LMFDB - Embedded newform 168.3.e.f.83.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,3,Mod(83,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.83"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 1])) N = Newforms(chi, 3, names="a")

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

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.57766844125$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			83.10
Character	$\chi$	$=$	168.83
Dual form			168.3.e.f.83.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36669 - 1.46019i) q^{2} +(2.87422 - 0.859555i) q^{3} +(-0.264297 + 3.99126i) q^{4} +6.07480i q^{5} +(-5.18330 - 3.02216i) q^{6} +(-1.74098 - 6.78004i) q^{7} +(6.18920 - 5.06891i) q^{8} +(7.52233 - 4.94111i) q^{9} +(8.87034 - 8.30239i) q^{10} +18.1021i q^{11} +(2.67106 + 11.6990i) q^{12} +19.5738 q^{13} +(-7.52075 + 11.8084i) q^{14} +(5.22162 + 17.4603i) q^{15} +(-15.8603 - 2.10975i) q^{16} +24.9998 q^{17} +(-17.4957 - 4.23104i) q^{18} -6.74068i q^{19} +(-24.2461 - 1.60555i) q^{20} +(-10.8318 - 17.9909i) q^{21} +(26.4324 - 24.7400i) q^{22} -11.2822 q^{23} +(13.4321 - 19.8891i) q^{24} -11.9032 q^{25} +(-26.7513 - 28.5814i) q^{26} +(17.3737 - 20.6677i) q^{27} +(27.5210 - 5.15676i) q^{28} -7.91470 q^{29} +(18.3590 - 31.4875i) q^{30} -12.4191 q^{31} +(18.5955 + 26.0424i) q^{32} +(15.5597 + 52.0294i) q^{33} +(-34.1670 - 36.5043i) q^{34} +(41.1874 - 10.5761i) q^{35} +(17.7331 + 31.3295i) q^{36} -2.65550i q^{37} +(-9.84265 + 9.21244i) q^{38} +(56.2594 - 16.8247i) q^{39} +(30.7926 + 37.5981i) q^{40} -32.9447 q^{41} +(-11.4664 + 40.4045i) q^{42} -51.6170 q^{43} +(-72.2501 - 4.78432i) q^{44} +(30.0162 + 45.6966i) q^{45} +(15.4194 + 16.4742i) q^{46} -36.7569i q^{47} +(-47.3995 + 7.56889i) q^{48} +(-42.9380 + 23.6078i) q^{49} +(16.2680 + 17.3808i) q^{50} +(71.8549 - 21.4887i) q^{51} +(-5.17328 + 78.1239i) q^{52} -24.9126 q^{53} +(-53.9233 + 2.87753i) q^{54} -109.966 q^{55} +(-45.1427 - 33.1382i) q^{56} +(-5.79398 - 19.3742i) q^{57} +(10.8170 + 11.5569i) q^{58} +18.3146 q^{59} +(-71.0687 + 16.2261i) q^{60} +68.9718 q^{61} +(16.9730 + 18.1341i) q^{62} +(-46.5971 - 42.3994i) q^{63} +(12.6124 - 62.7449i) q^{64} +118.907i q^{65} +(54.7074 - 93.8284i) q^{66} +28.6208 q^{67} +(-6.60735 + 99.7805i) q^{68} +(-32.4277 + 9.69769i) q^{69} +(-71.7336 - 45.6870i) q^{70} -86.9733 q^{71} +(21.5112 - 68.7115i) q^{72} +78.4472i q^{73} +(-3.87753 + 3.62925i) q^{74} +(-34.2123 + 10.2314i) q^{75} +(26.9038 + 1.78154i) q^{76} +(122.733 - 31.5154i) q^{77} +(-101.457 - 59.1550i) q^{78} +2.54780i q^{79} +(12.8163 - 96.3481i) q^{80} +(32.1709 - 74.3373i) q^{81} +(45.0253 + 48.1054i) q^{82} -84.3621 q^{83} +(74.6691 - 38.4775i) q^{84} +151.868i q^{85} +(70.5446 + 75.3705i) q^{86} +(-22.7486 + 6.80311i) q^{87} +(91.7577 + 112.037i) q^{88} -104.997 q^{89} +(25.7027 - 106.283i) q^{90} +(-34.0775 - 132.711i) q^{91} +(2.98186 - 45.0303i) q^{92} +(-35.6951 + 10.6749i) q^{93} +(-53.6719 + 50.2354i) q^{94} +40.9482 q^{95} +(75.8326 + 58.8678i) q^{96} -87.8707i q^{97} +(93.1549 + 30.4328i) q^{98} +(89.4443 + 136.170i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 44 q^{4} - 16 q^{9} - 76 q^{16} + 4 q^{18} + 32 q^{22} + 144 q^{25} + 108 q^{28} - 268 q^{30} - 176 q^{36} + 44 q^{42} + 128 q^{43} + 496 q^{46} - 464 q^{49} + 576 q^{51} + 128 q^{57} - 80 q^{58}+ \cdots - 64 q^{99}+O(q^{100}) $ 48 * q - 44 * q^4 - 16 * q^9 - 76 * q^16 + 4 * q^18 + 32 * q^22 + 144 * q^25 + 108 * q^28 - 268 * q^30 - 176 * q^36 + 44 * q^42 + 128 * q^43 + 496 * q^46 - 464 * q^49 + 576 * q^51 + 128 * q^57 - 80 * q^58 - 244 * q^60 - 212 * q^64 - 640 * q^67 - 336 * q^70 + 220 * q^72 - 84 * q^78 + 208 * q^81 + 308 * q^84 + 56 * q^88 + 320 * q^91 - 64 * q^99

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 $

$2$	−1.36669	−	1.46019i	−0.683347	−	0.730094i
$2$	−1.36669	−	1.46019i	−0.683347	−	0.730094i
$3$	2.87422	−	0.859555i	0.958075	−	0.286518i
$3$	2.87422	−	0.859555i	0.958075	−	0.286518i
$4$	−0.264297	+	3.99126i	−0.0660742	+	0.997815i
$5$			6.07480i			1.21496i	0.794335	+	0.607480i	$0.207819\pi$
$5$			6.07480i			1.21496i	−0.794335	+	0.607480i	$0.792181\pi$
$6$	−5.18330	−	3.02216i	−0.863883	−	0.503693i
$7$	−1.74098	−	6.78004i	−0.248712	−	0.968578i
$7$	−1.74098	−	6.78004i	−0.248712	−	0.968578i
$8$	6.18920	−	5.06891i	0.773650	−	0.633613i
$9$	7.52233	−	4.94111i	0.835815	−	0.549012i
$10$	8.87034	−	8.30239i	0.887034	−	0.830239i
$11$			18.1021i			1.64564i	0.568299	+	0.822822i	$0.307602\pi$
$11$			18.1021i			1.64564i	−0.568299	+	0.822822i	$0.692398\pi$
$12$	2.67106	+	11.6990i	0.222588	+	0.974913i
$13$	19.5738			1.50567			0.752837	−	0.658207i	$-0.228685\pi$
$13$	19.5738			1.50567			0.752837	+	0.658207i	$0.228685\pi$
$14$	−7.52075	+	11.8084i	−0.537196	+	0.843457i
$15$	5.22162	+	17.4603i	0.348108	+	1.16402i
$16$	−15.8603	−	2.10975i	−0.991268	−	0.131860i
$17$	24.9998			1.47057			0.735287	−	0.677756i	$-0.237047\pi$
$17$	24.9998			1.47057			0.735287	+	0.677756i	$0.237047\pi$
$18$	−17.4957	−	4.23104i	−0.971981	−	0.235058i
$19$		−	6.74068i		−	0.354772i	−0.984141	−	0.177386i	$-0.943236\pi$
$19$		−	6.74068i		−	0.354772i	0.984141	−	0.177386i	$-0.0567642\pi$
$20$	−24.2461	−	1.60555i	−1.21230	−	0.0802774i
$21$	−10.8318	−	17.9909i	−0.515799	−	0.856709i
$22$	26.4324	−	24.7400i	1.20147	−	1.12455i
$23$	−11.2822			−0.490532			−0.245266	−	0.969456i	$-0.578875\pi$
$23$	−11.2822			−0.490532			−0.245266	+	0.969456i	$0.578875\pi$
$24$	13.4321	−	19.8891i	0.559673	−	0.828714i
$25$	−11.9032			−0.476126
$26$	−26.7513	−	28.5814i	−1.02890	−	1.09928i
$27$	17.3737	−	20.6677i	0.643471	−	0.765470i
$28$	27.5210	−	5.15676i	0.982894	−	0.184170i
$29$	−7.91470			−0.272921			−0.136460	−	0.990646i	$-0.543573\pi$
$29$	−7.91470			−0.272921			−0.136460	+	0.990646i	$0.543573\pi$
$30$	18.3590	−	31.4875i	0.611967	−	1.04958i
$31$	−12.4191			−0.400615			−0.200307	−	0.979733i	$-0.564194\pi$
$31$	−12.4191			−0.400615			−0.200307	+	0.979733i	$0.564194\pi$
$32$	18.5955	+	26.0424i	0.581110	+	0.813825i
$33$	15.5597	+	52.0294i	0.471507	+	1.57665i
$34$	−34.1670	−	36.5043i	−1.00491	−	1.07366i
$35$	41.1874	−	10.5761i	1.17678	−	0.302174i
$36$	17.7331	+	31.3295i	0.492586	+	0.870264i
$37$		−	2.65550i		−	0.0717702i	−0.999356	−	0.0358851i	$-0.988575\pi$
$37$		−	2.65550i		−	0.0717702i	0.999356	−	0.0358851i	$-0.0114250\pi$
$38$	−9.84265	+	9.21244i	−0.259017	+	0.242433i
$39$	56.2594	−	16.8247i	1.44255	−	0.431403i
$40$	30.7926	+	37.5981i	0.769814	+	0.939953i
$41$	−32.9447			−0.803529			−0.401765	−	0.915743i	$-0.631603\pi$
$41$	−32.9447			−0.803529			−0.401765	+	0.915743i	$0.631603\pi$
$42$	−11.4664	+	40.4045i	−0.273008	+	0.962012i
$43$	−51.6170			−1.20039			−0.600197	−	0.799852i	$-0.704911\pi$
$43$	−51.6170			−1.20039			−0.600197	+	0.799852i	$0.704911\pi$
$44$	−72.2501	−	4.78432i	−1.64205	−	0.108735i
$45$	30.0162	+	45.6966i	0.667027	+	1.01548i
$46$	15.4194	+	16.4742i	0.335203	+	0.358134i
$47$		−	36.7569i		−	0.782061i	−0.920378	−	0.391030i	$-0.872119\pi$
$47$		−	36.7569i		−	0.782061i	0.920378	−	0.391030i	$-0.127881\pi$
$48$	−47.3995	+	7.56889i	−0.987489	+	0.157685i
$49$	−42.9380	+	23.6078i	−0.876285	+	0.481793i
$50$	16.2680	+	17.3808i	0.325359	+	0.347617i
$51$	71.8549	−	21.4887i	1.40892	−	0.421346i
$52$	−5.17328	+	78.1239i	−0.0994861	+	1.50238i
$53$	−24.9126			−0.470049			−0.235025	−	0.971989i	$-0.575517\pi$
$53$	−24.9126			−0.470049			−0.235025	+	0.971989i	$0.575517\pi$
$54$	−53.9233	+	2.87753i	−0.998579	+	0.0532875i
$55$	−109.966			−1.99939
$56$	−45.1427	−	33.1382i	−0.806119	−	0.591753i
$57$	−5.79398	−	19.3742i	−0.101649	−	0.339899i
$58$	10.8170	+	11.5569i	0.186499	+	0.199258i
$59$	18.3146			0.310416			0.155208	−	0.987882i	$-0.450395\pi$
$59$	18.3146			0.310416			0.155208	+	0.987882i	$0.450395\pi$
$60$	−71.0687	+	16.2261i	−1.18448	+	0.270435i
$61$	68.9718			1.13069			0.565343	−	0.824856i	$-0.308744\pi$
$61$	68.9718			1.13069			0.565343	+	0.824856i	$0.308744\pi$
$62$	16.9730	+	18.1341i	0.273759	+	0.292486i
$63$	−46.5971	−	42.3994i	−0.739637	−	0.673006i
$64$	12.6124	−	62.7449i	0.197069	−	0.980390i
$65$			118.907i			1.82933i
$66$	54.7074	−	93.8284i	0.828900	−	1.42164i
$67$	28.6208			0.427176			0.213588	−	0.976924i	$-0.431485\pi$
$67$	28.6208			0.427176			0.213588	+	0.976924i	$0.431485\pi$
$68$	−6.60735	+	99.7805i	−0.0971670	+	1.46736i
$69$	−32.4277	+	9.69769i	−0.469966	+	0.140546i
$70$	−71.7336	−	45.6870i	−1.02477	−	0.652672i
$71$	−86.9733			−1.22498			−0.612488	−	0.790480i	$-0.709831\pi$
