LMFDB - Embedded newform 144.5.m.a.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,5,Mod(19,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("144.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	144.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.8852746841$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + \cdots + 2097152 $ x^14 - 4x^13 + 15x^12 - 34x^11 + 62x^10 - 312x^9 + 1432x^8 - 4960x^7 + 11456x^6 - 19968x^5 + 31744x^4 - 139264x^3 + 491520x^2 - 1048576*x + 2097152
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{21} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.6
Root			$0.153862 - 2.82424i$ of defining polynomial
Character	$\chi$	$=$	144.19
Dual form			144.5.m.a.91.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.97810 + 2.67038i) q^{2} +(1.73818 + 15.9053i) q^{4} +(2.84710 - 2.84710i) q^{5} -76.7794 q^{7} +(-37.2967 + 52.0092i) q^{8} +O(q^{10})$	\(q+(2.97810 + 2.67038i) q^{2} +(1.73818 + 15.9053i) q^{4} +(2.84710 - 2.84710i) q^{5} -76.7794 q^{7} +(-37.2967 + 52.0092i) q^{8} +(16.0818 - 0.876123i) q^{10} +(-121.488 - 121.488i) q^{11} +(27.1604 + 27.1604i) q^{13} +(-228.657 - 205.030i) q^{14} +(-249.957 + 55.2924i) q^{16} +88.0613 q^{17} +(-261.112 + 261.112i) q^{19} +(50.2328 + 40.3352i) q^{20} +(-37.3847 - 686.220i) q^{22} -93.4210 q^{23} +608.788i q^{25} +(8.35791 + 153.415i) q^{26} +(-133.456 - 1221.20i) q^{28} +(-272.522 - 272.522i) q^{29} -1232.20i q^{31} +(-892.050 - 502.814i) q^{32} +(262.256 + 235.157i) q^{34} +(-218.599 + 218.599i) q^{35} +(-1046.16 + 1046.16i) q^{37} +(-1474.89 + 80.3506i) q^{38} +(41.8880 + 254.263i) q^{40} -915.267i q^{41} +(1116.82 + 1116.82i) q^{43} +(1721.13 - 2143.47i) q^{44} +(-278.217 - 249.469i) q^{46} +1720.70i q^{47} +3494.07 q^{49} +(-1625.69 + 1813.03i) q^{50} +(-384.784 + 479.203i) q^{52} +(-734.019 + 734.019i) q^{53} -691.775 q^{55} +(2863.62 - 3993.23i) q^{56} +(-83.8616 - 1539.33i) q^{58} +(1202.73 + 1202.73i) q^{59} +(580.221 + 580.221i) q^{61} +(3290.44 - 3669.61i) q^{62} +(-1313.91 - 3879.54i) q^{64} +154.657 q^{65} +(-1483.97 + 1483.97i) q^{67} +(153.066 + 1400.64i) q^{68} +(-1234.75 + 67.2681i) q^{70} -5571.73 q^{71} +6615.21i q^{73} +(-5909.20 + 321.929i) q^{74} +(-4606.93 - 3699.21i) q^{76} +(9327.75 + 9327.75i) q^{77} +5391.66i q^{79} +(-554.231 + 869.077i) q^{80} +(2444.11 - 2725.76i) q^{82} +(2554.07 - 2554.07i) q^{83} +(250.719 - 250.719i) q^{85} +(343.673 + 6308.34i) q^{86} +(10849.6 - 1787.39i) q^{88} +10962.7i q^{89} +(-2085.35 - 2085.35i) q^{91} +(-162.382 - 1485.89i) q^{92} +(-4594.92 + 5124.42i) q^{94} +1486.83i q^{95} +4713.20 q^{97} +(10405.7 + 9330.48i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} + 92 q^{8}+O(q^{10}) $ 14 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 + 92 * q^8	$ 14 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} + 92 q^{8} - 100 q^{10} - 94 q^{11} - 2 q^{13} - 44 q^{14} - 168 q^{16} + 4 q^{17} - 706 q^{19} - 1900 q^{20} + 900 q^{22} - 1148 q^{23} + 3416 q^{26} - 3784 q^{28} - 862 q^{29} - 3208 q^{32} + 7508 q^{34} - 1340 q^{35} - 1826 q^{37} - 3568 q^{38} - 5144 q^{40} + 1694 q^{43} + 14636 q^{44} - 5316 q^{46} + 682 q^{49} - 20070 q^{50} + 20452 q^{52} + 482 q^{53} - 11780 q^{55} + 6952 q^{56} - 20456 q^{58} + 2786 q^{59} - 3778 q^{61} + 11472 q^{62} + 15808 q^{64} + 2020 q^{65} + 7998 q^{67} - 18032 q^{68} + 15296 q^{70} - 19964 q^{71} + 23780 q^{74} - 23996 q^{76} + 9508 q^{77} - 1384 q^{80} + 16016 q^{82} + 17282 q^{83} + 9948 q^{85} + 4796 q^{86} + 7288 q^{88} - 28036 q^{91} + 14632 q^{92} + 432 q^{94} - 4 q^{97} + 12246 q^{98}+O(q^{100}) $ 14 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 + 92 * q^8 - 100 * q^10 - 94 * q^11 - 2 * q^13 - 44 * q^14 - 168 * q^16 + 4 * q^17 - 706 * q^19 - 1900 * q^20 + 900 * q^22 - 1148 * q^23 + 3416 * q^26 - 3784 * q^28 - 862 * q^29 - 3208 * q^32 + 7508 * q^34 - 1340 * q^35 - 1826 * q^37 - 3568 * q^38 - 5144 * q^40 + 1694 * q^43 + 14636 * q^44 - 5316 * q^46 + 682 * q^49 - 20070 * q^50 + 20452 * q^52 + 482 * q^53 - 11780 * q^55 + 6952 * q^56 - 20456 * q^58 + 2786 * q^59 - 3778 * q^61 + 11472 * q^62 + 15808 * q^64 + 2020 * q^65 + 7998 * q^67 - 18032 * q^68 + 15296 * q^70 - 19964 * q^71 + 23780 * q^74 - 23996 * q^76 + 9508 * q^77 - 1384 * q^80 + 16016 * q^82 + 17282 * q^83 + 9948 * q^85 + 4796 * q^86 + 7288 * q^88 - 28036 * q^91 + 14632 * q^92 + 432 * q^94 - 4 * q^97 + 12246 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	2.97810	+	2.67038i	0.744525	+	0.667594i
$2$	2.97810	+	2.67038i	0.744525	+	0.667594i
$3$		0			0
$3$		0			0
$4$	1.73818	+	15.9053i	0.108636	+	0.994082i
$5$	2.84710	−	2.84710i	0.113884	−	0.113884i	−0.647868	−	0.761752i	$-0.724339\pi$
$5$	2.84710	−	2.84710i	0.113884	−	0.113884i	0.761752	+	0.647868i	$0.224339\pi$
$6$		0			0
$7$	−76.7794			−1.56693			−0.783463	−	0.621439i	$-0.786549\pi$
$7$	−76.7794			−1.56693			−0.783463	+	0.621439i	$0.786549\pi$
$8$	−37.2967	+	52.0092i	−0.582761	+	0.812644i
$9$		0			0
$10$	16.0818	−	0.876123i	0.160818	−	0.00876123i
$11$	−121.488	−	121.488i	−1.00403	−	1.00403i	−0.999992	−	0.00403849i	$-0.998715\pi$
$11$	−121.488	−	121.488i	−1.00403	−	1.00403i	−0.00403849	−	0.999992i	$-0.501285\pi$
$12$		0			0
$13$	27.1604	+	27.1604i	0.160712	+	0.160712i	0.782882	−	0.622170i	$-0.213749\pi$
$13$	27.1604	+	27.1604i	0.160712	+	0.160712i	−0.622170	+	0.782882i	$0.713749\pi$
$14$	−228.657	−	205.030i	−1.16662	−	1.04607i
$15$		0			0
$16$	−249.957	+	55.2924i	−0.976396	+	0.215986i
$17$	88.0613			0.304710			0.152355	−	0.988326i	$-0.451314\pi$
$17$	88.0613			0.304710			0.152355	+	0.988326i	$0.451314\pi$
$18$		0			0
$19$	−261.112	+	261.112i	−0.723302	+	0.723302i	−0.969276	−	0.245974i	$-0.920892\pi$
$19$	−261.112	+	261.112i	−0.723302	+	0.723302i	0.245974	+	0.969276i	$0.420892\pi$
$20$	50.2328	+	40.3352i	0.125582	+	0.100838i
$21$		0			0
$22$	−37.3847	−	686.220i	−0.0772412	−	1.41781i
$23$	−93.4210			−0.176599			−0.0882996	−	0.996094i	$-0.528143\pi$
$23$	−93.4210			−0.176599			−0.0882996	+	0.996094i	$0.528143\pi$
$24$		0			0
$25$			608.788i			0.974061i
$26$	8.35791	+	153.415i	0.0123638	+	0.226945i
$27$		0			0
$28$	−133.456	−	1221.20i	−0.170224	−	1.55765i
$29$	−272.522	−	272.522i	−0.324045	−	0.324045i	0.526272	−	0.850316i	$-0.323590\pi$
$29$	−272.522	−	272.522i	−0.324045	−	0.324045i	−0.850316	+	0.526272i	$0.823590\pi$
$30$		0			0
$31$		−	1232.20i		−	1.28220i	−0.767455	−	0.641102i	$-0.778477\pi$
$31$		−	1232.20i		−	1.28220i	0.767455	−	0.641102i	$-0.221523\pi$
$32$	−892.050	−	502.814i	−0.871143	−	0.491030i
$33$		0			0
$34$	262.256	+	235.157i	0.226865	+	0.203423i
$35$	−218.599	+	218.599i	−0.178448	+	0.178448i
$36$		0			0
$37$	−1046.16	+	1046.16i	−0.764177	+	0.764177i	−0.977075	−	0.212898i	$-0.931710\pi$
$37$	−1046.16	+	1046.16i	−0.764177	+	0.764177i	0.212898	+	0.977075i	$0.431710\pi$
$38$	−1474.89	+	80.3506i	−1.02139	+	0.0556445i
$39$		0			0
$40$	41.8880	+	254.263i	0.0261800	+	0.158914i
$41$		−	915.267i		−	0.544478i	−0.962230	−	0.272239i	$-0.912236\pi$
$41$		−	915.267i		−	0.544478i	0.962230	−	0.272239i	$-0.0877641\pi$
$42$		0			0
$43$	1116.82	+	1116.82i	0.604013	+	0.604013i	0.941375	−	0.337362i	$-0.109535\pi$
$43$	1116.82	+	1116.82i	0.604013	+	0.604013i	−0.337362	+	0.941375i	$0.609535\pi$
$44$	1721.13	−	2143.47i	0.889014	−	1.10716i
$45$		0			0
$46$	−278.217	−	249.469i	−0.131483	−	0.117897i
$47$			1720.70i			0.778949i	0.921037	+	0.389475i	$0.127343\pi$
$47$			1720.70i			0.778949i	−0.921037	+	0.389475i	$0.872657\pi$
$48$		0			0
$49$	3494.07			1.45526
$50$	−1625.69	+	1813.03i	−0.650277	+	0.725213i
$51$		0			0
$52$	−384.784	+	479.203i	−0.142302	+	0.177220i
