LMFDB - Embedded newform 140.3.x.a.103.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,3,Mod(3,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("140.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	140.x (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.81472370104$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.30
Character	$\chi$	$=$	140.103
Dual form			140.3.x.a.87.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.937660 + 1.76658i) q^{2} +(0.677069 - 2.52686i) q^{3} +(-2.24159 + 3.31290i) q^{4} +(-0.838349 + 4.92922i) q^{5} +(5.09875 - 1.17324i) q^{6} +(5.54073 + 4.27788i) q^{7} +(-7.95433 - 0.853568i) q^{8} +(1.86765 + 1.07829i) q^{9} +O(q^{10})$	\(q+(0.937660 + 1.76658i) q^{2} +(0.677069 - 2.52686i) q^{3} +(-2.24159 + 3.31290i) q^{4} +(-0.838349 + 4.92922i) q^{5} +(5.09875 - 1.17324i) q^{6} +(5.54073 + 4.27788i) q^{7} +(-7.95433 - 0.853568i) q^{8} +(1.86765 + 1.07829i) q^{9} +(-9.49393 + 3.14092i) q^{10} +(-0.558108 + 0.322224i) q^{11} +(6.85350 + 7.90723i) q^{12} +(1.26172 - 1.26172i) q^{13} +(-2.36188 + 13.7993i) q^{14} +(11.8878 + 5.45581i) q^{15} +(-5.95057 - 14.8523i) q^{16} +(-5.07660 + 18.9461i) q^{17} +(-0.153658 + 4.31041i) q^{18} +(22.5524 + 13.0206i) q^{19} +(-14.4507 - 13.8266i) q^{20} +(14.5611 - 11.1042i) q^{21} +(-1.09255 - 0.683804i) q^{22} +(-8.50715 - 31.7491i) q^{23} +(-7.54248 + 19.5215i) q^{24} +(-23.5943 - 8.26481i) q^{25} +(3.41200 + 1.04586i) q^{26} +(20.6373 - 20.6373i) q^{27} +(-26.5922 + 8.76663i) q^{28} -39.4547i q^{29} +(1.50861 + 26.1164i) q^{30} +(-14.1092 - 24.4379i) q^{31} +(20.6581 - 24.4385i) q^{32} +(0.436336 + 1.62843i) q^{33} +(-38.2299 + 8.79681i) q^{34} +(-25.7317 + 23.7251i) q^{35} +(-7.75874 + 3.77025i) q^{36} +(4.16217 + 15.5334i) q^{37} +(-1.85548 + 52.0495i) q^{38} +(-2.33392 - 4.04247i) q^{39} +(10.8759 - 38.4930i) q^{40} +37.2770i q^{41} +(33.2698 + 15.3112i) q^{42} +(34.6421 - 34.6421i) q^{43} +(0.183554 - 2.57125i) q^{44} +(-6.88084 + 8.30205i) q^{45} +(48.1104 - 44.7984i) q^{46} +(-17.3586 - 64.7831i) q^{47} +(-41.5586 + 4.98019i) q^{48} +(12.3995 + 47.4052i) q^{49} +(-7.52304 - 49.4308i) q^{50} +(44.4369 + 25.6557i) q^{51} +(1.35169 + 7.00822i) q^{52} +(14.4231 - 53.8279i) q^{53} +(55.8081 + 17.1066i) q^{54} +(-1.12042 - 3.02117i) q^{55} +(-40.4214 - 38.7571i) q^{56} +(48.1709 - 48.1709i) q^{57} +(69.6998 - 36.9951i) q^{58} +(-48.7371 + 28.1384i) q^{59} +(-44.7221 + 27.1534i) q^{60} +(52.9920 + 30.5949i) q^{61} +(29.9417 - 47.8394i) q^{62} +(5.73535 + 13.9641i) q^{63} +(62.5428 + 13.5791i) q^{64} +(5.16154 + 7.27707i) q^{65} +(-2.46761 + 2.29773i) q^{66} +(-0.166368 + 0.620894i) q^{67} +(-51.3869 - 59.2876i) q^{68} -85.9854 q^{69} +(-66.0398 - 23.2109i) q^{70} +61.5119i q^{71} +(-13.9355 - 10.1712i) q^{72} +(57.8965 + 15.5133i) q^{73} +(-23.5383 + 21.9179i) q^{74} +(-36.8590 + 54.0237i) q^{75} +(-93.6893 + 45.5269i) q^{76} +(-4.47076 - 0.602163i) q^{77} +(4.95291 - 7.91351i) q^{78} +(-43.1677 + 74.7687i) q^{79} +(78.1988 - 16.8802i) q^{80} +(-28.4700 - 49.3115i) q^{81} +(-65.8527 + 34.9531i) q^{82} +(4.14603 + 4.14603i) q^{83} +(4.14725 + 73.1303i) q^{84} +(-89.1335 - 40.9071i) q^{85} +(93.6804 + 28.7154i) q^{86} +(-99.6964 - 26.7136i) q^{87} +(4.71442 - 2.08669i) q^{88} +(-26.4526 + 45.8173i) q^{89} +(-21.1181 - 4.37104i) q^{90} +(12.3884 - 1.59337i) q^{91} +(124.251 + 42.9851i) q^{92} +(-71.3039 + 19.1058i) q^{93} +(98.1679 - 91.4097i) q^{94} +(-83.0884 + 100.250i) q^{95} +(-47.7657 - 68.7467i) q^{96} +(-45.6253 - 45.6253i) q^{97} +(-72.1185 + 66.3546i) q^{98} -1.38980 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8}+O(q^{10}) $ 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8	$ 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8} - 6 q^{10} - 6 q^{12} - 28 q^{16} - 12 q^{17} - 36 q^{18} - 32 q^{21} - 24 q^{22} - 4 q^{25} - 12 q^{26} + 114 q^{28} + 28 q^{30} + 58 q^{32} - 156 q^{33} - 144 q^{36} - 4 q^{37} + 192 q^{38} + 54 q^{40} - 218 q^{42} - 12 q^{45} + 68 q^{46} - 332 q^{50} - 264 q^{52} - 4 q^{53} - 300 q^{56} - 24 q^{57} - 146 q^{58} - 434 q^{60} - 24 q^{61} + 92 q^{65} - 660 q^{66} - 72 q^{68} + 488 q^{70} - 80 q^{72} - 12 q^{73} - 156 q^{77} + 688 q^{78} + 588 q^{80} + 288 q^{81} + 798 q^{82} + 272 q^{85} - 72 q^{86} + 588 q^{88} + 524 q^{92} + 164 q^{93} + 1080 q^{96} - 766 q^{98}+O(q^{100}) $ 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8 - 6 * q^10 - 6 * q^12 - 28 * q^16 - 12 * q^17 - 36 * q^18 - 32 * q^21 - 24 * q^22 - 4 * q^25 - 12 * q^26 + 114 * q^28 + 28 * q^30 + 58 * q^32 - 156 * q^33 - 144 * q^36 - 4 * q^37 + 192 * q^38 + 54 * q^40 - 218 * q^42 - 12 * q^45 + 68 * q^46 - 332 * q^50 - 264 * q^52 - 4 * q^53 - 300 * q^56 - 24 * q^57 - 146 * q^58 - 434 * q^60 - 24 * q^61 + 92 * q^65 - 660 * q^66 - 72 * q^68 + 488 * q^70 - 80 * q^72 - 12 * q^73 - 156 * q^77 + 688 * q^78 + 588 * q^80 + 288 * q^81 + 798 * q^82 + 272 * q^85 - 72 * q^86 + 588 * q^88 + 524 * q^92 + 164 * q^93 + 1080 * q^96 - 766 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.937660	+	1.76658i	0.468830	+	0.883288i
$2$	0.937660	+	1.76658i	0.468830	+	0.883288i
$3$	0.677069	−	2.52686i	0.225690	−	0.842286i	−0.756437	−	0.654066i	$-0.773062\pi$
$3$	0.677069	−	2.52686i	0.225690	−	0.842286i	0.982127	−	0.188219i	$-0.0602716\pi$
$4$	−2.24159	+	3.31290i	−0.560397	+	0.828224i
$5$	−0.838349	+	4.92922i	−0.167670	+	0.985843i
$5$	−0.838349	+	4.92922i	−0.167670	+	0.985843i
$6$	5.09875	−	1.17324i	0.849791	−	0.195540i
$7$	5.54073	+	4.27788i	0.791533	+	0.611126i
$7$	5.54073	+	4.27788i	0.791533	+	0.611126i
$8$	−7.95433	−	0.853568i	−0.994292	−	0.106696i
$9$	1.86765	+	1.07829i	0.207516	+	0.119810i
$10$	−9.49393	+	3.14092i	−0.949393	+	0.314092i
$11$	−0.558108	+	0.322224i	−0.0507371	+	0.0292931i	−0.525154	−	0.851007i	$-0.675992\pi$
$11$	−0.558108	+	0.322224i	−0.0507371	+	0.0292931i	0.474417	+	0.880300i	$0.342659\pi$
$12$	6.85350	+	7.90723i	0.571125	+	0.658936i
$13$	1.26172	−	1.26172i	0.0970556	−	0.0970556i	−0.656912	−	0.753967i	$-0.728138\pi$
$13$	1.26172	−	1.26172i	0.0970556	−	0.0970556i	0.753967	+	0.656912i	$0.228138\pi$
$14$	−2.36188	+	13.7993i	−0.168706	+	0.985666i
$15$	11.8878	+	5.45581i	0.792520	+	0.363721i
$16$	−5.95057	−	14.8523i	−0.371910	−	0.928269i
$17$	−5.07660	+	18.9461i	−0.298623	+	1.11448i	0.639674	+	0.768647i	$0.279070\pi$
$17$	−5.07660	+	18.9461i	−0.298623	+	1.11448i	−0.938297	+	0.345831i	$0.887597\pi$
$18$	−0.153658	+	4.31041i	−0.00853658	+	0.239467i
$19$	22.5524	+	13.0206i	1.18697	+	0.685297i	0.957617	−	0.288046i	$-0.0930056\pi$
$19$	22.5524	+	13.0206i	1.18697	+	0.685297i	0.229353	+	0.973343i	$0.426339\pi$
$20$	−14.4507	−	13.8266i	−0.722537	−	0.691332i
$21$	14.5611	−	11.1042i	0.693383	−	0.528772i
$22$	−1.09255	−	0.683804i	−0.0496613	−	0.0310820i
$23$	−8.50715	−	31.7491i	−0.369876	−	1.38040i	−0.860689	−	0.509131i	$-0.829967\pi$
$23$	−8.50715	−	31.7491i	−0.369876	−	1.38040i	0.490813	−	0.871265i	$-0.336700\pi$
$24$	−7.54248	+	19.5215i	−0.314270	+	0.813397i
$25$	−23.5943	−	8.26481i	−0.943774	−	0.330592i
$26$	3.41200	+	1.04586i	0.131231	+	0.0402255i
$27$	20.6373	−	20.6373i	0.764344	−	0.764344i
$28$	−26.5922	+	8.76663i	−0.949722	+	0.313094i
$29$		−	39.4547i		−	1.36051i	−0.732977	−	0.680254i	$-0.761869\pi$
$29$		−	39.4547i		−	1.36051i	0.732977	−	0.680254i	$-0.238131\pi$
$30$	1.50861	+	26.1164i	0.0502869	+	0.870547i
$31$	−14.1092	−	24.4379i	−0.455136	−	0.788318i	0.543560	−	0.839370i	$-0.317076\pi$
$31$	−14.1092	−	24.4379i	−0.455136	−	0.788318i	−0.998696	+	0.0510518i	$0.983743\pi$
$32$	20.6581	−	24.4385i	0.645566	−	0.763704i
$33$	0.436336	+	1.62843i	0.0132223	+	0.0493463i
$34$	−38.2299	+	8.79681i	−1.12441	+	0.258730i
$35$	−25.7317	+	23.7251i	−0.735191	+	0.677860i
$36$	−7.75874	+	3.77025i	−0.215521	+	0.104729i
$37$	4.16217	+	15.5334i	0.112491	+	0.419823i	0.999087	−	0.0427221i	$-0.0136030\pi$
$37$	4.16217	+	15.5334i	0.112491	+	0.419823i	−0.886596	+	0.462545i	$0.846936\pi$
$38$	−1.85548	+	52.0495i	−0.0488283	+	1.36972i
$39$	−2.33392	−	4.04247i	−0.0598441	−	0.103653i
$40$	10.8759	−	38.4930i	0.271898	−	0.962326i
$41$			37.2770i			0.909195i	0.890697	+	0.454598i	$0.150217\pi$
$41$			37.2770i			0.909195i	−0.890697	+	0.454598i	$0.849783\pi$
$42$	33.2698	+	15.3112i	0.792137	+	0.364553i
$43$	34.6421	−	34.6421i	0.805630	−	0.805630i	−0.178339	−	0.983969i	$-0.557072\pi$
$43$	34.6421	−	34.6421i	0.805630	−	0.805630i	0.983969	+	0.178339i	$0.0570724\pi$
$44$	0.183554	−	2.57125i	0.00417169	−	0.0584374i
$45$	−6.88084	+	8.30205i	−0.152908	+	0.184490i
$46$	48.1104	−	44.7984i	1.04588	−	0.973878i
$47$	−17.3586	−	64.7831i	−0.369331	−	1.37836i	−0.861453	−	0.507837i	$-0.830445\pi$
$47$	−17.3586	−	64.7831i	−0.369331	−	1.37836i	0.492122	−	0.870526i	$-0.336221\pi$
$48$	−41.5586	+	4.98019i	−0.865804	+	0.103754i
$49$	12.3995	+	47.4052i	0.253050	+	0.967453i
$50$	−7.52304	−	49.4308i	−0.150461	−	0.988616i
$51$	44.4369	+	25.6557i	0.871312	+	0.503052i
$52$	1.35169	+	7.00822i	0.0259941	+	0.134773i
$53$	14.4231	−	53.8279i	0.272135	−	1.01562i	−0.685602	−	0.727976i	$-0.740461\pi$
$53$	14.4231	−	53.8279i	0.272135	−	1.01562i	0.957737	−	0.287645i	$-0.0928723\pi$
$54$	55.8081	+	17.1066i	1.03348	+	0.316789i
$55$	−1.12042	−	3.02117i	−0.0203713	−	0.0549304i
$56$	−40.4214	−	38.7571i	−0.721810	−	0.692091i
$57$	48.1709	−	48.1709i	0.845103	−	0.845103i
$58$	69.6998	−	36.9951i	1.20172	−	0.637847i
$59$	−48.7371	+	28.1384i	−0.826053	+	0.476922i	−0.852499	−	0.522729i	$-0.824914\pi$
$59$	−48.7371	+	28.1384i	−0.826053	+	0.476922i	0.0264466	+	0.999650i	$0.491581\pi$
$60$	−44.7221	+	27.1534i	−0.745368	+	0.452556i
$61$	52.9920	+	30.5949i	0.868721	+	0.501556i	0.866923	−	0.498442i	$-0.166094\pi$