$71$	−86.9733			−1.22498			−0.612488	+	0.790480i	$0.709831\pi$
$72$	21.5112	−	68.7115i	0.298767	−	0.954326i
$73$			78.4472i			1.07462i	0.843385	+	0.537310i	$0.180559\pi$
$73$			78.4472i			1.07462i	−0.843385	+	0.537310i	$0.819441\pi$
$74$	−3.87753	+	3.62925i	−0.0523990	+	0.0490440i
$75$	−34.2123	+	10.2314i	−0.456164	+	0.136419i
$76$	26.9038	+	1.78154i	0.353997	+	0.0234413i
$77$	122.733	−	31.5154i	1.59393	−	0.409291i
$78$	−101.457	−	59.1550i	−1.30072	−	0.758397i
$79$			2.54780i			0.0322506i	0.999870	+	0.0161253i	$0.00513306\pi$
$79$			2.54780i			0.0322506i	−0.999870	+	0.0161253i	$0.994867\pi$
$80$	12.8163	−	96.3481i	0.160204	−	1.20435i
$81$	32.1709	−	74.3373i	0.397172	−	0.917744i
$82$	45.0253	+	48.1054i	0.549089	+	0.586652i
$83$	−84.3621			−1.01641			−0.508206	−	0.861236i	$-0.669691\pi$
$83$	−84.3621			−1.01641			−0.508206	+	0.861236i	$0.669691\pi$
$84$	74.6691	−	38.4775i	0.888918	−	0.458066i
$85$			151.868i			1.78669i
$86$	70.5446	+	75.3705i	0.820286	+	0.876401i
$87$	−22.7486	+	6.80311i	−0.261478	+	0.0781967i
$88$	91.7577	+	112.037i	1.04270	+	1.27315i
$89$	−104.997			−1.17975			−0.589873	−	0.807496i	$-0.700822\pi$
$89$	−104.997			−1.17975			−0.589873	+	0.807496i	$0.700822\pi$
$90$	25.7027	−	106.283i	0.285586	−	1.18092i
$91$	−34.0775	−	132.711i	−0.374478	−	1.45836i
$92$	2.98186	−	45.0303i	0.0324115	−	0.489460i
$93$	−35.6951	+	10.6749i	−0.383819	+	0.114783i
$94$	−53.6719	+	50.2354i	−0.570978	+	0.534419i
$95$	40.9482			0.431034
$96$	75.8326	+	58.8678i	0.789923	+	0.613206i
$97$		−	87.8707i		−	0.905884i	−0.891540	−	0.452942i	$-0.850374\pi$
$97$		−	87.8707i		−	0.905884i	0.891540	−	0.452942i	$-0.149626\pi$
$98$	93.1549	+	30.4328i	0.950561	+	0.310539i
$99$	89.4443	+	136.170i	0.903478	+	1.37545i
$100$	3.14596	−	47.5086i	0.0314596	−	0.475086i
$101$			79.4339i			0.786475i	0.919437	+	0.393237i	$0.128645\pi$
$101$			79.4339i			0.786475i	−0.919437	+	0.393237i	$0.871355\pi$
$102$	−129.581	−	75.5533i	−1.27040	−	0.740718i
$103$	127.273			1.23566			0.617831	−	0.786311i	$-0.288012\pi$
$103$	127.273			1.23566			0.617831	+	0.786311i	$0.288012\pi$
$104$	121.146	−	99.2175i	1.16486	−	0.954014i
$105$	109.291	−	65.8009i	1.04087	−	0.626675i
$106$	34.0479	+	36.3771i	0.321207	+	0.343180i
$107$		−	172.021i		−	1.60768i	−0.594849	−	0.803838i	$-0.702788\pi$
$107$		−	172.021i		−	1.60768i	0.594849	−	0.803838i	$-0.297212\pi$
$108$	77.8983	+	74.8054i	0.721281	+	0.692643i
$109$		−	151.755i		−	1.39225i	−0.717920	−	0.696126i	$-0.754906\pi$
$109$		−	151.755i		−	1.39225i	0.717920	−	0.696126i	$-0.245094\pi$
$110$	150.290	+	160.572i	1.36628	+	1.45974i
$111$	−2.28255	−	7.63250i	−0.0205635	−	0.0687613i
$112$	13.3083	+	111.207i	0.118824	+	0.992915i
$113$		−	100.380i		−	0.888317i	−0.895948	−	0.444158i	$-0.853503\pi$
$113$		−	100.380i		−	0.888317i	0.895948	−	0.444158i	$-0.146497\pi$
$114$	−20.3714	+	34.9389i	−0.178696	+	0.306482i
$115$		−	68.5372i		−	0.595976i
$116$	2.09183	−	31.5896i	0.0180330	−	0.272324i
$117$	147.240	−	96.7160i	1.25846	−	0.826632i
$118$	−25.0304	−	26.7427i	−0.212122	−	0.226633i
$119$	−43.5241	−	169.499i	−0.365749	−	1.42437i
$120$	120.822	+	81.5976i	1.00685	+	0.679980i
$121$	−206.685			−1.70814
$122$	−94.2633	−	100.712i	−0.772650	−	0.825506i
$123$	−94.6905	+	28.3178i	−0.769841	+	0.230226i
$124$	3.28231	−	49.5677i	0.0264703	−	0.399739i
$125$			79.5607i			0.636485i
$126$	1.77299	+	125.988i	0.0140714	+	0.999901i
$127$		−	49.4402i		−	0.389293i	−0.980873	−	0.194646i	$-0.937644\pi$
$127$		−	49.4402i		−	0.389293i	0.980873	−	0.194646i	$-0.0623559\pi$
$128$	−108.857	+	67.3367i	−0.850443	+	0.526068i
$129$	−148.359	+	44.3676i	−1.15007	+	0.343935i
$130$	173.626	−	162.509i	1.33558	−	1.25007i
$131$	19.3183			0.147468			0.0737341	−	0.997278i	$-0.476508\pi$
$131$	19.3183			0.147468			0.0737341	+	0.997278i	$0.476508\pi$
$132$	−211.775	+	48.3517i	−1.60436	+	0.366301i
$133$	−45.7021	+	11.7354i	−0.343625	+	0.0882360i
$134$	−39.1159	−	41.7918i	−0.291910	−	0.311879i
$135$	125.552	+	105.542i	0.930015	+	0.781791i
$136$	154.729	−	126.721i	1.13771	−	0.931775i
$137$			33.9618i			0.247896i	0.992289	+	0.123948i	$0.0395557\pi$
$137$			33.9618i			0.247896i	−0.992289	+	0.123948i	$0.960444\pi$
$138$	58.4791	+	34.0967i	0.423762	+	0.247078i
$139$		−	19.0000i		−	0.136690i	−0.997662	−	0.0683452i	$-0.978228\pi$
$139$		−	19.0000i		−	0.136690i	0.997662	−	0.0683452i	$-0.0217719\pi$
$140$	31.3263	+	167.185i	0.223759	+	1.19418i
$141$	−31.5945	−	105.647i	−0.224075	−	0.749273i
$142$	118.866	+	126.997i	0.837084	+	0.894348i
$143$			354.326i			2.47780i
$144$	−129.731	+	62.4971i	−0.900909	+	0.434008i
$145$		−	48.0802i		−	0.331587i
$146$	114.548	−	107.213i	0.784573	−	0.734338i
$147$	−103.121	+	104.762i	−0.701504	+	0.712665i
$148$	10.5988	+	0.701839i	0.0716134	+	0.00474216i
$149$	−23.0598			−0.154764			−0.0773818	−	0.997002i	$-0.524656\pi$
$149$	−23.0598			−0.154764			−0.0773818	+	0.997002i	$0.524656\pi$
$150$	61.6976	+	35.9732i	0.411317	+	0.239821i
$151$			59.1812i			0.391929i	0.980611	+	0.195964i	$0.0627837\pi$
$151$			59.1812i			0.391929i	−0.980611	+	0.195964i	$0.937216\pi$
$152$	−34.1679	−	41.7194i	−0.224789	−	0.274470i
$153$	188.057	−	123.526i	1.22913	−	0.807363i
$154$	−213.757	−	136.141i	−1.38803	−	0.884034i
$155$		−	75.4432i		−	0.486730i
$156$	52.2826	+	228.992i	0.335145	+	1.46790i
$157$	−226.545			−1.44296			−0.721481	−	0.692434i	$-0.756538\pi$
$157$	−226.545			−1.44296			−0.721481	+	0.692434i	$0.756538\pi$
$158$	3.72026	−	3.48206i	0.0235459	−	0.0220383i
$159$	−71.6044	+	21.4137i	−0.450342	+	0.134678i
$160$	−158.202	+	112.964i	−0.988764	+	0.706025i
$161$	19.6421	+	76.4940i	0.122001	+	0.475118i
$162$	−152.514	+	54.6207i	−0.941446	+	0.337165i
$163$	−121.299			−0.744166			−0.372083	−	0.928200i	$-0.621356\pi$
$163$	−121.299			−0.744166			−0.372083	+	0.928200i	$0.621356\pi$
$164$	8.70717	−	131.491i	0.0530925	−	0.801773i
$165$	−316.068	+	94.5222i	−1.91557	+	0.572862i
$166$	115.297	+	123.185i	0.694562	+	0.742076i
$167$		−	35.0035i		−	0.209602i	−0.994493	−	0.104801i	$-0.966579\pi$
$167$		−	35.0035i		−	0.209602i	0.994493	−	0.104801i	$-0.0334205\pi$
$168$	−158.234	−	56.4440i	−0.941871	−	0.335976i
$169$	214.132			1.26705
$170$	221.756	−	207.558i	1.30445	−	1.22093i
$171$	−33.3064	−	50.7056i	−0.194774	−	0.296524i
$172$	13.6422	−	206.017i	0.0793151	−	1.19777i
$173$		−	112.273i		−	0.648978i	−0.945890	−	0.324489i	$-0.894808\pi$
$173$		−	112.273i		−	0.648978i	0.945890	−	0.324489i	$-0.105192\pi$
$174$	41.0242	+	23.9195i	0.235771	+	0.137468i
$175$	20.7232	+	80.7039i	0.118418	+	0.461165i
$176$	38.1909	−	287.104i	0.216994	−	1.63127i
$177$	52.6402	−	15.7424i	0.297402	−	0.0889399i
$178$	143.499	+	153.316i	0.806175	+	0.861325i
$179$		−	53.5854i		−	0.299360i	−0.988735	−	0.149680i	$-0.952176\pi$
$179$		−	53.5854i		−	0.299360i	0.988735	−	0.149680i	$-0.0478243\pi$
$180$	−190.320	+	107.725i	−1.05733	+	0.598472i
$181$	119.594			0.660742			0.330371	−	0.943851i	$-0.392826\pi$
$181$	119.594			0.660742			0.330371	+	0.943851i	$0.392826\pi$
$182$	−147.209	+	231.135i	−0.808842	+	1.26997i
$183$	198.240	−	59.2850i	1.08328	−	0.323962i
$184$	−69.8280	+	57.1886i	−0.379500	+	0.310807i
$185$	16.1316			0.0871979
$186$	64.3716	+	37.5324i	0.346084	+	0.201787i
$187$			452.548i			2.42004i
$188$	146.706	+	9.71472i	0.780352	+	0.0516740i
$189$	−170.375	−	81.8125i	−0.901456	−	0.432870i
$190$	−55.9637	−	59.7921i	−0.294546	−	0.314695i
$191$	−19.1768			−0.100402			−0.0502011	−	0.998739i	$-0.515986\pi$
$191$	−19.1768			−0.100402			−0.0502011	+	0.998739i	$0.515986\pi$
$192$	−17.6819	−	191.184i	−0.0920930	−	0.995750i
$193$	32.4372			0.168068			0.0840342	−	0.996463i	$-0.473220\pi$
$193$	32.4372			0.168068			0.0840342	+	0.996463i	$0.473220\pi$
$194$	−128.308	+	120.092i	−0.661380	+	0.619033i
$195$	102.207	+	341.764i	0.524137	+	1.75264i
$196$	−82.8767	−	177.616i	−0.422840	−	0.906204i
$197$	206.296			1.04719			0.523593	−	0.851968i	$-0.324591\pi$
$197$	206.296			1.04719			0.523593	+	0.851968i	$0.324591\pi$
$198$	76.5906	−	316.708i	0.386821	−	1.59953i
$199$	288.060			1.44754			0.723770	−	0.690041i	$-0.242408\pi$
$199$	288.060			1.44754			0.723770	+	0.690041i	$0.242408\pi$
$200$	−73.6710	+	60.3360i	−0.368355	+	0.301680i
$201$	82.2627	−	24.6012i	0.409267	−	0.122394i
$202$	115.988	−	108.562i	0.574200	−	0.537435i
$203$	13.7793	+	53.6620i	0.0678785	+	0.264345i
$204$	66.7758	+	292.471i	0.327332	+	1.43368i
$205$		−	200.132i		−	0.976255i
$206$	−173.943	−	185.843i	−0.844386	−	0.902149i
