LMFDB - Embedded newform 112.3.l.b.69.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [112,3,Mod(13,112)] 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("112.13"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(112, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	112.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [56] 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:	$3.05177896084$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			69.24
Character	$\chi$	$=$	112.69
Dual form			112.3.l.b.13.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.52993 + 1.28814i) q^{2} +(1.11083 + 1.11083i) q^{3} +(0.681387 + 3.94154i) q^{4} +(5.47687 - 5.47687i) q^{5} +(0.268590 + 3.13041i) q^{6} +(-3.11774 + 6.26735i) q^{7} +(-4.03478 + 6.90801i) q^{8} -6.53210i q^{9} +(15.4342 - 1.32426i) q^{10} +(2.57334 + 2.57334i) q^{11} +(-3.62148 + 5.13530i) q^{12} +(-11.1543 - 11.1543i) q^{13} +(-12.8432 + 5.57253i) q^{14} +12.1678 q^{15} +(-15.0714 + 5.37142i) q^{16} +24.6360i q^{17} +(8.41426 - 9.99367i) q^{18} +(-10.9902 - 10.9902i) q^{19} +(25.3191 + 17.8554i) q^{20} +(-10.4253 + 3.49869i) q^{21} +(0.622213 + 7.25186i) q^{22} -10.3758i q^{23} +(-12.1556 + 3.19168i) q^{24} -34.9921i q^{25} +(-2.69701 - 31.4335i) q^{26} +(17.2536 - 17.2536i) q^{27} +(-26.8274 - 8.01821i) q^{28} +(24.5610 - 24.5610i) q^{29} +(18.6159 + 15.6738i) q^{30} -14.5313i q^{31} +(-29.9774 - 11.1962i) q^{32} +5.71711i q^{33} +(-31.7347 + 37.6915i) q^{34} +(17.2500 + 51.4009i) q^{35} +(25.7465 - 4.45089i) q^{36} +(-2.55303 - 2.55303i) q^{37} +(-2.65734 - 30.9712i) q^{38} -24.7811i q^{39} +(15.7363 + 59.9322i) q^{40} -48.3838 q^{41} +(-20.4568 - 8.07647i) q^{42} +(46.0243 + 46.0243i) q^{43} +(-8.38947 + 11.8964i) q^{44} +(-35.7754 - 35.7754i) q^{45} +(13.3655 - 15.8743i) q^{46} -19.3308i q^{47} +(-22.7086 - 10.7751i) q^{48} +(-29.5593 - 39.0800i) q^{49} +(45.0748 - 53.5356i) q^{50} +(-27.3665 + 27.3665i) q^{51} +(36.3646 - 51.5653i) q^{52} +(8.08934 + 8.08934i) q^{53} +(48.6218 - 4.17177i) q^{54} +28.1877 q^{55} +(-30.7155 - 46.8248i) q^{56} -24.4166i q^{57} +(69.2148 - 5.93866i) q^{58} +(-61.0667 + 61.0667i) q^{59} +(8.29096 + 47.9597i) q^{60} +(75.6742 + 75.6742i) q^{61} +(18.7183 - 22.2319i) q^{62} +(40.9389 + 20.3654i) q^{63} +(-31.4411 - 55.7446i) q^{64} -122.181 q^{65} +(-7.36444 + 8.74679i) q^{66} +(-81.1264 + 81.1264i) q^{67} +(-97.1038 + 16.7867i) q^{68} +(11.5258 - 11.5258i) q^{69} +(-39.8203 + 100.860i) q^{70} +9.46404i q^{71} +(45.1238 + 26.3556i) q^{72} +36.7372 q^{73} +(-0.617301 - 7.19462i) q^{74} +(38.8704 - 38.8704i) q^{75} +(35.8297 - 50.8069i) q^{76} +(-24.1510 + 8.10501i) q^{77} +(31.9215 - 37.9134i) q^{78} +55.0332 q^{79} +(-53.1256 + 111.963i) q^{80} -20.4572 q^{81} +(-74.0239 - 62.3251i) q^{82} +(42.2965 + 42.2965i) q^{83} +(-20.8939 - 38.7077i) q^{84} +(134.928 + 134.928i) q^{85} +(11.1283 + 129.700i) q^{86} +54.5665 q^{87} +(-28.1595 + 7.39380i) q^{88} -8.11436 q^{89} +(-8.65021 - 100.818i) q^{90} +(104.684 - 35.1315i) q^{91} +(40.8967 - 7.06995i) q^{92} +(16.1418 - 16.1418i) q^{93} +(24.9008 - 29.5748i) q^{94} -120.384 q^{95} +(-20.8628 - 45.7370i) q^{96} +141.282i q^{97} +(5.11671 - 97.8663i) q^{98} +(16.8093 - 16.8093i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{2} - 8 q^{4} - 16 q^{8} + 40 q^{14} - 8 q^{15} + 48 q^{16} + 196 q^{18} - 20 q^{21} - 120 q^{22} - 96 q^{29} - 40 q^{30} - 184 q^{32} - 100 q^{35} + 160 q^{36} - 128 q^{37} - 144 q^{42} - 72 q^{43}+ \cdots + 8 q^{99}+O(q^{100}) $ 56 * q - 4 * q^2 - 8 * q^4 - 16 * q^8 + 40 * q^14 - 8 * q^15 + 48 * q^16 + 196 * q^18 - 20 * q^21 - 120 * q^22 - 96 * q^29 - 40 * q^30 - 184 * q^32 - 100 * q^35 + 160 * q^36 - 128 * q^37 - 144 * q^42 - 72 * q^43 - 448 * q^44 - 168 * q^46 + 192 * q^49 - 364 * q^50 - 128 * q^51 + 88 * q^53 + 56 * q^56 + 408 * q^58 + 504 * q^60 + 444 * q^63 + 256 * q^64 - 8 * q^65 + 440 * q^67 - 112 * q^70 + 592 * q^72 - 408 * q^74 + 12 * q^77 + 664 * q^78 - 8 * q^79 + 64 * q^81 - 576 * q^84 + 96 * q^85 + 256 * q^86 + 448 * q^88 - 388 * q^91 - 1192 * q^92 + 32 * q^93 - 776 * q^95 + 540 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.52993	+	1.28814i	0.764966	+	0.644070i
$2$	1.52993	+	1.28814i	0.764966	+	0.644070i
$3$	1.11083	+	1.11083i	0.370278	+	0.370278i	0.867578	−	0.497300i	$-0.165675\pi$
$3$	1.11083	+	1.11083i	0.370278	+	0.370278i	−0.497300	+	0.867578i	$0.665675\pi$
$4$	0.681387	+	3.94154i	0.170347	+	0.985384i
$5$	5.47687	−	5.47687i	1.09537	−	1.09537i	0.100429	−	0.994944i	$-0.467978\pi$
$5$	5.47687	−	5.47687i	1.09537	−	1.09537i	0.994944	−	0.100429i	$-0.0320216\pi$
$6$	0.268590	+	3.13041i	0.0447651	+	0.521735i
$7$	−3.11774	+	6.26735i	−0.445392	+	0.895336i
$7$	−3.11774	+	6.26735i	−0.445392	+	0.895336i
$8$	−4.03478	+	6.90801i	−0.504347	+	0.863501i
$9$		−	6.53210i		−	0.725789i
$10$	15.4342	−	1.32426i	1.54342	−	0.132426i
$11$	2.57334	+	2.57334i	0.233940	+	0.233940i	0.814335	−	0.580395i	$-0.197102\pi$
$11$	2.57334	+	2.57334i	0.233940	+	0.233940i	−0.580395	+	0.814335i	$0.697102\pi$
$12$	−3.62148	+	5.13530i	−0.301790	+	0.427942i
$13$	−11.1543	−	11.1543i	−0.858021	−	0.858021i	0.133084	−	0.991105i	$-0.457512\pi$
$13$	−11.1543	−	11.1543i	−0.858021	−	0.858021i	−0.991105	+	0.133084i	$0.957512\pi$
$14$	−12.8432	+	5.57253i	−0.917369	+	0.398038i
$15$	12.1678			0.811185
$16$	−15.0714	+	5.37142i	−0.941964	+	0.335714i
$17$			24.6360i			1.44918i	0.689181	+	0.724589i	$0.257971\pi$
$17$			24.6360i			1.44918i	−0.689181	+	0.724589i	$0.742029\pi$
$18$	8.41426	−	9.99367i	0.467459	−	0.555204i
$19$	−10.9902	−	10.9902i	−0.578432	−	0.578432i	0.356039	−	0.934471i	$-0.384127\pi$
$19$	−10.9902	−	10.9902i	−0.578432	−	0.578432i	−0.934471	+	0.356039i	$0.884127\pi$
$20$	25.3191	+	17.8554i	1.26596	+	0.892770i
$21$	−10.4253	+	3.49869i	−0.496442	+	0.166604i
$22$	0.622213	+	7.25186i	0.0282824	+	0.329630i
$23$		−	10.3758i		−	0.451122i	−0.974229	−	0.225561i	$-0.927578\pi$
$23$		−	10.3758i		−	0.451122i	0.974229	−	0.225561i	$-0.0724216\pi$
$24$	−12.1556	+	3.19168i	−0.506484	+	0.132987i
$25$		−	34.9921i		−	1.39969i
$26$	−2.69701	−	31.4335i	−0.103731	−	1.20898i
$27$	17.2536	−	17.2536i	0.639021	−	0.639021i
$28$	−26.8274	−	8.01821i	−0.958121	−	0.286365i
$29$	24.5610	−	24.5610i	0.846933	−	0.846933i	−0.142817	−	0.989749i	$-0.545616\pi$
$29$	24.5610	−	24.5610i	0.846933	−	0.846933i	0.989749	+	0.142817i	$0.0456159\pi$
$30$	18.6159	+	15.6738i	0.620529	+	0.522460i
$31$		−	14.5313i		−	0.468751i	−0.972146	−	0.234375i	$-0.924696\pi$
$31$		−	14.5313i		−	0.468751i	0.972146	−	0.234375i	$-0.0753045\pi$
$32$	−29.9774	−	11.1962i	−0.936794	−	0.349881i
$33$			5.71711i			0.173246i
$34$	−31.7347	+	37.6915i	−0.933373	+	1.10857i
$35$	17.2500	+	51.4009i	0.492856	+	1.46860i
$36$	25.7465	−	4.45089i	0.715181	−	0.123636i
$37$	−2.55303	−	2.55303i	−0.0690008	−	0.0690008i	0.671764	−	0.740765i	$-0.265537\pi$
$37$	−2.55303	−	2.55303i	−0.0690008	−	0.0690008i	−0.740765	+	0.671764i	$0.765537\pi$
$38$	−2.65734	−	30.9712i	−0.0699301	−	0.815032i
$39$		−	24.7811i		−	0.635412i
$40$	15.7363	+	59.9322i	0.393407	+	1.49830i
$41$	−48.3838			−1.18009			−0.590046	−	0.807369i	$-0.700890\pi$
$41$	−48.3838			−1.18009			−0.590046	+	0.807369i	$0.700890\pi$
$42$	−20.4568	−	8.07647i	−0.487066	−	0.192297i
$43$	46.0243	+	46.0243i	1.07033	+	1.07033i	0.997332	+	0.0729998i	$0.0232573\pi$
$43$	46.0243	+	46.0243i	1.07033	+	1.07033i	0.0729998	+	0.997332i	$0.476743\pi$
$44$	−8.38947	+	11.8964i	−0.190670	+	0.270372i
$45$	−35.7754	−	35.7754i	−0.795010	−	0.795010i
$46$	13.3655	−	15.8743i	0.290555	−	0.345093i
$47$		−	19.3308i		−	0.411294i	−0.978626	−	0.205647i	$-0.934070\pi$
$47$		−	19.3308i		−	0.411294i	0.978626	−	0.205647i	$-0.0659298\pi$
$48$	−22.7086	−	10.7751i	−0.473096	−	0.224481i
$49$	−29.5593	−	39.0800i	−0.603252	−	0.797551i
$50$	45.0748	−	53.5356i	0.901496	−	1.07071i
$51$	−27.3665	+	27.3665i	−0.536599	+	0.536599i
$52$	36.3646	−	51.5653i	0.699319	−	0.991641i
$53$	8.08934	+	8.08934i	0.152629	+	0.152629i	0.779291	−	0.626662i	$-0.215579\pi$
$53$	8.08934	+	8.08934i	0.152629	+	0.152629i	−0.626662	+	0.779291i	$0.715579\pi$
$54$	48.6218	−	4.17177i	0.900404	−	0.0772551i
$55$	28.1877			0.512503
$56$	−30.7155	−	46.8248i	−0.548491	−	0.836156i
$57$		−	24.4166i		−	0.428361i
$58$	69.2148	−	5.93866i	1.19336	−	0.102391i
$59$	−61.0667	+	61.0667i	−1.03503	+	1.03503i	−0.0356642	+	0.999364i	$0.511355\pi$
$59$	−61.0667	+	61.0667i	−1.03503	+	1.03503i	−0.999364	+	0.0356642i	$0.988645\pi$
$60$	8.29096	+	47.9597i	0.138183	+	0.799329i
$61$	75.6742	+	75.6742i	1.24056	+	1.24056i	0.959768	+	0.280793i	$0.0905975\pi$
$61$	75.6742	+	75.6742i	1.24056	+	1.24056i	0.280793	+	0.959768i	$0.409403\pi$
$62$	18.7183	−	22.2319i	0.301908	−	0.358578i
$63$	40.9389	+	20.3654i	0.649824	+	0.323260i
$64$	−31.4411	−	55.7446i	−0.491268	−	0.871009i
$65$	−122.181			−1.87971
$66$	−7.36444	+	8.74679i	−0.111582	+	0.132527i