$61$	52.9920	+	30.5949i	0.868721	+	0.501556i	0.00179799	+	0.999998i	$0.499428\pi$
$62$	29.9417	−	47.8394i	0.482931	−	0.771603i
$63$	5.73535	+	13.9641i	0.0910373	+	0.221652i
$64$	62.5428	+	13.5791i	0.977232	+	0.212174i
$65$	5.16154	+	7.27707i	0.0794083	+	0.111955i
$66$	−2.46761	+	2.29773i	−0.0373880	+	0.0348141i
$67$	−0.166368	+	0.620894i	−0.00248311	+	0.00926708i	−0.967156	−	0.254183i	$-0.918194\pi$
$67$	−0.166368	+	0.620894i	−0.00248311	+	0.00926708i	0.964673	+	0.263450i	$0.0848603\pi$
$68$	−51.3869	−	59.2876i	−0.755689	−	0.871877i
$69$	−85.9854			−1.24616
$70$	−66.0398	−	23.2109i	−0.943426	−	0.331584i
$71$			61.5119i			0.866365i	0.901306	+	0.433183i	$0.142610\pi$
$71$			61.5119i			0.866365i	−0.901306	+	0.433183i	$0.857390\pi$
$72$	−13.9355	−	10.1712i	−0.193548	−	0.141267i
$73$	57.8965	+	15.5133i	0.793103	+	0.212511i	0.632554	−	0.774516i	$-0.282007\pi$
$73$	57.8965	+	15.5133i	0.793103	+	0.212511i	0.160549	+	0.987028i	$0.448673\pi$
$74$	−23.5383	+	21.9179i	−0.318085	+	0.296188i
$75$	−36.8590	+	54.0237i	−0.491453	+	0.720316i
$76$	−93.6893	+	45.5269i	−1.23275	+	0.599038i
$77$	−4.47076	−	0.602163i	−0.0580619	−	0.00782030i
$78$	4.95291	−	7.91351i	0.0634988	−	0.101455i
$79$	−43.1677	+	74.7687i	−0.546427	+	0.946439i	0.452089	+	0.891973i	$0.350679\pi$
$79$	−43.1677	+	74.7687i	−0.546427	+	0.946439i	−0.998516	+	0.0544663i	$0.982654\pi$
$80$	78.1988	−	16.8802i	0.977486	−	0.211003i
$81$	−28.4700	−	49.3115i	−0.351482	−	0.608784i
$82$	−65.8527	+	34.9531i	−0.803082	+	0.426258i
$83$	4.14603	+	4.14603i	0.0499521	+	0.0499521i	0.731642	−	0.681689i	$-0.238754\pi$
$83$	4.14603	+	4.14603i	0.0499521	+	0.0499521i	−0.681689	+	0.731642i	$0.738754\pi$
$84$	4.14725	+	73.1303i	0.0493720	+	0.870599i
$85$	−89.1335	−	40.9071i	−1.04863	−	0.481260i
$86$	93.6804	+	28.7154i	1.08931	+	0.333900i
$87$	−99.6964	−	26.7136i	−1.14594	−	0.307053i
$88$	4.71442	−	2.08669i	0.0535729	−	0.0237124i
$89$	−26.4526	+	45.8173i	−0.297221	+	0.514801i	−0.975499	−	0.220004i	$-0.929393\pi$
$89$	−26.4526	+	45.8173i	−0.297221	+	0.514801i	0.678278	+	0.734805i	$0.262726\pi$
$90$	−21.1181	−	4.37104i	−0.234646	−	0.0485671i
$91$	12.3884	−	1.59337i	0.136136	−	0.0175096i
$92$	124.251	+	42.9851i	1.35055	+	0.467230i
$93$	−71.3039	+	19.1058i	−0.766709	+	0.205439i
$94$	98.1679	−	91.4097i	1.04434	−	0.972444i
$95$	−83.0884	+	100.250i	−0.874615	+	1.05526i
$96$	−47.7657	−	68.7467i	−0.497559	−	0.716111i
$97$	−45.6253	−	45.6253i	−0.470364	−	0.470364i	0.431668	−	0.902032i	$-0.357925\pi$
$97$	−45.6253	−	45.6253i	−0.470364	−	0.470364i	−0.902032	+	0.431668i	$0.857925\pi$
$98$	−72.1185	+	66.3546i	−0.735903	+	0.677087i
$99$	−1.38980			−0.0140384
$100$	80.2693	−	59.6393i	0.802693	−	0.596393i
$101$	−18.3643	+	10.6027i	−0.181825	+	0.104977i	−0.588150	−	0.808752i	$-0.700143\pi$
$101$	−18.3643	+	10.6027i	−0.181825	+	0.104977i	0.406325	+	0.913729i	$0.366810\pi$
$102$	−3.65600	+	102.558i	−0.0358431	+	1.00547i
$103$	36.2085	−	9.70203i	0.351538	−	0.0941945i	−0.0787286	−	0.996896i	$-0.525086\pi$
$103$	36.2085	−	9.70203i	0.351538	−	0.0941945i	0.430267	+	0.902702i	$0.358419\pi$
$104$	−11.1131	+	8.95920i	−0.106857	+	0.0861461i
$105$	42.5279	+	81.0838i	0.405027	+	0.772227i
$106$	108.615	−	24.9927i	1.02467	−	0.235780i
$107$	−25.2952	+	6.77783i	−0.236404	+	0.0633442i	−0.375076	−	0.926994i	$-0.622383\pi$
$107$	−25.2952	+	6.77783i	−0.236404	+	0.0633442i	0.138672	+	0.990338i	$0.455717\pi$
$108$	22.1089	+	114.629i	0.204712	+	1.06138i
$109$	122.945	−	70.9822i	1.12793	−	0.651213i	0.184520	−	0.982829i	$-0.440927\pi$
$109$	122.945	−	70.9822i	1.12793	−	0.651213i	0.943415	+	0.331616i	$0.107594\pi$
$110$	4.28656	−	4.81214i	0.0389687	−	0.0437467i
$111$	42.0689			0.378999
$112$	30.5659	−	107.748i	0.272910	−	0.962040i
$113$	−58.2140	−	58.2140i	−0.515168	−	0.515168i	0.400937	−	0.916106i	$-0.368685\pi$
$113$	−58.2140	−	58.2140i	−0.515168	−	0.515168i	−0.916106	+	0.400937i	$0.868685\pi$
$114$	130.265	+	39.9297i	1.14268	+	0.350260i
$115$	163.630	−	15.3167i	1.42287	−	0.133189i
$116$	130.709	+	88.4413i	1.12681	+	0.762425i
$117$	3.71695	−	0.995954i	0.0317688	−	0.00851243i
$118$	−95.4074	−	59.7136i	−0.808538	−	0.506048i
$119$	−109.177	+	83.2583i	−0.917456	+	0.699650i
$120$	−89.9026	−	53.5444i	−0.749189	−	0.446203i
$121$	−60.2923	+	104.429i	−0.498284	+	0.863053i
$122$	−4.35985	+	122.302i	−0.0357365	+	1.00248i
$123$	94.1936	+	25.2391i	0.765802	+	0.205196i
$124$	112.587	+	8.03729i	0.907961	+	0.0648168i
$125$	60.5193	−	109.373i	0.484155	−	0.874982i
$126$	−19.2908	+	23.2255i	−0.153101	+	0.184329i
$127$	−127.161	−	127.161i	−1.00127	−	1.00127i	−0.999999	−	0.00127018i	$-0.999596\pi$
$127$	−127.161	−	127.161i	−1.00127	−	1.00127i	−0.00127018	−	0.999999i	$-0.500404\pi$
$128$	34.6553	+	123.219i	0.270745	+	0.962651i
$129$	−64.0805	−	110.991i	−0.496748	−	0.860393i
$130$	−8.01573	+	15.9417i	−0.0616595	+	0.122628i
$131$	−52.1200	+	90.2745i	−0.397863	+	0.689118i	−0.993462	−	0.114163i	$-0.963581\pi$
$131$	−52.1200	+	90.2745i	−0.397863	+	0.689118i	0.595599	+	0.803282i	$0.296915\pi$
$132$	−6.37289	−	2.20473i	−0.0482795	−	0.0167025i
$133$	69.2562	+	168.621i	0.520723	+	1.26782i
$134$	−1.25285	+	0.288286i	−0.00934966	+	0.00215139i
$135$	84.4244	+	119.027i	0.625366	+	0.881681i
$136$	56.5527	−	146.370i	0.415829	−	1.07625i
$137$	40.8453	+	10.9445i	0.298141	+	0.0798865i	0.404789	−	0.914410i	$-0.367345\pi$
$137$	40.8453	+	10.9445i	0.298141	+	0.0798865i	−0.106648	+	0.994297i	$0.534012\pi$
$138$	−80.6250	−	151.900i	−0.584239	−	1.10072i
$139$		−	174.353i		−	1.25434i	−0.778882	−	0.627171i	$-0.784213\pi$
$139$		−	174.353i		−	1.25434i	0.778882	−	0.627171i	$-0.215787\pi$
$140$	−20.9190	−	138.428i	−0.149422	−	0.988774i
$141$	−175.451			−1.24433
$142$	−108.666	+	57.6773i	−0.765251	+	0.406178i
$143$	−0.297620	+	1.11073i	−0.00208126	+	0.00776738i
$144$	4.90148	−	34.1553i	0.0340380	−	0.237189i
$145$	194.481	+	33.0768i	1.34125	+	0.228116i
$146$	26.8818	+	116.825i	0.184122	+	0.800171i
$147$	128.181	+	0.764919i	0.871983	+	0.00520353i
$148$	−60.7906	−	21.0307i	−0.410747	−	0.142100i
$149$	−13.0466	−	7.53246i	−0.0875611	−	0.0505534i	0.455580	−	0.890195i	$-0.349432\pi$
$149$	−13.0466	−	7.53246i	−0.0875611	−	0.0505534i	−0.543141	+	0.839641i	$0.682765\pi$
$150$	−129.998	−	14.4584i	−0.866654	−	0.0963895i
$151$	117.614	−	67.9045i	0.778901	−	0.449699i	−0.0571395	−	0.998366i	$-0.518198\pi$
$151$	117.614	−	67.9045i	0.778901	−	0.449699i	0.836041	+	0.548667i	$0.184865\pi$
$152$	−168.276	−	122.821i	−1.10708	−	0.808030i
$153$	−29.9106	+	29.9106i	−0.195494	+	0.195494i
$154$	−3.12829	−	8.46257i	−0.0203136	−	0.0549518i
$155$	132.288	−	49.0599i	0.853471	−	0.316515i
$156$	18.6240	+	1.32951i	0.119384	+	0.00852252i
$157$	13.0021	−	48.5244i	0.0828158	−	0.309073i	−0.912076	−	0.410022i	$-0.865521\pi$
$157$	13.0021	−	48.5244i	0.0828158	−	0.309073i	0.994892	+	0.100949i	$0.0321878\pi$
$158$	−172.561	−	6.15151i	−1.09216	−	0.0389336i
$159$	−126.250	−	72.8905i	−0.794025	−	0.458431i
$160$	103.144	+	122.316i	0.644651	+	0.764477i
$161$	88.6830	−	212.306i	0.550826	−	1.31867i
$162$	60.4174	−	96.5319i	0.372947	−	0.595876i
$163$	−59.6892	−	222.763i	−0.366192	−	1.36665i	−0.865798	−	0.500393i	$-0.833189\pi$
$163$	−59.6892	−	222.763i	−0.366192	−	1.36665i	0.499607	−	0.866252i	$-0.333478\pi$
$164$	−123.495	−	83.5597i	−0.753017	−	0.509510i
$165$	−8.39267	+	0.785602i	−0.0508647	+	0.00476123i
$166$	−3.43671	+	11.2118i	−0.0207031	+	0.0675412i
$167$	−163.177	+	163.177i	−0.977109	+	0.977109i	−0.999744	−	0.0226344i	$-0.992795\pi$
$167$	−163.177	+	163.177i	−0.977109	+	0.977109i	0.0226344	+	0.999744i	$0.492795\pi$
$168$	−125.302	+	75.8978i	−0.745843	+	0.451773i
$169$			165.816i			0.981160i
$170$	−11.3114	−	195.818i	−0.0665376	−	1.15187i
$171$	28.0800	+	48.6359i	0.164210	+	0.284421i
$172$	37.1124	+	192.419i	0.215769	+	1.11871i
$173$	83.4680	+	311.507i	0.482474	+	1.80062i	0.591175	+	0.806543i	$0.298664\pi$
$173$	83.4680	+	311.507i	0.482474	+	1.80062i	−0.108701	+	0.994074i	$0.534669\pi$
$174$	−46.2898	−	201.170i	−0.266033	−	1.15615i
$175$	−95.3741	−	146.727i	−0.544995	−	0.838439i
$176$	8.10682	+	6.37177i	0.0460615	+	0.0362033i
$177$	38.1033	+	142.203i	0.215273	+	0.803409i
$178$	−105.743	−	3.76957i	−0.594064	−	0.0211773i
$179$	−19.7150	−	34.1473i	−0.110139	−	0.190767i	0.805687	−	0.592342i	$-0.201796\pi$
$179$	−19.7150	−	34.1473i	−0.110139	−	0.190767i	−0.915826	+	0.401575i	$0.868463\pi$
$180$	−12.0798	−	41.4053i	−0.0671101	−	0.230029i
$181$		−	105.427i		−	0.582470i	−0.956652	−	0.291235i	$-0.905934\pi$
$181$		−	105.427i		−	0.582470i	0.956652	−	0.291235i	$-0.0940661\pi$
$182$	14.4309	+	20.3910i	0.0792906	+	0.112038i
$183$	113.188	−	113.188i	0.618515	−	0.618515i
$184$	40.5687	+	259.804i	0.220482	+	1.41198i
$185$	−80.0571	+	7.49380i	−0.432741	+	0.0405070i
$186$	−100.611	−	108.049i	−0.540918	−	0.580909i
$187$	−3.27160	−	12.2098i	−0.0174952	−	0.0652929i
$188$	253.530	+	87.7098i	1.34857	+	0.466542i
$189$	202.630	−	26.0619i	1.07211	−	0.137893i
$190$	−255.008	−	52.7817i	−1.34215	−	0.277799i
$191$	−271.412	−	156.700i	−1.42100	−	0.820417i	−0.424620	−	0.905372i	$-0.639592\pi$
$191$	−271.412	−	156.700i	−1.42100	−	0.820417i	−0.996385	+	0.0849545i	$0.972925\pi$
$192$	76.6584	−	148.843i	0.399262	−	0.775223i
$193$	86.7193	−	323.641i	0.449323	−	1.67690i	−0.254940	−	0.966957i	$-0.582056\pi$
$193$	86.7193	−	323.641i	0.449323	−	1.67690i	0.704263	−	0.709939i	$-0.251278\pi$
$194$	37.8196	−	123.382i	0.194946	−	0.635988i
$195$	21.8828	−	8.11539i	0.112220	−	0.0416174i
$196$	−184.843	−	65.1848i	−0.943077	−	0.332575i
$197$	25.0339	−	25.0339i	0.127076	−	0.127076i	−0.640709	−	0.767784i	$-0.721359\pi$
