LMFDB - Embedded newform 24.5.b.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [24,5,Mod(19,24)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(24, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("24.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	24.b (of order $2$, degree $1$, 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:	$2.48087911401$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 20x^{6} - 6x^{5} + 121x^{4} + 18x^{3} - 114x^{2} + 72x + 144 $ x^8 + 20x^6 - 6x^5 + 121x^4 + 18x^3 - 114x^2 + 72x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.2
Root			$-0.866025 + 3.62169i$ of defining polynomial
Character	$\chi$	$=$	24.19
Dual form			24.5.b.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.56731 + 1.80951i) q^{2} +5.19615 q^{3} +(9.45137 - 12.9101i) q^{4} +38.1617i q^{5} +(-18.5363 + 9.40247i) q^{6} +42.0542i q^{7} +(-10.3550 + 63.1567i) q^{8} +27.0000 q^{9} +O(q^{10})$	\(q+(-3.56731 + 1.80951i) q^{2} +5.19615 q^{3} +(9.45137 - 12.9101i) q^{4} +38.1617i q^{5} +(-18.5363 + 9.40247i) q^{6} +42.0542i q^{7} +(-10.3550 + 63.1567i) q^{8} +27.0000 q^{9} +(-69.0539 - 136.135i) q^{10} +100.141 q^{11} +(49.1107 - 67.0830i) q^{12} -171.607i q^{13} +(-76.0973 - 150.020i) q^{14} +198.294i q^{15} +(-77.3433 - 244.037i) q^{16} -351.156 q^{17} +(-96.3173 + 48.8567i) q^{18} +494.248 q^{19} +(492.673 + 360.680i) q^{20} +218.520i q^{21} +(-357.233 + 181.205i) q^{22} -254.258i q^{23} +(-53.8059 + 328.172i) q^{24} -831.317 q^{25} +(310.524 + 612.174i) q^{26} +140.296 q^{27} +(542.925 + 397.469i) q^{28} -1388.76i q^{29} +(-358.815 - 707.376i) q^{30} +603.769i q^{31} +(717.494 + 730.602i) q^{32} +520.347 q^{33} +(1252.68 - 635.420i) q^{34} -1604.86 q^{35} +(255.187 - 348.574i) q^{36} +538.756i q^{37} +(-1763.14 + 894.346i) q^{38} -891.695i q^{39} +(-2410.17 - 395.163i) q^{40} +540.370 q^{41} +(-395.413 - 779.527i) q^{42} +2047.07 q^{43} +(946.467 - 1292.83i) q^{44} +1030.37i q^{45} +(460.081 + 907.016i) q^{46} -1830.56i q^{47} +(-401.887 - 1268.05i) q^{48} +632.448 q^{49} +(2965.56 - 1504.27i) q^{50} -1824.66 q^{51} +(-2215.47 - 1621.92i) q^{52} +3473.31i q^{53} +(-500.479 + 253.867i) q^{54} +3821.54i q^{55} +(-2656.00 - 435.469i) q^{56} +2568.19 q^{57} +(2512.98 + 4954.15i) q^{58} -1577.30 q^{59} +(2560.00 + 1874.15i) q^{60} -1057.51i q^{61} +(-1092.52 - 2153.83i) q^{62} +1135.46i q^{63} +(-3881.55 - 1307.97i) q^{64} +6548.81 q^{65} +(-1856.24 + 941.571i) q^{66} -517.305 q^{67} +(-3318.91 + 4533.47i) q^{68} -1321.16i q^{69} +(5725.03 - 2904.00i) q^{70} -1950.41i q^{71} +(-279.584 + 1705.23i) q^{72} -8306.47 q^{73} +(-974.882 - 1921.91i) q^{74} -4319.65 q^{75} +(4671.32 - 6380.82i) q^{76} +4211.34i q^{77} +(1613.53 + 3180.95i) q^{78} -11240.5i q^{79} +(9312.87 - 2951.55i) q^{80} +729.000 q^{81} +(-1927.67 + 977.804i) q^{82} -719.298 q^{83} +(2821.12 + 2065.31i) q^{84} -13400.7i q^{85} +(-7302.53 + 3704.19i) q^{86} -7216.23i q^{87} +(-1036.95 + 6324.57i) q^{88} -4185.54 q^{89} +(-1864.46 - 3675.63i) q^{90} +7216.78 q^{91} +(-3282.50 - 2403.08i) q^{92} +3137.27i q^{93} +(3312.42 + 6530.19i) q^{94} +18861.4i q^{95} +(3728.21 + 3796.32i) q^{96} -4891.42 q^{97} +(-2256.14 + 1144.42i) q^{98} +2703.80 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} + 216 q^{9}+O(q^{10}) $ 8 * q - 6 * q^2 + 8 * q^4 + 18 * q^6 - 180 * q^8 + 216 * q^9	$ 8 q - 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} + 216 q^{9} - 324 q^{10} + 192 q^{11} + 180 q^{12} + 420 q^{14} - 712 q^{16} + 240 q^{17} - 162 q^{18} - 704 q^{19} + 168 q^{20} + 592 q^{22} - 108 q^{24} - 664 q^{25} + 1008 q^{26} - 528 q^{28} + 468 q^{30} + 3624 q^{32} + 2716 q^{34} - 5184 q^{35} + 216 q^{36} - 6360 q^{38} + 408 q^{40} + 720 q^{41} - 2412 q^{42} + 10048 q^{43} - 6720 q^{44} + 2616 q^{46} - 3168 q^{48} - 1240 q^{49} + 5394 q^{50} - 4032 q^{51} + 2448 q^{52} + 486 q^{54} + 7512 q^{56} + 3744 q^{57} - 10740 q^{58} + 13056 q^{59} + 10656 q^{60} - 8724 q^{62} - 17632 q^{64} - 1344 q^{65} - 13680 q^{66} - 6656 q^{67} - 5616 q^{68} + 19800 q^{70} - 4860 q^{72} - 16880 q^{73} + 17400 q^{74} - 1152 q^{75} + 14320 q^{76} + 18720 q^{78} + 28512 q^{80} + 5832 q^{81} - 9740 q^{82} - 24000 q^{83} + 21960 q^{84} - 34344 q^{86} - 19616 q^{88} + 15600 q^{89} - 8748 q^{90} + 1344 q^{91} - 48096 q^{92} + 12120 q^{94} - 21528 q^{96} - 12176 q^{97} + 47778 q^{98} + 5184 q^{99}+O(q^{100}) $ 8 * q - 6 * q^2 + 8 * q^4 + 18 * q^6 - 180 * q^8 + 216 * q^9 - 324 * q^10 + 192 * q^11 + 180 * q^12 + 420 * q^14 - 712 * q^16 + 240 * q^17 - 162 * q^18 - 704 * q^19 + 168 * q^20 + 592 * q^22 - 108 * q^24 - 664 * q^25 + 1008 * q^26 - 528 * q^28 + 468 * q^30 + 3624 * q^32 + 2716 * q^34 - 5184 * q^35 + 216 * q^36 - 6360 * q^38 + 408 * q^40 + 720 * q^41 - 2412 * q^42 + 10048 * q^43 - 6720 * q^44 + 2616 * q^46 - 3168 * q^48 - 1240 * q^49 + 5394 * q^50 - 4032 * q^51 + 2448 * q^52 + 486 * q^54 + 7512 * q^56 + 3744 * q^57 - 10740 * q^58 + 13056 * q^59 + 10656 * q^60 - 8724 * q^62 - 17632 * q^64 - 1344 * q^65 - 13680 * q^66 - 6656 * q^67 - 5616 * q^68 + 19800 * q^70 - 4860 * q^72 - 16880 * q^73 + 17400 * q^74 - 1152 * q^75 + 14320 * q^76 + 18720 * q^78 + 28512 * q^80 + 5832 * q^81 - 9740 * q^82 - 24000 * q^83 + 21960 * q^84 - 34344 * q^86 - 19616 * q^88 + 15600 * q^89 - 8748 * q^90 + 1344 * q^91 - 48096 * q^92 + 12120 * q^94 - 21528 * q^96 - 12176 * q^97 + 47778 * q^98 + 5184 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/24\mathbb{Z}\right)^\times$.

$n$	$7$	$13$	$17$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−3.56731	+	1.80951i	−0.891827	+	0.452377i
$2$	−3.56731	+	1.80951i	−0.891827	+	0.452377i
$3$	5.19615			0.577350
$3$	5.19615			0.577350
$4$	9.45137	−	12.9101i	0.590711	−	0.806884i
$5$			38.1617i			1.52647i	0.646122	+	0.763234i	$0.276390\pi$
$5$			38.1617i			1.52647i	−0.646122	+	0.763234i	$0.723610\pi$
$6$	−18.5363	+	9.40247i	−0.514897	+	0.261180i
$7$			42.0542i			0.858248i	0.903246	+	0.429124i	$0.141178\pi$
$7$			42.0542i			0.858248i	−0.903246	+	0.429124i	$0.858822\pi$
$8$	−10.3550	+	63.1567i	−0.161796	+	0.986824i
$9$	27.0000			0.333333
$10$	−69.0539	−	136.135i	−0.690539	−	1.36135i
$11$	100.141			0.827610			0.413805	−	0.910366i	$-0.364200\pi$
$11$	100.141			0.827610			0.413805	+	0.910366i	$0.364200\pi$
$12$	49.1107	−	67.0830i	0.341047	−	0.465854i
$13$		−	171.607i		−	1.01543i	−0.861527	−	0.507713i	$-0.830491\pi$
$13$		−	171.607i		−	1.01543i	0.861527	−	0.507713i	$-0.169509\pi$
$14$	−76.0973	−	150.020i	−0.388252	−	0.765409i
$15$			198.294i			0.881307i
$16$	−77.3433	−	244.037i	−0.302122	−	0.953269i
$17$	−351.156			−1.21507			−0.607537	−	0.794292i	$-0.707842\pi$
$17$	−351.156			−1.21507			−0.607537	+	0.794292i	$0.707842\pi$
$18$	−96.3173	+	48.8567i	−0.297276	+	0.150792i
$19$	494.248			1.36911			0.684555	−	0.728962i	$-0.259997\pi$
$19$	494.248			1.36911			0.684555	+	0.728962i	$0.259997\pi$
$20$	492.673	+	360.680i	1.23168	+	0.901701i
$21$			218.520i			0.495510i
$22$	−357.233	+	181.205i	−0.738085	+	0.374391i
$23$		−	254.258i		−	0.480638i	−0.970694	−	0.240319i	$-0.922748\pi$
$23$		−	254.258i		−	0.480638i	0.970694	−	0.240319i	$-0.0772521\pi$
$24$	−53.8059	+	328.172i	−0.0934130	+	0.569743i
$25$	−831.317			−1.33011
$26$	310.524	+	612.174i	0.459355	+	0.905583i
$27$	140.296			0.192450
$28$	542.925	+	397.469i	0.692506	+	0.506976i
$29$		−	1388.76i		−	1.65132i	−0.564165	−	0.825662i	$-0.690802\pi$
$29$		−	1388.76i		−	1.65132i	0.564165	−	0.825662i	$-0.309198\pi$
$30$	−358.815	−	707.376i	−0.398683	−	0.785973i
$31$			603.769i			0.628271i	0.949378	+	0.314136i	$0.101715\pi$
$31$			603.769i			0.628271i	−0.949378	+	0.314136i	$0.898285\pi$
$32$	717.494	+	730.602i	0.700678	+	0.713478i
$33$	520.347			0.477821
$34$	1252.68	−	635.420i	1.08363	−	0.549671i
$35$	−1604.86			−1.31009
$36$	255.187	−	348.574i	0.196904	−	0.268961i
$37$			538.756i			0.393540i	0.980450	+	0.196770i	$0.0630451\pi$
$37$			538.756i			0.393540i	−0.980450	+	0.196770i	$0.936955\pi$
$38$	−1763.14	+	894.346i	−1.22101	+	0.619353i
$39$		−	891.695i		−	0.586256i
$40$	−2410.17	−	395.163i	−1.50636	−	0.246977i
$41$	540.370			0.321458			0.160729	−	0.986999i	$-0.448616\pi$
$41$	540.370			0.321458			0.160729	+	0.986999i	$0.448616\pi$
$42$	−395.413	−	779.527i	−0.224157	−	0.441909i
$43$	2047.07			1.10712			0.553561	−	0.832808i	$-0.313268\pi$
