LMFDB - Embedded newform 240.3.bg.a.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,3,Mod(97,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 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("240.97");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	240.bg (of order $4$, degree $2$, not 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:	$6.53952634465$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			193.1
Root			$-1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	240.193
Dual form			240.3.bg.a.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 - 1.22474i) q^{3} +(2.67423 - 4.22474i) q^{5} +(1.44949 - 1.44949i) q^{7} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.22474 - 1.22474i) q^{3} +(2.67423 - 4.22474i) q^{5} +(1.44949 - 1.44949i) q^{7} +3.00000i q^{9} +3.34847 q^{11} +(-10.4495 - 10.4495i) q^{13} +(-8.44949 + 1.89898i) q^{15} +(-2.65153 + 2.65153i) q^{17} -20.6969i q^{19} -3.55051 q^{21} +(-16.4495 - 16.4495i) q^{23} +(-10.6969 - 22.5959i) q^{25} +(3.67423 - 3.67423i) q^{27} -0.853572i q^{29} +18.6969 q^{31} +(-4.10102 - 4.10102i) q^{33} +(-2.24745 - 10.0000i) q^{35} +(38.0454 - 38.0454i) q^{37} +25.5959i q^{39} -28.6969 q^{41} +(-22.4949 - 22.4949i) q^{43} +(12.6742 + 8.02270i) q^{45} +(-19.7526 + 19.7526i) q^{47} +44.7980i q^{49} +6.49490 q^{51} +(28.6969 + 28.6969i) q^{53} +(8.95459 - 14.1464i) q^{55} +(-25.3485 + 25.3485i) q^{57} +111.934i q^{59} +94.0908 q^{61} +(4.34847 + 4.34847i) q^{63} +(-72.0908 + 16.2020i) q^{65} +(54.8990 - 54.8990i) q^{67} +40.2929i q^{69} +68.0000 q^{71} +(-39.7878 - 39.7878i) q^{73} +(-14.5732 + 40.7753i) q^{75} +(4.85357 - 4.85357i) q^{77} +24.4949i q^{79} -9.00000 q^{81} +(21.1464 + 21.1464i) q^{83} +(4.11123 + 18.2929i) q^{85} +(-1.04541 + 1.04541i) q^{87} +94.1816i q^{89} -30.2929 q^{91} +(-22.8990 - 22.8990i) q^{93} +(-87.4393 - 55.3485i) q^{95} +(14.5959 - 14.5959i) q^{97} +10.0454i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{5} - 4 q^{7}+O(q^{10}) $ 4 * q - 4 * q^5 - 4 * q^7	$ 4 q - 4 q^{5} - 4 q^{7} - 16 q^{11} - 32 q^{13} - 24 q^{15} - 40 q^{17} - 24 q^{21} - 56 q^{23} + 16 q^{25} + 16 q^{31} - 36 q^{33} + 40 q^{35} + 64 q^{37} - 56 q^{41} + 8 q^{43} + 36 q^{45} - 128 q^{47} - 72 q^{51} + 56 q^{53} + 124 q^{55} - 72 q^{57} + 200 q^{61} - 12 q^{63} - 112 q^{65} + 200 q^{67} + 272 q^{71} + 76 q^{73} - 24 q^{75} + 88 q^{77} - 36 q^{81} + 16 q^{83} + 232 q^{85} + 84 q^{87} + 16 q^{91} - 72 q^{93} - 144 q^{95} - 20 q^{97}+O(q^{100}) $ 4 * q - 4 * q^5 - 4 * q^7 - 16 * q^11 - 32 * q^13 - 24 * q^15 - 40 * q^17 - 24 * q^21 - 56 * q^23 + 16 * q^25 + 16 * q^31 - 36 * q^33 + 40 * q^35 + 64 * q^37 - 56 * q^41 + 8 * q^43 + 36 * q^45 - 128 * q^47 - 72 * q^51 + 56 * q^53 + 124 * q^55 - 72 * q^57 + 200 * q^61 - 12 * q^63 - 112 * q^65 + 200 * q^67 + 272 * q^71 + 76 * q^73 - 24 * q^75 + 88 * q^77 - 36 * q^81 + 16 * q^83 + 232 * q^85 + 84 * q^87 + 16 * q^91 - 72 * q^93 - 144 * q^95 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$4$		0			0
$5$	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	−0.595951	−	0.803021i	$-0.703225\pi$
$7$	1.44949	−	1.44949i	0.207070	−	0.207070i	0.803021	+	0.595951i	$0.203225\pi$
$8$		0			0
$9$			3.00000i			0.333333i
$10$		0			0
$11$	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	$0.942429\pi$
$14$		0			0
$15$	−8.44949	+	1.89898i	−0.563299	+	0.126599i
$16$		0			0
$17$	−2.65153	+	2.65153i	−0.155972	+	0.155972i	−0.780779	−	0.624807i	$-0.785178\pi$
$17$	−2.65153	+	2.65153i	−0.155972	+	0.155972i	0.624807	+	0.780779i	$0.285178\pi$
$18$		0			0
$19$		−	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
$22$		0			0
$23$	−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
$26$		0			0
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$		0			0
$29$		−	0.853572i		−	0.0294335i	−0.999892	−	0.0147168i	$-0.995315\pi$
$29$		−	0.853572i		−	0.0294335i	0.999892	−	0.0147168i	$-0.00468466\pi$
$30$		0			0
$31$	18.6969			0.603127			0.301564	−	0.953446i	$-0.402491\pi$
$31$	18.6969			0.603127			0.301564	+	0.953446i	$0.402491\pi$
$32$		0			0
$33$	−4.10102	−	4.10102i	−0.124273	−	0.124273i
$34$		0			0
$35$	−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	$-0.00912566\pi$
$38$		0			0
$39$			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	$0.613806\pi$
$42$		0			0
$43$	−22.4949	−	22.4949i	−0.523137	−	0.523137i	0.395380	−	0.918517i	$-0.370613\pi$
$43$	−22.4949	−	22.4949i	−0.523137	−	0.523137i	−0.918517	+	0.395380i	$0.870613\pi$
$44$		0			0
$45$	12.6742	+	8.02270i	0.281650	+	0.178282i
$46$		0			0
$47$	−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
$50$		0			0
$51$	6.49490			0.127351
$52$		0			0
$53$	28.6969	+	28.6969i	0.541452	+	0.541452i	0.923954	−	0.382503i	$-0.124938\pi$
$53$	28.6969	+	28.6969i	0.541452	+	0.541452i	−0.382503	+	0.923954i	$0.624938\pi$
$54$		0			0
$55$	8.95459	−	14.1464i	0.162811	−	0.257208i
$56$		0			0
$57$	−25.3485	+	25.3485i	−0.444710	+	0.444710i
$58$		0			0