$207$	−84.8687	+	55.7467i	−0.409994	+	0.269308i
$208$	−310.445	−	41.2958i	−1.49253	−	0.198537i
$209$	122.020			0.583829
$210$	−245.449	−	69.6558i	−1.16880	−	0.331694i
$211$	−75.0693			−0.355779			−0.177889	−	0.984050i	$-0.556927\pi$
$211$	−75.0693			−0.355779			−0.177889	+	0.984050i	$0.556927\pi$
$212$	6.58432	−	99.4327i	0.0310581	−	0.469022i
$213$	−249.981	+	74.7583i	−1.17362	+	0.350978i
$214$	−251.183	+	235.100i	−1.17375	+	1.09860i
$215$		−	313.563i		−	1.45843i
$216$	2.76679	−	215.982i	0.0128092	−	0.999918i
$217$	21.6213	+	84.2017i	0.0996375	+	0.388026i
$218$	−221.591	+	207.403i	−1.01647	+	0.951391i
$219$	67.4296	+	225.475i	0.307898	+	1.02957i
$220$	29.0638	−	438.905i	0.132108	−	1.99502i
$221$	489.339			2.21420
$222$	−8.02534	+	13.7642i	−0.0361502	+	0.0620011i
$223$	−222.340			−0.997039			−0.498519	−	0.866879i	$-0.666123\pi$
$223$	−222.340			−0.997039			−0.498519	+	0.866879i	$0.666123\pi$
$224$	144.194	−	171.418i	0.643724	−	0.765258i
$225$	−89.5395	+	58.8147i	−0.397953	+	0.261399i
$226$	−146.573	+	137.188i	−0.648555	+	0.607029i
$227$	146.952			0.647365			0.323682	−	0.946166i	$-0.395079\pi$
$227$	146.952			0.647365			0.323682	+	0.946166i	$0.395079\pi$
$228$	78.8588	−	18.0047i	0.345872	−	0.0789681i
$229$	−206.263			−0.900711			−0.450356	−	0.892849i	$-0.648703\pi$
$229$	−206.263			−0.900711			−0.450356	+	0.892849i	$0.648703\pi$
$230$	−100.077	+	93.6694i	−0.435118	+	0.407258i
$231$	325.673	−	196.078i	1.40984	−	0.848822i
$232$	−48.9856	+	40.1189i	−0.211145	+	0.172926i
$233$			76.1219i			0.326704i	0.986568	+	0.163352i	$0.0522306\pi$
$233$			76.1219i			0.326704i	−0.986568	+	0.163352i	$0.947769\pi$
$234$	−342.456	−	82.8173i	−1.46349	−	0.353920i
$235$	223.290			0.950172
$236$	−4.84048	+	73.0982i	−0.0205105	+	0.309738i
$237$	2.18997	+	7.32294i	0.00924038	+	0.0308985i
$238$	−188.017	+	295.207i	−0.789987	+	1.24037i
$239$	−332.370			−1.39067			−0.695335	−	0.718686i	$-0.744744\pi$
$239$	−332.370			−1.39067			−0.695335	+	0.718686i	$0.744744\pi$
$240$	−45.9794	−	287.942i	−0.191581	−	1.19976i
$241$		−	125.283i		−	0.519845i	−0.965629	−	0.259923i	$-0.916303\pi$
$241$		−	125.283i		−	0.519845i	0.965629	−	0.259923i	$-0.0836970\pi$
$242$	282.475	+	301.799i	1.16725	+	1.24710i
$243$	28.5696	−	241.315i	0.117570	−	0.993065i
$244$	−18.2290	+	275.284i	−0.0747091	+	1.12821i
$245$	−143.413	−	260.839i	−0.585359	−	1.06465i
$246$	170.762	+	99.5641i	0.694155	+	0.404732i
$247$		−	131.940i		−	0.534171i
$248$	−76.8640	+	62.9510i	−0.309935	+	0.253835i
$249$	−242.476	+	72.5139i	−0.973798	+	0.291220i
$250$	116.174	−	108.735i	0.464694	−	0.434940i
$251$	143.354			0.571131			0.285565	−	0.958359i	$-0.407819\pi$
$251$	143.354			0.571131			0.285565	+	0.958359i	$0.407819\pi$
$252$	181.542	−	174.775i	0.720406	−	0.693553i
$253$		−	204.232i		−	0.807240i
$254$	−72.1920	+	67.5696i	−0.284220	+	0.266022i
$255$	130.539	+	436.504i	0.511919	+	1.71178i
$256$	247.098	+	66.9226i	0.965226	+	0.261416i
$257$	301.716			1.17399			0.586996	−	0.809590i	$-0.300311\pi$
$257$	301.716			1.17399			0.586996	+	0.809590i	$0.300311\pi$
$258$	267.546	+	155.995i	1.03700	+	0.604631i
$259$	−18.0044	+	4.62317i	−0.0695150	+	0.0178501i
$260$	−474.587	−	31.4266i	−1.82533	−	0.120872i
$261$	−59.5370	+	39.1074i	−0.228111	+	0.149837i
$262$	−26.4022	−	28.2084i	−0.100772	−	0.107666i
$263$	−164.932			−0.627119			−0.313559	−	0.949569i	$-0.601521\pi$
$263$	−164.932			−0.627119			−0.313559	+	0.949569i	$0.601521\pi$
$264$	360.035	+	243.150i	1.36377	+	0.921022i
$265$		−	151.339i		−	0.571091i
$266$	79.5966	+	50.6949i	0.299235	+	0.190582i
$267$	−301.786	+	90.2510i	−1.13028	+	0.338019i
$268$	−7.56439	+	114.233i	−0.0282253	+	0.426243i
$269$			318.953i			1.18570i	0.805313	+	0.592850i	$0.201997\pi$
$269$			318.953i			1.18570i	−0.805313	+	0.592850i	$0.798003\pi$
$270$	−17.4804	−	327.573i	−0.0647422	−	1.21323i
$271$	158.506			0.584894			0.292447	−	0.956282i	$-0.405531\pi$
$271$	158.506			0.584894			0.292447	+	0.956282i	$0.405531\pi$
$272$	−396.504	−	52.7433i	−1.45773	−	0.193909i
$273$	−212.019	−	352.149i	−0.776625	−	1.28992i
$274$	49.5906	−	46.4154i	0.180988	−	0.169399i
$275$		−	215.472i		−	0.783534i
$276$	−30.1355	−	131.990i	−0.109187	−	0.478226i
$277$			393.719i			1.42137i	0.703512	+	0.710684i	$0.251614\pi$
$277$			393.719i			1.42137i	−0.703512	+	0.710684i	$0.748386\pi$
$278$	−27.7435	+	25.9671i	−0.0997968	+	0.0934069i
$279$	−93.4202	+	61.3639i	−0.334840	+	0.219942i
$280$	201.308	−	274.233i	0.718956	−	0.979402i
$281$			114.543i			0.407625i	0.979010	+	0.203813i	$0.0653334\pi$
$281$			114.543i			0.407625i	−0.979010	+	0.203813i	$0.934667\pi$
$282$	−111.085	+	190.522i	−0.393919	+	0.675609i
$283$		−	8.57843i		−	0.0303125i	−0.999885	−	0.0151562i	$-0.995175\pi$
$283$		−	8.57843i		−	0.0303125i	0.999885	−	0.0151562i	$-0.00482456\pi$
$284$	22.9868	−	347.133i	0.0809393	−	1.22230i
$285$	117.694	−	35.1972i	0.412963	−	0.123499i
$286$	517.382	−	484.255i	1.80903	−	1.69320i
$287$	57.3561	+	223.366i	0.199847	+	0.778280i
$288$	268.560	+	104.017i	0.932500	+	0.361170i
$289$	335.988			1.16259
$290$	−70.2061	+	65.7109i	−0.242090	+	0.226589i
$291$	−75.5297	−	252.560i	−0.259552	−	0.867904i
$292$	−313.103	−	20.7333i	−1.07227	−	0.0710046i
$293$			130.846i			0.446572i	0.974753	+	0.223286i	$0.0716784\pi$
$293$			130.846i			0.446572i	−0.974753	+	0.223286i	$0.928322\pi$
$294$	293.907	+	7.39894i	0.999683	+	0.0251665i
$295$			111.257i			0.377143i
$296$	−13.4605	−	16.4354i	−0.0454746	−	0.0555250i
$297$	374.128	+	314.500i	1.25969	+	1.05892i
$298$	31.5156	+	33.6716i	0.105757	+	0.112992i
$299$	−220.836			−0.738580
$300$	−31.7940	−	139.254i	−0.105980	−	0.464181i
$301$	89.8641	+	349.965i	0.298552	+	1.16268i
$302$	86.4157	−	80.8826i	0.286145	−	0.267823i
$303$	68.2778	+	228.311i	0.225339	+	0.753502i
$304$	−14.2212	+	106.909i	−0.0467801	+	0.351675i
$305$			418.990i			1.37374i
$306$	−437.387	−	105.775i	−1.42937	−	0.345670i
$307$			555.555i			1.80963i	0.425809	+	0.904813i	$0.359990\pi$
$307$			555.555i			1.80963i	−0.425809	+	0.904813i	$0.640010\pi$
$308$	93.3481	+	498.188i	0.303078	+	1.61749i
$309$	365.812	−	109.398i	1.18386	−	0.354040i
$310$	−110.161	+	103.108i	−0.355359	+	0.332606i
$311$		−	220.660i		−	0.709519i	−0.934958	−	0.354759i	$-0.884563\pi$
$311$		−	220.660i		−	0.709519i	0.934958	−	0.354759i	$-0.115437\pi$
$312$	262.918	−	389.305i	0.842684	−	1.24777i
$313$		−	477.460i		−	1.52543i	−0.646735	−	0.762715i	$-0.723866\pi$
$313$		−	477.460i		−	1.52543i	0.646735	−	0.762715i	$-0.276134\pi$
$314$	309.618	+	330.798i	0.986044	+	1.05350i
$315$	257.568	−	283.068i	0.817675	−	0.898629i
$316$	−10.1689	−	0.673374i	−0.0321801	−	0.00213093i
$317$	−281.998			−0.889584			−0.444792	−	0.895634i	$-0.646722\pi$
$317$	−281.998			−0.889584			−0.444792	+	0.895634i	$0.646722\pi$
$318$	129.129	+	75.2899i	0.406067	+	0.236761i
$319$		−	143.272i		−	0.449130i
$320$	381.163	+	76.6177i	1.19113	+	0.239430i
$321$	−147.862	−	494.428i	−0.460628	−	1.54027i
$322$	84.8508	−	133.225i	0.263512	−	0.413743i
$323$		−	168.515i		−	0.521719i
$324$	288.197	+	148.050i	0.889496	+	0.456943i
$325$	−232.989			−0.716890
$326$	165.779	+	177.119i	0.508523	+	0.543311i
$327$	−130.442	−	436.179i	−0.398906	−	1.33388i
$328$	−203.901	+	166.994i	−0.621650	+	0.509127i
$329$	−249.213	+	63.9930i	−0.757487	+	0.194508i
$330$	569.989	+	332.336i	1.72724	+	1.00708i
$331$	415.309			1.25471			0.627355	−	0.778733i	$-0.284138\pi$
$331$	415.309			1.25471			0.627355	+	0.778733i	$0.284138\pi$
$332$	22.2966	−	336.711i	0.0671585	−	1.01419i
$333$	−13.1211	−	19.9755i	−0.0394027	−	0.0599866i
$334$	−51.1117	+	47.8391i	−0.153029	+	0.143231i
$335$			173.866i			0.519002i
$336$	133.839	+	308.193i	0.398330	+	0.917242i
$337$	−288.093			−0.854874			−0.427437	−	0.904045i	$-0.640583\pi$
$337$	−288.093			−0.854874			−0.427437	+	0.904045i	$0.640583\pi$
$338$	−292.652	−	312.673i	−0.865836	−	0.925067i
$339$	−86.2819	−	288.514i	−0.254519	−	0.851074i
$340$	−606.146	−	40.1383i	−1.78278	−	0.118054i
$341$		−	224.811i		−	0.659269i
$342$	−28.5201	+	117.933i	−0.0833920	+	0.344832i
$343$	234.816	+	250.020i	0.684596	+	0.728923i
$344$	−319.468	+	261.642i	−0.928685	+	0.760586i
$345$	−58.9115	−	196.991i	−0.170758	−	0.570990i
$346$	−163.940	+	153.443i	−0.473815	+	0.443477i
$347$			144.584i			0.416670i	0.978058	+	0.208335i	$0.0668044\pi$
$347$			144.584i			0.416670i	−0.978058	+	0.208335i	$0.933196\pi$
$348$	−21.1406	−	92.5937i	−0.0607489	−	0.266074i
$349$	682.115			1.95448			0.977242	−	0.212128i	$-0.0680393\pi$
