LMFDB - Embedded newform 624.4.bv.h.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,4,Mod(49,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("624.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	624.bv (of order $6$, 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:	$36.8171918436$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 $ x^10 + 70x^8 + 1645x^6 + 14700x^4 + 44100x^2 + 27648
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.5
Root			$5.04537i$ of defining polynomial
Character	$\chi$	$=$	624.49
Dual form			624.4.bv.h.433.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 2.59808i) q^{3} +20.1174i q^{5} +(13.3609 + 7.71395i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 + 2.59808i) q^{3} +20.1174i q^{5} +(13.3609 + 7.71395i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-23.3283 + 13.4686i) q^{11} +(-3.96071 + 46.7045i) q^{13} +(-52.2665 + 30.1761i) q^{15} +(11.6167 - 20.1207i) q^{17} +(39.0399 + 22.5397i) q^{19} +46.2837i q^{21} +(71.0050 + 122.984i) q^{23} -279.710 q^{25} -27.0000 q^{27} +(-1.14534 - 1.98379i) q^{29} -37.7740i q^{31} +(-69.9849 - 40.4058i) q^{33} +(-155.185 + 268.787i) q^{35} +(271.793 - 156.920i) q^{37} +(-127.283 + 59.7666i) q^{39} +(5.08201 - 2.93410i) q^{41} +(180.449 - 312.547i) q^{43} +(-156.800 - 90.5283i) q^{45} +209.748i q^{47} +(-52.4900 - 90.9154i) q^{49} +69.7003 q^{51} +276.886 q^{53} +(-270.953 - 469.305i) q^{55} +135.238i q^{57} +(-470.415 - 271.594i) q^{59} +(-102.894 + 178.218i) q^{61} +(-120.249 + 69.4255i) q^{63} +(-939.573 - 79.6791i) q^{65} +(426.585 - 246.289i) q^{67} +(-213.015 + 368.953i) q^{69} +(-716.081 - 413.430i) q^{71} +66.1205i q^{73} +(-419.564 - 726.707i) q^{75} -415.584 q^{77} -317.642 q^{79} +(-40.5000 - 70.1481i) q^{81} +141.450i q^{83} +(404.777 + 233.698i) q^{85} +(3.43602 - 5.95136i) q^{87} +(555.399 - 320.660i) q^{89} +(-413.195 + 593.464i) q^{91} +(98.1396 - 56.6609i) q^{93} +(-453.440 + 785.381i) q^{95} +(-965.551 - 557.461i) q^{97} -242.435i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9}+O(q^{10}) $ 10 * q + 15 * q^3 - 30 * q^7 - 45 * q^9	$ 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9} - 60 q^{11} + 25 q^{13} - 45 q^{15} + 105 q^{17} - 180 q^{19} + 60 q^{23} - 960 q^{25} - 270 q^{27} - 495 q^{29} - 180 q^{33} - 60 q^{35} - 405 q^{37} - 345 q^{39} + 1065 q^{41} + 370 q^{43} - 135 q^{45} + 775 q^{49} + 630 q^{51} + 330 q^{53} + 260 q^{55} - 780 q^{59} - 1375 q^{61} + 270 q^{63} + 1605 q^{65} - 1590 q^{67} - 180 q^{69} - 1620 q^{71} - 1440 q^{75} - 4320 q^{77} - 1100 q^{79} - 405 q^{81} + 525 q^{85} + 1485 q^{87} + 2040 q^{89} - 4770 q^{91} - 990 q^{93} + 1380 q^{95} - 3750 q^{97}+O(q^{100}) $ 10 * q + 15 * q^3 - 30 * q^7 - 45 * q^9 - 60 * q^11 + 25 * q^13 - 45 * q^15 + 105 * q^17 - 180 * q^19 + 60 * q^23 - 960 * q^25 - 270 * q^27 - 495 * q^29 - 180 * q^33 - 60 * q^35 - 405 * q^37 - 345 * q^39 + 1065 * q^41 + 370 * q^43 - 135 * q^45 + 775 * q^49 + 630 * q^51 + 330 * q^53 + 260 * q^55 - 780 * q^59 - 1375 * q^61 + 270 * q^63 + 1605 * q^65 - 1590 * q^67 - 180 * q^69 - 1620 * q^71 - 1440 * q^75 - 4320 * q^77 - 1100 * q^79 - 405 * q^81 + 525 * q^85 + 1485 * q^87 + 2040 * q^89 - 4770 * q^91 - 990 * q^93 + 1380 * q^95 - 3750 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$		0			0
$5$			20.1174i			1.79935i	0.436556	+	0.899677i	$0.356198\pi$
$5$			20.1174i			1.79935i	−0.436556	+	0.899677i	$0.643802\pi$
$6$		0			0
$7$	13.3609	+	7.71395i	0.721423	+	0.416514i	0.815276	−	0.579072i	$-0.196585\pi$
$7$	13.3609	+	7.71395i	0.721423	+	0.416514i	−0.0938530	+	0.995586i	$0.529918\pi$
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	−23.3283	+	13.4686i	−0.639432	+	0.369176i	−0.784396	−	0.620261i	$-0.787027\pi$
$11$	−23.3283	+	13.4686i	−0.639432	+	0.369176i	0.144964	+	0.989437i	$0.453693\pi$
$12$		0			0
$13$	−3.96071	+	46.7045i	−0.0845002	+	0.996423i
$13$	−3.96071	+	46.7045i	−0.0845002	+	0.996423i
$14$		0			0
$15$	−52.2665	+	30.1761i	−0.899677	+	0.519429i
$16$		0			0
$17$	11.6167	−	20.1207i	0.165733	−	0.287059i	−0.771182	−	0.636615i	$-0.780334\pi$
$17$	11.6167	−	20.1207i	0.165733	−	0.287059i	0.936915	+	0.349556i	$0.113668\pi$
$18$		0			0
$19$	39.0399	+	22.5397i	0.471388	+	0.272156i	0.716821	−	0.697258i	$-0.245597\pi$
$19$	39.0399	+	22.5397i	0.471388	+	0.272156i	−0.245433	+	0.969414i	$0.578930\pi$
$20$		0			0
$21$			46.2837i			0.480949i
$22$		0			0
$23$	71.0050	+	122.984i	0.643720	+	1.11496i	0.984595	+	0.174848i	$0.0559434\pi$
$23$	71.0050	+	122.984i	0.643720	+	1.11496i	−0.340875	+	0.940109i	$0.610723\pi$
$24$		0			0
$25$	−279.710			−2.23768
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	−1.14534	−	1.98379i	−0.00733394	−	0.0127028i	0.862335	−	0.506338i	$-0.169001\pi$
$29$	−1.14534	−	1.98379i	−0.00733394	−	0.0127028i	−0.869669	+	0.493635i	$0.835668\pi$
$30$		0			0
$31$		−	37.7740i		−	0.218852i	−0.993995	−	0.109426i	$-0.965099\pi$
$31$		−	37.7740i		−	0.218852i	0.993995	−	0.109426i	$-0.0349012\pi$
$32$		0			0
$33$	−69.9849	−	40.4058i	−0.369176	−	0.213144i
$34$		0			0
$35$	−155.185	+	268.787i	−0.749456	+	1.29810i
$36$		0			0
$37$	271.793	−	156.920i	1.20764	−	0.697228i	0.245393	−	0.969424i	$-0.421083\pi$
$37$	271.793	−	156.920i	1.20764	−	0.697228i	0.962242	+	0.272195i	$0.0877497\pi$
$38$		0			0
$39$	−127.283	+	59.7666i	−0.522605	+	0.245393i
$40$		0			0
$41$	5.08201	−	2.93410i	0.0193580	−	0.0111763i	−0.490290	−	0.871559i	$-0.663109\pi$
$41$	5.08201	−	2.93410i	0.0193580	−	0.0111763i	0.509648	+	0.860383i	$0.329776\pi$
$42$		0			0
$43$	180.449	−	312.547i	0.639958	−	1.10844i	−0.345483	−	0.938425i	$-0.612285\pi$
$43$	180.449	−	312.547i	0.639958	−	1.10844i	0.985441	−	0.170015i	$-0.0543817\pi$
$44$		0			0
$45$	−156.800	−	90.5283i	−0.519429	−	0.299892i
$46$		0			0
$47$			209.748i			0.650956i	0.945550	+	0.325478i	$0.105525\pi$
$47$			209.748i			0.650956i	−0.945550	+	0.325478i	$0.894475\pi$
$48$		0			0
$49$	−52.4900	−	90.9154i	−0.153032	−	0.265060i
$50$		0			0
$51$	69.7003			0.191372
$52$		0			0
$53$	276.886			0.717609			0.358804	−	0.933413i	$-0.383185\pi$
$53$	276.886			0.717609			0.358804	+	0.933413i	$0.383185\pi$
$54$		0			0
$55$	−270.953	−	469.305i	−0.664278	−	1.15056i
$56$		0			0
$57$			135.238i			0.314259i
$58$		0			0
$59$	−470.415	−	271.594i	−1.03801	−	0.599298i	−0.118744	−	0.992925i	$-0.537887\pi$
$59$	−470.415	−	271.594i	−1.03801	−	0.599298i	−0.919270	+	0.393627i	$0.871220\pi$
$60$		0			0
$61$	−102.894	+	178.218i	−0.215971	+	0.374073i	−0.953573	−	0.301163i	$-0.902625\pi$
$61$	−102.894	+	178.218i	−0.215971	+	0.374073i	0.737601	+	0.675236i	$0.235958\pi$
$62$		0			0
$63$	−120.249	+	69.4255i	−0.240474	+	0.138838i
$64$		0			0
