LMFDB - Embedded newform 168.3.x.b.61.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,3,Mod(61,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 5]))

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

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

chi := DirichletCharacter("168.61");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	168.x (of order $6$, degree $2$, 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:	$4.57766844125$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			61.7
Character	$\chi$	$=$	168.61
Dual form			168.3.x.b.157.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32774 - 1.49570i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-0.474223 + 3.97179i) q^{4} +(4.33205 - 7.50333i) q^{5} +(1.09369 - 3.28692i) q^{6} +(2.39482 + 6.57760i) q^{7} +(6.57024 - 4.56420i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.32774 - 1.49570i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-0.474223 + 3.97179i) q^{4} +(4.33205 - 7.50333i) q^{5} +(1.09369 - 3.28692i) q^{6} +(2.39482 + 6.57760i) q^{7} +(6.57024 - 4.56420i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(-16.9745 + 3.48302i) q^{10} +(-9.70954 + 5.60581i) q^{11} +(-6.36837 + 2.72834i) q^{12} +15.6975 q^{13} +(6.65841 - 12.3153i) q^{14} +15.0067 q^{15} +(-15.5502 - 3.76703i) q^{16} +(29.3084 - 16.9212i) q^{17} +(5.87754 - 1.20602i) q^{18} +(6.81708 - 11.8075i) q^{19} +(27.7473 + 20.7642i) q^{20} +(-7.79243 + 9.28860i) q^{21} +(21.2763 + 7.07950i) q^{22} +(0.498987 - 0.864271i) q^{23} +(12.5363 + 5.90265i) q^{24} +(-25.0333 - 43.3590i) q^{25} +(-20.8422 - 23.4788i) q^{26} -5.19615 q^{27} +(-27.2605 + 6.39247i) q^{28} +13.0538i q^{29} +(-19.9249 - 22.4454i) q^{30} +(6.91318 - 3.99133i) q^{31} +(15.0123 + 28.2601i) q^{32} +(-16.8174 - 9.70954i) q^{33} +(-64.2228 - 21.3695i) q^{34} +(59.7284 + 10.5254i) q^{35} +(-9.60768 - 7.18975i) q^{36} +(11.3499 + 6.55286i) q^{37} +(-26.7118 + 5.48101i) q^{38} +(13.5945 + 23.5463i) q^{39} +(-5.78410 - 69.0710i) q^{40} +0.655069i q^{41} +(24.2392 - 0.677709i) q^{42} +5.93612i q^{43} +(-17.6606 - 41.2227i) q^{44} +(12.9962 + 22.5100i) q^{45} +(-1.95521 + 0.401192i) q^{46} +(-21.8643 - 12.6233i) q^{47} +(-7.81634 - 26.5877i) q^{48} +(-37.5297 + 31.5043i) q^{49} +(-31.6142 + 95.0116i) q^{50} +(50.7636 + 29.3084i) q^{51} +(-7.44414 + 62.3474i) q^{52} +(-57.5500 + 33.2265i) q^{53} +(6.89913 + 7.77187i) q^{54} +97.1385i q^{55} +(45.7560 + 32.2860i) q^{56} +23.6150 q^{57} +(19.5245 - 17.3320i) q^{58} +(-12.4419 - 21.5500i) q^{59} +(-7.11651 + 59.6033i) q^{60} +(-47.8480 + 82.8752i) q^{61} +(-15.1487 - 5.04059i) q^{62} +(-20.6813 - 3.64448i) q^{63} +(22.3361 - 59.9758i) q^{64} +(68.0026 - 117.784i) q^{65} +(7.80659 + 38.0455i) q^{66} +(-29.6779 + 17.1345i) q^{67} +(53.3087 + 124.431i) q^{68} +1.72854 q^{69} +(-63.5609 - 103.311i) q^{70} +61.8795 q^{71} +(2.00278 + 23.9163i) q^{72} +(-28.0314 + 16.1839i) q^{73} +(-5.26858 - 25.6765i) q^{74} +(43.3590 - 75.1000i) q^{75} +(43.6642 + 32.6754i) q^{76} +(-60.1254 - 50.4406i) q^{77} +(17.1683 - 51.5966i) q^{78} +(-23.6567 + 40.9746i) q^{79} +(-95.6296 + 100.360i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(0.979785 - 0.869760i) q^{82} -117.340 q^{83} +(-33.1970 - 35.3548i) q^{84} -293.214i q^{85} +(8.87865 - 7.88162i) q^{86} +(-19.5807 + 11.3049i) q^{87} +(-38.2080 + 81.1478i) q^{88} +(-101.251 - 58.4574i) q^{89} +(16.4127 - 49.3257i) q^{90} +(37.5928 + 103.252i) q^{91} +(3.19607 + 2.39173i) q^{92} +(11.9740 + 6.91318i) q^{93} +(10.1493 + 49.4629i) q^{94} +(-59.0638 - 102.302i) q^{95} +(-29.3891 + 46.9924i) q^{96} -48.9751i q^{97} +(96.9505 + 14.3036i) q^{98} -33.6348i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 2 q^{2} - 2 q^{4} + 26 q^{7} + 32 q^{8} - 90 q^{9}+O(q^{10}) $ 60 * q + 2 * q^2 - 2 * q^4 + 26 * q^7 + 32 * q^8 - 90 * q^9	$ 60 q + 2 q^{2} - 2 q^{4} + 26 q^{7} + 32 q^{8} - 90 q^{9} - 42 q^{10} - 14 q^{14} + 12 q^{15} + 6 q^{16} - 36 q^{17} + 6 q^{18} + 28 q^{22} - 28 q^{23} + 102 q^{24} - 204 q^{25} - 42 q^{26} + 186 q^{28} - 24 q^{30} + 18 q^{31} - 28 q^{32} - 30 q^{33} + 12 q^{36} - 414 q^{38} - 36 q^{39} + 18 q^{40} + 120 q^{42} - 48 q^{44} - 160 q^{46} + 828 q^{47} - 126 q^{49} - 332 q^{50} + 36 q^{52} + 36 q^{54} + 256 q^{56} - 312 q^{57} - 94 q^{58} + 150 q^{60} - 12 q^{63} + 988 q^{64} + 36 q^{65} - 108 q^{66} + 312 q^{68} + 222 q^{70} + 760 q^{71} - 48 q^{72} - 648 q^{73} - 294 q^{74} + 396 q^{78} + 114 q^{79} - 900 q^{80} - 270 q^{81} + 876 q^{82} - 96 q^{84} + 6 q^{86} - 174 q^{87} - 262 q^{88} - 72 q^{89} - 592 q^{92} - 540 q^{94} - 492 q^{95} - 258 q^{96} - 628 q^{98}+O(q^{100}) $ 60 * q + 2 * q^2 - 2 * q^4 + 26 * q^7 + 32 * q^8 - 90 * q^9 - 42 * q^10 - 14 * q^14 + 12 * q^15 + 6 * q^16 - 36 * q^17 + 6 * q^18 + 28 * q^22 - 28 * q^23 + 102 * q^24 - 204 * q^25 - 42 * q^26 + 186 * q^28 - 24 * q^30 + 18 * q^31 - 28 * q^32 - 30 * q^33 + 12 * q^36 - 414 * q^38 - 36 * q^39 + 18 * q^40 + 120 * q^42 - 48 * q^44 - 160 * q^46 + 828 * q^47 - 126 * q^49 - 332 * q^50 + 36 * q^52 + 36 * q^54 + 256 * q^56 - 312 * q^57 - 94 * q^58 + 150 * q^60 - 12 * q^63 + 988 * q^64 + 36 * q^65 - 108 * q^66 + 312 * q^68 + 222 * q^70 + 760 * q^71 - 48 * q^72 - 648 * q^73 - 294 * q^74 + 396 * q^78 + 114 * q^79 - 900 * q^80 - 270 * q^81 + 876 * q^82 - 96 * q^84 + 6 * q^86 - 174 * q^87 - 262 * q^88 - 72 * q^89 - 592 * q^92 - 540 * q^94 - 492 * q^95 - 258 * q^96 - 628 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.32774	−	1.49570i	−0.663869	−	0.747849i
$2$	−1.32774	−	1.49570i	−0.663869	−	0.747849i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$4$	−0.474223	+	3.97179i	−0.118556	+	0.992947i
$5$	4.33205	−	7.50333i	0.866410	−	1.50067i	0.000769783	−	1.00000i	$-0.499755\pi$
$5$	4.33205	−	7.50333i	0.866410	−	1.50067i	0.865640	−	0.500667i	$-0.166912\pi$
$6$	1.09369	−	3.28692i	0.182282	−	0.547820i
$7$	2.39482	+	6.57760i	0.342117	+	0.939657i
$7$	2.39482	+	6.57760i	0.342117	+	0.939657i
$8$	6.57024	−	4.56420i	0.821280	−	0.570525i
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$	−16.9745	+	3.48302i	−1.69745	+	0.348302i
$11$	−9.70954	+	5.60581i	−0.882686	+	0.509619i	−0.871543	−	0.490319i	$-0.836880\pi$
$11$	−9.70954	+	5.60581i	−0.882686	+	0.509619i	−0.0111427	+	0.999938i	$0.503547\pi$
$12$	−6.36837	+	2.72834i	−0.530698	+	0.227361i
$13$	15.6975			1.20750			0.603752	−	0.797172i	$-0.293672\pi$
$13$	15.6975			1.20750			0.603752	+	0.797172i	$0.293672\pi$
$14$	6.65841	−	12.3153i	0.475601	−	0.879661i
$15$	15.0067			1.00044
$16$	−15.5502	−	3.76703i	−0.971889	−	0.235439i
$17$	29.3084	−	16.9212i	1.72402	−	0.995364i	0.813923	−	0.580972i	$-0.197328\pi$
$17$	29.3084	−	16.9212i	1.72402	−	0.995364i	0.910099	−	0.414392i	$-0.136006\pi$
$18$	5.87754	−	1.20602i	0.326530	−	0.0670010i
$19$	6.81708	−	11.8075i	0.358793	−	0.621449i	−0.628966	−	0.777433i	$-0.716522\pi$
$19$	6.81708	−	11.8075i	0.358793	−	0.621449i	0.987760	+	0.155984i	$0.0498549\pi$
$20$	27.7473	+	20.7642i	1.38736	+	1.03821i
$21$	−7.79243	+	9.28860i	−0.371068	+	0.442314i
$22$	21.2763	+	7.07950i	0.967106	+	0.321795i
$23$	0.498987	−	0.864271i	0.0216951	−	0.0375770i	−0.854974	−	0.518671i	$-0.826427\pi$
$23$	0.498987	−	0.864271i	0.0216951	−	0.0375770i	0.876669	+	0.481094i	$0.159760\pi$
$24$	12.5363	+	5.90265i	0.522346	+	0.245944i
$25$	−25.0333	−	43.3590i	−1.00133	−	1.73436i
$26$	−20.8422	−	23.4788i	−0.801624	−	0.903030i
$27$	−5.19615			−0.192450
$28$	−27.2605	+	6.39247i	−0.973590	+	0.228302i
$29$			13.0538i			0.450130i	0.974344	+	0.225065i	$0.0722595\pi$
$29$			13.0538i			0.450130i	−0.974344	+	0.225065i	$0.927741\pi$
$30$	−19.9249	−	22.4454i	−0.664164	−	0.748181i
$31$	6.91318	−	3.99133i	0.223006	−	0.128753i	−0.384335	−	0.923194i	$-0.625569\pi$
$31$	6.91318	−	3.99133i	0.223006	−	0.128753i	0.607341	+	0.794441i	$0.292236\pi$
$32$	15.0123	+	28.2601i	0.469134	+	0.883127i
$33$	−16.8174	−	9.70954i	−0.509619	−	0.294229i
$34$	−64.2228	−	21.3695i	−1.88891	−	0.628516i
$35$	59.7284	+	10.5254i	1.70653	+	0.300725i
$36$	−9.60768	−	7.18975i	−0.266880	−	0.199715i
$37$	11.3499	+	6.55286i	0.306754	+	0.177104i	0.645473	−	0.763783i	$-0.276660\pi$
$37$	11.3499	+	6.55286i	0.306754	+	0.177104i	−0.338719	+	0.940887i	$0.609994\pi$
$38$	−26.7118	+	5.48101i	−0.702941	+	0.144237i
$39$	13.5945	+	23.5463i	0.348576	+	0.603752i
$40$	−5.78410	−	69.0710i	−0.144603	−	1.72678i
$41$			0.655069i			0.0159773i	0.999968	+	0.00798864i	$0.00254289\pi$
$41$			0.655069i			0.0159773i	−0.999968	+	0.00798864i	$0.997457\pi$
$42$	24.2392	−	0.677709i	0.577125	−	0.0161359i
$43$			5.93612i			0.138049i	0.997615	+	0.0690247i	$0.0219887\pi$
$43$			5.93612i			0.138049i	−0.997615	+	0.0690247i	$0.978011\pi$
$44$	−17.6606	−	41.2227i	−0.401377	−	0.936879i
$45$	12.9962	+	22.5100i	0.288803	+	0.500222i
$46$	−1.95521	+	0.401192i	−0.0425046	+	0.00872156i
$47$	−21.8643	−	12.6233i	−0.465197	−	0.268582i	0.249030	−	0.968496i	$-0.419888\pi$
$47$	−21.8643	−	12.6233i	−0.465197	−	0.268582i	−0.714227	+	0.699914i	$0.753222\pi$
$48$	−7.81634	−	26.5877i	−0.162841	−	0.553910i
$49$	−37.5297	+	31.5043i	−0.765912	+	0.642946i
$50$	−31.6142	+	95.0116i	−0.632285	+	1.90023i
$51$	50.7636	+	29.3084i	0.995364	+	0.574674i
$52$	−7.44414	+	62.3474i	−0.143157	+	1.19899i
$53$	−57.5500	+	33.2265i	−1.08585	+	0.626915i	−0.932468	−	0.361252i	$-0.882349\pi$
$53$	−57.5500	+	33.2265i	−1.08585	+	0.626915i	−0.153380	+	0.988167i	$0.549016\pi$