$197$	25.0339	−	25.0339i	0.127076	−	0.127076i	0.767784	+	0.640709i	$0.221359\pi$
$198$	−1.30316	−	2.45518i	−0.00658160	−	0.0123999i
$199$	109.510	−	63.2257i	0.550302	−	0.317717i	−0.198942	−	0.980011i	$-0.563750\pi$
$199$	109.510	−	63.2257i	0.550302	−	0.317717i	0.749244	+	0.662294i	$0.230417\pi$
$200$	180.623	+	85.8804i	0.903113	+	0.429402i
$201$	1.45627	+	0.840777i	0.00724512	+	0.00418297i
$202$	−35.9499	−	22.5003i	−0.177970	−	0.111388i
$203$	168.783	−	218.608i	0.831442	−	1.07689i
$204$	−184.604	+	89.7054i	−0.904921	+	0.439733i
$205$	−183.746	−	31.2511i	−0.896324	−	0.152445i
$206$	51.0906	+	54.8678i	0.248013	+	0.266349i
$207$	18.3463	−	68.4692i	0.0886293	−	0.330769i
$208$	−26.2474	−	11.2315i	−0.126190	−	0.0539977i
$209$	−16.7823			−0.0802979
$210$	−103.364	+	151.158i	−0.492210	+	0.719799i
$211$			296.925i			1.40723i	0.710584	+	0.703613i	$0.248431\pi$
$211$			296.925i			1.40723i	−0.710584	+	0.703613i	$0.751569\pi$
$212$	145.996	+	168.442i	0.688658	+	0.794540i
$213$	155.432	+	41.6478i	0.729727	+	0.195530i
$214$	−35.6919	−	38.3306i	−0.166784	−	0.179115i
$215$	141.716	+	199.800i	0.659145	+	0.929305i
$216$	−181.771	+	146.541i	−0.841533	+	0.678428i
$217$	26.3669	−	195.761i	0.121507	−	0.902126i
$218$	240.676	+	150.634i	1.10402	+	0.690983i
$219$	78.3999	−	135.793i	0.357991	−	0.620058i
$220$	12.5204	+	3.06038i	0.0569107	+	0.0139108i
$221$	17.4995	+	30.3100i	0.0791832	+	0.137149i
$222$	39.4463	+	74.3179i	0.177686	+	0.334765i
$223$	114.918	+	114.918i	0.515327	+	0.515327i	0.916154	−	0.400827i	$-0.131277\pi$
$223$	114.918	+	114.918i	0.515327	+	0.515327i	−0.400827	+	0.916154i	$0.631277\pi$
$224$	219.006	−	47.0344i	0.977707	−	0.209975i
$225$	−35.1541	−	40.8772i	−0.156240	−	0.181676i
$226$	48.2546	−	157.424i	0.213516	−	0.696568i
$227$	331.741	+	88.8898i	1.46142	+	0.391585i	0.899978	−	0.435935i	$-0.143582\pi$
$227$	331.741	+	88.8898i	1.46142	+	0.391585i	0.561437	+	0.827520i	$0.310249\pi$
$228$	51.6058	+	267.564i	0.226341	+	1.17353i
$229$	−65.0537	+	112.676i	−0.284077	+	0.492036i	−0.972385	−	0.233383i	$-0.925021\pi$
$229$	−65.0537	+	112.676i	−0.284077	+	0.492036i	0.688308	+	0.725419i	$0.258354\pi$
$230$	180.488	+	274.703i	0.784729	+	1.19436i
$231$	−4.54860	+	10.8893i	−0.0196909	+	0.0471397i
$232$	−33.6773	+	313.836i	−0.145161	+	1.35274i
$233$	−335.342	+	89.8546i	−1.43924	+	0.385642i	−0.892266	−	0.451511i	$-0.850885\pi$
$233$	−335.342	+	89.8546i	−1.43924	+	0.385642i	−0.546970	+	0.837152i	$0.684219\pi$
$234$	5.24466	+	5.63241i	0.0224131	+	0.0240701i
$235$	333.882	−	31.2533i	1.42078	−	0.132993i
$236$	16.0290	−	224.536i	0.0679194	−	0.951422i
$237$	159.702	+	159.702i	0.673849	+	0.673849i
$238$	−249.453	−	114.802i	−1.04812	−	0.482362i
$239$	−142.310			−0.595438			−0.297719	−	0.954654i	$-0.596226\pi$
$239$	−142.310			−0.595438			−0.297719	+	0.954654i	$0.596226\pi$
$240$	10.2922	−	209.026i	0.0428840	−	0.870943i
$241$	−235.581	+	136.013i	−0.977514	+	0.564368i	−0.901519	−	0.432740i	$-0.857547\pi$
$241$	−235.581	+	136.013i	−0.977514	+	0.564368i	−0.0759951	+	0.997108i	$0.524213\pi$
$242$	−241.016	−	8.59181i	−0.995935	−	0.0355033i
$243$	109.840	−	29.4316i	0.452017	−	0.121118i
$244$	−220.144	+	106.976i	−0.902230	+	0.438425i
$245$	−244.066	+	21.3775i	−0.996186	+	0.0872553i
$246$	43.7348	+	190.066i	0.177784	+	0.772626i
$247$	44.8834	−	12.0265i	0.181714	−	0.0486901i
$248$	91.3700	+	206.430i	0.368427	+	0.832380i
$249$	13.2836	−	7.66927i	0.0533477	−	0.0308003i
$250$	249.962	+	4.35757i	0.999848	+	0.0174303i
$251$	−126.724			−0.504876			−0.252438	−	0.967613i	$-0.581232\pi$
$251$	−126.724			−0.504876			−0.252438	+	0.967613i	$0.581232\pi$
$252$	−59.1178	−	12.3011i	−0.234594	−	0.0488137i
$253$	14.9782	+	14.9782i	0.0592025	+	0.0592025i
$254$	105.406	−	343.874i	0.414985	−	1.35383i
$255$	−163.716	+	197.531i	−0.642023	+	0.774630i
$256$	−185.182	+	176.759i	−0.723365	+	0.690465i
$257$	−261.070	+	69.9534i	−1.01583	+	0.272192i	−0.728065	−	0.685508i	$-0.759580\pi$
$257$	−261.070	+	69.9534i	−1.01583	+	0.272192i	−0.287769	+	0.957700i	$0.592914\pi$
$258$	135.988	−	217.275i	0.527085	−	0.842150i
$259$	−43.3887	+	103.872i	−0.167524	+	0.401050i
$260$	−35.6782	+	0.787456i	−0.137224	+	0.00302868i
$261$	42.5435	−	73.6875i	0.163002	−	0.282328i
$262$	−208.348	−	7.42723i	−0.795220	−	0.0283482i
$263$	−156.193	−	41.8517i	−0.593889	−	0.159132i	−0.0506590	−	0.998716i	$-0.516132\pi$
$263$	−156.193	−	41.8517i	−0.593889	−	0.159132i	−0.543230	+	0.839584i	$0.682799\pi$
$264$	−2.08079	−	13.3255i	−0.00788177	−	0.0504754i
$265$	253.238	+	116.221i	0.955614	+	0.438571i
$266$	−232.942	+	280.455i	−0.875723	+	1.05434i
$267$	97.8635	+	97.8635i	0.366530	+	0.366530i
$268$	−1.68403	−	1.94295i	−0.00628369	−	0.00724981i
$269$	−56.8221	−	98.4188i	−0.211235	−	0.365869i	0.740867	−	0.671652i	$-0.234415\pi$
$269$	−56.8221	−	98.4188i	−0.211235	−	0.365869i	−0.952101	+	0.305783i	$0.901082\pi$
$270$	−131.109	+	260.749i	−0.485588	+	0.965737i
$271$	−27.3351	+	47.3457i	−0.100867	+	0.174707i	−0.912042	−	0.410096i	$-0.865495\pi$
$271$	−27.3351	+	47.3457i	−0.100867	+	0.174707i	0.811175	+	0.584804i	$0.198828\pi$
$272$	311.602	−	37.3410i	1.14560	−	0.137283i
$273$	4.36156	−	32.3825i	0.0159764	−	0.118617i
$274$	18.9647	+	82.4185i	0.0692144	+	0.300797i
$275$	15.8313	−	2.99000i	0.0575684	−	0.0108727i
$276$	192.744	−	284.861i	0.698347	−	1.03210i
$277$	−376.857	−	100.979i	−1.36050	−	0.364544i	−0.496497	−	0.868038i	$-0.665381\pi$
$277$	−376.857	−	100.979i	−1.36050	−	0.364544i	−0.863998	+	0.503495i	$0.832047\pi$
$278$	308.009	−	163.484i	1.10795	−	0.588073i
$279$		−	60.8551i		−	0.218119i
$280$	224.929	−	166.754i	0.803319	−	0.595549i
$281$	289.114			1.02888			0.514438	−	0.857527i	$-0.328000\pi$
$281$	289.114			1.02888			0.514438	+	0.857527i	$0.328000\pi$
$282$	−164.513	−	309.947i	−0.583379	−	1.09910i
$283$	−58.9441	+	219.983i	−0.208283	+	0.777323i	0.780140	+	0.625604i	$0.215148\pi$
$283$	−58.9441	+	219.983i	−0.208283	+	0.777323i	−0.988424	+	0.151719i	$0.951519\pi$
$284$	−203.783	−	137.884i	−0.717545	−	0.485509i
$285$	197.061	+	277.829i	0.691441	+	0.974837i
$286$	−2.24127	+	0.515722i	−0.00783659	+	0.00180322i
$287$	−159.467	+	206.542i	−0.555633	+	0.719658i
$288$	64.9338	−	23.3672i	0.225465	−	0.0811360i
$289$	−82.9021	−	47.8635i	−0.286858	−	0.165618i
$290$	123.924	+	374.580i	0.427325	+	1.29166i
$291$	−146.180	+	84.3971i	−0.502337	+	0.290024i
$292$	−181.174	+	157.031i	−0.620460	+	0.537776i
$293$	304.796	−	304.796i	1.04026	−	1.04026i	0.0411045	−	0.999155i	$-0.486912\pi$
$293$	304.796	−	304.796i	1.04026	−	1.04026i	0.999155	−	0.0411045i	$-0.0130877\pi$
$294$	118.839	+	227.160i	0.404215	+	0.772652i
$295$	−97.8414	−	263.826i	−0.331666	−	0.894324i
$296$	−19.8485	−	127.111i	−0.0670556	−	0.429429i
$297$	−4.86801	+	18.1677i	−0.0163906	+	0.0611706i
$298$	1.07339	−	30.1107i	0.00360199	−	0.101043i
$299$	−50.7922	−	29.3249i	−0.169874	−	0.0980766i
$300$	−96.3521	−	243.209i	−0.321174	−	0.810696i
$301$	340.137	−	43.7479i	1.13002	−	0.145342i
$302$	230.241	+	144.103i	0.762386	+	0.477162i
$303$	14.3575	+	53.5828i	0.0473844	+	0.176841i
$304$	59.1869	−	412.436i	0.194694	−	1.35670i
$305$	−195.235	+	235.560i	−0.640114	+	0.772327i
$306$	−80.8854	−	24.7934i	−0.264331	−	0.0810243i
$307$	−233.770	+	233.770i	−0.761465	+	0.761465i	−0.976587	−	0.215122i	$-0.930985\pi$
$307$	−233.770	+	233.770i	−0.761465	+	0.761465i	0.215122	+	0.976587i	$0.430985\pi$
$308$	12.0165	−	13.4614i	0.0390147	−	0.0437058i
$309$		−	98.0625i		−	0.317355i
$310$	210.709	+	187.695i	0.679707	+	0.605469i
$311$	−260.298	−	450.850i	−0.836972	−	1.44968i	−0.892415	−	0.451216i	$-0.850991\pi$
$311$	−260.298	−	450.850i	−0.836972	−	1.44968i	0.0554434	−	0.998462i	$-0.482343\pi$
$312$	15.1143	+	34.1473i	0.0484431	+	0.109446i
$313$	−90.2104	−	336.670i	−0.288212	−	1.07562i	−0.946460	−	0.322821i	$-0.895369\pi$
$313$	−90.2104	−	336.670i	−0.288212	−	1.07562i	0.658248	−	0.752801i	$-0.271298\pi$
$314$	97.9137	−	22.5302i	0.311827	−	0.0717523i
$315$	−73.6401	+	16.5640i	−0.233778	+	0.0525842i
$316$	−150.937	−	310.611i	−0.477648	−	0.982946i
$317$	18.5313	+	69.1596i	0.0584582	+	0.218169i	0.988976	−	0.148079i	$-0.0473089\pi$
$317$	18.5313	+	69.1596i	0.0584582	+	0.218169i	−0.930517	+	0.366248i	$0.880642\pi$
$318$	10.3871	−	291.377i	0.0326637	−	0.916279i
$319$	12.7133	+	22.0200i	0.0398535	+	0.0690282i
$320$	−119.367	+	296.903i	−0.373023	+	0.927822i
$321$			68.5064i			0.213416i
$322$	458.209	−	42.4053i	1.42301	−	0.131693i
$323$	−361.180	+	361.180i	−1.11821	+	1.11821i
$324$	227.182	+	16.2179i	0.701179	+	0.0500552i
$325$	−40.1974	+	19.3416i	−0.123684	+	0.0595127i
$326$	337.560	−	314.322i	1.03546	−	0.964177i
$327$	−96.1198	−	358.724i	−0.293944	−	1.09701i
$328$	31.8185	−	296.514i	0.0970075	−	0.904005i
$329$	180.955	−	433.204i	0.550015	−	1.31673i
$330$	−9.25730	−	14.0897i	−0.0280524	−	0.0426960i
$331$	311.318	+	179.740i	0.940538	+	0.543020i	0.890129	−	0.455709i	$-0.150614\pi$
$331$	311.318	+	179.740i	0.940538	+	0.543020i	0.0504092	+	0.998729i	$0.483947\pi$
$332$	−23.0290	+	4.44167i	−0.0693646	+	0.0133785i
$333$	−8.97603	+	33.4990i	−0.0269550	+	0.100598i
$334$	−441.270	−	135.260i	−1.32117	−	0.404971i
$335$	−2.92105	−	1.34059i	−0.00871955	−	0.00400176i
$336$	−251.570	−	150.189i	−0.748719	−	0.446990i
$337$	117.957	−	117.957i	0.350022	−	0.350022i	−0.510096	−	0.860118i	$-0.670390\pi$
$337$	117.957	−	117.957i	0.350022	−	0.350022i	0.860118	+	0.510096i	$0.170390\pi$
$338$	−292.927	+	155.479i	−0.866648	+	0.459997i
$339$	−186.513	+	107.684i	−0.550187	+	0.317651i
$340$	335.322	−	203.593i	0.986240	−	0.598804i
$341$	15.7489	+	9.09265i	0.0461845	+	0.0266647i
$342$	−59.5897	+	95.2094i	−0.174239	+	0.278390i
$343$	−134.092	+	315.703i	−0.390938	+	0.920417i
