LMFDB - Embedded newform 45.3.g.b.28.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,3,Mod(28,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("45.28");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	45.g (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:	$1.22616118962$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			28.2
Root			$1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	45.28
Dual form			45.3.g.b.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.22474 - 2.22474i) q^{2} -5.89898i q^{4} +(-2.67423 + 4.22474i) q^{5} +(-1.44949 + 1.44949i) q^{7} +(-4.22474 - 4.22474i) q^{8} +O(q^{10})$	\(q+(2.22474 - 2.22474i) q^{2} -5.89898i q^{4} +(-2.67423 + 4.22474i) q^{5} +(-1.44949 + 1.44949i) q^{7} +(-4.22474 - 4.22474i) q^{8} +(3.44949 + 15.3485i) q^{10} +3.34847 q^{11} +(-10.4495 - 10.4495i) q^{13} +6.44949i q^{14} +4.79796 q^{16} +(2.65153 - 2.65153i) q^{17} +20.6969i q^{19} +(24.9217 + 15.7753i) q^{20} +(7.44949 - 7.44949i) q^{22} +(-16.4495 - 16.4495i) q^{23} +(-10.6969 - 22.5959i) q^{25} -46.4949 q^{26} +(8.55051 + 8.55051i) q^{28} +0.853572i q^{29} -18.6969 q^{31} +(27.5732 - 27.5732i) q^{32} -11.7980i q^{34} +(-2.24745 - 10.0000i) q^{35} +(38.0454 - 38.0454i) q^{37} +(46.0454 + 46.0454i) q^{38} +(29.1464 - 6.55051i) q^{40} +28.6969 q^{41} +(22.4949 + 22.4949i) q^{43} -19.7526i q^{44} -73.1918 q^{46} +(-19.7526 + 19.7526i) q^{47} +44.7980i q^{49} +(-74.0681 - 26.4722i) q^{50} +(-61.6413 + 61.6413i) q^{52} +(-28.6969 - 28.6969i) q^{53} +(-8.95459 + 14.1464i) q^{55} +12.2474 q^{56} +(1.89898 + 1.89898i) q^{58} +111.934i q^{59} +94.0908 q^{61} +(-41.5959 + 41.5959i) q^{62} -103.495i q^{64} +(72.0908 - 16.2020i) q^{65} +(-54.8990 + 54.8990i) q^{67} +(-15.6413 - 15.6413i) q^{68} +(-27.2474 - 17.2474i) q^{70} +68.0000 q^{71} +(-39.7878 - 39.7878i) q^{73} -169.283i q^{74} +122.091 q^{76} +(-4.85357 + 4.85357i) q^{77} -24.4949i q^{79} +(-12.8309 + 20.2702i) q^{80} +(63.8434 - 63.8434i) q^{82} +(21.1464 + 21.1464i) q^{83} +(4.11123 + 18.2929i) q^{85} +100.091 q^{86} +(-14.1464 - 14.1464i) q^{88} -94.1816i q^{89} +30.2929 q^{91} +(-97.0352 + 97.0352i) q^{92} +87.8888i q^{94} +(-87.4393 - 55.3485i) q^{95} +(14.5959 - 14.5959i) q^{97} +(99.6640 + 99.6640i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{5} + 4 q^{7} - 12 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^5 + 4 * q^7 - 12 * q^8	$ 4 q + 4 q^{2} + 4 q^{5} + 4 q^{7} - 12 q^{8} + 4 q^{10} - 16 q^{11} - 32 q^{13} - 20 q^{16} + 40 q^{17} + 36 q^{20} + 20 q^{22} - 56 q^{23} + 16 q^{25} - 88 q^{26} + 44 q^{28} - 16 q^{31} + 76 q^{32} + 40 q^{35} + 64 q^{37} + 96 q^{38} + 48 q^{40} + 56 q^{41} - 8 q^{43} - 136 q^{46} - 128 q^{47} - 164 q^{50} - 80 q^{52} - 56 q^{53} - 124 q^{55} - 12 q^{58} + 200 q^{61} - 88 q^{62} + 112 q^{65} - 200 q^{67} + 104 q^{68} - 60 q^{70} + 272 q^{71} + 76 q^{73} + 312 q^{76} - 88 q^{77} - 164 q^{80} + 128 q^{82} + 16 q^{83} + 232 q^{85} + 224 q^{86} + 12 q^{88} - 16 q^{91} - 104 q^{92} - 144 q^{95} - 20 q^{97} + 188 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^5 + 4 * q^7 - 12 * q^8 + 4 * q^10 - 16 * q^11 - 32 * q^13 - 20 * q^16 + 40 * q^17 + 36 * q^20 + 20 * q^22 - 56 * q^23 + 16 * q^25 - 88 * q^26 + 44 * q^28 - 16 * q^31 + 76 * q^32 + 40 * q^35 + 64 * q^37 + 96 * q^38 + 48 * q^40 + 56 * q^41 - 8 * q^43 - 136 * q^46 - 128 * q^47 - 164 * q^50 - 80 * q^52 - 56 * q^53 - 124 * q^55 - 12 * q^58 + 200 * q^61 - 88 * q^62 + 112 * q^65 - 200 * q^67 + 104 * q^68 - 60 * q^70 + 272 * q^71 + 76 * q^73 + 312 * q^76 - 88 * q^77 - 164 * q^80 + 128 * q^82 + 16 * q^83 + 232 * q^85 + 224 * q^86 + 12 * q^88 - 16 * q^91 - 104 * q^92 - 144 * q^95 - 20 * q^97 + 188 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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	$-0.0381431\pi$
$3$		0			0
$3$		0			0
$4$		−	5.89898i		−	1.47474i
$5$	−2.67423	+	4.22474i	−0.534847	+	0.844949i
$5$	−2.67423	+	4.22474i	−0.534847	+	0.844949i
$6$		0			0
$7$	−1.44949	+	1.44949i	−0.207070	+	0.207070i	−0.803021	−	0.595951i	$-0.796775\pi$
$7$	−1.44949	+	1.44949i	−0.207070	+	0.207070i	0.595951	+	0.803021i	$0.296775\pi$
$8$	−4.22474	−	4.22474i	−0.528093	−	0.528093i
$9$		0			0
$10$	3.44949	+	15.3485i	0.344949	+	1.53485i
$11$	3.34847			0.304406			0.152203	−	0.988349i	$-0.451363\pi$
$11$	3.34847			0.304406			0.152203	+	0.988349i	$0.451363\pi$
$12$		0			0
$13$	−10.4495	−	10.4495i	−0.803807	−	0.803807i	0.179881	−	0.983688i	$-0.442429\pi$
$13$	−10.4495	−	10.4495i	−0.803807	−	0.803807i	−0.983688	+	0.179881i	$0.942429\pi$
$14$			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	$0.214822\pi$
$18$		0			0
$19$			20.6969i			1.08931i	0.838659	+	0.544656i	$0.183340\pi$
$19$			20.6969i			1.08931i	−0.838659	+	0.544656i	$0.816660\pi$
$20$	24.9217	+	15.7753i	1.24608	+	0.788763i
$21$		0			0
$22$	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	$0.918773\pi$
$24$		0			0
$25$	−10.6969	−	22.5959i	−0.427878	−	0.903837i
$26$	−46.4949			−1.78827
$27$		0			0
$28$	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
$33$		0			0
$34$		−	11.7980i		−	0.346999i
$35$	−2.24745	−	10.0000i	−0.0642128	−	0.285714i
$36$		0			0
$37$	38.0454	−	38.0454i	1.02825	−	1.02825i	0.0286652	−	0.999589i	$-0.490874\pi$
$37$	38.0454	−	38.0454i	1.02825	−	1.02825i	0.999589	−	0.0286652i	$-0.00912566\pi$
$38$	46.0454	+	46.0454i	1.21172	+	1.21172i
$39$		0			0
$40$	29.1464	−	6.55051i	0.728661	−	0.163763i
$41$	28.6969			0.699925			0.349963	−	0.936764i	$-0.386194\pi$