$65$	−939.573	−	79.6791i	−1.79292	−	0.152046i
$66$		0			0
$67$	426.585	−	246.289i	0.777846	−	0.449090i	−0.0578203	−	0.998327i	$-0.518415\pi$
$67$	426.585	−	246.289i	0.777846	−	0.449090i	0.835666	+	0.549237i	$0.185082\pi$
$68$		0			0
$69$	−213.015	+	368.953i	−0.371652	+	0.643720i
$70$		0			0
$71$	−716.081	−	413.430i	−1.19695	−	0.691057i	−0.237073	−	0.971492i	$-0.576188\pi$
$71$	−716.081	−	413.430i	−1.19695	−	0.691057i	−0.959873	+	0.280435i	$0.909521\pi$
$72$		0			0
$73$			66.1205i			0.106011i	0.998594	+	0.0530056i	$0.0168801\pi$
$73$			66.1205i			0.106011i	−0.998594	+	0.0530056i	$0.983120\pi$
$74$		0			0
$75$	−419.564	−	726.707i	−0.645962	−	1.11884i
$76$		0			0
$77$	−415.584			−0.615068
$78$		0			0
$79$	−317.642			−0.452374			−0.226187	−	0.974084i	$-0.572626\pi$
$79$	−317.642			−0.452374			−0.226187	+	0.974084i	$0.572626\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			141.450i			0.187063i	0.995616	+	0.0935313i	$0.0298155\pi$
$83$			141.450i			0.187063i	−0.995616	+	0.0935313i	$0.970184\pi$
$84$		0			0
$85$	404.777	+	233.698i	0.516520	+	0.298213i
$86$		0			0
$87$	3.43602	−	5.95136i	0.00423425	−	0.00733394i
$88$		0			0
$89$	555.399	−	320.660i	0.661486	−	0.381909i	−0.131357	−	0.991335i	$-0.541933\pi$
$89$	555.399	−	320.660i	0.661486	−	0.381909i	0.792843	+	0.609426i	$0.208600\pi$
$90$		0			0
$91$	−413.195	+	593.464i	−0.475985	+	0.683648i
$92$		0			0
$93$	98.1396	−	56.6609i	0.109426	−	0.0631771i
$94$		0			0
$95$	−453.440	+	785.381i	−0.489705	+	0.848194i
$96$		0			0
$97$	−965.551	−	557.461i	−1.01069	−	0.583522i	−0.0992962	−	0.995058i	$-0.531659\pi$
$97$	−965.551	−	557.461i	−1.01069	−	0.583522i	−0.911394	+	0.411536i	$0.864992\pi$
$98$		0			0
$99$		−	242.435i		−	0.246117i
$100$		0			0
$101$	794.953	+	1376.90i	0.783177	+	1.35650i	0.930082	+	0.367351i	$0.119735\pi$
$101$	794.953	+	1376.90i	0.783177	+	1.35650i	−0.146906	+	0.989150i	$0.546931\pi$
$102$		0			0
$103$	527.502			0.504625			0.252312	−	0.967646i	$-0.418809\pi$
$103$	527.502			0.504625			0.252312	+	0.967646i	$0.418809\pi$
$104$		0			0
$105$	−931.107			−0.865398
$106$		0			0
$107$	875.982	+	1517.25i	0.791443	+	1.37082i	0.925073	+	0.379788i	$0.124003\pi$
$107$	875.982	+	1517.25i	0.791443	+	1.37082i	−0.133630	+	0.991031i	$0.542663\pi$
$108$		0			0
$109$		−	967.122i		−	0.849848i	−0.905229	−	0.424924i	$-0.860301\pi$
$109$		−	967.122i		−	0.849848i	0.905229	−	0.424924i	$-0.139699\pi$
$110$		0			0
$111$	815.379	+	470.759i	0.697228	+	0.402545i
$112$		0			0
$113$	−955.487	+	1654.95i	−0.795439	+	1.37774i	0.127120	+	0.991887i	$0.459427\pi$
$113$	−955.487	+	1654.95i	−0.795439	+	1.37774i	−0.922560	+	0.385854i	$0.873907\pi$
$114$		0			0
$115$	−2474.12	+	1428.44i	−2.00620	+	1.15828i
$116$		0			0
$117$	−346.203	−	241.041i	−0.273559	−	0.190464i
$118$		0			0
$119$	310.421	−	179.221i	0.239128	−	0.138061i
$120$		0			0
$121$	−302.694	+	524.281i	−0.227418	+	0.393900i
$122$		0			0
$123$	15.2460	+	8.80230i	0.0111763	+	0.00645266i
$124$		0			0
$125$		−	3112.35i		−	2.22702i
$126$		0			0
$127$	−616.557	−	1067.91i	−0.430792	−	0.746154i	0.566150	−	0.824302i	$-0.308432\pi$
$127$	−616.557	−	1067.91i	−0.430792	−	0.746154i	−0.996942	+	0.0781488i	$0.975099\pi$
$128$		0			0
$129$	1082.69			0.738960
$130$		0			0
$131$	1274.90			0.850292			0.425146	−	0.905125i	$-0.360223\pi$
$131$	1274.90			0.850292			0.425146	+	0.905125i	$0.360223\pi$
$132$		0			0
$133$	347.740	+	602.304i	0.226713	+	0.392679i
$134$		0			0
$135$		−	543.170i		−	0.346286i
$136$		0			0
$137$	−1759.18	−	1015.66i	−1.09706	−	0.633385i	−0.161609	−	0.986855i	$-0.551668\pi$
$137$	−1759.18	−	1015.66i	−1.09706	−	0.633385i	−0.935446	+	0.353470i	$0.885002\pi$
$138$		0			0
$139$	−722.832	+	1251.98i	−0.441078	+	0.763969i	−0.997770	−	0.0667498i	$-0.978737\pi$
$139$	−722.832	+	1251.98i	−0.441078	+	0.763969i	0.556692	+	0.830719i	$0.312070\pi$
$140$		0			0
$141$	−544.942	+	314.623i	−0.325478	+	0.187915i
$142$		0			0
$143$	−536.648	−	1142.88i	−0.313824	−	0.668340i
$144$		0			0
$145$	39.9086	−	23.0413i	0.0228568	−	0.0131964i
$146$		0			0
$147$	157.470	−	272.746i	0.0883532	−	0.153032i
$148$		0			0
$149$	836.856	+	483.159i	0.460120	+	0.265650i	0.712095	−	0.702083i	$-0.247747\pi$
$149$	836.856	+	483.159i	0.460120	+	0.265650i	−0.251975	+	0.967734i	$0.581080\pi$
$150$		0			0
$151$		−	1463.09i		−	0.788505i	−0.919002	−	0.394252i	$-0.871004\pi$
$151$		−	1463.09i		−	0.788505i	0.919002	−	0.394252i	$-0.128996\pi$
$152$		0			0
$153$	104.550	+	181.087i	0.0552445	+	0.0956862i
$154$		0			0
$155$	759.914			0.393792
$156$		0			0
$157$	−66.0424			−0.0335717			−0.0167859	−	0.999859i	$-0.505343\pi$
$157$	−66.0424			−0.0335717			−0.0167859	+	0.999859i	$0.505343\pi$
$158$		0			0
$159$	415.330	+	719.372i	0.207156	+	0.358804i
$160$		0			0
$161$			2190.92i			1.07247i
$162$		0			0
$163$	3052.95	+	1762.62i	1.46703	+	0.846988i	0.999319	−	0.0368953i	$-0.0117468\pi$
$163$	3052.95	+	1762.62i	1.46703	+	0.846988i	0.467707	+	0.883883i	$0.345080\pi$
$164$		0			0
$165$	812.859	−	1407.91i	0.383521	−	0.664278i
$166$		0			0
$167$	−225.731	+	130.326i	−0.104596	+	0.0603887i	−0.551386	−	0.834250i	$-0.685901\pi$
$167$	−225.731	+	130.326i	−0.104596	+	0.0603887i	0.446789	+	0.894639i	$0.352567\pi$
$168$		0			0
$169$	−2165.63	−	369.966i	−0.985719	−	0.168396i
$170$		0			0
$171$	−351.359	+	202.857i	−0.157129	+	0.0907186i
$172$		0			0
$173$	455.876	−	789.601i	0.200345	−	0.347007i	−0.748295	−	0.663366i	$-0.769127\pi$
$173$	455.876	−	789.601i	0.200345	−	0.347007i	0.948640	+	0.316359i	$0.102460\pi$
$174$		0			0
$175$	−3737.18	−	2157.66i	−1.61431	−	0.932023i
$176$		0			0
$177$		−	1629.57i		−	0.692009i
$178$		0			0
$179$	−1345.24	−	2330.03i	−0.561721	−	0.972930i	−0.997346	−	0.0728016i	$-0.976806\pi$
$179$	−1345.24	−	2330.03i	−0.561721	−	0.972930i	0.435625	−	0.900128i	$-0.356527\pi$
$180$		0			0
$181$	−4773.85			−1.96043			−0.980213	−	0.197944i	$-0.936573\pi$
$181$	−4773.85			−1.96043			−0.980213	+	0.197944i	$0.936573\pi$
$182$		0			0
$183$	−617.364			−0.249382
$184$		0			0
$185$	3156.82	+	5467.77i	1.25456	+	2.17296i
$186$		0			0
$187$			625.844i			0.244739i
$188$		0			0
$189$	−360.746	−	208.277i	−0.138838	−	0.0801582i
$190$		0			0
$191$	−1028.74	+	1781.82i	−0.389721	+	0.675017i	−0.992412	−	0.122958i	$-0.960762\pi$
$191$	−1028.74	+	1781.82i	−0.389721	+	0.675017i	0.602691	+	0.797975i	$0.294095\pi$
$192$		0			0
$193$	632.089	−	364.937i	0.235745	−	0.136107i	−0.377475	−	0.926020i	$-0.623207\pi$
$193$	632.089	−	364.937i	0.235745	−	0.136107i	0.613219	+	0.789913i	$0.289874\pi$
$194$		0			0
$195$	−1202.35	−	2560.60i	−0.441548	−	0.940351i
$196$		0			0
$197$	1473.21	−	850.557i	0.532801	−	0.307613i	−0.209355	−	0.977840i	$-0.567137\pi$
