LMFDB - Embedded newform 810.4.e.bh.541.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [810,4,Mod(271,810)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("810.271"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(810, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	810.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,8,0,-16,-20,0,-2,-64,0,-80,-36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$47.7915471046$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
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} + 254x^{6} + 23581x^{4} + 947376x^{2} + 13883076 $ x^8 + 254x^6 + 23581x^4 + 947376*x^2 + 13883076
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.1
Root			$7.40373i$ of defining polynomial
Character	$\chi$	$=$	810.541
Dual form			810.4.e.bh.271.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-15.8018 + 27.3694i) q^{7} -8.00000 q^{8} -10.0000 q^{10} +(-26.3335 + 45.6110i) q^{11} +(-33.5544 - 58.1179i) q^{13} +(31.6035 + 54.7389i) q^{14} +(-8.00000 + 13.8564i) q^{16} -19.4751 q^{17} +103.354 q^{19} +(-10.0000 + 17.3205i) q^{20} +(52.6671 + 91.2221i) q^{22} +(-77.2047 - 133.722i) q^{23} +(-12.5000 + 21.6506i) q^{25} -134.217 q^{26} +126.414 q^{28} +(41.9220 - 72.6110i) q^{29} +(57.8816 + 100.254i) q^{31} +(16.0000 + 27.7128i) q^{32} +(-19.4751 + 33.7319i) q^{34} +158.018 q^{35} +417.744 q^{37} +(103.354 - 179.014i) q^{38} +(20.0000 + 34.6410i) q^{40} +(74.2798 + 128.656i) q^{41} +(226.330 - 392.015i) q^{43} +210.668 q^{44} -308.819 q^{46} +(256.506 - 444.282i) q^{47} +(-327.891 - 567.924i) q^{49} +(25.0000 + 43.3013i) q^{50} +(-134.217 + 232.471i) q^{52} +139.549 q^{53} +263.335 q^{55} +(126.414 - 218.956i) q^{56} +(-83.8440 - 145.222i) q^{58} +(277.631 + 480.872i) q^{59} +(12.8106 - 22.1885i) q^{61} +231.526 q^{62} +64.0000 q^{64} +(-167.772 + 290.589i) q^{65} +(477.181 + 826.501i) q^{67} +(38.9502 + 67.4638i) q^{68} +(158.018 - 273.694i) q^{70} -49.5295 q^{71} -399.667 q^{73} +(417.744 - 723.553i) q^{74} +(-206.708 - 358.028i) q^{76} +(-832.232 - 1441.47i) q^{77} +(-375.436 + 650.275i) q^{79} +80.0000 q^{80} +297.119 q^{82} +(587.011 - 1016.73i) q^{83} +(48.6878 + 84.3297i) q^{85} +(-452.659 - 784.029i) q^{86} +(210.668 - 364.888i) q^{88} -1011.21 q^{89} +2120.87 q^{91} +(-308.819 + 534.890i) q^{92} +(-513.013 - 888.565i) q^{94} +(-258.385 - 447.535i) q^{95} +(-422.506 + 731.802i) q^{97} -1311.56 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 16 q^{4} - 20 q^{5} - 2 q^{7} - 64 q^{8} - 80 q^{10} - 36 q^{11} - 32 q^{13} + 4 q^{14} - 64 q^{16} - 180 q^{17} + 328 q^{19} - 80 q^{20} + 72 q^{22} + 42 q^{23} - 100 q^{25} - 128 q^{26}+ \cdots - 5352 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 - 16 * q^4 - 20 * q^5 - 2 * q^7 - 64 * q^8 - 80 * q^10 - 36 * q^11 - 32 * q^13 + 4 * q^14 - 64 * q^16 - 180 * q^17 + 328 * q^19 - 80 * q^20 + 72 * q^22 + 42 * q^23 - 100 * q^25 - 128 * q^26 + 16 * q^28 + 36 * q^29 - 446 * q^31 + 128 * q^32 - 180 * q^34 + 20 * q^35 + 1372 * q^37 + 328 * q^38 + 160 * q^40 + 108 * q^41 - 470 * q^43 + 288 * q^44 + 168 * q^46 + 804 * q^47 - 1338 * q^49 + 200 * q^50 - 128 * q^52 - 336 * q^53 + 360 * q^55 + 16 * q^56 - 72 * q^58 + 768 * q^59 - 596 * q^61 - 1784 * q^62 + 512 * q^64 - 160 * q^65 + 424 * q^67 + 360 * q^68 + 20 * q^70 - 696 * q^71 - 188 * q^73 + 1372 * q^74 - 656 * q^76 + 630 * q^77 - 1088 * q^79 + 640 * q^80 + 432 * q^82 + 522 * q^83 + 450 * q^85 + 940 * q^86 + 288 * q^88 - 2256 * q^89 + 5684 * q^91 + 168 * q^92 - 1608 * q^94 - 820 * q^95 - 2486 * q^97 - 5352 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$		0			0
$7$	−15.8018	+	27.3694i	−0.853214	+	1.47781i	0.0250771	+	0.999686i	$0.492017\pi$
$7$	−15.8018	+	27.3694i	−0.853214	+	1.47781i	−0.878292	+	0.478125i	$0.841316\pi$
$8$	−8.00000			−0.353553
$9$		0			0
$10$	−10.0000			−0.316228
$11$	−26.3335	+	45.6110i	−0.721806	+	1.25020i	0.238470	+	0.971150i	$0.423354\pi$
$11$	−26.3335	+	45.6110i	−0.721806	+	1.25020i	−0.960275	+	0.279054i	$0.909979\pi$
$12$		0			0
$13$	−33.5544	−	58.1179i	−0.715870	−	1.23992i	−0.962623	−	0.270844i	$-0.912697\pi$
$13$	−33.5544	−	58.1179i	−0.715870	−	1.23992i	0.246753	−	0.969078i	$-0.420636\pi$
$14$	31.6035	+	54.7389i	0.603314	+	1.04497i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−19.4751			−0.277848			−0.138924	−	0.990303i	$-0.544364\pi$
$17$	−19.4751			−0.277848			−0.138924	+	0.990303i	$0.544364\pi$
$18$		0			0
$19$	103.354			1.24795			0.623974	−	0.781445i	$-0.285517\pi$
$19$	103.354			1.24795			0.623974	+	0.781445i	$0.285517\pi$
$20$	−10.0000	+	17.3205i	−0.111803	+	0.193649i
$21$		0			0
$22$	52.6671	+	91.2221i	0.510394	+	0.884028i
$23$	−77.2047	−	133.722i	−0.699926	−	1.21231i	−0.968492	−	0.249046i	$-0.919883\pi$
$23$	−77.2047	−	133.722i	−0.699926	−	1.21231i	0.268566	−	0.963261i	$-0.413450\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−134.217			−1.01239
$27$		0			0
$28$	126.414			0.853214
$29$	41.9220	−	72.6110i	0.268439	−	0.464949i	−0.700020	−	0.714123i	$-0.746826\pi$
$29$	41.9220	−	72.6110i	0.268439	−	0.464949i	0.968459	+	0.249174i	$0.0801590\pi$
$30$		0			0
$31$	57.8816	+	100.254i	0.335350	+	0.580843i	0.983552	−	0.180625i	$-0.0578121\pi$
$31$	57.8816	+	100.254i	0.335350	+	0.580843i	−0.648202	+	0.761468i	$0.724479\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$		0			0
$34$	−19.4751	+	33.7319i	−0.0982340	+	0.170146i
$35$	158.018			0.763138
$36$		0			0
$37$	417.744			1.85613			0.928063	−	0.372424i	$-0.121473\pi$
$37$	417.744			1.85613			0.928063	+	0.372424i	$0.121473\pi$
$38$	103.354	−	179.014i	0.441216	−	0.764208i
$39$		0			0
$40$	20.0000	+	34.6410i	0.0790569	+	0.136931i
$41$	74.2798	+	128.656i	0.282940	+	0.490067i	0.972108	−	0.234535i	$-0.0753568\pi$
$41$	74.2798	+	128.656i	0.282940	+	0.490067i	−0.689167	+	0.724602i	$0.742023\pi$
$42$		0			0
$43$	226.330	−	392.015i	0.802674	−	1.39027i	−0.115177	−	0.993345i	$-0.536743\pi$
$43$	226.330	−	392.015i	0.802674	−	1.39027i	0.917850	−	0.396926i	$-0.129923\pi$
$44$	210.668			0.721806
$45$		0			0
$46$	−308.819			−0.989845
$47$	256.506	−	444.282i	0.796071	−	1.37883i	−0.126087	−	0.992019i	$-0.540242\pi$
$47$	256.506	−	444.282i	0.796071	−	1.37883i	0.922157	−	0.386815i	$-0.126425\pi$
$48$		0			0
$49$	−327.891	−	567.924i	−0.955950	−	1.65575i
$50$	25.0000	+	43.3013i	0.0707107	+	0.122474i
$51$		0			0
$52$	−134.217	+	232.471i	−0.357935	+	0.619961i
$53$	139.549			0.361671			0.180835	−	0.983513i	$-0.442120\pi$
$53$	139.549			0.361671			0.180835	+	0.983513i	$0.442120\pi$
$54$		0			0
$55$	263.335			0.645603
$56$	126.414	−	218.956i	0.301657	−	0.522485i
$57$		0			0
$58$	−83.8440	−	145.222i	−0.189815	−	0.328769i
$59$	277.631	+	480.872i	0.612619	+	1.06109i	0.990797	+	0.135355i	$0.0432174\pi$
$59$	277.631	+	480.872i	0.612619	+	1.06109i	−0.378178	+	0.925733i	$0.623449\pi$
$60$		0			0
$61$	12.8106	−	22.1885i	0.0268889	−	0.0465730i	−0.852268	−	0.523106i	$-0.824773\pi$
$61$	12.8106	−	22.1885i	0.0268889	−	0.0465730i	0.879157	+	0.476533i	$0.158107\pi$
$62$	231.526			0.474256
$63$		0			0
$64$	64.0000			0.125000
$65$	−167.772	+	290.589i	−0.320147	+	0.554510i
$66$		0			0