$43$	2047.07			1.10712			0.553561	+	0.832808i	$0.313268\pi$
$44$	946.467	−	1292.83i	0.488878	−	0.667785i
$45$			1030.37i			0.508823i
$46$	460.081	+	907.016i	0.217430	+	0.428646i
$47$		−	1830.56i		−	0.828685i	−0.910121	−	0.414342i	$-0.864012\pi$
$47$		−	1830.56i		−	0.828685i	0.910121	−	0.414342i	$-0.135988\pi$
$48$	−401.887	−	1268.05i	−0.174430	−	0.550370i
$49$	632.448			0.263410
$50$	2965.56	−	1504.27i	1.18623	−	0.601710i
$51$	−1824.66			−0.701523
$52$	−2215.47	−	1621.92i	−0.819330	−	0.599822i
$53$			3473.31i			1.23649i	0.785984	+	0.618247i	$0.212157\pi$
$53$			3473.31i			1.23649i	−0.785984	+	0.618247i	$0.787843\pi$
$54$	−500.479	+	253.867i	−0.171632	+	0.0870600i
$55$			3821.54i			1.26332i
$56$	−2656.00	−	435.469i	−0.846940	−	0.138861i
$57$	2568.19			0.790456
$58$	2512.98	+	4954.15i	0.747021	+	1.47270i
$59$	−1577.30			−0.453116			−0.226558	−	0.973998i	$-0.572747\pi$
$59$	−1577.30			−0.453116			−0.226558	+	0.973998i	$0.572747\pi$
$60$	2560.00	+	1874.15i	0.711112	+	0.520597i
$61$		−	1057.51i		−	0.284201i	−0.989852	−	0.142100i	$-0.954614\pi$
$61$		−	1057.51i		−	0.284201i	0.989852	−	0.142100i	$-0.0453856\pi$
$62$	−1092.52	−	2153.83i	−0.284215	−	0.560309i
$63$			1135.46i			0.286083i
$64$	−3881.55	−	1307.97i	−0.947644	−	0.319329i
$65$	6548.81			1.55001
$66$	−1856.24	+	941.571i	−0.426133	+	0.216155i
$67$	−517.305			−0.115238			−0.0576191	−	0.998339i	$-0.518351\pi$
$67$	−517.305			−0.115238			−0.0576191	+	0.998339i	$0.518351\pi$
$68$	−3318.91	+	4533.47i	−0.717756	+	0.980423i
$69$		−	1321.16i		−	0.277497i
$70$	5725.03	−	2904.00i	1.16837	−	0.592654i
$71$		−	1950.41i		−	0.386909i	−0.981109	−	0.193454i	$-0.938031\pi$
$71$		−	1950.41i		−	0.386909i	0.981109	−	0.193454i	$-0.0619692\pi$
$72$	−279.584	+	1705.23i	−0.0539320	+	0.328941i
$73$	−8306.47			−1.55873			−0.779364	−	0.626571i	$-0.784458\pi$
$73$	−8306.47			−1.55873			−0.779364	+	0.626571i	$0.784458\pi$
$74$	−974.882	−	1921.91i	−0.178028	−	0.350969i
$75$	−4319.65			−0.767938
$76$	4671.32	−	6380.82i	0.808747	−	1.10471i
$77$			4211.34i			0.710295i
$78$	1613.53	+	3180.95i	0.265209	+	0.522839i
$79$		−	11240.5i		−	1.80107i	−0.434782	−	0.900536i	$-0.643175\pi$
$79$		−	11240.5i		−	1.80107i	0.434782	−	0.900536i	$-0.356825\pi$
$80$	9312.87	−	2951.55i	1.45514	−	0.461180i
$81$	729.000			0.111111
$82$	−1927.67	+	977.804i	−0.286685	+	0.145420i
$83$	−719.298			−0.104413			−0.0522063	−	0.998636i	$-0.516625\pi$
$83$	−719.298			−0.104413			−0.0522063	+	0.998636i	$0.516625\pi$
$84$	2821.12	+	2065.31i	0.399819	+	0.292703i
$85$		−	13400.7i		−	1.85477i
$86$	−7302.53	+	3704.19i	−0.987362	+	0.500837i
$87$		−	7216.23i		−	0.953393i
$88$	−1036.95	+	6324.57i	−0.133904	+	0.816705i
$89$	−4185.54			−0.528410			−0.264205	−	0.964467i	$-0.585110\pi$
$89$	−4185.54			−0.528410			−0.264205	+	0.964467i	$0.585110\pi$
$90$	−1864.46	−	3675.63i	−0.230180	−	0.453782i
$91$	7216.78			0.871487
$92$	−3282.50	−	2403.08i	−0.387819	−	0.283918i
$93$			3137.27i			0.362733i
$94$	3312.42	+	6530.19i	0.374878	+	0.739043i
$95$			18861.4i			2.08990i
$96$	3728.21	+	3796.32i	0.404536	+	0.411927i
$97$	−4891.42			−0.519866			−0.259933	−	0.965627i	$-0.583701\pi$
$97$	−4891.42			−0.519866			−0.259933	+	0.965627i	$0.583701\pi$
$98$	−2256.14	+	1144.42i	−0.234916	+	0.119161i
$99$	2703.80			0.275870
$100$	−7857.08	+	10732.4i	−0.785708	+	1.07324i
$101$		−	3582.12i		−	0.351154i	−0.984466	−	0.175577i	$-0.943821\pi$
$101$		−	3582.12i		−	0.351154i	0.984466	−	0.175577i	$-0.0561791\pi$
$102$	6509.13	−	3301.74i	0.625637	−	0.317353i
$103$			17391.9i			1.63935i	0.572826	+	0.819677i	$0.305847\pi$
$103$			17391.9i			1.63935i	−0.572826	+	0.819677i	$0.694153\pi$
$104$	10838.1	+	1776.98i	1.00205	+	0.164292i
$105$	−8339.09			−0.756380
$106$	−6284.98	−	12390.4i	−0.559361	−	1.10274i
$107$	11793.1			1.03005			0.515027	−	0.857174i	$-0.327782\pi$
$107$	11793.1			1.03005			0.515027	+	0.857174i	$0.327782\pi$
$108$	1325.99	−	1811.24i	0.113682	−	0.155285i
$109$			10564.5i			0.889192i	0.895731	+	0.444596i	$0.146653\pi$
$109$			10564.5i			0.889192i	−0.895731	+	0.444596i	$0.853347\pi$
$110$	−6915.11	−	13632.6i	−0.571497	−	1.12666i
$111$			2799.46i			0.227210i
$112$	10262.8	−	3252.61i	0.818142	−	0.259296i
$113$	7408.35			0.580183			0.290091	−	0.956999i	$-0.406314\pi$
$113$	7408.35			0.580183			0.290091	+	0.956999i	$0.406314\pi$
$114$	−9161.52	+	4647.16i	−0.704950	+	0.357584i
$115$	9702.91			0.733680
$116$	−17929.1	−	13125.7i	−1.33243	−	0.975455i
$117$		−	4633.38i		−	0.338475i
$118$	5626.70	−	2854.13i	0.404101	−	0.204979i
$119$		−	14767.6i		−	1.04283i
$120$	−12523.6	−	2053.33i	−0.869695	−	0.142592i
$121$	−4612.82			−0.315062
$122$	1913.57	+	3772.47i	0.128566	+	0.253458i
$123$	2807.85			0.185594
$124$	7794.74	+	5706.44i	0.506942	+	0.371126i
$125$		−	7873.41i		−	0.503898i
$126$	−2054.63	−	4050.54i	−0.129417	−	0.255136i
$127$		−	443.504i		−	0.0274973i	−0.999905	−	0.0137487i	$-0.995624\pi$
$127$		−	443.504i		−	0.0274973i	0.999905	−	0.0137487i	$-0.00437647\pi$
$128$	16213.5	−	2357.76i	0.989591	−	0.143906i
$129$	10636.9			0.639198
$130$	−23361.6	+	11850.1i	−1.38234	+	0.701191i
$131$	106.777			0.00622209			0.00311105	−	0.999995i	$-0.499010\pi$
$131$	106.777			0.00622209			0.00311105	+	0.999995i	$0.499010\pi$
$132$	4917.99	−	6717.75i	0.282254	−	0.385546i
$133$			20785.2i			1.17504i
$134$	1845.38	−	936.066i	0.102773	−	0.0521311i
$135$			5353.94i			0.293769i
$136$	3636.21	−	22177.9i	0.196594	−	1.19906i
$137$	−29064.5			−1.54854			−0.774268	−	0.632858i	$-0.781882\pi$
$137$	−29064.5			−1.54854			−0.774268	+	0.632858i	$0.781882\pi$
$138$	2390.65	+	4712.99i	0.125533	+	0.247479i
$139$	−32437.6			−1.67888			−0.839440	−	0.543453i	$-0.817117\pi$
$139$	−32437.6			−1.67888			−0.839440	+	0.543453i	$0.817117\pi$
$140$	−15168.1	+	20719.0i	−0.773883	+	1.05709i
$141$		−	9511.89i		−	0.478441i
$142$	3529.28	+	6957.70i	0.175029	+	0.345056i
$143$		−	17184.8i		−	0.840376i
$144$	−2088.27	−	6589.00i	−0.100707	−	0.317756i
$145$	52997.6			2.52070
$146$	29631.7	−	15030.6i	1.39012	−	0.705133i
$147$	3286.29			0.152080
$148$	6955.41	+	5091.98i	0.317541	+	0.232468i
$149$			5874.77i			0.264617i	0.991209	+	0.132309i	$0.0422390\pi$
$149$			5874.77i			0.264617i	−0.991209	+	0.132309i	$0.957761\pi$
$150$	15409.5	−	7816.44i	0.684868	−	0.347397i
$151$		−	13831.1i		−	0.606599i	−0.952895	−	0.303300i	$-0.901912\pi$
$151$		−	13831.1i		−	0.606599i	0.952895	−	0.303300i	$-0.0980883\pi$
$152$	−5117.92	+	31215.1i	−0.221517	+	1.35107i
$153$	−9481.22			−0.405024
$154$	−7620.44	−	15023.1i	−0.321321	−	0.633460i
$155$	−23040.8			−0.959036
$156$	−11511.9	−	8427.74i	−0.473040	−	0.346308i
$157$		−	22719.2i		−	0.921708i	−0.887476	−	0.460854i	$-0.847543\pi$
$157$		−	22719.2i		−	0.921708i	0.887476	−	0.460854i	$-0.152457\pi$
$158$	20339.7	+	40098.3i	0.814763	+	1.60624i
$159$			18047.9i			0.713890i
$160$	−27881.0	+	27380.8i	−1.08910	+	1.06956i
$161$	10692.6			0.412507
$162$	−2600.57	+	1319.13i	−0.0990919	+	0.0502641i
$163$	−14332.3			−0.539438			−0.269719	−	0.962939i	$-0.586931\pi$
$163$	−14332.3			−0.539438			−0.269719	+	0.962939i	$0.586931\pi$
$164$	5107.24	−	6976.25i	0.189888	−	0.259379i
$165$			19857.3i			0.729379i
$166$	2565.96	−	1301.58i	0.0931180	−	0.0472338i
$167$			2863.09i			0.102660i	0.998682	+	0.0513301i	$0.0163461\pi$
$167$			2863.09i			0.102660i	−0.998682	+	0.0513301i	$0.983654\pi$
$168$	−13801.0	−	2262.76i	−0.488981	−	0.0801716i
$169$	−887.905			−0.0310880
$170$	24248.7	+	47804.5i	0.839055	+	1.65413i
$171$	13344.7			0.456370
$172$	19347.6	−	26428.0i	0.653989	−	0.893319i
$173$		−	14515.8i		−	0.485008i	−0.970150	−	0.242504i	$-0.922031\pi$
$173$		−	14515.8i		−	0.485008i	0.970150	−	0.242504i	$-0.0779688\pi$
$174$	13057.8	+	25742.5i	0.431293	+	0.850261i
$175$		−	34960.3i		−	1.14156i
$176$	−7745.22	−	24438.0i	−0.250039	−	0.788935i
$177$	−8195.87			−0.261606
$178$	14931.1	−	7573.76i	0.471250	−	0.239040i
$179$	−8072.26			−0.251935			−0.125968	−	0.992034i	$-0.540204\pi$
$179$	−8072.26			−0.251935			−0.125968	+	0.992034i	$0.540204\pi$
$180$	13302.2	+	9738.37i	0.410561	+	0.300567i
$181$			36860.1i			1.12512i	0.826756	+	0.562561i	$0.190184\pi$
$181$			36860.1i			1.12512i	−0.826756	+	0.562561i	$0.809816\pi$
$182$	−25744.5	+	13058.8i	−0.777215	+	0.394240i
$183$		−	5494.99i		−	0.164083i
$184$	16058.1	+	2632.83i	0.474306	+	0.0777654i