$197$	1473.21	−	850.557i	0.532801	−	0.307613i	0.742156	+	0.670227i	$0.233803\pi$
$198$		0			0
$199$	920.440	−	1594.25i	0.327881	−	0.567906i	−0.654211	−	0.756312i	$-0.726999\pi$
$199$	920.440	−	1594.25i	0.327881	−	0.567906i	0.982091	+	0.188407i	$0.0603323\pi$
$200$		0			0
$201$	1279.76	+	738.867i	0.449090	+	0.259282i
$202$		0			0
$203$		−	35.3404i		−	0.0122188i
$204$		0			0
$205$	59.0265	+	102.237i	0.0201102	+	0.0348319i
$206$		0			0
$207$	−1278.09			−0.429147
$208$		0			0
$209$	−1214.31			−0.401894
$210$		0			0
$211$	71.4850	+	123.816i	0.0233234	+	0.0403972i	0.877452	−	0.479665i	$-0.159242\pi$
$211$	71.4850	+	123.816i	0.0233234	+	0.0403972i	−0.854128	+	0.520063i	$0.825909\pi$
$212$		0			0
$213$		−	2480.58i		−	0.797964i
$214$		0			0
$215$	6287.63	+	3630.16i	1.99448	+	1.15151i
$216$		0			0
$217$	291.386	−	504.696i	0.0911548	−	0.157885i
$218$		0			0
$219$	−171.786	+	99.1807i	−0.0530056	+	0.0306028i
$220$		0			0
$221$	893.719	+	622.246i	0.272027	+	0.189397i
$222$		0			0
$223$	2025.39	−	1169.36i	0.608205	−	0.351148i	−0.164057	−	0.986451i	$-0.552458\pi$
$223$	2025.39	−	1169.36i	0.608205	−	0.351148i	0.772263	+	0.635303i	$0.219125\pi$
$224$		0			0
$225$	1258.69	−	2180.12i	0.372946	−	0.645962i
$226$		0			0
$227$	2840.01	+	1639.68i	0.830388	+	0.479425i	0.853986	−	0.520297i	$-0.174179\pi$
$227$	2840.01	+	1639.68i	0.830388	+	0.479425i	−0.0235973	+	0.999722i	$0.507512\pi$
$228$		0			0
$229$		−	1143.72i		−	0.330041i	−0.986290	−	0.165021i	$-0.947231\pi$
$229$		−	1143.72i		−	0.330041i	0.986290	−	0.165021i	$-0.0527690\pi$
$230$		0			0
$231$	−623.376	−	1079.72i	−0.177555	−	0.307534i
$232$		0			0
$233$	4238.17			1.19164			0.595819	−	0.803118i	$-0.296827\pi$
$233$	4238.17			1.19164			0.595819	+	0.803118i	$0.296827\pi$
$234$		0			0
$235$	−4219.59			−1.17130
$236$		0			0
$237$	−476.464	−	825.259i	−0.130589	−	0.226187i
$238$		0			0
$239$			3310.03i			0.895849i	0.894072	+	0.447924i	$0.147837\pi$
$239$			3310.03i			0.895849i	−0.894072	+	0.447924i	$0.852163\pi$
$240$		0			0
$241$	4938.82	+	2851.43i	1.32007	+	0.762145i	0.983740	−	0.179598i	$-0.0574798\pi$
$241$	4938.82	+	2851.43i	1.32007	+	0.762145i	0.336333	+	0.941743i	$0.390813\pi$
$242$		0			0
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$		0			0
$245$	1828.98	−	1055.96i	0.476936	−	0.275359i
$246$		0			0
$247$	−1207.33	+	1734.07i	−0.311015	+	0.446705i
$248$		0			0
$249$	−367.499	+	212.175i	−0.0935313	+	0.0540003i
$250$		0			0
$251$	1955.12	−	3386.36i	0.491657	−	0.851574i	−0.508297	−	0.861182i	$-0.669725\pi$
$251$	1955.12	−	3386.36i	0.491657	−	0.851574i	0.999954	+	0.00960748i	$0.00305820\pi$
$252$		0			0
$253$	−3312.85	−	1912.68i	−0.823230	−	0.475292i
$254$		0			0
$255$			1402.19i			0.344347i
$256$		0			0
$257$	3486.40	+	6038.63i	0.846209	+	1.46568i	0.884567	+	0.466413i	$0.154454\pi$
$257$	3486.40	+	6038.63i	0.846209	+	1.46568i	−0.0383576	+	0.999264i	$0.512213\pi$
$258$		0			0
$259$	4841.88			1.16162
$260$		0			0
$261$	20.6161			0.00488930
$262$		0			0
$263$	140.845	+	243.951i	0.0330224	+	0.0571965i	0.882064	−	0.471129i	$-0.156153\pi$
$263$	140.845	+	243.951i	0.0330224	+	0.0571965i	−0.849042	+	0.528326i	$0.822820\pi$
$264$		0			0
$265$			5570.23i			1.29123i
$266$		0			0
$267$	1666.20	+	961.980i	0.381909	+	0.220495i
$268$		0			0
$269$	−2166.56	+	3752.60i	−0.491070	+	0.850558i	−0.999947	−	0.0102813i	$-0.996727\pi$
$269$	−2166.56	+	3752.60i	−0.491070	+	0.850558i	0.508877	+	0.860839i	$0.330061\pi$
$270$		0			0
$271$	−371.175	+	214.298i	−0.0832003	+	0.0480357i	−0.541023	−	0.841008i	$-0.681963\pi$
$271$	−371.175	+	214.298i	−0.0832003	+	0.0480357i	0.457823	+	0.889044i	$0.348629\pi$
$272$		0			0
$273$	−2161.66	−	183.316i	−0.479229	−	0.0406403i
$274$		0			0
$275$	6525.15	−	3767.30i	1.43084	−	0.826096i
$276$		0			0
$277$	4469.37	−	7741.18i	0.969454	−	1.67914i	0.272313	−	0.962209i	$-0.412211\pi$
$277$	4469.37	−	7741.18i	0.969454	−	1.67914i	0.697140	−	0.716935i	$-0.254455\pi$
$278$		0			0
$279$	294.419	+	169.983i	0.0631771	+	0.0364753i
$280$		0			0
$281$			775.819i			0.164703i	0.996603	+	0.0823514i	$0.0262430\pi$
$281$			775.819i			0.164703i	−0.996603	+	0.0823514i	$0.973757\pi$
$282$		0			0
$283$	2007.27	+	3476.69i	0.421624	+	0.730274i	0.996098	−	0.0882484i	$-0.0281269\pi$
$283$	2007.27	+	3476.69i	0.421624	+	0.730274i	−0.574475	+	0.818522i	$0.694794\pi$
$284$		0			0
$285$	−2720.64			−0.565463
$286$		0			0
$287$	90.5340			0.0186204
$288$		0			0
$289$	2186.60	+	3787.31i	0.445065	+	0.770875i
$290$		0			0
$291$		−	3344.77i		−	0.673793i
$292$		0			0
$293$	4292.21	+	2478.11i	0.855814	+	0.494104i	0.862608	−	0.505873i	$-0.168829\pi$
$293$	4292.21	+	2478.11i	0.855814	+	0.494104i	−0.00679458	+	0.999977i	$0.502163\pi$
$294$		0			0
$295$	5463.77	−	9463.53i	1.07835	−	1.86776i
$296$		0			0
$297$	629.864	−	363.652i	0.123059	−	0.0710480i
$298$		0			0
$299$	−6025.15	+	2829.15i	−1.16536	+	0.547204i
$300$		0			0
$301$	4821.94	−	2783.95i	0.923362	−	0.533103i
$302$		0			0
$303$	−2384.86	+	4130.70i	−0.452167	+	0.783177i
$304$		0			0
$305$	−3585.28	−	2069.96i	−0.673090	−	0.388608i
$306$		0			0
$307$			3894.90i			0.724084i	0.932162	+	0.362042i	$0.117920\pi$
$307$			3894.90i			0.724084i	−0.932162	+	0.362042i	$0.882080\pi$
$308$		0			0
$309$	791.254	+	1370.49i	0.145673	+	0.252312i
$310$		0			0
$311$	3097.44			0.564758			0.282379	−	0.959303i	$-0.408876\pi$
$311$	3097.44			0.564758			0.282379	+	0.959303i	$0.408876\pi$
$312$		0			0
$313$	4487.36			0.810353			0.405177	−	0.914238i	$-0.367210\pi$
$313$	4487.36			0.810353			0.405177	+	0.914238i	$0.367210\pi$
$314$		0			0
$315$	−1396.66	−	2419.09i	−0.249819	−	0.432699i
$316$		0			0
$317$		−	6820.62i		−	1.20847i	−0.796807	−	0.604233i	$-0.793479\pi$
$317$		−	6820.62i		−	1.20847i	0.796807	−	0.604233i	$-0.206521\pi$
$318$		0			0
$319$	53.4377	+	30.8523i	0.00937911	+	0.00541503i
$320$		0			0
$321$	−2627.95	+	4551.74i	−0.456940	+	0.791443i
$322$		0			0
$323$	907.031	−	523.675i	0.156249	−	0.0902106i
$324$		0			0
$325$	1107.85	−	13063.7i	0.189084	−	2.22967i
$326$		0			0
$327$	2512.66	−	1450.68i	0.424924	−	0.245330i
$328$		0			0
$329$	−1617.99	+	2802.44i	−0.271132	+	0.469615i
$330$		0			0
$331$	−4341.35	−	2506.48i	−0.720913	−	0.416219i	0.0941759	−	0.995556i	$-0.469978\pi$
$331$	−4341.35	−	2506.48i	−0.720913	−	0.416219i	−0.815088	+	0.579337i	$0.803312\pi$
$332$		0			0
$333$			2824.56i			0.464819i
$334$		0			0
$335$	4954.70	+	8581.78i	0.808071	+	1.39962i
$336$		0			0
$337$	−3220.79			−0.520616			−0.260308	−	0.965526i	$-0.583824\pi$
$337$	−3220.79			−0.520616			−0.260308	+	0.965526i	$0.583824\pi$
$338$		0			0
$339$	−5732.92			−0.918494
$340$		0			0
$341$	508.762	+	881.202i	0.0807948	+	0.139941i
$342$		0			0
$343$		−	6911.39i		−	1.08799i
$344$		0			0