$67$	−81.1264	+	81.1264i	−1.21084	+	1.21084i	−0.240091	+	0.970750i	$0.577177\pi$
$67$	−81.1264	+	81.1264i	−1.21084	+	1.21084i	−0.970750	+	0.240091i	$0.922823\pi$
$68$	−97.1038	+	16.7867i	−1.42800	+	0.246863i
$69$	11.5258	−	11.5258i	0.167041	−	0.167041i
$70$	−39.8203	+	100.860i	−0.568862	+	1.44086i
$71$			9.46404i			0.133296i	0.997777	+	0.0666481i	$0.0212305\pi$
$71$			9.46404i			0.133296i	−0.997777	+	0.0666481i	$0.978769\pi$
$72$	45.1238	+	26.3556i	0.626719	+	0.366049i
$73$	36.7372			0.503249			0.251625	−	0.967825i	$-0.419035\pi$
$73$	36.7372			0.503249			0.251625	+	0.967825i	$0.419035\pi$
$74$	−0.617301	−	7.19462i	−0.00834191	−	0.0972246i
$75$	38.8704	−	38.8704i	0.518273	−	0.518273i
$76$	35.8297	−	50.8069i	0.471444	−	0.668512i
$77$	−24.1510	+	8.10501i	−0.313650	+	0.105260i
$78$	31.9215	−	37.9134i	0.409250	−	0.486069i
$79$	55.0332			0.696622			0.348311	−	0.937379i	$-0.386755\pi$
$79$	55.0332			0.696622			0.348311	+	0.937379i	$0.386755\pi$
$80$	−53.1256	+	111.963i	−0.664070	+	1.39953i
$81$	−20.4572			−0.252558
$82$	−74.0239	−	62.3251i	−0.902731	−	0.760063i
$83$	42.2965	+	42.2965i	0.509597	+	0.509597i	0.914403	−	0.404806i	$-0.132661\pi$
$83$	42.2965	+	42.2965i	0.509597	+	0.509597i	−0.404806	+	0.914403i	$0.632661\pi$
$84$	−20.8939	−	38.7077i	−0.248736	−	0.460805i
$85$	134.928	+	134.928i	1.58739	+	1.58739i
$86$	11.1283	+	129.700i	0.129399	+	1.50814i
$87$	54.5665			0.627201
$88$	−28.1595	+	7.39380i	−0.319994	+	0.0840204i
$89$	−8.11436			−0.0911726			−0.0455863	−	0.998960i	$-0.514516\pi$
$89$	−8.11436			−0.0911726			−0.0455863	+	0.998960i	$0.514516\pi$
$90$	−8.65021	−	100.818i	−0.0961134	−	1.12020i
$91$	104.684	−	35.1315i	1.15037	−	0.386061i
$92$	40.8967	−	7.06995i	0.444529	−	0.0768472i
$93$	16.1418	−	16.1418i	0.173568	−	0.173568i
$94$	24.9008	−	29.5748i	0.264902	−	0.314626i
$95$	−120.384			−1.26720
$96$	−20.8628	−	45.7370i	−0.217321	−	0.476427i
$97$			141.282i			1.45651i	0.685306	+	0.728255i	$0.259669\pi$
$97$			141.282i			1.45651i	−0.685306	+	0.728255i	$0.740331\pi$
$98$	5.11671	−	97.8663i	0.0522113	−	0.998636i
$99$	16.8093	−	16.8093i	0.169791	−	0.169791i
$100$	137.923	−	23.8432i	1.37923	−	0.238432i
$101$	91.1516	−	91.1516i	0.902491	−	0.902491i	−0.0931601	−	0.995651i	$-0.529697\pi$
$101$	91.1516	−	91.1516i	0.902491	−	0.902491i	0.995651	+	0.0931601i	$0.0296969\pi$
$102$	−77.1209	+	6.61700i	−0.756087	+	0.0648726i
$103$	−168.367			−1.63463			−0.817313	−	0.576193i	$-0.804538\pi$
$103$	−168.367			−1.63463			−0.817313	+	0.576193i	$0.804538\pi$
$104$	122.059	−	32.0488i	1.17364	−	0.308161i
$105$	−37.9360	+	76.2597i	−0.361295	+	0.726283i
$106$	1.95594	+	22.7964i	0.0184522	+	0.215060i
$107$	−60.2166	−	60.2166i	−0.562772	−	0.562772i	0.367322	−	0.930094i	$-0.380275\pi$
$107$	−60.2166	−	60.2166i	−0.562772	−	0.562772i	−0.930094	+	0.367322i	$0.880275\pi$
$108$	79.7620	+	56.2492i	0.738537	+	0.520826i
$109$	3.71167	−	3.71167i	0.0340520	−	0.0340520i	−0.689876	−	0.723928i	$-0.742335\pi$
$109$	3.71167	−	3.71167i	0.0340520	−	0.0340520i	0.723928	+	0.689876i	$0.242335\pi$
$110$	43.1253	+	36.3097i	0.392048	+	0.330088i
$111$		−	5.67198i		−	0.0510989i
$112$	13.3242	−	111.205i	0.118966	−	0.992898i
$113$	44.1451			0.390664			0.195332	−	0.980737i	$-0.437422\pi$
$113$	44.1451			0.390664			0.195332	+	0.980737i	$0.437422\pi$
$114$	31.4520	−	37.3557i	0.275895	−	0.327682i
$115$	−56.8270	−	56.8270i	−0.494147	−	0.494147i
$116$	113.544	+	80.0727i	0.978826	+	0.690282i
$117$	−72.8608	+	72.8608i	−0.622742	+	0.622742i
$118$	−172.090	+	14.7654i	−1.45839	+	0.125131i
$119$	−154.403	−	76.8088i	−1.29750	−	0.645452i
$120$	−49.0943	+	84.0551i	−0.409119	+	0.700459i
$121$		−	107.756i		−	0.890544i
$122$	18.2974	+	213.256i	0.149979	+	1.74800i
$123$	−53.7463	−	53.7463i	−0.436962	−	0.436962i
$124$	57.2755	−	9.90142i	0.461899	−	0.0798501i
$125$	−54.7256	−	54.7256i	−0.437805	−	0.437805i
$126$	36.4003	+	83.8928i	0.288891	+	0.665816i
$127$	101.945			0.802715			0.401358	−	0.915921i	$-0.368538\pi$
$127$	101.945			0.802715			0.401358	+	0.915921i	$0.368538\pi$
$128$	23.7040	−	125.786i	0.185188	−	0.982703i
$129$			102.251i			0.792640i
$130$	−186.929	−	157.386i	−1.43791	−	1.21066i
$131$	96.2909	+	96.2909i	0.735045	+	0.735045i	0.971615	−	0.236569i	$-0.0760231\pi$
$131$	96.2909	+	96.2909i	0.735045	+	0.735045i	−0.236569	+	0.971615i	$0.576023\pi$
$132$	−22.5342	+	3.89556i	−0.170714	+	0.0295118i
$133$	103.144	−	34.6148i	0.775520	−	0.260262i
$134$	−228.620	+	19.6157i	−1.70612	+	0.146386i
$135$		−	188.991i		−	1.39993i
$136$	−170.186	−	99.4009i	−1.25137	−	0.730889i
$137$			44.6517i			0.325925i	0.986632	+	0.162963i	$0.0521050\pi$
$137$			44.6517i			0.325925i	−0.986632	+	0.162963i	$0.947895\pi$
$138$	32.4806	−	2.78684i	0.235366	−	0.0201945i
$139$	−6.91394	+	6.91394i	−0.0497406	+	0.0497406i	−0.731540	−	0.681799i	$-0.761198\pi$
$139$	−6.91394	+	6.91394i	−0.0497406	+	0.0497406i	0.681799	+	0.731540i	$0.261198\pi$
$140$	−190.845	+	103.015i	−1.36318	+	0.735824i
$141$	21.4733	−	21.4733i	0.152293	−	0.152293i
$142$	−12.1910	+	14.4793i	−0.0858522	+	0.101967i
$143$		−	57.4075i		−	0.401451i
$144$	35.0867	+	98.4480i	0.243657	+	0.683667i
$145$		−	269.035i		−	1.85541i
$146$	56.2054	+	47.3227i	0.384969	+	0.324128i
$147$	10.5758	−	76.2469i	0.0719445	−	0.518686i
$148$	8.32325	−	11.8025i	0.0562382	−	0.0797463i
$149$	−86.9376	−	86.9376i	−0.583474	−	0.583474i	0.352382	−	0.935856i	$-0.385372\pi$
$149$	−86.9376	−	86.9376i	−0.583474	−	0.583474i	−0.935856	+	0.352382i	$0.885372\pi$
$150$	109.540	−	9.39856i	0.730265	−	0.0626570i
$151$		−	136.089i		−	0.901251i	−0.892713	−	0.450626i	$-0.851201\pi$
$151$		−	136.089i		−	0.901251i	0.892713	−	0.450626i	$-0.148799\pi$
$152$	120.264	−	31.5774i	0.791207	−	0.207746i
$153$	160.925			1.05180
$154$	−47.3899	−	18.7098i	−0.307726	−	0.121492i
$155$	−79.5858	−	79.5858i	−0.513457	−	0.513457i
$156$	97.6755	−	16.8855i	0.626125	−	0.108240i
$157$	−61.2224	−	61.2224i	−0.389952	−	0.389952i	0.484719	−	0.874670i	$-0.338922\pi$
$157$	−61.2224	−	61.2224i	−0.389952	−	0.389952i	−0.874670	+	0.484719i	$0.838922\pi$
$158$	84.1970	+	70.8905i	0.532893	+	0.448674i
$159$			17.9718i			0.113030i
$160$	−225.502	+	102.862i	−1.40939	+	0.642889i
$161$	65.0289	+	32.3491i	0.403906	+	0.200926i
$162$	−31.2981	−	26.3517i	−0.193198	−	0.162665i
$163$	168.015	−	168.015i	1.03077	−	1.03077i	0.0312561	−	0.999511i	$-0.490049\pi$
$163$	168.015	−	168.015i	1.03077	−	1.03077i	0.999511	−	0.0312561i	$-0.00995075\pi$
$164$	−32.9681	−	190.706i	−0.201025	−	1.16284i
$165$	31.3118	+	31.3118i	0.189769	+	0.189769i
$166$	10.2270	+	119.195i	0.0616082	+	0.718041i
$167$	−118.309			−0.708434			−0.354217	−	0.935163i	$-0.615253\pi$
$167$	−118.309			−0.708434			−0.354217	+	0.935163i	$0.615253\pi$
$168$	17.8947	−	86.1343i	0.106516	−	0.512704i
$169$			79.8354i			0.472399i
$170$	32.6246	+	380.238i	0.191909	+	2.23669i
$171$	−71.7891	+	71.7891i	−0.419820	+	0.419820i
$172$	−150.046	+	212.767i	−0.872360	+	1.23702i
$173$	8.88388	+	8.88388i	0.0513519	+	0.0513519i	0.732316	−	0.680965i	$-0.238439\pi$
$173$	8.88388	+	8.88388i	0.0513519	+	0.0513519i	−0.680965	+	0.732316i	$0.738439\pi$
$174$	83.4830	+	70.2893i	0.479787	+	0.403961i
$175$	219.308	+	109.097i	1.25319	+	0.623409i
$176$	−52.6064	−	24.9614i	−0.298900	−	0.141826i
$177$	−135.670			−0.766496
$178$	−12.4144	−	10.4524i	−0.0697440	−	0.0587216i
$179$	−134.233	+	134.233i	−0.749904	+	0.749904i	−0.974461	−	0.224557i	$-0.927907\pi$
$179$	−134.233	+	134.233i	−0.749904	+	0.749904i	0.224557	+	0.974461i	$0.427907\pi$
$180$	116.633	−	165.387i	0.647963	−	0.918817i
$181$	−9.12602	+	9.12602i	−0.0504200	+	0.0504200i	−0.731867	−	0.681447i	$-0.761351\pi$
$181$	−9.12602	+	9.12602i	−0.0504200	+	0.0504200i	0.681447	+	0.731867i	$0.261351\pi$
$182$	205.414	+	81.0986i	1.12865	+	0.445597i
$183$			168.123i			0.918705i
$184$	71.6762	+	41.8641i	0.389545	+	0.227522i
$185$	−27.9652			−0.151163
$186$	45.4888	−	3.90296i	0.244564	−	0.0209837i
$187$	−63.3969	+	63.3969i	−0.339021	+	0.339021i
$188$	76.1931	−	13.1718i	0.405282	−	0.0700625i
$189$	54.3420	+	161.926i	0.287524	+	0.856754i
$190$	−184.179	−	155.071i	−0.969364	−	0.816165i
$191$	−182.482			−0.955405			−0.477702	−	0.878522i	$-0.658530\pi$
$191$	−182.482			−0.955405			−0.477702	+	0.878522i	$0.658530\pi$
$192$	26.9970	−	96.8488i	0.140610	−	0.504421i
$193$	378.766			1.96252			0.981258	−	0.192699i	$-0.0617240\pi$
$193$	378.766			1.96252			0.981258	+	0.192699i	$0.0617240\pi$
$194$	−181.991	+	216.151i	−0.938095	+	1.11418i
$195$	−135.723	−	135.723i	−0.696013	−	0.696013i
$196$	133.894	−	143.138i	0.683132	−	0.730295i
$197$	128.998	+	128.998i	0.654811	+	0.654811i	0.954148	−	0.299337i	$-0.0967653\pi$
$197$	128.998	+	128.998i	0.654811	+	0.654811i	−0.299337	+	0.954148i	$0.596765\pi$
$198$	47.3699	−	4.06435i	0.239242	−	0.0205270i
$199$	274.793			1.38087			0.690436	−	0.723394i	$-0.257419\pi$
$199$	274.793			1.38087			0.690436	+	0.723394i	$0.257419\pi$