$185$	−20559.8			−0.600726
$186$	−5676.92	−	11191.6i	−0.164092	−	0.323495i
$187$	−35165.1			−1.00561
$188$	−23632.8	−	17301.3i	−0.668652	−	0.489513i
$189$			5900.04i			0.165170i
$190$	−34129.8	−	67284.3i	−0.945423	−	1.86383i
$191$			2132.11i			0.0584444i	0.999573	+	0.0292222i	$0.00930304\pi$
$191$			2132.11i			0.0584444i	−0.999573	+	0.0292222i	$0.990697\pi$
$192$	−20169.1	−	6796.41i	−0.547123	−	0.184365i
$193$	33387.8			0.896341			0.448170	−	0.893948i	$-0.352076\pi$
$193$	33387.8			0.896341			0.448170	+	0.893948i	$0.352076\pi$
$194$	17449.2	−	8851.06i	0.463631	−	0.235175i
$195$	34028.6			0.894901
$196$	5977.50	−	8164.99i	0.155599	−	0.212541i
$197$		−	40238.1i		−	1.03682i	−0.855131	−	0.518412i	$-0.826523\pi$
$197$		−	40238.1i		−	1.03682i	0.855131	−	0.518412i	$-0.173477\pi$
$198$	−9645.29	+	4892.55i	−0.246028	+	0.124797i
$199$			2284.56i			0.0576894i	0.999584	+	0.0288447i	$0.00918283\pi$
$199$			2284.56i			0.0576894i	−0.999584	+	0.0288447i	$0.990817\pi$
$200$	8608.25	−	52503.3i	0.215206	−	1.31258i
$201$	−2687.99			−0.0665328
$202$	6481.88	+	12778.5i	0.158854	+	0.313169i
$203$	58403.3			1.41725
$204$	−17245.5	+	23556.6i	−0.414397	+	0.566047i
$205$			20621.5i			0.490695i
$206$	−31470.8	−	62042.3i	−0.741605	−	1.46202i
$207$		−	6864.96i		−	0.160213i
$208$	−41878.4	+	13272.6i	−0.967973	+	0.306782i
$209$	49494.4			1.13309
$210$	29748.1	−	15089.6i	0.674560	−	0.342169i
$211$	13228.5			0.297129			0.148565	−	0.988903i	$-0.452535\pi$
$211$	13228.5			0.297129			0.148565	+	0.988903i	$0.452535\pi$
$212$	44840.9	+	32827.6i	0.997707	+	0.730410i
$213$		−	10134.6i		−	0.223382i
$214$	−42069.6	+	21339.7i	−0.918630	+	0.465973i
$215$			78119.7i			1.68999i
$216$	−1452.76	+	8860.65i	−0.0311377	+	0.189914i
$217$	−25391.0			−0.539213
$218$	−19116.5	−	37686.8i	−0.402250	−	0.793005i
$219$	−43161.7			−0.899932
$220$	49336.7	+	36118.8i	1.01935	+	0.746257i
$221$			60260.8i			1.23382i
$222$	−5065.64	−	9986.52i	−0.102785	−	0.202632i
$223$			59636.9i			1.19924i	0.800286	+	0.599619i	$0.204681\pi$
$223$			59636.9i			1.19924i	−0.800286	+	0.599619i	$0.795319\pi$
$224$	−30724.8	+	30173.6i	−0.612341	+	0.601355i
$225$	−22445.6			−0.443369
$226$	−26427.9	+	13405.5i	−0.517423	+	0.262461i
$227$	−10099.9			−0.196005			−0.0980024	−	0.995186i	$-0.531245\pi$
$227$	−10099.9			−0.196005			−0.0980024	+	0.995186i	$0.531245\pi$
$228$	24272.9	−	33155.7i	0.466930	−	0.637806i
$229$		−	33647.7i		−	0.641630i	−0.947142	−	0.320815i	$-0.896043\pi$
$229$		−	33647.7i		−	0.641630i	0.947142	−	0.320815i	$-0.103957\pi$
$230$	−34613.3	+	17557.5i	−0.654315	+	0.331900i
$231$			21882.7i			0.410089i
$232$	87709.8	+	14380.6i	1.62957	+	0.267178i
$233$	−74833.7			−1.37843			−0.689216	−	0.724556i	$-0.742045\pi$
$233$	−74833.7			−1.37843			−0.689216	+	0.724556i	$0.742045\pi$
$234$	8384.14	+	16528.7i	0.153118	+	0.301861i
$235$	69857.5			1.26496
$236$	−14907.6	+	20363.1i	−0.267660	+	0.365612i
$237$		−	58407.3i		−	1.03985i
$238$	26722.0	+	52680.5i	0.471754	+	0.930028i
$239$		−	24812.5i		−	0.434384i	−0.976129	−	0.217192i	$-0.930310\pi$
$239$		−	24812.5i		−	0.434384i	0.976129	−	0.217192i	$-0.0696898\pi$
$240$	48391.1	−	15336.7i	0.840123	−	0.266262i
$241$	−15222.1			−0.262084			−0.131042	−	0.991377i	$-0.541832\pi$
$241$	−15222.1			−0.262084			−0.131042	+	0.991377i	$0.541832\pi$
$242$	16455.4	−	8346.93i	0.280981	−	0.142527i
$243$	3788.00			0.0641500
$244$	−13652.6	−	9994.93i	−0.229317	−	0.167880i
$245$			24135.3i			0.402087i
$246$	−10016.5	+	5080.82i	−0.165517	+	0.0839583i
$247$		−	84816.4i		−	1.39023i
$248$	−38132.1	−	6252.00i	−0.619993	−	0.101652i
$249$	−3737.58			−0.0602827
$250$	14247.0	+	28086.9i	0.227952	+	0.449390i
$251$	91146.1			1.44674			0.723370	−	0.690461i	$-0.242592\pi$
$251$	91146.1			1.44674			0.723370	+	0.690461i	$0.242592\pi$
$252$	14659.0	+	10731.7i	0.230835	+	0.168992i
$253$		−	25461.6i		−	0.397781i
$254$	802.524	+	1582.12i	0.0124391	+	0.0245228i
$255$		−	69632.2i		−	1.07085i
$256$	−53572.0	+	37749.2i	−0.817444	+	0.576008i
$257$	−24844.7			−0.376156			−0.188078	−	0.982154i	$-0.560226\pi$
$257$	−24844.7			−0.376156			−0.188078	+	0.982154i	$0.560226\pi$
$258$	−37945.1	+	19247.5i	−0.570054	+	0.289158i
$259$	−22656.9			−0.337755
$260$	61895.2	−	84546.1i	0.915610	−	1.25068i
$261$		−	37496.6i		−	0.550442i
$262$	−380.908	+	193.214i	−0.00554903	+	0.00281473i
$263$		−	65761.8i		−	0.950741i	−0.879786	−	0.475371i	$-0.842314\pi$
$263$		−	65761.8i		−	0.950741i	0.879786	−	0.475371i	$-0.157686\pi$
$264$	−5388.17	+	32863.4i	−0.0773096	+	0.471525i
$265$	−132548.			−1.88747
$266$	−37611.0	−	74147.2i	−0.531559	−	1.04793i
$267$	−21748.7			−0.305078
$268$	−4889.24	+	6678.47i	−0.0680725	+	0.0929839i
$269$		−	3022.19i		−	0.0417654i	−0.999782	−	0.0208827i	$-0.993352\pi$
$269$		−	3022.19i		−	0.0417654i	0.999782	−	0.0208827i	$-0.00664765\pi$
$270$	−9687.99	−	19099.2i	−0.132894	−	0.261991i
$271$			145358.i			1.97925i	0.143665	+	0.989626i	$0.454111\pi$
$271$			145358.i			1.97925i	−0.143665	+	0.989626i	$0.545889\pi$
$272$	27159.6	+	85695.1i	0.367101	+	1.15829i
$273$	37499.5			0.503153
$274$	103682.	−	52592.4i	1.38103	−	0.700522i
$275$	−83248.7			−1.10081
$276$	−17056.4	−	12486.8i	−0.223908	−	0.163920i
$277$		−	120910.i		−	1.57580i	−0.615802	−	0.787901i	$-0.711168\pi$
$277$		−	120910.i		−	1.57580i	0.615802	−	0.787901i	$-0.288832\pi$
$278$	115715.	−	58696.1i	1.49727	−	0.759486i
$279$			16301.8i			0.209424i
$280$	16618.2	−	101358.i	0.211967	−	1.29283i
$281$	139506.			1.76677			0.883383	−	0.468653i	$-0.155260\pi$
$281$	139506.			1.76677			0.883383	+	0.468653i	$0.155260\pi$
$282$	17211.8	+	33931.8i	0.216436	+	0.426687i
$283$	−52948.2			−0.661117			−0.330558	−	0.943786i	$-0.607237\pi$
$283$	−52948.2			−0.661117			−0.330558	+	0.943786i	$0.607237\pi$
$284$	−25180.0	−	18434.0i	−0.312190	−	0.228551i
$285$			98006.6i			1.20661i
$286$	31096.1	+	61303.6i	0.380166	+	0.749470i
$287$			22724.8i			0.275890i
$288$	19372.3	+	19726.2i	0.233559	+	0.237826i
$289$	39789.6			0.476403
$290$	−189059.	+	95899.6i	−2.24802	+	1.14030i
$291$	−25416.6			−0.300145
$292$	−78507.5	+	107238.i	−0.920757	+	1.25771i
$293$		−	22036.7i		−	0.256691i	−0.991730	−	0.128346i	$-0.959033\pi$
$293$		−	22036.7i		−	0.256691i	0.991730	−	0.128346i	$-0.0409667\pi$
$294$	−11723.2	+	5946.57i	−0.135629	+	0.0687974i
$295$		−	60192.3i		−	0.691667i
$296$	−34026.1	−	5578.79i	−0.388354	−	0.0636732i
$297$	14049.4			0.159274
$298$	−10630.4	−	20957.1i	−0.119707	−	0.235993i
$299$	−43632.4			−0.488052
$300$	−40826.6	+	55767.3i	−0.453629	+	0.619636i
$301$			86087.8i			0.950186i
$302$	25027.4	+	49339.7i	0.274411	+	0.540981i
$303$		−	18613.3i		−	0.202739i
$304$	−38226.8	−	120615.i	−0.413638	−	1.30513i
$305$	40356.5			0.433824
$306$	33822.4	−	17156.3i	0.361212	−	0.183224i
$307$	144674.			1.53502			0.767510	−	0.641037i	$-0.221496\pi$
$307$	144674.			1.53502			0.767510	+	0.641037i	$0.221496\pi$
$308$	54368.9	+	39802.9i	0.573125	+	0.419578i
$309$			90371.0i			0.946481i
$310$	82193.8	−	41692.6i	0.855294	−	0.433846i
$311$			58811.2i			0.608050i	0.952664	+	0.304025i	$0.0983306\pi$
$311$			58811.2i			0.608050i	−0.952664	+	0.304025i	$0.901669\pi$
$312$	56316.6	+	9233.46i	0.578532	+	0.0948539i
$313$	91670.3			0.935707			0.467853	−	0.883806i	$-0.345028\pi$
$313$	91670.3			0.935707			0.467853	+	0.883806i	$0.345028\pi$
$314$	41110.5	+	81046.3i	0.416959	+	0.822004i
$315$	−43331.2			−0.436696
$316$	−145116.	−	106238.i	−1.45325	−	1.06391i
$317$			68445.4i			0.681124i	0.940222	+	0.340562i	$0.110617\pi$
$317$			68445.4i			0.681124i	−0.940222	+	0.340562i	$0.889383\pi$
$318$	−32657.7	−	64382.3i	−0.322947	−	0.636667i
$319$		−	139072.i		−	1.36665i
$320$	49914.4	−	148127.i	0.487445	−	1.44655i
$321$	61278.7			0.594702
$322$	−38143.8	+	19348.3i	−0.367885	+	0.186609i
$323$	−173558.			−1.66357
$324$	6890.05	−	9411.49i	0.0656345	−	0.0896537i
$325$			142660.i			1.35062i
$326$	51127.8	−	25934.4i	0.481085	−	0.244029i
$327$			54894.7i			0.513375i
$328$	−5595.51	+	34128.0i	−0.0520106	+	0.317222i
$329$	76982.8			0.711217
$330$	−35932.0	−	70837.2i	−0.329954	−	0.650479i
$331$	45633.5			0.416513			0.208256	−	0.978074i	$-0.433221\pi$
$331$	45633.5			0.416513			0.208256	+	0.978074i	$0.433221\pi$
$332$	−6798.35	+	9286.24i	−0.0616776	+	0.0842488i
$333$			14546.4i			0.131180i
$334$	−5180.78	−	10213.5i	−0.0464411	−	0.0915552i
