LMFDB - Embedded newform 72.5.b.d.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,5,Mod(19,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, 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("72.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	72.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:	$7.44263734204$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 24)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.7
Root			$-0.866025 + 3.62169i$ of defining polynomial
Character	$\chi$	$=$	72.19
Dual form			72.5.b.d.19.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.56731 - 1.80951i) q^{2} +(9.45137 - 12.9101i) q^{4} -38.1617i q^{5} +42.0542i q^{7} +(10.3550 - 63.1567i) q^{8} +O(q^{10})$	\(q+(3.56731 - 1.80951i) q^{2} +(9.45137 - 12.9101i) q^{4} -38.1617i q^{5} +42.0542i q^{7} +(10.3550 - 63.1567i) q^{8} +(-69.0539 - 136.135i) q^{10} -100.141 q^{11} -171.607i q^{13} +(76.0973 + 150.020i) q^{14} +(-77.3433 - 244.037i) q^{16} +351.156 q^{17} +494.248 q^{19} +(-492.673 - 360.680i) q^{20} +(-357.233 + 181.205i) q^{22} +254.258i q^{23} -831.317 q^{25} +(-310.524 - 612.174i) q^{26} +(542.925 + 397.469i) q^{28} +1388.76i q^{29} +603.769i q^{31} +(-717.494 - 730.602i) q^{32} +(1252.68 - 635.420i) q^{34} +1604.86 q^{35} +538.756i q^{37} +(1763.14 - 894.346i) q^{38} +(-2410.17 - 395.163i) q^{40} -540.370 q^{41} +2047.07 q^{43} +(-946.467 + 1292.83i) q^{44} +(460.081 + 907.016i) q^{46} +1830.56i q^{47} +632.448 q^{49} +(-2965.56 + 1504.27i) q^{50} +(-2215.47 - 1621.92i) q^{52} -3473.31i q^{53} +3821.54i q^{55} +(2656.00 + 435.469i) q^{56} +(2512.98 + 4954.15i) q^{58} +1577.30 q^{59} -1057.51i q^{61} +(1092.52 + 2153.83i) q^{62} +(-3881.55 - 1307.97i) q^{64} -6548.81 q^{65} -517.305 q^{67} +(3318.91 - 4533.47i) q^{68} +(5725.03 - 2904.00i) q^{70} +1950.41i q^{71} -8306.47 q^{73} +(974.882 + 1921.91i) q^{74} +(4671.32 - 6380.82i) q^{76} -4211.34i q^{77} -11240.5i q^{79} +(-9312.87 + 2951.55i) q^{80} +(-1927.67 + 977.804i) q^{82} +719.298 q^{83} -13400.7i q^{85} +(7302.53 - 3704.19i) q^{86} +(-1036.95 + 6324.57i) q^{88} +4185.54 q^{89} +7216.78 q^{91} +(3282.50 + 2403.08i) q^{92} +(3312.42 + 6530.19i) q^{94} -18861.4i q^{95} -4891.42 q^{97} +(2256.14 - 1144.42i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{2} + 8 q^{4} + 180 q^{8}+O(q^{10}) $ 8 * q + 6 * q^2 + 8 * q^4 + 180 * q^8	$ 8 q + 6 q^{2} + 8 q^{4} + 180 q^{8} - 324 q^{10} - 192 q^{11} - 420 q^{14} - 712 q^{16} - 240 q^{17} - 704 q^{19} - 168 q^{20} + 592 q^{22} - 664 q^{25} - 1008 q^{26} - 528 q^{28} - 3624 q^{32} + 2716 q^{34} + 5184 q^{35} + 6360 q^{38} + 408 q^{40} - 720 q^{41} + 10048 q^{43} + 6720 q^{44} + 2616 q^{46} - 1240 q^{49} - 5394 q^{50} + 2448 q^{52} - 7512 q^{56} - 10740 q^{58} - 13056 q^{59} + 8724 q^{62} - 17632 q^{64} + 1344 q^{65} - 6656 q^{67} + 5616 q^{68} + 19800 q^{70} - 16880 q^{73} - 17400 q^{74} + 14320 q^{76} - 28512 q^{80} - 9740 q^{82} + 24000 q^{83} + 34344 q^{86} - 19616 q^{88} - 15600 q^{89} + 1344 q^{91} + 48096 q^{92} + 12120 q^{94} - 12176 q^{97} - 47778 q^{98}+O(q^{100}) $ 8 * q + 6 * q^2 + 8 * q^4 + 180 * q^8 - 324 * q^10 - 192 * q^11 - 420 * q^14 - 712 * q^16 - 240 * q^17 - 704 * q^19 - 168 * q^20 + 592 * q^22 - 664 * q^25 - 1008 * q^26 - 528 * q^28 - 3624 * q^32 + 2716 * q^34 + 5184 * q^35 + 6360 * q^38 + 408 * q^40 - 720 * q^41 + 10048 * q^43 + 6720 * q^44 + 2616 * q^46 - 1240 * q^49 - 5394 * q^50 + 2448 * q^52 - 7512 * q^56 - 10740 * q^58 - 13056 * q^59 + 8724 * q^62 - 17632 * q^64 + 1344 * q^65 - 6656 * q^67 + 5616 * q^68 + 19800 * q^70 - 16880 * q^73 - 17400 * q^74 + 14320 * q^76 - 28512 * q^80 - 9740 * q^82 + 24000 * q^83 + 34344 * q^86 - 19616 * q^88 - 15600 * q^89 + 1344 * q^91 + 48096 * q^92 + 12120 * q^94 - 12176 * q^97 - 47778 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$1$

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
$3$		0			0
$3$		0			0
$4$	9.45137	−	12.9101i	0.590711	−	0.806884i
$5$		−	38.1617i		−	1.52647i	−0.646122	−	0.763234i	$-0.723610\pi$
$5$		−	38.1617i		−	1.52647i	0.646122	−	0.763234i	$-0.276390\pi$
$6$		0			0
$7$			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
$9$		0			0
$10$	−69.0539	−	136.135i	−0.690539	−	1.36135i
$11$	−100.141			−0.827610			−0.413805	−	0.910366i	$-0.635800\pi$
$11$	−100.141			−0.827610			−0.413805	+	0.910366i	$0.635800\pi$
$12$		0			0
$13$		−	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
$15$		0			0
$16$	−77.3433	−	244.037i	−0.302122	−	0.953269i
$17$	351.156			1.21507			0.607537	−	0.794292i	$-0.292158\pi$
$17$	351.156			1.21507			0.607537	+	0.794292i	$0.292158\pi$
$18$		0			0
$19$	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
$21$		0			0
$22$	−357.233	+	181.205i	−0.738085	+	0.374391i
$23$			254.258i			0.480638i	0.970694	+	0.240319i	$0.0772521\pi$
$23$			254.258i			0.480638i	−0.970694	+	0.240319i	$0.922748\pi$
$24$		0			0
$25$	−831.317			−1.33011
$26$	−310.524	−	612.174i	−0.459355	−	0.905583i
$27$		0			0
$28$	542.925	+	397.469i	0.692506	+	0.506976i
$29$			1388.76i			1.65132i	0.564165	+	0.825662i	$0.309198\pi$
$29$			1388.76i			1.65132i	−0.564165	+	0.825662i	$0.690802\pi$
$30$		0			0
$31$			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
$33$		0			0
$34$	1252.68	−	635.420i	1.08363	−	0.549671i
$35$	1604.86			1.31009
$36$		0			0
$37$			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
$39$		0			0
$40$	−2410.17	−	395.163i	−1.50636	−	0.246977i
$41$	−540.370			−0.321458			−0.160729	−	0.986999i	$-0.551384\pi$
$41$	−540.370			−0.321458			−0.160729	+	0.986999i	$0.551384\pi$
$42$		0			0
$43$	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