$200$	241.726	+	141.186i	1.20863	+	0.705928i
$201$	−180.236			−0.896696
$202$	256.872	−	22.0397i	1.27164	−	0.109107i
$203$	77.3576	+	230.508i	0.381072	+	1.13551i
$204$	−126.513	−	89.2190i	−0.620164	−	0.437348i
$205$	−264.992	+	264.992i	−1.29264	+	1.29264i
$206$	−257.590	−	216.880i	−1.25043	−	1.05281i
$207$	−67.7758			−0.327419
$208$	228.025	+	108.196i	1.09627	+	0.520175i
$209$		−	56.5631i		−	0.270637i
$210$	−156.273	+	67.8053i	−0.744156	+	0.322882i
$211$	81.1914	−	81.1914i	0.384793	−	0.384793i	−0.488032	−	0.872826i	$-0.662285\pi$
$211$	81.1914	−	81.1914i	0.384793	−	0.384793i	0.872826	+	0.488032i	$0.162285\pi$
$212$	−26.3725	+	37.3964i	−0.124398	+	0.176398i
$213$	−10.5130	+	10.5130i	−0.0493567	+	0.0493567i
$214$	−14.5599	−	169.695i	−0.0680368	−	0.792966i
$215$	504.138			2.34483
$216$	49.5735	+	188.802i	0.229507	+	0.874084i
$217$	91.0725	+	45.3048i	0.419689	+	0.208778i
$218$	10.4598	−	0.897452i	0.0479806	−	0.00411675i
$219$	40.8089	+	40.8089i	0.186342	+	0.186342i
$220$	19.2067	+	111.103i	0.0873033	+	0.505013i
$221$	274.797	−	274.797i	1.24343	−	1.24343i
$222$	7.30631	−	8.67775i	0.0329113	−	0.0390889i
$223$		−	265.113i		−	1.18885i	−0.804152	−	0.594424i	$-0.797380\pi$
$223$		−	265.113i		−	1.18885i	0.804152	−	0.594424i	$-0.202620\pi$
$224$	163.632	−	152.972i	0.730502	−	0.682911i
$225$	−228.572			−1.01588
$226$	67.5390	+	56.8650i	0.298845	+	0.251615i
$227$	35.0233	+	35.0233i	0.154288	+	0.154288i	0.780030	−	0.625742i	$-0.215204\pi$
$227$	35.0233	+	35.0233i	0.154288	+	0.154288i	−0.625742	+	0.780030i	$0.715204\pi$
$228$	96.2389	−	16.6372i	0.422100	−	0.0729700i
$229$	−16.7509	+	16.7509i	−0.0731481	+	0.0731481i	−0.742734	−	0.669586i	$-0.766471\pi$
$229$	−16.7509	+	16.7509i	−0.0731481	+	0.0731481i	0.669586	+	0.742734i	$0.266471\pi$
$230$	−13.7403	−	160.143i	−0.0597404	−	0.696272i
$231$	−35.8311	−	17.8245i	−0.155113	−	0.0771622i
$232$	70.5695	+	268.766i	0.304179	+	1.15848i
$233$			162.893i			0.699113i	0.936915	+	0.349556i	$0.113668\pi$
$233$			162.893i			0.699113i	−0.936915	+	0.349556i	$0.886332\pi$
$234$	−205.327	+	17.6171i	−0.877466	+	0.0752869i
$235$	−105.872	−	105.872i	−0.450520	−	0.450520i
$236$	−282.306	−	199.086i	−1.19621	−	0.843587i
$237$	61.1327	+	61.1327i	0.257944	+	0.257944i
$238$	−137.285	−	316.405i	−0.576828	−	1.32943i
$239$	−458.835			−1.91981			−0.959906	−	0.280321i	$-0.909559\pi$
$239$	−458.835			−1.91981			−0.959906	+	0.280321i	$0.909559\pi$
$240$	−183.386	+	65.3583i	−0.764107	+	0.272326i
$241$		−	6.17751i		−	0.0256328i	−0.999918	−	0.0128164i	$-0.995920\pi$
$241$		−	6.17751i		−	0.0256328i	0.999918	−	0.0128164i	$-0.00407970\pi$
$242$	138.805	−	164.859i	0.573573	−	0.681236i
$243$	−178.007	−	178.007i	−0.732538	−	0.732538i
$244$	−246.709	+	349.836i	−1.01110	+	1.43376i
$245$	−375.928	−	52.1432i	−1.53440	−	0.212830i
$246$	−12.9954	−	151.461i	−0.0528269	−	0.615696i
$247$			245.176i			0.992614i
$248$	100.382	+	58.6304i	0.404767	+	0.236413i
$249$			93.9688i			0.377385i
$250$	−13.2322	−	154.221i	−0.0529288	−	0.616883i
$251$	19.6790	−	19.6790i	0.0784025	−	0.0784025i	−0.666818	−	0.745221i	$-0.732344\pi$
$251$	19.6790	−	19.6790i	0.0784025	−	0.0784025i	0.745221	+	0.666818i	$0.232344\pi$
$252$	−52.3757	+	175.239i	−0.207840	+	0.695393i
$253$	26.7005	−	26.7005i	0.105536	−	0.105536i
$254$	155.969	+	131.319i	0.614050	+	0.517005i
$255$			299.766i			1.17555i
$256$	198.296	−	161.910i	0.774592	−	0.632461i
$257$			46.6133i			0.181375i	0.995879	+	0.0906873i	$0.0289064\pi$
$257$			46.6133i			0.181375i	−0.995879	+	0.0906873i	$0.971094\pi$
$258$	−131.713	+	156.437i	−0.510516	+	0.606343i
$259$	23.9604	−	8.04103i	0.0925112	−	0.0310465i
$260$	−83.2525	−	481.580i	−0.320202	−	1.85223i
$261$	−160.435	−	160.435i	−0.614694	−	0.614694i
$262$	23.2824	+	271.355i	0.0888639	+	1.03571i
$263$			233.528i			0.887940i	0.896042	+	0.443970i	$0.146430\pi$
$263$			233.528i			0.887940i	−0.896042	+	0.443970i	$0.853570\pi$
$264$	−39.4938	−	23.0673i	−0.149598	−	0.0873760i
$265$	88.6085			0.334372
$266$	202.392	+	79.9058i	0.760874	+	0.300398i
$267$	−9.01371	−	9.01371i	−0.0337592	−	0.0337592i
$268$	−375.041	−	264.484i	−1.39941	−	0.986881i
$269$	118.706	+	118.706i	0.441286	+	0.441286i	0.892444	−	0.451158i	$-0.148989\pi$
$269$	118.706	+	118.706i	0.441286	+	0.441286i	−0.451158	+	0.892444i	$0.648989\pi$
$270$	243.447	−	289.144i	0.901656	−	1.07090i
$271$			131.992i			0.487055i	0.969894	+	0.243527i	$0.0783046\pi$
$271$			131.992i			0.487055i	−0.969894	+	0.243527i	$0.921695\pi$
$272$	−132.331	−	371.300i	−0.486510	−	1.36507i
$273$	155.312	+	77.2610i	0.568907	+	0.283007i
$274$	−57.5177	+	68.3141i	−0.209919	+	0.249322i
$275$	90.0467	−	90.0467i	0.327443	−	0.327443i
$276$	53.2829	+	37.5758i	0.193054	+	0.136144i
$277$	−249.565	−	249.565i	−0.900958	−	0.900958i	0.0945613	−	0.995519i	$-0.469855\pi$
$277$	−249.565	−	249.565i	−0.900958	−	0.900958i	−0.995519	+	0.0945613i	$0.969855\pi$
$278$	−19.4840	+	1.67173i	−0.0700863	+	0.00601343i
$279$	−94.9197			−0.340214
$280$	−424.678	−	88.2283i	−1.51671	−	0.315101i
$281$		−	344.044i		−	1.22436i	−0.790720	−	0.612178i	$-0.790294\pi$
$281$		−	344.044i		−	1.22436i	0.790720	−	0.612178i	$-0.209706\pi$
$282$	60.5133	−	5.19207i	0.214586	−	0.0184116i
$283$	141.638	−	141.638i	0.500489	−	0.500489i	−0.411101	−	0.911590i	$-0.634856\pi$
$283$	141.638	−	141.638i	0.500489	−	0.500489i	0.911590	+	0.411101i	$0.134856\pi$
$284$	−37.3028	+	6.44867i	−0.131348	+	0.0227066i
$285$	−133.726	−	133.726i	−0.469216	−	0.469216i
$286$	73.9489	−	87.8295i	0.258563	−	0.307096i
$287$	150.848	−	303.238i	0.525604	−	1.05658i
$288$	−73.1347	+	195.815i	−0.253940	+	0.679914i
$289$	−317.934			−1.10012
$290$	346.555	−	411.606i	1.19502	−	1.41933i
$291$	−156.940	+	156.940i	−0.539314	+	0.539314i
$292$	25.0323	+	144.801i	0.0857269	+	0.495894i
$293$	82.6004	−	82.6004i	0.281913	−	0.281913i	−0.551959	−	0.833871i	$-0.686119\pi$
$293$	82.6004	−	82.6004i	0.281913	−	0.281913i	0.833871	+	0.551959i	$0.186119\pi$
$294$	114.397	−	103.029i	0.389106	−	0.350440i
$295$			668.908i			2.26748i
$296$	27.9372	−	7.33544i	0.0943826	−	0.0247819i
$297$	88.7986			0.298985
$298$	−21.0208	−	244.997i	−0.0705396	−	0.822136i
$299$	−115.735	+	115.735i	−0.387072	+	0.387072i
$300$	179.695	+	126.723i	0.598984	+	0.422412i
$301$	−431.942	+	144.958i	−1.43502	+	0.481589i
$302$	175.302	−	208.207i	0.580469	−	0.689427i
$303$	202.509			0.668345
$304$	224.671	+	106.605i	0.739050	+	0.350675i
$305$	828.916			2.71776
$306$	246.204	+	207.294i	0.804589	+	0.677431i
$307$	200.953	+	200.953i	0.654570	+	0.654570i	0.954090	−	0.299520i	$-0.0968265\pi$
$307$	200.953	+	200.953i	0.654570	+	0.654570i	−0.299520	+	0.954090i	$0.596826\pi$
$308$	−48.4024	−	89.6696i	−0.157151	−	0.291135i
$309$	−187.027	−	187.027i	−0.605266	−	0.605266i
$310$	−19.2432	−	224.279i	−0.0620748	−	0.723480i
$311$	−463.074			−1.48898			−0.744491	−	0.667632i	$-0.767308\pi$
$311$	−463.074			−1.48898			−0.744491	+	0.667632i	$0.767308\pi$
$312$	171.188	+	99.9861i	0.548679	+	0.320468i
$313$	−1.09088			−0.00348523			−0.00174262	−	0.999998i	$-0.500555\pi$
$313$	−1.09088			−0.00348523			−0.00174262	+	0.999998i	$0.500555\pi$
$314$	−14.8031	−	172.529i	−0.0471435	−	0.549456i
$315$	335.756	−	112.679i	1.06589	−	0.357710i
$316$	37.4989	+	216.915i	0.118667	+	0.686441i
$317$	51.1667	−	51.1667i	0.161409	−	0.161409i	−0.621782	−	0.783191i	$-0.713591\pi$
$317$	51.1667	−	51.1667i	0.161409	−	0.161409i	0.783191	+	0.621782i	$0.213591\pi$
$318$	−23.1502	+	27.4957i	−0.0727995	+	0.0864644i
$319$	126.408			0.396263
$320$	−477.504	−	133.107i	−1.49220	−	0.415958i
$321$		−	133.781i		−	0.416764i
$322$	57.8195	+	133.258i	0.179564	+	0.413846i
$323$	270.755	−	270.755i	0.838252	−	0.838252i
$324$	−13.9393	−	80.6327i	−0.0430224	−	0.248866i
$325$	−390.312	+	390.312i	−1.20096	+	1.20096i
$326$	473.479	−	40.6247i	1.45239	−	0.124616i
$327$	8.24610			0.0252174
$328$	195.218	−	334.236i	0.595176	−	1.01901i
$329$	121.153	+	60.2685i	0.368246	+	0.183187i
$330$	7.57094	+	88.2390i	0.0229423	+	0.267391i
$331$	28.8219	+	28.8219i	0.0870753	+	0.0870753i	0.749303	−	0.662228i	$-0.230389\pi$
$331$	28.8219	+	28.8219i	0.0870753	+	0.0870753i	−0.662228	+	0.749303i	$0.730389\pi$
$332$	−137.893	+	195.534i	−0.415340	+	0.588957i
$333$	−16.6766	+	16.6766i	−0.0500800	+	0.0500800i
$334$	−181.004	−	152.398i	−0.541928	−	0.456282i
$335$			888.637i			2.65265i
$336$	138.331	−	108.729i	0.411699	−	0.323598i
$337$	−84.7524			−0.251491			−0.125745	−	0.992063i	$-0.540132\pi$
$337$	−84.7524			−0.251491			−0.125745	+	0.992063i	$0.540132\pi$
$338$	−102.839	+	122.143i	−0.304258	+	0.361369i
$339$	49.0378	+	49.0378i	0.144654	+	0.144654i
$340$	−439.886	+	623.763i	−1.29378	+	1.83460i
$341$	37.3939	−	37.3939i	0.109660	−	0.109660i
$342$	−202.307	+	17.3580i	−0.591541	+	0.0507545i
$343$	337.086	−	63.4174i	0.982759	−	0.184890i
$344$	−503.634	+	132.238i	−1.46405	+	0.384414i