$335$		−	19741.2i		−	0.175908i
$336$	53326.9	−	16901.0i	0.472354	−	0.149705i
$337$	−178174.			−1.56886			−0.784430	−	0.620217i	$-0.787045\pi$
$337$	−178174.			−1.56886			−0.784430	+	0.620217i	$0.787045\pi$
$338$	3167.43	−	1606.67i	0.0277251	−	0.0140635i
$339$	38494.9			0.334969
$340$	−173005.	−	126655.i	−1.49658	−	1.09563i
$341$			60461.9i			0.519963i
$342$	−47604.7	+	24147.3i	−0.407003	+	0.206451i
$343$			127569.i			1.08432i
$344$	−21197.3	+	129286.i	−0.179128	+	1.09254i
$345$	50417.8			0.423590
$346$	26266.5	+	51782.3i	0.219406	+	0.432543i
$347$	22112.6			0.183646			0.0918228	−	0.995775i	$-0.470731\pi$
$347$	22112.6			0.183646			0.0918228	+	0.995775i	$0.470731\pi$
$348$	−93162.5	−	68203.2i	−0.769277	−	0.563179i
$349$		−	186409.i		−	1.53044i	−0.643772	−	0.765218i	$-0.722631\pi$
$349$		−	186409.i		−	1.53044i	0.643772	−	0.765218i	$-0.277369\pi$
$350$	63261.0	+	124714.i	0.516416	+	1.01808i
$351$		−	24075.8i		−	0.195419i
$352$	71850.4	+	73163.0i	0.579888	+	0.590481i
$353$	−15985.3			−0.128284			−0.0641420	−	0.997941i	$-0.520431\pi$
$353$	−15985.3			−0.128284			−0.0641420	+	0.997941i	$0.520431\pi$
$354$	29237.2	−	14830.5i	0.233308	−	0.118345i
$355$	74430.9			0.590604
$356$	−39559.0	+	54035.8i	−0.312137	+	0.426365i
$357$		−	76734.6i		−	0.602081i
$358$	28796.2	−	14606.8i	0.224683	−	0.113970i
$359$		−	130882.i		−	1.01553i	−0.861497	−	0.507763i	$-0.830473\pi$
$359$		−	130882.i		−	1.01553i	0.861497	−	0.507763i	$-0.169527\pi$
$360$	−65074.6	−	10669.4i	−0.502119	−	0.0823256i
$361$	113961.			0.874460
$362$	−66698.7	−	131491.i	−0.508979	−	1.00341i
$363$	−23968.9			−0.181901
$364$	68208.5	−	93169.6i	0.514796	−	0.703188i
$365$		−	316989.i		−	2.37935i
$366$	9943.22	+	19602.3i	0.0742275	+	0.146334i
$367$			157598.i			1.17009i	0.811001	+	0.585045i	$0.198923\pi$
$367$			157598.i			1.17009i	−0.811001	+	0.585045i	$0.801077\pi$
$368$	−62048.3	+	19665.1i	−0.458178	+	0.145212i
$369$	14590.0			0.107153
$370$	73343.3	−	37203.2i	0.535743	−	0.271754i
$371$	−146067.			−1.06122
$372$	40502.6	+	29651.5i	0.292683	+	0.214270i
$373$		−	43982.6i		−	0.316128i	−0.987429	−	0.158064i	$-0.949475\pi$
$373$		−	43982.6i		−	0.316128i	0.987429	−	0.158064i	$-0.0505252\pi$
$374$	125445.	−	63631.4i	0.896827	−	0.454913i
$375$		−	40911.4i		−	0.290926i
$376$	115612.	+	18955.4i	0.817766	+	0.134078i
$377$	−238321.			−1.67680
$378$	−10676.2	−	21047.2i	−0.0747190	−	0.147303i
$379$	−163953.			−1.14141			−0.570703	−	0.821156i	$-0.693329\pi$
$379$	−163953.			−1.14141			−0.570703	+	0.821156i	$0.693329\pi$
$380$	243503.	+	178266.i	1.68631	+	1.23453i
$381$		−	2304.51i		−	0.0158756i
$382$	−3858.07	−	7605.89i	−0.0264389	−	0.0521223i
$383$		−	274654.i		−	1.87236i	−0.351525	−	0.936179i	$-0.614337\pi$
$383$		−	274654.i		−	1.87236i	0.351525	−	0.936179i	$-0.385663\pi$
$384$	84247.6	−	12251.3i	0.571341	−	0.0830843i
$385$	−160712.			−1.08424
$386$	−119105.	+	60415.5i	−0.799381	+	0.405484i
$387$	55270.9			0.369041
$388$	−46230.6	+	63148.9i	−0.307090	+	0.419472i
$389$			192557.i			1.27251i	0.771480	+	0.636253i	$0.219517\pi$
$389$			192557.i			1.27251i	−0.771480	+	0.636253i	$0.780483\pi$
$390$	−121391.	+	61575.0i	−0.798097	+	0.404833i
$391$			89284.2i			0.584011i
$392$	−6548.97	+	39943.3i	−0.0426187	+	0.259939i
$393$	554.831			0.00359233
$394$	72811.2	+	143542.i	0.469036	+	0.924668i
$395$	428956.			2.74928
$396$	25554.6	−	34906.4i	0.162959	−	0.222595i
$397$			152788.i			0.969410i	0.874678	+	0.484705i	$0.161073\pi$
$397$			152788.i			0.969410i	−0.874678	+	0.484705i	$0.838927\pi$
$398$	−4133.93	−	8149.73i	−0.0260974	−	0.0514490i
$399$			108003.i			0.678407i
$400$	64296.8	+	202872.i	0.401855	+	1.26795i
$401$	−181363.			−1.12787			−0.563936	−	0.825819i	$-0.690713\pi$
$401$	−181363.			−1.12787			−0.563936	+	0.825819i	$0.690713\pi$
$402$	9588.90	−	4863.94i	0.0593358	−	0.0300979i
$403$	103611.			0.637962
$404$	−46245.7	−	33856.0i	−0.283341	−	0.207430i
$405$			27819.9i			0.169608i
$406$	−208343.	+	105681.i	−1.26394	+	0.641129i
$407$			53951.4i			0.325697i
$408$	18894.3	−	115240.i	0.113504	−	0.692280i
$409$	115126.			0.688217			0.344109	−	0.938930i	$-0.388181\pi$
$409$	115126.			0.688217			0.344109	+	0.938930i	$0.388181\pi$
$410$	−37314.7	−	73563.1i	−0.221979	−	0.437615i
$411$	−151023.			−0.894048
$412$	224532.	+	164377.i	1.32277	+	0.968383i
$413$		−	66331.8i		−	0.388886i
$414$	12422.2	+	24489.4i	0.0724766	+	0.142882i
$415$		−	27449.7i		−	0.159383i
$416$	125376.	−	123127.i	0.724484	−	0.711486i
$417$	−168551.			−0.969301
$418$	−176562.	+	89560.5i	−1.01052	+	0.512583i
$419$	−62276.3			−0.354727			−0.177364	−	0.984145i	$-0.556757\pi$
$419$	−62276.3			−0.354727			−0.177364	+	0.984145i	$0.556757\pi$
$420$	−78815.8	+	107659.i	−0.446802	+	0.610311i
$421$			28425.3i			0.160377i	0.996780	+	0.0801884i	$0.0255522\pi$
$421$			28425.3i			0.160377i	−0.996780	+	0.0801884i	$0.974448\pi$
$422$	−47190.1	+	23937.1i	−0.264988	+	0.134414i
$423$		−	49425.2i		−	0.276228i
$424$	−219363.	−	35966.0i	−1.22020	−	0.200060i
$425$	291922.			1.61618
$426$	18338.7	+	36153.3i	0.101053	+	0.199218i
$427$	44472.8			0.243915
$428$	111461.	−	152250.i	0.608464	−	0.831134i
$429$		−	89295.1i		−	0.485191i
$430$	−141358.	−	278677.i	−0.764511	−	1.50718i
$431$			337494.i			1.81682i	0.418081	+	0.908410i	$0.362703\pi$
$431$			337494.i			1.81682i	−0.418081	+	0.908410i	$0.637297\pi$
$432$	−10851.0	−	34237.4i	−0.0581434	−	0.183457i
$433$	−27404.4			−0.146165			−0.0730827	−	0.997326i	$-0.523284\pi$
$433$	−27404.4			−0.146165			−0.0730827	+	0.997326i	$0.523284\pi$
$434$	90577.4	−	45945.2i	0.480884	−	0.243927i
$435$	275384.			1.45532
$436$	136389.	+	99848.9i	0.717474	+	0.525255i
$437$		−	125666.i		−	0.658047i
$438$	153971.	−	78101.3i	0.802584	−	0.407109i
$439$		−	152979.i		−	0.793787i	−0.917865	−	0.396894i	$-0.870088\pi$
$439$		−	152979.i		−	0.793787i	0.917865	−	0.396894i	$-0.129912\pi$
$440$	−241356.	−	39571.9i	−1.24668	−	0.204400i
$441$	17076.1			0.0878034
$442$	−109042.	−	214969.i	−0.558150	−	1.10035i
$443$	−206035.			−1.04987			−0.524933	−	0.851143i	$-0.675910\pi$
$443$	−206035.			−1.04987			−0.524933	+	0.851143i	$0.675910\pi$
$444$	36141.4	+	26458.7i	0.183332	+	0.134215i
$445$		−	159727.i		−	0.806601i
$446$	−107913.	−	212743.i	−0.542507	−	1.06951i
$447$			30526.2i			0.152777i
$448$	55005.6	−	163235.i	0.274063	−	0.813314i
$449$	−189831.			−0.941615			−0.470808	−	0.882236i	$-0.656037\pi$
$449$	−189831.			−0.941615			−0.470808	+	0.882236i	$0.656037\pi$
$450$	80070.2	−	40615.4i	0.395408	−	0.200570i
$451$	54113.1			0.266042
$452$	70019.1	−	95642.8i	0.342720	−	0.468140i
$453$		−	71868.3i		−	0.350220i
$454$	36029.6	−	18275.9i	0.174802	−	0.0886680i
$455$			275405.i			1.33030i
$456$	−26593.5	+	162199.i	−0.127893	+	0.780041i
$457$	89739.8			0.429687			0.214844	−	0.976648i	$-0.431076\pi$
$457$	89739.8			0.429687			0.214844	+	0.976648i	$0.431076\pi$
$458$	60885.8	+	120032.i	0.290259	+	0.572223i
$459$	−49265.8			−0.233841
$460$	91705.8	−	125266.i	0.433392	−	0.591994i
$461$			282353.i			1.32859i	0.747472	+	0.664294i	$0.231268\pi$
$461$			282353.i			1.32859i	−0.747472	+	0.664294i	$0.768732\pi$
$462$	−39597.0	−	78062.5i	−0.185515	−	0.365728i
$463$		−	276727.i		−	1.29089i	−0.763807	−	0.645445i	$-0.776672\pi$
$463$		−	276727.i		−	1.29089i	0.763807	−	0.645445i	$-0.223328\pi$
$464$	−338910.	+	107412.i	−1.57416	+	0.498902i
$465$	−119724.			−0.553700
$466$	266955.	−	135412.i	1.22932	−	0.623570i
$467$	367707.			1.68604			0.843021	−	0.537881i	$-0.180775\pi$
$467$	367707.			1.68604			0.843021	+	0.537881i	$0.180775\pi$
$468$	−59817.6	−	43791.8i	−0.273110	−	0.199941i
$469$		−	21754.8i		−	0.0989030i
$470$	−249203.	+	126408.i	−1.12813	+	0.572239i
$471$		−	118052.i		−	0.532149i
$472$	16332.8	−	99616.9i	0.0733124	−	0.447145i
$473$	204995.			0.916266
$474$	105688.	+	208357.i	0.470404	+	0.927365i
$475$	−410877.			−1.82106
$476$	−190651.	−	139574.i	−0.841446	−	0.616013i
$477$			93779.4i			0.412165i
$478$	44898.3	+	88513.7i	0.196505	+	0.387395i
$479$			286130.i			1.24708i	0.781793	+	0.623538i	$0.214305\pi$
$479$			286130.i			1.24708i	−0.781793	+	0.623538i	$0.785695\pi$
$480$	−144874.	+	142275.i	−0.628793	+	0.617512i
$481$	92454.1			0.399610
$482$	54301.9	−	27544.5i	0.233733	−	0.118561i
$483$	55560.4			0.238161
$484$	−43597.5	+	59552.2i	−0.186110	+	0.254218i
$485$		−	186665.i		−	0.793560i