$45$		0			0
$46$	460.081	+	907.016i	0.217430	+	0.428646i
$47$			1830.56i			0.828685i	0.910121	+	0.414342i	$0.135988\pi$
$47$			1830.56i			0.828685i	−0.910121	+	0.414342i	$0.864012\pi$
$48$		0			0
$49$	632.448			0.263410
$50$	−2965.56	+	1504.27i	−1.18623	+	0.601710i
$51$		0			0
$52$	−2215.47	−	1621.92i	−0.819330	−	0.599822i
$53$		−	3473.31i		−	1.23649i	−0.785984	−	0.618247i	$-0.787843\pi$
$53$		−	3473.31i		−	1.23649i	0.785984	−	0.618247i	$-0.212157\pi$
$54$		0			0
$55$			3821.54i			1.26332i
$56$	2656.00	+	435.469i	0.846940	+	0.138861i
$57$		0			0
$58$	2512.98	+	4954.15i	0.747021	+	1.47270i
$59$	1577.30			0.453116			0.226558	−	0.973998i	$-0.427253\pi$
$59$	1577.30			0.453116			0.226558	+	0.973998i	$0.427253\pi$
$60$		0			0
$61$		−	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
$63$		0			0
$64$	−3881.55	−	1307.97i	−0.947644	−	0.319329i
$65$	−6548.81			−1.55001
$66$		0			0
$67$	−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
$69$		0			0
$70$	5725.03	−	2904.00i	1.16837	−	0.592654i
$71$			1950.41i			0.386909i	0.981109	+	0.193454i	$0.0619692\pi$
$71$			1950.41i			0.386909i	−0.981109	+	0.193454i	$0.938031\pi$
$72$		0			0
$73$	−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
$75$		0			0
$76$	4671.32	−	6380.82i	0.808747	−	1.10471i
$77$		−	4211.34i		−	0.710295i
$78$		0			0
$79$		−	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
$81$		0			0
$82$	−1927.67	+	977.804i	−0.286685	+	0.145420i
$83$	719.298			0.104413			0.0522063	−	0.998636i	$-0.483375\pi$
$83$	719.298			0.104413			0.0522063	+	0.998636i	$0.483375\pi$
$84$		0			0
$85$		−	13400.7i		−	1.85477i
$86$	7302.53	−	3704.19i	0.987362	−	0.500837i
$87$		0			0
$88$	−1036.95	+	6324.57i	−0.133904	+	0.816705i
$89$	4185.54			0.528410			0.264205	−	0.964467i	$-0.414890\pi$
$89$	4185.54			0.528410			0.264205	+	0.964467i	$0.414890\pi$
$90$		0			0
$91$	7216.78			0.871487
$92$	3282.50	+	2403.08i	0.387819	+	0.283918i
$93$		0			0
$94$	3312.42	+	6530.19i	0.374878	+	0.739043i
$95$		−	18861.4i		−	2.08990i
$96$		0			0
$97$	−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
$99$		0			0
$100$	−7857.08	+	10732.4i	−0.785708	+	1.07324i
$101$			3582.12i			0.351154i	0.984466	+	0.175577i	$0.0561791\pi$
$101$			3582.12i			0.351154i	−0.984466	+	0.175577i	$0.943821\pi$
$102$		0			0
$103$			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
$105$		0			0
$106$	−6284.98	−	12390.4i	−0.559361	−	1.10274i
$107$	−11793.1			−1.03005			−0.515027	−	0.857174i	$-0.672218\pi$
$107$	−11793.1			−1.03005			−0.515027	+	0.857174i	$0.672218\pi$
$108$		0			0
$109$			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
$111$		0			0
$112$	10262.8	−	3252.61i	0.818142	−	0.259296i
$113$	−7408.35			−0.580183			−0.290091	−	0.956999i	$-0.593686\pi$
$113$	−7408.35			−0.580183			−0.290091	+	0.956999i	$0.593686\pi$
$114$		0			0
$115$	9702.91			0.733680
$116$	17929.1	+	13125.7i	1.33243	+	0.975455i
$117$		0			0
$118$	5626.70	−	2854.13i	0.404101	−	0.204979i
$119$			14767.6i			1.04283i
$120$		0			0
$121$	−4612.82			−0.315062
$122$	−1913.57	−	3772.47i	−0.128566	−	0.253458i
$123$		0			0
$124$	7794.74	+	5706.44i	0.506942	+	0.371126i
$125$			7873.41i			0.503898i
$126$		0			0
$127$		−	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
$129$		0			0
$130$	−23361.6	+	11850.1i	−1.38234	+	0.701191i
$131$	−106.777			−0.00622209			−0.00311105	−	0.999995i	$-0.500990\pi$
$131$	−106.777			−0.00622209			−0.00311105	+	0.999995i	$0.500990\pi$
$132$		0			0
$133$			20785.2i			1.17504i
$134$	−1845.38	+	936.066i	−0.102773	+	0.0521311i
$135$		0			0
$136$	3636.21	−	22177.9i	0.196594	−	1.19906i
$137$	29064.5			1.54854			0.774268	−	0.632858i	$-0.218118\pi$
$137$	29064.5			1.54854			0.774268	+	0.632858i	$0.218118\pi$
$138$		0			0
$139$	−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
$141$		0			0
$142$	3529.28	+	6957.70i	0.175029	+	0.345056i
$143$			17184.8i			0.840376i
$144$		0			0
$145$	52997.6			2.52070
$146$	−29631.7	+	15030.6i	−1.39012	+	0.705133i
$147$		0			0
$148$	6955.41	+	5091.98i	0.317541	+	0.232468i
$149$		−	5874.77i		−	0.264617i	−0.991209	−	0.132309i	$-0.957761\pi$
$149$		−	5874.77i		−	0.264617i	0.991209	−	0.132309i	$-0.0422390\pi$
$150$		0			0
$151$		−	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
$153$		0			0
$154$	−7620.44	−	15023.1i	−0.321321	−	0.633460i
$155$	23040.8			0.959036
$156$		0			0
$157$		−	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
$159$		0			0
$160$	−27881.0	+	27380.8i	−1.08910	+	1.06956i
$161$	−10692.6			−0.412507
$162$		0			0
$163$	−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
$165$		0			0
$166$	2565.96	−	1301.58i	0.0931180	−	0.0472338i
$167$		−	2863.09i		−	0.102660i	−0.998682	−	0.0513301i	$-0.983654\pi$
$167$		−	2863.09i		−	0.102660i	0.998682	−	0.0513301i	$-0.0163461\pi$
$168$		0			0
$169$	−887.905			−0.0310880
$170$	−24248.7	−	47804.5i	−0.839055	−	1.65413i
$171$		0			0
$172$	19347.6	−	26428.0i	0.653989	−	0.893319i
$173$			14515.8i			0.485008i	0.970150	+	0.242504i	$0.0779688\pi$
$173$			14515.8i			0.485008i	−0.970150	+	0.242504i	$0.922031\pi$
$174$		0			0
$175$		−	34960.3i		−	1.14156i
$176$	7745.22	+	24438.0i	0.250039	+	0.788935i
$177$		0			0
$178$	14931.1	−	7573.76i	0.471250	−	0.239040i
$179$	8072.26			0.251935			0.125968	−	0.992034i	$-0.459796\pi$
$179$	8072.26			0.251935			0.125968	+	0.992034i	$0.459796\pi$
$180$		0			0
$181$			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
$183$		0			0
$184$	16058.1	+	2632.83i	0.474306	+	0.0777654i
$185$	20559.8			0.600726
$186$		0			0
$187$	−35165.1			−1.00561
$188$	23632.8	+	17301.3i	0.668652	+	0.489513i
$189$		0			0
