LMFDB - Embedded newform 21.5.h.b.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,5,Mod(2,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("21.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	21.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17076922476$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 103 x^{14} + 7227 x^{12} - 270898 x^{10} + 7374256 x^{8} - 115494792 x^{6} + 1245573504 x^{4} + \cdots + 5639409216 $ x^16 - 103x^14 + 7227x^12 - 270898x^10 + 7374256x^8 - 115494792x^6 + 1245573504x^4 - 2908017504*x^2 + 5639409216
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.5
Root			$1.34450 - 0.776250i$ of defining polynomial
Character	$\chi$	$=$	21.11
Dual form			21.5.h.b.2.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34450 - 0.776250i) q^{2} +(8.38348 + 3.27372i) q^{3} +(-6.79487 + 11.7691i) q^{4} +(23.4142 - 13.5182i) q^{5} +(13.8128 - 2.10615i) q^{6} +(-27.0847 - 40.8340i) q^{7} +45.9381i q^{8} +(59.5656 + 54.8903i) q^{9} +O(q^{10})$	\(q+(1.34450 - 0.776250i) q^{2} +(8.38348 + 3.27372i) q^{3} +(-6.79487 + 11.7691i) q^{4} +(23.4142 - 13.5182i) q^{5} +(13.8128 - 2.10615i) q^{6} +(-27.0847 - 40.8340i) q^{7} +45.9381i q^{8} +(59.5656 + 54.8903i) q^{9} +(20.9870 - 36.3506i) q^{10} +(-130.154 - 75.1445i) q^{11} +(-95.4933 + 76.4213i) q^{12} -189.322 q^{13} +(-68.1129 - 33.8770i) q^{14} +(240.548 - 36.6782i) q^{15} +(-73.0586 - 126.541i) q^{16} +(136.932 + 79.0575i) q^{17} +(122.695 + 27.5624i) q^{18} +(67.5003 + 116.914i) q^{19} +367.418i q^{20} +(-93.3851 - 430.999i) q^{21} -233.323 q^{22} +(791.290 - 456.852i) q^{23} +(-150.388 + 385.121i) q^{24} +(52.9840 - 91.7711i) q^{25} +(-254.545 + 146.961i) q^{26} +(319.672 + 655.172i) q^{27} +(664.616 - 41.2996i) q^{28} +177.015i q^{29} +(294.946 - 236.039i) q^{30} +(-134.801 + 233.483i) q^{31} +(-832.991 - 480.928i) q^{32} +(-845.142 - 1056.06i) q^{33} +245.473 q^{34} +(-1186.17 - 589.961i) q^{35} +(-1050.75 + 328.059i) q^{36} +(205.859 + 356.558i) q^{37} +(181.509 + 104.794i) q^{38} +(-1587.18 - 619.788i) q^{39} +(621.000 + 1075.60i) q^{40} +1725.66i q^{41} +(-460.120 - 506.990i) q^{42} +811.064 q^{43} +(1768.76 - 1021.19i) q^{44} +(2136.70 + 479.994i) q^{45} +(709.262 - 1228.48i) q^{46} +(-211.453 + 122.082i) q^{47} +(-198.225 - 1300.03i) q^{48} +(-933.837 + 2211.96i) q^{49} -164.515i q^{50} +(889.152 + 1111.05i) q^{51} +(1286.42 - 2228.15i) q^{52} +(1865.65 + 1077.13i) q^{53} +(938.377 + 632.737i) q^{54} -4063.27 q^{55} +(1875.84 - 1244.22i) q^{56} +(183.145 + 1201.12i) q^{57} +(137.408 + 237.997i) q^{58} +(-1222.75 - 705.954i) q^{59} +(-1202.82 + 3080.24i) q^{60} +(-938.815 - 1626.08i) q^{61} +418.558i q^{62} +(628.076 - 3918.99i) q^{63} +844.594 q^{64} +(-4432.84 + 2559.30i) q^{65} +(-1956.06 - 763.835i) q^{66} +(1002.10 - 1735.69i) q^{67} +(-1860.87 + 1074.37i) q^{68} +(8129.37 - 1239.55i) q^{69} +(-2052.77 + 127.560i) q^{70} -5336.08i q^{71} +(-2521.55 + 2736.33i) q^{72} +(-2600.24 + 4503.75i) q^{73} +(553.556 + 319.596i) q^{74} +(744.623 - 595.906i) q^{75} -1834.62 q^{76} +(456.732 + 7349.98i) q^{77} +(-2615.08 + 398.742i) q^{78} +(-4936.13 - 8549.63i) q^{79} +(-3421.22 - 1975.24i) q^{80} +(535.114 + 6539.14i) q^{81} +(1339.54 + 2320.15i) q^{82} -9012.89i q^{83} +(5707.00 + 1829.53i) q^{84} +4274.86 q^{85} +(1090.48 - 629.588i) q^{86} +(-579.496 + 1484.00i) q^{87} +(3451.99 - 5979.02i) q^{88} +(11344.1 - 6549.50i) q^{89} +(3245.40 - 1013.26i) q^{90} +(5127.74 + 7730.80i) q^{91} +12417.0i q^{92} +(-1894.46 + 1516.10i) q^{93} +(-189.533 + 328.280i) q^{94} +(3160.94 + 1824.97i) q^{95} +(-5408.95 - 6758.83i) q^{96} -7271.60 q^{97} +(461.482 + 3698.87i) q^{98} +(-3628.00 - 11620.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 78 q^{4} + 28 q^{6} - 168 q^{7} + 62 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 78 * q^4 + 28 * q^6 - 168 * q^7 + 62 * q^9	$ 16 q + 8 q^{3} + 78 q^{4} + 28 q^{6} - 168 q^{7} + 62 q^{9} - 98 q^{10} + 436 q^{12} - 492 q^{13} - 856 q^{15} + 150 q^{16} - 884 q^{18} - 1326 q^{19} + 2170 q^{21} + 3244 q^{22} + 630 q^{24} + 2094 q^{25} + 1028 q^{27} - 854 q^{28} + 340 q^{30} - 2504 q^{31} - 616 q^{33} - 7728 q^{34} - 9644 q^{36} + 1342 q^{37} - 2626 q^{39} + 5754 q^{40} - 1582 q^{42} + 1460 q^{43} - 1330 q^{45} + 8844 q^{46} + 25864 q^{48} + 5572 q^{49} + 7794 q^{51} + 9536 q^{52} - 18578 q^{54} - 35140 q^{55} + 11696 q^{57} - 12446 q^{58} - 18890 q^{60} + 15012 q^{61} - 13076 q^{63} + 7660 q^{64} - 