LMFDB - Embedded newform 210.3.v.a.193.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(37,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("210.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.v (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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.5
Character	$\chi$	$=$	210.193
Dual form			210.3.v.a.37.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 - 0.366025i) q^{2} +(1.67303 - 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-4.60928 - 1.93765i) q^{5} -2.44949 q^{6} +(-1.45688 + 6.84672i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})$	\(q+(-1.36603 - 0.366025i) q^{2} +(1.67303 - 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-4.60928 - 1.93765i) q^{5} -2.44949 q^{6} +(-1.45688 + 6.84672i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +(5.58717 + 4.33400i) q^{10} +(-6.59836 + 11.4287i) q^{11} +(3.34607 + 0.896575i) q^{12} +(10.7755 + 10.7755i) q^{13} +(4.49620 - 8.81953i) q^{14} +(-8.58011 - 1.17547i) q^{15} +(2.00000 + 3.46410i) q^{16} +(2.10467 + 7.85475i) q^{17} +(-4.09808 + 1.09808i) q^{18} +(-8.35848 + 4.82577i) q^{19} +(-6.04586 - 7.96540i) q^{20} +(0.631897 + 12.1079i) q^{21} +(13.1967 - 13.1967i) q^{22} +(6.06684 - 22.6417i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(17.4910 + 17.8624i) q^{25} +(-10.7755 - 18.6638i) q^{26} +(3.67423 - 3.67423i) q^{27} +(-9.37010 + 10.4020i) q^{28} +41.4745i q^{29} +(11.2904 + 4.74626i) q^{30} +(-18.0882 + 31.3297i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(-5.91593 + 22.0785i) q^{33} -11.5001i q^{34} +(19.9817 - 28.7355i) q^{35} +6.00000 q^{36} +(-4.68858 - 1.25630i) q^{37} +(13.1843 - 3.53271i) q^{38} +(22.8583 + 13.1973i) q^{39} +(5.34326 + 13.0939i) q^{40} -7.31247 q^{41} +(3.56860 - 16.7710i) q^{42} +(48.7061 + 48.7061i) q^{43} +(-22.8574 + 13.1967i) q^{44} +(-14.8818 + 1.87976i) q^{45} +(-16.5749 + 28.7086i) q^{46} +(-51.9641 - 13.9237i) q^{47} +(4.89898 + 4.89898i) q^{48} +(-44.7550 - 19.9496i) q^{49} +(-17.3551 - 30.8026i) q^{50} +(7.04237 + 12.1977i) q^{51} +(7.88823 + 29.4393i) q^{52} +(45.4596 - 12.1809i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(52.5586 - 39.8928i) q^{55} +(16.6072 - 10.7797i) q^{56} +(-11.8207 + 11.8207i) q^{57} +(15.1807 - 56.6552i) q^{58} +(-1.15330 - 0.665857i) q^{59} +(-13.6857 - 10.6161i) q^{60} +(-29.7996 - 51.6144i) q^{61} +(36.1764 - 36.1764i) q^{62} +(6.48500 + 19.9736i) q^{63} +8.00000i q^{64} +(-28.7882 - 70.5467i) q^{65} +(16.1626 - 27.9945i) q^{66} +(-31.5356 - 117.692i) q^{67} +(-4.20935 + 15.7095i) q^{68} -40.6001i q^{69} +(-37.8135 + 31.9397i) q^{70} -82.6803 q^{71} +(-8.19615 - 2.19615i) q^{72} +(49.5667 - 13.2814i) q^{73} +(5.94488 + 3.43228i) q^{74} +(37.2705 + 22.0433i) q^{75} -19.3031 q^{76} +(-68.6360 - 61.8273i) q^{77} +(-26.3945 - 26.3945i) q^{78} +(-26.3388 + 15.2067i) q^{79} +(-2.50634 - 19.8423i) q^{80} +(4.50000 - 7.79423i) q^{81} +(9.98902 + 2.67655i) q^{82} +(-32.2690 - 32.2690i) q^{83} +(-11.0134 + 21.6034i) q^{84} +(5.51873 - 40.2829i) q^{85} +(-48.7061 - 84.3614i) q^{86} +(18.5925 + 69.3881i) q^{87} +(36.0541 - 9.66067i) q^{88} +(-19.1540 + 11.0586i) q^{89} +(21.0169 + 2.87930i) q^{90} +(-89.4755 + 58.0783i) q^{91} +(33.1498 - 33.1498i) q^{92} +(-16.2174 + 60.5243i) q^{93} +(65.8878 + 38.0403i) q^{94} +(47.8773 - 6.04752i) q^{95} +(-4.89898 - 8.48528i) q^{96} +(128.645 - 128.645i) q^{97} +(53.8344 + 43.6332i) q^{98} +39.5902i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 8 q^{7} - 64 q^{8}+O(q^{10}) $ 32 * q - 16 * q^2 - 8 * q^7 - 64 * q^8	$ 32 q - 16 q^{2} - 8 q^{7} - 64 q^{8} + 4 q^{10} - 32 q^{11} - 32 q^{13} + 64 q^{16} - 56 q^{17} - 48 q^{18} - 16 q^{20} - 48 q^{21} + 64 q^{22} - 48 q^{23} + 68 q^{25} + 32 q^{26} + 40 q^{28} + 12 q^{30} + 160 q^{31} + 64 q^{32} + 12 q^{33} + 152 q^{35} + 192 q^{36} + 44 q^{37} - 64 q^{38} + 8 q^{40} - 80 q^{41} - 48 q^{42} - 184 q^{43} - 12 q^{45} - 96 q^{46} - 228 q^{47} - 96 q^{50} + 192 q^{51} + 32 q^{52} + 48 q^{53} + 104 q^{55} + 32 q^{56} + 144 q^{57} - 112 q^{58} + 24 q^{60} + 216 q^{61} - 320 q^{62} + 84 q^{63} - 384 q^{65} + 24 q^{66} + 112 q^{68} - 24 q^{70} + 368 q^{71} - 96 q^{72} + 52 q^{73} + 48 q^{75} + 256 q^{76} - 836 q^{77} - 240 q^{78} + 144 q^{81} + 40 q^{82} - 736 q^{83} - 72 q^{85} + 184 q^{86} - 72 q^{87} + 64 q^{88} + 24 q^{90} + 216 q^{91} + 192 q^{92} - 216 q^{93} + 272 q^{95} - 408 q^{97} + 200 q^{98}+O(q^{100}) $ 32 * q - 16 * q^2 - 8 * q^7 - 64 * q^8 + 4 * q^10 - 32 * q^11 - 32 * q^13 + 64 * q^16 - 56 * q^17 - 48 * q^18 - 16 * q^20 - 48 * q^21 + 64 * q^22 - 48 * q^23 + 68 * q^25 + 32 * q^26 + 40 * q^28 + 12 * q^30 + 160 * q^31 + 64 * q^32 + 12 * q^33 + 152 * q^35 + 192 * q^36 + 44 * q^37 - 64 * q^38 + 8 * q^40 - 80 * q^41 - 48 * q^42 - 184 * q^43 - 12 * q^45 - 96 * q^46 - 228 * q^47 - 96 * q^50 + 192 * q^51 + 32 * q^52 + 48 * q^53 + 104 * q^55 + 32 * q^56 + 144 * q^57 - 112 * q^58 + 24 * q^60 + 216 * q^61 - 320 * q^62 + 84 * q^63 - 384 * q^65 + 24 * q^66 + 112 * q^68 - 24 * q^70 + 368 * q^71 - 96 * q^72 + 52 * q^73 + 48 * q^75 + 256 * q^76 - 836 * q^77 - 240 * q^78 + 144 * q^81 + 40 * q^82 - 736 * q^83 - 72 * q^85 + 184 * q^86 - 72 * q^87 + 64 * q^88 + 24 * q^90 + 216 * q^91 + 192 * q^92 - 216 * q^93 + 272 * q^95 - 408 * q^97 + 200 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.36603	−	0.366025i	−0.683013	−	0.183013i
$2$	−1.36603	−	0.366025i	−0.683013	−	0.183013i
$3$	1.67303	−	0.448288i	0.557678	−	0.149429i
$3$	1.67303	−	0.448288i	0.557678	−	0.149429i
$4$	1.73205	+	1.00000i	0.433013	+	0.250000i
$5$	−4.60928	−	1.93765i	−0.921857	−	0.387531i
$5$	−4.60928	−	1.93765i	−0.921857	−	0.387531i
$6$	−2.44949			−0.408248
$7$	−1.45688	+	6.84672i	−0.208125	+	0.978102i
$7$	−1.45688	+	6.84672i	−0.208125	+	0.978102i
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$	2.59808	−	1.50000i	0.288675	−	0.166667i
$10$	5.58717	+	4.33400i	0.558717	+	0.433400i
$11$	−6.59836	+	11.4287i	−0.599851	+	1.03897i	0.392992	+	0.919542i	$0.371440\pi$
$11$	−6.59836	+	11.4287i	−0.599851	+	1.03897i	−0.992843	+	0.119430i	$0.961893\pi$
$12$	3.34607	+	0.896575i	0.278839	+	0.0747146i
$13$	10.7755	+	10.7755i	0.828886	+	0.828886i	0.987363	−	0.158476i	$-0.0506582\pi$
$13$	10.7755	+	10.7755i	0.828886	+	0.828886i	−0.158476	+	0.987363i	$0.550658\pi$
$14$	4.49620	−	8.81953i	0.321157	−	0.629967i
$15$	−8.58011	−	1.17547i	−0.572007	−	0.0783647i
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	2.10467	+	7.85475i	0.123804	+	0.462044i	0.999794	−	0.0202855i	$-0.00645751\pi$
$17$	2.10467	+	7.85475i	0.123804	+	0.462044i	−0.875990	+	0.482329i	$0.839791\pi$
$18$	−4.09808	+	1.09808i	−0.227671	+	0.0610042i
$19$	−8.35848	+	4.82577i	−0.439920	+	0.253988i	−0.703564	−	0.710632i	$-0.748409\pi$
$19$	−8.35848	+	4.82577i	−0.439920	+	0.253988i	0.263644	+	0.964620i	$0.415076\pi$
$20$	−6.04586	−	7.96540i	−0.302293	−	0.398270i
$21$	0.631897	+	12.1079i	0.0300903	+	0.576566i
$22$	13.1967	−	13.1967i	0.599851	−	0.599851i
$23$	6.06684	−	22.6417i	0.263776	−	0.984424i	−0.699220	−	0.714907i	$-0.746469\pi$
$23$	6.06684	−	22.6417i	0.263776	−	0.984424i	0.962996	−	0.269517i	$-0.0868641\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$	17.4910	+	17.8624i	0.699640	+	0.714495i
$26$	−10.7755	−	18.6638i	−0.414443	−	0.717837i
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	−9.37010	+	10.4020i	−0.334646	+	0.371499i
$29$			41.4745i			1.43015i	0.699046	+	0.715077i	$0.253608\pi$
$29$			41.4745i			1.43015i	−0.699046	+	0.715077i	$0.746392\pi$
$30$	11.2904	+	4.74626i	0.376346	+	0.158209i
$31$	−18.0882	+	31.3297i	−0.583490	+	1.01063i	0.411572	+	0.911377i	$0.364980\pi$
$31$	−18.0882	+	31.3297i	−0.583490	+	1.01063i	−0.995062	+	0.0992569i	$0.968353\pi$
$32$	−1.46410	−	5.46410i	−0.0457532	−	0.170753i
$33$	−5.91593	+	22.0785i	−0.179271	+	0.669047i
$34$		−	11.5001i		−	0.338240i
$35$	19.9817	−	28.7355i	0.570906	−	0.821015i
$36$	6.00000			0.166667
$37$	−4.68858	−	1.25630i	−0.126718	−	0.0339541i	0.194902	−	0.980823i	$-0.437561\pi$
$37$	−4.68858	−	1.25630i	−0.126718	−	0.0339541i	−0.321621	+	0.946869i	$0.604228\pi$
$38$	13.1843	−	3.53271i	0.346954	−	0.0929661i
$39$	22.8583	+	13.1973i	0.586111	+	0.338391i
$40$	5.34326	+	13.0939i	0.133582	+	0.327347i
$41$	−7.31247			−0.178353			−0.0891764	−	0.996016i	$-0.528424\pi$
$41$	−7.31247			−0.178353			−0.0891764	+	0.996016i	$0.528424\pi$
$42$	3.56860	−	16.7710i	0.0849668	−	0.399309i
$43$	48.7061	+	48.7061i	1.13270	+	1.13270i	0.989727	+	0.142972i	$0.0456660\pi$
$43$	48.7061	+	48.7061i	1.13270	+	1.13270i	0.142972	+	0.989727i	$0.454334\pi$
$44$	−22.8574	+	13.1967i	−0.519486	+	0.299925i
$45$	−14.8818	+	1.87976i	−0.330706	+	0.0417724i
$46$	−16.5749	+	28.7086i	−0.360324	+	0.624100i
$47$	−51.9641	−	13.9237i	−1.10562	−	0.296250i	−0.340568	−	0.940220i	$-0.610619\pi$
$47$	−51.9641	−	13.9237i	−1.10562	−	0.296250i	−0.765051	+	0.643970i	$0.777286\pi$
$48$	4.89898	+	4.89898i	0.102062	+	0.102062i
$49$	−44.7550	−	19.9496i	−0.913368	−	0.407135i
$50$	−17.3551	−	30.8026i	−0.347101	−	0.616052i
$51$	7.04237	+	12.1977i	0.138086	+	0.239172i
$52$	7.88823	+	29.4393i	0.151697	+	0.566140i
$53$	45.4596	−	12.1809i	0.857728	−	0.229827i	0.196954	−	0.980413i	$-0.436895\pi$
$53$	45.4596	−	12.1809i	0.857728	−	0.229827i	0.660774	+	0.750585i	$0.270228\pi$
$54$	−6.36396	+	3.67423i	−0.117851	+	0.0680414i
$55$	52.5586	−	39.8928i	0.955610	−	0.725323i
$56$	16.6072	−	10.7797i	0.296557	−	0.192494i
$57$	−11.8207	+	11.8207i	−0.207380	+	0.207380i
$58$	15.1807	−	56.6552i	0.261736	−	0.976813i
