296 q^{19} +(12.5543 - 71.0607i) q^{20} +(-83.4915 - 47.8557i) q^{21} +(24.5567 + 2.15254i) q^{22} -177.747i q^{23} +(102.408 - 57.7638i) 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} +(-84.2249 - 102.375i) 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} +(41.6254 - 211.951i) 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} +(223.428 + 155.460i) 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} +(-302.813 + 137.464i) 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} +(-246.225 - 311.187i) 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} +(212.029 + 309.256i) q^{60} +157.196 q^{61} +(-12.8845 + 146.989i) q^{62} +(483.826 - 126.329i) q^{63} +(443.150 + 256.442i) q^{64} +473.198i q^{65} +(-98.9160 + 81.3793i) 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} +(-169.633 + 586.918i) 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} +(-595.400 + 489.842i) 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} +(-591.140 - 493.211i) 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} +(684.944 + 73.2171i) 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} +(887.164 - 312.532i) 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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