17192 q^{66} + 8658 q^{67} + 53676 q^{69} + 13790 q^{70} + 21312 q^{72} + 12322 q^{73} - 19514 q^{75} - 84520 q^{76} - 32120 q^{78} - 40168 q^{79} - 23986 q^{81} + 47348 q^{82} - 5992 q^{84} + 22536 q^{85} - 1162 q^{87} + 56430 q^{88} + 139636 q^{90} - 17878 q^{91} + 8556 q^{93} + 6468 q^{94} - 40894 q^{96} - 28268 q^{97} - 47812 q^{99}+O(q^{100}) $ 16 * q + 8 * q^3 + 78 * q^4 + 28 * q^6 - 168 * q^7 + 62 * q^9 - 98 * q^10 + 436 * q^12 - 492 * q^13 - 856 * q^15 + 150 * q^16 - 884 * q^18 - 1326 * q^19 + 2170 * q^21 + 3244 * q^22 + 630 * q^24 + 2094 * q^25 + 1028 * q^27 - 854 * q^28 + 340 * q^30 - 2504 * q^31 - 616 * q^33 - 7728 * q^34 - 9644 * q^36 + 1342 * q^37 - 2626 * q^39 + 5754 * q^40 - 1582 * q^42 + 1460 * q^43 - 1330 * q^45 + 8844 * q^46 + 25864 * q^48 + 5572 * q^49 + 7794 * q^51 + 9536 * q^52 - 18578 * q^54 - 35140 * q^55 + 11696 * q^57 - 12446 * q^58 - 18890 * q^60 + 15012 * q^61 - 13076 * q^63 + 7660 * q^64 - 17192 * q^66 + 8658 * q^67 + 53676 * q^69 + 13790 * q^70 + 21312 * q^72 + 12322 * q^73 - 19514 * q^75 - 84520 * q^76 - 32120 * q^78 - 40168 * q^79 - 23986 * q^81 + 47348 * q^82 - 5992 * q^84 + 22536 * q^85 - 1162 * q^87 + 56430 * q^88 + 139636 * q^90 - 17878 * q^91 + 8556 * q^93 + 6468 * q^94 - 40894 * q^96 - 28268 * q^97 - 47812 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.34450	−	0.776250i	0.336126	−	0.194062i	−0.322432	−	0.946593i	$-0.604500\pi$
$2$	1.34450	−	0.776250i	0.336126	−	0.194062i	0.658558	+	0.752530i	$0.271167\pi$
$3$	8.38348	+	3.27372i	0.931498	+	0.363746i
$3$	8.38348	+	3.27372i	0.931498	+	0.363746i
$4$	−6.79487	+	11.7691i	−0.424680	+	0.735567i
$5$	23.4142	−	13.5182i	0.936569	−	0.540728i	0.0476860	−	0.998862i	$-0.484815\pi$
$5$	23.4142	−	13.5182i	0.936569	−	0.540728i	0.888883	+	0.458134i	$0.151482\pi$
$6$	13.8128	−	2.10615i	0.383690	−	0.0585042i
$7$	−27.0847	−	40.8340i	−0.552749	−	0.833348i
$7$	−27.0847	−	40.8340i	−0.552749	−	0.833348i
$8$			45.9381i			0.717782i
$9$	59.5656	+	54.8903i	0.735377	+	0.677658i
$10$	20.9870	−	36.3506i	0.209870	−	0.363506i
$11$	−130.154	−	75.1445i	−1.07565	−	0.621029i	−0.145933	−	0.989295i	$-0.546618\pi$
$11$	−130.154	−	75.1445i	−1.07565	−	0.621029i	−0.929720	+	0.368266i	$0.879952\pi$
$12$	−95.4933	+	76.4213i	−0.663148	+	0.530703i
$13$	−189.322			−1.12025			−0.560126	−	0.828408i	$-0.689247\pi$
$13$	−189.322			−1.12025			−0.560126	+	0.828408i	$0.689247\pi$
$14$	−68.1129	−	33.8770i	−0.347515	−	0.172842i
$15$	240.548	−	36.6782i	1.06910	−	0.163014i
$16$	−73.0586	−	126.541i	−0.285385	−	0.494301i
$17$	136.932	+	79.0575i	0.473812	+	0.273555i	0.717834	−	0.696214i	$-0.245134\pi$
$17$	136.932	+	79.0575i	0.473812	+	0.273555i	−0.244022	+	0.969770i	$0.578467\pi$
$18$	122.695	+	27.5624i	0.378687	+	0.0850693i
$19$	67.5003	+	116.914i	0.186981	+	0.323861i	0.944242	−	0.329251i	$-0.106796\pi$
$19$	67.5003	+	116.914i	0.186981	+	0.323861i	−0.757261	+	0.653112i	$0.773463\pi$
$20$			367.418i			0.918545i
$21$	−93.3851	−	430.999i	−0.211758	−	0.977322i
$22$	−233.323			−0.482073
$23$	791.290	−	456.852i	1.49582	−	0.863614i	0.495835	−	0.868417i	$-0.334862\pi$
$23$	791.290	−	456.852i	1.49582	−	0.863614i	0.999988	+	0.00480324i	$0.00152892\pi$
$24$	−150.388	+	385.121i	−0.261091	+	0.668613i
$25$	52.9840	−	91.7711i	0.0847745	−	0.146834i
$26$	−254.545	+	146.961i	−0.376546	+	0.217399i
$27$	319.672	+	655.172i	0.438507	+	0.898728i
$28$	664.616	−	41.2996i	0.847724	−	0.0526781i
$29$			177.015i			0.210481i	0.994447	+	0.105241i	$0.0335613\pi$
$29$			177.015i			0.210481i	−0.994447	+	0.105241i	$0.966439\pi$
$30$	294.946	−	236.039i	0.327717	−	0.262265i
$31$	−134.801	+	233.483i	−0.140272	+	0.242958i	−0.927599	−	0.373577i	$-0.878131\pi$
$31$	−134.801	+	233.483i	−0.140272	+	0.242958i	0.787327	+	0.616536i	$0.211464\pi$
$32$	−832.991	−	480.928i	−0.813468	−	0.469656i
$33$	−845.142	−	1056.06i	−0.776072	−	0.969752i
$34$	245.473			0.212347
$35$	−1186.17	−	589.961i	−0.968303	−	0.481601i
$36$	−1050.75	+	328.059i	−0.810762	+	0.253132i
$37$	205.859	+	356.558i	0.150372	+	0.260451i	0.931364	−	0.364089i	$-0.118620\pi$
$37$	205.859	+	356.558i	0.150372	+	0.260451i	−0.780992	+	0.624540i	$0.785286\pi$
$38$	181.509	+	104.794i	0.125699	+	0.0725722i
$39$	−1587.18	−	619.788i	−1.04351	−	0.407487i
$40$	621.000	+	1075.60i	0.388125	+	0.672253i
$41$			1725.66i			1.02657i	0.858219	+	0.513283i	$0.171571\pi$
$41$			1725.66i			1.02657i	−0.858219	+	0.513283i	$0.828429\pi$
$42$	−460.120	−	506.990i	−0.260839	−	0.287409i
