LMFDB - Embedded newform 75.3.f.c.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(7,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("75.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.f (of order $4$, 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:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.2
Root			$1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	75.43
Dual form			75.3.f.c.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.22474 - 2.22474i) q^{2} +(-1.22474 - 1.22474i) q^{3} -5.89898i q^{4} -5.44949 q^{6} +(1.44949 - 1.44949i) q^{7} +(-4.22474 - 4.22474i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(2.22474 - 2.22474i) q^{2} +(-1.22474 - 1.22474i) q^{3} -5.89898i q^{4} -5.44949 q^{6} +(1.44949 - 1.44949i) q^{7} +(-4.22474 - 4.22474i) q^{8} +3.00000i q^{9} -3.34847 q^{11} +(-7.22474 + 7.22474i) q^{12} +(10.4495 + 10.4495i) q^{13} -6.44949i q^{14} +4.79796 q^{16} +(2.65153 - 2.65153i) q^{17} +(6.67423 + 6.67423i) q^{18} +20.6969i q^{19} -3.55051 q^{21} +(-7.44949 + 7.44949i) q^{22} +(-16.4495 - 16.4495i) q^{23} +10.3485i q^{24} +46.4949 q^{26} +(3.67423 - 3.67423i) q^{27} +(-8.55051 - 8.55051i) q^{28} -0.853572i q^{29} -18.6969 q^{31} +(27.5732 - 27.5732i) q^{32} +(4.10102 + 4.10102i) q^{33} -11.7980i q^{34} +17.6969 q^{36} +(-38.0454 + 38.0454i) q^{37} +(46.0454 + 46.0454i) q^{38} -25.5959i q^{39} -28.6969 q^{41} +(-7.89898 + 7.89898i) q^{42} +(-22.4949 - 22.4949i) q^{43} +19.7526i q^{44} -73.1918 q^{46} +(-19.7526 + 19.7526i) q^{47} +(-5.87628 - 5.87628i) q^{48} +44.7980i q^{49} -6.49490 q^{51} +(61.6413 - 61.6413i) q^{52} +(-28.6969 - 28.6969i) q^{53} -16.3485i q^{54} -12.2474 q^{56} +(25.3485 - 25.3485i) q^{57} +(-1.89898 - 1.89898i) q^{58} -111.934i q^{59} +94.0908 q^{61} +(-41.5959 + 41.5959i) q^{62} +(4.34847 + 4.34847i) q^{63} -103.495i q^{64} +18.2474 q^{66} +(54.8990 - 54.8990i) q^{67} +(-15.6413 - 15.6413i) q^{68} +40.2929i q^{69} -68.0000 q^{71} +(12.6742 - 12.6742i) q^{72} +(39.7878 + 39.7878i) q^{73} +169.283i q^{74} +122.091 q^{76} +(-4.85357 + 4.85357i) q^{77} +(-56.9444 - 56.9444i) q^{78} -24.4949i q^{79} -9.00000 q^{81} +(-63.8434 + 63.8434i) q^{82} +(21.1464 + 21.1464i) q^{83} +20.9444i q^{84} -100.091 q^{86} +(-1.04541 + 1.04541i) q^{87} +(14.1464 + 14.1464i) q^{88} +94.1816i q^{89} +30.2929 q^{91} +(-97.0352 + 97.0352i) q^{92} +(22.8990 + 22.8990i) q^{93} +87.8888i q^{94} -67.5403 q^{96} +(-14.5959 + 14.5959i) q^{97} +(99.6640 + 99.6640i) q^{98} -10.0454i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 12 q^{6} - 4 q^{7} - 12 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 12 * q^6 - 4 * q^7 - 12 * q^8	$ 4 q + 4 q^{2} - 12 q^{6} - 4 q^{7} - 12 q^{8} + 16 q^{11} - 24 q^{12} + 32 q^{13} - 20 q^{16} + 40 q^{17} + 12 q^{18} - 24 q^{21} - 20 q^{22} - 56 q^{23} + 88 q^{26} - 44 q^{28} - 16 q^{31} + 76 q^{32} + 36 q^{33} + 12 q^{36} - 64 q^{37} + 96 q^{38} - 56 q^{41} - 12 q^{42} + 8 q^{43} - 136 q^{46} - 128 q^{47} - 48 q^{48} + 72 q^{51} + 80 q^{52} - 56 q^{53} + 72 q^{57} + 12 q^{58} + 200 q^{61} - 88 q^{62} - 12 q^{63} + 24 q^{66} + 200 q^{67} + 104 q^{68} - 272 q^{71} + 36 q^{72} - 76 q^{73} + 312 q^{76} - 88 q^{77} - 120 q^{78} - 36 q^{81} - 128 q^{82} + 16 q^{83} - 224 q^{86} + 84 q^{87} - 12 q^{88} - 16 q^{91} - 104 q^{92} + 72 q^{93} - 84 q^{96} + 20 q^{97} + 188 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 12 * q^6 - 4 * q^7 - 12 * q^8 + 16 * q^11 - 24 * q^12 + 32 * q^13 - 20 * q^16 + 40 * q^17 + 12 * q^18 - 24 * q^21 - 20 * q^22 - 56 * q^23 + 88 * q^26 - 44 * q^28 - 16 * q^31 + 76 * q^32 + 36 * q^33 + 12 * q^36 - 64 * q^37 + 96 * q^38 - 56 * q^41 - 12 * q^42 + 8 * q^43 - 136 * q^46 - 128 * q^47 - 48 * q^48 + 72 * q^51 + 80 * q^52 - 56 * q^53 + 72 * q^57 + 12 * q^58 + 200 * q^61 - 88 * q^62 - 12 * q^63 + 24 * q^66 + 200 * q^67 + 104 * q^68 - 272 * q^71 + 36 * q^72 - 76 * q^73 + 312 * q^76 - 88 * q^77 - 120 * q^78 - 36 * q^81 - 128 * q^82 + 16 * q^83 - 224 * q^86 + 84 * q^87 - 12 * q^88 - 16 * q^91 - 104 * q^92 + 72 * q^93 - 84 * q^96 + 20 * q^97 + 188 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	2.22474	−	2.22474i	1.11237	−	1.11237i	0.119543	−	0.992829i	$-0.461857\pi$
$2$	2.22474	−	2.22474i	1.11237	−	1.11237i	0.992829	−	0.119543i	$-0.0381431\pi$
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$4$		−	5.89898i		−	1.47474i
$5$		0			0
$5$		0			0
$6$	−5.44949			−0.908248
$7$	1.44949	−	1.44949i	0.207070	−	0.207070i	−0.595951	−	0.803021i	$-0.703225\pi$
$7$	1.44949	−	1.44949i	0.207070	−	0.207070i	0.803021	+	0.595951i	$0.203225\pi$
$8$	−4.22474	−	4.22474i	−0.528093	−	0.528093i
$9$			3.00000i			0.333333i
$10$		0			0
$11$	−3.34847			−0.304406			−0.152203	−	0.988349i	$-0.548637\pi$
$11$	−3.34847			−0.304406			−0.152203	+	0.988349i	$0.548637\pi$
$12$	−7.22474	+	7.22474i	−0.602062	+	0.602062i
$13$	10.4495	+	10.4495i	0.803807	+	0.803807i	0.983688	−	0.179881i	$-0.0575714\pi$
$13$	10.4495	+	10.4495i	0.803807	+	0.803807i	−0.179881	+	0.983688i	$0.557571\pi$
$14$		−	6.44949i		−	0.460678i
$15$		0			0
$16$	4.79796			0.299872
$17$	2.65153	−	2.65153i	0.155972	−	0.155972i	−0.624807	−	0.780779i	$-0.714822\pi$
$17$	2.65153	−	2.65153i	0.155972	−	0.155972i	0.780779	+	0.624807i	$0.214822\pi$
$18$	6.67423	+	6.67423i	0.370791	+	0.370791i
$19$			20.6969i			1.08931i	0.838659	+	0.544656i	$0.183340\pi$
$19$			20.6969i			1.08931i	−0.838659	+	0.544656i	$0.816660\pi$
$20$		0			0
$21$	−3.55051			−0.169072
$22$	−7.44949	+	7.44949i	−0.338613	+	0.338613i
$23$	−16.4495	−	16.4495i	−0.715195	−	0.715195i	0.252422	−	0.967617i	$-0.418773\pi$
$23$	−16.4495	−	16.4495i	−0.715195	−	0.715195i	−0.967617	+	0.252422i	$0.918773\pi$
$24$			10.3485i			0.431186i
$25$		0			0
$26$	46.4949			1.78827
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	−8.55051	−	8.55051i	−0.305375	−	0.305375i
$29$		−	0.853572i		−	0.0294335i	−0.999892	−	0.0147168i	$-0.995315\pi$
$29$		−	0.853572i		−	0.0294335i	0.999892	−	0.0147168i	$-0.00468466\pi$
$30$		0			0
$31$	−18.6969			−0.603127			−0.301564	−	0.953446i	$-0.597509\pi$
$31$	−18.6969			−0.603127			−0.301564	+	0.953446i	$0.597509\pi$
$32$	27.5732	−	27.5732i	0.861663	−	0.861663i
$33$	4.10102	+	4.10102i	0.124273	+	0.124273i
$34$		−	11.7980i		−	0.346999i
$35$		0			0
$36$	17.6969			0.491582
$37$	−38.0454	+	38.0454i	−1.02825	+	1.02825i	−0.0286652	+	0.999589i	$0.509126\pi$
$37$	−38.0454	+	38.0454i	−1.02825	+	1.02825i	−0.999589	+	0.0286652i	$0.990874\pi$
$38$	46.0454	+	46.0454i	1.21172	+	1.21172i
$39$		−	25.5959i		−	0.656306i
$40$		0			0
$41$	−28.6969			−0.699925			−0.349963	−	0.936764i	$-0.613806\pi$
$41$	−28.6969			−0.699925			−0.349963	+	0.936764i	$0.613806\pi$
$42$	−7.89898	+	7.89898i	−0.188071	+	0.188071i
$43$	−22.4949	−	22.4949i	−0.523137	−	0.523137i	0.395380	−	0.918517i	$-0.370613\pi$
$43$	−22.4949	−	22.4949i	−0.523137	−	0.523137i	−0.918517	+	0.395380i	$0.870613\pi$
$44$			19.7526i			0.448922i
$45$		0			0
$46$	−73.1918			−1.59113
$47$	−19.7526	+	19.7526i	−0.420267	+	0.420267i	−0.885296	−	0.465029i	$-0.846044\pi$
$47$	−19.7526	+	19.7526i	−0.420267	+	0.420267i	0.465029	+	0.885296i	$0.346044\pi$
$48$	−5.87628	−	5.87628i	−0.122422	−	0.122422i
$49$			44.7980i			0.914244i
$50$		0			0
$51$	−6.49490			−0.127351
$52$	61.6413	−	61.6413i	1.18541	−	1.18541i
$53$	−28.6969	−	28.6969i	−0.541452	−	0.541452i	0.382503	−	0.923954i	$-0.375062\pi$
$53$	−28.6969	−	28.6969i	−0.541452	−	0.541452i	−0.923954	+	0.382503i	$0.875062\pi$
$54$		−	16.3485i		−	0.302749i
$55$		0			0
$56$	−12.2474			−0.218704
$57$	25.3485	−	25.3485i	0.444710	−	0.444710i
$58$	−1.89898	−	1.89898i	−0.0327410	−	0.0327410i
$59$		−	111.934i		−	1.89719i	−0.316493	−	0.948595i	$-0.602505\pi$