$345$		−	126.251i		−	0.365944i
$346$	2.14805	+	25.0354i	0.00620823	+	0.0723567i
$347$	−38.7326	−	38.7326i	−0.111621	−	0.111621i	0.649090	−	0.760711i	$-0.275150\pi$
$347$	−38.7326	−	38.7326i	−0.111621	−	0.111621i	−0.760711	+	0.649090i	$0.775150\pi$
$348$	37.1809	+	215.076i	0.106842	+	0.618034i
$349$	−3.91040	−	3.91040i	−0.0112046	−	0.0112046i	0.701482	−	0.712687i	$-0.252522\pi$
$349$	−3.91040	−	3.91040i	−0.0112046	−	0.0112046i	−0.712687	+	0.701482i	$0.752522\pi$
$350$	194.995	+	449.410i	0.557128	+	1.28403i
$351$	−384.902			−1.09659
$352$	−48.3305	−	105.954i	−0.137302	−	0.301005i
$353$		−	620.142i		−	1.75678i	−0.477949	−	0.878388i	$-0.658620\pi$
$353$		−	620.142i		−	1.75678i	0.477949	−	0.878388i	$-0.341380\pi$
$354$	−207.566	−	174.762i	−0.586344	−	0.493677i
$355$	51.8333	+	51.8333i	0.146009	+	0.146009i
$356$	−5.52902	−	31.9831i	−0.0155310	−	0.0898400i
$357$	−86.1938	−	256.838i	−0.241439	−	0.719433i
$358$	−378.278	+	32.4564i	−1.05664	+	0.0906603i
$359$			343.001i			0.955435i	0.878514	+	0.477717i	$0.158536\pi$
$359$			343.001i			0.955435i	−0.878514	+	0.477717i	$0.841464\pi$
$360$	391.483	−	102.791i	1.08745	−	0.285531i
$361$		−	119.430i		−	0.330832i
$362$	−25.7178	+	2.20660i	−0.0710436	+	0.00609557i
$363$	119.699	−	119.699i	0.329749	−	0.329749i
$364$	209.803	+	388.677i	0.576381	+	1.06779i
$365$	201.205	−	201.205i	0.551246	−	0.551246i
$366$	−216.566	+	257.217i	−0.591711	+	0.702778i
$367$		−	680.088i		−	1.85310i	−0.376171	−	0.926550i	$-0.622760\pi$
$367$		−	680.088i		−	1.85310i	0.376171	−	0.926550i	$-0.377240\pi$
$368$	55.7329	+	156.378i	0.151448	+	0.424941i
$369$			316.048i			0.856498i
$370$	−42.7849	−	36.0231i	−0.115635	−	0.0973597i
$371$	−75.9193	+	25.4782i	−0.204634	+	0.0686745i
$372$	74.6224	+	52.6248i	0.200598	+	0.141464i
$373$	−32.9618	−	32.9618i	−0.0883694	−	0.0883694i	0.661540	−	0.749910i	$-0.269903\pi$
$373$	−32.9618	−	32.9618i	−0.0883694	−	0.0883694i	−0.749910	+	0.661540i	$0.769903\pi$
$374$	−178.657	+	15.3289i	−0.477693	+	0.0409862i
$375$		−	121.582i		−	0.324219i
$376$	133.537	+	77.9955i	0.355152	+	0.207435i
$377$	−547.921			−1.45337
$378$	−125.444	+	317.737i	−0.331864	+	0.840573i
$379$	−217.828	−	217.828i	−0.574745	−	0.574745i	0.358706	−	0.933451i	$-0.383218\pi$
$379$	−217.828	−	217.828i	−0.574745	−	0.574745i	−0.933451	+	0.358706i	$0.883218\pi$
$380$	−82.0280	−	474.497i	−0.215863	−	1.24868i
$381$	113.244	+	113.244i	0.297228	+	0.297228i
$382$	−279.186	−	235.063i	−0.730853	−	0.615348i
$383$		−	263.286i		−	0.687430i	−0.939074	−	0.343715i	$-0.888315\pi$
$383$		−	263.286i		−	0.687430i	0.939074	−	0.343715i	$-0.111685\pi$
$384$	166.059	−	113.396i	0.432444	−	0.295302i
$385$	−87.8820	+	176.662i	−0.228265	+	0.458863i
$386$	579.486	+	487.903i	1.50126	+	1.26400i
$387$	300.635	−	300.635i	0.776835	−	0.776835i
$388$	−556.866	+	96.2674i	−1.43522	+	0.248112i
$389$	28.5590	+	28.5590i	0.0734164	+	0.0734164i	0.742862	−	0.669445i	$-0.233468\pi$
$389$	28.5590	+	28.5590i	0.0734164	+	0.0734164i	−0.669445	+	0.742862i	$0.733468\pi$
$390$	−32.8166	−	382.476i	−0.0841452	−	0.980708i
$391$	255.619			0.653757
$392$	389.230	−	46.5172i	0.992934	−	0.118666i
$393$			213.926i			0.544342i
$394$	31.1906	+	363.525i	0.0791640	+	0.922653i
$395$	301.409	−	301.409i	0.763062	−	0.763062i
$396$	77.7082	+	54.8009i	0.196233	+	0.138386i
$397$	263.058	+	263.058i	0.662615	+	0.662615i	0.955996	−	0.293380i	$-0.0947803\pi$
$397$	263.058	+	263.058i	0.662615	+	0.662615i	−0.293380	+	0.955996i	$0.594780\pi$
$398$	420.415	+	353.972i	1.05632	+	0.889378i
$399$	153.027	+	76.1247i	0.383527	+	0.190789i
$400$	187.958	+	527.381i	0.469894	+	1.31845i
$401$	372.578			0.929123			0.464562	−	0.885541i	$-0.346212\pi$
$401$	372.578			0.929123			0.464562	+	0.885541i	$0.346212\pi$
$402$	−275.749	−	232.169i	−0.685942	−	0.577535i
$403$	−162.086	+	162.086i	−0.402198	+	0.402198i
$404$	421.387	+	297.168i	1.04304	+	0.735564i
$405$	−112.041	+	112.041i	−0.276645	+	0.276645i
$406$	−178.574	+	452.309i	−0.439838	+	1.11406i
$407$		−	13.1396i		−	0.0322841i
$408$	−78.6303	−	299.466i	−0.192721	−	0.733986i
$409$	−561.999			−1.37408			−0.687040	−	0.726620i	$-0.741090\pi$
$409$	−561.999			−1.37408			−0.687040	+	0.726620i	$0.741090\pi$
$410$	−746.766	+	64.0728i	−1.82138	+	0.156275i
$411$	−49.6006	+	49.6006i	−0.120683	+	0.120683i
$412$	−114.723	−	663.623i	−0.278453	−	1.61074i
$413$	−192.336	−	573.116i	−0.465704	−	1.38769i
$414$	−103.692	−	87.3048i	−0.250465	−	0.210881i
$415$	463.305			1.11640
$416$	209.491	+	459.261i	0.503583	+	1.10399i
$417$	−15.3605			−0.0368357
$418$	72.8613	−	86.5377i	0.174309	−	0.207028i
$419$	−238.635	−	238.635i	−0.569534	−	0.569534i	0.362464	−	0.931998i	$-0.381936\pi$
$419$	−238.635	−	238.635i	−0.569534	−	0.569534i	−0.931998	+	0.362464i	$0.881936\pi$
$420$	−326.430	−	97.5638i	−0.777213	−	0.232295i
$421$	503.838	+	503.838i	1.19676	+	1.19676i	0.975130	+	0.221635i	$0.0711393\pi$
$421$	503.838	+	503.838i	1.19676	+	1.19676i	0.221635	+	0.975130i	$0.428861\pi$
$422$	228.803	−	19.6314i	0.542188	−	0.0465199i
$423$	−126.271			−0.298512
$424$	−88.5200	+	23.2425i	−0.208773	+	0.0548173i
$425$	862.068			2.02839
$426$	−29.6263	+	2.54195i	−0.0695453	+	0.00596702i
$427$	−710.210	+	238.344i	−1.66326	+	0.558183i
$428$	196.315	−	278.377i	0.458680	−	0.650413i
$429$	63.7701	−	63.7701i	0.148648	−	0.148648i
$430$	771.296	+	649.400i	1.79371	+	1.51023i
$431$	−580.398			−1.34663			−0.673315	−	0.739355i	$-0.735130\pi$
$431$	−580.398			−1.34663			−0.673315	+	0.739355i	$0.735130\pi$
$432$	−167.360	+	352.712i	−0.387407	+	0.816463i
$433$		−	161.231i		−	0.372359i	−0.982516	−	0.186179i	$-0.940389\pi$
$433$		−	161.231i		−	0.372359i	0.982516	−	0.186179i	$-0.0596106\pi$
$434$	80.9759	+	186.627i	0.186580	+	0.430017i
$435$	298.853	−	298.853i	0.687019	−	0.687019i
$436$	17.1588	+	12.1006i	0.0393550	+	0.0277537i
$437$	−114.032	+	114.032i	−0.260944	+	0.260944i
$438$	9.86726	+	115.003i	0.0225280	+	0.262563i
$439$	−171.458			−0.390564			−0.195282	−	0.980747i	$-0.562562\pi$
$439$	−171.458			−0.390564			−0.195282	+	0.980747i	$0.562562\pi$
$440$	−113.731	+	194.721i	−0.258480	+	0.442547i
$441$	−255.274	+	193.085i	−0.578853	+	0.437833i
$442$	774.398	−	66.4436i	1.75203	−	0.150325i
$443$	362.506	+	362.506i	0.818298	+	0.818298i	0.985861	−	0.167563i	$-0.0535898\pi$
$443$	362.506	+	362.506i	0.818298	+	0.818298i	−0.167563	+	0.985861i	$0.553590\pi$
$444$	22.3563	−	3.86481i	0.0503521	−	0.00870453i
$445$	−44.4413	+	44.4413i	−0.0998681	+	0.0998681i
$446$	341.503	−	405.605i	0.765701	−	0.909428i
$447$		−	193.147i		−	0.432095i
$448$	447.396	−	23.2554i	0.998652	−	0.0519093i
$449$	−680.601			−1.51582			−0.757908	−	0.652362i	$-0.773778\pi$
$449$	−680.601			−1.51582			−0.757908	+	0.652362i	$0.773778\pi$
$450$	−349.700	−	294.433i	−0.777111	−	0.654296i
$451$	−124.508	−	124.508i	−0.276071	−	0.276071i
$452$	30.0799	+	173.999i	0.0665484	+	0.384954i
$453$	151.172	−	151.172i	0.333713	−	0.333713i
$454$	8.46834	+	98.6981i	0.0186527	+	0.217397i
$455$	380.929	−	765.750i	0.837206	−	1.68297i
$456$	168.670	+	98.5155i	0.369890	+	0.216043i
$457$			76.4527i			0.167293i	0.996496	+	0.0836463i	$0.0266566\pi$
$457$			76.4527i			0.167293i	−0.996496	+	0.0836463i	$0.973343\pi$
$458$	−47.2053	+	4.05023i	−0.103068	+	0.00884331i
$459$	425.060	+	425.060i	0.926056	+	0.926056i
$460$	185.264	−	262.707i	0.402749	−	0.571102i
$461$	9.52689	+	9.52689i	0.0206657	+	0.0206657i	0.717364	−	0.696698i	$-0.245348\pi$
$461$	9.52689	+	9.52689i	0.0206657	+	0.0206657i	−0.696698	+	0.717364i	$0.745348\pi$
$462$	−31.8587	−	73.4257i	−0.0689583	−	0.158930i
$463$	108.583			0.234521			0.117260	−	0.993101i	$-0.462589\pi$
$463$	108.583			0.234521			0.117260	+	0.993101i	$0.462589\pi$
$464$	−238.242	+	502.098i	−0.513453	+	1.08211i
$465$		−	176.813i		−	0.380243i
$466$	−209.829	+	249.216i	−0.450278	+	0.534797i
$467$	−428.836	−	428.836i	−0.918278	−	0.918278i	0.0786261	−	0.996904i	$-0.474947\pi$
$467$	−428.836	−	428.836i	−0.918278	−	0.918278i	−0.996904	+	0.0786261i	$0.974947\pi$
$468$	−336.830	−	237.537i	−0.719722	−	0.507558i
$469$	−255.516	−	761.379i	−0.544811	−	1.62341i
$470$	−25.5990	−	298.356i	−0.0544660	−	0.634799i
$471$		−	136.016i		−	0.288781i
$472$	−175.459	−	668.239i	−0.371734	−	1.41576i
$473$			236.872i			0.500787i
$474$	14.7814	+	172.276i	0.0311844	+	0.363452i
$475$	−384.571	+	384.571i	−0.809623	+	0.809623i
$476$	197.537	−	660.920i	0.414994	−	1.38849i
$477$	52.8404	−	52.8404i	0.110776	−	0.110776i
$478$	−701.987	−	591.044i	−1.46859	−	1.23649i
$479$			678.346i			1.41617i	0.706127	+	0.708085i	$0.250441\pi$
$479$			678.346i			1.41617i	−0.706127	+	0.708085i	$0.749559\pi$
$480$	−364.758	−	136.233i	−0.759913	−	0.283818i
$481$			56.9543i			0.118408i
$482$	7.95750	−	9.45117i	0.0165093	−	0.0196082i
$483$	36.3017	+	108.171i	0.0751589	+	0.223956i
$484$	424.724	−	73.4234i	0.877528	−	0.151701i
$485$	773.780	+	773.780i	1.59542	+	1.59542i