$43$	811.064			0.438650			0.219325	−	0.975652i	$-0.429615\pi$
$43$	811.064			0.438650			0.219325	+	0.975652i	$0.429615\pi$
$44$	1768.76	−	1021.19i	0.913616	−	0.527476i
$45$	2136.70	+	479.994i	1.05516	+	0.237034i
$46$	709.262	−	1228.48i	0.335190	−	0.580566i
$47$	−211.453	+	122.082i	−0.0957234	+	0.0552659i	−0.547098	−	0.837069i	$-0.684267\pi$
$47$	−211.453	+	122.082i	−0.0957234	+	0.0552659i	0.451374	+	0.892335i	$0.350934\pi$
$48$	−198.225	−	1300.03i	−0.0860354	−	0.564248i
$49$	−933.837	+	2211.96i	−0.388937	+	0.921264i
$50$		−	164.515i		−	0.0658062i
$51$	889.152	+	1111.05i	0.341850	+	0.427163i
$52$	1286.42	−	2228.15i	0.475748	−	0.824019i
$53$	1865.65	+	1077.13i	0.664168	+	0.383458i	0.793863	−	0.608096i	$-0.208067\pi$
$53$	1865.65	+	1077.13i	0.664168	+	0.383458i	−0.129695	+	0.991554i	$0.541400\pi$
$54$	938.377	+	632.737i	0.321803	+	0.216988i
$55$	−4063.27			−1.34323
$56$	1875.84	−	1244.22i	0.598162	−	0.396753i
$57$	183.145	+	1201.12i	0.0563695	+	0.369690i
$58$	137.408	+	237.997i	0.0408465	+	0.0707482i
$59$	−1222.75	−	705.954i	−0.351263	−	0.202802i	0.313978	−	0.949430i	$-0.398338\pi$
$59$	−1222.75	−	705.954i	−0.351263	−	0.202802i	−0.665242	+	0.746628i	$0.731671\pi$
$60$	−1202.82	+	3080.24i	−0.334117	+	0.855623i
$61$	−938.815	−	1626.08i	−0.252302	−	0.437000i	0.711857	−	0.702324i	$-0.247854\pi$
$61$	−938.815	−	1626.08i	−0.252302	−	0.437000i	−0.964159	+	0.265324i	$0.914521\pi$
$62$			418.558i			0.108886i
$63$	628.076	−	3918.99i	0.158245	−	0.987400i
$64$	844.594			0.206200
$65$	−4432.84	+	2559.30i	−1.04919	+	0.605752i
$66$	−1956.06	−	763.835i	−0.449050	−	0.175352i
$67$	1002.10	−	1735.69i	0.223235	−	0.386655i	−0.732553	−	0.680710i	$-0.761672\pi$
$67$	1002.10	−	1735.69i	0.223235	−	0.386655i	0.955788	+	0.294055i	$0.0950049\pi$
$68$	−1860.87	+	1074.37i	−0.402436	+	0.232347i
$69$	8129.37	−	1239.55i	1.70749	−	0.260355i
$70$	−2052.77	+	127.560i	−0.418932	+	0.0260327i
$71$		−	5336.08i		−	1.05854i	−0.848455	−	0.529268i	$-0.822467\pi$
$71$		−	5336.08i		−	1.05854i	0.848455	−	0.529268i	$-0.177533\pi$
$72$	−2521.55	+	2736.33i	−0.486411	+	0.527841i
$73$	−2600.24	+	4503.75i	−0.487942	+	0.845140i	−0.999904	−	0.0138681i	$-0.995586\pi$
$73$	−2600.24	+	4503.75i	−0.487942	+	0.845140i	0.511962	+	0.859008i	$0.328919\pi$
$74$	553.556	+	319.596i	0.101088	+	0.0583630i
$75$	744.623	−	595.906i	0.132377	−	0.105939i
$76$	−1834.62			−0.317629
$77$	456.732	+	7349.98i	0.0770336	+	1.23967i
$78$	−2615.08	+	398.742i	−0.429829	+	0.0655394i
$79$	−4936.13	−	8549.63i	−0.790920	−	1.36991i	−0.925398	−	0.378997i	$-0.876269\pi$
$79$	−4936.13	−	8549.63i	−0.790920	−	1.36991i	0.134478	−	0.990917i	$-0.457064\pi$
$80$	−3421.22	−	1975.24i	−0.534566	−	0.308632i
$81$	535.114	+	6539.14i	0.0815598	+	0.996668i
$82$	1339.54	+	2320.15i	0.199218	+	0.345056i
$83$		−	9012.89i		−	1.30830i	−0.756364	−	0.654151i	$-0.773026\pi$
$83$		−	9012.89i		−	1.30830i	0.756364	−	0.654151i	$-0.226974\pi$
$84$	5707.00	+	1829.53i	0.808815	+	0.259287i
$85$	4274.86			0.591676
$86$	1090.48	−	629.588i	0.147442	−	0.0851255i
$87$	−579.496	+	1484.00i	−0.0765618	+	0.196063i
$88$	3451.99	−	5979.02i	0.445763	−	0.772085i
$89$	11344.1	−	6549.50i	1.43215	−	0.826853i	0.434866	−	0.900495i	$-0.356796\pi$
$89$	11344.1	−	6549.50i	1.43215	−	0.826853i	0.997285	+	0.0736421i	$0.0234623\pi$
$90$	3245.40	−	1013.26i	0.400666	−	0.125094i
$91$	5127.74	+	7730.80i	0.619218	+	0.933559i
$92$			12417.0i			1.46704i
$93$	−1894.46	+	1516.10i	−0.219038	+	0.175292i
$94$	−189.533	+	328.280i	−0.0214501	+	0.0371526i
$95$	3160.94	+	1824.97i	0.350242	+	0.202212i
$96$	−5408.95	−	6758.83i	−0.586908	−	0.733380i
$97$	−7271.60			−0.772835			−0.386417	−	0.922324i	$-0.626288\pi$
$97$	−7271.60			−0.772835			−0.386417	+	0.922324i	$0.626288\pi$
$98$	461.482	+	3698.87i	0.0480511	+	0.385139i
$99$	−3628.00	−	11620.2i	−0.370166	−	1.18561i
$100$	720.040	+	1247.15i	0.0720040	+	0.124715i
$101$	3261.86	+	1883.24i	0.319759	+	0.184613i	0.651285	−	0.758833i	$-0.274230\pi$
$101$	3261.86	+	1883.24i	0.319759	+	0.184613i	−0.331526	+	0.943446i	$0.607563\pi$
$102$	2057.92	+	803.610i	0.197801	+	0.0772405i
$103$	9164.79	+	15873.9i	0.863869	+	1.49627i	0.868166	+	0.496274i	$0.165299\pi$
$103$	9164.79	+	15873.9i	0.863869	+	1.49627i	−0.00429677	+	0.999991i	$0.501368\pi$
$104$		−	8697.11i		−	0.804096i
$105$	−8012.88	−	8829.11i	−0.726792	−	0.800826i
$106$	3344.49			0.297659
$107$	−16425.5	+	9483.24i	−1.43466	+	0.828303i	−0.997472	−	0.0710650i	$-0.977360\pi$