$345$	−7422.37	−	4285.31i	−1.15828	−	0.668734i
$346$		0			0
$347$	−1680.36	+	2910.46i	−0.259960	+	0.450265i	−0.966231	−	0.257677i	$-0.917043\pi$
$347$	−1680.36	+	2910.46i	−0.259960	+	0.450265i	0.706271	+	0.707942i	$0.250376\pi$
$348$		0			0
$349$	3976.20	−	2295.66i	0.609859	−	0.352102i	−0.163051	−	0.986618i	$-0.552134\pi$
$349$	3976.20	−	2295.66i	0.609859	−	0.352102i	0.772910	+	0.634515i	$0.218800\pi$
$350$		0			0
$351$	106.939	−	1261.02i	0.0162621	−	0.191762i
$352$		0			0
$353$	1506.96	−	870.044i	0.227216	−	0.131183i	−0.382071	−	0.924133i	$-0.624789\pi$
$353$	1506.96	−	870.044i	0.227216	−	0.131183i	0.609287	+	0.792950i	$0.291456\pi$
$354$		0			0
$355$	8317.12	−	14405.7i	1.24346	−	2.15373i
$356$		0			0
$357$	931.262	+	537.664i	0.138061	+	0.0797093i
$358$		0			0
$359$			1425.49i			0.209567i	0.994495	+	0.104784i	$0.0334150\pi$
$359$			1425.49i			0.209567i	−0.994495	+	0.104784i	$0.966585\pi$
$360$		0			0
$361$	−2413.42	−	4180.17i	−0.351862	−	0.609443i
$362$		0			0
$363$	−1816.16			−0.262600
$364$		0			0
$365$	−1330.17			−0.190752
$366$		0			0
$367$	5424.61	+	9395.69i	0.771559	+	1.33638i	0.936708	+	0.350111i	$0.113856\pi$
$367$	5424.61	+	9395.69i	0.771559	+	1.33638i	−0.165149	+	0.986269i	$0.552811\pi$
$368$		0			0
$369$			52.8138i			0.00745089i
$370$		0			0
$371$	3699.46	+	2135.89i	0.517700	+	0.298894i
$372$		0			0
$373$	247.374	−	428.465i	0.0343393	−	0.0594774i	−0.848345	−	0.529444i	$-0.822401\pi$
$373$	247.374	−	428.465i	0.0343393	−	0.0594774i	0.882684	+	0.469966i	$0.155734\pi$
$374$		0			0
$375$	8086.13	−	4668.53i	1.11351	−	0.642885i
$376$		0			0
$377$	97.1882	−	45.6354i	0.0132770	−	0.00623433i
$378$		0			0
$379$	−10949.4	+	6321.66i	−1.48400	+	0.856786i	−0.999835	−	0.0181912i	$-0.994209\pi$
$379$	−10949.4	+	6321.66i	−1.48400	+	0.856786i	−0.484163	+	0.874978i	$0.660876\pi$
$380$		0			0
$381$	1849.67	−	3203.72i	0.248718	−	0.430792i
$382$		0			0
$383$	−2010.48	−	1160.75i	−0.268227	−	0.154861i	0.359855	−	0.933008i	$-0.382826\pi$
$383$	−2010.48	−	1160.75i	−0.268227	−	0.154861i	−0.628082	+	0.778147i	$0.716160\pi$
$384$		0			0
$385$		−	8360.47i		−	1.10673i
$386$		0			0
$387$	1624.04	+	2812.92i	0.213319	+	0.369480i
$388$		0			0
$389$	10477.6			1.36564			0.682821	−	0.730586i	$-0.260753\pi$
$389$	10477.6			1.36564			0.682821	+	0.730586i	$0.260753\pi$
$390$		0			0
$391$	3299.38			0.426744
$392$		0			0
$393$	1912.35	+	3312.28i	0.245458	+	0.425146i
$394$		0			0
$395$		−	6390.14i		−	0.813982i
$396$		0			0
$397$	1530.14	+	883.424i	0.193439	+	0.111682i	0.593592	−	0.804766i	$-0.297709\pi$
$397$	1530.14	+	883.424i	0.193439	+	0.111682i	−0.400152	+	0.916449i	$0.631043\pi$
$398$		0			0
$399$	−1043.22	+	1806.91i	−0.130893	+	0.226713i
$400$		0			0
$401$	−4331.55	+	2500.82i	−0.539420	+	0.311434i	−0.744844	−	0.667239i	$-0.767476\pi$
$401$	−4331.55	+	2500.82i	−0.539420	+	0.311434i	0.205424	+	0.978673i	$0.434143\pi$
$402$		0			0
$403$	1764.21	+	149.612i	0.218069	+	0.0184930i
$404$		0			0
$405$	1411.20	−	814.754i	0.173143	−	0.0999641i
$406$		0			0
$407$	−4226.98	+	7321.34i	−0.514800	+	0.891660i
$408$		0			0
$409$	−9706.92	−	5604.29i	−1.17354	−	0.677541i	−0.219025	−	0.975719i	$-0.570288\pi$
$409$	−9706.92	−	5604.29i	−1.17354	−	0.677541i	−0.954510	+	0.298178i	$0.903621\pi$
$410$		0			0
$411$		−	6093.96i		−	0.731370i
$412$		0			0
$413$	−4190.13	−	7257.51i	−0.499232	−	0.864695i
$414$		0			0
$415$	−2845.61			−0.336592
$416$		0			0
$417$	−4336.99			−0.509313
$418$		0			0
$419$	1642.59	+	2845.06i	0.191518	+	0.331719i	0.945753	−	0.324885i	$-0.105326\pi$
$419$	1642.59	+	2845.06i	0.191518	+	0.331719i	−0.754236	+	0.656604i	$0.771992\pi$
$420$		0			0
$421$			13289.9i			1.53850i	0.638948	+	0.769250i	$0.279370\pi$
$421$			13289.9i			1.53850i	−0.638948	+	0.769250i	$0.720630\pi$
$422$		0			0
$423$	−1634.83	−	943.868i	−0.187915	−	0.108493i
$424$		0			0
$425$	−3249.31	+	5627.96i	−0.370858	+	0.642344i
$426$		0			0
$427$	−2749.52	+	1587.44i	−0.311613	+	0.179910i
$428$		0			0
$429$	2164.32	−	3108.58i	0.243577	−	0.349845i
$430$		0			0
$431$	−11857.8	+	6846.13i	−1.32523	+	0.765119i	−0.984557	−	0.175064i	$-0.943987\pi$
$431$	−11857.8	+	6846.13i	−1.32523	+	0.765119i	−0.340668	+	0.940184i	$0.610653\pi$
$432$		0			0
$433$	−5001.26	+	8662.43i	−0.555070	+	0.961409i	0.442829	+	0.896606i	$0.353975\pi$
$433$	−5001.26	+	8662.43i	−0.555070	+	0.961409i	−0.997898	+	0.0648023i	$0.979358\pi$
$434$		0			0
$435$	119.726	+	69.1238i	0.0131964	+	0.00761892i
$436$		0			0
$437$			6401.73i			0.700769i
$438$		0			0
$439$	−2243.60	−	3886.04i	−0.243921	−	0.422484i	0.717907	−	0.696139i	$-0.245100\pi$
$439$	−2243.60	−	3886.04i	−0.243921	−	0.422484i	−0.961828	+	0.273656i	$0.911767\pi$
$440$		0			0
$441$	944.821			0.102021
$442$		0			0
$443$	−2035.35			−0.218290			−0.109145	−	0.994026i	$-0.534811\pi$
$443$	−2035.35			−0.218290			−0.109145	+	0.994026i	$0.534811\pi$
$444$		0			0
$445$	6450.84	+	11173.2i	0.687190	+	1.19025i
$446$		0			0
$447$			2898.95i			0.306747i
$448$		0			0
$449$	−3096.55	−	1787.79i	−0.325468	−	0.187909i	0.328359	−	0.944553i	$-0.393504\pi$
$449$	−3096.55	−	1787.79i	−0.325468	−	0.187909i	−0.653827	+	0.756644i	$0.726838\pi$
$450$		0			0
$451$	−79.0365	+	136.895i	−0.00825207	+	0.0142930i
$452$		0			0
$453$	3801.21	−	2194.63i	0.394252	−	0.227622i
$454$		0			0
$455$	−11939.0	−	8312.41i	−1.23012	−	0.856465i
$456$		0			0
$457$	−6978.95	+	4029.30i	−0.714358	+	0.412435i	−0.812672	−	0.582721i	$-0.801988\pi$
$457$	−6978.95	+	4029.30i	−0.714358	+	0.412435i	0.0983147	+	0.995155i	$0.468655\pi$
$458$		0			0
$459$	−313.651	+	543.260i	−0.0318954	+	0.0552445i
$460$		0			0
$461$	10125.7	+	5846.07i	1.02300	+	0.590626i	0.914970	−	0.403522i	$-0.132214\pi$
$461$	10125.7	+	5846.07i	1.02300	+	0.590626i	0.108025	+	0.994148i	$0.465547\pi$
$462$		0			0
$463$		−	1732.40i		−	0.173891i	−0.996213	−	0.0869455i	$-0.972289\pi$
$463$		−	1732.40i		−	0.173891i	0.996213	−	0.0869455i	$-0.0277106\pi$
$464$		0			0
$465$	1139.87	+	1974.31i	0.113678	+	0.196896i
$466$		0			0
$467$	10769.9			1.06718			0.533588	−	0.845745i	$-0.320843\pi$
$467$	10769.9			1.06718			0.533588	+	0.845745i	$0.320843\pi$
$468$		0			0
$469$	7599.44			0.748208
$470$		0			0
$471$	−99.0636	−	171.583i	−0.00969132	−	0.0167859i
$472$		0			0
$473$			9721.58i			0.945029i
$474$		0			0
$475$	−10919.8	−	6304.57i	−1.05481	−	0.608997i
$476$		0			0
$477$	−1245.99	+	2158.12i	−0.119601	+	0.207156i
$478$		0			0
$479$	−6851.68	+	3955.82i	−0.653572	+	0.377340i	−0.789824	−	0.613334i	$-0.789828\pi$
$479$	−6851.68	+	3955.82i	−0.653572	+	0.377340i	0.136251	+	0.990674i	$0.456495\pi$
$480$		0			0
$481$	6252.37	+	13315.5i	0.592689	+	1.26223i
$482$		0			0
$483$	−5692.17	+	3286.37i	−0.536237	+	0.309597i