$67$	477.181	+	826.501i	0.870103	+	1.50706i	0.861889	+	0.507096i	$0.169281\pi$
$67$	477.181	+	826.501i	0.870103	+	1.50706i	0.00821346	+	0.999966i	$0.497386\pi$
$68$	38.9502	+	67.4638i	0.0694619	+	0.120312i
$69$		0			0
$70$	158.018	−	273.694i	0.269810	−	0.467325i
$71$	−49.5295			−0.0827897			−0.0413949	−	0.999143i	$-0.513180\pi$
$71$	−49.5295			−0.0827897			−0.0413949	+	0.999143i	$0.513180\pi$
$72$		0			0
$73$	−399.667			−0.640788			−0.320394	−	0.947284i	$-0.603815\pi$
$73$	−399.667			−0.640788			−0.320394	+	0.947284i	$0.603815\pi$
$74$	417.744	−	723.553i	0.656239	−	1.13664i
$75$		0			0
$76$	−206.708	−	358.028i	−0.311987	−	0.540377i
$77$	−832.232	−	1441.47i	−1.23171	−	2.13338i
$78$		0			0
$79$	−375.436	+	650.275i	−0.534682	+	0.926096i	0.464497	+	0.885575i	$0.346235\pi$
$79$	−375.436	+	650.275i	−0.534682	+	0.926096i	−0.999179	+	0.0405214i	$0.987098\pi$
$80$	80.0000			0.111803
$81$		0			0
$82$	297.119			0.400138
$83$	587.011	−	1016.73i	0.776299	−	1.34459i	−0.157762	−	0.987477i	$-0.550428\pi$
$83$	587.011	−	1016.73i	0.776299	−	1.34459i	0.934061	−	0.357113i	$-0.116239\pi$
$84$		0			0
$85$	48.6878	+	84.3297i	0.0621286	+	0.107610i
$86$	−452.659	−	784.029i	−0.567576	−	0.983070i
$87$		0			0
$88$	210.668	−	364.888i	0.255197	−	0.442014i
$89$	−1011.21			−1.20436			−0.602182	−	0.798359i	$-0.705702\pi$
$89$	−1011.21			−1.20436			−0.602182	+	0.798359i	$0.705702\pi$
$90$		0			0
$91$	2120.87			2.44316
$92$	−308.819	+	534.890i	−0.349963	+	0.606154i
$93$		0			0
$94$	−513.013	−	888.565i	−0.562907	−	0.974983i
$95$	−258.385	−	447.535i	−0.279049	−	0.483328i
$96$		0			0
$97$	−422.506	+	731.802i	−0.442258	+	0.766013i	−0.997857	−	0.0654373i	$-0.979156\pi$
$97$	−422.506	+	731.802i	−0.442258	+	0.766013i	0.555599	+	0.831451i	$0.312489\pi$
$98$	−1311.56			−1.35192
$99$		0			0
$100$	100.000			0.100000
$101$	757.515	−	1312.05i	0.746292	−	1.29262i	−0.203296	−	0.979117i	$-0.565165\pi$
$101$	757.515	−	1312.05i	0.746292	−	1.29262i	0.949589	−	0.313499i	$-0.101501\pi$
$102$		0			0
$103$	30.3883	+	52.6341i	0.0290704	+	0.0503514i	0.880195	−	0.474613i	$-0.157412\pi$
$103$	30.3883	+	52.6341i	0.0290704	+	0.0503514i	−0.851124	+	0.524964i	$0.824079\pi$
$104$	268.435	+	464.943i	0.253098	+	0.438379i
$105$		0			0
$106$	139.549	−	241.706i	0.127870	−	0.221477i
$107$	222.983			0.201463			0.100732	−	0.994914i	$-0.467882\pi$
$107$	222.983			0.201463			0.100732	+	0.994914i	$0.467882\pi$
$108$		0			0
$109$	−398.980			−0.350599			−0.175300	−	0.984515i	$-0.556089\pi$
$109$	−398.980			−0.350599			−0.175300	+	0.984515i	$0.556089\pi$
$110$	263.335	−	456.110i	0.228255	−	0.395349i
$111$		0			0
$112$	−252.828	−	437.911i	−0.213304	−	0.369453i
$113$	3.94448	+	6.83204i	0.00328376	+	0.00568765i	0.867663	−	0.497153i	$-0.165621\pi$
$113$	3.94448	+	6.83204i	0.00328376	+	0.00568765i	−0.864379	+	0.502841i	$0.832288\pi$
$114$		0			0
$115$	−386.024	+	668.612i	−0.313016	+	0.542160i
$116$	−335.376			−0.268439
$117$		0			0
$118$	1110.53			0.866375
$119$	307.741	−	533.023i	0.237064	−	0.410606i
$120$		0			0
$121$	−721.411	−	1249.52i	−0.542007	−	0.938783i
$122$	−25.6211	−	44.3771i	−0.0190133	−	0.0329321i
$123$		0			0
$124$	231.526	−	401.016i	0.167675	−	0.290422i
$125$	125.000			0.0894427
$126$		0			0
$127$	867.604			0.606200			0.303100	−	0.952959i	$-0.401978\pi$
$127$	867.604			0.606200			0.303100	+	0.952959i	$0.401978\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$		0			0
$130$	335.544	+	581.179i	0.226378	+	0.392098i
$131$	−393.441	−	681.460i	−0.262406	−	0.454500i	0.704475	−	0.709729i	$-0.251182\pi$
$131$	−393.441	−	681.460i	−0.262406	−	0.454500i	−0.966881	+	0.255229i	$0.917849\pi$
$132$		0			0
$133$	−1633.17	+	2828.74i	−1.06477	+	1.84423i
$134$	1908.72			1.23051
$135$		0			0
$136$	155.801			0.0982340
$137$	−41.6309	+	72.1069i	−0.0259618	+	0.0449672i	−0.878714	−	0.477348i	$-0.841598\pi$
$137$	−41.6309	+	72.1069i	−0.0259618	+	0.0449672i	0.852753	+	0.522315i	$0.174932\pi$
$138$		0			0
$139$	−454.730	−	787.615i	−0.277480	−	0.480609i	0.693278	−	0.720670i	$-0.256166\pi$
$139$	−454.730	−	787.615i	−0.277480	−	0.480609i	−0.970758	+	0.240061i	$0.922833\pi$
$140$	−316.035	−	547.389i	−0.190785	−	0.330449i
$141$		0			0
$142$	−49.5295	+	85.7876i	−0.0292706	+	0.0506981i
$143$	3534.42			2.06687
$144$		0			0
$145$	−419.220			−0.240099
$146$	−399.667	+	692.244i	−0.226553	+	0.392401i
$147$		0			0
$148$	−835.487	−	1447.11i	−0.464031	−	0.803726i
$149$	−1558.65	−	2699.65i	−0.856975	−	1.48432i	−0.874801	−	0.484483i	$-0.839008\pi$
$149$	−1558.65	−	2699.65i	−0.856975	−	1.48432i	0.0178259	−	0.999841i	$-0.494326\pi$
$150$		0			0
$151$	857.118	−	1484.57i	0.461929	−	0.800084i	−0.537128	−	0.843501i	$-0.680491\pi$
$151$	857.118	−	1484.57i	0.461929	−	0.800084i	0.999057	+	0.0434164i	$0.0138242\pi$
$152$	−826.831			−0.441216
$153$		0			0
$154$	−3328.93			−1.74190
$155$	289.408	−	501.270i	0.149973	−	0.259761i
$156$		0			0
$157$	1935.54	+	3352.46i	0.983906	+	1.70418i	0.646699	+	0.762745i	$0.276149\pi$
$157$	1935.54	+	3352.46i	0.983906	+	1.70418i	0.337207	+	0.941430i	$0.390518\pi$
$158$	750.872	+	1300.55i	0.378077	+	0.654849i
$159$		0			0
$160$	80.0000	−	138.564i	0.0395285	−	0.0684653i
$161$	4879.88			2.38875
$162$		0			0
$163$	1192.36			0.572963			0.286482	−	0.958086i	$-0.407514\pi$
$163$	1192.36			0.572963			0.286482	+	0.958086i	$0.407514\pi$
$164$	297.119	−	514.625i	0.141470	−	0.245034i
$165$		0			0
$166$	−1174.02	−	2033.47i	−0.548926	−	0.950768i
$167$	−280.195	−	485.312i	−0.129833	−	0.224877i	0.793779	−	0.608207i	$-0.208111\pi$
$167$	−280.195	−	485.312i	−0.129833	−	0.224877i	−0.923612	+	0.383329i	$0.874777\pi$
$168$		0			0
$169$	−1153.29	+	1997.56i	−0.524939	+	0.909221i
$170$	194.751			0.0878631
$171$		0			0
$172$	−1810.64			−0.802674
$173$	934.699	−	1618.95i	0.410774	−	0.711481i	−0.584201	−	0.811609i	$-0.698592\pi$
$173$	934.699	−	1618.95i	0.410774	−	0.711481i	0.994975	+	0.100128i	$0.0319253\pi$
$174$		0			0
$175$	−395.044	−	684.236i	−0.170643	−	0.295562i
$176$	−421.337	−	729.777i	−0.180451	−	0.312551i
$177$		0			0
$178$	−1011.21	+	1751.47i	−0.425807	+	0.737519i
$179$	1700.66			0.710130			0.355065	−	0.934842i	$-0.384459\pi$
$179$	1700.66			0.710130			0.355065	+	0.934842i	$0.384459\pi$
$180$		0			0
$181$	−544.922			−0.223777			−0.111889	−	0.993721i	$-0.535690\pi$
$181$	−544.922			−0.223777			−0.111889	+	0.993721i	$0.535690\pi$
$182$	2120.87	−	3673.46i	0.863788	−	1.49612i
$183$		0			0
$184$	617.638	+	1069.78i	0.247461	+	0.428615i
$185$	−1044.36	−	1808.88i	−0.415042	−	0.718874i
$186$		0			0
$187$	512.849	−	888.280i	0.200552	−	0.347366i
$188$	−2052.05			−0.796071
$189$		0			0
$190$	−1033.54			−0.394636
$191$	−1119.54	+	1939.10i	−0.424122	+	0.734600i	−0.996338	−	0.0855025i	$-0.972750\pi$
$191$	−1119.54	+	1939.10i	−0.424122	+	0.734600i	0.572216	+	0.820103i	$0.306084\pi$
$192$		0			0
$193$	368.762	+	638.715i	0.137534	+	0.238216i	0.926563	−	0.376140i	$-0.122749\pi$
$193$	368.762	+	638.715i	0.137534	+	0.238216i	−0.789029	+	0.614357i	$0.789416\pi$
$194$	845.013	+	1463.60i	0.312724	+	0.541653i
$195$		0			0
$196$	−1311.56	+	2271.69i	−0.477975	+	0.827877i
$197$	−1104.80			−0.399562			−0.199781	−	0.979841i	$-0.564023\pi$