$53$	−734.019	+	734.019i	−0.261310	+	0.261310i	−0.825586	−	0.564276i	$-0.809155\pi$
$53$	−734.019	+	734.019i	−0.261310	+	0.261310i	0.564276	+	0.825586i	$0.309155\pi$
$54$		0			0
$55$	−691.775			−0.228686
$56$	2863.62	−	3993.23i	0.913143	−	1.27335i
$57$		0			0
$58$	−83.8616	−	1539.33i	−0.0249291	−	0.457590i
$59$	1202.73	+	1202.73i	0.345512	+	0.345512i	0.858435	−	0.512923i	$-0.171437\pi$
$59$	1202.73	+	1202.73i	0.345512	+	0.345512i	−0.512923	+	0.858435i	$0.671437\pi$
$60$		0			0
$61$	580.221	+	580.221i	0.155932	+	0.155932i	0.780761	−	0.624830i	$-0.214832\pi$
$61$	580.221	+	580.221i	0.155932	+	0.155932i	−0.624830	+	0.780761i	$0.714832\pi$
$62$	3290.44	−	3669.61i	0.855993	−	0.954634i
$63$		0			0
$64$	−1313.91	−	3879.54i	−0.320779	−	0.947154i
$65$	154.657			0.0366051
$66$		0			0
$67$	−1483.97	+	1483.97i	−0.330580	+	0.330580i	−0.852807	−	0.522227i	$-0.825101\pi$
$67$	−1483.97	+	1483.97i	−0.330580	+	0.330580i	0.522227	+	0.852807i	$0.325101\pi$
$68$	153.066	+	1400.64i	0.0331025	+	0.302907i
$69$		0			0
$70$	−1234.75	+	67.2681i	−0.251990	+	0.0137282i
$71$	−5571.73			−1.10528			−0.552641	−	0.833419i	$-0.686380\pi$
$71$	−5571.73			−1.10528			−0.552641	+	0.833419i	$0.686380\pi$
$72$		0			0
$73$			6615.21i			1.24136i	0.784064	+	0.620681i	$0.213144\pi$
$73$			6615.21i			1.24136i	−0.784064	+	0.620681i	$0.786856\pi$
$74$	−5909.20	+	321.929i	−1.07911	+	0.0587890i
$75$		0			0
$76$	−4606.93	−	3699.21i	−0.797598	−	0.640445i
$77$	9327.75	+	9327.75i	1.57324	+	1.57324i
$78$		0			0
$79$			5391.66i			0.863910i	0.901895	+	0.431955i	$0.142176\pi$
$79$			5391.66i			0.863910i	−0.901895	+	0.431955i	$0.857824\pi$
$80$	−554.231	+	869.077i	−0.0865986	+	0.135793i
$81$		0			0
$82$	2444.11	−	2725.76i	0.363490	−	0.405378i
$83$	2554.07	−	2554.07i	0.370747	−	0.370747i	−0.497002	−	0.867749i	$-0.665566\pi$
$83$	2554.07	−	2554.07i	0.370747	−	0.370747i	0.867749	+	0.497002i	$0.165566\pi$
$84$		0			0
$85$	250.719	−	250.719i	0.0347017	−	0.0347017i
$86$	343.673	+	6308.34i	0.0464674	+	0.852939i
$87$		0			0
$88$	10849.6	−	1787.39i	1.40103	−	0.230809i
$89$			10962.7i			1.38400i	0.721898	+	0.691999i	$0.243270\pi$
$89$			10962.7i			1.38400i	−0.721898	+	0.691999i	$0.756730\pi$
$90$		0			0
$91$	−2085.35	−	2085.35i	−0.251824	−	0.251824i
$92$	−162.382	−	1485.89i	−0.0191850	−	0.175554i
$93$		0			0
$94$	−4594.92	+	5124.42i	−0.520022	+	0.579948i
$95$			1486.83i			0.164745i
$96$		0			0
$97$	4713.20			0.500925			0.250462	−	0.968126i	$-0.419417\pi$
$97$	4713.20			0.500925			0.250462	+	0.968126i	$0.419417\pi$
$98$	10405.7	+	9330.48i	1.08347	+	0.971520i
$99$		0			0
$100$	−9682.96	+	1058.18i	−0.968296	+	0.105818i
$101$	11381.0	−	11381.0i	1.11568	−	1.11568i	0.123307	−	0.992369i	$-0.460650\pi$
$101$	11381.0	−	11381.0i	1.11568	−	1.11568i	0.992369	−	0.123307i	$-0.0393499\pi$
$102$		0			0
$103$	175.758			0.0165668			0.00828342	−	0.999966i	$-0.497363\pi$
$103$	175.758			0.0165668			0.00828342	+	0.999966i	$0.497363\pi$
$104$	−2425.58	+	399.597i	−0.224258	+	0.0369450i
$105$		0			0
$106$	−4146.09	+	225.876i	−0.369000	+	0.0201028i
$107$	−15151.8	−	15151.8i	−1.32342	−	1.32342i	−0.910988	−	0.412432i	$-0.864679\pi$
$107$	−15151.8	−	15151.8i	−1.32342	−	1.32342i	−0.412432	−	0.910988i	$-0.635321\pi$
$108$		0			0
$109$	−2349.51	−	2349.51i	−0.197754	−	0.197754i	0.601283	−	0.799036i	$-0.294657\pi$
$109$	−2349.51	−	2349.51i	−0.197754	−	0.197754i	−0.799036	+	0.601283i	$0.794657\pi$
$110$	−2060.18	−	1847.30i	−0.170263	−	0.152669i
$111$		0			0
$112$	19191.6	−	4245.32i	1.52994	−	0.338434i
$113$	8526.30			0.667734			0.333867	−	0.942620i	$-0.391646\pi$
$113$	8526.30			0.667734			0.333867	+	0.942620i	$0.391646\pi$
$114$		0			0
$115$	−265.979	+	265.979i	−0.0201118	+	0.0201118i
$116$	3860.85	−	4808.23i	0.286924	−	0.357330i
$117$		0			0
$118$	370.108	+	6793.57i	0.0265806	+	0.487904i
$119$	−6761.29			−0.477459
$120$		0			0
$121$			14877.5i			1.01615i
$122$	178.548	+	3277.37i	0.0119960	+	0.220194i
$123$		0			0
$124$	19598.5	−	2141.78i	1.27462	−	0.139294i
$125$	3512.72	+	3512.72i	0.224814	+	0.224814i
$126$		0			0
$127$		−	2844.31i		−	0.176347i	−0.996105	−	0.0881737i	$-0.971897\pi$
$127$		−	2844.31i		−	0.176347i	0.996105	−	0.0881737i	$-0.0281031\pi$
$128$	6446.87	−	15062.3i	0.393486	−	0.919331i
$129$		0			0
$130$	460.583	+	412.991i	0.0272534	+	0.0244373i
$131$	6989.87	−	6989.87i	0.407311	−	0.407311i	−0.473489	−	0.880800i	$-0.657006\pi$
$131$	6989.87	−	6989.87i	0.407311	−	0.407311i	0.880800	+	0.473489i	$0.157006\pi$
$132$		0			0
$133$	20048.0	−	20048.0i	1.13336	−	1.13336i
$134$	−8382.19	+	456.655i	−0.466818	+	0.0254319i
$135$		0			0
$136$	−3284.40	+	4580.00i	−0.177573	+	0.247621i
$137$			3669.69i			0.195519i	0.995210	+	0.0977594i	$0.0311676\pi$
$137$			3669.69i			0.195519i	−0.995210	+	0.0977594i	$0.968832\pi$
$138$		0			0
$139$	4401.33	+	4401.33i	0.227800	+	0.227800i	0.811773	−	0.583973i	$-0.198503\pi$
$139$	4401.33	+	4401.33i	0.227800	+	0.227800i	−0.583973	+	0.811773i	$0.698503\pi$
$140$	−3856.84	−	3096.91i	−0.196778	−	0.158006i
$141$		0			0
$142$	−16593.2	−	14878.6i	−0.822911	−	0.737880i
$143$		−	6599.30i		−	0.322720i
$144$		0			0
$145$	−1551.79			−0.0738071
$146$	−17665.1	+	19700.8i	−0.828725	+	0.924225i
$147$		0			0
$148$	−18457.9	−	14821.1i	−0.842671	−	0.676637i
$149$	−15737.5	+	15737.5i	−0.708863	+	0.708863i	−0.966296	−	0.257433i	$-0.917123\pi$
$149$	−15737.5	+	15737.5i	−0.708863	+	0.708863i	0.257433	+	0.966296i	$0.417123\pi$
$150$		0			0
$151$	−41972.2			−1.84080			−0.920402	−	0.390974i	$-0.872138\pi$
$151$	−41972.2			−1.84080			−0.920402	+	0.390974i	$0.872138\pi$
$152$	−3841.61	−	23318.9i	−0.166275	−	1.00930i
$153$		0			0
$154$	2870.38	+	52687.6i	0.121031	+	2.22160i
$155$	−3508.19	−	3508.19i	−0.146023	−	0.146023i
$156$		0			0
$157$	−24735.4	−	24735.4i	−1.00351	−	1.00351i	−0.999994	−	0.00351271i	$-0.998882\pi$
$157$	−24735.4	−	24735.4i	−1.00351	−	1.00351i	−0.00351271	−	0.999994i	$-0.501118\pi$
$158$	−14397.8	+	16056.9i	−0.576741	+	0.643203i
$159$		0			0
$160$	−3971.32	+	1108.19i	−0.155130	+	0.0432888i
$161$	7172.80			0.276718
$162$		0			0
$163$	24429.8	−	24429.8i	0.919483	−	0.919483i	−0.0775084	−	0.996992i	$-0.524696\pi$
$163$	24429.8	−	24429.8i	0.919483	−	0.919483i	0.996992	+	0.0775084i	$0.0246965\pi$
$164$	14557.6	−	1590.90i	0.541255	−	0.0591499i
$165$		0			0
$166$	14426.6	−	785.951i	0.523539	−	0.0285220i
$167$	−52178.2			−1.87093			−0.935463	−	0.353425i	$-0.885017\pi$
$167$	−52178.2			−1.87093			−0.935463	+	0.353425i	$0.885017\pi$
$168$		0			0
$169$		−	27085.6i		−	0.948343i
$170$	1416.18	−	77.1525i	0.0490029	−	0.00266964i
$171$		0			0
$172$	−15822.1	+	19704.6i	−0.534821	+	0.666056i
$173$	−26316.2	−	26316.2i	−0.879289	−	0.879289i	0.114172	−	0.993461i	$-0.463578\pi$
$173$	−26316.2	−	26316.2i	−0.879289	−	0.879289i	−0.993461	+	0.114172i	$0.963578\pi$
$174$		0			0
$175$		−	46742.4i		−	1.52628i
$176$	37084.1	+	23649.4i	1.19719	+	0.763475i
$177$		0			0
$178$	−29274.4	+	32647.9i	−0.923949	+	1.03042i
$179$	−4815.78	+	4815.78i	−0.150301	+	0.150301i	−0.778252	−	0.627952i	$-0.783894\pi$
$179$	−4815.78	+	4815.78i	−0.150301	+	0.150301i	0.627952	+	0.778252i	$0.283894\pi$
$180$		0			0
$181$	−23924.9	+	23924.9i	−0.730286	+	0.730286i	−0.970676	−	0.240391i	$-0.922724\pi$
$181$	−23924.9	+	23924.9i	−0.730286	+	0.730286i	0.240391	+	0.970676i	$0.422724\pi$
$182$	−641.715	−	11779.1i	−0.0193731	−	0.355606i
$183$		0			0
$184$	3484.29	−	4858.75i	0.102915	−	0.143512i
$185$			5957.04i			0.174055i
$186$		0			0
$187$	−10698.4	−	10698.4i	−0.305939	−	0.305939i
$188$	−27368.2	+	2990.88i	−0.774339	+	0.0846219i
$189$		0			0
$190$	−3970.38	+	4427.92i	−0.109983	+	0.122657i