$41$	28.6969			0.699925			0.349963	+	0.936764i	$0.386194\pi$
$42$		0			0
$43$	22.4949	+	22.4949i	0.523137	+	0.523137i	0.918517	−	0.395380i	$-0.129387\pi$
$43$	22.4949	+	22.4949i	0.523137	+	0.523137i	−0.395380	+	0.918517i	$0.629387\pi$
$44$		−	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	$0.346044\pi$
$48$		0			0
$49$			44.7980i			0.914244i
$50$	−74.0681	−	26.4722i	−1.48136	−	0.529444i
$51$		0			0
$52$	−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	$0.875062\pi$
$54$		0			0
$55$	−8.95459	+	14.1464i	−0.162811	+	0.257208i
$56$	12.2474			0.218704
$57$		0			0
$58$	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
$63$		0			0
$64$		−	103.495i		−	1.61711i
$65$	72.0908	−	16.2020i	1.10909	−	0.249262i
$66$		0			0
$67$	−54.8990	+	54.8990i	−0.819388	+	0.819388i	−0.986019	−	0.166631i	$-0.946711\pi$
$67$	−54.8990	+	54.8990i	−0.819388	+	0.819388i	0.166631	+	0.986019i	$0.446711\pi$
$68$	−15.6413	−	15.6413i	−0.230019	−	0.230019i
$69$		0			0
$70$	−27.2474	−	17.2474i	−0.389249	−	0.246392i
$71$	68.0000			0.957746			0.478873	−	0.877884i	$-0.341045\pi$
$71$	68.0000			0.957746			0.478873	+	0.877884i	$0.341045\pi$
$72$		0			0
$73$	−39.7878	−	39.7878i	−0.545038	−	0.545038i	0.379964	−	0.925001i	$-0.375936\pi$
$73$	−39.7878	−	39.7878i	−0.545038	−	0.545038i	−0.925001	+	0.379964i	$0.875936\pi$
$74$		−	169.283i		−	2.28760i
$75$		0			0
$76$	122.091			1.60646
$77$	−4.85357	+	4.85357i	−0.0630334	+	0.0630334i
$78$		0			0
$79$		−	24.4949i		−	0.310062i	−0.987910	−	0.155031i	$-0.950452\pi$
$79$		−	24.4949i		−	0.310062i	0.987910	−	0.155031i	$-0.0495477\pi$
$80$	−12.8309	+	20.2702i	−0.160386	+	0.253377i
$81$		0			0
$82$	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	$0.692340\pi$
$84$		0			0
$85$	4.11123	+	18.2929i	0.0483674	+	0.215210i
$86$	100.091			1.16385
$87$		0			0
$88$	−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
$93$		0			0
$94$			87.8888i			0.934987i
$95$	−87.4393	−	55.3485i	−0.920414	−	0.582615i
$96$		0			0
$97$	14.5959	−	14.5959i	0.150473	−	0.150473i	−0.627856	−	0.778329i	$-0.716067\pi$
$97$	14.5959	−	14.5959i	0.150473	−	0.150473i	0.778329	+	0.627856i	$0.216067\pi$
$98$	99.6640	+	99.6640i	1.01698	+	1.01698i
$99$		0			0
$100$	−133.293	+	63.1010i	−1.33293	+	0.631010i
$101$	−173.621			−1.71902			−0.859509	−	0.511120i	$-0.829231\pi$
$101$	−173.621			−1.71902			−0.859509	+	0.511120i	$0.829231\pi$
$102$		0			0
$103$	−64.7526	−	64.7526i	−0.628666	−	0.628666i	0.319067	−	0.947732i	$-0.396631\pi$
$103$	−64.7526	−	64.7526i	−0.628666	−	0.628666i	−0.947732	+	0.319067i	$0.896631\pi$
$104$			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	$0.240023\pi$
$108$		0			0
$109$		−	39.3031i		−	0.360579i	−0.983614	−	0.180289i	$-0.942297\pi$
$109$		−	39.3031i		−	0.360579i	0.983614	−	0.180289i	$-0.0577034\pi$
$110$	11.5505	+	51.3939i	0.105005	+	0.467217i
$111$		0			0
$112$	−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	$0.778639\pi$
$114$		0			0
$115$	113.485	−	25.5051i	0.986823	−	0.221784i
$116$	5.03520			0.0434069
$117$		0			0
$118$	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
$123$		0			0
$124$			110.293i			0.889459i
$125$	124.068	+	15.2350i	0.992545	+	0.121880i
$126$		0			0
$127$	−114.621	+	114.621i	−0.902527	+	0.902527i	−0.995654	−	0.0931273i	$-0.970314\pi$
$127$	−114.621	+	114.621i	−0.902527	+	0.902527i	0.0931273	+	0.995654i	$0.470314\pi$
$128$	−119.957	−	119.957i	−0.937163	−	0.937163i
$129$		0			0
$130$	124.338	−	196.429i	0.956448	−	1.51099i
$131$	26.1362			0.199513			0.0997566	−	0.995012i	$-0.468194\pi$
$131$	26.1362			0.199513			0.0997566	+	0.995012i	$0.468194\pi$
$132$		0			0
$133$	−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	$0.274061\pi$
$138$		0			0
$139$		−	83.1714i		−	0.598356i	−0.954197	−	0.299178i	$-0.903288\pi$
$139$		−	83.1714i		−	0.598356i	0.954197	−	0.299178i	$-0.0967124\pi$
$140$	−58.9898	+	13.2577i	−0.421356	+	0.0946975i
$141$		0			0
$142$	151.283	−	151.283i	1.06537	−	1.06537i
$143$	−34.9898	−	34.9898i	−0.244684	−	0.244684i
$144$		0			0
$145$	−3.60612	−	2.28265i	−0.0248698	−	0.0157424i
$146$	−177.035			−1.21257
$147$		0			0
$148$	−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
$153$		0			0
$154$			21.5959i			0.140233i
$155$	50.0000	−	78.9898i	0.322581	−	0.509612i
$156$		0			0
$157$	51.1464	−	51.1464i	0.325773	−	0.325773i	−0.525203	−	0.850977i	$-0.676011\pi$
$157$	51.1464	−	51.1464i	0.325773	−	0.325773i	0.850977	+	0.525203i	$0.176011\pi$
$158$	−54.4949	−	54.4949i	−0.344904	−	0.344904i
$159$		0			0
$160$	42.7526	+	190.227i	0.267203	+	1.18892i
$161$	47.6867			0.296191
$162$		0			0
$163$	189.394	+	189.394i	1.16193	+	1.16193i	0.984054	+	0.177872i	$0.0569213\pi$
$163$	189.394	+	189.394i	1.16193	+	1.16193i	0.177872	+	0.984054i	$0.443079\pi$
$164$		−	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	$0.384773\pi$
$168$		0			0
$169$			49.3837i			0.292211i
$170$	49.8434	+	31.5505i	0.293196	+	0.185591i
$171$		0			0
$172$	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	$0.704792\pi$
$174$		0			0
$175$	48.2577	+	17.2474i	0.275758	+	0.0985568i
$176$	16.0658			0.0912831
$177$		0			0
$178$	−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
$183$		0			0
$184$			138.990i			0.755379i
$185$	58.9898	+	262.474i	0.318864	+	1.41878i
$186$		0			0
$187$	8.87857	−	8.87857i	0.0474790	−	0.0474790i
$188$	116.520	+	116.520i	0.619787	+	0.619787i
$189$		0			0
$190$	−317.666	+	71.3939i	−1.67193	+	0.375757i