$190$	−34129.8	−	67284.3i	−0.945423	−	1.86383i
$191$		−	2132.11i		−	0.0584444i	−0.999573	−	0.0292222i	$-0.990697\pi$
$191$		−	2132.11i		−	0.0584444i	0.999573	−	0.0292222i	$-0.00930304\pi$
$192$		0			0
$193$	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
$195$		0			0
$196$	5977.50	−	8164.99i	0.155599	−	0.212541i
$197$			40238.1i			1.03682i	0.855131	+	0.518412i	$0.173477\pi$
$197$			40238.1i			1.03682i	−0.855131	+	0.518412i	$0.826523\pi$
$198$		0			0
$199$			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
$201$		0			0
$202$	6481.88	+	12778.5i	0.158854	+	0.313169i
$203$	−58403.3			−1.41725
$204$		0			0
$205$			20621.5i			0.490695i
$206$	31470.8	+	62042.3i	0.741605	+	1.46202i
$207$		0			0
$208$	−41878.4	+	13272.6i	−0.967973	+	0.306782i
$209$	−49494.4			−1.13309
$210$		0			0
$211$	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
$213$		0			0
$214$	−42069.6	+	21339.7i	−0.918630	+	0.465973i
$215$		−	78119.7i		−	1.68999i
$216$		0			0
$217$	−25391.0			−0.539213
$218$	19116.5	+	37686.8i	0.402250	+	0.793005i
$219$		0			0
$220$	49336.7	+	36118.8i	1.01935	+	0.746257i
$221$		−	60260.8i		−	1.23382i
$222$		0			0
$223$			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
$225$		0			0
$226$	−26427.9	+	13405.5i	−0.517423	+	0.262461i
$227$	10099.9			0.196005			0.0980024	−	0.995186i	$-0.468755\pi$
$227$	10099.9			0.196005			0.0980024	+	0.995186i	$0.468755\pi$
$228$		0			0
$229$		−	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
$231$		0			0
$232$	87709.8	+	14380.6i	1.62957	+	0.267178i
$233$	74833.7			1.37843			0.689216	−	0.724556i	$-0.257955\pi$
$233$	74833.7			1.37843			0.689216	+	0.724556i	$0.257955\pi$
$234$		0			0
$235$	69857.5			1.26496
$236$	14907.6	−	20363.1i	0.267660	−	0.365612i
$237$		0			0
$238$	26722.0	+	52680.5i	0.471754	+	0.930028i
$239$			24812.5i			0.434384i	0.976129	+	0.217192i	$0.0696898\pi$
$239$			24812.5i			0.434384i	−0.976129	+	0.217192i	$0.930310\pi$
$240$		0			0
$241$	−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
$243$		0			0
$244$	−13652.6	−	9994.93i	−0.229317	−	0.167880i
$245$		−	24135.3i		−	0.402087i
$246$		0			0
$247$		−	84816.4i		−	1.39023i
$248$	38132.1	+	6252.00i	0.619993	+	0.101652i
$249$		0			0
$250$	14247.0	+	28086.9i	0.227952	+	0.449390i
$251$	−91146.1			−1.44674			−0.723370	−	0.690461i	$-0.757408\pi$
$251$	−91146.1			−1.44674			−0.723370	+	0.690461i	$0.757408\pi$
$252$		0			0
$253$		−	25461.6i		−	0.397781i
$254$	−802.524	−	1582.12i	−0.0124391	−	0.0245228i
$255$		0			0
$256$	−53572.0	+	37749.2i	−0.817444	+	0.576008i
$257$	24844.7			0.376156			0.188078	−	0.982154i	$-0.439774\pi$
$257$	24844.7			0.376156			0.188078	+	0.982154i	$0.439774\pi$
$258$		0			0
$259$	−22656.9			−0.337755
$260$	−61895.2	+	84546.1i	−0.915610	+	1.25068i
$261$		0			0
$262$	−380.908	+	193.214i	−0.00554903	+	0.00281473i
$263$			65761.8i			0.950741i	0.879786	+	0.475371i	$0.157686\pi$
$263$			65761.8i			0.950741i	−0.879786	+	0.475371i	$0.842314\pi$
$264$		0			0
$265$	−132548.			−1.88747
$266$	37611.0	+	74147.2i	0.531559	+	1.04793i
$267$		0			0
$268$	−4889.24	+	6678.47i	−0.0680725	+	0.0929839i
$269$			3022.19i			0.0417654i	0.999782	+	0.0208827i	$0.00664765\pi$
$269$			3022.19i			0.0417654i	−0.999782	+	0.0208827i	$0.993352\pi$
$270$		0			0
$271$			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
$273$		0			0
$274$	103682.	−	52592.4i	1.38103	−	0.700522i
$275$	83248.7			1.10081
$276$		0			0
$277$		−	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
$279$		0			0
$280$	16618.2	−	101358.i	0.211967	−	1.29283i
$281$	−139506.			−1.76677			−0.883383	−	0.468653i	$-0.844740\pi$
$281$	−139506.			−1.76677			−0.883383	+	0.468653i	$0.844740\pi$
$282$		0			0
$283$	−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
$285$		0			0
$286$	31096.1	+	61303.6i	0.380166	+	0.749470i
$287$		−	22724.8i		−	0.275890i
$288$		0			0
$289$	39789.6			0.476403
$290$	189059.	−	95899.6i	2.24802	−	1.14030i
$291$		0			0
$292$	−78507.5	+	107238.i	−0.920757	+	1.25771i
$293$			22036.7i			0.256691i	0.991730	+	0.128346i	$0.0409667\pi$
$293$			22036.7i			0.256691i	−0.991730	+	0.128346i	$0.959033\pi$
$294$		0			0
$295$		−	60192.3i		−	0.691667i
$296$	34026.1	+	5578.79i	0.388354	+	0.0636732i
$297$		0			0
$298$	−10630.4	−	20957.1i	−0.119707	−	0.235993i
$299$	43632.4			0.488052
$300$		0			0
$301$			86087.8i			0.950186i
$302$	−25027.4	−	49339.7i	−0.274411	−	0.540981i
$303$		0			0
$304$	−38226.8	−	120615.i	−0.413638	−	1.30513i
$305$	−40356.5			−0.433824
$306$		0			0
$307$	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
$309$		0			0
$310$	82193.8	−	41692.6i	0.855294	−	0.433846i
$311$		−	58811.2i		−	0.608050i	−0.952664	−	0.304025i	$-0.901669\pi$
$311$		−	58811.2i		−	0.608050i	0.952664	−	0.304025i	$-0.0983306\pi$
$312$		0			0
$313$	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
$315$		0			0
$316$	−145116.	−	106238.i	−1.45325	−	1.06391i
$317$		−	68445.4i		−	0.681124i	−0.940222	−	0.340562i	$-0.889383\pi$
$317$		−	68445.4i		−	0.681124i	0.940222	−	0.340562i	$-0.110617\pi$
$318$		0			0
$319$		−	139072.i		−	1.36665i
$320$	−49914.4	+	148127.i	−0.487445	+	1.44655i
$321$		0			0
$322$	−38143.8	+	19348.3i	−0.367885	+	0.186609i
$323$	173558.			1.66357
$324$		0			0
$325$			142660.i			1.35062i
$326$	−51127.8	+	25934.4i	−0.481085	+	0.244029i
$327$		0			0
$328$	−5595.51	+	34128.0i	−0.0520106	+	0.317222i
$329$	−76982.8			−0.711217
$330$		0			0
$331$	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
$333$		0			0
$334$	−5180.78	−	10213.5i	−0.0464411	−	0.0915552i
$335$			19741.2i			0.175908i
$336$		0			0
$337$	−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
$339$		0			0