$197$	−1104.80			−0.399562			−0.199781	+	0.979841i	$0.564023\pi$
$198$		0			0
$199$	4004.57			1.42651			0.713257	−	0.700902i	$-0.247219\pi$
$199$	4004.57			1.42651			0.713257	+	0.700902i	$0.247219\pi$
$200$	100.000	−	173.205i	0.0353553	−	0.0612372i
$201$		0			0
$202$	−1515.03	−	2624.11i	−0.527708	−	0.914018i
$203$	1324.88	+	2294.76i	0.458071	+	0.793403i
$204$		0			0
$205$	371.399	−	643.282i	0.126535	−	0.219165i
$206$	121.553			0.0411117
$207$		0			0
$208$	1073.74			0.357935
$209$	−2721.67	+	4714.07i	−0.900775	+	1.56019i
$210$		0			0
$211$	778.258	+	1347.98i	0.253922	+	0.439806i	0.964602	−	0.263710i	$-0.0849460\pi$
$211$	778.258	+	1347.98i	0.253922	+	0.439806i	−0.710680	+	0.703515i	$0.751613\pi$
$212$	−279.098	−	483.413i	−0.0904177	−	0.156608i
$213$		0			0
$214$	222.983	−	386.218i	0.0712280	−	0.123371i
$215$	−2263.30			−0.717933
$216$		0			0
$217$	−3658.52			−1.14450
$218$	−398.980	+	691.053i	−0.123956	+	0.214697i
$219$		0			0
$220$	−526.671	−	912.221i	−0.161401	−	0.279554i
$221$	653.475	+	1131.85i	0.198903	+	0.344510i
$222$		0			0
$223$	2151.77	−	3726.97i	0.646156	−	1.11918i	−0.337877	−	0.941190i	$-0.609709\pi$
$223$	2151.77	−	3726.97i	0.646156	−	1.11918i	0.984033	−	0.177985i	$-0.0569580\pi$
$224$	−1011.31			−0.301657
$225$		0			0
$226$	15.7779			0.00464394
$227$	1209.36	−	2094.67i	0.353604	−	0.612460i	−0.633274	−	0.773928i	$-0.718289\pi$
$227$	1209.36	−	2094.67i	0.353604	−	0.612460i	0.986878	+	0.161468i	$0.0516228\pi$
$228$		0			0
$229$	−100.905	−	174.772i	−0.0291178	−	0.0504335i	0.851099	−	0.525005i	$-0.175936\pi$
$229$	−100.905	−	174.772i	−0.0291178	−	0.0504335i	−0.880217	+	0.474571i	$0.842603\pi$
$230$	772.047	+	1337.22i	0.221336	+	0.383365i
$231$		0			0
$232$	−335.376	+	580.888i	−0.0949074	+	0.164384i
$233$	187.810			0.0528062			0.0264031	−	0.999651i	$-0.491595\pi$
$233$	187.810			0.0528062			0.0264031	+	0.999651i	$0.491595\pi$
$234$		0			0
$235$	−2565.06			−0.712027
$236$	1110.53	−	1923.49i	0.306310	−	0.530544i
$237$		0			0
$238$	−615.482	−	1066.05i	−0.167629	−	0.290342i
$239$	−1706.45	−	2955.65i	−0.461844	−	0.799938i	0.537209	−	0.843449i	$-0.319479\pi$
$239$	−1706.45	−	2955.65i	−0.461844	−	0.799938i	−0.999053	+	0.0435116i	$0.986145\pi$
$240$		0			0
$241$	−582.337	+	1008.64i	−0.155650	+	0.269593i	−0.933295	−	0.359109i	$-0.883080\pi$
$241$	−582.337	+	1008.64i	−0.155650	+	0.269593i	0.777646	+	0.628703i	$0.216414\pi$
$242$	−2885.64			−0.766513
$243$		0			0
$244$	−102.484			−0.0268889
$245$	−1639.45	+	2839.62i	−0.427514	+	0.740476i
$246$		0			0
$247$	−3467.97	−	6006.70i	−0.893367	−	1.54736i
$248$	−463.053	−	802.031i	−0.118564	−	0.205359i
$249$		0			0
$250$	125.000	−	216.506i	0.0316228	−	0.0547723i
$251$	−4345.22			−1.09270			−0.546351	−	0.837556i	$-0.683983\pi$
$251$	−4345.22			−1.09270			−0.546351	+	0.837556i	$0.683983\pi$
$252$		0			0
$253$	8132.29			2.02084
$254$	867.604	−	1502.73i	0.214324	−	0.371220i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−669.053	−	1158.83i	−0.162391	−	0.281269i	0.773335	−	0.633998i	$-0.218587\pi$
$257$	−669.053	−	1158.83i	−0.162391	−	0.281269i	−0.935726	+	0.352729i	$0.885254\pi$
$258$		0			0
$259$	−6601.08	+	11433.4i	−1.58367	+	2.74300i
$260$	1342.17			0.320147
$261$		0			0
$262$	−1573.77			−0.371098
$263$	−2391.83	+	4142.77i	−0.560785	+	0.971308i	0.436643	+	0.899635i	$0.356167\pi$
$263$	−2391.83	+	4142.77i	−0.560785	+	0.971308i	−0.997428	+	0.0716734i	$0.977166\pi$
$264$		0			0
$265$	−348.873	−	604.266i	−0.0808721	−	0.140075i
$266$	3266.34	+	5657.47i	0.752904	+	1.30407i
$267$		0			0
$268$	1908.72	−	3306.00i	0.435051	−	0.753531i
$269$	6102.65			1.38322			0.691608	−	0.722273i	$-0.256903\pi$
$269$	6102.65			1.38322			0.691608	+	0.722273i	$0.256903\pi$
$270$		0			0
$271$	−422.742			−0.0947591			−0.0473796	−	0.998877i	$-0.515087\pi$
$271$	−422.742			−0.0947591			−0.0473796	+	0.998877i	$0.515087\pi$
$272$	155.801	−	269.855i	0.0347310	−	0.0601558i
$273$		0			0
$274$	83.2619	+	144.214i	0.0183578	+	0.0317966i
$275$	−658.339	−	1140.28i	−0.144361	−	0.250041i
$276$		0			0
$277$	1641.28	−	2842.78i	0.356011	−	0.616629i	−0.631280	−	0.775555i	$-0.717470\pi$
$277$	1641.28	−	2842.78i	0.356011	−	0.616629i	0.987290	+	0.158926i	$0.0508033\pi$
$278$	−1818.92			−0.392416
$279$		0			0
$280$	−1264.14			−0.269810
$281$	−320.964	+	555.926i	−0.0681391	+	0.118020i	−0.898082	−	0.439828i	$-0.855040\pi$
$281$	−320.964	+	555.926i	−0.0681391	+	0.118020i	0.829943	+	0.557848i	$0.188373\pi$
$282$		0			0
$283$	3613.55	+	6258.84i	0.759021	+	1.31466i	0.943350	+	0.331799i	$0.107655\pi$
$283$	3613.55	+	6258.84i	0.759021	+	1.31466i	−0.184329	+	0.982865i	$0.559011\pi$
$284$	99.0590	+	171.575i	0.0206974	+	0.0358490i
$285$		0			0
$286$	3534.42	−	6121.80i	0.730751	−	1.26570i
$287$	−4695.00			−0.965635
$288$		0			0
$289$	−4533.72			−0.922801
$290$	−419.220	+	726.110i	−0.0848877	+	0.147030i
$291$		0			0
$292$	799.335	+	1384.49i	0.160197	+	0.277469i
$293$	−1862.21	−	3225.45i	−0.371303	−	0.643115i	0.618464	−	0.785813i	$-0.287755\pi$
$293$	−1862.21	−	3225.45i	−0.371303	−	0.643115i	−0.989766	+	0.142698i	$0.954422\pi$
$294$		0			0
$295$	1388.16	−	2404.36i	0.273972	−	0.474533i
$296$	−3341.95			−0.656239
$297$		0			0
$298$	−6234.58			−1.21195
$299$	−5181.11	+	8973.94i	−1.00211	+	1.73571i
$300$		0			0
$301$	7152.81	+	12389.0i	1.36971	+	2.37240i
$302$	−1714.24	−	2969.14i	−0.326633	−	0.565745i
$303$		0			0
$304$	−826.831	+	1432.11i	−0.155993	+	0.270188i
$305$	−128.106			−0.0240502
$306$		0			0
$307$	−5190.35			−0.964914			−0.482457	−	0.875920i	$-0.660256\pi$
$307$	−5190.35			−0.964914			−0.482457	+	0.875920i	$0.660256\pi$
$308$	−3328.93	+	5765.87i	−0.615855	+	1.06669i
$309$		0			0
$310$	−578.816	−	1002.54i	−0.106047	−	0.183679i
$311$	−1815.68	−	3144.86i	−0.331055	−	0.573403i	0.651664	−	0.758507i	$-0.274071\pi$
$311$	−1815.68	−	3144.86i	−0.331055	−	0.573403i	−0.982719	+	0.185104i	$0.940738\pi$
$312$		0			0
$313$	1819.45	−	3151.37i	0.328566	−	0.569093i	−0.653661	−	0.756787i	$-0.726768\pi$
$313$	1819.45	−	3151.37i	0.328566	−	0.569093i	0.982228	+	0.187694i	$0.0601013\pi$
$314$	7742.18			1.39145
$315$		0			0
$316$	3003.49			0.534682
$317$	2050.60	−	3551.75i	0.363323	−	0.629293i	−0.625183	−	0.780478i	$-0.714976\pi$
$317$	2050.60	−	3551.75i	0.363323	−	0.629293i	0.988505	+	0.151185i	$0.0483090\pi$
$318$		0			0
$319$	2207.91	+	3824.21i	0.387521	+	0.671206i
$320$	−160.000	−	277.128i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	4879.88	−	8452.20i	0.844550	−	1.46280i
$323$	−2012.83			−0.346739
$324$		0			0
$325$	1677.72			0.286348
$326$	1192.36	−	2065.23i	0.202573	−	0.350867i
$327$		0			0
$328$	−594.238	−	1029.25i	−0.100035	−	0.173265i
$329$	8106.50	+	14040.9i	1.35844	+	2.35288i
$330$		0			0
$331$	2891.20	−	5007.70i	0.480105	−	0.831566i	−0.519635	−	0.854388i	$-0.673932\pi$
$331$	2891.20	−	5007.70i	0.480105	−	0.831566i	0.999740	+	0.0228228i	$0.00726535\pi$
$332$	−4696.09			−0.776299
$333$		0			0
$334$	−1120.78			−0.183612
$335$	2385.90	−	4132.51i	0.389122	−	0.673979i
$336$		0			0
$337$	5165.11	+	8946.23i	0.834901	+	1.44609i	0.894111	+	0.447845i	$0.147808\pi$
$337$	5165.11	+	8946.23i	0.834901	+	1.44609i	−0.0592108	+	0.998245i	$0.518858\pi$