$54$	6.89913	+	7.77187i	0.127762	+	0.143924i
$55$			97.1385i			1.76616i
$56$	45.7560	+	32.2860i	0.817072	+	0.576536i
$57$	23.6150			0.414299
$58$	19.5245	−	17.3320i	0.336629	−	0.298827i
$59$	−12.4419	−	21.5500i	−0.210879	−	0.365254i	0.741111	−	0.671383i	$-0.234299\pi$
$59$	−12.4419	−	21.5500i	−0.210879	−	0.365254i	−0.951990	+	0.306129i	$0.900966\pi$
$60$	−7.11651	+	59.6033i	−0.118608	+	0.993388i
$61$	−47.8480	+	82.8752i	−0.784394	+	1.35861i	0.144966	+	0.989437i	$0.453693\pi$
$61$	−47.8480	+	82.8752i	−0.784394	+	1.35861i	−0.929360	+	0.369174i	$0.879641\pi$
$62$	−15.1487	−	5.04059i	−0.244334	−	0.0812999i
$63$	−20.6813	−	3.64448i	−0.328275	−	0.0578489i
$64$	22.3361	−	59.9758i	0.349002	−	0.937122i
$65$	68.0026	−	117.784i	1.04619	−	1.81206i
$66$	7.80659	+	38.0455i	0.118282	+	0.576447i
$67$	−29.6779	+	17.1345i	−0.442953	+	0.255739i	−0.704850	−	0.709357i	$-0.748985\pi$
$67$	−29.6779	+	17.1345i	−0.442953	+	0.255739i	0.261896	+	0.965096i	$0.415652\pi$
$68$	53.3087	+	124.431i	0.783952	+	1.82987i
$69$	1.72854			0.0250513
$70$	−63.5609	−	103.311i	−0.908013	−	1.47587i
$71$	61.8795			0.871542			0.435771	−	0.900058i	$-0.356476\pi$
$71$	61.8795			0.871542			0.435771	+	0.900058i	$0.356476\pi$
$72$	2.00278	+	23.9163i	0.0278164	+	0.332171i
$73$	−28.0314	+	16.1839i	−0.383992	+	0.221698i	−0.679554	−	0.733626i	$-0.737827\pi$
$73$	−28.0314	+	16.1839i	−0.383992	+	0.221698i	0.295562	+	0.955324i	$0.404493\pi$
$74$	−5.26858	−	25.6765i	−0.0711970	−	0.346979i
$75$	43.3590	−	75.1000i	0.578120	−	1.00133i
$76$	43.6642	+	32.6754i	0.574529	+	0.429939i
$77$	−60.1254	−	50.4406i	−0.780849	−	0.655073i
$78$	17.1683	−	51.5966i	0.220106	−	0.661494i
$79$	−23.6567	+	40.9746i	−0.299452	+	0.518666i	−0.976011	−	0.217723i	$-0.930137\pi$
$79$	−23.6567	+	40.9746i	−0.299452	+	0.518666i	0.676559	+	0.736389i	$0.263471\pi$
$80$	−95.6296	+	100.360i	−1.19537	+	1.25449i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	0.979785	−	0.869760i	0.0119486	−	0.0106068i
$83$	−117.340			−1.41374			−0.706870	−	0.707343i	$-0.749894\pi$
$83$	−117.340			−1.41374			−0.706870	+	0.707343i	$0.749894\pi$
$84$	−33.1970	−	35.3548i	−0.395202	−	0.420890i
$85$		−	293.214i		−	3.44957i
$86$	8.87865	−	7.88162i	0.103240	−	0.0916467i
$87$	−19.5807	+	11.3049i	−0.225065	+	0.129941i
$88$	−38.2080	+	81.1478i	−0.434182	+	0.922134i
$89$	−101.251	−	58.4574i	−1.13765	−	0.656824i	−0.191805	−	0.981433i	$-0.561434\pi$
$89$	−101.251	−	58.4574i	−1.13765	−	0.656824i	−0.945848	+	0.324609i	$0.894767\pi$
$90$	16.4127	−	49.3257i	0.182363	−	0.548063i
$91$	37.5928	+	103.252i	0.413108	+	1.13464i
$92$	3.19607	+	2.39173i	0.0347399	+	0.0259971i
$93$	11.9740	+	6.91318i	0.128753	+	0.0743353i
$94$	10.1493	+	49.4629i	0.107972	+	0.526201i
$95$	−59.0638	−	102.302i	−0.621725	−	1.07686i
$96$	−29.3891	+	46.9924i	−0.306136	+	0.489504i
$97$		−	48.9751i		−	0.504898i	−0.967610	−	0.252449i	$-0.918764\pi$
$97$		−	48.9751i		−	0.504898i	0.967610	−	0.252449i	$-0.0812360\pi$
$98$	96.9505	+	14.3036i	0.989291	+	0.145955i
$99$		−	33.6348i		−	0.339746i
$100$	184.084	−	78.8652i	1.84084	−	0.788652i
$101$	49.8929	+	86.4170i	0.493989	+	0.855614i	0.999976	−	0.00692737i	$-0.00220507\pi$
$101$	49.8929	+	86.4170i	0.493989	+	0.855614i	−0.505987	+	0.862541i	$0.668872\pi$
$102$	−23.5643	−	114.841i	−0.231022	−	1.12589i
$103$	125.370	+	72.3824i	1.21718	+	0.702742i	0.964315	−	0.264759i	$-0.0852922\pi$
$103$	125.370	+	72.3824i	1.21718	+	0.702742i	0.252870	+	0.967500i	$0.418626\pi$
$104$	103.137	−	71.6468i	0.991699	−	0.688911i
$105$	35.9382	+	98.7078i	0.342269	+	0.940075i
$106$	126.108	+	41.9613i	1.18970	+	0.395861i
$107$	−35.5663	−	20.5342i	−0.332396	−	0.191909i	0.324509	−	0.945883i	$-0.394801\pi$
$107$	−35.5663	−	20.5342i	−0.332396	−	0.191909i	−0.656904	+	0.753974i	$0.728134\pi$
$108$	2.46414	−	20.6380i	0.0228161	−	0.191093i
$109$	114.967	−	66.3763i	1.05474	−	0.608957i	0.130771	−	0.991413i	$-0.458255\pi$
$109$	114.967	−	66.3763i	1.05474	−	0.608957i	0.923974	+	0.382455i	$0.124921\pi$
$110$	145.290	−	128.975i	1.32082	−	1.17250i
$111$			22.6998i			0.204502i
$112$	−12.4620	−	111.305i	−0.111267	−	0.993790i
$113$	−150.727			−1.33386			−0.666932	−	0.745119i	$-0.732393\pi$
$113$	−150.727			−1.33386			−0.666932	+	0.745119i	$0.732393\pi$
$114$	−31.3546	−	35.3210i	−0.275040	−	0.309833i
$115$	−4.32327	−	7.48813i	−0.0375937	−	0.0651142i
$116$	−51.8468	−	6.19040i	−0.446956	−	0.0533655i
$117$	−23.5463	+	40.7834i	−0.201251	+	0.348576i
$118$	−15.7127	+	47.2220i	−0.133158	+	0.400186i
$119$	181.489	+	152.256i	1.52512	+	1.27946i
$120$	98.5974	−	68.4934i	0.821645	−	0.570779i
$121$	2.35014	−	4.07057i	0.0194227	−	0.0336410i
$122$	187.486	−	38.4704i	1.53677	−	0.315331i
$123$	−0.982603	+	0.567306i	−0.00798864	+	0.00461225i
$124$	12.5743	+	29.3505i	0.101406	+	0.236698i
$125$	−217.180			−1.73744
$126$	22.0084	+	35.7719i	0.174670	+	0.283904i
$127$	−144.141			−1.13497			−0.567484	−	0.823385i	$-0.692083\pi$
$127$	−144.141			−1.13497			−0.567484	+	0.823385i	$0.692083\pi$
$128$	−119.362	+	46.2241i	−0.932517	+	0.361126i
$129$	−8.90419	+	5.14083i	−0.0690247	+	0.0398514i
$130$	−266.459	+	54.6749i	−2.04968	+	0.420576i
$131$	125.999	−	218.236i	0.961822	−	1.66592i	0.243901	−	0.969800i	$-0.421573\pi$
$131$	125.999	−	218.236i	0.961822	−	1.66592i	0.717921	−	0.696124i	$-0.245094\pi$
$132$	46.5395	−	62.1908i	0.352572	−	0.471142i
$133$	93.9908	+	16.5631i	0.706698	+	0.124535i
$134$	65.0325	+	21.6390i	0.485317	+	0.161485i
$135$	−22.5100	+	38.9885i	−0.166741	+	0.288803i
$136$	115.331	−	244.946i	0.848024	−	1.80107i
$137$	92.7717	+	160.685i	0.677165	+	1.17288i	0.975831	+	0.218527i	$0.0701252\pi$
$137$	92.7717	+	160.685i	0.677165	+	1.17288i	−0.298666	+	0.954358i	$0.596541\pi$
$138$	−2.29505	−	2.58538i	−0.0166308	−	0.0187346i
$139$	−177.155			−1.27449			−0.637247	−	0.770660i	$-0.719927\pi$
$139$	−177.155			−1.27449			−0.637247	+	0.770660i	$0.719927\pi$
$140$	−70.1292	+	232.237i	−0.500923	+	1.65884i
$141$		−	43.7286i		−	0.310132i
$142$	−82.1597	−	92.5530i	−0.578590	−	0.651781i
$143$	−152.416	+	87.9974i	−1.06585	+	0.615367i
$144$	33.1124	−	34.7501i	0.229947	−	0.241320i
$145$	97.9468	+	56.5496i	0.675495	+	0.389997i
$146$	61.4247	+	20.4385i	0.420717	+	0.139990i
$147$	−79.7582	−	29.0110i	−0.542572	−	0.197354i
$148$	−31.4089	+	41.9718i	−0.212223	+	0.283593i
$149$	−20.5747	−	11.8788i	−0.138085	−	0.0797237i	0.429366	−	0.903131i	$-0.358737\pi$
$149$	−20.5747	−	11.8788i	−0.138085	−	0.0797237i	−0.567451	+	0.823407i	$0.692070\pi$
$150$	−169.896	+	34.8611i	−1.13264	+	0.232408i
$151$	−44.8515	−	77.6850i	−0.297030	−	0.514470i	0.678425	−	0.734669i	$-0.262663\pi$
$151$	−44.8515	−	77.6850i	−0.297030	−	0.514470i	−0.975455	+	0.220199i	$0.929329\pi$
$152$	−9.10208	−	108.693i	−0.0598821	−	0.715084i
$153$			101.527i			0.663576i
$154$	4.38683	+	156.901i	0.0284859	+	1.01884i
$155$		−	69.1626i		−	0.446210i
$156$	−99.9678	+	42.8282i	−0.640820	+	0.274540i
$157$	96.7479	+	167.572i	0.616229	+	1.06734i	0.990168	+	0.139886i	$0.0446737\pi$
$157$	96.7479	+	167.572i	0.616229	+	1.06734i	−0.373939	+	0.927453i	$0.621993\pi$
$158$	92.6956	−	19.0203i	0.586681	−	0.120382i
$159$	−99.6795	−	57.5500i	−0.626915	−	0.361950i
$160$	277.079	+	9.78186i	1.73174	+	0.0611366i
$161$	6.87981	+	1.21237i	0.0427318	+	0.00753022i
$162$	−5.68299	+	17.0793i	−0.0350802	+	0.105428i
$163$	64.8970	+	37.4683i	0.398141	+	0.229867i	0.685682	−	0.727902i	$-0.259504\pi$
$163$	64.8970	+	37.4683i	0.398141	+	0.229867i	−0.287540	+	0.957769i	$0.592838\pi$
$164$	−2.60180	−	0.310649i	−0.0158646	−	0.00189420i
$165$	−145.708	+	84.1244i	−0.883078	+	0.509845i
$166$	155.797	+	175.506i	0.938539	+	1.05726i
$167$		−	311.218i		−	1.86358i	−0.362997	−	0.931790i	$-0.618246\pi$
$167$		−	311.218i		−	1.86358i	0.362997	−	0.931790i	$-0.381754\pi$
$168$	−8.80309	+	96.5945i	−0.0523994	+	0.574968i
$169$	77.4130			0.458065
$170$	−438.559	+	389.311i	−2.57976	+	2.29007i
$171$	20.4512	+	35.4226i	0.119598	+	0.207150i
$172$	−23.5770	−	2.81505i	−0.137076	−	0.0163666i
$173$	−3.52322	+	6.10239i	−0.0203654	+	0.0352739i	−0.876028	−	0.482259i	$-0.839816\pi$
$173$	−3.52322	+	6.10239i	−0.0203654	+	0.0352739i	0.855663	+	0.517533i	$0.173150\pi$
$174$	42.9067	+	14.2768i	0.246590	+	0.0820506i
$175$	225.248	−	268.496i	1.28713	−	1.53426i
$176$	172.103	−	50.5954i	0.977857	−	0.287474i
$177$	21.5500	−	37.3256i	0.121751	−	0.210879i
$178$	47.0004	+	229.057i	0.264047	+	1.28684i
$179$	42.0060	−	24.2522i	0.234670	−	0.135487i	−0.378054	−	0.925783i	$-0.623407\pi$
$179$	42.0060	−	24.2522i	0.234670	−	0.135487i	0.612725	+	0.790296i	$0.290073\pi$
$180$	−95.5680	+	40.9432i	−0.530934	+	0.227462i
$181$	100.024			0.552617			0.276308	−	0.961069i	$-0.410889\pi$
$181$	100.024			0.552617			0.276308	+	0.961069i	$0.410889\pi$
$182$	104.521	−	193.319i	0.574290	−	1.06219i
$183$	−165.750			−0.905740
$184$	−0.666242	−	7.95595i	−0.00362088	−	0.0432388i
$185$	98.3365	−	56.7746i	0.531549	−	0.306890i
$186$	−5.55828	−	27.0884i	−0.0298832	−	0.145636i
$187$	−189.714	+	328.594i	−1.01451	+	1.75719i
$188$	60.5058	−	80.8540i	0.321840	−	0.430075i
$189$	−12.4438	−	34.1782i	−0.0658405	−	0.180837i
$190$	−74.5909	+	224.171i	−0.392584	+	1.17985i
$191$	32.6745	−	56.5938i	0.171071	−	0.296303i	−0.767724	−	0.640781i	$-0.778611\pi$
$191$	32.6745	−	56.5938i	0.171071	−	0.296303i	0.938794	+	0.344478i	$0.111944\pi$
$192$	109.307	−	18.4364i	0.569309	−	0.0960228i
$193$	−49.2249	−	85.2601i	−0.255051	−	0.441762i	0.709858	−	0.704345i	$-0.248759\pi$