$344$	−305.124	+	245.985i	−0.886989	+	0.715074i
$345$	72.0858	−	423.840i	0.208944	−	1.22852i
$346$	−472.036	+	439.540i	−1.36427	+	1.27035i
$347$	69.9880	−	261.199i	0.201695	−	0.752734i	−0.788737	−	0.614731i	$-0.789265\pi$
$347$	69.9880	−	261.199i	0.201695	−	0.752734i	0.990432	−	0.138004i	$-0.0440686\pi$
$348$	311.978	−	270.403i	0.896488	−	0.777021i
$349$	−121.966			−0.349473			−0.174737	−	0.984615i	$-0.555907\pi$
$349$	−121.966			−0.349473			−0.174737	+	0.984615i	$0.555907\pi$
$350$	169.776	−	306.066i	0.485074	−	0.874473i
$351$		−	52.0771i		−	0.148368i
$352$	−3.65479	+	20.2959i	−0.0103829	+	0.0576588i
$353$	119.867	+	32.1183i	0.339567	+	0.0909866i	0.424573	−	0.905394i	$-0.360424\pi$
$353$	119.867	+	32.1183i	0.339567	+	0.0909866i	−0.0850061	+	0.996380i	$0.527091\pi$
$354$	−215.485	+	200.651i	−0.608715	+	0.566810i
$355$	−303.206	−	51.5685i	−0.854101	−	0.145263i
$356$	−92.4921	−	190.338i	−0.259809	−	0.534658i
$357$	136.461	+	332.247i	0.382244	+	0.930664i
$358$	41.8379	−	66.8465i	0.116866	−	0.186722i
$359$	−111.679	+	193.434i	−0.311084	+	0.538813i	−0.978597	−	0.205785i	$-0.934025\pi$
$359$	−111.679	+	193.434i	−0.311084	+	0.538813i	0.667513	+	0.744598i	$0.267359\pi$
$360$	61.8189	−	60.1640i	0.171719	−	0.167122i
$361$	158.575	+	274.659i	0.439265	+	0.760829i
$362$	186.245	−	98.8547i	0.514489	−	0.273079i
$363$	223.056	+	223.056i	0.614479	+	0.614479i
$364$	−22.4910	+	44.6131i	−0.0617883	+	0.122563i
$365$	−125.006	+	272.379i	−0.342482	+	0.746244i
$366$	306.088	+	93.8237i	0.836306	+	0.256349i
$367$	−68.9030	−	18.4625i	−0.187747	−	0.0503066i	0.163721	−	0.986507i	$-0.447650\pi$
$367$	−68.9030	−	18.4625i	−0.187747	−	0.0503066i	−0.351467	+	0.936200i	$0.614317\pi$
$368$	−420.925	+	315.276i	−1.14382	+	0.856728i
$369$	−40.1953	+	69.6203i	−0.108930	+	0.188673i
$370$	−88.3047	−	134.400i	−0.238661	−	0.363244i
$371$	310.184	−	236.546i	0.836076	−	0.637589i
$372$	96.5384	−	279.050i	0.259512	−	0.750134i
$373$	−719.170	+	192.701i	−1.92807	+	0.516625i	−0.947849	+	0.318720i	$0.896747\pi$
$373$	−719.170	+	192.701i	−1.92807	+	0.516625i	−0.980221	+	0.197905i	$0.936586\pi$
$374$	18.5019	−	17.2282i	0.0494702	−	0.0460646i
$375$	−235.394	−	226.977i	−0.627716	−	0.605271i
$376$	82.7791	+	530.123i	0.220157	+	1.40990i
$377$	−49.7809	−	49.7809i	−0.132045	−	0.132045i
$378$	236.038	+	333.524i	0.624439	+	0.882338i
$379$	156.437			0.412761			0.206381	−	0.978472i	$-0.433831\pi$
$379$	156.437			0.412761			0.206381	+	0.978472i	$0.433831\pi$
$380$	−145.868	−	499.982i	−0.383862	−	1.31574i
$381$	−407.415	+	235.221i	−1.06933	+	0.617379i
$382$	22.3301	−	626.401i	0.0584558	−	1.63979i
$383$	−370.610	+	99.3048i	−0.967651	+	0.259281i	−0.707836	−	0.706377i	$-0.750328\pi$
$383$	−370.610	+	99.3048i	−0.967651	+	0.259281i	−0.259815	+	0.965658i	$0.583662\pi$
$384$	334.822	−	4.14103i	0.871932	−	0.0107839i
$385$	6.71625	−	21.5325i	0.0174448	−	0.0559287i
$386$	653.050	−	150.269i	1.69184	−	0.389297i
$387$	102.053	−	27.3451i	0.263703	−	0.0706591i
$388$	253.425	−	48.8788i	0.653157	−	0.125976i
$389$	281.101	−	162.294i	0.722624	−	0.417207i	−0.0930934	−	0.995657i	$-0.529676\pi$
$389$	281.101	−	162.294i	0.722624	−	0.417207i	0.815718	+	0.578450i	$0.196342\pi$
$390$	34.8551	+	31.0482i	0.0893721	+	0.0796108i
$391$	644.709			1.64887
$392$	−58.1660	−	387.661i	−0.148383	−	0.988930i
$393$	192.822	+	192.822i	0.490641	+	0.490641i
$394$	67.6976	+	20.7510i	0.171821	+	0.0526676i
$395$	−332.361	−	275.465i	−0.841421	−	0.697381i
$396$	3.11535	−	4.60426i	0.00786706	−	0.0116269i
$397$	138.453	−	37.0983i	0.348747	−	0.0934466i	−0.0801931	−	0.996779i	$-0.525554\pi$
$397$	138.453	−	37.0983i	0.348747	−	0.0934466i	0.428940	+	0.903333i	$0.358887\pi$
$398$	214.376	+	134.174i	0.538634	+	0.337120i
$399$	472.971	−	60.8327i	1.18539	−	0.152463i
$400$	17.6482	+	399.610i	0.0441206	+	0.999026i
$401$	170.872	−	295.960i	0.426115	−	0.738054i	−0.570408	−	0.821361i	$-0.693215\pi$
$401$	170.872	−	295.960i	0.426115	−	0.738054i	0.996524	+	0.0833076i	$0.0265484\pi$
$402$	−0.119813	+	3.36097i	−0.000298042	+	0.00836063i
$403$	−48.6357	−	13.0319i	−0.120684	−	0.0323372i
$404$	6.03978	−	84.6059i	0.0149500	−	0.209421i
$405$	266.935	−	98.9946i	0.659099	−	0.244431i
$406$	544.449	+	93.1874i	1.34101	+	0.229526i
$407$	−7.32819	−	7.32819i	−0.0180054	−	0.0180054i
$408$	−331.567	−	242.004i	−0.812665	−	0.593146i
$409$	218.405	+	378.289i	0.533999	+	0.924913i	0.999211	+	0.0397137i	$0.0126446\pi$
$409$	218.405	+	378.289i	0.533999	+	0.924913i	−0.465212	+	0.885199i	$0.654022\pi$
$410$	−117.084	−	353.905i	−0.285571	−	0.863183i
$411$	55.3101	−	95.8000i	0.134575	−	0.233090i
$412$	−49.0226	+	141.703i	−0.118987	+	0.343939i
$413$	−390.412	−	52.5842i	−0.945307	−	0.127323i
$414$	138.159	−	31.7907i	0.333717	−	0.0767892i
$415$	−23.9125	+	16.9608i	−0.0576204	+	0.0408695i
$416$	−4.76983	−	56.8995i	−0.0114659	−	0.136778i
$417$	−440.566	−	118.049i	−1.05651	−	0.283092i
$418$	−15.7360	−	29.6471i	−0.0376460	−	0.0709262i
$419$		−	220.568i		−	0.526415i	−0.964739	−	0.263207i	$-0.915220\pi$
$419$		−	220.568i		−	0.526415i	0.964739	−	0.263207i	$-0.0847803\pi$
$420$	−363.952	−	40.8661i	−0.866553	−	0.0973002i
$421$	−366.483			−0.870506			−0.435253	−	0.900308i	$-0.643341\pi$
$421$	−366.483			−0.870506			−0.435253	+	0.900308i	$0.643341\pi$
$422$	−524.540	+	278.414i	−1.24299	+	0.659749i
$423$	37.4350	−	139.709i	0.0884989	−	0.330282i
$424$	−160.672	+	415.854i	−0.378944	+	0.980788i
$425$	276.365	−	405.064i	0.650270	−	0.953092i
$426$	72.1681	+	313.634i	0.169409	+	0.736230i
$427$	162.733	+	396.212i	0.381108	+	0.927896i
$428$	34.2472	−	98.9935i	0.0800168	−	0.231293i
$429$	2.60516	+	1.50409i	0.00607263	+	0.00350603i
$430$	−220.081	+	437.697i	−0.511817	+	1.01790i
$431$	−480.892	+	277.643i	−1.11576	+	0.644184i	−0.940315	−	0.340306i	$-0.889469\pi$
$431$	−480.892	+	277.643i	−1.11576	+	0.644184i	−0.175444	+	0.984489i	$0.556136\pi$
$432$	−429.315	−	183.708i	−0.993784	−	0.425249i
$433$	−100.349	+	100.349i	−0.231753	+	0.231753i	−0.813424	−	0.581671i	$-0.802399\pi$
$433$	−100.349	+	100.349i	−0.231753	+	0.231753i	0.581671	+	0.813424i	$0.302399\pi$
$434$	370.551	−	136.978i	0.853803	−	0.315618i
$435$	215.257	−	469.030i	0.494845	−	1.07823i
$436$	−40.4349	+	566.416i	−0.0927406	+	1.29912i
$437$	221.537	−	826.788i	0.506950	−	1.89196i
$438$	313.401	+	11.1722i	0.715527	+	0.0255073i
$439$	661.421	+	381.871i	1.50665	+	0.869867i	0.999970	+	0.00773403i	$0.00246184\pi$
$439$	661.421	+	381.871i	1.50665	+	0.869867i	0.506683	+	0.862132i	$0.330871\pi$
$440$	6.33343	+	24.9878i	0.0143942	+	0.0567904i
$441$	−27.9585	+	101.906i	−0.0633981	+	0.231080i
$442$	−37.1364	+	59.3347i	−0.0840190	+	0.134241i
$443$	−85.3378	−	318.485i	−0.192636	−	0.718928i	−0.992866	−	0.119235i	$-0.961956\pi$
$443$	−85.3378	−	318.485i	−0.192636	−	0.718928i	0.800230	−	0.599693i	$-0.204711\pi$
$444$	−94.3011	+	139.370i	−0.212390	+	0.313896i
$445$	−203.667	−	168.802i	−0.457678	−	0.379330i
$446$	−95.2574	+	310.765i	−0.213582	+	0.696783i
$447$	−27.8669	+	27.8669i	−0.0623420	+	0.0623420i
$448$	288.443	+	342.789i	0.643847	+	0.765154i
$449$			677.978i			1.50997i	0.655740	+	0.754987i	$0.272357\pi$
$449$			677.978i			1.50997i	−0.655740	+	0.754987i	$0.727643\pi$
$450$	39.2502	−	100.431i	0.0872226	−	0.223181i
$451$	−12.0115	−	20.8046i	−0.0266331	−	0.0461299i
$452$	323.349	−	62.3652i	0.715374	−	0.137976i
$453$	−91.9521	−	343.170i	−0.202985	−	0.757550i
$454$	154.030	+	669.395i	0.339273	+	1.47444i
$455$	−2.53171	+	62.4008i	−0.00556420	+	0.137145i
$456$	−424.284	+	342.050i	−0.930448	+	0.750110i
$457$	182.433	+	680.851i	0.399198	+	1.48983i	0.814511	+	0.580149i	$0.197005\pi$
$457$	182.433	+	680.851i	0.399198	+	1.48983i	−0.415313	+	0.909679i	$0.636328\pi$
$458$	−260.049	−	9.27031i	−0.567794	−	0.0202409i
$459$	286.229	+	495.764i	0.623593	+	1.08009i
$460$	−316.049	+	576.423i	−0.687062	+	1.25309i
$461$		−	303.314i		−	0.657947i	−0.944339	−	0.328973i	$-0.893297\pi$
$461$		−	303.314i		−	0.657947i	0.944339	−	0.328973i	$-0.106703\pi$
$462$	−23.5018	+	2.17499i	−0.0508696	+	0.00470777i
$463$	−429.736	+	429.736i	−0.928155	+	0.928155i	−0.997587	−	0.0694313i	$-0.977882\pi$
$463$	−429.736	+	429.736i	−0.928155	+	0.928155i	0.0694313	+	0.997587i	$0.477882\pi$
$464$	−585.993	+	234.778i	−1.26292	+	0.505987i
$465$	−34.3992	−	367.490i	−0.0739767	−	0.790301i
$466$	−473.172	−	508.154i	−1.01539	−	1.09046i
$467$	135.299	+	504.944i	0.289720	+	1.08125i	0.945321	+	0.326142i	$0.105749\pi$
$467$	135.299	+	504.944i	0.289720	+	1.08125i	−0.655601	+	0.755108i	$0.727585\pi$
$468$	−5.03238	+	14.5464i	−0.0107529	+	0.0310820i
$469$	−3.57791	+	2.72851i	−0.00762882	+	0.00581771i
$470$	368.279	+	560.524i	0.783573	+	1.19260i
$471$	−113.811	−	65.7088i	−0.241637	−	0.139509i
$472$	411.689	−	182.222i	0.872223	−	0.386063i
$473$	−8.17152	+	30.4965i	−0.0172759	+	0.0644747i
$474$	−132.380	+	431.873i	−0.279283	+	0.911124i
$475$	−424.496	−	493.605i	−0.893677	−	1.03917i
$476$	−31.0956	−	548.324i	−0.0653270	−	1.15194i
$477$	84.9792	−	84.9792i	0.178154	−	0.178154i
$478$	−133.438	−	251.401i	−0.279159	−	0.525943i
$479$	578.757	−	334.145i	1.20826	−	0.697589i	0.245881	−	0.969300i	$-0.420923\pi$
$479$	578.757	−	334.145i	1.20826	−	0.697589i	0.962379	+	0.271710i	$0.0875893\pi$
$480$	378.912	−	177.814i	0.789399	−	0.370445i
$481$	24.8504	+	14.3474i	0.0516641	+	0.0298283i
$482$	−461.171	−	288.638i	−0.956787	−	0.598834i
$483$	−476.422	−	367.835i	−0.986381	−	0.761563i
$484$	−210.813	−	433.830i	−0.435564	−	0.896343i
$485$	263.147	−	186.647i	0.542571	−	0.384839i
$486$	154.986	+	166.444i	0.318901	+	0.342478i
$487$	19.7639	−	73.7600i	0.0405830	−	0.151458i	−0.942661	−	0.333751i	$-0.891685\pi$