$338$	2306.58	+	3995.12i	0.371188	+	0.642916i
$339$		0			0
$340$	194.751	−	337.319i	0.0310643	−	0.0538050i
$341$	−6096.91			−0.968230
$342$		0			0
$343$	9885.00			1.55609
$344$	−1810.64	+	3136.12i	−0.283788	+	0.491535i
$345$		0			0
$346$	−1869.40	−	3237.89i	−0.290461	−	0.503093i
$347$	2207.94	+	3824.26i	0.341580	+	0.591635i	0.984726	−	0.174109i	$-0.0557045\pi$
$347$	2207.94	+	3824.26i	0.341580	+	0.591635i	−0.643146	+	0.765744i	$0.722371\pi$
$348$		0			0
$349$	2922.40	−	5061.75i	0.448231	−	0.776359i	−0.550040	−	0.835138i	$-0.685388\pi$
$349$	2922.40	−	5061.75i	0.448231	−	0.776359i	0.998271	+	0.0587795i	$0.0187209\pi$
$350$	−1580.18			−0.241325
$351$		0			0
$352$	−1685.35			−0.255197
$353$	6315.79	−	10939.3i	0.952282	−	1.64940i	0.211814	−	0.977310i	$-0.432063\pi$
$353$	6315.79	−	10939.3i	0.952282	−	1.64940i	0.740468	−	0.672091i	$-0.234604\pi$
$354$		0			0
$355$	123.824	+	214.469i	0.0185123	+	0.0320643i
$356$	2022.43	+	3502.95i	0.301091	+	0.521505i
$357$		0			0
$358$	1700.66	−	2945.63i	0.251069	−	0.434864i
$359$	12417.4			1.82553			0.912766	−	0.408484i	$-0.133942\pi$
$359$	12417.4			1.82553			0.912766	+	0.408484i	$0.133942\pi$
$360$		0			0
$361$	3823.01			0.557372
$362$	−544.922	+	943.832i	−0.0791173	+	0.137035i
$363$		0			0
$364$	−4241.74	−	7346.91i	−0.610790	−	1.05792i
$365$	999.168	+	1730.61i	0.143285	+	0.248176i
$366$		0			0
$367$	801.493	−	1388.23i	0.113999	−	0.197452i	−0.803380	−	0.595466i	$-0.796967\pi$
$367$	801.493	−	1388.23i	0.113999	−	0.197452i	0.917379	+	0.398014i	$0.130301\pi$
$368$	2470.55			0.349963
$369$		0			0
$370$	−4177.44			−0.586958
$371$	−2205.12	+	3819.38i	−0.308583	+	0.534481i
$372$		0			0
$373$	1706.77	+	2956.21i	0.236925	+	0.410367i	0.959830	−	0.280581i	$-0.0905270\pi$
$373$	1706.77	+	2956.21i	0.236925	+	0.410367i	−0.722905	+	0.690947i	$0.757194\pi$
$374$	−1025.70	−	1776.56i	−0.141812	−	0.245625i
$375$		0			0
$376$	−2052.05	+	3554.26i	−0.281453	+	0.487492i
$377$	−5626.66			−0.768668
$378$		0			0
$379$	−3087.00			−0.418386			−0.209193	−	0.977874i	$-0.567084\pi$
$379$	−3087.00			−0.418386			−0.209193	+	0.977874i	$0.567084\pi$
$380$	−1033.54	+	1790.14i	−0.139525	+	0.241664i
$381$		0			0
$382$	2239.08	+	3878.21i	0.299899	+	0.519441i
$383$	5667.92	+	9817.13i	0.756181	+	1.30974i	0.944785	+	0.327690i	$0.106270\pi$
$383$	5667.92	+	9817.13i	0.756181	+	1.30974i	−0.188605	+	0.982053i	$0.560396\pi$
$384$		0			0
$385$	−4161.16	+	7207.34i	−0.550837	+	0.954078i
$386$	1475.05			0.194503
$387$		0			0
$388$	3380.05			0.442258
$389$	−5414.94	+	9378.94i	−0.705779	+	1.22245i	0.260630	+	0.965439i	$0.416070\pi$
$389$	−5414.94	+	9378.94i	−0.705779	+	1.22245i	−0.966410	+	0.257007i	$0.917264\pi$
$390$		0			0
$391$	1503.57	+	2604.26i	0.194473	+	0.336837i
$392$	2623.13	+	4543.39i	0.337979	+	0.585397i
$393$		0			0
$394$	−1104.80	+	1913.57i	−0.141266	+	0.244681i
$395$	3754.36			0.478234
$396$		0			0
$397$	3974.56			0.502462			0.251231	−	0.967927i	$-0.419165\pi$
$397$	3974.56			0.502462			0.251231	+	0.967927i	$0.419165\pi$
$398$	4004.57	−	6936.12i	0.504349	−	0.873558i
$399$		0			0
$400$	−200.000	−	346.410i	−0.0250000	−	0.0433013i
$401$	6655.92	+	11528.4i	0.828880	+	1.43566i	0.898918	+	0.438118i	$0.144355\pi$
$401$	6655.92	+	11528.4i	0.828880	+	1.43566i	−0.0700379	+	0.997544i	$0.522312\pi$
$402$		0			0
$403$	3884.36	−	6727.91i	0.480134	−	0.831616i
$404$	−6060.12			−0.746292
$405$		0			0
$406$	5299.53			0.647811
$407$	−11000.7	+	19053.7i	−1.33976	+	2.32053i
$408$		0			0
$409$	−3210.71	−	5561.12i	−0.388165	−	0.672321i	0.604038	−	0.796956i	$-0.293558\pi$
$409$	−3210.71	−	5561.12i	−0.388165	−	0.672321i	−0.992203	+	0.124634i	$0.960224\pi$
$410$	−742.798	−	1286.56i	−0.0894736	−	0.154973i
$411$		0			0
$412$	121.553	−	210.536i	0.0145352	−	0.0251757i
$413$	−17548.3			−2.09078
$414$		0			0
$415$	−5870.11			−0.694343
$416$	1073.74	−	1859.77i	0.126549	−	0.219189i
$417$		0			0
$418$	5443.34	+	9428.15i	0.636944	+	1.10322i
$419$	−2313.43	−	4006.98i	−0.269734	−	0.467193i	0.699059	−	0.715064i	$-0.253602\pi$
$419$	−2313.43	−	4006.98i	−0.269734	−	0.467193i	−0.968793	+	0.247871i	$0.920269\pi$
$420$		0			0
$421$	−2575.50	+	4460.90i	−0.298153	+	0.516416i	−0.975713	−	0.219051i	$-0.929704\pi$
$421$	−2575.50	+	4460.90i	−0.298153	+	0.516416i	0.677561	+	0.735467i	$0.263037\pi$
$422$	3113.03			0.359100
$423$		0			0
$424$	−1116.39			−0.127870
$425$	243.439	−	421.649i	0.0277848	−	0.0481246i
$426$		0			0
$427$	404.859	+	701.236i	0.0458840	+	0.0794735i
$428$	−445.966	−	772.435i	−0.0503658	−	0.0872361i
$429$		0			0
$430$	−2263.30	+	3920.15i	−0.253828	+	0.439642i
$431$	2452.29			0.274067			0.137033	−	0.990566i	$-0.456243\pi$
$431$	2452.29			0.274067			0.137033	+	0.990566i	$0.456243\pi$
$432$		0			0
$433$	11033.4			1.22456			0.612279	−	0.790642i	$-0.290253\pi$
$433$	11033.4			1.22456			0.612279	+	0.790642i	$0.290253\pi$
$434$	−3658.52	+	6336.75i	−0.404642	+	0.700861i
$435$		0			0
$436$	797.959	+	1382.11i	0.0876498	+	0.151814i
$437$	−7979.40	−	13820.7i	−0.873470	−	1.51290i
$438$		0			0
$439$	410.002	−	710.144i	0.0445748	−	0.0772057i	−0.842877	−	0.538106i	$-0.819140\pi$
$439$	410.002	−	710.144i	0.0445748	−	0.0772057i	0.887452	+	0.460900i	$0.152473\pi$
$440$	−2106.68			−0.228255
$441$		0			0
$442$	2613.90			0.281291
$443$	−3353.20	+	5807.91i	−0.359628	+	0.622894i	−0.987899	−	0.155101i	$-0.950430\pi$
$443$	−3353.20	+	5807.91i	−0.359628	+	0.622894i	0.628271	+	0.777995i	$0.283763\pi$
$444$		0			0
$445$	2528.03	+	4378.68i	0.269304	+	0.466448i
$446$	−4303.53	−	7453.94i	−0.456902	−	0.791377i
$447$		0			0
$448$	−1011.31	+	1751.64i	−0.106652	+	0.184726i
$449$	−9873.94			−1.03782			−0.518908	−	0.854830i	$-0.673661\pi$
$449$	−9873.94			−1.03782			−0.518908	+	0.854830i	$0.673661\pi$
$450$		0			0
$451$	−7824.20			−0.816912
$452$	15.7779	−	27.3281i	0.00164188	−	0.00284382i
$453$		0			0
$454$	−2418.72	−	4189.35i	−0.250036	−	0.433074i
$455$	−5302.18	−	9183.64i	−0.546308	−	0.946232i
$456$		0			0
$457$	6540.21	−	11328.0i	0.669449	−	1.15952i	−0.308610	−	0.951189i	$-0.599864\pi$
$457$	6540.21	−	11328.0i	0.669449	−	1.15952i	0.978058	−	0.208331i	$-0.0668030\pi$
$458$	−403.619			−0.0411788
$459$		0			0
$460$	3088.19			0.313016
$461$	−4784.40	+	8286.83i	−0.483366	+	0.837215i	−0.999818	−	0.0191014i	$-0.993919\pi$
$461$	−4784.40	+	8286.83i	−0.483366	+	0.837215i	0.516451	+	0.856317i	$0.327253\pi$
$462$		0			0
$463$	−160.312	−	277.669i	−0.0160915	−	0.0278712i	0.857868	−	0.513871i	$-0.171789\pi$
$463$	−160.312	−	277.669i	−0.0160915	−	0.0278712i	−0.873959	+	0.486000i	$0.838456\pi$
$464$	670.752	+	1161.78i	0.0671097	+	0.116237i
$465$		0			0
$466$	187.810	−	325.296i	0.0186698	−	0.0323370i
$467$	4083.18			0.404597			0.202299	−	0.979324i	$-0.435159\pi$
$467$	4083.18			0.404597			0.202299	+	0.979324i	$0.435159\pi$
$468$		0			0
$469$	−30161.2			−2.96954
$470$	−2565.06	+	4442.82i	−0.251740	+	0.436026i
$471$		0			0
$472$	−2221.05	−	3846.97i	−0.216594	−	0.375151i
$473$	11920.1	+	20646.3i	1.15875	+	2.00701i
$474$		0			0
$475$	−1291.92	+	2237.68i	−0.124795	+	0.216151i
$476$	−2461.93			−0.237064
$477$		0			0
$478$	−6825.78			−0.653147
$479$	1286.40	−	2228.11i	0.122708	−	0.212537i	−0.798127	−	0.602490i	$-0.794175\pi$