$191$	40.0908			0.209900			0.104950	−	0.994478i	$-0.466532\pi$
$191$	40.0908			0.209900			0.104950	+	0.994478i	$0.466532\pi$
$192$		0			0
$193$	77.5653	+	77.5653i	0.401893	+	0.401893i	0.878900	−	0.477007i	$-0.158278\pi$
$193$	77.5653	+	77.5653i	0.401893	+	0.401893i	−0.477007	+	0.878900i	$0.658278\pi$
$194$		−	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	$0.172336\pi$
$198$		0			0
$199$		−	251.394i		−	1.26329i	−0.775259	−	0.631643i	$-0.782381\pi$
$199$		−	251.394i		−	1.26329i	0.775259	−	0.631643i	$-0.217619\pi$
$200$	−50.2702	+	140.654i	−0.251351	+	0.703269i
$201$		0			0
$202$	−386.262	+	386.262i	−1.91219	+	1.91219i
$203$	−1.23724	−	1.23724i	−0.00609480	−	0.00609480i
$204$		0			0
$205$	−76.7423	+	121.237i	−0.374353	+	0.591401i
$206$	−288.116			−1.39862
$207$		0			0
$208$	−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
$213$		0			0
$214$		−	21.1010i		−	0.0986029i
$215$	−155.192	+	34.8786i	−0.721822	+	0.162226i
$216$		0			0
$217$	27.1010	−	27.1010i	0.124889	−	0.124889i
$218$	−87.4393	−	87.4393i	−0.401098	−	0.401098i
$219$		0			0
$220$	83.4495	+	52.8230i	0.379316	+	0.240104i
$221$	−55.4143			−0.250743
$222$		0			0
$223$	−33.4291	−	33.4291i	−0.149906	−	0.149906i	0.628170	−	0.778076i	$-0.283804\pi$
$223$	−33.4291	−	33.4291i	−0.149906	−	0.149906i	−0.778076	+	0.628170i	$0.783804\pi$
$224$			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	$0.228992\pi$
$228$		0			0
$229$			243.798i			1.06462i	0.846550	+	0.532310i	$0.178676\pi$
$229$			243.798i			1.06462i	−0.846550	+	0.532310i	$0.821324\pi$
$230$	195.732	−	309.217i	0.851009	−	1.34442i
$231$		0			0
$232$	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	$0.913281\pi$
$234$		0			0
$235$	−30.6265	−	136.272i	−0.130326	−	0.579883i
$236$	660.297			2.79787
$237$		0			0
$238$	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
$243$		0			0
$244$		−	555.040i		−	2.27475i
$245$	−189.260	−	119.800i	−0.772490	−	0.488981i
$246$		0			0
$247$	216.272	−	216.272i	0.875597	−	0.875597i
$248$	78.9898	+	78.9898i	0.318507	+	0.318507i
$249$		0			0
$250$	309.914	−	242.126i	1.23966	−	0.968504i
$251$	404.742			1.61252			0.806260	−	0.591562i	$-0.201488\pi$
$251$	404.742			1.61252			0.806260	+	0.591562i	$0.201488\pi$
$252$		0			0
$253$	−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	$0.171039\pi$
$258$		0			0
$259$			110.293i			0.425841i
$260$	−95.5755	−	425.262i	−0.367598	−	1.63562i
$261$		0			0
$262$	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	$0.378928\pi$
$264$		0			0
$265$	197.980	−	44.4949i	0.747093	−	0.167905i
$266$	−133.485			−0.501822
$267$		0			0
$268$	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
$273$		0			0
$274$			65.1010i			0.237595i
$275$	−35.8184	−	75.6617i	−0.130249	−	0.275134i
$276$		0			0
$277$	−285.510	+	285.510i	−1.03072	+	1.03072i	−0.0312080	+	0.999513i	$0.509935\pi$
$277$	−285.510	+	285.510i	−1.03072	+	1.03072i	−0.999513	+	0.0312080i	$0.990065\pi$
$278$	−185.035	−	185.035i	−0.665594	−	0.665594i
$279$		0			0
$280$	−32.7526	+	51.7423i	−0.116973	+	0.184794i
$281$	−372.697			−1.32632			−0.663162	−	0.748476i	$-0.730786\pi$
$281$	−372.697			−1.32632			−0.663162	+	0.748476i	$0.730786\pi$
$282$		0			0
$283$	−77.1918	−	77.1918i	−0.272763	−	0.272763i	0.557449	−	0.830211i	$-0.311780\pi$
$283$	−77.1918	−	77.1918i	−0.272763	−	0.272763i	−0.830211	+	0.557449i	$0.811780\pi$
$284$		−	401.131i		−	1.41243i
$285$		0			0
$286$	−155.687			−0.544359
$287$	−41.5959	+	41.5959i	−0.144934	+	0.144934i
$288$		0			0
$289$			274.939i			0.951345i
$290$	−13.1010	+	2.94439i	−0.0451759	+	0.0101531i
$291$		0			0
$292$	−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	$0.556590\pi$
$294$		0			0
$295$	−472.893	−	299.338i	−1.60303	−	1.01471i
$296$	−321.464			−1.08603
$297$		0			0
$298$	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
$303$		0			0
$304$			99.3031i			0.326655i
$305$	−251.621	+	397.510i	−0.824987	+	1.30331i
$306$		0			0
$307$	168.969	−	168.969i	0.550389	−	0.550389i	−0.376164	−	0.926553i	$-0.622757\pi$
$307$	168.969	−	168.969i	0.550389	−	0.550389i	0.926553	+	0.376164i	$0.122757\pi$
$308$	28.6311	+	28.6311i	0.0929582	+	0.0929582i
$309$		0			0
$310$	−64.4949	−	286.969i	−0.208048	−	0.925708i
$311$	−354.302			−1.13923			−0.569617	−	0.821910i	$-0.692909\pi$
$311$	−354.302			−1.13923			−0.569617	+	0.821910i	$0.692909\pi$
$312$		0			0
$313$	152.373	+	152.373i	0.486816	+	0.486816i	0.907300	−	0.420484i	$-0.138140\pi$
$313$	152.373	+	152.373i	0.486816	+	0.486816i	−0.420484	+	0.907300i	$0.638140\pi$
$314$		−	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	$-0.151978\pi$
$318$		0			0
$319$			2.85816i			0.00895975i
$320$	437.240	+	276.770i	1.36637	+	0.864905i
$321$		0			0
$322$	106.091	−	106.091i	0.329475	−	0.329475i
$323$	54.8786	+	54.8786i	0.169903	+	0.169903i
$324$		0			0
$325$	−124.338	+	347.893i	−0.382579	+	1.07044i
$326$	842.706			2.58499
$327$		0			0
$328$	−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
$333$		0			0
$334$			431.757i			1.29269i
$335$	−85.1214	−	378.747i	−0.254094	−	1.13059i
$336$		0			0
$337$	292.192	−	292.192i	0.867038	−	0.867038i	−0.125105	−	0.992143i	$-0.539927\pi$
$337$	292.192	−	292.192i	0.867038	−	0.867038i	0.992143	+	0.125105i	$0.0399269\pi$
$338$	109.866	+	109.866i	0.325048	+	0.325048i
$339$		0			0
$340$	107.909	−	24.2520i	0.317380	−	0.0713295i
$341$	−62.6061			−0.183596
$342$		0			0
$343$	−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	$0.476149\pi$
$348$		0			0
