LMFDB - Embedded newform 225.4.e.e.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(76,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("225.76");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.e (of order $3$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Character	$\chi$	$=$	225.151
Dual form			225.4.e.e.76.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.77209 + 4.80141i) q^{2} +(0.320819 - 5.18624i) q^{3} +(-11.3690 - 19.6917i) q^{4} +(24.0119 + 15.9171i) q^{6} +(12.8563 - 22.2678i) q^{7} +81.7101 q^{8} +(-26.7942 - 3.32769i) q^{9} +O(q^{10})$	\(q+(-2.77209 + 4.80141i) q^{2} +(0.320819 - 5.18624i) q^{3} +(-11.3690 - 19.6917i) q^{4} +(24.0119 + 15.9171i) q^{6} +(12.8563 - 22.2678i) q^{7} +81.7101 q^{8} +(-26.7942 - 3.32769i) q^{9} +(-3.12792 + 5.41771i) q^{11} +(-105.773 + 52.6449i) q^{12} +(-7.62998 - 13.2155i) q^{13} +(71.2779 + 123.457i) q^{14} +(-135.556 + 234.790i) q^{16} +36.0074 q^{17} +(90.2535 - 119.425i) q^{18} -52.7512 q^{19} +(-111.362 - 73.8199i) q^{21} +(-17.3418 - 30.0368i) q^{22} +(-41.8670 - 72.5158i) q^{23} +(26.2142 - 423.768i) q^{24} +84.6040 q^{26} +(-25.8543 + 137.893i) q^{27} -584.654 q^{28} +(-59.5457 + 103.136i) q^{29} +(-138.331 - 239.596i) q^{31} +(-424.708 - 735.615i) q^{32} +(27.0941 + 17.9602i) q^{33} +(-99.8157 + 172.886i) q^{34} +(239.095 + 565.454i) q^{36} +117.553 q^{37} +(146.231 - 253.280i) q^{38} +(-70.9867 + 35.3311i) q^{39} +(79.6608 + 137.977i) q^{41} +(663.144 - 330.057i) q^{42} +(-147.482 + 255.446i) q^{43} +142.245 q^{44} +464.237 q^{46} +(41.6458 - 72.1327i) q^{47} +(1174.19 + 778.352i) q^{48} +(-159.070 - 275.518i) q^{49} +(11.5519 - 186.743i) q^{51} +(-173.490 + 300.494i) q^{52} -149.018 q^{53} +(-590.411 - 506.390i) q^{54} +(1050.49 - 1819.51i) q^{56} +(-16.9236 + 273.580i) q^{57} +(-330.132 - 571.806i) q^{58} +(-317.731 - 550.325i) q^{59} +(-298.575 + 517.148i) q^{61} +1533.86 q^{62} +(-418.575 + 553.865i) q^{63} +2540.42 q^{64} +(-161.342 + 80.3021i) q^{66} +(-165.008 - 285.802i) q^{67} +(-409.367 - 709.045i) q^{68} +(-389.516 + 193.868i) q^{69} -1149.79 q^{71} +(-2189.35 - 271.906i) q^{72} +130.284 q^{73} +(-325.869 + 564.422i) q^{74} +(599.728 + 1038.76i) q^{76} +(80.4271 + 139.304i) q^{77} +(27.1426 - 438.777i) q^{78} +(368.918 - 638.984i) q^{79} +(706.853 + 178.325i) q^{81} -883.309 q^{82} +(-184.951 + 320.345i) q^{83} +(-187.568 + 3032.16i) q^{84} +(-817.665 - 1416.24i) q^{86} +(515.785 + 341.906i) q^{87} +(-255.583 + 442.682i) q^{88} -225.638 q^{89} -392.374 q^{91} +(-951.972 + 1648.86i) q^{92} +(-1286.98 + 640.549i) q^{93} +(230.892 + 399.917i) q^{94} +(-3951.33 + 1966.64i) q^{96} +(-5.95671 + 10.3173i) q^{97} +1763.83 q^{98} +(101.838 - 134.754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} - q^{3} - 48 q^{4} - 13 q^{6} + 6 q^{7} + 90 q^{8} - 61 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 - q^3 - 48 * q^4 - 13 * q^6 + 6 * q^7 + 90 * q^8 - 61 * q^9	\( 24 q - 4 q^{2} - q^{3} - 48 q^{4} - 13 q^{6} + 6 q^{7} + 90 q^{8} - 61 q^{9} - 29 q^{11} - 77 q^{12} + 24 q^{13} + 69 q^{14} - 192 q^{16} + 158 q^{17} + 125 q^{18} - 150 q^{19} - 60 q^{21} - 18 q^{22} - 318 q^{23} + 342 q^{24} - 308 q^{26} - 394 q^{27} - 192 q^{28} - 106 q^{29} - 60 q^{31} - 914 q^{32} - 80 q^{33} + 108 q^{34} + 1303 q^{36} + 168 q^{37} - 640 q^{38} - 410 q^{39} + 353 q^{41} + 1521 q^{42} - 426 q^{43} + 1142 q^{44} + 540 q^{46} - 1210 q^{47} + 2680 q^{48} - 666 q^{49} - 1369 q^{51} - 75 q^{52} + 896 q^{53} - 2128 q^{54} + 570 q^{56} + 1544 q^{57} + 594 q^{58} - 482 q^{59} - 402 q^{61} + 5088 q^{62} - 1038 q^{63} + 1950 q^{64} + 2041 q^{66} - 201 q^{67} - 3437 q^{68} + 2856 q^{69} - 1888 q^{71} - 5493 q^{72} + 906 q^{73} - 10 q^{74} + 462 q^{76} - 2652 q^{77} - 4589 q^{78} - 258 q^{79} + 3071 q^{81} - 1746 q^{82} - 3012 q^{83} - 2703 q^{84} - 1952 q^{86} + 2708 q^{87} - 216 q^{88} - 1476 q^{89} - 1236 q^{91} - 5232 q^{92} + 3024 q^{93} - 63 q^{94} - 10424 q^{96} - 318 q^{97} + 15022 q^{98} - 1697 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 - q^3 - 48 * q^4 - 13 * q^6 + 6 * q^7 + 90 * q^8 - 61 * q^9 - 29 * q^11 - 77 * q^12 + 24 * q^13 + 69 * q^14 - 192 * q^16 + 158 * q^17 + 125 * q^18 - 150 * q^19 - 60 * q^21 - 18 * q^22 - 318 * q^23 + 342 * q^24 - 308 * q^26 - 394 * q^27 - 192 * q^28 - 106 * q^29 - 60 * q^31 - 914 * q^32 - 80 * q^33 + 108 * q^34 + 1303 * q^36 + 168 * q^37 - 640 * q^38 - 410 * q^39 + 353 * q^41 + 1521 * q^42 - 426 * q^43 + 1142 * q^44 + 540 * q^46 - 1210 * q^47 + 2680 * q^48 - 666 * q^49 - 1369 * q^51 - 75 * q^52 + 896 * q^53 - 2128 * q^54 + 570 * q^56 + 1544 * q^57 + 594 * q^58 - 482 * q^59 - 402 * q^61 + 5088 * q^62 - 1038 * q^63 + 1950 * q^64 + 2041 * q^66 - 201 * q^67 - 3437 * q^68 + 2856 * q^69 - 1888 * q^71 - 5493 * q^72 + 906 * q^73 - 10 * q^74 + 462 * q^76 - 2652 * q^77 - 4589 * q^78 - 258 * q^79 + 3071 * q^81 - 1746 * q^82 - 3012 * q^83 - 2703 * q^84 - 1952 * q^86 + 2708 * q^87 - 216 * q^88 - 1476 * q^89 - 1236 * q^91 - 5232 * q^92 + 3024 * q^93 - 63 * q^94 - 10424 * q^96 - 318 * q^97 + 15022 * q^98 - 1697 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−2.77209	+	4.80141i	−0.980083	+	1.69755i	−0.318058	+	0.948071i	$0.603031\pi$
$2$	−2.77209	+	4.80141i	−0.980083	+	1.69755i	−0.662025	+	0.749482i	$0.730303\pi$
$3$	0.320819	−	5.18624i	0.0617417	−	0.998092i
$3$	0.320819	−	5.18624i	0.0617417	−	0.998092i
$4$	−11.3690	−	19.6917i	−1.42112	−	2.46146i
$5$		0			0
$5$		0			0
$6$	24.0119	+	15.9171i	1.63380	+	1.08302i
$7$	12.8563	−	22.2678i	0.694177	−	1.20235i	−0.276281	−	0.961077i	$-0.589102\pi$
$7$	12.8563	−	22.2678i	0.694177	−	1.20235i	0.970457	−	0.241272i	$-0.0775646\pi$
$8$	81.7101			3.61111
$9$	−26.7942	−	3.32769i	−0.992376	−	0.123248i
$10$		0			0
$11$	−3.12792	+	5.41771i	−0.0857366	+	0.148500i	−0.905705	−	0.423909i	$-0.860658\pi$
$11$	−3.12792	+	5.41771i	−0.0857366	+	0.148500i	0.819968	+	0.572409i	$0.193991\pi$
$12$	−105.773	+	52.6449i	−2.54451	+	1.26644i
$13$	−7.62998	−	13.2155i	−0.162783	−	0.281948i	0.773083	−	0.634305i	$-0.218714\pi$
$13$	−7.62998	−	13.2155i	−0.162783	−	0.281948i	−0.935866	+	0.352357i	$0.885380\pi$
$14$	71.2779	+	123.457i	1.36070	+	2.35680i
$15$		0			0
$16$	−135.556	+	234.790i	−2.11806	+	3.66859i
$17$	36.0074			0.513710			0.256855	−	0.966450i	$-0.417314\pi$
$17$	36.0074			0.513710			0.256855	+	0.966450i	$0.417314\pi$
$18$	90.2535	−	119.425i	1.18183	−	1.56382i
$19$	−52.7512			−0.636945			−0.318472	−	0.947932i	$-0.603170\pi$
$19$	−52.7512			−0.636945			−0.318472	+	0.947932i	$0.603170\pi$
$20$		0			0
$21$	−111.362	−	73.8199i	−1.15720	−	0.767087i
$22$	−17.3418	−	30.0368i	−0.168058	−	0.291085i
$23$	−41.8670	−	72.5158i	−0.379560	−	0.657417i	0.611438	−	0.791292i	$-0.290591\pi$
$23$	−41.8670	−	72.5158i	−0.379560	−	0.657417i	−0.990998	+	0.133875i	$0.957258\pi$
$24$	26.2142	−	423.768i	0.222956	−	3.60422i
$25$		0			0
$26$	84.6040			0.638162
$27$	−25.8543	+	137.893i	−0.184284	+	0.982873i
$28$	−584.654			−3.94604
$29$	−59.5457	+	103.136i	−0.381288	+	0.660411i	−0.991247	−	0.132023i	$-0.957853\pi$
$29$	−59.5457	+	103.136i	−0.381288	+	0.660411i	0.609958	+	0.792433i	$0.291186\pi$
$30$		0			0
$31$	−138.331	−	239.596i	−0.801449	−	1.38815i	−0.918663	−	0.395043i	$-0.870730\pi$
$31$	−138.331	−	239.596i	−0.801449	−	1.38815i	0.117214	−	0.993107i	$-0.462604\pi$
$32$	−424.708	−	735.615i	−2.34620	−	4.06374i
$33$	27.0941	+	17.9602i	0.142923	+	0.0947417i
$34$	−99.8157	+	172.886i	−0.503478	+	0.872050i
$35$		0			0
$36$	239.095	+	565.454i	1.10692	+	2.61784i
$37$	117.553			0.522315			0.261158	−	0.965296i	$-0.415896\pi$
$37$	117.553			0.522315			0.261158	+	0.965296i	$0.415896\pi$
$38$	146.231	−	253.280i	0.624258	−	1.08125i
$39$	−70.9867	+	35.3311i	−0.291461	+	0.145064i
$40$		0			0
$41$	79.6608	+	137.977i	0.303437	+	0.525569i	0.976912	−	0.213641i	$-0.0685324\pi$
$41$	79.6608	+	137.977i	0.303437	+	0.525569i	−0.673475	+	0.739210i	$0.735199\pi$
$42$	663.144	−	330.057i	2.43632	−	1.21259i
$43$	−147.482	+	255.446i	−0.523040	+	0.905932i	0.476600	+	0.879120i	$0.341869\pi$
$43$	−147.482	+	255.446i	−0.523040	+	0.905932i	−0.999640	+	0.0268122i	$0.991464\pi$
$44$	142.245			0.487370
$45$		0			0
$46$	464.237			1.48800
$47$	41.6458	−	72.1327i	0.129248	−	0.223865i	−0.794137	−	0.607738i	$-0.792077\pi$
$47$	41.6458	−	72.1327i	0.129248	−	0.223865i	0.923386	+	0.383874i	$0.125410\pi$
