LMFDB - Embedded newform 75.3.f.c.7.2

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			7.2
Root			$1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	75.7
Dual form			75.3.f.c.43.2

$q$-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 $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	2.22474	+	2.22474i	1.11237	+	1.11237i	0.992829	+	0.119543i	$0.0381431\pi$
$2$	2.22474	+	2.22474i	1.11237	+	1.11237i	0.119543	+	0.992829i	$0.461857\pi$
$3$	−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	0.803021	−	0.595951i	$-0.203225\pi$
$7$	1.44949	+	1.44949i	0.207070	+	0.207070i	−0.595951	+	0.803021i	$0.703225\pi$
$8$	−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	−0.179881	−	0.983688i	$-0.557571\pi$
$13$	10.4495	−	10.4495i	0.803807	−	0.803807i	0.983688	+	0.179881i	$0.0575714\pi$
$14$			6.44949i			0.460678i
$15$		0			0
$16$	4.79796			0.299872
$17$	2.65153	+	2.65153i	0.155972	+	0.155972i	0.780779	−	0.624807i	$-0.214822\pi$
$17$	2.65153	+	2.65153i	0.155972	+	0.155972i	−0.624807	+	0.780779i	$0.714822\pi$
$18$	6.67423	−	6.67423i	0.370791	−	0.370791i
$19$		−	20.6969i		−	1.08931i	−0.838659	−	0.544656i	$-0.816660\pi$
$19$		−	20.6969i		−	1.08931i	0.838659	−	0.544656i	$-0.183340\pi$
$20$		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	−0.967617	−	0.252422i	$-0.918773\pi$
$23$	−16.4495	+	16.4495i	−0.715195	+	0.715195i	0.252422	+	0.967617i	$0.418773\pi$
$24$		−	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	$0.00468466\pi$
$29$			0.853572i			0.0294335i	−0.999892	+	0.0147168i	$0.995315\pi$
$30$		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	−0.999589	−	0.0286652i	$-0.990874\pi$
$37$	−38.0454	−	38.0454i	−1.02825	−	1.02825i	−0.0286652	−	0.999589i	$-0.509126\pi$
$38$	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	−0.918517	−	0.395380i	$-0.870613\pi$
$43$	−22.4949	+	22.4949i	−0.523137	+	0.523137i	0.395380	+	0.918517i	$0.370613\pi$
$44$		−	19.7526i		−	0.448922i
$45$		0			0
$46$	−73.1918			−1.59113
$47$	−19.7526	−	19.7526i	−0.420267	−	0.420267i	0.465029	−	0.885296i	$-0.346044\pi$
$47$	−19.7526	−	19.7526i	−0.420267	−	0.420267i	−0.885296	+	0.465029i	$0.846044\pi$
$48$	−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	−0.923954	−	0.382503i	$-0.875062\pi$
$53$	−28.6969	+	28.6969i	−0.541452	+	0.541452i	0.382503	+	0.923954i	$0.375062\pi$
$54$			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	$0.397495\pi$
$59$			111.934i			1.89719i	−0.316493	+	0.948595i	$0.602505\pi$
$60$		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	0.986019	−	0.166631i	$-0.0532890\pi$
$67$	54.8990	+	54.8990i	0.819388	+	0.819388i	−0.166631	+	0.986019i	$0.553289\pi$
$68$	−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	−0.379964	−	0.925001i	$-0.624064\pi$
$73$	39.7878	−	39.7878i	0.545038	−	0.545038i	0.925001	+	0.379964i	$0.124064\pi$
$74$		−	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	$0.0495477\pi$
$79$			24.4949i			0.310062i	−0.987910	+	0.155031i	$0.950452\pi$
$80$		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	−0.568149	−	0.822926i	$-0.692340\pi$