$349$		−	574.009i		−	1.64473i	−0.568964	−	0.822363i	$-0.692655\pi$
$349$		−	574.009i		−	1.64473i	0.568964	−	0.822363i	$-0.307345\pi$
$350$	145.732	−	68.9898i	0.416378	−	0.197114i
$351$		0			0
$352$	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	$0.929265\pi$
$354$		0			0
$355$	−181.848	+	287.283i	−0.512248	+	0.809247i
$356$	−555.576			−1.56061
$357$		0			0
$358$	−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
$363$		0			0
$364$		−	178.697i		−	0.490926i
$365$	274.495	−	61.6913i	0.752041	−	0.169017i
$366$		0			0
$367$	−240.510	+	240.510i	−0.655340	+	0.655340i	−0.954274	−	0.298934i	$-0.903369\pi$
$367$	−240.510	+	240.510i	−0.655340	+	0.655340i	0.298934	+	0.954274i	$0.403369\pi$
$368$	−78.9240	−	78.9240i	−0.214467	−	0.214467i
$369$		0			0
$370$	715.176	+	452.702i	1.93291	+	1.22352i
$371$	83.1918			0.224237
$372$		0			0
$373$	−330.207	−	330.207i	−0.885272	−	0.885272i	0.108792	−	0.994065i	$-0.465302\pi$
$373$	−330.207	−	330.207i	−0.885272	−	0.885272i	−0.994065	+	0.108792i	$0.965302\pi$
$374$		−	39.5051i		−	0.105629i
$375$		0			0
$376$	166.899			0.443880
$377$	8.91939	−	8.91939i	0.0236589	−	0.0236589i
$378$		0			0
$379$			210.000i			0.554090i	0.960857	+	0.277045i	$0.0893551\pi$
$379$			210.000i			0.554090i	−0.960857	+	0.277045i	$0.910645\pi$
$380$	−326.499	+	515.803i	−0.859209	+	1.35738i
$381$		0			0
$382$	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	$0.852013\pi$
$384$		0			0
$385$	−7.52551	−	33.4847i	−0.0195468	−	0.0869732i
$386$	345.126			0.894109
$387$		0			0
$388$	−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
$393$		0			0
$394$		−	299.464i		−	0.760062i
$395$	103.485	+	65.5051i	0.261987	+	0.165836i
$396$		0			0
$397$	45.2577	−	45.2577i	0.113999	−	0.113999i	−0.647806	−	0.761805i	$-0.724313\pi$
$397$	45.2577	−	45.2577i	0.113999	−	0.113999i	0.761805	+	0.647806i	$0.224313\pi$
$398$	−559.287	−	559.287i	−1.40524	−	1.40524i
$399$		0			0
$400$	−51.3235	−	108.414i	−0.128309	−	0.271036i
$401$	520.302			1.29751			0.648756	−	0.760997i	$-0.275290\pi$
$401$	520.302			1.29751			0.648756	+	0.760997i	$0.275290\pi$
$402$		0			0
$403$	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
$408$		0			0
$409$		−	347.110i		−	0.848680i	−0.905503	−	0.424340i	$-0.860506\pi$
$409$		−	347.110i		−	0.848680i	0.905503	−	0.424340i	$-0.139494\pi$
$410$	98.9898	+	440.454i	0.241439	+	1.07428i
$411$		0			0
$412$	−381.974	+	381.974i	−0.927121	+	0.927121i
$413$	−162.247	−	162.247i	−0.392851	−	0.392851i
$414$		0			0
$415$	−145.889	+	32.7878i	−0.351539	+	0.0790066i
$416$	−576.252			−1.38522
$417$		0			0
$418$	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
$423$		0			0
$424$			242.474i			0.571874i
$425$	−88.2770	−	31.5505i	−0.207711	−	0.0742365i
$426$		0			0
$427$	−136.384	+	136.384i	−0.319400	+	0.319400i
$428$	−27.9750	−	27.9750i	−0.0653622	−	0.0653622i
$429$		0			0
$430$	−267.666	+	422.858i	−0.622480	+	0.983391i
$431$	−187.364			−0.434720			−0.217360	−	0.976092i	$-0.569745\pi$
$431$	−187.364			−0.434720			−0.217360	+	0.976092i	$0.569745\pi$
$432$		0			0
$433$	154.848	+	154.848i	0.357617	+	0.357617i	0.862934	−	0.505317i	$-0.168624\pi$
$433$	154.848	+	154.848i	0.357617	+	0.357617i	−0.505317	+	0.862934i	$0.668624\pi$
$434$		−	120.586i		−	0.277847i
$435$		0			0
$436$	−231.848			−0.531761
$437$	340.454	−	340.454i	0.779071	−	0.779071i
$438$		0			0
$439$			252.929i			0.576147i	0.957608	+	0.288074i	$0.0930148\pi$
$439$			252.929i			0.576147i	−0.957608	+	0.288074i	$0.906985\pi$
$440$	97.5959	−	21.9342i	0.221809	−	0.0498504i
$441$		0			0
$442$	−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	$0.515350\pi$
$444$		0			0
$445$	397.893	+	251.864i	0.894142	+	0.565986i
$446$	−148.742			−0.333503
$447$		0			0
$448$	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
$453$		0			0
$454$		−	94.2020i		−	0.207493i
$455$	−81.0102	+	127.980i	−0.178044	+	0.281274i
$456$		0			0
$457$	285.747	−	285.747i	0.625267	−	0.625267i	−0.321607	−	0.946873i	$-0.604223\pi$
$457$	285.747	−	285.747i	0.625267	−	0.625267i	0.946873	+	0.321607i	$0.104223\pi$
$458$	542.388	+	542.388i	1.18425	+	1.18425i
$459$		0			0
$460$	−150.454	−	669.444i	−0.327074	−	1.45531i
$461$	−526.620			−1.14234			−0.571171	−	0.820831i	$-0.693511\pi$
$461$	−526.620			−1.14234			−0.571171	+	0.820831i	$0.693511\pi$
$462$		0			0
$463$	335.702	+	335.702i	0.725057	+	0.725057i	0.969631	−	0.244573i	$-0.0786479\pi$
$463$	335.702	+	335.702i	0.725057	+	0.725057i	−0.244573	+	0.969631i	$0.578648\pi$
$464$			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	$0.984812\pi$
$468$		0			0
$469$		−	159.151i		−	0.339341i
$470$	−371.308	−	235.035i	−0.790016	−	0.500075i
$471$		0			0
$472$	472.893	−	472.893i	1.00189	−	1.00189i
$473$	75.3235	+	75.3235i	0.159246	+	0.159246i
$474$		0			0
$475$	467.666	−	221.394i	0.984561	−	0.466092i
$476$	45.3439			0.0952603
$477$		0			0
$478$	−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
$483$		0			0
$484$			647.636i			1.33809i
$485$	22.6311	+	100.697i	0.0466621	+	0.207623i
$486$		0			0
$487$	−120.682	+	120.682i	−0.247807	+	0.247807i	−0.820070	−	0.572263i	$-0.806066\pi$
$487$	−120.682	+	120.682i	−0.247807	+	0.247807i	0.572263	+	0.820070i	$0.306066\pi$
$488$	−397.510	−	397.510i	−0.814569	−	0.814569i
$489$		0			0
$490$	−687.580	+	154.530i	−1.40322	+	0.315368i
$491$	105.682			0.215239			0.107619	−	0.994192i	$-0.465677\pi$
$491$	105.682			0.215239			0.107619	+	0.994192i	$0.465677\pi$
$492$		0			0
$493$	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