$340$	−173005.	−	126655.i	−1.49658	−	1.09563i
$341$		−	60461.9i		−	0.519963i
$342$		0			0
$343$			127569.i			1.08432i
$344$	21197.3	−	129286.i	0.179128	−	1.09254i
$345$		0			0
$346$	26266.5	+	51782.3i	0.219406	+	0.432543i
$347$	−22112.6			−0.183646			−0.0918228	−	0.995775i	$-0.529269\pi$
$347$	−22112.6			−0.183646			−0.0918228	+	0.995775i	$0.529269\pi$
$348$		0			0
$349$		−	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
$351$		0			0
$352$	71850.4	+	73163.0i	0.579888	+	0.590481i
$353$	15985.3			0.128284			0.0641420	−	0.997941i	$-0.479569\pi$
$353$	15985.3			0.128284			0.0641420	+	0.997941i	$0.479569\pi$
$354$		0			0
$355$	74430.9			0.590604
$356$	39559.0	−	54035.8i	0.312137	−	0.426365i
$357$		0			0
$358$	28796.2	−	14606.8i	0.224683	−	0.113970i
$359$			130882.i			1.01553i	0.861497	+	0.507763i	$0.169527\pi$
$359$			130882.i			1.01553i	−0.861497	+	0.507763i	$0.830473\pi$
$360$		0			0
$361$	113961.			0.874460
$362$	66698.7	+	131491.i	0.508979	+	1.00341i
$363$		0			0
$364$	68208.5	−	93169.6i	0.514796	−	0.703188i
$365$			316989.i			2.37935i
$366$		0			0
$367$			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
$369$		0			0
$370$	73343.3	−	37203.2i	0.535743	−	0.271754i
$371$	146067.			1.06122
$372$		0			0
$373$		−	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
$375$		0			0
$376$	115612.	+	18955.4i	0.817766	+	0.134078i
$377$	238321.			1.67680
$378$		0			0
$379$	−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
$381$		0			0
$382$	−3858.07	−	7605.89i	−0.0264389	−	0.0521223i
$383$			274654.i			1.87236i	0.351525	+	0.936179i	$0.385663\pi$
$383$			274654.i			1.87236i	−0.351525	+	0.936179i	$0.614337\pi$
$384$		0			0
$385$	−160712.			−1.08424
$386$	119105.	−	60415.5i	0.799381	−	0.405484i
$387$		0			0
$388$	−46230.6	+	63148.9i	−0.307090	+	0.419472i
$389$		−	192557.i		−	1.27251i	−0.771480	−	0.636253i	$-0.780483\pi$
$389$		−	192557.i		−	1.27251i	0.771480	−	0.636253i	$-0.219517\pi$
$390$		0			0
$391$			89284.2i			0.584011i
$392$	6548.97	−	39943.3i	0.0426187	−	0.259939i
$393$		0			0
$394$	72811.2	+	143542.i	0.469036	+	0.924668i
$395$	−428956.			−2.74928
$396$		0			0
$397$			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
$399$		0			0
$400$	64296.8	+	202872.i	0.401855	+	1.26795i
$401$	181363.			1.12787			0.563936	−	0.825819i	$-0.309287\pi$
$401$	181363.			1.12787			0.563936	+	0.825819i	$0.309287\pi$
$402$		0			0
$403$	103611.			0.637962
$404$	46245.7	+	33856.0i	0.283341	+	0.207430i
$405$		0			0
$406$	−208343.	+	105681.i	−1.26394	+	0.641129i
$407$		−	53951.4i		−	0.325697i
$408$		0			0
$409$	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
$411$		0			0
$412$	224532.	+	164377.i	1.32277	+	0.968383i
$413$			66331.8i			0.388886i
$414$		0			0
$415$		−	27449.7i		−	0.159383i
$416$	−125376.	+	123127.i	−0.724484	+	0.711486i
$417$		0			0
$418$	−176562.	+	89560.5i	−1.01052	+	0.512583i
$419$	62276.3			0.354727			0.177364	−	0.984145i	$-0.443243\pi$
$419$	62276.3			0.354727			0.177364	+	0.984145i	$0.443243\pi$
$420$		0			0
$421$			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
$423$		0			0
$424$	−219363.	−	35966.0i	−1.22020	−	0.200060i
$425$	−291922.			−1.61618
$426$		0			0
$427$	44472.8			0.243915
$428$	−111461.	+	152250.i	−0.608464	+	0.831134i
$429$		0			0
$430$	−141358.	−	278677.i	−0.764511	−	1.50718i
$431$		−	337494.i		−	1.81682i	−0.418081	−	0.908410i	$-0.637297\pi$
$431$		−	337494.i		−	1.81682i	0.418081	−	0.908410i	$-0.362703\pi$
$432$		0			0
$433$	−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
$435$		0			0
$436$	136389.	+	99848.9i	0.717474	+	0.525255i
$437$			125666.i			0.658047i
$438$		0			0
$439$		−	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
$441$		0			0
$442$	−109042.	−	214969.i	−0.558150	−	1.10035i
$443$	206035.			1.04987			0.524933	−	0.851143i	$-0.324090\pi$
$443$	206035.			1.04987			0.524933	+	0.851143i	$0.324090\pi$
$444$		0			0
$445$		−	159727.i		−	0.806601i
$446$	107913.	+	212743.i	0.542507	+	1.06951i
$447$		0			0
$448$	55005.6	−	163235.i	0.274063	−	0.813314i
$449$	189831.			0.941615			0.470808	−	0.882236i	$-0.343963\pi$
$449$	189831.			0.941615			0.470808	+	0.882236i	$0.343963\pi$
$450$		0			0
$451$	54113.1			0.266042
$452$	−70019.1	+	95642.8i	−0.342720	+	0.468140i
$453$		0			0
$454$	36029.6	−	18275.9i	0.174802	−	0.0886680i
$455$		−	275405.i		−	1.33030i
$456$		0			0
$457$	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
$459$		0			0
$460$	91705.8	−	125266.i	0.433392	−	0.591994i
$461$		−	282353.i		−	1.32859i	−0.747472	−	0.664294i	$-0.768732\pi$
$461$		−	282353.i		−	1.32859i	0.747472	−	0.664294i	$-0.231268\pi$
$462$		0			0
$463$		−	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
$465$		0			0
$466$	266955.	−	135412.i	1.22932	−	0.623570i
$467$	−367707.			−1.68604			−0.843021	−	0.537881i	$-0.819225\pi$
$467$	−367707.			−1.68604			−0.843021	+	0.537881i	$0.819225\pi$
$468$		0			0
$469$		−	21754.8i		−	0.0989030i
$470$	249203.	−	126408.i	1.12813	−	0.572239i
$471$		0			0
$472$	16332.8	−	99616.9i	0.0733124	−	0.447145i
$473$	−204995.			−0.916266
$474$		0			0
$475$	−410877.			−1.82106
$476$	190651.	+	139574.i	0.841446	+	0.616013i
$477$		0			0
$478$	44898.3	+	88513.7i	0.196505	+	0.387395i
$479$		−	286130.i		−	1.24708i	−0.781793	−	0.623538i	$-0.785695\pi$
$479$		−	286130.i		−	1.24708i	0.781793	−	0.623538i	$-0.214305\pi$
$480$		0			0
$481$	92454.1			0.399610
$482$	−54301.9	+	27544.5i	−0.233733	+	0.118561i
$483$		0			0
$484$	−43597.5	+	59552.2i	−0.186110	+	0.254218i
$485$			186665.i			0.793560i
$486$		0			0
$487$		−	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
$489$		0			0
$490$	−43673.0	−	86098.0i	−0.181895	−	0.358592i