$107$	−16425.5	+	9483.24i	−1.43466	+	0.828303i	−0.437192	+	0.899368i	$0.644027\pi$
$108$	−9882.90	−	689.576i	−0.847299	−	0.0591200i
$109$	1392.76	−	2412.34i	0.117226	−	0.203042i	−0.801441	−	0.598073i	$-0.795933\pi$
$109$	1392.76	−	2412.34i	0.117226	−	0.203042i	0.918667	+	0.395032i	$0.129266\pi$
$110$	−5463.09	+	3154.12i	−0.451495	+	0.260671i
$111$	558.545	+	3663.12i	0.0453327	+	0.297307i
$112$	−3188.42	+	6410.61i	−0.254179	+	0.511050i
$113$		−	9331.38i		−	0.730784i	−0.930854	−	0.365392i	$-0.880935\pi$
$113$		−	9331.38i		−	0.730784i	0.930854	−	0.365392i	$-0.119065\pi$
$114$	1178.61	+	1472.75i	0.0906902	+	0.113323i
$115$	12351.6	−	21393.7i	0.933961	−	1.61767i
$116$	−2083.30	−	1202.79i	−0.154823	−	0.0893871i
$117$	−11277.1	−	10392.0i	−0.823807	−	0.759147i
$118$	−2191.98			−0.157425
$119$	−480.516	−	7732.72i	−0.0339323	−	0.546057i
$120$	1684.92	+	11050.3i	0.117009	+	0.767381i
$121$	3972.88	+	6881.23i	0.271353	+	0.469997i
$122$	−2524.48	−	1457.51i	−0.169610	−	0.0979246i
$123$	−5649.32	+	14467.0i	−0.373410	+	0.956245i
$124$	−1831.92	−	3172.98i	−0.119141	−	0.206359i
$125$			14032.8i			0.898097i
$126$	−2197.66	−	5756.64i	−0.138427	−	0.362600i
$127$	−6294.79			−0.390278			−0.195139	−	0.980776i	$-0.562516\pi$
$127$	−6294.79			−0.390278			−0.195139	+	0.980776i	$0.562516\pi$
$128$	14463.4	−	8350.46i	0.882777	−	0.509672i
$129$	6799.54	+	2655.19i	0.408602	+	0.159557i
$130$	−3973.31	+	6881.98i	−0.235107	+	0.407218i
$131$	−8388.93	+	4843.35i	−0.488837	+	0.282230i	−0.724092	−	0.689704i	$-0.757741\pi$
$131$	−8388.93	+	4843.35i	−0.488837	+	0.282230i	0.235255	+	0.971934i	$0.424407\pi$
$132$	18171.5	−	2770.75i	1.04290	−	0.159019i
$133$	2945.84	−	5922.89i	0.166535	−	0.334835i
$134$		−	3111.53i		−	0.173286i
$135$	16341.6	+	11019.0i	0.896660	+	0.604607i
$136$	−3631.75	+	6290.37i	−0.196353	+	0.340094i
$137$	−5175.49	−	2988.07i	−0.275747	−	0.159203i	0.355749	−	0.934581i	$-0.384226\pi$
$137$	−5175.49	−	2988.07i	−0.275747	−	0.159203i	−0.631496	+	0.775379i	$0.717559\pi$
$138$	9967.77	−	7977.00i	0.523408	−	0.418872i
$139$	−12834.8			−0.664295			−0.332147	−	0.943227i	$-0.607773\pi$
$139$	−12834.8			−0.664295			−0.332147	+	0.943227i	$0.607773\pi$
$140$	15003.2	−	9951.41i	0.765468	−	0.507725i
$141$	−2172.37	+	331.239i	−0.109269	+	0.0166611i
$142$	−4142.13	−	7174.38i	−0.205422	−	0.355801i
$143$	24641.1	+	14226.5i	1.20500	+	0.695708i
$144$	2594.10	−	11547.7i	0.125101	−	0.556891i
$145$	2392.92	+	4144.66i	0.113813	+	0.197130i
$146$			8073.75i			0.378765i
$147$	−15070.1	+	15486.8i	−0.697400	+	0.716682i
$148$	−5595.14			−0.255439
$149$	12863.0	−	7426.43i	0.579386	−	0.334509i	−0.181503	−	0.983390i	$-0.558096\pi$
$149$	12863.0	−	7426.43i	0.579386	−	0.334509i	0.760890	+	0.648881i	$0.224763\pi$
$150$	538.577	−	1379.21i	0.0239367	−	0.0612983i
$151$	16528.1	−	28627.5i	0.724885	−	1.25554i	−0.234136	−	0.972204i	$-0.575226\pi$
$151$	16528.1	−	28627.5i	0.724885	−	1.25554i	0.959021	−	0.283334i	$-0.0914405\pi$
$152$	−5370.80	+	3100.83i	−0.232462	+	0.134212i
$153$	3816.92	+	12225.3i	0.163054	+	0.522249i
$154$	6319.50	+	9527.54i	0.266466	+	0.401735i
$155$			7289.10i			0.303396i
$156$	18079.0	−	14468.3i	0.742892	−	0.594521i
$157$	−15205.4	+	26336.6i	−0.616878	+	1.06846i	0.373174	+	0.927762i	$0.378270\pi$
$157$	−15205.4	+	26336.6i	−0.616878	+	1.06846i	−0.990052	+	0.140703i	$0.955064\pi$
$158$	−13273.3	−	7663.34i	−0.531698	−	0.306976i
$159$	12114.4	+	15137.7i	0.479190	+	0.598779i
$160$	−26005.1			−1.01583
$161$	−40087.0	−	19937.9i	−1.54651	−	0.769179i
$162$	5795.47	+	8376.52i	0.220830	+	0.319178i
$163$	−17596.1	−	30477.4i	−0.662281	−	1.14710i	−0.980015	−	0.198924i	$-0.936255\pi$
$163$	−17596.1	−	30477.4i	−0.662281	−	1.14710i	0.317734	−	0.948180i	$-0.397078\pi$
$164$	−20309.4	−	11725.6i	−0.755108	−	0.435962i
$165$	−34064.4	−	13302.0i	−1.25122	−	0.488595i
$166$	−6996.25	−	12117.9i	−0.253892	−	0.439754i
$167$			22533.6i			0.807975i	0.914764	+	0.403988i	$0.132376\pi$
$167$			22533.6i			0.807975i	−0.914764	+	0.403988i	$0.867624\pi$
$168$	19799.3	−	4289.93i	0.701504	−	0.151996i
$169$	7281.99			0.254963
$170$	5747.57	−	3318.36i	0.198878	−	0.114822i
$171$	−2396.75	+	10669.2i	−0.0819653	+	0.364870i
$172$	−5511.08	+	9545.46i	−0.186286	+	0.322656i
$173$	98.1196	−	56.6494i	0.00327841	−	0.00189279i	−0.498360	−	0.866970i	$-0.666064\pi$
$173$	98.1196	−	56.6494i	0.00327841	−	0.00189279i	0.501638	+	0.865077i	$0.332731\pi$
$174$	372.820	+	2445.08i	0.0123140	+	0.0807596i
$175$	−5182.44	+	322.040i	−0.169223	+	0.0105156i