$487$	19.7639	−	73.7600i	0.0405830	−	0.151458i	0.983244	+	0.182293i	$0.0583521\pi$
$488$	−395.401	−	288.595i	−0.810248	−	0.591382i
$489$	−603.304			−1.23375
$490$	−266.616	−	411.116i	−0.544113	−	0.839012i
$491$		−	576.776i		−	1.17470i	−0.809334	−	0.587348i	$-0.800172\pi$
$491$		−	576.776i		−	1.17470i	0.809334	−	0.587348i	$-0.199828\pi$
$492$	−294.758	+	255.478i	−0.599101	+	0.519264i
$493$	747.514	+	200.296i	1.51626	+	0.406279i
$494$	63.3310	+	68.0132i	0.128200	+	0.137679i
$495$	1.16514	−	6.85061i	0.00235381	−	0.0138396i
$496$	−279.001	+	354.973i	−0.562502	+	0.715672i
$497$	−263.141	+	340.821i	−0.529458	+	0.685757i
$498$	26.0038	+	16.2753i	0.0522165	+	0.0326813i
$499$	−46.7510	+	80.9751i	−0.0936894	+	0.162275i	−0.909061	−	0.416663i	$-0.863199\pi$
$499$	−46.7510	+	80.9751i	−0.0936894	+	0.162275i	0.815371	+	0.578938i	$0.196533\pi$
$500$	226.681	+	445.663i	0.453363	+	0.891326i
$501$	301.843	+	522.808i	0.602482	+	1.04353i
$502$	−118.824	−	223.868i	−0.236701	−	0.445952i
$503$	167.376	+	167.376i	0.332756	+	0.332756i	0.853632	−	0.520876i	$-0.174395\pi$
$503$	167.376	+	167.376i	0.332756	+	0.332756i	−0.520876	+	0.853632i	$0.674395\pi$
$504$	−33.7016	−	115.970i	−0.0668683	−	0.230100i
$505$	−36.8670	−	99.4105i	−0.0730040	−	0.196852i
$506$	−12.4157	+	40.5047i	−0.0245370	+	0.0800487i
$507$	418.994	+	112.269i	0.826417	+	0.221438i
$508$	706.315	−	136.229i	1.39038	−	0.268167i
$509$	−276.998	+	479.774i	−0.544200	+	0.942582i	0.454457	+	0.890769i	$0.349833\pi$
$509$	−276.998	+	479.774i	−0.544200	+	0.942582i	−0.998657	+	0.0518134i	$0.983500\pi$
$510$	−502.463	−	104.000i	−0.985222	−	0.203922i
$511$	254.425	+	333.630i	0.497897	+	0.652896i
$512$	−485.896	−	161.398i	−0.949015	−	0.315230i
$513$	734.132	−	196.710i	1.43106	−	0.383450i
$514$	−368.372	−	395.607i	−0.716678	−	0.769663i
$515$	17.4681	+	186.613i	0.0339186	+	0.362355i
$516$	511.343	+	36.5033i	0.990974	+	0.0707429i
$517$	30.5626	+	30.5626i	0.0591153	+	0.0591153i
$518$	−224.182	+	20.7471i	−0.432783	+	0.0400522i
$519$	843.647			1.62552
$520$	−34.8451	−	62.2900i	−0.0670099	−	0.119788i
$521$	−211.634	+	122.187i	−0.406207	+	0.234524i	−0.689159	−	0.724610i	$-0.742020\pi$
$521$	−211.634	+	122.187i	−0.406207	+	0.234524i	0.282952	+	0.959134i	$0.408686\pi$
$522$	170.066	+	6.06255i	0.325797	+	0.0116141i
$523$	263.556	−	70.6195i	0.503930	−	0.135028i	0.00210689	−	0.999998i	$-0.499329\pi$
$523$	263.556	−	70.6195i	0.503930	−	0.135028i	0.501824	+	0.864970i	$0.332663\pi$
$524$	−182.238	−	375.026i	−0.347783	−	0.715699i
$525$	−435.333	+	141.652i	−0.829205	+	0.269814i
$526$	−72.5214	−	315.169i	−0.137873	−	0.599181i
$527$	534.629	−	143.254i	1.01448	−	0.271828i
$528$	21.5894	−	16.1706i	0.0408891	−	0.0306262i
$529$	−477.506	+	275.688i	−0.902659	+	0.521150i
$530$	32.1369	+	556.340i	0.0606356	+	1.04970i
$531$	−121.365			−0.228559
$532$	−713.866	−	148.539i	−1.34185	−	0.279209i
$533$	47.0332	+	47.0332i	0.0882425	+	0.0882425i
$534$	−81.1207	+	264.646i	−0.151911	+	0.495592i
$535$	−12.2032	−	130.368i	−0.0228097	−	0.243678i
$536$	1.85332	−	4.79679i	0.00345769	−	0.00894924i
$537$	−99.6337	+	26.6968i	−0.185538	+	0.0497147i
$538$	120.585	−	192.664i	0.224135	−	0.358112i
$539$	−22.1953	−	22.4618i	−0.0411787	−	0.0416731i
$540$	−583.569	+	12.8800i	−1.08068	+	0.0238518i
$541$	338.495	−	586.290i	0.625683	−	1.08372i	−0.362725	−	0.931896i	$-0.618154\pi$
$541$	338.495	−	586.290i	0.625683	−	1.08372i	0.988408	−	0.151819i	$-0.0485131\pi$
$542$	−109.271	−	3.89531i	−0.201607	−	0.00718693i
$543$	−266.399	−	71.3814i	−0.490606	−	0.131457i
$544$	358.142	+	515.456i	0.658350	+	0.947529i
$545$	246.816	+	665.530i	0.452873	+	1.22116i
$546$	61.2958	−	22.6587i	0.112263	−	0.0414994i
$547$	−87.5088	−	87.5088i	−0.159980	−	0.159980i	0.622578	−	0.782558i	$-0.286085\pi$
$547$	−87.5088	−	87.5088i	−0.159980	−	0.159980i	−0.782558	+	0.622578i	$0.786085\pi$
$548$	−127.816	+	110.783i	−0.233241	+	0.202159i
$549$	65.9802	+	114.281i	0.120182	+	0.208162i
$550$	20.1265	+	25.1636i	0.0365935	+	0.0457520i
$551$	513.726	−	889.800i	0.932352	−	1.61488i
$552$	683.956	+	73.3944i	1.23905	+	0.132961i
$553$	−559.033	+	229.607i	−1.01091	+	0.415203i
$554$	−174.977	−	760.431i	−0.315844	−	1.37262i
$555$	−35.2684	+	207.367i	−0.0635467	+	0.373633i
$556$	577.615	+	390.829i	1.03888	+	0.702929i
$557$	1036.68	+	277.778i	1.86119	+	0.498704i	0.999955	−	0.00950515i	$-0.00302563\pi$
$557$	1036.68	+	277.778i	1.86119	+	0.498704i	0.861234	+	0.508209i	$0.169692\pi$
$558$	107.505	−	57.0613i	0.192662	−	0.102260i
$559$		−	87.4174i		−	0.156382i
$560$	505.491	+	240.997i	0.902662	+	0.430351i
$561$	−33.0675			−0.0589438
$562$	271.091	+	510.743i	0.482368	+	0.908795i
$563$	−125.046	+	466.676i	−0.222106	+	0.828910i	0.761438	+	0.648238i	$0.224494\pi$
$563$	−125.046	+	466.676i	−0.222106	+	0.828910i	−0.983543	+	0.180672i	$0.942173\pi$
$564$	393.288	−	581.249i	0.697319	−	1.03058i
$565$	335.753	−	238.146i	0.594253	−	0.421497i
$566$	−443.886	+	102.139i	−0.784250	+	0.180458i
$567$	53.2040	−	395.013i	0.0938342	−	0.696673i
$568$	52.5046	−	489.287i	0.0924377	−	0.861420i
$569$	677.527	+	391.170i	1.19073	+	0.687470i	0.958473	−	0.285184i	$-0.0920547\pi$
$569$	677.527	+	391.170i	1.19073	+	0.687470i	0.232260	+	0.972654i	$0.425388\pi$
$570$	−306.030	+	608.631i	−0.536894	+	1.06777i
$571$	−51.9834	+	30.0127i	−0.0910393	+	0.0525616i	−0.544828	−	0.838548i	$-0.683405\pi$
$571$	−51.9834	+	30.0127i	−0.0910393	+	0.0525616i	0.453789	+	0.891109i	$0.350072\pi$
$572$	−3.01261	−	3.47580i	−0.00526679	−	0.00607657i
$573$	−579.722	+	579.722i	−1.01173	+	1.01173i
$574$	−514.398	−	88.0439i	−0.896163	−	0.153387i
$575$	−61.6798	+	819.409i	−0.107269	+	1.42506i
$576$	102.166	+	92.8001i	0.177371	+	0.161111i
$577$	64.6534	−	241.290i	0.112051	−	0.418180i	−0.886998	−	0.461772i	$-0.847214\pi$
$577$	64.6534	−	241.290i	0.112051	−	0.418180i	0.999049	+	0.0435925i	$0.0138803\pi$
$578$	6.82067	−	191.333i	0.0118005	−	0.331025i
$579$	−759.079	−	438.255i	−1.31102	−	0.756917i
$580$	−545.526	+	570.150i	−0.940562	+	0.983018i
$581$	5.23582	+	40.7082i	0.00901175	+	0.0700658i
$582$	−286.161	−	179.103i	−0.491686	−	0.307736i
$583$	9.29496	+	34.6893i	0.0159433	+	0.0595013i
$584$	−447.287	−	172.817i	−0.765902	−	0.295919i
$585$	1.79317	+	19.1566i	0.00306525	+	0.0327463i
$586$	824.241	+	252.651i	1.40655	+	0.431144i
$587$	492.666	−	492.666i	0.839295	−	0.839295i	−0.149471	−	0.988766i	$-0.547757\pi$
$587$	492.666	−	492.666i	0.839295	−	0.839295i	0.988766	+	0.149471i	$0.0477572\pi$
$588$	−289.864	+	422.937i	−0.492966	+	0.719281i
$589$		−	734.844i		−	1.24761i
$590$	374.326	−	420.223i	0.634451	−	0.712242i
$591$	−46.3074	−	80.2068i	−0.0783543	−	0.135714i
$592$	205.940	−	154.251i	0.347872	−	0.260559i
$593$	−264.225	−	986.103i	−0.445574	−	1.66290i	−0.714416	−	0.699721i	$-0.753308\pi$
$593$	−264.225	−	986.103i	−0.445574	−	1.66290i	0.268842	−	0.963184i	$-0.413359\pi$
$594$	−36.6591	+	8.43537i	−0.0617157	+	0.0142010i
$595$	−318.869	−	607.958i	−0.535915	−	1.02178i
$596$	54.1994	−	26.3374i	0.0909385	−	0.0441902i
$597$	−85.6164	−	319.525i	−0.143411	−	0.535217i
$598$	4.17887	−	117.225i	0.00698808	−	0.196029i
$599$	258.556	+	447.832i	0.431646	+	0.747632i	0.997015	−	0.0772053i	$-0.0245997\pi$
$599$	258.556	+	447.832i	0.431646	+	0.747632i	−0.565369	+	0.824838i	$0.691266\pi$
$600$	339.302	−	398.261i	0.565503	−	0.663768i
$601$		−	480.120i		−	0.798868i	−0.916762	−	0.399434i	$-0.869207\pi$
$601$		−	480.120i		−	0.798868i	0.916762	−	0.399434i	$-0.130793\pi$
$602$	396.217	+	559.858i	0.658168	+	0.929997i
$603$	−0.980219	+	0.980219i	−0.00162557	+	0.00162557i
$604$	−38.6817	+	541.857i	−0.0640425	+	0.897115i
$605$	−464.209	−	384.742i	−0.767288	−	0.635938i
$606$	−81.1957	+	75.6060i	−0.133986	+	0.124762i
$607$	3.63081	+	13.5503i	0.00598156	+	0.0223235i	0.968852	−	0.247640i	$-0.0796550\pi$
$607$	3.63081	+	13.5503i	0.00598156	+	0.0223235i	−0.962871	+	0.269964i	$0.912988\pi$
$608$	784.096	−	282.166i	1.28963	−	0.464089i
$609$	−438.114	−	574.502i	−0.719399	−	0.943354i
$610$	−599.198	−	124.023i	−0.982292	−	0.203316i
$611$	−103.640	−	59.8366i	−0.169624	−	0.0979322i
$612$	−32.0435	−	166.138i	−0.0523586	−	0.271467i
$613$	117.457	−	438.357i	0.191611	−	0.715101i	−0.801507	−	0.597985i	$-0.795968\pi$
$613$	117.457	−	438.357i	0.191611	−	0.715101i	0.993118	−	0.117116i	$-0.0373650\pi$
$614$	−632.169	−	193.776i	−1.02959	−	0.315596i
$615$	−203.376	+	443.142i	−0.330693	+	0.720556i
$616$	35.0480	+	8.60591i	0.0568960	+	0.0139706i
$617$	−157.692	+	157.692i	−0.255578	+	0.255578i	−0.823253	−	0.567675i	$-0.807843\pi$
$617$	−157.692	+	157.692i	−0.255578	+	0.255578i	0.567675	+	0.823253i	$0.307843\pi$
$618$	173.235	−	91.9493i	0.280316	−	0.148785i
$619$	−177.812	+	102.660i	−0.287257	+	0.165848i	−0.636704	−	0.771108i	$-0.719703\pi$
$619$	−177.812	+	102.660i	−0.287257	+	0.165848i	0.349447	+	0.936956i	$0.386369\pi$
$620$	−134.005	+	548.228i	−0.216137	+	0.884239i
$621$	−830.780	−	479.651i	−1.33781	−	0.772385i
$622$	552.389	−	882.580i	0.888086	−	1.41894i
$623$	−342.568	+	140.700i	−0.549868	+	0.225843i
$624$	−46.1518	+	58.7190i	−0.0739612	+	0.0941010i
$625$	488.386	+	390.005i	0.781417	+	0.624009i
$626$	510.166	−	475.045i	0.814962	−	0.758858i
$627$	−11.3627	+	42.4063i	−0.0181224	+	0.0676337i
$628$	131.611	+	151.846i	0.209572	+	0.241794i
$629$	−315.428			−0.501476
$630$	−98.3110	−	114.560i	−0.156049	−	0.181841i
$631$		−	433.020i		−	0.686244i	−0.939291	−	0.343122i	$-0.888516\pi$
$631$		−	433.020i		−	0.686244i	0.939291	−	0.343122i	$-0.111484\pi$
$632$	407.191	−	557.889i	0.644289	−	0.882735i
$633$	750.286	+	201.038i	1.18529	+	0.317596i
$634$	−104.800	+	97.5851i	−0.165299	+	0.153920i