$48$	1174.19	+	778.352i	3.53082	+	2.34053i
$49$	−159.070	−	275.518i	−0.463762	−	0.803260i
$50$		0			0
$51$	11.5519	−	186.743i	0.0317173	−	0.512730i
$52$	−173.490	+	300.494i	−0.462669	+	0.801366i
$53$	−149.018			−0.386212			−0.193106	−	0.981178i	$-0.561856\pi$
$53$	−149.018			−0.386212			−0.193106	+	0.981178i	$0.561856\pi$
$54$	−590.411	−	506.390i	−1.48787	−	1.27613i
$55$		0			0
$56$	1050.49	−	1819.51i	2.50675	−	4.34182i
$57$	−16.9236	+	273.580i	−0.0393260	+	0.635729i
$58$	−330.132	−	571.806i	−0.747388	−	1.29451i
$59$	−317.731	−	550.325i	−0.701102	−	1.21434i	−0.968080	−	0.250641i	$-0.919359\pi$
$59$	−317.731	−	550.325i	−0.701102	−	1.21434i	0.266978	−	0.963703i	$-0.413975\pi$
$60$		0			0
$61$	−298.575	+	517.148i	−0.626699	+	1.08548i	0.361510	+	0.932368i	$0.382261\pi$
$61$	−298.575	+	517.148i	−0.626699	+	1.08548i	−0.988210	+	0.153107i	$0.951072\pi$
$62$	1533.86			3.14194
$63$	−418.575	+	553.865i	−0.837071	+	1.10763i
$64$	2540.42			4.96175
$65$		0			0
$66$	−161.342	+	80.3021i	−0.300906	+	0.149765i
$67$	−165.008	−	285.802i	−0.300879	−	0.521138i	0.675456	−	0.737400i	$-0.263947\pi$
$67$	−165.008	−	285.802i	−0.300879	−	0.521138i	−0.976335	+	0.216262i	$0.930613\pi$
$68$	−409.367	−	709.045i	−0.730045	−	1.26448i
$69$	−389.516	+	193.868i	−0.679598	+	0.338246i
$70$		0			0
$71$	−1149.79			−1.92189			−0.960947	−	0.276732i	$-0.910749\pi$
$71$	−1149.79			−1.92189			−0.960947	+	0.276732i	$0.910749\pi$
$72$	−2189.35	−	271.906i	−3.58358	−	0.445062i
$73$	130.284			0.208885			0.104442	−	0.994531i	$-0.466694\pi$
$73$	130.284			0.208885			0.104442	+	0.994531i	$0.466694\pi$
$74$	−325.869	+	564.422i	−0.511912	+	0.886658i
$75$		0			0
$76$	599.728	+	1038.76i	0.905177	+	1.56781i
$77$	80.4271	+	139.304i	0.119033	+	0.206171i
$78$	27.1426	−	438.777i	0.0394012	−	0.636945i
$79$	368.918	−	638.984i	0.525398	−	0.910017i	−0.474164	−	0.880437i	$-0.657250\pi$
$79$	368.918	−	638.984i	0.525398	−	0.910017i	0.999562	−	0.0295801i	$-0.00941703\pi$
$80$		0			0
$81$	706.853	+	178.325i	0.969620	+	0.244616i
$82$	−883.309			−1.18957
$83$	−184.951	+	320.345i	−0.244591	+	0.423644i	−0.962016	−	0.272991i	$-0.911987\pi$
$83$	−184.951	+	320.345i	−0.244591	+	0.423644i	0.717426	+	0.696635i	$0.245320\pi$
$84$	−187.568	+	3032.16i	−0.243635	+	3.93852i
$85$		0			0
$86$	−817.665	−	1416.24i	−1.02525	−	1.77578i
$87$	515.785	+	341.906i	0.635609	+	0.421336i
$88$	−255.583	+	442.682i	−0.309605	+	0.536251i
$89$	−225.638			−0.268737			−0.134369	−	0.990931i	$-0.542901\pi$
$89$	−225.638			−0.268737			−0.134369	+	0.990931i	$0.542901\pi$
$90$		0			0
$91$	−392.374			−0.452000
$92$	−951.972	+	1648.86i	−1.07880	+	1.86854i
$93$	−1286.98	+	640.549i	−1.43498	+	0.714213i
$94$	230.892	+	399.917i	0.253348	+	0.438812i
$95$		0			0
$96$	−3951.33	+	1966.64i	−4.20084	+	2.09082i
$97$	−5.95671	+	10.3173i	−0.00623518	+	0.0107996i	−0.869126	−	0.494590i	$-0.835318\pi$
$97$	−5.95671	+	10.3173i	−0.00623518	+	0.0107996i	0.862891	+	0.505390i	$0.168651\pi$
$98$	1763.83			1.81810
$99$	101.838	−	134.754i	0.103385	−	0.136801i
$100$		0			0
$101$	−383.267	+	663.838i	−0.377589	+	0.654003i	−0.990711	−	0.135985i	$-0.956580\pi$
$101$	−383.267	+	663.838i	−0.377589	+	0.654003i	0.613122	+	0.789988i	$0.289913\pi$
$102$	864.605	+	573.133i	0.839300	+	0.556359i
$103$	−774.737	−	1341.88i	−0.741137	−	1.28369i	−0.951978	−	0.306166i	$-0.900954\pi$
$103$	−774.737	−	1341.88i	−0.741137	−	1.28369i	0.210841	−	0.977520i	$-0.432380\pi$
$104$	−623.447	−	1079.84i	−0.587827	−	1.01815i
$105$		0			0
$106$	413.093	−	715.497i	0.378520	−	0.655615i
$107$	1218.43			1.10084			0.550421	−	0.834887i	$-0.314467\pi$
$107$	1218.43			1.10084			0.550421	+	0.834887i	$0.314467\pi$
$108$	3009.29	−	1058.59i	2.68119	−	0.943178i
$109$	−1327.27			−1.16633			−0.583163	−	0.812355i	$-0.698185\pi$
$109$	−1327.27			−1.16633			−0.583163	+	0.812355i	$0.698185\pi$
$110$		0			0
$111$	37.7134	−	609.660i	0.0322486	−	0.521319i
$112$	3485.51	+	6037.08i	2.94062	+	5.09330i
$113$	−216.828	−	375.557i	−0.180509	−	0.312650i	0.761545	−	0.648112i	$-0.224441\pi$
$113$	−216.828	−	375.557i	−0.180509	−	0.312650i	−0.942054	+	0.335462i	$0.891108\pi$
$114$	−1266.66	−	839.646i	−1.04064	−	0.689825i
$115$		0			0
$116$	2707.90			2.16743
$117$	160.462	+	379.489i	0.126792	+	0.299861i
$118$	3523.11			2.74855
$119$	462.922	−	801.805i	0.356605	−	0.617658i
$120$		0			0
$121$	645.932	+	1118.79i	0.485298	+	0.840562i
$122$	−1655.36	−	2867.16i	−1.22843	−	2.12771i
$123$	741.136	−	368.875i	0.543301	−	0.270409i
$124$	−3145.36	+	5447.92i	−2.27792	+	3.94547i
$125$		0			0
$126$	−1499.00	−	3545.11i	−1.05986	−	2.50654i
$127$	−1850.18			−1.29273			−0.646365	−	0.763028i	$-0.723712\pi$
$127$	−1850.18			−1.29273			−0.646365	+	0.763028i	$0.723712\pi$
$128$	−3644.61	+	6312.65i	−2.51673	+	4.35910i
$129$	1277.49	+	846.827i	0.871911	+	0.577976i
$130$		0			0
$131$	638.716	+	1106.29i	0.425991	+	0.737839i	0.996512	−	0.0834443i	$-0.0265921\pi$
$131$	638.716	+	1106.29i	0.425991	+	0.737839i	−0.570521	+	0.821283i	$0.693259\pi$
$132$	45.6350	−	737.717i	0.0300910	−	0.486440i
$133$	−678.186	+	1174.65i	−0.442152	+	0.765830i
$134$	1829.67			1.17954
$135$		0			0
$136$	2942.17			1.85506
$137$	766.766	−	1328.08i	0.478170	−	0.828214i	−0.521517	−	0.853241i	$-0.674634\pi$
$137$	766.766	−	1328.08i	0.478170	−	0.828214i	0.999687	+	0.0250268i	$0.00796711\pi$
$138$	148.936	−	2407.64i	0.0918717	−	1.48516i
$139$	−766.669	−	1327.91i	−0.467828	−	0.810301i	0.531497	−	0.847060i	$-0.321630\pi$
$139$	−766.669	−	1327.91i	−0.467828	−	0.810301i	−0.999324	+	0.0367593i	$0.988297\pi$
$140$		0			0
$141$	−360.737	−	239.127i	−0.215457	−	0.142823i
$142$	3187.31	−	5520.59i	1.88362	−	3.26252i
$143$	95.4638			0.0558258
$144$	4413.42	−	5839.91i	2.55406	−	3.37958i
$145$		0			0
$146$	−361.159	+	625.545i	−0.204724	+	0.354593i
$147$	−1479.94	+	736.586i	−0.830361	+	0.413283i
$148$	−1336.46	−	2314.82i	−0.742275	−	1.28566i
$149$	1251.54	+	2167.73i	0.688120	+	1.19186i	0.972445	+	0.233131i	$0.0748971\pi$
$149$	1251.54	+	2167.73i	0.688120	+	1.19186i	−0.284325	+	0.958728i	$0.591770\pi$
$150$		0			0
$151$	760.321	−	1316.92i	0.409762	−	0.709729i	−0.585101	−	0.810961i	$-0.698945\pi$
$151$	760.321	−	1316.92i	0.409762	−	0.709729i	0.994863	+	0.101232i	$0.0322784\pi$
$152$	−4310.30			−2.30008
$153$	−964.786	−	119.821i	−0.509793	−	0.0633136i
$154$	−891.805			−0.466648
$155$		0			0
$156$	1502.78	+	996.167i	0.771271	+	0.511264i
$157$	−1296.44	−	2245.50i	−0.659026	−	1.14147i	−0.980868	−	0.194674i	$-0.937635\pi$
$157$	−1296.44	−	2245.50i	−0.659026	−	1.14147i	0.321842	−	0.946793i	$-0.395698\pi$
$158$	2045.35	+	3542.65i	1.02987	+	1.78378i
$159$	−47.8079	+	772.845i	−0.0238454	+	0.385475i
$160$		0			0
$161$	−2153.03			−1.05393
$162$	−2815.67	+	2899.55i	−1.36556	+	1.40624i
$163$	−675.580			−0.324635			−0.162318	−	0.986739i	$-0.551897\pi$
$163$	−675.580			−0.324635			−0.162318	+	0.986739i	$0.551897\pi$
$164$	1811.33	−	3137.31i	0.862444	−	1.49380i
$165$		0			0
$166$	−1025.40	−	1776.05i	−0.479438	−	0.830412i
$167$	1947.97	+	3373.97i	0.902623	+	1.56339i	0.824076	+	0.566479i	$0.191695\pi$
$167$	1947.97	+	3373.97i	0.902623	+	1.56339i	0.0785470	+	0.996910i	$0.474972\pi$
$168$	−9099.38	−	6031.84i	−4.17876	−	2.77004i
$169$	982.067	−	1700.99i	0.447004	−	0.774233i
$170$		0			0
$171$	1413.42	+	175.540i	0.632088	+	0.0785020i
$172$	6706.87			2.97322
$173$	25.8304	−	44.7396i	0.0113517	−	0.0196618i	−0.860294	−	0.509799i	$-0.829720\pi$
$173$	25.8304	−	44.7396i	0.0113517	−	0.0196618i	0.871645	+	0.490137i	$0.163053\pi$
$174$	−3071.44	+	1528.70i	−1.33819	+	0.666037i
$175$		0			0
$176$	−848.017	−	1468.81i	−0.363191	−	0.629066i
$177$	−2956.05	+	1471.27i	−1.25531	+	0.624788i
$178$	625.490	−	1083.38i	0.263385	−	0.456195i
$179$	4553.37			1.90131			0.950656	−	0.310247i	$-0.100412\pi$
$179$	4553.37			1.90131			0.950656	+	0.310247i	$0.100412\pi$
$180$		0			0
$181$	2441.01			1.00243			0.501213	−	0.865324i	$-0.332887\pi$
$181$	2441.01			1.00243			0.501213	+	0.865324i	$0.332887\pi$
$182$	1087.70	−	1883.95i	0.442997	−	0.767294i
$183$	2586.26	+	1714.39i	1.04471	+	0.692523i
$184$	−3420.96	−	5925.28i	−1.37063	−	2.37401i
$185$		0			0
$186$	492.092	−	7954.97i	0.193989	−	3.13595i
$187$	−112.628	+	195.078i	−0.0440437	+	0.0762860i
$188$	−1893.88			−0.734711
$189$	2738.19	+	2348.52i	1.05383	+	0.903861i
$190$		0			0