$479$	1286.40	−	2228.11i	0.122708	−	0.212537i	0.920835	+	0.389953i	$0.127509\pi$
$480$		0			0
$481$	−14017.1	−	24278.4i	−1.32874	−	2.30145i
$482$	1164.67	+	2017.27i	0.110061	+	0.190631i
$483$		0			0
$484$	−2885.64	+	4998.08i	−0.271003	+	0.469391i
$485$	4225.06			0.395568
$486$		0			0
$487$	7204.59			0.670372			0.335186	−	0.942152i	$-0.391201\pi$
$487$	7204.59			0.670372			0.335186	+	0.942152i	$0.391201\pi$
$488$	−102.484	+	177.508i	−0.00950667	+	0.0164660i
$489$		0			0
$490$	3278.91	+	5679.24i	0.302298	+	0.523595i
$491$	−865.439	−	1498.98i	−0.0795452	−	0.137776i	0.823509	−	0.567304i	$-0.192013\pi$
$491$	−865.439	−	1498.98i	−0.0795452	−	0.137776i	−0.903054	+	0.429527i	$0.858680\pi$
$492$		0			0
$493$	−816.436	+	1414.11i	−0.0745850	+	0.129185i
$494$	−13871.9			−1.26341
$495$		0			0
$496$	−1852.21			−0.167675
$497$	782.653	−	1355.59i	0.0706374	−	0.122348i
$498$		0			0
$499$	−9723.03	−	16840.8i	−0.872270	−	1.51082i	−0.859643	−	0.510895i	$-0.829314\pi$
$499$	−9723.03	−	16840.8i	−0.872270	−	1.51082i	−0.0126270	−	0.999920i	$-0.504019\pi$
$500$	−250.000	−	433.013i	−0.0223607	−	0.0387298i
$501$		0			0
$502$	−4345.22	+	7526.15i	−0.386328	+	0.669140i
$503$	6493.41			0.575600			0.287800	−	0.957691i	$-0.407076\pi$
$503$	6493.41			0.575600			0.287800	+	0.957691i	$0.407076\pi$
$504$		0			0
$505$	−7575.15			−0.667504
$506$	8132.29	−	14085.5i	0.714475	−	1.23751i
$507$		0			0
$508$	−1735.21	−	3005.47i	−0.151550	−	0.262492i
$509$	−4932.71	−	8543.70i	−0.429545	−	0.743994i	0.567288	−	0.823520i	$-0.307993\pi$
$509$	−4932.71	−	8543.70i	−0.429545	−	0.743994i	−0.996833	+	0.0795257i	$0.974659\pi$
$510$		0			0
$511$	6315.44	−	10938.7i	0.546730	−	0.946963i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	−2676.21			−0.229655
$515$	151.942	−	263.171i	0.0130007	−	0.0225178i
$516$		0			0
$517$	13509.4	+	23399.1i	1.14922	+	1.99050i
$518$	13202.2	+	22866.8i	1.11983	+	1.93960i
$519$		0			0
$520$	1342.17	−	2324.71i	0.113189	−	0.196049i
$521$	−5324.37			−0.447726			−0.223863	−	0.974621i	$-0.571867\pi$
$521$	−5324.37			−0.447726			−0.223863	+	0.974621i	$0.571867\pi$
$522$		0			0
$523$	6262.02			0.523554			0.261777	−	0.965128i	$-0.415691\pi$
$523$	6262.02			0.523554			0.261777	+	0.965128i	$0.415691\pi$
$524$	−1573.77	+	2725.84i	−0.131203	+	0.227250i
$525$		0			0
$526$	4783.66	+	8285.54i	0.396535	+	0.686819i
$527$	−1127.25	−	1952.46i	−0.0931762	−	0.161386i
$528$		0			0
$529$	−5837.63	+	10111.1i	−0.479792	+	0.831025i
$530$	−1395.49			−0.114370
$531$		0			0
$532$	13065.4			1.06477
$533$	4984.82	−	8633.96i	0.405097	−	0.701648i
$534$		0			0
$535$	−557.457	−	965.544i	−0.0450485	−	0.0780264i
$536$	−3817.45	−	6612.01i	−0.307628	−	0.532827i
$537$		0			0
$538$	6102.65	−	10570.1i	0.489041	−	0.847044i
$539$	34538.1			2.76004
$540$		0			0
$541$	23066.3			1.83308			0.916542	−	0.399938i	$-0.130968\pi$
$541$	23066.3			1.83308			0.916542	+	0.399938i	$0.130968\pi$
$542$	−422.742	+	732.210i	−0.0335024	+	0.0580279i
$543$		0			0
$544$	−311.602	−	539.710i	−0.0245585	−	0.0425366i
$545$	997.449	+	1727.63i	0.0783964	+	0.135786i
$546$		0			0
$547$	6770.53	−	11726.9i	0.529227	−	0.916648i	−0.470192	−	0.882564i	$-0.655815\pi$
$547$	6770.53	−	11726.9i	0.529227	−	0.916648i	0.999419	−	0.0340838i	$-0.0108513\pi$
$548$	333.048			0.0259618
$549$		0			0
$550$	−2633.35			−0.204157
$551$	4332.80	−	7504.63i	0.334997	−	0.580232i
$552$		0			0
$553$	−11865.1	−	20551.0i	−0.912397	−	1.58032i
$554$	−3282.56	−	5685.56i	−0.251738	−	0.436022i
$555$		0			0
$556$	−1818.92	+	3150.46i	−0.138740	+	0.240305i
$557$	10550.8			0.802603			0.401302	−	0.915946i	$-0.368558\pi$
$557$	10550.8			0.802603			0.401302	+	0.915946i	$0.368558\pi$
$558$		0			0
$559$	−30377.4			−2.29844
$560$	−1264.14	+	2189.56i	−0.0953923	+	0.165224i
$561$		0			0
$562$	641.928	+	1111.85i	0.0481816	+	0.0834531i
$563$	−11506.2	−	19929.3i	−0.861328	−	1.49186i	−0.870648	−	0.491907i	$-0.836300\pi$
$563$	−11506.2	−	19929.3i	−0.861328	−	1.49186i	0.00931961	−	0.999957i	$-0.497033\pi$
$564$		0			0
$565$	19.7224	−	34.1602i	0.00146854	−	0.00254359i
$566$	14454.2			1.07342
$567$		0			0
$568$	396.236			0.0292706
$569$	10644.4	−	18436.6i	0.784245	−	1.35835i	−0.145204	−	0.989402i	$-0.546384\pi$
$569$	10644.4	−	18436.6i	0.784245	−	1.35835i	0.929449	−	0.368950i	$-0.120283\pi$
$570$		0			0
$571$	11019.6	+	19086.5i	0.807628	+	1.39885i	0.914502	+	0.404581i	$0.132582\pi$
$571$	11019.6	+	19086.5i	0.807628	+	1.39885i	−0.106874	+	0.994273i	$0.534084\pi$
$572$	−7068.84	−	12243.6i	−0.516719	−	0.894983i
$573$		0			0
$574$	−4695.00	+	8131.98i	−0.341404	+	0.591328i
$575$	3860.24			0.279970
$576$		0			0
$577$	8130.59			0.586622			0.293311	−	0.956017i	$-0.405243\pi$
$577$	8130.59			0.586622			0.293311	+	0.956017i	$0.405243\pi$
$578$	−4533.72	+	7852.63i	−0.326259	+	0.565098i
$579$		0			0
$580$	838.440	+	1452.22i	0.0600247	+	0.103966i
$581$	18551.6	+	32132.3i	1.32470	+	2.29445i
$582$		0			0
$583$	−3674.82	+	6364.98i	−0.261056	+	0.452162i
$584$	3197.34			0.226553
$585$		0			0
$586$	−7448.85			−0.525101
$587$	4447.17	−	7702.72i	0.312699	−	0.541611i	−0.666247	−	0.745731i	$-0.732100\pi$
$587$	4447.17	−	7702.72i	0.312699	−	0.541611i	0.978946	+	0.204121i	$0.0654335\pi$
$588$		0			0
$589$	5982.29	+	10361.6i	0.418499	+	0.724861i
$590$	−2776.31	−	4808.72i	−0.193727	−	0.335545i
$591$		0			0
$592$	−3341.95	+	5788.43i	−0.232016	+	0.401863i
$593$	−6979.35			−0.483318			−0.241659	−	0.970361i	$-0.577691\pi$
$593$	−6979.35			−0.483318			−0.241659	+	0.970361i	$0.577691\pi$
$594$		0			0
$595$	−3077.41			−0.212036
$596$	−6234.58	+	10798.6i	−0.428487	+	0.742162i
$597$		0			0
$598$	10362.2	+	17947.9i	0.708600	+	1.22733i
$599$	−11997.3	−	20779.9i	−0.818355	−	1.41743i	−0.906893	−	0.421360i	$-0.861553\pi$
$599$	−11997.3	−	20779.9i	−0.818355	−	1.41743i	0.0885379	−	0.996073i	$-0.471781\pi$
$600$		0			0
$601$	−7805.56	+	13519.6i	−0.529776	+	0.917599i	0.469621	+	0.882868i	$0.344391\pi$
$601$	−7805.56	+	13519.6i	−0.529776	+	0.917599i	−0.999397	+	0.0347309i	$0.988943\pi$
$602$	28611.3			1.93706
$603$		0			0
$604$	−6856.94			−0.461929
$605$	−3607.05	+	6247.60i	−0.242393	+	0.419837i
$606$		0			0
$607$	−12900.5	−	22344.4i	−0.862630	−	1.49412i	−0.869382	−	0.494141i	$-0.835482\pi$
$607$	−12900.5	−	22344.4i	−0.862630	−	1.49412i	0.00675169	−	0.999977i	$-0.497851\pi$
$608$	1653.66	+	2864.23i	0.110304	+	0.191052i
$609$		0			0
$610$	−128.106	+	221.885i	−0.00850302	+	0.0147277i
$611$	−34427.6			−2.27953
$612$		0			0
$613$	6249.09			0.411743			0.205871	−	0.978579i	$-0.433997\pi$
$613$	6249.09			0.411743			0.205871	+	0.978579i	$0.433997\pi$
$614$	−5190.35	+	8989.94i	−0.341149	+	0.590887i
$615$		0			0
$616$	6657.86	+	11531.7i	0.435475	+	0.754265i
$617$	−5715.09	−	9898.83i	−0.372903	−	0.645886i	0.617108	−	0.786878i	$-0.288304\pi$
$617$	−5715.09	−	9898.83i	−0.372903	−	0.645886i	−0.990011	+	0.140992i	$0.954971\pi$
$618$		0			0
$619$	4365.08	−	7560.55i	0.283437	−	0.490927i	−0.688792	−	0.724959i	$-0.741859\pi$
$619$	4365.08	−	7560.55i	0.283437	−	0.490927i	0.972229	+	0.234032i	$0.0751920\pi$
$620$	−2315.26			−0.149973
$621$		0			0
$622$	−7262.73			−0.468182