$193$	−49.2249	−	85.2601i	−0.255051	−	0.441762i	−0.964909	+	0.262583i	$0.915426\pi$
$194$	−73.2520	+	65.0261i	−0.377587	+	0.335186i
$195$	235.568			1.20804
$196$	−107.331	−	164.000i	−0.547608	−	0.836735i
$197$			78.4827i			0.398390i	0.979960	+	0.199195i	$0.0638326\pi$
$197$			78.4827i			0.398390i	−0.979960	+	0.199195i	$0.936167\pi$
$198$	−50.3076	+	44.6583i	−0.254079	+	0.225547i
$199$	−89.5798	+	51.7189i	−0.450150	+	0.259894i	−0.707894	−	0.706319i	$-0.750354\pi$
$199$	−89.5798	+	51.7189i	−0.450150	+	0.259894i	0.257744	+	0.966213i	$0.417021\pi$
$200$	−362.374	−	170.622i	−1.81187	−	0.853109i
$201$	−51.4036	−	29.6779i	−0.255739	−	0.147651i
$202$	63.0090	−	189.364i	0.311926	−	0.937444i
$203$	−85.8625	+	31.2614i	−0.422968	+	0.153997i
$204$	−140.480	+	187.724i	−0.688627	+	0.920214i
$205$	4.91520	+	2.83779i	0.0239766	+	0.0138429i
$206$	−58.1963	−	283.621i	−0.282506	−	1.37680i
$207$	1.49696	+	2.59281i	0.00723170	+	0.0125257i
$208$	−244.100	−	59.1331i	−1.17356	−	0.284294i
$209$			152.861i			0.731392i
$210$	99.9205	−	184.811i	0.475812	−	0.880052i
$211$		−	4.82651i		−	0.0228745i	−0.999935	−	0.0114372i	$-0.996359\pi$
$211$		−	4.82651i		−	0.0228745i	0.999935	−	0.0114372i	$-0.00364066\pi$
$212$	−104.677	−	244.333i	−0.493760	−	1.15251i
$213$	53.5892	+	92.8192i	0.251592	+	0.435771i
$214$	16.5098	+	80.4606i	0.0771485	+	0.375984i
$215$	44.5407	+	25.7156i	0.207166	+	0.119607i
$216$	−34.1400	+	23.7163i	−0.158055	+	0.109798i
$217$	42.8092	+	35.9137i	0.197277	+	0.165501i
$218$	−251.925	−	83.8258i	−1.15562	−	0.384522i
$219$	−48.5518	−	28.0314i	−0.221698	−	0.127997i
$220$	−385.814	−	46.0654i	−1.75370	−	0.209388i
$221$	460.070	−	265.621i	2.08176	−	1.20191i
$222$	33.9520	−	30.1393i	0.152937	−	0.135763i
$223$			81.4317i			0.365164i	0.983191	+	0.182582i	$0.0584456\pi$
$223$			81.4317i			0.365164i	−0.983191	+	0.182582i	$0.941554\pi$
$224$	−149.932	+	166.423i	−0.669338	+	0.742958i
$225$	150.200			0.667555
$226$	200.125	+	225.441i	0.885511	+	0.997528i
$227$	158.218	+	274.041i	0.696995	+	1.20723i	0.969504	+	0.245077i	$0.0788132\pi$
$227$	158.218	+	274.041i	0.696995	+	1.20723i	−0.272509	+	0.962153i	$0.587854\pi$
$228$	−11.1988	+	93.7940i	−0.0491176	+	0.411377i
$229$	84.9134	−	147.074i	0.370801	−	0.642246i	−0.618888	−	0.785479i	$-0.712417\pi$
$229$	84.9134	−	147.074i	0.370801	−	0.642246i	0.989689	+	0.143233i	$0.0457499\pi$
$230$	−5.45980	+	16.4086i	−0.0237383	+	0.0713417i
$231$	23.5908	−	133.871i	0.102125	−	0.579528i
$232$	59.5801	+	85.7664i	0.256811	+	0.369683i
$233$	−73.4322	+	127.188i	−0.315160	+	0.545873i	−0.979471	−	0.201583i	$-0.935391\pi$
$233$	−73.4322	+	127.188i	−0.315160	+	0.545873i	0.664312	+	0.747456i	$0.268725\pi$
$234$	92.2630	−	18.9315i	0.394286	−	0.0809040i
$235$	−189.434	+	109.370i	−0.806104	+	0.465404i
$236$	91.4921	−	39.1970i	0.387678	−	0.166089i
$237$	−81.9492			−0.345777
$238$	−13.2417	−	473.608i	−0.0556374	−	1.98995i
$239$	−163.827			−0.685471			−0.342735	−	0.939432i	$-0.611353\pi$
$239$	−163.827			−0.685471			−0.342735	+	0.939432i	$0.611353\pi$
$240$	−233.357	−	56.5305i	−0.972321	−	0.235544i
$241$	−139.660	+	80.6329i	−0.579503	+	0.334576i	−0.760936	−	0.648827i	$-0.775260\pi$
$241$	−139.660	+	80.6329i	−0.579503	+	0.334576i	0.181433	+	0.983403i	$0.441927\pi$
$242$	−9.20871	+	1.88954i	−0.0380525	+	0.00780803i
$243$	7.79423	−	13.5000i	0.0320750	−	0.0555556i
$244$	−306.472	−	229.344i	−1.25603	−	0.939933i
$245$	73.8070	+	418.076i	0.301253	+	1.70643i
$246$	2.15316	+	0.716443i	0.00875268	+	0.00291237i
$247$	107.011	−	185.349i	0.433244	−	0.750401i
$248$	27.2041	−	57.7772i	0.109694	−	0.232972i
$249$	−101.620	−	176.011i	−0.408112	−	0.706870i
$250$	288.358	+	324.835i	1.15343	+	1.29934i
$251$	−107.745			−0.429263			−0.214631	−	0.976695i	$-0.568855\pi$
$251$	−107.745			−0.429263			−0.214631	+	0.976695i	$0.568855\pi$
$252$	24.2827	−	80.4136i	0.0963598	−	0.319102i
$253$			11.1889i			0.0442249i
$254$	191.381	+	215.591i	0.753470	+	0.848784i
$255$	439.821	−	253.931i	1.72479	−	0.995806i
$256$	227.619	+	117.156i	0.889137	+	0.457642i
$257$	10.8076	+	6.23980i	0.0420531	+	0.0242794i	0.520879	−	0.853630i	$-0.325604\pi$
$257$	10.8076	+	6.23980i	0.0420531	+	0.0242794i	−0.478826	+	0.877910i	$0.658938\pi$
$258$	19.5116	+	6.49229i	0.0756262	+	0.0251639i
$259$	−15.9212	+	90.3479i	−0.0614717	+	0.348834i
$260$	435.564	+	325.948i	1.67525	+	1.25365i
$261$	−33.9147	−	19.5807i	−0.129941	−	0.0750217i
$262$	−493.708	+	101.304i	−1.88438	+	0.386658i
$263$	−213.667	−	370.083i	−0.812423	−	1.40716i	−0.911163	−	0.412045i	$-0.864815\pi$
$263$	−213.667	−	370.083i	−0.812423	−	1.40716i	0.0987400	−	0.995113i	$-0.468519\pi$
$264$	−154.811	+	12.9641i	−0.586405	+	0.0491063i
$265$			575.755i			2.17266i
$266$	−100.022	−	162.573i	−0.376022	−	0.611178i
$267$		−	202.502i		−	0.758436i
$268$	−53.9808	−	126.000i	−0.201421	−	0.470149i
$269$	−44.8327	−	77.6525i	−0.166664	−	0.288671i	0.770581	−	0.637342i	$-0.219966\pi$
$269$	−44.8327	−	77.6525i	−0.166664	−	0.288671i	−0.937245	+	0.348671i	$0.886633\pi$
$270$	88.2023	−	18.0983i	0.326675	−	0.0670308i
$271$	358.921	+	207.223i	1.32443	+	0.764661i	0.984432	−	0.175764i	$-0.0562396\pi$
$271$	358.921	+	207.223i	1.32443	+	0.764661i	0.340000	+	0.940425i	$0.389573\pi$
$272$	−519.494	+	152.723i	−1.90991	+	0.561481i
$273$	−122.322	+	145.808i	−0.448066	+	0.534096i
$274$	117.160	−	352.106i	0.427591	−	1.28506i
$275$	486.124	+	280.664i	1.76772	+	1.02060i
$276$	−0.819715	+	6.86541i	−0.00296998	+	0.0248747i
$277$	155.672	−	89.8772i	0.561992	−	0.324466i	−0.191953	−	0.981404i	$-0.561482\pi$
$277$	155.672	−	89.8772i	0.561992	−	0.324466i	0.753945	+	0.656938i	$0.228149\pi$
$278$	235.215	+	264.970i	0.846097	+	0.953129i
$279$			23.9480i			0.0858350i
$280$	440.470	−	203.458i	1.57311	−	0.726636i
$281$	139.706			0.497175			0.248588	−	0.968609i	$-0.420034\pi$
$281$	139.706			0.497175			0.248588	+	0.968609i	$0.420034\pi$
$282$	−65.4047	+	58.0601i	−0.231932	+	0.205887i
$283$	−131.928	−	228.505i	−0.466176	−	0.807440i	0.533078	−	0.846066i	$-0.321035\pi$
$283$	−131.928	−	228.505i	−0.466176	−	0.807440i	−0.999254	+	0.0386263i	$0.987702\pi$
$284$	−29.3447	+	245.772i	−0.103326	+	0.865395i
$285$	102.302	−	177.191i	0.358953	−	0.621725i
$286$	333.986	+	111.131i	1.16778	+	0.388569i
$287$	−4.30878	+	1.56877i	−0.0150132	+	0.00546610i
$288$	−95.9402	−	3.38703i	−0.333126	−	0.0117605i
$289$	428.154	−	741.584i	1.48150	−	2.56603i
$290$	−45.4666	−	221.582i	−0.156781	−	0.764075i
$291$	73.4627	−	42.4137i	0.252449	−	0.145752i
$292$	−50.9861	−	119.010i	−0.174610	−	0.407567i
$293$	−330.985			−1.12964			−0.564821	−	0.825213i	$-0.691055\pi$
$293$	−330.985			−1.12964			−0.564821	+	0.825213i	$0.691055\pi$
$294$	62.5063	+	157.813i	0.212606	+	0.536779i
$295$	−215.595			−0.730831
$296$	104.480	−	8.74930i	0.352973	−	0.0295584i
$297$	50.4523	−	29.1286i	0.169873	−	0.0980762i
$298$	9.55072	+	46.5456i	0.0320494	+	0.156193i
$299$	7.83287	−	13.5669i	0.0261969	−	0.0453744i
$300$	277.719	+	207.827i	0.925731	+	0.692756i
$301$	−39.0455	+	14.2159i	−0.129719	+	0.0472291i
$302$	−56.6423	+	170.230i	−0.187557	+	0.563674i
$303$	−86.4170	+	149.679i	−0.285205	+	0.493989i
$304$	−150.486	+	157.929i	−0.495021	+	0.519505i
$305$	414.560	+	718.039i	1.35921	+	2.35423i
$306$	151.854	−	134.801i	0.496255	−	0.440528i
$307$	−4.65829			−0.0151736			−0.00758680	−	0.999971i	$-0.502415\pi$
$307$	−4.65829			−0.0151736			−0.00758680	+	0.999971i	$0.502415\pi$
$308$	228.852	−	214.885i	0.743027	−	0.697679i
$309$			250.740i			0.811456i
$310$	−103.446	+	91.8298i	−0.333698	+	0.296225i
$311$	−276.765	+	159.790i	−0.889919	+	0.513795i	−0.873916	−	0.486077i	$-0.838428\pi$
$311$	−276.765	+	159.790i	−0.889919	+	0.513795i	−0.0160032	+	0.999872i	$0.505094\pi$
$312$	196.789	+	92.6571i	0.630734	+	0.296978i
$313$	−372.667	−	215.159i	−1.19063	−	0.687410i	−0.232180	−	0.972673i	$-0.574586\pi$
$313$	−372.667	−	215.159i	−1.19063	−	0.687410i	−0.958449	+	0.285262i	$0.907919\pi$
$314$	122.182	−	367.198i	0.389114	−	1.16942i
$315$	−116.938	+	139.391i	−0.371233	+	0.442511i
$316$	−151.524	−	113.391i	−0.479506	−	0.358831i
$317$	−34.9652	−	20.1872i	−0.110300	−	0.0636819i	0.443835	−	0.896109i	$-0.353618\pi$
$317$	−34.9652	−	20.1872i	−0.110300	−	0.0636819i	−0.554135	+	0.832427i	$0.686951\pi$
$318$	46.2709	+	225.502i	0.145506	+	0.709125i
$319$	−73.1769	−	126.746i	−0.229395	−	0.397323i
$320$	−353.257	−	427.414i	−1.10393	−	1.33567i
$321$		−	71.1327i		−	0.221597i
$322$	−7.32126	−	11.8998i	−0.0227368	−	0.0369560i
$323$		−	461.412i		−	1.42852i
$324$	33.0910	−	14.1768i	0.102133	−	0.0437557i
$325$	−392.962	−	680.630i	−1.20911	−	2.09424i
$326$	−30.1250	−	146.814i	−0.0924079	−	0.450351i
$327$	199.129	+	114.967i	0.608957	+	0.351582i
$328$	2.98987	+	4.30396i	0.00911545	+	0.0131218i
$329$	30.6704	−	174.045i	0.0932230	−	0.529013i
$330$	319.287	+	106.240i	0.967535	+	0.321938i
$331$	189.572	+	109.449i	0.572725	+	0.330663i	0.758237	−	0.651979i	$-0.226061\pi$
$331$	189.572	+	109.449i	0.572725	+	0.330663i	−0.185512	+	0.982642i	$0.559394\pi$
$332$	55.6456	−	466.052i	0.167607	−	1.40377i
$333$	−34.0496	+	19.6586i	−0.102251	+	0.0590348i
$334$	−465.488	+	413.216i	−1.39368	+	1.23717i
$335$			296.910i			0.886300i
$336$	156.164	−	115.085i	0.464775	−	0.342516i
$337$	−415.576			−1.23316			−0.616582	−	0.787291i	$-0.711483\pi$
$337$	−415.576			−1.23316			−0.616582	+	0.787291i	$0.711483\pi$
$338$	−102.784	−	115.786i	−0.304095	−	0.342563i
$339$	−130.533	−	226.090i	−0.385053	−	0.666932i