$486$	−13512.9	+	6854.40i	−0.0572107	+	0.0290200i
$487$		−	61310.2i		−	0.258508i	−0.991611	−	0.129254i	$-0.958742\pi$
$487$		−	61310.2i		−	0.258508i	0.991611	−	0.129254i	$-0.0412583\pi$
$488$	66789.0	+	10950.5i	0.280456	+	0.0459826i
$489$	−74472.9			−0.311445
$490$	−43673.0	−	86098.0i	−0.181895	−	0.358592i
$491$	422941.			1.75435			0.877175	−	0.480170i	$-0.159425\pi$
$491$	422941.			1.75435			0.877175	+	0.480170i	$0.159425\pi$
$492$	26538.0	−	36249.7i	0.109632	−	0.149752i
$493$			487673.i			2.00648i
$494$	153476.	+	302566.i	0.628907	+	1.23984i
$495$			103182.i			0.421107i
$496$	147342.	−	46697.4i	0.598912	−	0.189815i
$497$	82022.7			0.332064
$498$	13333.1	−	6763.19i	0.0537617	−	0.0272705i
$499$	−324563.			−1.30346			−0.651730	−	0.758451i	$-0.725957\pi$
$499$	−324563.			−1.30346			−0.651730	+	0.758451i	$0.725957\pi$
$500$	−101647.	−	74414.5i	−0.406587	−	0.297658i
$501$			14877.1i			0.0592709i
$502$	−325146.	+	164929.i	−1.29024	+	0.654471i
$503$		−	185687.i		−	0.733915i	−0.930238	−	0.366958i	$-0.880399\pi$
$503$		−	185687.i		−	0.733915i	0.930238	−	0.366958i	$-0.119601\pi$
$504$	−71712.1	−	11757.7i	−0.282313	−	0.0462871i
$505$	136700.			0.536026
$506$	46072.9	+	90829.3i	0.179947	+	0.354752i
$507$	−4613.69			−0.0179487
$508$	−5725.70	−	4191.72i	−0.0221871	−	0.0162429i
$509$			401954.i			1.55146i	0.631064	+	0.775731i	$0.282618\pi$
$509$			401954.i			1.55146i	−0.631064	+	0.775731i	$0.717382\pi$
$510$	126000.	+	248399.i	0.484429	+	0.955015i
$511$		−	349321.i		−	1.33778i
$512$	122800.	−	231602.i	0.468446	−	0.883492i
$513$	69341.1			0.263485
$514$	88628.8	−	44956.7i	0.335466	−	0.170164i
$515$	−663705.			−2.50242
$516$	100533.	−	137324.i	0.377581	−	0.515758i
$517$		−	183314.i		−	0.685828i
$518$	80824.2	−	40997.8i	0.301219	−	0.152792i
$519$		−	75426.3i		−	0.280020i
$520$	−67812.6	+	413602.i	−0.250786	+	1.52959i
$521$	63089.4			0.232424			0.116212	−	0.993224i	$-0.462925\pi$
$521$	63089.4			0.232424			0.116212	+	0.993224i	$0.462925\pi$
$522$	67850.4	+	133762.i	0.249007	+	0.490899i
$523$	−183735.			−0.671722			−0.335861	−	0.941912i	$-0.609027\pi$
$523$	−183735.			−0.671722			−0.335861	+	0.941912i	$0.609027\pi$
$524$	1009.19	−	1378.51i	0.00367546	−	0.00502051i
$525$		−	181659.i		−	0.659081i
$526$	118997.	+	234593.i	0.430093	+	0.847897i
$527$		−	212017.i		−	0.763395i
$528$	−40245.3	−	126984.i	−0.144360	−	0.455492i
$529$	215194.			0.768987
$530$	472838.	−	239846.i	1.68330	−	0.853848i
$531$	−42587.0			−0.151039
$532$	268340.	+	196449.i	0.948117	+	0.694106i
$533$		−	92731.2i		−	0.326416i
$534$	77584.2	−	39354.4i	0.272076	−	0.138010i
$535$			450045.i			1.57235i
$536$	5356.67	−	32671.3i	0.0186451	−	0.113720i
$537$	−41944.7			−0.145455
$538$	5468.67	+	10781.1i	0.0188937	+	0.0372475i
$539$	63333.8			0.218001
$540$	69120.1	+	50602.1i	0.237037	+	0.173532i
$541$		−	436991.i		−	1.49306i	−0.665350	−	0.746531i	$-0.731718\pi$
$541$		−	436991.i		−	1.49306i	0.665350	−	0.746531i	$-0.268282\pi$
$542$	−263027.	−	518538.i	−0.895368	−	1.76515i
$543$			191531.i			0.649590i
$544$	−251952.	−	256555.i	−0.851374	−	0.866928i
$545$	−403159.			−1.35732
$546$	−133772.	+	67855.6i	−0.448725	+	0.227615i
$547$	44994.9			0.150379			0.0751897	−	0.997169i	$-0.476044\pi$
$547$	44994.9			0.150379			0.0751897	+	0.997169i	$0.476044\pi$
$548$	−274699.	+	375226.i	−0.914736	+	1.24949i
$549$		−	28552.8i		−	0.0947336i
$550$	296974.	−	150639.i	0.981732	−	0.497981i
$551$		−	686394.i		−	2.26084i
$552$	83440.3	+	13680.6i	0.273841	+	0.0448979i
$553$	472709.			1.54577
$554$	218787.	+	431322.i	0.712856	+	1.40534i
$555$	−106832.			−0.346829
$556$	−306580.	+	418774.i	−0.991732	+	1.35466i
$557$		−	181185.i		−	0.583999i	−0.956419	−	0.291999i	$-0.905680\pi$
$557$		−	181185.i		−	0.583999i	0.956419	−	0.291999i	$-0.0943205\pi$
$558$	−29498.1	−	58153.4i	−0.0947384	−	0.186770i
$559$		−	351291.i		−	1.12420i
$560$	124125.	+	391645.i	0.395807	+	1.24887i
$561$	−182723.			−0.580587
$562$	−497659.	+	252436.i	−1.57565	+	0.799243i
$563$	−252429.			−0.796382			−0.398191	−	0.917302i	$-0.630362\pi$
$563$	−252429.			−0.796382			−0.398191	+	0.917302i	$0.630362\pi$
$564$	−122800.	−	89900.4i	−0.386046	−	0.282620i
$565$			282715.i			0.885631i
$566$	188882.	−	95810.1i	0.589602	−	0.299074i
$567$			30657.5i			0.0953609i
$568$	123181.	+	20196.4i	0.381811	+	0.0626004i
$569$	244576.			0.755423			0.377711	−	0.925923i	$-0.376711\pi$
$569$	244576.			0.755423			0.377711	+	0.925923i	$0.376711\pi$
$570$	−177344.	−	349620.i	−0.545840	−	1.07608i
$571$	−320074.			−0.981699			−0.490849	−	0.871244i	$-0.663313\pi$
$571$	−320074.			−0.981699			−0.490849	+	0.871244i	$0.663313\pi$
$572$	−221859.	−	162420.i	−0.678085	−	0.496419i
$573$			11078.8i			0.0337429i
$574$	−41120.7	−	81066.4i	−0.124806	−	0.246047i
$575$			211369.i			0.639301i
$576$	−104802.	−	35315.2i	−0.315881	−	0.106443i
$577$	−214829.			−0.645269			−0.322635	−	0.946524i	$-0.604569\pi$
$577$	−214829.			−0.645269			−0.322635	+	0.946524i	$0.604569\pi$
$578$	−141942.	+	71999.6i	−0.424869	+	0.215514i
$579$	173488.			0.517503
$580$	500900.	−	684207.i	1.48900	−	2.03391i
$581$		−	30249.5i		−	0.0896119i
$582$	90668.7	−	45991.5i	0.267677	−	0.135779i
$583$			347820.i			1.02333i
$584$	86013.1	−	524609.i	0.252196	−	1.53819i
$585$	176818.			0.516672
$586$	39875.5	+	78611.6i	0.116121	+	0.228924i
$587$	674424.			1.95730			0.978649	−	0.205537i	$-0.0658942\pi$
$587$	674424.			1.95730			0.978649	+	0.205537i	$0.0658942\pi$
$588$	31060.0	−	42426.5i	0.0898352	−	0.122711i
$589$			298412.i			0.860172i
$590$	108918.	+	214724.i	0.312894	+	0.616847i
$591$		−	209083.i		−	0.598611i
$592$	131476.	−	41669.1i	0.375149	−	0.118897i
$593$	−337443.			−0.959601			−0.479800	−	0.877378i	$-0.659291\pi$
$593$	−337443.			−0.959601			−0.479800	+	0.877378i	$0.659291\pi$
$594$	−50118.4	+	25422.4i	−0.142044	+	0.0720517i
$595$	563556.			1.59185
$596$	75844.1	+	55524.6i	0.213515	+	0.156312i
$597$			11870.9i			0.0333070i
$598$	155650.	−	78953.1i	0.435258	−	0.220784i
$599$			308879.i			0.860864i	0.902623	+	0.430432i	$0.141639\pi$
$599$			308879.i			0.860864i	−0.902623	+	0.430432i	$0.858361\pi$
$600$	44729.8	−	272815.i	0.124249	−	0.757820i
$601$	−505644.			−1.39990			−0.699948	−	0.714193i	$-0.746794\pi$
$601$	−505644.			−1.39990			−0.699948	+	0.714193i	$0.746794\pi$
$602$	−155776.	−	307102.i	−0.429842	−	0.847401i
$603$	−13967.2			−0.0384128
$604$	−178561.	−	130722.i	−0.489455	−	0.358324i
$605$		−	176033.i		−	0.480932i
$606$	33680.8	+	66399.2i	0.0917144	+	0.180808i
$607$			662175.i			1.79720i	0.438773	+	0.898598i	$0.355413\pi$
$607$			662175.i			1.79720i	−0.438773	+	0.898598i	$0.644587\pi$
$608$	354620.	+	361099.i	0.959304	+	0.976829i
$609$	303472.			0.818248
$610$	−143964.	+	73025.3i	−0.386896	+	0.196252i
$611$	−314137.			−0.841467
$612$	−89610.5	+	122404.i	−0.239252	+	0.326808i
$613$			470942.i			1.25328i	0.779311	+	0.626638i	$0.215569\pi$
$613$			470942.i			1.25328i	−0.779311	+	0.626638i	$0.784431\pi$
$614$	−516097.	+	261789.i	−1.36897	+	0.694407i
$615$			107152.i			0.283303i
$616$	−265974.	−	43608.2i	−0.700936	−	0.114923i
$617$	−239921.			−0.630229			−0.315114	−	0.949054i	$-0.602043\pi$
$617$	−239921.			−0.630229			−0.315114	+	0.949054i	$0.602043\pi$
$618$	−163527.	−	322381.i	−0.428166	−	0.844097i
$619$	730806.			1.90731			0.953653	−	0.300907i	$-0.0972895\pi$
$619$	730806.			1.90731			0.953653	+	0.300907i	$0.0972895\pi$
$620$	−217768.	+	297461.i	−0.566513	+	0.773831i
$621$		−	35671.4i		−	0.0924989i
$622$	−106419.	−	209798.i	−0.275068	−	0.542275i
$623$		−	176019.i		−	0.453507i
$624$	−217607.	+	68966.6i	−0.558860	+	0.177121i
$625$	−219110.			−0.560922
$626$	−327016.	+	165878.i	−0.834489	+	0.423292i
$627$	257181.			0.654189
$628$	−293308.	−	214727.i	−0.743711	−	0.544463i
$629$		−	189187.i		−	0.478179i
$630$	154576.	−	78408.1i	0.389458	−	0.197551i
$631$		−	242358.i		−	0.608693i	−0.952561	−	0.304346i	$-0.901562\pi$
$631$		−	242358.i		−	0.608693i	0.952561	−	0.304346i	$-0.0984380\pi$
$632$	709913.	+	116395.i	1.77734	+	0.291406i
$633$	68737.3			0.171548
$634$	−123853.	−	244166.i	−0.308125	−	0.607444i
$635$	16924.9			0.0419738
$636$	233000.	+	170577.i	0.576026	+	0.421703i
$637$		−	108532.i		−	0.267473i
$638$	251652.	+	496112.i	0.618242	+	1.21882i
$639$		−	52661.0i		−	0.128970i
$640$	89976.2	+	618734.i	0.219668	+	1.51058i