$83$	21.1464	−	21.1464i	0.254776	−	0.254776i	0.822926	+	0.568149i	$0.192340\pi$
$84$		−	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	$-0.822526\pi$
$89$		−	94.1816i		−	1.05822i	0.848553	−	0.529110i	$-0.177474\pi$
$90$		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	0.627856	−	0.778329i	$-0.283933\pi$
$97$	−14.5959	−	14.5959i	−0.150473	−	0.150473i	−0.778329	+	0.627856i	$0.783933\pi$
$98$	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	−0.319067	−	0.947732i	$-0.603369\pi$
$103$	64.7526	−	64.7526i	0.628666	−	0.628666i	0.947732	+	0.319067i	$0.103369\pi$
$104$			88.2929i			0.848970i
$105$		0			0
$106$	−127.687			−1.20459
$107$	4.74235	+	4.74235i	0.0443210	+	0.0443210i	0.728920	−	0.684599i	$-0.240023\pi$
$107$	4.74235	+	4.74235i	0.0443210	+	0.0443210i	−0.684599	+	0.728920i	$0.740023\pi$
$108$	−21.6742	+	21.6742i	−0.200687	+	0.200687i
$109$			39.3031i			0.360579i	0.983614	+	0.180289i	$0.0577034\pi$
$109$			39.3031i			0.360579i	−0.983614	+	0.180289i	$0.942297\pi$
$110$		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	−0.767781	−	0.640713i	$-0.778639\pi$
$113$	−14.3587	+	14.3587i	−0.127068	+	0.127068i	0.640713	+	0.767781i	$0.278639\pi$
$114$			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	0.995654	−	0.0931273i	$-0.0296864\pi$
$127$	114.621	+	114.621i	0.902527	+	0.902527i	−0.0931273	+	0.995654i	$0.529686\pi$
$128$	−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	0.651689	−	0.758486i	$-0.274061\pi$
$137$	−14.6311	−	14.6311i	−0.106796	−	0.106796i	−0.758486	+	0.651689i	$0.774061\pi$
$138$	89.6413	−	89.6413i	0.649575	−	0.649575i
$139$			83.1714i			0.598356i	0.954197	+	0.299178i	$0.0967124\pi$
$139$			83.1714i			0.598356i	−0.954197	+	0.299178i	$0.903288\pi$
$140$		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	$0.130927\pi$
$149$			119.146i			0.799640i	−0.916594	+	0.399820i	$0.869073\pi$
$150$		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	0.525203	−	0.850977i	$-0.323989\pi$
$157$	−51.1464	−	51.1464i	−0.325773	−	0.325773i	−0.850977	+	0.525203i	$0.823989\pi$
$158$	−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	−0.177872	+	0.984054i	$0.556921\pi$
$163$	−189.394	+	189.394i	−1.16193	+	1.16193i	−0.984054	+	0.177872i	$0.943079\pi$
$164$		−	169.283i		−	1.03221i
$165$		0			0
$166$	94.0908			0.566812
$167$	−97.0352	−	97.0352i	−0.581049	−	0.581049i	0.354142	−	0.935192i	$-0.384773\pi$
$167$	−97.0352	−	97.0352i	−0.581049	−	0.581049i	−0.935192	+	0.354142i	$0.884773\pi$
$168$	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	−0.599897	−	0.800077i	$-0.704792\pi$
$173$	34.6311	−	34.6311i	0.200180	−	0.200180i	0.800077	+	0.599897i	$0.204792\pi$
$174$		−	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	$-0.828474\pi$
$179$		−	183.712i		−	1.02632i	0.858292	−	0.513161i	$-0.171526\pi$
$180$		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	−0.878900	−	0.477007i	$-0.841722\pi$
$193$	−77.5653	+	77.5653i	−0.401893	+	0.401893i	0.477007	+	0.878900i	$0.341722\pi$
$194$		−	64.9444i		−	0.334765i
$195$		0			0
$196$	264.262			1.34828
$197$	67.3031	+	67.3031i	0.341640	+	0.341640i	0.856984	−	0.515344i	$-0.172336\pi$