$59$			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	$0.219639\pi$
$62$		0			0
$63$	4.34847	+	4.34847i	0.0690233	+	0.0690233i
$64$		0			0
$65$	−72.0908	+	16.2020i	−1.10909	+	0.249262i
$66$		0			0
$67$	54.8990	−	54.8990i	0.819388	−	0.819388i	−0.166631	−	0.986019i	$-0.553289\pi$
$67$	54.8990	−	54.8990i	0.819388	−	0.819388i	0.986019	+	0.166631i	$0.0532890\pi$
$68$		0			0
$69$			40.2929i			0.583954i
$70$		0			0
$71$	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	$0.875936\pi$
$74$		0			0
$75$	−14.5732	+	40.7753i	−0.194310	+	0.543670i
$76$		0			0
$77$	4.85357	−	4.85357i	0.0630334	−	0.0630334i
$78$		0			0
$79$			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
$82$		0			0
$83$	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
$86$		0			0
$87$	−1.04541	+	1.04541i	−0.0120162	+	0.0120162i
$88$		0			0
$89$			94.1816i			1.05822i	0.848553	+	0.529110i	$0.177474\pi$
$89$			94.1816i			1.05822i	−0.848553	+	0.529110i	$0.822526\pi$
$90$		0			0
$91$	−30.2929			−0.332889
$92$		0			0
$93$	−22.8990	−	22.8990i	−0.246226	−	0.246226i
$94$		0			0
$95$	−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	$0.216067\pi$
$98$		0			0
$99$			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	$0.170769\pi$
$102$		0			0
$103$	64.7526	+	64.7526i	0.628666	+	0.628666i	0.947732	−	0.319067i	$-0.103369\pi$
$103$	64.7526	+	64.7526i	0.628666	+	0.628666i	−0.319067	+	0.947732i	$0.603369\pi$
$104$		0			0
$105$	−9.49490	+	15.0000i	−0.0904276	+	0.142857i
$106$		0			0
$107$	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	$-0.0577034\pi$
$110$		0			0
$111$	−93.1918			−0.839566
$112$		0			0
$113$	14.3587	+	14.3587i	0.127068	+	0.127068i	0.767781	−	0.640713i	$-0.221361\pi$
$113$	14.3587	+	14.3587i	0.127068	+	0.127068i	−0.640713	+	0.767781i	$0.721361\pi$
$114$		0			0
$115$	−113.485	+	25.5051i	−0.986823	+	0.221784i
$116$		0			0
$117$	31.3485	−	31.3485i	0.267936	−	0.267936i
$118$		0			0
$119$			7.68673i			0.0645944i
$120$		0			0
$121$	−109.788			−0.907337
$122$		0			0
$123$	35.1464	+	35.1464i	0.285743	+	0.285743i
$124$		0			0
$125$	−124.068	−	15.2350i	−0.992545	−	0.121880i
$126$		0			0
$127$	114.621	−	114.621i	0.902527	−	0.902527i	−0.0931273	−	0.995654i	$-0.529686\pi$
$127$	114.621	−	114.621i	0.902527	−	0.902527i	0.995654	+	0.0931273i	$0.0296864\pi$
$128$		0			0
$129$			55.1010i			0.427140i
$130$		0			0
$131$	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
$134$		0			0
$135$	−5.69694	−	25.3485i	−0.0421995	−	0.187766i
$136$		0			0
$137$	14.6311	−	14.6311i	0.106796	−	0.106796i	−0.651689	−	0.758486i	$-0.725939\pi$
$137$	14.6311	−	14.6311i	0.106796	−	0.106796i	0.758486	+	0.651689i	$0.225939\pi$
$138$		0			0
$139$			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
$142$		0			0
$143$	−34.9898	−	34.9898i	−0.244684	−	0.244684i
$144$		0			0
$145$	−3.60612	−	2.28265i	−0.0248698	−	0.0157424i
$146$		0			0
$147$	54.8661	−	54.8661i	0.373239	−	0.373239i
$148$		0			0
$149$		−	119.146i		−	0.799640i	−0.916594	−	0.399820i	$-0.869073\pi$
$149$		−	119.146i		−	0.799640i	0.916594	−	0.399820i	$-0.130927\pi$
$150$		0			0
$151$	144.969			0.960062			0.480031	−	0.877251i	$-0.340625\pi$
$151$	144.969			0.960062			0.480031	+	0.877251i	$0.340625\pi$
$152$		0			0
$153$	−7.95459	−	7.95459i	−0.0519908	−	0.0519908i
$154$		0			0
$155$	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	$0.176011\pi$
$158$		0			0
$159$		−	70.2929i		−	0.442093i
$160$		0			0
$161$	−47.6867			−0.296191
$162$		0			0
$163$	−189.394	−	189.394i	−1.16193	−	1.16193i	−0.984054	−	0.177872i	$-0.943079\pi$
$163$	−189.394	−	189.394i	−1.16193	−	1.16193i	−0.177872	−	0.984054i	$-0.556921\pi$
$164$		0			0
$165$	−28.2929	+	6.35867i	−0.171472	+	0.0385374i
$166$		0			0
$167$	−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
$170$		0			0
$171$	62.0908			0.363104
$172$		0			0
$173$	−34.6311	−	34.6311i	−0.200180	−	0.200180i	0.599897	−	0.800077i	$-0.295208\pi$
$173$	−34.6311	−	34.6311i	−0.200180	−	0.200180i	−0.800077	+	0.599897i	$0.795208\pi$
$174$		0			0
$175$	−48.2577	−	17.2474i	−0.275758	−	0.0985568i
$176$		0			0
$177$	137.091	−	137.091i	0.774524	−	0.774524i
$178$		0			0
$179$		−	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	$0.519117\pi$
$182$		0			0
$183$	−115.237	−	115.237i	−0.629712	−	0.629712i
$184$		0			0
$185$	−58.9898	−	262.474i	−0.318864	−	1.41878i
$186$		0			0
$187$	−8.87857	+	8.87857i	−0.0474790	+	0.0474790i
$188$		0			0
$189$		−	10.6515i		−	0.0563573i
$190$		0			0
$191$	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	$0.658278\pi$
$194$		0			0
$195$	108.136	+	68.4495i	0.554545	+	0.351023i
$196$		0			0
$197$	−67.3031	+	67.3031i	−0.341640	+	0.341640i	−0.856984	−	0.515344i	$-0.827664\pi$
$197$	−67.3031	+	67.3031i	−0.341640	+	0.341640i	0.515344	+	0.856984i	$0.327664\pi$
$198$		0			0
$199$			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
$202$		0			0
$203$	−1.23724	−	1.23724i	−0.00609480	−	0.00609480i
$204$		0			0
$205$	−76.7423	+	121.237i	−0.374353	+	0.591401i
$206$		0			0