$641$	684663.			1.66633			0.833165	−	0.553025i	$-0.186527\pi$
$641$	684663.			1.66633			0.833165	+	0.553025i	$0.186527\pi$
$642$	−218600.	+	110884.i	−0.530371	+	0.269029i
$643$	415456.			1.00485			0.502427	−	0.864620i	$-0.332441\pi$
$643$	415456.			1.00485			0.502427	+	0.864620i	$0.332441\pi$
$644$	101060.	−	138043.i	0.243672	−	0.332845i
$645$			405922.i			0.975715i
$646$	619136.	−	314055.i	1.48361	−	0.752559i
$647$			743379.i			1.77583i	0.460007	+	0.887915i	$0.347847\pi$
$647$			743379.i			1.77583i	−0.460007	+	0.887915i	$0.652153\pi$
$648$	−7548.76	+	46041.3i	−0.0179773	+	0.109647i
$649$	−157952.			−0.375003
$650$	−258144.	−	508911.i	−0.610991	−	1.20452i
$651$	−131935.			−0.311315
$652$	−135460.	+	185032.i	−0.318652	+	0.435263i
$653$		−	318695.i		−	0.747393i	−0.927551	−	0.373697i	$-0.878090\pi$
$653$		−	318695.i		−	0.747393i	0.927551	−	0.373697i	$-0.121910\pi$
$654$	−99332.3	−	195826.i	−0.232239	−	0.457842i
$655$			4074.81i			0.00949783i
$656$	−41794.0	−	131870.i	−0.0971195	−	0.306436i
$657$	−224275.			−0.519576
$658$	−274621.	+	139301.i	−0.634282	+	0.321738i
$659$	−661853.			−1.52402			−0.762010	−	0.647566i	$-0.775787\pi$
$659$	−661853.			−1.52402			−0.762010	+	0.647566i	$0.775787\pi$
$660$	256361.	+	187679.i	0.588524	+	0.430852i
$661$		−	477462.i		−	1.09279i	−0.837529	−	0.546394i	$-0.816000\pi$
$661$		−	477462.i		−	1.09279i	0.837529	−	0.546394i	$-0.184000\pi$
$662$	−162789.	+	82574.2i	−0.371457	+	0.188421i
$663$			313124.i			0.712344i
$664$	7448.30	−	45428.6i	0.0168936	−	0.103037i
$665$	−793199.			−1.79366
$666$	−26321.8	−	51891.5i	−0.0593427	−	0.116990i
$667$	−353104.			−0.793690
$668$	36962.9	+	27060.1i	0.0828349	+	0.0606425i
$669$			309882.i			0.692380i
$670$	35721.9	+	70423.1i	0.0795765	+	0.156879i
$671$		−	105900.i		−	0.235207i
$672$	−159651.	+	156787.i	−0.353535	+	0.347193i
$673$	7442.28			0.0164314			0.00821572	−	0.999966i	$-0.497385\pi$
$673$	7442.28			0.0164314			0.00821572	+	0.999966i	$0.497385\pi$
$674$	635601.	−	322407.i	1.39915	−	0.709716i
$675$	−116631.			−0.255979
$676$	−8391.92	+	11463.0i	−0.0183640	+	0.0250844i
$677$			55653.5i			0.121427i	0.998155	+	0.0607135i	$0.0193376\pi$
$677$			55653.5i			0.121427i	−0.998155	+	0.0607135i	$0.980662\pi$
$678$	−137323.	+	69656.8i	−0.298734	+	0.151532i
$679$		−	205705.i		−	0.446174i
$680$	846346.	+	138764.i	1.83033	+	0.300095i
$681$	−52480.8			−0.113163
$682$	−109406.	−	215686.i	−0.235219	−	0.463717i
$683$	323036.			0.692484			0.346242	−	0.938145i	$-0.387458\pi$
$683$	323036.			0.692484			0.346242	+	0.938145i	$0.387458\pi$
$684$	126126.	−	172282.i	0.269582	−	0.368237i
$685$		−	1.10915e6i		−	2.36379i
$686$	−230837.	−	455078.i	−0.490521	−	0.967025i
$687$		−	174839.i		−	0.370445i
$688$	−158327.	−	499561.i	−0.334486	−	1.05539i
$689$	596044.			1.25557
$690$	−179856.	+	91231.4i	−0.377769	+	0.191622i
$691$	154529.			0.323633			0.161816	−	0.986821i	$-0.448265\pi$
$691$	154529.			0.323633			0.161816	+	0.986821i	$0.448265\pi$
$692$	−187401.	−	137194.i	−0.391345	−	0.286499i
$693$			113706.i			0.236765i
$694$	−78882.4	+	40012.9i	−0.163780	+	0.0830770i
$695$		−	1.23788e6i		−	2.56276i
$696$	455754.	+	74723.7i	0.940831	+	0.154255i
$697$	−189754.			−0.390595
$698$	337308.	+	664977.i	0.692333	+	1.36488i
$699$	−388847.			−0.795838
$700$	−451343.	−	330423.i	−0.921108	−	0.674333i
$701$		−	53163.0i		−	0.108187i	−0.998536	−	0.0540933i	$-0.982773\pi$
$701$		−	53163.0i		−	0.108187i	0.998536	−	0.0540933i	$-0.0172269\pi$
$702$	43565.3	+	85885.7i	0.0884029	+	0.174280i
$703$			266279.i			0.538799i
$704$	−388701.	−	130981.i	−0.784279	−	0.264280i
$705$	362990.			0.730326
$706$	57024.6	−	28925.6i	0.114407	−	0.0580327i
$707$	150643.			0.301377
$708$	−77462.2	+	105810.i	−0.154534	+	0.211086i
$709$		−	280896.i		−	0.558795i	−0.960176	−	0.279397i	$-0.909865\pi$
$709$		−	280896.i		−	0.558795i	0.960176	−	0.279397i	$-0.0901347\pi$
$710$	−265518.	+	134683.i	−0.526717	+	0.267176i
$711$		−	303493.i		−	0.600357i
$712$	43341.0	−	264345.i	0.0854947	−	0.521448i
$713$	153513.			0.301971
$714$	138852.	+	273736.i	0.272367	+	0.536952i
$715$	655803.			1.28281
$716$	−76293.9	+	104214.i	−0.148821	+	0.203282i
$717$		−	128929.i		−	0.250792i
$718$	236832.	+	466896.i	0.459400	+	0.905673i
$719$		−	367010.i		−	0.709937i	−0.934878	−	0.354968i	$-0.884492\pi$
$719$		−	367010.i		−	0.709937i	0.934878	−	0.354968i	$-0.115508\pi$
$720$	251447.	−	79691.9i	0.485045	−	0.153727i
$721$	−731402.			−1.40697
$722$	−406532.	+	206212.i	−0.779867	+	0.395585i
$723$	−79096.3			−0.151314
$724$	475870.	+	348379.i	0.907843	+	0.664622i
$725$			1.15450e6i			2.19644i
$726$	85504.5	−	43371.9i	0.162224	−	0.0822878i
$727$		−	340510.i		−	0.644261i	−0.946695	−	0.322130i	$-0.895601\pi$
$727$		−	340510.i		−	0.644261i	0.946695	−	0.322130i	$-0.104399\pi$
$728$	−74729.4	+	455788.i	−0.141003	+	0.860004i
$729$	19683.0			0.0370370
$730$	573594.	+	1.13080e6i	1.07636	+	2.12197i
$731$	−718841.			−1.34524
$732$	−70941.1	−	51935.2i	−0.132396	−	0.0969258i
$733$			815103.i			1.51707i	0.651635	+	0.758533i	$0.274084\pi$
$733$			815103.i			1.51707i	−0.651635	+	0.758533i	$0.725916\pi$
$734$	−285175.	−	562201.i	−0.529321	−	1.04352i
$735$			125411.i			0.232145i
$736$	185761.	−	182428.i	0.342925	−	0.336773i
$737$	−51803.3			−0.0953723
$738$	−52047.0	+	26400.7i	−0.0955615	+	0.0484733i
$739$	−994330.			−1.82071			−0.910357	−	0.413824i	$-0.864193\pi$
$739$	−994330.			−1.82071			−0.910357	+	0.413824i	$0.864193\pi$
$740$	−194319.	+	265430.i	−0.354855	+	0.484716i
$741$		−	440719.i		−	0.802648i
$742$	521067.	−	264310.i	0.946424	−	0.480071i
$743$			917401.i			1.66181i	0.556414	+	0.830905i	$0.312177\pi$
$743$			917401.i			1.66181i	−0.556414	+	0.830905i	$0.687823\pi$
$744$	−198140.	−	32486.3i	−0.357953	−	0.0586887i
$745$	−224191.			−0.403930
$746$	79586.8	+	156899.i	0.143009	+	0.281931i
$747$	−19421.1			−0.0348042
$748$	−332358.	+	453986.i	−0.594022	+	0.811407i
$749$			495948.i			0.884042i
$750$	74029.5	+	145944.i	0.131608	+	0.259455i
$751$			507595.i			0.899989i	0.893031	+	0.449994i	$0.148574\pi$
$751$			507595.i			0.899989i	−0.893031	+	0.449994i	$0.851426\pi$
$752$	−446725.	+	141582.i	−0.789960	+	0.250364i
$753$	473609.			0.835276
$754$	850166.	−	431244.i	1.49541	−	0.758544i
$755$	527817.			0.925954
$756$	76170.3	+	55763.4i	0.133273	+	0.0975676i
$757$		−	71291.0i		−	0.124406i	−0.998064	−	0.0622032i	$-0.980187\pi$
$757$		−	71291.0i		−	0.124406i	0.998064	−	0.0622032i	$-0.0198127\pi$
$758$	584870.	−	296674.i	1.01794	−	0.516346i
$759$		−	132302.i		−	0.229659i
$760$	−1.19122e6	−	195309.i	−2.06237	−	0.338138i
$761$	206970.			0.357387			0.178693	−	0.983905i	$-0.442813\pi$
$761$	206970.			0.357387			0.178693	+	0.983905i	$0.442813\pi$
$762$	4170.03	+	8220.91i	0.00718174	+	0.0141583i
$763$	−444281.			−0.763147
$764$	27525.8	+	20151.4i	0.0471578	+	0.0345237i
$765$		−	361820.i		−	0.618257i
$766$	496989.	+	979776.i	0.847011	+	1.66982i
$767$			270675.i			0.460105i
$768$	−278368.	+	196151.i	−0.471952	+	0.332558i
$769$	931878.			1.57582			0.787910	−	0.615791i	$-0.211163\pi$
$769$	931878.			1.57582			0.787910	+	0.615791i	$0.211163\pi$
$770$	573309.	−	290809.i	0.966957	−	0.490486i
$771$	−129097.			−0.217174
$772$	315560.	−	431041.i	0.529478	−	0.723243i
$773$		−	184225.i		−	0.308312i	−0.988047	−	0.154156i	$-0.950734\pi$
$773$		−	184225.i		−	0.308312i	0.988047	−	0.154156i	$-0.0492658\pi$
$774$	−197168.	+	100013.i	−0.329121	+	0.166946i
$775$		−	501923.i		−	0.835668i
$776$	50650.4	−	308926.i	0.0841124	−	0.513017i
$777$	−117729.			−0.195003
$778$	−348433.	−	686910.i	−0.575653	−	1.13486i
$779$	267077.			0.440111
$780$	321617.	−	439314.i	0.528628	−	0.722081i
$781$		−	195315.i		−	0.320210i
$782$	−161560.	−	318504.i	−0.264193	−	0.520837i
$783$		−	194838.i		−	0.317798i
$784$	−48915.6	−	154341.i	−0.0795820	−	0.251101i
$785$	867003.			1.40696
$786$	−1979.25	+	1003.97i	−0.00320373	+	0.00162509i
$787$	936929.			1.51271			0.756357	−	0.654158i	$-0.226977\pi$
$787$	936929.			1.51271			0.756357	+	0.654158i	$0.226977\pi$
$788$	−519480.	−	380305.i	−0.836597	−	0.612463i
$789$		−	341709.i		−	0.548911i
$790$	−1.53022e6	+	776200.i	−2.45188	+	1.24371i
$791$			311552.i			0.497941i
$792$	−27997.7	+	170763.i	−0.0446347	+	0.272235i
$793$	−181476.			−0.288585
$794$	−276471.	−	545041.i	−0.438539	−	0.864546i
$795$	−688737.			−1.08973