$491$	−422941.			−1.75435			−0.877175	−	0.480170i	$-0.840575\pi$
$491$	−422941.			−1.75435			−0.877175	+	0.480170i	$0.840575\pi$
$492$		0			0
$493$			487673.i			2.00648i
$494$	−153476.	−	302566.i	−0.628907	−	1.23984i
$495$		0			0
$496$	147342.	−	46697.4i	0.598912	−	0.189815i
$497$	−82022.7			−0.332064
$498$		0			0
$499$	−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
$501$		0			0
$502$	−325146.	+	164929.i	−1.29024	+	0.654471i
$503$			185687.i			0.733915i	0.930238	+	0.366958i	$0.119601\pi$
$503$			185687.i			0.733915i	−0.930238	+	0.366958i	$0.880399\pi$
$504$		0			0
$505$	136700.			0.536026
$506$	−46072.9	−	90829.3i	−0.179947	−	0.354752i
$507$		0			0
$508$	−5725.70	−	4191.72i	−0.0221871	−	0.0162429i
$509$		−	401954.i		−	1.55146i	−0.631064	−	0.775731i	$-0.717382\pi$
$509$		−	401954.i		−	1.55146i	0.631064	−	0.775731i	$-0.282618\pi$
$510$		0			0
$511$		−	349321.i		−	1.33778i
$512$	−122800.	+	231602.i	−0.468446	+	0.883492i
$513$		0			0
$514$	88628.8	−	44956.7i	0.335466	−	0.170164i
$515$	663705.			2.50242
$516$		0			0
$517$		−	183314.i		−	0.685828i
$518$	−80824.2	+	40997.8i	−0.301219	+	0.152792i
$519$		0			0
$520$	−67812.6	+	413602.i	−0.250786	+	1.52959i
$521$	−63089.4			−0.232424			−0.116212	−	0.993224i	$-0.537075\pi$
$521$	−63089.4			−0.232424			−0.116212	+	0.993224i	$0.537075\pi$
$522$		0			0
$523$	−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
$525$		0			0
$526$	118997.	+	234593.i	0.430093	+	0.847897i
$527$			212017.i			0.763395i
$528$		0			0
$529$	215194.			0.768987
$530$	−472838.	+	239846.i	−1.68330	+	0.853848i
$531$		0			0
$532$	268340.	+	196449.i	0.948117	+	0.694106i
$533$			92731.2i			0.326416i
$534$		0			0
$535$			450045.i			1.57235i
$536$	−5356.67	+	32671.3i	−0.0186451	+	0.113720i
$537$		0			0
$538$	5468.67	+	10781.1i	0.0188937	+	0.0372475i
$539$	−63333.8			−0.218001
$540$		0			0
$541$		−	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
$543$		0			0
$544$	−251952.	−	256555.i	−0.851374	−	0.866928i
$545$	403159.			1.35732
$546$		0			0
$547$	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
$549$		0			0
$550$	296974.	−	150639.i	0.981732	−	0.497981i
$551$			686394.i			2.26084i
$552$		0			0
$553$	472709.			1.54577
$554$	−218787.	−	431322.i	−0.712856	−	1.40534i
$555$		0			0
$556$	−306580.	+	418774.i	−0.991732	+	1.35466i
$557$			181185.i			0.583999i	0.956419	+	0.291999i	$0.0943205\pi$
$557$			181185.i			0.583999i	−0.956419	+	0.291999i	$0.905680\pi$
$558$		0			0
$559$		−	351291.i		−	1.12420i
$560$	−124125.	−	391645.i	−0.395807	−	1.24887i
$561$		0			0
$562$	−497659.	+	252436.i	−1.57565	+	0.799243i
$563$	252429.			0.796382			0.398191	−	0.917302i	$-0.369638\pi$
$563$	252429.			0.796382			0.398191	+	0.917302i	$0.369638\pi$
$564$		0			0
$565$			282715.i			0.885631i
$566$	−188882.	+	95810.1i	−0.589602	+	0.299074i
$567$		0			0
$568$	123181.	+	20196.4i	0.381811	+	0.0626004i
$569$	−244576.			−0.755423			−0.377711	−	0.925923i	$-0.623289\pi$
$569$	−244576.			−0.755423			−0.377711	+	0.925923i	$0.623289\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$	−41120.7	−	81066.4i	−0.124806	−	0.246047i
$575$		−	211369.i		−	0.639301i
$576$		0			0
$577$	−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
$579$		0			0
$580$	500900.	−	684207.i	1.48900	−	2.03391i
$581$			30249.5i			0.0896119i
$582$		0			0
$583$			347820.i			1.02333i
$584$	−86013.1	+	524609.i	−0.252196	+	1.53819i
$585$		0			0
$586$	39875.5	+	78611.6i	0.116121	+	0.228924i
$587$	−674424.			−1.95730			−0.978649	−	0.205537i	$-0.934106\pi$
$587$	−674424.			−1.95730			−0.978649	+	0.205537i	$0.934106\pi$
$588$		0			0
$589$			298412.i			0.860172i
$590$	−108918.	−	214724.i	−0.312894	−	0.616847i
$591$		0			0
$592$	131476.	−	41669.1i	0.375149	−	0.118897i
$593$	337443.			0.959601			0.479800	−	0.877378i	$-0.340709\pi$
$593$	337443.			0.959601			0.479800	+	0.877378i	$0.340709\pi$
$594$		0			0
$595$	563556.			1.59185
$596$	−75844.1	−	55524.6i	−0.213515	−	0.156312i
$597$		0			0
$598$	155650.	−	78953.1i	0.435258	−	0.220784i
$599$		−	308879.i		−	0.860864i	−0.902623	−	0.430432i	$-0.858361\pi$
$599$		−	308879.i		−	0.860864i	0.902623	−	0.430432i	$-0.141639\pi$
$600$		0			0
$601$	−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
$603$		0			0
$604$	−178561.	−	130722.i	−0.489455	−	0.358324i
$605$			176033.i			0.480932i
$606$		0			0
$607$			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
$609$		0			0
$610$	−143964.	+	73025.3i	−0.386896	+	0.196252i
$611$	314137.			0.841467
$612$		0			0
$613$			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
$615$		0			0
$616$	−265974.	−	43608.2i	−0.700936	−	0.114923i
$617$	239921.			0.630229			0.315114	−	0.949054i	$-0.397957\pi$
$617$	239921.			0.630229			0.315114	+	0.949054i	$0.397957\pi$
$618$		0			0
$619$	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
$621$		0			0
$622$	−106419.	−	209798.i	−0.275068	−	0.542275i
$623$			176019.i			0.453507i
$624$		0			0
$625$	−219110.			−0.560922
$626$	327016.	−	165878.i	0.834489	−	0.423292i
$627$		0			0
$628$	−293308.	−	214727.i	−0.743711	−	0.544463i
$629$			189187.i			0.478179i
$630$		0			0
$631$		−	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
$633$		0			0
$634$	−123853.	−	244166.i	−0.308125	−	0.607444i
$635$	−16924.9			−0.0419738
$636$		0			0
$637$		−	108532.i		−	0.267473i
$638$	−251652.	−	496112.i	−0.618242	−	1.21882i
$639$		0			0
$640$	89976.2	+	618734.i	0.219668	+	1.51058i
$641$	−684663.			−1.66633			−0.833165	−	0.553025i	$-0.813473\pi$
$641$	−684663.			−1.66633			−0.833165	+	0.553025i	$0.813473\pi$
$642$		0			0
$643$	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