$349$	682.115			1.95448			0.977242	+	0.212128i	$0.0680393\pi$
$350$	89.5206	−	140.557i	0.255773	−	0.401592i
$351$	340.069	−	404.544i	0.968857	−	1.15255i
$352$	−471.421	+	336.618i	−1.33927	+	0.956300i
$353$	−388.643			−1.10097			−0.550486	−	0.834844i	$-0.685558\pi$
$353$	−388.643			−1.10097			−0.550486	+	0.834844i	$0.685558\pi$
$354$	−94.9298	−	55.3495i	−0.268163	−	0.156355i
$355$		−	528.345i		−	1.48830i
$356$	27.7504	−	419.072i	0.0779507	−	1.17717i
$357$	−270.792	−	449.768i	−0.758521	−	1.25985i
$358$	−78.2448	+	73.2348i	−0.218561	+	0.204567i
$359$	275.437			0.767234			0.383617	−	0.923492i	$-0.374678\pi$
$359$	275.437			0.767234			0.383617	+	0.923492i	$0.374678\pi$
$360$	417.408	+	130.676i	1.15947	+	0.362990i
$361$	315.563			0.874137
$362$	−163.449	−	174.630i	−0.451516	−	0.482404i
$363$	−594.060	+	177.657i	−1.63653	+	0.489414i
$364$	538.690	−	100.937i	1.47992	−	0.277300i
$365$	−476.551			−1.30562
$366$	−357.501	−	208.444i	−0.976779	−	0.569518i
$367$	−361.491			−0.984988			−0.492494	−	0.870316i	$-0.663915\pi$
$367$	−361.491			−0.984988			−0.492494	+	0.870316i	$0.663915\pi$
$368$	178.939	+	23.8027i	0.486249	+	0.0646813i
$369$	−247.821	+	162.783i	−0.671602	+	0.441147i
$370$	−22.0470	−	23.5552i	−0.0595864	−	0.0636627i
$371$	43.3724	+	168.909i	0.116907	+	0.455279i
$372$	−33.1720	−	145.290i	−0.0891720	−	0.390564i
$373$		−	479.653i		−	1.28593i	−0.765895	−	0.642966i	$-0.777704\pi$
$373$		−	479.653i		−	1.28593i	0.765895	−	0.642966i	$-0.222296\pi$
$374$	660.805	−	618.494i	1.76686	−	1.65373i
$375$	68.3868	+	228.675i	0.182365	+	0.609801i
$376$	−186.317	−	227.496i	−0.495524	−	0.605041i
$377$	−154.920			−0.410929
$378$	113.389	+	360.592i	0.299971	+	0.953948i
$379$	500.585			1.32080			0.660402	−	0.750912i	$-0.270386\pi$
$379$	500.585			1.32080			0.660402	+	0.750912i	$0.270386\pi$
$380$	−10.8225	+	163.435i	−0.0284802	+	0.430092i
$381$	−42.4965	−	142.102i	−0.111539	−	0.372972i
$382$	26.2088	+	28.0017i	0.0686095	+	0.0733030i
$383$			208.298i			0.543859i	0.962317	+	0.271929i	$0.0876617\pi$
$383$			208.298i			0.543859i	−0.962317	+	0.271929i	$0.912338\pi$
$384$	−254.999	+	287.109i	−0.664060	+	0.747679i
$385$	191.449	+	745.577i	0.497271	+	1.93656i
$386$	−44.3317	−	47.3644i	−0.114849	−	0.122706i
$387$	−388.280	+	255.045i	−1.00331	+	0.659031i
$388$	350.715	+	23.2239i	0.903904	+	0.0598555i
$389$	26.9990			0.0694063			0.0347031	−	0.999398i	$-0.488951\pi$
$389$	26.9990			0.0694063			0.0347031	+	0.999398i	$0.488951\pi$
$390$	359.355	−	616.328i	0.921422	−	1.58033i
$391$	−282.053			−0.721363
$392$	−146.086	+	363.762i	−0.372668	+	0.927965i
$393$	55.5252	−	16.6052i	0.141286	−	0.0422523i
$394$	−281.943	−	301.231i	−0.715592	−	0.764545i
$395$	−15.4773			−0.0391831
$396$	−567.129	+	321.006i	−1.43214	+	0.810621i
$397$	−177.923			−0.448168			−0.224084	−	0.974570i	$-0.571939\pi$
$397$	−177.923			−0.448168			−0.224084	+	0.974570i	$0.571939\pi$
$398$	−393.690	−	420.622i	−0.989172	−	1.05684i
$399$	−121.271	+	73.0136i	−0.303937	+	0.182991i
$400$	188.787	+	25.1127i	0.471969	+	0.0627818i
$401$		−	357.559i		−	0.891667i	−0.895116	−	0.445834i	$-0.852907\pi$
$401$		−	357.559i		−	0.891667i	0.895116	−	0.445834i	$-0.147093\pi$
$402$	−148.350	−	86.4967i	−0.369030	−	0.215166i
$403$	−243.087			−0.603195
$404$	−317.041	−	20.9941i	−0.784756	−	0.0519657i
$405$	451.584	+	195.432i	1.11502	+	0.482548i
$406$	59.5244	−	93.4599i	0.146612	−	0.230197i
$407$	48.0700			0.118108
$408$	335.801	−	497.223i	0.823040	−	1.21868i
$409$			678.281i			1.65839i	0.558960	+	0.829195i	$0.311201\pi$
$409$			678.281i			1.65839i	−0.558960	+	0.829195i	$0.688799\pi$
$410$	−292.231	+	273.520i	−0.712758	+	0.667121i
$411$	29.1920	+	97.6139i	0.0710268	+	0.237503i
$412$	−33.6379	+	507.980i	−0.0816453	+	1.23296i
$413$	−31.8853	−	124.174i	−0.0772041	−	0.300662i
$414$	197.390	+	47.7355i	0.476788	+	0.115303i
$415$		−	512.483i		−	1.23490i
$416$	363.984	+	509.747i	0.874962	+	1.22535i
$417$	−16.3315	−	54.6102i	−0.0391643	−	0.130960i
$418$	−166.764	−	178.172i	−0.398958	−	0.426250i
$419$	−585.142			−1.39652			−0.698261	−	0.715844i	$-0.746042\pi$
$419$	−585.142			−1.39652			−0.698261	+	0.715844i	$0.746042\pi$
$420$	233.743	+	453.600i	0.556531	+	1.08000i
$421$			455.654i			1.08231i	0.840922	+	0.541156i	$0.182013\pi$
$421$			455.654i			1.08231i	−0.840922	+	0.541156i	$0.817987\pi$
$422$	102.597	+	109.615i	0.243120	+	0.259752i
$423$	−181.620	−	276.497i	−0.429361	−	0.653658i
$424$	−154.189	+	126.280i	−0.363654	+	0.297829i
$425$	−297.576			−0.700179
$426$	450.809	+	262.847i	1.05824	+	0.617012i
$427$	−120.079	−	467.632i	−0.281214	−	1.09516i
$428$	686.581	+	45.4646i	1.60416	+	0.106226i
$429$	304.562	+	1018.41i	0.709935	+	2.37392i
$430$	−457.860	+	428.544i	−1.06479	+	0.996614i
$431$	−503.991			−1.16935			−0.584677	−	0.811266i	$-0.698779\pi$
$431$	−503.991			−1.16935			−0.584677	+	0.811266i	$0.698779\pi$
$432$	−319.156	+	291.142i	−0.738787	+	0.673939i
$433$			52.6642i			0.121626i	0.998149	+	0.0608132i	$0.0193694\pi$
$433$			52.6642i			0.121626i	−0.998149	+	0.0608132i	$0.980631\pi$
$434$	93.4006	−	146.649i	0.215209	−	0.337901i
$435$	−41.3275	−	138.193i	−0.0950058	−	0.317686i
$436$	605.695	+	40.1085i	1.38921	+	0.0919919i
$437$			76.0499i			0.174027i
$438$	237.080	−	406.615i	0.541278	−	0.928345i
$439$	−622.938			−1.41899			−0.709497	−	0.704709i	$-0.751078\pi$
$439$	−622.938			−1.41899			−0.709497	+	0.704709i	$0.751078\pi$
$440$	−680.604	+	557.410i	−1.54683	+	1.26684i
$441$	−206.345	+	389.747i	−0.467902	+	0.883780i
$442$	−668.777	−	714.527i	−1.51307	−	1.61658i
$443$			667.216i			1.50613i	0.657946	+	0.753065i	$0.271425\pi$
$443$			667.216i			1.50613i	−0.657946	+	0.753065i	$0.728575\pi$
$444$	31.0665	−	7.09299i	0.0699697	−	0.0159752i
$445$		−	637.838i		−	1.43334i
$446$	303.870	+	324.658i	0.681323	+	0.727932i
$447$	−66.2789	+	19.8211i	−0.148275	+	0.0443426i
$448$	−447.371	+	23.7252i	−0.998597	+	0.0529580i
$449$		−	364.939i		−	0.812781i	−0.913700	−	0.406390i	$-0.866787\pi$
$449$		−	364.939i		−	0.812781i	0.913700	−	0.406390i	$-0.133213\pi$
$450$	208.254	+	50.3627i	0.462786	+	0.111917i
$451$		−	596.368i		−	1.32232i
$452$	400.642	+	26.5300i	0.886376	+	0.0586948i
$453$	50.8695	+	170.100i	0.112295	+	0.375497i
$454$	−200.838	−	214.577i	−0.442375	−	0.472637i
$455$	806.192	−	207.014i	1.77185	−	0.454976i
$456$	−134.066	−	90.5418i	−0.294005	−	0.198557i
$457$	171.296			0.374827			0.187413	−	0.982281i	$-0.439990\pi$
$457$	171.296			0.374827			0.187413	+	0.982281i	$0.439990\pi$
$458$	281.898	+	301.182i	0.615498	+	0.657604i
$459$	434.339	−	516.688i	0.946272	−	1.12568i
$460$	273.550	+	18.1142i	0.594674	+	0.0393786i
$461$			306.409i			0.664662i	0.943163	+	0.332331i	$0.107835\pi$
$461$			306.409i			0.664662i	−0.943163	+	0.332331i	$0.892165\pi$
$462$	−731.405	−	207.565i	−1.58313	−	0.449275i
$463$			758.757i			1.63878i	0.573233	+	0.819392i	$0.305689\pi$
$463$			758.757i			1.63878i	−0.573233	+	0.819392i	$0.694311\pi$
$464$	125.529	+	16.6981i	0.270538	+	0.0359872i
$465$	−64.8476	−	216.841i	−0.139457	−	0.466324i
$466$	111.152	−	104.035i	0.238524	−	0.223252i
$467$	306.493			0.656301			0.328151	−	0.944625i	$-0.393575\pi$
$467$	306.493			0.656301			0.328151	+	0.944625i	$0.393575\pi$
$468$	347.103	+	613.236i	0.741674	+	1.31033i
$469$	−49.8283	−	194.050i	−0.106244	−	0.413754i
$470$	−305.170	−	326.046i	−0.649297	−	0.693715i
$471$	−651.141	+	194.728i	−1.38247	+	0.413435i
$472$	113.352	−	92.8348i	0.240154	−	0.196684i
$473$		−	934.374i		−	1.97542i
$474$	7.69984	−	13.2060i	0.0162444	−	0.0278607i
$475$			80.2353i			0.168916i
$476$	688.020	−	128.918i	1.44542	−	0.270836i
$477$	−187.401	+	123.096i	−0.392874	+	0.258063i
$478$	454.248	+	485.323i	0.950310	+	1.01532i
$479$			304.767i			0.636257i	0.948048	+	0.318128i	$0.103054\pi$
$479$			304.767i			0.636257i	−0.948048	+	0.318128i	$0.896946\pi$
$480$	−357.610	+	460.668i	−0.745021	+	0.959724i
$481$		−	51.9781i		−	0.108063i
$482$	−182.936	+	171.223i	−0.379536	+	0.355235i
$483$	122.207	+	202.977i	0.253016	+	0.420243i
$484$	54.6262	−	824.934i	0.112864	−	1.70441i
$485$	533.797			1.10061
$486$	−391.411	+	288.086i	−0.805372	+	0.592770i
$487$		−	552.223i		−	1.13393i	−0.823743	−	0.566964i	$-0.808118\pi$
$487$		−	552.223i		−	1.13393i	0.823743	−	0.566964i	$-0.191882\pi$
$488$	426.880	−	349.612i	0.874755	−	0.716417i
$489$	−348.641	+	104.263i	−0.712966	+	0.213217i
$490$	−184.873	+	565.897i	−0.377292	+	1.15489i
$491$		−	249.139i		−	0.507411i	−0.967281	−	0.253706i	$-0.918351\pi$