$176$			21959.8i			0.708929i
$177$	−7939.79	−	9921.28i	−0.253433	−	0.316680i
$178$	10168.1	−	17611.7i	0.320922	−	0.555853i
$179$	8131.13	+	4694.51i	0.253773	+	0.146516i	0.621490	−	0.783422i	$-0.286527\pi$
$179$	8131.13	+	4694.51i	0.253773	+	0.146516i	−0.367718	+	0.929937i	$0.619861\pi$
$180$	−20167.7	+	21885.5i	−0.622459	+	0.675477i
$181$	51233.0			1.56384			0.781921	−	0.623377i	$-0.214240\pi$
$181$	51233.0			1.56384			0.781921	+	0.623377i	$0.214240\pi$
$182$	12895.3	+	6413.68i	0.389304	+	0.193626i
$183$	−2547.23	−	16705.6i	−0.0760618	−	0.498838i
$184$	20986.9	+	36350.3i	0.619887	+	1.07368i
$185$	9640.05	+	5565.69i	0.281667	+	0.162620i
$186$	−1370.24	+	3508.98i	−0.0396069	+	0.101427i
$187$	−11881.5	−	20579.3i	−0.339771	−	0.588501i
$188$		−	3318.14i		−	0.0938812i
$189$	18095.1	−	30798.6i	0.506568	−	0.862200i
$190$	5666.52			0.156967
$191$	26381.4	−	15231.3i	0.723155	−	0.417514i	−0.0927578	−	0.995689i	$-0.529568\pi$
$191$	26381.4	−	15231.3i	0.723155	−	0.417514i	0.815913	+	0.578175i	$0.196235\pi$
$192$	7080.64	+	2764.96i	0.192075	+	0.0750043i
$193$	−8998.44	+	15585.8i	−0.241575	+	0.418421i	−0.961163	−	0.275981i	$-0.910997\pi$
$193$	−8998.44	+	15585.8i	−0.241575	+	0.418421i	0.719588	+	0.694402i	$0.244331\pi$
$194$	−9776.70	+	5644.58i	−0.259770	+	0.149978i
$195$	−45541.1	+	6944.00i	−1.19766	+	0.182617i
$196$	−19687.3	−	26020.4i	−0.512478	−	0.677331i
$197$		−	26557.8i		−	0.684321i	−0.939642	−	0.342160i	$-0.888841\pi$
$197$		−	26557.8i		−	0.684321i	0.939642	−	0.342160i	$-0.111159\pi$
$198$	−13898.0	−	12807.2i	−0.354506	−	0.326681i
$199$	−17871.8	+	30954.9i	−0.451297	+	0.781669i	−0.998467	−	0.0553522i	$-0.982372\pi$
$199$	−17871.8	+	30954.9i	−0.451297	+	0.781669i	0.547170	+	0.837022i	$0.315705\pi$
$200$	4215.78	+	2433.98i	0.105395	+	0.0608496i
$201$	14083.3	−	11270.5i	0.348587	−	0.278967i
$202$	5847.45			0.143306
$203$	7228.23	−	4794.39i	0.175404	−	0.116343i
$204$	−19117.7	+	2915.03i	−0.459384	+	0.0700458i
$205$	23327.8	+	40405.0i	0.555094	+	0.961451i
$206$	24644.2	+	14228.3i	0.580738	+	0.335289i
$207$	72210.4	+	16221.5i	1.68523	+	0.378574i
$208$	13831.6	+	23957.1i	0.319703	+	0.553742i
$209$		−	20289.1i		−	0.464483i
$210$	−17626.9	−	5650.78i	−0.399704	−	0.128136i
$211$	37798.3			0.848999			0.424499	−	0.905428i	$-0.360450\pi$
$211$	37798.3			0.848999			0.424499	+	0.905428i	$0.360450\pi$
$212$	−25353.7	+	14638.0i	−0.564117	+	0.325693i
$213$	17468.8	−	44734.9i	0.385038	−	0.986024i
$214$	−14722.7	+	25500.5i	−0.321485	+	0.556829i
$215$	18990.4	−	10964.1i	0.410826	−	0.237191i
$216$	−30097.4	+	14685.1i	−0.645091	+	0.314753i
$217$	13185.1	−	819.331i	0.280004	−	0.0173996i
$218$		−	4324.53i		−	0.0909968i
$219$	−36543.1	+	29244.7i	−0.761933	+	0.609759i
$220$	27609.4	−	47820.9i	0.570443	−	0.988036i
$221$	−25924.2	−	14967.4i	−0.530788	−	0.306451i
$222$	3594.46	+	4491.51i	0.0729336	+	0.0911353i
$223$	19785.6			0.397868			0.198934	−	0.980013i	$-0.436252\pi$
$223$	19785.6			0.397868			0.198934	+	0.980013i	$0.436252\pi$
$224$	2923.10	+	47040.2i	0.0582570	+	0.937504i
$225$	8193.36	−	2558.09i	0.161844	−	0.0505301i
$226$	−7243.48	−	12546.1i	−0.141818	−	0.245636i
$227$	−54163.5	−	31271.3i	−1.05113	−	0.606868i	−0.128162	−	0.991753i	$-0.540908\pi$
$227$	−54163.5	−	31271.3i	−1.05113	−	0.606868i	−0.922965	+	0.384885i	$0.874241\pi$
$228$	−15380.5	−	6006.04i	−0.295871	−	0.115536i
$229$	−18665.5	−	32329.5i	−0.355933	−	0.616494i	0.631344	−	0.775503i	$-0.282503\pi$
$229$	−18665.5	−	32329.5i	−0.355933	−	0.616494i	−0.987277	+	0.159009i	$0.949170\pi$
$230$		−	38351.8i		−	0.724987i
$231$	−20232.7	+	63113.6i	−0.379167	+	1.18277i
$232$	−8131.72			−0.151080
$233$	−48791.5	+	28169.8i	−0.898736	+	0.518885i	−0.876790	−	0.480874i	$-0.840320\pi$
$233$	−48791.5	+	28169.8i	−0.898736	+	0.518885i	−0.0219459	+	0.999759i	$0.506986\pi$
$234$	−23228.9	−	5218.19i	−0.424225	−	0.0952989i
$235$	−3300.67	+	5716.93i	−0.0597677	+	0.103521i
$236$	16616.8	−	9593.73i	0.298349	−	0.172252i
$237$	−13392.9	−	87835.2i	−0.238440	−	1.56377i
$238$	−6648.57	−	10023.7i	−0.117375	−	0.176959i
$239$			33343.9i			0.583742i	0.956458	+	0.291871i	$0.0942778\pi$
$239$			33343.9i			0.583742i	−0.956458	+	0.291871i	$0.905722\pi$
$240$	−22215.4	−	27759.5i	−0.385683	−	0.481936i
$241$	−11384.0	+	19717.6i	−0.196002	+	0.339485i	−0.947228	−	0.320559i	$-0.896129\pi$
$241$	−11384.0	+	19717.6i	−0.196002	+	0.339485i	0.751227	+	0.660044i	$0.229463\pi$
$242$	10683.1	+	6167.89i	0.182418	+	0.105319i
$243$	−16921.2	+	56572.6i	−0.286562	+	0.958062i