$645$		0			0
$646$	619136.	−	314055.i	1.48361	−	0.752559i
$647$		−	743379.i		−	1.77583i	−0.460007	−	0.887915i	$-0.652153\pi$
$647$		−	743379.i		−	1.77583i	0.460007	−	0.887915i	$-0.347847\pi$
$648$		0			0
$649$	−157952.			−0.375003
$650$	258144.	+	508911.i	0.610991	+	1.20452i
$651$		0			0
$652$	−135460.	+	185032.i	−0.318652	+	0.435263i
$653$			318695.i			0.747393i	0.927551	+	0.373697i	$0.121910\pi$
$653$			318695.i			0.747393i	−0.927551	+	0.373697i	$0.878090\pi$
$654$		0			0
$655$			4074.81i			0.00949783i
$656$	41794.0	+	131870.i	0.0971195	+	0.306436i
$657$		0			0
$658$	−274621.	+	139301.i	−0.634282	+	0.321738i
$659$	661853.			1.52402			0.762010	−	0.647566i	$-0.224213\pi$
$659$	661853.			1.52402			0.762010	+	0.647566i	$0.224213\pi$
$660$		0			0
$661$		−	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
$663$		0			0
$664$	7448.30	−	45428.6i	0.0168936	−	0.103037i
$665$	793199.			1.79366
$666$		0			0
$667$	−353104.			−0.793690
$668$	−36962.9	−	27060.1i	−0.0828349	−	0.0606425i
$669$		0			0
$670$	35721.9	+	70423.1i	0.0795765	+	0.156879i
$671$			105900.i			0.235207i
$672$		0			0
$673$	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
$675$		0			0
$676$	−8391.92	+	11463.0i	−0.0183640	+	0.0250844i
$677$		−	55653.5i		−	0.121427i	−0.998155	−	0.0607135i	$-0.980662\pi$
$677$		−	55653.5i		−	0.121427i	0.998155	−	0.0607135i	$-0.0193376\pi$
$678$		0			0
$679$		−	205705.i		−	0.446174i
$680$	−846346.	−	138764.i	−1.83033	−	0.300095i
$681$		0			0
$682$	−109406.	−	215686.i	−0.235219	−	0.463717i
$683$	−323036.			−0.692484			−0.346242	−	0.938145i	$-0.612542\pi$
$683$	−323036.			−0.692484			−0.346242	+	0.938145i	$0.612542\pi$
$684$		0			0
$685$		−	1.10915e6i		−	2.36379i
$686$	230837.	+	455078.i	0.490521	+	0.967025i
$687$		0			0
$688$	−158327.	−	499561.i	−0.334486	−	1.05539i
$689$	−596044.			−1.25557
$690$		0			0
$691$	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
$693$		0			0
$694$	−78882.4	+	40012.9i	−0.163780	+	0.0830770i
$695$			1.23788e6i			2.56276i
$696$		0			0
$697$	−189754.			−0.390595
$698$	−337308.	−	664977.i	−0.692333	−	1.36488i
$699$		0			0
$700$	−451343.	−	330423.i	−0.921108	−	0.674333i
$701$			53163.0i			0.108187i	0.998536	+	0.0540933i	$0.0172269\pi$
$701$			53163.0i			0.108187i	−0.998536	+	0.0540933i	$0.982773\pi$
$702$		0			0
$703$			266279.i			0.538799i
$704$	388701.	+	130981.i	0.784279	+	0.264280i
$705$		0			0
$706$	57024.6	−	28925.6i	0.114407	−	0.0580327i
$707$	−150643.			−0.301377
$708$		0			0
$709$		−	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
$711$		0			0
$712$	43341.0	−	264345.i	0.0854947	−	0.521448i
$713$	−153513.			−0.301971
$714$		0			0
$715$	655803.			1.28281
$716$	76293.9	−	104214.i	0.148821	−	0.203282i
$717$		0			0
$718$	236832.	+	466896.i	0.459400	+	0.905673i
$719$			367010.i			0.709937i	0.934878	+	0.354968i	$0.115508\pi$
$719$			367010.i			0.709937i	−0.934878	+	0.354968i	$0.884492\pi$
$720$		0			0
$721$	−731402.			−1.40697
$722$	406532.	−	206212.i	0.779867	−	0.395585i
$723$		0			0
$724$	475870.	+	348379.i	0.907843	+	0.664622i
$725$		−	1.15450e6i		−	2.19644i
$726$		0			0
$727$		−	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
$729$		0			0
$730$	573594.	+	1.13080e6i	1.07636	+	2.12197i
$731$	718841.			1.34524
$732$		0			0
$733$			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
$735$		0			0
$736$	185761.	−	182428.i	0.342925	−	0.336773i
$737$	51803.3			0.0953723
$738$		0			0
$739$	−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
$741$		0			0
$742$	521067.	−	264310.i	0.946424	−	0.480071i
$743$		−	917401.i		−	1.66181i	−0.556414	−	0.830905i	$-0.687823\pi$
$743$		−	917401.i		−	1.66181i	0.556414	−	0.830905i	$-0.312177\pi$
$744$		0			0
$745$	−224191.			−0.403930
$746$	−79586.8	−	156899.i	−0.143009	−	0.281931i
$747$		0			0
$748$	−332358.	+	453986.i	−0.594022	+	0.811407i
$749$		−	495948.i		−	0.884042i
$750$		0			0
$751$			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
$753$		0			0
$754$	850166.	−	431244.i	1.49541	−	0.758544i
$755$	−527817.			−0.925954
$756$		0			0
$757$		−	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
$759$		0			0
$760$	−1.19122e6	−	195309.i	−2.06237	−	0.338138i
$761$	−206970.			−0.357387			−0.178693	−	0.983905i	$-0.557187\pi$
$761$	−206970.			−0.357387			−0.178693	+	0.983905i	$0.557187\pi$
$762$		0			0
$763$	−444281.			−0.763147
$764$	−27525.8	−	20151.4i	−0.0471578	−	0.0345237i
$765$		0			0
$766$	496989.	+	979776.i	0.847011	+	1.66982i
$767$		−	270675.i		−	0.460105i
$768$		0			0
$769$	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
$771$		0			0
$772$	315560.	−	431041.i	0.529478	−	0.723243i
$773$			184225.i			0.308312i	0.988047	+	0.154156i	$0.0492658\pi$
$773$			184225.i			0.308312i	−0.988047	+	0.154156i	$0.950734\pi$
$774$		0			0
$775$		−	501923.i		−	0.835668i
$776$	−50650.4	+	308926.i	−0.0841124	+	0.513017i
$777$		0			0
$778$	−348433.	−	686910.i	−0.575653	−	1.13486i
$779$	−267077.			−0.440111
$780$		0			0
$781$		−	195315.i		−	0.320210i
$782$	161560.	+	318504.i	0.264193	+	0.520837i
$783$		0			0
$784$	−48915.6	−	154341.i	−0.0795820	−	0.251101i
$785$	−867003.			−1.40696
$786$		0			0
$787$	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
$789$		0			0
$790$	−1.53022e6	+	776200.i	−2.45188	+	1.24371i
$791$		−	311552.i		−	0.497941i
$792$		0			0
$793$	−181476.			−0.288585
$794$	276471.	+	545041.i	0.438539	+	0.864546i
$795$		0			0
$796$	29494.0	+	21592.2i	0.0465487	+	0.0340778i
$797$		−	239720.i		−	0.377388i	−0.982036	−	0.188694i	$-0.939575\pi$
$797$		−	239720.i		−	0.377388i	0.982036	−	0.188694i	$-0.0604255\pi$
$798$		0			0
$799$			642814.i			1.00691i