$486$	−43.0406	−	501.636i	−0.0885608	−	1.03217i
$487$		−	737.584i		−	1.51455i	−0.653098	−	0.757273i	$-0.726531\pi$
$487$		−	737.584i		−	1.51455i	0.653098	−	0.757273i	$-0.273469\pi$
$488$	−828.087	+	217.429i	−1.69690	+	0.445552i
$489$	373.274			0.763341
$490$	−507.977	−	564.024i	−1.03669	−	1.15107i
$491$	−524.855	−	524.855i	−1.06895	−	1.06895i	−0.997440	−	0.0715115i	$-0.977218\pi$
$491$	−524.855	−	524.855i	−1.06895	−	1.06895i	−0.0715115	−	0.997440i	$-0.522782\pi$
$492$	175.221	−	248.465i	0.356140	−	0.505011i
$493$	605.087	+	605.087i	1.22736	+	1.22736i
$494$	−315.821	+	375.102i	−0.639313	+	0.759316i
$495$		−	184.125i		−	0.371969i
$496$	78.0536	+	219.007i	0.157366	+	0.441546i
$497$	−59.3144	−	29.5064i	−0.119345	−	0.0593691i
$498$	−121.045	+	143.766i	−0.243062	+	0.288687i
$499$	61.5115	−	61.5115i	0.123270	−	0.123270i	−0.642781	−	0.766050i	$-0.722219\pi$
$499$	61.5115	−	61.5115i	0.123270	−	0.123270i	0.766050	+	0.642781i	$0.222219\pi$
$500$	178.414	−	252.992i	0.356828	−	0.505985i
$501$	−131.421	−	131.421i	−0.262318	−	0.262318i
$502$	55.4569	−	4.75823i	0.110472	−	0.00947854i
$503$	64.6784			0.128585			0.0642927	−	0.997931i	$-0.479521\pi$
$503$	64.6784			0.128585			0.0642927	+	0.997931i	$0.479521\pi$
$504$	−305.864	+	200.637i	−0.606873	+	0.398089i
$505$		−	998.450i		−	1.97713i
$506$	75.2440	−	6.45596i	0.148704	−	0.0127588i
$507$	−88.6838	+	88.6838i	−0.174919	+	0.174919i
$508$	69.4639	+	401.819i	0.136740	+	0.790983i
$509$	−392.205	−	392.205i	−0.770541	−	0.770541i	0.207660	−	0.978201i	$-0.433415\pi$
$509$	−392.205	−	392.205i	−0.770541	−	0.770541i	−0.978201	+	0.207660i	$0.933415\pi$
$510$	−386.140	+	458.621i	−0.757138	+	0.899258i
$511$	−114.537	+	230.245i	−0.224143	+	0.450577i
$512$	511.942	+	7.72126i	0.999886	+	0.0150806i
$513$	−379.241			−0.739261
$514$	−60.0445	+	71.3152i	−0.116818	+	0.138745i
$515$	−922.121	+	922.121i	−1.79053	+	1.79053i
$516$	−403.025	+	69.6722i	−0.781055	+	0.135024i
$517$	49.7447	−	49.7447i	0.0962180	−	0.0962180i
$518$	47.0158	+	18.5621i	0.0907641	+	0.0358342i
$519$			19.7370i			0.0380289i
$520$	492.973	−	844.026i	0.948024	−	1.62313i
$521$	537.133			1.03097			0.515483	−	0.856900i	$-0.327613\pi$
$521$	537.133			1.03097			0.515483	+	0.856900i	$0.327613\pi$
$522$	−38.7919	−	452.118i	−0.0743140	−	0.866126i
$523$	−282.626	+	282.626i	−0.540394	+	0.540394i	−0.923644	−	0.383251i	$-0.874805\pi$
$523$	−282.626	+	282.626i	−0.540394	+	0.540394i	0.383251	+	0.923644i	$0.374805\pi$
$524$	−313.923	+	445.146i	−0.599089	+	0.849514i
$525$	122.427	+	364.803i	0.233194	+	0.694862i
$526$	−300.817	+	357.282i	−0.571896	+	0.679244i
$527$	357.993			0.679303
$528$	−30.7090	−	86.1649i	−0.0581610	−	0.163191i
$529$	421.342			0.796489
$530$	135.565	+	114.140i	0.255783	+	0.215359i
$531$	398.893	+	398.893i	0.751212	+	0.751212i
$532$	206.717	+	382.960i	0.388565	+	0.719850i
$533$	539.686	+	539.686i	1.01254	+	1.01254i
$534$	−2.17944	−	25.4013i	−0.00408135	−	0.0475679i
$535$	−659.596			−1.23289
$536$	−233.095	−	887.749i	−0.434878	−	1.65625i
$537$	−298.221			−0.555346
$538$	28.7021	+	334.522i	0.0533496	+	0.621788i
$539$	24.4998	−	176.632i	0.0454542	−	0.327704i
$540$	744.915	−	128.776i	1.37947	−	0.238474i
$541$	−53.3102	+	53.3102i	−0.0985401	+	0.0985401i	−0.754658	−	0.656118i	$-0.772197\pi$
$541$	−53.3102	+	53.3102i	−0.0985401	+	0.0985401i	0.656118	+	0.754658i	$0.272197\pi$
$542$	−170.024	+	201.939i	−0.313698	+	0.372581i
$543$	−20.2750			−0.0373388
$544$	275.830	−	738.525i	0.507040	−	1.35758i
$545$		−	40.6567i		−	0.0745994i
$546$	138.093	+	318.267i	0.252918	+	0.582907i
$547$	301.530	−	301.530i	0.551244	−	0.551244i	−0.375556	−	0.926800i	$-0.622548\pi$
$547$	301.530	−	301.530i	0.551244	−	0.551244i	0.926800	+	0.375556i	$0.122548\pi$
$548$	−175.996	+	30.4251i	−0.321161	+	0.0555203i
$549$	494.312	−	494.312i	0.900385	−	0.900385i
$550$	253.758	−	21.7726i	0.461378	−	0.0395865i
$551$	−539.862			−0.979786
$552$	33.1163	+	126.124i	0.0599933	+	0.228486i
$553$	−171.579	+	344.912i	−0.310270	+	0.623711i
$554$	−60.3428	−	703.293i	−0.108922	−	1.26948i
$555$	−31.0647	−	31.0647i	−0.0559724	−	0.0559724i
$556$	−31.9626	−	22.5405i	−0.0574867	−	0.0405404i
$557$	−524.220	+	524.220i	−0.941148	+	0.941148i	−0.998362	−	0.0572135i	$-0.981778\pi$
$557$	−524.220	+	524.220i	−0.941148	+	0.941148i	0.0572135	+	0.998362i	$0.481778\pi$
$558$	−145.221	−	122.270i	−0.260252	−	0.219122i
$559$		−	1026.73i		−	1.83673i
$560$	−536.078	−	682.028i	−0.957282	−	1.21791i
$561$	−140.847			−0.251064
$562$	443.177	−	526.364i	0.788571	−	0.936591i
$563$	608.657	+	608.657i	1.08110	+	1.08110i	0.996407	+	0.0846888i	$0.0269896\pi$
$563$	608.657	+	608.657i	1.08110	+	1.08110i	0.0846888	+	0.996407i	$0.473010\pi$
$564$	99.2694	+	70.0062i	0.176010	+	0.124124i
$565$	241.777	−	241.777i	0.427923	−	0.427923i
$566$	399.148	−	34.2470i	0.705208	−	0.0605071i
$567$	63.7802	−	128.212i	0.112487	−	0.226124i
$568$	−65.3776	−	38.1853i	−0.115101	−	0.0672276i
$569$			576.735i			1.01359i	0.862066	+	0.506797i	$0.169170\pi$
$569$			576.735i			1.01359i	−0.862066	+	0.506797i	$0.830830\pi$
$570$	−32.3340	−	376.851i	−0.0567262	−	0.661142i
$571$	−401.402	−	401.402i	−0.702980	−	0.702980i	0.262069	−	0.965049i	$-0.415595\pi$
$571$	−401.402	−	401.402i	−0.702980	−	0.702980i	−0.965049	+	0.262069i	$0.915595\pi$
$572$	226.274	−	39.1167i	0.395583	−	0.0683858i
$573$	−202.708	−	202.708i	−0.353765	−	0.353765i
$574$	621.401	−	269.620i	1.08258	−	0.469721i
$575$	−363.072			−0.631430
$576$	−364.129	+	205.377i	−0.632168	+	0.356557i
$577$			933.829i			1.61842i	0.587519	+	0.809210i	$0.300105\pi$
$577$			933.829i			1.61842i	−0.587519	+	0.809210i	$0.699895\pi$
$578$	−486.418	−	409.544i	−0.841554	−	0.708554i
$579$	420.746	+	420.746i	0.726676	+	0.726676i
$580$	1060.41	−	183.317i	1.82830	−	0.316064i
$581$	−396.957	+	133.217i	−0.683231	+	0.229290i
$582$	−442.269	+	37.9469i	−0.759913	+	0.0652008i
$583$			41.6333i			0.0714121i
$584$	−148.226	+	253.781i	−0.253812	+	0.434556i
$585$			798.097i			1.36427i
$586$	232.774	−	19.9721i	0.397225	−	0.0340821i
$587$	415.106	−	415.106i	0.707165	−	0.707165i	−0.258773	−	0.965938i	$-0.583318\pi$
$587$	415.106	−	415.106i	0.707165	−	0.707165i	0.965938	+	0.258773i	$0.0833181\pi$
$588$	307.736	−	10.2686i	0.523361	−	0.0174635i
$589$	−159.702	+	159.702i	−0.271140	+	0.271140i
$590$	−861.647	+	1023.38i	−1.46042	+	1.73455i
$591$			286.590i			0.484924i
$592$	52.1912	+	24.7644i	0.0881608	+	0.0418317i
$593$			818.826i			1.38082i	0.723419	+	0.690409i	$0.242570\pi$
$593$			818.826i			1.38082i	−0.723419	+	0.690409i	$0.757430\pi$
$594$	135.856	+	114.385i	0.228714	+	0.192568i
$595$	−1266.31	+	424.971i	−2.12826	+	0.714237i
$596$	283.430	−	401.906i	0.475553	−	0.674339i
$597$	305.250	+	305.250i	0.511306	+	0.511306i
$598$	−326.149	+	27.9837i	−0.545399	+	0.0467955i
$599$		−	503.564i		−	0.840674i	−0.907368	−	0.420337i	$-0.861912\pi$
$599$		−	503.564i		−	0.840674i	0.907368	−	0.420337i	$-0.138088\pi$
$600$	111.684	+	425.351i	0.186140	+	0.708918i
$601$	110.475			0.183819			0.0919093	−	0.995767i	$-0.470703\pi$
$601$	110.475			0.183819			0.0919093	+	0.995767i	$0.470703\pi$
$602$	−847.569	−	334.626i	−1.40792	−	0.555857i
$603$	529.925	+	529.925i	0.878815	+	0.878815i
$604$	536.400	−	92.7292i	0.888079	−	0.153525i
$605$	−590.164	−	590.164i	−0.975478	−	0.975478i
$606$	309.824	+	260.859i	0.511261	+	0.430461i
$607$		−	169.212i		−	0.278769i	−0.990238	−	0.139384i	$-0.955488\pi$
$607$		−	169.212i		−	0.278769i	0.990238	−	0.139384i	$-0.0445123\pi$
$608$	206.410	+	452.507i	0.339489	+	0.744254i
$609$	−170.124	+	341.987i	−0.279350	+	0.561555i
$610$	1268.18	+	1067.76i	2.07899	+	1.75043i
$611$	−215.621	+	215.621i	−0.352898	+	0.352898i
$612$	109.652	+	634.292i	0.179170	+	1.03642i
$613$	199.765	+	199.765i	0.325881	+	0.325881i	0.851018	−	0.525137i	$-0.175986\pi$
$613$	199.765	+	199.765i	0.325881	+	0.325881i	−0.525137	+	0.851018i	$0.675986\pi$
$614$	48.5888	+	566.300i	0.0791349	+	0.922313i
$615$	−588.723			−0.957273
$616$	41.4546	−	199.537i	0.0672965	−	0.323924i
$617$		−	166.208i		−	0.269381i	−0.990888	−	0.134690i	$-0.956996\pi$
$617$		−	166.208i		−	0.269381i	0.990888	−	0.134690i	$-0.0430040\pi$
$618$	−45.2217	−	527.057i	−0.0731742	−	0.852842i
$619$	474.519	−	474.519i	0.766589	−	0.766589i	−0.210915	−	0.977504i	$-0.567644\pi$
$619$	474.519	−	474.519i	0.766589	−	0.766589i	0.977504	+	0.210915i	$0.0676444\pi$
$620$	259.462	−	367.919i	0.418487	−	0.593418i
$621$	−179.020	−	179.020i	−0.288277	−	0.288277i
$622$	−708.471	−	596.504i	−1.13902	−	0.959010i
$623$	25.2985	−	50.8555i	0.0406075	−	0.0816301i
$624$	133.110	+	373.486i	0.213317	+	0.598535i
$625$	275.354			0.440566
$626$	−1.66897	−	1.40520i	−0.00266609	−	0.00224474i
$627$	62.8322	−	62.8322i	0.100211	−	0.100211i
$628$	199.594	−	283.026i	0.317825	−	0.450679i
$629$	62.8965	−	62.8965i	0.0999944	−	0.0999944i
$630$	658.829	+	260.110i	1.04576	+	0.412873i