$207$	49.3485	−	49.3485i	0.238398	−	0.238398i
$208$		0			0
$209$		−	69.3031i		−	0.331594i
$210$		0			0
$211$	−264.788			−1.25492			−0.627459	−	0.778649i	$-0.715905\pi$
$211$	−264.788			−1.25492			−0.627459	+	0.778649i	$0.715905\pi$
$212$		0			0
$213$	−83.2827	−	83.2827i	−0.390998	−	0.390998i
$214$		0			0
$215$	−155.192	+	34.8786i	−0.721822	+	0.162226i
$216$		0			0
$217$	27.1010	−	27.1010i	0.124889	−	0.124889i
$218$		0			0
$219$			97.4597i			0.445021i
$220$		0			0
$221$	55.4143			0.250743
$222$		0			0
$223$	33.4291	+	33.4291i	0.149906	+	0.149906i	0.778076	−	0.628170i	$-0.216196\pi$
$223$	33.4291	+	33.4291i	0.149906	+	0.149906i	−0.628170	+	0.778076i	$0.716196\pi$
$224$		0			0
$225$	67.7878	−	32.0908i	0.301279	−	0.142626i
$226$		0			0
$227$	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	$0.821324\pi$
$230$		0			0
$231$	−11.8888			−0.0514666
$232$		0			0
$233$	161.712	+	161.712i	0.694042	+	0.694042i	0.963119	−	0.269077i	$-0.0867186\pi$
$233$	161.712	+	161.712i	0.694042	+	0.694042i	−0.269077	+	0.963119i	$0.586719\pi$
$234$		0			0
$235$	30.6265	+	136.272i	0.130326	+	0.579883i
$236$		0			0
$237$	30.0000	−	30.0000i	0.126582	−	0.126582i
$238$		0			0
$239$		−	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	$0.589382\pi$
$242$		0			0
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$		0			0
$245$	189.260	+	119.800i	0.772490	+	0.488981i
$246$		0			0
$247$	−216.272	+	216.272i	−0.875597	+	0.875597i
$248$		0			0
$249$		−	51.7980i		−	0.208024i
$250$		0			0
$251$	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
$254$		0			0
$255$	17.3689	−	27.4393i	0.0681133	−	0.107605i
$256$		0			0
$257$	−89.2372	+	89.2372i	−0.347227	+	0.347227i	−0.859076	−	0.511849i	$-0.828961\pi$
$257$	−89.2372	+	89.2372i	−0.347227	+	0.347227i	0.511849	+	0.859076i	$0.328961\pi$
$258$		0			0
$259$		−	110.293i		−	0.425841i
$260$		0			0
$261$	2.56072			0.00981117
$262$		0			0
$263$	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
$266$		0			0
$267$	115.348	−	115.348i	0.432017	−	0.432017i
$268$		0			0
$269$			3.50052i			0.0130131i	0.999979	+	0.00650653i	$0.00207111\pi$
$269$			3.50052i			0.0130131i	−0.999979	+	0.00650653i	$0.997929\pi$
$270$		0			0
$271$	103.576			0.382197			0.191099	−	0.981571i	$-0.438795\pi$
$271$	103.576			0.382197			0.191099	+	0.981571i	$0.438795\pi$
$272$		0			0
$273$	37.1010	+	37.1010i	0.135901	+	0.135901i
$274$		0			0
$275$	−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	$0.990065\pi$
$278$		0			0
$279$			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	$0.269214\pi$
$282$		0			0
$283$	77.1918	+	77.1918i	0.272763	+	0.272763i	0.830211	−	0.557449i	$-0.188220\pi$
$283$	77.1918	+	77.1918i	0.272763	+	0.272763i	−0.557449	+	0.830211i	$0.688220\pi$
$284$		0			0
$285$	39.3031	+	174.879i	0.137905	+	0.613609i
$286$		0			0
$287$	−41.5959	+	41.5959i	−0.144934	+	0.144934i
$288$		0			0
$289$			274.939i			0.951345i
$290$		0			0
$291$	−35.7526			−0.122861
$292$		0			0
$293$	−236.565	−	236.565i	−0.807390	−	0.807390i	0.176848	−	0.984238i	$-0.443410\pi$
$293$	−236.565	−	236.565i	−0.807390	−	0.807390i	−0.984238	+	0.176848i	$0.943410\pi$
$294$		0			0
$295$	472.893	+	299.338i	1.60303	+	1.01471i
$296$		0			0
$297$	12.3031	−	12.3031i	0.0414244	−	0.0414244i
$298$		0			0
$299$			343.778i			1.14976i
$300$		0			0
$301$	−65.2122			−0.216652
$302$		0			0
$303$	−212.641	−	212.641i	−0.701787	−	0.701787i
$304$		0			0
$305$	251.621	−	397.510i	0.824987	−	1.30331i
$306$		0			0
$307$	−168.969	+	168.969i	−0.550389	+	0.550389i	−0.926553	−	0.376164i	$-0.877243\pi$
$307$	−168.969	+	168.969i	−0.550389	+	0.550389i	0.376164	+	0.926553i	$0.377243\pi$
$308$		0			0
$309$		−	158.611i		−	0.513303i
$310$		0			0
$311$	−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	$0.638140\pi$
$314$		0			0
$315$	30.0000	−	6.74235i	0.0952381	−	0.0214043i
$316$		0			0
$317$	−427.217	+	427.217i	−1.34769	+	1.34769i	−0.459519	+	0.888168i	$0.651978\pi$
$317$	−427.217	+	427.217i	−1.34769	+	1.34769i	−0.888168	+	0.459519i	$0.848022\pi$
$318$		0			0
$319$		−	2.85816i		−	0.00895975i
$320$		0			0
$321$	−11.6163			−0.0361879
$322$		0			0
$323$	54.8786	+	54.8786i	0.169903	+	0.169903i
$324$		0			0
$325$	−124.338	+	347.893i	−0.382579	+	1.07044i
$326$		0			0
$327$	−48.1362	+	48.1362i	−0.147206	+	0.147206i
$328$		0			0
$329$			57.2622i			0.174049i
$330$		0			0
$331$	−489.423			−1.47862			−0.739310	−	0.673365i	$-0.764848\pi$
$331$	−489.423			−1.47862			−0.739310	+	0.673365i	$0.764848\pi$
$332$		0			0
$333$	114.136	+	114.136i	0.342751	+	0.342751i
$334$		0			0
$335$	−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	$0.0399269\pi$
$338$		0			0
$339$		−	35.1714i		−	0.103751i
$340$		0			0
$341$	62.6061			0.183596
$342$		0			0
$343$	135.959	+	135.959i	0.396382	+	0.396382i
$344$		0			0
$345$	170.227	+	107.753i	0.493412	+	0.312326i
$346$		0			0
$347$	−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	$-0.307345\pi$
$350$		0			0
$351$	−76.7878			−0.218769
$352$		0			0