$800$	596465.	+	607361.i	0.931976	+	0.949002i
$801$		0			0
$802$	646977.	−	328177.i	1.00587	−	0.510223i
$803$	831816.			1.29002
$804$		0			0
$805$			408048.i			0.629679i
$806$	369612.	−	187485.i	0.568952	−	0.288599i
$807$		0			0
$808$	226235.	+	37092.7i	0.346527	+	0.0568154i
$809$	−598514.			−0.914486			−0.457243	−	0.889342i	$-0.651163\pi$
$809$	−598514.			−0.914486			−0.457243	+	0.889342i	$0.651163\pi$
$810$		0			0
$811$	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
$813$		0			0
$814$	−97625.5	−	192461.i	−0.147338	−	0.290466i
$815$			546946.i			0.823435i
$816$		0			0
$817$	1.01176e6			1.51577
$818$	410689.	−	208321.i	0.613771	−	0.311334i
$819$		0			0
$820$	266226.	+	194901.i	0.395934	+	0.289859i
$821$			18495.4i			0.0274396i	0.999906	+	0.0137198i	$0.00436728\pi$
$821$			18495.4i			0.0274396i	−0.999906	+	0.0137198i	$0.995633\pi$
$822$		0			0
$823$		−	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
$825$		0			0
$826$	120028.	+	236626.i	0.175923	+	0.346819i
$827$	−239745.			−0.350540			−0.175270	−	0.984520i	$-0.556080\pi$
$827$	−239745.			−0.350540			−0.175270	+	0.984520i	$0.556080\pi$
$828$		0			0
$829$			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
$831$		0			0
$832$	−224457.	+	666100.i	−0.324254	+	0.962261i
$833$	222088.			0.320063
$834$		0			0
$835$	−109260.			−0.156708
$836$	−467790.	+	638980.i	−0.669327	+	0.914270i
$837$		0			0
$838$	222159.	−	112689.i	0.316355	−	0.160470i
$839$		−	376178.i		−	0.534403i	−0.963641	−	0.267202i	$-0.913901\pi$
$839$		−	376178.i		−	0.534403i	0.963641	−	0.267202i	$-0.0860990\pi$
$840$		0			0
$841$	−1.22138e6			−1.72687
$842$	51435.9	+	101402.i	0.0725507	+	0.143028i
$843$		0			0
$844$	125027.	−	170782.i	0.175517	−	0.239749i
$845$			33884.0i			0.0474549i
$846$		0			0
$847$		−	193988.i		−	0.270401i
$848$	−847617.	+	268637.i	−1.17871	+	0.373572i
$849$		0			0
$850$	−1.04138e6	+	528235.i	−1.44135	+	0.731121i
$851$	−136983.			−0.189150
$852$		0			0
$853$		−	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
$855$		0			0
$856$	−122117.	+	744813.i	−0.166659	+	1.01648i
$857$	767295.			1.04472			0.522361	−	0.852724i	$-0.325051\pi$
$857$	767295.			1.04472			0.522361	+	0.852724i	$0.325051\pi$
$858$		0			0
$859$	−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
$861$		0			0
$862$	−610698.	−	1.20395e6i	−0.821887	−	1.62029i
$863$			605487.i			0.812987i	0.913654	+	0.406493i	$0.133249\pi$
$863$			605487.i			0.812987i	−0.913654	+	0.406493i	$0.866751\pi$
$864$		0			0
$865$	553948.			0.740350
$866$	−97760.0	+	49588.5i	−0.130354	+	0.0661219i
$867$		0			0
$868$	−239980.	+	327801.i	−0.318519	+	0.435082i
$869$			1.12563e6i			1.49058i
$870$		0			0
$871$			88773.0i			0.117016i
$872$	667219.	+	109395.i	0.877476	+	0.143868i
$873$		0			0
$874$	227394.	+	448291.i	0.297685	+	0.586864i
$875$	−331110.			−0.432470
$876$		0			0
$877$			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
$879$		0			0
$880$	932598.	−	295571.i	1.20428	−	0.381677i
$881$	−218679.			−0.281745			−0.140872	−	0.990028i	$-0.544991\pi$
$881$	−218679.			−0.281745			−0.140872	+	0.990028i	$0.544991\pi$
$882$		0			0
$883$	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
$885$		0			0
$886$	734991.	−	372822.i	0.936299	−	0.474935i
$887$		−	932038.i		−	1.18464i	−0.805703	−	0.592320i	$-0.798212\pi$
$887$		−	932038.i		−	1.18464i	0.805703	−	0.592320i	$-0.201788\pi$
$888$		0			0
$889$	18651.2			0.0235995
$890$	−289028.	−	569796.i	−0.364888	−	0.719349i
$891$		0			0
$892$	769920.	+	563650.i	0.967645	+	0.708402i
$893$			904754.i			1.13456i
$894$		0			0
$895$		−	308051.i		−	0.384571i
$896$	−99153.6	−	681844.i	−0.123507	−	0.849315i
$897$		0			0
$898$	677184.	−	343500.i	0.839758	−	0.425965i
$899$	−838492.			−1.03748
$900$		0			0
$901$		−	1.21968e6i		−	1.50243i
$902$	193038.	−	97918.1i	0.237263	−	0.120351i
$903$		0			0
$904$	−76713.1	+	467887.i	−0.0938713	+	0.572538i
$905$	1.40665e6			1.71746
$906$		0			0
$907$	−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
$909$		0			0
$910$	−498347.	−	982454.i	−0.601796	−	1.18639i
$911$		−	1.42062e6i		−	1.71175i	−0.517184	−	0.855874i	$-0.673020\pi$
$911$		−	1.42062e6i		−	1.71175i	0.517184	−	0.855874i	$-0.326980\pi$
$912$		0			0
$913$	−72031.1			−0.0864129
$914$	320129.	−	162385.i	0.383207	−	0.194381i
$915$		0			0
$916$	−434397.	−	318017.i	−0.517721	−	0.379018i
$917$		−	4490.43i		−	0.00534010i
$918$		0			0
$919$			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
$921$		0			0
$922$	−510919.	−	1.00724e6i	−0.601022	−	1.18487i
$923$	334703.			0.392877
$924$		0			0
$925$		−	447877.i		−	0.523450i
$926$	−500739.	−	987169.i	−0.583968	−	1.15125i
$927$		0			0
$928$	1.01463e6	−	996430.i	1.17818	−	1.15705i
$929$	1.13677e6			1.31717			0.658585	−	0.752506i	$-0.271155\pi$
$929$	1.13677e6			1.31717			0.658585	+	0.752506i	$0.271155\pi$
$930$		0			0
$931$	312586.			0.360637
$932$	707280.	−	966113.i	0.814254	−	1.11223i
$933$		0			0
$934$	−1.31172e6	+	665369.i	−1.50366	+	0.762726i
$935$			1.34196e6i			1.53503i
$936$		0			0
$937$	−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
$939$		0			0
$940$	660249.	−	901870.i	0.747226	−	1.02068i
$941$		−	184285.i		−	0.208118i	−0.994571	−	0.104059i	$-0.966817\pi$
$941$		−	184285.i		−	0.208118i	0.994571	−	0.104059i	$-0.0331831\pi$
$942$		0			0
$943$		−	137393.i		−	0.154505i
$944$	−121993.	−	384918.i	−0.136896	−	0.431941i
$945$		0			0
$946$	−731281.	+	370940.i	−0.817150	+	0.414497i
$947$	−477705.			−0.532672			−0.266336	−	0.963880i	$-0.585813\pi$
$947$	−477705.			−0.532672			−0.266336	+	0.963880i	$0.585813\pi$
$948$		0			0
$949$			1.42545e6i			1.58277i
$950$	−1.46573e6	+	743485.i	−1.62407	+	0.823806i