$631$			326.927i			0.518110i	0.965863	+	0.259055i	$0.0834111\pi$
$631$			326.927i			0.518110i	−0.965863	+	0.259055i	$0.916589\pi$
$632$	−222.047	+	380.170i	−0.351340	+	0.601534i
$633$	180.380			0.284961
$634$	144.191	−	12.3717i	0.227431	−	0.0195137i
$635$	558.338	−	558.338i	0.879273	−	0.879273i
$636$	−70.8366	+	12.2458i	−0.111378	+	0.0192544i
$637$	−106.196	+	765.621i	−0.166712	+	1.20192i
$638$	193.395	+	162.831i	0.303128	+	0.255221i
$639$	61.8200			0.0967449
$640$	−559.090	−	818.737i	−0.873577	−	1.27928i
$641$	−468.475			−0.730850			−0.365425	−	0.930841i	$-0.619076\pi$
$641$	−468.475			−0.730850			−0.365425	+	0.930841i	$0.619076\pi$
$642$	172.329	−	204.676i	0.268425	−	0.318810i
$643$	162.961	+	162.961i	0.253438	+	0.253438i	0.822379	−	0.568941i	$-0.192647\pi$
$643$	162.961	+	162.961i	0.253438	+	0.253438i	−0.568941	+	0.822379i	$0.692647\pi$
$644$	−83.1955	+	278.356i	−0.129186	+	0.432230i
$645$	560.013	+	560.013i	0.868237	+	0.868237i
$646$	763.008	−	65.4664i	1.18113	−	0.101341i
$647$	648.535			1.00237			0.501186	−	0.865340i	$-0.332897\pi$
$647$	648.535			1.00237			0.501186	+	0.865340i	$0.332897\pi$
$648$	82.5401	−	141.318i	0.127377	−	0.218084i
$649$	−314.291			−0.484269
$650$	−1099.93	+	94.3742i	−1.69220	+	0.145191i
$651$	50.8404	+	151.493i	0.0780958	+	0.232707i
$652$	776.721	+	547.754i	1.19129	+	0.840114i
$653$	198.998	−	198.998i	0.304744	−	0.304744i	−0.538122	−	0.842867i	$-0.680866\pi$
$653$	198.998	−	198.998i	0.304744	−	0.304744i	0.842867	+	0.538122i	$0.180866\pi$
$654$	12.6160	+	10.6221i	0.0192905	+	0.0162418i
$655$	1054.75			1.61030
$656$	729.213	−	259.890i	1.11160	−	0.396174i
$657$		−	239.971i		−	0.365253i
$658$	107.721	+	248.269i	0.163710	+	0.377308i
$659$	273.506	−	273.506i	0.415032	−	0.415032i	−0.468455	−	0.883487i	$-0.655189\pi$
$659$	273.506	−	273.506i	0.415032	−	0.415032i	0.883487	+	0.468455i	$0.155189\pi$
$660$	−102.081	+	144.752i	−0.154669	+	0.219322i
$661$	418.775	−	418.775i	0.633547	−	0.633547i	−0.315409	−	0.948956i	$-0.602142\pi$
$661$	418.775	−	418.775i	0.633547	−	0.633547i	0.948956	+	0.315409i	$0.102142\pi$
$662$	6.96890	+	81.2223i	0.0105270	+	0.122692i
$663$	610.507			0.920826
$664$	−462.842	+	121.528i	−0.697051	+	0.183024i
$665$	375.326	−	754.488i	0.564400	−	1.13457i
$666$	−46.9960	+	4.03227i	−0.0705645	+	0.00605446i
$667$	−254.841	−	254.841i	−0.382070	−	0.382070i
$668$	−80.6139	−	466.317i	−0.120679	−	0.698080i
$669$	294.496	−	294.496i	0.440204	−	0.440204i
$670$	−1144.69	+	1359.55i	−1.70849	+	2.02919i
$671$			389.471i			0.580434i
$672$	351.695	+	11.8419i	0.523355	+	0.0176218i
$673$	−1171.54			−1.74077			−0.870383	−	0.492375i	$-0.836129\pi$
$673$	−1171.54			−1.74077			−0.870383	+	0.492375i	$0.836129\pi$
$674$	−129.666	−	109.173i	−0.192382	−	0.161978i
$675$	−603.740	−	603.740i	−0.894429	−	0.894429i
$676$	−314.674	+	54.3988i	−0.465494	+	0.0804716i
$677$	−104.959	+	104.959i	−0.155035	+	0.155035i	−0.780362	−	0.625328i	$-0.784965\pi$
$677$	−104.959	+	104.959i	−0.155035	+	0.155035i	0.625328	+	0.780362i	$0.284965\pi$
$678$	11.8569	+	138.192i	0.0174881	+	0.203823i
$679$	−885.461	−	440.480i	−1.30407	−	0.648718i
$680$	−1476.49	+	387.680i	−2.17131	+	0.570118i
$681$			77.8100i			0.114259i
$682$	105.379	−	9.04154i	0.154514	−	0.0132574i
$683$	598.937	+	598.937i	0.876921	+	0.876921i	0.993215	−	0.116294i	$-0.0371016\pi$
$683$	598.937	+	598.937i	0.876921	+	0.876921i	−0.116294	+	0.993215i	$0.537102\pi$
$684$	−331.876	−	234.043i	−0.485198	−	0.342169i
$685$	244.552	+	244.552i	0.357010	+	0.357010i
$686$	597.410	+	337.190i	0.870860	+	0.491531i
$687$	−37.2150			−0.0541703
$688$	−940.867	−	446.435i	−1.36754	−	0.648889i
$689$		−	180.461i		−	0.261918i
$690$	162.629	−	193.155i	0.235694	−	0.279935i
$691$	397.739	+	397.739i	0.575599	+	0.575599i	0.933688	−	0.358089i	$-0.116571\pi$
$691$	397.739	+	397.739i	0.575599	+	0.575599i	−0.358089	+	0.933688i	$0.616571\pi$
$692$	−28.9628	+	41.0695i	−0.0418537	+	0.0593490i
$693$	52.9427	+	157.757i	0.0763964	+	0.227643i
$694$	−9.36522	−	109.151i	−0.0134946	−	0.157278i
$695$			75.7335i			0.108969i
$696$	−220.164	+	376.946i	−0.316327	+	0.541588i
$697$		−	1191.98i		−	1.71016i
$698$	−0.945502	−	11.0198i	−0.00135459	−	0.0157877i
$699$	−180.947	+	180.947i	−0.258866	+	0.258866i
$700$	−280.574	+	938.747i	−0.400821	+	1.34107i
$701$	848.967	−	848.967i	1.21108	−	1.21108i	0.240409	−	0.970672i	$-0.422718\pi$
$701$	848.967	−	848.967i	1.21108	−	1.21108i	0.970672	−	0.240409i	$-0.0772815\pi$
$702$	−588.874	−	495.808i	−0.838852	−	0.706279i
$703$			56.1166i			0.0798245i
$704$	62.5410	−	224.358i	0.0888366	−	0.318691i
$705$		−	235.213i		−	0.333635i
$706$	798.830	−	948.775i	1.13149	−	1.34387i
$707$	287.092	+	855.466i	0.406070	+	1.20999i
$708$	−92.4436	−	534.747i	−0.130570	−	0.755293i
$709$	250.885	+	250.885i	0.353857	+	0.353857i	0.861542	−	0.507685i	$-0.169499\pi$
$709$	250.885	+	250.885i	0.353857	+	0.353857i	−0.507685	+	0.861542i	$0.669499\pi$
$710$	12.5329	+	146.070i	0.0176519	+	0.205732i
$711$		−	359.482i		−	0.505601i
$712$	32.7396	−	56.0541i	0.0459827	−	0.0787276i
$713$	−150.774			−0.211464
$714$	198.972	−	503.974i	0.278672	−	0.705846i
$715$	−314.413	−	314.413i	−0.439738	−	0.439738i
$716$	−620.548	−	437.619i	−0.866687	−	0.611200i
$717$	−509.690	−	509.690i	−0.710864	−	0.710864i
$718$	−441.834	+	524.769i	−0.615367	+	0.730875i
$719$			1326.17i			1.84446i	0.386642	+	0.922230i	$0.373635\pi$
$719$			1326.17i			1.84446i	−0.386642	+	0.922230i	$0.626365\pi$
$720$	731.352	+	347.022i	1.01577	+	0.481974i
$721$	524.924	−	1055.21i	0.728050	−	1.46354i
$722$	153.843	−	182.721i	0.213079	−	0.253076i
$723$	6.86219	−	6.86219i	0.00949127	−	0.00949127i
$724$	−42.1889	−	29.7522i	−0.0582719	−	0.0410942i
$725$	−859.444	−	859.444i	−1.18544	−	1.18544i
$726$	337.320	−	28.9422i	0.464628	−	0.0398653i
$727$	135.744			0.186719			0.0933593	−	0.995632i	$-0.470239\pi$
$727$	135.744			0.186719			0.0933593	+	0.995632i	$0.470239\pi$
$728$	−179.687	+	864.905i	−0.246823	+	1.18806i
$729$		−	211.357i		−	0.289927i
$730$	567.010	−	48.6497i	0.776726	−	0.0666434i
$731$	−1133.86	+	1133.86i	−1.55110	+	1.55110i
$732$	−662.663	+	114.557i	−0.905277	+	0.156498i
$733$	−340.606	−	340.606i	−0.464674	−	0.464674i	0.435510	−	0.900184i	$-0.356568\pi$
$733$	−340.606	−	340.606i	−0.464674	−	0.464674i	−0.900184	+	0.435510i	$0.856568\pi$
$734$	876.049	−	1040.49i	1.19353	−	1.41756i
$735$	−359.672	−	475.516i	−0.489349	−	0.646961i
$736$	−116.170	+	311.040i	−0.157839	+	0.422609i
$737$	−417.532			−0.566529
$738$	−407.114	+	483.532i	−0.551645	+	0.655192i
$739$	422.281	−	422.281i	0.571423	−	0.571423i	−0.361103	−	0.932526i	$-0.617600\pi$
$739$	422.281	−	422.281i	0.571423	−	0.571423i	0.932526	+	0.361103i	$0.117600\pi$
$740$	−19.0551	−	110.226i	−0.0257502	−	0.148954i
$741$	−272.349	+	272.349i	−0.367543	+	0.367543i
$742$	−148.971	−	58.8147i	−0.200769	−	0.0792651i
$743$			125.612i			0.169061i	0.996421	+	0.0845303i	$0.0269390\pi$
$743$			125.612i			0.169061i	−0.996421	+	0.0845303i	$0.973061\pi$
$744$	46.3792	+	176.636i	0.0623376	+	0.237415i
$745$	−952.292			−1.27824
$746$	−7.96989	−	92.8887i	−0.0106835	−	0.124516i
$747$	276.285	−	276.285i	0.369860	−	0.369860i
$748$	−293.079	−	206.683i	−0.391817	−	0.276315i
$749$	565.138	−	189.658i	0.754524	−	0.253216i
$750$	156.615	−	186.012i	0.208820	−	0.248017i
$751$	−964.776			−1.28465			−0.642327	−	0.766430i	$-0.722031\pi$
$751$	−964.776			−1.28465			−0.642327	+	0.766430i	$0.722031\pi$
$752$	103.834	+	291.343i	0.138077	+	0.387424i
$753$	43.7202			0.0580614
$754$	−838.282	−	705.799i	−1.11178	−	0.936073i
$755$	−745.341	−	745.341i	−0.987207	−	0.987207i
$756$	−601.211	+	324.525i	−0.795253	+	0.429266i
$757$	−313.133	−	313.133i	−0.413650	−	0.413650i	0.469358	−	0.883008i	$-0.344485\pi$
$757$	−313.133	−	313.133i	−0.413650	−	0.413650i	−0.883008	+	0.469358i	$0.844485\pi$
$758$	−52.6691	−	613.857i	−0.0694843	−	0.809837i
$759$	59.3196			0.0781550
$760$	485.722	−	831.613i	0.639108	−	1.09423i
$761$	−1428.00			−1.87648			−0.938242	−	0.345980i	$-0.887547\pi$
$761$	−1428.00			−1.87648			−0.938242	+	0.345980i	$0.887547\pi$
$762$	27.3814	+	319.129i	0.0359336	+	0.418805i
$763$	11.6903	+	34.8344i	0.0153215	+	0.0456545i
$764$	−124.341	−	719.261i	−0.162750	−	0.941441i
$765$	881.365	−	881.365i	1.15211	−	1.15211i
$766$	339.149	−	402.809i	0.442753	−	0.525861i
$767$	1362.31			1.77615
$768$	400.129	+	40.4184i	0.521001	+	0.0526281i
$769$			870.738i			1.13230i	0.824303	+	0.566149i	$0.191567\pi$
$769$			870.738i			1.13230i	−0.824303	+	0.566149i	$0.808433\pi$
$770$	−362.019	+	157.077i	−0.470155	+	0.203996i
$771$	−51.7796	+	51.7796i	−0.0671590	+	0.0671590i
$772$	258.086	+	1492.92i	0.334308	+	1.93383i
$773$	−3.78212	+	3.78212i	−0.00489279	+	0.00489279i	−0.709549	−	0.704656i	$-0.751101\pi$
$773$	−3.78212	+	3.78212i	−0.00489279	+	0.00489279i	0.704656	+	0.709549i	$0.251101\pi$
$774$	847.211	−	72.6911i	1.09459	−	0.0939161i
$775$	−508.480			−0.656104