$635$	733.411	−	520.200i	1.15498	−	0.819212i
$636$	524.479	−	254.863i	0.824652	−	0.400728i
$637$	75.4569	+	44.1675i	0.118457	+	0.0693368i
$638$	−26.9793	+	43.1062i	−0.0422873	+	0.0675646i
$639$	−66.3275	+	114.883i	−0.103799	+	0.179785i
$640$	−636.428	+	67.5228i	−0.994419	+	0.105504i
$641$	590.003	+	1021.92i	0.920441	+	1.59425i	0.798733	+	0.601685i	$0.205504\pi$
$641$	590.003	+	1021.92i	0.920441	+	1.59425i	0.121708	+	0.992566i	$0.461163\pi$
$642$	−121.022	+	64.2357i	−0.188508	+	0.100056i
$643$	−514.374	−	514.374i	−0.799959	−	0.799959i	0.183130	−	0.983089i	$-0.441377\pi$
$643$	−514.374	−	514.374i	−0.799959	−	0.799959i	−0.983089	+	0.183130i	$0.941377\pi$
$644$	504.557	+	769.700i	0.783473	+	1.19519i
$645$	600.819	−	222.818i	0.931502	−	0.345454i
$646$	−976.717	−	299.388i	−1.51195	−	0.463450i
$647$	305.194	+	81.7765i	0.471707	+	0.126393i	0.486838	−	0.873492i	$-0.338150\pi$
$647$	305.194	+	81.7765i	0.471707	+	0.126393i	−0.0151317	+	0.999886i	$0.504817\pi$
$648$	184.369	+	416.541i	0.284521	+	0.642811i
$649$	18.1337	−	31.4085i	0.0279410	−	0.0483952i
$650$	−71.8600	−	52.8760i	−0.110554	−	0.0813476i
$651$	−476.808	−	199.169i	−0.732425	−	0.305944i
$652$	871.790	+	301.599i	1.33710	+	0.462575i
$653$	238.875	−	64.0064i	0.365812	−	0.0980190i	−0.0712305	−	0.997460i	$-0.522693\pi$
$653$	238.875	−	64.0064i	0.365812	−	0.0980190i	0.437042	+	0.899441i	$0.356026\pi$
$654$	543.586	−	506.164i	0.831171	−	0.773951i
$655$	−401.288	−	332.592i	−0.612653	−	0.507774i
$656$	553.649	−	221.819i	0.843977	−	0.338139i
$657$	91.4024	+	91.4024i	0.139121	+	0.139121i
$658$	934.962	−	86.5267i	1.42091	−	0.131500i
$659$	−1249.17			−1.89555			−0.947774	−	0.318944i	$-0.896672\pi$
$659$	−1249.17			−1.89555			−0.947774	+	0.318944i	$0.896672\pi$
$660$	16.2103	−	29.5650i	0.0245610	−	0.0447955i
$661$	−728.977	+	420.875i	−1.10284	+	0.636724i	−0.936965	−	0.349423i	$-0.886378\pi$
$661$	−728.977	+	420.875i	−1.10284	+	0.636724i	−0.165874	+	0.986147i	$0.553044\pi$
$662$	−25.6133	+	718.502i	−0.0386909	+	1.08535i
$663$	88.4374	−	23.6967i	0.133390	−	0.0357417i
$664$	−29.4400	−	36.5178i	−0.0443373	−	0.0549967i
$665$	−889.228	+	200.016i	−1.33718	+	0.300776i
$666$	−67.5950	+	15.5538i	−0.101494	+	0.0233541i
$667$	−1252.65	+	335.647i	−1.87804	+	0.503219i
$668$	−174.813	−	906.366i	−0.261696	−	1.35683i
$669$	368.188	−	212.574i	0.550356	−	0.317748i
$670$	−0.370692	−	6.41727i	−0.000553272	−	0.00957802i
$671$	−39.4337			−0.0587685
$672$	29.4331	−	585.243i	0.0437993	−	0.870898i
$673$	92.7955	+	92.7955i	0.137883	+	0.137883i	0.772680	−	0.634796i	$-0.218916\pi$
$673$	92.7955	+	92.7955i	0.137883	+	0.137883i	−0.634796	+	0.772680i	$0.718916\pi$
$674$	318.985	+	97.7769i	0.473271	+	0.145070i
$675$	−657.486	+	316.360i	−0.974054	+	0.468681i
$676$	−549.332	−	371.691i	−0.812621	−	0.549839i
$677$	−755.783	+	202.512i	−1.11637	+	0.299131i	−0.769414	−	0.638750i	$-0.779452\pi$
$677$	−755.783	+	202.512i	−1.11637	+	0.299131i	−0.346957	+	0.937881i	$0.612785\pi$
$678$	−365.117	−	228.520i	−0.538521	−	0.337050i
$679$	−57.6180	−	447.977i	−0.0848572	−	0.659760i
$680$	674.081	+	401.470i	0.991295	+	0.590397i
$681$	449.224	−	778.078i	0.659653	−	1.14255i
$682$	−1.29573	+	36.3475i	−0.00189989	+	0.0532955i
$683$	677.578	+	181.557i	0.992062	+	0.265822i	0.718116	−	0.695923i	$-0.245005\pi$
$683$	677.578	+	181.557i	0.992062	+	0.265822i	0.273945	+	0.961745i	$0.411671\pi$
$684$	−224.070	−	15.9957i	−0.327587	−	0.0233855i
$685$	−88.1902	+	192.160i	−0.128745	+	0.280525i
$686$	−683.446	+	59.1389i	−0.996277	+	0.0862083i
$687$	240.671	+	240.671i	0.350322	+	0.350322i
$688$	−720.655	−	308.375i	−1.04746	−	0.448219i
$689$	−49.7179	−	86.1139i	−0.0721595	−	0.124984i
$690$	816.339	−	270.073i	1.18310	−	0.391410i
$691$	−478.756	+	829.230i	−0.692846	+	1.20004i	0.278056	+	0.960565i	$0.410310\pi$
$691$	−478.756	+	829.230i	−0.692846	+	1.20004i	−0.970902	+	0.239479i	$0.923023\pi$
$692$	−1219.09	−	421.749i	−1.76169	−	0.609464i
$693$	−7.70050	−	5.94539i	−0.0111118	−	0.00857921i
$694$	527.053	−	121.276i	0.759442	−	0.174750i
$695$	859.426	+	146.169i	1.23658	+	0.210315i
$696$	770.217	+	297.586i	1.10663	+	0.427567i
$697$	−706.254	−	189.240i	−1.01328	−	0.271507i
$698$	−114.363	−	215.463i	−0.163844	−	0.308686i
$699$			908.199i			1.29928i
$700$	699.880	+	12.9367i	0.999829	+	0.0184811i
$701$	350.252			0.499646			0.249823	−	0.968291i	$-0.419628\pi$
$701$	350.252			0.499646			0.249823	+	0.968291i	$0.419628\pi$
$702$	91.9982	−	48.8306i	0.131052	−	0.0695592i
$703$	−108.388	+	404.511i	−0.154180	+	0.575407i
$704$	−39.2812	+	12.5742i	−0.0557971	+	0.0178610i
$705$	147.089	−	864.833i	0.208637	−	1.22671i
$706$	55.6551	+	241.870i	0.0788316	+	0.342593i
$707$	−147.109	−	19.8139i	−0.208075	−	0.0280254i
$708$	−556.517	−	192.529i	−0.786041	−	0.271934i
$709$	414.586	+	239.361i	0.584748	+	0.337604i	0.763018	−	0.646377i	$-0.223717\pi$
$709$	414.586	+	239.361i	0.584748	+	0.337604i	−0.178270	+	0.983982i	$0.557050\pi$
$710$	−193.204	−	583.990i	−0.272118	−	0.822521i
$711$	−161.244	+	93.0943i	−0.226785	+	0.130934i
$712$	249.521	−	341.867i	0.350451	−	0.480150i
$713$	−655.851	+	655.851i	−0.919848	+	0.919848i
$714$	−458.986	+	552.604i	−0.642837	+	0.773955i
$715$	−5.22554	−	2.39822i	−0.00730845	−	0.00335415i
$716$	157.319	+	11.2306i	0.219720	+	0.0156852i
$717$	−96.3535	+	359.596i	−0.134384	+	0.501529i
$718$	−446.433	−	15.9146i	−0.621773	−	0.0221651i
$719$	−60.5018	−	34.9307i	−0.0841471	−	0.0485824i	0.457336	−	0.889294i	$-0.348804\pi$
$719$	−60.5018	−	34.9307i	−0.0841471	−	0.0485824i	−0.541483	+	0.840712i	$0.682137\pi$
$720$	164.249	+	52.7945i	0.228124	+	0.0733256i
$721$	242.126	+	101.139i	0.335819	+	0.140276i
$722$	−336.518	+	537.671i	−0.466091	+	0.744697i
$723$	184.180	+	687.369i	0.254744	+	0.950718i
$724$	349.269	+	236.324i	0.482415	+	0.326414i
$725$	−326.086	+	930.908i	−0.449774	+	1.28401i
$726$	−184.895	+	603.196i	−0.254676	+	0.830849i
$727$	−11.4198	+	11.4198i	−0.0157081	+	0.0157081i	−0.714917	−	0.699209i	$-0.753536\pi$
$727$	−11.4198	+	11.4198i	−0.0157081	+	0.0157081i	0.699209	+	0.714917i	$0.253536\pi$
$728$	−99.9013	+	2.09988i	−0.137227	+	0.00288446i
$729$		−	809.938i		−	1.11103i
$730$	−598.392	+	34.5659i	−0.819714	+	0.0473506i
$731$	480.469	+	832.197i	0.657276	+	1.13844i
$732$	121.260	+	628.702i	0.165655	+	0.858883i
$733$	−21.8756	−	81.6409i	−0.0298439	−	0.111379i	0.949397	−	0.314078i	$-0.101695\pi$
$733$	−21.8756	−	81.6409i	−0.0298439	−	0.111379i	−0.979241	+	0.202699i	$0.935029\pi$
$734$	−31.9922	−	139.034i	−0.0435860	−	0.189420i
$735$	−111.231	+	631.193i	−0.151335	+	0.858766i
$736$	−951.643	−	447.975i	−1.29299	−	0.608661i
$737$	−0.107216	−	0.400134i	−0.000145476	−	0.000542923i
$738$	−160.679	−	5.72793i	−0.217722	−	0.00776142i
$739$	−500.966	−	867.699i	−0.677897	−	1.17415i	−0.975613	−	0.219498i	$-0.929558\pi$
$739$	−500.966	−	867.699i	−0.677897	−	1.17415i	0.297716	−	0.954655i	$-0.403775\pi$
$740$	154.629	−	282.019i	0.208958	−	0.381106i
$741$		−	121.557i		−	0.164044i
$742$	708.723	+	326.165i	0.955153	+	0.439575i
$743$	298.718	−	298.718i	0.402043	−	0.402043i	−0.476910	−	0.878952i	$-0.658243\pi$
$743$	298.718	−	298.718i	0.402043	−	0.402043i	0.878952	+	0.476910i	$0.158243\pi$
$744$	583.483	−	91.1114i	0.784252	−	0.122462i
$745$	48.0667	−	57.9947i	0.0645191	−	0.0778452i
$746$	−1014.76	−	1089.78i	−1.36027	−	1.46083i
$747$	3.27271	+	12.2139i	0.00438114	+	0.0163506i
$748$	47.7833	+	16.5308i	0.0638814	+	0.0221000i
$749$	−169.149	−	70.6557i	−0.225833	−	0.0943334i
$750$	180.253	−	628.668i	0.240337	−	0.838224i
$751$	443.386	+	255.989i	0.590394	+	0.340864i	0.765253	−	0.643729i	$-0.222614\pi$
$751$	443.386	+	255.989i	0.590394	+	0.340864i	−0.174859	+	0.984593i	$0.555947\pi$
$752$	−858.884	+	643.311i	−1.14213	+	0.855466i
$753$	−85.8009	+	320.213i	−0.113945	+	0.425250i
$754$	41.2643	−	134.619i	0.0547271	−	0.178540i
$755$	236.114	+	636.673i	0.312734	+	0.843275i
$756$	−367.872	+	729.711i	−0.486603	+	0.965226i
$757$	176.573	−	176.573i	0.233254	−	0.233254i	−0.580796	−	0.814049i	$-0.697258\pi$
$757$	176.573	−	176.573i	0.233254	−	0.233254i	0.814049	+	0.580796i	$0.197258\pi$
$758$	146.684	+	276.357i	0.193515	+	0.364587i
$759$	47.9891	−	27.7065i	0.0632268	−	0.0365040i
$760$	746.483	−	726.500i	0.982214	−	0.955921i
$761$	−418.956	−	241.884i	−0.550534	−	0.317851i	0.198803	−	0.980039i	$-0.436294\pi$
$761$	−418.956	−	241.884i	−0.550534	−	0.317851i	−0.749337	+	0.662189i	$0.769628\pi$
$762$	−797.553	−	499.173i	−1.04666	−	0.655082i
$763$	984.858	+	132.650i	1.29077	+	0.173853i
$764$	1127.52	−	547.903i	1.47582	−	0.717151i
$765$	−122.360	−	172.511i	−0.159948	−	0.225505i
$766$	−522.936	−	561.598i	−0.682684	−	0.733156i
$767$	−25.9899	+	96.9956i	−0.0338851	+	0.126461i
$768$	321.264	+	587.605i	0.418313	+	0.765111i
$769$	101.094			0.131462			0.0657310	−	0.997837i	$-0.479062\pi$
$769$	101.094			0.131462			0.0657310	+	0.997837i	$0.479062\pi$
$770$	44.3364	−	8.32541i	0.0575798	−	0.0108122i
$771$			707.049i			0.917054i
$772$	877.800	+	1012.76i	1.13705	+	1.31187i
$773$	517.121	+	138.562i	0.668979	+	0.179252i	0.577295	−	0.816536i	$-0.304108\pi$
$773$	517.121	+	138.562i	0.668979	+	0.179252i	0.0916841	+	0.995788i	$0.470775\pi$
$774$	143.998	+	154.645i	0.186044	+	0.199799i
$775$	130.923	+	693.205i	0.168933	+	0.894459i
$776$	323.974	+	401.863i	0.417493	+	0.517865i
$777$	233.092	+	179.966i	0.299990	+	0.231616i
$778$	550.281	+	344.410i	0.707302	+	0.442687i
$779$	−485.371	+	840.687i	−0.623069	+	1.07919i
$780$	−22.1668	+	90.6869i	−0.0284190	+	0.116265i
$781$	−19.8206	−	34.3303i	−0.0253785	−	0.0439569i
$782$	604.518	+	1138.93i	0.773041	+	1.45643i
$783$	−814.239	−	814.239i	−1.03990	−	1.03990i
$784$	630.292	−	466.248i	0.803944	−	0.594705i