$191$	−663.053	+	1148.44i	−0.251188	+	0.435070i	−0.963853	−	0.266434i	$-0.914154\pi$
$191$	−663.053	+	1148.44i	−0.251188	+	0.435070i	0.712665	+	0.701504i	$0.247488\pi$
$192$	815.015	−	13175.2i	0.306347	−	4.95229i
$193$	724.098	+	1254.17i	0.270061	+	0.467759i	0.968877	−	0.247542i	$-0.0796229\pi$
$193$	724.098	+	1254.17i	0.270061	+	0.467759i	−0.698816	+	0.715301i	$0.746290\pi$
$194$	−33.0251	−	57.2012i	−0.0122220	−	0.0211691i
$195$		0			0
$196$	−3616.94	+	6264.73i	−1.31813	+	2.28306i
$197$	2398.84			0.867564			0.433782	−	0.901018i	$-0.357179\pi$
$197$	2398.84			0.867564			0.433782	+	0.901018i	$0.357179\pi$
$198$	364.704	+	862.519i	0.130901	+	0.309578i
$199$	3109.15			1.10755			0.553773	−	0.832667i	$-0.313187\pi$
$199$	3109.15			1.10755			0.553773	+	0.832667i	$0.313187\pi$
$200$		0			0
$201$	−1535.17	+	764.078i	−0.538720	+	0.268129i
$202$	−2124.90	−	3680.44i	−0.740137	−	1.28195i
$203$	1531.08	+	2651.91i	0.529363	+	0.916883i
$204$	−3808.61	+	1895.60i	−1.30714	+	0.650582i
$205$		0			0
$206$	8590.57			2.90550
$207$	880.481	+	2082.32i	0.295641	+	0.699185i
$208$	4137.16			1.37914
$209$	165.001	−	285.791i	0.0546095	−	0.0945864i
$210$		0			0
$211$	1654.80	+	2866.19i	0.539910	+	0.935151i	0.998908	+	0.0467139i	$0.0148749\pi$
$211$	1654.80	+	2866.19i	0.539910	+	0.935151i	−0.458999	+	0.888437i	$0.651792\pi$
$212$	1694.19	+	2934.42i	0.548855	+	0.950645i
$213$	−368.873	+	5963.07i	−0.118661	+	1.91823i
$214$	−3377.60	+	5850.18i	−1.07892	+	1.86874i
$215$		0			0
$216$	−2112.56	+	11267.3i	−0.665469	+	3.54926i
$217$	−7113.69			−2.22539
$218$	3679.32	−	6372.76i	1.14310	−	1.97990i
$219$	41.7976	−	675.683i	0.0128969	−	0.208486i
$220$		0			0
$221$	−274.735	−	475.856i	−0.0836231	−	0.144839i
$222$	2822.68	+	1871.11i	0.853360	+	0.565679i
$223$	1399.42	−	2423.86i	0.420233	−	0.727865i	−0.575729	−	0.817641i	$-0.695282\pi$
$223$	1399.42	−	2423.86i	0.420233	−	0.727865i	0.995962	+	0.0897754i	$0.0286149\pi$
$224$	−21840.7			−6.51471
$225$		0			0
$226$	2404.27			0.707653
$227$	1564.59	−	2709.94i	0.457468	−	0.792358i	−0.541358	−	0.840792i	$-0.682090\pi$
$227$	1564.59	−	2709.94i	0.457468	−	0.792358i	0.998826	+	0.0484343i	$0.0154231\pi$
$228$	5579.66	−	2777.08i	1.62071	−	0.806651i
$229$	−1487.79	−	2576.93i	−0.429327	−	0.743616i	0.567487	−	0.823383i	$-0.307916\pi$
$229$	−1487.79	−	2576.93i	−0.429327	−	0.743616i	−0.996814	+	0.0797667i	$0.974582\pi$
$230$		0			0
$231$	748.265	−	372.423i	0.213127	−	0.106076i
$232$	−4865.49	+	8427.27i	−1.37687	+	2.38482i
$233$	925.895			0.260332			0.130166	−	0.991492i	$-0.458449\pi$
$233$	925.895			0.260332			0.130166	+	0.991492i	$0.458449\pi$
$234$	−2266.89	−	281.536i	−0.633297	−	0.0786521i
$235$		0			0
$236$	−7224.55	+	12513.3i	−1.99271	+	3.45147i
$237$	−3195.57	−	2118.29i	−0.875842	−	0.580582i
$238$	2566.53	+	4445.36i	0.699005	+	1.21071i
$239$	−1305.41	−	2261.04i	−0.353305	−	0.611942i	0.633521	−	0.773725i	$-0.281609\pi$
$239$	−1305.41	−	2261.04i	−0.353305	−	0.611942i	−0.986826	+	0.161783i	$0.948276\pi$
$240$		0			0
$241$	334.737	−	579.781i	0.0894700	−	0.154967i	−0.817817	−	0.575478i	$-0.804816\pi$
$241$	334.737	−	579.781i	0.0894700	−	0.154967i	0.907287	+	0.420511i	$0.138149\pi$
$242$	−7162.34			−1.90253
$243$	1151.61	−	3608.70i	0.304016	−	0.952667i
$244$	13578.0			3.56247
$245$		0			0
$246$	−283.382	+	4581.05i	−0.0734464	+	1.18731i
$247$	402.490	+	697.134i	0.103684	+	0.179585i
$248$	−11303.0	−	19577.4i	−2.89412	−	5.01276i
$249$	1602.05	+	1061.97i	0.407734	+	0.270281i
$250$		0			0
$251$	−6463.00			−1.62526			−0.812631	−	0.582778i	$-0.801966\pi$
$251$	−6463.00			−1.62526			−0.812631	+	0.582778i	$0.801966\pi$
$252$	15665.3	+	1945.55i	3.91596	+	0.486341i
$253$	523.827			0.130169
$254$	5128.87	−	8883.46i	1.26698	−	2.19448i
$255$		0			0
$256$	−10044.7	−	17398.0i	−2.45233	−	4.24755i
$257$	−1417.66	−	2455.47i	−0.344091	−	0.595984i	0.641097	−	0.767460i	$-0.278480\pi$
$257$	−1417.66	−	2455.47i	−0.344091	−	0.595984i	−0.985188	+	0.171476i	$0.945146\pi$
$258$	−7607.27	+	3786.25i	−1.83569	+	0.913650i
$259$	1511.31	−	2617.66i	0.362579	−	0.628005i
$260$		0			0
$261$	1938.68	−	2565.30i	0.459775	−	0.608383i
$262$	−7082.32			−1.67003
$263$	−816.837	+	1414.80i	−0.191515	+	0.331713i	−0.945752	−	0.324888i	$-0.894673\pi$
$263$	−816.837	+	1414.80i	−0.191515	+	0.331713i	0.754238	+	0.656601i	$0.228007\pi$
$264$	2213.86	+	1467.53i	0.516112	+	0.342123i
$265$		0			0
$266$	−3759.99	−	6512.49i	−0.866691	−	1.50115i
$267$	−72.3891	+	1170.21i	−0.0165923	+	0.268224i
$268$	−3751.94	+	6498.55i	−0.855173	+	1.48120i
$269$	−4870.30			−1.10389			−0.551947	−	0.833880i	$-0.686115\pi$
$269$	−4870.30			−1.10389			−0.551947	+	0.833880i	$0.686115\pi$
$270$		0			0
$271$	−3913.17			−0.877153			−0.438576	−	0.898694i	$-0.644517\pi$
$271$	−3913.17			−0.877153			−0.438576	+	0.898694i	$0.644517\pi$
$272$	−4881.02	+	8454.17i	−1.08807	+	1.88459i
$273$	−125.881	+	2034.95i	−0.0279072	+	0.451138i
$274$	4251.09	+	7363.11i	0.937291	+	1.62344i
$275$		0			0
$276$	8245.99	+	5466.14i	1.79837	+	1.19211i
$277$	409.072	−	708.534i	0.0887320	−	0.153688i	−0.818243	−	0.574872i	$-0.805052\pi$
$277$	409.072	−	708.534i	0.0887320	−	0.153688i	0.906975	+	0.421184i	$0.138385\pi$
$278$	8501.11			1.83404
$279$	2909.15	+	6880.08i	0.624252	+	1.47634i
$280$		0			0
$281$	2581.48	−	4471.25i	0.548035	−	0.949225i	−0.450374	−	0.892840i	$-0.648709\pi$
$281$	2581.48	−	4471.25i	0.548035	−	0.949225i	0.998409	−	0.0563851i	$-0.0179574\pi$
$282$	2148.14	−	1069.16i	0.453617	−	0.225772i
$283$	−3573.29	−	6189.11i	−0.750565	−	1.30002i	−0.947549	−	0.319610i	$-0.896448\pi$
$283$	−3573.29	−	6189.11i	−0.750565	−	1.30002i	0.196984	−	0.980407i	$-0.436885\pi$
$284$	13071.9	+	22641.2i	2.73125	+	4.73067i
$285$		0			0
$286$	−264.635	+	458.360i	−0.0547139	+	0.0947672i
$287$	4096.58			0.842556
$288$	8931.78	+	21123.5i	1.82747	+	4.32192i
$289$	−3616.47			−0.736102
$290$		0			0
$291$	51.5971	+	34.2029i	0.0103941	+	0.00689007i
$292$	−1481.20	−	2565.51i	−0.296851	−	0.514161i
$293$	−732.548	−	1268.81i	−0.146061	−	0.252985i	0.783707	−	0.621130i	$-0.213326\pi$
$293$	−732.548	−	1268.81i	−0.146061	−	0.252985i	−0.929768	+	0.368145i	$0.879993\pi$
$294$	565.871	−	9147.65i	0.112253	−	1.81463i
$295$		0			0
$296$	9605.31			1.88614
$297$	−666.196	−	571.390i	−0.130157	−	0.111634i
$298$	−13877.5			−2.69766
$299$	−638.889	+	1106.59i	−0.123572	+	0.214032i
$300$		0			0
$301$	3792.14	+	6568.19i	0.726165	+	1.25775i
$302$	4215.36	+	7301.22i	0.803202	+	1.39119i
$303$	3319.86	+	2200.68i	0.629442	+	0.417248i
$304$	7150.74	−	12385.4i	1.34909	−	2.33669i
$305$		0			0
$306$	3249.79	−	4300.17i	0.607118	−	0.803348i
$307$	790.554			0.146968			0.0734842	−	0.997296i	$-0.476588\pi$
$307$	790.554			0.146968			0.0734842	+	0.997296i	$0.476588\pi$
$308$	1828.75	−	3167.49i	0.338321	−	0.585988i
$309$	−7207.88	+	3587.47i	−1.32700	+	0.660466i
$310$		0			0
$311$	−1962.65	−	3399.42i	−0.357852	−	0.619817i	0.629750	−	0.776798i	$-0.283157\pi$
$311$	−1962.65	−	3399.42i	−0.357852	−	0.619817i	−0.987602	+	0.156981i	$0.949824\pi$
$312$	−5800.33	+	2886.91i	−1.05250	+	0.523843i
$313$	2871.19	−	4973.04i	0.518495	−	0.898060i	−0.481274	−	0.876570i	$-0.659826\pi$
$313$	2871.19	−	4973.04i	0.518495	−	0.898060i	0.999769	−	0.0214900i	$-0.00684100\pi$
$314$	14375.4			2.58360
$315$		0			0
$316$	−16776.9			−2.98663
$317$	4068.35	−	7046.59i	0.720824	−	1.24850i	−0.239846	−	0.970811i	$-0.577097\pi$
$317$	4068.35	−	7046.59i	0.720824	−	1.24850i	0.960670	−	0.277693i	$-0.0895697\pi$
$318$	−3578.21	−	2371.94i	−0.630994	−	0.418276i
$319$	−372.508	−	645.203i	−0.0653807	−	0.113243i
$320$		0			0
$321$	390.896	−	6319.07i	0.0679679	−	1.09874i
$322$	5968.39	−	10337.5i	1.03294	−	1.78910i
$323$	−1899.43			−0.327205
$324$	−4524.68	−	15946.5i	−0.775837	−	2.73431i
$325$		0			0
$326$	1872.77	−	3243.73i	0.318169	−	0.551085i
$327$	−425.814	+	6883.54i	−0.0720109	+	1.16410i
$328$	6509.10	+	11274.1i	1.09575	+	1.89789i
$329$	−1070.83	−	1854.72i	−0.179442	−	0.310803i
$330$		0			0
$331$	3163.47	−	5479.29i	0.525317	−	0.909876i	−0.474248	−	0.880391i	$-0.657280\pi$
$331$	3163.47	−	5479.29i	0.525317	−	0.909876i	0.999565	−	0.0294849i	$-0.00938671\pi$
$332$	8410.84			1.39038
$333$	−3149.74	−	391.181i	−0.518333	−	0.0643742i
$334$	−21599.8			−3.53858
$335$		0			0
$336$	32427.9	−	16139.9i	5.26515	−	2.62054i
$337$	2387.01	+	4134.42i	0.385842	+	0.668297i	0.991886	−	0.127134i	$-0.0405778\pi$