$197$	67.3031	+	67.3031i	0.341640	+	0.341640i	−0.515344	+	0.856984i	$0.672336\pi$
$198$	−22.3485	+	22.3485i	−0.112871	+	0.112871i
$199$			251.394i			1.26329i	0.775259	+	0.631643i	$0.217619\pi$
$199$			251.394i			1.26329i	−0.775259	+	0.631643i	$0.782381\pi$
$200$		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	−0.628170	−	0.778076i	$-0.716196\pi$
$223$	33.4291	−	33.4291i	0.149906	−	0.149906i	0.778076	+	0.628170i	$0.216196\pi$
$224$			79.9342i			0.356849i
$225$		0			0
$226$	−63.8888			−0.282694
$227$	21.1714	+	21.1714i	0.0932662	+	0.0932662i	0.752200	−	0.658934i	$-0.228992\pi$
$227$	21.1714	+	21.1714i	0.0932662	+	0.0932662i	−0.658934	+	0.752200i	$0.728992\pi$
$228$	−149.530	+	149.530i	−0.655834	+	0.655834i
$229$		−	243.798i		−	1.06462i	−0.846550	−	0.532310i	$-0.821324\pi$
$229$		−	243.798i		−	1.06462i	0.846550	−	0.532310i	$-0.178676\pi$
$230$		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	−0.963119	−	0.269077i	$-0.913281\pi$
$233$	−161.712	+	161.712i	−0.694042	+	0.694042i	0.269077	+	0.963119i	$0.413281\pi$
$234$		−	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	$-0.760923\pi$
$239$		−	326.202i		−	1.36486i	0.730950	−	0.682431i	$-0.239077\pi$
$240$		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	0.859076	−	0.511849i	$-0.171039\pi$
$257$	89.2372	+	89.2372i	0.347227	+	0.347227i	−0.511849	+	0.859076i	$0.671039\pi$
$258$	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	0.371253	−	0.928532i	$-0.378928\pi$
$263$	341.843	−	341.843i	1.29978	−	1.29978i	0.928532	−	0.371253i	$-0.121072\pi$
$264$			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	$-0.997929\pi$
$269$		−	3.50052i		−	0.0130131i	0.999979	−	0.00650653i	$-0.00207111\pi$
$270$		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	0.999513	+	0.0312080i	$0.00993542\pi$
$277$	285.510	+	285.510i	1.03072	+	1.03072i	0.0312080	+	0.999513i	$0.490065\pi$
$278$	−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	−0.557449	−	0.830211i	$-0.688220\pi$
$283$	77.1918	−	77.1918i	0.272763	−	0.272763i	0.830211	+	0.557449i	$0.188220\pi$
$284$		−	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	−0.176848	−	0.984238i	$-0.556590\pi$
$293$	236.565	−	236.565i	0.807390	−	0.807390i	0.984238	+	0.176848i	$0.0565901\pi$
$294$			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	0.376164	−	0.926553i	$-0.377243\pi$
$307$	−168.969	−	168.969i	−0.550389	−	0.550389i	−0.926553	+	0.376164i	$0.877243\pi$
$308$	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	−0.907300	−	0.420484i	$-0.861860\pi$
$313$	−152.373	+	152.373i	−0.486816	+	0.486816i	0.420484	+	0.907300i	$0.361860\pi$
$314$		−	227.576i		−	0.724763i
$315$		0			0
$316$	−144.495			−0.457262
$317$	427.217	+	427.217i	1.34769	+	1.34769i	0.888168	+	0.459519i	$0.151978\pi$
$317$	427.217	+	427.217i	1.34769	+	1.34769i	0.459519	+	0.888168i	$0.348022\pi$
$318$	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	0.125105	−	0.992143i	$-0.460073\pi$
$337$	−292.192	−	292.192i	−0.867038	−	0.867038i	−0.992143	+	0.125105i	$0.960073\pi$