$59$		−	111.934i		−	1.89719i	0.316493	−	0.948595i	$-0.397495\pi$
$60$		0			0
$61$	94.0908			1.54247			0.771236	−	0.636549i	$-0.219639\pi$
$61$	94.0908			1.54247			0.771236	+	0.636549i	$0.219639\pi$
$62$	−41.5959	+	41.5959i	−0.670902	+	0.670902i
$63$	4.34847	+	4.34847i	0.0690233	+	0.0690233i
$64$		−	103.495i		−	1.61711i
$65$		0			0
$66$	18.2474			0.276476
$67$	54.8990	−	54.8990i	0.819388	−	0.819388i	−0.166631	−	0.986019i	$-0.553289\pi$
$67$	54.8990	−	54.8990i	0.819388	−	0.819388i	0.986019	+	0.166631i	$0.0532890\pi$
$68$	−15.6413	−	15.6413i	−0.230019	−	0.230019i
$69$			40.2929i			0.583954i
$70$		0			0
$71$	−68.0000			−0.957746			−0.478873	−	0.877884i	$-0.658955\pi$
$71$	−68.0000			−0.957746			−0.478873	+	0.877884i	$0.658955\pi$
$72$	12.6742	−	12.6742i	0.176031	−	0.176031i
$73$	39.7878	+	39.7878i	0.545038	+	0.545038i	0.925001	−	0.379964i	$-0.124064\pi$
$73$	39.7878	+	39.7878i	0.545038	+	0.545038i	−0.379964	+	0.925001i	$0.624064\pi$
$74$			169.283i			2.28760i
$75$		0			0
$76$	122.091			1.60646
$77$	−4.85357	+	4.85357i	−0.0630334	+	0.0630334i
$78$	−56.9444	−	56.9444i	−0.730056	−	0.730056i
$79$		−	24.4949i		−	0.310062i	−0.987910	−	0.155031i	$-0.950452\pi$
$79$		−	24.4949i		−	0.310062i	0.987910	−	0.155031i	$-0.0495477\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	−63.8434	+	63.8434i	−0.778578	+	0.778578i
$83$	21.1464	+	21.1464i	0.254776	+	0.254776i	0.822926	−	0.568149i	$-0.192340\pi$
$83$	21.1464	+	21.1464i	0.254776	+	0.254776i	−0.568149	+	0.822926i	$0.692340\pi$
$84$			20.9444i			0.249338i
$85$		0			0
$86$	−100.091			−1.16385
$87$	−1.04541	+	1.04541i	−0.0120162	+	0.0120162i
$88$	14.1464	+	14.1464i	0.160755	+	0.160755i
$89$			94.1816i			1.05822i	0.848553	+	0.529110i	$0.177474\pi$
$89$			94.1816i			1.05822i	−0.848553	+	0.529110i	$0.822526\pi$
$90$		0			0
$91$	30.2929			0.332889
$92$	−97.0352	+	97.0352i	−1.05473	+	1.05473i
$93$	22.8990	+	22.8990i	0.246226	+	0.246226i
$94$			87.8888i			0.934987i
$95$		0			0
$96$	−67.5403			−0.703545
$97$	−14.5959	+	14.5959i	−0.150473	+	0.150473i	−0.778329	−	0.627856i	$-0.783933\pi$
$97$	−14.5959	+	14.5959i	−0.150473	+	0.150473i	0.627856	+	0.778329i	$0.283933\pi$
$98$	99.6640	+	99.6640i	1.01698	+	1.01698i
$99$		−	10.0454i		−	0.101469i
$100$		0			0
$101$	173.621			1.71902			0.859509	−	0.511120i	$-0.170769\pi$
$101$	173.621			1.71902			0.859509	+	0.511120i	$0.170769\pi$
$102$	−14.4495	+	14.4495i	−0.141662	+	0.141662i
$103$	64.7526	+	64.7526i	0.628666	+	0.628666i	0.947732	−	0.319067i	$-0.103369\pi$
$103$	64.7526	+	64.7526i	0.628666	+	0.628666i	−0.319067	+	0.947732i	$0.603369\pi$
$104$		−	88.2929i		−	0.848970i
$105$		0			0
$106$	−127.687			−1.20459
$107$	4.74235	−	4.74235i	0.0443210	−	0.0443210i	−0.684599	−	0.728920i	$-0.740023\pi$
$107$	4.74235	−	4.74235i	0.0443210	−	0.0443210i	0.728920	+	0.684599i	$0.240023\pi$
$108$	−21.6742	−	21.6742i	−0.200687	−	0.200687i
$109$		−	39.3031i		−	0.360579i	−0.983614	−	0.180289i	$-0.942297\pi$
$109$		−	39.3031i		−	0.360579i	0.983614	−	0.180289i	$-0.0577034\pi$
$110$		0			0
$111$	93.1918			0.839566
$112$	6.95459	−	6.95459i	0.0620946	−	0.0620946i
$113$	−14.3587	−	14.3587i	−0.127068	−	0.127068i	0.640713	−	0.767781i	$-0.278639\pi$
$113$	−14.3587	−	14.3587i	−0.127068	−	0.127068i	−0.767781	+	0.640713i	$0.778639\pi$
$114$		−	112.788i		−	0.989366i
$115$		0			0
$116$	−5.03520			−0.0434069
$117$	−31.3485	+	31.3485i	−0.267936	+	0.267936i
$118$	−249.025	−	249.025i	−2.11038	−	2.11038i
$119$		−	7.68673i		−	0.0645944i
$120$		0			0
$121$	−109.788			−0.907337
$122$	209.328	−	209.328i	1.71580	−	1.71580i
$123$	35.1464	+	35.1464i	0.285743	+	0.285743i
$124$			110.293i			0.889459i
$125$		0			0
$126$	19.3485			0.153559
$127$	114.621	−	114.621i	0.902527	−	0.902527i	−0.0931273	−	0.995654i	$-0.529686\pi$
$127$	114.621	−	114.621i	0.902527	−	0.902527i	0.995654	+	0.0931273i	$0.0296864\pi$
$128$	−119.957	−	119.957i	−0.937163	−	0.937163i
$129$			55.1010i			0.427140i
$130$		0			0
$131$	−26.1362			−0.199513			−0.0997566	−	0.995012i	$-0.531806\pi$
$131$	−26.1362			−0.199513			−0.0997566	+	0.995012i	$0.531806\pi$
$132$	24.1918	−	24.1918i	0.183271	−	0.183271i
$133$	30.0000	+	30.0000i	0.225564	+	0.225564i
$134$		−	244.272i		−	1.82293i
$135$		0			0
$136$	−22.4041			−0.164736
$137$	−14.6311	+	14.6311i	−0.106796	+	0.106796i	−0.758486	−	0.651689i	$-0.774061\pi$
$137$	−14.6311	+	14.6311i	−0.106796	+	0.106796i	0.651689	+	0.758486i	$0.274061\pi$
$138$	89.6413	+	89.6413i	0.649575	+	0.649575i
$139$		−	83.1714i		−	0.598356i	−0.954197	−	0.299178i	$-0.903288\pi$
$139$		−	83.1714i		−	0.598356i	0.954197	−	0.299178i	$-0.0967124\pi$
$140$		0			0
$141$	48.3837			0.343147
$142$	−151.283	+	151.283i	−1.06537	+	1.06537i
$143$	−34.9898	−	34.9898i	−0.244684	−	0.244684i
$144$			14.3939i			0.0999575i
$145$		0			0
$146$	177.035			1.21257
$147$	54.8661	−	54.8661i	0.373239	−	0.373239i
$148$	224.429	+	224.429i	1.51641	+	1.51641i
$149$		−	119.146i		−	0.799640i	−0.916594	−	0.399820i	$-0.869073\pi$
$149$		−	119.146i		−	0.799640i	0.916594	−	0.399820i	$-0.130927\pi$
$150$		0			0
$151$	−144.969			−0.960062			−0.480031	−	0.877251i	$-0.659375\pi$
$151$	−144.969			−0.960062			−0.480031	+	0.877251i	$0.659375\pi$
$152$	87.4393	−	87.4393i	0.575258	−	0.575258i
$153$	7.95459	+	7.95459i	0.0519908	+	0.0519908i
$154$			21.5959i			0.140233i
$155$		0			0
$156$	−150.990			−0.967883
$157$	−51.1464	+	51.1464i	−0.325773	+	0.325773i	−0.850977	−	0.525203i	$-0.823989\pi$
$157$	−51.1464	+	51.1464i	−0.325773	+	0.325773i	0.525203	+	0.850977i	$0.323989\pi$
$158$	−54.4949	−	54.4949i	−0.344904	−	0.344904i
$159$			70.2929i			0.442093i
$160$		0			0
$161$	−47.6867			−0.296191
$162$	−20.0227	+	20.0227i	−0.123597	+	0.123597i
$163$	−189.394	−	189.394i	−1.16193	−	1.16193i	−0.984054	−	0.177872i	$-0.943079\pi$
$163$	−189.394	−	189.394i	−1.16193	−	1.16193i	−0.177872	−	0.984054i	$-0.556921\pi$
$164$			169.283i			1.03221i
$165$		0			0
$166$	94.0908			0.566812
$167$	−97.0352	+	97.0352i	−0.581049	+	0.581049i	−0.935192	−	0.354142i	$-0.884773\pi$
$167$	−97.0352	+	97.0352i	−0.581049	+	0.581049i	0.354142	+	0.935192i	$0.384773\pi$
$168$	15.0000	+	15.0000i	0.0892857	+	0.0892857i
$169$			49.3837i			0.292211i
$170$		0			0
$171$	−62.0908			−0.363104
$172$	−132.697	+	132.697i	−0.771494	+	0.771494i
$173$	34.6311	+	34.6311i	0.200180	+	0.200180i	0.800077	−	0.599897i	$-0.204792\pi$
$173$	34.6311	+	34.6311i	0.200180	+	0.200180i	−0.599897	+	0.800077i	$0.704792\pi$
$174$			4.65153i			0.0267329i
$175$		0			0
$176$	−16.0658			−0.0912831
$177$	−137.091	+	137.091i	−0.774524	+	0.774524i
$178$	209.530	+	209.530i	1.17714	+	1.17714i
$179$			183.712i			1.02632i	0.858292	+	0.513161i	$0.171526\pi$
$179$			183.712i			1.02632i	−0.858292	+	0.513161i	$0.828474\pi$
$180$		0			0
$181$	−21.7276			−0.120042			−0.0600209	−	0.998197i	$-0.519117\pi$
$181$	−21.7276			−0.120042			−0.0600209	+	0.998197i	$0.519117\pi$
$182$	67.3939	−	67.3939i	0.370296	−	0.370296i
$183$	−115.237	−	115.237i	−0.629712	−	0.629712i
$184$			138.990i			0.755379i
$185$		0			0
$186$	101.889			0.547789
$187$	−8.87857	+	8.87857i	−0.0474790	+	0.0474790i
$188$	116.520	+	116.520i	0.619787	+	0.619787i
$189$		−	10.6515i		−	0.0563573i
$190$		0			0
$191$	−40.0908			−0.209900			−0.104950	−	0.994478i	$-0.533468\pi$
$191$	−40.0908			−0.209900			−0.104950	+	0.994478i	$0.533468\pi$
$192$	−126.755	+	126.755i	−0.660181	+	0.660181i
$193$	−77.5653	−	77.5653i	−0.401893	−	0.401893i	0.477007	−	0.878900i	$-0.341722\pi$
$193$	−77.5653	−	77.5653i	−0.401893	−	0.401893i	−0.878900	+	0.477007i	$0.841722\pi$
$194$			64.9444i			0.334765i
$195$		0			0
$196$	264.262			1.34828
$197$	67.3031	−	67.3031i	0.341640	−	0.341640i	−0.515344	−	0.856984i	$-0.672336\pi$