$623$	15978.9	−	27676.3i	1.02758	−	1.77982i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−3638.89	−	6302.75i	−0.232331	−	0.402410i
$627$		0			0
$628$	7742.18	−	13409.8i	0.491953	−	0.852088i
$629$	−8135.61			−0.515720
$630$		0			0
$631$	−4394.10			−0.277221			−0.138610	−	0.990347i	$-0.544264\pi$
$631$	−4394.10			−0.277221			−0.138610	+	0.990347i	$0.544264\pi$
$632$	3003.49	−	5202.20i	0.189039	−	0.327424i
$633$		0			0
$634$	−4101.20	−	7103.49i	−0.256908	−	0.444977i
$635$	−2169.01	−	3756.83i	−0.135550	−	0.234780i
$636$		0			0
$637$	−22004.3	+	38112.6i	−1.36867	+	2.37061i
$638$	8831.64			0.548037
$639$		0			0
$640$	−640.000			−0.0395285
$641$	5308.39	−	9194.41i	0.327097	−	0.566548i	−0.654838	−	0.755769i	$-0.727263\pi$
$641$	5308.39	−	9194.41i	0.327097	−	0.566548i	0.981934	+	0.189221i	$0.0605964\pi$
$642$		0			0
$643$	−10062.5	−	17428.8i	−0.617148	−	1.06893i	−0.990003	−	0.141043i	$-0.954954\pi$
$643$	−10062.5	−	17428.8i	−0.617148	−	1.06893i	0.372855	−	0.927890i	$-0.378379\pi$
$644$	−9759.76	−	16904.4i	−0.597187	−	1.03436i
$645$		0			0
$646$	−2012.83	+	3486.32i	−0.122591	+	0.212334i
$647$	−2621.86			−0.159314			−0.0796568	−	0.996822i	$-0.525382\pi$
$647$	−2621.86			−0.159314			−0.0796568	+	0.996822i	$0.525382\pi$
$648$		0			0
$649$	−29244.1			−1.76877
$650$	1677.72	−	2905.89i	0.101239	−	0.175352i
$651$		0			0
$652$	−2384.72	−	4130.46i	−0.143241	−	0.248100i
$653$	−14260.1	−	24699.2i	−0.854579	−	1.48017i	−0.877035	−	0.480426i	$-0.840482\pi$
$653$	−14260.1	−	24699.2i	−0.854579	−	1.48017i	0.0224567	−	0.999748i	$-0.492851\pi$
$654$		0			0
$655$	−1967.21	+	3407.30i	−0.117351	+	0.203258i
$656$	−2376.95			−0.141470
$657$		0			0
$658$	32426.0			1.92112
$659$	−3281.43	+	5683.60i	−0.193970	+	0.335966i	−0.946562	−	0.322521i	$-0.895470\pi$
$659$	−3281.43	+	5683.60i	−0.193970	+	0.335966i	0.752592	+	0.658487i	$0.228803\pi$
$660$		0			0
$661$	873.679	+	1513.26i	0.0514103	+	0.0890452i	0.890585	−	0.454816i	$-0.150295\pi$
$661$	873.679	+	1513.26i	0.0514103	+	0.0890452i	−0.839175	+	0.543861i	$0.816962\pi$
$662$	−5782.40	−	10015.4i	−0.339485	−	0.588006i
$663$		0			0
$664$	−4696.09	+	8133.86i	−0.274463	+	0.475384i
$665$	16331.7			0.952356
$666$		0			0
$667$	−12946.3			−0.751548
$668$	−1120.78	+	1941.25i	−0.0649165	+	0.112439i
$669$		0			0
$670$	−4771.81	−	8265.01i	−0.275151	−	0.476575i
$671$	674.695	+	1168.61i	0.0388172	+	0.0672333i
$672$		0			0
$673$	−1263.96	+	2189.24i	−0.0723954	+	0.125392i	−0.899951	−	0.435992i	$-0.856398\pi$
$673$	−1263.96	+	2189.24i	−0.0723954	+	0.125392i	0.827555	+	0.561384i	$0.189731\pi$
$674$	20660.4			1.18073
$675$		0			0
$676$	9226.32			0.524939
$677$	−3024.20	+	5238.07i	−0.171683	+	0.297364i	−0.939008	−	0.343894i	$-0.888254\pi$
$677$	−3024.20	+	5238.07i	−0.171683	+	0.297364i	0.767325	+	0.641258i	$0.221587\pi$
$678$		0			0
$679$	−13352.7	−	23127.5i	−0.754682	−	1.30715i
$680$	−389.502	−	674.638i	−0.0219658	−	0.0380459i
$681$		0			0
$682$	−6096.91	+	10560.2i	−0.342321	+	0.592917i
$683$	−23230.8			−1.30147			−0.650733	−	0.759307i	$-0.725538\pi$
$683$	−23230.8			−1.30147			−0.650733	+	0.759307i	$0.725538\pi$
$684$		0			0
$685$	416.309			0.0232210
$686$	9885.00	−	17121.3i	0.550162	−	0.952908i
$687$		0			0
$688$	3621.28	+	6272.23i	0.200668	+	0.347568i
$689$	−4682.48	−	8110.30i	−0.258909	−	0.448444i
$690$		0			0
$691$	11215.2	−	19425.2i	0.617431	−	1.06942i	−0.372522	−	0.928024i	$-0.621507\pi$
$691$	11215.2	−	19425.2i	0.617431	−	1.06942i	0.989953	−	0.141399i	$-0.0451599\pi$
$692$	−7477.59			−0.410774
$693$		0			0
$694$	8831.76			0.483068
$695$	−2273.65	+	3938.08i	−0.124093	+	0.214935i
$696$		0			0
$697$	−1446.61	−	2505.60i	−0.0786143	−	0.136164i
$698$	−5844.80	−	10123.5i	−0.316947	−	0.548969i
$699$		0			0
$700$	−1580.18	+	2736.94i	−0.0853214	+	0.147781i
$701$	16185.3			0.872054			0.436027	−	0.899934i	$-0.356385\pi$
$701$	16185.3			0.872054			0.436027	+	0.899934i	$0.356385\pi$
$702$		0			0
$703$	43175.4			2.31635
$704$	−1685.35	+	2919.11i	−0.0902257	+	0.156275i
$705$		0			0
$706$	−12631.6	−	21878.5i	−0.673365	−	1.16630i
$707$	23940.1	+	41465.5i	1.27349	+	2.20576i
$708$		0			0
$709$	−17703.7	+	30663.7i	−0.937765	+	1.62426i	−0.168138	+	0.985763i	$0.553775\pi$
$709$	−17703.7	+	30663.7i	−0.937765	+	1.62426i	−0.769627	+	0.638494i	$0.779558\pi$
$710$	495.295			0.0261804
$711$		0			0
$712$	8089.71			0.425807
$713$	8937.47	−	15480.1i	0.469440	−	0.813094i
$714$		0			0
$715$	−8836.05	−	15304.5i	−0.462167	−	0.800497i
$716$	−3401.32	−	5891.26i	−0.177532	−	0.307495i
$717$		0			0
$718$	12417.4	−	21507.6i	0.645423	−	1.11790i
$719$	5469.90			0.283718			0.141859	−	0.989887i	$-0.454692\pi$
$719$	5469.90			0.283718			0.141859	+	0.989887i	$0.454692\pi$
$720$		0			0
$721$	−1920.75			−0.0992131
$722$	3823.01	−	6621.65i	0.197061	−	0.341319i
$723$		0			0
$724$	1089.84	+	1887.66i	0.0559443	+	0.0968985i
$725$	1048.05	+	1815.28i	0.0536877	+	0.0929899i
$726$		0			0
$727$	2742.28	−	4749.77i	0.139898	−	0.242310i	−0.787560	−	0.616238i	$-0.788656\pi$
$727$	2742.28	−	4749.77i	0.139898	−	0.242310i	0.927458	+	0.373928i	$0.121989\pi$
$728$	−16967.0			−0.863788
$729$		0			0
$730$	3996.67			0.202635
$731$	−4407.80	+	7634.53i	−0.223021	+	0.386284i
$732$		0			0
$733$	3339.41	+	5784.03i	0.168273	+	0.291457i	0.937813	−	0.347142i	$-0.112848\pi$
$733$	3339.41	+	5784.03i	0.168273	+	0.291457i	−0.769540	+	0.638599i	$0.779514\pi$
$734$	−1602.99	−	2776.45i	−0.0806094	−	0.139620i
$735$		0			0
$736$	2470.55	−	4279.12i	0.123731	−	0.214308i
$737$	−50263.4			−2.51218
$738$		0			0
$739$	31170.0			1.55156			0.775782	−	0.631002i	$-0.217356\pi$
$739$	31170.0			1.55156			0.775782	+	0.631002i	$0.217356\pi$
$740$	−4177.44	+	7235.53i	−0.207521	+	0.359437i
$741$		0			0
$742$	4410.24	+	7638.77i	0.218201	+	0.377935i
$743$	−1407.51	−	2437.87i	−0.0694972	−	0.120373i	0.829183	−	0.558977i	$-0.188806\pi$
$743$	−1407.51	−	2437.87i	−0.0694972	−	0.120373i	−0.898680	+	0.438605i	$0.855473\pi$
$744$		0			0
$745$	−7793.23	+	13498.3i	−0.383251	+	0.663810i
$746$	6827.08			0.335063
$747$		0			0
$748$	−4102.79			−0.200552
$749$	−3523.52	+	6102.91i	−0.171891	+	0.297724i
$750$		0			0
$751$	3995.76	+	6920.87i	0.194151	+	0.336280i	0.946622	−	0.322346i	$-0.104471\pi$
$751$	3995.76	+	6920.87i	0.194151	+	0.336280i	−0.752471	+	0.658626i	$0.771138\pi$
$752$	4104.10	+	7108.52i	0.199018	+	0.344709i
$753$		0			0
$754$	−5626.66	+	9745.67i	−0.271765	+	0.470711i
$755$	−8571.18			−0.413162
$756$		0			0
$757$	−16253.4			−0.780371			−0.390185	−	0.920736i	$-0.627589\pi$
$757$	−16253.4			−0.780371			−0.390185	+	0.920736i	$0.627589\pi$
$758$	−3087.00	+	5346.84i	−0.147922	+	0.256208i
$759$		0			0
$760$	2067.08	+	3580.28i	0.0986589	+	0.170882i
$761$	−2768.92	−	4795.91i	−0.131897	−	0.228452i	0.792511	−	0.609858i	$-0.208773\pi$
$761$	−2768.92	−	4795.91i	−0.131897	−	0.228452i	−0.924408	+	0.381406i	$0.875440\pi$
$762$		0			0
$763$	6304.58	−	10919.8i	0.299136	−	0.518119i
$764$	8956.34			0.424122
$765$		0			0
$766$	22671.7			1.06940
$767$	18631.5	−	32270.7i	0.877111	−	1.51920i
$768$		0			0
$769$	−6966.69	−	12066.7i	−0.326691	−	0.565845i	0.655162	−	0.755488i	$-0.272600\pi$
$769$	−6966.69	−	12066.7i	−0.326691	−	0.565845i	−0.981853	+	0.189643i	$0.939267\pi$