$337$	2387.01	+	4134.42i	0.385842	+	0.668297i	−0.606044	+	0.795431i	$0.707244\pi$
$338$	5444.76	+	9430.60i	0.876201	+	1.51762i
$339$	−2017.29	+	1004.04i	−0.323198	+	0.160861i
$340$		0			0
$341$	1730.75			0.274854
$342$	−4760.97	+	6299.80i	−0.752760	+	0.996065i
$343$	639.195			0.100622
$344$	−12050.7	+	20872.5i	−1.88876	+	3.27142i
$345$		0			0
$346$	143.209	+	248.045i	0.0222513	+	0.0385404i
$347$	−909.717	−	1575.68i	−0.140738	−	0.243766i	0.787037	−	0.616906i	$-0.211614\pi$
$347$	−909.717	−	1575.68i	−0.140738	−	0.243766i	−0.927775	+	0.373141i	$0.878281\pi$
$348$	868.746	−	14043.8i	0.133821	−	2.16330i
$349$	1488.69	−	2578.48i	0.228331	−	0.395481i	−0.728982	−	0.684532i	$-0.760006\pi$
$349$	1488.69	−	2578.48i	0.228331	−	0.395481i	0.957314	+	0.289051i	$0.0933397\pi$
$350$		0			0
$351$	2019.60	−	710.445i	0.307117	−	0.108036i
$352$	5313.80			0.804621
$353$	3473.89	−	6016.95i	0.523786	−	0.907223i	−0.475831	−	0.879537i	$-0.657853\pi$
$353$	3473.89	−	6016.95i	0.523786	−	0.907223i	0.999617	−	0.0276865i	$-0.00881401\pi$
$354$	1130.28	−	18271.7i	0.169700	−	2.74331i
$355$		0			0
$356$	2565.28	+	4443.19i	0.381909	+	0.661485i
$357$	−4009.84	−	2658.06i	−0.594463	−	0.394060i
$358$	−12622.4	+	21862.6i	−1.86344	+	3.22758i
$359$	−3665.56			−0.538887			−0.269444	−	0.963016i	$-0.586840\pi$
$359$	−3665.56			−0.538887			−0.269444	+	0.963016i	$0.586840\pi$
$360$		0			0
$361$	−4076.31			−0.594302
$362$	−6766.71	+	11720.3i	−0.982460	+	1.70167i
$363$	6009.53	−	2991.03i	0.868921	−	0.432475i
$364$	4460.90	+	7726.50i	0.642348	+	1.11258i
$365$		0			0
$366$	−15400.9	+	7665.24i	−2.19950	+	1.09472i
$367$	4831.54	−	8368.48i	0.687206	−	1.19028i	−0.285532	−	0.958369i	$-0.592170\pi$
$367$	4831.54	−	8368.48i	0.687206	−	1.19028i	0.972738	−	0.231906i	$-0.0744963\pi$
$368$	22701.3			3.21573
$369$	−1675.30	−	3962.05i	−0.236349	−	0.558960i
$370$		0			0
$371$	−1915.83	+	3318.31i	−0.268099	+	0.464362i
$372$	27245.1	+	18060.4i	3.79730	+	2.51717i
$373$	−3011.86	−	5216.70i	−0.418092	−	0.724157i	0.577655	−	0.816281i	$-0.303968\pi$
$373$	−3011.86	−	5216.70i	−0.418092	−	0.724157i	−0.995748	+	0.0921237i	$0.970634\pi$
$374$	−624.431	−	1081.55i	−0.0863330	−	0.149533i
$375$		0			0
$376$	3402.89	−	5893.97i	0.466730	−	0.808400i
$377$	1817.33			0.248269
$378$	−18866.7	+	6636.85i	−2.56719	+	0.903076i
$379$	−1229.32			−0.166613			−0.0833063	−	0.996524i	$-0.526548\pi$
$379$	−1229.32			−0.166613			−0.0833063	+	0.996524i	$0.526548\pi$
$380$		0			0
$381$	−593.573	+	9595.47i	−0.0798154	+	1.29026i
$382$	−3676.09	−	6367.17i	−0.492369	−	0.852809i
$383$	−1066.80	−	1847.75i	−0.142326	−	0.246515i	0.786046	−	0.618168i	$-0.212125\pi$
$383$	−1066.80	−	1847.75i	−0.142326	−	0.246515i	−0.928372	+	0.371652i	$0.878791\pi$
$384$	31569.7	+	20927.0i	4.19540	+	2.78106i
$385$		0			0
$386$	−8029.07			−1.05873
$387$	4801.69	−	6353.67i	0.630707	−	0.834562i
$388$	270.887			0.0354439
$389$	−4920.76	+	8523.01i	−0.641369	+	1.11088i	0.343759	+	0.939058i	$0.388300\pi$
$389$	−4920.76	+	8523.01i	−0.641369	+	1.11088i	−0.985127	+	0.171825i	$0.945033\pi$
$390$		0			0
$391$	−1507.52	−	2611.10i	−0.194984	−	0.337722i
$392$	−12997.7	−	22512.6i	−1.67470	−	2.90066i
$393$	5942.39	−	2957.61i	0.762732	−	0.379623i
$394$	−6649.80	+	11517.8i	−0.850284	+	1.47274i
$395$		0			0
$396$	−3811.34	−	473.348i	−0.483654	−	0.0600672i
$397$	2548.71			0.322207			0.161104	−	0.986938i	$-0.448495\pi$
$397$	2548.71			0.322207			0.161104	+	0.986938i	$0.448495\pi$
$398$	−8618.85	+	14928.3i	−1.08549	+	1.88012i
$399$	5874.46	+	3894.09i	0.737069	+	0.488592i
$400$		0			0
$401$	6552.50	+	11349.3i	0.816001	+	1.41335i	0.908607	+	0.417652i	$0.137147\pi$
$401$	6552.50	+	11349.3i	0.816001	+	1.41335i	−0.0926064	+	0.995703i	$0.529520\pi$
$402$	586.992	−	9489.08i	0.0728271	−	1.17729i
$403$	−2110.92	+	3656.22i	−0.260924	+	0.451934i
$404$	17429.4			2.14640
$405$		0			0
$406$	−16977.2			−2.07528
$407$	−367.697	+	636.871i	−0.0447815	+	0.0775639i
$408$	943.903	−	15258.8i	0.114535	−	1.85152i
$409$	−3108.62	−	5384.29i	−0.375823	−	0.650944i	0.614627	−	0.788818i	$-0.289306\pi$
$409$	−3108.62	−	5384.29i	−0.375823	−	0.650944i	−0.990450	+	0.137874i	$0.955973\pi$
$410$		0			0
$411$	−6641.73	−	4402.70i	−0.797111	−	0.528393i
$412$	−17616.0	+	30511.7i	−2.10649	+	3.64856i
$413$	−16339.4			−1.94675
$414$	−12438.8	−	1544.84i	−1.47666	−	0.183393i
$415$		0			0
$416$	−6481.02	+	11225.5i	−0.763842	+	1.32301i
$417$	−7132.82	+	3550.11i	−0.837640	+	0.416906i
$418$	914.798	+	1584.48i	0.107044	+	0.185405i
$419$	−4214.03	−	7298.91i	−0.491334	−	0.851015i	0.508617	−	0.860993i	$-0.330157\pi$
$419$	−4214.03	−	7298.91i	−0.491334	−	0.851015i	−0.999950	+	0.00997827i	$0.996824\pi$
$420$		0			0
$421$	6389.69	−	11067.3i	0.739702	−	1.28120i	−0.212928	−	0.977068i	$-0.568300\pi$
$421$	6389.69	−	11067.3i	0.739702	−	1.28120i	0.952629	−	0.304133i	$-0.0983668\pi$
$422$	−18349.0			−2.11662
$423$	−1355.90	+	1794.15i	−0.155854	+	0.206228i
$424$	−12176.3			−1.39465
$425$		0			0
$426$	−27608.5	−	18301.3i	−3.14000	−	2.08146i
$427$	7677.17	+	13297.2i	0.870080	+	1.50702i
$428$	−13852.3	−	23992.9i	−1.56443	−	2.70968i
$429$	30.6266	−	495.098i	0.00344678	−	0.0557193i
$430$		0			0
$431$	3149.70			0.352009			0.176005	−	0.984389i	$-0.443683\pi$
$431$	3149.70			0.352009			0.176005	+	0.984389i	$0.443683\pi$
$432$	−28871.3	−	24762.6i	−3.21544	−	2.75785i
$433$	6999.89			0.776890			0.388445	−	0.921472i	$-0.373012\pi$
$433$	6999.89			0.776890			0.388445	+	0.921472i	$0.373012\pi$
$434$	19719.8	−	34155.7i	2.18106	−	3.77771i
$435$		0			0
$436$	15089.7	+	26136.2i	1.65749	+	2.87086i
$437$	2208.53	+	3825.29i	0.241759	+	0.418738i
$438$	3128.36	+	2073.74i	0.341276	+	0.226227i
$439$	3861.15	−	6687.71i	0.419778	−	0.727077i	−0.576139	−	0.817352i	$-0.695441\pi$
$439$	3861.15	−	6687.71i	0.419778	−	0.727077i	0.995917	+	0.0902746i	$0.0287745\pi$
$440$		0			0
$441$	3345.32	+	7911.61i	0.361226	+	0.854293i
$442$	3046.37			0.327830
$443$	−3324.37	+	5757.97i	−0.356536	+	0.617538i	−0.987380	−	0.158372i	$-0.949376\pi$
$443$	−3324.37	+	5757.97i	−0.356536	+	0.617538i	0.630844	+	0.775910i	$0.282709\pi$
$444$	−12434.0	+	6188.58i	−1.32903	+	0.661480i
$445$		0			0
$446$	7758.64	+	13438.4i	0.823727	+	1.42674i
$447$	11643.9	−	5795.32i	1.23207	−	0.613220i
$448$	32660.4	−	56569.5i	3.44433	−	5.96576i
$449$	−11416.8			−1.19998			−0.599989	−	0.800008i	$-0.704829\pi$
$449$	−11416.8			−1.19998			−0.599989	+	0.800008i	$0.704829\pi$
$450$		0			0
$451$	−996.690			−0.104063
$452$	−4930.23	+	8539.41i	−0.513050	+	0.888629i
$453$	−6585.91	−	4365.70i	−0.683075	−	0.452800i
$454$	8674.35	+	15024.4i	0.896713	+	1.55315i
$455$		0			0
$456$	−1382.83	+	22354.3i	−0.142011	+	2.29569i
$457$	−5595.73	+	9692.09i	−0.572773	+	0.992072i	0.423507	+	0.905893i	$0.360799\pi$
$457$	−5595.73	+	9692.09i	−0.572773	+	0.992072i	−0.996280	+	0.0861787i	$0.972534\pi$
$458$	16497.2			1.68310
$459$	−930.944	+	4965.17i	−0.0946683	+	0.504912i
$460$		0			0
$461$	2450.93	−	4245.14i	0.247617	−	0.428885i	−0.715247	−	0.698871i	$-0.753686\pi$
$461$	2450.93	−	4245.14i	0.247617	−	0.428885i	0.962864	+	0.269987i	$0.0870193\pi$
$462$	−286.108	+	4625.12i	−0.0288116	+	0.465757i
$463$	−1065.82	−	1846.06i	−0.106982	−	0.185299i	0.807564	−	0.589780i	$-0.200786\pi$
$463$	−1065.82	−	1846.06i	−0.106982	−	0.185299i	−0.914546	+	0.404481i	$0.867452\pi$
$464$	−16143.6	−	27961.5i	−1.61519	−	2.79758i
$465$		0			0
$466$	−2566.67	+	4445.60i	−0.255147	+	0.441928i
$467$	17877.0			1.77141			0.885707	−	0.464246i	$-0.153675\pi$
$467$	17877.0			1.77141			0.885707	+	0.464246i	$0.153675\pi$
$468$	5648.48	−	7474.16i	0.557908	−	0.738234i
$469$	−8485.57			−0.835452
$470$		0			0
$471$	−12061.6	+	6003.24i	−1.17998	+	0.587293i
$472$	−25961.8	−	44967.2i	−2.53176	−	4.38513i
$473$	−922.621	−	1598.03i	−0.0896874	−	0.155343i
$474$	19029.2	−	9471.11i	1.84397	−	0.917769i
$475$		0			0
$476$	−21051.8			−2.02712
$477$	3992.82	+	495.887i	0.383268	+	0.0475998i
$478$	14474.9			1.38507
$479$	−10208.9	+	17682.3i	−0.973811	+	1.68669i	−0.290006	+	0.957025i	$0.593657\pi$
$479$	−10208.9	+	17682.3i	−0.973811	+	1.68669i	−0.683805	+	0.729665i	$0.739676\pi$
$480$		0			0
$481$	−896.930	−	1553.53i	−0.0850239	−	0.147266i
$482$	1855.84	+	3214.41i	0.175376	+	0.303760i
$483$	−690.732	+	11166.1i	−0.0650712	+	1.05192i
$484$	14687.2	−	25439.0i	1.37934	−	2.38908i
$485$		0			0