$484$		0			0
$485$	11214.7	−	19424.4i	1.04996	−	1.81859i
$486$		0			0
$487$	9495.78	+	5482.39i	0.883562	+	0.510125i	0.871831	−	0.489806i	$-0.162933\pi$
$487$	9495.78	+	5482.39i	0.883562	+	0.510125i	0.0117307	+	0.999931i	$0.496266\pi$
$488$		0			0
$489$			10575.7i			0.978018i
$490$		0			0
$491$	4569.69	+	7914.93i	0.420014	+	0.727486i	0.995940	−	0.0900157i	$-0.0286917\pi$
$491$	4569.69	+	7914.93i	0.420014	+	0.727486i	−0.575926	+	0.817502i	$0.695358\pi$
$492$		0			0
$493$	−53.2204			−0.00486192
$494$		0			0
$495$	4877.16			0.442852
$496$		0			0
$497$	−6378.35	−	11047.6i	−0.575670	−	0.997090i
$498$		0			0
$499$		−	12577.5i		−	1.12835i	−0.825655	−	0.564175i	$-0.809194\pi$
$499$		−	12577.5i		−	1.12835i	0.825655	−	0.564175i	$-0.190806\pi$
$500$		0			0
$501$	−677.193	−	390.978i	−0.0603887	−	0.0348655i
$502$		0			0
$503$	6607.30	−	11444.2i	0.585696	−	1.01446i	−0.409092	−	0.912493i	$-0.634155\pi$
$503$	6607.30	−	11444.2i	0.585696	−	1.01446i	0.994788	−	0.101962i	$-0.0325120\pi$
$504$		0			0
$505$	−27699.6	+	15992.4i	−2.44083	+	1.40921i
$506$		0			0
$507$	−2287.24	−	6181.41i	−0.200355	−	0.541471i
$508$		0			0
$509$	−18809.9	+	10859.9i	−1.63798	+	0.945689i	−0.656454	+	0.754366i	$0.727945\pi$
$509$	−18809.9	+	10859.9i	−1.63798	+	0.945689i	−0.981527	+	0.191323i	$0.938722\pi$
$510$		0			0
$511$	−510.050	+	883.432i	−0.0441551	+	0.0764789i
$512$		0			0
$513$	−1054.08	−	608.572i	−0.0907186	−	0.0523764i
$514$		0			0
$515$			10612.0i			0.907999i
$516$		0			0
$517$	−2825.02	−	4893.07i	−0.240317	−	0.416242i
$518$		0			0
$519$	2735.26			0.231338
$520$		0			0
$521$	−4627.05			−0.389088			−0.194544	−	0.980894i	$-0.562323\pi$
$521$	−4627.05			−0.389088			−0.194544	+	0.980894i	$0.562323\pi$
$522$		0			0
$523$	6891.98	+	11937.3i	0.576224	+	0.998049i	0.995907	+	0.0903788i	$0.0288078\pi$
$523$	6891.98	+	11937.3i	0.576224	+	0.998049i	−0.419683	+	0.907671i	$0.637859\pi$
$524$		0			0
$525$		−	12946.0i		−	1.07621i
$526$		0			0
$527$	−760.040	−	438.809i	−0.0628233	−	0.0362710i
$528$		0			0
$529$	−3999.93	+	6928.07i	−0.328752	+	0.569415i
$530$		0			0
$531$	4233.74	−	2444.35i	0.346005	−	0.199766i
$532$		0			0
$533$	116.907	+	248.974i	0.00950061	+	0.0202331i
$534$		0			0
$535$	−30523.0	+	17622.5i	−2.46659	+	1.42409i
$536$		0			0
$537$	4035.73	−	6990.08i	0.324310	−	0.561721i
$538$		0			0
$539$	2449.01	+	1413.93i	0.195707	+	0.112992i
$540$		0			0
$541$			454.638i			0.0361302i	0.999837	+	0.0180651i	$0.00575061\pi$
$541$			454.638i			0.0361302i	−0.999837	+	0.0180651i	$0.994249\pi$
$542$		0			0
$543$	−7160.77	−	12402.8i	−0.565926	−	0.980213i
$544$		0			0
$545$	19456.0			1.52918
$546$		0			0
$547$	−11611.4			−0.907621			−0.453810	−	0.891098i	$-0.649936\pi$
$547$	−11611.4			−0.907621			−0.453810	+	0.891098i	$0.649936\pi$
$548$		0			0
$549$	−926.047	−	1603.96i	−0.0719904	−	0.124691i
$550$		0			0
$551$		−	103.263i		−	0.00798390i
$552$		0			0
$553$	−4244.00	−	2450.28i	−0.326353	−	0.188420i
$554$		0			0
$555$	−9470.45	+	16403.3i	−0.724321	+	1.25456i
$556$		0			0
$557$	4229.61	−	2441.97i	0.321749	−	0.185762i	−0.330423	−	0.943833i	$-0.607191\pi$
$557$	4229.61	−	2441.97i	0.321749	−	0.185762i	0.652172	+	0.758071i	$0.273858\pi$
$558$		0			0
$559$	13882.6	+	9665.69i	1.05040	+	0.731333i
$560$		0			0
$561$	−1625.99	+	938.766i	−0.122370	+	0.0706501i
$562$		0			0
$563$	−9808.67	+	16989.1i	−0.734256	+	1.27177i	0.220793	+	0.975321i	$0.429136\pi$
$563$	−9808.67	+	16989.1i	−0.734256	+	1.27177i	−0.955049	+	0.296448i	$0.904198\pi$
$564$		0			0
$565$	−33293.3	−	19221.9i	−2.47905	−	1.43128i
$566$		0			0
$567$		−	1249.66i		−	0.0925587i
$568$		0			0
$569$	3737.59	+	6473.70i	0.275374	+	0.476963i	0.970230	−	0.242187i	$-0.0778648\pi$
$569$	3737.59	+	6473.70i	0.275374	+	0.476963i	−0.694855	+	0.719150i	$0.744531\pi$
$570$		0			0
$571$	−7799.56			−0.571631			−0.285816	−	0.958285i	$-0.592265\pi$
$571$	−7799.56			−0.571631			−0.285816	+	0.958285i	$0.592265\pi$
$572$		0			0
$573$	−6172.42			−0.450011
$574$		0			0
$575$	−19860.8	−	34399.9i	−1.44044	−	2.49491i
$576$		0			0
$577$		−	13136.1i		−	0.947771i	−0.880587	−	0.473885i	$-0.842851\pi$
$577$		−	13136.1i		−	0.947771i	0.880587	−	0.473885i	$-0.157149\pi$
$578$		0			0
$579$	1896.27	+	1094.81i	0.136107	+	0.0785816i
$580$		0			0
$581$	−1091.14	+	1889.91i	−0.0779142	+	0.134951i
$582$		0			0
$583$	−6459.29	+	3729.27i	−0.458862	+	0.264924i
$584$		0			0
$585$	4849.12	−	6964.69i	0.342712	−	0.492230i
$586$		0			0
$587$	19183.1	−	11075.3i	1.34884	−	0.778754i	0.360756	−	0.932660i	$-0.382519\pi$
$587$	19183.1	−	11075.3i	1.34884	−	0.778754i	0.988085	+	0.153907i	$0.0491855\pi$
$588$		0			0
$589$	851.414	−	1474.69i	0.0595618	−	0.103164i
$590$		0			0
$591$	4419.63	+	2551.67i	0.307613	+	0.177600i
$592$		0			0
$593$		−	22770.3i		−	1.57684i	−0.615138	−	0.788419i	$-0.710900\pi$
$593$		−	22770.3i		−	1.57684i	0.615138	−	0.788419i	$-0.289100\pi$
$594$		0			0
$595$	3605.47	+	6244.86i	0.248420	+	0.430276i
$596$		0			0
$597$	5522.64			0.378604
$598$		0			0
$599$	7214.11			0.492088			0.246044	−	0.969259i	$-0.420869\pi$
$599$	7214.11			0.492088			0.246044	+	0.969259i	$0.420869\pi$
$600$		0			0
$601$	−13638.4	−	23622.4i	−0.925658	−	1.60329i	−0.790499	−	0.612464i	$-0.790179\pi$
$601$	−13638.4	−	23622.4i	−0.925658	−	1.60329i	−0.135160	−	0.990824i	$-0.543155\pi$
$602$		0			0
$603$			4433.20i			0.299393i
$604$		0			0
$605$	−10547.2	−	6089.41i	−0.708765	−	0.409206i
$606$		0			0
$607$	5783.08	−	10016.6i	0.386701	−	0.669787i	−0.605302	−	0.795996i	$-0.706948\pi$
$607$	5783.08	−	10016.6i	0.386701	−	0.669787i	0.992004	+	0.126209i	$0.0402810\pi$
$608$		0			0
$609$	91.8170	−	53.0106i	0.00610938	−	0.00352725i
$610$		0			0
$611$	−9796.20	−	830.752i	−0.648628	−	0.0550059i
$612$		0			0
$613$	−21197.3	+	12238.3i	−1.39666	+	0.806362i	−0.994041	−	0.109006i	$-0.965233\pi$
$613$	−21197.3	+	12238.3i	−1.39666	+	0.806362i	−0.402619	+	0.915368i	$0.631900\pi$
$614$		0			0
$615$	−177.079	+	306.711i	−0.0116106	+	0.0201102i
$616$		0			0
$617$	2098.62	+	1211.64i	0.136933	+	0.0790581i	0.566901	−	0.823786i	$-0.308142\pi$
$617$	2098.62	+	1211.64i	0.136933	+	0.0790581i	−0.429969	+	0.902844i	$0.641475\pi$
$618$		0			0
$619$		−	17223.4i		−	1.11836i	−0.829045	−	0.559182i	$-0.811115\pi$
$619$		−	17223.4i		−	1.11836i	0.829045	−	0.559182i	$-0.188885\pi$
$620$		0			0
$621$	−1917.14	−	3320.58i	−0.123884	−	0.214573i
$622$		0			0
$623$	9894.22			0.636282
$624$		0			0
$625$	27648.7			1.76952
$626$		0			0
$627$	−1821.47	−	3154.88i	−0.116017	−	0.200947i
$628$		0			0
$629$		−	7291.57i		−	0.462216i
$630$		0			0
$631$	8004.31	+	4621.29i	0.504987	+	0.291554i	0.730771	−	0.682623i	$-0.239161\pi$
$631$	8004.31	+	4621.29i	0.504987	+	0.291554i	−0.225784	+	0.974177i	$0.572494\pi$