$59$	−1.15330	−	0.665857i	−0.0195474	−	0.0112857i	0.490194	−	0.871613i	$-0.336926\pi$
$59$	−1.15330	−	0.665857i	−0.0195474	−	0.0112857i	−0.509742	+	0.860327i	$0.670259\pi$
$60$	−13.6857	−	10.6161i	−0.228095	−	0.176935i
$61$	−29.7996	−	51.6144i	−0.488518	−	0.846138i	0.511395	−	0.859346i	$-0.329129\pi$
$61$	−29.7996	−	51.6144i	−0.488518	−	0.846138i	−0.999913	+	0.0132077i	$0.995796\pi$
$62$	36.1764	−	36.1764i	0.583490	−	0.583490i
$63$	6.48500	+	19.9736i	0.102936	+	0.317041i
$64$			8.00000i			0.125000i
$65$	−28.7882	−	70.5467i	−0.442896	−	1.08533i
$66$	16.1626	−	27.9945i	0.244888	−	0.424159i
$67$	−31.5356	−	117.692i	−0.470680	−	1.75660i	−0.637335	−	0.770587i	$-0.719963\pi$
$67$	−31.5356	−	117.692i	−0.470680	−	1.75660i	0.166654	−	0.986015i	$-0.446704\pi$
$68$	−4.20935	+	15.7095i	−0.0619021	+	0.231022i
$69$		−	40.6001i		−	0.588407i
$70$	−37.8135	+	31.9397i	−0.540192	+	0.456281i
$71$	−82.6803			−1.16451			−0.582256	−	0.813006i	$-0.697830\pi$
$71$	−82.6803			−1.16451			−0.582256	+	0.813006i	$0.697830\pi$
$72$	−8.19615	−	2.19615i	−0.113835	−	0.0305021i
$73$	49.5667	−	13.2814i	0.678996	−	0.181936i	0.0971923	−	0.995266i	$-0.469014\pi$
$73$	49.5667	−	13.2814i	0.678996	−	0.181936i	0.581804	+	0.813329i	$0.302347\pi$
$74$	5.94488	+	3.43228i	0.0803362	+	0.0463821i
$75$	37.2705	+	22.0433i	0.496940	+	0.293911i
$76$	−19.3031			−0.253988
$77$	−68.6360	−	61.8273i	−0.891377	−	0.802952i
$78$	−26.3945	−	26.3945i	−0.338391	−	0.338391i
$79$	−26.3388	+	15.2067i	−0.333403	+	0.192490i	−0.657351	−	0.753585i	$-0.728323\pi$
$79$	−26.3388	+	15.2067i	−0.333403	+	0.192490i	0.323948	+	0.946075i	$0.394990\pi$
$80$	−2.50634	−	19.8423i	−0.0313293	−	0.248029i
$81$	4.50000	−	7.79423i	0.0555556	−	0.0962250i
$82$	9.98902	+	2.67655i	0.121817	+	0.0326408i
$83$	−32.2690	−	32.2690i	−0.388784	−	0.388784i	0.485470	−	0.874253i	$-0.338649\pi$
$83$	−32.2690	−	32.2690i	−0.388784	−	0.388784i	−0.874253	+	0.485470i	$0.838649\pi$
$84$	−11.0134	+	21.6034i	−0.131112	+	0.257183i
$85$	5.51873	−	40.2829i	0.0649263	−	0.473916i
$86$	−48.7061	−	84.3614i	−0.566350	−	0.980946i
$87$	18.5925	+	69.3881i	0.213707	+	0.797565i
$88$	36.0541	−	9.66067i	0.409706	−	0.109780i
$89$	−19.1540	+	11.0586i	−0.215214	+	0.124254i	−0.603732	−	0.797187i	$-0.706320\pi$
$89$	−19.1540	+	11.0586i	−0.215214	+	0.124254i	0.388518	+	0.921441i	$0.372987\pi$
$90$	21.0169	+	2.87930i	0.233521	+	0.0319923i
$91$	−89.4755	+	58.0783i	−0.983248	+	0.638223i
$92$	33.1498	−	33.1498i	0.360324	−	0.360324i
$93$	−16.2174	+	60.5243i	−0.174381	+	0.650798i
$94$	65.8878	+	38.0403i	0.700934	+	0.404685i
$95$	47.8773	−	6.04752i	0.503972	−	0.0636581i
$96$	−4.89898	−	8.48528i	−0.0510310	−	0.0883883i
$97$	128.645	−	128.645i	1.32623	−	1.32623i	0.417603	−	0.908630i	$-0.362870\pi$
$97$	128.645	−	128.645i	1.32623	−	1.32623i	0.908630	−	0.417603i	$-0.137130\pi$
$98$	53.8344	+	43.6332i	0.549331	+	0.445237i
$99$			39.5902i			0.399901i
$100$	12.4329	+	48.4296i	0.124329	+	0.484296i
$101$	25.4347	−	44.0541i	0.251828	−	0.436179i	−0.712201	−	0.701976i	$-0.752302\pi$
$101$	25.4347	−	44.0541i	0.251828	−	0.436179i	0.964029	+	0.265796i	$0.0856348\pi$
$102$	−5.15537	−	19.2401i	−0.0505429	−	0.188629i
$103$	−31.7417	+	118.462i	−0.308172	+	1.15011i	0.622009	+	0.783010i	$0.286317\pi$
$103$	−31.7417	+	118.462i	−0.308172	+	1.15011i	−0.930181	+	0.367102i	$0.880350\pi$
$104$		−	43.1021i		−	0.414443i
$105$	20.5483	−	57.0330i	0.195698	−	0.543172i
$106$	−66.5574			−0.627900
$107$	187.250	+	50.1735i	1.75000	+	0.468912i	0.984627	−	0.174673i	$-0.0558868\pi$
$107$	187.250	+	50.1735i	1.75000	+	0.468912i	0.765375	+	0.643584i	$0.222553\pi$
$108$	10.0382	−	2.68973i	0.0929463	−	0.0249049i
$109$	58.3978	+	33.7160i	0.535760	+	0.309321i	0.743359	−	0.668893i	$-0.233232\pi$
$109$	58.3978	+	33.7160i	0.535760	+	0.309321i	−0.207599	+	0.978214i	$0.566565\pi$
$110$	−86.3981	+	35.2568i	−0.785437	+	0.320516i
$111$	−8.40733			−0.0757417
$112$	−26.6315	+	8.64666i	−0.237781	+	0.0772023i
$113$	85.9828	+	85.9828i	0.760910	+	0.760910i	0.976487	−	0.215577i	$-0.0691632\pi$
$113$	85.9828	+	85.9828i	0.760910	+	0.760910i	−0.215577	+	0.976487i	$0.569163\pi$
$114$	20.4740	−	11.8207i	0.179597	−	0.103690i
$115$	−71.8356	+	92.6068i	−0.624658	+	0.805277i
$116$	−41.4745	+	71.8359i	−0.357538	+	0.619275i
$117$	44.1589	+	11.8323i	0.377427	+	0.101131i
$118$	1.33171	+	1.33171i	0.0112857	+	0.0112857i
$119$	−56.8455	+	2.96670i	−0.477693	+	0.0249303i
$120$	14.8093	+	19.5112i	0.123411	+	0.162593i
$121$	−26.5767	−	46.0322i	−0.219642	−	0.380432i
$122$	21.8148	+	81.4140i	0.178810	+	0.667328i
$123$	−12.2340	+	3.27809i	−0.0994634	+	0.0266511i
$124$	−62.6593	+	36.1764i	−0.505317	+	0.291745i
$125$	−46.0099	−	116.224i	−0.368079	−	0.929794i
$126$	−1.54783	−	29.6581i	−0.0122843	−	0.235382i
$127$	−111.649	+	111.649i	−0.879125	+	0.879125i	−0.993444	−	0.114319i	$-0.963531\pi$
$127$	−111.649	+	111.649i	−0.879125	+	0.879125i	0.114319	+	0.993444i	$0.463531\pi$
$128$	2.92820	−	10.9282i	0.0228766	−	0.0853766i
$129$	103.321	+	59.6525i	0.800939	+	0.462422i
$130$	13.5036	+	106.906i	0.103874	+	0.822352i
$131$	36.8045	+	63.7473i	0.280951	+	0.486621i	0.971619	−	0.236551i	$-0.0760170\pi$
$131$	36.8045	+	63.7473i	0.280951	+	0.486621i	−0.690669	+	0.723171i	$0.742684\pi$
$132$	−32.3252	+	32.3252i	−0.244888	+	0.244888i
$133$	−20.8634	−	64.2587i	−0.156868	−	0.483148i
$134$			172.314i			1.28592i
$135$	−24.0550	+	9.81620i	−0.178185	+	0.0727126i
$136$	11.5001	−	19.9188i	0.0845599	−	0.146462i
$137$	61.7203	+	230.343i	0.450513	+	1.68134i	0.700953	+	0.713207i	$0.252758\pi$
$137$	61.7203	+	230.343i	0.450513	+	1.68134i	−0.250440	+	0.968132i	$0.580575\pi$
$138$	−14.8607	+	55.4607i	−0.107686	+	0.401889i
$139$		−	185.128i		−	1.33186i	−0.746015	−	0.665930i	$-0.768035\pi$
$139$		−	185.128i		−	1.33186i	0.746015	−	0.665930i	$-0.231965\pi$
$140$	63.3449	−	29.7897i	0.452463	−	0.212784i
$141$	−93.1794			−0.660847
$142$	112.943	+	30.2631i	0.795376	+	0.213120i
$143$	−194.251	+	52.0494i	−1.35840	+	0.363982i
$144$	10.3923	+	6.00000i	0.0721688	+	0.0416667i
$145$	80.3631	−	191.168i	0.554228	−	1.31840i
$146$	−72.5707			−0.497060
$147$	−83.8198	−	13.3133i	−0.570203	−	0.0905664i
$148$	−6.86455	−	6.86455i	−0.0463821	−	0.0463821i
$149$	−43.7077	+	25.2346i	−0.293340	+	0.169360i	−0.639447	−	0.768835i	$-0.720837\pi$
$149$	−43.7077	+	25.2346i	−0.293340	+	0.169360i	0.346107	+	0.938195i	$0.387503\pi$
$150$	−42.8440	−	43.7537i	−0.285627	−	0.291692i
$151$	−16.5824	+	28.7216i	−0.109817	+	0.190209i	−0.915696	−	0.401871i	$-0.868360\pi$
$151$	−16.5824	+	28.7216i	−0.109817	+	0.190209i	0.805879	+	0.592080i	$0.201693\pi$
$152$	26.3685	+	7.06542i	0.173477	+	0.0464830i
$153$	17.2502	+	17.2502i	0.112747	+	0.112747i
$154$	71.1282	+	109.580i	0.461871	+	0.711560i
$155$	144.080	−	109.359i	0.929546	−	0.705540i
$156$	26.3945	+	45.7167i	0.169196	+	0.293056i
$157$	−58.5850	−	218.642i	−0.373153	−	1.39262i	−0.856025	−	0.516934i	$-0.827073\pi$
$157$	−58.5850	−	218.642i	−0.373153	−	1.39262i	0.482873	−	0.875690i	$-0.339593\pi$
$158$	41.5456	−	11.1321i	0.262947	−	0.0704564i
$159$	70.5948	−	40.7579i	0.443992	−	0.256339i
$160$	−3.83907	+	28.0225i	−0.0239942	+	0.175141i
$161$	146.183	+	74.5241i	0.907969	+	0.462883i
$162$	−9.00000	+	9.00000i	−0.0555556	+	0.0555556i
$163$	44.6896	−	166.784i	0.274169	−	1.02321i	−0.682227	−	0.731141i	$-0.738988\pi$
$163$	44.6896	−	166.784i	0.274169	−	1.02321i	0.956396	−	0.292073i	$-0.0943451\pi$
$164$	−12.6656	−	7.31247i	−0.0772291	−	0.0445882i
$165$	70.0487	−	90.3033i	0.424538	−	0.547293i
$166$	32.2690	+	55.8916i	0.194392	+	0.336697i
$167$	−158.459	+	158.459i	−0.948854	+	0.948854i	−0.998754	−	0.0498998i	$-0.984110\pi$
$167$	−158.459	+	158.459i	−0.948854	+	0.948854i	0.0498998	+	0.998754i	$0.484110\pi$
$168$	22.9520	−	25.4795i	0.136619	−	0.151664i
$169$			63.2238i			0.374105i
$170$	−22.2833	+	53.0074i	−0.131078	+	0.311809i
$171$	−14.4773	+	25.0755i	−0.0846627	+	0.146640i
$172$	35.6553	+	133.067i	0.207298	+	0.773648i
$173$	−10.9342	+	40.8069i	−0.0632033	+	0.235878i	−0.990300	−	0.138944i	$-0.955629\pi$
$173$	−10.9342	+	40.8069i	−0.0632033	+	0.235878i	0.927097	+	0.374822i	$0.122296\pi$
$174$		−	101.591i		−	0.583858i
$175$	−147.781	+	93.7326i	−0.844462	+	0.535615i
$176$	−52.7869			−0.299925
$177$	−2.22800	−	0.596991i	−0.0125876	−	0.00337283i
$178$	30.2126	−	8.09545i	0.169734	−	0.0454800i
$179$	294.348	+	169.942i	1.64440	+	0.949398i	0.979241	+	0.202700i	$0.0649716\pi$
$179$	294.348	+	169.942i	1.64440	+	0.949398i	0.665164	+	0.746697i	$0.268362\pi$
$180$	−27.6557	−	11.6259i	−0.153643	−	0.0645884i
$181$	37.6015			0.207743			0.103871	−	0.994591i	$-0.466877\pi$
$181$	37.6015			0.207743			0.103871	+	0.994591i	$0.466877\pi$
$182$	143.484	−	46.5862i	0.788374	−	0.255968i
$183$	−72.9938	−	72.9938i	−0.398873	−	0.398873i
$184$	−57.4172	+	33.1498i	−0.312050	+	0.180162i
$185$	19.1767	+	14.8755i	0.103658	+	0.0804080i
$186$	44.3068	−	76.7417i	0.238209	−	0.412590i
$187$	−103.657	−	27.7748i	−0.554315	−	0.148528i
$188$	−76.0807	−	76.0807i	−0.404685	−	0.404685i
$189$	19.8035	+	30.5093i	0.104781	+	0.161425i
$190$	−67.6152	−	9.26324i	−0.355869	−	0.0487539i
$191$	141.603	+	245.263i	0.741375	+	1.28410i	0.951870	+	0.306503i	$0.0991591\pi$
$191$	141.603	+	245.263i	0.741375	+	1.28410i	−0.210495	+	0.977595i	$0.567508\pi$
$192$	3.58630	+	13.3843i	0.0186787	+	0.0697097i
$193$	152.834	−	40.9517i	0.791885	−	0.212185i	0.159867	−	0.987139i	$-0.448894\pi$
$193$	152.834	−	40.9517i	0.791885	−	0.212185i	0.632018	+	0.774954i	$0.282227\pi$
$194$	−222.819	+	128.645i	−1.14855	+	0.663116i