$197$	67.3031	−	67.3031i	0.341640	−	0.341640i	0.856984	+	0.515344i	$0.172336\pi$
$198$	−22.3485	−	22.3485i	−0.112871	−	0.112871i
$199$		−	251.394i		−	1.26329i	−0.775259	−	0.631643i	$-0.782381\pi$
$199$		−	251.394i		−	1.26329i	0.775259	−	0.631643i	$-0.217619\pi$
$200$		0			0
$201$	−134.474			−0.669027
$202$	386.262	−	386.262i	1.91219	−	1.91219i
$203$	−1.23724	−	1.23724i	−0.00609480	−	0.00609480i
$204$			38.3133i			0.187810i
$205$		0			0
$206$	288.116			1.39862
$207$	49.3485	−	49.3485i	0.238398	−	0.238398i
$208$	50.1362	+	50.1362i	0.241040	+	0.241040i
$209$		−	69.3031i		−	0.331594i
$210$		0			0
$211$	264.788			1.25492			0.627459	−	0.778649i	$-0.284095\pi$
$211$	264.788			1.25492			0.627459	+	0.778649i	$0.284095\pi$
$212$	−169.283	+	169.283i	−0.798503	+	0.798503i
$213$	83.2827	+	83.2827i	0.390998	+	0.390998i
$214$		−	21.1010i		−	0.0986029i
$215$		0			0
$216$	−31.0454			−0.143729
$217$	−27.1010	+	27.1010i	−0.124889	+	0.124889i
$218$	−87.4393	−	87.4393i	−0.401098	−	0.401098i
$219$		−	97.4597i		−	0.445021i
$220$		0			0
$221$	55.4143			0.250743
$222$	207.328	−	207.328i	0.933910	−	0.933910i
$223$	33.4291	+	33.4291i	0.149906	+	0.149906i	0.778076	−	0.628170i	$-0.216196\pi$
$223$	33.4291	+	33.4291i	0.149906	+	0.149906i	−0.628170	+	0.778076i	$0.716196\pi$
$224$		−	79.9342i		−	0.356849i
$225$		0			0
$226$	−63.8888			−0.282694
$227$	21.1714	−	21.1714i	0.0932662	−	0.0932662i	−0.658934	−	0.752200i	$-0.728992\pi$
$227$	21.1714	−	21.1714i	0.0932662	−	0.0932662i	0.752200	+	0.658934i	$0.228992\pi$
$228$	−149.530	−	149.530i	−0.655834	−	0.655834i
$229$			243.798i			1.06462i	0.846550	+	0.532310i	$0.178676\pi$
$229$			243.798i			1.06462i	−0.846550	+	0.532310i	$0.821324\pi$
$230$		0			0
$231$	11.8888			0.0514666
$232$	−3.60612	+	3.60612i	−0.0155436	+	0.0155436i
$233$	−161.712	−	161.712i	−0.694042	−	0.694042i	0.269077	−	0.963119i	$-0.413281\pi$
$233$	−161.712	−	161.712i	−0.694042	−	0.694042i	−0.963119	+	0.269077i	$0.913281\pi$
$234$			139.485i			0.596088i
$235$		0			0
$236$	−660.297			−2.79787
$237$	−30.0000	+	30.0000i	−0.126582	+	0.126582i
$238$	−17.1010	−	17.1010i	−0.0718530	−	0.0718530i
$239$			326.202i			1.36486i	0.730950	+	0.682431i	$0.239077\pi$
$239$			326.202i			1.36486i	−0.730950	+	0.682431i	$0.760923\pi$
$240$		0			0
$241$	−133.576			−0.554255			−0.277128	−	0.960833i	$-0.589382\pi$
$241$	−133.576			−0.554255			−0.277128	+	0.960833i	$0.589382\pi$
$242$	−244.250	+	244.250i	−1.00930	+	1.00930i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$		−	555.040i		−	2.27475i
$245$		0			0
$246$	156.384			0.635706
$247$	−216.272	+	216.272i	−0.875597	+	0.875597i
$248$	78.9898	+	78.9898i	0.318507	+	0.318507i
$249$		−	51.7980i		−	0.208024i
$250$		0			0
$251$	−404.742			−1.61252			−0.806260	−	0.591562i	$-0.798512\pi$
$251$	−404.742			−1.61252			−0.806260	+	0.591562i	$0.798512\pi$
$252$	25.6515	−	25.6515i	0.101792	−	0.101792i
$253$	55.0806	+	55.0806i	0.217710	+	0.217710i
$254$		−	510.005i		−	2.00789i
$255$		0			0
$256$	−119.767			−0.467841
$257$	89.2372	−	89.2372i	0.347227	−	0.347227i	−0.511849	−	0.859076i	$-0.671039\pi$
$257$	89.2372	−	89.2372i	0.347227	−	0.347227i	0.859076	+	0.511849i	$0.171039\pi$
$258$	122.586	+	122.586i	0.475138	+	0.475138i
$259$			110.293i			0.425841i
$260$		0			0
$261$	2.56072			0.00981117
$262$	−58.1464	+	58.1464i	−0.221933	+	0.221933i
$263$	341.843	+	341.843i	1.29978	+	1.29978i	0.928532	+	0.371253i	$0.121072\pi$
$263$	341.843	+	341.843i	1.29978	+	1.29978i	0.371253	+	0.928532i	$0.378928\pi$
$264$		−	34.6515i		−	0.131256i
$265$		0			0
$266$	133.485			0.501822
$267$	115.348	−	115.348i	0.432017	−	0.432017i
$268$	−323.848	−	323.848i	−1.20839	−	1.20839i
$269$			3.50052i			0.0130131i	0.999979	+	0.00650653i	$0.00207111\pi$
$269$			3.50052i			0.0130131i	−0.999979	+	0.00650653i	$0.997929\pi$
$270$		0			0
$271$	−103.576			−0.382197			−0.191099	−	0.981571i	$-0.561205\pi$
$271$	−103.576			−0.382197			−0.191099	+	0.981571i	$0.561205\pi$
$272$	12.7219	−	12.7219i	0.0467718	−	0.0467718i
$273$	−37.1010	−	37.1010i	−0.135901	−	0.135901i
$274$			65.1010i			0.237595i
$275$		0			0
$276$	237.687			0.861184
$277$	285.510	−	285.510i	1.03072	−	1.03072i	0.0312080	−	0.999513i	$-0.490065\pi$
$277$	285.510	−	285.510i	1.03072	−	1.03072i	0.999513	−	0.0312080i	$-0.00993542\pi$
$278$	−185.035	−	185.035i	−0.665594	−	0.665594i
$279$		−	56.0908i		−	0.201042i
$280$		0			0
$281$	372.697			1.32632			0.663162	−	0.748476i	$-0.269214\pi$
$281$	372.697			1.32632			0.663162	+	0.748476i	$0.269214\pi$
$282$	107.641	−	107.641i	0.381707	−	0.381707i
$283$	77.1918	+	77.1918i	0.272763	+	0.272763i	0.830211	−	0.557449i	$-0.188220\pi$
$283$	77.1918	+	77.1918i	0.272763	+	0.272763i	−0.557449	+	0.830211i	$0.688220\pi$
$284$			401.131i			1.41243i
$285$		0			0
$286$	−155.687			−0.544359
$287$	−41.5959	+	41.5959i	−0.144934	+	0.144934i
$288$	82.7196	+	82.7196i	0.287221	+	0.287221i
$289$			274.939i			0.951345i
$290$		0			0
$291$	35.7526			0.122861
$292$	234.707	−	234.707i	0.803792	−	0.803792i
$293$	236.565	+	236.565i	0.807390	+	0.807390i	0.984238	−	0.176848i	$-0.0565901\pi$
$293$	236.565	+	236.565i	0.807390	+	0.807390i	−0.176848	+	0.984238i	$0.556590\pi$
$294$		−	244.126i		−	0.830361i
$295$		0			0
$296$	321.464			1.08603
$297$	−12.3031	+	12.3031i	−0.0414244	+	0.0414244i
$298$	−265.070	−	265.070i	−0.889498	−	0.889498i
$299$		−	343.778i		−	1.14976i
$300$		0			0
$301$	−65.2122			−0.216652
$302$	−322.520	+	322.520i	−1.06795	+	1.06795i
$303$	−212.641	−	212.641i	−0.701787	−	0.701787i
$304$			99.3031i			0.326655i
$305$		0			0
$306$	35.3939			0.115666
$307$	−168.969	+	168.969i	−0.550389	+	0.550389i	−0.926553	−	0.376164i	$-0.877243\pi$
$307$	−168.969	+	168.969i	−0.550389	+	0.550389i	0.376164	+	0.926553i	$0.377243\pi$
$308$	28.6311	+	28.6311i	0.0929582	+	0.0929582i
$309$		−	158.611i		−	0.513303i
$310$		0			0
$311$	354.302			1.13923			0.569617	−	0.821910i	$-0.307091\pi$
$311$	354.302			1.13923			0.569617	+	0.821910i	$0.307091\pi$
$312$	−108.136	+	108.136i	−0.346590	+	0.346590i
$313$	−152.373	−	152.373i	−0.486816	−	0.486816i	0.420484	−	0.907300i	$-0.361860\pi$
$313$	−152.373	−	152.373i	−0.486816	−	0.486816i	−0.907300	+	0.420484i	$0.861860\pi$
$314$			227.576i			0.724763i
$315$		0			0
$316$	−144.495			−0.457262
$317$	427.217	−	427.217i	1.34769	−	1.34769i	0.459519	−	0.888168i	$-0.348022\pi$
$317$	427.217	−	427.217i	1.34769	−	1.34769i	0.888168	−	0.459519i	$-0.151978\pi$
$318$	156.384	+	156.384i	0.491773	+	0.491773i
$319$			2.85816i			0.00895975i
$320$		0			0
$321$	−11.6163			−0.0361879
$322$	−106.091	+	106.091i	−0.329475	+	0.329475i
$323$	54.8786	+	54.8786i	0.169903	+	0.169903i
$324$			53.0908i			0.163861i
$325$		0			0
$326$	−842.706			−2.58499
$327$	−48.1362	+	48.1362i	−0.147206	+	0.147206i
$328$	121.237	+	121.237i	0.369626	+	0.369626i
$329$			57.2622i			0.174049i
$330$		0			0
$331$	489.423			1.47862			0.739310	−	0.673365i	$-0.235152\pi$
$331$	489.423			1.47862			0.739310	+	0.673365i	$0.235152\pi$
$332$	124.742	−	124.742i	0.375730	−	0.375730i
$333$	−114.136	−	114.136i	−0.342751	−	0.342751i
$334$			431.757i			1.29269i
$335$		0			0
$336$	−17.0352			−0.0507000
$337$	−292.192	+	292.192i	−0.867038	+	0.867038i	−0.992143	−	0.125105i	$-0.960073\pi$
$337$	−292.192	+	292.192i	−0.867038	+	0.867038i	0.125105	+	0.992143i	$0.460073\pi$
$338$	109.866	+	109.866i	0.325048	+	0.325048i
$339$			35.1714i			0.103751i
$340$		0			0
$341$	62.6061			0.183596
$342$	−138.136	+	138.136i	−0.403907	+	0.403907i
$343$	135.959	+	135.959i	0.396382	+	0.396382i
$344$			190.070i			0.552530i
$345$		0			0
$346$	154.091			0.445349
$347$	−320.050	+	320.050i	−0.922334	+	0.922334i	−0.997194	−	0.0748598i	$-0.976149\pi$