$491$		−	249.139i		−	0.507411i	0.967281	−	0.253706i	$-0.0816494\pi$
$492$	−87.9972	−	385.418i	−0.178856	−	0.783371i
$493$	−197.866			−0.401350
$494$	−192.658	+	180.322i	−0.389995	+	0.365024i
$495$	−827.204	+	543.356i	−1.67112	+	1.09769i
$496$	196.970	+	26.2011i	0.397117	+	0.0528249i
$497$	151.419	+	589.683i	0.304666	+	1.18648i
$498$	437.274	+	254.956i	0.878060	+	0.511960i
$499$	−590.912			−1.18419			−0.592096	−	0.805867i	$-0.701699\pi$
$499$	−590.912			−1.18419			−0.592096	+	0.805867i	$0.701699\pi$
$500$	−317.547	−	21.0276i	−0.635095	−	0.0420552i
$501$	−30.0874	−	100.608i	−0.0600547	−	0.200814i
$502$	−195.921	−	209.323i	−0.390280	−	0.416979i
$503$		−	1004.52i		−	1.99706i	−0.0542280	−	0.998529i	$-0.517270\pi$
$503$		−	1004.52i		−	1.99706i	0.0542280	−	0.998529i	$-0.482730\pi$
$504$	−503.317	−	26.2216i	−0.998646	−	0.0520270i
$505$	−482.545			−0.955535
$506$	−298.217	+	279.122i	−0.589361	+	0.551625i
$507$	615.463	−	184.058i	1.21393	−	0.363033i
$508$	197.329	+	13.0669i	0.388442	+	0.0257222i
$509$		−	12.5080i		−	0.0245736i	−0.999925	−	0.0122868i	$-0.996089\pi$
$509$		−	12.5080i		−	0.0245736i	0.999925	−	0.0122868i	$-0.00391111\pi$
$510$	458.971	−	787.179i	0.899943	−	1.54349i
$511$	531.875	−	136.575i	1.04085	−	0.267270i
$512$	−239.988	−	452.272i	−0.468726	−	0.883344i
$513$	−139.314	−	117.111i	−0.271568	−	0.228286i
$514$	−412.353	−	440.562i	−0.802243	−	0.857124i
$515$			773.159i			1.50128i
$516$	−137.872	−	603.864i	−0.267194	−	1.17028i
$517$	665.376			1.28699
$518$	31.3572	+	19.9713i	0.0605351	+	0.0385547i
$519$	−96.5049	−	322.698i	−0.185944	−	0.621769i
$520$	602.726	+	735.936i	1.15909	+	1.41526i
$521$	87.7148			0.168358			0.0841792	−	0.996451i	$-0.473173\pi$
$521$	87.7148			0.168358			0.0841792	+	0.996451i	$0.473173\pi$
$522$	138.473	+	33.4874i	0.265274	+	0.0641521i
$523$			158.064i			0.302225i	0.988517	+	0.151112i	$0.0482855\pi$
$523$			158.064i			0.302225i	−0.988517	+	0.151112i	$0.951714\pi$
$524$	−5.10577	+	77.1045i	−0.00974384	+	0.147146i
$525$	128.932	+	214.148i	0.245586	+	0.407902i
$526$	225.412	+	240.832i	0.428540	+	0.457856i
$527$	−310.473			−0.589134
$528$	−137.013	−	858.029i	−0.259494	−	1.62506i
$529$	−401.711			−0.759379
$530$	−220.983	+	206.834i	−0.416950	+	0.390253i
$531$	137.768	−	90.4942i	0.259450	−	0.170422i
$532$	−34.7601	−	185.510i	−0.0653385	−	0.348704i
$533$	−644.851			−1.20985
$534$	544.232	+	317.319i	1.01916	+	0.594230i
$535$	1044.99			1.95326
$536$	177.140	−	145.076i	0.330485	−	0.270665i
$537$	−46.0596	−	154.016i	−0.0857720	−	0.286809i
$538$	465.732	−	435.912i	0.865672	−	0.810245i
$539$	−427.351	−	777.267i	−0.792859	−	1.44205i
$540$	−454.428	+	473.217i	−0.841533	+	0.876327i
$541$			413.272i			0.763905i	0.924182	+	0.381952i	$0.124748\pi$
$541$			413.272i			0.763905i	−0.924182	+	0.381952i	$0.875252\pi$
$542$	−216.629	−	231.449i	−0.399685	−	0.427027i
$543$	343.741	−	102.798i	0.633040	−	0.189315i
$544$	464.884	+	651.054i	0.854566	+	1.19679i
$545$	921.883			1.69153
$546$	−224.440	+	790.867i	−0.411061	+	1.44848i
$547$	596.199			1.08994			0.544972	−	0.838454i	$-0.316540\pi$
$547$	596.199			1.08994			0.544972	+	0.838454i	$0.316540\pi$
$548$	−135.550	−	8.97599i	−0.247355	−	0.0163796i
$549$	518.829	−	340.797i	0.945043	−	0.620759i
$550$	−314.629	+	294.484i	−0.572053	+	0.535425i
$551$			53.3504i			0.0968247i
$552$	−151.545	+	224.394i	−0.274537	+	0.406510i
$553$	17.2742	−	4.43566i	0.0312372	−	0.00802109i
$554$	574.903	−	538.093i	1.03773	−	0.971287i
$555$	46.3659	−	13.8660i	0.0835421	−	0.0249838i
$556$	75.8338	+	5.02163i	0.136392	+	0.00903170i
$557$	144.131			0.258763			0.129381	−	0.991595i	$-0.458701\pi$
$557$	144.131			0.258763			0.129381	+	0.991595i	$0.458701\pi$
$558$	217.280	+	52.5455i	0.389390	+	0.0941675i
$559$	−1010.34			−1.80740
$560$	−675.557	+	80.8449i	−1.20635	+	0.144366i
$561$	388.989	+	1300.72i	0.693386	+	2.31858i
$562$	167.254	−	156.545i	0.297605	−	0.278550i
$563$	346.190			0.614902			0.307451	−	0.951564i	$-0.400524\pi$
$563$	346.190			0.614902			0.307451	+	0.951564i	$0.400524\pi$
$564$	430.017	−	98.1797i	0.762441	−	0.174077i
$565$	609.787			1.07927
$566$	−12.5261	+	11.7241i	−0.0221310	+	0.0207139i
$567$	−560.019	−	88.7007i	−0.987688	−	0.156439i
$568$	−538.295	+	440.860i	−0.947703	+	0.776161i
$569$			112.196i			0.197182i	0.995128	+	0.0985908i	$0.0314335\pi$
$569$			112.196i			0.197182i	−0.995128	+	0.0985908i	$0.968567\pi$
$570$	−212.247	−	123.752i	−0.372363	−	0.217109i
$571$	−758.845			−1.32898			−0.664488	−	0.747299i	$-0.731350\pi$
$571$	−758.845			−1.32898			−0.664488	+	0.747299i	$0.731350\pi$
$572$	−1414.21	−	93.6471i	−2.47239	−	0.163719i
$573$	−55.1185	+	16.4835i	−0.0961928	+	0.0287670i
$574$	247.769	−	389.024i	0.431653	−	0.677743i
$575$	134.294			0.233555
$576$	−215.155	−	534.307i	−0.373533	−	0.927617i
$577$			461.263i			0.799415i	0.916643	+	0.399708i	$0.130888\pi$
$577$			461.263i			0.799415i	−0.916643	+	0.399708i	$0.869112\pi$
$578$	−459.193	−	490.606i	−0.794451	−	0.848799i
$579$	93.2318	−	27.8815i	0.161022	−	0.0481547i
$580$	191.900	+	12.7074i	0.330863	+	0.0219094i
$581$	146.873	+	571.979i	0.252793	+	0.984473i
$582$	−265.559	+	455.460i	−0.456288	+	0.782577i
$583$		−	450.970i		−	0.773533i
$584$	397.641	+	485.525i	0.680893	+	0.831379i
$585$	587.530	+	894.455i	1.00432	+	1.52898i
$586$	191.059	−	178.826i	0.326039	−	0.305164i
$587$	921.720			1.57022			0.785110	−	0.619356i	$-0.212606\pi$
$587$	921.720			1.57022			0.785110	+	0.619356i	$0.212606\pi$
$588$	−390.877	−	439.271i	−0.664757	−	0.747060i
$589$			83.7128i			0.142127i
$590$	162.456	−	152.055i	0.275350	−	0.257720i
$591$	592.940	−	177.323i	1.00328	−	0.300038i
$592$	−5.60245	+	42.1170i	−0.00946359	+	0.0711436i
$593$	394.929			0.665986			0.332993	−	0.942929i	$-0.391942\pi$
$593$	394.929			0.665986			0.332993	+	0.942929i	$0.391942\pi$
$594$	−52.0892	−	976.123i	−0.0876923	−	1.64331i
$595$	1029.67	−	264.400i	1.73055	−	0.444370i
$596$	6.09462	−	92.0375i	0.0102259	−	0.154425i
$597$	827.950	−	247.604i	1.38685	−	0.414747i
$598$	301.815	+	322.461i	0.504707	+	0.539233i
$599$	916.058			1.52931			0.764656	−	0.644439i	$-0.222909\pi$
$599$	916.058			1.52931			0.764656	+	0.644439i	$0.222909\pi$
$600$	−159.885	+	236.743i	−0.266475	+	0.394572i
$601$		−	890.305i		−	1.48137i	−0.671851	−	0.740687i	$-0.734500\pi$
$601$		−	890.305i		−	1.48137i	0.671851	−	0.740687i	$-0.265500\pi$
$602$	388.198	−	609.514i	0.644848	−	1.01248i
$603$	215.295	−	141.418i	0.357040	−	0.234525i
$604$	−236.208	−	15.6414i	−0.391072	−	0.0258964i
$605$		−	1255.57i		−	2.07532i
$606$	240.062	−	411.730i	0.396142	−	0.679422i
$607$	−83.0019			−0.136741			−0.0683706	−	0.997660i	$-0.521780\pi$
$607$	−83.0019			−0.136741			−0.0683706	+	0.997660i	$0.521780\pi$
$608$	175.543	−	125.346i	0.288723	−	0.206162i
$609$	85.7303	+	142.392i	0.140772	+	0.233814i
$610$	611.804	−	572.630i	1.00296	−	0.938738i
$611$		−	719.470i		−	1.17753i
$612$	443.323	+	783.230i	0.724385	+	1.27979i
$613$			721.671i			1.17728i	0.808397	+	0.588638i	$0.200336\pi$
$613$			721.671i			1.17728i	−0.808397	+	0.588638i	$0.799664\pi$
$614$	811.215	−	759.274i	1.32120	−	1.23660i
$615$	−172.025	−	575.225i	−0.279715	−	0.935326i
$616$	599.870	−	817.176i	0.973815	−	1.32658i
$617$			111.394i			0.180541i	0.995917	+	0.0902707i	$0.0287732\pi$
$617$			111.394i			0.180541i	−0.995917	+	0.0902707i	$0.971227\pi$
$618$	−659.694	−	384.640i	−1.06747	−	0.622395i
$619$		−	454.283i		−	0.733898i	−0.930241	−	0.366949i	$-0.880402\pi$
$619$		−	454.283i		−	0.733898i	0.930241	−	0.366949i	$-0.119598\pi$
$620$	301.113	+	19.9394i	0.485667	+	0.0321603i
$621$	−196.014	+	233.178i	−0.315643	+	0.375488i
$622$	−322.206	+	301.575i	−0.518015	+	0.484847i
$623$	182.798	+	711.887i	0.293416	+	1.14268i
$624$	−927.786	+	148.152i	−1.48684	+	0.237422i
$625$	−780.894			−1.24943
$626$	−697.181	+	652.541i	−1.11371	+	1.04240i
$627$	350.714	−	104.883i	0.559352	−	0.167278i
$628$	59.8751	−	904.200i	0.0953425	−	1.43981i
$629$		−	66.3868i		−	0.105543i
$630$	−765.349	+	10.7706i	−1.21484	+	0.0170961i
$631$			948.810i			1.50366i	0.659357	+	0.751830i	$0.270829\pi$
$631$			948.810i			1.50366i	−0.659357	+	0.751830i	$0.729171\pi$
$632$	12.9145	+	15.7688i	0.0204344	+	0.0249507i
$633$	−215.766	+	64.5262i	−0.340863	+	0.101937i
$634$	385.405	+	411.770i	0.607895	+	0.649480i
$635$	300.339			0.472975
$636$	−66.5430	−	291.451i	−0.104627	−	0.458257i
$637$	−840.457	+	462.094i	−1.31940	+	0.725423i
$638$	−209.205	+	195.810i	−0.327907	+	0.306912i