$486$	14134.5	+	15533.0i	1.31924	+	1.44978i
$487$	8337.59			0.775795			0.387898	−	0.921702i	$-0.373201\pi$
$487$	8337.59			0.775795			0.387898	+	0.921702i	$0.373201\pi$
$488$	−24396.6	+	42256.2i	−2.26308	+	3.91977i
$489$	−216.739	+	3503.72i	−0.0200435	+	0.324016i
$490$		0			0
$491$	−8132.34	−	14085.6i	−0.747469	−	1.29465i	−0.949032	−	0.315179i	$-0.897935\pi$
$491$	−8132.34	−	14085.6i	−0.747469	−	1.29465i	0.201563	−	0.979476i	$-0.435398\pi$
$492$	−15689.7	−	10400.5i	−1.43770	−	0.953029i
$493$	−2144.08	+	3713.66i	−0.195871	+	0.339259i
$494$	−4462.96			−0.406474
$495$		0			0
$496$	75006.2			6.79008
$497$	−14782.0	+	25603.2i	−1.33413	+	2.31079i
$498$	−9540.00	+	4748.20i	−0.858429	+	0.427253i
$499$	8055.83	+	13953.1i	0.722702	+	1.25176i	0.959913	+	0.280299i	$0.0904336\pi$
$499$	8055.83	+	13953.1i	0.722702	+	1.25176i	−0.237210	+	0.971458i	$0.576233\pi$
$500$		0			0
$501$	18123.2	−	9020.18i	1.61614	−	0.804375i
$502$	17916.0	−	31031.5i	1.59289	−	2.75897i
$503$	9219.89			0.817285			0.408643	−	0.912695i	$-0.366002\pi$
$503$	9219.89			0.817285			0.408643	+	0.912695i	$0.366002\pi$
$504$	−34201.8	+	45256.4i	−3.02276	+	3.99976i
$505$		0			0
$506$	−1452.10	+	2515.10i	−0.127576	+	0.220968i
$507$	−8506.67	−	5638.94i	−0.745157	−	0.493953i
$508$	21034.7	+	36433.1i	1.83713	+	3.18200i
$509$	−4283.42	−	7419.11i	−0.373005	−	0.646063i	0.617022	−	0.786946i	$-0.288339\pi$
$509$	−4283.42	−	7419.11i	−0.373005	−	0.646063i	−0.990026	+	0.140883i	$0.955006\pi$
$510$		0			0
$511$	1674.97	−	2901.14i	0.145003	−	0.251152i
$512$	53065.9			4.58048
$513$	1363.84	−	7274.03i	0.117378	−	0.626036i
$514$	15719.6			1.34895
$515$		0			0
$516$	2151.69	−	34783.4i	0.183572	−	2.96755i
$517$	260.530	+	451.250i	0.0221626	+	0.0383868i
$518$	8378.96	+	14512.8i	0.710715	+	1.23099i
$519$	−223.743	−	148.316i	−0.0189234	−	0.0125440i
$520$		0			0
$521$	−2450.94			−0.206099			−0.103050	−	0.994676i	$-0.532860\pi$
$521$	−2450.94			−0.206099			−0.103050	+	0.994676i	$0.532860\pi$
$522$	6942.82	+	16419.6i	0.582144	+	1.37676i
$523$	20897.8			1.74722			0.873609	−	0.486628i	$-0.161773\pi$
$523$	20897.8			1.74722			0.873609	+	0.486628i	$0.161773\pi$
$524$	14523.1	−	25154.8i	1.21077	−	2.09712i
$525$		0			0
$526$	−4528.70	−	7843.94i	−0.375400	−	0.650213i
$527$	−4980.92	−	8627.20i	−0.411712	−	0.713106i
$528$	−7889.65	+	3926.80i	−0.650290	+	0.323659i
$529$	2577.80	−	4464.89i	0.211868	−	0.366967i
$530$		0			0
$531$	6682.01	+	15802.8i	0.546091	+	1.29149i
$532$	30841.2			2.51341
$533$	1215.62	−	2105.52i	0.0987887	−	0.171107i
$534$	−5418.00	−	3591.51i	−0.439063	−	0.291048i
$535$		0			0
$536$	−13482.8	−	23352.9i	−1.08651	−	1.88189i
$537$	1460.81	−	23614.9i	0.117390	−	1.89768i
$538$	13500.9	−	23384.3i	1.08191	−	1.87392i
$539$	1990.24			0.159046
$540$		0			0
$541$	−9960.84			−0.791590			−0.395795	−	0.918339i	$-0.629531\pi$
$541$	−9960.84			−0.791590			−0.395795	+	0.918339i	$0.629531\pi$
$542$	10847.7	−	18788.7i	0.859682	−	1.48901i
$543$	783.123	−	12659.7i	0.0618914	−	1.00051i
$544$	−15292.6	−	26487.6i	−1.20527	−	2.08758i
$545$		0			0
$546$	−9421.65	−	6245.47i	−0.738478	−	0.489526i
$547$	−4297.17	+	7442.93i	−0.335894	+	0.581785i	−0.983656	−	0.180057i	$-0.942372\pi$
$547$	−4297.17	+	7442.93i	−0.335894	+	0.581785i	0.647762	+	0.761843i	$0.275705\pi$
$548$	−34869.4			−2.71815
$549$	9720.98	−	12863.0i	0.755704	−	0.999960i
$550$		0			0
$551$	3141.10	−	5440.55i	0.242859	−	0.420645i
$552$	−31827.4	+	15841.0i	−2.45410	+	1.22144i
$553$	−9485.85	−	16430.0i	−0.729438	−	1.26342i
$554$	2267.97	+	3928.24i	0.173929	+	0.301255i
$555$		0			0
$556$	−17432.5	+	30194.0i	−1.32968	+	2.30308i
$557$	−9469.85			−0.720378			−0.360189	−	0.932879i	$-0.617288\pi$
$557$	−9469.85			−0.720378			−0.360189	+	0.932879i	$0.617288\pi$
$558$	−41098.5	−	5104.21i	−3.11799	−	0.387238i
$559$	4501.13			0.340568
$560$		0			0
$561$	975.585	+	646.701i	0.0734211	+	0.0486697i
$562$	14312.2	+	24789.4i	1.07424	+	1.86064i
$563$	4.38733	+	7.59907i	0.000328426	+	0.000568850i	0.866190	−	0.499716i	$-0.166562\pi$
$563$	4.38733	+	7.59907i	0.000328426	+	0.000568850i	−0.865861	+	0.500284i	$0.833229\pi$
$564$	−607.595	+	9822.14i	−0.0453623	+	0.733310i
$565$		0			0
$566$	39621.9			2.94246
$567$	13058.4	−	13447.5i	0.967202	−	0.996015i
$568$	−93949.2			−6.94018
$569$	123.467	−	213.851i	0.00909667	−	0.0157559i	−0.861441	−	0.507857i	$-0.830438\pi$
$569$	123.467	−	213.851i	0.00909667	−	0.0157559i	0.870538	+	0.492101i	$0.163771\pi$
$570$		0			0
$571$	−1723.59	−	2985.35i	−0.126323	−	0.218797i	0.795927	−	0.605393i	$-0.206984\pi$
$571$	−1723.59	−	2985.35i	−0.126323	−	0.218797i	−0.922249	+	0.386596i	$0.873651\pi$
$572$	−1085.33	−	1879.84i	−0.0793354	−	0.137413i
$573$	5743.37	+	3807.19i	0.418731	+	0.277570i
$574$	−11356.1	+	19669.4i	−0.825775	+	1.43028i
$575$		0			0
$576$	−68068.3	−	8453.72i	−4.92392	−	0.611525i
$577$	−21137.2			−1.52505			−0.762525	−	0.646959i	$-0.776040\pi$
$577$	−21137.2			−1.52505			−0.762525	+	0.646959i	$0.776040\pi$
$578$	10025.2	−	17364.1i	0.721441	−	1.24957i
$579$	6736.76	−	3352.98i	0.483541	−	0.240665i
$580$		0			0
$581$	4755.59	+	8236.92i	0.339578	+	0.588167i
$582$	−307.254	+	152.925i	−0.0218833	+	0.0108916i
$583$	466.117	−	807.339i	0.0331125	−	0.0573526i
$584$	10645.5			0.754305
$585$		0			0
$586$	8122.77			0.572608
$587$	2655.50	−	4599.47i	0.186720	−	0.323408i	−0.757435	−	0.652910i	$-0.773548\pi$
$587$	2655.50	−	4599.47i	0.186720	−	0.323408i	0.944155	+	0.329503i	$0.106881\pi$
$588$	31330.0	+	20768.2i	2.19732	+	1.45657i
$589$	7297.10	+	12638.9i	0.510478	+	0.884174i
$590$		0			0
$591$	769.593	−	12440.9i	0.0535648	−	0.865908i
$592$	−15935.1	+	27600.4i	−1.10630	+	1.91616i
$593$	−11575.8			−0.801624			−0.400812	−	0.916160i	$-0.631272\pi$
$593$	−11575.8			−0.801624			−0.400812	+	0.916160i	$0.631272\pi$
$594$	4590.23	−	1614.73i	0.317070	−	0.111537i
$595$		0			0
$596$	28457.4	−	49289.7i	1.95581	−	3.38756i
$597$	997.475	−	16124.8i	0.0683818	−	1.10543i
$598$	−3542.12	−	6135.13i	−0.242221	−	0.419539i
$599$	3563.32	+	6171.85i	0.243061	+	0.420993i	0.961585	−	0.274509i	$-0.0885153\pi$
$599$	3563.32	+	6171.85i	0.243061	+	0.420993i	−0.718524	+	0.695502i	$0.755182\pi$
$600$		0			0
$601$	3860.93	−	6687.32i	0.262047	−	0.453879i	−0.704739	−	0.709467i	$-0.748936\pi$
$601$	3860.93	−	6687.32i	0.262047	−	0.453879i	0.966786	+	0.255588i	$0.0822690\pi$
$602$	−42048.7			−2.84681
$603$	3470.18	+	8206.90i	0.234356	+	0.554247i
$604$	−34576.4			−2.32929
$605$		0			0
$606$	−19769.3	+	9839.49i	−1.32521	+	0.659574i
$607$	7180.72	+	12437.4i	0.480159	+	0.831659i	0.999741	−	0.0227612i	$-0.00724573\pi$
$607$	7180.72	+	12437.4i	0.480159	+	0.831659i	−0.519582	+	0.854420i	$0.673912\pi$
$608$	22403.8	+	38804.6i	1.49440	+	2.58838i
$609$	14244.6	−	7089.76i	0.947817	−	0.471743i
$610$		0			0
$611$	−1271.03			−0.0841575
$612$	8609.17	+	20360.5i	0.568636	+	1.34481i
$613$	12086.0			0.796330			0.398165	−	0.917314i	$-0.369647\pi$
$613$	12086.0			0.796330			0.398165	+	0.917314i	$0.369647\pi$
$614$	−2191.49	+	3795.77i	−0.144041	+	0.249487i
$615$		0			0
$616$	6571.71	+	11382.5i	0.429840	+	0.744505i
$617$	−12617.9	−	21854.8i	−0.823301	−	1.42600i	−0.903210	−	0.429198i	$-0.858796\pi$
$617$	−12617.9	−	21854.8i	−0.823301	−	1.42600i	0.0799090	−	0.996802i	$-0.474537\pi$
$618$	2756.02	−	44552.7i	0.179391	−	2.89996i
$619$	2452.72	−	4248.24i	0.159262	−	0.275850i	−0.775341	−	0.631543i	$-0.782422\pi$
$619$	2452.72	−	4248.24i	0.159262	−	0.275850i	0.934603	+	0.355693i	$0.115755\pi$
$620$		0			0
$621$	11081.9	−	3898.34i	0.716104	−	0.251908i
$622$	21762.6			1.40290
$623$	−2900.88	+	5024.47i	−0.186551	+	0.323116i
$624$	1327.28	−	21456.3i	0.0851503	−	1.37651i
$625$		0			0
$626$	15918.4	+	27571.5i	1.01634	+	1.76035i
$627$	−1429.24	−	947.423i	−0.0910342	−	0.0603452i
$628$	−29478.4	+	51058.1i	−1.87312	+	3.24433i
$629$	4232.79			0.268318
$630$		0			0
$631$	−11240.9			−0.709181			−0.354590	−	0.935022i	$-0.615380\pi$
$631$	−11240.9			−0.709181			−0.354590	+	0.935022i	$0.615380\pi$
$632$	30144.3	−	52211.5i	1.89727	−	3.28617i
$633$	15395.6	−	7662.64i	0.966702	−	0.481142i
$634$	22555.7	+	39067.6i	1.41293	+	2.44727i
$635$		0			0
$636$	15762.1	−	7845.05i	0.982719	−	0.489114i
$637$	−2427.41	+	4204.39i	−0.150985	+	0.261514i
$638$	4130.51			0.256314
$639$	30807.5	+	3826.13i	1.90724	+	0.236869i
$640$		0			0
$641$	−5579.48	+	9663.94i	−0.343800	+	0.595480i	−0.985135	−	0.171781i	$-0.945048\pi$