$347$	−320.050	+	320.050i	−0.922334	+	0.922334i	0.0748598	+	0.997194i	$0.476149\pi$
$348$	6.16684	+	6.16684i	0.0177208	+	0.0177208i
$349$		−	574.009i		−	1.64473i	−0.568964	−	0.822363i	$-0.692655\pi$
$349$		−	574.009i		−	1.64473i	0.568964	−	0.822363i	$-0.307345\pi$
$350$		0			0
$351$	76.7878			0.218769
$352$	−92.3281	+	92.3281i	−0.262296	+	0.262296i
$353$	−266.520	−	266.520i	−0.755014	−	0.755014i	0.220396	−	0.975410i	$-0.429265\pi$
$353$	−266.520	−	266.520i	−0.755014	−	0.755014i	−0.975410	+	0.220396i	$0.929265\pi$
$354$			609.984i			1.72312i
$355$		0			0
$356$	555.576			1.56061
$357$	−9.41429	+	9.41429i	−0.0263706	+	0.0263706i
$358$	408.712	+	408.712i	1.14165	+	1.14165i
$359$			216.272i			0.602430i	0.953556	+	0.301215i	$0.0973922\pi$
$359$			216.272i			0.602430i	−0.953556	+	0.301215i	$0.902608\pi$
$360$		0			0
$361$	−67.3633			−0.186602
$362$	−48.3383	+	48.3383i	−0.133531	+	0.133531i
$363$	134.462	+	134.462i	0.370419	+	0.370419i
$364$		−	178.697i		−	0.490926i
$365$		0			0
$366$	−512.747			−1.40095
$367$	240.510	−	240.510i	0.655340	−	0.655340i	−0.298934	−	0.954274i	$-0.596631\pi$
$367$	240.510	−	240.510i	0.655340	−	0.655340i	0.954274	+	0.298934i	$0.0966311\pi$
$368$	−78.9240	−	78.9240i	−0.214467	−	0.214467i
$369$		−	86.0908i		−	0.233308i
$370$		0			0
$371$	−83.1918			−0.224237
$372$	135.081	−	135.081i	0.363120	−	0.363120i
$373$	330.207	+	330.207i	0.885272	+	0.885272i	0.994065	−	0.108792i	$-0.0346983\pi$
$373$	330.207	+	330.207i	0.885272	+	0.885272i	−0.108792	+	0.994065i	$0.534698\pi$
$374$			39.5051i			0.105629i
$375$		0			0
$376$	166.899			0.443880
$377$	8.91939	−	8.91939i	0.0236589	−	0.0236589i
$378$	−23.6969	−	23.6969i	−0.0626903	−	0.0626903i
$379$			210.000i			0.554090i	0.960857	+	0.277045i	$0.0893551\pi$
$379$			210.000i			0.554090i	−0.960857	+	0.277045i	$0.910645\pi$
$380$		0			0
$381$	−280.763			−0.736910
$382$	−89.1918	+	89.1918i	−0.233486	+	0.233486i
$383$	−170.631	−	170.631i	−0.445512	−	0.445512i	0.448347	−	0.893859i	$-0.352013\pi$
$383$	−170.631	−	170.631i	−0.445512	−	0.445512i	−0.893859	+	0.448347i	$0.852013\pi$
$384$			293.833i			0.765191i
$385$		0			0
$386$	−345.126			−0.894109
$387$	67.4847	−	67.4847i	0.174379	−	0.174379i
$388$	86.1010	+	86.1010i	0.221910	+	0.221910i
$389$		−	547.337i		−	1.40704i	−0.710677	−	0.703518i	$-0.751611\pi$
$389$		−	547.337i		−	1.40704i	0.710677	−	0.703518i	$-0.248389\pi$
$390$		0			0
$391$	−87.2327			−0.223101
$392$	189.260	−	189.260i	0.482806	−	0.482806i
$393$	32.0102	+	32.0102i	0.0814509	+	0.0814509i
$394$		−	299.464i		−	0.760062i
$395$		0			0
$396$	−59.2577			−0.149641
$397$	−45.2577	+	45.2577i	−0.113999	+	0.113999i	−0.761805	−	0.647806i	$-0.775687\pi$
$397$	−45.2577	+	45.2577i	−0.113999	+	0.113999i	0.647806	+	0.761805i	$0.275687\pi$
$398$	−559.287	−	559.287i	−1.40524	−	1.40524i
$399$		−	73.4847i		−	0.184172i
$400$		0			0
$401$	−520.302			−1.29751			−0.648756	−	0.760997i	$-0.724710\pi$
$401$	−520.302			−1.29751			−0.648756	+	0.760997i	$0.724710\pi$
$402$	−299.171	+	299.171i	−0.744208	+	0.744208i
$403$	−195.373	−	195.373i	−0.484798	−	0.484798i
$404$		−	1024.19i		−	2.53511i
$405$		0			0
$406$	−5.50510			−0.0135594
$407$	127.394	−	127.394i	0.313007	−	0.313007i
$408$	27.4393	+	27.4393i	0.0672531	+	0.0672531i
$409$		−	347.110i		−	0.848680i	−0.905503	−	0.424340i	$-0.860506\pi$
$409$		−	347.110i		−	0.848680i	0.905503	−	0.424340i	$-0.139494\pi$
$410$		0			0
$411$	35.8388			0.0871990
$412$	381.974	−	381.974i	0.927121	−	0.927121i
$413$	−162.247	−	162.247i	−0.392851	−	0.392851i
$414$		−	219.576i		−	0.530376i
$415$		0			0
$416$	576.252			1.38522
$417$	−101.864	+	101.864i	−0.244278	+	0.244278i
$418$	−154.182	−	154.182i	−0.368856	−	0.368856i
$419$			583.398i			1.39236i	0.717868	+	0.696180i	$0.245118\pi$
$419$			583.398i			1.39236i	−0.717868	+	0.696180i	$0.754882\pi$
$420$		0			0
$421$	213.151			0.506297			0.253148	−	0.967427i	$-0.418534\pi$
$421$	213.151			0.506297			0.253148	+	0.967427i	$0.418534\pi$
$422$	589.085	−	589.085i	1.39594	−	1.39594i
$423$	−59.2577	−	59.2577i	−0.140089	−	0.140089i
$424$			242.474i			0.571874i
$425$		0			0
$426$	370.565			0.869872
$427$	136.384	−	136.384i	0.319400	−	0.319400i
$428$	−27.9750	−	27.9750i	−0.0653622	−	0.0653622i
$429$			85.7071i			0.199784i
$430$		0			0
$431$	187.364			0.434720			0.217360	−	0.976092i	$-0.430255\pi$
$431$	187.364			0.434720			0.217360	+	0.976092i	$0.430255\pi$
$432$	17.6288	−	17.6288i	0.0408075	−	0.0408075i
$433$	−154.848	−	154.848i	−0.357617	−	0.357617i	0.505317	−	0.862934i	$-0.331376\pi$
$433$	−154.848	−	154.848i	−0.357617	−	0.357617i	−0.862934	+	0.505317i	$0.831376\pi$
$434$			120.586i			0.277847i
$435$		0			0
$436$	−231.848			−0.531761
$437$	340.454	−	340.454i	0.779071	−	0.779071i
$438$	−216.823	−	216.823i	−0.495030	−	0.495030i
$439$			252.929i			0.576147i	0.957608	+	0.288074i	$0.0930148\pi$
$439$			252.929i			0.576147i	−0.957608	+	0.288074i	$0.906985\pi$
$440$		0			0
$441$	−134.394			−0.304748
$442$	123.283	−	123.283i	0.278920	−	0.278920i
$443$	421.131	+	421.131i	0.950633	+	0.950633i	0.998838	−	0.0482041i	$-0.0153498\pi$
$443$	421.131	+	421.131i	0.950633	+	0.950633i	−0.0482041	+	0.998838i	$0.515350\pi$
$444$		−	549.737i		−	1.23815i
$445$		0			0
$446$	148.742			0.333503
$447$	−145.924	+	145.924i	−0.326452	+	0.326452i
$448$	−150.015	−	150.015i	−0.334854	−	0.334854i
$449$		−	297.909i		−	0.663495i	−0.943368	−	0.331747i	$-0.892362\pi$
$449$		−	297.909i		−	0.663495i	0.943368	−	0.331747i	$-0.107638\pi$
$450$		0			0
$451$	96.0908			0.213062
$452$	−84.7015	+	84.7015i	−0.187393	+	0.187393i
$453$	177.551	+	177.551i	0.391944	+	0.391944i
$454$		−	94.2020i		−	0.207493i
$455$		0			0
$456$	−214.182			−0.469697
$457$	−285.747	+	285.747i	−0.625267	+	0.625267i	−0.946873	−	0.321607i	$-0.895777\pi$
$457$	−285.747	+	285.747i	−0.625267	+	0.625267i	0.321607	+	0.946873i	$0.395777\pi$
$458$	542.388	+	542.388i	1.18425	+	1.18425i
$459$		−	19.4847i		−	0.0424503i
$460$		0			0
$461$	526.620			1.14234			0.571171	−	0.820831i	$-0.306489\pi$
$461$	526.620			1.14234			0.571171	+	0.820831i	$0.306489\pi$
$462$	26.4495	−	26.4495i	0.0572500	−	0.0572500i
$463$	−335.702	−	335.702i	−0.725057	−	0.725057i	0.244573	−	0.969631i	$-0.421352\pi$
$463$	−335.702	−	335.702i	−0.725057	−	0.725057i	−0.969631	+	0.244573i	$0.921352\pi$
$464$		−	4.09540i		−	0.00882630i
$465$		0			0
$466$	−719.535			−1.54407
$467$	−488.742	+	488.742i	−1.04656	+	1.04656i	−0.0476956	+	0.998862i	$0.515188\pi$
$467$	−488.742	+	488.742i	−1.04656	+	1.04656i	−0.998862	+	0.0476956i	$0.984812\pi$
$468$	184.924	+	184.924i	0.395137	+	0.395137i
$469$		−	159.151i		−	0.339341i
$470$		0			0
$471$	125.283			0.265993
$472$	−472.893	+	472.893i	−1.00189	+	1.00189i
$473$	75.3235	+	75.3235i	0.159246	+	0.159246i
$474$			133.485i			0.281613i
$475$		0			0
$476$	−45.3439			−0.0952603
$477$	86.0908	−	86.0908i	0.180484	−	0.180484i
$478$	725.716	+	725.716i	1.51823	+	1.51823i
$479$			184.949i			0.386115i	0.981187	+	0.193057i	$0.0618404\pi$
$479$			184.949i			0.386115i	−0.981187	+	0.193057i	$0.938160\pi$
$480$		0			0
$481$	−795.110			−1.65304
$482$	−297.171	+	297.171i	−0.616538	+	0.616538i
$483$	58.4041	+	58.4041i	0.120919	+	0.120919i
$484$			647.636i			1.33809i
$485$		0			0
$486$	49.0454			0.100916
$487$	120.682	−	120.682i	0.247807	−	0.247807i	−0.572263	−	0.820070i	$-0.693934\pi$
$487$	120.682	−	120.682i	0.247807	−	0.247807i	0.820070	+	0.572263i	$0.193934\pi$
$488$	−397.510	−	397.510i	−0.814569	−	0.814569i
$489$			463.918i			0.948708i
$490$		0			0
$491$	−105.682			−0.215239			−0.107619	−	0.994192i	$-0.534323\pi$
$491$	−105.682			−0.215239			−0.107619	+	0.994192i	$0.534323\pi$
$492$	207.328	−	207.328i	0.421398	−	0.421398i