$195$	−79.7889	−	105.121i	−0.409174	−	0.539084i
$196$	−57.5683	−	79.3088i	−0.293716	−	0.404637i
$197$	188.004	−	188.004i	0.954337	−	0.954337i	−0.0446654	−	0.999002i	$-0.514222\pi$
$197$	188.004	−	188.004i	0.954337	−	0.954337i	0.999002	+	0.0446654i	$0.0142222\pi$
$198$	14.4910	−	54.0812i	0.0731869	−	0.273137i
$199$	4.52064	+	2.60999i	0.0227168	+	0.0131155i	0.511315	−	0.859393i	$-0.329158\pi$
$199$	4.52064	+	2.60999i	0.0227168	+	0.0131155i	−0.488599	+	0.872509i	$0.662492\pi$
$200$	0.742760	−	70.7068i	0.00371380	−	0.353534i
$201$	−105.520	−	182.766i	−0.524976	−	0.909284i
$202$	−50.8693	+	50.8693i	−0.251828	+	0.251828i
$203$	−283.964	−	60.4232i	−1.39884	−	0.297651i
$204$			28.1695i			0.138086i
$205$	33.7052	+	14.1690i	0.164416	+	0.0691172i
$206$	86.7199	−	150.203i	0.420970	−	0.729142i
$207$	−18.2005	−	67.9252i	−0.0879252	−	0.328141i
$208$	−15.7765	+	58.8786i	−0.0758484	+	0.283070i
$209$		−	127.369i		−	0.609420i
$210$	−48.9450	+	70.3874i	−0.233071	+	0.335178i
$211$	49.9660			0.236806			0.118403	−	0.992966i	$-0.462223\pi$
$211$	49.9660			0.236806			0.118403	+	0.992966i	$0.462223\pi$
$212$	90.9191	+	24.3617i	0.428864	+	0.114914i
$213$	−138.327	+	37.0646i	−0.649422	+	0.174012i
$214$	−237.424	−	137.077i	−1.10946	−	0.640545i
$215$	−130.125	−	318.876i	−0.605231	−	1.48314i
$216$	−14.6969			−0.0680414
$217$	−188.153	−	169.488i	−0.867065	−	0.781051i
$218$	−67.4320	−	67.4320i	−0.309321	−	0.309321i
$219$	76.9729	−	44.4403i	0.351474	−	0.202924i
$220$	130.927	−	16.5378i	0.595122	−	0.0751716i
$221$	−61.9601	+	107.318i	−0.280362	+	0.485602i
$222$	11.4846	+	3.07730i	0.0517325	+	0.0138617i
$223$	211.407	+	211.407i	0.948013	+	0.948013i	0.998714	−	0.0507005i	$-0.0161454\pi$
$223$	211.407	+	211.407i	0.948013	+	0.948013i	−0.0507005	+	0.998714i	$0.516145\pi$
$224$	39.5442	−	2.06377i	0.176536	−	0.00921324i
$225$	72.2365	+	20.1713i	0.321051	+	0.0896504i
$226$	−85.9828	−	148.927i	−0.380455	−	0.658967i
$227$	11.7221	+	43.7476i	0.0516393	+	0.192721i	0.986927	−	0.161168i	$-0.0515260\pi$
$227$	11.7221	+	43.7476i	0.0516393	+	0.192721i	−0.935288	+	0.353888i	$0.884859\pi$
$228$	−32.2947	+	8.65334i	−0.141643	+	0.0379532i
$229$	−84.7804	+	48.9480i	−0.370220	+	0.213747i	−0.673555	−	0.739138i	$-0.735233\pi$
$229$	−84.7804	+	48.9480i	−0.370220	+	0.213747i	0.303335	+	0.952884i	$0.401900\pi$
$230$	132.026	−	100.210i	0.574025	−	0.435694i
$231$	−142.547	−	72.6704i	−0.617085	−	0.314590i
$232$	82.9489	−	82.9489i	0.357538	−	0.357538i
$233$	−47.1774	+	176.069i	−0.202478	+	0.755659i	0.787725	+	0.616027i	$0.211259\pi$
$233$	−47.1774	+	176.069i	−0.202478	+	0.755659i	−0.990203	+	0.139632i	$0.955408\pi$
$234$	−55.9913	−	32.3266i	−0.239279	−	0.138148i
$235$	212.538	+	164.867i	0.904416	+	0.701561i
$236$	−1.33171	−	2.30660i	−0.00564286	−	0.00977372i
$237$	−37.2488	+	37.2488i	−0.157168	+	0.157168i
$238$	78.7382	+	16.7543i	0.330833	+	0.0703962i
$239$			68.1419i			0.285112i	0.989787	+	0.142556i	$0.0455322\pi$
$239$			68.1419i			0.285112i	−0.989787	+	0.142556i	$0.954468\pi$
$240$	−13.0883	−	32.0733i	−0.0545345	−	0.133639i
$241$	136.691	−	236.756i	0.567183	−	0.982389i	−0.429660	−	0.902991i	$-0.641367\pi$
$241$	136.691	−	236.756i	0.567183	−	0.982389i	0.996843	−	0.0793984i	$-0.0252999\pi$
$242$	19.4555	+	72.6089i	0.0803946	+	0.300037i
$243$	4.03459	−	15.0573i	0.0166032	−	0.0619642i
$244$		−	119.198i		−	0.488518i
$245$	167.633	+	178.673i	0.684217	+	0.729278i
$246$	17.9118			0.0728123
$247$	−142.067	−	38.0668i	−0.575171	−	0.154117i
$248$	98.8357	−	26.4829i	0.398531	−	0.106786i
$249$	−68.4530	−	39.5214i	−0.274912	−	0.158720i
$250$	20.3097	+	175.606i	0.0812387	+	0.702425i
$251$	102.144			0.406947			0.203473	−	0.979081i	$-0.434777\pi$
$251$	102.144			0.406947			0.203473	+	0.979081i	$0.434777\pi$
$252$	−8.74126	+	41.0803i	−0.0346875	+	0.163017i
$253$	218.734	+	218.734i	0.864563	+	0.864563i
$254$	193.381	−	111.649i	0.761344	−	0.439562i
$255$	−8.82530	−	69.8686i	−0.0346090	−	0.273994i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−344.764	−	92.3792i	−1.34149	−	0.359452i	−0.484506	−	0.874788i	$-0.661000\pi$
$257$	−344.764	−	92.3792i	−1.34149	−	0.359452i	−0.856988	+	0.515336i	$0.827667\pi$
$258$	−119.305	−	119.305i	−0.462422	−	0.462422i
$259$	15.4322	−	30.2711i	0.0595838	−	0.116877i
$260$	20.6840	−	150.979i	0.0795538	−	0.580687i
$261$	62.2117	+	107.754i	0.238359	+	0.412850i
$262$	−26.9428	−	100.552i	−0.102835	−	0.383786i
$263$	−186.615	+	50.0033i	−0.709562	+	0.190126i	−0.595509	−	0.803348i	$-0.703050\pi$
$263$	−186.615	+	50.0033i	−0.709562	+	0.190126i	−0.114052	+	0.993475i	$0.536383\pi$
$264$	55.9889	−	32.3252i	0.212079	−	0.122444i
$265$	−233.138	−	31.9398i	−0.879767	−	0.120528i
$266$	4.97963	+	95.4156i	0.0187204	+	0.358705i
$267$	−27.0879	+	27.0879i	−0.101453	+	0.101453i
$268$	63.0712	−	235.385i	0.235340	−	0.878301i
$269$	−244.880	−	141.381i	−0.910334	−	0.525582i	−0.0297956	−	0.999556i	$-0.509486\pi$
$269$	−244.880	−	141.381i	−0.910334	−	0.525582i	−0.880539	+	0.473974i	$0.842819\pi$
$270$	36.4527	−	4.60445i	0.135010	−	0.0170535i
$271$	256.230	+	443.803i	0.945497	+	1.63765i	0.754752	+	0.656010i	$0.227757\pi$
$271$	256.230	+	443.803i	0.945497	+	1.63765i	0.190745	+	0.981640i	$0.438910\pi$
$272$	−23.0003	+	23.0003i	−0.0845599	+	0.0845599i
$273$	−123.660	+	137.278i	−0.452966	+	0.502849i
$274$		−	337.246i		−	1.23083i
$275$	−319.556	+	82.0369i	−1.16202	+	0.298316i
$276$	40.6001	−	70.3214i	0.147102	−	0.254788i
$277$	−34.4217	−	128.464i	−0.124266	−	0.463767i	0.875546	−	0.483134i	$-0.160502\pi$
$277$	−34.4217	−	128.464i	−0.124266	−	0.463767i	−0.999812	+	0.0193668i	$0.993835\pi$
$278$	−67.7617	+	252.890i	−0.243747	+	0.909677i
$279$			108.529i			0.388993i
$280$	−97.4345	+	17.5076i	−0.347980	+	0.0625273i
$281$	456.720			1.62534			0.812670	−	0.582724i	$-0.198013\pi$
$281$	456.720			1.62534			0.812670	+	0.582724i	$0.198013\pi$
$282$	127.285	+	34.1060i	0.451367	+	0.120943i
$283$	−90.4360	+	24.2323i	−0.319562	+	0.0856264i	−0.415034	−	0.909806i	$-0.636230\pi$
$283$	−90.4360	+	24.2323i	−0.319562	+	0.0856264i	0.0954725	+	0.995432i	$0.469564\pi$
$284$	−143.207	−	82.6803i	−0.504248	−	0.291128i
$285$	77.3893	−	31.5805i	0.271541	−	0.110809i
$286$	284.403			0.994417
$287$	10.6534	−	50.0664i	0.0371197	−	0.174447i
$288$	−12.0000	−	12.0000i	−0.0416667	−	0.0416667i
$289$	193.014	−	111.437i	0.667868	−	0.385594i
$290$	−179.750	+	231.725i	−0.619828	+	0.799051i
$291$	157.557	−	272.896i	0.541432	−	0.937788i
$292$	99.1334	+	26.5627i	0.339498	+	0.0909682i
$293$	41.1011	+	41.1011i	0.140277	+	0.140277i	0.773758	−	0.633481i	$-0.218375\pi$
$293$	41.1011	+	41.1011i	0.140277	+	0.140277i	−0.633481	+	0.773758i	$0.718375\pi$
$294$	109.627	+	48.8664i	0.372881	+	0.166212i
$295$	4.02568	+	5.30382i	0.0136464	+	0.0179790i
$296$	6.86455	+	11.8898i	0.0231911	+	0.0401681i
$297$	17.7478	+	66.2356i	0.0597568	+	0.223016i
$298$	68.9423	−	18.4730i	0.231350	−	0.0619900i
$299$	309.350	−	178.603i	1.03462	−	0.597335i
$300$	42.5111	+	75.4507i	0.141704	+	0.251502i
$301$	−404.435	+	262.518i	−1.34364	+	0.872152i
$302$	33.1648	−	33.1648i	0.109817	−	0.109817i
$303$	22.8041	−	85.1060i	0.0752610	−	0.280878i
$304$	−33.4339	−	19.3031i	−0.109980	−	0.0634970i
$305$	37.3440	+	295.647i	0.122439	+	0.969334i
$306$	−17.2502	−	29.8783i	−0.0563733	−	0.0976414i
$307$	−219.450	+	219.450i	−0.714822	+	0.714822i	−0.967540	−	0.252718i	$-0.918676\pi$
$307$	−219.450	+	219.450i	−0.714822	+	0.714822i	0.252718	+	0.967540i	$0.418676\pi$
$308$	−57.0538	−	175.724i	−0.185240	−	0.570533i
$309$			212.419i			0.687442i
$310$	−236.844	+	96.6499i	−0.764014	+	0.311774i
$311$	239.292	−	414.465i	0.769427	−	1.33269i	−0.168447	−	0.985711i	$-0.553875\pi$
$311$	239.292	−	414.465i	0.769427	−	1.33269i	0.937874	−	0.346976i	$-0.112791\pi$
$312$	−19.3221	−	72.1112i	−0.0619299	−	0.231126i
$313$	99.3245	−	370.684i	0.317331	−	1.18429i	−0.604470	−	0.796628i	$-0.706615\pi$
$313$	99.3245	−	370.684i	0.317331	−	1.18429i	0.921800	−	0.387666i	$-0.126718\pi$
$314$			320.114i			1.01947i
$315$	8.81071	−	104.630i	0.0279705	−	0.332158i
$316$	−60.8270			−0.192490
$317$	141.782	+	37.9902i	0.447260	+	0.119843i	0.475417	−	0.879760i	$-0.342297\pi$
$317$	141.782	+	37.9902i	0.447260	+	0.119843i	−0.0281569	+	0.999604i	$0.508964\pi$
$318$	−111.353	+	29.8369i	−0.350166	+	0.0938267i
$319$	−473.999	−	273.663i	−1.48589	−	0.857879i
$320$	15.5012	−	36.8743i	0.0484413	−	0.115232i
$321$	335.768			1.04601
$322$	−172.412	−	155.309i	−0.535441	−	0.482325i
$323$	−55.4971	−	55.4971i	−0.171818	−	0.171818i
$324$	15.5885	−	9.00000i	0.0481125	−	0.0277778i
$325$	−4.00181	+	380.951i	−0.0123133	+	1.17216i
$326$	−122.094	+	211.473i	−0.374522	+	0.648692i
$327$	112.816	+	30.2289i	0.345003	+	0.0924432i
$328$	14.6249	+	14.6249i	0.0445882	+	0.0445882i
$329$	171.037	−	335.498i	0.519870	−	1.01975i
$330$	−128.742	+	97.7169i	−0.390126	+	0.296112i
$331$	29.0788	+	50.3660i	0.0878515	+	0.152163i	0.906603	−	0.421985i	$-0.138667\pi$
$331$	29.0788	+	50.3660i	0.0878515	+	0.152163i	−0.818751	+	0.574148i	$0.805333\pi$
$332$	−23.6226	−	88.1607i	−0.0711524	−	0.265544i
$333$	−14.0657	+	3.76890i	−0.0422394	+	0.0113180i
$334$	274.459	−	158.459i	0.821732	−	0.474427i
$335$	−82.6905	+	603.583i	−0.246837	+	1.80174i
$336$	−40.6791	+	26.4047i	−0.121069	+	0.0785854i
$337$	−296.066	+	296.066i	−0.878534	+	0.878534i	−0.993383	−	0.114849i	$-0.963362\pi$
$337$	−296.066	+	296.066i	−0.878534	+	0.878534i	0.114849	+	0.993383i	$0.463362\pi$
$338$	23.1415	−	86.3653i	0.0684660	−	0.255519i
$339$	182.397	+	105.307i	0.538045	+	0.310640i