$340$	1164.58	+	139.049i	3.42525	+	0.408967i
$341$	−44.7492	+	77.5080i	−0.131229	+	0.227296i
$342$	25.8276	−	77.6207i	0.0755192	−	0.226961i
$343$	−297.100	−	171.408i	−0.866180	−	0.499732i
$344$	27.0937	+	39.0018i	0.0787607	+	0.113377i
$345$	7.48813	−	12.9698i	0.0217047	−	0.0375937i
$346$	13.8052	−	2.83271i	0.0398995	−	0.00818702i
$347$	−156.085	+	90.1160i	−0.449814	+	0.259700i	−0.707752	−	0.706461i	$-0.750290\pi$
$347$	−156.085	+	90.1160i	−0.449814	+	0.259700i	0.257938	+	0.966162i	$0.416957\pi$
$348$	−35.6151	−	83.1313i	−0.102342	−	0.238883i
$349$	−131.310			−0.376247			−0.188123	−	0.982145i	$-0.560240\pi$
$349$	−131.310			−0.376247			−0.188123	+	0.982145i	$0.560240\pi$
$350$	−700.659	+	19.5899i	−2.00188	+	0.0559710i
$351$	−81.5668			−0.232384
$352$	−304.183	−	190.236i	−0.864156	−	0.540444i
$353$	359.128	−	207.342i	1.01736	−	0.587372i	0.104021	−	0.994575i	$-0.466829\pi$
$353$	359.128	−	207.342i	1.01736	−	0.587372i	0.913338	+	0.407203i	$0.133496\pi$
$354$	−84.4405	+	17.3264i	−0.238533	+	0.0489447i
$355$	268.065	−	464.302i	0.755112	−	1.30789i
$356$	280.196	−	374.426i	0.787068	−	1.05176i
$357$	−71.2092	+	404.091i	−0.199465	+	1.13191i
$358$	−92.0468	−	30.6277i	−0.257114	−	0.0855523i
$359$	−193.471	+	335.101i	−0.538915	+	0.933429i	0.460048	+	0.887894i	$0.347832\pi$
$359$	−193.471	+	335.101i	−0.538915	+	0.933429i	−0.998963	+	0.0455343i	$0.985501\pi$
$360$	188.128	+	88.5790i	0.522578	+	0.246053i
$361$	87.5549	+	151.650i	0.242534	+	0.420082i
$362$	−132.805	−	149.605i	−0.366865	−	0.413274i
$363$	8.14113			0.0224274
$364$	−427.923	+	100.346i	−1.17561	+	0.275676i
$365$			280.439i			0.768325i
$366$	220.073	+	247.913i	0.601293	+	0.677357i
$367$	393.315	−	227.081i	1.07170	−	0.618748i	0.143057	−	0.989714i	$-0.454307\pi$
$367$	393.315	−	227.081i	1.07170	−	0.618748i	0.928646	+	0.370966i	$0.120973\pi$
$368$	−11.0151	+	11.5599i	−0.0299323	+	0.0314128i
$369$	−1.70192	−	0.982603i	−0.00461225	−	0.00266288i
$370$	−215.483	−	71.6999i	−0.582386	−	0.193783i
$371$	−356.372	−	298.969i	−0.960573	−	0.805847i
$372$	−33.1361	+	44.2798i	−0.0890754	+	0.119032i
$373$	394.924	+	228.009i	1.05878	+	0.611285i	0.925094	−	0.379739i	$-0.123986\pi$
$373$	394.924	+	228.009i	1.05878	+	0.611285i	0.133683	+	0.991024i	$0.457319\pi$
$374$	743.368	−	152.532i	1.98761	−	0.407840i
$375$	−188.083	−	325.770i	−0.501555	−	0.868719i
$376$	−201.269	+	16.8545i	−0.535290	+	0.0448259i
$377$			204.912i			0.543534i
$378$	−34.5981	+	63.9920i	−0.0915294	+	0.169291i
$379$			31.8832i			0.0841245i	0.999115	+	0.0420623i	$0.0133928\pi$
$379$			31.8832i			0.0841245i	−0.999115	+	0.0420623i	$0.986607\pi$
$380$	434.330	−	186.075i	1.14297	−	0.489672i
$381$	−124.830	−	216.211i	−0.327637	−	0.567484i
$382$	−128.030	+	26.2707i	−0.335158	+	0.0687714i
$383$	500.563	+	289.000i	1.30695	+	0.754569i	0.981586	−	0.191019i	$-0.0611793\pi$
$383$	500.563	+	289.000i	1.30695	+	0.754569i	0.325366	+	0.945588i	$0.394513\pi$
$384$	−172.707	−	139.012i	−0.449757	−	0.362011i
$385$	−638.939	+	232.629i	−1.65958	+	0.604232i
$386$	−62.1655	+	186.829i	−0.161050	+	0.484012i
$387$	−15.4225	−	8.90419i	−0.0398514	−	0.0230082i
$388$	194.519	+	23.2251i	0.501337	+	0.0598586i
$389$	343.343	−	198.229i	0.882631	−	0.509587i	0.0111058	−	0.999938i	$-0.496465\pi$
$389$	343.343	−	198.229i	0.882631	−	0.509587i	0.871525	+	0.490351i	$0.163131\pi$
$390$	−312.772	−	352.338i	−0.801980	−	0.903431i
$391$		−	33.7738i		−	0.0863781i
$392$	−102.787	+	378.284i	−0.262212	+	0.965010i
$393$	436.472			1.11062
$394$	117.386	−	104.205i	0.297935	−	0.264478i
$395$	204.964	+	355.008i	0.518896	+	0.898755i
$396$	133.591	+	15.9504i	0.337350	+	0.0402788i
$397$	−98.9328	+	171.357i	−0.249201	+	0.431629i	−0.963304	−	0.268412i	$-0.913501\pi$
$397$	−98.9328	+	171.357i	−0.249201	+	0.431629i	0.714103	+	0.700040i	$0.246835\pi$
$398$	196.294	+	65.3152i	0.493202	+	0.164108i
$399$	56.5538	+	155.330i	0.141739	+	0.389299i
$400$	225.939	+	768.543i	0.564848	+	1.92136i
$401$	−23.4522	+	40.6205i	−0.0584844	+	0.101298i	−0.893785	−	0.448495i	$-0.851960\pi$
$401$	−23.4522	+	40.6205i	−0.0584844	+	0.101298i	0.835301	+	0.549793i	$0.185293\pi$
$402$	23.8614	+	116.289i	0.0593566	+	0.289275i
$403$	108.520	−	62.6541i	0.269281	−	0.155469i
$404$	−366.890	+	157.183i	−0.908144	+	0.389067i
$405$	−77.9769			−0.192536
$406$	160.761	+	86.9174i	0.395962	+	0.214082i
$407$	−146.936			−0.361023
$408$	467.298	−	39.1322i	1.14534	−	0.0959122i
$409$	104.273	−	60.2022i	0.254947	−	0.147194i	−0.367080	−	0.930189i	$-0.619643\pi$
$409$	104.273	−	60.2022i	0.254947	−	0.147194i	0.622027	+	0.782996i	$0.286309\pi$
$410$	−2.28162	−	11.1195i	−0.00556492	−	0.0271207i
$411$	−160.685	+	278.315i	−0.390962	+	0.677165i
$412$	−346.941	+	463.618i	−0.842090	+	1.12529i
$413$	111.951	−	133.446i	0.271068	−	0.323114i
$414$	1.89049	−	5.68158i	0.00456641	−	0.0137236i
$415$	−508.325	+	880.445i	−1.22488	+	2.12155i
$416$	235.656	+	443.614i	0.566481	+	1.06638i
$417$	−153.420	−	265.732i	−0.367915	−	0.637247i
$418$	228.634	−	202.959i	0.546970	−	0.485548i
$419$	546.963			1.30540			0.652701	−	0.757616i	$-0.273636\pi$
$419$	546.963			1.30540			0.652701	+	0.757616i	$0.273636\pi$
$420$	−409.090	+	95.9296i	−0.974023	+	0.228404i
$421$		−	302.426i		−	0.718351i	−0.933270	−	0.359176i	$-0.883058\pi$
$421$		−	302.426i		−	0.718351i	0.933270	−	0.359176i	$-0.116942\pi$
$422$	−7.21900	+	6.40834i	−0.0171066	+	0.0151856i
$423$	65.5928	−	37.8700i	0.155066	−	0.0895273i
$424$	−226.465	+	480.976i	−0.534115	+	1.13438i
$425$	−1467.37	−	847.187i	−3.45264	−	1.99338i
$426$	67.6770	−	203.393i	0.158866	−	0.477448i
$427$	−659.708	−	116.254i	−1.54498	−	0.272258i
$428$	98.4240	−	131.524i	0.229963	−	0.307300i
$429$	−263.992	−	152.416i	−0.615367	−	0.355282i
$430$	−20.6756	−	100.763i	−0.0480829	−	0.234333i
$431$	281.450	+	487.485i	0.653015	+	1.13106i	0.982387	+	0.186856i	$0.0598296\pi$
$431$	281.450	+	487.485i	0.653015	+	1.13106i	−0.329372	+	0.944200i	$0.606837\pi$
$432$	80.8013	+	19.5741i	0.187040	+	0.0453103i
$433$		−	204.891i		−	0.473189i	−0.971609	−	0.236594i	$-0.923969\pi$
$433$		−	204.891i		−	0.473189i	0.971609	−	0.236594i	$-0.0760312\pi$
$434$	−3.12342	−	111.714i	−0.00719682	−	0.257405i
$435$			195.894i			0.450330i
$436$	209.113	+	488.103i	0.479616	+	1.11950i
$437$	−6.80327	−	11.7836i	−0.0155681	−	0.0269648i
$438$	22.5376	+	109.837i	0.0514557	+	0.250770i
$439$	−246.898	−	142.546i	−0.562409	−	0.324707i	0.191703	−	0.981453i	$-0.438599\pi$
$439$	−246.898	−	142.546i	−0.562409	−	0.324707i	−0.754112	+	0.656746i	$0.771932\pi$
$440$	443.360	+	638.224i	1.00764	+	1.45051i
$441$	−25.5561	−	144.761i	−0.0579504	−	0.328257i
$442$	−1008.14	−	335.449i	−2.28086	−	0.758935i
$443$	−705.036	−	407.052i	−1.59150	−	0.918854i	−0.993050	−	0.117696i	$-0.962449\pi$
$443$	−705.036	−	407.052i	−1.59150	−	0.918854i	−0.598453	−	0.801158i	$-0.704218\pi$
$444$	−90.1587	−	10.7648i	−0.203060	−	0.0242449i
$445$	−877.250	+	506.481i	−1.97135	+	1.13816i
$446$	121.797	−	108.120i	0.273088	−	0.242421i
$447$		−	41.1495i		−	0.0920570i
$448$	447.988	+	3.28694i	0.999973	+	0.00733692i
$449$	−451.470			−1.00550			−0.502750	−	0.864432i	$-0.667678\pi$
$449$	−451.470			−1.00550			−0.502750	+	0.864432i	$0.667678\pi$
$450$	−199.426	−	224.654i	−0.443169	−	0.499230i
$451$	−3.67219	−	6.36042i	−0.00814233	−	0.0141029i
$452$	71.4780	−	598.654i	0.158137	−	1.32446i
$453$	77.6850	−	134.554i	0.171490	−	0.297030i
$454$	199.811	−	600.501i	0.440112	−	1.32269i
$455$	937.589	+	165.223i	2.06064	+	0.363127i
$456$	155.157	−	107.784i	0.340256	−	0.236368i
$457$	334.931	−	580.117i	0.732890	−	1.26940i	−0.222753	−	0.974875i	$-0.571504\pi$
$457$	334.931	−	580.117i	0.732890	−	1.26940i	0.955643	−	0.294528i	$-0.0951625\pi$
$458$	−332.721	+	68.2714i	−0.726466	+	0.149064i
$459$	−152.291	+	87.9251i	−0.331788	+	0.191558i
$460$	31.7915	−	13.6201i	0.0691119	−	0.0296089i
$461$	426.215			0.924544			0.462272	−	0.886738i	$-0.347034\pi$
$461$	426.215			0.924544			0.462272	+	0.886738i	$0.347034\pi$
$462$	−231.553	+	142.461i	−0.501197	+	0.308357i
$463$	−5.80051			−0.0125281			−0.00626405	−	0.999980i	$-0.501994\pi$
$463$	−5.80051			−0.0125281			−0.00626405	+	0.999980i	$0.501994\pi$
$464$	49.1740	−	202.989i	0.105978	−	0.437477i
$465$	103.744	−	59.8965i	0.223105	−	0.128810i
$466$	287.734	−	59.0404i	0.617455	−	0.126696i
$467$	−215.428	+	373.132i	−0.461302	+	0.798998i	−0.999026	−	0.0441227i	$-0.985951\pi$
$467$	−215.428	+	373.132i	−0.461302	+	0.798998i	0.537724	+	0.843121i	$0.319284\pi$
$468$	−150.817	−	112.861i	−0.322258	−	0.241157i
$469$	−183.777	−	154.175i	−0.391849	−	0.328732i
$470$	415.104	+	138.122i	0.883199	+	0.293876i
$471$	−167.572	+	290.244i	−0.355780	+	0.616229i
$472$	−180.104	−	84.8012i	−0.381577	−	0.179664i
$473$	−33.2768	−	57.6371i	−0.0703526	−	0.121854i
$474$	108.807	+	122.571i	0.229551	+	0.258589i
$475$	−682.616			−1.43709
$476$	−690.793	+	648.633i	−1.45125	+	1.36268i
$477$		−	199.359i		−	0.417943i
$478$	217.520	+	245.036i	0.455063	+	0.512628i
$479$	−290.926	+	167.966i	−0.607362	+	0.350661i	−0.771932	−	0.635705i	$-0.780710\pi$
$479$	−290.926	+	167.966i	−0.607362	+	0.350661i	0.164570	+	0.986365i	$0.447376\pi$
$480$	225.284	+	424.089i	0.469342	+	0.883519i
$481$	178.165	+	102.864i	0.370406	+	0.213854i
$482$	306.035	+	101.830i	0.634927	+	0.211266i
$483$	4.13955	+	11.3697i	0.00857049	+	0.0235397i
$484$	15.0529	+	11.2646i	0.0311011	+	0.0232740i
$485$	−367.477	−	212.163i	−0.757684	−	0.437449i