$770$	8322.32	+	14414.7i	0.389501	+	0.674635i
$771$		0			0
$772$	1475.05	−	2554.86i	0.0687670	−	0.119108i
$773$	33075.0			1.53897			0.769486	−	0.638663i	$-0.220512\pi$
$773$	33075.0			1.53897			0.769486	+	0.638663i	$0.220512\pi$
$774$		0			0
$775$	−2894.08			−0.134140
$776$	3380.05	−	5854.42i	0.156362	−	0.270827i
$777$		0			0
$778$	10829.9	+	18757.9i	0.499061	+	0.864399i
$779$	7677.10	+	13297.1i	0.353095	+	0.611578i
$780$		0			0
$781$	1304.29	−	2259.09i	0.0597581	−	0.103504i
$782$	6014.28			0.275026
$783$		0			0
$784$	10492.5			0.477975
$785$	9677.72	−	16762.3i	0.440016	−	0.762131i
$786$		0			0
$787$	−17371.4	−	30088.2i	−0.786817	−	1.36281i	−0.927908	−	0.372810i	$-0.878394\pi$
$787$	−17371.4	−	30088.2i	−0.786817	−	1.36281i	0.141091	−	0.989997i	$-0.454939\pi$
$788$	2209.60	+	3827.13i	0.0998904	+	0.173015i
$789$		0			0
$790$	3754.36	−	6502.75i	0.169081	−	0.292857i
$791$	−249.319			−0.0112070
$792$		0			0
$793$	−1719.40			−0.0769959
$794$	3974.56	−	6884.14i	0.177647	−	0.307694i
$795$		0			0
$796$	−8009.14	−	13872.2i	−0.356629	−	0.617699i
$797$	13308.0	+	23050.1i	0.591459	+	1.02444i	0.994036	+	0.109052i	$0.0347814\pi$
$797$	13308.0	+	23050.1i	0.591459	+	1.02444i	−0.402577	+	0.915386i	$0.631885\pi$
$798$		0			0
$799$	−4995.49	+	8652.45i	−0.221186	+	0.383106i
$800$	−800.000			−0.0353553
$801$		0			0
$802$	26623.7			1.17221
$803$	10524.7	−	18229.2i	0.462524	−	0.801116i
$804$		0			0
$805$	−12199.7	−	21130.5i	−0.534140	−	0.925158i
$806$	−7768.72	−	13455.8i	−0.339506	−	0.588041i
$807$		0			0
$808$	−6060.12	+	10496.4i	−0.263854	+	0.457009i
$809$	15155.9			0.658656			0.329328	−	0.944216i	$-0.393178\pi$
$809$	15155.9			0.658656			0.329328	+	0.944216i	$0.393178\pi$
$810$		0			0
$811$	15130.7			0.655130			0.327565	−	0.944829i	$-0.393772\pi$
$811$	15130.7			0.655130			0.327565	+	0.944829i	$0.393772\pi$
$812$	5299.53	−	9179.05i	0.229036	−	0.396701i
$813$		0			0
$814$	22001.3	+	38107.4i	0.947354	+	1.64087i
$815$	−2980.91	−	5163.08i	−0.128118	−	0.221908i
$816$		0			0
$817$	23392.0	−	40516.2i	1.00169	−	1.73499i
$818$	−12842.8			−0.548948
$819$		0			0
$820$	−2971.19			−0.126535
$821$	10966.2	−	18994.0i	0.466165	−	0.807422i	−0.533088	−	0.846060i	$-0.678969\pi$
$821$	10966.2	−	18994.0i	0.466165	−	0.807422i	0.999253	+	0.0386378i	$0.0123019\pi$
$822$		0			0
$823$	1015.31	+	1758.57i	0.0430029	+	0.0744833i	0.886726	−	0.462296i	$-0.152974\pi$
$823$	1015.31	+	1758.57i	0.0430029	+	0.0744833i	−0.843723	+	0.536779i	$0.819641\pi$
$824$	−243.107	−	421.073i	−0.0102779	−	0.0178019i
$825$		0			0
$826$	−17548.3	+	30394.5i	−0.739203	+	1.28034i
$827$	30865.0			1.29780			0.648901	−	0.760873i	$-0.275229\pi$
$827$	30865.0			1.29780			0.648901	+	0.760873i	$0.275229\pi$
$828$		0			0
$829$	−22051.0			−0.923840			−0.461920	−	0.886921i	$-0.652839\pi$
$829$	−22051.0			−0.923840			−0.461920	+	0.886921i	$0.652839\pi$
$830$	−5870.11	+	10167.3i	−0.245487	+	0.425197i
$831$		0			0
$832$	−2147.48	−	3719.54i	−0.0894837	−	0.154990i
$833$	6385.71	+	11060.4i	0.265608	+	0.460047i
$834$		0			0
$835$	−1400.97	+	2426.56i	−0.0580631	+	0.100568i
$836$	21773.4			0.900775
$837$		0			0
$838$	−9253.72			−0.381461
$839$	−13100.6	+	22690.9i	−0.539074	+	0.933703i	0.459880	+	0.887981i	$0.347892\pi$
$839$	−13100.6	+	22690.9i	−0.539074	+	0.933703i	−0.998954	+	0.0457225i	$0.985441\pi$
$840$		0			0
$841$	8679.59	+	15033.5i	0.355881	+	0.616405i
$842$	5151.01	+	8921.81i	0.210826	+	0.365161i
$843$		0			0
$844$	3113.03	−	5391.93i	0.126961	−	0.219903i
$845$	11532.9			0.469519
$846$		0			0
$847$	45598.2			1.84979
$848$	−1116.39	+	1933.65i	−0.0452089	+	0.0783040i
$849$		0			0
$850$	−486.878	−	843.297i	−0.0196468	−	0.0340292i
$851$	−32251.8	−	55861.7i	−1.29915	−	2.25019i
$852$		0			0
$853$	4813.43	−	8337.11i	0.193211	−	0.334651i	−0.753102	−	0.657904i	$-0.771443\pi$
$853$	4813.43	−	8337.11i	0.193211	−	0.334651i	0.946313	+	0.323253i	$0.104777\pi$
$854$	1619.43			0.0648898
$855$		0			0
$856$	−1783.86			−0.0712280
$857$	10634.1	−	18418.8i	0.423867	−	0.734160i	−0.572447	−	0.819942i	$-0.694006\pi$
$857$	10634.1	−	18418.8i	0.423867	−	0.734160i	0.996314	+	0.0857822i	$0.0273389\pi$
$858$		0			0
$859$	12007.9	+	20798.3i	0.476954	+	0.826109i	0.999651	−	0.0264093i	$-0.00840731\pi$
$859$	12007.9	+	20798.3i	0.476954	+	0.826109i	−0.522697	+	0.852519i	$0.675074\pi$
$860$	4526.59	+	7840.29i	0.179483	+	0.310874i
$861$		0			0
$862$	2452.29	−	4247.49i	0.0968971	−	0.167831i
$863$	−38716.4			−1.52714			−0.763569	−	0.645726i	$-0.776555\pi$
$863$	−38716.4			−1.52714			−0.763569	+	0.645726i	$0.776555\pi$
$864$		0			0
$865$	−9346.99			−0.367407
$866$	11033.4	−	19110.5i	0.432946	−	0.749885i
$867$		0			0
$868$	7317.05	+	12673.5i	0.286125	+	0.495584i
$869$	−19773.1	−	34248.1i	−0.771873	−	1.33692i
$870$		0			0
$871$	32023.0	−	55465.4i	1.24576	−	2.15772i
$872$	3191.84			0.123956
$873$		0			0
$874$	−31917.6			−1.23527
$875$	−1975.22	+	3421.18i	−0.0763138	+	0.132179i
$876$		0			0
$877$	−22641.3	−	39216.0i	−0.871772	−	1.50995i	−0.860162	−	0.510021i	$-0.829638\pi$
$877$	−22641.3	−	39216.0i	−0.871772	−	1.50995i	−0.0116099	−	0.999933i	$-0.503696\pi$
$878$	−820.004	−	1420.29i	−0.0315191	−	0.0545927i
$879$		0			0
$880$	−2106.68	+	3648.88i	−0.0807003	+	0.139777i
$881$	−7095.59			−0.271347			−0.135673	−	0.990754i	$-0.543320\pi$
$881$	−7095.59			−0.271347			−0.135673	+	0.990754i	$0.543320\pi$
$882$		0			0
$883$	798.332			0.0304258			0.0152129	−	0.999884i	$-0.495157\pi$
$883$	798.332			0.0304258			0.0152129	+	0.999884i	$0.495157\pi$
$884$	2613.90	−	4527.41i	0.0994514	−	0.172255i
$885$		0			0
$886$	6706.40	+	11615.8i	0.254295	+	0.440453i
$887$	21005.5	+	36382.6i	0.795147	+	1.37724i	0.922746	+	0.385410i	$0.125940\pi$
$887$	21005.5	+	36382.6i	0.795147	+	1.37724i	−0.127598	+	0.991826i	$0.540727\pi$
$888$		0			0
$889$	−13709.7	+	23745.8i	−0.517218	+	0.895849i
$890$	10112.1			0.380853
$891$		0			0
$892$	−17214.1			−0.646156
$893$	26510.9	−	45918.3i	0.993454	−	1.72071i
$894$		0			0
$895$	−4251.65	−	7364.07i	−0.158790	−	0.275032i
$896$	2022.62	+	3503.29i	0.0754142	+	0.130621i
$897$		0			0
$898$	−9873.94	+	17102.2i	−0.366924	+	0.635531i
$899$	9706.05			0.360083
$900$		0			0
$901$	−2717.74			−0.100489
$902$	−7824.20	+	13551.9i	−0.288822	+	0.500254i
$903$		0			0
$904$	−31.5558	−	54.6563i	−0.00116099	−	0.00201089i
$905$	1362.30	+	2359.58i	0.0500381	+	0.0866686i
$906$		0			0
$907$	−5094.26	+	8823.51i	−0.186496	+	0.323021i	−0.944080	−	0.329717i	$-0.893047\pi$
$907$	−5094.26	+	8823.51i	−0.186496	+	0.323021i	0.757583	+	0.652738i	$0.226380\pi$
$908$	−9674.88			−0.353604
$909$		0			0
$910$	−21208.7			−0.772595
$911$	13329.3	−	23087.0i	0.484762	−	0.839633i	−0.515084	−	0.857140i	$-0.672239\pi$
$911$	13329.3	−	23087.0i	0.484762	−	0.839633i	0.999847	+	0.0175064i	$0.00557273\pi$
$912$		0			0
$913$	30916.2	+	53548.4i	1.12067	+	1.94106i
$914$	−13080.4	−	22656.0i	−0.473372	−	0.819904i
$915$		0			0
$916$	−403.619	+	699.089i	−0.0145589	+	0.0252168i
$917$	24868.3			0.895553
$918$		0			0
$919$	−6192.18			−0.222265			−0.111132	−	0.993806i	$-0.535448\pi$
$919$	−6192.18			−0.222265			−0.111132	+	0.993806i	$0.535448\pi$