$191$		−	45079.4i		−	1.23569i	−0.786298	−	0.617847i	$-0.788005\pi$
$191$		−	45079.4i		−	1.23569i	0.786298	−	0.617847i	$-0.211995\pi$
$192$		0			0
$193$	50286.0			1.34999			0.674997	−	0.737820i	$-0.264145\pi$
$193$	50286.0			1.34999			0.674997	+	0.737820i	$0.264145\pi$
$194$	14036.4	+	12586.0i	0.372951	+	0.334415i
$195$		0			0
$196$	6073.31	+	55574.2i	0.158093	+	1.44664i
$197$	25662.2	−	25662.2i	0.661243	−	0.661243i	−0.294430	−	0.955673i	$-0.595130\pi$
$197$	25662.2	−	25662.2i	0.661243	−	0.661243i	0.955673	+	0.294430i	$0.0951297\pi$
$198$		0			0
$199$	−44599.1			−1.12621			−0.563106	−	0.826385i	$-0.690394\pi$
$199$	−44599.1			−1.12621			−0.563106	+	0.826385i	$0.690394\pi$
$200$	−31662.6	−	22705.8i	−0.791564	−	0.567645i
$201$		0			0
$202$	64285.4	−	3502.21i	1.57547	−	0.0858302i
$203$	20924.0	+	20924.0i	0.507754	+	0.507754i
$204$		0			0
$205$	−2605.86	−	2605.86i	−0.0620073	−	0.0620073i
$206$	523.424	+	469.339i	0.0123344	+	0.0110599i
$207$		0			0
$208$	−8290.70	−	5287.17i	−0.191630	−	0.122207i
$209$	63443.8			1.45244
$210$		0			0
$211$	25828.5	−	25828.5i	0.580143	−	0.580143i	−0.354800	−	0.934942i	$-0.615451\pi$
$211$	25828.5	−	25828.5i	0.580143	−	0.580143i	0.934942	+	0.354800i	$0.115451\pi$
$212$	−12950.6	−	10398.9i	−0.288151	−	0.231375i
$213$		0			0
$214$	−4662.59	−	85584.8i	−0.101812	−	1.86883i
$215$	6359.40			0.137575
$216$		0			0
$217$			94607.4i			2.00912i
$218$	−723.003	−	13271.2i	−0.0152134	−	0.279252i
$219$		0			0
$220$	−1202.43	−	11002.9i	−0.0248435	−	0.227333i
$221$	2391.78	+	2391.78i	0.0489707	+	0.0489707i
$222$		0			0
$223$			72650.0i			1.46092i	0.682957	+	0.730459i	$0.260694\pi$
$223$			72650.0i			1.46092i	−0.682957	+	0.730459i	$0.739306\pi$
$224$	68491.1	+	38605.8i	1.36502	+	0.769407i
$225$		0			0
$226$	25392.2	+	22768.4i	0.497145	+	0.445776i
$227$	−18858.2	+	18858.2i	−0.365972	+	0.365972i	−0.866006	−	0.500034i	$-0.833321\pi$
$227$	−18858.2	+	18858.2i	−0.365972	+	0.365972i	0.500034	+	0.866006i	$0.333321\pi$
$228$		0			0
$229$	41675.9	−	41675.9i	0.794721	−	0.794721i	−0.187537	−	0.982258i	$-0.560050\pi$
$229$	41675.9	−	41675.9i	0.794721	−	0.794721i	0.982258	+	0.187537i	$0.0600504\pi$
$230$	−1502.38	+	81.8483i	−0.0284003	+	0.00154723i
$231$		0			0
$232$	24337.8	−	4009.48i	0.452174	−	0.0744923i
$233$			2767.61i			0.0509792i	0.999675	+	0.0254896i	$0.00811447\pi$
$233$			2767.61i			0.0509792i	−0.999675	+	0.0254896i	$0.991886\pi$
$234$		0			0
$235$	4899.00	+	4899.00i	0.0887099	+	0.0887099i
$236$	−17039.2	+	21220.3i	−0.305932	+	0.381002i
$237$		0			0
$238$	−20135.8	−	18055.2i	−0.355480	−	0.318749i
$239$			49981.8i			0.875016i	0.899215	+	0.437508i	$0.144139\pi$
$239$			49981.8i			0.875016i	−0.899215	+	0.437508i	$0.855861\pi$
$240$		0			0
$241$	−44076.0			−0.758872			−0.379436	−	0.925218i	$-0.623882\pi$
$241$	−44076.0			−0.758872			−0.379436	+	0.925218i	$0.623882\pi$
$242$	−39728.6	+	44306.7i	−0.678378	+	0.756552i
$243$		0			0
$244$	−8220.07	+	10237.1i	−0.138069	+	0.171948i
$245$	9947.97	−	9947.97i	0.165730	−	0.165730i
$246$		0			0
$247$	−14183.8			−0.232487
$248$	64085.7	+	45957.0i	1.04198	+	0.747219i
$249$		0			0
$250$	1080.95	+	19841.5i	0.0172952	+	0.317464i
$251$	31786.2	+	31786.2i	0.504534	+	0.504534i	0.912844	−	0.408309i	$-0.133881\pi$
$251$	31786.2	+	31786.2i	0.504534	+	0.504534i	−0.408309	+	0.912844i	$0.633881\pi$
$252$		0			0
$253$	11349.5	+	11349.5i	0.177311	+	0.177311i
$254$	7595.38	−	8470.64i	0.117729	−	0.131295i
$255$		0			0
$256$	59421.5	−	27641.5i	0.906700	−	0.421776i
$257$	−70865.6			−1.07292			−0.536462	−	0.843924i	$-0.680240\pi$
$257$	−70865.6			−1.07292			−0.536462	+	0.843924i	$0.680240\pi$
$258$		0			0
$259$	80323.4	−	80323.4i	1.19741	−	1.19741i
$260$	268.820	+	2459.86i	0.00397663	+	0.0363885i
$261$		0			0
$262$	39482.1	−	2150.95i	0.575172	−	0.0313349i
$263$	113289.			1.63786			0.818929	−	0.573894i	$-0.194568\pi$
$263$	113289.			1.63786			0.818929	+	0.573894i	$0.194568\pi$
$264$		0			0
$265$			4179.65i			0.0595180i
$266$	113241.	−	6169.27i	1.60044	−	0.0871908i
$267$		0			0
$268$	−26182.5	−	21023.6i	−0.364536	−	0.292711i
$269$	−70652.7	−	70652.7i	−0.976393	−	0.976393i	0.0233352	−	0.999728i	$-0.492572\pi$
$269$	−70652.7	−	70652.7i	−0.976393	−	0.976393i	−0.999728	+	0.0233352i	$0.992572\pi$
$270$		0			0
$271$			110180.i			1.50025i	0.661294	+	0.750126i	$0.270007\pi$
$271$			110180.i			1.50025i	−0.661294	+	0.750126i	$0.729993\pi$
$272$	−22011.6	+	4869.12i	−0.297518	+	0.0658132i
$273$		0			0
$274$	−9799.47	+	10928.7i	−0.130527	+	0.145569i
$275$	73960.2	−	73960.2i	0.977987	−	0.977987i
$276$		0			0
$277$	34611.0	−	34611.0i	0.451081	−	0.451081i	−0.444632	−	0.895713i	$-0.646666\pi$
$277$	34611.0	−	34611.0i	0.451081	−	0.451081i	0.895713	+	0.444632i	$0.146666\pi$
$278$	1354.40	+	24860.8i	0.0175249	+	0.321681i
$279$		0			0
$280$	−3216.13	−	19522.1i	−0.0410221	−	0.249007i
$281$			147980.i			1.87408i	0.349216	+	0.937042i	$0.386448\pi$
$281$			147980.i			1.87408i	−0.349216	+	0.937042i	$0.613552\pi$
$282$		0			0
$283$	39761.2	+	39761.2i	0.496463	+	0.496463i	0.910335	−	0.413872i	$-0.135824\pi$
$283$	39761.2	+	39761.2i	0.496463	+	0.496463i	−0.413872	+	0.910335i	$0.635824\pi$
$284$	−9684.65	−	88620.1i	−0.120073	−	1.09874i
$285$		0			0
$286$	17622.6	−	19653.4i	0.215446	−	0.240273i
$287$			70273.6i			0.853156i
$288$		0			0
$289$	−75766.2			−0.907152
$290$	−4621.40	−	4143.87i	−0.0549512	−	0.0492732i
$291$		0			0
$292$	−105217.	+	11498.4i	−1.23401	+	0.134856i
$293$	708.909	−	708.909i	0.00825763	−	0.00825763i	−0.702966	−	0.711224i	$-0.748141\pi$
$293$	708.909	−	708.909i	0.00825763	−	0.00825763i	0.711224	+	0.702966i	$0.248141\pi$
$294$		0			0
$295$	6848.56			0.0786965
$296$	−15391.6	−	93428.1i	−0.175671	−	1.06634i
$297$		0			0
$298$	−88892.8	+	4842.81i	−1.00100	+	0.0545337i
$299$	−2537.35	−	2537.35i	−0.0283816	−	0.0283816i
$300$		0			0
$301$	−85748.8	−	85748.8i	−0.946444	−	0.946444i
$302$	−124997.	−	112081.i	−1.37052	−	1.22891i
$303$		0			0
$304$	50829.4	−	79704.5i	0.550007	−	0.862453i
$305$	3303.90			0.0355162
$306$		0			0
$307$	−20597.1	+	20597.1i	−0.218539	+	0.218539i	−0.807883	−	0.589344i	$-0.799386\pi$
$307$	−20597.1	+	20597.1i	−0.218539	+	0.218539i	0.589344	+	0.807883i	$0.299386\pi$
$308$	−132147.	+	164574.i	−1.39302	+	1.73484i
$309$		0			0
$310$	−1079.56	−	19816.0i	−0.0112337	−	0.206201i
$311$	−82310.6			−0.851011			−0.425505	−	0.904956i	$-0.639904\pi$
$311$	−82310.6			−0.851011			−0.425505	+	0.904956i	$0.639904\pi$
$312$		0			0
$313$			120415.i			1.22911i	0.788872	+	0.614557i	$0.210665\pi$
$313$			120415.i			1.22911i	−0.788872	+	0.614557i	$0.789335\pi$
$314$	−7611.70	−	139718.i	−0.0772009	−	1.41707i
$315$		0			0
$316$	−85756.0	+	9371.65i	−0.858797	+	0.0938517i
$317$	−14795.3	−	14795.3i	−0.147233	−	0.147233i	0.629648	−	0.776881i	$-0.283199\pi$
$317$	−14795.3	−	14795.3i	−0.147233	−	0.147233i	−0.776881	+	0.629648i	$0.783199\pi$
$318$		0			0
$319$			66216.1i			0.650702i
$320$	−14786.3	−	7304.61i	−0.144397	−	0.0713340i
$321$		0			0
$322$	21361.3	+	19154.1i	0.206023	+	0.184735i
$323$	−22993.9	+	22993.9i	−0.220398	+	0.220398i
$324$		0			0
$325$	−16534.9	+	16534.9i	−0.156543	+	0.156543i
$326$	137991.	−	7517.63i	1.29842	−	0.0707369i
$327$		0			0
$328$	47602.3	+	34136.4i	0.442467	+	0.317300i
$329$		−	132114.i		−	1.22056i
$330$		0			0
$331$	82868.2	+	82868.2i	0.756366	+	0.756366i	0.975659	−	0.219293i	$-0.0703752\pi$
$331$	82868.2	+	82868.2i	0.756366	+	0.756366i	−0.219293	+	0.975659i	$0.570375\pi$
$332$	45062.8	+	36183.9i	0.408829	+	0.328276i
$333$		0			0
$334$	−155392.	−	139336.i	−1.39295	−	1.24902i
$335$			8450.04i			0.0752955i
$336$		0			0