$338$	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	0.0748598	−	0.997194i	$-0.476149\pi$
$347$	−320.050	−	320.050i	−0.922334	−	0.922334i	−0.997194	+	0.0748598i	$0.976149\pi$
$348$	6.16684	−	6.16684i	0.0177208	−	0.0177208i
$349$			574.009i			1.64473i	0.568964	+	0.822363i	$0.307345\pi$
$349$			574.009i			1.64473i	−0.568964	+	0.822363i	$0.692655\pi$
$350$		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	−0.975410	−	0.220396i	$-0.929265\pi$
$353$	−266.520	+	266.520i	−0.755014	+	0.755014i	0.220396	+	0.975410i	$0.429265\pi$
$354$		−	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	$-0.902608\pi$
$359$		−	216.272i		−	0.602430i	0.953556	−	0.301215i	$-0.0973922\pi$
$360$		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	0.954274	−	0.298934i	$-0.0966311\pi$
$367$	240.510	+	240.510i	0.655340	+	0.655340i	−0.298934	+	0.954274i	$0.596631\pi$
$368$	−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	−0.108792	−	0.994065i	$-0.534698\pi$
$373$	330.207	−	330.207i	0.885272	−	0.885272i	0.994065	+	0.108792i	$0.0346983\pi$
$374$		−	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	$-0.910645\pi$
$379$		−	210.000i		−	0.554090i	0.960857	−	0.277045i	$-0.0893551\pi$
$380$		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	−0.893859	−	0.448347i	$-0.852013\pi$
$383$	−170.631	+	170.631i	−0.445512	+	0.445512i	0.448347	+	0.893859i	$0.352013\pi$
$384$		−	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	$0.248389\pi$
$389$			547.337i			1.40704i	−0.710677	+	0.703518i	$0.751611\pi$
$390$		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	0.647806	−	0.761805i	$-0.275687\pi$
$397$	−45.2577	−	45.2577i	−0.113999	−	0.113999i	−0.761805	+	0.647806i	$0.775687\pi$
$398$	−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	$0.139494\pi$
$409$			347.110i			0.848680i	−0.905503	+	0.424340i	$0.860506\pi$
$410$		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	$-0.754882\pi$
$419$		−	583.398i		−	1.39236i	0.717868	−	0.696180i	$-0.245118\pi$
$420$		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	−0.862934	−	0.505317i	$-0.831376\pi$
$433$	−154.848	+	154.848i	−0.357617	+	0.357617i	0.505317	+	0.862934i	$0.331376\pi$
$434$		−	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	$-0.906985\pi$
$439$		−	252.929i		−	0.576147i	0.957608	−	0.288074i	$-0.0930148\pi$
$440$		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	−0.0482041	−	0.998838i	$-0.515350\pi$
$443$	421.131	−	421.131i	0.950633	−	0.950633i	0.998838	+	0.0482041i	$0.0153498\pi$
$444$			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	$0.107638\pi$
$449$			297.909i			0.663495i	−0.943368	+	0.331747i	$0.892362\pi$
$450$		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	0.321607	−	0.946873i	$-0.395777\pi$
$457$	−285.747	−	285.747i	−0.625267	−	0.625267i	−0.946873	+	0.321607i	$0.895777\pi$
$458$	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	−0.969631	−	0.244573i	$-0.921352\pi$
$463$	−335.702	+	335.702i	−0.725057	+	0.725057i	0.244573	+	0.969631i	$0.421352\pi$
$464$			4.09540i			0.00882630i
$465$		0			0
$466$	−719.535			−1.54407
$467$	−488.742	−	488.742i	−1.04656	−	1.04656i	−0.998862	−	0.0476956i	$-0.984812\pi$