$796$	29494.0	+	21592.2i	0.0465487	+	0.0340778i
$797$			239720.i			0.377388i	0.982036	+	0.188694i	$0.0604255\pi$
$797$			239720.i			0.377388i	−0.982036	+	0.188694i	$0.939575\pi$
$798$	−195432.	−	385280.i	−0.306896	−	0.605022i
$799$			642814.i			1.00691i
$800$	−596465.	−	607361.i	−0.931976	−	0.949002i
$801$	−113009.			−0.176137
$802$	646977.	−	328177.i	1.00587	−	0.510223i
$803$	−831816.			−1.29002
$804$	−25405.2	+	34702.4i	−0.0393017	+	0.0536843i
$805$			408048.i			0.629679i
$806$	−369612.	+	187485.i	−0.568952	+	0.288599i
$807$		−	15703.7i		−	0.0241133i
$808$	226235.	+	37092.7i	0.346527	+	0.0568154i
$809$	598514.			0.914486			0.457243	−	0.889342i	$-0.348837\pi$
$809$	598514.			0.914486			0.457243	+	0.889342i	$0.348837\pi$
$810$	−50340.3	−	99242.1i	−0.0767266	−	0.151261i
$811$	17550.1			0.0266831			0.0133416	−	0.999911i	$-0.495753\pi$
$811$	17550.1			0.0266831			0.0133416	+	0.999911i	$0.495753\pi$
$812$	551991.	−	753995.i	0.837182	−	1.14355i
$813$			755304.i			1.14272i
$814$	−97625.5	−	192461.i	−0.147338	−	0.290466i
$815$		−	546946.i		−	0.823435i
$816$	141125.	+	445285.i	0.211946	+	0.668740i
$817$	1.01176e6			1.51577
$818$	−410689.	+	208321.i	−0.613771	+	0.311334i
$819$	194853.			0.290496
$820$	266226.	+	194901.i	0.395934	+	0.289859i
$821$		−	18495.4i		−	0.0274396i	−0.999906	−	0.0137198i	$-0.995633\pi$
$821$		−	18495.4i		−	0.0274396i	0.999906	−	0.0137198i	$-0.00436728\pi$
$822$	538747.	−	273278.i	0.797336	−	0.404446i
$823$		−	425107.i		−	0.627622i	−0.949485	−	0.313811i	$-0.898394\pi$
$823$		−	425107.i		−	0.627622i	0.949485	−	0.313811i	$-0.101606\pi$
$824$	−1.09842e6	−	180092.i	−1.61775	−	0.265241i
$825$	−432573.			−0.635553
$826$	120028.	+	236626.i	0.175923	+	0.346819i
$827$	239745.			0.350540			0.175270	−	0.984520i	$-0.443920\pi$
$827$	239745.			0.350540			0.175270	+	0.984520i	$0.443920\pi$
$828$	−88627.6	−	64883.3i	−0.129273	−	0.0946394i
$829$			904750.i			1.31650i	0.752801	+	0.658248i	$0.228702\pi$
$829$			904750.i			1.31650i	−0.752801	+	0.658248i	$0.771298\pi$
$830$	49670.4	+	97921.4i	0.0721010	+	0.142142i
$831$		−	628265.i		−	0.909790i
$832$	−224457.	+	666100.i	−0.324254	+	0.962261i
$833$	−222088.			−0.320063
$834$	601273.	−	304994.i	0.864449	−	0.438489i
$835$	−109260.			−0.156708
$836$	467790.	−	638980.i	0.669327	−	0.914270i
$837$			84706.4i			0.120911i
$838$	222159.	−	112689.i	0.316355	−	0.160470i
$839$			376178.i			0.534403i	0.963641	+	0.267202i	$0.0860990\pi$
$839$			376178.i			0.534403i	−0.963641	+	0.267202i	$0.913901\pi$
$840$	86350.9	−	526670.i	0.122379	−	0.746414i
$841$	−1.22138e6			−1.72687
$842$	−51435.9	−	101402.i	−0.0725507	−	0.143028i
$843$	724892.			1.02004
$844$	125027.	−	170782.i	0.175517	−	0.239749i
$845$		−	33884.0i		−	0.0474549i
$846$	89435.3	+	176315.i	0.124959	+	0.246348i
$847$		−	193988.i		−	0.270401i
$848$	847617.	−	268637.i	1.17871	−	0.373572i
$849$	−275127.			−0.381696
$850$	−1.04138e6	+	528235.i	−1.44135	+	0.731121i
$851$	136983.			0.189150
$852$	−130839.	−	95786.0i	−0.180243	−	0.131954i
$853$		−	662654.i		−	0.910729i	−0.890305	−	0.455364i	$-0.849509\pi$
$853$		−	662654.i		−	0.910729i	0.890305	−	0.455364i	$-0.150491\pi$
$854$	−158648.	+	80473.8i	−0.217530	+	0.110341i
$855$			509257.i			0.696634i
$856$	−122117.	+	744813.i	−0.166659	+	1.01648i
$857$	−767295.			−1.04472			−0.522361	−	0.852724i	$-0.674949\pi$
$857$	−767295.			−1.04472			−0.522361	+	0.852724i	$0.674949\pi$
$858$	161580.	+	318543.i	0.219489	+	0.432707i
$859$	−823262.			−1.11571			−0.557856	−	0.829938i	$-0.688376\pi$
$859$	−823262.			−1.11571			−0.557856	+	0.829938i	$0.688376\pi$
$860$	1.00854e6	+	738338.i	1.36362	+	0.998294i
$861$			118082.i			0.159285i
$862$	−610698.	−	1.20395e6i	−0.821887	−	1.62029i
$863$		−	605487.i		−	0.812987i	−0.913654	−	0.406493i	$-0.866751\pi$
$863$		−	605487.i		−	0.812987i	0.913654	−	0.406493i	$-0.133249\pi$
$864$	100662.	+	102501.i	0.134845	+	0.137309i
$865$	553948.			0.740350
$866$	97760.0	−	49588.5i	0.130354	−	0.0661219i
$867$	206753.			0.275051
$868$	−239980.	+	327801.i	−0.318519	+	0.435082i
$869$		−	1.12563e6i		−	1.49058i
$870$	−982378.	+	498309.i	−1.29790	+	0.658355i
$871$			88773.0i			0.117016i
$872$	−667219.	−	109395.i	−0.877476	−	0.143868i
$873$	−132068.			−0.173289
$874$	227394.	+	448291.i	0.297685	+	0.586864i
$875$	331110.			0.432470
$876$	−407937.	+	557223.i	−0.531600	+	0.726141i
$877$			578472.i			0.752114i	0.926597	+	0.376057i	$0.122720\pi$
$877$			578472.i			0.752114i	−0.926597	+	0.376057i	$0.877280\pi$
$878$	276817.	+	545725.i	0.359091	+	0.707921i
$879$		−	114506.i		−	0.148201i
$880$	932598.	−	295571.i	1.20428	−	0.381677i
$881$	218679.			0.281745			0.140872	−	0.990028i	$-0.455009\pi$
$881$	218679.			0.281745			0.140872	+	0.990028i	$0.455009\pi$
$882$	−60915.7	+	30899.3i	−0.0783054	+	0.0397202i
$883$	302510.			0.387988			0.193994	−	0.981003i	$-0.437856\pi$
$883$	302510.			0.387988			0.193994	+	0.981003i	$0.437856\pi$
$884$	777975.	+	569547.i	0.995546	+	0.728828i
$885$		−	312768.i		−	0.399334i
$886$	734991.	−	372822.i	0.936299	−	0.474935i
$887$			932038.i			1.18464i	0.805703	+	0.592320i	$0.201788\pi$
$887$			932038.i			1.18464i	−0.805703	+	0.592320i	$0.798212\pi$
$888$	−176805.	−	28988.2i	−0.224216	−	0.0367617i
$889$	18651.2			0.0235995
$890$	289028.	+	569796.i	0.364888	+	0.719349i
$891$	73002.6			0.0919566
$892$	769920.	+	563650.i	0.967645	+	0.708402i
$893$		−	904754.i		−	1.13456i
$894$	−55237.4	−	108896.i	−0.0691127	−	0.136250i
$895$		−	308051.i		−	0.384571i
$896$	99153.6	+	681844.i	0.123507	+	0.849315i
$897$	−226720.			−0.281777
$898$	677184.	−	343500.i	0.839758	−	0.425965i
$899$	838492.			1.03748
$900$	−212141.	+	289775.i	−0.261903	+	0.357747i
$901$		−	1.21968e6i		−	1.50243i
$902$	−193038.	+	97918.1i	−0.237263	+	0.120351i
$903$			447325.i			0.548590i
$904$	−76713.1	+	467887.i	−0.0938713	+	0.572538i
$905$	−1.40665e6			−1.71746
$906$	130046.	+	256376.i	0.158431	+	0.312336i
$907$	−553592.			−0.672938			−0.336469	−	0.941695i	$-0.609233\pi$
$907$	−553592.			−0.672938			−0.336469	+	0.941695i	$0.609233\pi$
$908$	−95458.2	+	130392.i	−0.115782	+	0.158153i
$909$		−	96717.3i		−	0.117051i
$910$	−498347.	−	982454.i	−0.601796	−	1.18639i
$911$			1.42062e6i			1.71175i	0.517184	+	0.855874i	$0.326980\pi$
$911$			1.42062e6i			1.71175i	−0.517184	+	0.855874i	$0.673020\pi$
$912$	−198632.	−	626733.i	−0.238814	−	0.753517i
$913$	−72031.1			−0.0864129
$914$	−320129.	+	162385.i	−0.383207	+	0.194381i
$915$	209698.			0.250468
$916$	−434397.	−	318017.i	−0.517721	−	0.379018i
$917$			4490.43i			0.00534010i
$918$	175746.	−	89146.9i	0.208546	−	0.105784i
$919$			212699.i			0.251845i	0.992040	+	0.125923i	$0.0401891\pi$
$919$			212699.i			0.251845i	−0.992040	+	0.125923i	$0.959811\pi$
$920$	−100473.	+	612804.i	−0.118707	+	0.724013i
$921$	751748.			0.886244
$922$	−510919.	−	1.00724e6i	−0.601022	−	1.18487i
$923$	−334703.			−0.392877
$924$	282509.	+	206822.i	0.330894	+	0.242244i
$925$		−	447877.i		−	0.523450i
$926$	500739.	+	987169.i	0.583968	+	1.15125i
$927$			469581.i			0.546451i
$928$	1.01463e6	−	996430.i	1.17818	−	1.15705i
$929$	−1.13677e6			−1.31717			−0.658585	−	0.752506i	$-0.728845\pi$
$929$	−1.13677e6			−1.31717			−0.658585	+	0.752506i	$0.728845\pi$
$930$	427092.	−	216641.i	0.493804	−	0.250481i
$931$	312586.			0.360637
$932$	−707280.	+	966113.i	−0.814254	+	1.11223i
$933$			305592.i			0.351058i
$934$	−1.31172e6	+	665369.i	−1.50366	+	0.762726i
$935$		−	1.34196e6i		−	1.53503i
$936$	292629.	+	47978.5i	0.334015	+	0.0547640i
$937$	−285636.			−0.325337			−0.162669	−	0.986681i	$-0.552010\pi$
$937$	−285636.			−0.325337			−0.162669	+	0.986681i	$0.552010\pi$
$938$	39365.5	+	77606.1i	0.0447414	+	0.0882044i
$939$	476333.			0.540231
$940$	660249.	−	901870.i	0.747226	−	1.02068i
$941$			184285.i			0.208118i	0.994571	+	0.104059i	$0.0331831\pi$
$941$			184285.i			0.208118i	−0.994571	+	0.104059i	$0.966817\pi$
$942$	213617.	+	421129.i	0.240732	+	0.474584i
$943$		−	137393.i		−	0.154505i
$944$	121993.	+	384918.i	0.136896	+	0.431941i
$945$	−225156.			−0.252127
$946$	−731281.	+	370940.i	−0.817150	+	0.414497i
$947$	477705.			0.532672			0.266336	−	0.963880i	$-0.414187\pi$
$947$	477705.			0.532672			0.266336	+	0.963880i	$0.414187\pi$
$948$	−754046.	−	552029.i	−0.839037	−	0.614250i
$949$			1.42545e6i			1.58277i
$950$	1.46573e6	−	743485.i	1.62407	−	0.823806i