$641$	−5579.48	+	9663.94i	−0.343800	+	0.595480i	0.641335	+	0.767261i	$0.278381\pi$
$642$	29256.8	+	19393.9i	1.79856	+	1.19224i
$643$	13622.4	+	23594.7i	0.835483	+	1.44710i	0.893636	+	0.448792i	$0.148146\pi$
$643$	13622.4	+	23594.7i	0.835483	+	1.44710i	−0.0581529	+	0.998308i	$0.518521\pi$
$644$	24477.7	+	42396.7i	1.49776	+	2.59420i
$645$		0			0
$646$	5265.40	−	9119.93i	0.320688	−	0.555447i
$647$	−31360.6			−1.90559			−0.952793	−	0.303620i	$-0.901805\pi$
$647$	−31360.6			−1.90559			−0.952793	+	0.303620i	$0.901805\pi$
$648$	57757.1	+	14571.0i	3.50141	+	0.883337i
$649$	3975.34			0.240440
$650$		0			0
$651$	−2282.21	+	36893.3i	−0.137399	+	2.22114i
$652$	7680.67	+	13303.3i	0.461347	+	0.799076i
$653$	3537.24	+	6126.67i	0.211980	+	0.367160i	0.952334	−	0.305057i	$-0.0986756\pi$
$653$	3537.24	+	6126.67i	0.211980	+	0.367160i	−0.740354	+	0.672217i	$0.765342\pi$
$654$	−31870.3	−	21126.3i	−1.90554	−	1.26316i
$655$		0			0
$656$	−43194.0			−2.57080
$657$	−3490.84	−	433.544i	−0.207292	−	0.0257446i
$658$	11873.7			0.703473
$659$	−9249.31	+	16020.3i	−0.546740	+	0.946982i	0.451755	+	0.892142i	$0.350798\pi$
$659$	−9249.31	+	16020.3i	−0.546740	+	0.946982i	−0.998495	+	0.0548399i	$0.982535\pi$
$660$		0			0
$661$	−3200.38	−	5543.23i	−0.188321	−	0.326182i	0.756369	−	0.654145i	$-0.226971\pi$
$661$	−3200.38	−	5543.23i	−0.188321	−	0.326182i	−0.944691	+	0.327963i	$0.893638\pi$
$662$	17538.9	+	30378.2i	1.02971	+	1.78351i
$663$	−2556.04	+	1272.18i	−0.149726	+	0.0745209i
$664$	−15112.4	+	26175.4i	−0.883245	+	1.52982i
$665$		0			0
$666$	10609.6	−	14038.8i	0.617288	−	0.816806i
$667$	9972.01			0.578887
$668$	44292.8	−	76717.4i	2.56548	−	4.44354i
$669$	−12121.8	−	8035.34i	−0.700531	−	0.464371i
$670$		0			0
$671$	−1867.84	−	3235.19i	−0.107462	−	0.186130i
$672$	−7006.92	+	113271.i	−0.402229	+	6.50228i
$673$	−7115.68	+	12324.7i	−0.407562	+	0.705918i	−0.994616	−	0.103630i	$-0.966954\pi$
$673$	−7115.68	+	12324.7i	−0.407562	+	0.705918i	0.587054	+	0.809548i	$0.300288\pi$
$674$	−26468.0			−1.51263
$675$		0			0
$676$	−44660.4			−2.54099
$677$	−9953.99	+	17240.8i	−0.565085	+	0.978756i	0.431956	+	0.901894i	$0.357823\pi$
$677$	−9953.99	+	17240.8i	−0.565085	+	0.978756i	−0.997042	+	0.0768620i	$0.975510\pi$
$678$	771.336	−	12469.1i	0.0436917	−	0.706303i
$679$	153.163	+	265.286i	0.00865663	+	0.0149937i
$680$		0			0
$681$	−13552.5	−	8983.72i	−0.762601	−	0.505517i
$682$	−4797.79	+	8310.02i	−0.269380	+	0.466579i
$683$	26204.1			1.46804			0.734021	−	0.679126i	$-0.237641\pi$
$683$	26204.1			1.46804			0.734021	+	0.679126i	$0.237641\pi$
$684$	−12612.5	−	29828.4i	−0.705047	−	1.66742i
$685$		0			0
$686$	−1771.91	+	3069.03i	−0.0986177	+	0.170811i
$687$	−13841.9	+	6889.30i	−0.768705	+	0.382596i
$688$	−39984.1	−	69254.4i	−2.21567	−	3.83765i
$689$	1137.01	+	1969.35i	0.0628687	+	0.108892i
$690$		0			0
$691$	13281.2	−	23003.8i	0.731176	−	1.26643i	−0.225205	−	0.974311i	$-0.572305\pi$
$691$	13281.2	−	23003.8i	0.731176	−	1.26643i	0.956381	−	0.292122i	$-0.0943614\pi$
$692$	−1174.66			−0.0645289
$693$	−1691.42	−	4000.16i	−0.0927151	−	0.219269i
$694$	10087.3			0.551741
$695$		0			0
$696$	42144.9	+	27937.2i	2.29526	+	1.52149i
$697$	2868.38	+	4968.17i	0.155879	+	0.269990i
$698$	8253.56	+	14295.6i	0.447567	+	0.775209i
$699$	297.045	−	4801.91i	0.0160734	−	0.259836i
$700$		0			0
$701$	35417.5			1.90827			0.954137	−	0.299372i	$-0.0967771\pi$
$701$	35417.5			1.90827			0.954137	+	0.299372i	$0.0967771\pi$
$702$	−2187.38	+	11666.3i	−0.117603	+	0.627232i
$703$	−6201.08			−0.332686
$704$	−7946.22	+	13763.3i	−0.425404	+	0.736821i
$705$		0			0
$706$	19259.9	+	33359.1i	1.02671	+	1.77831i
$707$	9854.81	+	17069.0i	0.524227	+	0.907987i
$708$	62579.2	+	41482.8i	3.32185	+	2.20200i
$709$	8339.20	−	14443.9i	0.441728	−	0.765096i	−0.556090	−	0.831122i	$-0.687699\pi$
$709$	8339.20	−	14443.9i	0.441728	−	0.765096i	0.997818	+	0.0660267i	$0.0210322\pi$
$710$		0			0
$711$	−12011.2	+	15893.4i	−0.633550	+	0.838324i
$712$	−18436.9			−0.970439
$713$	−11583.0	+	20062.3i	−0.608396	+	1.05377i
$714$	23878.1	−	11884.5i	1.25156	−	0.622920i
$715$		0			0
$716$	−51767.2	−	89663.5i	−2.70200	−	4.68000i
$717$	−12145.1	+	6044.78i	−0.632588	+	0.314849i
$718$	10161.3	−	17599.8i	0.528154	−	0.914790i
$719$	3273.36			0.169786			0.0848928	−	0.996390i	$-0.472945\pi$
$719$	3273.36			0.169786			0.0848928	+	0.996390i	$0.472945\pi$
$720$		0			0
$721$	−39841.1			−2.05792
$722$	11299.9	−	19572.0i	0.582465	−	1.00886i
$723$	−2899.49	−	1922.03i	−0.149147	−	0.0988672i
$724$	−27751.8	−	48067.6i	−1.42457	−	2.46743i
$725$		0			0
$726$	−2297.82	+	37145.6i	−0.117465	+	1.89890i
$727$	16970.3	−	29393.3i	0.865738	−	1.49950i	−0.000573784	−	1.00000i	$-0.500183\pi$
$727$	16970.3	−	29393.3i	0.865738	−	1.49950i	0.866312	−	0.499503i	$-0.166484\pi$
$728$	−32060.9			−1.63222
$729$	−18346.1	−	7130.26i	−0.932079	−	0.362255i
$730$		0			0
$731$	−5310.42	+	9197.92i	−0.268691	+	0.465386i
$732$	4356.09	−	70418.8i	0.219953	−	3.55567i
$733$	−952.351	−	1649.52i	−0.0479890	−	0.0831193i	0.841033	−	0.540984i	$-0.181948\pi$
$733$	−952.351	−	1649.52i	−0.0479890	−	0.0831193i	−0.889022	+	0.457864i	$0.848615\pi$
$734$	26787.0	+	46396.4i	1.34704	+	2.33314i
$735$		0			0
$736$	−35562.5	+	61596.0i	−1.78105	+	3.08486i
$737$	2064.52			0.103185
$738$	23667.5	+	2939.38i	1.18051	+	0.146612i
$739$	23159.4			1.15282			0.576408	−	0.817162i	$-0.304454\pi$
$739$	23159.4			1.15282			0.576408	+	0.817162i	$0.304454\pi$
$740$		0			0
$741$	3744.63	−	1863.76i	0.185644	−	0.0923979i
$742$	−10621.7	−	18397.3i	−0.525519	−	0.910226i
$743$	−10943.4	−	18954.5i	−0.540342	−	0.935900i	−0.998884	−	0.0472272i	$-0.984962\pi$
$743$	−10943.4	−	18954.5i	−0.540342	−	0.935900i	0.458542	−	0.888673i	$-0.348372\pi$
$744$	−105159.	+	52339.3i	−5.18189	+	2.57910i
$745$		0			0
$746$	33396.7			1.63906
$747$	6021.62	−	7967.91i	0.294939	−	0.390268i
$748$	5121.87			0.250367
$749$	15664.5	−	27131.8i	0.764179	−	1.32360i
$750$		0			0
$751$	15830.7	+	27419.5i	0.769200	+	1.33229i	0.937997	+	0.346643i	$0.112678\pi$
$751$	15830.7	+	27419.5i	0.769200	+	1.33229i	−0.168797	+	0.985651i	$0.553988\pi$
$752$	11290.7	+	19556.1i	0.547512	+	0.948319i
$753$	−2073.45	+	33518.7i	−0.100346	+	1.62216i
$754$	−5037.81	+	8725.74i	−0.243324	+	0.421449i
$755$		0			0
$756$	15115.8	−	80619.9i	0.727191	−	3.87846i
$757$	−29482.4			−1.41553			−0.707764	−	0.706449i	$-0.750296\pi$
$757$	−29482.4			−1.41553			−0.707764	+	0.706449i	$0.750296\pi$
$758$	3407.80	−	5902.48i	0.163294	−	0.282834i
$759$	168.054	−	2716.69i	0.00803684	−	0.129920i
$760$		0			0
$761$	13012.0	+	22537.4i	0.619822	+	1.07356i	0.989518	+	0.144410i	$0.0461284\pi$
$761$	13012.0	+	22537.4i	0.619822	+	1.07356i	−0.369696	+	0.929153i	$0.620538\pi$
$762$	−44426.3	−	29449.5i	−2.11207	−	1.40006i
$763$	−17063.8	+	29555.4i	−0.809636	+	1.40233i
$764$	30153.0			1.42788
$765$		0			0
$766$	11829.0			0.557964
$767$	−4848.56	+	8397.94i	−0.228254	+	0.395348i
$768$	−93452.6	+	46512.8i	−4.39086	+	2.18540i
$769$	−839.198	−	1453.53i	−0.0393527	−	0.0681609i	0.845678	−	0.533693i	$-0.179196\pi$
$769$	−839.198	−	1453.53i	−0.0393527	−	0.0681609i	−0.885031	+	0.465532i	$0.845863\pi$
$770$		0			0
$771$	−13189.5	+	6564.59i	−0.616092	+	0.306638i
$772$	16464.5	−	28517.4i	0.767580	−	1.32949i
$773$	−25777.0			−1.19940			−0.599698	−	0.800226i	$-0.704713\pi$
$773$	−25777.0			−1.19940			−0.599698	+	0.800226i	$0.704713\pi$
$774$	17195.8	+	40667.8i	0.798568	+	1.88860i
$775$		0			0
$776$	−486.724	+	843.030i	−0.0225159	+	0.0389987i
$777$	−13090.9	−	8677.79i	−0.604421	−	0.400661i
$778$	−27281.6	−	47253.1i	−1.25719	−	2.17752i
$779$	−4202.20	−	7278.43i	−0.193273	−	0.334758i
$780$		0			0
$781$	3596.44	−	6229.21i	0.164777	−	0.285402i
$782$	16716.0			0.764401
$783$	−12682.3	−	10877.5i	−0.578835	−	0.496461i
$784$	86251.9			3.92911
$785$		0			0
$786$	−2272.14	+	36730.6i	−0.103110	+	1.66684i
$787$	20408.3	+	35348.2i	0.924368	+	1.60105i	0.792574	+	0.609775i	$0.208740\pi$
$787$	20408.3	+	35348.2i	0.924368	+	1.60105i	0.131794	+	0.991277i	$0.457926\pi$
$788$	−27272.4	−	47237.1i	−1.23292	−	2.13547i
$789$	7075.45	+	4690.21i	0.319256	+	0.211630i
$790$		0			0
$791$	−11150.4			−0.501219
$792$	8321.23	−	11010.8i	0.373336	−	0.494004i
$793$	9112.50			0.408063
$794$	−7065.27	+	12237.4i	−0.315790	+	0.546964i
$795$		0			0
$796$	−35347.9	−	61224.4i	−1.57396	−	2.72618i