$467$	−488.742	−	488.742i	−1.04656	−	1.04656i	−0.0476956	−	0.998862i	$-0.515188\pi$
$468$	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	$-0.938160\pi$
$479$		−	184.949i		−	0.386115i	0.981187	−	0.193057i	$-0.0618404\pi$
$480$		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	0.820070	−	0.572263i	$-0.193934\pi$
$487$	120.682	+	120.682i	0.247807	+	0.247807i	−0.572263	+	0.820070i	$0.693934\pi$
$488$	−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	$-0.734320\pi$
$499$		−	739.585i		−	1.48213i	0.671431	−	0.741067i	$-0.265680\pi$
$500$		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	−0.176357	−	0.984326i	$-0.556431\pi$
$503$	406.409	−	406.409i	0.807970	−	0.807970i	0.984326	+	0.176357i	$0.0564312\pi$
$504$			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	$0.0611962\pi$
$509$			194.511i			0.382143i	−0.981576	+	0.191071i	$0.938804\pi$
$510$		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	−0.558716	−	0.829359i	$-0.688706\pi$
$523$	141.546	−	141.546i	0.270642	−	0.270642i	0.829359	+	0.558716i	$0.188706\pi$
$524$		−	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	0.985491	−	0.169728i	$-0.0542889\pi$
$547$	446.222	+	446.222i	0.815763	+	0.815763i	−0.169728	+	0.985491i	$0.554289\pi$
$548$	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	0.488308	−	0.872672i	$-0.337614\pi$
$557$	−214.091	−	214.091i	−0.384364	−	0.384364i	−0.872672	+	0.488308i	$0.837614\pi$
$558$	−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	−0.217579	+	0.976043i	$0.569816\pi$
$563$	−672.009	+	672.009i	−1.19362	+	1.19362i	−0.976043	+	0.217579i	$0.930184\pi$
$564$			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	$-0.674003\pi$
$569$		−	972.161i		−	1.70854i	0.519827	−	0.854272i	$-0.325997\pi$
$570$		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	0.991671	−	0.128797i	$-0.0411114\pi$
$577$	497.879	+	497.879i	0.862874	+	0.862874i	−0.128797	+	0.991671i	$0.541111\pi$
$578$	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	0.412279	−	0.911058i	$-0.364733\pi$
$587$	−292.783	−	292.783i	−0.498779	−	0.498779i	−0.911058	+	0.412279i	$0.864733\pi$
$588$	−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	−0.976498	−	0.215524i	$-0.930854\pi$
$593$	−451.258	+	451.258i	−0.760974	+	0.760974i	0.215524	+	0.976498i	$0.430854\pi$
$594$		−	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	$0.00873154\pi$
$599$			32.8582i			0.0548550i	−0.999624	+	0.0274275i	$0.991268\pi$
$600$		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	0.585778	−	0.810472i	$-0.300789\pi$
$607$	−136.389	−	136.389i	−0.224694	−	0.224694i	−0.810472	+	0.585778i	$0.800789\pi$
$608$	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	−0.696661	−	0.717400i	$-0.745332\pi$
$613$	12.7128	−	12.7128i	0.0207386	−	0.0207386i	0.717400	+	0.696661i	$0.245332\pi$
$614$		−	751.828i		−	1.22447i
$615$		0			0
$616$	41.0102			0.0665750
$617$	398.752	+	398.752i	0.646275	+	0.646275i	0.952091	−	0.305816i	$-0.0989292\pi$
$617$	398.752	+	398.752i	0.646275	+	0.646275i	−0.305816	+	0.952091i	$0.598929\pi$