$340$	49.8416	−	64.2533i	0.146593	−	0.188980i
$341$	−238.705	−	413.449i	−0.700014	−	1.21246i
$342$	28.9546	−	28.9546i	0.0846627	−	0.0846627i
$343$	201.792	−	277.361i	0.588315	−	0.808632i
$344$		−	194.824i		−	0.566350i
$345$	−78.6688	+	187.137i	−0.228026	+	0.542427i
$346$	29.8727	−	51.7411i	0.0863373	−	0.149541i
$347$	−33.2690	−	124.162i	−0.0958760	−	0.357814i	0.901275	−	0.433248i	$-0.142633\pi$
$347$	−33.2690	−	124.162i	−0.0958760	−	0.357814i	−0.997151	+	0.0754337i	$0.975966\pi$
$348$	−37.1850	+	138.776i	−0.106853	+	0.398782i
$349$		−	335.241i		−	0.960576i	−0.877111	−	0.480288i	$-0.840532\pi$
$349$		−	335.241i		−	0.960576i	0.877111	−	0.480288i	$-0.159468\pi$
$350$	236.181	−	73.9496i	0.674803	−	0.211285i
$351$	79.1836			0.225594
$352$	72.1082	+	19.3213i	0.204853	+	0.0548902i
$353$	−28.0127	+	7.50598i	−0.0793561	+	0.0212634i	−0.298279	−	0.954479i	$-0.596412\pi$
$353$	−28.0127	+	7.50598i	−0.0793561	+	0.0212634i	0.218923	+	0.975742i	$0.429746\pi$
$354$	2.82499	+	1.63101i	0.00798021	+	0.00460737i
$355$	381.097	+	160.206i	1.07351	+	0.451284i
$356$	−44.2343			−0.124254
$357$	−93.7744	+	30.4465i	−0.262673	+	0.0852844i
$358$	−339.884	−	339.884i	−0.949398	−	0.949398i
$359$	−237.071	+	136.873i	−0.660366	+	0.381262i	−0.792416	−	0.609981i	$-0.791177\pi$
$359$	−237.071	+	136.873i	−0.660366	+	0.381262i	0.132050	+	0.991243i	$0.457844\pi$
$360$	33.5230	+	26.0040i	0.0931195	+	0.0722333i
$361$	−133.924	+	231.963i	−0.370980	+	0.642556i
$362$	−51.3646	−	13.7631i	−0.141891	−	0.0380196i
$363$	−65.0994	−	65.0994i	−0.179337	−	0.179337i
$364$	−213.055	+	11.1191i	−0.585315	+	0.0305469i
$365$	−254.202	−	34.8255i	−0.696443	−	0.0954123i
$366$	72.9938	+	126.429i	0.199437	+	0.345434i
$367$	73.2224	+	273.270i	0.199516	+	0.744604i	0.991051	+	0.133481i	$0.0426154\pi$
$367$	73.2224	+	273.270i	0.199516	+	0.744604i	−0.791535	+	0.611123i	$0.790718\pi$
$368$	90.5670	−	24.2673i	0.246106	−	0.0659439i
$369$	−18.9984	+	10.9687i	−0.0514860	+	0.0297255i
$370$	−20.7511	−	27.3394i	−0.0560840	−	0.0738904i
$371$	17.1699	+	328.995i	0.0462800	+	0.886778i
$372$	−88.6137	+	88.6137i	−0.238209	+	0.238209i
$373$	86.9270	−	324.416i	0.233048	−	0.869747i	−0.745971	−	0.665979i	$-0.768014\pi$
$373$	86.9270	−	324.416i	0.233048	−	0.869747i	0.979019	−	0.203769i	$-0.0653191\pi$
$374$	131.432	+	75.8821i	0.351422	+	0.202893i
$375$	−129.078	−	173.821i	−0.344208	−	0.463524i
$376$	76.0807	+	131.776i	0.202342	+	0.350467i
$377$	−446.909	+	446.909i	−1.18544	+	1.18544i
$378$	−15.8849	−	48.9251i	−0.0420236	−	0.129432i
$379$			479.313i			1.26468i	0.774692	+	0.632339i	$0.217905\pi$
$379$			479.313i			1.26468i	−0.774692	+	0.632339i	$0.782095\pi$
$380$	88.9734	+	37.4027i	0.234141	+	0.0984281i
$381$	−136.741	+	236.843i	−0.358901	+	0.621635i
$382$	−103.660	−	386.865i	−0.271362	−	1.01274i
$383$	105.779	−	394.771i	0.276184	−	1.03073i	−0.678859	−	0.734268i	$-0.737525\pi$
$383$	105.779	−	394.771i	0.276184	−	1.03073i	0.955044	−	0.296465i	$-0.0958079\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	196.563	+	417.972i	0.510554	+	1.08564i
$386$	−223.764			−0.579700
$387$	199.601	+	53.4830i	0.515765	+	0.138199i
$388$	351.464	−	94.1744i	0.905834	−	0.242717i
$389$	427.944	+	247.074i	1.10011	+	0.635151i	0.936251	−	0.351332i	$-0.114271\pi$
$389$	427.944	+	247.074i	1.10011	+	0.635151i	0.163863	+	0.986483i	$0.447605\pi$
$390$	70.5165	+	172.803i	0.180811	+	0.443086i
$391$	190.614			0.487504
$392$	49.6108	+	129.409i	0.126558	+	0.330126i
$393$	90.1523	+	90.1523i	0.229395	+	0.229395i
$394$	−325.633	+	188.004i	−0.826480	+	0.477168i
$395$	150.869	−	19.0567i	0.381946	−	0.0482447i
$396$	−39.5902	+	68.5722i	−0.0999752	+	0.173162i
$397$	557.198	+	149.301i	1.40352	+	0.376073i	0.879608	−	0.475699i	$-0.157805\pi$
$397$	557.198	+	149.301i	1.40352	+	0.376073i	0.523914	+	0.851771i	$0.324471\pi$
$398$	−5.21998	−	5.21998i	−0.0131155	−	0.0131155i
$399$	−63.7116	−	98.1541i	−0.159678	−	0.246000i
$400$	−26.8951	+	96.3154i	−0.0672378	+	0.240788i
$401$	−200.253	−	346.849i	−0.499384	−	0.864959i	0.500615	−	0.865670i	$-0.333107\pi$
$401$	−200.253	−	346.849i	−0.499384	−	0.864959i	−1.00000		0.000710769i	$0.999774\pi$
$402$	77.2461	+	288.286i	0.192154	+	0.717130i
$403$	−532.503	+	142.684i	−1.32135	+	0.354054i
$404$	88.1083	−	50.8693i	0.218090	−	0.125914i
$405$	−35.8443	+	27.2064i	−0.0885044	+	0.0671762i
$406$	365.785	+	186.478i	0.900949	+	0.459304i
$407$	45.2948	−	45.2948i	0.111289	−	0.111289i
$408$	10.3107	−	38.4802i	0.0252714	−	0.0943143i
$409$	−579.420	−	334.528i	−1.41667	−	0.817917i	−0.420669	−	0.907214i	$-0.638205\pi$
$409$	−579.420	−	334.528i	−1.41667	−	0.817917i	−0.996005	+	0.0892974i	$0.971538\pi$
$410$	−40.8560	−	31.6922i	−0.0996488	−	0.0772981i
$411$	206.520	+	357.704i	0.502482	+	0.870325i
$412$	−173.440	+	173.440i	−0.420970	+	0.420970i
$413$	6.23915	−	6.92624i	0.0151069	−	0.0167705i
$414$			99.4494i			0.240216i
$415$	86.2110	+	211.263i	0.207737	+	0.509069i
$416$	43.1021	−	74.6550i	0.103611	−	0.179459i
$417$	−82.9908	−	309.726i	−0.199019	−	0.742748i
$418$	−46.6202	+	173.989i	−0.111532	+	0.416241i
$419$			19.3686i			0.0462258i	0.999733	+	0.0231129i	$0.00735772\pi$
$419$			19.3686i			0.0462258i	−0.999733	+	0.0231129i	$0.992642\pi$
$420$	92.6237	−	78.2359i	0.220533	−	0.186276i
$421$	−337.581			−0.801854			−0.400927	−	0.916110i	$-0.631312\pi$
$421$	−337.581			−0.801854			−0.400927	+	0.916110i	$0.631312\pi$
$422$	−68.2548	−	18.2888i	−0.161741	−	0.0433384i
$423$	−155.892	+	41.7712i	−0.368540	+	0.0987499i
$424$	−115.281	−	66.5574i	−0.271889	−	0.156975i
$425$	−103.492	+	174.982i	−0.243510	+	0.411722i
$426$	202.525			0.475410
$427$	396.804	−	128.834i	0.929283	−	0.301718i
$428$	274.153	+	274.153i	0.640545	+	0.640545i
$429$	−301.655	+	174.161i	−0.703159	+	0.405969i
$430$	61.0370	+	483.221i	0.141947	+	1.12377i
$431$	123.164	−	213.326i	0.285763	−	0.494955i	−0.687031	−	0.726628i	$-0.741086\pi$
$431$	123.164	−	213.326i	0.285763	−	0.494955i	0.972794	+	0.231673i	$0.0744198\pi$
$432$	20.0764	+	5.37945i	0.0464731	+	0.0124524i
$433$	480.212	+	480.212i	1.10904	+	1.10904i	0.993277	+	0.115758i	$0.0369298\pi$
$433$	480.212	+	480.212i	1.10904	+	1.10904i	0.115758	+	0.993277i	$0.463070\pi$
$434$	194.985	+	300.394i	0.449274	+	0.692152i
$435$	48.7520	−	355.855i	0.112074	−	0.818058i
$436$	67.4320	+	116.796i	0.154661	+	0.267880i
$437$	58.5544	+	218.528i	0.133992	+	0.500064i
$438$	−121.413	+	32.5326i	−0.277199	+	0.0742752i
$439$	−309.357	+	178.607i	−0.704685	+	0.406850i	−0.809090	−	0.587685i	$-0.800040\pi$
$439$	−309.357	+	178.607i	−0.704685	+	0.406850i	0.104405	+	0.994535i	$0.466706\pi$
$440$	−184.903	−	25.3316i	−0.420233	−	0.0575717i
$441$	−146.201	+	15.3019i	−0.331522	+	0.0346981i
$442$	123.920	−	123.920i	0.280362	−	0.280362i
$443$	206.262	−	769.781i	0.465603	−	1.73765i	−0.189280	−	0.981923i	$-0.560615\pi$
$443$	206.262	−	769.781i	0.465603	−	1.73765i	0.654883	−	0.755731i	$-0.272718\pi$
$444$	−14.5619	−	8.40733i	−0.0327971	−	0.0189354i
$445$	109.714	−	13.8583i	0.246549	−	0.0311423i
$446$	−211.407	−	366.168i	−0.474007	−	0.821004i
$447$	−61.8120	+	61.8120i	−0.138282	+	0.138282i
$448$	−54.7737	−	11.6550i	−0.122263	−	0.0260156i
$449$		−	838.986i		−	1.86857i	−0.356531	−	0.934283i	$-0.616041\pi$
$449$		−	838.986i		−	1.86857i	0.356531	−	0.934283i	$-0.383959\pi$
$450$	−91.2937	−	53.9950i	−0.202875	−	0.119989i
$451$	48.2503	−	83.5720i	0.106985	−	0.185304i
$452$	62.9438	+	234.909i	0.139256	+	0.519711i
$453$	−14.8674	+	55.4858i	−0.0328198	+	0.122485i
$454$		−	64.0509i		−	0.141081i
$455$	524.954	−	94.3270i	1.15374	−	0.207312i
$456$	47.2827			0.103690
$457$	445.251	+	119.305i	0.974291	+	0.261060i	0.710638	−	0.703557i	$-0.248406\pi$
$457$	445.251	+	119.305i	0.974291	+	0.261060i	0.263652	+	0.964618i	$0.415073\pi$
$458$	133.728	−	35.8324i	0.291983	−	0.0782367i
$459$	36.5932	+	21.1271i	0.0797238	+	0.0460286i
$460$	−217.030	+	88.5641i	−0.471804	+	0.192531i
$461$	583.525			1.26578			0.632890	−	0.774241i	$-0.281868\pi$
$461$	583.525			1.26578			0.632890	+	0.774241i	$0.281868\pi$
$462$	168.123	+	151.445i	0.363903	+	0.327804i
$463$	235.910	+	235.910i	0.509525	+	0.509525i	0.914381	−	0.404856i	$-0.132678\pi$
$463$	235.910	+	235.910i	0.509525	+	0.509525i	−0.404856	+	0.914381i	$0.632678\pi$
$464$	−143.672	+	82.9489i	−0.309637	+	0.178769i
$465$	192.026	−	247.550i	0.412958	−	0.532365i
$466$	128.891	−	223.246i	0.276591	−	0.479069i
$467$	−223.045	−	59.7647i	−0.477612	−	0.127976i	0.0119785	−	0.999928i	$-0.496187\pi$
$467$	−223.045	−	59.7647i	−0.477612	−	0.127976i	−0.489590	+	0.871952i	$0.662854\pi$
$468$	64.6531	+	64.6531i	0.138148	+	0.138148i
$469$	851.750	−	44.4519i	1.81610	−	0.0947801i
$470$	−229.987	−	303.006i	−0.489333	−	0.644695i
$471$	−196.029	−	339.532i	−0.416198	−	0.720875i
$472$	0.974883	+	3.63831i	0.00206543	+	0.00770829i
$473$	−878.027	+	235.267i	−1.85629	+	0.497392i
$474$	64.5167	−	37.2488i	0.136111	−	0.0785839i
$475$	−232.398	−	64.8948i	−0.489259	−	0.136621i
$476$	−101.426	−	51.7070i	−0.213080	−	0.108628i
$477$	99.8361	−	99.8361i	0.209300	−	0.209300i
$478$	24.9416	−	93.0835i	0.0521792	−	0.194735i
$479$	−497.384	−	287.165i	−1.03838	−	0.599509i	−0.119006	−	0.992894i	$-0.537971\pi$
$479$	−497.384	−	287.165i	−1.03838	−	0.599509i	−0.919374	+	0.393385i	$0.871304\pi$
$480$	6.13926	+	48.6036i	0.0127901	+	0.101257i
$481$	−36.9846	−	64.0592i	−0.0768910	−	0.133179i
$482$	−273.382	+	273.382i	−0.567183	+	0.567183i
$483$	277.977	+	59.1493i	0.575522	+	0.122462i
$484$		−	106.307i		−	0.219642i
$485$	−842.228	+	343.691i	−1.73655	+	0.708641i
$486$	−11.0227	+	19.0919i	−0.0226805	+	0.0392837i