$797$	−4974.78	−	8616.57i	−0.221099	−	0.382954i	0.734043	−	0.679103i	$-0.237631\pi$
$797$	−4974.78	−	8616.57i	−0.221099	−	0.382954i	−0.955142	+	0.296148i	$0.904298\pi$
$798$	−34981.6	+	17410.9i	−1.55180	+	0.772354i
$799$	1499.56	−	2597.31i	0.0663961	−	0.115001i
$800$		0			0
$801$	6045.78	+	750.854i	0.266688	+	0.0331212i
$802$	−72656.6			−3.19899
$803$	−407.517	+	705.840i	−0.0179091	+	0.0310194i
$804$	32499.4	+	21543.3i	1.42558	+	0.944993i
$805$		0			0
$806$	−11703.3	−	20270.8i	−0.511454	−	0.885865i
$807$	−1562.48	+	25258.5i	−0.0681562	+	1.10179i
$808$	−31316.8	+	54242.3i	−1.36352	+	2.36168i
$809$	−32596.2			−1.41659			−0.708295	−	0.705917i	$-0.750535\pi$
$809$	−32596.2			−1.41659			−0.708295	+	0.705917i	$0.750535\pi$
$810$		0			0
$811$	−7399.23			−0.320373			−0.160186	−	0.987087i	$-0.551210\pi$
$811$	−7399.23			−0.320373			−0.160186	+	0.987087i	$0.551210\pi$
$812$	34813.6	−	60299.0i	1.50458	−	2.60601i
$813$	−1255.42	+	20294.7i	−0.0541569	+	0.875479i
$814$	−2038.58	−	3530.93i	−0.0877792	−	0.152038i
$815$		0			0
$816$	42279.4	+	28026.4i	1.81382	+	1.20235i
$817$	7779.83	−	13475.1i	0.333148	−	0.577029i
$818$	34469.6			1.47335
$819$	10513.3	+	1305.70i	0.448554	+	0.0557080i
$820$		0			0
$821$	8699.04	−	15067.2i	0.369791	−	0.640497i	−0.619741	−	0.784806i	$-0.712763\pi$
$821$	8699.04	−	15067.2i	0.369791	−	0.640497i	0.989533	+	0.144309i	$0.0460959\pi$
$822$	39550.7	−	19685.0i	1.67821	−	0.835270i
$823$	−2634.82	−	4563.64i	−0.111597	−	0.193291i	0.804818	−	0.593522i	$-0.202263\pi$
$823$	−2634.82	−	4563.64i	−0.111597	−	0.193291i	−0.916414	+	0.400231i	$0.868930\pi$
$824$	−63303.9	−	109645.i	−2.67633	−	4.63554i
$825$		0			0
$826$	45294.3	−	78452.1i	1.90798	−	3.30472i
$827$	9005.90			0.378677			0.189338	−	0.981912i	$-0.439366\pi$
$827$	9005.90			0.378677			0.189338	+	0.981912i	$0.439366\pi$
$828$	30994.2	−	41012.0i	1.30087	−	1.72134i
$829$	5545.90			0.232349			0.116174	−	0.993229i	$-0.462937\pi$
$829$	5545.90			0.232349			0.116174	+	0.993229i	$0.462937\pi$
$830$		0			0
$831$	−3543.39	−	2348.86i	−0.147917	−	0.0980517i
$832$	−19383.3	−	33572.9i	−0.807688	−	1.39896i
$833$	−5727.71	−	9920.68i	−0.238239	−	0.412642i
$834$	2727.32	−	44088.8i	0.113237	−	1.83054i
$835$		0			0
$836$	−7503.60			−0.310427
$837$	36615.1	−	12880.3i	1.51207	−	0.531909i
$838$	46726.7			1.92619
$839$	2041.47	−	3535.92i	0.0840038	−	0.145499i	−0.820962	−	0.570982i	$-0.806563\pi$
$839$	2041.47	−	3535.92i	0.0840038	−	0.145499i	0.904966	+	0.425483i	$0.139896\pi$
$840$		0			0
$841$	5103.12	+	8838.86i	0.209239	+	0.362412i
$842$	35425.6	+	61359.0i	1.44994	+	2.51137i
$843$	−22360.8	−	14822.6i	−0.913578	−	0.605597i
$844$	37626.8	−	65171.4i	1.53456	−	2.65793i
$845$		0			0
$846$	−4855.76	−	11483.8i	−0.197334	−	0.466691i
$847$	33217.3			1.34753
$848$	20200.3	−	34988.0i	0.818022	−	1.41686i
$849$	−33244.6	+	16546.3i	−1.34388	+	0.668868i
$850$		0			0
$851$	−4921.61	−	8524.48i	−0.198250	−	0.343379i
$852$	121616.	−	60530.3i	4.89027	−	2.43396i
$853$	11838.3	−	20504.5i	0.475188	−	0.823049i	−0.524409	−	0.851467i	$-0.675714\pi$
$853$	11838.3	−	20504.5i	0.475188	−	0.823049i	0.999596	+	0.0284177i	$0.00904686\pi$
$854$	−85127.3			−3.41100
$855$		0			0
$856$	99558.1			3.97527
$857$	−8275.86	+	14334.2i	−0.329869	+	0.571351i	−0.982486	−	0.186338i	$-0.940338\pi$
$857$	−8275.86	+	14334.2i	−0.329869	+	0.571351i	0.652616	+	0.757689i	$0.273671\pi$
$858$	2292.27	+	1519.51i	0.0912083	+	0.0604606i
$859$	50.2878	+	87.1010i	0.00199744	+	0.00345966i	0.867022	−	0.498269i	$-0.166031\pi$
$859$	50.2878	+	87.1010i	0.00199744	+	0.00345966i	−0.865025	+	0.501729i	$0.832698\pi$
$860$		0			0
$861$	1314.26	−	21245.9i	0.0520209	−	0.840949i
$862$	−8731.27	+	15123.0i	−0.344998	+	0.597554i
$863$	−21496.8			−0.847924			−0.423962	−	0.905680i	$-0.639361\pi$
$863$	−21496.8			−0.847924			−0.423962	+	0.905680i	$0.639361\pi$
$864$	112417.	−	39545.5i	4.42650	−	1.55714i
$865$		0			0
$866$	−19404.4	+	33609.3i	−0.761417	+	1.31881i
$867$	−1160.23	+	18755.9i	−0.0454482	+	0.734698i
$868$	80875.5	+	140081.i	3.16255	+	5.47770i
$869$	2307.89	+	3997.38i	0.0900918	+	0.156044i
$870$		0			0
$871$	−2518.01	+	4361.32i	−0.0979558	+	0.169664i
$872$	−108451.			−4.21173
$873$	193.938	−	256.622i	0.00751867	−	0.00994884i
$874$	−24489.1			−0.947774
$875$		0			0
$876$	−13780.5	+	6858.77i	−0.531508	+	0.264539i
$877$	7609.29	+	13179.7i	0.292984	+	0.507464i	0.974514	−	0.224327i	$-0.0720183\pi$
$877$	7609.29	+	13179.7i	0.292984	+	0.507464i	−0.681530	+	0.731791i	$0.738685\pi$
$878$	21406.9	+	37077.9i	0.822835	+	1.42519i
$879$	−6815.37	+	3392.11i	−0.261521	+	0.130163i
$880$		0			0
$881$	−29944.2			−1.14511			−0.572557	−	0.819865i	$-0.694048\pi$
$881$	−29944.2			−1.14511			−0.572557	+	0.819865i	$0.694048\pi$
$882$	−47260.4	−	5869.49i	−1.80424	−	0.224077i
$883$	−22598.4			−0.861265			−0.430633	−	0.902527i	$-0.641710\pi$
$883$	−22598.4			−0.861265			−0.430633	+	0.902527i	$0.641710\pi$
$884$	−6246.93	+	10820.0i	−0.237678	+	0.411670i
$885$		0			0
$886$	−18430.9	−	31923.3i	−0.698869	−	1.21048i
$887$	−18103.2	−	31355.7i	−0.685283	−	1.18694i	−0.973348	−	0.229334i	$-0.926345\pi$
$887$	−18103.2	−	31355.7i	−0.685283	−	1.18694i	0.288065	−	0.957611i	$-0.406988\pi$
$888$	3081.57	−	49815.4i	0.116453	−	1.88254i
$889$	−23786.5	+	41199.4i	−0.897383	+	1.55431i
$890$		0			0
$891$	−3177.09	+	3271.74i	−0.119458	+	0.123016i
$892$	−63639.9			−2.38881
$893$	−2196.87	+	3805.08i	−0.0823240	+	0.142589i
$894$	−4452.17	+	71972.1i	−0.166558	+	2.69251i
$895$		0			0
$896$	93712.6	+	162315.i	3.49411	+	6.05197i
$897$	5534.07	+	3668.45i	0.205994	+	0.136551i
$898$	31648.3	−	54816.5i	1.17608	−	2.03703i
$899$	32948.0			1.22233
$900$		0			0
$901$	−5365.76			−0.198401
$902$	2762.92	−	4785.51i	0.101990	−	0.176652i
$903$	35280.8	−	17559.8i	1.30019	−	0.647123i
$904$	−17717.0	−	30686.8i	−0.651836	−	1.12901i
$905$		0			0
$906$	39218.3	−	19519.5i	1.43812	−	0.715775i
$907$	−14719.9	+	25495.6i	−0.538883	+	0.933372i	0.460082	+	0.887876i	$0.347820\pi$
$907$	−14719.9	+	25495.6i	−0.538883	+	0.933372i	−0.998965	+	0.0454956i	$0.985513\pi$
$908$	−71151.1			−2.60047
$909$	12478.4	−	16511.6i	0.455314	−	0.602480i
$910$		0			0
$911$	18064.0	−	31287.8i	0.656956	−	1.13788i	−0.324443	−	0.945905i	$-0.605177\pi$
$911$	18064.0	−	31287.8i	0.656956	−	1.13788i	0.981400	−	0.191977i	$-0.0614898\pi$
$912$	−61939.8	−	41058.9i	−2.24894	−	1.49079i
$913$	−1157.02	−	2004.03i	−0.0419408	−	0.0726436i
$914$	−31023.8	−	53734.7i	−1.12273	−	1.94462i
$915$		0			0
$916$	−33829.3	+	58594.1i	−1.22025	+	2.11354i
$917$	32846.2			1.18285
$918$	−21259.1	−	18233.8i	−0.764331	−	0.655560i
$919$	−9547.59			−0.342705			−0.171353	−	0.985210i	$-0.554814\pi$
$919$	−9547.59			−0.342705			−0.171353	+	0.985210i	$0.554814\pi$
$920$		0			0
$921$	253.625	−	4100.00i	0.00907407	−	0.146688i
$922$	13588.4	+	23535.8i	0.485369	+	0.840685i
$923$	8772.84	+	15195.0i	0.312851	+	0.541874i
$924$	−15840.7	−	10500.5i	−0.563982	−	0.373855i
$925$		0			0
$926$	11818.2			0.419407
$927$	16293.0	+	38532.7i	0.577275	+	1.36524i
$928$	101158.			3.57831
$929$	−9245.91	+	16014.4i	−0.326532	+	0.565570i	−0.981821	−	0.189808i	$-0.939213\pi$
$929$	−9245.91	+	16014.4i	−0.326532	+	0.565570i	0.655289	+	0.755378i	$0.272547\pi$
$930$		0			0
$931$	8391.15	+	14533.9i	0.295391	+	0.511632i
$932$	−10526.5	−	18232.4i	−0.369964	−	0.640797i
$933$	−18259.8	+	9088.19i	−0.640729	+	0.318900i
$934$	−49556.8	+	85834.8i	−1.73613	+	3.00707i
$935$		0			0
$936$	13111.3	+	31008.1i	0.457861	+	1.08283i
$937$	−268.075			−0.00934644			−0.00467322	−	0.999989i	$-0.501488\pi$
$937$	−268.075			−0.00934644			−0.00467322	+	0.999989i	$0.501488\pi$
$938$	23522.8	−	40742.7i	0.818812	−	1.41822i
$939$	−24870.2	−	16486.1i	−0.864334	−	0.572954i
$940$		0			0
$941$	15216.2	+	26355.3i	0.527137	+	0.913027i	0.999500	+	0.0316233i	$0.0100677\pi$
$941$	15216.2	+	26355.3i	0.527137	+	0.913027i	−0.472363	+	0.881404i	$0.656599\pi$
$942$	4611.90	−	74554.3i	0.159516	−	2.57867i
$943$	6670.33	−	11553.3i	0.230345	−	0.398970i
$944$	172281.			5.93991
$945$		0			0
$946$	10230.4			0.351604
$947$	14910.6	−	25825.8i	0.511645	−	0.886195i	−0.488264	−	0.872696i	$-0.662370\pi$
$947$	14910.6	−	25825.8i	0.511645	−	0.886195i	0.999909	−	0.0134993i	$-0.00429708\pi$
$948$	−5382.35	+	87008.9i	−0.184399	+	2.98093i
$949$	−994.063	−	1721.77i	−0.0340028	−	0.0588946i