$618$	−352.868	+	352.868i	−0.570984	+	0.570984i
$619$			819.131i			1.32331i	0.749807	+	0.661656i	$0.230146\pi$
$619$			819.131i			1.32331i	−0.749807	+	0.661656i	$0.769854\pi$
$620$		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	0.211349	−	0.977411i	$-0.432214\pi$
$643$	764.372	−	764.372i	1.18876	−	1.18876i	0.977411	−	0.211349i	$-0.0677856\pi$
$644$		−	281.303i		−	0.436806i
$645$		0			0
$646$	244.182			0.377990
$647$	−321.287	−	321.287i	−0.496580	−	0.496580i	0.413792	−	0.910372i	$-0.364204\pi$
$647$	−321.287	−	321.287i	−0.496580	−	0.496580i	−0.910372	+	0.413792i	$0.864204\pi$
$648$	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	−0.565015	−	0.825081i	$-0.691130\pi$
$653$	169.823	−	169.823i	0.260066	−	0.260066i	0.825081	+	0.565015i	$0.191130\pi$
$654$		−	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	$0.259289\pi$
$659$			958.763i			1.45488i	−0.686174	+	0.727438i	$0.740711\pi$
$660$		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	−0.818806	−	0.574070i	$-0.805364\pi$
$673$	−164.707	+	164.707i	−0.244736	+	0.244736i	0.574070	+	0.818806i	$0.305364\pi$
$674$		−	1300.10i		−	1.92894i
$675$		0			0
$676$	291.313			0.430937
$677$	−544.388	−	544.388i	−0.804119	−	0.804119i	0.179618	−	0.983736i	$-0.442514\pi$
$677$	−544.388	−	544.388i	−0.804119	−	0.804119i	−0.983736	+	0.179618i	$0.942514\pi$
$678$	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	−0.165452	+	0.986218i	$0.552908\pi$
$683$	−786.590	+	786.590i	−1.15167	+	1.15167i	−0.986218	+	0.165452i	$0.947092\pi$
$684$		−	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	$-0.827588\pi$
$709$		−	731.049i		−	1.03110i	0.856860	−	0.515549i	$-0.172412\pi$
$710$		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	$0.144172\pi$
$719$			629.271i			0.875204i	−0.899169	+	0.437602i	$0.855828\pi$
$720$		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	0.717940	−	0.696105i	$-0.245085\pi$
$727$	15.8740	+	15.8740i	0.0218349	+	0.0218349i	−0.696105	+	0.717940i	$0.745085\pi$
$728$	−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	−0.386016	−	0.922492i	$-0.626149\pi$
$733$	393.237	−	393.237i	0.536476	−	0.536476i	0.922492	+	0.386016i	$0.126149\pi$
$734$			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	$-0.958460\pi$
$739$		−	192.334i		−	0.260262i	0.991497	−	0.130131i	$-0.0415398\pi$
$740$		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	−0.676385	−	0.736548i	$-0.736454\pi$
$743$	44.7015	−	44.7015i	0.0601636	−	0.0601636i	0.736548	+	0.676385i	$0.236454\pi$
$744$			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	0.845552	−	0.533894i	$-0.179272\pi$
$757$	235.925	+	235.925i	0.311658	+	0.311658i	−0.533894	+	0.845552i	$0.679272\pi$
$758$	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	$-0.712304\pi$
$769$		−	1208.40i		−	1.57139i	0.618612	−	0.785697i	$-0.287696\pi$
$770$		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	0.0562070	−	0.998419i	$-0.482099\pi$
$773$	815.226	−	815.226i	1.05463	−	1.05463i	0.998419	−	0.0562070i	$-0.0179007\pi$
$774$			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	−0.999435	−	0.0336150i	$-0.989298\pi$