$632$		0			0
$633$	−214.455	+	371.447i	−0.0134657	+	0.0233234i
$634$		0			0
$635$	21483.5	−	12403.5i	1.34259	−	0.775147i
$636$		0			0
$637$	4454.06	−	2091.43i	0.277043	−	0.130087i
$638$		0			0
$639$	6444.73	−	3720.87i	0.398982	−	0.230352i
$640$		0			0
$641$	−5799.42	+	10044.9i	−0.357353	+	0.618953i	−0.987518	−	0.157508i	$-0.949654\pi$
$641$	−5799.42	+	10044.9i	−0.357353	+	0.618953i	0.630165	+	0.776461i	$0.282987\pi$
$642$		0			0
$643$	−21965.8	−	12682.0i	−1.34720	−	0.777804i	−0.359345	−	0.933205i	$-0.617000\pi$
$643$	−21965.8	−	12682.0i	−1.34720	−	0.777804i	−0.987852	+	0.155401i	$0.950333\pi$
$644$		0			0
$645$			21781.0i			1.32965i
$646$		0			0
$647$	3295.05	+	5707.19i	0.200219	+	0.346789i	0.948599	−	0.316481i	$-0.102501\pi$
$647$	3295.05	+	5707.19i	0.200219	+	0.346789i	−0.748380	+	0.663270i	$0.769168\pi$
$648$		0			0
$649$	14632.0			0.884985
$650$		0			0
$651$	1748.32			0.105257
$652$		0			0
$653$	−7849.12	−	13595.1i	−0.470382	−	0.814726i	0.529044	−	0.848594i	$-0.322551\pi$
$653$	−7849.12	−	13595.1i	−0.470382	−	0.814726i	−0.999426	+	0.0338683i	$0.989217\pi$
$654$		0			0
$655$			25647.6i			1.52998i
$656$		0			0
$657$	−515.358	−	297.542i	−0.0306028	−	0.0176685i
$658$		0			0
$659$	1420.41	−	2460.22i	0.0839624	−	0.145427i	−0.820986	−	0.570948i	$-0.806576\pi$
$659$	1420.41	−	2460.22i	0.0839624	−	0.145427i	0.904949	+	0.425521i	$0.139909\pi$
$660$		0			0
$661$	18029.9	−	10409.5i	1.06094	−	0.612533i	0.135247	−	0.990812i	$-0.456817\pi$
$661$	18029.9	−	10409.5i	1.06094	−	0.612533i	0.925692	+	0.378279i	$0.123484\pi$
$662$		0			0
$663$	−276.063	+	3255.32i	−0.0161710	+	0.190688i
$664$		0			0
$665$	−12116.8	+	6995.63i	−0.706569	+	0.407938i
$666$		0			0
$667$	162.650	−	281.718i	0.00944202	−	0.0163541i
$668$		0			0
$669$	6076.16	+	3508.07i	0.351148	+	0.202735i
$670$		0			0
$671$		−	5543.36i		−	0.318925i
$672$		0			0
$673$	15632.3	+	27075.9i	0.895364	+	1.55082i	0.833354	+	0.552740i	$0.186418\pi$
$673$	15632.3	+	27075.9i	0.895364	+	1.55082i	0.0620102	+	0.998076i	$0.480249\pi$
$674$		0			0
$675$	7552.16			0.430641
$676$		0			0
$677$	−27953.2			−1.58689			−0.793447	−	0.608639i	$-0.791716\pi$
$677$	−27953.2			−1.58689			−0.793447	+	0.608639i	$0.791716\pi$
$678$		0			0
$679$	−8600.46	−	14896.4i	−0.486090	−	0.841933i
$680$		0			0
$681$			9838.09i			0.553592i
$682$		0			0
$683$	−30059.7	−	17354.9i	−1.68404	−	0.972282i	−0.958926	−	0.283655i	$-0.908453\pi$
$683$	−30059.7	−	17354.9i	−1.68404	−	0.972282i	−0.725116	−	0.688627i	$-0.758214\pi$
$684$		0			0
$685$	20432.4	−	35390.0i	1.13968	−	1.97399i
$686$		0			0
$687$	2971.48	−	1715.59i	0.165021	−	0.0952747i
$688$		0			0
$689$	−1096.67	+	12931.8i	−0.0606381	+	0.715042i
$690$		0			0
$691$	−10271.7	+	5930.39i	−0.565492	+	0.326487i	−0.755347	−	0.655325i	$-0.772532\pi$
$691$	−10271.7	+	5930.39i	−0.565492	+	0.326487i	0.189855	+	0.981812i	$0.439198\pi$
$692$		0			0
$693$	1870.13	−	3239.16i	0.102511	−	0.177555i
$694$		0			0
$695$	−25186.6	−	14541.5i	−1.37465	−	0.793655i
$696$		0			0
$697$		−	136.338i		−	0.00740916i
$698$		0			0
$699$	6357.26	+	11011.1i	0.343996	+	0.595819i
$700$		0			0
$701$	−16100.5			−0.867486			−0.433743	−	0.901037i	$-0.642807\pi$
$701$	−16100.5			−0.867486			−0.433743	+	0.901037i	$0.642807\pi$
$702$		0			0
$703$	14147.7			0.759019
$704$		0			0
$705$	−6329.39	−	10962.8i	−0.338125	−	0.585650i
$706$		0			0
$707$			24528.9i			1.30482i
$708$		0			0
$709$	24651.8	+	14232.7i	1.30581	+	0.753910i	0.981394	−	0.192005i	$-0.0614990\pi$
$709$	24651.8	+	14232.7i	1.30581	+	0.753910i	0.324416	+	0.945915i	$0.394832\pi$
$710$		0			0
$711$	1429.39	−	2475.78i	0.0753957	−	0.130589i
$712$		0			0
$713$	4645.60	−	2682.14i	0.244010	−	0.140879i
$714$		0			0
$715$	22991.8	−	10796.0i	1.20258	−	0.564680i
$716$		0			0
$717$	−8599.70	+	4965.04i	−0.447924	+	0.258609i
$718$		0			0
$719$	13911.0	−	24094.6i	0.721550	−	1.24976i	−0.238829	−	0.971062i	$-0.576763\pi$
$719$	13911.0	−	24094.6i	0.721550	−	1.24976i	0.960378	−	0.278699i	$-0.0899033\pi$
$720$		0			0
$721$	7047.93	+	4069.13i	0.364048	+	0.210183i
$722$		0			0
$723$			17108.6i			0.880049i
$724$		0			0
$725$	320.363	+	554.884i	0.0164110	+	0.0284247i
$726$		0			0
$727$	866.153			0.0441869			0.0220934	−	0.999756i	$-0.492967\pi$
$727$	866.153			0.0441869			0.0220934	+	0.999756i	$0.492967\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−4192.45	−	7261.53i	−0.212125	−	0.367411i
$732$		0			0
$733$			23120.1i			1.16502i	0.812823	+	0.582511i	$0.197930\pi$
$733$			23120.1i			1.16502i	−0.812823	+	0.582511i	$0.802070\pi$
$734$		0			0
$735$	5486.94	+	3167.89i	0.275359	+	0.158979i
$736$		0			0
$737$	−6634.34	+	11491.0i	−0.331586	+	0.574324i
$738$		0			0
$739$	−17983.1	+	10382.6i	−0.895156	+	0.516819i	−0.875626	−	0.482990i	$-0.839551\pi$
$739$	−17983.1	+	10382.6i	−0.895156	+	0.516819i	−0.0195308	+	0.999809i	$0.506217\pi$
$740$		0			0
$741$	−6316.24	−	535.639i	−0.313135	−	0.0265549i
$742$		0			0
$743$	−32039.3	+	18497.9i	−1.58198	+	0.913354i	−0.587405	+	0.809293i	$0.699850\pi$
$743$	−32039.3	+	18497.9i	−1.58198	+	0.913354i	−0.994571	+	0.104061i	$0.966816\pi$
$744$		0			0
$745$	−9719.90	+	16835.4i	−0.477999	+	0.827919i
$746$		0			0
$747$	−1102.50	−	636.526i	−0.0540003	−	0.0311771i
$748$		0			0
$749$			27029.1i			1.31859i
$750$		0			0
$751$	17214.6	+	29816.5i	0.836443	+	1.44876i	0.892851	+	0.450353i	$0.148702\pi$
$751$	17214.6	+	29816.5i	0.836443	+	1.44876i	−0.0564080	+	0.998408i	$0.517965\pi$
$752$		0			0
$753$	11730.7			0.567716
$754$		0			0
$755$	29433.5			1.41880
$756$		0			0
$757$	−2134.44	−	3696.96i	−0.102480	−	0.177501i	0.810226	−	0.586118i	$-0.199345\pi$
$757$	−2134.44	−	3696.96i	−0.102480	−	0.177501i	−0.912706	+	0.408617i	$0.866011\pi$
$758$		0			0
$759$		−	11476.1i		−	0.548820i
$760$		0			0
$761$	6358.45	+	3671.05i	0.302883	+	0.174869i	0.643737	−	0.765247i	$-0.277383\pi$
$761$	6358.45	+	3671.05i	0.302883	+	0.174869i	−0.340854	+	0.940116i	$0.610716\pi$
$762$		0			0
$763$	7460.33	−	12921.7i	0.353974	−	0.613100i
$764$		0			0
$765$	−3642.99	+	2103.28i	−0.172173	+	0.0994044i
$766$		0			0
$767$	14547.9	−	20894.8i	0.684867	−	0.983661i
$768$		0			0
$769$	12755.2	−	7364.23i	0.598134	−	0.345333i	−0.170173	−	0.985414i	$-0.554433\pi$
$769$	12755.2	−	7364.23i	0.598134	−	0.345333i	0.768307	+	0.640081i	$0.221099\pi$
$770$		0			0
$771$	−10459.2	+	18115.9i	−0.488559	+	0.846209i
$772$		0			0
$773$	8606.05	+	4968.71i	0.400437	+	0.231193i	0.686673	−	0.726967i	$-0.259071\pi$
$773$	8606.05	+	4968.71i	0.400437	+	0.231193i	−0.286235	+	0.958159i	$0.592404\pi$
$774$		0			0
$775$			10565.7i			0.489719i
$776$		0			0
$777$	7262.83	+	12579.6i	0.335331	+	0.580811i
$778$		0			0
$779$	264.535			0.0121668