$950$		0			0
$951$	−35240.1	−	23360.1i	−1.20162	−	0.796534i
$952$	37825.5	−	65515.6i	1.28774	−	2.23043i
$953$	41109.5			1.39734			0.698671	−	0.715443i	$-0.253775\pi$
$953$	41109.5			1.39734			0.698671	+	0.715443i	$0.253775\pi$
$954$	−13449.4	+	17796.5i	−0.456437	+	0.603965i
$955$		0			0
$956$	−29682.4	+	51411.4i	−1.00418	+	1.73929i
$957$	−3465.68	+	1724.92i	−0.117063	+	0.0582642i
$958$	−56599.9	−	98033.9i	−1.90883	−	3.30619i
$959$	−19715.6	−	34148.4i	−0.663868	−	1.14985i
$960$		0			0
$961$	−23375.2	+	40487.0i	−0.784640	+	1.35904i
$962$	9945.49			0.333322
$963$	−32646.8	−	4054.56i	−1.09245	−	0.135676i
$964$	−15222.5			−0.508592
$965$		0			0
$966$	−51698.2	−	34270.0i	−1.72191	−	1.14143i
$967$	−21303.0	−	36897.9i	−0.708437	−	1.22705i	−0.965437	−	0.260638i	$-0.916067\pi$
$967$	−21303.0	−	36897.9i	−0.708437	−	1.22705i	0.256999	−	0.966412i	$-0.417266\pi$
$968$	52779.2	+	91416.3i	1.75247	+	3.03536i
$969$	−609.374	+	9850.90i	−0.0202022	+	0.326580i
$970$		0			0
$971$	−33410.2			−1.10421			−0.552103	−	0.833776i	$-0.686175\pi$
$971$	−33410.2			−1.10421			−0.552103	+	0.833776i	$0.686175\pi$
$972$	−84154.0	+	18350.1i	−2.77700	+	0.605536i
$973$	−39426.2			−1.29902
$974$	−23112.6	+	40032.1i	−0.760344	+	1.31695i
$975$		0			0
$976$	−80947.4	−	140205.i	−2.65478	−	4.59821i
$977$	4192.37	+	7261.40i	0.137283	+	0.237782i	0.926467	−	0.376375i	$-0.122830\pi$
$977$	4192.37	+	7261.40i	0.137283	+	0.237782i	−0.789184	+	0.614157i	$0.789496\pi$
$978$	−16222.0	−	10753.3i	−0.530390	−	0.351587i
$979$	705.778	−	1222.44i	0.0230406	−	0.0399075i
$980$		0			0
$981$	35563.1	+	4416.74i	1.15743	+	0.143747i
$982$	90174.4			2.93033
$983$	−9777.09	+	16934.4i	−0.317234	+	0.549465i	−0.979910	−	0.199441i	$-0.936087\pi$
$983$	−9777.09	+	16934.4i	−0.317234	+	0.549465i	0.662676	+	0.748906i	$0.269421\pi$
$984$	60558.4	−	30140.8i	1.96192	−	0.976477i
$985$		0			0
$986$	−11887.2	−	20589.2i	−0.383941	−	0.665004i
$987$	−9962.58	+	4958.52i	−0.321289	+	0.159910i
$988$	9151.82	−	15851.4i	0.294695	−	0.510426i
$989$	24698.5			0.794101
$990$		0			0
$991$	32644.3			1.04640			0.523199	−	0.852210i	$-0.324738\pi$
$991$	32644.3			1.04640			0.523199	+	0.852210i	$0.324738\pi$
$992$	−117500.	+	203516.i	−3.76072	+	6.51375i
$993$	−27402.0	−	18164.4i	−0.875706	−	0.580492i
$994$	−81954.3	−	141949.i	−2.61512	−	4.52953i
$995$		0			0
$996$	2698.36	−	43620.6i	0.0858441	−	1.38772i
$997$	10695.6	−	18525.3i	0.339752	−	0.588469i	−0.644634	−	0.764492i	$-0.722990\pi$
$997$	10695.6	−	18525.3i	0.339752	−	0.588469i	0.984386	+	0.176023i	$0.0563234\pi$
$998$	−89326.0			−2.83323
$999$	−3039.26	+	16209.8i	−0.0962541	+	0.513370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.e.e.151.1	yes	24
5.2	odd	4		225.4.k.e.124.1		48
5.3	odd	4		225.4.k.e.124.24		48
5.4	even	2		225.4.e.f.151.12	yes	24
9.2	odd	6		2025.4.a.be.1.1		12
9.4	even	3	inner	225.4.e.e.76.1	✓	24
9.7	even	3		2025.4.a.bi.1.12		12
45.4	even	6		225.4.e.f.76.12	yes	24
45.13	odd	12		225.4.k.e.49.1		48
45.22	odd	12		225.4.k.e.49.24		48
45.29	odd	6		2025.4.a.bj.1.12		12
45.34	even	6		2025.4.a.bf.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.e.e.76.1	✓	24	9.4	even	3	inner
225.4.e.e.151.1	yes	24	1.1	even	1	trivial
225.4.e.f.76.12	yes	24	45.4	even	6
225.4.e.f.151.12	yes	24	5.4	even	2
225.4.k.e.49.1		48	45.13	odd	12
225.4.k.e.49.24		48	45.22	odd	12
225.4.k.e.124.1		48	5.2	odd	4
225.4.k.e.124.24		48	5.3	odd	4
2025.4.a.be.1.1		12	9.2	odd	6
2025.4.a.bf.1.1		12	45.34	even	6
2025.4.a.bi.1.12		12	9.7	even	3
2025.4.a.bj.1.12		12	45.29	odd	6

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.77209 + 4.80141i) q^{2} +(0.320819 - 5.18624i) q^{3} +(-11.3690 - 19.6917i) q^{4} +(24.0119 + 15.9171i) q^{6} +(12.8563 - 22.2678i) q^{7} +81.7101 q^{8} +(-26.7942 - 3.32769i) q^{9} +O(q^{10})\)	\(q+(-2.77209 + 4.80141i) q^{2} +(0.320819 - 5.18624i) q^{3} +(-11.3690 - 19.6917i) q^{4} +(24.0119 + 15.9171i) q^{6} +(12.8563 - 22.2678i) q^{7} +81.7101 q^{8} +(-26.7942 - 3.32769i) q^{9} +(-3.12792 + 5.41771i) q^{11} +(-105.773 + 52.6449i) q^{12} +(-7.62998 - 13.2155i) q^{13} +(71.2779 + 123.457i) q^{14} +(-135.556 + 234.790i) q^{16} +36.0074 q^{17} +(90.2535 - 119.425i) q^{18} -52.7512 q^{19} +(-111.362 - 73.8199i) q^{21} +(-17.3418 - 30.0368i) q^{22} +(-41.8670 - 72.5158i) q^{23} +(26.2142 - 423.768i) q^{24} +84.6040 q^{26} +(-25.8543 + 137.893i) q^{27} -584.654 q^{28} +(-59.5457 + 103.136i) q^{29} +(-138.331 - 239.596i) q^{31} +(-424.708 - 735.615i) q^{32} +(27.0941 + 17.9602i) q^{33} +(-99.8157 + 172.886i) q^{34} +(239.095 + 565.454i) q^{36} +117.553 q^{37} +(146.231 - 253.280i) q^{38} +(-70.9867 + 35.3311i) q^{39} +(79.6608 + 137.977i) q^{41} +(663.144 - 330.057i) q^{42} +(-147.482 + 255.446i) q^{43} +142.245 q^{44} +464.237 q^{46} +(41.6458 - 72.1327i) q^{47} +(1174.19 + 778.352i) q^{48} +(-159.070 - 275.518i) q^{49} +(11.5519 - 186.743i) q^{51} +(-173.490 + 300.494i) q^{52} -149.018 q^{53} +(-590.411 - 506.390i) q^{54} +(1050.49 - 1819.51i) q^{56} +(-16.9236 + 273.580i) q^{57} +(-330.132 - 571.806i) q^{58} +(-317.731 - 550.325i) q^{59} +(-298.575 + 517.148i) q^{61} +1533.86 q^{62} +(-418.575 + 553.865i) q^{63} +2540.42 q^{64} +(-161.342 + 80.3021i) q^{66} +(-165.008 - 285.802i) q^{67} +(-409.367 - 709.045i) q^{68} +(-389.516 + 193.868i) q^{69} -1149.79 q^{71} +(-2189.35 - 271.906i) q^{72} +130.284 q^{73} +(-325.869 + 564.422i) q^{74} +(599.728 + 1038.76i) q^{76} +(80.4271 + 139.304i) q^{77} +(27.1426 - 438.777i) q^{78} +(368.918 - 638.984i) q^{79} +(706.853 + 178.325i) q^{81} -883.309 q^{82} +(-184.951 + 320.345i) q^{83} +(-187.568 + 3032.16i) q^{84} +(-817.665 - 1416.24i) q^{86} +(515.785 + 341.906i) q^{87} +(-255.583 + 442.682i) q^{88} -225.638 q^{89} -392.374 q^{91} +(-951.972 + 1648.86i) q^{92} +(-1286.98 + 640.549i) q^{93} +(230.892 + 399.917i) q^{94} +(-3951.33 + 1966.64i) q^{96} +(-5.95671 + 10.3173i) q^{97} +1763.83 q^{98} +(101.838 - 134.754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} - q^{3} - 48 q^{4} - 13 q^{6} + 6 q^{7} + 90 q^{8} - 61 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 - q^3 - 48 * q^4 - 13 * q^6 + 6 * q^7 + 90 * q^8 - 61 * q^9	\( 24 q - 4 q^{2} - q^{3} - 48 q^{4} - 13 q^{6} + 6 q^{7} + 90 q^{8} - 61 q^{9} - 29 q^{11} - 77 q^{12} + 24 q^{13} + 69 q^{14} - 192 q^{16} + 158 q^{17} + 125 q^{18} - 150 q^{19} - 60 q^{21} - 18 q^{22} - 318 q^{23} + 342 q^{24} - 308 q^{26} - 394 q^{27} - 192 q^{28} - 106 q^{29} - 60 q^{31} - 914 q^{32} - 80 q^{33} + 108 q^{34} + 1303 q^{36} + 168 q^{37} - 640 q^{38} - 410 q^{39} + 353 q^{41} + 1521 q^{42} - 426 q^{43} + 1142 q^{44} + 540 q^{46} - 1210 q^{47} + 2680 q^{48} - 666 q^{49} - 1369 q^{51} - 75 q^{52} + 896 q^{53} - 2128 q^{54} + 570 q^{56} + 1544 q^{57} + 594 q^{58} - 482 q^{59} - 402 q^{61} + 5088 q^{62} - 1038 q^{63} + 1950 q^{64} + 2041 q^{66} - 201 q^{67} - 3437 q^{68} + 2856 q^{69} - 1888 q^{71} - 5493 q^{72} + 906 q^{73} - 10 q^{74} + 462 q^{76} - 2652 q^{77} - 4589 q^{78} - 258 q^{79} + 3071 q^{81} - 1746 q^{82} - 3012 q^{83} - 2703 q^{84} - 1952 q^{86} + 2708 q^{87} - 216 q^{88} - 1476 q^{89} - 1236 q^{91} - 5232 q^{92} + 3024 q^{93} - 63 q^{94} - 10424 q^{96} - 318 q^{97} + 15022 q^{98} - 1697 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 - q^3 - 48 * q^4 - 13 * q^6 + 6 * q^7 + 90 * q^8 - 61 * q^9 - 29 * q^11 - 77 * q^12 + 24 * q^13 + 69 * q^14 - 192 * q^16 + 158 * q^17 + 125 * q^18 - 150 * q^19 - 60 * q^21 - 18 * q^22 - 318 * q^23 + 342 * q^24 - 308 * q^26 - 394 * q^27 - 192 * q^28 - 106 * q^29 - 60 * q^31 - 914 * q^32 - 80 * q^33 + 108 * q^34 + 1303 * q^36 + 168 * q^37 - 640 * q^38 - 410 * q^39 + 353 * q^41 + 1521 * q^42 - 426 * q^43 + 1142 * q^44 + 540 * q^46 - 1210 * q^47 + 2680 * q^48 - 666 * q^49 - 1369 * q^51 - 75 * q^52 + 896 * q^53 - 2128 * q^54 + 570 * q^56 + 1544 * q^57 + 594 * q^58 - 482 * q^59 - 402 * q^61 + 5088 * q^62 - 1038 * q^63 + 1950 * q^64 + 2041 * q^66 - 201 * q^67 - 3437 * q^68 + 2856 * q^69 - 1888 * q^71 - 5493 * q^72 + 906 * q^73 - 10 * q^74 + 462 * q^76 - 2652 * q^77 - 4589 * q^78 - 258 * q^79 + 3071 * q^81 - 1746 * q^82 - 3012 * q^83 - 2703 * q^84 - 1952 * q^86 + 2708 * q^87 - 216 * q^88 - 1476 * q^89 - 1236 * q^91 - 5232 * q^92 + 3024 * q^93 - 63 * q^94 - 10424 * q^96 - 318 * q^97 + 15022 * q^98 - 1697 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more