$787$	−813.010	−	813.010i	−1.03305	−	1.03305i	−0.0336150	−	0.999435i	$-0.510702\pi$
$788$	−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	0.484375	−	0.874860i	$-0.339047\pi$
$797$	−311.217	−	311.217i	−0.390485	−	0.390485i	−0.874860	+	0.484375i	$0.839047\pi$
$798$	−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	$-0.970448\pi$
$809$		−	150.000i		−	0.185414i	0.995693	−	0.0927070i	$-0.0295520\pi$
$810$		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	−0.865638	−	0.500670i	$-0.833087\pi$
$823$	−300.369	+	300.369i	−0.364968	+	0.364968i	0.500670	+	0.865638i	$0.333087\pi$
$824$			547.126i			0.663988i
$825$		0			0
$826$	−721.918			−0.873993
$827$	1030.76	+	1030.76i	1.24638	+	1.24638i	0.957307	+	0.289073i	$0.0933469\pi$
$827$	1030.76	+	1030.76i	1.24638	+	1.24638i	0.289073	+	0.957307i	$0.406653\pi$
$828$	−291.106	+	291.106i	−0.351577	+	0.351577i
$829$			37.4235i			0.0451429i	0.999745	+	0.0225714i	$0.00718533\pi$
$829$			37.4235i			0.0451429i	−0.999745	+	0.0225714i	$0.992815\pi$
$830$		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	$-0.759035\pi$
$839$		−	1152.37i		−	1.37351i	0.726890	−	0.686754i	$-0.240965\pi$
$840$		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	−0.985270	−	0.171003i	$-0.945299\pi$
$853$	−694.570	+	694.570i	−0.814267	+	0.814267i	0.171003	+	0.985270i	$0.445299\pi$
$854$			606.838i			0.710583i
$855$		0			0
$856$	−40.0704			−0.0468112
$857$	−417.176	−	417.176i	−0.486786	−	0.486786i	0.420504	−	0.907291i	$-0.361853\pi$
$857$	−417.176	−	417.176i	−0.486786	−	0.486786i	−0.907291	+	0.420504i	$0.861853\pi$
$858$	190.677	−	190.677i	0.222234	−	0.222234i
$859$			486.867i			0.566784i	0.959004	+	0.283392i	$0.0914597\pi$
$859$			486.867i			0.566784i	−0.959004	+	0.283392i	$0.908540\pi$
$860$		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	−0.427432	−	0.904047i	$-0.640582\pi$
$863$	411.319	−	411.319i	0.476615	−	0.476615i	0.904047	+	0.427432i	$0.140582\pi$
$864$			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	0.491627	−	0.870806i	$-0.336402\pi$
$877$	−332.540	−	332.540i	−0.379179	−	0.379179i	−0.870806	+	0.491627i	$0.836402\pi$
$878$	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	−0.144698	−	0.989476i	$-0.546221\pi$
$883$	745.939	−	745.939i	0.844778	−	0.844778i	0.989476	+	0.144698i	$0.0462211\pi$
$884$			326.888i			0.369783i
$885$		0			0
$886$	1873.82			2.11492
$887$	386.207	+	386.207i	0.435408	+	0.435408i	0.890463	−	0.455055i	$-0.150381\pi$
$887$	386.207	+	386.207i	0.435408	+	0.435408i	−0.455055	+	0.890463i	$0.650381\pi$
$888$	−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	0.998964	+	0.0455146i	$0.0144928\pi$
$907$	947.342	+	947.342i	1.04448	+	1.04448i	0.0455146	+	0.998964i	$0.485507\pi$
$908$	−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	$0.0720652\pi$
$919$			412.577i			0.448941i	−0.974481	+	0.224470i	$0.927935\pi$
$920$		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	$-0.973981\pi$
$929$		−	151.707i		−	0.163302i	0.996661	−	0.0816508i	$-0.0260192\pi$
$930$		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	0.259214	−	0.965820i	$-0.416537\pi$