$493$	−2.26327	−	2.26327i	−0.00459082	−	0.00459082i
$494$			962.302i			1.94798i
$495$		0			0
$496$	−89.7071			−0.180861
$497$	−98.5653	+	98.5653i	−0.198321	+	0.198321i
$498$	−115.237	−	115.237i	−0.231400	−	0.231400i
$499$			739.585i			1.48213i	0.671431	+	0.741067i	$0.265680\pi$
$499$			739.585i			1.48213i	−0.671431	+	0.741067i	$0.734320\pi$
$500$		0			0
$501$	237.687			0.474425
$502$	−900.448	+	900.448i	−1.79372	+	1.79372i
$503$	406.409	+	406.409i	0.807970	+	0.807970i	0.984326	−	0.176357i	$-0.0564312\pi$
$503$	406.409	+	406.409i	0.807970	+	0.807970i	−0.176357	+	0.984326i	$0.556431\pi$
$504$		−	36.7423i		−	0.0729015i
$505$		0			0
$506$	245.081			0.484349
$507$	60.4824	−	60.4824i	0.119295	−	0.119295i
$508$	−676.146	−	676.146i	−1.33100	−	1.33100i
$509$		−	194.511i		−	0.382143i	−0.981576	−	0.191071i	$-0.938804\pi$
$509$		−	194.511i		−	0.382143i	0.981576	−	0.191071i	$-0.0611962\pi$
$510$		0			0
$511$	115.344			0.225722
$512$	213.376	−	213.376i	0.416750	−	0.416750i
$513$	76.0454	+	76.0454i	0.148237	+	0.148237i
$514$		−	397.060i		−	0.772491i
$515$		0			0
$516$	325.040			0.629922
$517$	66.1408	−	66.1408i	0.127932	−	0.127932i
$518$	245.373	+	245.373i	0.473694	+	0.473694i
$519$		−	84.8286i		−	0.163446i
$520$		0			0
$521$	−589.605			−1.13168			−0.565840	−	0.824515i	$-0.691448\pi$
$521$	−589.605			−1.13168			−0.565840	+	0.824515i	$0.691448\pi$
$522$	5.69694	−	5.69694i	0.0109137	−	0.0109137i
$523$	141.546	+	141.546i	0.270642	+	0.270642i	0.829359	−	0.558716i	$-0.188706\pi$
$523$	141.546	+	141.546i	0.270642	+	0.270642i	−0.558716	+	0.829359i	$0.688706\pi$
$524$			154.177i			0.294231i
$525$		0			0
$526$	1521.03			2.89169
$527$	−49.5755	+	49.5755i	−0.0940712	+	0.0940712i
$528$	19.6765	+	19.6765i	0.0372662	+	0.0372662i
$529$			12.1714i			0.0230084i
$530$		0			0
$531$	335.803			0.632397
$532$	176.969	−	176.969i	0.332649	−	0.332649i
$533$	−299.868	−	299.868i	−0.562605	−	0.562605i
$534$		−	513.242i		−	0.961127i
$535$		0			0
$536$	−463.868			−0.865426
$537$	225.000	−	225.000i	0.418994	−	0.418994i
$538$	7.78775	+	7.78775i	0.0144754	+	0.0144754i
$539$		−	150.005i		−	0.278302i
$540$		0			0
$541$	431.303			0.797233			0.398617	−	0.917118i	$-0.369490\pi$
$541$	431.303			0.797233			0.398617	+	0.917118i	$0.369490\pi$
$542$	−230.429	+	230.429i	−0.425146	+	0.425146i
$543$	26.6107	+	26.6107i	0.0490068	+	0.0490068i
$544$		−	146.222i		−	0.268791i
$545$		0			0
$546$	−165.081			−0.302345
$547$	446.222	−	446.222i	0.815763	−	0.815763i	−0.169728	−	0.985491i	$-0.554289\pi$
$547$	446.222	−	446.222i	0.815763	−	0.815763i	0.985491	+	0.169728i	$0.0542889\pi$
$548$	86.3087	+	86.3087i	0.157498	+	0.157498i
$549$			282.272i			0.514157i
$550$		0			0
$551$	17.6663			0.0320623
$552$	170.227	−	170.227i	0.308382	−	0.308382i
$553$	−35.5051	−	35.5051i	−0.0642045	−	0.0642045i
$554$		−	1270.37i		−	2.29309i
$555$		0			0
$556$	−490.627			−0.882422
$557$	−214.091	+	214.091i	−0.384364	+	0.384364i	−0.872672	−	0.488308i	$-0.837614\pi$
$557$	−214.091	+	214.091i	−0.384364	+	0.384364i	0.488308	+	0.872672i	$0.337614\pi$
$558$	−124.788	−	124.788i	−0.223634	−	0.223634i
$559$		−	470.120i		−	0.841003i
$560$		0			0
$561$	21.7480			0.0387664
$562$	829.156	−	829.156i	1.47537	−	1.47537i
$563$	−672.009	−	672.009i	−1.19362	−	1.19362i	−0.976043	−	0.217579i	$-0.930184\pi$
$563$	−672.009	−	672.009i	−1.19362	−	1.19362i	−0.217579	−	0.976043i	$-0.569816\pi$
$564$		−	285.414i		−	0.506054i
$565$		0			0
$566$	343.464			0.606827
$567$	−13.0454	+	13.0454i	−0.0230078	+	0.0230078i
$568$	287.283	+	287.283i	0.505779	+	0.505779i
$569$			972.161i			1.70854i	0.519827	+	0.854272i	$0.325997\pi$
$569$			972.161i			1.70854i	−0.519827	+	0.854272i	$0.674003\pi$
$570$		0			0
$571$	−924.030			−1.61827			−0.809133	−	0.587626i	$-0.800063\pi$
$571$	−924.030			−1.61827			−0.809133	+	0.587626i	$0.800063\pi$
$572$	−206.404	+	206.404i	−0.360846	+	0.360846i
$573$	49.1010	+	49.1010i	0.0856911	+	0.0856911i
$574$			185.081i			0.322440i
$575$		0			0
$576$	310.485			0.539036
$577$	497.879	−	497.879i	0.862874	−	0.862874i	−0.128797	−	0.991671i	$-0.541111\pi$
$577$	497.879	−	497.879i	0.862874	−	0.862874i	0.991671	+	0.128797i	$0.0411114\pi$
$578$	611.669	+	611.669i	1.05825	+	1.05825i
$579$			189.995i			0.328144i
$580$		0			0
$581$	61.3031			0.105513
$582$	79.5403	−	79.5403i	0.136667	−	0.136667i
$583$	96.0908	+	96.0908i	0.164821	+	0.164821i
$584$		−	336.186i		−	0.575661i
$585$		0			0
$586$	1052.59			1.79624
$587$	−292.783	+	292.783i	−0.498779	+	0.498779i	−0.911058	−	0.412279i	$-0.864733\pi$
$587$	−292.783	+	292.783i	−0.498779	+	0.498779i	0.412279	+	0.911058i	$0.364733\pi$
$588$	−323.654	−	323.654i	−0.550432	−	0.550432i
$589$		−	386.969i		−	0.656994i
$590$		0			0
$591$	−164.858			−0.278948
$592$	−182.540	+	182.540i	−0.308345	+	0.308345i
$593$	−451.258	−	451.258i	−0.760974	−	0.760974i	0.215524	−	0.976498i	$-0.430854\pi$
$593$	−451.258	−	451.258i	−0.760974	−	0.760974i	−0.976498	+	0.215524i	$0.930854\pi$
$594$			54.7423i			0.0921588i
$595$		0			0
$596$	−702.842			−1.17927
$597$	−307.893	+	307.893i	−0.515734	+	0.515734i
$598$	−764.817	−	764.817i	−1.27896	−	1.27896i
$599$		−	32.8582i		−	0.0548550i	−0.999624	−	0.0274275i	$-0.991268\pi$
$599$		−	32.8582i		−	0.0548550i	0.999624	−	0.0274275i	$-0.00873154\pi$
$600$		0			0
$601$	−184.484			−0.306961			−0.153481	−	0.988152i	$-0.549048\pi$
$601$	−184.484			−0.306961			−0.153481	+	0.988152i	$0.549048\pi$
$602$	−145.081	+	145.081i	−0.240998	+	0.240998i
$603$	164.697	+	164.697i	0.273129	+	0.273129i
$604$			855.171i			1.41585i
$605$		0			0
$606$	−946.145			−1.56130
$607$	−136.389	+	136.389i	−0.224694	+	0.224694i	−0.810472	−	0.585778i	$-0.800789\pi$
$607$	−136.389	+	136.389i	−0.224694	+	0.224694i	0.585778	+	0.810472i	$0.300789\pi$
$608$	570.681	+	570.681i	0.938620	+	0.938620i
$609$			3.03062i			0.00497638i
$610$		0			0
$611$	−412.808			−0.675627
$612$	46.9240	−	46.9240i	0.0766732	−	0.0766732i
$613$	12.7128	+	12.7128i	0.0207386	+	0.0207386i	0.717400	−	0.696661i	$-0.245332\pi$
$613$	12.7128	+	12.7128i	0.0207386	+	0.0207386i	−0.696661	+	0.717400i	$0.745332\pi$
$614$			751.828i			1.22447i
$615$		0			0
$616$	41.0102			0.0665750
$617$	398.752	−	398.752i	0.646275	−	0.646275i	−0.305816	−	0.952091i	$-0.598929\pi$
$617$	398.752	−	398.752i	0.646275	−	0.646275i	0.952091	+	0.305816i	$0.0989292\pi$
$618$	−352.868	−	352.868i	−0.570984	−	0.570984i
$619$		−	819.131i		−	1.32331i	−0.749807	−	0.661656i	$-0.769854\pi$
$619$		−	819.131i		−	1.32331i	0.749807	−	0.661656i	$-0.230146\pi$
$620$		0			0
$621$	−120.879			−0.194651
$622$	788.232	−	788.232i	1.26725	−	1.26725i
$623$	136.515	+	136.515i	0.219126	+	0.219126i
$624$		−	122.808i		−	0.196808i
$625$		0			0
$626$	−677.984			−1.08304
$627$	−84.8786	+	84.8786i	−0.135373	+	0.135373i
$628$	301.712	+	301.712i	0.480433	+	0.480433i
$629$			201.757i			0.320759i
$630$		0			0
$631$	105.485			0.167171			0.0835853	−	0.996501i	$-0.473363\pi$
$631$	105.485			0.167171			0.0835853	+	0.996501i	$0.473363\pi$
$632$	−103.485	+	103.485i	−0.163742	+	0.163742i
$633$	−324.297	−	324.297i	−0.512318	−	0.512318i
$634$		−	1900.90i		−	2.99826i
$635$		0			0
$636$	414.656			0.651975
$637$	−468.116	+	468.116i	−0.734876	+	0.734876i
$638$	6.35867	+	6.35867i	0.00996657	+	0.00996657i
$639$		−	204.000i		−	0.319249i
$640$		0			0
$641$	164.788			0.257079			0.128540	−	0.991704i	$-0.458971\pi$
$641$	164.788			0.257079			0.128540	+	0.991704i	$0.458971\pi$
$642$	−25.8434	+	25.8434i	−0.0402545	+	0.0402545i
$643$	764.372	+	764.372i	1.18876	+	1.18876i	0.977411	+	0.211349i	$0.0677856\pi$
$643$	764.372	+	764.372i	1.18876	+	1.18876i	0.211349	+	0.977411i	$0.432214\pi$
$644$			281.303i			0.436806i
$645$		0			0