$776$	−975.974	−	570.040i	−1.25770	−	0.734587i
$777$	35.5483	+	17.6838i	0.0457507	+	0.0227590i
$778$	6.90533	+	80.4813i	0.00887574	+	0.103446i
$779$	531.748	+	531.748i	0.682603	+	0.682603i
$780$	442.476	−	627.435i	0.567277	−	0.804404i
$781$	−24.3542	+	24.3542i	−0.0311833	+	0.0311833i
$782$	391.080	+	329.273i	0.500102	+	0.421065i
$783$		−	847.532i		−	1.08242i
$784$	655.417	+	430.215i	0.835991	+	0.548744i
$785$	−670.614			−0.854285
$786$	−275.567	+	327.293i	−0.350594	+	0.416403i
$787$	376.678	+	376.678i	0.478626	+	0.478626i	0.904692	−	0.426066i	$-0.140101\pi$
$787$	376.678	+	376.678i	0.478626	+	0.478626i	−0.426066	+	0.904692i	$0.640101\pi$
$788$	−420.552	+	596.347i	−0.533696	+	0.756785i
$789$	−259.411	+	259.411i	−0.328784	+	0.328784i
$790$	849.394	−	72.8783i	1.07518	−	0.0922510i
$791$	−137.633	+	276.672i	−0.173999	+	0.349776i
$792$	48.2970	+	183.941i	0.0609811	+	0.232248i
$793$		−	1688.18i		−	2.12885i
$794$	63.6053	+	741.318i	0.0801075	+	0.933649i
$795$	98.4293	+	98.4293i	0.123810	+	0.123810i
$796$	187.241	+	1083.11i	0.235227	+	1.36069i
$797$	1054.97	+	1054.97i	1.32367	+	1.32367i	0.910778	+	0.412896i	$0.135483\pi$
$797$	1054.97	+	1054.97i	1.32367	+	1.32367i	0.412896	+	0.910778i	$0.364517\pi$
$798$	136.062	+	313.586i	0.170504	+	0.392965i
$799$	476.234			0.596038
$800$	−391.779	+	1048.97i	−0.489724	+	1.31122i
$801$			53.0038i			0.0661720i
$802$	570.020	+	479.933i	0.710748	+	0.598421i
$803$	94.5373	+	94.5373i	0.117730	+	0.117730i
$804$	−122.810	−	710.406i	−0.152749	−	0.883590i
$805$	533.326	−	178.983i	0.662517	−	0.222339i
$806$	−456.769	+	39.1910i	−0.566711	+	0.0486241i
$807$			263.725i			0.326797i
$808$	261.899	+	997.452i	0.324133	+	1.23447i
$809$			826.800i			1.02200i	0.859580	+	0.511001i	$0.170725\pi$
$809$			826.800i			1.02200i	−0.859580	+	0.511001i	$0.829275\pi$
$810$	−315.740	+	27.0906i	−0.389803	+	0.0334452i
$811$	−185.728	+	185.728i	−0.229012	+	0.229012i	−0.812280	−	0.583268i	$-0.801774\pi$
$811$	−185.728	+	185.728i	−0.229012	+	0.229012i	0.583268	+	0.812280i	$0.301774\pi$
$812$	−855.844	+	461.973i	−1.05400	+	0.568932i
$813$	−146.621	+	146.621i	−0.180346	+	0.180346i
$814$	16.9257	−	20.1027i	0.0207932	−	0.0246962i
$815$		−	1840.39i		−	2.25815i
$816$	265.455	−	559.450i	0.325313	−	0.685600i
$817$		−	1011.63i		−	1.23823i
$818$	−859.820	−	723.933i	−1.05112	−	0.885004i
$819$	−229.483	−	683.805i	−0.280199	−	0.834927i
$820$	−1225.04	−	863.912i	−1.49395	−	1.05355i
$821$	−293.780	−	293.780i	−0.357832	−	0.357832i	0.505181	−	0.863013i	$-0.331426\pi$
$821$	−293.780	−	293.780i	−0.357832	−	0.357832i	−0.863013	+	0.505181i	$0.831426\pi$
$822$	−139.778	+	11.9930i	−0.170047	+	0.0145901i
$823$		−	118.012i		−	0.143393i	−0.997427	−	0.0716964i	$-0.977159\pi$
$823$		−	118.012i		−	0.143393i	0.997427	−	0.0716964i	$-0.0228413\pi$
$824$	679.322	−	1163.08i	0.824420	−	1.41150i
$825$	200.054			0.242489
$826$	443.993	−	1124.58i	0.537522	−	1.36148i
$827$	36.0081	+	36.0081i	0.0435406	+	0.0435406i	0.728542	−	0.685001i	$-0.240198\pi$
$827$	36.0081	+	36.0081i	0.0435406	+	0.0435406i	−0.685001	+	0.728542i	$0.740198\pi$
$828$	−46.1816	−	267.141i	−0.0557748	−	0.322634i
$829$	−52.8642	−	52.8642i	−0.0637686	−	0.0637686i	0.674503	−	0.738272i	$-0.264358\pi$
$829$	−52.8642	−	52.8642i	−0.0637686	−	0.0637686i	−0.738272	+	0.674503i	$0.764358\pi$
$830$	708.825	+	596.802i	0.854006	+	0.719039i
$831$		−	554.451i		−	0.667209i
$832$	−271.087	+	972.492i	−0.325825	+	1.16886i
$833$	962.776	−	728.225i	1.15579	−	0.874220i
$834$	−23.5005	−	19.7865i	−0.0281780	−	0.0237248i
$835$	−647.960	+	647.960i	−0.776000	+	0.776000i
$836$	222.946	−	38.5414i	0.266681	−	0.0461021i
$837$	−250.716	−	250.716i	−0.299542	−	0.299542i
$838$	−57.6999	−	672.490i	−0.0688543	−	0.802494i
$839$	1257.63			1.49897			0.749484	−	0.662023i	$-0.230302\pi$
$839$	1257.63			1.49897			0.749484	+	0.662023i	$0.230302\pi$
$840$	−373.739	−	569.753i	−0.444928	−	0.678278i
$841$		−	365.490i		−	0.434589i
$842$	121.824	+	1419.85i	0.144684	+	1.68629i
$843$	382.176	−	382.176i	0.453352	−	0.453352i
$844$	375.341	+	264.696i	0.444717	+	0.313621i
$845$	437.248	+	437.248i	0.517453	+	0.517453i
$846$	−193.186	−	162.654i	−0.228352	−	0.192263i
$847$	675.344	+	335.955i	0.797336	+	0.396641i
$848$	−165.369	−	78.4666i	−0.195011	−	0.0925314i
$849$	314.674			0.370640
$850$	1318.91	+	1110.46i	1.55165	+	1.30643i
$851$	−26.4897	+	26.4897i	−0.0311278	+	0.0311278i
$852$	−48.6007	−	34.2739i	−0.0570430	−	0.0402275i
$853$	−906.916	+	906.916i	−1.06321	+	1.06321i	−0.0653442	+	0.997863i	$0.520815\pi$
$853$	−906.916	+	906.916i	−1.06321	+	1.06321i	−0.997863	+	0.0653442i	$0.979185\pi$
$854$	−1393.59	−	550.200i	−1.63184	−	0.644262i
$855$			786.359i			0.919718i
$856$	658.937	−	173.016i	0.769786	−	0.202122i
$857$	1015.16			1.18455			0.592273	−	0.805737i	$-0.298231\pi$
$857$	1015.16			1.18455			0.592273	+	0.805737i	$0.298231\pi$
$858$	179.709	−	15.4191i	0.209451	−	0.0179710i
$859$	851.483	−	851.483i	0.991249	−	0.991249i	−0.00871336	−	0.999962i	$-0.502774\pi$
$859$	851.483	−	851.483i	0.991249	−	0.991249i	0.999962	+	0.00871336i	$0.00277359\pi$
$860$	343.513	+	1987.08i	0.399433	+	2.31055i
$861$	504.414	−	169.280i	0.585847	−	0.196608i
$862$	−887.970	−	747.634i	−1.03013	−	0.867325i
$863$	−873.705			−1.01240			−0.506202	−	0.862415i	$-0.668951\pi$
$863$	−873.705			−1.01240			−0.506202	+	0.862415i	$0.668951\pi$
$864$	−710.392	+	324.043i	−0.822213	+	0.375050i
$865$	97.3116			0.112499
$866$	207.689	−	246.673i	0.239825	−	0.284842i
$867$	−353.172	−	353.172i	−0.407350	−	0.407350i
$868$	−116.515	+	389.836i	−0.134234	+	0.449120i
$869$	141.619	+	141.619i	0.162968	+	0.162968i
$870$	842.190	−	72.2603i	0.968035	−	0.0830578i
$871$	1809.81			2.07785
$872$	10.6645	+	40.6160i	0.0122299	+	0.0465780i
$873$	922.865			1.05712
$874$	−321.352	+	27.5721i	−0.367679	+	0.0315470i
$875$	513.605	−	172.364i	0.586977	−	0.196988i
$876$	−133.043	+	188.657i	−0.151876	+	0.215361i
$877$	−1140.58	+	1140.58i	−1.30055	+	1.30055i	−0.372525	+	0.928022i	$0.621508\pi$
$877$	−1140.58	+	1140.58i	−1.30055	+	1.30055i	−0.928022	+	0.372525i	$0.878492\pi$
$878$	−262.319	−	220.862i	−0.298769	−	0.251551i
$879$	183.511			0.208772
$880$	−424.829	+	151.408i	−0.482760	+	0.172055i
$881$			626.678i			0.711325i	0.934614	+	0.355663i	$0.115745\pi$
$881$			626.678i			0.711325i	−0.934614	+	0.355663i	$0.884255\pi$
$882$	−639.272	−	33.4228i	−0.724799	−	0.0378944i
$883$	101.385	−	101.385i	0.114819	−	0.114819i	−0.647363	−	0.762182i	$-0.724128\pi$
$883$	101.385	−	101.385i	0.114819	−	0.114819i	0.762182	+	0.647363i	$0.224128\pi$
$884$	1270.37	+	895.879i	1.43706	+	1.01344i
$885$	−743.045	+	743.045i	−0.839599	+	0.839599i
$886$	87.6510	+	1021.57i	0.0989289	+	1.15301i
$887$	−966.644			−1.08979			−0.544895	−	0.838504i	$-0.683431\pi$
$887$	−966.644			−1.08979			−0.544895	+	0.838504i	$0.683431\pi$
$888$	39.1821	+	22.8852i	0.0441240	+	0.0257716i
$889$	−317.838	+	638.924i	−0.357523	+	0.718700i
$890$	−125.239	+	10.7455i	−0.140718	+	0.0120736i
$891$	−52.6433	−	52.6433i	−0.0590834	−	0.0590834i
$892$	1044.95	−	180.644i	1.17147	−	0.202516i
$893$	−212.450	+	212.450i	−0.237905	+	0.237905i
$894$	248.800	−	295.501i	0.278300	−	0.330538i
$895$			1470.35i			1.64285i
$896$	714.442	+	540.730i	0.797368	+	0.603493i
$897$	−257.124			−0.286649
$898$	−1041.27	−	876.710i	−1.15955	−	0.976292i
$899$	−356.903	−	356.903i	−0.397000	−	0.397000i
$900$	−155.746	−	900.925i	−0.173051	−	1.00103i
$901$	−199.289	+	199.289i	−0.221187	+	0.221187i
$902$	−30.1050	−	350.873i	−0.0333758	−	0.388994i
$903$	−640.840	−	318.791i	−0.709679	−	0.353036i
$904$	−178.115	+	304.954i	−0.197030	+	0.337339i
$905$			99.9640i			0.110457i
$906$	426.014	−	36.5522i	0.470214	−	0.0403446i
$907$	5.22275	+	5.22275i	0.00575826	+	0.00575826i	0.709980	−	0.704222i	$-0.248704\pi$
$907$	5.22275	+	5.22275i	0.00575826	+	0.00575826i	−0.704222	+	0.709980i	$0.748704\pi$
$908$	−114.181	+	161.910i	−0.125750	+	0.178315i
$909$	−595.411	−	595.411i	−0.655018	−	0.655018i
$910$	1569.19	−	680.857i	1.72438	−	0.748194i
$911$	−1180.89			−1.29626			−0.648130	−	0.761530i	$-0.724449\pi$
$911$	−1180.89			−1.29626			−0.648130	+	0.761530i	$0.724449\pi$
$912$	131.152	+	367.993i	0.143807	+	0.403501i
$913$			217.687i			0.238430i
$914$	−98.4818	+	116.967i	−0.107748	+	0.127973i
$915$	920.787	+	920.787i	1.00632	+	1.00632i
$916$	−77.4382	−	54.6105i	−0.0845395	−	0.0596184i
$917$	−903.699	+	303.278i	−0.985495	+	0.330729i
$918$	102.776	+	1197.85i	0.111956	+	1.30485i
$919$			541.429i			0.589150i	0.955628	+	0.294575i	$0.0951781\pi$
$919$			541.429i			0.589150i	−0.955628	+	0.294575i	$0.904822\pi$
$920$	621.845	−	163.277i	0.675919	−	0.177475i
$921$			446.451i			0.484746i
$922$	2.30352	+	26.8475i	0.00249840	+	0.0291187i
$923$	105.564	−	105.564i	0.114371	−	0.114371i
$924$	45.8410	−	153.375i	0.0496114	−	0.165990i
$925$	−89.3359	+	89.3359i	−0.0965794	+	0.0965794i