$487$	−197.500	−	737.079i	−0.405544	−	1.51351i	−0.803051	−	0.595911i	$-0.796791\pi$
$487$	−197.500	−	737.079i	−0.405544	−	1.51351i	0.397507	−	0.917599i	$-0.369875\pi$
$488$	−43.6297	+	162.828i	−0.0894050	+	0.333664i
$489$		−	299.069i		−	0.611592i
$490$	−163.592	−	305.430i	−0.333862	−	0.623327i
$491$	267.633			0.545077			0.272538	−	0.962145i	$-0.412137\pi$
$491$	267.633			0.545077			0.272538	+	0.962145i	$0.412137\pi$
$492$	−24.4680	−	6.55618i	−0.0497317	−	0.0133256i
$493$	−325.771	+	87.2902i	−0.660794	+	0.177059i
$494$	180.134	+	104.000i	0.364644	+	0.210527i
$495$	76.7120	−	182.482i	0.154974	−	0.368651i
$496$	−144.705			−0.291745
$497$	120.455	−	566.089i	0.242364	−	1.13901i
$498$	79.0427	+	79.0427i	0.158720	+	0.158720i
$499$	−328.627	+	189.733i	−0.658572	+	0.380227i	−0.791733	−	0.610868i	$-0.790821\pi$
$499$	−328.627	+	189.733i	−0.658572	+	0.380227i	0.133161	+	0.991094i	$0.457487\pi$
$500$	36.5328	−	247.316i	0.0730656	−	0.494633i
$501$	−194.071	+	336.142i	−0.387368	+	0.670941i
$502$	−139.531	−	37.3871i	−0.277950	−	0.0744764i
$503$	−344.318	−	344.318i	−0.684530	−	0.684530i	0.276488	−	0.961017i	$-0.410829\pi$
$503$	−344.318	−	344.318i	−0.684530	−	0.684530i	−0.961017	+	0.276488i	$0.910829\pi$
$504$	26.9772	−	52.9172i	0.0535262	−	0.104994i
$505$	−202.597	+	153.774i	−0.401183	+	0.304504i
$506$	−218.734	−	378.859i	−0.432281	−	0.748733i
$507$	28.3425	+	105.776i	0.0559023	+	0.208630i
$508$	−305.030	+	81.7326i	−0.600453	+	0.160891i
$509$	−217.653	+	125.662i	−0.427608	+	0.246880i	−0.698327	−	0.715779i	$-0.746072\pi$
$509$	−217.653	+	125.662i	−0.427608	+	0.246880i	0.270719	+	0.962658i	$0.412739\pi$
$510$	−13.5181	+	98.6725i	−0.0265060	+	0.193476i
$511$	18.7211	+	358.718i	0.0366363	+	0.701993i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	−12.9800	+	48.4421i	−0.0253022	+	0.0944290i
$514$	437.143	+	252.385i	0.850473	+	0.491021i
$515$	375.844	−	484.519i	0.729794	−	0.940813i
$516$	119.305	+	206.642i	0.231211	+	0.400470i
$517$	502.008	−	502.008i	0.971002	−	0.971002i
$518$	−32.1608	+	35.7025i	−0.0620864	+	0.0689237i
$519$			73.1729i			0.140988i
$520$	−83.5169	+	198.670i	−0.160609	+	0.382057i
$521$	−146.018	+	252.911i	−0.280266	+	0.485434i	−0.971450	−	0.237244i	$-0.923756\pi$
$521$	−146.018	+	252.911i	−0.280266	+	0.485434i	0.691184	+	0.722678i	$0.257089\pi$
$522$	−45.5421	−	169.966i	−0.0872454	−	0.325604i
$523$	199.320	−	743.873i	0.381109	−	1.42232i	−0.463100	−	0.886306i	$-0.653263\pi$
$523$	199.320	−	743.873i	0.381109	−	1.42232i	0.844209	−	0.536014i	$-0.180070\pi$
$524$			147.218i			0.280951i
$525$	−205.223	+	223.066i	−0.390901	+	0.424888i
$526$	273.223			0.519435
$527$	−284.156	−	76.1394i	−0.539196	−	0.144477i
$528$	−88.3142	+	23.6637i	−0.167262	+	0.0448176i
$529$	−17.7146	−	10.2276i	−0.0334870	−	0.0193337i
$530$	306.782	+	128.965i	0.578834	+	0.243330i
$531$	−3.99514			−0.00752381
$532$	28.1222	−	132.163i	0.0528613	−	0.248426i
$533$	−78.7957	−	78.7957i	−0.147834	−	0.147834i
$534$	46.9176	−	27.0879i	0.0878607	−	0.0507264i
$535$	−765.870	−	594.090i	−1.43153	−	1.11045i
$536$	−172.314	+	298.456i	−0.321481	+	0.556821i
$537$	568.638	+	152.366i	1.05892	+	0.283736i
$538$	282.763	+	282.763i	0.525582	+	0.525582i
$539$	523.308	−	379.857i	0.970887	−	0.704743i
$540$	−51.4807	−	7.05282i	−0.0953345	−	0.0130608i
$541$	82.6003	+	143.068i	0.152681	+	0.264451i	0.932212	−	0.361912i	$-0.117876\pi$
$541$	82.6003	+	143.068i	0.152681	+	0.264451i	−0.779531	+	0.626363i	$0.784543\pi$
$542$	−187.573	−	700.033i	−0.346076	−	1.29157i
$543$	62.9085	−	16.8563i	0.115854	−	0.0310429i
$544$	39.8377	−	23.0003i	0.0732310	−	0.0422800i
$545$	−203.842	−	268.561i	−0.374022	−	0.492773i
$546$	219.169	−	142.262i	0.401409	−	0.260554i
$547$	172.204	−	172.204i	0.314815	−	0.314815i	−0.531956	−	0.846772i	$-0.678543\pi$
$547$	172.204	−	172.204i	0.314815	−	0.314815i	0.846772	+	0.531956i	$0.178543\pi$
$548$	−123.441	+	460.687i	−0.225257	+	0.840670i
$549$	−154.843	−	89.3988i	−0.282046	−	0.162839i
$550$	466.549	+	4.90100i	0.848270	+	0.00891090i
$551$	−200.146	−	346.664i	−0.363242	−	0.629154i
$552$	−81.2001	+	81.2001i	−0.147102	+	0.147102i
$553$	−65.7438	−	202.489i	−0.118886	−	0.366164i
$554$			188.084i			0.339501i
$555$	38.7518	+	16.2905i	0.0698230	+	0.0293522i
$556$	185.128	−	320.652i	0.332965	−	0.576712i
$557$	−6.64563	−	24.8018i	−0.0119311	−	0.0445275i	0.959704	−	0.281014i	$-0.0906708\pi$
$557$	−6.64563	−	24.8018i	−0.0119311	−	0.0445275i	−0.971635	+	0.236487i	$0.924004\pi$
$558$	39.7244	−	148.254i	0.0711907	−	0.265687i
$559$			1049.67i			1.87776i
$560$	139.506	+	11.7476i	0.249118	+	0.0209779i
$561$	−185.872			−0.331323
$562$	−623.892	−	167.171i	−1.11013	−	0.297458i
$563$	813.352	−	217.937i	1.44468	−	0.387100i	0.550507	−	0.834831i	$-0.314434\pi$
$563$	813.352	−	217.937i	1.44468	−	0.387100i	0.894168	+	0.447731i	$0.147768\pi$
$564$	−161.392	−	93.1794i	−0.286155	−	0.165212i
$565$	−229.714	−	562.924i	−0.406574	−	0.996326i
$566$	132.408			0.233936
$567$	46.8089	+	42.1654i	0.0825554	+	0.0743659i
$568$	165.361	+	165.361i	0.291128	+	0.291128i
$569$	−88.8020	+	51.2699i	−0.156067	+	0.0901052i	−0.576000	−	0.817450i	$-0.695387\pi$
$569$	−88.8020	+	51.2699i	−0.156067	+	0.0901052i	0.419933	+	0.907555i	$0.362054\pi$
$570$	−117.275	+	14.8133i	−0.205746	+	0.0259883i
$571$	313.449	−	542.910i	0.548947	−	0.950805i	−0.449400	−	0.893331i	$-0.648362\pi$
$571$	313.449	−	542.910i	0.548947	−	0.950805i	0.998347	−	0.0574739i	$-0.0183046\pi$
$572$	−388.502	−	104.099i	−0.679199	−	0.181991i
$573$	346.854	+	346.854i	0.605330	+	0.605330i
$574$	−32.8783	+	64.4926i	−0.0572793	+	0.112356i
$575$	510.551	−	287.659i	0.887914	−	0.500276i
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	256.448	+	957.078i	0.444451	+	1.65871i	0.717381	+	0.696681i	$0.245341\pi$
$577$	256.448	+	957.078i	0.444451	+	1.65871i	−0.272930	+	0.962034i	$0.587993\pi$
$578$	−304.451	+	81.5773i	−0.526731	+	0.141137i
$579$	237.338	−	137.027i	0.409910	−	0.236661i
$580$	330.361	−	250.749i	0.569587	−	0.432326i
$581$	267.949	−	173.925i	0.461186	−	0.299355i
$582$	−315.114	+	315.114i	−0.541432	+	0.541432i
$583$	−160.747	+	599.917i	−0.275724	+	1.02902i
$584$	−125.696	−	72.5707i	−0.215233	−	0.124265i
$585$	−180.614	−	140.103i	−0.308742	−	0.239493i
$586$	−41.1011	−	71.1892i	−0.0701384	−	0.121483i
$587$	−625.656	+	625.656i	−1.06585	+	1.06585i	−0.0681813	+	0.997673i	$0.521720\pi$
$587$	−625.656	+	625.656i	−1.06585	+	1.06585i	−0.997673	+	0.0681813i	$0.978280\pi$
$588$	−131.867	−	106.879i	−0.224263	−	0.181767i
$589$		−	349.158i		−	0.592798i
$590$	−3.55785	−	8.71865i	−0.00603026	−	0.0147774i
$591$	230.257	−	398.817i	0.389606	−	0.674818i
$592$	−5.02520	−	18.7543i	−0.00848852	−	0.0316796i
$593$	−143.959	+	537.263i	−0.242764	+	0.906009i	0.731730	+	0.681595i	$0.238713\pi$
$593$	−143.959	+	537.263i	−0.242764	+	0.906009i	−0.974494	+	0.224414i	$0.927953\pi$
$594$		−	96.9757i		−	0.163259i
$595$	267.765	+	96.4724i	0.450026	+	0.162138i
$596$	−100.938			−0.169360
$597$	8.73320	+	2.34005i	0.0146285	+	0.00391969i
$598$	−487.953	+	130.747i	−0.815975	+	0.218640i
$599$	179.972	+	103.907i	0.300454	+	0.173467i	0.642647	−	0.766163i	$-0.277836\pi$
$599$	179.972	+	103.907i	0.300454	+	0.173467i	−0.342193	+	0.939630i	$0.611170\pi$
$600$	−30.4543	−	118.628i	−0.0507572	−	0.197713i
$601$	−803.576			−1.33707			−0.668533	−	0.743683i	$-0.733077\pi$
$601$	−803.576			−1.33707			−0.668533	+	0.743683i	$0.733077\pi$
$602$	648.557	−	210.572i	1.07734	−	0.349788i
$603$	−258.470	−	258.470i	−0.428641	−	0.428641i
$604$	−57.4431	+	33.1648i	−0.0951045	+	0.0549086i
$605$	33.3052	+	263.672i	0.0550499	+	0.435821i
$606$	−62.3019	+	107.910i	−0.102808	+	0.178070i
$607$	−241.467	−	64.7010i	−0.397805	−	0.106591i	0.0543700	−	0.998521i	$-0.482685\pi$
$607$	−241.467	−	64.7010i	−0.397805	−	0.106591i	−0.452175	+	0.891929i	$0.649352\pi$
$608$	38.6062	+	38.6062i	0.0634970	+	0.0634970i
$609$	−502.168	+	26.2076i	−0.824578	+	0.0430338i
$610$	57.2014	−	417.530i	0.0937728	−	0.684475i
$611$	−409.905	−	709.976i	−0.670875	−	1.16199i
$612$	12.6280	+	47.1285i	0.0206340	+	0.0770073i
$613$	508.814	−	136.336i	0.830039	−	0.222408i	0.181308	−	0.983426i	$-0.441967\pi$
$613$	508.814	−	136.336i	0.830039	−	0.222408i	0.648731	+	0.761018i	$0.275300\pi$
$614$	380.099	−	219.450i	0.619054	−	0.357411i
$615$	62.7418	+	8.59559i	0.102019	+	0.0139766i
$616$	13.6175	+	260.927i	0.0221063	+	0.423582i
$617$	−188.817	+	188.817i	−0.306025	+	0.306025i	−0.843365	−	0.537340i	$-0.819429\pi$
$617$	−188.817	+	188.817i	−0.306025	+	0.306025i	0.537340	+	0.843365i	$0.319429\pi$
$618$	77.7509	−	290.170i	0.125811	−	0.469531i
$619$	93.0351	+	53.7139i	0.150299	+	0.0867752i	0.573263	−	0.819371i	$-0.305677\pi$
$619$	93.0351	+	53.7139i	0.150299	+	0.0867752i	−0.422964	+	0.906146i	$0.639010\pi$
$620$	358.912	−	45.3352i	0.578890	−	0.0731213i
$621$	−60.9001	−	105.482i	−0.0980678	−	0.169858i
$622$	−478.584	+	478.584i	−0.769427	+	0.769427i
$623$	−47.8099	−	147.253i	−0.0767415	−	0.236361i
$624$			105.578i			0.169196i
$625$	−13.1295	+	624.862i	−0.0210073	+	0.999779i
$626$	−271.359	+	470.008i	−0.433482	+	0.750812i
$627$	−57.0978	−	213.092i	−0.0910651	−	0.339860i
$628$	117.170	−	437.284i	0.186576	−	0.696312i
$629$		−	39.4717i		−	0.0627531i
$630$	−50.3328	+	139.702i	−0.0798933	+	0.221749i
$631$	−494.190			−0.783185			−0.391593	−	0.920139i	$-0.628076\pi$
$631$	−494.190			−0.783185			−0.391593	+	0.920139i	$0.628076\pi$
$632$	83.0912	+	22.2642i	0.131473	+	0.0352282i
$633$	83.5947	−	22.3991i	0.132061	−	0.0353857i
$634$	−179.772	−	103.791i	−0.283552	−	0.163709i