$353$	266.520	+	266.520i	0.755014	+	0.755014i	0.975410	−	0.220396i	$-0.0707351\pi$
$353$	266.520	+	266.520i	0.755014	+	0.755014i	−0.220396	+	0.975410i	$0.570735\pi$
$354$		0			0
$355$	181.848	−	287.283i	0.512248	−	0.809247i
$356$		0			0
$357$	9.41429	−	9.41429i	0.0263706	−	0.0263706i
$358$		0			0
$359$		−	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
$362$		0			0
$363$	134.462	+	134.462i	0.370419	+	0.370419i
$364$		0			0
$365$	−274.495	+	61.6913i	−0.752041	+	0.169017i
$366$		0			0
$367$	240.510	−	240.510i	0.655340	−	0.655340i	−0.298934	−	0.954274i	$-0.596631\pi$
$367$	240.510	−	240.510i	0.655340	−	0.655340i	0.954274	+	0.298934i	$0.0966311\pi$
$368$		0			0
$369$		−	86.0908i		−	0.233308i
$370$		0			0
$371$	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	$0.965302\pi$
$374$		0			0
$375$	133.293	+	170.611i	0.355448	+	0.454962i
$376$		0			0
$377$	−8.91939	+	8.91939i	−0.0236589	+	0.0236589i
$378$		0			0
$379$		−	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
$382$		0			0
$383$	−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
$386$		0			0
$387$	67.4847	−	67.4847i	0.174379	−	0.174379i
$388$		0			0
$389$		−	547.337i		−	1.40704i	−0.710677	−	0.703518i	$-0.751611\pi$
$389$		−	547.337i		−	1.40704i	0.710677	−	0.703518i	$-0.248389\pi$
$390$		0			0
$391$	87.2327			0.223101
$392$		0			0
$393$	−32.0102	−	32.0102i	−0.0814509	−	0.0814509i
$394$		0			0
$395$	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	$0.224313\pi$
$398$		0			0
$399$			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	$0.724710\pi$
$402$		0			0
$403$	−195.373	−	195.373i	−0.484798	−	0.484798i
$404$		0			0
$405$	−24.0681	+	38.0227i	−0.0594274	+	0.0938832i
$406$		0			0
$407$	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	$-0.139494\pi$
$410$		0			0
$411$	−35.8388			−0.0871990
$412$		0			0
$413$	162.247	+	162.247i	0.392851	+	0.392851i
$414$		0			0
$415$	145.889	−	32.7878i	0.351539	−	0.0790066i
$416$		0			0
$417$	101.864	−	101.864i	0.244278	−	0.244278i
$418$		0			0
$419$		−	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	$0.418534\pi$
$422$		0			0
$423$	−59.2577	−	59.2577i	−0.140089	−	0.140089i
$424$		0			0
$425$	88.2770	+	31.5505i	0.207711	+	0.0742365i
$426$		0			0
$427$	136.384	−	136.384i	0.319400	−	0.319400i
$428$		0			0
$429$			85.7071i			0.199784i
$430$		0			0
$431$	−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	$0.668624\pi$
$434$		0			0
$435$	1.62092	+	7.21225i	0.00372624	+	0.0165799i
$436$		0			0
$437$	−340.454	+	340.454i	−0.779071	+	0.779071i
$438$		0			0
$439$		−	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
$442$		0			0
$443$	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
$446$		0			0
$447$	−145.924	+	145.924i	−0.326452	+	0.326452i
$448$		0			0
$449$		−	297.909i		−	0.663495i	−0.943368	−	0.331747i	$-0.892362\pi$
$449$		−	297.909i		−	0.663495i	0.943368	−	0.331747i	$-0.107638\pi$
$450$		0			0
$451$	−96.0908			−0.213062
$452$		0			0
$453$	−177.551	−	177.551i	−0.391944	−	0.391944i
$454$		0			0
$455$	−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	$0.104223\pi$
$458$		0			0
$459$			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	$0.306489\pi$
$462$		0			0
$463$	−335.702	−	335.702i	−0.725057	−	0.725057i	0.244573	−	0.969631i	$-0.421352\pi$
$463$	−335.702	−	335.702i	−0.725057	−	0.725057i	−0.969631	+	0.244573i	$0.921352\pi$
$464$		0			0
$465$	−157.980	+	35.5051i	−0.339741	+	0.0763551i
$466$		0			0
$467$	−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
$470$		0			0
$471$	−125.283			−0.265993
$472$		0			0
$473$	−75.3235	−	75.3235i	−0.159246	−	0.159246i
$474$		0			0
$475$	−467.666	+	221.394i	−0.984561	+	0.466092i
$476$		0			0
$477$	−86.0908	+	86.0908i	−0.180484	+	0.180484i
$478$		0			0
$479$		−	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
$482$		0			0
$483$	58.4041	+	58.4041i	0.120919	+	0.120919i
$484$		0			0
$485$	−22.6311	−	100.697i	−0.0466621	−	0.207623i
$486$		0			0
$487$	120.682	−	120.682i	0.247807	−	0.247807i	−0.572263	−	0.820070i	$-0.693934\pi$
$487$	120.682	−	120.682i	0.247807	−	0.247807i	0.820070	+	0.572263i	$0.193934\pi$
$488$		0			0
$489$			463.918i			0.948708i
$490$		0			0
$491$	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
$494$		0			0
$495$	42.4393	+	26.8638i	0.0857359	+	0.0542703i
$496$		0			0
$497$	98.5653	−	98.5653i	0.198321	−	0.198321i
$498$		0			0
$499$		−	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
$502$		0			0
$503$	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
$506$		0			0
$507$	60.4824	−	60.4824i	0.119295	−	0.119295i
$508$		0			0
$509$		−	194.511i		−	0.382143i	−0.981576	−	0.191071i	$-0.938804\pi$
$509$		−	194.511i		−	0.382143i	0.981576	−	0.191071i	$-0.0611962\pi$
$510$		0			0
$511$	−115.344			−0.225722
$512$		0			0
$513$	−76.0454	−	76.0454i	−0.148237	−	0.148237i
$514$		0			0
$515$	446.727	−	100.399i	0.867430	−	0.194950i
$516$		0			0
$517$	−66.1408	+	66.1408i	−0.127932	+	0.127932i
$518$		0			0
$519$			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	$0.691448\pi$