$780$		0			0
$781$	22273.3			1.02049
$782$		0			0
$783$	30.9242	+	53.5623i	0.00141142	+	0.00244465i
$784$		0			0
$785$		−	1328.60i		−	0.0604074i
$786$		0			0
$787$	31441.1	+	18152.5i	1.42408	+	0.822194i	0.996645	−	0.0818508i	$-0.0260831\pi$
$787$	31441.1	+	18152.5i	1.42408	+	0.822194i	0.427437	+	0.904045i	$0.359416\pi$
$788$		0			0
$789$	−422.536	+	731.854i	−0.0190655	+	0.0330224i
$790$		0			0
$791$	−25532.4	+	14741.2i	−1.14770	+	0.662623i
$792$		0			0
$793$	−7916.04	−	5511.49i	−0.354485	−	0.246808i
$794$		0			0
$795$	−14471.9	+	8355.35i	−0.645616	+	0.372747i
$796$		0			0
$797$	−4575.37	+	7924.77i	−0.203347	+	0.352208i	−0.949605	−	0.313449i	$-0.898515\pi$
$797$	−4575.37	+	7924.77i	−0.203347	+	0.352208i	0.746258	+	0.665657i	$0.231849\pi$
$798$		0			0
$799$	4220.29	+	2436.59i	0.186863	+	0.107885i
$800$		0			0
$801$			5771.88i			0.254606i
$802$		0			0
$803$	−890.550	−	1542.48i	−0.0391368	−	0.0677869i
$804$		0			0
$805$	−44075.5			−1.92976
$806$		0			0
$807$	−12999.4			−0.567038
$808$		0			0
$809$	−15174.9	−	26283.8i	−0.659484	−	1.14226i	−0.980749	−	0.195271i	$-0.937441\pi$
$809$	−15174.9	−	26283.8i	−0.659484	−	1.14226i	0.321265	−	0.946989i	$-0.395892\pi$
$810$		0			0
$811$		−	4238.72i		−	0.183529i	−0.995781	−	0.0917643i	$-0.970749\pi$
$811$		−	4238.72i		−	0.183529i	0.995781	−	0.0917643i	$-0.0292506\pi$
$812$		0			0
$813$	−1113.53	−	642.894i	−0.0480357	−	0.0277334i
$814$		0			0
$815$	−35459.3	+	61417.3i	−1.52403	+	2.63970i
$816$		0			0
$817$	14089.4	−	8134.53i	0.603337	−	0.348337i
$818$		0			0
$819$	−2766.22	−	5891.13i	−0.118021	−	0.251346i
$820$		0			0
$821$	−5139.41	+	2967.24i	−0.218473	+	0.126136i	−0.605243	−	0.796041i	$-0.706924\pi$
$821$	−5139.41	+	2967.24i	−0.218473	+	0.126136i	0.386770	+	0.922176i	$0.373591\pi$
$822$		0			0
$823$	11229.8	−	19450.6i	0.475633	−	0.823820i	−0.523978	−	0.851732i	$-0.675552\pi$
$823$	11229.8	−	19450.6i	0.475633	−	0.823820i	0.999610	+	0.0279120i	$0.00888582\pi$
$824$		0			0
$825$	19575.4	+	11301.9i	0.826096	+	0.476947i
$826$		0			0
$827$		−	20138.4i		−	0.846772i	−0.905949	−	0.423386i	$-0.860841\pi$
$827$		−	20138.4i		−	0.846772i	0.905949	−	0.423386i	$-0.139159\pi$
$828$		0			0
$829$	2922.85	+	5062.53i	0.122455	+	0.212098i	0.920735	−	0.390188i	$-0.127590\pi$
$829$	2922.85	+	5062.53i	0.122455	+	0.212098i	−0.798281	+	0.602286i	$0.794257\pi$
$830$		0			0
$831$	26816.2			1.11943
$832$		0			0
$833$	−2439.05			−0.101450
$834$		0			0
$835$	−2621.82	−	4541.12i	−0.108661	−	0.188206i
$836$		0			0
$837$			1019.90i			0.0421180i
$838$		0			0
$839$	−24058.1	−	13889.9i	−0.989961	−	0.571554i	−0.0846986	−	0.996407i	$-0.526993\pi$
$839$	−24058.1	−	13889.9i	−0.989961	−	0.571554i	−0.905263	+	0.424852i	$0.860326\pi$
$840$		0			0
$841$	12191.9	−	21116.9i	0.499892	−	0.865839i
$842$		0			0
$843$	−2015.64	+	1163.73i	−0.0823514	+	0.0475456i
$844$		0			0
$845$	7442.75	−	43566.7i	0.303004	−	1.77366i
$846$		0			0
$847$	−8088.55	+	4669.92i	−0.328130	+	0.189446i
$848$		0			0
$849$	−6021.80	+	10430.1i	−0.243425	+	0.421624i
$850$		0			0
$851$	38597.3	+	22284.2i	1.55476	+	0.897640i
$852$		0			0
$853$			16480.5i			0.661526i	0.943714	+	0.330763i	$0.107306\pi$
$853$			16480.5i			0.661526i	−0.943714	+	0.330763i	$0.892694\pi$
$854$		0			0
$855$	−4080.96	−	7068.43i	−0.163235	−	0.282731i
$856$		0			0
$857$	45445.2			1.81141			0.905704	−	0.423910i	$-0.139343\pi$
$857$	45445.2			1.81141			0.905704	+	0.423910i	$0.139343\pi$
$858$		0			0
$859$	28243.1			1.12182			0.560909	−	0.827877i	$-0.310452\pi$
$859$	28243.1			1.12182			0.560909	+	0.827877i	$0.310452\pi$
$860$		0			0
$861$	135.801	+	235.214i	0.00537524	+	0.00931020i
$862$		0			0
$863$		−	328.319i		−	0.0129503i	−0.999979	−	0.00647514i	$-0.997939\pi$
$863$		−	328.319i		−	0.0129503i	0.999979	−	0.00647514i	$-0.00206112\pi$
$864$		0			0
$865$	15884.7	+	9171.05i	0.624389	+	0.360491i
$866$		0			0
$867$	−6559.81	+	11361.9i	−0.256958	+	0.445065i
$868$		0			0
$869$	7410.06	−	4278.20i	0.289262	−	0.167006i
$870$		0			0
$871$	9813.24	+	20898.9i	0.381755	+	0.813012i
$872$		0			0
$873$	8689.96	−	5017.15i	0.336897	−	0.194507i
$874$		0			0
$875$	24008.5	−	41584.0i	0.927584	−	1.60662i
$876$		0			0
$877$	36788.7	+	21240.0i	1.41650	+	0.817815i	0.995989	−	0.0894746i	$-0.0285188\pi$
$877$	36788.7	+	21240.0i	1.41650	+	0.817815i	0.420507	+	0.907289i	$0.361852\pi$
$878$		0			0
$879$			14868.6i			0.570542i
$880$		0			0
$881$	−2610.47	−	4521.47i	−0.0998287	−	0.172908i	0.811785	−	0.583956i	$-0.198496\pi$
$881$	−2610.47	−	4521.47i	−0.0998287	−	0.172908i	−0.911614	+	0.411048i	$0.865163\pi$
$882$		0			0
$883$	11790.3			0.449349			0.224674	−	0.974434i	$-0.427868\pi$
$883$	11790.3			0.449349			0.224674	+	0.974434i	$0.427868\pi$
$884$		0			0
$885$	32782.6			1.24517
$886$		0			0
$887$	−24676.2	−	42740.4i	−0.934097	−	1.61790i	−0.776236	−	0.630443i	$-0.782873\pi$
$887$	−24676.2	−	42740.4i	−0.934097	−	1.61790i	−0.157861	−	0.987461i	$-0.550460\pi$
$888$		0			0
$889$		−	19024.4i		−	0.717724i
$890$		0			0
$891$	1889.59	+	1090.96i	0.0710480	+	0.0410196i
$892$		0			0
$893$	−4727.67	+	8188.56i	−0.177162	+	0.306853i
$894$		0			0
$895$	46874.1	−	27062.8i	1.75065	−	1.01074i
$896$		0			0
$897$	−16388.1	−	11410.1i	−0.610013	−	0.424717i
$898$		0			0
$899$	−74.9355	+	43.2640i	−0.00278002	+	0.00160505i
$900$		0			0
$901$	3216.51	−	5571.16i	0.118932	−	0.205996i
$902$		0			0
$903$	14465.8	+	8351.84i	0.533103	+	0.307787i
$904$		0			0
$905$		−	96037.3i		−	3.52750i
$906$		0			0
$907$	−3044.47	−	5273.17i	−0.111455	−	0.193046i	0.804902	−	0.593408i	$-0.202218\pi$
$907$	−3044.47	−	5273.17i	−0.111455	−	0.193046i	−0.916357	+	0.400362i	$0.868884\pi$
$908$		0			0
$909$	−14309.2			−0.522118
$910$		0			0
$911$	30301.7			1.10202			0.551010	−	0.834499i	$-0.314243\pi$
$911$	30301.7			1.10202			0.551010	+	0.834499i	$0.314243\pi$
$912$		0			0
$913$	−1905.14	−	3299.80i	−0.0690590	−	0.119614i
$914$		0			0
$915$		−	12419.8i		−	0.448726i
$916$		0			0
$917$	17033.8	+	9834.49i	0.613421	+	0.354159i
$918$		0			0
$919$	17347.9	−	30047.4i	0.622692	−	1.07853i	−0.366290	−	0.930501i	$-0.619372\pi$
$919$	17347.9	−	30047.4i	0.622692	−	1.07853i	0.988982	−	0.148034i	$-0.0472945\pi$
$920$		0			0
$921$	−10119.3	+	5842.36i	−0.362042	+	0.209025i
$922$		0			0
$923$	22145.2	−	31806.7i	0.789728	−	1.13427i
$924$		0			0
$925$	−76023.1	+	43892.0i	−2.70230	+	1.56017i
$926$		0			0
$927$	−2373.76	+	4111.47i	−0.0841041	+	0.145673i
$928$		0			0
$929$	−14714.5	−	8495.40i	−0.519662	−	0.300027i	0.217134	−	0.976142i	$-0.430329\pi$
$929$	−14714.5	−	8495.40i	−0.519662	−	0.300027i	−0.736796	+	0.676115i	$0.763662\pi$
$930$		0			0
$931$		−	4732.44i		−	0.166594i
$932$		0			0
$933$	4646.16	+	8047.38i	0.163032	+	0.282379i