$646$	244.182			0.377990
$647$	−321.287	+	321.287i	−0.496580	+	0.496580i	−0.910372	−	0.413792i	$-0.864204\pi$
$647$	−321.287	+	321.287i	−0.496580	+	0.496580i	0.413792	+	0.910372i	$0.364204\pi$
$648$	38.0227	+	38.0227i	0.0586770	+	0.0586770i
$649$			374.808i			0.577516i
$650$		0			0
$651$	66.3837			0.101972
$652$	−1117.23	+	1117.23i	−1.71354	+	1.71354i
$653$	169.823	+	169.823i	0.260066	+	0.260066i	0.825081	−	0.565015i	$-0.191130\pi$
$653$	169.823	+	169.823i	0.260066	+	0.260066i	−0.565015	+	0.825081i	$0.691130\pi$
$654$			214.182i			0.327495i
$655$		0			0
$656$	−137.687			−0.209888
$657$	−119.363	+	119.363i	−0.181679	+	0.181679i
$658$	127.394	+	127.394i	0.193608	+	0.193608i
$659$		−	958.763i		−	1.45488i	−0.686174	−	0.727438i	$-0.740711\pi$
$659$		−	958.763i		−	1.45488i	0.686174	−	0.727438i	$-0.259289\pi$
$660$		0			0
$661$	396.393			0.599687			0.299843	−	0.953988i	$-0.403066\pi$
$661$	396.393			0.599687			0.299843	+	0.953988i	$0.403066\pi$
$662$	1088.84	−	1088.84i	1.64478	−	1.64478i
$663$	−67.8684	−	67.8684i	−0.102366	−	0.102366i
$664$		−	178.677i		−	0.269091i
$665$		0			0
$666$	−507.848			−0.762534
$667$	−14.0408	+	14.0408i	−0.0210507	+	0.0210507i
$668$	572.409	+	572.409i	0.856899	+	0.856899i
$669$		−	81.8842i		−	0.122398i
$670$		0			0
$671$	−315.060			−0.469538
$672$	−97.8990	+	97.8990i	−0.145683	+	0.145683i
$673$	−164.707	−	164.707i	−0.244736	−	0.244736i	0.574070	−	0.818806i	$-0.305364\pi$
$673$	−164.707	−	164.707i	−0.244736	−	0.244736i	−0.818806	+	0.574070i	$0.805364\pi$
$674$			1300.10i			1.92894i
$675$		0			0
$676$	291.313			0.430937
$677$	−544.388	+	544.388i	−0.804119	+	0.804119i	−0.983736	−	0.179618i	$-0.942514\pi$
$677$	−544.388	+	544.388i	−0.804119	+	0.804119i	0.179618	+	0.983736i	$0.442514\pi$
$678$	78.2474	+	78.2474i	0.115409	+	0.115409i
$679$			42.3133i			0.0623170i
$680$		0			0
$681$	−51.8592			−0.0761515
$682$	139.283	−	139.283i	0.204227	−	0.204227i
$683$	−786.590	−	786.590i	−1.15167	−	1.15167i	−0.986218	−	0.165452i	$-0.947092\pi$
$683$	−786.590	−	786.590i	−1.15167	−	1.15167i	−0.165452	−	0.986218i	$-0.552908\pi$
$684$			366.272i			0.535486i
$685$		0			0
$686$	604.949			0.881850
$687$	298.590	−	298.590i	0.434629	−	0.434629i
$688$	−107.930	−	107.930i	−0.156874	−	0.156874i
$689$		−	599.737i		−	0.870445i
$690$		0			0
$691$	356.879			0.516467			0.258233	−	0.966083i	$-0.416860\pi$
$691$	356.879			0.516467			0.258233	+	0.966083i	$0.416860\pi$
$692$	204.288	−	204.288i	0.295214	−	0.295214i
$693$	−14.5607	−	14.5607i	−0.0210111	−	0.0210111i
$694$			1424.06i			2.05196i
$695$		0			0
$696$	8.83316			0.0126913
$697$	−76.0908	+	76.0908i	−0.109169	+	0.109169i
$698$	−1277.02	−	1277.02i	−1.82955	−	1.82955i
$699$			396.111i			0.566683i
$700$		0			0
$701$	885.680			1.26345			0.631726	−	0.775192i	$-0.282347\pi$
$701$	885.680			1.26345			0.631726	+	0.775192i	$0.282347\pi$
$702$	170.833	−	170.833i	0.243352	−	0.243352i
$703$	−787.423	−	787.423i	−1.12009	−	1.12009i
$704$			346.549i			0.492258i
$705$		0			0
$706$	−1185.88			−1.67971
$707$	251.662	−	251.662i	0.355957	−	0.355957i
$708$	808.696	+	808.696i	1.14223	+	1.14223i
$709$			731.049i			1.03110i	0.856860	+	0.515549i	$0.172412\pi$
$709$			731.049i			1.03110i	−0.856860	+	0.515549i	$0.827588\pi$
$710$		0			0
$711$	73.4847			0.103354
$712$	397.893	−	397.893i	0.558839	−	0.558839i
$713$	307.555	+	307.555i	0.431354	+	0.431354i
$714$			41.8888i			0.0586678i
$715$		0			0
$716$	1083.71			1.51356
$717$	399.514	−	399.514i	0.557203	−	0.557203i
$718$	481.151	+	481.151i	0.670127	+	0.670127i
$719$		−	629.271i		−	0.875204i	−0.899169	−	0.437602i	$-0.855828\pi$
$719$		−	629.271i		−	0.875204i	0.899169	−	0.437602i	$-0.144172\pi$
$720$		0			0
$721$	187.716			0.260356
$722$	−149.866	+	149.866i	−0.207571	+	0.207571i
$723$	163.596	+	163.596i	0.226274	+	0.226274i
$724$			128.170i			0.177031i
$725$		0			0
$726$	598.287			0.824087
$727$	15.8740	−	15.8740i	0.0218349	−	0.0218349i	−0.696105	−	0.717940i	$-0.745085\pi$
$727$	15.8740	−	15.8740i	0.0218349	−	0.0218349i	0.717940	+	0.696105i	$0.245085\pi$
$728$	−127.980	−	127.980i	−0.175796	−	0.175796i
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	−119.292			−0.163190
$732$	−679.782	+	679.782i	−0.928664	+	0.928664i
$733$	393.237	+	393.237i	0.536476	+	0.536476i	0.922492	−	0.386016i	$-0.126149\pi$
$733$	393.237	+	393.237i	0.536476	+	0.536476i	−0.386016	+	0.922492i	$0.626149\pi$
$734$		−	1070.15i		−	1.45796i
$735$		0			0
$736$	−907.131			−1.23251
$737$	−183.828	+	183.828i	−0.249427	+	0.249427i
$738$	−191.530	−	191.530i	−0.259526	−	0.259526i
$739$			192.334i			0.260262i	0.991497	+	0.130131i	$0.0415398\pi$
$739$			192.334i			0.260262i	−0.991497	+	0.130131i	$0.958460\pi$
$740$		0			0
$741$	529.757			0.714922
$742$	−185.081	+	185.081i	−0.249435	+	0.249435i
$743$	44.7015	+	44.7015i	0.0601636	+	0.0601636i	0.736548	−	0.676385i	$-0.236454\pi$
$743$	44.7015	+	44.7015i	0.0601636	+	0.0601636i	−0.676385	+	0.736548i	$0.736454\pi$
$744$		−	193.485i		−	0.260060i
$745$		0			0
$746$	1469.25			1.96951
$747$	−63.4393	+	63.4393i	−0.0849254	+	0.0849254i
$748$	52.3745	+	52.3745i	0.0700194	+	0.0700194i
$749$		−	13.7480i		−	0.0183551i
$750$		0			0
$751$	227.787			0.303311			0.151656	−	0.988433i	$-0.451540\pi$
$751$	227.787			0.303311			0.151656	+	0.988433i	$0.451540\pi$
$752$	−94.7719	+	94.7719i	−0.126027	+	0.126027i
$753$	495.706	+	495.706i	0.658308	+	0.658308i
$754$		−	39.6867i		−	0.0526349i
$755$		0			0
$756$	−62.8332			−0.0831126
$757$	235.925	−	235.925i	0.311658	−	0.311658i	−0.533894	−	0.845552i	$-0.679272\pi$
$757$	235.925	−	235.925i	0.311658	−	0.311658i	0.845552	+	0.533894i	$0.179272\pi$
$758$	467.196	+	467.196i	0.616354	+	0.616354i
$759$		−	134.919i		−	0.177759i
$760$		0			0
$761$	−881.242			−1.15801			−0.579003	−	0.815326i	$-0.696558\pi$
$761$	−881.242			−1.15801			−0.579003	+	0.815326i	$0.696558\pi$
$762$	−624.626	+	624.626i	−0.819719	+	0.819719i
$763$	−56.9694	−	56.9694i	−0.0746650	−	0.0746650i
$764$			236.495i			0.309548i
$765$		0			0
$766$	−759.221			−0.991151
$767$	1169.66	−	1169.66i	1.52497	−	1.52497i
$768$	146.684	+	146.684i	0.190995	+	0.190995i
$769$			1208.40i			1.57139i	0.618612	+	0.785697i	$0.287696\pi$
$769$			1208.40i			1.57139i	−0.618612	+	0.785697i	$0.712304\pi$
$770$		0			0
$771$	−218.586			−0.283509
$772$	−457.556	+	457.556i	−0.592689	+	0.592689i
$773$	815.226	+	815.226i	1.05463	+	1.05463i	0.998419	+	0.0562070i	$0.0179007\pi$
$773$	815.226	+	815.226i	1.05463	+	1.05463i	0.0562070	+	0.998419i	$0.482099\pi$
$774$		−	300.272i		−	0.387949i
$775$		0			0
$776$	123.328			0.158928
$777$	135.081	−	135.081i	0.173849	−	0.173849i
$778$	−1217.69	−	1217.69i	−1.56515	−	1.56515i
$779$		−	593.939i		−	0.762437i
$780$		0			0
$781$	227.696			0.291544
$782$	−194.070	+	194.070i	−0.248172	+	0.248172i
$783$	−3.13622	−	3.13622i	−0.00400539	−	0.00400539i
$784$			214.939i			0.274157i
$785$		0			0
$786$	142.429			0.181207
$787$	−813.010	+	813.010i	−1.03305	+	1.03305i	−0.0336150	+	0.999435i	$0.510702\pi$
$787$	−813.010	+	813.010i	−1.03305	+	1.03305i	−0.999435	+	0.0336150i	$0.989298\pi$
$788$	−397.019	−	397.019i	−0.503832	−	0.503832i
$789$		−	837.342i		−	1.06127i
$790$		0			0
$791$	−41.6255			−0.0526239
$792$	−42.4393	+	42.4393i	−0.0535850	+	0.0535850i
$793$	983.201	+	983.201i	1.23985	+	1.23985i
$794$			201.373i			0.253619i
$795$		0			0
$796$	−1482.97			−1.86302
$797$	−311.217	+	311.217i	−0.390485	+	0.390485i	−0.874860	−	0.484375i	$-0.839047\pi$
$797$	−311.217	+	311.217i	−0.390485	+	0.390485i	0.484375	+	0.874860i	$0.339047\pi$
$798$	−163.485	−	163.485i	−0.204868	−	0.204868i
$799$			104.749i			0.131100i
$800$		0			0
$801$	−282.545			−0.352740
$802$	−1157.54	+	1157.54i	−1.44332	+	1.44332i