$951$		0			0
$952$	932672.	+	152918.i	1.02909	+	0.168727i
$953$	1.40115e6			1.54276			0.771380	−	0.636375i	$-0.219567\pi$
$953$	1.40115e6			1.54276			0.771380	+	0.636375i	$0.219567\pi$
$954$		0			0
$955$	−81365.0			−0.0892135
$956$	320332.	+	234512.i	0.350497	+	0.256595i
$957$		0			0
$958$	−517755.	−	1.02071e6i	−0.564148	−	1.11218i
$959$			1.22228e6i			1.32903i
$960$		0			0
$961$	558984.			0.605275
$962$	329812.	−	167296.i	0.356383	−	0.180774i
$963$		0			0
$964$	−143870.	+	196519.i	−0.154816	+	0.211471i
$965$		−	1.27414e6i		−	1.36824i
$966$		0			0
$967$		−	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
$969$		0			0
$970$	337772.	+	665892.i	0.358988	+	0.707718i
$971$	−29888.2			−0.0317002			−0.0158501	−	0.999874i	$-0.505045\pi$
$971$	−29888.2			−0.0317002			−0.0158501	+	0.999874i	$0.505045\pi$
$972$		0			0
$973$		−	1.36414e6i		−	1.44090i
$974$	−110941.	−	218712.i	−0.116943	−	0.230545i
$975$		0			0
$976$	−258072.	+	81791.4i	−0.270920	+	0.0858634i
$977$	−1.28420e6			−1.34537			−0.672687	−	0.739927i	$-0.734860\pi$
$977$	−1.28420e6			−1.34537			−0.672687	+	0.739927i	$0.734860\pi$
$978$		0			0
$979$	−419143.			−0.437317
$980$	−311590.	−	228112.i	−0.324438	−	0.237517i
$981$		0			0
$982$	−1.50876e6	+	765314.i	−1.56458	+	0.793627i
$983$			1.30863e6i			1.35428i	0.735852	+	0.677142i	$0.236782\pi$
$983$			1.30863e6i			1.35428i	−0.735852	+	0.677142i	$0.763218\pi$
$984$		0			0
$985$	1.53556e6			1.58268
$986$	882448.	+	1.73968e6i	0.907685	+	1.78943i
$987$		0			0
$988$	−1.09499e6	−	801631.i	−1.12175	−	0.821222i
$989$			520483.i			0.532126i
$990$		0			0
$991$		−	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
$993$		0			0
$994$	−292600.	+	148421.i	−0.296143	+	0.150218i
$995$	87182.7			0.0880611
$996$		0			0
$997$			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
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.5.b.a.19.1	✓	8	24.11	even	2
24.5.b.a.19.2	yes	8	3.2	odd	2
72.5.b.d.19.7		8	1.1	even	1	trivial
72.5.b.d.19.8		8	8.3	odd	2	inner
96.5.b.a.79.1		8	24.5	odd	2
96.5.b.a.79.4		8	12.11	even	2
288.5.b.d.271.1		8	4.3	odd	2
288.5.b.d.271.8		8	8.5	even	2
768.5.g.k.511.1		16	48.5	odd	4
768.5.g.k.511.8		16	48.35	even	4
768.5.g.k.511.9		16	48.11	even	4
768.5.g.k.511.16		16	48.29	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	72.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(3.56731 - 1.80951i) q^{2} +(9.45137 - 12.9101i) q^{4} -38.1617i q^{5} +42.0542i q^{7} +(10.3550 - 63.1567i) q^{8} +O(q^{10})\)	\(q+(3.56731 - 1.80951i) q^{2} +(9.45137 - 12.9101i) q^{4} -38.1617i q^{5} +42.0542i q^{7} +(10.3550 - 63.1567i) q^{8} +(-69.0539 - 136.135i) q^{10} -100.141 q^{11} -171.607i q^{13} +(76.0973 + 150.020i) q^{14} +(-77.3433 - 244.037i) q^{16} +351.156 q^{17} +494.248 q^{19} +(-492.673 - 360.680i) q^{20} +(-357.233 + 181.205i) q^{22} +254.258i q^{23} -831.317 q^{25} +(-310.524 - 612.174i) q^{26} +(542.925 + 397.469i) q^{28} +1388.76i q^{29} +603.769i q^{31} +(-717.494 - 730.602i) q^{32} +(1252.68 - 635.420i) q^{34} +1604.86 q^{35} +538.756i q^{37} +(1763.14 - 894.346i) q^{38} +(-2410.17 - 395.163i) q^{40} -540.370 q^{41} +2047.07 q^{43} +(-946.467 + 1292.83i) q^{44} +(460.081 + 907.016i) q^{46} +1830.56i q^{47} +632.448 q^{49} +(-2965.56 + 1504.27i) q^{50} +(-2215.47 - 1621.92i) q^{52} -3473.31i q^{53} +3821.54i q^{55} +(2656.00 + 435.469i) q^{56} +(2512.98 + 4954.15i) q^{58} +1577.30 q^{59} -1057.51i q^{61} +(1092.52 + 2153.83i) q^{62} +(-3881.55 - 1307.97i) q^{64} -6548.81 q^{65} -517.305 q^{67} +(3318.91 - 4533.47i) q^{68} +(5725.03 - 2904.00i) q^{70} +1950.41i q^{71} -8306.47 q^{73} +(974.882 + 1921.91i) q^{74} +(4671.32 - 6380.82i) q^{76} -4211.34i q^{77} -11240.5i q^{79} +(-9312.87 + 2951.55i) q^{80} +(-1927.67 + 977.804i) q^{82} +719.298 q^{83} -13400.7i q^{85} +(7302.53 - 3704.19i) q^{86} +(-1036.95 + 6324.57i) q^{88} +4185.54 q^{89} +7216.78 q^{91} +(3282.50 + 2403.08i) q^{92} +(3312.42 + 6530.19i) q^{94} -18861.4i q^{95} -4891.42 q^{97} +(2256.14 - 1144.42i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{2} + 8 q^{4} + 180 q^{8}+O(q^{10}) \) 8 * q + 6 * q^2 + 8 * q^4 + 180 * q^8	\( 8 q + 6 q^{2} + 8 q^{4} + 180 q^{8} - 324 q^{10} - 192 q^{11} - 420 q^{14} - 712 q^{16} - 240 q^{17} - 704 q^{19} - 168 q^{20} + 592 q^{22} - 664 q^{25} - 1008 q^{26} - 528 q^{28} - 3624 q^{32} + 2716 q^{34} + 5184 q^{35} + 6360 q^{38} + 408 q^{40} - 720 q^{41} + 10048 q^{43} + 6720 q^{44} + 2616 q^{46} - 1240 q^{49} - 5394 q^{50} + 2448 q^{52} - 7512 q^{56} - 10740 q^{58} - 13056 q^{59} + 8724 q^{62} - 17632 q^{64} + 1344 q^{65} - 6656 q^{67} + 5616 q^{68} + 19800 q^{70} - 16880 q^{73} - 17400 q^{74} + 14320 q^{76} - 28512 q^{80} - 9740 q^{82} + 24000 q^{83} + 34344 q^{86} - 19616 q^{88} - 15600 q^{89} + 1344 q^{91} + 48096 q^{92} + 12120 q^{94} - 12176 q^{97} - 47778 q^{98}+O(q^{100}) \) 8 * q + 6 * q^2 + 8 * q^4 + 180 * q^8 - 324 * q^10 - 192 * q^11 - 420 * q^14 - 712 * q^16 - 240 * q^17 - 704 * q^19 - 168 * q^20 + 592 * q^22 - 664 * q^25 - 1008 * q^26 - 528 * q^28 - 3624 * q^32 + 2716 * q^34 + 5184 * q^35 + 6360 * q^38 + 408 * q^40 - 720 * q^41 + 10048 * q^43 + 6720 * q^44 + 2616 * q^46 - 1240 * q^49 - 5394 * q^50 + 2448 * q^52 - 7512 * q^56 - 10740 * q^58 - 13056 * q^59 + 8724 * q^62 - 17632 * q^64 + 1344 * q^65 - 6656 * q^67 + 5616 * q^68 + 19800 * q^70 - 16880 * q^73 - 17400 * q^74 + 14320 * q^76 - 28512 * q^80 - 9740 * q^82 + 24000 * q^83 + 34344 * q^86 - 19616 * q^88 - 15600 * q^89 + 1344 * q^91 + 48096 * q^92 + 12120 * q^94 - 12176 * q^97 - 47778 * q^98

Introduction

L-functions

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