$486$	−30.5406	+	6.26665i	−0.0628408	+	0.0128943i
$487$	334.353	+	579.116i	0.686556	+	1.18915i	0.972945	+	0.231036i	$0.0742117\pi$
$487$	334.353	+	579.116i	0.686556	+	1.18915i	−0.286389	+	0.958113i	$0.592455\pi$
$488$	63.8861	+	762.898i	0.130914	+	1.56332i
$489$			129.794i			0.265427i
$490$	527.319	−	665.488i	1.07616	−	1.35814i
$491$			729.226i			1.48518i	0.669744	+	0.742592i	$0.266404\pi$
$491$			729.226i			1.48518i	−0.669744	+	0.742592i	$0.733596\pi$
$492$	−1.78725	−	4.17172i	−0.00363262	−	0.00847911i
$493$	220.885	+	382.585i	0.448044	+	0.776034i
$494$	−419.309	+	86.0384i	−0.848804	+	0.174167i
$495$	−252.373	−	145.708i	−0.509845	−	0.294359i
$496$	−122.537	+	36.0239i	−0.247050	+	0.0726288i
$497$	148.190	+	407.018i	0.298169	+	0.818951i
$498$	−128.334	+	385.689i	−0.257699	+	0.774475i
$499$	696.518	+	402.135i	1.39583	+	0.805882i	0.993952	−	0.109812i	$-0.0350250\pi$
$499$	696.518	+	402.135i	1.39583	+	0.805882i	0.401876	+	0.915694i	$0.368358\pi$
$500$	102.992	−	862.593i	0.205983	−	1.72519i
$501$	466.827	−	269.523i	0.931790	−	0.537969i
$502$	143.057	+	161.154i	0.284974	+	0.321024i
$503$		−	383.284i		−	0.761997i	−0.924576	−	0.380998i	$-0.875580\pi$
$503$		−	383.284i		−	0.761997i	0.924576	−	0.380998i	$-0.124420\pi$
$504$	−152.516	+	70.4487i	−0.302610	+	0.139779i
$505$	864.554			1.71199
$506$	16.7352	−	14.8559i	0.0330735	−	0.0293595i
$507$	67.0416	+	116.119i	0.132232	+	0.229033i
$508$	68.3550	−	572.497i	0.134557	−	1.12696i
$509$	−46.4944	+	80.5307i	−0.0913446	+	0.158214i	−0.908077	−	0.418803i	$-0.862450\pi$
$509$	−46.4944	+	80.5307i	−0.0913446	+	0.158214i	0.816733	+	0.577016i	$0.195783\pi$
$510$	−963.770	−	320.686i	−1.88975	−	0.628795i
$511$	−173.582	−	145.622i	−0.339690	−	0.284974i
$512$	−126.988	−	496.002i	−0.248023	−	0.968754i
$513$	−35.4226	+	61.3537i	−0.0690498	+	0.119598i
$514$	−5.01687	−	24.4498i	−0.00976045	−	0.0475677i
$515$	1086.22	−	627.128i	2.10916	−	1.21773i
$516$	−16.1957	−	37.8035i	−0.0313871	−	0.0732625i
$517$	283.056			0.547498
$518$	156.272	−	96.1451i	0.301684	−	0.185608i
$519$	−12.2048			−0.0235160
$520$	−90.7962	−	1084.25i	−0.174608	−	2.08509i
$521$	−407.887	+	235.494i	−0.782893	+	0.452003i	−0.837454	−	0.546507i	$-0.815957\pi$
$521$	−407.887	+	235.494i	−0.782893	+	0.452003i	0.0545619	+	0.998510i	$0.482624\pi$
$522$	15.7431	+	76.7241i	0.0301592	+	0.146981i
$523$	347.347	−	601.622i	0.664143	−	1.15033i	−0.315374	−	0.948967i	$-0.602130\pi$
$523$	347.347	−	601.622i	0.664143	−	1.15033i	0.979517	−	0.201362i	$-0.0645367\pi$
$524$	807.036	+	603.933i	1.54015	+	1.15254i
$525$	597.814	+	105.347i	1.13869	+	0.200661i
$526$	−269.838	+	810.955i	−0.512999	+	1.54174i
$527$	135.076	−	233.959i	0.256311	−	0.443944i
$528$	224.939	+	214.337i	0.426020	+	0.405942i
$529$	264.002	+	457.265i	0.499059	+	0.864395i
$530$	861.156	−	764.452i	1.62482	−	1.44236i
$531$	74.6512			0.140586
$532$	−110.358	+	365.457i	−0.207440	+	0.686950i
$533$			10.2830i			0.0192926i
$534$	−302.882	+	268.870i	−0.567195	+	0.503502i
$535$	−308.150	+	177.911i	−0.575982	+	0.332543i
$536$	−116.785	+	248.034i	−0.217883	+	0.462749i
$537$	72.7565	+	42.0060i	0.135487	+	0.0782234i
$538$	−56.6186	+	170.158i	−0.105239	+	0.316280i
$539$	187.789	−	516.277i	0.348402	−	0.957842i
$540$	−144.179	−	107.894i	−0.266998	−	0.199804i
$541$	112.726	+	65.0826i	0.208367	+	0.120301i	0.600552	−	0.799586i	$-0.294948\pi$
$541$	112.726	+	65.0826i	0.208367	+	0.120301i	−0.392185	+	0.919886i	$0.628281\pi$
$542$	−166.610	−	811.976i	−0.307398	−	1.49811i
$543$	86.6230	+	150.035i	0.159527	+	0.276308i
$544$	918.180	+	574.231i	1.68783	+	1.05557i
$545$		−	1150.18i		−	2.11043i
$546$	380.497	−	10.6384i	0.696880	−	0.0194842i
$547$			795.308i			1.45395i	0.686666	+	0.726973i	$0.259073\pi$
$547$			795.308i			1.45395i	−0.686666	+	0.726973i	$0.740927\pi$
$548$	−682.202	+	292.269i	−1.24489	+	0.533337i
$549$	−143.544	−	248.626i	−0.261465	−	0.452870i
$550$	−225.657	−	1099.74i	−0.410286	−	1.99953i
$551$	154.133	+	88.9886i	0.279733	+	0.161504i
$552$	11.3569	−	7.88941i	0.0205742	−	0.0142924i
$553$	−326.168	−	57.4776i	−0.589816	−	0.103938i
$554$	−341.120	−	113.505i	−0.615741	−	0.204882i
$555$	170.324	+	98.3365i	0.306890	+	0.177183i
$556$	84.0108	−	703.621i	0.151099	−	1.26551i
$557$	−456.727	+	263.691i	−0.819976	+	0.473413i	−0.850408	−	0.526124i	$-0.823645\pi$
$557$	−456.727	+	263.691i	−0.819976	+	0.473413i	0.0304323	+	0.999537i	$0.490312\pi$
$558$	35.8189	−	31.7966i	0.0641916	−	0.0569832i
$559$			93.1826i			0.166695i
$560$	−889.141	−	388.671i	−1.58775	−	0.694055i
$561$	−657.188			−1.17146
$562$	−185.493	−	208.958i	−0.330059	−	0.371812i
$563$	36.9792	+	64.0499i	0.0656825	+	0.113765i	0.896997	−	0.442038i	$-0.145744\pi$
$563$	36.9792	+	64.0499i	0.0656825	+	0.113765i	−0.831314	+	0.555803i	$0.812411\pi$
$564$	173.681	+	20.7371i	0.307944	+	0.0367679i
$565$	−652.955	+	1130.95i	−1.15567	+	2.00168i
$566$	−166.610	+	500.719i	−0.294363	+	0.884663i
$567$	40.4906	−	48.2650i	0.0714121	−	0.0851234i
$568$	406.563	−	282.430i	0.715780	−	0.497236i
$569$	341.691	−	591.826i	0.600512	−	1.04012i	−0.392232	−	0.919866i	$-0.628297\pi$
$569$	341.691	−	591.826i	0.600512	−	1.04012i	0.992744	−	0.120250i	$-0.0383697\pi$
$570$	−400.855	+	82.2517i	−0.703254	+	0.144301i
$571$	473.012	−	273.094i	0.828392	−	0.478273i	−0.0249095	−	0.999690i	$-0.507930\pi$
$571$	473.012	−	273.094i	0.828392	−	0.478273i	0.853302	+	0.521417i	$0.174596\pi$
$572$	−277.228	−	647.095i	−0.484664	−	1.13128i
$573$	113.188			0.197535
$574$	8.06734	+	4.36172i	0.0140546	+	0.00759881i
$575$	−49.9652			−0.0868960
$576$	122.318	+	147.995i	0.212357	+	0.256935i
$577$	556.261	−	321.157i	0.964057	−	0.556599i	0.0666378	−	0.997777i	$-0.478773\pi$
$577$	556.261	−	321.157i	0.964057	−	0.556599i	0.897419	+	0.441179i	$0.145439\pi$
$578$	−1677.66	+	344.241i	−2.90253	+	0.595572i
$579$	85.2601	−	147.675i	0.147254	−	0.255051i
$580$	−271.052	+	362.207i	−0.467331	+	0.624495i
$581$	−281.009	−	771.819i	−0.483665	−	1.32843i
$582$	−160.977	−	53.5637i	−0.276593	−	0.0920338i
$583$	372.523	−	645.228i	0.638975	−	1.10674i
$584$	−110.306	+	234.273i	−0.188881	+	0.401153i
$585$	204.008	+	353.352i	0.348731	+	0.604020i
$586$	439.462	+	495.054i	0.749935	+	0.844802i
$587$	−271.221			−0.462046			−0.231023	−	0.972948i	$-0.574207\pi$
$587$	−271.221			−0.462046			−0.231023	+	0.972948i	$0.574207\pi$
$588$	153.049	−	303.025i	0.260287	−	0.515349i
$589$		−	108.837i		−	0.184782i
$590$	286.254	+	322.465i	0.485176	+	0.546551i
$591$	−117.724	+	67.9680i	−0.199195	+	0.115005i
$592$	−151.808	−	144.654i	−0.256433	−	0.244348i
$593$	280.252	+	161.804i	0.472600	+	0.272856i	0.717328	−	0.696736i	$-0.245365\pi$
$593$	280.252	+	161.804i	0.472600	+	0.272856i	−0.244727	+	0.969592i	$0.578698\pi$
$594$	−110.555	−	36.7861i	−0.186120	−	0.0619295i
$595$	1928.64	−	702.194i	3.24142	−	1.18016i
$596$	56.9372	−	76.0853i	0.0955323	−	0.127660i
$597$	−155.157	−	89.5798i	−0.259894	−	0.150050i
$598$	−30.6920	+	6.29773i	−0.0513245	+	0.0105313i
$599$	−47.3860	−	82.0750i	−0.0791086	−	0.137020i	0.823757	−	0.566943i	$-0.191874\pi$
$599$	−47.3860	−	82.0750i	−0.0791086	−	0.137020i	−0.902866	+	0.429923i	$0.858541\pi$
$600$	−57.8924	−	691.324i	−0.0964873	−	1.15221i
$601$		−	297.172i		−	0.494463i	−0.968956	−	0.247232i	$-0.920479\pi$
$601$		−	297.172i		−	0.494463i	0.968956	−	0.247232i	$-0.0795209\pi$
$602$	73.1049	+	39.5252i	0.121437	+	0.0656564i
$603$		−	102.807i		−	0.170493i
$604$	329.818	−	141.301i	0.546057	−	0.233941i
$605$	−20.3619	−	35.2678i	−0.0336560	−	0.0582939i
$606$	338.613	−	69.4803i	0.558767	−	0.114654i
$607$	625.913	+	361.371i	1.03116	+	0.595339i	0.917316	−	0.398160i	$-0.130351\pi$
$607$	625.913	+	361.371i	1.03116	+	0.595339i	0.113841	+	0.993499i	$0.463684\pi$
$608$	436.021	+	15.3931i	0.717140	+	0.0253176i
$609$	−121.251	−	101.721i	−0.199099	−	0.167029i
$610$	523.542	−	1573.43i	0.858266	−	2.57939i
$611$	−343.216	−	198.156i	−0.561728	−	0.324314i
$612$	−403.245	−	48.1465i	−0.658896	−	0.0786708i
$613$	−54.1732	+	31.2769i	−0.0883740	+	0.0510227i	−0.543536	−	0.839386i	$-0.682915\pi$
$613$	−54.1732	+	31.2769i	−0.0883740	+	0.0510227i	0.455162	+	0.890409i	$0.349581\pi$
$614$	6.18499	+	6.96740i	0.0100733	+	0.0113476i
$615$			9.83040i			0.0159844i
$616$	−625.259	−	56.9827i	−1.01503	−	0.0925043i
$617$	648.161			1.05050			0.525252	−	0.850947i	$-0.323971\pi$
$617$	648.161			1.05050			0.525252	+	0.850947i	$0.323971\pi$
$618$	375.031	−	332.917i	0.606847	−	0.538701i
$619$	−440.821	−	763.525i	−0.712151	−	1.23348i	−0.964048	−	0.265727i	$-0.914388\pi$
$619$	−440.821	−	763.525i	−0.712151	−	1.23348i	0.251898	−	0.967754i	$-0.418945\pi$
$620$	274.699	+	32.7985i	0.443063	+	0.0529008i
$621$	−2.59281	+	4.49088i	−0.00417522	+	0.00723170i
$622$	606.469	+	201.797i	0.975031	+	0.324432i
$623$	142.031	−	805.985i	0.227979	−	1.29372i
$624$	−122.697	−	417.361i	−0.196631	−	0.668848i
$625$	−315.001	+	545.598i	−0.504002	+	0.872957i
$626$	172.991	+	843.073i	0.276343	+	1.34676i
$627$	−229.291	+	132.381i	−0.365696	+	0.211135i
$628$	−711.442	+	304.796i	−1.13287	+	0.485344i
$629$	443.529			0.705133
$630$	363.750	−	10.1702i	0.577381	−	0.0161431i
$631$	983.113			1.55802			0.779012	−	0.627009i	$-0.215721\pi$
$631$	983.113			1.55802			0.779012	+	0.627009i	$0.215721\pi$
$632$	31.5862	+	377.187i	0.0499781	+	0.596815i
$633$	7.23977	−	4.17988i	0.0114372	−	0.00660329i
$634$	16.2307	+	79.1006i	0.0256005	+	0.124764i
$635$	−624.426	+	1081.54i	−0.983347	+	1.70321i
$636$	275.847	−	368.614i	0.433721	−	0.579582i