$635$	730.958	−	298.285i	1.15111	−	0.469739i
$636$	163.032			0.256339
$637$	−267.291	−	697.227i	−0.419609	−	1.09455i
$638$	547.327	+	547.327i	0.857879	+	0.857879i
$639$	−214.810	+	124.021i	−0.336166	+	0.194085i
$640$	−34.6720	+	44.6974i	−0.0541750	+	0.0698396i
$641$	−209.798	+	363.381i	−0.327298	+	0.566897i	−0.981975	−	0.189012i	$-0.939471\pi$
$641$	−209.798	+	363.381i	−0.327298	+	0.566897i	0.654677	+	0.755909i	$0.272805\pi$
$642$	−458.667	−	122.900i	−0.714435	−	0.191432i
$643$	−192.944	−	192.944i	−0.300069	−	0.300069i	0.540972	−	0.841041i	$-0.318057\pi$
$643$	−192.944	−	192.944i	−0.300069	−	0.300069i	−0.841041	+	0.540972i	$0.818057\pi$
$644$	178.672	+	275.263i	0.277441	+	0.427426i
$645$	−360.651	−	475.156i	−0.559149	−	0.736676i
$646$	55.4971	+	96.1238i	0.0859088	+	0.148798i
$647$	91.8957	+	342.959i	0.142033	+	0.530076i	0.999870	+	0.0161528i	$0.00514181\pi$
$647$	91.8957	+	342.959i	0.142033	+	0.530076i	−0.857836	+	0.513923i	$0.828192\pi$
$648$	−24.5885	+	6.58846i	−0.0379452	+	0.0101674i
$649$	15.2198	−	8.78713i	0.0234511	−	0.0135395i
$650$	144.904	−	518.924i	0.222930	−	0.798345i
$651$	−390.766	−	199.212i	−0.600254	−	0.306010i
$652$	244.189	−	244.189i	0.374522	−	0.374522i
$653$	−101.202	+	377.692i	−0.154981	+	0.578395i	0.844126	+	0.536144i	$0.180120\pi$
$653$	−101.202	+	377.692i	−0.154981	+	0.578395i	−0.999107	+	0.0422513i	$0.986547\pi$
$654$	−143.045	−	82.5870i	−0.218723	−	0.126280i
$655$	−46.1224	−	365.144i	−0.0704158	−	0.557471i
$656$	−14.6249	−	25.3311i	−0.0222941	−	0.0386145i
$657$	108.856	−	108.856i	0.165687	−	0.165687i
$658$	−356.442	+	395.695i	−0.541705	+	0.601360i
$659$		−	325.611i		−	0.494099i	−0.969003	−	0.247050i	$-0.920539\pi$
$659$		−	325.611i		−	0.494099i	0.969003	−	0.247050i	$-0.0794610\pi$
$660$	211.631	−	86.3611i	0.320653	−	0.130850i
$661$	−127.822	+	221.394i	−0.193377	+	0.334938i	−0.946367	−	0.323093i	$-0.895277\pi$
$661$	−127.822	+	221.394i	−0.193377	+	0.334938i	0.752990	+	0.658032i	$0.228611\pi$
$662$	−21.2872	−	79.4448i	−0.0321559	−	0.120007i
$663$	−55.5519	+	207.322i	−0.0837886	+	0.312703i
$664$			129.076i			0.194392i
$665$	−28.3457	+	336.613i	−0.0426250	+	0.506185i
$666$	20.5937			0.0309214
$667$	939.054	+	251.619i	1.40788	+	0.377240i
$668$	−432.917	+	116.000i	−0.648080	+	0.173652i
$669$	448.462	+	258.920i	0.670347	+	0.387025i
$670$	333.884	−	794.242i	0.498334	−	1.18544i
$671$	786.514			1.17215
$672$	65.2335	−	21.1799i	0.0970737	−	0.0315177i
$673$	74.4755	+	74.4755i	0.110662	+	0.110662i	0.760270	−	0.649608i	$-0.225067\pi$
$673$	74.4755	+	74.4755i	0.110662	+	0.110662i	−0.649608	+	0.760270i	$0.725067\pi$
$674$	512.801	−	296.066i	0.760833	−	0.439267i
$675$	129.897	+	1.36454i	0.192439	+	0.00202154i
$676$	−63.2238	+	109.507i	−0.0935264	+	0.161992i
$677$	291.039	+	77.9835i	0.429894	+	0.115190i	0.467277	−	0.884111i	$-0.345235\pi$
$677$	291.039	+	77.9835i	0.429894	+	0.115190i	−0.0373822	+	0.999301i	$0.511902\pi$
$678$	−210.614	−	210.614i	−0.310640	−	0.310640i
$679$	693.374	+	1068.21i	1.02117	+	1.57321i
$680$	−91.6032	+	69.5283i	−0.134711	+	0.102248i
$681$	39.2230	+	67.9362i	0.0575962	+	0.0997595i
$682$	174.744	+	652.153i	0.256223	+	0.956237i
$683$	−682.280	+	182.816i	−0.998945	+	0.267667i	−0.721004	−	0.692931i	$-0.756319\pi$
$683$	−682.280	+	182.816i	−0.998945	+	0.267667i	−0.277942	+	0.960598i	$0.589652\pi$
$684$	−50.1509	+	28.9546i	−0.0733200	+	0.0423313i
$685$	161.839	−	1181.31i	0.236261	−	1.72454i
$686$	−377.174	+	305.021i	−0.549816	+	0.444637i
$687$	−119.898	+	119.898i	−0.174523	+	0.174523i
$688$	−71.3106	+	266.135i	−0.103649	+	0.386824i
$689$	621.106	+	358.596i	0.901460	+	0.520458i
$690$	175.961	−	226.839i	0.255015	−	0.328753i
$691$	363.308	+	629.267i	0.525771	+	0.910662i	0.999549	+	0.0300178i	$0.00955639\pi$
$691$	363.308	+	629.267i	0.525771	+	0.910662i	−0.473779	+	0.880644i	$0.657110\pi$
$692$	−59.7454	+	59.7454i	−0.0863373	+	0.0863373i
$693$	−271.063	−	57.6780i	−0.391144	−	0.0832294i
$694$			181.785i			0.261938i
$695$	−358.715	+	853.309i	−0.516136	+	1.22778i
$696$	101.591	−	175.961i	0.145964	−	0.252818i
$697$	−15.3904	−	57.4376i	−0.0220809	−	0.0824069i
$698$	−122.707	+	457.948i	−0.175798	+	0.656086i
$699$			315.718i			0.451670i
$700$	−349.697	+	14.5688i	−0.499567	+	0.0208126i
$701$	−693.038			−0.988642			−0.494321	−	0.869279i	$-0.664583\pi$
$701$	−693.038			−0.988642			−0.494321	+	0.869279i	$0.664583\pi$
$702$	−108.167	−	28.9832i	−0.154084	−	0.0412866i
$703$	45.2520	−	12.1252i	0.0643699	−	0.0172479i
$704$	−91.4296	−	52.7869i	−0.129872	−	0.0749814i
$705$	429.491	+	180.549i	0.609206	+	0.256098i
$706$	41.0134			0.0580927
$707$	264.571	+	238.325i	0.374216	+	0.337094i
$708$	−3.26202	−	3.26202i	−0.00460737	−	0.00460737i
$709$	−222.013	+	128.179i	−0.313135	+	0.180789i	−0.648329	−	0.761361i	$-0.724532\pi$
$709$	−222.013	+	128.179i	−0.313135	+	0.180789i	0.335193	+	0.942149i	$0.391198\pi$
$710$	−461.949	−	358.336i	−0.650633	−	0.504699i
$711$	−45.6202	+	79.0165i	−0.0641635	+	0.111134i
$712$	60.4252	+	16.1909i	0.0848669	+	0.0227400i
$713$	599.620	+	599.620i	0.840982	+	0.840982i
$714$	139.242	−	7.26691i	0.195017	−	0.0101777i
$715$	996.212	+	136.480i	1.39330	+	0.190882i
$716$	339.884	+	588.697i	0.474699	+	0.822202i
$717$	30.5472	+	114.004i	0.0426041	+	0.159001i
$718$	373.945	−	100.198i	0.520814	−	0.139552i
$719$	−527.096	+	304.319i	−0.733096	+	0.423253i	−0.819554	−	0.573002i	$-0.805779\pi$
$719$	−527.096	+	304.319i	−0.733096	+	0.423253i	0.0864576	+	0.996256i	$0.472445\pi$
$720$	−36.2752	−	47.7924i	−0.0503822	−	0.0663783i
$721$	−764.829	−	389.910i	−1.06079	−	0.540791i
$722$	267.848	−	267.848i	0.370980	−	0.370980i
$723$	122.554	−	457.377i	0.169507	−	0.632610i
$724$	65.1277	+	37.6015i	0.0899553	+	0.0519357i
$725$	−740.833	+	725.430i	−1.02184	+	1.00059i
$726$	65.0994	+	112.755i	0.0896686	+	0.155311i
$727$	−549.001	+	549.001i	−0.755160	+	0.755160i	−0.975437	−	0.220278i	$-0.929304\pi$
$727$	−549.001	+	549.001i	−0.755160	+	0.755160i	0.220278	+	0.975437i	$0.429304\pi$
$728$	295.108	+	62.7944i	0.405368	+	0.0862561i
$729$		−	27.0000i		−	0.0370370i
$730$	334.499	+	140.617i	0.458218	+	0.192626i
$731$	−280.063	+	485.084i	−0.383124	+	0.663590i
$732$	−53.4352	−	199.423i	−0.0729989	−	0.272436i
$733$	−156.408	+	583.723i	−0.213381	+	0.796347i	0.773350	+	0.633980i	$0.218580\pi$
$733$	−156.408	+	583.723i	−0.213381	+	0.796347i	−0.986730	+	0.162368i	$0.948087\pi$
$734$		−	400.095i		−	0.545088i
$735$	360.553	+	223.778i	0.490548	+	0.304460i
$736$	−132.599			−0.180162
$737$	1553.15	+	416.166i	2.10740	+	0.564676i
$738$	29.9671	−	8.02965i	0.0406058	−	0.0108803i
$739$	532.900	+	307.670i	0.721109	+	0.416333i	0.815161	−	0.579235i	$-0.196649\pi$
$739$	532.900	+	307.670i	0.721109	+	0.416333i	−0.0940517	+	0.995567i	$0.529982\pi$
$740$	18.3396	+	44.9418i	0.0247832	+	0.0607322i
$741$	−254.748			−0.343790
$742$	96.9659	−	455.700i	0.130682	−	0.614151i
$743$	236.059	+	236.059i	0.317710	+	0.317710i	0.847887	−	0.530177i	$-0.177874\pi$
$743$	236.059	+	236.059i	0.317710	+	0.317710i	−0.530177	+	0.847887i	$0.677874\pi$
$744$	153.483	−	88.6137i	0.206295	−	0.119104i
$745$	250.357	−	31.6233i	0.336050	−	0.0424474i
$746$	−237.489	+	411.343i	−0.318350	+	0.551398i
$747$	−132.241	−	35.4339i	−0.177029	−	0.0474349i
$748$	−151.764	−	151.764i	−0.202893	−	0.202893i
$749$	−616.324	+	1208.95i	−0.822863	+	1.61409i
$750$	112.701	+	284.690i	0.150268	+	0.379587i
$751$	−676.879	−	1172.39i	−0.901303	−	1.56110i	−0.825804	−	0.563957i	$-0.809279\pi$
$751$	−676.879	−	1172.39i	−0.901303	−	1.56110i	−0.0754985	−	0.997146i	$-0.524055\pi$
$752$	−55.6949	−	207.856i	−0.0740624	−	0.276405i
$753$	170.890	−	45.7897i	0.226945	−	0.0608097i
$754$	774.069	−	446.909i	1.02662	−	0.592718i
$755$	132.085	−	100.255i	0.174948	−	0.132788i
$756$	3.79138	+	72.6473i	0.00501506	+	0.0960943i
$757$	−435.838	+	435.838i	−0.575744	+	0.575744i	−0.933728	−	0.357984i	$-0.883464\pi$
$757$	−435.838	+	435.838i	−0.575744	+	0.575744i	0.357984	+	0.933728i	$0.383464\pi$
$758$	175.441	−	654.753i	0.231452	−	0.863791i
$759$	464.006	+	267.894i	0.611338	+	0.352956i
$760$	−107.850	−	83.6596i	−0.141907	−	0.110078i
$761$	560.575	+	970.944i	0.736629	+	1.27588i	0.954005	+	0.299792i	$0.0969171\pi$
$761$	560.575	+	970.944i	0.736629	+	1.27588i	−0.217375	+	0.976088i	$0.569750\pi$
$762$	273.483	−	273.483i	0.358901	−	0.358901i
$763$	−315.922	+	350.713i	−0.414053	+	0.459650i
$764$			566.410i			0.741375i
$765$	−46.0862	−	112.936i	−0.0602434	−	0.147629i
$766$	−288.992	+	500.550i	−0.377275	+	0.653459i
$767$	−5.25244	−	19.6024i	−0.00684803	−	0.0255572i
$768$	−7.17260	+	26.7685i	−0.00933933	+	0.0348548i
$769$		−	103.197i		−	0.134196i	−0.997746	−	0.0670980i	$-0.978626\pi$
$769$		−	103.197i		−	0.134196i	0.997746	−	0.0670980i	$-0.0213740\pi$
$770$	−115.522	−	642.908i	−0.150028	−	0.834945i
$771$	−618.214			−0.801834
$772$	305.667	+	81.9034i	0.395942	+	0.106092i
$773$	1022.68	−	274.026i	1.32300	−	0.354496i	0.472898	−	0.881117i	$-0.343208\pi$
$773$	1022.68	−	274.026i	1.32300	−	0.354496i	0.850100	+	0.526621i	$0.176541\pi$
$774$	−253.084	−	146.118i	−0.326982	−	0.188783i
$775$	−876.003	+	224.889i	−1.13033	+	0.290179i
$776$	−514.578			−0.663116
$777$	12.2484	−	57.5626i	0.0157638	−	0.0740831i
$778$	−494.148	−	494.148i	−0.635151	−	0.635151i
$779$	61.1211	−	35.2883i	0.0784610	−	0.0452995i
$780$	−33.0769	−	261.865i	−0.0424063	−	0.335724i
$781$	545.555	−	944.928i	0.698534	−	1.20990i
$782$	−260.383	−	69.7695i	−0.332971	−	0.0892193i
$783$	152.387	+	152.387i	0.194619	+	0.194619i
$784$	−20.4025	−	194.935i	−0.0260236	−	0.248642i