$522$		0			0
$523$	141.546	+	141.546i	0.270642	+	0.270642i	0.829359	−	0.558716i	$-0.188706\pi$
$523$	141.546	+	141.546i	0.270642	+	0.270642i	−0.558716	+	0.829359i	$0.688706\pi$
$524$		0			0
$525$	37.9796	+	80.2270i	0.0723421	+	0.152813i
$526$		0			0
$527$	−49.5755	+	49.5755i	−0.0940712	+	0.0940712i
$528$		0			0
$529$			12.1714i			0.0230084i
$530$		0			0
$531$	−335.803			−0.632397
$532$		0			0
$533$	299.868	+	299.868i	0.562605	+	0.562605i
$534$		0			0
$535$	−7.35306	−	32.7173i	−0.0137440	−	0.0611539i
$536$		0			0
$537$	−225.000	+	225.000i	−0.418994	+	0.418994i
$538$		0			0
$539$			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	$0.369490\pi$
$542$		0			0
$543$	26.6107	+	26.6107i	0.0490068	+	0.0490068i
$544$		0			0
$545$	−166.045	−	105.106i	−0.304670	−	0.192854i
$546$		0			0
$547$	446.222	−	446.222i	0.815763	−	0.815763i	−0.169728	−	0.985491i	$-0.554289\pi$
$547$	446.222	−	446.222i	0.815763	−	0.815763i	0.985491	+	0.169728i	$0.0542889\pi$
$548$		0			0
$549$			282.272i			0.514157i
$550$		0			0
$551$	−17.6663			−0.0320623
$552$		0			0
$553$	35.5051	+	35.5051i	0.0642045	+	0.0642045i
$554$		0			0
$555$	−249.217	+	393.712i	−0.449039	+	0.709391i
$556$		0			0
$557$	214.091	−	214.091i	0.384364	−	0.384364i	−0.488308	−	0.872672i	$-0.662386\pi$
$557$	214.091	−	214.091i	0.384364	−	0.384364i	0.872672	+	0.488308i	$0.162386\pi$
$558$		0			0
$559$			470.120i			0.841003i
$560$		0			0
$561$	21.7480			0.0387664
$562$		0			0
$563$	−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
$566$		0			0
$567$	−13.0454	+	13.0454i	−0.0230078	+	0.0230078i
$568$		0			0
$569$			972.161i			1.70854i	0.519827	+	0.854272i	$0.325997\pi$
$569$			972.161i			1.70854i	−0.519827	+	0.854272i	$0.674003\pi$
$570$		0			0
$571$	924.030			1.61827			0.809133	−	0.587626i	$-0.199937\pi$
$571$	924.030			1.61827			0.809133	+	0.587626i	$0.199937\pi$
$572$		0			0
$573$	−49.1010	−	49.1010i	−0.0856911	−	0.0856911i
$574$		0			0
$575$	−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	$0.458889\pi$
$578$		0			0
$579$		−	189.995i		−	0.328144i
$580$		0			0
$581$	61.3031			0.105513
$582$		0			0
$583$	96.0908	+	96.0908i	0.164821	+	0.164821i
$584$		0			0
$585$	−48.6061	−	216.272i	−0.0830874	−	0.369696i
$586$		0			0
$587$	−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
$590$		0			0
$591$	164.858			0.278948
$592$		0			0
$593$	451.258	+	451.258i	0.760974	+	0.760974i	0.976498	−	0.215524i	$-0.0691461\pi$
$593$	451.258	+	451.258i	0.760974	+	0.760974i	−0.215524	+	0.976498i	$0.569146\pi$
$594$		0			0
$595$	32.4745	+	20.5561i	0.0545790	+	0.0345481i
$596$		0			0
$597$	307.893	−	307.893i	0.515734	−	0.515734i
$598$		0			0
$599$			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	$0.549048\pi$
$602$		0			0
$603$	164.697	+	164.697i	0.273129	+	0.273129i
$604$		0			0
$605$	−293.598	+	463.825i	−0.485286	+	0.766653i
$606$		0			0
$607$	−136.389	+	136.389i	−0.224694	+	0.224694i	−0.810472	−	0.585778i	$-0.800789\pi$
$607$	−136.389	+	136.389i	−0.224694	+	0.224694i	0.585778	+	0.810472i	$0.300789\pi$
$608$		0			0
$609$			3.03062i			0.00497638i
$610$		0			0
$611$	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	$0.754668\pi$
$614$		0			0
$615$	242.474	−	54.4949i	0.394267	−	0.0886096i
$616$		0			0
$617$	−398.752	+	398.752i	−0.646275	+	0.646275i	−0.952091	−	0.305816i	$-0.901071\pi$
$617$	−398.752	+	398.752i	−0.646275	+	0.646275i	0.305816	+	0.952091i	$0.401071\pi$
$618$		0			0
$619$			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
$622$		0			0
$623$	136.515	+	136.515i	0.219126	+	0.219126i
$624$		0			0
$625$	−396.151	+	483.414i	−0.633842	+	0.773463i
$626$		0			0
$627$	−84.8786	+	84.8786i	−0.135373	+	0.135373i
$628$		0			0
$629$			201.757i			0.320759i
$630$		0			0
$631$	−105.485			−0.167171			−0.0835853	−	0.996501i	$-0.526637\pi$
$631$	−105.485			−0.167171			−0.0835853	+	0.996501i	$0.526637\pi$
$632$		0			0
$633$	324.297	+	324.297i	0.512318	+	0.512318i
$634$		0			0
$635$	−177.721	−	790.767i	−0.279875	−	1.24530i
$636$		0			0
$637$	468.116	−	468.116i	0.734876	−	0.734876i
$638$		0			0
$639$			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	$0.458971\pi$
$642$		0			0
$643$	764.372	+	764.372i	1.18876	+	1.18876i	0.977411	+	0.211349i	$0.0677856\pi$
$643$	764.372	+	764.372i	1.18876	+	1.18876i	0.211349	+	0.977411i	$0.432214\pi$
$644$		0			0
$645$	232.788	+	147.353i	0.360911	+	0.228454i
$646$		0			0
$647$	−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
$650$		0			0
$651$	−66.3837			−0.101972
$652$		0			0
$653$	−169.823	−	169.823i	−0.260066	−	0.260066i	0.565015	−	0.825081i	$-0.308870\pi$
$653$	−169.823	−	169.823i	−0.260066	−	0.260066i	−0.825081	+	0.565015i	$0.808870\pi$
$654$		0			0
$655$	69.8944	−	110.419i	0.106709	−	0.168578i
$656$		0			0
$657$	119.363	−	119.363i	0.181679	−	0.181679i
$658$		0			0
$659$			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	$0.403066\pi$
$662$		0			0
$663$	−67.8684	−	67.8684i	−0.102366	−	0.102366i