$637$	−589.124	+	494.541i	−0.924841	+	0.776359i
$638$	−92.4142	+	277.736i	−0.144850	+	0.435323i
$639$	−92.8192	+	160.768i	−0.145257	+	0.251592i
$640$	−170.249	+	1095.86i	−0.266013	+	1.71228i
$641$	340.966	+	590.571i	0.531929	+	0.921328i	0.999305	+	0.0372695i	$0.0118660\pi$
$641$	340.966	+	590.571i	0.531929	+	0.921328i	−0.467376	+	0.884058i	$0.654801\pi$
$642$	−106.393	+	94.4456i	−0.165721	+	0.147111i
$643$	−1.19182			−0.00185353			−0.000926763	−	1.00000i	$-0.500295\pi$
$643$	−1.19182			−0.00185353			−0.000926763		1.00000i	$0.500295\pi$
$644$	−8.07783	+	26.7502i	−0.0125432	+	0.0415376i
$645$			89.0814i			0.138111i
$646$	−690.133	+	612.635i	−1.06832	+	0.948351i
$647$	−250.570	+	144.667i	−0.387280	+	0.223596i	−0.680981	−	0.732301i	$-0.738446\pi$
$647$	−250.570	+	144.667i	−0.387280	+	0.223596i	0.293701	+	0.955897i	$0.405113\pi$
$648$	−65.1405	−	30.6711i	−0.100525	−	0.0473319i
$649$	241.610	+	139.493i	0.372280	+	0.214936i
$650$	−496.266	+	1491.45i	−0.763486	+	2.29454i
$651$	−16.7966	+	95.3159i	−0.0258013	+	0.146415i
$652$	−179.592	+	239.989i	−0.275448	+	0.368081i
$653$	222.449	+	128.431i	0.340656	+	0.196678i	0.660562	−	0.750771i	$-0.270318\pi$
$653$	222.449	+	128.431i	0.340656	+	0.196678i	−0.319906	+	0.947449i	$0.603651\pi$
$654$	−92.4350	−	450.483i	−0.141338	−	0.688812i
$655$	−1091.67	−	1890.82i	−1.66666	−	2.88675i
$656$	2.46766	−	10.1865i	0.00376168	−	0.0155282i
$657$		−	97.1037i		−	0.147799i
$658$	−301.041	+	185.213i	−0.457509	+	0.281478i
$659$		−	114.610i		−	0.173915i	−0.996212	−	0.0869576i	$-0.972286\pi$
$659$		−	114.610i		−	0.173915i	0.996212	−	0.0869576i	$-0.0277145\pi$
$660$	−265.027	−	618.615i	−0.401555	−	0.937295i
$661$	364.595	+	631.497i	0.551581	+	0.955366i	0.998161	+	0.0606225i	$0.0193086\pi$
$661$	364.595	+	631.497i	0.551581	+	0.955366i	−0.446580	+	0.894744i	$0.647358\pi$
$662$	−87.9987	−	428.863i	−0.132929	−	0.647829i
$663$	796.864	+	460.070i	1.20191	+	0.693921i
$664$	−770.955	+	535.566i	−1.16108	+	0.806575i
$665$	531.452	−	633.492i	0.799175	−	0.952620i
$666$	74.6123	+	24.8265i	0.112030	+	0.0372771i
$667$	11.2820	+	6.51367i	0.0169145	+	0.00976562i
$668$	1236.09	+	147.587i	1.85044	+	0.220938i
$669$	−122.148	+	70.5219i	−0.182582	+	0.105414i
$670$	444.088	−	394.219i	0.662818	−	0.588387i
$671$		−	1072.91i		−	1.59897i
$672$	−379.479	−	80.7714i	−0.564700	−	0.120196i
$673$	−423.130			−0.628723			−0.314361	−	0.949303i	$-0.601790\pi$
$673$	−423.130			−0.628723			−0.314361	+	0.949303i	$0.601790\pi$
$674$	551.777	+	621.577i	0.818660	+	0.922221i
$675$	130.077	+	225.300i	0.192707	+	0.333778i
$676$	−36.7110	+	307.468i	−0.0543063	+	0.454834i
$677$	−200.455	+	347.198i	−0.296093	+	0.512849i	−0.975239	−	0.221155i	$-0.929017\pi$
$677$	−200.455	+	347.198i	−0.296093	+	0.512849i	0.679145	+	0.734004i	$0.262351\pi$
$678$	−164.848	+	495.426i	−0.243139	+	0.730717i
$679$	322.139	−	117.287i	0.474431	−	0.172734i
$680$	−1338.29	−	1926.49i	−1.96807	−	2.83307i
$681$	−274.041	+	474.653i	−0.402410	+	0.696995i
$682$	175.344	−	35.9789i	0.257102	−	0.0527550i
$683$	−1155.01	+	666.848i	−1.69109	+	0.976351i	−0.737450	+	0.675402i	$0.763970\pi$
$683$	−1155.01	+	666.848i	−1.69109	+	0.976351i	−0.953640	+	0.300950i	$0.902696\pi$
$684$	−150.389	+	64.4298i	−0.219868	+	0.0941956i
$685$	1607.57			2.34681
$686$	138.096	+	671.956i	0.201306	+	0.979528i
$687$	294.149			0.428164
$688$	22.3616	−	92.3081i	0.0325023	−	0.134169i
$689$	−903.393	+	521.574i	−1.31117	+	0.757002i
$690$	−29.3412	+	6.02055i	−0.0425235	+	0.00872543i
$691$	542.994	−	940.493i	0.785809	−	1.36106i	−0.142706	−	0.989765i	$-0.545580\pi$
$691$	542.994	−	940.493i	0.785809	−	1.36106i	0.928515	−	0.371295i	$-0.121086\pi$
$692$	−22.5666	−	16.8874i	−0.0326107	−	0.0244037i
$693$	221.237	−	80.5494i	0.319245	−	0.116233i
$694$	342.027	+	113.806i	0.492834	+	0.163986i
$695$	−767.443	+	1329.25i	−1.10423	+	1.91259i
$696$	−77.0518	+	163.646i	−0.110707	+	0.235124i
$697$	11.0845	+	19.1990i	0.0159032	+	0.0275452i
$698$	174.345	+	196.400i	0.249778	+	0.281376i
$699$	−254.377			−0.363915
$700$	959.592	+	1021.96i	1.37085	+	1.45995i
$701$		−	656.518i		−	0.936544i	−0.883584	−	0.468272i	$-0.844877\pi$
$701$		−	656.518i		−	0.936544i	0.883584	−	0.468272i	$-0.155123\pi$
$702$	108.299	+	121.999i	0.154273	+	0.173788i
$703$	154.746	−	89.3427i	0.220122	−	0.127088i
$704$	119.339	+	707.550i	0.169516	+	1.00504i
$705$	−328.110	−	189.434i	−0.465404	−	0.268701i
$706$	−786.949	−	261.850i	−1.11466	−	0.370892i
$707$	−448.932	+	535.128i	−0.634982	+	0.756900i
$708$	138.030	+	103.293i	0.194958	+	0.145893i
$709$	−746.403	−	430.936i	−1.05275	−	0.607808i	−0.129335	−	0.991601i	$-0.541284\pi$
$709$	−746.403	−	430.936i	−1.05275	−	0.607808i	−0.923419	+	0.383793i	$0.874618\pi$
$710$	−1050.38	+	215.527i	−1.47940	+	0.303560i
$711$	−70.9701	−	122.924i	−0.0998173	−	0.172889i
$712$	−932.056	+	78.0516i	−1.30907	+	0.109623i
$713$		−	7.96649i		−	0.0111732i
$714$	698.945	−	430.019i	0.978914	−	0.602268i
$715$			1524.84i			2.13264i
$716$	76.4043	+	178.340i	0.106710	+	0.249078i
$717$	−141.879	−	245.741i	−0.197878	−	0.342735i
$718$	758.088	−	155.553i	1.05583	−	0.216647i
$719$	−598.298	−	345.428i	−0.832126	−	0.480428i	0.0224543	−	0.999748i	$-0.492852\pi$
$719$	−598.298	−	345.428i	−0.832126	−	0.480428i	−0.854580	+	0.519320i	$0.826185\pi$
$720$	−117.297	−	398.992i	−0.162913	−	0.554156i
$721$	−175.864	+	997.977i	−0.243917	+	1.38416i
$722$	110.572	−	332.307i	0.153147	−	0.460259i
$723$	−241.899	−	139.660i	−0.334576	−	0.193168i
$724$	−47.4335	+	397.273i	−0.0655159	+	0.548719i
$725$	565.998	−	326.779i	0.780687	−	0.450730i
$726$	−10.8093	−	12.1767i	−0.0148888	−	0.0167723i
$727$			930.093i			1.27936i	0.768642	+	0.639679i	$0.220933\pi$
$727$			930.093i			1.27936i	−0.768642	+	0.639679i	$0.779067\pi$
$728$	718.258	+	506.811i	0.986618	+	0.696169i
$729$	27.0000			0.0370370
$730$	419.451	−	372.349i	0.574591	−	0.510067i
$731$	100.446	+	173.978i	0.137409	+	0.238000i
$732$	78.6027	−	658.326i	0.107381	−	0.899353i
$733$	340.313	−	589.440i	0.464275	−	0.804147i	−0.534894	−	0.844919i	$-0.679648\pi$
$733$	340.313	−	589.440i	0.464275	−	0.804147i	0.999168	+	0.0407720i	$0.0129817\pi$
$734$	−861.864	−	286.777i	−1.17420	−	0.390704i
$735$	−563.195	+	472.775i	−0.766252	+	0.643231i
$736$	31.9153	+	1.12672i	0.0433632	+	0.00153087i
$737$	192.106	−	332.737i	0.260659	−	0.451475i
$738$	0.790025	+	3.85020i	0.00107049	+	0.00521707i
$739$	−571.849	+	330.157i	−0.773815	+	0.446762i	−0.834234	−	0.551411i	$-0.814090\pi$
$739$	−571.849	+	330.157i	−0.773815	+	0.446762i	0.0604187	+	0.998173i	$0.480756\pi$
$740$	178.863	+	417.496i	0.241707	+	0.564183i
$741$	370.698			0.500268
$742$	26.0014	+	929.978i	0.0350424	+	1.25334i
$743$	−178.644			−0.240435			−0.120218	−	0.992748i	$-0.538359\pi$
$743$	−178.644			−0.240435			−0.120218	+	0.992748i	$0.538359\pi$
$744$	110.225	−	9.23040i	0.148152	−	0.0124065i
$745$	−178.262	+	102.919i	−0.239277	+	0.138147i
$746$	−183.322	−	893.423i	−0.245740	−	1.19762i
$747$	176.011	−	304.860i	0.235623	−	0.408112i
$748$	−1215.14	−	909.331i	−1.62452	−	1.21568i
$749$	49.8911	−	283.117i	0.0666102	−	0.377993i
$750$	−237.528	+	713.853i	−0.316704	+	0.951804i
$751$	−379.327	+	657.013i	−0.505095	+	0.874851i	0.494887	+	0.868957i	$0.335209\pi$
$751$	−379.327	+	657.013i	−0.505095	+	0.874851i	−0.999983	+	0.00589360i	$0.998124\pi$
$752$	292.442	+	278.659i	0.388886	+	0.370558i
$753$	−93.3099	−	161.617i	−0.123918	−	0.214631i
$754$	306.487	−	272.070i	0.406481	−	0.360835i
$755$	−777.195			−1.02940
$756$	141.650	−	33.2162i	0.187368	−	0.0439368i
$757$			121.445i			0.160430i	0.996778	+	0.0802148i	$0.0255606\pi$
$757$			121.445i			0.160430i	−0.996778	+	0.0802148i	$0.974439\pi$
$758$	47.6876	−	42.3325i	0.0629124	−	0.0558477i
$759$	−16.7834	+	9.68987i	−0.0221125	+	0.0127666i
$760$	−854.989	−	402.567i	−1.12498	−	0.529693i
$761$	266.676	+	153.966i	0.350429	+	0.202320i	0.664874	−	0.746955i	$-0.268485\pi$
$761$	266.676	+	153.966i	0.350429	+	0.202320i	−0.314445	+	0.949276i	$0.601818\pi$
$762$	−157.646	+	473.780i	−0.206884	+	0.621758i
$763$	711.923	+	597.249i	0.933057	+	0.782764i
$764$	209.284	+	156.614i	0.273932	+	0.204992i
$765$	761.792	+	439.821i	0.995806	+	0.574929i
$766$	−232.359	−	1132.41i	−0.303341	−	1.47834i
$767$	−195.307	−	338.281i	−0.254637	−	0.441045i
$768$	21.3893	+	442.889i	0.0278507	+	0.576678i
$769$		−	92.7247i		−	0.120578i	−0.998181	−	0.0602891i	$-0.980798\pi$
$769$		−	92.7247i		−	0.120578i	0.998181	−	0.0602891i	$-0.0192023\pi$
$770$	1196.29	+	646.788i	1.55362	+	0.839985i
$771$			21.6153i			0.0280354i
$772$	361.979	−	155.079i	0.468884	−	0.200879i
$773$	527.812	+	914.197i	0.682809	+	1.18266i	0.974120	+	0.226032i	$0.0725754\pi$
$773$	527.812	+	914.197i	0.682809	+	1.18266i	−0.291311	+	0.956629i	$0.594091\pi$
$774$	7.15907	+	34.8898i	0.00924945	+	0.0450773i
$775$	−346.120	−	199.832i	−0.446606	−	0.257848i
$776$	−223.532	−	321.778i	−0.288057	−	0.414663i
$777$	−149.310	+	54.3618i	−0.192162	+	0.0699637i
$778$	−752.361	−	250.341i	−0.967045	−	0.321775i
$779$	7.73474	+	4.46565i	0.00992906	+	0.00573255i
$780$	−111.712	+	935.626i	−0.143220	+	1.19952i
$781$	−600.821	+	346.884i	−0.769297	+	0.444154i
$782$	−50.5154	+	44.8428i	−0.0645978	+	0.0573437i
$783$		−	67.8294i		−	0.0866276i
$784$	702.273	−	348.524i	0.895756	−	0.444546i
$785$	1676.47			2.13563
$786$	−579.521	−	652.830i	−0.737304	−	0.830573i
$787$	113.609	+	196.776i	0.144357	+	0.250033i	0.929133	−	0.369746i	$-0.120555\pi$