$498$		0			0
$499$			739.585i			1.48213i	0.671431	+	0.741067i	$0.265680\pi$
$499$			739.585i			1.48213i	−0.671431	+	0.741067i	$0.734320\pi$
$500$	89.8707	−	731.875i	0.179741	−	1.46375i
$501$		0			0
$502$	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	$0.556431\pi$
$504$		0			0
$505$	464.303	−	733.504i	0.919412	−	1.45248i
$506$	−245.081			−0.484349
$507$		0			0
$508$	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
$513$		0			0
$514$		−	397.060i		−	0.772491i
$515$	446.727	−	100.399i	0.867430	−	0.194950i
$516$		0			0
$517$	−66.1408	+	66.1408i	−0.127932	+	0.127932i
$518$	245.373	+	245.373i	0.473694	+	0.473694i
$519$		0			0
$520$	−373.015	−	236.116i	−0.717336	−	0.454069i
$521$	589.605			1.13168			0.565840	−	0.824515i	$-0.308552\pi$
$521$	589.605			1.13168			0.565840	+	0.824515i	$0.308552\pi$
$522$		0			0
$523$	−141.546	−	141.546i	−0.270642	−	0.270642i	0.558716	−	0.829359i	$-0.311294\pi$
$523$	−141.546	−	141.546i	−0.270642	−	0.270642i	−0.829359	+	0.558716i	$0.811294\pi$
$524$		−	154.177i		−	0.294231i
$525$		0			0
$526$	1521.03			2.89169
$527$	−49.5755	+	49.5755i	−0.0940712	+	0.0940712i
$528$		0			0
$529$			12.1714i			0.0230084i
$530$	341.464	−	539.444i	0.644272	−	1.01782i
$531$		0			0
$532$	−176.969	+	176.969i	−0.332649	+	0.332649i
$533$	−299.868	−	299.868i	−0.562605	−	0.562605i
$534$		0			0
$535$	7.35306	+	32.7173i	0.0137440	+	0.0611539i
$536$	463.868			0.865426
$537$		0			0
$538$	−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
$543$		0			0
$544$		−	146.222i		−	0.268791i
$545$	166.045	+	105.106i	0.304670	+	0.192854i
$546$		0			0
$547$	−446.222	+	446.222i	−0.815763	+	0.815763i	−0.985491	−	0.169728i	$-0.945711\pi$
$547$	−446.222	+	446.222i	−0.815763	+	0.815763i	0.169728	+	0.985491i	$0.445711\pi$
$548$	86.3087	+	86.3087i	0.157498	+	0.157498i
$549$		0			0
$550$	−248.015	−	88.6413i	−0.450936	−	0.161166i
$551$	−17.6663			−0.0320623
$552$		0			0
$553$	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	$0.337614\pi$
$558$		0			0
$559$		−	470.120i		−	0.841003i
$560$	−10.7832	−	47.9796i	−0.0192557	−	0.0856778i
$561$		0			0
$562$	−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	$-0.569816\pi$
$564$		0			0
$565$	99.0602	−	22.2633i	0.175328	−	0.0394040i
$566$	−343.464			−0.606827
$567$		0			0
$568$	−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
$573$		0			0
$574$			185.081i			0.322440i
$575$	−195.732	+	547.650i	−0.340404	+	0.952436i
$576$		0			0
$577$	−497.879	+	497.879i	−0.862874	+	0.862874i	−0.991671	−	0.128797i	$-0.958889\pi$
$577$	−497.879	+	497.879i	−0.862874	+	0.862874i	0.128797	+	0.991671i	$0.458889\pi$
$578$	611.669	+	611.669i	1.05825	+	1.05825i
$579$		0			0
$580$	−13.4653	+	21.2724i	−0.0232161	+	0.0366766i
$581$	−61.3031			−0.105513
$582$		0			0
$583$	−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	$0.364733\pi$
$588$		0			0
$589$		−	386.969i		−	0.656994i
$590$	−1718.02	+	386.116i	−2.91190	+	0.654434i
$591$		0			0
$592$	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	$0.930854\pi$
$594$		0			0
$595$	−32.4745	−	20.5561i	−0.0545790	−	0.0345481i
$596$	702.842			1.17927
$597$		0			0
$598$	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
$603$		0			0
$604$			855.171i			1.41585i
$605$	293.598	−	463.825i	0.485286	−	0.766653i
$606$		0			0
$607$	136.389	−	136.389i	0.224694	−	0.224694i	−0.585778	−	0.810472i	$-0.699211\pi$
$607$	136.389	−	136.389i	0.224694	−	0.224694i	0.810472	+	0.585778i	$0.199211\pi$
$608$	570.681	+	570.681i	0.938620	+	0.938620i
$609$		0			0
$610$	324.565	+	1444.15i	0.532074	+	2.36746i
$611$	412.808			0.675627
$612$		0			0
$613$	−12.7128	−	12.7128i	−0.0207386	−	0.0207386i	0.696661	−	0.717400i	$-0.254668\pi$
$613$	−12.7128	−	12.7128i	−0.0207386	−	0.0207386i	−0.717400	+	0.696661i	$0.754668\pi$
$614$		−	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	$0.0989292\pi$
$618$		0			0
$619$		−	819.131i		−	1.32331i	−0.749807	−	0.661656i	$-0.769854\pi$
$619$		−	819.131i		−	1.32331i	0.749807	−	0.661656i	$-0.230146\pi$
$620$	−465.959	−	294.949i	−0.751547	−	0.475724i
$621$		0			0
$622$	−788.232	+	788.232i	−1.26725	+	1.26725i
$623$	136.515	+	136.515i	0.219126	+	0.219126i
$624$		0			0
$625$	−396.151	+	483.414i	−0.633842	+	0.773463i
$626$	677.984			1.08304
$627$		0			0
$628$	−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
$633$		0			0
$634$		−	1900.90i		−	2.99826i
$635$	−177.721	−	790.767i	−0.279875	−	1.24530i
$636$		0			0
$637$	468.116	−	468.116i	0.734876	−	0.734876i
$638$	6.35867	+	6.35867i	0.00996657	+	0.00996657i
$639$		0			0
$640$	827.580	−	185.994i	1.29309	−	0.290616i
$641$	−164.788			−0.257079			−0.128540	−	0.991704i	$-0.541029\pi$
$641$	−164.788			−0.257079			−0.128540	+	0.991704i	$0.541029\pi$
$642$		0			0
$643$	−764.372	−	764.372i	−1.18876	−	1.18876i	−0.977411	−	0.211349i	$-0.932214\pi$
$643$	−764.372	−	764.372i	−1.18876	−	1.18876i	−0.211349	−	0.977411i	$-0.567786\pi$
$644$		−	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	$0.364204\pi$
$648$		0			0
$649$			374.808i			0.577516i
$650$	497.353	+	1050.59i	0.765159	+	1.61630i
$651$		0			0
$652$	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	$0.691130\pi$
$654$		0			0
$655$	−69.8944	+	110.419i	−0.106709	+	0.168578i
$656$	137.687			0.209888
$657$		0			0
$658$	−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
$663$		0			0
$664$		−	178.677i		−	0.269091i
$665$	206.969	−	46.5153i	0.311232	−	0.0699478i
$666$		0			0
$667$	14.0408	−	14.0408i	0.0210507	−	0.0210507i