$785$	228.287	+	104.770i	0.290812	+	0.133466i
$786$	−159.833	+	521.436i	−0.203350	+	0.663405i
$787$	−1019.92	−	273.286i	−1.29595	−	0.347250i	−0.456035	−	0.889962i	$-0.650731\pi$
$787$	−1019.92	−	273.286i	−1.29595	−	0.347250i	−0.839919	+	0.542712i	$0.817397\pi$
$788$	26.8190	+	139.050i	0.0340343	+	0.176460i
$789$	−211.507	+	366.340i	−0.268069	+	0.464310i
$790$	174.989	−	845.435i	0.221505	−	1.07017i
$791$	−73.5158	−	571.581i	−0.0929403	−	0.722606i
$792$	11.0549	+	1.18629i	0.0139582	+	0.00149784i
$793$	105.464	−	28.2589i	0.132993	−	0.0356354i
$794$	195.358	+	209.802i	0.246043	+	0.264234i
$795$	465.134	−	561.206i	0.585075	−	0.705919i
$796$	−36.0164	+	504.522i	−0.0452467	+	0.633821i
$797$	50.6148	+	50.6148i	0.0635066	+	0.0635066i	0.738147	−	0.674640i	$-0.235701\pi$
$797$	50.6148	+	50.6148i	0.0635066	+	0.0635066i	−0.674640	+	0.738147i	$0.735701\pi$
$798$	550.952	+	778.500i	0.690416	+	0.975563i
$799$	1315.51			1.64645
$800$	−689.395	+	405.876i	−0.861743	+	0.507345i
$801$	−98.8083	+	57.0470i	−0.123356	+	0.0712197i
$802$	683.055	+	24.3497i	0.851690	+	0.0303613i
$803$	−37.3113	+	9.99753i	−0.0464649	+	0.0124502i
$804$	−6.04976	+	2.93979i	−0.00752458	+	0.00365646i
$805$	972.154	+	615.124i	1.20764	+	0.764130i
$806$	−22.5819	−	98.1383i	−0.0280173	−	0.121760i
$807$	−287.163	+	76.9450i	−0.355840	+	0.0953470i
$808$	155.126	−	68.6618i	0.191988	−	0.0849775i
$809$	595.173	−	343.623i	0.735689	−	0.424750i	−0.0848105	−	0.996397i	$-0.527028\pi$
$809$	595.173	−	343.623i	0.735689	−	0.424750i	0.820500	+	0.571647i	$0.193695\pi$
$810$	425.176	+	378.738i	0.524908	+	0.467578i
$811$	−662.912			−0.817401			−0.408701	−	0.912669i	$-0.634018\pi$
$811$	−662.912			−0.817401			−0.408701	+	0.912669i	$0.634018\pi$
$812$	345.885	+	1049.19i	0.425967	+	1.29210i
$813$	101.128	+	101.128i	0.124389	+	0.124389i
$814$	6.07446	−	19.8172i	0.00746248	−	0.0243454i
$815$	1148.09	−	107.468i	1.40870	−	0.131862i
$816$	116.621	−	812.656i	0.142918	−	0.995902i
$817$	1232.33	−	330.201i	1.50835	−	0.404162i
$818$	−463.487	+	740.537i	−0.566610	+	0.905302i
$819$	24.8552	+	10.3824i	0.0303482	+	0.0126769i
$820$	515.416	−	538.681i	0.628556	−	0.656928i
$821$	−138.451	+	239.805i	−0.168638	+	0.292089i	−0.937941	−	0.346795i	$-0.887270\pi$
$821$	−138.451	+	239.805i	−0.168638	+	0.292089i	0.769304	+	0.638883i	$0.220603\pi$
$822$	221.100	+	7.88183i	0.268978	+	0.00958861i
$823$	1156.67	+	309.930i	1.40544	+	0.376585i	0.880294	−	0.474429i	$-0.157346\pi$
$823$	1156.67	+	309.930i	1.40544	+	0.376585i	0.525142	+	0.851015i	$0.324012\pi$
$824$	−296.296	+	46.2668i	−0.359582	+	0.0561490i
$825$	3.16359	−	42.0279i	0.00383465	−	0.0509429i
$826$	−273.180	−	738.999i	−0.330726	−	0.894672i
$827$	251.811	+	251.811i	0.304488	+	0.304488i	0.842767	−	0.538279i	$-0.180925\pi$
$827$	251.811	+	251.811i	0.304488	+	0.304488i	−0.538279	+	0.842767i	$0.680925\pi$
$828$	185.707	+	214.259i	0.224283	+	0.258767i
$829$	523.792	+	907.235i	0.631836	+	1.09437i	0.987176	+	0.159635i	$0.0510319\pi$
$829$	523.792	+	907.235i	0.631836	+	1.09437i	−0.355340	+	0.934737i	$0.615635\pi$
$830$	−52.3844	−	26.3397i	−0.0631138	−	0.0317346i
$831$	−510.317	+	883.895i	−0.614100	+	1.06365i
$832$	96.0448	−	61.7786i	0.115438	−	0.0742532i
$833$	−961.091	−	5.73528i	−1.15377	−	0.00688509i
$834$	−204.558	−	888.984i	−0.245273	−	1.06593i
$835$	−667.536	−	941.136i	−0.799445	−	1.12711i
$836$	37.6189	−	55.5979i	0.0449987	−	0.0665046i
$837$	−795.507	−	213.156i	−0.950427	−	0.254666i
$838$	389.650	−	206.818i	0.464976	−	0.246799i
$839$		−	959.140i		−	1.14319i	−0.820534	−	0.571597i	$-0.806324\pi$
$839$		−	959.140i		−	1.14319i	0.820534	−	0.571597i	$-0.193676\pi$
$840$	−269.070	−	681.268i	−0.320322	−	0.811033i
$841$	−715.676			−0.850982
$842$	−343.637	−	647.421i	−0.408119	−	0.768908i
$843$	195.750	−	730.551i	0.232207	−	0.866608i
$844$	−983.680	−	665.583i	−1.16550	−	0.788605i
$845$	−817.343	−	139.012i	−0.967270	−	0.164511i
$846$	281.909	−	64.8680i	0.333225	−	0.0766762i
$847$	−780.800	+	320.692i	−0.921842	+	0.378621i
$848$	−885.294	+	106.090i	−1.04398	+	0.125106i
$849$	515.955	+	297.887i	0.607721	+	0.350868i
$850$	974.713	+	108.408i	1.14672	+	0.127539i
$851$	457.765	−	264.291i	0.537914	−	0.310565i
$852$	−486.389	+	421.572i	−0.570879	+	0.494803i
$853$	−410.134	+	410.134i	−0.480814	+	0.480814i	−0.905391	−	0.424578i	$-0.860423\pi$
$853$	−410.134	+	410.134i	−0.480814	+	0.480814i	0.424578	+	0.905391i	$0.360423\pi$
$854$	−547.350	+	658.992i	−0.640926	+	0.771654i
$855$	−263.278	+	97.6383i	−0.307927	+	0.114197i
$856$	206.992	−	32.3219i	0.241813	−	0.0377593i
$857$	139.794	−	521.719i	0.163120	−	0.608773i	−0.835152	−	0.550019i	$-0.814621\pi$
$857$	139.794	−	521.719i	0.163120	−	0.608773i	0.998272	−	0.0587542i	$-0.0187128\pi$
$858$	−0.214336	+	6.01254i	−0.000249809	+	0.00700762i
$859$	−919.568	−	530.913i	−1.07051	−	0.618059i	−0.142189	−	0.989839i	$-0.545414\pi$
$859$	−919.568	−	530.913i	−1.07051	−	0.618059i	−0.928321	+	0.371780i	$0.878748\pi$
$860$	−979.588	+	21.6205i	−1.13906	+	0.0251402i
$861$	413.932	+	542.792i	0.480757	+	0.630421i
$862$	−941.391	−	589.198i	−1.09210	−	0.683524i
$863$	10.5966	+	39.5469i	0.0122788	+	0.0458249i	0.971793	−	0.235834i	$-0.0757821\pi$
$863$	10.5966	+	39.5469i	0.0122788	+	0.0458249i	−0.959515	+	0.281659i	$0.909115\pi$
$864$	−78.0175	−	930.673i	−0.0902980	−	1.07717i
$865$	−1605.46	+	150.280i	−1.85602	+	0.173734i
$866$	−271.367	−	83.1810i	−0.313357	−	0.0960520i
$867$	−177.075	+	177.075i	−0.204238	+	0.204238i
$868$	589.433	+	526.167i	0.679070	+	0.606183i
$869$		−	55.6387i		−	0.0640261i
$870$	1030.42	−	59.5217i	1.18439	−	0.0684158i
$871$	0.573486	+	0.993307i	0.000658423	+	0.00114042i
$872$	−1038.53	+	459.675i	−1.19098	+	0.527150i
$873$	−36.0148	−	134.409i	−0.0412541	−	0.153962i
$874$	1668.31	−	383.883i	1.90882	−	0.439226i
$875$	803.205	−	347.111i	0.917949	−	0.396698i
$876$	274.127	+	564.122i	0.312930	+	0.643975i
$877$	−58.4893	−	218.285i	−0.0666925	−	0.248900i	0.924529	−	0.381112i	$-0.124459\pi$
$877$	−58.4893	−	218.285i	−0.0666925	−	0.248900i	−0.991221	+	0.132212i	$0.957792\pi$
$878$	−54.4176	+	1526.52i	−0.0619791	+	1.73863i
$879$	−563.808	−	976.544i	−0.641420	−	1.11097i
$880$	−38.2042	+	34.6185i	−0.0434139	+	0.0393392i
$881$		−	684.953i		−	0.777472i	−0.921349	−	0.388736i	$-0.872912\pi$
$881$		−	684.953i		−	0.777472i	0.921349	−	0.388736i	$-0.127088\pi$
$882$	−206.241	+	46.1625i	−0.233833	+	0.0523385i
$883$	646.910	−	646.910i	0.732627	−	0.732627i	−0.238512	−	0.971139i	$-0.576660\pi$
$883$	646.910	−	646.910i	0.732627	−	0.732627i	0.971139	+	0.238512i	$0.0766598\pi$
$884$	−139.641	−	9.96855i	−0.157964	−	0.0112766i
$885$	−732.895	+	68.6032i	−0.828130	+	0.0775177i
$886$	482.611	−	449.386i	0.544707	−	0.507208i
$887$	−43.7451	−	163.259i	−0.0493181	−	0.184057i	0.936873	−	0.349670i	$-0.113706\pi$
$887$	−43.7451	−	163.259i	−0.0493181	−	0.184057i	−0.986191	+	0.165613i	$0.947040\pi$
$888$	−334.630	−	35.9087i	−0.376835	−	0.0404377i
$889$	−160.586	−	1248.55i	−0.180637	−	1.40444i
$890$	107.231	−	518.072i	0.120484	−	0.582103i
$891$	31.7787	+	18.3474i	0.0356663	+	0.0205920i
$892$	−638.309	+	123.112i	−0.715593	+	0.138018i
$893$	452.040	−	1687.04i	0.506204	−	1.88918i
$894$	−75.3587	−	23.0993i	−0.0842938	−	0.0258382i
$895$	184.847	−	68.5519i	0.206533	−	0.0765943i
$896$	−335.102	+	830.977i	−0.373997	+	0.927430i
$897$	−108.490	+	108.490i	−0.120947	+	0.120947i
$898$	−1197.70	+	635.713i	−1.33374	+	0.707921i
$899$	−964.190	+	556.675i	−1.07251	+	0.619216i
$900$	214.223	−	24.8319i	0.238025	−	0.0275910i
$901$	946.609	+	546.525i	1.05062	+	0.606576i
$902$	25.4902	−	40.7269i	0.0282596	−	0.0451518i
$903$	119.752	−	889.099i	0.132616	−	0.984605i
$904$	413.364	+	512.743i	0.457261	+	0.567194i
$905$	519.673	+	88.3847i	0.574224	+	0.0976626i
$906$	520.016	−	484.217i	0.573970	−	0.534456i
$907$	−122.919	+	458.740i	−0.135523	+	0.505777i	0.864473	+	0.502680i	$0.167653\pi$
$907$	−122.919	+	458.740i	−0.135523	+	0.505777i	−0.999995	+	0.00309728i	$0.999014\pi$
$908$	−1038.11	+	899.770i	−1.14329	+	0.990936i
$909$	−45.7308			−0.0503089
$910$	−112.610	+	54.0382i	−0.123747	+	0.0593827i
$911$		−	40.2633i		−	0.0441968i	−0.999756	−	0.0220984i	$-0.992965\pi$
$911$		−	40.2633i		−	0.0441968i	0.999756	−	0.0220984i	$-0.00703472\pi$
$912$	−1002.09	−	428.804i	−1.09879	−	0.470180i
$913$	−3.64988	−	0.977982i	−0.00399768	−	0.00107117i
$914$	−1031.72	+	960.689i	−1.12879	+	1.05108i
$915$	463.038	+	652.821i	0.506053	+	0.713465i
$916$	−227.461	−	468.090i	−0.248320	−	0.511015i
$917$	−674.967	+	277.224i	−0.736060	+	0.302316i
$918$	−607.419	+	970.504i	−0.661676	+	1.05719i
$919$	710.887	−	1231.29i	0.773544	−	1.33982i	−0.162065	−	0.986780i	$-0.551815\pi$
$919$	710.887	−	1231.29i	0.773544	−	1.33982i	0.935609	−	0.353038i	$-0.114851\pi$
$920$	−1314.64	−	17.8351i	−1.42896	−	0.0193860i
$921$	432.424	+	748.981i	0.469516	+	0.813226i
$922$	535.827	−	284.405i	0.581157	−	0.308465i
$923$	77.6110	+	77.6110i	0.0840856	+	0.0840856i
$924$	−25.8790	−	39.4783i	−0.0280075	−	0.0427254i
$925$	30.1772	−	400.901i	0.0326240	−	0.433407i
$926$	−1162.11	−	356.215i	−1.25498	−	0.384682i
$927$	78.0862	+	20.9231i	0.0842353	+	0.0225708i
$928$	−964.216	−	815.061i	−1.03903	−	0.878298i
$929$	438.592	−	759.663i	0.472112	−	0.817722i	−0.527379	−	0.849630i	$-0.676825\pi$
$929$	438.592	−	759.663i	0.472112	−	0.817722i	0.999491	+	0.0319085i	$0.0101585\pi$
$930$	616.944	−	405.349i	0.663381	−	0.435859i
$931$	−337.608	+	1230.55i	−0.362630	+	1.32175i
$932$	454.019	−	1312.37i	0.487145	−	1.40812i
$933$	−1315.47	+	352.480i	−1.40994	+	0.377792i
$934$	−765.157	+	712.482i	−0.819226	+	0.762828i
$935$	62.9274	−	5.89037i	0.0673020	−	0.00629986i