$785$	−153.618	+	1121.30i	−0.195691	+	1.42841i
$786$	−90.1523	−	156.148i	−0.114698	−	0.198662i
$787$	−17.0043	−	63.4609i	−0.0216065	−	0.0806365i	0.954281	−	0.298912i	$-0.0966236\pi$
$787$	−17.0043	−	63.4609i	−0.0216065	−	0.0806365i	−0.975887	+	0.218275i	$0.929957\pi$
$788$	513.637	−	137.629i	0.651824	−	0.174656i
$789$	−289.797	+	167.314i	−0.367296	+	0.212059i
$790$	−213.066	−	29.1899i	−0.269703	−	0.0369492i
$791$	−713.966	+	463.434i	−0.902612	+	0.585883i
$792$	79.1803	−	79.1803i	0.0999752	−	0.0999752i
$793$	235.066	−	877.279i	0.296426	−	1.10628i
$794$	−706.499	−	407.898i	−0.889798	−	0.513725i
$795$	−404.366	+	51.0767i	−0.508637	+	0.0642474i
$796$	5.21998	+	9.04127i	0.00655776	+	0.0113584i
$797$	376.938	−	376.938i	0.472946	−	0.472946i	−0.429921	−	0.902867i	$-0.641458\pi$
$797$	376.938	−	376.938i	0.472946	−	0.472946i	0.902867	+	0.429921i	$0.141458\pi$
$798$	51.1047	+	157.401i	0.0640410	+	0.197244i
$799$		−	437.470i		−	0.547521i
$800$	71.9933	−	121.725i	0.0899916	−	0.152156i
$801$	−33.1758	+	57.4621i	−0.0414179	+	0.0717380i
$802$	146.595	+	547.102i	0.182787	+	0.682172i
$803$	−175.270	+	654.118i	−0.218269	+	0.814593i
$804$		−	422.080i		−	0.524976i
$805$	−529.397	−	626.755i	−0.657636	−	0.778577i
$806$	779.639			0.967294
$807$	−473.072	−	126.759i	−0.586210	−	0.157075i
$808$	−138.978	+	37.2389i	−0.172002	+	0.0460878i
$809$	936.058	+	540.433i	1.15706	+	0.668026i	0.950597	−	0.310429i	$-0.100473\pi$
$809$	936.058	+	540.433i	1.15706	+	0.668026i	0.206459	+	0.978455i	$0.433806\pi$
$810$	58.9224	−	24.0447i	0.0727437	−	0.0296848i
$811$	−588.576			−0.725741			−0.362870	−	0.931840i	$-0.618203\pi$
$811$	−588.576			−0.725741			−0.362870	+	0.931840i	$0.618203\pi$
$812$	−431.417	−	388.620i	−0.531301	−	0.478596i
$813$	627.632	+	627.632i	0.771995	+	0.771995i
$814$	−78.4529	+	45.2948i	−0.0963795	+	0.0556447i
$815$	−529.156	+	682.161i	−0.649272	+	0.837008i
$816$	−28.1695	+	48.7910i	−0.0345214	+	0.0597929i
$817$	−642.153	−	172.064i	−0.785989	−	0.210605i
$818$	669.056	+	669.056i	0.817917	+	0.817917i
$819$	−145.347	+	285.105i	−0.177469	+	0.348114i
$820$	44.2102	+	58.2467i	0.0539148	+	0.0710326i
$821$	−291.956	−	505.682i	−0.355610	−	0.615934i	0.631612	−	0.775284i	$-0.282393\pi$
$821$	−291.956	−	505.682i	−0.355610	−	0.615934i	−0.987222	+	0.159350i	$0.949060\pi$
$822$	−151.183	−	564.224i	−0.183921	−	0.686404i
$823$	−1215.19	+	325.609i	−1.47654	+	0.395637i	−0.905167	−	0.425056i	$-0.860255\pi$
$823$	−1215.19	+	325.609i	−1.47654	+	0.395637i	−0.571370	+	0.820693i	$0.693588\pi$
$824$	300.407	−	173.440i	0.364571	−	0.210485i
$825$	−497.851	+	280.503i	−0.603456	+	0.340004i
$826$	−11.0580	+	7.17773i	−0.0133874	+	0.00868974i
$827$	613.456	−	613.456i	0.741784	−	0.741784i	−0.231137	−	0.972921i	$-0.574245\pi$
$827$	613.456	−	613.456i	0.741784	−	0.741784i	0.972921	+	0.231137i	$0.0742445\pi$
$828$	36.4010	−	135.850i	0.0439626	−	0.164071i
$829$	−721.377	−	416.487i	−0.870177	−	0.502397i	−0.00276996	−	0.999996i	$-0.500882\pi$
$829$	−721.377	−	416.487i	−0.870177	−	0.502397i	−0.867407	+	0.497599i	$0.834215\pi$
$830$	−40.4387	−	320.147i	−0.0487213	−	0.385719i
$831$	−115.177	−	199.493i	−0.138601	−	0.240064i
$832$	−86.2042	+	86.2042i	−0.103611	+	0.103611i
$833$	62.5046	−	393.527i	0.0750356	−	0.472421i
$834$			453.470i			0.543729i
$835$	1037.42	−	423.343i	1.24242	−	0.506998i
$836$	127.369	−	220.609i	0.152355	−	0.263887i
$837$	48.6523	+	181.573i	0.0581270	+	0.216933i
$838$	7.08941	−	26.4580i	0.00845991	−	0.0315728i
$839$			553.700i			0.659953i	0.943989	+	0.329976i	$0.107041\pi$
$839$			553.700i			0.659953i	−0.943989	+	0.329976i	$0.892959\pi$
$840$	−155.163	+	72.9696i	−0.184717	+	0.0868685i
$841$	−879.131			−1.04534
$842$	461.144	+	123.563i	0.547676	+	0.146749i
$843$	764.108	−	204.742i	0.906415	−	0.242873i
$844$	86.5436	+	49.9660i	0.102540	+	0.0592014i
$845$	122.506	−	291.417i	0.144977	−	0.344872i
$846$	228.242			0.269790
$847$	353.888	−	114.900i	0.417814	−	0.135655i
$848$	133.115	+	133.115i	0.156975	+	0.156975i
$849$	−140.439	+	81.0827i	−0.165417	+	0.0955038i
$850$	205.420	−	201.149i	0.241671	−	0.236646i
$851$	−56.8897	+	98.5358i	−0.0668504	+	0.115788i
$852$	−276.654	−	74.1292i	−0.324711	−	0.0870061i
$853$	299.589	+	299.589i	0.351218	+	0.351218i	0.860563	−	0.509344i	$-0.170112\pi$
$853$	299.589	+	299.589i	0.351218	+	0.351218i	−0.509344	+	0.860563i	$0.670112\pi$
$854$	−589.200	+	30.7497i	−0.689930	+	0.0360067i
$855$	115.318	−	87.5279i	0.134874	−	0.102372i
$856$	−274.153	−	474.847i	−0.320273	−	0.554728i
$857$	−356.960	−	1332.19i	−0.416523	−	1.55448i	−0.781766	−	0.623572i	$-0.785681\pi$
$857$	−356.960	−	1332.19i	−0.416523	−	1.55448i	0.365243	−	0.930912i	$-0.380986\pi$
$858$	475.816	−	127.494i	0.554564	−	0.148595i
$859$	−284.064	+	164.005i	−0.330692	+	0.190925i	−0.656148	−	0.754632i	$-0.727815\pi$
$859$	−284.064	+	164.005i	−0.330692	+	0.190925i	0.325456	+	0.945557i	$0.394482\pi$
$860$	93.4930	−	682.433i	0.108713	−	0.793527i
$861$	−4.62073	−	88.5385i	−0.00536670	−	0.102832i
$862$	−246.327	+	246.327i	−0.285763	+	0.285763i
$863$	91.1301	−	340.102i	0.105597	−	0.394093i	−0.892815	−	0.450423i	$-0.851273\pi$
$863$	91.1301	−	340.102i	0.105597	−	0.394093i	0.998412	+	0.0563301i	$0.0179399\pi$
$864$	−25.4558	−	14.6969i	−0.0294628	−	0.0170103i
$865$	129.468	−	166.904i	0.149674	−	0.192953i
$866$	−480.212	−	831.752i	−0.554518	−	0.960453i
$867$	272.963	−	272.963i	0.314836	−	0.314836i
$868$	−156.402	−	481.715i	−0.180187	−	0.554971i
$869$		−	401.358i		−	0.461862i
$870$	−196.849	+	468.263i	−0.226263	+	0.538233i
$871$	928.385	−	1608.01i	1.06588	−	1.84616i
$872$	−49.3636	−	184.228i	−0.0566097	−	0.211270i
$873$	141.262	−	527.195i	0.161812	−	0.603889i
$874$		−	319.947i		−	0.366072i
$875$	862.785	−	145.692i	0.986041	−	0.166506i
$876$	177.761			0.202924
$877$	1150.23	+	308.205i	1.31156	+	0.351430i	0.845808	−	0.533487i	$-0.179119\pi$
$877$	1150.23	+	308.205i	1.31156	+	0.351430i	0.465748	+	0.884917i	$0.345785\pi$
$878$	487.964	−	130.750i	0.555767	−	0.148917i
$879$	87.1886	+	50.3384i	0.0991907	+	0.0572678i
$880$	243.310	+	102.283i	0.276488	+	0.116230i
$881$	804.709			0.913404			0.456702	−	0.889620i	$-0.349031\pi$
$881$	804.709			0.913404			0.456702	+	0.889620i	$0.349031\pi$
$882$	205.316	+	32.6107i	0.232784	+	0.0369736i
$883$	3.52555	+	3.52555i	0.00399269	+	0.00399269i	0.709100	−	0.705108i	$-0.249101\pi$
$883$	3.52555	+	3.52555i	0.00399269	+	0.00399269i	−0.705108	+	0.709100i	$0.749101\pi$
$884$	−214.636	+	123.920i	−0.242801	+	0.140181i
$885$	9.11273	+	7.06880i	0.0102969	+	0.00798734i
$886$	−563.519	+	976.043i	−0.636025	+	1.10163i
$887$	470.654	+	126.111i	0.530613	+	0.142177i	0.514171	−	0.857688i	$-0.328100\pi$
$887$	470.654	+	126.111i	0.530613	+	0.142177i	0.0164416	+	0.999865i	$0.494766\pi$
$888$	16.8147	+	16.8147i	0.0189354	+	0.0189354i
$889$	−601.769	−	927.086i	−0.676906	−	1.04284i
$890$	−154.945	−	21.2273i	−0.174095	−	0.0238510i
$891$	59.3852	+	102.858i	0.0666501	+	0.115441i
$892$	154.761	+	577.575i	0.173499	+	0.647505i
$893$	501.534	−	134.386i	0.561628	−	0.150488i
$894$	107.061	−	61.8120i	0.119756	−	0.0691409i
$895$	−1027.45	−	1353.66i	−1.14799	−	1.51247i
$896$	70.5563	+	35.9696i	0.0787458	+	0.0401447i
$897$	437.487	−	437.487i	0.487722	−	0.487722i
$898$	−307.090	+	1146.08i	−0.341971	+	1.27625i
$899$	−1299.38	−	750.198i	−1.44536	−	0.834480i
$900$	104.946	+	107.174i	0.116607	+	0.119083i
$901$	191.355	+	331.437i	0.212381	+	0.367854i
$902$	−96.5006	+	96.5006i	−0.106985	+	0.106985i
$903$	−558.950	+	620.504i	−0.618992	+	0.687159i
$904$		−	343.931i		−	0.380455i
$905$	−173.316	−	72.8586i	−0.191509	−	0.0805067i
$906$	40.6184	−	70.3532i	0.0448327	−	0.0776525i
$907$	−42.8777	−	160.022i	−0.0472742	−	0.176430i	0.938252	−	0.345952i	$-0.112444\pi$
$907$	−42.8777	−	160.022i	−0.0472742	−	0.176430i	−0.985526	+	0.169523i	$0.945777\pi$
$908$	−23.4442	+	87.4951i	−0.0258197	+	0.0963603i
$909$		−	152.608i		−	0.167886i
$910$	−751.626	−	63.2933i	−0.825963	−	0.0695531i
$911$	−6.95825			−0.00763803			−0.00381902	−	0.999993i	$-0.501216\pi$
$911$	−6.95825			−0.00763803			−0.00381902	+	0.999993i	$0.501216\pi$
$912$	−64.5894	−	17.3067i	−0.0708217	−	0.0189766i
$913$	581.716	−	155.870i	0.637148	−	0.170723i
$914$	−564.555	−	325.946i	−0.617676	−	0.356615i
$915$	195.013	+	477.886i	0.213129	+	0.522280i
$916$	−195.792			−0.213747
$917$	−490.079	+	159.118i	−0.534438	+	0.173520i
$918$	−42.2542	−	42.2542i	−0.0460286	−	0.0460286i
$919$	−161.798	+	93.4143i	−0.176059	+	0.101648i	−0.585440	−	0.810716i	$-0.699078\pi$
$919$	−161.798	+	93.4143i	−0.176059	+	0.101648i	0.409381	+	0.912364i	$0.365745\pi$
$920$	328.885	−	41.5424i	0.357484	−	0.0451548i
$921$	−268.771	+	465.525i	−0.291825	+	0.505456i
$922$	−797.110	−	213.585i	−0.864544	−	0.231654i
$923$	−890.924	−	890.924i	−0.965248	−	0.965248i
$924$	−174.228	−	268.416i	−0.188558	−	0.290493i
$925$	−59.5674	−	105.723i	−0.0643972	−	0.114295i
$926$	−235.910	−	408.608i	−0.254762	−	0.441261i
$927$	95.2250	+	355.385i	0.102724	+	0.383371i
$928$	226.621	−	60.7228i	0.244203	−	0.0654341i
$929$	−938.697	+	541.957i	−1.01044	+	0.583377i	−0.911320	−	0.411699i	$-0.864936\pi$
$929$	−938.697	+	541.957i	−1.01044	+	0.583377i	−0.0991182	+	0.995076i	$0.531602\pi$
$930$	−352.921	+	267.873i	−0.379485	+	0.288035i
$931$	470.357	−	49.2289i	0.505216	−	0.0528774i
$932$	−257.782	+	257.782i	−0.276591	+	0.276591i
$933$	214.543	−	800.686i	0.229950	−	0.858184i
$934$	282.809	+	163.280i	0.302794	+	0.174818i
$935$	423.966	+	328.873i	0.453440	+	0.351736i
$936$	−64.6531	−	111.983i	−0.0690739	−	0.119639i