$337$	78854.4			0.694331			0.347165	−	0.937804i	$-0.387144\pi$
$337$	78854.4			0.694331			0.347165	+	0.937804i	$0.387144\pi$
$338$	72328.8	−	80663.8i	0.633108	−	0.706066i
$339$		0			0
$340$	4423.56	+	3551.98i	0.0382661	+	0.0307264i
$341$	−149697.	+	149697.i	−1.28737	+	1.28737i
$342$		0			0
$343$	−83925.2			−0.713352
$344$	−99738.7	+	16431.2i	−0.842843	+	0.138852i
$345$		0			0
$346$	−8098.15	−	148647.i	−0.0676447	−	1.24166i
$347$	59543.0	+	59543.0i	0.494506	+	0.494506i	0.909723	−	0.415216i	$-0.136294\pi$
$347$	59543.0	+	59543.0i	0.494506	+	0.494506i	−0.415216	+	0.909723i	$0.636294\pi$
$348$		0			0
$349$	−756.172	−	756.172i	−0.00620826	−	0.00620826i	0.703996	−	0.710204i	$-0.251397\pi$
$349$	−756.172	−	756.172i	−0.00620826	−	0.00620826i	−0.710204	+	0.703996i	$0.751397\pi$
$350$	124820.	−	139203.i	1.01894	−	1.13635i
$351$		0			0
$352$	47287.4	+	169459.i	0.381645	+	1.36766i
$353$	−23723.5			−0.190384			−0.0951918	−	0.995459i	$-0.530346\pi$
$353$	−23723.5			−0.190384			−0.0951918	+	0.995459i	$0.530346\pi$
$354$		0			0
$355$	−15863.3	+	15863.3i	−0.125874	+	0.125874i
$356$	−174364.	+	19055.0i	−1.37581	+	0.150352i
$357$		0			0
$358$	−27201.8	+	1481.93i	−0.212242	+	0.0115628i
$359$	−146064.			−1.13333			−0.566663	−	0.823950i	$-0.691766\pi$
$359$	−146064.			−1.13333			−0.566663	+	0.823950i	$0.691766\pi$
$360$		0			0
$361$		−	6038.12i		−	0.0463327i
$362$	−135139.	+	7362.28i	−1.03125	+	0.0561817i
$363$		0			0
$364$	29543.5	−	36792.9i	0.222976	−	0.277691i
$365$	18834.2	+	18834.2i	0.141371	+	0.141371i
$366$		0			0
$367$		−	151129.i		−	1.12206i	−0.827797	−	0.561028i	$-0.810406\pi$
$367$		−	151129.i		−	1.12206i	0.827797	−	0.561028i	$-0.189594\pi$
$368$	23351.3	−	5165.47i	0.172431	−	0.0381430i
$369$		0			0
$370$	−15907.5	+	17740.7i	−0.116198	+	0.129588i
$371$	56357.5	−	56357.5i	0.409453	−	0.409453i
$372$		0			0
$373$	26207.7	−	26207.7i	0.188370	−	0.188370i	−0.606621	−	0.794991i	$-0.707476\pi$
$373$	26207.7	−	26207.7i	0.188370	−	0.188370i	0.794991	+	0.606621i	$0.207476\pi$
$374$	−3292.15	−	60429.5i	−0.0235362	−	0.432022i
$375$		0			0
$376$	−89492.2	−	64176.4i	−0.633008	−	0.453941i
$377$		−	14803.6i		−	0.104156i
$378$		0			0
$379$	110424.	+	110424.i	0.768752	+	0.768752i	0.977887	−	0.209135i	$-0.0670647\pi$
$379$	110424.	+	110424.i	0.768752	+	0.768752i	−0.209135	+	0.977887i	$0.567065\pi$
$380$	−23648.4	+	2584.36i	−0.163770	+	0.0178973i
$381$		0			0
$382$	120379.	−	134251.i	0.824942	−	0.920006i
$383$		−	10514.9i		−	0.0716819i	−0.999358	−	0.0358409i	$-0.988589\pi$
$383$		−	10514.9i		−	0.0716819i	0.999358	−	0.0358409i	$-0.0114110\pi$
$384$		0			0
$385$	53114.1			0.358334
$386$	149757.	+	134282.i	1.00511	+	0.901249i
$387$		0			0
$388$	8192.37	+	74964.9i	0.0544185	+	0.497960i
$389$	166762.	−	166762.i	1.10204	−	1.10204i	0.107877	−	0.994164i	$-0.465595\pi$
$389$	166762.	−	166762.i	1.10204	−	1.10204i	0.994164	−	0.107877i	$-0.0344054\pi$
$390$		0			0
$391$	−8226.78			−0.0538116
$392$	−130317.	+	181724.i	−0.848066	+	1.18260i
$393$		0			0
$394$	144952.	−	7896.89i	0.933755	−	0.0508702i
$395$	15350.6	+	15350.6i	0.0983855	+	0.0983855i
$396$		0			0
$397$	−192542.	−	192542.i	−1.22164	−	1.22164i	−0.967048	−	0.254594i	$-0.918058\pi$
$397$	−192542.	−	192542.i	−1.22164	−	1.22164i	−0.254594	−	0.967048i	$-0.581942\pi$
$398$	−132821.	−	119096.i	−0.838494	−	0.751853i
$399$		0			0
$400$	−33661.4	−	152171.i	−0.210384	−	0.951070i
$401$	−91157.6			−0.566897			−0.283448	−	0.958987i	$-0.591478\pi$
$401$	−91157.6			−0.566897			−0.283448	+	0.958987i	$0.591478\pi$
$402$		0			0
$403$	33467.0	−	33467.0i	0.206066	−	0.206066i
$404$	200801.	+	161236.i	1.23027	+	0.987870i
$405$		0			0
$406$	6438.84	+	118189.i	0.0390621	+	0.717010i
$407$	254191.			1.53451
$408$		0			0
$409$		−	107774.i		−	0.644272i	−0.946693	−	0.322136i	$-0.895599\pi$
$409$		−	107774.i		−	0.644272i	0.946693	−	0.322136i	$-0.104401\pi$
$410$	−801.887	−	14719.1i	−0.00477029	−	0.0875618i
$411$		0			0
$412$	305.497	+	2795.48i	0.00179975	+	0.0164688i
$413$	−92344.5	−	92344.5i	−0.541391	−	0.541391i
$414$		0			0
$415$		−	14543.4i		−	0.0844442i
$416$	−10571.8	−	37885.0i	−0.0610888	−	0.218918i
$417$		0			0
$418$	188942.	+	169419.i	1.08137	+	0.969637i
$419$	118524.	−	118524.i	0.675115	−	0.675115i	−0.283776	−	0.958891i	$-0.591587\pi$
$419$	118524.	−	118524.i	0.675115	−	0.675115i	0.958891	+	0.283776i	$0.0915871\pi$
$420$		0			0
$421$	−226616.	+	226616.i	−1.27858	+	1.27858i	−0.337113	+	0.941464i	$0.609451\pi$
$421$	−226616.	+	226616.i	−1.27858	+	1.27858i	−0.941464	+	0.337113i	$0.890549\pi$
$422$	145892.	−	7948.08i	0.819231	−	0.0446310i
$423$		0			0
$424$	−10799.2	−	65552.2i	−0.0600706	−	0.364633i
$425$			53610.7i			0.296807i
$426$		0			0
$427$	−44549.0	−	44549.0i	−0.244333	−	0.244333i
$428$	214658.	−	267331.i	1.17182	−	1.45936i
$429$		0			0
$430$	18938.9	+	16982.0i	0.102428	+	0.0918442i
$431$			5397.51i			0.0290562i	0.999894	+	0.0145281i	$0.00462460\pi$
$431$			5397.51i			0.0290562i	−0.999894	+	0.0145281i	$0.995375\pi$
$432$		0			0
$433$	163835.			0.873840			0.436920	−	0.899500i	$-0.356069\pi$
$433$	163835.			0.873840			0.436920	+	0.899500i	$0.356069\pi$
$434$	−252638.	+	281751.i	−1.34128	+	1.49584i
$435$		0			0
$436$	33285.9	−	41453.6i	0.175100	−	0.218067i
$437$	24393.4	−	24393.4i	0.127735	−	0.127735i
$438$		0			0
$439$	158472.			0.822289			0.411144	−	0.911570i	$-0.365129\pi$
$439$	158472.			0.822289			0.411144	+	0.911570i	$0.365129\pi$
$440$	25800.9	−	35978.7i	0.133269	−	0.185840i
$441$		0			0
$442$	736.008	+	13509.9i	0.00376737	+	0.0691524i
$443$	137929.	+	137929.i	0.702826	+	0.702826i	0.965016	−	0.262190i	$-0.0844448\pi$
$443$	137929.	+	137929.i	0.702826	+	0.702826i	−0.262190	+	0.965016i	$0.584445\pi$
$444$		0			0
$445$	31211.8	+	31211.8i	0.157615	+	0.157615i
$446$	−194003.	+	216359.i	−0.975300	+	1.08769i
$447$		0			0
$448$	100881.	+	297869.i	0.502638	+	1.48412i
$449$	−327336.			−1.62368			−0.811841	−	0.583879i	$-0.801534\pi$
$449$	−327336.			−1.62368			−0.811841	+	0.583879i	$0.801534\pi$
$450$		0			0
$451$	−111194.	+	111194.i	−0.546672	+	0.546672i
$452$	14820.2	+	135613.i	0.0725400	+	0.663782i
$453$		0			0
$454$	−106520.	+	5803.13i	−0.516797	+	0.0281547i
$455$	−11874.4			−0.0573575
$456$		0			0
$457$			154510.i			0.739817i	0.929068	+	0.369909i	$0.120611\pi$
$457$			154510.i			0.739817i	−0.929068	+	0.369909i	$0.879389\pi$
$458$	235406.	−	12824.7i	1.12224	−	0.0611388i
$459$		0			0
$460$	−4692.80	−	3768.16i	−0.0221777	−	0.0178079i
$461$	−19296.3	−	19296.3i	−0.0907971	−	0.0907971i	0.660249	−	0.751046i	$-0.270451\pi$
$461$	−19296.3	−	19296.3i	−0.0907971	−	0.0907971i	−0.751046	+	0.660249i	$0.770451\pi$
$462$		0			0
$463$			26503.6i			0.123635i	0.998087	+	0.0618176i	$0.0196897\pi$
$463$			26503.6i			0.123635i	−0.998087	+	0.0618176i	$0.980310\pi$
$464$	83187.2	+	53050.5i	0.386385	+	0.246407i
$465$		0			0
$466$	−7390.56	+	8242.22i	−0.0340334	+	0.0379553i
$467$	−111797.	+	111797.i	−0.512622	+	0.512622i	−0.915329	−	0.402707i	$-0.868069\pi$
$467$	−111797.	+	111797.i	−0.512622	+	0.512622i	0.402707	+	0.915329i	$0.368069\pi$
$468$		0			0
$469$	113939.	−	113939.i	0.517994	−	0.517994i
$470$	1507.54	+	27671.9i	0.00682455	+	0.125269i
$471$		0			0
$472$	−107411.	+	17695.1i	−0.482129	+	0.0794272i
$473$		−	271360.i		−	1.21290i
$474$		0			0
$475$	−158962.	−	158962.i	−0.704541	−	0.704541i
$476$	−11752.3	−	107540.i	−0.0518692	−	0.474633i
$477$		0			0
$478$	−133470.	+	148851.i	−0.584155	+	0.651471i
$479$			225380.i			0.982301i	0.871075	+	0.491150i	$0.163423\pi$
$479$			225380.i			0.982301i	−0.871075	+	0.491150i	$0.836577\pi$
$480$		0			0
$481$	−56828.1			−0.245625
$482$	−131263.	−	117700.i	−0.564999	−	0.506618i