$787$	113.609	+	196.776i	0.144357	+	0.250033i	−0.784776	+	0.619779i	$0.787222\pi$
$788$	−311.717	−	37.2183i	−0.395580	−	0.0472314i
$789$	370.083	−	641.002i	0.469053	−	0.812423i
$790$	258.846	−	777.922i	0.327654	−	0.984712i
$791$	−360.963	−	991.419i	−0.456337	−	1.25337i
$792$	−153.516	−	220.989i	−0.193834	−	0.279027i
$793$	−751.097	+	1300.94i	−0.947159	+	1.64053i
$794$	387.654	−	79.5431i	0.488230	−	0.100180i
$795$	−863.633	+	498.619i	−1.08633	+	0.627193i
$796$	−162.936	−	380.319i	−0.204693	−	0.477787i
$797$	−623.447			−0.782243			−0.391121	−	0.920339i	$-0.627913\pi$
$797$	−623.447			−0.782243			−0.391121	+	0.920339i	$0.627913\pi$
$798$	157.239	−	290.825i	0.197041	−	0.364443i
$799$	−854.409			−1.06935
$800$	849.520	−	1358.36i	1.06190	−	1.69795i
$801$	303.753	−	175.372i	0.379218	−	0.218941i
$802$	91.8944	−	18.8559i	0.114582	−	0.0235111i
$803$	181.448	−	314.277i	0.225963	−	0.391379i
$804$	142.251	−	190.090i	0.176929	−	0.236431i
$805$	38.9005	−	46.3695i	0.0483236	−	0.0576019i
$806$	−237.798	−	79.1250i	−0.295034	−	0.0981699i
$807$	77.6525	−	134.498i	0.0962237	−	0.166664i
$808$	722.233	+	340.059i	0.893852	+	0.420865i
$809$	−466.973	−	808.821i	−0.577222	−	0.999778i	−0.995796	−	0.0915957i	$-0.970803\pi$
$809$	−466.973	−	808.821i	−0.577222	−	0.999778i	0.418574	−	0.908183i	$-0.362530\pi$
$810$	103.533	+	116.630i	0.127818	+	0.143988i
$811$	−110.425			−0.136159			−0.0680795	−	0.997680i	$-0.521687\pi$
$811$	−110.425			−0.136159			−0.0680795	+	0.997680i	$0.521687\pi$
$812$	−83.4458	−	355.853i	−0.102766	−	0.438242i
$813$			717.842i			0.882955i
$814$	195.093	+	219.772i	0.239672	+	0.269990i
$815$	562.274	−	324.629i	0.689907	−	0.398318i
$816$	−678.980	−	646.980i	−0.832083	−	0.792867i
$817$	70.0909	+	40.4670i	0.0857906	+	0.0495312i
$818$	−228.492	−	76.0285i	−0.279330	−	0.0929444i
$819$	−324.646	−	57.2094i	−0.396394	−	0.0698527i
$820$	−13.6020	+	18.1764i	−0.0165878	+	0.0221663i
$821$	−771.380	−	445.357i	−0.939562	−	0.542456i	−0.0497389	−	0.998762i	$-0.515839\pi$
$821$	−771.380	−	445.357i	−0.939562	−	0.542456i	−0.889823	+	0.456306i	$0.849172\pi$
$822$	629.623	−	129.193i	0.765965	−	0.157169i
$823$	−352.585	−	610.696i	−0.428415	−	0.742036i	0.568318	−	0.822809i	$-0.307594\pi$
$823$	−352.585	−	610.696i	−0.428415	−	0.742036i	−0.996733	+	0.0807732i	$0.974261\pi$
$824$	1154.08	−	96.6441i	1.40058	−	0.117287i
$825$			972.248i			1.17848i
$826$	−348.236	+	9.73641i	−0.421594	+	0.0117874i
$827$		−	721.630i		−	0.872588i	−0.899804	−	0.436294i	$-0.856291\pi$
$827$		−	721.630i		−	0.872588i	0.899804	−	0.436294i	$-0.143709\pi$
$828$	−11.0080	+	4.71604i	−0.0132947	+	0.00569570i
$829$	−401.589	−	695.572i	−0.484426	−	0.839050i	0.515414	−	0.856941i	$-0.327638\pi$
$829$	−401.589	−	695.572i	−0.484426	−	0.839050i	−0.999840	+	0.0178913i	$0.994305\pi$
$830$	1991.80	−	408.699i	2.39976	−	0.492409i
$831$	269.632	+	155.672i	0.324466	+	0.187331i
$832$	350.622	−	941.473i	0.421421	−	1.13158i
$833$	−566.843	+	1558.39i	−0.680484	+	1.87081i
$834$	−193.753	+	582.293i	−0.232317	+	0.698193i
$835$	−2335.17	−	1348.21i	−2.79661	−	1.61463i
$836$	−607.131	−	72.4902i	−0.726233	−	0.0867107i
$837$	−35.9220	+	20.7396i	−0.0429175	+	0.0247784i
$838$	−726.224	−	818.091i	−0.866615	−	0.976243i
$839$		−	1150.33i		−	1.37107i	−0.728037	−	0.685537i	$-0.759567\pi$
$839$		−	1150.33i		−	1.37107i	0.728037	−	0.685537i	$-0.240433\pi$
$840$	686.645	+	484.505i	0.817435	+	0.576792i
$841$	670.599			0.797383
$842$	−452.338	+	401.542i	−0.537218	+	0.476891i
$843$	120.989	+	209.559i	0.143522	+	0.248588i
$844$	19.1699	+	2.28884i	0.0227131	+	0.00271190i
$845$	335.357	−	580.855i	0.396872	−	0.687403i
$846$	−143.732	−	47.8256i	−0.169896	−	0.0565314i
$847$	32.4027	+	5.71003i	0.0382559	+	0.00674148i
$848$	1020.08	−	299.887i	1.20292	−	0.353640i
$849$	228.505	−	395.783i	0.269147	−	0.466176i
$850$	681.149	+	3319.59i	0.801352	+	3.90540i
$851$	11.3269	−	6.53958i	0.0133101	−	0.00768459i
$852$	−394.072	+	168.828i	−0.462525	+	0.198155i
$853$	247.862			0.290576			0.145288	−	0.989389i	$-0.453589\pi$
$853$	247.862			0.290576			0.145288	+	0.989389i	$0.453589\pi$
$854$	702.038	+	1141.08i	0.822059	+	1.33616i
$855$	354.383			0.414483
$856$	−327.402	+	27.4171i	−0.382479	+	0.0320293i
$857$	−1410.46	+	814.329i	−1.64581	+	0.950209i	−0.667099	+	0.744969i	$0.732464\pi$
$857$	−1410.46	+	814.329i	−1.64581	+	0.950209i	−0.978712	+	0.205241i	$0.934202\pi$
$858$	122.544	+	597.221i	0.142826	+	0.696062i
$859$	490.166	−	848.992i	0.570624	−	0.988349i	−0.425878	−	0.904780i	$-0.640035\pi$
$859$	490.166	−	848.992i	0.570624	−	0.988349i	0.996502	−	0.0835688i	$-0.0266318\pi$
$860$	−123.259	+	164.711i	−0.143325	+	0.191525i
$861$	−6.08467	−	5.10458i	−0.00706698	−	0.00592866i
$862$	355.439	−	1068.22i	0.412342	−	1.23923i
$863$	333.473	−	577.592i	0.386411	−	0.669284i	−0.605552	−	0.795805i	$-0.707048\pi$
$863$	333.473	−	577.592i	0.386411	−	0.669284i	0.991964	+	0.126521i	$0.0403811\pi$
$864$	−78.0061	−	146.844i	−0.0902849	−	0.169958i
$865$	30.5255	+	52.8717i	0.0352896	+	0.0611234i
$866$	−306.455	+	272.041i	−0.353874	+	0.314135i
$867$	1483.17			1.71069
$868$	−162.943	+	152.998i	−0.187722	+	0.176265i
$869$		−	530.460i		−	0.610426i
$870$	292.998	−	260.095i	0.336779	−	0.298960i
$871$	−465.870	+	268.970i	−0.534868	+	0.308806i
$872$	452.407	−	960.842i	0.518815	−	1.10188i
$873$	127.241	+	73.4627i	0.145752	+	0.0841497i
$874$	−8.59175	+	25.8212i	−0.00983038	+	0.0295437i
$875$	−520.106	−	1428.52i	−0.594407	−	1.63260i
$876$	134.359	−	179.544i	0.153378	−	0.204959i
$877$	−729.217	−	421.013i	−0.831490	−	0.480061i	0.0228726	−	0.999738i	$-0.492719\pi$
$877$	−729.217	−	421.013i	−0.831490	−	0.480061i	−0.854363	+	0.519677i	$0.826052\pi$
$878$	114.609	+	558.549i	0.130534	+	0.636160i
$879$	−286.642	−	496.478i	−0.326100	−	0.564821i
$880$	365.924	−	1510.53i	0.415823	−	1.71651i
$881$		−	24.6644i		−	0.0279959i	−0.999902	−	0.0139980i	$-0.995544\pi$
$881$		−	24.6644i		−	0.0279959i	0.999902	−	0.0139980i	$-0.00445584\pi$
$882$	−182.588	+	230.430i	−0.207015	+	0.261258i
$883$		−	1434.33i		−	1.62439i	−0.583389	−	0.812193i	$-0.698273\pi$
$883$		−	1434.33i		−	1.62439i	0.583389	−	0.812193i	$-0.301727\pi$
$884$	836.816	+	1953.26i	0.946625	+	2.20957i
$885$	−186.711	−	323.393i	−0.210973	−	0.365416i
$886$	327.275	+	1594.98i	0.369385	+	1.80020i
$887$	−192.616	−	111.207i	−0.217155	−	0.125374i	0.387477	−	0.921879i	$-0.373347\pi$
$887$	−192.616	−	111.207i	−0.217155	−	0.125374i	−0.604632	+	0.796505i	$0.706680\pi$
$888$	103.606	+	149.143i	0.116674	+	0.167954i
$889$	−345.191	−	948.101i	−0.388292	−	1.06648i
$890$	1922.30	+	639.627i	2.15989	+	0.718682i
$891$	87.3859	+	50.4523i	0.0980762	+	0.0566243i
$892$	−323.429	−	38.6168i	−0.362589	−	0.0432924i
$893$	−298.101	+	172.109i	−0.333820	+	0.192731i
$894$	−61.5472	+	54.6357i	−0.0688447	+	0.0611138i
$895$		−	420.246i		−	0.469549i
$896$	−589.894	−	674.419i	−0.658364	−	0.752699i
$897$	27.1339			0.0302496
$898$	599.433	+	675.262i	0.667520	+	0.751962i
$899$	52.1019	+	90.2432i	0.0579554	+	0.100382i
$900$	−71.2283	+	596.562i	−0.0791425	+	0.662847i
$901$	−1124.46	+	1947.63i	−1.24802	+	2.16163i
$902$	−4.63756	+	13.9375i	−0.00514142	+	0.0154517i
$903$	−55.1383	−	46.2568i	−0.0610612	−	0.0512257i
$904$	−990.310	+	687.946i	−1.09548	+	0.761003i
$905$	433.307	−	750.510i	0.478793	−	0.829293i
$906$	−304.398	+	62.4597i	−0.335980	+	0.0689401i
$907$	130.244	−	75.1964i	0.143599	−	0.0829067i	−0.426479	−	0.904497i	$-0.640246\pi$
$907$	130.244	−	75.1964i	0.143599	−	0.0829067i	0.570078	+	0.821591i	$0.306913\pi$
$908$	−1163.46	+	498.451i	−1.28135	+	0.548955i
$909$	−299.357			−0.329326
$910$	−997.750	−	1621.72i	−1.09643	−	1.78211i
$911$	661.735			0.726383			0.363192	−	0.931714i	$-0.381687\pi$
$911$	661.735			0.726383			0.363192	+	0.931714i	$0.381687\pi$
$912$	−367.219	−	88.9586i	−0.402653	−	0.0975423i
$913$	1139.32	−	657.788i	1.24789	−	0.720469i
$914$	−1312.38	+	269.288i	−1.43586	+	0.294626i
$915$	−718.039	+	1243.68i	−0.784743	+	1.35921i
$916$	543.880	+	407.004i	0.593756	+	0.444328i
$917$	1737.21	+	306.133i	1.89445	+	0.333842i
$918$	333.712	+	111.039i	0.363520	+	0.120958i
$919$	−185.915	+	322.014i	−0.202301	+	0.350396i	−0.949269	−	0.314464i	$-0.898175\pi$
$919$	−185.915	+	322.014i	−0.202301	+	0.350396i	0.746968	+	0.664860i	$0.231509\pi$
$920$	−62.5823	−	29.4665i	−0.0680242	−	0.0320288i
$921$	−4.03420	−	6.98744i	−0.00438024	−	0.00758680i
$922$	−565.902	−	637.488i	−0.613776	−	0.691419i
$923$	971.356			1.05239
$924$	520.520	+	157.182i	0.563333	+	0.170111i
$925$		−	656.159i		−	0.709361i
$926$	7.70156	+	8.67581i	0.00831702	+	0.00936912i
$927$	−376.110	+	217.147i	−0.405728	+	0.234247i
$928$	−368.901	+	195.967i	−0.397522	+	0.211171i
$929$	1452.82	+	838.787i	1.56386	+	0.902892i	0.996861	+	0.0791705i	$0.0252271\pi$
$929$	1452.82	+	838.787i	1.56386	+	0.902892i	0.566994	+	0.823722i	$0.308106\pi$
$930$	−227.332	−	75.6425i	−0.244443	−	0.0813360i
$931$	116.145	+	657.900i	0.124753	+	0.706659i
$932$	−470.342	−	351.973i	−0.504659	−	0.377653i
$933$	−479.371	−	276.765i	−0.513795	−	0.296640i
$934$	844.124	−	173.207i	0.903774	−	0.185446i
$935$	1643.70	+	2846.97i	1.75797	+	3.04489i
$936$	31.4388	+	375.427i	0.0335884	+	0.401097i
$937$			1609.04i			1.71723i	0.512623	+	0.858614i	$0.328674\pi$
$937$			1609.04i			1.71723i	−0.512623	+	0.858614i	$0.671326\pi$
$938$	13.4086	+	479.579i	0.0142949	+	0.511279i
$939$		−	745.334i		−	0.793753i
$940$	−344.560	−	804.259i	−0.366554	−	0.855595i