$934$		0			0
$935$	−12590.3			−0.440372
$936$		0			0
$937$	9307.86			0.324519			0.162260	−	0.986748i	$-0.448122\pi$
$937$	9307.86			0.324519			0.162260	+	0.986748i	$0.448122\pi$
$938$		0			0
$939$	6731.04	+	11658.5i	0.233929	+	0.405177i
$940$		0			0
$941$		−	52285.3i		−	1.81132i	−0.424006	−	0.905659i	$-0.639377\pi$
$941$		−	52285.3i		−	1.81132i	0.424006	−	0.905659i	$-0.360623\pi$
$942$		0			0
$943$	721.697	+	416.672i	0.0249222	+	0.0143889i
$944$		0			0
$945$	4189.98	−	7257.26i	0.144233	−	0.249819i
$946$		0			0
$947$	−10694.1	+	6174.26i	−0.366962	+	0.211865i	−0.672130	−	0.740433i	$-0.734621\pi$
$947$	−10694.1	+	6174.26i	−0.366962	+	0.211865i	0.305169	+	0.952298i	$0.401287\pi$
$948$		0			0
$949$	−3088.13	−	261.884i	−0.105632	−	0.00895797i
$950$		0			0
$951$	17720.5	−	10230.9i	0.604233	−	0.348854i
$952$		0			0
$953$	−12815.5	+	22197.1i	−0.435609	+	0.754497i	−0.997345	−	0.0728193i	$-0.976800\pi$
$953$	−12815.5	+	22197.1i	−0.435609	+	0.754497i	0.561736	+	0.827317i	$0.310134\pi$
$954$		0			0
$955$	−35845.7	−	20695.5i	−1.21459	−	0.701247i
$956$		0			0
$957$			185.114i			0.00625274i
$958$		0			0
$959$	−15669.5	−	27140.4i	−0.527627	−	0.913878i
$960$		0			0
$961$	28364.1			0.952104
$962$		0			0
$963$	−15767.7			−0.527629
$964$		0			0
$965$	7341.57	+	12716.0i	0.244905	+	0.424188i
$966$		0			0
$967$		−	11185.6i		−	0.371981i	−0.982552	−	0.185991i	$-0.940451\pi$
$967$		−	11185.6i		−	0.371981i	0.982552	−	0.185991i	$-0.0595494\pi$
$968$		0			0
$969$	2721.09	+	1571.02i	0.0902106	+	0.0520831i
$970$		0			0
$971$	−11770.6	+	20387.3i	−0.389019	+	0.673801i	−0.992318	−	0.123714i	$-0.960519\pi$
$971$	−11770.6	+	20387.3i	−0.389019	+	0.673801i	0.603299	+	0.797515i	$0.293853\pi$
$972$		0			0
$973$	−19315.4	+	11151.8i	−0.636408	+	0.367430i
$974$		0			0
$975$	35602.3	−	16717.3i	1.16942	−	0.549109i
$976$		0			0
$977$	−20956.8	+	12099.4i	−0.686251	+	0.396207i	−0.802206	−	0.597047i	$-0.796341\pi$
$977$	−20956.8	+	12099.4i	−0.686251	+	0.396207i	0.115955	+	0.993254i	$0.463007\pi$
$978$		0			0
$979$	−8637.68	+	14960.9i	−0.281983	+	0.488409i
$980$		0			0
$981$	7537.97	+	4352.05i	0.245330	+	0.141641i
$982$		0			0
$983$			33757.4i			1.09532i	0.836702	+	0.547658i	$0.184480\pi$
$983$			33757.4i			1.09532i	−0.836702	+	0.547658i	$0.815520\pi$
$984$		0			0
$985$	17111.0	+	29637.1i	0.553504	+	0.958697i
$986$		0			0
$987$	−9707.93			−0.313077
$988$		0			0
$989$	51251.1			1.64782
$990$		0			0
$991$	12649.3	+	21909.2i	0.405466	+	0.702288i	0.994376	−	0.105911i	$-0.0337758\pi$
$991$	12649.3	+	21909.2i	0.405466	+	0.702288i	−0.588909	+	0.808199i	$0.700442\pi$
$992$		0			0
$993$		−	15038.9i		−	0.480608i
$994$		0			0
$995$	32072.1	+	18516.8i	1.02186	+	0.589973i
$996$		0			0
$997$	14383.0	−	24912.2i	0.456886	−	0.791350i	−0.541908	−	0.840438i	$-0.682298\pi$
$997$	14383.0	−	24912.2i	0.456886	−	0.791350i	0.998794	+	0.0490874i	$0.0156313\pi$
$998$		0			0
$999$	−7338.41	+	4236.83i	−0.232409	+	0.134182i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.4.bv.h.49.5		10
4.3	odd	2		39.4.j.c.10.5	yes	10
12.11	even	2		117.4.q.e.10.1		10
13.4	even	6	inner	624.4.bv.h.433.1		10
52.3	odd	6		507.4.b.i.337.9		10
52.11	even	12		507.4.a.r.1.2		10
52.15	even	12		507.4.a.r.1.9		10
52.23	odd	6		507.4.b.i.337.2		10
52.43	odd	6		39.4.j.c.4.5	✓	10
156.11	odd	12		1521.4.a.bk.1.9		10
156.95	even	6		117.4.q.e.82.1		10
156.119	odd	12		1521.4.a.bk.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.c.4.5	✓	10	52.43	odd	6
39.4.j.c.10.5	yes	10	4.3	odd	2
117.4.q.e.10.1		10	12.11	even	2
117.4.q.e.82.1		10	156.95	even	6
507.4.a.r.1.2		10	52.11	even	12
507.4.a.r.1.9		10	52.15	even	12
507.4.b.i.337.2		10	52.23	odd	6
507.4.b.i.337.9		10	52.3	odd	6
624.4.bv.h.49.5		10	1.1	even	1	trivial
624.4.bv.h.433.1		10	13.4	even	6	inner
1521.4.a.bk.1.2		10	156.119	odd	12
1521.4.a.bk.1.9		10	156.11	odd	12

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	624.bv (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{3} +20.1174i q^{5} +(13.3609 + 7.71395i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 2.59808i) q^{3} +20.1174i q^{5} +(13.3609 + 7.71395i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-23.3283 + 13.4686i) q^{11} +(-3.96071 + 46.7045i) q^{13} +(-52.2665 + 30.1761i) q^{15} +(11.6167 - 20.1207i) q^{17} +(39.0399 + 22.5397i) q^{19} +46.2837i q^{21} +(71.0050 + 122.984i) q^{23} -279.710 q^{25} -27.0000 q^{27} +(-1.14534 - 1.98379i) q^{29} -37.7740i q^{31} +(-69.9849 - 40.4058i) q^{33} +(-155.185 + 268.787i) q^{35} +(271.793 - 156.920i) q^{37} +(-127.283 + 59.7666i) q^{39} +(5.08201 - 2.93410i) q^{41} +(180.449 - 312.547i) q^{43} +(-156.800 - 90.5283i) q^{45} +209.748i q^{47} +(-52.4900 - 90.9154i) q^{49} +69.7003 q^{51} +276.886 q^{53} +(-270.953 - 469.305i) q^{55} +135.238i q^{57} +(-470.415 - 271.594i) q^{59} +(-102.894 + 178.218i) q^{61} +(-120.249 + 69.4255i) q^{63} +(-939.573 - 79.6791i) q^{65} +(426.585 - 246.289i) q^{67} +(-213.015 + 368.953i) q^{69} +(-716.081 - 413.430i) q^{71} +66.1205i q^{73} +(-419.564 - 726.707i) q^{75} -415.584 q^{77} -317.642 q^{79} +(-40.5000 - 70.1481i) q^{81} +141.450i q^{83} +(404.777 + 233.698i) q^{85} +(3.43602 - 5.95136i) q^{87} +(555.399 - 320.660i) q^{89} +(-413.195 + 593.464i) q^{91} +(98.1396 - 56.6609i) q^{93} +(-453.440 + 785.381i) q^{95} +(-965.551 - 557.461i) q^{97} -242.435i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9}+O(q^{10}) \) 10 * q + 15 * q^3 - 30 * q^7 - 45 * q^9	\( 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9} - 60 q^{11} + 25 q^{13} - 45 q^{15} + 105 q^{17} - 180 q^{19} + 60 q^{23} - 960 q^{25} - 270 q^{27} - 495 q^{29} - 180 q^{33} - 60 q^{35} - 405 q^{37} - 345 q^{39} + 1065 q^{41} + 370 q^{43} - 135 q^{45} + 775 q^{49} + 630 q^{51} + 330 q^{53} + 260 q^{55} - 780 q^{59} - 1375 q^{61} + 270 q^{63} + 1605 q^{65} - 1590 q^{67} - 180 q^{69} - 1620 q^{71} - 1440 q^{75} - 4320 q^{77} - 1100 q^{79} - 405 q^{81} + 525 q^{85} + 1485 q^{87} + 2040 q^{89} - 4770 q^{91} - 990 q^{93} + 1380 q^{95} - 3750 q^{97}+O(q^{100}) \) 10 * q + 15 * q^3 - 30 * q^7 - 45 * q^9 - 60 * q^11 + 25 * q^13 - 45 * q^15 + 105 * q^17 - 180 * q^19 + 60 * q^23 - 960 * q^25 - 270 * q^27 - 495 * q^29 - 180 * q^33 - 60 * q^35 - 405 * q^37 - 345 * q^39 + 1065 * q^41 + 370 * q^43 - 135 * q^45 + 775 * q^49 + 630 * q^51 + 330 * q^53 + 260 * q^55 - 780 * q^59 - 1375 * q^61 + 270 * q^63 + 1605 * q^65 - 1590 * q^67 - 180 * q^69 - 1620 * q^71 - 1440 * q^75 - 4320 * q^77 - 1100 * q^79 - 405 * q^81 + 525 * q^85 + 1485 * q^87 + 2040 * q^89 - 4770 * q^91 - 990 * q^93 + 1380 * q^95 - 3750 * q^97

Introduction

L-functions

Modular forms

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