$639$	−654.242	+	429.744i	−1.02385	+	0.672527i
$640$	−409.056	−	661.282i	−0.639151	−	1.03325i
$641$		−	849.888i		−	1.32588i	−0.748673	−	0.662939i	$-0.769309\pi$
$641$		−	849.888i		−	1.32588i	0.748673	−	0.662939i	$-0.230691\pi$
$642$	−519.876	+	891.637i	−0.809775	+	1.38884i
$643$			641.678i			0.997944i	0.866618	+	0.498972i	$0.166289\pi$
$643$			641.678i			0.997944i	−0.866618	+	0.498972i	$0.833711\pi$
$644$	−310.499	+	58.1798i	−0.482141	+	0.0903413i
$645$	−269.524	−	901.249i	−0.417867	−	1.39729i
$646$	−246.064	+	230.309i	−0.380904	+	0.356515i
$647$		−	448.130i		−	0.692628i	−0.938119	−	0.346314i	$-0.887433\pi$
$647$		−	448.130i		−	0.692628i	0.938119	−	0.346314i	$-0.112567\pi$
$648$	−177.696	−	623.160i	−0.274223	−	0.961666i
$649$			331.532i			0.510835i
$650$	318.425	+	340.208i	0.489885	+	0.523397i
$651$	134.521	+	223.430i	0.206637	+	0.343210i
$652$	32.0589	−	484.136i	0.0491701	−	0.742539i
$653$	−961.093			−1.47181			−0.735905	−	0.677084i	$-0.763243\pi$
$653$	−961.093			−1.47181			−0.735905	+	0.677084i	$0.763243\pi$
$654$	−458.629	+	786.593i	−0.701268	+	1.20274i
$655$			117.355i			0.179168i
$656$	522.513	+	69.5052i	0.796513	+	0.105953i
$657$	387.616	+	590.106i	0.589978	+	0.898182i
$658$	434.040	+	276.439i	0.659635	+	0.420120i
$659$			808.891i			1.22745i	0.789519	+	0.613726i	$0.210330\pi$
$659$			808.891i			1.22745i	−0.789519	+	0.613726i	$0.789670\pi$
$660$	−293.727	−	1286.49i	−0.445040	−	1.94923i
$661$	−574.628			−0.869331			−0.434666	−	0.900592i	$-0.643133\pi$
$661$	−574.628			−0.869331			−0.434666	+	0.900592i	$0.643133\pi$
$662$	−567.600	−	606.429i	−0.857402	−	0.916056i
$663$	1406.47	−	420.614i	2.12137	−	0.634410i
$664$	−522.134	+	427.624i	−0.786347	+	0.644012i
$665$	−71.2901	−	277.631i	−0.107203	−	0.417490i
$666$	−11.2355	+	46.4597i	−0.0168701	+	0.0697593i
$667$	89.2954			0.133876
$668$	139.708	+	9.25131i	0.209144	+	0.0138493i
$669$	−639.054	+	191.113i	−0.955237	+	0.285670i
$670$	253.877	−	237.621i	0.378920	−	0.354658i
$671$			1248.53i			1.86070i
$672$	267.103	−	616.636i	0.397475	−	0.917613i
$673$	781.072			1.16058			0.580291	−	0.814409i	$-0.302939\pi$
$673$	781.072			1.16058			0.580291	+	0.814409i	$0.302939\pi$
$674$	393.734	+	420.669i	0.584176	+	0.624139i
$675$	−206.802	+	246.011i	−0.306373	+	0.364460i
$676$	−56.5943	+	854.655i	−0.0837194	+	1.26428i
$677$			974.030i			1.43874i	0.694625	+	0.719372i	$0.255570\pi$
$677$			974.030i			1.43874i	−0.694625	+	0.719372i	$0.744430\pi$
$678$	−303.364	+	520.298i	−0.447439	+	0.767402i
$679$	−595.767	+	152.981i	−0.877419	+	0.225304i
$680$	769.807	+	939.944i	1.13207	+	1.38227i
$681$	422.372	−	126.313i	0.620224	−	0.185482i
$682$	−328.266	+	307.247i	−0.481328	+	0.450509i
$683$			1124.97i			1.64711i	0.567239	+	0.823553i	$0.308012\pi$
$683$			1124.97i			1.64711i	−0.567239	+	0.823553i	$0.691988\pi$
$684$	211.182	−	119.533i	0.308746	−	0.174756i
$685$	−206.311			−0.301184
$686$	44.1547	−	684.578i	0.0643655	−	0.997926i
$687$	−592.846	+	177.294i	−0.862949	+	0.258070i
$688$	818.660	+	108.899i	1.18991	+	0.158283i
$689$	−487.633			−0.707740
$690$	−207.130	+	355.249i	−0.300189	+	0.514853i
$691$			1048.93i			1.51799i	0.651094	+	0.758997i	$0.274310\pi$
$691$			1048.93i			1.51799i	−0.651094	+	0.758997i	$0.725690\pi$
$692$	448.111	+	29.6734i	0.647559	+	0.0428807i
$693$	767.517	−	843.505i	1.10753	−	1.21718i
$694$	211.120	−	197.603i	0.304208	−	0.284730i
$695$	115.421			0.166073
$696$	−106.311	+	157.416i	−0.152746	+	0.226173i
$697$	−823.610			−1.18165
$698$	−932.242	−	996.016i	−1.33559	−	1.42696i
$699$	65.4310	+	218.792i	0.0936065	+	0.313006i
$700$	−327.587	+	61.3817i	−0.467982	+	0.0876882i
$701$	708.010			1.01000			0.505000	−	0.863119i	$-0.331492\pi$
$701$	708.010			1.01000			0.505000	+	0.863119i	$0.331492\pi$
$702$	−1055.48	+	56.3240i	−1.50353	+	0.0802336i
$703$	−17.8999			−0.0254621
$704$	1135.81	+	228.311i	1.61337	+	0.324305i
$705$	641.787	−	191.930i	0.910336	−	0.272242i
$706$	531.156	+	567.492i	0.752346	+	0.803813i
$707$	538.566	−	138.293i	0.761762	−	0.195605i
$708$	48.9192	+	214.261i	0.0690950	+	0.302629i
$709$		−	989.361i		−	1.39543i	−0.716374	−	0.697716i	$-0.754200\pi$
$709$		−	989.361i		−	1.39543i	0.716374	−	0.697716i	$-0.245800\pi$
$710$	−771.483	+	722.086i	−1.08660	+	1.01702i
$711$	12.5889	+	19.1654i	0.0177059	+	0.0269555i
$712$	−649.850	+	532.222i	−0.912710	+	0.747502i
$713$	140.115			0.196514
$714$	−286.656	+	1010.10i	−0.401479	+	1.41471i
$715$	−2152.46			−3.01043
$716$	213.873	+	14.1624i	0.298706	+	0.0197800i
$717$	−955.307	+	285.690i	−1.33237	+	0.398452i
$718$	−376.438	−	402.190i	−0.524287	−	0.560153i
$719$			404.601i			0.562728i	0.959601	+	0.281364i	$0.0907868\pi$
$719$			404.601i			0.562728i	−0.959601	+	0.281364i	$0.909213\pi$
$720$	−379.657	−	788.089i	−0.527302	−	1.09457i
$721$	−221.580	−	862.918i	−0.307323	−	1.19683i
$722$	−431.278	−	460.782i	−0.597338	−	0.638202i
$723$	−107.687	−	360.091i	−0.148945	−	0.498051i
$724$	−31.6084	+	477.332i	−0.0436580	+	0.659298i
$725$	94.2098			0.129945
$726$	1071.31	+	624.636i	1.47563	+	0.860380i
$727$	861.158			1.18454			0.592268	−	0.805741i	$-0.298233\pi$
$727$	861.158			1.18454			0.592268	+	0.805741i	$0.298233\pi$
$728$	−883.612	−	648.638i	−1.21375	−	0.890987i
$729$	−125.308	−	718.150i	−0.171890	−	0.985116i
$730$	651.299	+	695.854i	0.892190	+	0.953224i
$731$	−1290.41			−1.76527
$732$	184.228	+	806.898i	0.251677	+	1.10232i
$733$	392.419			0.535360			0.267680	−	0.963508i	$-0.413743\pi$
$733$	392.419			0.535360			0.267680	+	0.963508i	$0.413743\pi$
$734$	494.047	+	527.844i	0.673089	+	0.719134i
$735$	−636.407	−	626.440i	−0.865859	−	0.852299i
$736$	−209.799	−	293.816i	−0.285053	−	0.399207i
$737$			518.096i			0.702980i
$738$	576.389	+	139.390i	0.781016	+	0.188876i
$739$	−226.762			−0.306849			−0.153425	−	0.988160i	$-0.549030\pi$
$739$	−226.762			−0.306849			−0.153425	+	0.988160i	$0.549030\pi$
$740$	−4.26353	+	64.3854i	−0.00576153	+	0.0870074i
$741$	−113.410	−	379.226i	−0.153050	−	0.511776i
$742$	187.361	−	294.178i	0.252509	−	0.396466i
$743$	693.032			0.932748			0.466374	−	0.884588i	$-0.345560\pi$
$743$	693.032			0.932748			0.466374	+	0.884588i	$0.345560\pi$
$744$	−166.815	+	247.004i	−0.224213	+	0.331995i
$745$		−	140.083i		−	0.188031i
$746$	−700.383	+	655.538i	−0.938851	+	0.878738i
$747$	−634.600	+	416.842i	−0.849532	+	0.558022i
$748$	−1806.23	−	119.607i	−2.41475	−	0.159902i
$749$	−1166.31	+	299.486i	−1.55716	+	0.399847i
$750$	240.445	−	412.387i	0.320593	−	0.549849i
$751$		−	698.204i		−	0.929700i	−0.885390	−	0.464850i	$-0.846108\pi$
$751$		−	698.204i		−	0.929700i	0.885390	−	0.464850i	$-0.153892\pi$
$752$	−77.5479	+	582.975i	−0.103122	+	0.775232i
$753$	412.031	−	123.220i	0.547186	−	0.163639i
$754$	211.729	+	226.213i	0.280807	+	0.300017i
$755$	−359.514			−0.476178
$756$	371.564	−	658.389i	0.491487	−	0.870885i
$757$			549.022i			0.725260i	0.931933	+	0.362630i	$0.118121\pi$
$757$			549.022i			0.725260i	−0.931933	+	0.362630i	$0.881879\pi$
$758$	−684.146	−	730.948i	−0.902567	−	0.964311i
$759$	−175.548	−	587.008i	−0.231289	−	0.773397i
$760$	253.437	−	207.563i	0.333470	−	0.273109i
$761$	390.469			0.513100			0.256550	−	0.966531i	$-0.417414\pi$
$761$	390.469			0.513100			0.256550	+	0.966531i	$0.417414\pi$
$762$	−149.416	+	256.263i	−0.196084	+	0.336303i
$763$	−1028.91	+	264.203i	−1.34850	+	0.346269i
$764$	5.06837	−	76.5396i	0.00663399	−	0.100183i
$765$	750.398	+	1142.41i	0.980913	+	1.49334i
$766$	304.154	−	284.679i	0.397068	−	0.371644i
$767$	358.485			0.467385
$768$	767.738	−	20.0436i	0.999659	−	0.0260984i
$769$		−	1361.61i		−	1.77063i	−0.464993	−	0.885314i	$-0.653943\pi$
$769$		−	1361.61i		−	1.77063i	0.464993	−	0.885314i	$-0.346057\pi$
$770$	827.030	−	1298.53i	1.07406	−	1.68640i
$771$	867.199	−	259.341i	1.12477	−	0.336370i
$772$	−8.57304	+	129.465i	−0.0111050	+	0.167701i
$773$		−	1328.35i		−	1.71843i	−0.511614	−	0.859215i	$-0.670952\pi$
$773$		−	1328.35i		−	1.71843i	0.511614	−	0.859215i	$-0.329048\pi$
$774$	903.073	+	218.393i	1.16676	+	0.282162i
$775$	147.826			0.190743
$776$	−445.408	−	543.850i	−0.573980	−	0.700837i
$777$	−47.7748	+	28.7638i	−0.0614862	+	0.0370190i
$778$	−36.8994	−	39.4237i	−0.0474286	−	0.0506731i
$779$			222.070i			0.285070i
$780$	−1391.08	+	317.606i	−1.78344	+	0.407187i
$781$		−	1574.40i		−	2.01588i
$782$	385.480	+	411.850i	0.492941	+	0.526663i
$783$	−137.508	+	163.579i	−0.175616	+	0.208913i
$784$	730.816	−	283.839i	0.932163	−	0.362039i
$785$		−	1376.22i		−	1.75314i