$803$	−133.228	−	133.228i	−0.165913	−	0.165913i
$804$			793.262i			0.986645i
$805$		0			0
$806$	−869.312			−1.07855
$807$	4.28724	−	4.28724i	0.00531256	−	0.00531256i
$808$	−733.504	−	733.504i	−0.907802	−	0.907802i
$809$			150.000i			0.185414i	0.995693	+	0.0927070i	$0.0295520\pi$
$809$			150.000i			0.185414i	−0.995693	+	0.0927070i	$0.970448\pi$
$810$		0			0
$811$	−132.847			−0.163806			−0.0819032	−	0.996640i	$-0.526100\pi$
$811$	−132.847			−0.163806			−0.0819032	+	0.996640i	$0.526100\pi$
$812$	−7.29847	+	7.29847i	−0.00898827	+	0.00898827i
$813$	126.854	+	126.854i	0.156031	+	0.156031i
$814$		−	566.838i		−	0.696361i
$815$		0			0
$816$	−31.1623			−0.0381890
$817$	465.576	−	465.576i	0.569860	−	0.569860i
$818$	−772.232	−	772.232i	−0.944048	−	0.944048i
$819$			90.8786i			0.110963i
$820$		0			0
$821$	509.893			0.621064			0.310532	−	0.950563i	$-0.399493\pi$
$821$	509.893			0.621064			0.310532	+	0.950563i	$0.399493\pi$
$822$	79.7321	−	79.7321i	0.0969977	−	0.0969977i
$823$	−300.369	−	300.369i	−0.364968	−	0.364968i	0.500670	−	0.865638i	$-0.333087\pi$
$823$	−300.369	−	300.369i	−0.364968	−	0.364968i	−0.865638	+	0.500670i	$0.833087\pi$
$824$		−	547.126i		−	0.663988i
$825$		0			0
$826$	−721.918			−0.873993
$827$	1030.76	−	1030.76i	1.24638	−	1.24638i	0.289073	−	0.957307i	$-0.406653\pi$
$827$	1030.76	−	1030.76i	1.24638	−	1.24638i	0.957307	−	0.289073i	$-0.0933469\pi$
$828$	−291.106	−	291.106i	−0.351577	−	0.351577i
$829$		−	37.4235i		−	0.0451429i	−0.999745	−	0.0225714i	$-0.992815\pi$
$829$		−	37.4235i		−	0.0451429i	0.999745	−	0.0225714i	$-0.00718533\pi$
$830$		0			0
$831$	−699.353			−0.841580
$832$	1081.47	−	1081.47i	1.29984	−	1.29984i
$833$	118.783	+	118.783i	0.142597	+	0.142597i
$834$			453.242i			0.543455i
$835$		0			0
$836$	−408.817			−0.489016
$837$	−68.6969	+	68.6969i	−0.0820752	+	0.0820752i
$838$	1297.91	+	1297.91i	1.54882	+	1.54882i
$839$			1152.37i			1.37351i	0.726890	+	0.686754i	$0.240965\pi$
$839$			1152.37i			1.37351i	−0.726890	+	0.686754i	$0.759035\pi$
$840$		0			0
$841$	840.271			0.999134
$842$	474.207	−	474.207i	0.563191	−	0.563191i
$843$	−456.459	−	456.459i	−0.541469	−	0.541469i
$844$		−	1561.98i		−	1.85068i
$845$		0			0
$846$	−263.666			−0.311662
$847$	−159.136	+	159.136i	−0.187882	+	0.187882i
$848$	−137.687	−	137.687i	−0.162366	−	0.162366i
$849$		−	189.081i		−	0.222710i
$850$		0			0
$851$	1251.66			1.47081
$852$	491.283	−	491.283i	0.576623	−	0.576623i
$853$	−694.570	−	694.570i	−0.814267	−	0.814267i	0.171003	−	0.985270i	$-0.445299\pi$
$853$	−694.570	−	694.570i	−0.814267	−	0.814267i	−0.985270	+	0.171003i	$0.945299\pi$
$854$		−	606.838i		−	0.710583i
$855$		0			0
$856$	−40.0704			−0.0468112
$857$	−417.176	+	417.176i	−0.486786	+	0.486786i	−0.907291	−	0.420504i	$-0.861853\pi$
$857$	−417.176	+	417.176i	−0.486786	+	0.486786i	0.420504	+	0.907291i	$0.361853\pi$
$858$	190.677	+	190.677i	0.222234	+	0.222234i
$859$		−	486.867i		−	0.566784i	−0.959004	−	0.283392i	$-0.908540\pi$
$859$		−	486.867i		−	0.566784i	0.959004	−	0.283392i	$-0.0914597\pi$
$860$		0			0
$861$	101.889			0.118338
$862$	416.838	−	416.838i	0.483570	−	0.483570i
$863$	411.319	+	411.319i	0.476615	+	0.476615i	0.904047	−	0.427432i	$-0.140582\pi$
$863$	411.319	+	411.319i	0.476615	+	0.476615i	−0.427432	+	0.904047i	$0.640582\pi$
$864$		−	202.621i		−	0.234515i
$865$		0			0
$866$	−688.994			−0.795606
$867$	336.730	−	336.730i	0.388385	−	0.388385i
$868$	159.868	+	159.868i	0.184180	+	0.184180i
$869$			82.0204i			0.0943848i
$870$		0			0
$871$	1147.33			1.31726
$872$	−166.045	+	166.045i	−0.190419	+	0.190419i
$873$	−43.7878	−	43.7878i	−0.0501578	−	0.0501578i
$874$		−	1514.85i		−	1.73323i
$875$		0			0
$876$	−574.913			−0.656293
$877$	−332.540	+	332.540i	−0.379179	+	0.379179i	−0.870806	−	0.491627i	$-0.836402\pi$
$877$	−332.540	+	332.540i	−0.379179	+	0.379179i	0.491627	+	0.870806i	$0.336402\pi$
$878$	562.702	+	562.702i	0.640890	+	0.640890i
$879$		−	579.464i		−	0.659231i
$880$		0			0
$881$	533.151			0.605166			0.302583	−	0.953123i	$-0.402151\pi$
$881$	533.151			0.605166			0.302583	+	0.953123i	$0.402151\pi$
$882$	−298.992	+	298.992i	−0.338993	+	0.338993i
$883$	745.939	+	745.939i	0.844778	+	0.844778i	0.989476	−	0.144698i	$-0.0462211\pi$
$883$	745.939	+	745.939i	0.844778	+	0.844778i	−0.144698	+	0.989476i	$0.546221\pi$
$884$		−	326.888i		−	0.369783i
$885$		0			0
$886$	1873.82			2.11492
$887$	386.207	−	386.207i	0.435408	−	0.435408i	−0.455055	−	0.890463i	$-0.650381\pi$
$887$	386.207	−	386.207i	0.435408	−	0.435408i	0.890463	+	0.455055i	$0.150381\pi$
$888$	−393.712	−	393.712i	−0.443369	−	0.443369i
$889$		−	332.284i		−	0.373772i
$890$		0			0
$891$	30.1362			0.0338229
$892$	197.197	−	197.197i	0.221073	−	0.221073i
$893$	−408.817	−	408.817i	−0.457802	−	0.457802i
$894$			649.287i			0.726272i
$895$		0			0
$896$	−347.753			−0.388117
$897$	−421.040	+	421.040i	−0.469387	+	0.469387i
$898$	−662.772	−	662.772i	−0.738053	−	0.738053i
$899$			15.9592i			0.0177521i
$900$		0			0
$901$	−152.182			−0.168903
$902$	213.778	−	213.778i	0.237004	−	0.237004i
$903$	79.8684	+	79.8684i	0.0884478	+	0.0884478i
$904$			121.323i			0.134207i
$905$		0			0
$906$	790.009			0.871975
$907$	947.342	−	947.342i	1.04448	−	1.04448i	0.0455146	−	0.998964i	$-0.485507\pi$
$907$	947.342	−	947.342i	1.04448	−	1.04448i	0.998964	−	0.0455146i	$-0.0144928\pi$
$908$	−124.890	−	124.890i	−0.137544	−	0.137544i
$909$			520.863i			0.573006i
$910$		0			0
$911$	−1149.36			−1.26165			−0.630824	−	0.775926i	$-0.717283\pi$
$911$	−1149.36			−1.26165			−0.630824	+	0.775926i	$0.717283\pi$
$912$	121.621	−	121.621i	0.133356	−	0.133356i
$913$	−70.8082	−	70.8082i	−0.0775555	−	0.0775555i
$914$			1271.43i			1.39106i
$915$		0			0
$916$	1438.16			1.57004
$917$	−37.8842	+	37.8842i	−0.0413132	+	0.0413132i
$918$	−43.3485	−	43.3485i	−0.0472206	−	0.0472206i
$919$		−	412.577i		−	0.448941i	−0.974481	−	0.224470i	$-0.927935\pi$
$919$		−	412.577i		−	0.448941i	0.974481	−	0.224470i	$-0.0720652\pi$
$920$		0			0
$921$	413.889			0.449391
$922$	1171.59	−	1171.59i	1.27071	−	1.27071i
$923$	−710.565	−	710.565i	−0.769843	−	0.769843i
$924$		−	70.1316i		−	0.0759000i
$925$		0			0
$926$	−1493.70			−1.61307
$927$	−194.258	+	194.258i	−0.209555	+	0.209555i
$928$	−23.5357	−	23.5357i	−0.0253618	−	0.0253618i
$929$			151.707i			0.163302i	0.996661	+	0.0816508i	$0.0260192\pi$
$929$			151.707i			0.163302i	−0.996661	+	0.0816508i	$0.973981\pi$
$930$		0			0
$931$	−927.181			−0.995898
$932$	−953.934	+	953.934i	−1.02353	+	1.02353i
$933$	−433.930	−	433.930i	−0.465091	−	0.465091i
$934$			2174.65i			2.32832i
$935$		0			0
$936$	264.879			0.282990
$937$	−662.090	+	662.090i	−0.706606	+	0.706606i	−0.965820	−	0.259214i	$-0.916537\pi$
$937$	−662.090	+	662.090i	−0.706606	+	0.706606i	0.259214	+	0.965820i	$0.416537\pi$
$938$	−354.070	−	354.070i	−0.377474	−	0.377474i
$939$			373.237i			0.397484i
$940$		0			0
$941$	−1533.77			−1.62994			−0.814969	−	0.579505i	$-0.803246\pi$
$941$	−1533.77			−1.62994			−0.814969	+	0.579505i	$0.803246\pi$
$942$	278.722	−	278.722i	0.295883	−	0.295883i
$943$	472.050	+	472.050i	0.500583	+	0.500583i
$944$		−	537.056i		−	0.568915i
$945$		0			0
$946$	335.151			0.354282
$947$	−1173.19	+	1173.19i	−1.23885	+	1.23885i	−0.278377	+	0.960472i	$0.589796\pi$
$947$	−1173.19	+	1173.19i	−1.23885	+	1.23885i	−0.960472	+	0.278377i	$0.910204\pi$
$948$	176.969	+	176.969i	0.186677	+	0.186677i
$949$			831.523i			0.876210i
$950$		0			0
$951$	−1046.46			−1.10038
$952$	−32.4745	+	32.4745i	−0.0341119	+	0.0341119i
$953$	145.501	+	145.501i	0.152676	+	0.152676i	0.779312	−	0.626636i	$-0.215569\pi$
$953$	145.501	+	145.501i	0.152676	+	0.152676i	−0.626636	+	0.779312i	$0.715569\pi$
$954$		−	383.060i		−	0.401531i