$936$	−30.4160	+	4.74948i	−0.0324957	+	0.00507423i
$937$	−926.803	−	926.803i	−0.989117	−	0.989117i	0.0108239	−	0.999941i	$-0.496555\pi$
$937$	−926.803	−	926.803i	−0.989117	−	0.989117i	−0.999941	+	0.0108239i	$0.996555\pi$
$938$	−8.17499	−	3.76225i	−0.00871534	−	0.00401093i
$939$	−911.795			−0.971027
$940$	−644.888	+	1176.17i	−0.686051	+	1.25125i
$941$	370.909	−	214.144i	0.394164	−	0.227571i	−0.289799	−	0.957088i	$-0.593588\pi$
$941$	370.909	−	214.144i	0.394164	−	0.227571i	0.683963	+	0.729517i	$0.260255\pi$
$942$	9.36367	−	262.668i	0.00994020	−	0.278841i
$943$	1183.51	−	317.121i	1.25505	−	0.336289i
$944$	707.933	+	556.419i	0.749929	+	0.589427i
$945$	−41.4098	+	1020.65i	−0.0438199	+	1.08006i
$946$	−61.5366	+	14.1598i	−0.0650492	+	0.0149680i
$947$	1338.70	−	358.703i	1.41362	−	0.378778i	0.530404	−	0.847745i	$-0.322040\pi$
$947$	1338.70	−	358.703i	1.41362	−	0.378778i	0.883216	+	0.468967i	$0.155374\pi$
$948$	−887.064	+	171.090i	−0.935721	+	0.180475i
$949$	92.6229	−	53.4759i	0.0976005	−	0.0563497i
$950$	473.958	−	1212.74i	0.498903	−	1.27657i
$951$	187.303			0.196954
$952$	939.499	−	569.074i	0.986869	−	0.597767i
$953$	477.877	+	477.877i	0.501445	+	0.501445i	0.911887	−	0.410442i	$-0.134626\pi$
$953$	477.877	+	477.877i	0.501445	+	0.501445i	−0.410442	+	0.911887i	$0.634626\pi$
$954$	229.804	+	70.4407i	0.240885	+	0.0738373i
$955$	999.945	−	1206.48i	1.04706	−	1.26333i
$956$	319.000	−	471.457i	0.333682	−	0.493156i
$957$	64.2491	−	17.2155i	0.0671360	−	0.0179890i
$958$	1132.97	+	709.104i	1.18264	+	0.740192i
$959$	179.494	+	235.372i	0.187168	+	0.245434i
$960$	669.412	+	502.648i	0.697304	+	0.523591i
$961$	82.3603	−	142.652i	0.0857027	−	0.148441i
$962$	−2.04454	+	57.3531i	−0.00212530	+	0.0596187i
$963$	−54.5509	−	14.6169i	−0.0566469	−	0.0151785i
$964$	77.4794	−	1085.34i	0.0803728	−	1.12587i
$965$	1522.60	+	698.783i	1.57782	+	0.724127i
$966$	203.087	−	1186.54i	0.210235	−	1.22830i
$967$	−709.757	−	709.757i	−0.733978	−	0.733978i	0.237427	−	0.971405i	$-0.423696\pi$
$967$	−709.757	−	709.757i	−0.733978	−	0.733978i	−0.971405	+	0.237427i	$0.923696\pi$
$968$	568.723	−	779.203i	0.587524	−	0.804961i
$969$	668.107	+	1157.19i	0.689481	+	1.19422i
$970$	576.468	+	289.858i	0.594297	+	0.298822i
$971$	398.922	−	690.953i	0.410836	−	0.711589i	−0.584145	−	0.811649i	$-0.698570\pi$
$971$	398.922	−	690.953i	0.410836	−	0.711589i	0.994981	+	0.100060i	$0.0319036\pi$
$972$	−148.713	+	429.863i	−0.152997	+	0.442246i
$973$	745.863	−	966.046i	0.766560	−	0.992853i
$974$	148.835	−	34.2473i	0.152808	−	0.0351615i
$975$	21.6571	+	114.669i	0.0222124	+	0.117609i
$976$	139.073	−	969.110i	0.142493	−	0.992940i
$977$	750.302	+	201.043i	0.767965	+	0.205776i	0.621472	−	0.783436i	$-0.286535\pi$
$977$	750.302	+	201.043i	0.767965	+	0.205776i	0.146493	+	0.989212i	$0.453202\pi$
$978$	−565.694	−	1065.78i	−0.578420	−	1.08976i
$979$		−	34.0947i		−	0.0348260i
$980$	476.273	−	856.484i	0.485993	−	0.873963i
$981$	306.157			0.312086
$982$	1018.92	−	540.819i	1.03760	−	0.550733i
$983$	−23.3428	+	87.1164i	−0.0237465	+	0.0886230i	−0.976782	−	0.214235i	$-0.931274\pi$
$983$	−23.3428	+	87.1164i	−0.0237465	+	0.0886230i	0.953036	+	0.302858i	$0.0979408\pi$
$984$	−727.704	−	281.161i	−0.739537	−	0.285733i
$985$	102.410	+	144.385i	0.103970	+	0.146583i
$986$	347.076	+	1508.35i	0.352004	+	1.52977i
$987$	−972.125	−	750.556i	−0.984929	−	0.760442i
$988$	−60.7676	+	175.652i	−0.0615057	+	0.177786i
$989$	−1394.56	−	805.150i	−1.41007	−	0.814105i
$990$	13.1946	−	4.36524i	0.0133279	−	0.00440934i
$991$	−190.013	+	109.704i	−0.191739	+	0.110700i	−0.592796	−	0.805353i	$-0.701976\pi$
$991$	−190.013	+	109.704i	−0.191739	+	0.110700i	0.401058	+	0.916053i	$0.368643\pi$
$992$	−888.696	−	160.032i	−0.895862	−	0.161323i
$993$	664.960	−	664.960i	0.669648	−	0.669648i
$994$	−848.824	−	145.284i	−0.853947	−	0.146161i
$995$	219.845	+	592.804i	0.220950	+	0.595783i
$996$	−4.36879	+	61.1984i	−0.00438633	+	0.0614442i
$997$	53.9220	−	201.240i	0.0540842	−	0.201845i	−0.933597	−	0.358325i	$-0.883348\pi$
$997$	53.9220	−	201.240i	0.0540842	−	0.201845i	0.987681	+	0.156480i	$0.0500146\pi$
$998$	−186.885	−	6.66214i	−0.187260	−	0.00667549i
$999$	406.464	+	234.672i	0.406871	+	0.234907i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.3.x.a.103.30	yes	176
4.3	odd	2	inner	140.3.x.a.103.21	yes	176
5.2	odd	4	inner	140.3.x.a.47.9	yes	176
7.3	odd	6	inner	140.3.x.a.3.1	✓	176
20.7	even	4	inner	140.3.x.a.47.1	yes	176
28.3	even	6	inner	140.3.x.a.3.9	yes	176
35.17	even	12	inner	140.3.x.a.87.21	yes	176
140.87	odd	12	inner	140.3.x.a.87.30	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.3.x.a.3.1	✓	176	7.3	odd	6	inner
140.3.x.a.3.9	yes	176	28.3	even	6	inner
140.3.x.a.47.1	yes	176	20.7	even	4	inner
140.3.x.a.47.9	yes	176	5.2	odd	4	inner
140.3.x.a.87.21	yes	176	35.17	even	12	inner
140.3.x.a.87.30	yes	176	140.87	odd	12	inner
140.3.x.a.103.21	yes	176	4.3	odd	2	inner
140.3.x.a.103.30	yes	176	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	140.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.937660 + 1.76658i) q^{2} +(0.677069 - 2.52686i) q^{3} +(-2.24159 + 3.31290i) q^{4} +(-0.838349 + 4.92922i) q^{5} +(5.09875 - 1.17324i) q^{6} +(5.54073 + 4.27788i) q^{7} +(-7.95433 - 0.853568i) q^{8} +(1.86765 + 1.07829i) q^{9} +O(q^{10})\)	\(q+(0.937660 + 1.76658i) q^{2} +(0.677069 - 2.52686i) q^{3} +(-2.24159 + 3.31290i) q^{4} +(-0.838349 + 4.92922i) q^{5} +(5.09875 - 1.17324i) q^{6} +(5.54073 + 4.27788i) q^{7} +(-7.95433 - 0.853568i) q^{8} +(1.86765 + 1.07829i) q^{9} +(-9.49393 + 3.14092i) q^{10} +(-0.558108 + 0.322224i) q^{11} +(6.85350 + 7.90723i) q^{12} +(1.26172 - 1.26172i) q^{13} +(-2.36188 + 13.7993i) q^{14} +(11.8878 + 5.45581i) q^{15} +(-5.95057 - 14.8523i) q^{16} +(-5.07660 + 18.9461i) q^{17} +(-0.153658 + 4.31041i) q^{18} +(22.5524 + 13.0206i) q^{19} +(-14.4507 - 13.8266i) q^{20} +(14.5611 - 11.1042i) q^{21} +(-1.09255 - 0.683804i) q^{22} +(-8.50715 - 31.7491i) q^{23} +(-7.54248 + 19.5215i) q^{24} +(-23.5943 - 8.26481i) q^{25} +(3.41200 + 1.04586i) q^{26} +(20.6373 - 20.6373i) q^{27} +(-26.5922 + 8.76663i) q^{28} -39.4547i q^{29} +(1.50861 + 26.1164i) q^{30} +(-14.1092 - 24.4379i) q^{31} +(20.6581 - 24.4385i) q^{32} +(0.436336 + 1.62843i) q^{33} +(-38.2299 + 8.79681i) q^{34} +(-25.7317 + 23.7251i) q^{35} +(-7.75874 + 3.77025i) q^{36} +(4.16217 + 15.5334i) q^{37} +(-1.85548 + 52.0495i) q^{38} +(-2.33392 - 4.04247i) q^{39} +(10.8759 - 38.4930i) q^{40} +37.2770i q^{41} +(33.2698 + 15.3112i) q^{42} +(34.6421 - 34.6421i) q^{43} +(0.183554 - 2.57125i) q^{44} +(-6.88084 + 8.30205i) q^{45} +(48.1104 - 44.7984i) q^{46} +(-17.3586 - 64.7831i) q^{47} +(-41.5586 + 4.98019i) q^{48} +(12.3995 + 47.4052i) q^{49} +(-7.52304 - 49.4308i) q^{50} +(44.4369 + 25.6557i) q^{51} +(1.35169 + 7.00822i) q^{52} +(14.4231 - 53.8279i) q^{53} +(55.8081 + 17.1066i) q^{54} +(-1.12042 - 3.02117i) q^{55} +(-40.4214 - 38.7571i) q^{56} +(48.1709 - 48.1709i) q^{57} +(69.6998 - 36.9951i) q^{58} +(-48.7371 + 28.1384i) q^{59} +(-44.7221 + 27.1534i) q^{60} +(52.9920 + 30.5949i) q^{61} +(29.9417 - 47.8394i) q^{62} +(5.73535 + 13.9641i) q^{63} +(62.5428 + 13.5791i) q^{64} +(5.16154 + 7.27707i) q^{65} +(-2.46761 + 2.29773i) q^{66} +(-0.166368 + 0.620894i) q^{67} +(-51.3869 - 59.2876i) q^{68} -85.9854 q^{69} +(-66.0398 - 23.2109i) q^{70} +61.5119i q^{71} +(-13.9355 - 10.1712i) q^{72} +(57.8965 + 15.5133i) q^{73} +(-23.5383 + 21.9179i) q^{74} +(-36.8590 + 54.0237i) q^{75} +(-93.6893 + 45.5269i) q^{76} +(-4.47076 - 0.602163i) q^{77} +(4.95291 - 7.91351i) q^{78} +(-43.1677 + 74.7687i) q^{79} +(78.1988 - 16.8802i) q^{80} +(-28.4700 - 49.3115i) q^{81} +(-65.8527 + 34.9531i) q^{82} +(4.14603 + 4.14603i) q^{83} +(4.14725 + 73.1303i) q^{84} +(-89.1335 - 40.9071i) q^{85} +(93.6804 + 28.7154i) q^{86} +(-99.6964 - 26.7136i) q^{87} +(4.71442 - 2.08669i) q^{88} +(-26.4526 + 45.8173i) q^{89} +(-21.1181 - 4.37104i) q^{90} +(12.3884 - 1.59337i) q^{91} +(124.251 + 42.9851i) q^{92} +(-71.3039 + 19.1058i) q^{93} +(98.1679 - 91.4097i) q^{94} +(-83.0884 + 100.250i) q^{95} +(-47.7657 - 68.7467i) q^{96} +(-45.6253 - 45.6253i) q^{97} +(-72.1185 + 66.3546i) q^{98} -1.38980 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8}+O(q^{10}) \) 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8	\( 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8} - 6 q^{10} - 6 q^{12} - 28 q^{16} - 12 q^{17} - 36 q^{18} - 32 q^{21} - 24 q^{22} - 4 q^{25} - 12 q^{26} + 114 q^{28} + 28 q^{30} + 58 q^{32} - 156 q^{33} - 144 q^{36} - 4 q^{37} + 192 q^{38} + 54 q^{40} - 218 q^{42} - 12 q^{45} + 68 q^{46} - 332 q^{50} - 264 q^{52} - 4 q^{53} - 300 q^{56} - 24 q^{57} - 146 q^{58} - 434 q^{60} - 24 q^{61} + 92 q^{65} - 660 q^{66} - 72 q^{68} + 488 q^{70} - 80 q^{72} - 12 q^{73} - 156 q^{77} + 688 q^{78} + 588 q^{80} + 288 q^{81} + 798 q^{82} + 272 q^{85} - 72 q^{86} + 588 q^{88} + 524 q^{92} + 164 q^{93} + 1080 q^{96} - 766 q^{98}+O(q^{100}) \) 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8 - 6 * q^10 - 6 * q^12 - 28 * q^16 - 12 * q^17 - 36 * q^18 - 32 * q^21 - 24 * q^22 - 4 * q^25 - 12 * q^26 + 114 * q^28 + 28 * q^30 + 58 * q^32 - 156 * q^33 - 144 * q^36 - 4 * q^37 + 192 * q^38 + 54 * q^40 - 218 * q^42 - 12 * q^45 + 68 * q^46 - 332 * q^50 - 264 * q^52 - 4 * q^53 - 300 * q^56 - 24 * q^57 - 146 * q^58 - 434 * q^60 - 24 * q^61 + 92 * q^65 - 660 * q^66 - 72 * q^68 + 488 * q^70 - 80 * q^72 - 12 * q^73 - 156 * q^77 + 688 * q^78 + 588 * q^80 + 288 * q^81 + 798 * q^82 + 272 * q^85 - 72 * q^86 + 588 * q^88 + 524 * q^92 + 164 * q^93 + 1080 * q^96 - 766 * q^98

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