$786$	−100.133	−	58.3831i	−0.127395	−	0.0742787i
$787$			584.219i			0.742337i	0.928566	+	0.371168i	$0.121043\pi$
$787$			584.219i			0.742337i	−0.928566	+	0.371168i	$0.878957\pi$
$788$	−54.5233	+	823.380i	−0.0691920	+	1.04490i
$789$	−474.052	+	141.768i	−0.600827	+	0.179681i
$790$	21.1528	+	22.5998i	0.0267757	+	0.0286074i
$791$	−680.579	+	174.759i	−0.860404	+	0.220935i
$792$	1243.82	+	389.398i	1.57048	+	0.491664i
$793$	1350.04			1.70244
$794$	243.166	+	259.801i	0.306254	+	0.327205i
$795$	−130.084	−	434.982i	−0.163628	−	0.547148i
$796$	−76.1334	+	1149.72i	−0.0956450	+	1.44438i
$797$		−	1505.41i		−	1.88885i	−0.328725	−	0.944426i	$-0.606619\pi$
$797$		−	1505.41i		−	1.88885i	0.328725	−	0.944426i	$-0.393381\pi$
$798$	272.354	+	77.2910i	0.341295	+	0.0968559i
$799$		−	918.913i		−	1.15008i
$800$	−221.345	−	309.987i	−0.276682	−	0.387483i
$801$	−789.825	+	518.803i	−0.986049	+	0.647694i
$802$	−522.103	+	488.673i	−0.651001	+	0.609318i
$803$	−1420.06			−1.76844
$804$	76.4478	+	334.834i	0.0950844	+	0.416460i
$805$	−464.685	+	119.322i	−0.577249	+	0.148226i
$806$	332.226	+	354.953i	0.412191	+	0.440389i
$807$	274.158	+	916.744i	0.339725	+	1.13599i
$808$	402.643	+	491.633i	0.498321	+	0.608456i
$809$		−	472.140i		−	0.583609i	−0.956478	−	0.291805i	$-0.905744\pi$
$809$		−	472.140i		−	0.583609i	0.956478	−	0.291805i	$-0.0942557\pi$
$810$	−331.809	−	926.493i	−0.409641	−	1.14382i
$811$			652.885i			0.805037i	0.915412	+	0.402518i	$0.131865\pi$
$811$			652.885i			0.805037i	−0.915412	+	0.402518i	$0.868135\pi$
$812$	−217.821	+	40.8142i	−0.268252	+	0.0502638i
$813$	455.582	−	136.245i	0.560372	−	0.167583i
$814$	−65.6970	−	70.1913i	−0.0807089	−	0.0862301i
$815$		−	736.867i		−	0.904131i
$816$	−1184.98	+	189.220i	−1.45218	+	0.231888i
$817$			347.933i			0.425867i
$818$	990.418	−	927.003i	1.21078	−	1.13326i
$819$	−912.081	−	829.915i	−1.11365	−	1.01333i
$820$	798.780	+	52.8943i	0.974122	+	0.0645053i
$821$	−733.742			−0.893718			−0.446859	−	0.894605i	$-0.647457\pi$
$821$	−733.742			−0.893718			−0.446859	+	0.894605i	$0.647457\pi$
$822$	102.638	−	176.034i	0.124864	−	0.214153i
$823$			1037.88i			1.26109i	0.776151	+	0.630547i	$0.217169\pi$
$823$			1037.88i			1.26109i	−0.776151	+	0.630547i	$0.782831\pi$
$824$	787.719	−	645.136i	0.955970	−	0.782932i
$825$	−185.210	−	619.314i	−0.224497	−	0.750684i
$826$	−137.739	+	216.266i	−0.166754	+	0.261823i
$827$		−	223.798i		−	0.270615i	−0.990804	−	0.135307i	$-0.956798\pi$
$827$		−	223.798i		−	0.270615i	0.990804	−	0.135307i	$-0.0432022\pi$
$828$	−200.069	−	353.466i	−0.241629	−	0.426892i
$829$	1405.14			1.69498			0.847489	−	0.530813i	$-0.178113\pi$
$829$	1405.14			1.69498			0.847489	+	0.530813i	$0.178113\pi$
$830$	−748.321	+	700.407i	−0.901592	+	0.843864i
$831$	338.423	+	1131.64i	0.407248	+	1.36178i
$832$	246.872	−	1228.15i	0.296721	−	1.47615i
$833$	−1073.44	+	590.191i	−1.28864	+	0.708512i
$834$	−57.4209	+	98.4824i	−0.0688500	+	0.118084i
$835$	212.639			0.254658
$836$	−32.2495	+	487.014i	−0.0385760	+	0.582553i
$837$	−215.765	+	256.673i	−0.257784	+	0.306659i
$838$	799.710	+	854.418i	0.954308	+	1.01959i
$839$		−	1148.14i		−	1.36846i	−0.729264	−	0.684232i	$-0.760137\pi$
$839$		−	1148.14i		−	1.36846i	0.729264	−	0.684232i	$-0.239863\pi$
$840$	342.886	−	961.241i	0.408197	−	1.14433i
$841$	−778.358			−0.925514
$842$	665.340	−	622.739i	0.790190	−	0.739595i
$843$	98.4557	+	329.222i	0.116792	+	0.390536i
$844$	19.8406	−	299.621i	0.0235078	−	0.355001i
$845$			1300.81i			1.53942i
$846$	−155.520	+	643.086i	−0.183829	+	0.760149i
$847$	359.835	+	1401.34i	0.424835	+	1.65447i
$848$	395.121	+	52.5594i	0.465945	+	0.0619805i
$849$	−7.37363	−	24.6563i	−0.00868508	−	0.0290416i
$850$	406.695	+	434.517i	0.478465	+	0.511196i
$851$			29.9599i			0.0352056i
$852$	−232.311	−	1017.50i	−0.272665	−	1.19425i
$853$	−1532.59			−1.79671			−0.898354	−	0.439272i	$-0.855237\pi$
$853$	−1532.59			−1.79671			−0.898354	+	0.439272i	$0.855237\pi$
$854$	−518.720	+	814.447i	−0.607400	+	0.953685i
$855$	308.026	−	202.330i	0.360265	−	0.236643i
$856$	−871.959	−	1064.67i	−1.01864	−	1.24378i
$857$	1277.93			1.49117			0.745583	−	0.666413i	$-0.232171\pi$
$857$	1277.93			1.49117			0.745583	+	0.666413i	$0.232171\pi$
$858$	1070.83	−	1836.57i	1.24805	−	2.14053i
$859$		−	1201.25i		−	1.39843i	−0.714912	−	0.699215i	$-0.753533\pi$
$859$		−	1201.25i		−	1.39843i	0.714912	−	0.699215i	$-0.246467\pi$
$860$	1251.51	+	82.8735i	1.45524	+	0.0963646i
$861$	356.850	+	592.705i	0.414460	+	0.688391i
$862$	688.802	+	735.922i	0.799074	+	0.853738i
$863$	805.185			0.933007			0.466504	−	0.884519i	$-0.345513\pi$
$863$	805.185			0.933007			0.466504	+	0.884519i	$0.345513\pi$
$864$	861.310	+	68.1264i	0.996886	+	0.0788500i
$865$	682.036			0.788481
$866$	76.8996	−	71.9758i	0.0887986	−	0.0831130i
$867$	965.705	−	288.800i	1.11385	−	0.333103i
$868$	−341.785	+	64.0421i	−0.393762	+	0.0737812i
$869$	−46.1204			−0.0530729
$870$	−145.306	+	249.214i	−0.167018	+	0.286453i
$871$	560.217			0.643188
$872$	−769.234	−	939.245i	−0.882149	−	1.07712i
$873$	−434.179	−	660.993i	−0.497341	−	0.757151i
$874$	111.047	−	103.937i	0.127056	−	0.118921i
$875$	539.425	−	138.514i	0.616486	−	0.158301i
$876$	−917.750	+	209.537i	−1.04766	+	0.239197i
$877$		−	848.540i		−	0.967548i	−0.875193	−	0.483774i	$-0.839266\pi$
$877$		−	848.540i		−	0.967548i	0.875193	−	0.483774i	$-0.160734\pi$
$878$	851.366	+	909.607i	0.969665	+	1.03600i
$879$	112.469	+	376.080i	0.127951	+	0.427849i
$880$	1744.10	+	232.002i	1.98193	+	0.263639i
$881$	−862.906			−0.979462			−0.489731	−	0.871874i	$-0.662905\pi$
$881$	−862.906			−0.979462			−0.489731	+	0.871874i	$0.662905\pi$
$882$	851.114	−	231.363i	0.964982	−	0.262316i
$883$	577.379			0.653883			0.326942	−	0.945045i	$-0.393982\pi$
$883$	577.379			0.653883			0.326942	+	0.945045i	$0.393982\pi$
$884$	−129.331	+	1953.08i	−0.146302	+	2.20937i
$885$	95.6317	+	319.778i	0.108058	+	0.361331i
$886$	974.260	−	911.879i	1.09962	−	1.02921i
$887$			927.468i			1.04562i	0.852448	+	0.522812i	$0.175117\pi$
$887$			927.468i			1.04562i	−0.852448	+	0.522812i	$0.824883\pi$
$888$	−52.8156	−	35.6691i	−0.0594770	−	0.0401679i
$889$	−335.207	+	86.0744i	−0.377060	+	0.0968216i
$890$	−931.363	+	871.728i	−1.04647	+	0.979470i
$891$	1345.66	+	582.361i	1.51028	+	0.653604i
$892$	58.7636	−	887.415i	0.0658785	−	0.994860i
$893$	−247.766			−0.277454
$894$	119.526	+	69.6903i	0.133698	+	0.0779533i
$895$	325.520			0.363710
$896$	646.063	+	620.821i	0.721052	+	0.692881i
$897$	−634.731	+	189.820i	−0.707615	+	0.211617i
$898$	−532.879	+	498.759i	−0.593406	+	0.555411i
$899$	98.2930			0.109336
$900$	−211.080	−	372.920i	−0.234533	−	0.414355i
$901$	−622.809			−0.691242
$902$	−870.809	+	815.052i	−0.965420	+	0.903605i
$903$	559.104	+	928.636i	0.619163	+	1.02839i
$904$	−508.816	−	621.271i	−0.562849	−	0.687246i
$905$			726.511i			0.802774i
$906$	178.855	−	306.754i	0.197412	−	0.338580i
$907$	1113.64			1.22783			0.613915	−	0.789372i	$-0.289594\pi$
$907$	1113.64			1.22783			0.613915	+	0.789372i	$0.289594\pi$
$908$	−38.8389	+	586.522i	−0.0427741	+	0.645950i
$909$	392.491	+	597.528i	0.431784	+	0.657347i
$910$	−1404.10	−	894.266i	−1.54296	−	0.982710i
$911$	245.394			0.269368			0.134684	−	0.990889i	$-0.456998\pi$
$911$	245.394			0.269368			0.134684	+	0.990889i	$0.456998\pi$
$912$	51.0194	+	319.505i	0.0559423	+	0.350334i
$913$		−	1527.13i		−	1.67265i
$914$	−234.109	−	250.124i	−0.256137	−	0.273659i
$915$	360.144	+	1204.27i	0.393601	+	1.31614i
$916$	54.5146	−	823.248i	0.0595137	−	0.898743i
$917$	−33.6328	−	130.979i	−0.0366770	−	0.142834i
$918$	−1348.07	+	71.9375i	−1.46848	+	0.0783632i
$919$		−	590.705i		−	0.642770i	−0.946949	−	0.321385i	$-0.895852\pi$
$919$		−	590.705i		−	0.642770i	0.946949	−	0.321385i	$-0.104148\pi$
$920$	−347.409	−	424.191i	−0.377618	−	0.461077i
$921$	477.530	+	1596.79i	0.518491	+	1.73376i
$922$	447.415	−	418.767i	0.485266	−	0.454195i
$923$	−1702.39			−1.84441
$924$	696.523	+	1351.67i	0.753813	+	1.46284i
$925$			31.6088i			0.0341717i
$926$	1107.93	−	1036.99i	1.19647	−	1.11986i
$927$	957.391	−	628.870i	1.03278	−	0.678393i
$928$	−147.178	−	206.118i	−0.158597	−	0.222110i
$929$	−1503.25			−1.61814			−0.809070	−	0.587712i	$-0.800029\pi$
$929$	−1503.25			−1.61814			−0.809070	+	0.587712i	$0.800029\pi$
$930$	−228.001	+	391.044i	−0.245163	+	0.420478i
$931$	159.133	+	289.431i	0.170927	+	0.310882i
$932$	−303.822	−	20.1188i	−0.325990	−	0.0215867i
$933$	−189.670	−	634.227i	−0.203290	−	0.679772i
$934$	−418.881	−	447.537i	−0.448481	−	0.479161i