$244$	25516.5			0.428590
$245$	8036.61	+	64415.0i	0.133888	+	1.07314i
$246$	3634.50	+	23836.3i	0.0600585	+	0.393883i
$247$	−12779.3	−	22134.4i	−0.209466	−	0.362806i
$248$	−10725.8	−	6192.52i	−0.174391	−	0.100685i
$249$	29505.6	−	75559.4i	0.475890	−	1.21868i
$250$	10892.9	+	18867.1i	0.174287	+	0.301874i
$251$			7754.35i			0.123083i	0.998105	+	0.0615415i	$0.0196016\pi$
$251$			7754.35i			0.123083i	−0.998105	+	0.0615415i	$0.980398\pi$
$252$	41855.2	+	34020.9i	0.659095	+	0.535728i
$253$	−137319.			−2.14532
$254$	−8463.38	+	4886.33i	−0.131183	+	0.0757383i
$255$	35838.2	+	13994.7i	0.551146	+	0.215220i
$256$	6207.34	−	10751.4i	0.0947165	−	0.164054i
$257$	67989.8	−	39253.9i	1.02938	−	0.594315i	0.112576	−	0.993643i	$-0.464090\pi$
$257$	67989.8	−	39253.9i	1.02938	−	0.594315i	0.916808	+	0.399328i	$0.130757\pi$
$258$	11203.1	−	1708.22i	0.168306	−	0.0256629i
$259$	8984.07	−	18063.3i	0.133929	−	0.269276i
$260$		−	69560.5i		−	1.02900i
$261$	−9716.39	+	10544.0i	−0.142634	+	0.154783i
$262$	−7519.30	+	13023.8i	−0.109541	+	0.189730i
$263$	78978.6	+	45598.3i	1.14182	+	0.659231i	0.946881	−	0.321584i	$-0.104215\pi$
$263$	78978.6	+	45598.3i	1.14182	+	0.659231i	0.194940	+	0.980815i	$0.437549\pi$
$264$	48513.3	−	38824.2i	0.696070	−	0.557051i
$265$	58243.6			0.829386
$266$	−636.945	−	10250.1i	−0.00900199	−	0.144865i
$267$	116544.	−	17770.4i	1.63481	−	0.249272i
$268$	13618.3	+	23587.6i	0.189607	+	0.328409i
$269$	−32588.6	−	18815.1i	−0.450362	−	0.260017i	0.257621	−	0.966246i	$-0.417061\pi$
$269$	−32588.6	−	18815.1i	−0.450362	−	0.260017i	−0.707983	+	0.706229i	$0.750395\pi$
$270$	30524.9	+	2129.86i	0.418722	+	0.0292162i
$271$	−38788.5	−	67183.6i	−0.528158	−	0.914797i	−0.999461	−	0.0328253i	$-0.989549\pi$
$271$	−38788.5	−	67183.6i	−0.528158	−	0.914797i	0.471303	−	0.881971i	$-0.343784\pi$
$272$		−	23103.3i		−	0.312274i
$273$	17679.9	+	81597.8i	0.237222	+	1.09485i
$274$	−9277.96			−0.123581
$275$	−13792.2	+	7962.92i	−0.182376	+	0.105295i
$276$	−40649.7	+	104098.i	−0.533629	+	1.36654i
$277$	−73193.1	+	126774.i	−0.953917	+	1.65223i	−0.217089	+	0.976152i	$0.569656\pi$
$277$	−73193.1	+	126774.i	−0.953917	+	1.65223i	−0.736828	+	0.676080i	$0.763677\pi$
$278$	−17256.5	+	9963.04i	−0.223287	+	0.128915i
$279$	−20845.5	+	6508.26i	−0.267796	+	0.0836096i
$280$	27101.6	−	54490.4i	0.345684	−	0.695030i
$281$			25825.2i			0.327062i	0.986538	+	0.163531i	$0.0522884\pi$
$281$			25825.2i			0.327062i	−0.986538	+	0.163531i	$0.947712\pi$
$282$	−2663.64	+	2131.66i	−0.0334948	+	0.0268052i
$283$	−1511.18	+	2617.45i	−0.0188688	+	0.0326817i	−0.875306	−	0.483570i	$-0.839340\pi$
$283$	−1511.18	+	2617.45i	−0.0188688	+	0.0326817i	0.856437	+	0.516252i	$0.172673\pi$
$284$	62800.6	+	36258.0i	0.778623	+	0.449538i
$285$	20525.2	+	25647.6i	0.252696	+	0.315760i
$286$	44173.4			0.540043
$287$	70465.6	−	46739.0i	0.855487	−	0.567434i
$288$	−23219.3	−	74369.9i	−0.279940	−	0.896628i
$289$	−29260.3	−	50680.4i	−0.350335	−	0.606798i
$290$	6434.59	+	3715.01i	0.0765112	+	0.0441737i
$291$	−60961.3	−	23805.2i	−0.719894	−	0.281116i
$292$	−35336.6	−	61204.8i	−0.414438	−	0.717827i
$293$			6471.42i			0.0753814i	0.999289	+	0.0376907i	$0.0120002\pi$
$293$			6471.42i			0.0753814i	−0.999289	+	0.0376907i	$0.988000\pi$
$294$	−8240.23	+	32520.2i	−0.0953334	+	0.376235i
$295$	−38172.9			−0.438643
$296$	−16379.6	+	9456.76i	−0.186947	+	0.107934i
$297$	7626.02	−	109295.i	0.0864540	−	1.23904i
$298$	11529.5	−	19969.7i	0.129831	−	0.224874i
$299$	−149809.	+	86492.3i	−1.67570	+	0.967464i
$300$	1953.64	+	12812.6i	0.0217071	+	0.142363i
$301$	−21967.4	−	33119.0i	−0.242463	−	0.365548i
$302$		−	51319.7i		−	0.562692i
$303$	21180.6	+	26466.5i	0.230703	+	0.288278i
$304$	9862.95	−	17083.1i	0.106723	−	0.184850i
$305$	−43963.3	−	25382.2i	−0.472596	−	0.272854i
$306$	14621.8	+	13474.1i	0.156155	+	0.143899i
$307$	−2922.17			−0.0310048			−0.0155024	−	0.999880i	$-0.504935\pi$
$307$	−2922.17			−0.0310048			−0.0155024	+	0.999880i	$0.504935\pi$
$308$	−89605.8	−	44566.9i	−0.944571	−	0.469797i
$309$	24866.3	+	163081.i	0.260432	+	1.70800i
$310$	5658.16	+	9800.22i	0.0588779	+	0.101979i
$311$	−48400.9	−	27944.3i	−0.500418	−	0.288916i	0.228468	−	0.973551i	$-0.426628\pi$
$311$	−48400.9	−	27944.3i	−0.500418	−	0.288916i	−0.728886	+	0.684635i	$0.759962\pi$
$312$	28471.9	−	72912.0i	0.292487	−	0.749014i
$313$	71971.2	+	124658.i	0.734633	+	1.27242i	0.954884	+	0.296978i	$0.0959789\pi$
$313$	71971.2	+	124658.i	0.734633	+	1.27242i	−0.220251	+	0.975443i	$0.570688\pi$