$483$		0			0
$484$	−236631.	+	25859.7i	−1.01014	+	0.110391i
$485$	13419.0	−	13419.0i	0.0570473	−	0.0570473i
$486$		0			0
$487$	8483.58			0.0357702			0.0178851	−	0.999840i	$-0.494307\pi$
$487$	8483.58			0.0357702			0.0178851	+	0.999840i	$0.494307\pi$
$488$	−51817.2	+	8536.50i	−0.217588	+	0.0358460i
$489$		0			0
$490$	56190.9	−	3061.23i	0.234031	−	0.0127498i
$491$	−69265.0	−	69265.0i	−0.287310	−	0.287310i	0.548706	−	0.836016i	$-0.315121\pi$
$491$	−69265.0	−	69265.0i	−0.287310	−	0.287310i	−0.836016	+	0.548706i	$0.815121\pi$
$492$		0			0
$493$	−23998.6	−	23998.6i	−0.0987399	−	0.0987399i
$494$	−42240.8	−	37876.1i	−0.173092	−	0.155207i
$495$		0			0
$496$	68131.3	+	307997.i	0.276938	+	1.25194i
$497$	427794.			1.73190
$498$		0			0
$499$	86869.4	−	86869.4i	0.348872	−	0.348872i	−0.510817	−	0.859689i	$-0.670657\pi$
$499$	86869.4	−	86869.4i	0.348872	−	0.348872i	0.859689	+	0.510817i	$0.170657\pi$
$500$	−49765.1	+	61976.6i	−0.199061	+	0.247906i
$501$		0			0
$502$	9781.39	+	179544.i	0.0388144	+	0.712463i
$503$	−112271.			−0.443745			−0.221872	−	0.975076i	$-0.571217\pi$
$503$	−112271.			−0.443745			−0.221872	+	0.975076i	$0.571217\pi$
$504$		0			0
$505$		−	64805.7i		−	0.254115i
$506$	3492.52	+	64107.4i	0.0136407	+	0.250384i
$507$		0			0
$508$	45239.6	−	4943.91i	0.175304	−	0.0191577i
$509$	167589.	+	167589.i	0.646861	+	0.646861i	0.952233	−	0.305372i	$-0.0987808\pi$
$509$	167589.	+	167589.i	0.646861	+	0.646861i	−0.305372	+	0.952233i	$0.598781\pi$
$510$		0			0
$511$		−	507912.i		−	1.94512i
$512$	250776.	+	76358.6i	0.956636	+	0.291285i
$513$		0			0
$514$	−211045.	−	189238.i	−0.798820	−	0.716278i
$515$	500.399	−	500.399i	0.00188670	−	0.00188670i
$516$		0			0
$517$	209044.	−	209044.i	0.782089	−	0.782089i
$518$	453705.	−	24717.5i	1.69088	−	0.0921180i
$519$		0			0
$520$	−5768.18	+	8043.56i	−0.0213320	+	0.0297469i
$521$			287463.i			1.05903i	0.848302	+	0.529513i	$0.177625\pi$
$521$			287463.i			1.05903i	−0.848302	+	0.529513i	$0.822375\pi$
$522$		0			0
$523$	−203069.	−	203069.i	−0.742404	−	0.742404i	0.230636	−	0.973040i	$-0.425919\pi$
$523$	−203069.	−	203069.i	−0.742404	−	0.742404i	−0.973040	+	0.230636i	$0.925919\pi$
$524$	123326.	+	99026.4i	0.449149	+	0.360652i
$525$		0			0
$526$	337386.	+	302524.i	1.21943	+	1.09343i
$527$		−	108509.i		−	0.390701i
$528$		0			0
$529$	−271114.			−0.968813
$530$	−11161.2	+	12447.4i	−0.0397339	+	0.0443126i
$531$		0			0
$532$	353717.	+	284023.i	1.24978	+	1.00353i
$533$	24859.0	−	24859.0i	0.0875042	−	0.0875042i
$534$		0			0
$535$	−86277.6			−0.301433
$536$	−21833.0	−	132528.i	−0.0759946	−	0.461293i
$537$		0			0
$538$	−21741.6	−	399080.i	−0.0751150	−	1.37878i
$539$	−424486.	−	424486.i	−1.46112	−	1.46112i
$540$		0			0
$541$	308972.	+	308972.i	1.05566	+	1.05566i	0.998357	+	0.0573036i	$0.0182503\pi$
$541$	308972.	+	308972.i	1.05566	+	1.05566i	0.0573036	+	0.998357i	$0.481750\pi$
$542$	−294222.	+	328127.i	−1.00156	+	1.11698i
$543$		0			0
$544$	−78555.1	−	44278.5i	−0.265446	−	0.149622i
$545$	−13378.6			−0.0450420
$546$		0			0
$547$	−8623.13	+	8623.13i	−0.0288198	+	0.0288198i	−0.721370	−	0.692550i	$-0.756487\pi$
$547$	−8623.13	+	8623.13i	−0.0288198	+	0.0288198i	0.692550	+	0.721370i	$0.256487\pi$
$548$	−58367.6	+	6378.57i	−0.194362	+	0.0212404i
$549$		0			0
$550$	417763.	−	22759.4i	1.38103	−	0.0752376i
$551$	142317.			0.468765
$552$		0			0
$553$		−	413968.i		−	1.35368i
$554$	195499.	−	10650.6i	0.636980	−	0.0347022i
$555$		0			0
$556$	−62354.2	+	77654.8i	−0.201705	+	0.251199i
$557$	208785.	+	208785.i	0.672961	+	0.672961i	0.958398	−	0.285437i	$-0.0921387\pi$
$557$	208785.	+	208785.i	0.672961	+	0.672961i	−0.285437	+	0.958398i	$0.592139\pi$
$558$		0			0
$559$			60666.5i			0.194145i
$560$	42553.5	−	66727.2i	0.135694	−	0.212778i
$561$		0			0
$562$	−395161.	+	440698.i	−1.25113	+	1.39530i
$563$	−127891.	+	127891.i	−0.403480	+	0.403480i	−0.879458	−	0.475977i	$-0.842094\pi$
$563$	−127891.	+	127891.i	−0.403480	+	0.403480i	0.475977	+	0.879458i	$0.342094\pi$
$564$		0			0
$565$	24275.2	−	24275.2i	0.0760443	−	0.0760443i
$566$	12235.5	+	224590.i	0.0381935	+	0.701065i
$567$		0			0
$568$	207807.	−	289781.i	0.644116	−	0.898201i
$569$		−	488561.i		−	1.50902i	−0.656290	−	0.754509i	$-0.727875\pi$
$569$		−	488561.i		−	1.50902i	0.656290	−	0.754509i	$-0.272125\pi$
$570$		0			0
$571$	−17324.2	−	17324.2i	−0.0531352	−	0.0531352i	0.680040	−	0.733175i	$-0.261962\pi$
$571$	−17324.2	−	17324.2i	−0.0531352	−	0.0531352i	−0.733175	+	0.680040i	$0.761962\pi$
$572$	104964.	−	11470.7i	0.320810	−	0.0350590i
$573$		0			0
$574$	−187657.	+	209282.i	−0.569562	+	0.635197i
$575$		−	56873.6i		−	0.172018i
$576$		0			0
$577$	−9362.93			−0.0281229			−0.0140615	−	0.999901i	$-0.504476\pi$
$577$	−9362.93			−0.0281229			−0.0140615	+	0.999901i	$0.504476\pi$
$578$	−225639.	−	202324.i	−0.675397	−	0.605609i
$579$		0			0
$580$	−2697.29	−	24681.8i	−0.00801810	−	0.0733702i
$581$	−196100.	+	196100.i	−0.580932	+	0.580932i
$582$		0			0
$583$	178348.			0.524725
$584$	−344052.	−	246726.i	−1.00878	−	0.723417i
$585$		0			0
$586$	4004.26	−	218.149i	0.0116608	−	0.000635268i
$587$	−46301.5	−	46301.5i	−0.134375	−	0.134375i	0.636720	−	0.771095i	$-0.280291\pi$
$587$	−46301.5	−	46301.5i	−0.134375	−	0.134375i	−0.771095	+	0.636720i	$0.780291\pi$
$588$		0			0
$589$	321742.	+	321742.i	0.927422	+	0.927422i
$590$	20395.7	+	18288.2i	0.0585916	+	0.0525373i
$591$		0			0
$592$	203650.	−	319340.i	0.581088	−	0.911191i
$593$	194145.			0.552099			0.276049	−	0.961143i	$-0.410975\pi$
$593$	194145.			0.552099			0.276049	+	0.961143i	$0.410975\pi$
$594$		0			0
$595$	−19250.1	+	19250.1i	−0.0543749	+	0.0543749i
$596$	−277664.	−	222955.i	−0.781676	−	0.627660i
$597$		0			0
$598$	−780.804	−	14332.2i	−0.00218343	−	0.0400783i
$599$	−474516.			−1.32250			−0.661252	−	0.750164i	$-0.729975\pi$
$599$	−474516.			−1.32250			−0.661252	+	0.750164i	$0.729975\pi$
$600$		0			0
$601$		−	87515.3i		−	0.242290i	−0.992635	−	0.121145i	$-0.961343\pi$
$601$		−	87515.3i		−	0.242290i	0.992635	−	0.121145i	$-0.0386566\pi$
$602$	−26387.0	−	484350.i	−0.0728110	−	1.33649i
$603$		0			0
$604$	−72955.0	−	667580.i	−0.199977	−	1.82991i
$605$	42357.8	+	42357.8i	0.115724	+	0.115724i
$606$		0			0
$607$			687260.i			1.86528i	0.360808	+	0.932640i	$0.382501\pi$
$607$			687260.i			1.86528i	−0.360808	+	0.932640i	$0.617499\pi$
$608$	364216.	−	101634.i	0.985263	−	0.274937i
$609$		0			0
$610$	9839.34	+	8822.65i	0.0264427	+	0.0237104i
$611$	−46734.8	+	46734.8i	−0.125187	+	0.125187i
$612$		0			0
$613$	−220862.	+	220862.i	−0.587761	+	0.587761i	−0.937025	−	0.349263i	$-0.886432\pi$
$613$	−220862.	+	220862.i	−0.587761	+	0.587761i	0.349263	+	0.937025i	$0.386432\pi$
$614$	−116342.	+	6338.23i	−0.308603	+	0.0168124i
$615$		0			0
$616$	−833023.	+	137234.i	−2.19531	+	0.361661i
$617$			518967.i			1.36323i	0.731711	+	0.681615i	$0.238722\pi$
$617$			518967.i			1.36323i	−0.731711	+	0.681615i	$0.761278\pi$
$618$		0			0
$619$	−77555.3	−	77555.3i	−0.202409	−	0.202409i	0.598622	−	0.801031i	$-0.295715\pi$
$619$	−77555.3	−	77555.3i	−0.202409	−	0.202409i	−0.801031	+	0.598622i	$0.795715\pi$
$620$	49701.1	−	61896.8i	0.129295	−	0.161022i
$621$		0			0
$622$	−245129.	−	219800.i	−0.633599	−	0.568130i
$623$		−	841705.i		−	2.16862i
$624$		0			0
$625$	−360490.			−0.922855
$626$	−321554.	+	358609.i	−0.820550	+	0.915107i
$627$		0			0
$628$	350430.	−	436419.i	0.888550	−	1.10658i
$629$	−92126.1	+	92126.1i	−0.232853	+	0.232853i
$630$		0			0
$631$	344653.			0.865612			0.432806	−	0.901487i	$-0.357523\pi$
$631$	344653.			0.865612			0.432806	+	0.901487i	$0.357523\pi$
$632$	−280416.	−	201091.i	−0.702051	−	0.503453i
$633$		0			0