$664$		0			0
$665$	−206.969	+	46.5153i	−0.311232	+	0.0699478i
$666$		0			0
$667$	−14.0408	+	14.0408i	−0.0210507	+	0.0210507i
$668$		0			0
$669$		−	81.8842i		−	0.122398i
$670$		0			0
$671$	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	$0.694636\pi$
$674$		0			0
$675$	−122.326	−	43.7196i	−0.181223	−	0.0647698i
$676$		0			0
$677$	544.388	−	544.388i	0.804119	−	0.804119i	−0.179618	−	0.983736i	$-0.557486\pi$
$677$	544.388	−	544.388i	0.804119	−	0.804119i	0.983736	+	0.179618i	$0.0574861\pi$
$678$		0			0
$679$		−	42.3133i		−	0.0623170i
$680$		0			0
$681$	−51.8592			−0.0761515
$682$		0			0
$683$	−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
$686$		0			0
$687$	298.590	−	298.590i	0.434629	−	0.434629i
$688$		0			0
$689$		−	599.737i		−	0.870445i
$690$		0			0
$691$	−356.879			−0.516467			−0.258233	−	0.966083i	$-0.583140\pi$
$691$	−356.879			−0.516467			−0.258233	+	0.966083i	$0.583140\pi$
$692$		0			0
$693$	14.5607	+	14.5607i	0.0210111	+	0.0210111i
$694$		0			0
$695$	351.378	+	222.420i	0.505580	+	0.320029i
$696$		0			0
$697$	76.0908	−	76.0908i	0.109169	−	0.109169i
$698$		0			0
$699$		−	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	$0.282347\pi$
$702$		0			0
$703$	−787.423	−	787.423i	−1.12009	−	1.12009i
$704$		0			0
$705$	129.389	−	204.409i	0.183531	−	0.289941i
$706$		0			0
$707$	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	$0.827588\pi$
$710$		0			0
$711$	−73.4847			−0.103354
$712$		0			0
$713$	−307.555	−	307.555i	−0.431354	−	0.431354i
$714$		0			0
$715$	−241.394	+	54.2520i	−0.337614	+	0.0758770i
$716$		0			0
$717$	−399.514	+	399.514i	−0.557203	+	0.557203i
$718$		0			0
$719$			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
$722$		0			0
$723$	163.596	+	163.596i	0.226274	+	0.226274i
$724$		0			0
$725$	−19.2872	+	9.13061i	−0.0266031	+	0.0125939i
$726$		0			0
$727$	15.8740	−	15.8740i	0.0218349	−	0.0218349i	−0.696105	−	0.717940i	$-0.745085\pi$
$727$	15.8740	−	15.8740i	0.0218349	−	0.0218349i	0.717940	+	0.696105i	$0.245085\pi$
$728$		0			0
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	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	$0.873851\pi$
$734$		0			0
$735$	−85.0704	−	378.520i	−0.115742	−	0.514993i
$736$		0			0
$737$	183.828	−	183.828i	0.249427	−	0.249427i
$738$		0			0
$739$		−	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
$742$		0			0
$743$	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
$746$		0			0
$747$	−63.4393	+	63.4393i	−0.0849254	+	0.0849254i
$748$		0			0
$749$		−	13.7480i		−	0.0183551i
$750$		0			0
$751$	−227.787			−0.303311			−0.151656	−	0.988433i	$-0.548460\pi$
$751$	−227.787			−0.303311			−0.151656	+	0.988433i	$0.548460\pi$
$752$		0			0
$753$	−495.706	−	495.706i	−0.658308	−	0.658308i
$754$		0			0
$755$	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	$0.320728\pi$
$758$		0			0
$759$			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	$0.696558\pi$
$762$		0			0
$763$	−56.9694	−	56.9694i	−0.0746650	−	0.0746650i
$764$		0			0
$765$	−54.8786	+	12.3337i	−0.0717367	+	0.0161225i
$766$		0			0
$767$	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	$0.712304\pi$
$770$		0			0
$771$	218.586			0.283509
$772$		0			0
$773$	−815.226	−	815.226i	−1.05463	−	1.05463i	−0.998419	−	0.0562070i	$-0.982099\pi$
$773$	−815.226	−	815.226i	−1.05463	−	1.05463i	−0.0562070	−	0.998419i	$-0.517901\pi$
$774$		0			0
$775$	−200.000	−	422.474i	−0.258065	−	0.545128i
$776$		0			0
$777$	−135.081	+	135.081i	−0.173849	+	0.173849i
$778$		0			0
$779$			593.939i			0.762437i
$780$		0			0
$781$	227.696			0.291544
$782$		0			0
$783$	−3.13622	−	3.13622i	−0.00400539	−	0.00400539i
$784$		0			0
$785$	−79.3031	−	352.858i	−0.101023	−	0.449501i
$786$		0			0
$787$	−813.010	+	813.010i	−1.03305	+	1.03305i	−0.0336150	+	0.999435i	$0.510702\pi$
$787$	−813.010	+	813.010i	−1.03305	+	1.03305i	−0.999435	+	0.0336150i	$0.989298\pi$
$788$		0			0
$789$		−	837.342i		−	1.06127i
$790$		0			0
$791$	41.6255			0.0526239
$792$		0			0
$793$	−983.201	−	983.201i	−1.23985	−	1.23985i
$794$		0			0
$795$	−296.969	−	187.980i	−0.373546	−	0.236452i
$796$		0			0
$797$	311.217	−	311.217i	0.390485	−	0.390485i	−0.484375	−	0.874860i	$-0.660953\pi$
$797$	311.217	−	311.217i	0.390485	−	0.390485i	0.874860	+	0.484375i	$0.160953\pi$
$798$		0			0
$799$		−	104.749i		−	0.131100i
$800$		0			0
$801$	−282.545			−0.352740
$802$		0			0
$803$	−133.228	−	133.228i	−0.165913	−	0.165913i
$804$		0			0
$805$	−127.526	+	201.464i	−0.158417	+	0.250266i
$806$		0			0
$807$	4.28724	−	4.28724i	0.00531256	−	0.00531256i
$808$		0			0
$809$			150.000i			0.185414i	0.995693	+	0.0927070i	$0.0295520\pi$
$809$			150.000i			0.185414i	−0.995693	+	0.0927070i	$0.970448\pi$
$810$		0			0
$811$	132.847			0.163806			0.0819032	−	0.996640i	$-0.473900\pi$
$811$	132.847			0.163806			0.0819032	+	0.996640i	$0.473900\pi$
$812$		0			0
$813$	−126.854	−	126.854i	−0.156031	−	0.156031i
$814$		0			0
$815$	−1306.62	+	293.657i	−1.60322	+	0.360316i
$816$		0			0
$817$	−465.576	+	465.576i	−0.569860	+	0.569860i