$937$	−662.090	−	662.090i	−0.706606	−	0.706606i	−0.965820	+	0.259214i	$0.916537\pi$
$938$	−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	−0.960472	−	0.278377i	$-0.910204\pi$
$947$	−1173.19	−	1173.19i	−1.23885	−	1.23885i	−0.278377	−	0.960472i	$-0.589796\pi$
$948$	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	−0.626636	−	0.779312i	$-0.715569\pi$
$953$	145.501	−	145.501i	0.152676	−	0.152676i	0.779312	+	0.626636i	$0.215569\pi$
$954$			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	−0.976789	−	0.214204i	$-0.931284\pi$
$967$	−1151.69	−	1151.69i	−1.19099	−	1.19099i	−0.214204	−	0.976789i	$-0.568716\pi$
$968$	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	0.246242	−	0.969208i	$-0.420804\pi$
$977$	−706.338	−	706.338i	−0.722966	−	0.722966i	−0.969208	+	0.246242i	$0.920804\pi$
$978$	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	−0.635286	−	0.772277i	$-0.719118\pi$
$983$	134.663	−	134.663i	0.136992	−	0.136992i	0.772277	+	0.635286i	$0.219118\pi$
$984$			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	0.991944	+	0.126679i	$0.0404318\pi$
$997$	1115.27	+	1115.27i	1.11862	+	1.11862i	0.126679	+	0.991944i	$0.459568\pi$
$998$	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.7.2		4
3.2	odd	2		225.3.g.a.82.1		4
4.3	odd	2		1200.3.bg.k.1057.2		4
5.2	odd	4		15.3.f.a.13.1	yes	4
5.3	odd	4	inner	75.3.f.c.43.2		4
5.4	even	2		15.3.f.a.7.1	✓	4
15.2	even	4		45.3.g.b.28.2		4
15.8	even	4		225.3.g.a.118.1		4
15.14	odd	2		45.3.g.b.37.2		4
20.3	even	4		1200.3.bg.k.193.2		4
20.7	even	4		240.3.bg.a.193.1		4
20.19	odd	2		240.3.bg.a.97.1		4
40.19	odd	2		960.3.bg.h.577.2		4
40.27	even	4		960.3.bg.h.193.2		4
40.29	even	2		960.3.bg.i.577.1		4
40.37	odd	4		960.3.bg.i.193.1		4
45.2	even	12		405.3.l.f.28.1		8
45.4	even	6		405.3.l.h.217.2		8
45.7	odd	12		405.3.l.h.28.2		8
45.14	odd	6		405.3.l.f.217.1		8
45.22	odd	12		405.3.l.h.298.1		8
45.29	odd	6		405.3.l.f.352.2		8
45.32	even	12		405.3.l.f.298.2		8
45.34	even	6		405.3.l.h.352.1		8
60.47	odd	4		720.3.bh.k.433.1		4
60.59	even	2		720.3.bh.k.577.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.3.f.a.7.1	✓	4	5.4	even	2
15.3.f.a.13.1	yes	4	5.2	odd	4
45.3.g.b.28.2		4	15.2	even	4
45.3.g.b.37.2		4	15.14	odd	2
75.3.f.c.7.2		4	1.1	even	1	trivial
75.3.f.c.43.2		4	5.3	odd	4	inner
225.3.g.a.82.1		4	3.2	odd	2
225.3.g.a.118.1		4	15.8	even	4
240.3.bg.a.97.1		4	20.19	odd	2
240.3.bg.a.193.1		4	20.7	even	4
405.3.l.f.28.1		8	45.2	even	12
405.3.l.f.217.1		8	45.14	odd	6
405.3.l.f.298.2		8	45.32	even	12
405.3.l.f.352.2		8	45.29	odd	6
405.3.l.h.28.2		8	45.7	odd	12
405.3.l.h.217.2		8	45.4	even	6
405.3.l.h.298.1		8	45.22	odd	12
405.3.l.h.352.1		8	45.34	even	6
720.3.bh.k.433.1		4	60.47	odd	4
720.3.bh.k.577.1		4	60.59	even	2
960.3.bg.h.193.2		4	40.27	even	4
960.3.bg.h.577.2		4	40.19	odd	2
960.3.bg.i.193.1		4	40.37	odd	4
960.3.bg.i.577.1		4	40.29	even	2
1200.3.bg.k.193.2		4	20.3	even	4
1200.3.bg.k.1057.2		4	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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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