$634$	−4552.88	−	83571.0i	−0.0113268	−	0.207911i
$635$	−8098.03	−	8098.03i	−0.0200832	−	0.0200832i
$636$		0			0
$637$	94900.2	+	94900.2i	0.233877	+	0.233877i
$638$	−176822.	+	197198.i	−0.434405	+	0.484464i
$639$		0			0
$640$	−24529.0	−	61238.8i	−0.0598853	−	0.149509i
$641$	183353.			0.446243			0.223122	−	0.974791i	$-0.428375\pi$
$641$	183353.			0.446243			0.223122	+	0.974791i	$0.428375\pi$
$642$		0			0
$643$	−541900.	+	541900.i	−1.31068	+	1.31068i	−0.389768	+	0.920913i	$0.627445\pi$
$643$	−541900.	+	541900.i	−1.31068	+	1.31068i	−0.920913	+	0.389768i	$0.872555\pi$
$644$	12467.6	+	114086.i	0.0300615	+	0.275080i
$645$		0			0
$646$	−129880.	+	7075.78i	−0.311228	+	0.0169555i
$647$	358562.			0.856555			0.428278	−	0.903647i	$-0.359121\pi$
$647$	358562.			0.856555			0.428278	+	0.903647i	$0.359121\pi$
$648$		0			0
$649$		−	292233.i		−	0.693808i
$650$	−93397.0	+	5088.19i	−0.221058	+	0.0120431i
$651$		0			0
$652$	431026.	+	346099.i	1.01393	+	0.814152i
$653$	73642.4	+	73642.4i	0.172704	+	0.172704i	0.788166	−	0.615463i	$-0.211031\pi$
$653$	73642.4	+	73642.4i	0.172704	+	0.172704i	−0.615463	+	0.788166i	$0.711031\pi$
$654$		0			0
$655$		−	39801.7i		−	0.0927725i
$656$	50607.3	+	228778.i	0.117600	+	0.531626i
$657$		0			0
$658$	352795.	−	393449.i	0.814836	−	0.908735i
$659$	−22081.7	+	22081.7i	−0.0508467	+	0.0508467i	−0.732073	−	0.681226i	$-0.761447\pi$
$659$	−22081.7	+	22081.7i	−0.0508467	+	0.0508467i	0.681226	+	0.732073i	$0.261447\pi$
$660$		0			0
$661$	20869.3	−	20869.3i	0.0477644	−	0.0477644i	−0.682821	−	0.730586i	$-0.739247\pi$
$661$	20869.3	−	20869.3i	0.0477644	−	0.0477644i	0.730586	+	0.682821i	$0.239247\pi$
$662$	25500.6	+	468079.i	0.0581881	+	1.06808i
$663$		0			0
$664$	37576.8	+	228094.i	0.0852283	+	0.517342i
$665$		−	114157.i		−	0.258143i
$666$		0			0
$667$	25459.3	+	25459.3i	0.0572261	+	0.0572261i
$668$	−90694.9	−	829911.i	−0.203250	−	1.85985i
$669$		0			0
$670$	−22564.8	+	25165.1i	−0.0502669	+	0.0560594i
$671$		−	140979.i		−	0.313120i
$672$		0			0
$673$	379771.			0.838479			0.419239	−	0.907876i	$-0.362297\pi$
$673$	379771.			0.838479			0.419239	+	0.907876i	$0.362297\pi$
$674$	234837.	+	210571.i	0.516947	+	0.463531i
$675$		0			0
$676$	430805.	−	47079.6i	0.942731	−	0.103024i
$677$	156167.	−	156167.i	0.340731	−	0.340731i	−0.515911	−	0.856642i	$-0.672546\pi$
$677$	156167.	−	156167.i	0.340731	−	0.340731i	0.856642	+	0.515911i	$0.172546\pi$
$678$		0			0
$679$	−361877.			−0.784912
$680$	3688.71	+	22390.7i	0.00797731	+	0.0484228i
$681$		0			0
$682$	−845560.	+	46065.4i	−1.81792	+	0.0990390i
$683$	−164044.	−	164044.i	−0.351656	−	0.351656i	0.509070	−	0.860725i	$-0.329990\pi$
$683$	−164044.	−	164044.i	−0.351656	−	0.351656i	−0.860725	+	0.509070i	$0.829990\pi$
$684$		0			0
$685$	10448.0	+	10448.0i	0.0222665	+	0.0222665i
$686$	−249938.	−	224112.i	−0.531109	−	0.476230i
$687$		0			0
$688$	−340909.	−	217406.i	−0.720215	−	0.459298i
$689$	−39872.4			−0.0839912
$690$		0			0
$691$	−288207.	+	288207.i	−0.603599	+	0.603599i	−0.941266	−	0.337667i	$-0.890362\pi$
$691$	−288207.	+	288207.i	−0.603599	+	0.603599i	0.337667	+	0.941266i	$0.390362\pi$
$692$	372825.	−	464310.i	0.778562	−	0.969607i
$693$		0			0
$694$	18322.8	+	336327.i	0.0380429	+	0.698302i
$695$	25062.1			0.0518856
$696$		0			0
$697$		−	80599.7i		−	0.165908i
$698$	−232.693	−	4271.22i	−0.000477608	−	0.00876681i
$699$		0			0
$700$	743451.	−	81246.4i	1.51725	−	0.165809i
$701$	−323248.	−	323248.i	−0.657808	−	0.657808i	0.297053	−	0.954861i	$-0.403996\pi$
$701$	−323248.	−	323248.i	−0.657808	−	0.657808i	−0.954861	+	0.297053i	$0.903996\pi$
$702$		0			0
$703$		−	546329.i		−	1.10546i
$704$	−311692.	+	630941.i	−0.628899	+	1.27304i
$705$		0			0
$706$	−70651.0	−	63350.7i	−0.141745	−	0.127099i
$707$	−873826.	+	873826.i	−1.74818	+	1.74818i
$708$		0			0
$709$	−580085.	+	580085.i	−1.15398	+	1.15398i	−0.168235	+	0.985747i	$0.553807\pi$
$709$	−580085.	+	580085.i	−1.15398	+	1.15398i	−0.985747	+	0.168235i	$0.946193\pi$
$710$	−89603.4	+	4881.52i	−0.177749	+	0.00968364i
$711$		0			0
$712$	−570159.	−	408871.i	−1.12470	−	0.806540i
$713$			115113.i			0.226436i
$714$		0			0
$715$	−18788.9	−	18788.9i	−0.0367526	−	0.0367526i
$716$	−84967.2	−	68225.8i	−0.165739	−	0.133083i
$717$		0			0
$718$	−434994.	−	390046.i	−0.843789	−	0.756601i
$719$			332243.i			0.642684i	0.946963	+	0.321342i	$0.104134\pi$
$719$			332243.i			0.642684i	−0.946963	+	0.321342i	$0.895866\pi$
$720$		0			0
$721$	−13494.5			−0.0259590
$722$	16124.1	−	17982.1i	0.0309314	−	0.0344959i
$723$		0			0
$724$	−422118.	−	338947.i	−0.805299	−	0.646628i
$725$	165908.	−	165908.i	0.315639	−	0.315639i
$726$		0			0
$727$	362311.			0.685508			0.342754	−	0.939425i	$-0.388640\pi$
$727$	362311.			0.685508			0.342754	+	0.939425i	$0.388640\pi$
$728$	186234.	−	30680.8i	0.351396	−	0.0578900i
$729$		0			0
$730$	5795.74	+	106384.i	0.0108758	+	0.199633i
$731$	98348.7	+	98348.7i	0.184049	+	0.184049i
$732$		0			0
$733$	377844.	+	377844.i	0.703242	+	0.703242i	0.965105	−	0.261863i	$-0.0843369\pi$
$733$	377844.	+	377844.i	0.703242	+	0.703242i	−0.261863	+	0.965105i	$0.584337\pi$
$734$	403570.	−	450076.i	0.749078	−	0.835399i
$735$		0			0
$736$	83336.2	+	46973.4i	0.153843	+	0.0867155i
$737$	360569.			0.663825
$738$		0			0
$739$	467502.	−	467502.i	0.856042	−	0.856042i	−0.134828	−	0.990869i	$-0.543048\pi$
$739$	467502.	−	467502.i	0.856042	−	0.856042i	0.990869	+	0.134828i	$0.0430480\pi$
$740$	−94748.5	+	10354.4i	−0.173025	+	0.0189086i
$741$		0			0
$742$	318334.	−	17342.6i	0.578196	−	0.0314997i
$743$	555820.			1.00683			0.503415	−	0.864045i	$-0.332077\pi$
$743$	555820.			1.00683			0.503415	+	0.864045i	$0.332077\pi$
$744$		0			0
$745$			89612.4i			0.161456i
$746$	148034.	−	8064.75i	0.266001	−	0.0144915i
$747$		0			0
$748$	151565.	−	188756.i	0.270892	−	0.337364i
$749$	1.16335e6	+	1.16335e6i	2.07370	+	2.07370i
$750$		0			0
$751$			308308.i			0.546644i	0.961923	+	0.273322i	$0.0881224\pi$
$751$			308308.i			0.546644i	−0.961923	+	0.273322i	$0.911878\pi$
$752$	−95141.6	−	430102.i	−0.168242	−	0.760563i
$753$		0			0
$754$	39531.1	−	44086.5i	0.0695339	−	0.0775467i
$755$	−119499.	+	119499.i	−0.209638	+	0.209638i
$756$		0			0
$757$	34980.2	−	34980.2i	0.0610423	−	0.0610423i	−0.675927	−	0.736969i	$-0.736256\pi$
$757$	34980.2	−	34980.2i	0.0610423	−	0.0610423i	0.736969	+	0.675927i	$0.236256\pi$
$758$	33980.3	+	623729.i	0.0591410	+	1.08557i
$759$		0			0
$760$	−77328.6	−	55453.7i	−0.133879	−	0.0960070i
$761$			545745.i			0.942368i	0.882035	+	0.471184i	$0.156173\pi$
$761$			545745.i			0.942368i	−0.882035	+	0.471184i	$0.843827\pi$
$762$		0			0
$763$	180394.	+	180394.i	0.309866	+	0.309866i
$764$	717001.	−	78355.8i	1.22838	−	0.134241i
$765$		0			0
$766$	28078.9	−	31314.6i	0.0478544	−	0.0533690i
$767$			65332.9i			0.111056i
$768$		0			0
$769$	510362.			0.863030			0.431515	−	0.902106i	$-0.357979\pi$
$769$	510362.			0.863030			0.431515	+	0.902106i	$0.357979\pi$
$770$	158179.	+	141835.i	0.266789	+	0.239222i
$771$		0			0
$772$	87405.8	+	799814.i	0.146658	+	1.34200i
$773$	−596763.	+	596763.i	−0.998718	+	0.998718i	−0.999999	−	0.00128103i	$-0.999592\pi$
$773$	−596763.	+	596763.i	−0.998718	+	0.998718i	0.00128103	+	0.999999i	$0.499592\pi$
$774$		0			0
$775$	750148.			1.24895
$776$	−175787.	+	245130.i	−0.291919	+	0.407073i
$777$		0			0
$778$	941952.	−	51316.8i	1.55621	−	0.0847813i
$779$	238987.	+	238987.i	0.393822	+	0.393822i
$780$		0			0
$781$	676897.	+	676897.i	1.10974	+	1.10974i
$782$	−24500.2	−	21968.6i	−0.0400641	−	0.0359243i
$783$		0			0
$784$	−873369.	+	193196.i	−1.42091	+	0.314315i
$785$	−140849.			−0.228567
$786$		0			0
$787$	−463254.	+	463254.i	−0.747945	+	0.747945i	−0.974093	−	0.226148i	$-0.927387\pi$