$926$	166.125	+	139.870i	0.179400	+	0.151048i
$927$			1099.79i			1.18639i
$928$	−1011.27	+	461.286i	−1.08973	+	0.497076i
$929$		−	362.906i		−	0.390641i	−0.980739	−	0.195321i	$-0.937425\pi$
$929$		−	362.906i		−	0.390641i	0.980739	−	0.195321i	$-0.0625748\pi$
$930$	227.760	−	270.512i	0.244904	−	0.290873i
$931$	−104.634	+	754.361i	−0.112389	+	0.810269i
$932$	−642.050	+	110.993i	−0.688894	+	0.119092i
$933$	−514.398	−	514.398i	−0.551337	−	0.551337i
$934$	−103.689	−	1208.49i	−0.111016	−	1.29389i
$935$			694.433i			0.742709i
$936$	−209.346	−	797.300i	−0.223660	−	0.851816i
$937$	−1172.13			−1.25094			−0.625469	−	0.780249i	$-0.715092\pi$
$937$	−1172.13			−1.25094			−0.625469	+	0.780249i	$0.715092\pi$
$938$	589.841	−	1494.00i	0.628828	−	1.59275i
$939$	−1.21178	−	1.21178i	−0.00129050	−	0.00129050i
$940$	345.159	−	489.439i	0.367191	−	0.520680i
$941$	−930.677	−	930.677i	−0.989030	−	0.989030i	0.0109108	−	0.999940i	$-0.496527\pi$
$941$	−930.677	−	930.677i	−0.989030	−	0.989030i	−0.999940	+	0.0109108i	$0.996527\pi$
$942$	175.207	−	208.095i	0.185995	−	0.220908i
$943$			502.021i			0.532366i
$944$	592.347	−	1248.38i	0.627486	−	1.32243i
$945$	1184.47	+	589.226i	1.25341	+	0.623519i
$946$	−305.125	+	362.398i	−0.322542	+	0.383085i
$947$	265.946	−	265.946i	0.280830	−	0.280830i	−0.552610	−	0.833440i	$-0.686368\pi$
$947$	265.946	−	265.946i	0.280830	−	0.280830i	0.833440	+	0.552610i	$0.186368\pi$
$948$	−199.302	+	282.612i	−0.210234	+	0.298114i
$949$	−409.777	−	409.777i	−0.431798	−	0.431798i
$950$	−1083.75	+	92.9861i	−1.14079	+	0.0978801i
$951$	113.675			0.119532
$952$	1153.58	−	756.708i	1.21174	−	0.794861i
$953$			1378.60i			1.44659i	0.690540	+	0.723294i	$0.257373\pi$
$953$			1378.60i			1.44659i	−0.690540	+	0.723294i	$0.742627\pi$
$954$	148.908	−	12.7764i	0.156088	−	0.0133924i
$955$	−999.431	+	999.431i	−1.04653	+	1.04653i
$956$	−312.644	−	1808.52i	−0.327034	−	1.89175i
$957$	140.418	+	140.418i	0.146727	+	0.146727i
$958$	−873.805	+	1037.82i	−0.912113	+	1.08332i
$959$	−279.848	−	139.213i	−0.291812	−	0.145164i
$960$	−382.569	−	678.287i	−0.398509	−	0.706549i
$961$	749.842			0.780273
$962$	−73.3652	+	87.1363i	−0.0762632	+	0.0905782i
$963$	−393.340	+	393.340i	−0.408453	+	0.408453i
$964$	24.3489	−	4.20928i	0.0252582	−	0.00436647i
$965$	2074.45	−	2074.45i	2.14969	−	2.14969i
$966$	−83.7999	+	212.256i	−0.0867494	+	0.219726i
$967$			1533.12i			1.58544i	0.609584	+	0.792722i	$0.291337\pi$
$967$			1533.12i			1.58544i	−0.609584	+	0.792722i	$0.708663\pi$
$968$	744.378	+	434.771i	0.768986	+	0.449143i
$969$	601.528			0.620772
$970$	187.094	+	2180.57i	0.192880	+	2.24801i
$971$	−44.2230	+	44.2230i	−0.0455437	+	0.0455437i	−0.729512	−	0.683968i	$-0.760253\pi$
$971$	−44.2230	+	44.2230i	−0.0455437	+	0.0455437i	0.683968	+	0.729512i	$0.260253\pi$
$972$	580.328	−	822.911i	0.597046	−	0.846617i
$973$	−21.7762	−	64.8880i	−0.0223805	−	0.0666886i
$974$	950.112	−	1128.45i	0.975474	−	1.15858i
$975$	−867.143			−0.889377
$976$	−1547.00	−	734.040i	−1.58504	−	0.752090i
$977$	−623.770			−0.638454			−0.319227	−	0.947678i	$-0.603423\pi$
$977$	−623.770			−0.638454			−0.319227	+	0.947678i	$0.603423\pi$
$978$	571.084	+	480.829i	0.583930	+	0.491645i
$979$	−20.8810	−	20.8810i	−0.0213289	−	0.0213289i
$980$	−50.6283	−	1517.27i	−0.0516615	−	1.54823i
$981$	−24.2450	−	24.2450i	−0.0247146	−	0.0247146i
$982$	−126.906	−	1479.08i	−0.129232	−	1.50619i
$983$	−1124.01			−1.14345			−0.571724	−	0.820446i	$-0.693725\pi$
$983$	−1124.01			−1.14345			−0.571724	+	0.820446i	$0.693725\pi$
$984$	588.135	−	154.426i	0.597698	−	0.156937i
$985$	1413.01			1.43453
$986$	146.305	+	1705.18i	0.148382	+	1.72939i
$987$	67.6324	+	201.529i	0.0685232	+	0.204183i
$988$	−966.368	+	167.059i	−0.978106	+	0.169088i
$989$	477.539	−	477.539i	0.482851	−	0.482851i
$990$	237.179	−	281.698i	0.239574	−	0.284544i
$991$	392.328			0.395891			0.197946	−	0.980213i	$-0.436573\pi$
$991$	392.328			0.395891			0.197946	+	0.980213i	$0.436573\pi$
$992$	−162.695	+	435.610i	−0.164007	+	0.439123i
$993$			64.0327i			0.0644841i
$994$	−52.7386	−	121.548i	−0.0530570	−	0.122282i
$995$	1505.01	−	1505.01i	1.51257	−	1.51257i
$996$	−370.382	+	64.0291i	−0.371869	+	0.0642863i
$997$	744.756	−	744.756i	0.746997	−	0.746997i	−0.226917	−	0.973914i	$-0.572865\pi$
$997$	744.756	−	744.756i	0.746997	−	0.746997i	0.973914	+	0.226917i	$0.0728648\pi$
$998$	173.344	−	14.8730i	0.173691	−	0.0149028i
$999$	−88.0977			−0.0881859

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.3.l.b.69.24	yes	56
4.3	odd	2		448.3.l.b.433.11		56
7.6	odd	2	inner	112.3.l.b.69.23	yes	56
16.3	odd	4		448.3.l.b.209.18		56
16.13	even	4	inner	112.3.l.b.13.23	✓	56
28.27	even	2		448.3.l.b.433.18		56
112.13	odd	4	inner	112.3.l.b.13.24	yes	56
112.83	even	4		448.3.l.b.209.11		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.3.l.b.13.23	✓	56	16.13	even	4	inner
112.3.l.b.13.24	yes	56	112.13	odd	4	inner
112.3.l.b.69.23	yes	56	7.6	odd	2	inner
112.3.l.b.69.24	yes	56	1.1	even	1	trivial
448.3.l.b.209.11		56	112.83	even	4
448.3.l.b.209.18		56	16.3	odd	4
448.3.l.b.433.11		56	4.3	odd	2
448.3.l.b.433.18		56	28.27	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:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	112.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.52993 + 1.28814i) q^{2} +(1.11083 + 1.11083i) q^{3} +(0.681387 + 3.94154i) q^{4} +(5.47687 - 5.47687i) q^{5} +(0.268590 + 3.13041i) q^{6} +(-3.11774 + 6.26735i) q^{7} +(-4.03478 + 6.90801i) q^{8} -6.53210i q^{9} +(15.4342 - 1.32426i) q^{10} +(2.57334 + 2.57334i) q^{11} +(-3.62148 + 5.13530i) q^{12} +(-11.1543 - 11.1543i) q^{13} +(-12.8432 + 5.57253i) q^{14} +12.1678 q^{15} +(-15.0714 + 5.37142i) q^{16} +24.6360i q^{17} +(8.41426 - 9.99367i) q^{18} +(-10.9902 - 10.9902i) q^{19} +(25.3191 + 17.8554i) q^{20} +(-10.4253 + 3.49869i) q^{21} +(0.622213 + 7.25186i) q^{22} -10.3758i q^{23} +(-12.1556 + 3.19168i) q^{24} -34.9921i q^{25} +(-2.69701 - 31.4335i) q^{26} +(17.2536 - 17.2536i) q^{27} +(-26.8274 - 8.01821i) q^{28} +(24.5610 - 24.5610i) q^{29} +(18.6159 + 15.6738i) q^{30} -14.5313i q^{31} +(-29.9774 - 11.1962i) q^{32} +5.71711i q^{33} +(-31.7347 + 37.6915i) q^{34} +(17.2500 + 51.4009i) q^{35} +(25.7465 - 4.45089i) q^{36} +(-2.55303 - 2.55303i) q^{37} +(-2.65734 - 30.9712i) q^{38} -24.7811i q^{39} +(15.7363 + 59.9322i) q^{40} -48.3838 q^{41} +(-20.4568 - 8.07647i) q^{42} +(46.0243 + 46.0243i) q^{43} +(-8.38947 + 11.8964i) q^{44} +(-35.7754 - 35.7754i) q^{45} +(13.3655 - 15.8743i) q^{46} -19.3308i q^{47} +(-22.7086 - 10.7751i) q^{48} +(-29.5593 - 39.0800i) q^{49} +(45.0748 - 53.5356i) q^{50} +(-27.3665 + 27.3665i) q^{51} +(36.3646 - 51.5653i) q^{52} +(8.08934 + 8.08934i) q^{53} +(48.6218 - 4.17177i) q^{54} +28.1877 q^{55} +(-30.7155 - 46.8248i) q^{56} -24.4166i q^{57} +(69.2148 - 5.93866i) q^{58} +(-61.0667 + 61.0667i) q^{59} +(8.29096 + 47.9597i) q^{60} +(75.6742 + 75.6742i) q^{61} +(18.7183 - 22.2319i) q^{62} +(40.9389 + 20.3654i) q^{63} +(-31.4411 - 55.7446i) q^{64} -122.181 q^{65} +(-7.36444 + 8.74679i) q^{66} +(-81.1264 + 81.1264i) q^{67} +(-97.1038 + 16.7867i) q^{68} +(11.5258 - 11.5258i) q^{69} +(-39.8203 + 100.860i) q^{70} +9.46404i q^{71} +(45.1238 + 26.3556i) q^{72} +36.7372 q^{73} +(-0.617301 - 7.19462i) q^{74} +(38.8704 - 38.8704i) q^{75} +(35.8297 - 50.8069i) q^{76} +(-24.1510 + 8.10501i) q^{77} +(31.9215 - 37.9134i) q^{78} +55.0332 q^{79} +(-53.1256 + 111.963i) q^{80} -20.4572 q^{81} +(-74.0239 - 62.3251i) q^{82} +(42.2965 + 42.2965i) q^{83} +(-20.8939 - 38.7077i) q^{84} +(134.928 + 134.928i) q^{85} +(11.1283 + 129.700i) q^{86} +54.5665 q^{87} +(-28.1595 + 7.39380i) q^{88} -8.11436 q^{89} +(-8.65021 - 100.818i) q^{90} +(104.684 - 35.1315i) q^{91} +(40.8967 - 7.06995i) q^{92} +(16.1418 - 16.1418i) q^{93} +(24.9008 - 29.5748i) q^{94} -120.384 q^{95} +(-20.8628 - 45.7370i) q^{96} +141.282i q^{97} +(5.11671 - 97.8663i) q^{98} +(16.8093 - 16.8093i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{2} - 8 q^{4} - 16 q^{8} + 40 q^{14} - 8 q^{15} + 48 q^{16} + 196 q^{18} - 20 q^{21} - 120 q^{22} - 96 q^{29} - 40 q^{30} - 184 q^{32} - 100 q^{35} + 160 q^{36} - 128 q^{37} - 144 q^{42} - 72 q^{43}+ \cdots + 8 q^{99}+O(q^{100}) \) 56 * q - 4 * q^2 - 8 * q^4 - 16 * q^8 + 40 * q^14 - 8 * q^15 + 48 * q^16 + 196 * q^18 - 20 * q^21 - 120 * q^22 - 96 * q^29 - 40 * q^30 - 184 * q^32 - 100 * q^35 + 160 * q^36 - 128 * q^37 - 144 * q^42 - 72 * q^43 - 448 * q^44 - 168 * q^46 + 192 * q^49 - 364 * q^50 - 128 * q^51 + 88 * q^53 + 56 * q^56 + 408 * q^58 + 504 * q^60 + 444 * q^63 + 256 * q^64 - 8 * q^65 + 440 * q^67 - 112 * q^70 + 592 * q^72 - 408 * q^74 + 12 * q^77 + 664 * q^78 - 8 * q^79 + 64 * q^81 - 576 * q^84 + 96 * q^85 + 256 * q^86 + 448 * q^88 - 388 * q^91 - 1192 * q^92 + 32 * q^93 - 776 * q^95 + 540 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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