$314$			47212.9i			0.478852i
$315$	−38271.8	−	100251.i	−0.385707	−	1.01034i
$316$	134162.			1.34355
$317$	60342.6	−	34838.8i	0.600490	−	0.346693i	−0.168744	−	0.985660i	$-0.553971\pi$
$317$	60342.6	−	34838.8i	0.600490	−	0.346693i	0.769234	+	0.638967i	$0.220638\pi$
$318$	28038.5	+	10948.9i	0.277269	+	0.108272i
$319$	13301.7	−	23039.2i	0.130715	−	0.226405i
$320$	19775.5	−	11417.4i	0.193120	−	0.111498i
$321$	−168748.	+	25730.3i	−1.63768	+	0.249710i
$322$	−69373.9	+	4310.93i	−0.669089	+	0.0415776i
$323$			21345.6i			0.204599i
$324$	−80595.6	−	38134.8i	−0.767753	−	0.363272i
$325$	−10031.1	+	17374.3i	−0.0949687	+	0.164491i
$326$	−47316.2	−	27318.0i	−0.445220	−	0.257048i
$327$	19573.5	−	15664.3i	0.183052	−	0.146492i
$328$	−79273.4			−0.736851
$329$	10712.3	+	5327.91i	0.0989667	+	0.0492227i
$330$	−56125.4	+	8557.87i	−0.515385	+	0.0785847i
$331$	51757.8	+	89647.1i	0.472410	+	0.818239i	0.999502	−	0.0315700i	$-0.0100507\pi$
$331$	51757.8	+	89647.1i	0.472410	+	0.818239i	−0.527091	+	0.849809i	$0.676717\pi$
$332$	106073.	+	61241.4i	0.962343	+	0.555609i
$333$	−7309.47	+	32538.2i	−0.0659170	+	0.293431i
$334$	17491.7	+	30296.5i	0.156798	+	0.271581i
$335$		−	54186.5i		−	0.482838i
$336$	−47716.5	+	43305.2i	−0.422659	+	0.383585i
$337$	91896.2			0.809166			0.404583	−	0.914501i	$-0.367417\pi$
$337$	91896.2			0.809166			0.404583	+	0.914501i	$0.367417\pi$
$338$	9790.66	−	5652.64i	0.0856996	−	0.0494787i
$339$	30548.3	−	78229.5i	0.265820	−	0.680724i
$340$	−29047.1	+	50311.1i	−0.251273	+	0.435217i
$341$	35089.9	−	20259.2i	0.301768	−	0.174226i
$342$	5059.50	+	16205.2i	0.0432569	+	0.138549i
$343$	115616.	−	21777.8i	0.982718	−	0.185109i
$344$			37258.7i			0.314855i
$345$	173586.	−	138918.i	1.45840	−	1.16713i
$346$	87.9482	−	152.331i	0.000734640	−	0.00127243i
$347$	−79222.8	−	45739.3i	−0.657948	−	0.379866i	0.133547	−	0.991043i	$-0.457363\pi$
$347$	−79222.8	−	45739.3i	−0.657948	−	0.379866i	−0.791495	+	0.611176i	$0.790697\pi$
$348$	−13527.7	−	16903.7i	−0.111703	−	0.139580i
$349$	52408.6			0.430281			0.215140	−	0.976583i	$-0.430979\pi$
$349$	52408.6			0.430281			0.215140	+	0.976583i	$0.430979\pi$
$350$	−6717.83	+	4455.85i	−0.0548394	+	0.0363743i
$351$	−60521.0	−	124039.i	−0.491238	−	1.00680i
$352$	72278.1	+	125189.i	0.583340	+	1.01037i
$353$	189241.	+	109258.i	1.51868	+	0.876809i	0.999758	+	0.0219854i	$0.00699874\pi$
$353$	189241.	+	109258.i	1.51868	+	0.876809i	0.518919	+	0.854823i	$0.326335\pi$
$354$	−18376.5	−	7175.94i	−0.146641	−	0.0572627i
$355$	−72134.2	−	124940.i	−0.572380	−	0.991391i
$356$			178012.i			1.40459i
$357$	21286.3	−	66400.2i	0.167018	−	0.520994i
$358$	14576.4			0.113733
$359$	166638.	−	96208.6i	1.29296	−	0.746491i	0.313783	−	0.949495i	$-0.398404\pi$
$359$	166638.	−	96208.6i	1.29296	−	0.746491i	0.979178	+	0.203003i	$0.0650702\pi$
$360$	−22050.0	+	98155.9i	−0.170139	+	0.757376i
$361$	56047.9	−	97077.8i	0.430076	−	0.744913i
$362$	68883.0	−	39769.6i	0.525648	−	0.303483i
$363$	10779.4	+	70694.7i	0.0818051	+	0.536505i
$364$	−125827.	+	7818.94i	−0.949664	+	0.0590127i
$365$			140602.i			1.05538i
$366$	−16392.5	−	20483.4i	−0.122372	−	0.152912i
$367$	−46018.8	+	79707.0i	−0.341667	+	0.591785i	−0.984742	−	0.174018i	$-0.944325\pi$
$367$	−46018.8	+	79707.0i	−0.341667	+	0.591785i	0.643075	+	0.765803i	$0.277658\pi$
$368$	−115621.	−	66753.9i	−0.853771	−	0.492925i
$369$	−94721.9	+	102790.i	−0.695661	+	0.754914i
$370$	17281.4			0.126234
$371$	−6546.87	−	105356.i	−0.0475648	−	0.765439i
$372$	−4970.43	−	32597.8i	−0.0359177	−	0.235560i
$373$	−42456.9	−	73537.5i	−0.305162	−	0.528556i	0.672135	−	0.740428i	$-0.265377\pi$
$373$	−42456.9	−	73537.5i	−0.305162	−	0.528556i	−0.977297	+	0.211872i	$0.932044\pi$
$374$	−31949.3	−	18446.0i	−0.228412	−	0.131874i
$375$	−45939.3	+	117643.i	−0.326679	+	0.836576i
$376$	−5608.23	−	9713.74i	−0.0396689	−	0.0687085i
$377$		−	33512.9i		−	0.235792i
$378$	421.525	−	55455.2i	0.00295012	−	0.388114i
$379$	−183134.			−1.27494			−0.637472	−	0.770474i	$-0.720020\pi$
$379$	−183134.			−1.27494			−0.637472	+	0.770474i	$0.720020\pi$
$380$	−42956.3	+	24800.8i	−0.297481	+	0.171751i
$381$	−52772.3	−	20607.4i	−0.363543	−	0.141962i
$382$	23646.6	−	40957.1i	0.162047	−	0.280674i
$383$	−32777.8	+	18924.3i	−0.223451	+	0.129009i	−0.607547	−	0.794284i	$-0.707846\pi$
$383$	−32777.8	+	18924.3i	−0.223451	+	0.129009i	0.384096	+	0.923293i	$0.374513\pi$
$384$	148591.	−	22656.8i	1.00770	−	0.153651i
$385$	110053.	+	165920.i	0.742470	+	1.11938i