$787$	−463254.	+	463254.i	−0.747945	+	0.747945i	0.226148	+	0.974093i	$0.427387\pi$
$788$	452770.	+	363560.i	0.729165	+	0.585495i
$789$		0			0
$790$	4723.76	+	86707.5i	0.00756891	+	0.138932i
$791$	−654644.			−1.04629
$792$		0			0
$793$			31518.0i			0.0501202i
$794$	−59249.8	−	1.08757e6i	−0.0939823	−	1.72510i
$795$		0			0
$796$	−77521.1	−	709363.i	−0.122347	−	1.11955i
$797$	−406283.	−	406283.i	−0.639605	−	0.639605i	0.310853	−	0.950458i	$-0.399385\pi$
$797$	−406283.	−	406283.i	−0.639605	−	0.639605i	−0.950458	+	0.310853i	$0.899385\pi$
$798$		0			0
$799$			151527.i			0.237354i
$800$	306107.	−	543070.i	0.478293	−	0.848546i
$801$		0			0
$802$	−271476.	−	243425.i	−0.422069	−	0.378457i
$803$	803667.	−	803667.i	1.24636	−	1.24636i
$804$		0			0
$805$	20421.7	−	20421.7i	0.0315137	−	0.0315137i
$806$	189037.	−	10298.6i	0.290990	−	0.0158529i
$807$		0			0
$808$	167443.	+	1.01639e6i	0.256475	+	1.55682i
$809$		−	766553.i		−	1.17124i	−0.810587	−	0.585619i	$-0.800852\pi$
$809$		−	766553.i		−	1.17124i	0.810587	−	0.585619i	$-0.199148\pi$
$810$		0			0
$811$	−418641.	−	418641.i	−0.636503	−	0.636503i	0.313188	−	0.949691i	$-0.398603\pi$
$811$	−418641.	−	418641.i	−0.636503	−	0.636503i	−0.949691	+	0.313188i	$0.898603\pi$
$812$	−296434.	+	369173.i	−0.449589	+	0.559909i
$813$		0			0
$814$	757006.	+	678785.i	1.14248	+	1.02443i
$815$		−	139108.i		−	0.209429i
$816$		0			0
$817$	−583231.			−0.873769
$818$	287798.	−	320963.i	0.430112	−	0.479677i
$819$		0			0
$820$	36917.5	−	45976.4i	0.0549041	−	0.0683766i
$821$	23229.7	−	23229.7i	0.0344633	−	0.0344633i	−0.689665	−	0.724128i	$-0.742242\pi$
$821$	23229.7	−	23229.7i	0.0344633	−	0.0344633i	0.724128	+	0.689665i	$0.242242\pi$
$822$		0			0
$823$	−41797.3			−0.0617090			−0.0308545	−	0.999524i	$-0.509823\pi$
$823$	−41797.3			−0.0617090			−0.0308545	+	0.999524i	$0.509823\pi$
$824$	−6555.17	+	9141.01i	−0.00965450	+	0.0134629i
$825$		0			0
$826$	−28416.7	−	521606.i	−0.0416498	−	0.764509i
$827$	349889.	+	349889.i	0.511587	+	0.511587i	0.915013	−	0.403425i	$-0.132180\pi$
$827$	349889.	+	349889.i	0.511587	+	0.511587i	−0.403425	+	0.915013i	$0.632180\pi$
$828$		0			0
$829$	213369.	+	213369.i	0.310472	+	0.310472i	0.845092	−	0.534621i	$-0.179545\pi$
$829$	213369.	+	213369.i	0.310472	+	0.310472i	−0.534621	+	0.845092i	$0.679545\pi$
$830$	38836.4	−	43311.8i	0.0563745	−	0.0628709i
$831$		0			0
$832$	69683.4	−	141056.i	0.100666	−	0.203772i
$833$	307692.			0.443432
$834$		0			0
$835$	−148557.	+	148557.i	−0.213069	+	0.213069i
$836$	110276.	+	1.00909e6i	0.157787	+	1.44384i
$837$		0			0
$838$	669479.	−	36472.7i	0.953343	−	0.0519374i
$839$	7789.74			0.0110662			0.00553311	−	0.999985i	$-0.498239\pi$
$839$	7789.74			0.0110662			0.00553311	+	0.999985i	$0.498239\pi$
$840$		0			0
$841$		−	558745.i		−	0.789990i
$842$	−1.28004e6	+	69735.4i	−1.80550	+	0.0983624i
$843$		0			0
$844$	455705.	+	365916.i	0.639734	+	0.513685i
$845$	−77115.5	−	77115.5i	−0.108001	−	0.108001i
$846$		0			0
$847$		−	1.14229e6i		−	1.59224i
$848$	142888.	−	224059.i	0.198703	−	0.311581i
$849$		0			0
$850$	−143161.	+	159658.i	−0.198146	+	0.220980i
$851$	97733.2	−	97733.2i	0.134953	−	0.134953i
$852$		0			0
$853$	485860.	−	485860.i	0.667749	−	0.667749i	−0.289445	−	0.957195i	$-0.593471\pi$
$853$	485860.	−	485860.i	0.667749	−	0.667749i	0.957195	+	0.289445i	$0.0934708\pi$
$854$	−13708.8	−	251634.i	−0.0187968	−	0.345028i
$855$		0			0
$856$	1.35315e6	−	222921.i	1.84671	−	0.304232i
$857$		−	1.01914e6i		−	1.38763i	−0.720154	−	0.693814i	$-0.755929\pi$
$857$		−	1.01914e6i		−	1.38763i	0.720154	−	0.693814i	$-0.244071\pi$
$858$		0			0
$859$	232567.	+	232567.i	0.315182	+	0.315182i	0.846913	−	0.531731i	$-0.178458\pi$
$859$	232567.	+	232567.i	0.315182	+	0.315182i	−0.531731	+	0.846913i	$0.678458\pi$
$860$	11053.8	+	101148.i	0.0149456	+	0.136761i
$861$		0			0
$862$	−14413.4	+	16074.3i	−0.0193978	+	0.0216331i
$863$			739852.i			0.993398i	0.867923	+	0.496699i	$0.165455\pi$
$863$			739852.i			0.993398i	−0.867923	+	0.496699i	$0.834545\pi$
$864$		0			0
$865$	−149850.			−0.200274
$866$	487919.	+	437502.i	0.650596	+	0.583371i
$867$		0			0
$868$	−1.50476e6	+	164444.i	−1.99723	+	0.218263i
$869$	655020.	−	655020.i	0.867392	−	0.867392i
$870$		0			0
$871$	−80610.5			−0.106256
$872$	209825.	−	34567.2i	0.275947	−	0.0454602i
$873$		0			0
$874$	137785.	−	7506.44i	0.180377	−	0.00982677i
$875$	−269704.	−	269704.i	−0.352267	−	0.352267i
$876$		0			0
$877$	−828805.	−	828805.i	−1.07759	−	1.07759i	−0.996725	−	0.0808636i	$-0.974232\pi$
$877$	−828805.	−	828805.i	−1.07759	−	1.07759i	−0.0808636	−	0.996725i	$-0.525768\pi$
$878$	471947.	+	423181.i	0.612215	+	0.548955i
$879$		0			0
$880$	172914.	−	38249.9i	0.223288	−	0.0493930i
$881$	−1.20631e6			−1.55420			−0.777099	−	0.629379i	$-0.783310\pi$
$881$	−1.20631e6			−1.55420			−0.777099	+	0.629379i	$0.783310\pi$
$882$		0			0
$883$	381765.	−	381765.i	0.489637	−	0.489637i	−0.418555	−	0.908192i	$-0.637463\pi$
$883$	381765.	−	381765.i	0.489637	−	0.489637i	0.908192	+	0.418555i	$0.137463\pi$
$884$	−33884.6	+	42199.3i	−0.0433609	+	0.0540008i
$885$		0			0
$886$	42444.1	+	779088.i	0.0540692	+	0.992474i
$887$	1.44154e6			1.83223			0.916113	−	0.400919i	$-0.131309\pi$
$887$	1.44154e6			1.83223			0.916113	+	0.400919i	$0.131309\pi$
$888$		0			0
$889$			218384.i			0.276323i
$890$	9604.63	+	176299.i	0.0121255	+	0.222572i
$891$		0			0
$892$	−1.15552e6	+	126278.i	−1.45227	+	0.158708i
$893$	−449295.	−	449295.i	−0.563416	−	0.563416i
$894$		0			0
$895$			27422.0i			0.0342337i
$896$	−494987.	+	1.15647e6i	−0.616563	+	1.44052i
$897$		0			0
$898$	−974840.	−	874110.i	−1.20887	−	1.08396i
$899$	−335801.	+	335801.i	−0.415492	+	0.415492i
$900$		0			0
$901$	−64638.6	+	64638.6i	−0.0796238	+	0.0796238i
$902$	−628075.	+	34217.0i	−0.771967	+	0.0420561i
$903$		0			0
$904$	−318003.	+	443446.i	−0.389129	+	0.542630i
$905$			136233.i			0.166336i
$906$		0			0
$907$	−208093.	−	208093.i	−0.252955	−	0.252955i	0.569226	−	0.822181i	$-0.307243\pi$
$907$	−208093.	−	208093.i	−0.252955	−	0.252955i	−0.822181	+	0.569226i	$0.807243\pi$
$908$	−332724.	−	267166.i	−0.403564	−	0.324049i
$909$		0			0
$910$	−35363.3	−	31709.2i	−0.0427041	−	0.0382915i
$911$			861726.i			1.03832i	0.854676	+	0.519162i	$0.173756\pi$
$911$			861726.i			1.03832i	−0.854676	+	0.519162i	$0.826244\pi$
$912$		0			0
$913$	−620577.			−0.744482
$914$	−412600.	+	460147.i	−0.493898	+	0.550813i
$915$		0			0
$916$	735309.	+	590429.i	0.876353	+	0.703682i
$917$	−536678.	+	536678.i	−0.638227	+	0.638227i
$918$		0			0
$919$	−368829.			−0.436711			−0.218355	−	0.975869i	$-0.570069\pi$
$919$	−368829.			−0.436711			−0.218355	+	0.975869i	$0.570069\pi$
$920$	−3913.22	−	23753.5i	−0.00462336	−	0.0280641i
$921$		0			0
$922$	−5937.94	−	108995.i	−0.00698512	−	0.128216i
$923$	−151330.	−	151330.i	−0.177632	−	0.177632i
$924$		0			0
$925$	−636889.	−	636889.i	−0.744355	−	0.744355i
$926$	−70774.5	+	78930.3i	−0.0825382	+	0.0920496i
$927$		0			0
$928$	106075.	+	380131.i	0.123174	+	0.441405i
$929$	−842458.			−0.976151			−0.488076	−	0.872801i	$-0.662301\pi$
$929$	−842458.			−0.976151			−0.488076	+	0.872801i	$0.662301\pi$
$930$		0			0
$931$	−912344.	+	912344.i	−1.05259	+	1.05259i
$932$	−44019.7	+	4810.59i	−0.0506775	+	0.00553817i
$933$		0			0
$934$	−631484.	+	34402.7i	−0.723883	+	0.0394366i
$935$	−60918.6			−0.0696830
$936$		0			0
$937$			41186.1i			0.0469107i	0.999725	+	0.0234553i	$0.00746675\pi$
$937$			41186.1i			0.0469107i	−0.999725	+	0.0234553i	$0.992533\pi$
$938$	643579.	−	35061.7i	0.731470	−	0.0398499i
$939$		0			0
$940$	−69404.8	+	86435.5i	−0.0785478	+	0.0978220i