$937$	790.801	−	790.801i	0.843971	−	0.843971i	−0.145401	−	0.989373i	$-0.546447\pi$
$937$	790.801	−	790.801i	0.843971	−	0.843971i	0.989373	+	0.145401i	$0.0464474\pi$
$938$	−1179.78	−	251.040i	−1.25776	−	0.267633i
$939$		−	664.692i		−	0.707872i
$940$	203.260	+	498.095i	0.216234	+	0.529889i
$941$	−33.5626	+	58.1322i	−0.0356670	+	0.0617770i	−0.883308	−	0.468793i	$-0.844689\pi$
$941$	−33.5626	+	58.1322i	−0.0356670	+	0.0617770i	0.847641	+	0.530570i	$0.178022\pi$
$942$	143.503	+	535.561i	0.152339	+	0.568536i
$943$	−44.3636	+	165.567i	−0.0470451	+	0.175575i
$944$		−	5.32686i		−	0.00564286i
$945$	−32.1636	−	178.999i	−0.0340356	−	0.189417i
$946$	1285.52			1.35890
$947$	144.558	+	38.7341i	0.152648	+	0.0409019i	0.334334	−	0.942455i	$-0.391489\pi$
$947$	144.558	+	38.7341i	0.152648	+	0.0409019i	−0.181686	+	0.983357i	$0.558155\pi$
$948$	−101.765	+	27.2680i	−0.107348	+	0.0287637i
$949$	677.221	+	390.994i	0.713615	+	0.412006i
$950$	293.709	+	173.712i	0.309167	+	0.182854i
$951$	254.236			0.267335
$952$	119.624	+	107.758i	0.125656	+	0.113191i
$953$	−778.354	−	778.354i	−0.816741	−	0.816741i	0.168893	−	0.985634i	$-0.445981\pi$
$953$	−778.354	−	778.354i	−0.816741	−	0.816741i	−0.985634	+	0.168893i	$0.945981\pi$
$954$	−172.921	+	99.8361i	−0.181259	+	0.104650i
$955$	−177.452	−	1404.86i	−0.185814	−	1.47106i
$956$	−68.1419	+	118.025i	−0.0712781	+	0.123457i
$957$	−915.696	−	245.360i	−0.956840	−	0.256384i
$958$	574.329	+	574.329i	0.599509	+	0.599509i
$959$	−1667.02	+	86.9997i	−1.73828	+	0.0907192i
$960$	9.40376	−	68.6409i	0.00979559	−	0.0715009i
$961$	−173.865	−	301.143i	−0.180921	−	0.313364i
$962$	27.0746	+	101.044i	0.0281441	+	0.105035i
$963$	561.751	−	150.521i	0.583334	−	0.156304i
$964$	473.511	−	273.382i	0.491194	−	0.283591i
$965$	−783.804	−	107.381i	−0.812232	−	0.111275i
$966$	−358.074	−	182.546i	−0.370677	−	0.188971i
$967$	−959.028	+	959.028i	−0.991756	+	0.991756i	−0.999966	−	0.00821072i	$-0.997386\pi$
$967$	−959.028	+	959.028i	−0.991756	+	0.991756i	0.00821072	+	0.999966i	$0.497386\pi$
$968$	−38.9110	+	145.218i	−0.0401973	+	0.150018i
$969$	−117.727	−	67.9698i	−0.121493	−	0.0701443i
$970$	1276.30	−	161.214i	1.31578	−	0.166200i
$971$	417.900	+	723.824i	0.430381	+	0.745442i	0.996906	−	0.0786028i	$-0.0250459\pi$
$971$	417.900	+	723.824i	0.430381	+	0.745442i	−0.566525	+	0.824045i	$0.691713\pi$
$972$	22.0454	−	22.0454i	0.0226805	−	0.0226805i
$973$	1267.52	+	269.709i	1.30269	+	0.277193i
$974$			1079.16i			1.10797i
$975$	164.081	+	639.138i	0.168288	+	0.655526i
$976$	119.198	−	206.458i	0.122130	−	0.211535i
$977$	−256.830	−	958.504i	−0.262877	−	0.981069i	−0.963537	−	0.267574i	$-0.913778\pi$
$977$	−256.830	−	958.504i	−0.262877	−	0.981069i	0.700661	−	0.713495i	$-0.252889\pi$
$978$	−109.467	+	408.535i	−0.111929	+	0.417725i
$979$		−	291.874i		−	0.298135i
$980$	111.676	+	477.104i	0.113955	+	0.486841i
$981$	202.296			0.206214
$982$	−365.593	−	97.9603i	−0.372294	−	0.0997559i
$983$	1160.43	−	310.936i	1.18050	−	0.316313i	0.385373	−	0.922761i	$-0.374073\pi$
$983$	1160.43	−	310.936i	1.18050	−	0.316313i	0.795124	+	0.606447i	$0.207406\pi$
$984$	31.0242	+	17.9118i	0.0315286	+	0.0182031i
$985$	−1230.85	+	502.278i	−1.24960	+	0.509927i
$986$	476.962			0.483735
$987$	135.751	−	637.973i	0.137539	−	0.646376i
$988$	−208.001	−	208.001i	−0.210527	−	0.210527i
$989$	1398.28	−	807.298i	1.41383	−	0.816278i
$990$	−171.584	+	221.197i	−0.173317	+	0.223431i
$991$	−134.710	+	233.324i	−0.135933	+	0.235443i	−0.925954	−	0.377637i	$-0.876737\pi$
$991$	−134.710	+	233.324i	−0.135933	+	0.235443i	0.790020	+	0.613081i	$0.210070\pi$
$992$	197.671	+	52.9659i	0.199266	+	0.0533930i
$993$	71.2283	+	71.2283i	0.0717304	+	0.0717304i
$994$	−371.748	+	729.202i	−0.373991	+	0.733604i
$995$	−15.7796	−	20.7896i	−0.0158589	−	0.0208941i
$996$	−79.0427	−	136.906i	−0.0793601	−	0.137456i
$997$	−194.401	−	725.514i	−0.194986	−	0.727697i	−0.992271	−	0.124093i	$-0.960398\pi$
$997$	−194.401	−	725.514i	−0.194986	−	0.727697i	0.797285	−	0.603603i	$-0.206269\pi$
$998$	518.360	−	138.894i	0.519399	−	0.139173i
$999$	−21.8429	+	12.6110i	−0.0218647	+	0.0126236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.v.a.193.5	yes	32
5.2	odd	4	inner	210.3.v.a.67.3	yes	32
7.2	even	3	inner	210.3.v.a.163.3	yes	32
35.2	odd	12	inner	210.3.v.a.37.5	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.v.a.37.5	✓	32	35.2	odd	12	inner
210.3.v.a.67.3	yes	32	5.2	odd	4	inner
210.3.v.a.163.3	yes	32	7.2	even	3	inner
210.3.v.a.193.5	yes	32	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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 - 0.366025i) q^{2} +(1.67303 - 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-4.60928 - 1.93765i) q^{5} -2.44949 q^{6} +(-1.45688 + 6.84672i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\)	\(q+(-1.36603 - 0.366025i) q^{2} +(1.67303 - 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-4.60928 - 1.93765i) q^{5} -2.44949 q^{6} +(-1.45688 + 6.84672i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +(5.58717 + 4.33400i) q^{10} +(-6.59836 + 11.4287i) q^{11} +(3.34607 + 0.896575i) q^{12} +(10.7755 + 10.7755i) q^{13} +(4.49620 - 8.81953i) q^{14} +(-8.58011 - 1.17547i) q^{15} +(2.00000 + 3.46410i) q^{16} +(2.10467 + 7.85475i) q^{17} +(-4.09808 + 1.09808i) q^{18} +(-8.35848 + 4.82577i) q^{19} +(-6.04586 - 7.96540i) q^{20} +(0.631897 + 12.1079i) q^{21} +(13.1967 - 13.1967i) q^{22} +(6.06684 - 22.6417i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(17.4910 + 17.8624i) q^{25} +(-10.7755 - 18.6638i) q^{26} +(3.67423 - 3.67423i) q^{27} +(-9.37010 + 10.4020i) q^{28} +41.4745i q^{29} +(11.2904 + 4.74626i) q^{30} +(-18.0882 + 31.3297i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(-5.91593 + 22.0785i) q^{33} -11.5001i q^{34} +(19.9817 - 28.7355i) q^{35} +6.00000 q^{36} +(-4.68858 - 1.25630i) q^{37} +(13.1843 - 3.53271i) q^{38} +(22.8583 + 13.1973i) q^{39} +(5.34326 + 13.0939i) q^{40} -7.31247 q^{41} +(3.56860 - 16.7710i) q^{42} +(48.7061 + 48.7061i) q^{43} +(-22.8574 + 13.1967i) q^{44} +(-14.8818 + 1.87976i) q^{45} +(-16.5749 + 28.7086i) q^{46} +(-51.9641 - 13.9237i) q^{47} +(4.89898 + 4.89898i) q^{48} +(-44.7550 - 19.9496i) q^{49} +(-17.3551 - 30.8026i) q^{50} +(7.04237 + 12.1977i) q^{51} +(7.88823 + 29.4393i) q^{52} +(45.4596 - 12.1809i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(52.5586 - 39.8928i) q^{55} +(16.6072 - 10.7797i) q^{56} +(-11.8207 + 11.8207i) q^{57} +(15.1807 - 56.6552i) q^{58} +(-1.15330 - 0.665857i) q^{59} +(-13.6857 - 10.6161i) q^{60} +(-29.7996 - 51.6144i) q^{61} +(36.1764 - 36.1764i) q^{62} +(6.48500 + 19.9736i) q^{63} +8.00000i q^{64} +(-28.7882 - 70.5467i) q^{65} +(16.1626 - 27.9945i) q^{66} +(-31.5356 - 117.692i) q^{67} +(-4.20935 + 15.7095i) q^{68} -40.6001i q^{69} +(-37.8135 + 31.9397i) q^{70} -82.6803 q^{71} +(-8.19615 - 2.19615i) q^{72} +(49.5667 - 13.2814i) q^{73} +(5.94488 + 3.43228i) q^{74} +(37.2705 + 22.0433i) q^{75} -19.3031 q^{76} +(-68.6360 - 61.8273i) q^{77} +(-26.3945 - 26.3945i) q^{78} +(-26.3388 + 15.2067i) q^{79} +(-2.50634 - 19.8423i) q^{80} +(4.50000 - 7.79423i) q^{81} +(9.98902 + 2.67655i) q^{82} +(-32.2690 - 32.2690i) q^{83} +(-11.0134 + 21.6034i) q^{84} +(5.51873 - 40.2829i) q^{85} +(-48.7061 - 84.3614i) q^{86} +(18.5925 + 69.3881i) q^{87} +(36.0541 - 9.66067i) q^{88} +(-19.1540 + 11.0586i) q^{89} +(21.0169 + 2.87930i) q^{90} +(-89.4755 + 58.0783i) q^{91} +(33.1498 - 33.1498i) q^{92} +(-16.2174 + 60.5243i) q^{93} +(65.8878 + 38.0403i) q^{94} +(47.8773 - 6.04752i) q^{95} +(-4.89898 - 8.48528i) q^{96} +(128.645 - 128.645i) q^{97} +(53.8344 + 43.6332i) q^{98} +39.5902i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 8 q^{7} - 64 q^{8}+O(q^{10}) \) 32 * q - 16 * q^2 - 8 * q^7 - 64 * q^8	\( 32 q - 16 q^{2} - 8 q^{7} - 64 q^{8} + 4 q^{10} - 32 q^{11} - 32 q^{13} + 64 q^{16} - 56 q^{17} - 48 q^{18} - 16 q^{20} - 48 q^{21} + 64 q^{22} - 48 q^{23} + 68 q^{25} + 32 q^{26} + 40 q^{28} + 12 q^{30} + 160 q^{31} + 64 q^{32} + 12 q^{33} + 152 q^{35} + 192 q^{36} + 44 q^{37} - 64 q^{38} + 8 q^{40} - 80 q^{41} - 48 q^{42} - 184 q^{43} - 12 q^{45} - 96 q^{46} - 228 q^{47} - 96 q^{50} + 192 q^{51} + 32 q^{52} + 48 q^{53} + 104 q^{55} + 32 q^{56} + 144 q^{57} - 112 q^{58} + 24 q^{60} + 216 q^{61} - 320 q^{62} + 84 q^{63} - 384 q^{65} + 24 q^{66} + 112 q^{68} - 24 q^{70} + 368 q^{71} - 96 q^{72} + 52 q^{73} + 48 q^{75} + 256 q^{76} - 836 q^{77} - 240 q^{78} + 144 q^{81} + 40 q^{82} - 736 q^{83} - 72 q^{85} + 184 q^{86} - 72 q^{87} + 64 q^{88} + 24 q^{90} + 216 q^{91} + 192 q^{92} - 216 q^{93} + 272 q^{95} - 408 q^{97} + 200 q^{98}+O(q^{100}) \) 32 * q - 16 * q^2 - 8 * q^7 - 64 * q^8 + 4 * q^10 - 32 * q^11 - 32 * q^13 + 64 * q^16 - 56 * q^17 - 48 * q^18 - 16 * q^20 - 48 * q^21 + 64 * q^22 - 48 * q^23 + 68 * q^25 + 32 * q^26 + 40 * q^28 + 12 * q^30 + 160 * q^31 + 64 * q^32 + 12 * q^33 + 152 * q^35 + 192 * q^36 + 44 * q^37 - 64 * q^38 + 8 * q^40 - 80 * q^41 - 48 * q^42 - 184 * q^43 - 12 * q^45 - 96 * q^46 - 228 * q^47 - 96 * q^50 + 192 * q^51 + 32 * q^52 + 48 * q^53 + 104 * q^55 + 32 * q^56 + 144 * q^57 - 112 * q^58 + 24 * q^60 + 216 * q^61 - 320 * q^62 + 84 * q^63 - 384 * q^65 + 24 * q^66 + 112 * q^68 - 24 * q^70 + 368 * q^71 - 96 * q^72 + 52 * q^73 + 48 * q^75 + 256 * q^76 - 836 * q^77 - 240 * q^78 + 144 * q^81 + 40 * q^82 - 736 * q^83 - 72 * q^85 + 184 * q^86 - 72 * q^87 + 64 * q^88 + 24 * q^90 + 216 * q^91 + 192 * q^92 - 216 * q^93 + 272 * q^95 - 408 * q^97 + 200 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more