$951$			355653.i			0.393247i
$952$	932672.	+	152918.i	1.02909	+	0.168727i
$953$	−1.40115e6			−1.54276			−0.771380	−	0.636375i	$-0.780433\pi$
$953$	−1.40115e6			−1.54276			−0.771380	+	0.636375i	$0.780433\pi$
$954$	−169695.	−	334540.i	−0.186454	−	0.367580i
$955$	−81365.0			−0.0892135
$956$	−320332.	−	234512.i	−0.350497	−	0.256595i
$957$		−	722639.i		−	0.789037i
$958$	−517755.	−	1.02071e6i	−0.564148	−	1.11218i
$959$		−	1.22228e6i		−	1.32903i
$960$	259363.	−	769689.i	0.281427	−	0.835165i
$961$	558984.			0.605275
$962$	−329812.	+	167296.i	−0.356383	+	0.180774i
$963$	318413.			0.343351
$964$	−143870.	+	196519.i	−0.154816	+	0.211471i
$965$			1.27414e6i			1.36824i
$966$	−198201.	+	100537.i	−0.212398	+	0.107739i
$967$		−	877370.i		−	0.938275i	−0.883125	−	0.469137i	$-0.844565\pi$
$967$		−	877370.i		−	0.938275i	0.883125	−	0.469137i	$-0.155435\pi$
$968$	47765.6	−	291331.i	0.0509758	−	0.310911i
$969$	−901836.			−0.960461
$970$	337772.	+	665892.i	0.358988	+	0.707718i
$971$	29888.2			0.0317002			0.0158501	−	0.999874i	$-0.494955\pi$
$971$	29888.2			0.0317002			0.0158501	+	0.999874i	$0.494955\pi$
$972$	35801.7	−	48903.5i	0.0378941	−	0.0517616i
$973$		−	1.36414e6i		−	1.44090i
$974$	110941.	+	218712.i	0.116943	+	0.230545i
$975$			741281.i			0.779783i
$976$	−258072.	+	81791.4i	−0.270920	+	0.0858634i
$977$	1.28420e6			1.34537			0.672687	−	0.739927i	$-0.265140\pi$
$977$	1.28420e6			1.34537			0.672687	+	0.739927i	$0.265140\pi$
$978$	265668.	−	134759.i	0.277755	−	0.140890i
$979$	−419143.			−0.437317
$980$	311590.	+	228112.i	0.324438	+	0.237517i
$981$			285241.i			0.296397i
$982$	−1.50876e6	+	765314.i	−1.56458	+	0.793627i
$983$		−	1.30863e6i		−	1.35428i	−0.735852	−	0.677142i	$-0.763218\pi$
$983$		−	1.30863e6i		−	1.35428i	0.735852	−	0.677142i	$-0.236782\pi$
$984$	−29075.1	+	177334.i	−0.0300283	+	0.183148i
$985$	1.53556e6			1.58268
$986$	−882448.	−	1.73968e6i	−0.907685	−	1.78943i
$987$	400015.			0.410621
$988$	−1.09499e6	−	801631.i	−1.12175	−	0.821222i
$989$		−	520483.i		−	0.532126i
$990$	−186708.	−	368081.i	−0.190499	−	0.375554i
$991$		−	958452.i		−	0.975940i	−0.872860	−	0.487970i	$-0.837737\pi$
$991$		−	958452.i		−	0.975940i	0.872860	−	0.487970i	$-0.162263\pi$
$992$	−441114.	+	433200.i	−0.448258	+	0.440216i
$993$	237119.			0.240474
$994$	−292600.	+	148421.i	−0.296143	+	0.150218i
$995$	−87182.7			−0.0880611
$996$	−35325.3	+	48252.7i	−0.0356096	+	0.0486411i
$997$			1.30519e6i			1.31306i	0.754301	+	0.656529i	$0.227976\pi$
$997$			1.30519e6i			1.31306i	−0.754301	+	0.656529i	$0.772024\pi$
$998$	1.15782e6	−	587299.i	1.16246	−	0.589655i
$999$			75585.3i			0.0757367i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.5.b.a.19.2	yes	8
3.2	odd	2		72.5.b.d.19.7		8
4.3	odd	2		96.5.b.a.79.4		8
8.3	odd	2	inner	24.5.b.a.19.1	✓	8
8.5	even	2		96.5.b.a.79.1		8
12.11	even	2		288.5.b.d.271.1		8
16.3	odd	4		768.5.g.k.511.8		16
16.5	even	4		768.5.g.k.511.1		16
16.11	odd	4		768.5.g.k.511.9		16
16.13	even	4		768.5.g.k.511.16		16
24.5	odd	2		288.5.b.d.271.8		8
24.11	even	2		72.5.b.d.19.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.5.b.a.19.1	✓	8	8.3	odd	2	inner
24.5.b.a.19.2	yes	8	1.1	even	1	trivial
72.5.b.d.19.7		8	3.2	odd	2
72.5.b.d.19.8		8	24.11	even	2
96.5.b.a.79.1		8	8.5	even	2
96.5.b.a.79.4		8	4.3	odd	2
288.5.b.d.271.1		8	12.11	even	2
288.5.b.d.271.8		8	24.5	odd	2
768.5.g.k.511.1		16	16.5	even	4
768.5.g.k.511.8		16	16.3	odd	4
768.5.g.k.511.9		16	16.11	odd	4
768.5.g.k.511.16		16	16.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	24.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.56731 + 1.80951i) q^{2} +5.19615 q^{3} +(9.45137 - 12.9101i) q^{4} +38.1617i q^{5} +(-18.5363 + 9.40247i) q^{6} +42.0542i q^{7} +(-10.3550 + 63.1567i) q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q+(-3.56731 + 1.80951i) q^{2} +5.19615 q^{3} +(9.45137 - 12.9101i) q^{4} +38.1617i q^{5} +(-18.5363 + 9.40247i) q^{6} +42.0542i q^{7} +(-10.3550 + 63.1567i) q^{8} +27.0000 q^{9} +(-69.0539 - 136.135i) q^{10} +100.141 q^{11} +(49.1107 - 67.0830i) q^{12} -171.607i q^{13} +(-76.0973 - 150.020i) q^{14} +198.294i q^{15} +(-77.3433 - 244.037i) q^{16} -351.156 q^{17} +(-96.3173 + 48.8567i) q^{18} +494.248 q^{19} +(492.673 + 360.680i) q^{20} +218.520i q^{21} +(-357.233 + 181.205i) q^{22} -254.258i q^{23} +(-53.8059 + 328.172i) q^{24} -831.317 q^{25} +(310.524 + 612.174i) q^{26} +140.296 q^{27} +(542.925 + 397.469i) q^{28} -1388.76i q^{29} +(-358.815 - 707.376i) q^{30} +603.769i q^{31} +(717.494 + 730.602i) q^{32} +520.347 q^{33} +(1252.68 - 635.420i) q^{34} -1604.86 q^{35} +(255.187 - 348.574i) q^{36} +538.756i q^{37} +(-1763.14 + 894.346i) q^{38} -891.695i q^{39} +(-2410.17 - 395.163i) q^{40} +540.370 q^{41} +(-395.413 - 779.527i) q^{42} +2047.07 q^{43} +(946.467 - 1292.83i) q^{44} +1030.37i q^{45} +(460.081 + 907.016i) q^{46} -1830.56i q^{47} +(-401.887 - 1268.05i) q^{48} +632.448 q^{49} +(2965.56 - 1504.27i) q^{50} -1824.66 q^{51} +(-2215.47 - 1621.92i) q^{52} +3473.31i q^{53} +(-500.479 + 253.867i) q^{54} +3821.54i q^{55} +(-2656.00 - 435.469i) q^{56} +2568.19 q^{57} +(2512.98 + 4954.15i) q^{58} -1577.30 q^{59} +(2560.00 + 1874.15i) q^{60} -1057.51i q^{61} +(-1092.52 - 2153.83i) q^{62} +1135.46i q^{63} +(-3881.55 - 1307.97i) q^{64} +6548.81 q^{65} +(-1856.24 + 941.571i) q^{66} -517.305 q^{67} +(-3318.91 + 4533.47i) q^{68} -1321.16i q^{69} +(5725.03 - 2904.00i) q^{70} -1950.41i q^{71} +(-279.584 + 1705.23i) q^{72} -8306.47 q^{73} +(-974.882 - 1921.91i) q^{74} -4319.65 q^{75} +(4671.32 - 6380.82i) q^{76} +4211.34i q^{77} +(1613.53 + 3180.95i) q^{78} -11240.5i q^{79} +(9312.87 - 2951.55i) q^{80} +729.000 q^{81} +(-1927.67 + 977.804i) q^{82} -719.298 q^{83} +(2821.12 + 2065.31i) q^{84} -13400.7i q^{85} +(-7302.53 + 3704.19i) q^{86} -7216.23i q^{87} +(-1036.95 + 6324.57i) q^{88} -4185.54 q^{89} +(-1864.46 - 3675.63i) q^{90} +7216.78 q^{91} +(-3282.50 - 2403.08i) q^{92} +3137.27i q^{93} +(3312.42 + 6530.19i) q^{94} +18861.4i q^{95} +(3728.21 + 3796.32i) q^{96} -4891.42 q^{97} +(-2256.14 + 1144.42i) q^{98} +2703.80 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} + 216 q^{9}+O(q^{10}) \) 8 * q - 6 * q^2 + 8 * q^4 + 18 * q^6 - 180 * q^8 + 216 * q^9	\( 8 q - 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} + 216 q^{9} - 324 q^{10} + 192 q^{11} + 180 q^{12} + 420 q^{14} - 712 q^{16} + 240 q^{17} - 162 q^{18} - 704 q^{19} + 168 q^{20} + 592 q^{22} - 108 q^{24} - 664 q^{25} + 1008 q^{26} - 528 q^{28} + 468 q^{30} + 3624 q^{32} + 2716 q^{34} - 5184 q^{35} + 216 q^{36} - 6360 q^{38} + 408 q^{40} + 720 q^{41} - 2412 q^{42} + 10048 q^{43} - 6720 q^{44} + 2616 q^{46} - 3168 q^{48} - 1240 q^{49} + 5394 q^{50} - 4032 q^{51} + 2448 q^{52} + 486 q^{54} + 7512 q^{56} + 3744 q^{57} - 10740 q^{58} + 13056 q^{59} + 10656 q^{60} - 8724 q^{62} - 17632 q^{64} - 1344 q^{65} - 13680 q^{66} - 6656 q^{67} - 5616 q^{68} + 19800 q^{70} - 4860 q^{72} - 16880 q^{73} + 17400 q^{74} - 1152 q^{75} + 14320 q^{76} + 18720 q^{78} + 28512 q^{80} + 5832 q^{81} - 9740 q^{82} - 24000 q^{83} + 21960 q^{84} - 34344 q^{86} - 19616 q^{88} + 15600 q^{89} - 8748 q^{90} + 1344 q^{91} - 48096 q^{92} + 12120 q^{94} - 21528 q^{96} - 12176 q^{97} + 47778 q^{98} + 5184 q^{99}+O(q^{100}) \) 8 * q - 6 * q^2 + 8 * q^4 + 18 * q^6 - 180 * q^8 + 216 * q^9 - 324 * q^10 + 192 * q^11 + 180 * q^12 + 420 * q^14 - 712 * q^16 + 240 * q^17 - 162 * q^18 - 704 * q^19 + 168 * q^20 + 592 * q^22 - 108 * q^24 - 664 * q^25 + 1008 * q^26 - 528 * q^28 + 468 * q^30 + 3624 * q^32 + 2716 * q^34 - 5184 * q^35 + 216 * q^36 - 6360 * q^38 + 408 * q^40 + 720 * q^41 - 2412 * q^42 + 10048 * q^43 - 6720 * q^44 + 2616 * q^46 - 3168 * q^48 - 1240 * q^49 + 5394 * q^50 - 4032 * q^51 + 2448 * q^52 + 486 * q^54 + 7512 * q^56 + 3744 * q^57 - 10740 * q^58 + 13056 * q^59 + 10656 * q^60 - 8724 * q^62 - 17632 * q^64 - 1344 * q^65 - 13680 * q^66 - 6656 * q^67 - 5616 * q^68 + 19800 * q^70 - 4860 * q^72 - 16880 * q^73 + 17400 * q^74 - 1152 * q^75 + 14320 * q^76 + 18720 * q^78 + 28512 * q^80 + 5832 * q^81 - 9740 * q^82 - 24000 * q^83 + 21960 * q^84 - 34344 * q^86 - 19616 * q^88 + 15600 * q^89 - 8748 * q^90 + 1344 * q^91 - 48096 * q^92 + 12120 * q^94 - 21528 * q^96 - 12176 * q^97 + 47778 * q^98 + 5184 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more