$818$		0			0
$819$		−	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	$0.399493\pi$
$822$		0			0
$823$	−300.369	−	300.369i	−0.364968	−	0.364968i	0.500670	−	0.865638i	$-0.333087\pi$
$823$	−300.369	−	300.369i	−0.364968	−	0.364968i	−0.865638	+	0.500670i	$0.833087\pi$
$824$		0			0
$825$	−48.7980	+	136.535i	−0.0591490	+	0.165497i
$826$		0			0
$827$	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	$-0.00718533\pi$
$830$		0			0
$831$	699.353			0.841580
$832$		0			0
$833$	−118.783	−	118.783i	−0.142597	−	0.142597i
$834$		0			0
$835$	150.454	+	669.444i	0.180185	+	0.801729i
$836$		0			0
$837$	68.6969	−	68.6969i	0.0820752	−	0.0820752i
$838$		0			0
$839$		−	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
$842$		0			0
$843$	−456.459	−	456.459i	−0.541469	−	0.541469i
$844$		0			0
$845$	208.633	+	132.064i	0.246903	+	0.156288i
$846$		0			0
$847$	−159.136	+	159.136i	−0.187882	+	0.187882i
$848$		0			0
$849$		−	189.081i		−	0.222710i
$850$		0			0
$851$	−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	$0.554701\pi$
$854$		0			0
$855$	166.045	−	262.318i	0.194205	−	0.306805i
$856$		0			0
$857$	417.176	−	417.176i	0.486786	−	0.486786i	−0.420504	−	0.907291i	$-0.638147\pi$
$857$	417.176	−	417.176i	0.486786	−	0.486786i	0.907291	+	0.420504i	$0.138147\pi$
$858$		0			0
$859$			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
$862$		0			0
$863$	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
$866$		0			0
$867$	336.730	−	336.730i	0.388385	−	0.388385i
$868$		0			0
$869$			82.0204i			0.0943848i
$870$		0			0
$871$	−1147.33			−1.31726
$872$		0			0
$873$	43.7878	+	43.7878i	0.0501578	+	0.0501578i
$874$		0			0
$875$	−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	$0.163598\pi$
$878$		0			0
$879$			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	$0.402151\pi$
$882$		0			0
$883$	745.939	+	745.939i	0.844778	+	0.844778i	0.989476	−	0.144698i	$-0.0462211\pi$
$883$	745.939	+	745.939i	0.844778	+	0.844778i	−0.144698	+	0.989476i	$0.546221\pi$
$884$		0			0
$885$	−212.561	−	945.787i	−0.240182	−	1.06869i
$886$		0			0
$887$	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
$890$		0			0
$891$	−30.1362			−0.0338229
$892$		0			0
$893$	408.817	+	408.817i	0.457802	+	0.457802i
$894$		0			0
$895$	−776.135	−	491.288i	−0.867190	−	0.548925i
$896$		0			0
$897$	421.040	−	421.040i	0.469387	−	0.469387i
$898$		0			0
$899$		−	15.9592i		−	0.0177521i
$900$		0			0
$901$	−152.182			−0.168903
$902$		0			0
$903$	79.8684	+	79.8684i	0.0884478	+	0.0884478i
$904$		0			0
$905$	−58.1046	+	91.7934i	−0.0642040	+	0.101429i
$906$		0			0
$907$	947.342	−	947.342i	1.04448	−	1.04448i	0.0455146	−	0.998964i	$-0.485507\pi$
$907$	947.342	−	947.342i	1.04448	−	1.04448i	0.998964	−	0.0455146i	$-0.0144928\pi$
$908$		0			0
$909$			520.863i			0.573006i
$910$		0			0
$911$	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
$914$		0			0
$915$	−795.019	+	178.677i	−0.868874	+	0.195275i
$916$		0			0
$917$	37.8842	−	37.8842i	0.0413132	−	0.0413132i
$918$		0			0
$919$			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
$922$		0			0
$923$	−710.565	−	710.565i	−0.769843	−	0.769843i
$924$		0			0
$925$	−1266.64	−	452.702i	−1.36934	−	0.489407i
$926$		0			0
$927$	−194.258	+	194.258i	−0.209555	+	0.209555i
$928$		0			0
$929$			151.707i			0.163302i	0.996661	+	0.0816508i	$0.0260192\pi$
$929$			151.707i			0.163302i	−0.996661	+	0.0816508i	$0.973981\pi$
$930$		0			0
$931$	927.181			0.995898
$932$		0			0
$933$	433.930	+	433.930i	0.465091	+	0.465091i
$934$		0			0
$935$	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	$0.0834635\pi$
$938$		0			0
$939$		−	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	$0.803246\pi$
$942$		0			0
$943$	472.050	+	472.050i	0.500583	+	0.500583i
$944$		0			0
$945$	−45.0000	−	28.4847i	−0.0476190	−	0.0301425i
$946$		0			0
$947$	−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
$950$		0			0
$951$	1046.46			1.10038
$952$		0			0
$953$	−145.501	−	145.501i	−0.152676	−	0.152676i	0.626636	−	0.779312i	$-0.284431\pi$
$953$	−145.501	−	145.501i	−0.152676	−	0.152676i	−0.779312	+	0.626636i	$0.784431\pi$
$954$		0			0
$955$	107.212	−	169.373i	0.112264	−	0.177354i
$956$		0			0
$957$	−3.50052	+	3.50052i	−0.00365780	+	0.00365780i
$958$		0			0
$959$		−	42.4153i		−	0.0442287i
$960$		0			0
$961$	−611.424			−0.636238
$962$		0			0
$963$	14.2270	+	14.2270i	0.0147737	+	0.0147737i
$964$		0			0
$965$	535.121	−	120.266i	0.554530	−	0.124628i
$966$		0			0
$967$	−1151.69	+	1151.69i	−1.19099	+	1.19099i	−0.214204	+	0.976789i	$0.568716\pi$
$967$	−1151.69	+	1151.69i	−1.19099	+	1.19099i	−0.976789	+	0.214204i	$0.931284\pi$
$968$		0			0
$969$		−	134.424i		−	0.138725i
$970$		0			0
$971$	−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
$974$		0			0
$975$	578.363	−	273.798i	0.593193	−	0.280818i
$976$		0			0
$977$	706.338	−	706.338i	0.722966	−	0.722966i	−0.246242	−	0.969208i	$-0.579196\pi$
$977$	706.338	−	706.338i	0.722966	−	0.722966i	0.969208	+	0.246242i	$0.0791958\pi$