$668$	572.409	+	572.409i	0.856899	+	0.856899i
$669$		0			0
$670$	−1031.99	−	653.242i	−1.54028	−	0.974988i
$671$	315.060			0.469538
$672$		0			0
$673$	164.707	+	164.707i	0.244736	+	0.244736i	0.818806	−	0.574070i	$-0.194636\pi$
$673$	164.707	+	164.707i	0.244736	+	0.244736i	−0.574070	+	0.818806i	$0.694636\pi$
$674$		−	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	$0.442514\pi$
$678$		0			0
$679$			42.3133i			0.0623170i
$680$	59.9138	−	94.6515i	0.0881085	−	0.139193i
$681$		0			0
$682$	−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	$-0.552908\pi$
$684$		0			0
$685$	−22.6857	−	100.940i	−0.0331178	−	0.147357i
$686$	−604.949			−0.881850
$687$		0			0
$688$	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
$693$		0			0
$694$			1424.06i			2.05196i
$695$	351.378	+	222.420i	0.505580	+	0.320029i
$696$		0			0
$697$	76.0908	−	76.0908i	0.109169	−	0.109169i
$698$	−1277.02	−	1277.02i	−1.82955	−	1.82955i
$699$		0			0
$700$	101.742	−	284.671i	0.145346	−	0.406673i
$701$	−885.680			−1.26345			−0.631726	−	0.775192i	$-0.717653\pi$
$701$	−885.680			−1.26345			−0.631726	+	0.775192i	$0.717653\pi$
$702$		0			0
$703$	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
$708$		0			0
$709$			731.049i			1.03110i	0.856860	+	0.515549i	$0.172412\pi$
$709$			731.049i			1.03110i	−0.856860	+	0.515549i	$0.827588\pi$
$710$	234.565	+	1043.70i	0.330374	+	1.46999i
$711$		0			0
$712$	−397.893	+	397.893i	−0.558839	+	0.558839i
$713$	307.555	+	307.555i	0.431354	+	0.431354i
$714$		0			0
$715$	241.394	−	54.2520i	0.337614	−	0.0758770i
$716$	−1083.71			−1.51356
$717$		0			0
$718$	−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
$723$		0			0
$724$			128.170i			0.177031i
$725$	19.2872	−	9.13061i	0.0266031	−	0.0125939i
$726$		0			0
$727$	−15.8740	+	15.8740i	−0.0218349	+	0.0218349i	−0.717940	−	0.696105i	$-0.754915\pi$
$727$	−15.8740	+	15.8740i	−0.0218349	+	0.0218349i	0.696105	+	0.717940i	$0.254915\pi$
$728$	−127.980	−	127.980i	−0.175796	−	0.175796i
$729$		0			0
$730$	473.434	−	747.929i	0.648539	−	1.02456i
$731$	119.292			0.163190
$732$		0			0
$733$	−393.237	−	393.237i	−0.536476	−	0.536476i	0.386016	−	0.922492i	$-0.373851\pi$
$733$	−393.237	−	393.237i	−0.536476	−	0.536476i	−0.922492	+	0.386016i	$0.873851\pi$
$734$			1070.15i			1.45796i
$735$		0			0
$736$	−907.131			−1.23251
$737$	−183.828	+	183.828i	−0.249427	+	0.249427i
$738$		0			0
$739$			192.334i			0.260262i	0.991497	+	0.130131i	$0.0415398\pi$
$739$			192.334i			0.260262i	−0.991497	+	0.130131i	$0.958460\pi$
$740$	1548.33	−	347.980i	2.09234	−	0.470243i
$741$		0			0
$742$	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	$0.736454\pi$
$744$		0			0
$745$	−503.363	−	318.626i	−0.675655	−	0.427685i
$746$	−1469.25			−1.96951
$747$		0			0
$748$	−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
$753$		0			0
$754$		−	39.6867i		−	0.0526349i
$755$	387.682	−	612.459i	0.513486	−	0.811204i
$756$		0			0
$757$	−235.925	+	235.925i	−0.311658	+	0.311658i	−0.845552	−	0.533894i	$-0.820728\pi$
$757$	−235.925	+	235.925i	−0.311658	+	0.311658i	0.533894	+	0.845552i	$0.320728\pi$
$758$	467.196	+	467.196i	0.616354	+	0.616354i
$759$		0			0
$760$	135.576	+	603.242i	0.178389	+	0.793739i
$761$	881.242			1.15801			0.579003	−	0.815326i	$-0.303442\pi$
$761$	881.242			1.15801			0.579003	+	0.815326i	$0.303442\pi$
$762$		0			0
$763$	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
$768$		0			0
$769$			1208.40i			1.57139i	0.618612	+	0.785697i	$0.287696\pi$
$769$			1208.40i			1.57139i	−0.618612	+	0.785697i	$0.712304\pi$
$770$	−91.2372	−	57.7526i	−0.118490	−	0.0750033i
$771$		0			0
$772$	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	$0.482099\pi$
$774$		0			0
$775$	200.000	+	422.474i	0.258065	+	0.545128i
$776$	−123.328			−0.158928
$777$		0			0
$778$	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
$783$		0			0
$784$			214.939i			0.274157i
$785$	79.3031	+	352.858i	0.101023	+	0.449501i
$786$		0			0
$787$	813.010	−	813.010i	1.03305	−	1.03305i	0.0336150	−	0.999435i	$-0.489298\pi$
$787$	813.010	−	813.010i	1.03305	−	1.03305i	0.999435	−	0.0336150i	$-0.0107020\pi$
$788$	−397.019	−	397.019i	−0.503832	−	0.503832i
$789$		0			0
$790$	375.959	−	84.4949i	0.475898	−	0.106956i
$791$	41.6255			0.0526239
$792$		0			0
$793$	−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	$0.339047\pi$
$798$		0			0
$799$			104.749i			0.131100i
$800$	−917.991	−	328.093i	−1.14749	−	0.410116i
$801$		0			0
$802$	1157.54	−	1157.54i	1.44332	−	1.44332i
$803$	−133.228	−	133.228i	−0.165913	−	0.165913i
$804$		0			0
$805$	−127.526	+	201.464i	−0.158417	+	0.250266i
$806$	869.312			1.07855
$807$		0			0
$808$	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
$813$		0			0
$814$		−	566.838i		−	0.696361i
$815$	−1306.62	+	293.657i	−1.60322	+	0.360316i
$816$		0			0
$817$	−465.576	+	465.576i	−0.569860	+	0.569860i
$818$	−772.232	−	772.232i	−0.944048	−	0.944048i
$819$		0			0
$820$	715.176	+	452.702i	0.872166	+	0.552075i
$821$	−509.893			−0.621064			−0.310532	−	0.950563i	$-0.600507\pi$
$821$	−509.893			−0.621064			−0.310532	+	0.950563i	$0.600507\pi$
$822$		0			0
$823$	300.369	+	300.369i	0.364968	+	0.364968i	0.865638	−	0.500670i	$-0.166913\pi$
$823$	300.369	+	300.369i	0.364968	+	0.364968i	−0.500670	+	0.865638i	$0.666913\pi$
$824$			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	$-0.0933469\pi$
$828$		0			0
$829$		−	37.4235i		−	0.0451429i	−0.999745	−	0.0225714i	$-0.992815\pi$