$941$	−495362.	−	495362.i	−0.559427	−	0.559427i	0.369717	−	0.929144i	$-0.379454\pi$
$941$	−495362.	−	495362.i	−0.559427	−	0.559427i	−0.929144	+	0.369717i	$0.879454\pi$
$942$		0			0
$943$			85505.2i			0.0961544i
$944$	−367132.	−	234129.i	−0.411982	−	0.262731i
$945$		0			0
$946$	724633.	−	808137.i	0.809722	−	0.903031i
$947$	825578.	−	825578.i	0.920573	−	0.920573i	−0.0764965	−	0.997070i	$-0.524373\pi$
$947$	825578.	−	825578.i	0.920573	−	0.920573i	0.997070	+	0.0764965i	$0.0243734\pi$
$948$		0			0
$949$	−179672.	+	179672.i	−0.199502	+	0.199502i
$950$	−48916.5	−	897893.i	−0.0542011	−	0.994895i
$951$		0			0
$952$	252174.	−	351649.i	0.278244	−	0.388004i
$953$		−	1.06311e6i		−	1.17055i	−0.810834	−	0.585276i	$-0.800986\pi$
$953$		−	1.06311e6i		−	1.17055i	0.810834	−	0.585276i	$-0.199014\pi$
$954$		0			0
$955$	−128345.	−	128345.i	−0.140726	−	0.140726i
$956$	−794975.	+	86877.1i	−0.869837	+	0.0950582i
$957$		0			0
$958$	−601850.	+	671205.i	−0.655778	+	0.731348i
$959$		−	281757.i		−	0.306364i
$960$		0			0
$961$	−594793.			−0.644050
$962$	−169240.	−	151752.i	−0.182874	−	0.163978i
$963$		0			0
$964$	−76611.9	−	701043.i	−0.0824408	−	0.754381i
$965$	143169.	−	143169.i	0.153743	−	0.153743i
$966$		0			0
$967$	1.03910e6			1.11123			0.555615	−	0.831440i	$-0.312483\pi$
$967$	1.03910e6			1.11123			0.555615	+	0.831440i	$0.312483\pi$
$968$	−773767.	−	554882.i	−0.825771	−	0.592175i
$969$		0			0
$970$	75796.7	−	4129.34i	0.0805577	−	0.00438872i
$971$	−624932.	−	624932.i	−0.662818	−	0.662818i	0.293225	−	0.956043i	$-0.405271\pi$
$971$	−624932.	−	624932.i	−0.662818	−	0.662818i	−0.956043	+	0.293225i	$0.905271\pi$
$972$		0			0
$973$	−337931.	−	337931.i	−0.356946	−	0.356946i
$974$	25265.0	+	22654.4i	0.0266318	+	0.0238800i
$975$		0			0
$976$	−177112.	−	112949.i	−0.185930	−	0.118572i
$977$	−1.37121e6			−1.43653			−0.718264	−	0.695771i	$-0.755063\pi$
$977$	−1.37121e6			−1.43653			−0.718264	+	0.695771i	$0.755063\pi$
$978$		0			0
$979$	1.33183e6	−	1.33183e6i	1.38958	−	1.38958i
$980$	175517.	+	140934.i	0.182754	+	0.146745i
$981$		0			0
$982$	−21314.5	−	391242.i	−0.0221031	−	0.405716i
$983$	−838159.			−0.867400			−0.433700	−	0.901057i	$-0.642792\pi$
$983$	−838159.			−0.867400			−0.433700	+	0.901057i	$0.642792\pi$
$984$		0			0
$985$		−	146126.i		−	0.150610i
$986$	−7384.97	−	135556.i	−0.00759617	−	0.139432i
$987$		0			0
$988$	−24653.9	−	225598.i	−0.0252564	−	0.231111i
$989$	−104335.	−	104335.i	−0.106668	−	0.106668i
$990$		0			0
$991$			817540.i			0.832457i	0.909260	+	0.416228i	$0.136648\pi$
$991$			817540.i			0.832457i	−0.909260	+	0.416228i	$0.863352\pi$
$992$	−619567.	+	1.09918e6i	−0.629601	+	1.11698i
$993$		0			0
$994$	1.27401e6	+	1.14237e6i	1.28944	+	1.15620i
$995$	−126978.	+	126978.i	−0.128258	+	0.128258i
$996$		0			0
$997$	−243046.	+	243046.i	−0.244511	+	0.244511i	−0.818713	−	0.574203i	$-0.805312\pi$
$997$	−243046.	+	243046.i	−0.244511	+	0.244511i	0.574203	+	0.818713i	$0.305312\pi$
$998$	490680.	−	26731.9i	0.492649	−	0.0268391i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.5.m.a.19.6		14
3.2	odd	2		16.5.f.a.3.2	✓	14
4.3	odd	2		576.5.m.a.559.4		14
12.11	even	2		64.5.f.a.47.7		14
16.5	even	4		576.5.m.a.271.4		14
16.11	odd	4	inner	144.5.m.a.91.6		14
24.5	odd	2		128.5.f.b.95.7		14
24.11	even	2		128.5.f.a.95.1		14
48.5	odd	4		64.5.f.a.15.7		14
48.11	even	4		16.5.f.a.11.2	yes	14
48.29	odd	4		128.5.f.a.31.1		14
48.35	even	4		128.5.f.b.31.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.5.f.a.3.2	✓	14	3.2	odd	2
16.5.f.a.11.2	yes	14	48.11	even	4
64.5.f.a.15.7		14	48.5	odd	4
64.5.f.a.47.7		14	12.11	even	2
128.5.f.a.31.1		14	48.29	odd	4
128.5.f.a.95.1		14	24.11	even	2
128.5.f.b.31.7		14	48.35	even	4
128.5.f.b.95.7		14	24.5	odd	2
144.5.m.a.19.6		14	1.1	even	1	trivial
144.5.m.a.91.6		14	16.11	odd	4	inner
576.5.m.a.271.4		14	16.5	even	4
576.5.m.a.559.4		14	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	144.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.97810 + 2.67038i) q^{2} +(1.73818 + 15.9053i) q^{4} +(2.84710 - 2.84710i) q^{5} -76.7794 q^{7} +(-37.2967 + 52.0092i) q^{8} +O(q^{10})\)	\(q+(2.97810 + 2.67038i) q^{2} +(1.73818 + 15.9053i) q^{4} +(2.84710 - 2.84710i) q^{5} -76.7794 q^{7} +(-37.2967 + 52.0092i) q^{8} +(16.0818 - 0.876123i) q^{10} +(-121.488 - 121.488i) q^{11} +(27.1604 + 27.1604i) q^{13} +(-228.657 - 205.030i) q^{14} +(-249.957 + 55.2924i) q^{16} +88.0613 q^{17} +(-261.112 + 261.112i) q^{19} +(50.2328 + 40.3352i) q^{20} +(-37.3847 - 686.220i) q^{22} -93.4210 q^{23} +608.788i q^{25} +(8.35791 + 153.415i) q^{26} +(-133.456 - 1221.20i) q^{28} +(-272.522 - 272.522i) q^{29} -1232.20i q^{31} +(-892.050 - 502.814i) q^{32} +(262.256 + 235.157i) q^{34} +(-218.599 + 218.599i) q^{35} +(-1046.16 + 1046.16i) q^{37} +(-1474.89 + 80.3506i) q^{38} +(41.8880 + 254.263i) q^{40} -915.267i q^{41} +(1116.82 + 1116.82i) q^{43} +(1721.13 - 2143.47i) q^{44} +(-278.217 - 249.469i) q^{46} +1720.70i q^{47} +3494.07 q^{49} +(-1625.69 + 1813.03i) q^{50} +(-384.784 + 479.203i) q^{52} +(-734.019 + 734.019i) q^{53} -691.775 q^{55} +(2863.62 - 3993.23i) q^{56} +(-83.8616 - 1539.33i) q^{58} +(1202.73 + 1202.73i) q^{59} +(580.221 + 580.221i) q^{61} +(3290.44 - 3669.61i) q^{62} +(-1313.91 - 3879.54i) q^{64} +154.657 q^{65} +(-1483.97 + 1483.97i) q^{67} +(153.066 + 1400.64i) q^{68} +(-1234.75 + 67.2681i) q^{70} -5571.73 q^{71} +6615.21i q^{73} +(-5909.20 + 321.929i) q^{74} +(-4606.93 - 3699.21i) q^{76} +(9327.75 + 9327.75i) q^{77} +5391.66i q^{79} +(-554.231 + 869.077i) q^{80} +(2444.11 - 2725.76i) q^{82} +(2554.07 - 2554.07i) q^{83} +(250.719 - 250.719i) q^{85} +(343.673 + 6308.34i) q^{86} +(10849.6 - 1787.39i) q^{88} +10962.7i q^{89} +(-2085.35 - 2085.35i) q^{91} +(-162.382 - 1485.89i) q^{92} +(-4594.92 + 5124.42i) q^{94} +1486.83i q^{95} +4713.20 q^{97} +(10405.7 + 9330.48i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} + 92 q^{8}+O(q^{10}) \) 14 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 + 92 * q^8	\( 14 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} + 92 q^{8} - 100 q^{10} - 94 q^{11} - 2 q^{13} - 44 q^{14} - 168 q^{16} + 4 q^{17} - 706 q^{19} - 1900 q^{20} + 900 q^{22} - 1148 q^{23} + 3416 q^{26} - 3784 q^{28} - 862 q^{29} - 3208 q^{32} + 7508 q^{34} - 1340 q^{35} - 1826 q^{37} - 3568 q^{38} - 5144 q^{40} + 1694 q^{43} + 14636 q^{44} - 5316 q^{46} + 682 q^{49} - 20070 q^{50} + 20452 q^{52} + 482 q^{53} - 11780 q^{55} + 6952 q^{56} - 20456 q^{58} + 2786 q^{59} - 3778 q^{61} + 11472 q^{62} + 15808 q^{64} + 2020 q^{65} + 7998 q^{67} - 18032 q^{68} + 15296 q^{70} - 19964 q^{71} + 23780 q^{74} - 23996 q^{76} + 9508 q^{77} - 1384 q^{80} + 16016 q^{82} + 17282 q^{83} + 9948 q^{85} + 4796 q^{86} + 7288 q^{88} - 28036 q^{91} + 14632 q^{92} + 432 q^{94} - 4 q^{97} + 12246 q^{98}+O(q^{100}) \) 14 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 + 92 * q^8 - 100 * q^10 - 94 * q^11 - 2 * q^13 - 44 * q^14 - 168 * q^16 + 4 * q^17 - 706 * q^19 - 1900 * q^20 + 900 * q^22 - 1148 * q^23 + 3416 * q^26 - 3784 * q^28 - 862 * q^29 - 3208 * q^32 + 7508 * q^34 - 1340 * q^35 - 1826 * q^37 - 3568 * q^38 - 5144 * q^40 + 1694 * q^43 + 14636 * q^44 - 5316 * q^46 + 682 * q^49 - 20070 * q^50 + 20452 * q^52 + 482 * q^53 - 11780 * q^55 + 6952 * q^56 - 20456 * q^58 + 2786 * q^59 - 3778 * q^61 + 11472 * q^62 + 15808 * q^64 + 2020 * q^65 + 7998 * q^67 - 18032 * q^68 + 15296 * q^70 - 19964 * q^71 + 23780 * q^74 - 23996 * q^76 + 9508 * q^77 - 1384 * q^80 + 16016 * q^82 + 17282 * q^83 + 9948 * q^85 + 4796 * q^86 + 7288 * q^88 - 28036 * q^91 + 14632 * q^92 + 432 * q^94 - 4 * q^97 + 12246 * q^98

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