$978$		0			0
$979$			315.364i			0.322129i
$980$		0			0
$981$	117.909			0.120193
$982$		0			0
$983$	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
$986$		0			0
$987$	70.1316	−	70.1316i	0.0710554	−	0.0710554i
$988$		0			0
$989$			740.059i			0.748290i
$990$		0			0
$991$	1131.94			1.14222			0.571109	−	0.820874i	$-0.306513\pi$
$991$	1131.94			1.14222			0.571109	+	0.820874i	$0.306513\pi$
$992$		0			0
$993$	599.419	+	599.419i	0.603644	+	0.603644i
$994$		0			0
$995$	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	$0.959568\pi$
$998$		0			0
$999$		−	279.576i		−	0.279855i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.3.bg.a.193.1		4
3.2	odd	2		720.3.bh.k.433.1		4
4.3	odd	2		15.3.f.a.13.1	yes	4
5.2	odd	4	inner	240.3.bg.a.97.1		4
5.3	odd	4		1200.3.bg.k.1057.2		4
5.4	even	2		1200.3.bg.k.193.2		4
8.3	odd	2		960.3.bg.i.193.1		4
8.5	even	2		960.3.bg.h.193.2		4
12.11	even	2		45.3.g.b.28.2		4
15.2	even	4		720.3.bh.k.577.1		4
20.3	even	4		75.3.f.c.7.2		4
20.7	even	4		15.3.f.a.7.1	✓	4
20.19	odd	2		75.3.f.c.43.2		4
36.7	odd	6		405.3.l.h.28.2		8
36.11	even	6		405.3.l.f.28.1		8
36.23	even	6		405.3.l.f.298.2		8
36.31	odd	6		405.3.l.h.298.1		8
40.27	even	4		960.3.bg.i.577.1		4
40.37	odd	4		960.3.bg.h.577.2		4
60.23	odd	4		225.3.g.a.82.1		4
60.47	odd	4		45.3.g.b.37.2		4
60.59	even	2		225.3.g.a.118.1		4
180.7	even	12		405.3.l.h.352.1		8
180.47	odd	12		405.3.l.f.352.2		8
180.67	even	12		405.3.l.h.217.2		8
180.167	odd	12		405.3.l.f.217.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.3.f.a.7.1	✓	4	20.7	even	4
15.3.f.a.13.1	yes	4	4.3	odd	2
45.3.g.b.28.2		4	12.11	even	2
45.3.g.b.37.2		4	60.47	odd	4
75.3.f.c.7.2		4	20.3	even	4
75.3.f.c.43.2		4	20.19	odd	2
225.3.g.a.82.1		4	60.23	odd	4
225.3.g.a.118.1		4	60.59	even	2
240.3.bg.a.97.1		4	5.2	odd	4	inner
240.3.bg.a.193.1		4	1.1	even	1	trivial
405.3.l.f.28.1		8	36.11	even	6
405.3.l.f.217.1		8	180.167	odd	12
405.3.l.f.298.2		8	36.23	even	6
405.3.l.f.352.2		8	180.47	odd	12
405.3.l.h.28.2		8	36.7	odd	6
405.3.l.h.217.2		8	180.67	even	12
405.3.l.h.298.1		8	36.31	odd	6
405.3.l.h.352.1		8	180.7	even	12
720.3.bh.k.433.1		4	3.2	odd	2
720.3.bh.k.577.1		4	15.2	even	4
960.3.bg.h.193.2		4	8.5	even	2
960.3.bg.h.577.2		4	40.37	odd	4
960.3.bg.i.193.1		4	8.3	odd	2
960.3.bg.i.577.1		4	40.27	even	4
1200.3.bg.k.193.2		4	5.4	even	2
1200.3.bg.k.1057.2		4	5.3	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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	240.bg (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 1.22474i) q^{3} +(2.67423 - 4.22474i) q^{5} +(1.44949 - 1.44949i) q^{7} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.22474 - 1.22474i) q^{3} +(2.67423 - 4.22474i) q^{5} +(1.44949 - 1.44949i) q^{7} +3.00000i q^{9} +3.34847 q^{11} +(-10.4495 - 10.4495i) q^{13} +(-8.44949 + 1.89898i) q^{15} +(-2.65153 + 2.65153i) q^{17} -20.6969i q^{19} -3.55051 q^{21} +(-16.4495 - 16.4495i) q^{23} +(-10.6969 - 22.5959i) q^{25} +(3.67423 - 3.67423i) q^{27} -0.853572i q^{29} +18.6969 q^{31} +(-4.10102 - 4.10102i) q^{33} +(-2.24745 - 10.0000i) q^{35} +(38.0454 - 38.0454i) q^{37} +25.5959i q^{39} -28.6969 q^{41} +(-22.4949 - 22.4949i) q^{43} +(12.6742 + 8.02270i) q^{45} +(-19.7526 + 19.7526i) q^{47} +44.7980i q^{49} +6.49490 q^{51} +(28.6969 + 28.6969i) q^{53} +(8.95459 - 14.1464i) q^{55} +(-25.3485 + 25.3485i) q^{57} +111.934i q^{59} +94.0908 q^{61} +(4.34847 + 4.34847i) q^{63} +(-72.0908 + 16.2020i) q^{65} +(54.8990 - 54.8990i) q^{67} +40.2929i q^{69} +68.0000 q^{71} +(-39.7878 - 39.7878i) q^{73} +(-14.5732 + 40.7753i) q^{75} +(4.85357 - 4.85357i) q^{77} +24.4949i q^{79} -9.00000 q^{81} +(21.1464 + 21.1464i) q^{83} +(4.11123 + 18.2929i) q^{85} +(-1.04541 + 1.04541i) q^{87} +94.1816i q^{89} -30.2929 q^{91} +(-22.8990 - 22.8990i) q^{93} +(-87.4393 - 55.3485i) q^{95} +(14.5959 - 14.5959i) q^{97} +10.0454i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5} - 4 q^{7}+O(q^{10}) \) 4 * q - 4 * q^5 - 4 * q^7	\( 4 q - 4 q^{5} - 4 q^{7} - 16 q^{11} - 32 q^{13} - 24 q^{15} - 40 q^{17} - 24 q^{21} - 56 q^{23} + 16 q^{25} + 16 q^{31} - 36 q^{33} + 40 q^{35} + 64 q^{37} - 56 q^{41} + 8 q^{43} + 36 q^{45} - 128 q^{47} - 72 q^{51} + 56 q^{53} + 124 q^{55} - 72 q^{57} + 200 q^{61} - 12 q^{63} - 112 q^{65} + 200 q^{67} + 272 q^{71} + 76 q^{73} - 24 q^{75} + 88 q^{77} - 36 q^{81} + 16 q^{83} + 232 q^{85} + 84 q^{87} + 16 q^{91} - 72 q^{93} - 144 q^{95} - 20 q^{97}+O(q^{100}) \) 4 * q - 4 * q^5 - 4 * q^7 - 16 * q^11 - 32 * q^13 - 24 * q^15 - 40 * q^17 - 24 * q^21 - 56 * q^23 + 16 * q^25 + 16 * q^31 - 36 * q^33 + 40 * q^35 + 64 * q^37 - 56 * q^41 + 8 * q^43 + 36 * q^45 - 128 * q^47 - 72 * q^51 + 56 * q^53 + 124 * q^55 - 72 * q^57 + 200 * q^61 - 12 * q^63 - 112 * q^65 + 200 * q^67 + 272 * q^71 + 76 * q^73 - 24 * q^75 + 88 * q^77 - 36 * q^81 + 16 * q^83 + 232 * q^85 + 84 * q^87 + 16 * q^91 - 72 * q^93 - 144 * q^95 - 20 * q^97

Introduction

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