$829$		−	37.4235i		−	0.0451429i	0.999745	−	0.0225714i	$-0.00718533\pi$
$830$	−251.621	+	397.510i	−0.303158	+	0.478927i
$831$		0			0
$832$	−1081.47	+	1081.47i	−1.29984	+	1.29984i
$833$	118.783	+	118.783i	0.142597	+	0.142597i
$834$		0			0
$835$	−150.454	−	669.444i	−0.180185	−	0.801729i
$836$	408.817			0.489016
$837$		0			0
$838$	−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
$843$		0			0
$844$		−	1561.98i		−	1.85068i
$845$	−208.633	−	132.064i	−0.246903	−	0.156288i
$846$		0			0
$847$	159.136	−	159.136i	0.187882	−	0.187882i
$848$	−137.687	−	137.687i	−0.162366	−	0.162366i
$849$		0			0
$850$	−266.586	+	126.202i	−0.313630	+	0.148473i
$851$	−1251.66			−1.47081
$852$		0			0
$853$	694.570	+	694.570i	0.814267	+	0.814267i	0.985270	−	0.171003i	$-0.0547009\pi$
$853$	694.570	+	694.570i	0.814267	+	0.814267i	−0.171003	+	0.985270i	$0.554701\pi$
$854$			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	$0.361853\pi$
$858$		0			0
$859$		−	486.867i		−	0.566784i	−0.959004	−	0.283392i	$-0.908540\pi$
$859$		−	486.867i		−	0.566784i	0.959004	−	0.283392i	$-0.0914597\pi$
$860$	205.748	+	915.473i	0.239242	+	1.06450i
$861$		0			0
$862$	−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	$0.640582\pi$
$864$		0			0
$865$	−238.919	+	53.6959i	−0.276207	+	0.0620762i
$866$	688.994			0.795606
$867$		0			0
$868$	−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
$873$		0			0
$874$		−	1514.85i		−	1.73323i
$875$	−201.918	+	157.753i	−0.230764	+	0.180289i
$876$		0			0
$877$	332.540	−	332.540i	0.379179	−	0.379179i	−0.491627	−	0.870806i	$-0.663598\pi$
$877$	332.540	−	332.540i	0.379179	−	0.379179i	0.870806	+	0.491627i	$0.163598\pi$
$878$	562.702	+	562.702i	0.640890	+	0.640890i
$879$		0			0
$880$	−42.9638	+	67.8740i	−0.0488225	+	0.0771295i
$881$	−533.151			−0.605166			−0.302583	−	0.953123i	$-0.597849\pi$
$881$	−533.151			−0.605166			−0.302583	+	0.953123i	$0.597849\pi$
$882$		0			0
$883$	−745.939	−	745.939i	−0.844778	−	0.844778i	0.144698	−	0.989476i	$-0.453779\pi$
$883$	−745.939	−	745.939i	−0.844778	−	0.844778i	−0.989476	+	0.144698i	$0.953779\pi$
$884$			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	$0.150381\pi$
$888$		0			0
$889$		−	332.284i		−	0.373772i
$890$	1445.54	−	324.879i	1.62421	−	0.365032i
$891$		0			0
$892$	−197.197	+	197.197i	−0.221073	+	0.221073i
$893$	−408.817	−	408.817i	−0.457802	−	0.457802i
$894$		0			0
$895$	776.135	+	491.288i	0.867190	+	0.548925i
$896$	347.753			0.388117
$897$		0			0
$898$	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
$903$		0			0
$904$			121.323i			0.134207i
$905$	58.1046	−	91.7934i	0.0642040	−	0.101429i
$906$		0			0
$907$	−947.342	+	947.342i	−1.04448	+	1.04448i	−0.0455146	+	0.998964i	$0.514493\pi$
$907$	−947.342	+	947.342i	−1.04448	+	1.04448i	−0.998964	+	0.0455146i	$0.985507\pi$
$908$	−124.890	−	124.890i	−0.137544	−	0.137544i
$909$		0			0
$910$	104.495	+	464.949i	0.114830	+	0.510933i
$911$	1149.36			1.26165			0.630824	−	0.775926i	$-0.282717\pi$
$911$	1149.36			1.26165			0.630824	+	0.775926i	$0.282717\pi$
$912$		0			0
$913$	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
$918$		0			0
$919$		−	412.577i		−	0.448941i	−0.974481	−	0.224470i	$-0.927935\pi$
$919$		−	412.577i		−	0.448941i	0.974481	−	0.224470i	$-0.0720652\pi$
$920$	−587.196	−	371.691i	−0.638257	−	0.404012i
$921$		0			0
$922$	−1171.59	+	1171.59i	−1.27071	+	1.27071i
$923$	−710.565	−	710.565i	−0.769843	−	0.769843i
$924$		0			0
$925$	−1266.64	−	452.702i	−1.36934	−	0.489407i
$926$	1493.70			1.61307
$927$		0			0
$928$	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
$933$		0			0
$934$			2174.65i			2.32832i
$935$	13.7663	+	61.2531i	0.0147233	+	0.0655113i
$936$		0			0
$937$	662.090	−	662.090i	0.706606	−	0.706606i	−0.259214	−	0.965820i	$-0.583463\pi$
$937$	662.090	−	662.090i	0.706606	−	0.706606i	0.965820	+	0.259214i	$0.0834635\pi$
$938$	−354.070	−	354.070i	−0.377474	−	0.377474i
$939$		0			0
$940$	−803.868	+	180.665i	−0.855179	+	0.192197i
$941$	1533.77			1.62994			0.814969	−	0.579505i	$-0.196754\pi$
$941$	1533.77			1.62994			0.814969	+	0.579505i	$0.196754\pi$
$942$		0			0
$943$	−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	$0.910204\pi$
$948$		0			0
$949$			831.523i			0.876210i
$950$	547.893	−	1532.98i	0.576730	−	1.61367i
$951$		0			0
$952$	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	$0.715569\pi$
$954$		0			0
$955$	−107.212	+	169.373i	−0.112264	+	0.177354i
$956$	−1924.26			−2.01282
$957$		0			0
$958$	−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
$963$		0			0
$964$			787.959i			0.817385i
$965$	−535.121	+	120.266i	−0.554530	+	0.124628i
$966$		0			0
$967$	1151.69	−	1151.69i	1.19099	−	1.19099i	0.214204	−	0.976789i	$-0.431284\pi$
$967$	1151.69	−	1151.69i	1.19099	−	1.19099i	0.976789	−	0.214204i	$-0.0687158\pi$
$968$	463.825	+	463.825i	0.479158	+	0.479158i
$969$		0			0
$970$	274.373	+	173.677i	0.282859	+	0.179048i
$971$	−72.4383			−0.0746017			−0.0373009	−	0.999304i	$-0.511876\pi$
$971$	−72.4383			−0.0746017			−0.0373009	+	0.999304i	$0.511876\pi$
$972$		0			0
$973$	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	$0.420804\pi$
$978$		0			0
$979$		−	315.364i		−	0.322129i
$980$	−706.699	+	1116.44i	−0.721122	+	1.13923i
$981$		0			0
$982$	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	$0.719118\pi$
$984$		0			0
$985$	104.354	+	464.322i	0.105943	+	0.471393i
$986$	10.0704			0.0102134
$987$		0			0
$988$	−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
$993$		0			0
$994$			438.565i			0.441213i