$955$		0			0
$956$	1924.26			2.01282
$957$	3.50052	−	3.50052i	0.00365780	−	0.00365780i
$958$	411.464	+	411.464i	0.429503	+	0.429503i
$959$			42.4153i			0.0442287i
$960$		0			0
$961$	−611.424			−0.636238
$962$	−1768.92	+	1768.92i	−1.83879	+	1.83879i
$963$	14.2270	+	14.2270i	0.0147737	+	0.0147737i
$964$			787.959i			0.817385i
$965$		0			0
$966$	259.868			0.269015
$967$	−1151.69	+	1151.69i	−1.19099	+	1.19099i	−0.214204	+	0.976789i	$0.568716\pi$
$967$	−1151.69	+	1151.69i	−1.19099	+	1.19099i	−0.976789	+	0.214204i	$0.931284\pi$
$968$	463.825	+	463.825i	0.479158	+	0.479158i
$969$		−	134.424i		−	0.138725i
$970$		0			0
$971$	72.4383			0.0746017			0.0373009	−	0.999304i	$-0.488124\pi$
$971$	72.4383			0.0746017			0.0373009	+	0.999304i	$0.488124\pi$
$972$	65.0227	−	65.0227i	0.0668958	−	0.0668958i
$973$	−120.556	−	120.556i	−0.123901	−	0.123901i
$974$		−	536.974i		−	0.551308i
$975$		0			0
$976$	451.444			0.462545
$977$	−706.338	+	706.338i	−0.722966	+	0.722966i	−0.969208	−	0.246242i	$-0.920804\pi$
$977$	−706.338	+	706.338i	−0.722966	+	0.722966i	0.246242	+	0.969208i	$0.420804\pi$
$978$	1032.10	+	1032.10i	1.05532	+	1.05532i
$979$		−	315.364i		−	0.322129i
$980$		0			0
$981$	117.909			0.120193
$982$	−235.116	+	235.116i	−0.239425	+	0.239425i
$983$	134.663	+	134.663i	0.136992	+	0.136992i	0.772277	−	0.635286i	$-0.219118\pi$
$983$	134.663	+	134.663i	0.136992	+	0.136992i	−0.635286	+	0.772277i	$0.719118\pi$
$984$		−	296.969i		−	0.301798i
$985$		0			0
$986$	−10.0704			−0.0102134
$987$	70.1316	−	70.1316i	0.0710554	−	0.0710554i
$988$	1275.79	+	1275.79i	1.29128	+	1.29128i
$989$			740.059i			0.748290i
$990$		0			0
$991$	−1131.94			−1.14222			−0.571109	−	0.820874i	$-0.693487\pi$
$991$	−1131.94			−1.14222			−0.571109	+	0.820874i	$0.693487\pi$
$992$	−515.535	+	515.535i	−0.519692	+	0.519692i
$993$	−599.419	−	599.419i	−0.603644	−	0.603644i
$994$			438.565i			0.441213i
$995$		0			0
$996$	−305.555			−0.306782
$997$	1115.27	−	1115.27i	1.11862	−	1.11862i	0.126679	−	0.991944i	$-0.459568\pi$
$997$	1115.27	−	1115.27i	1.11862	−	1.11862i	0.991944	−	0.126679i	$-0.0404318\pi$
$998$	1645.39	+	1645.39i	1.64868	+	1.64868i
$999$			279.576i			0.279855i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.f.c.43.2		4
3.2	odd	2		225.3.g.a.118.1		4
4.3	odd	2		1200.3.bg.k.193.2		4
5.2	odd	4	inner	75.3.f.c.7.2		4
5.3	odd	4		15.3.f.a.7.1	✓	4
5.4	even	2		15.3.f.a.13.1	yes	4
15.2	even	4		225.3.g.a.82.1		4
15.8	even	4		45.3.g.b.37.2		4
15.14	odd	2		45.3.g.b.28.2		4
20.3	even	4		240.3.bg.a.97.1		4
20.7	even	4		1200.3.bg.k.1057.2		4
20.19	odd	2		240.3.bg.a.193.1		4
40.3	even	4		960.3.bg.h.577.2		4
40.13	odd	4		960.3.bg.i.577.1		4
40.19	odd	2		960.3.bg.h.193.2		4
40.29	even	2		960.3.bg.i.193.1		4
45.4	even	6		405.3.l.h.298.1		8
45.13	odd	12		405.3.l.h.217.2		8
45.14	odd	6		405.3.l.f.298.2		8
45.23	even	12		405.3.l.f.217.1		8
45.29	odd	6		405.3.l.f.28.1		8
45.34	even	6		405.3.l.h.28.2		8
45.38	even	12		405.3.l.f.352.2		8
45.43	odd	12		405.3.l.h.352.1		8
60.23	odd	4		720.3.bh.k.577.1		4
60.59	even	2		720.3.bh.k.433.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.3.f.a.7.1	✓	4	5.3	odd	4
15.3.f.a.13.1	yes	4	5.4	even	2
45.3.g.b.28.2		4	15.14	odd	2
45.3.g.b.37.2		4	15.8	even	4
75.3.f.c.7.2		4	5.2	odd	4	inner
75.3.f.c.43.2		4	1.1	even	1	trivial
225.3.g.a.82.1		4	15.2	even	4
225.3.g.a.118.1		4	3.2	odd	2
240.3.bg.a.97.1		4	20.3	even	4
240.3.bg.a.193.1		4	20.19	odd	2
405.3.l.f.28.1		8	45.29	odd	6
405.3.l.f.217.1		8	45.23	even	12
405.3.l.f.298.2		8	45.14	odd	6
405.3.l.f.352.2		8	45.38	even	12
405.3.l.h.28.2		8	45.34	even	6
405.3.l.h.217.2		8	45.13	odd	12
405.3.l.h.298.1		8	45.4	even	6
405.3.l.h.352.1		8	45.43	odd	12
720.3.bh.k.433.1		4	60.59	even	2
720.3.bh.k.577.1		4	60.23	odd	4
960.3.bg.h.193.2		4	40.19	odd	2
960.3.bg.h.577.2		4	40.3	even	4
960.3.bg.i.193.1		4	40.29	even	2
960.3.bg.i.577.1		4	40.13	odd	4
1200.3.bg.k.193.2		4	4.3	odd	2
1200.3.bg.k.1057.2		4	20.7	even	4

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.22474 - 2.22474i) q^{2} +(-1.22474 - 1.22474i) q^{3} -5.89898i q^{4} -5.44949 q^{6} +(1.44949 - 1.44949i) q^{7} +(-4.22474 - 4.22474i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(2.22474 - 2.22474i) q^{2} +(-1.22474 - 1.22474i) q^{3} -5.89898i q^{4} -5.44949 q^{6} +(1.44949 - 1.44949i) q^{7} +(-4.22474 - 4.22474i) q^{8} +3.00000i q^{9} -3.34847 q^{11} +(-7.22474 + 7.22474i) q^{12} +(10.4495 + 10.4495i) q^{13} -6.44949i q^{14} +4.79796 q^{16} +(2.65153 - 2.65153i) q^{17} +(6.67423 + 6.67423i) q^{18} +20.6969i q^{19} -3.55051 q^{21} +(-7.44949 + 7.44949i) q^{22} +(-16.4495 - 16.4495i) q^{23} +10.3485i q^{24} +46.4949 q^{26} +(3.67423 - 3.67423i) q^{27} +(-8.55051 - 8.55051i) q^{28} -0.853572i q^{29} -18.6969 q^{31} +(27.5732 - 27.5732i) q^{32} +(4.10102 + 4.10102i) q^{33} -11.7980i q^{34} +17.6969 q^{36} +(-38.0454 + 38.0454i) q^{37} +(46.0454 + 46.0454i) q^{38} -25.5959i q^{39} -28.6969 q^{41} +(-7.89898 + 7.89898i) q^{42} +(-22.4949 - 22.4949i) q^{43} +19.7526i q^{44} -73.1918 q^{46} +(-19.7526 + 19.7526i) q^{47} +(-5.87628 - 5.87628i) q^{48} +44.7980i q^{49} -6.49490 q^{51} +(61.6413 - 61.6413i) q^{52} +(-28.6969 - 28.6969i) q^{53} -16.3485i q^{54} -12.2474 q^{56} +(25.3485 - 25.3485i) q^{57} +(-1.89898 - 1.89898i) q^{58} -111.934i q^{59} +94.0908 q^{61} +(-41.5959 + 41.5959i) q^{62} +(4.34847 + 4.34847i) q^{63} -103.495i q^{64} +18.2474 q^{66} +(54.8990 - 54.8990i) q^{67} +(-15.6413 - 15.6413i) q^{68} +40.2929i q^{69} -68.0000 q^{71} +(12.6742 - 12.6742i) q^{72} +(39.7878 + 39.7878i) q^{73} +169.283i q^{74} +122.091 q^{76} +(-4.85357 + 4.85357i) q^{77} +(-56.9444 - 56.9444i) q^{78} -24.4949i q^{79} -9.00000 q^{81} +(-63.8434 + 63.8434i) q^{82} +(21.1464 + 21.1464i) q^{83} +20.9444i q^{84} -100.091 q^{86} +(-1.04541 + 1.04541i) q^{87} +(14.1464 + 14.1464i) q^{88} +94.1816i q^{89} +30.2929 q^{91} +(-97.0352 + 97.0352i) q^{92} +(22.8990 + 22.8990i) q^{93} +87.8888i q^{94} -67.5403 q^{96} +(-14.5959 + 14.5959i) q^{97} +(99.6640 + 99.6640i) q^{98} -10.0454i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 12 q^{6} - 4 q^{7} - 12 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 12 * q^6 - 4 * q^7 - 12 * q^8	\( 4 q + 4 q^{2} - 12 q^{6} - 4 q^{7} - 12 q^{8} + 16 q^{11} - 24 q^{12} + 32 q^{13} - 20 q^{16} + 40 q^{17} + 12 q^{18} - 24 q^{21} - 20 q^{22} - 56 q^{23} + 88 q^{26} - 44 q^{28} - 16 q^{31} + 76 q^{32} + 36 q^{33} + 12 q^{36} - 64 q^{37} + 96 q^{38} - 56 q^{41} - 12 q^{42} + 8 q^{43} - 136 q^{46} - 128 q^{47} - 48 q^{48} + 72 q^{51} + 80 q^{52} - 56 q^{53} + 72 q^{57} + 12 q^{58} + 200 q^{61} - 88 q^{62} - 12 q^{63} + 24 q^{66} + 200 q^{67} + 104 q^{68} - 272 q^{71} + 36 q^{72} - 76 q^{73} + 312 q^{76} - 88 q^{77} - 120 q^{78} - 36 q^{81} - 128 q^{82} + 16 q^{83} - 224 q^{86} + 84 q^{87} - 12 q^{88} - 16 q^{91} - 104 q^{92} + 72 q^{93} - 84 q^{96} + 20 q^{97} + 188 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 12 * q^6 - 4 * q^7 - 12 * q^8 + 16 * q^11 - 24 * q^12 + 32 * q^13 - 20 * q^16 + 40 * q^17 + 12 * q^18 - 24 * q^21 - 20 * q^22 - 56 * q^23 + 88 * q^26 - 44 * q^28 - 16 * q^31 + 76 * q^32 + 36 * q^33 + 12 * q^36 - 64 * q^37 + 96 * q^38 - 56 * q^41 - 12 * q^42 + 8 * q^43 - 136 * q^46 - 128 * q^47 - 48 * q^48 + 72 * q^51 + 80 * q^52 - 56 * q^53 + 72 * q^57 + 12 * q^58 + 200 * q^61 - 88 * q^62 - 12 * q^63 + 24 * q^66 + 200 * q^67 + 104 * q^68 - 272 * q^71 + 36 * q^72 - 76 * q^73 + 312 * q^76 - 88 * q^77 - 120 * q^78 - 36 * q^81 - 128 * q^82 + 16 * q^83 - 224 * q^86 + 84 * q^87 - 12 * q^88 - 16 * q^91 - 104 * q^92 + 72 * q^93 - 84 * q^96 + 20 * q^97 + 188 * q^98

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