$920$	3088.19	−	5348.90i	0.110668	−	0.191683i
$921$		0			0
$922$	9568.81	+	16573.7i	0.341792	+	0.592001i
$923$	1661.93	+	2878.55i	0.0592666	+	0.102653i
$924$		0			0
$925$	−5221.80	+	9044.41i	−0.185613	+	0.321490i
$926$	−641.250			−0.0227568
$927$		0			0
$928$	2683.01			0.0949074
$929$	4552.34	−	7884.88i	0.160772	−	0.278466i	−0.774374	−	0.632729i	$-0.781935\pi$
$929$	4552.34	−	7884.88i	0.160772	−	0.278466i	0.935146	+	0.354263i	$0.115268\pi$
$930$		0			0
$931$	−33888.8	−	58697.1i	−1.19297	−	2.06629i
$932$	−375.620	−	650.593i	−0.0132015	−	0.0228657i
$933$		0			0
$934$	4083.18	−	7072.27i	0.143047	−	0.247764i
$935$	−5128.49			−0.179379
$936$		0			0
$937$	−52517.5			−1.83103			−0.915513	−	0.402289i	$-0.868215\pi$
$937$	−52517.5			−1.83103			−0.915513	+	0.402289i	$0.868215\pi$
$938$	−30161.2	+	52240.7i	−1.04989	+	1.81846i
$939$		0			0
$940$	5130.13	+	8885.65i	0.178007	+	0.308317i
$941$	26558.0	+	45999.8i	0.920048	+	1.59357i	0.799338	+	0.600882i	$0.205184\pi$
$941$	26558.0	+	45999.8i	0.920048	+	1.59357i	0.120710	+	0.992688i	$0.461483\pi$
$942$		0			0
$943$	11469.5	−	19865.8i	0.396074	−	0.686021i
$944$	−8884.21			−0.306310
$945$		0			0
$946$	47680.5			1.63872
$947$	−27937.4	+	48388.9i	−0.958651	+	1.66043i	−0.232867	+	0.972509i	$0.574811\pi$
$947$	−27937.4	+	48388.9i	−0.958651	+	1.66043i	−0.725784	+	0.687923i	$0.758523\pi$
$948$		0			0
$949$	13410.6	+	23227.8i	0.458721	+	0.794528i
$950$	2583.85	+	4475.35i	0.0882432	+	0.152842i
$951$		0			0
$952$	−2461.93	+	4264.18i	−0.0838147	+	0.145171i
$953$	−26732.4			−0.908655			−0.454327	−	0.890835i	$-0.650120\pi$
$953$	−26732.4			−0.908655			−0.454327	+	0.890835i	$0.650120\pi$
$954$		0			0
$955$	11195.4			0.379346
$956$	−6825.78	+	11822.6i	−0.230922	+	0.399969i
$957$		0			0
$958$	−2572.80	−	4456.23i	−0.0867677	−	0.150286i
$959$	−1315.68	−	2278.83i	−0.0443020	−	0.0767334i
$960$		0			0
$961$	8194.94	−	14194.0i	0.275081	−	0.476454i
$962$	−56068.5			−1.87913
$963$		0			0
$964$	4658.69			0.155650
$965$	1843.81	−	3193.57i	0.0615071	−	0.106533i
$966$		0			0
$967$	2540.47	+	4400.23i	0.0844841	+	0.146331i	0.905171	−	0.425047i	$-0.139742\pi$
$967$	2540.47	+	4400.23i	0.0844841	+	0.146331i	−0.820687	+	0.571378i	$0.806409\pi$
$968$	5771.29	+	9996.16i	0.191628	+	0.331910i
$969$		0			0
$970$	4225.06	−	7318.02i	0.139854	−	0.242235i
$971$	4341.74			0.143495			0.0717473	−	0.997423i	$-0.477142\pi$
$971$	4341.74			0.143495			0.0717473	+	0.997423i	$0.477142\pi$
$972$		0			0
$973$	28742.1			0.946999
$974$	7204.59	−	12478.7i	0.237012	−	0.410517i
$975$		0			0
$976$	204.969	+	355.017i	0.00672223	+	0.0116432i
$977$	13212.2	+	22884.2i	0.432647	+	0.749366i	0.997100	−	0.0760985i	$-0.0242464\pi$
$977$	13212.2	+	22884.2i	0.432647	+	0.749366i	−0.564453	+	0.825465i	$0.690913\pi$
$978$		0			0
$979$	26628.8	−	46122.5i	0.869317	−	1.50570i
$980$	13115.6			0.427514
$981$		0			0
$982$	−3461.76			−0.112494
$983$	5221.57	−	9044.02i	0.169422	−	0.293448i	−0.768795	−	0.639496i	$-0.779143\pi$
$983$	5221.57	−	9044.02i	0.169422	−	0.293448i	0.938217	+	0.346048i	$0.112476\pi$
$984$		0			0
$985$	2762.00	+	4783.92i	0.0893447	+	0.154750i
$986$	1632.87	+	2828.22i	0.0527396	+	0.0913476i
$987$		0			0
$988$	−13871.9	+	24026.8i	−0.446684	+	0.773679i
$989$	−69894.9			−2.24725
$990$		0			0
$991$	−6631.49			−0.212569			−0.106285	−	0.994336i	$-0.533895\pi$
$991$	−6631.49			−0.212569			−0.106285	+	0.994336i	$0.533895\pi$
$992$	−1852.21	+	3208.13i	−0.0592820	+	0.102680i
$993$		0			0
$994$	−1565.31	−	2711.19i	−0.0499482	−	0.0865128i
$995$	−10011.4	−	17340.3i	−0.318978	−	0.552487i
$996$		0			0
$997$	−20120.0	+	34848.9i	−0.639125	+	1.10700i	0.346500	+	0.938050i	$0.387370\pi$
$997$	−20120.0	+	34848.9i	−0.639125	+	1.10700i	−0.985625	+	0.168947i	$0.945963\pi$
$998$	−38892.1			−1.23358
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.4.e.bh.541.1		8
3.2	odd	2		810.4.e.bg.541.1		8
9.2	odd	6		810.4.a.u.1.4	yes	4
9.4	even	3	inner	810.4.e.bh.271.1		8
9.5	odd	6		810.4.e.bg.271.1		8
9.7	even	3		810.4.a.t.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
810.4.a.t.1.4	✓	4	9.7	even	3
810.4.a.u.1.4	yes	4	9.2	odd	6
810.4.e.bg.271.1		8	9.5	odd	6
810.4.e.bg.541.1		8	3.2	odd	2
810.4.e.bh.271.1		8	9.4	even	3	inner
810.4.e.bh.541.1		8	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	810.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-15.8018 + 27.3694i) q^{7} -8.00000 q^{8} -10.0000 q^{10} +(-26.3335 + 45.6110i) q^{11} +(-33.5544 - 58.1179i) q^{13} +(31.6035 + 54.7389i) q^{14} +(-8.00000 + 13.8564i) q^{16} -19.4751 q^{17} +103.354 q^{19} +(-10.0000 + 17.3205i) q^{20} +(52.6671 + 91.2221i) q^{22} +(-77.2047 - 133.722i) q^{23} +(-12.5000 + 21.6506i) q^{25} -134.217 q^{26} +126.414 q^{28} +(41.9220 - 72.6110i) q^{29} +(57.8816 + 100.254i) q^{31} +(16.0000 + 27.7128i) q^{32} +(-19.4751 + 33.7319i) q^{34} +158.018 q^{35} +417.744 q^{37} +(103.354 - 179.014i) q^{38} +(20.0000 + 34.6410i) q^{40} +(74.2798 + 128.656i) q^{41} +(226.330 - 392.015i) q^{43} +210.668 q^{44} -308.819 q^{46} +(256.506 - 444.282i) q^{47} +(-327.891 - 567.924i) q^{49} +(25.0000 + 43.3013i) q^{50} +(-134.217 + 232.471i) q^{52} +139.549 q^{53} +263.335 q^{55} +(126.414 - 218.956i) q^{56} +(-83.8440 - 145.222i) q^{58} +(277.631 + 480.872i) q^{59} +(12.8106 - 22.1885i) q^{61} +231.526 q^{62} +64.0000 q^{64} +(-167.772 + 290.589i) q^{65} +(477.181 + 826.501i) q^{67} +(38.9502 + 67.4638i) q^{68} +(158.018 - 273.694i) q^{70} -49.5295 q^{71} -399.667 q^{73} +(417.744 - 723.553i) q^{74} +(-206.708 - 358.028i) q^{76} +(-832.232 - 1441.47i) q^{77} +(-375.436 + 650.275i) q^{79} +80.0000 q^{80} +297.119 q^{82} +(587.011 - 1016.73i) q^{83} +(48.6878 + 84.3297i) q^{85} +(-452.659 - 784.029i) q^{86} +(210.668 - 364.888i) q^{88} -1011.21 q^{89} +2120.87 q^{91} +(-308.819 + 534.890i) q^{92} +(-513.013 - 888.565i) q^{94} +(-258.385 - 447.535i) q^{95} +(-422.506 + 731.802i) q^{97} -1311.56 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 16 q^{4} - 20 q^{5} - 2 q^{7} - 64 q^{8} - 80 q^{10} - 36 q^{11} - 32 q^{13} + 4 q^{14} - 64 q^{16} - 180 q^{17} + 328 q^{19} - 80 q^{20} + 72 q^{22} + 42 q^{23} - 100 q^{25} - 128 q^{26}+ \cdots - 5352 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 - 16 * q^4 - 20 * q^5 - 2 * q^7 - 64 * q^8 - 80 * q^10 - 36 * q^11 - 32 * q^13 + 4 * q^14 - 64 * q^16 - 180 * q^17 + 328 * q^19 - 80 * q^20 + 72 * q^22 + 42 * q^23 - 100 * q^25 - 128 * q^26 + 16 * q^28 + 36 * q^29 - 446 * q^31 + 128 * q^32 - 180 * q^34 + 20 * q^35 + 1372 * q^37 + 328 * q^38 + 160 * q^40 + 108 * q^41 - 470 * q^43 + 288 * q^44 + 168 * q^46 + 804 * q^47 - 1338 * q^49 + 200 * q^50 - 128 * q^52 - 336 * q^53 + 360 * q^55 + 16 * q^56 - 72 * q^58 + 768 * q^59 - 596 * q^61 - 1784 * q^62 + 512 * q^64 - 160 * q^65 + 424 * q^67 + 360 * q^68 + 20 * q^70 - 696 * q^71 - 188 * q^73 + 1372 * q^74 - 656 * q^76 + 630 * q^77 - 1088 * q^79 + 640 * q^80 + 432 * q^82 + 522 * q^83 + 450 * q^85 + 940 * q^86 + 288 * q^88 - 2256 * q^89 + 5684 * q^91 + 168 * q^92 - 1608 * q^94 - 820 * q^95 - 2486 * q^97 - 5352 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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