$935$	−2749.14			−2.94025
$936$	421.055	−	1344.94i	0.449845	−	1.43690i
$937$			493.211i			0.526373i	0.964745	+	0.263186i	$0.0847734\pi$
$937$			493.211i			0.526373i	−0.964745	+	0.263186i	$0.915227\pi$
$938$	−215.250	+	337.966i	−0.229478	+	0.360305i
$939$	−410.403	−	1372.33i	−0.437063	−	1.46148i
$940$	−59.0149	+	891.210i	−0.0627818	+	0.948096i
$941$			614.183i			0.652692i	0.945250	+	0.326346i	$0.105817\pi$
$941$			614.183i			0.652692i	−0.945250	+	0.326346i	$0.894183\pi$
$942$	1174.25	+	684.655i	1.24655	+	0.726810i
$943$	371.690			0.394157
$944$	−290.474	−	38.6392i	−0.307706	−	0.0409314i
$945$	496.994	−	1034.99i	0.525920	−	1.09523i
$946$	−1364.36	+	1277.00i	−1.44224	+	1.34990i
$947$		−	455.433i		−	0.480922i	−0.970659	−	0.240461i	$-0.922701\pi$
$947$		−	455.433i		−	0.480922i	0.970659	−	0.240461i	$-0.0772986\pi$
$948$	−29.8065	+	6.80531i	−0.0314415	+	0.00717859i
$949$			1535.51i			1.61803i
$950$	117.159	−	109.657i	0.123325	−	0.115429i
$951$	−810.526	+	242.393i	−0.852288	+	0.254882i
$952$	−1128.56	−	828.447i	−1.18546	−	0.870217i
$953$			1786.71i			1.87483i	0.348213	+	0.937415i	$0.386789\pi$
$953$			1786.71i			1.87483i	−0.348213	+	0.937415i	$0.613211\pi$
$954$	435.863	+	105.406i	0.456879	+	0.110489i
$955$		−	116.495i		−	0.121985i
$956$	87.8443	−	1326.58i	0.0918874	−	1.38763i
$957$	−123.151	−	411.797i	−0.128684	−	0.430300i
$958$	445.017	−	416.523i	0.464527	−	0.434784i
$959$	230.263	−	59.1269i	0.240107	−	0.0616547i
$960$	1161.40	−	107.414i	1.20980	−	0.111889i
$961$	−806.767			−0.839508
$962$	−75.8977	+	71.0381i	−0.0788958	+	0.0738442i
$963$	−849.975	−	1294.00i	−0.882632	−	1.34372i
$964$	500.036	+	33.1118i	0.518709	+	0.0343483i
$965$			197.049i			0.204196i
$966$	129.366	−	455.853i	0.133919	−	0.471897i
$967$		−	1359.05i		−	1.40543i	−0.711472	−	0.702715i	$-0.751971\pi$
$967$		−	1359.05i		−	1.40543i	0.711472	−	0.702715i	$-0.248029\pi$
$968$	−1279.22	+	1047.67i	−1.32150	+	1.08230i
$969$	−144.848	−	484.351i	−0.149482	−	0.499846i
$970$	−729.537	−	779.444i	−0.752100	−	0.803550i
$971$	1016.98			1.04735			0.523676	−	0.851918i	$-0.324560\pi$
$971$	1016.98			1.04735			0.523676	+	0.851918i	$0.324560\pi$
$972$	955.599	+	177.807i	0.983126	+	0.182929i
$973$	−128.821	+	33.0786i	−0.132395	+	0.0339965i
$974$	−806.349	+	754.719i	−0.827873	+	0.774866i
$975$	−669.664	+	200.267i	−0.686834	+	0.205402i
$976$	−1093.91	−	145.513i	−1.12081	−	0.149092i
$977$		−	126.755i		−	0.129739i	−0.997894	−	0.0648697i	$-0.979337\pi$
$977$		−	126.755i		−	0.129739i	0.997894	−	0.0648697i	$-0.0206632\pi$
$978$	628.729	+	366.585i	0.642872	+	0.374831i
$979$		−	1900.67i		−	1.94144i
$980$	1078.98	−	503.459i	1.10100	−	0.513734i
$981$	−749.840	−	1141.55i	−0.764363	−	1.16366i
$982$	−363.790	+	340.497i	−0.370458	+	0.346738i
$983$			155.672i			0.158364i	0.996860	+	0.0791822i	$0.0252309\pi$
$983$			155.672i			0.158364i	−0.996860	+	0.0791822i	$0.974769\pi$
$984$	−442.518	+	655.241i	−0.449714	+	0.665896i
$985$			1253.21i			1.27229i
$986$	270.422	+	288.921i	0.274261	+	0.293023i
$987$	−661.289	+	398.143i	−0.669999	+	0.403387i
$988$	526.608	+	34.8714i	0.533004	+	0.0352949i
$989$	582.354			0.588832
$990$	1923.94	+	465.272i	1.94337	+	0.469972i
$991$		−	358.585i		−	0.361841i	−0.983498	−	0.180921i	$-0.942092\pi$
$991$		−	358.585i		−	0.361841i	0.983498	−	0.180921i	$-0.0579077\pi$
$992$	−230.939	−	323.422i	−0.232801	−	0.326030i
$993$	1193.69	−	356.981i	1.20211	−	0.359497i
$994$	654.105	−	1027.02i	0.658053	−	1.03322i
$995$			1749.91i			1.75870i
$996$	−225.336	−	986.949i	−0.226241	−	0.990912i
$997$	753.699			0.755967			0.377983	−	0.925812i	$-0.376618\pi$
$997$	753.699			0.755967			0.377983	+	0.925812i	$0.376618\pi$
$998$	807.596	+	862.843i	0.809214	+	0.864572i
$999$	−54.8831	−	46.1359i	−0.0549380	−	0.0461821i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.3.e.f.83.10	yes	48
3.2	odd	2	inner	168.3.e.f.83.39	yes	48
4.3	odd	2		672.3.e.f.335.4		48
7.6	odd	2	inner	168.3.e.f.83.9	✓	48
8.3	odd	2	inner	168.3.e.f.83.38	yes	48
8.5	even	2		672.3.e.f.335.3		48
12.11	even	2		672.3.e.f.335.47		48
21.20	even	2	inner	168.3.e.f.83.40	yes	48
24.5	odd	2		672.3.e.f.335.48		48
24.11	even	2	inner	168.3.e.f.83.11	yes	48
28.27	even	2		672.3.e.f.335.46		48
56.13	odd	2		672.3.e.f.335.45		48
56.27	even	2	inner	168.3.e.f.83.37	yes	48
84.83	odd	2		672.3.e.f.335.1		48
168.83	odd	2	inner	168.3.e.f.83.12	yes	48
168.125	even	2		672.3.e.f.335.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.e.f.83.9	✓	48	7.6	odd	2	inner
168.3.e.f.83.10	yes	48	1.1	even	1	trivial
168.3.e.f.83.11	yes	48	24.11	even	2	inner
168.3.e.f.83.12	yes	48	168.83	odd	2	inner
168.3.e.f.83.37	yes	48	56.27	even	2	inner
168.3.e.f.83.38	yes	48	8.3	odd	2	inner
168.3.e.f.83.39	yes	48	3.2	odd	2	inner
168.3.e.f.83.40	yes	48	21.20	even	2	inner
672.3.e.f.335.1		48	84.83	odd	2
672.3.e.f.335.2		48	168.125	even	2
672.3.e.f.335.3		48	8.5	even	2
672.3.e.f.335.4		48	4.3	odd	2
672.3.e.f.335.45		48	56.13	odd	2
672.3.e.f.335.46		48	28.27	even	2
672.3.e.f.335.47		48	12.11	even	2
672.3.e.f.335.48		48	24.5	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	168.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36669 - 1.46019i) q^{2} +(2.87422 - 0.859555i) q^{3} +(-0.264297 + 3.99126i) q^{4} +6.07480i q^{5} +(-5.18330 - 3.02216i) q^{6} +(-1.74098 - 6.78004i) q^{7} +(6.18920 - 5.06891i) q^{8} +(7.52233 - 4.94111i) q^{9} +(8.87034 - 8.30239i) q^{10} +18.1021i q^{11} +(2.67106 + 11.6990i) q^{12} +19.5738 q^{13} +(-7.52075 + 11.8084i) q^{14} +(5.22162 + 17.4603i) q^{15} +(-15.8603 - 2.10975i) q^{16} +24.9998 q^{17} +(-17.4957 - 4.23104i) q^{18} -6.74068i q^{19} +(-24.2461 - 1.60555i) q^{20} +(-10.8318 - 17.9909i) q^{21} +(26.4324 - 24.7400i) q^{22} -11.2822 q^{23} +(13.4321 - 19.8891i) q^{24} -11.9032 q^{25} +(-26.7513 - 28.5814i) q^{26} +(17.3737 - 20.6677i) q^{27} +(27.5210 - 5.15676i) q^{28} -7.91470 q^{29} +(18.3590 - 31.4875i) q^{30} -12.4191 q^{31} +(18.5955 + 26.0424i) q^{32} +(15.5597 + 52.0294i) q^{33} +(-34.1670 - 36.5043i) q^{34} +(41.1874 - 10.5761i) q^{35} +(17.7331 + 31.3295i) q^{36} -2.65550i q^{37} +(-9.84265 + 9.21244i) q^{38} +(56.2594 - 16.8247i) q^{39} +(30.7926 + 37.5981i) q^{40} -32.9447 q^{41} +(-11.4664 + 40.4045i) q^{42} -51.6170 q^{43} +(-72.2501 - 4.78432i) q^{44} +(30.0162 + 45.6966i) q^{45} +(15.4194 + 16.4742i) q^{46} -36.7569i q^{47} +(-47.3995 + 7.56889i) q^{48} +(-42.9380 + 23.6078i) q^{49} +(16.2680 + 17.3808i) q^{50} +(71.8549 - 21.4887i) q^{51} +(-5.17328 + 78.1239i) q^{52} -24.9126 q^{53} +(-53.9233 + 2.87753i) q^{54} -109.966 q^{55} +(-45.1427 - 33.1382i) q^{56} +(-5.79398 - 19.3742i) q^{57} +(10.8170 + 11.5569i) q^{58} +18.3146 q^{59} +(-71.0687 + 16.2261i) q^{60} +68.9718 q^{61} +(16.9730 + 18.1341i) q^{62} +(-46.5971 - 42.3994i) q^{63} +(12.6124 - 62.7449i) q^{64} +118.907i q^{65} +(54.7074 - 93.8284i) q^{66} +28.6208 q^{67} +(-6.60735 + 99.7805i) q^{68} +(-32.4277 + 9.69769i) q^{69} +(-71.7336 - 45.6870i) q^{70} -86.9733 q^{71} +(21.5112 - 68.7115i) q^{72} +78.4472i q^{73} +(-3.87753 + 3.62925i) q^{74} +(-34.2123 + 10.2314i) q^{75} +(26.9038 + 1.78154i) q^{76} +(122.733 - 31.5154i) q^{77} +(-101.457 - 59.1550i) q^{78} +2.54780i q^{79} +(12.8163 - 96.3481i) q^{80} +(32.1709 - 74.3373i) q^{81} +(45.0253 + 48.1054i) q^{82} -84.3621 q^{83} +(74.6691 - 38.4775i) q^{84} +151.868i q^{85} +(70.5446 + 75.3705i) q^{86} +(-22.7486 + 6.80311i) q^{87} +(91.7577 + 112.037i) q^{88} -104.997 q^{89} +(25.7027 - 106.283i) q^{90} +(-34.0775 - 132.711i) q^{91} +(2.98186 - 45.0303i) q^{92} +(-35.6951 + 10.6749i) q^{93} +(-53.6719 + 50.2354i) q^{94} +40.9482 q^{95} +(75.8326 + 58.8678i) q^{96} -87.8707i q^{97} +(93.1549 + 30.4328i) q^{98} +(89.4443 + 136.170i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 44 q^{4} - 16 q^{9} - 76 q^{16} + 4 q^{18} + 32 q^{22} + 144 q^{25} + 108 q^{28} - 268 q^{30} - 176 q^{36} + 44 q^{42} + 128 q^{43} + 496 q^{46} - 464 q^{49} + 576 q^{51} + 128 q^{57} - 80 q^{58}+ \cdots - 64 q^{99}+O(q^{100}) \) 48 * q - 44 * q^4 - 16 * q^9 - 76 * q^16 + 4 * q^18 + 32 * q^22 + 144 * q^25 + 108 * q^28 - 268 * q^30 - 176 * q^36 + 44 * q^42 + 128 * q^43 + 496 * q^46 - 464 * q^49 + 576 * q^51 + 128 * q^57 - 80 * q^58 - 244 * q^60 - 212 * q^64 - 640 * q^67 - 336 * q^70 + 220 * q^72 - 84 * q^78 + 208 * q^81 + 308 * q^84 + 56 * q^88 + 320 * q^91 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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