$995$	1062.07	+	672.286i	1.06741	+	0.675665i
$996$		0			0
$997$	−1115.27	+	1115.27i	−1.11862	+	1.11862i	−0.126679	+	0.991944i	$0.540432\pi$
$997$	−1115.27	+	1115.27i	−1.11862	+	1.11862i	−0.991944	+	0.126679i	$0.959568\pi$
$998$	1645.39	+	1645.39i	1.64868	+	1.64868i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.3.g.b.28.2		4
3.2	odd	2		15.3.f.a.13.1	yes	4
4.3	odd	2		720.3.bh.k.433.1		4
5.2	odd	4	inner	45.3.g.b.37.2		4
5.3	odd	4		225.3.g.a.82.1		4
5.4	even	2		225.3.g.a.118.1		4
9.2	odd	6		405.3.l.h.28.2		8
9.4	even	3		405.3.l.f.298.2		8
9.5	odd	6		405.3.l.h.298.1		8
9.7	even	3		405.3.l.f.28.1		8
12.11	even	2		240.3.bg.a.193.1		4
15.2	even	4		15.3.f.a.7.1	✓	4
15.8	even	4		75.3.f.c.7.2		4
15.14	odd	2		75.3.f.c.43.2		4
20.7	even	4		720.3.bh.k.577.1		4
24.5	odd	2		960.3.bg.i.193.1		4
24.11	even	2		960.3.bg.h.193.2		4
45.2	even	12		405.3.l.h.352.1		8
45.7	odd	12		405.3.l.f.352.2		8
45.22	odd	12		405.3.l.f.217.1		8
45.32	even	12		405.3.l.h.217.2		8
60.23	odd	4		1200.3.bg.k.1057.2		4
60.47	odd	4		240.3.bg.a.97.1		4
60.59	even	2		1200.3.bg.k.193.2		4
120.77	even	4		960.3.bg.i.577.1		4
120.107	odd	4		960.3.bg.h.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.3.f.a.7.1	✓	4	15.2	even	4
15.3.f.a.13.1	yes	4	3.2	odd	2
45.3.g.b.28.2		4	1.1	even	1	trivial
45.3.g.b.37.2		4	5.2	odd	4	inner
75.3.f.c.7.2		4	15.8	even	4
75.3.f.c.43.2		4	15.14	odd	2
225.3.g.a.82.1		4	5.3	odd	4
225.3.g.a.118.1		4	5.4	even	2
240.3.bg.a.97.1		4	60.47	odd	4
240.3.bg.a.193.1		4	12.11	even	2
405.3.l.f.28.1		8	9.7	even	3
405.3.l.f.217.1		8	45.22	odd	12
405.3.l.f.298.2		8	9.4	even	3
405.3.l.f.352.2		8	45.7	odd	12
405.3.l.h.28.2		8	9.2	odd	6
405.3.l.h.217.2		8	45.32	even	12
405.3.l.h.298.1		8	9.5	odd	6
405.3.l.h.352.1		8	45.2	even	12
720.3.bh.k.433.1		4	4.3	odd	2
720.3.bh.k.577.1		4	20.7	even	4
960.3.bg.h.193.2		4	24.11	even	2
960.3.bg.h.577.2		4	120.107	odd	4
960.3.bg.i.193.1		4	24.5	odd	2
960.3.bg.i.577.1		4	120.77	even	4
1200.3.bg.k.193.2		4	60.59	even	2
1200.3.bg.k.1057.2		4	60.23	odd	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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	45.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.22474 - 2.22474i) q^{2} -5.89898i q^{4} +(-2.67423 + 4.22474i) q^{5} +(-1.44949 + 1.44949i) q^{7} +(-4.22474 - 4.22474i) q^{8} +O(q^{10})\)	\(q+(2.22474 - 2.22474i) q^{2} -5.89898i q^{4} +(-2.67423 + 4.22474i) q^{5} +(-1.44949 + 1.44949i) q^{7} +(-4.22474 - 4.22474i) q^{8} +(3.44949 + 15.3485i) q^{10} +3.34847 q^{11} +(-10.4495 - 10.4495i) q^{13} +6.44949i q^{14} +4.79796 q^{16} +(2.65153 - 2.65153i) q^{17} +20.6969i q^{19} +(24.9217 + 15.7753i) q^{20} +(7.44949 - 7.44949i) q^{22} +(-16.4495 - 16.4495i) q^{23} +(-10.6969 - 22.5959i) q^{25} -46.4949 q^{26} +(8.55051 + 8.55051i) q^{28} +0.853572i q^{29} -18.6969 q^{31} +(27.5732 - 27.5732i) q^{32} -11.7980i q^{34} +(-2.24745 - 10.0000i) q^{35} +(38.0454 - 38.0454i) q^{37} +(46.0454 + 46.0454i) q^{38} +(29.1464 - 6.55051i) q^{40} +28.6969 q^{41} +(22.4949 + 22.4949i) q^{43} -19.7526i q^{44} -73.1918 q^{46} +(-19.7526 + 19.7526i) q^{47} +44.7980i q^{49} +(-74.0681 - 26.4722i) q^{50} +(-61.6413 + 61.6413i) q^{52} +(-28.6969 - 28.6969i) q^{53} +(-8.95459 + 14.1464i) q^{55} +12.2474 q^{56} +(1.89898 + 1.89898i) q^{58} +111.934i q^{59} +94.0908 q^{61} +(-41.5959 + 41.5959i) q^{62} -103.495i q^{64} +(72.0908 - 16.2020i) q^{65} +(-54.8990 + 54.8990i) q^{67} +(-15.6413 - 15.6413i) q^{68} +(-27.2474 - 17.2474i) q^{70} +68.0000 q^{71} +(-39.7878 - 39.7878i) q^{73} -169.283i q^{74} +122.091 q^{76} +(-4.85357 + 4.85357i) q^{77} -24.4949i q^{79} +(-12.8309 + 20.2702i) q^{80} +(63.8434 - 63.8434i) q^{82} +(21.1464 + 21.1464i) q^{83} +(4.11123 + 18.2929i) q^{85} +100.091 q^{86} +(-14.1464 - 14.1464i) q^{88} -94.1816i q^{89} +30.2929 q^{91} +(-97.0352 + 97.0352i) q^{92} +87.8888i q^{94} +(-87.4393 - 55.3485i) q^{95} +(14.5959 - 14.5959i) q^{97} +(99.6640 + 99.6640i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{5} + 4 q^{7} - 12 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^5 + 4 * q^7 - 12 * q^8	\( 4 q + 4 q^{2} + 4 q^{5} + 4 q^{7} - 12 q^{8} + 4 q^{10} - 16 q^{11} - 32 q^{13} - 20 q^{16} + 40 q^{17} + 36 q^{20} + 20 q^{22} - 56 q^{23} + 16 q^{25} - 88 q^{26} + 44 q^{28} - 16 q^{31} + 76 q^{32} + 40 q^{35} + 64 q^{37} + 96 q^{38} + 48 q^{40} + 56 q^{41} - 8 q^{43} - 136 q^{46} - 128 q^{47} - 164 q^{50} - 80 q^{52} - 56 q^{53} - 124 q^{55} - 12 q^{58} + 200 q^{61} - 88 q^{62} + 112 q^{65} - 200 q^{67} + 104 q^{68} - 60 q^{70} + 272 q^{71} + 76 q^{73} + 312 q^{76} - 88 q^{77} - 164 q^{80} + 128 q^{82} + 16 q^{83} + 232 q^{85} + 224 q^{86} + 12 q^{88} - 16 q^{91} - 104 q^{92} - 144 q^{95} - 20 q^{97} + 188 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^5 + 4 * q^7 - 12 * q^8 + 4 * q^10 - 16 * q^11 - 32 * q^13 - 20 * q^16 + 40 * q^17 + 36 * q^20 + 20 * q^22 - 56 * q^23 + 16 * q^25 - 88 * q^26 + 44 * q^28 - 16 * q^31 + 76 * q^32 + 40 * q^35 + 64 * q^37 + 96 * q^38 + 48 * q^40 + 56 * q^41 - 8 * q^43 - 136 * q^46 - 128 * q^47 - 164 * q^50 - 80 * q^52 - 56 * q^53 - 124 * q^55 - 12 * q^58 + 200 * q^61 - 88 * q^62 + 112 * q^65 - 200 * q^67 + 104 * q^68 - 60 * q^70 + 272 * q^71 + 76 * q^73 + 312 * q^76 - 88 * q^77 - 164 * q^80 + 128 * q^82 + 16 * q^83 + 232 * q^85 + 224 * q^86 + 12 * q^88 - 16 * q^91 - 104 * q^92 - 144 * q^95 - 20 * q^97 + 188 * q^98

Introduction

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