$941$	−443.422	−	768.030i	−0.471224	−	0.816185i	0.528234	−	0.849099i	$-0.322854\pi$
$941$	−443.422	−	768.030i	−0.471224	−	0.816185i	−0.999458	+	0.0329144i	$0.989521\pi$
$942$	656.609	−	134.730i	0.697037	−	0.143026i
$943$	0.566157	+	0.326871i	0.000600379	+	0.000346629i
$944$	112.295	+	381.976i	0.118956	+	0.404635i
$945$	−310.358	−	54.6915i	−0.328421	−	0.0578746i
$946$	−42.0248	+	126.299i	−0.0444237	+	0.133508i
$947$	1169.78	+	675.375i	1.23525	+	0.713173i	0.968120	−	0.250487i	$-0.0805907\pi$
$947$	1169.78	+	675.375i	1.23525	+	0.713173i	0.267132	+	0.963660i	$0.413924\pi$
$948$	38.8622	−	325.485i	0.0409939	−	0.343339i
$949$	−440.024	+	254.048i	−0.463672	+	0.267701i
$950$	906.335	+	1020.99i	0.954037	+	1.07472i
$951$		−	69.9304i		−	0.0735335i
$952$	1887.35	+	172.003i	1.98251	+	0.180675i
$953$	−630.482			−0.661576			−0.330788	−	0.943705i	$-0.607315\pi$
$953$	−630.482			−0.661576			−0.330788	+	0.943705i	$0.607315\pi$
$954$	−298.181	+	264.696i	−0.312558	+	0.277460i
$955$	−283.095	−	490.335i	−0.296434	−	0.513439i
$956$	77.6908	−	650.688i	0.0812665	−	0.680636i
$957$	126.746	−	219.531i	0.132441	−	0.229395i
$958$	637.501	+	212.122i	0.665450	+	0.221422i
$959$	−834.752	+	995.027i	−0.870440	+	1.03757i
$960$	335.191	−	900.037i	0.349157	−	0.937538i
$961$	−448.639	+	777.065i	−0.466846	+	0.808600i
$962$	−82.7037	−	403.058i	−0.0859706	−	0.418979i
$963$	106.699	−	61.6027i	0.110799	−	0.0639696i
$964$	−254.027	−	592.939i	−0.263513	−	0.615082i
$965$	−852.979			−0.883916
$966$	11.5093	−	21.2874i	0.0119144	−	0.0220367i
$967$	810.364			0.838018			0.419009	−	0.907982i	$-0.362377\pi$
$967$	810.364			0.838018			0.419009	+	0.907982i	$0.362377\pi$
$968$	−3.13788	−	37.4711i	−0.00324161	−	0.0387098i
$969$	692.118	−	399.595i	0.714261	−	0.412379i
$970$	170.581	+	831.330i	0.175857	+	0.857042i
$971$	281.062	−	486.813i	0.289456	−	0.501352i	−0.684224	−	0.729272i	$-0.739859\pi$
$971$	281.062	−	486.813i	0.289456	−	0.501352i	0.973680	+	0.227919i	$0.0731923\pi$
$972$	49.9230	+	37.3590i	0.0513611	+	0.0384352i
$973$	−424.253	−	1165.25i	−0.436026	−	1.19759i
$974$	422.250	−	1269.00i	0.433521	−	1.30288i
$975$	680.630	−	1178.89i	0.698082	−	1.20911i
$976$	1056.24	−	1108.48i	1.08221	−	1.13574i
$977$	−68.7246	−	119.035i	−0.0703425	−	0.121837i	0.828709	−	0.559680i	$-0.189076\pi$
$977$	−68.7246	−	119.035i	−0.0703425	−	0.121837i	−0.899051	+	0.437843i	$0.855743\pi$
$978$	194.133	−	172.332i	0.198500	−	0.176209i
$979$	1310.80			1.33892
$980$	−1695.51	+	94.8844i	−1.73011	+	0.0968208i
$981$			398.258i			0.405971i
$982$	1090.70	−	968.221i	1.11069	−	0.985968i
$983$	533.162	−	307.821i	0.542382	−	0.313145i	−0.203662	−	0.979041i	$-0.565284\pi$
$983$	533.162	−	307.821i	0.542382	−	0.313145i	0.746044	+	0.665897i	$0.231951\pi$
$984$	−3.86664	+	8.21214i	−0.00392951	+	0.00834567i
$985$	588.882	+	339.991i	0.597850	+	0.345169i
$986$	278.953	−	838.350i	0.282914	−	0.850254i
$987$	287.629	−	104.722i	0.291417	−	0.106101i
$988$	685.420	+	512.924i	0.693745	+	0.519153i
$989$	5.13042	+	2.96205i	0.00518748	+	0.00299499i
$990$	117.151	+	570.936i	0.118334	+	0.576703i
$991$	−45.9802	−	79.6401i	−0.0463978	−	0.0803634i	0.841894	−	0.539643i	$-0.181441\pi$
$991$	−45.9802	−	79.6401i	−0.0463978	−	0.0803634i	−0.888292	+	0.459280i	$0.848108\pi$
$992$	216.578	+	135.448i	0.218325	+	0.136540i
$993$			379.144i			0.381817i
$994$	412.019	−	762.061i	0.414506	−	0.766661i
$995$			896.196i			0.900700i
$996$	747.268	−	320.144i	0.750269	−	0.321430i
$997$	199.505	+	345.553i	0.200105	+	0.346593i	0.948562	−	0.316591i	$-0.102538\pi$
$997$	199.505	+	345.553i	0.200105	+	0.346593i	−0.748457	+	0.663184i	$0.769205\pi$
$998$	−323.321	−	1575.71i	−0.323969	−	1.57887i
$999$	−58.9757	−	34.0496i	−0.0590348	−	0.0340837i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.3.x.b.61.7	✓	60
4.3	odd	2		672.3.bf.b.145.15		60
7.3	odd	6	inner	168.3.x.b.157.28	yes	60
8.3	odd	2		672.3.bf.b.145.16		60
8.5	even	2	inner	168.3.x.b.61.28	yes	60
28.3	even	6		672.3.bf.b.241.16		60
56.3	even	6		672.3.bf.b.241.15		60
56.45	odd	6	inner	168.3.x.b.157.7	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.x.b.61.7	✓	60	1.1	even	1	trivial
168.3.x.b.61.28	yes	60	8.5	even	2	inner
168.3.x.b.157.7	yes	60	56.45	odd	6	inner
168.3.x.b.157.28	yes	60	7.3	odd	6	inner
672.3.bf.b.145.15		60	4.3	odd	2
672.3.bf.b.145.16		60	8.3	odd	2
672.3.bf.b.241.15		60	56.3	even	6
672.3.bf.b.241.16		60	28.3	even	6

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	168.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32774 - 1.49570i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-0.474223 + 3.97179i) q^{4} +(4.33205 - 7.50333i) q^{5} +(1.09369 - 3.28692i) q^{6} +(2.39482 + 6.57760i) q^{7} +(6.57024 - 4.56420i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.32774 - 1.49570i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-0.474223 + 3.97179i) q^{4} +(4.33205 - 7.50333i) q^{5} +(1.09369 - 3.28692i) q^{6} +(2.39482 + 6.57760i) q^{7} +(6.57024 - 4.56420i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(-16.9745 + 3.48302i) q^{10} +(-9.70954 + 5.60581i) q^{11} +(-6.36837 + 2.72834i) q^{12} +15.6975 q^{13} +(6.65841 - 12.3153i) q^{14} +15.0067 q^{15} +(-15.5502 - 3.76703i) q^{16} +(29.3084 - 16.9212i) q^{17} +(5.87754 - 1.20602i) q^{18} +(6.81708 - 11.8075i) q^{19} +(27.7473 + 20.7642i) q^{20} +(-7.79243 + 9.28860i) q^{21} +(21.2763 + 7.07950i) q^{22} +(0.498987 - 0.864271i) q^{23} +(12.5363 + 5.90265i) q^{24} +(-25.0333 - 43.3590i) q^{25} +(-20.8422 - 23.4788i) q^{26} -5.19615 q^{27} +(-27.2605 + 6.39247i) q^{28} +13.0538i q^{29} +(-19.9249 - 22.4454i) q^{30} +(6.91318 - 3.99133i) q^{31} +(15.0123 + 28.2601i) q^{32} +(-16.8174 - 9.70954i) q^{33} +(-64.2228 - 21.3695i) q^{34} +(59.7284 + 10.5254i) q^{35} +(-9.60768 - 7.18975i) q^{36} +(11.3499 + 6.55286i) q^{37} +(-26.7118 + 5.48101i) q^{38} +(13.5945 + 23.5463i) q^{39} +(-5.78410 - 69.0710i) q^{40} +0.655069i q^{41} +(24.2392 - 0.677709i) q^{42} +5.93612i q^{43} +(-17.6606 - 41.2227i) q^{44} +(12.9962 + 22.5100i) q^{45} +(-1.95521 + 0.401192i) q^{46} +(-21.8643 - 12.6233i) q^{47} +(-7.81634 - 26.5877i) q^{48} +(-37.5297 + 31.5043i) q^{49} +(-31.6142 + 95.0116i) q^{50} +(50.7636 + 29.3084i) q^{51} +(-7.44414 + 62.3474i) q^{52} +(-57.5500 + 33.2265i) q^{53} +(6.89913 + 7.77187i) q^{54} +97.1385i q^{55} +(45.7560 + 32.2860i) q^{56} +23.6150 q^{57} +(19.5245 - 17.3320i) q^{58} +(-12.4419 - 21.5500i) q^{59} +(-7.11651 + 59.6033i) q^{60} +(-47.8480 + 82.8752i) q^{61} +(-15.1487 - 5.04059i) q^{62} +(-20.6813 - 3.64448i) q^{63} +(22.3361 - 59.9758i) q^{64} +(68.0026 - 117.784i) q^{65} +(7.80659 + 38.0455i) q^{66} +(-29.6779 + 17.1345i) q^{67} +(53.3087 + 124.431i) q^{68} +1.72854 q^{69} +(-63.5609 - 103.311i) q^{70} +61.8795 q^{71} +(2.00278 + 23.9163i) q^{72} +(-28.0314 + 16.1839i) q^{73} +(-5.26858 - 25.6765i) q^{74} +(43.3590 - 75.1000i) q^{75} +(43.6642 + 32.6754i) q^{76} +(-60.1254 - 50.4406i) q^{77} +(17.1683 - 51.5966i) q^{78} +(-23.6567 + 40.9746i) q^{79} +(-95.6296 + 100.360i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(0.979785 - 0.869760i) q^{82} -117.340 q^{83} +(-33.1970 - 35.3548i) q^{84} -293.214i q^{85} +(8.87865 - 7.88162i) q^{86} +(-19.5807 + 11.3049i) q^{87} +(-38.2080 + 81.1478i) q^{88} +(-101.251 - 58.4574i) q^{89} +(16.4127 - 49.3257i) q^{90} +(37.5928 + 103.252i) q^{91} +(3.19607 + 2.39173i) q^{92} +(11.9740 + 6.91318i) q^{93} +(10.1493 + 49.4629i) q^{94} +(-59.0638 - 102.302i) q^{95} +(-29.3891 + 46.9924i) q^{96} -48.9751i q^{97} +(96.9505 + 14.3036i) q^{98} -33.6348i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 2 q^{2} - 2 q^{4} + 26 q^{7} + 32 q^{8} - 90 q^{9}+O(q^{10}) \) 60 * q + 2 * q^2 - 2 * q^4 + 26 * q^7 + 32 * q^8 - 90 * q^9	\( 60 q + 2 q^{2} - 2 q^{4} + 26 q^{7} + 32 q^{8} - 90 q^{9} - 42 q^{10} - 14 q^{14} + 12 q^{15} + 6 q^{16} - 36 q^{17} + 6 q^{18} + 28 q^{22} - 28 q^{23} + 102 q^{24} - 204 q^{25} - 42 q^{26} + 186 q^{28} - 24 q^{30} + 18 q^{31} - 28 q^{32} - 30 q^{33} + 12 q^{36} - 414 q^{38} - 36 q^{39} + 18 q^{40} + 120 q^{42} - 48 q^{44} - 160 q^{46} + 828 q^{47} - 126 q^{49} - 332 q^{50} + 36 q^{52} + 36 q^{54} + 256 q^{56} - 312 q^{57} - 94 q^{58} + 150 q^{60} - 12 q^{63} + 988 q^{64} + 36 q^{65} - 108 q^{66} + 312 q^{68} + 222 q^{70} + 760 q^{71} - 48 q^{72} - 648 q^{73} - 294 q^{74} + 396 q^{78} + 114 q^{79} - 900 q^{80} - 270 q^{81} + 876 q^{82} - 96 q^{84} + 6 q^{86} - 174 q^{87} - 262 q^{88} - 72 q^{89} - 592 q^{92} - 540 q^{94} - 492 q^{95} - 258 q^{96} - 628 q^{98}+O(q^{100}) \) 60 * q + 2 * q^2 - 2 * q^4 + 26 * q^7 + 32 * q^8 - 90 * q^9 - 42 * q^10 - 14 * q^14 + 12 * q^15 + 6 * q^16 - 36 * q^17 + 6 * q^18 + 28 * q^22 - 28 * q^23 + 102 * q^24 - 204 * q^25 - 42 * q^26 + 186 * q^28 - 24 * q^30 + 18 * q^31 - 28 * q^32 - 30 * q^33 + 12 * q^36 - 414 * q^38 - 36 * q^39 + 18 * q^40 + 120 * q^42 - 48 * q^44 - 160 * q^46 + 828 * q^47 - 126 * q^49 - 332 * q^50 + 36 * q^52 + 36 * q^54 + 256 * q^56 - 312 * q^57 - 94 * q^58 + 150 * q^60 - 12 * q^63 + 988 * q^64 + 36 * q^65 - 108 * q^66 + 312 * q^68 + 222 * q^70 + 760 * q^71 - 48 * q^72 - 648 * q^73 - 294 * q^74 + 396 * q^78 + 114 * q^79 - 900 * q^80 - 270 * q^81 + 876 * q^82 - 96 * q^84 + 6 * q^86 - 174 * q^87 - 262 * q^88 - 72 * q^89 - 592 * q^92 - 540 * q^94 - 492 * q^95 - 258 * q^96 - 628 * q^98

Introduction

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