$386$			27940.2i			0.187523i
$387$	48311.5	+	44519.5i	0.322573	+	0.297255i
$388$	49409.6	−	85579.9i	0.328207	−	0.568471i
$389$	−89369.6	−	51597.6i	−0.590596	−	0.340981i	0.174737	−	0.984615i	$-0.444092\pi$
$389$	−89369.6	−	51597.6i	−0.590596	−	0.340981i	−0.765333	+	0.643634i	$0.777426\pi$
$390$	−55839.8	+	44687.5i	−0.367126	+	0.293803i
$391$	144470.			0.944984
$392$	−101613.	−	42898.7i	−0.661267	−	0.279172i
$393$	−86184.2	+	13141.2i	−0.558011	+	0.0850842i
$394$	−20615.5	−	35707.1i	−0.132801	−	0.230018i
$395$	−231151.	−	133455.i	−1.48150	−	0.855346i
$396$	161411.	+	36259.7i	1.02930	+	0.231225i
$397$	−24990.0	−	43284.0i	−0.158557	−	0.274629i	0.775791	−	0.630989i	$-0.217351\pi$
$397$	−24990.0	−	43284.0i	−0.158557	−	0.274629i	−0.934349	+	0.356360i	$0.884018\pi$
$398$			55492.0i			0.350319i
$399$	44086.3	−	40010.6i	0.276922	−	0.251321i
$400$	−15483.8			−0.0967735
$401$	−34183.1	+	19735.6i	−0.212580	+	0.122733i	−0.602510	−	0.798111i	$-0.705833\pi$
$401$	−34183.1	+	19735.6i	−0.212580	+	0.122733i	0.389930	+	0.920845i	$0.372499\pi$
$402$	10186.3	−	26085.4i	0.0630322	−	0.161416i
$403$	25520.9	−	44203.6i	0.157140	−	0.272174i
$404$	−44327.9	+	25592.7i	−0.271590	+	0.156803i
$405$	100927.	+	145875.i	0.615313	+	0.889347i
$406$	5996.73	−	12057.0i	0.0363800	−	0.0731454i
$407$		−	61876.6i		−	0.373540i
$408$	−51039.6	+	40845.9i	−0.306610	+	0.245374i
$409$	−63030.3	+	109172.i	−0.376793	+	0.652625i	−0.990594	−	0.136836i	$-0.956307\pi$
$409$	−63030.3	+	109172.i	−0.376793	+	0.652625i	0.613800	+	0.789461i	$0.289640\pi$
$410$	62728.7	+	36216.4i	0.373163	+	0.215446i
$411$	−33606.6	−	41993.6i	−0.198948	−	0.248599i
$412$	−249094.			−1.46747
$413$	4290.82	+	69050.3i	0.0251559	+	0.404823i
$414$	109679.	−	34243.4i	0.639916	−	0.199791i
$415$	−121838.	−	211030.i	−0.707436	−	1.22531i
$416$	157704.	+	91050.4i	0.911289	+	0.526133i
$417$	−107601.	−	42017.6i	−0.618789	−	0.241635i
$418$	−15749.4	−	27278.8i	−0.0901388	−	0.156125i
$419$			12103.1i			0.0689394i	0.999406	+	0.0344697i	$0.0109742\pi$
$419$			12103.1i			0.0689394i	−0.999406	+	0.0344697i	$0.989026\pi$
$420$	158357.	−	34311.4i	0.897715	−	0.194509i
$421$	60950.0			0.343882			0.171941	−	0.985107i	$-0.444996\pi$
$421$	60950.0			0.343882			0.171941	+	0.985107i	$0.444996\pi$
$422$	50819.9	−	29340.9i	0.285371	−	0.164759i
$423$	−19296.4	−	4334.80i	−0.107844	−	0.0242264i
$424$	−49481.4	+	85704.2i	−0.275239	+	0.476728i
$425$	14510.4	−	8377.57i	0.0803343	−	0.0463810i
$426$	−11238.6	−	73706.4i	−0.0619288	−	0.406150i
$427$	−40971.7	+	82377.4i	−0.224713	+	0.451806i
$428$		−	257750.i		−	1.40705i
$429$	160004.	+	199936.i	0.869395	+	1.08637i
$430$	17021.8	−	29482.6i	0.0920595	−	0.159452i
$431$	210524.	+	121546.i	1.13331	+	0.654315i	0.944764	−	0.327750i	$-0.106290\pi$
$431$	210524.	+	121546.i	1.13331	+	0.654315i	0.188542	+	0.982065i	$0.439624\pi$
$432$	59551.5	−	88317.6i	0.319099	−	0.473238i
$433$	−274713.			−1.46522			−0.732611	−	0.680648i	$-0.761698\pi$
$433$	−274713.			−1.46522			−0.732611	+	0.680648i	$0.761698\pi$
$434$	17091.4	−	11336.5i	0.0907400	−	0.0601867i
$435$	6492.58	+	42580.5i	0.0343114	+	0.225026i
$436$	18927.3	+	32783.1i	0.0995671	+	0.172455i
$437$	106825.	+	61675.3i	0.559382	+	0.322960i
$438$	−26431.2	+	67686.1i	−0.137774	+	0.352819i
$439$	106155.	+	183867.i	0.550824	+	0.954056i	0.998215	+	0.0597173i	$0.0190199\pi$
$439$	106155.	+	183867.i	0.550824	+	0.954056i	−0.447391	+	0.894338i	$0.647647\pi$
$440$		−	186659.i		−	0.964147i
$441$	−177039.	+	80497.8i	−0.910317	+	0.413911i
$442$	−46473.6			−0.237882
$443$	−187991.	+	108537.i	−0.957921	+	0.553056i	−0.895532	−	0.444996i	$-0.853205\pi$
$443$	−187991.	+	108537.i	−0.957921	+	0.553056i	−0.0623882	+	0.998052i	$0.519872\pi$
$444$	−46906.7	−	18316.9i	−0.237941	−	0.0929150i
$445$	177075.	−	306703.i	0.894206	−	1.54881i
$446$	26601.8	−	15358.5i	0.133734	−	0.0772111i
$447$	132148.	−	20149.7i	0.661374	−	0.100845i
$448$	−22875.6	−	34488.2i	−0.113977	−	0.171836i
$449$			271648.i			1.34745i	0.738980	+	0.673727i	$0.235308\pi$
$449$			271648.i			1.34745i	−0.738980	+	0.673727i	$0.764692\pi$
$450$	9030.30	−	9799.45i	0.0445941	−	0.0483924i
$451$	129674.	−	224601.i	0.637527	−	1.10423i
$452$	109822.	+	63405.6i	0.537540	+	0.310349i
$453$	232281.	−	185890.i	1.13193	−	0.905857i
$454$	−97097.4			−0.471081
$455$	224569.	+	111693.i	1.08474	+	0.539514i
$456$	−55177.3	+	8413.31i	−0.265357	+	0.0404610i
$457$	−38605.7	−	66867.0i	−0.184850	−	0.320169i	0.758676	−	0.651468i	$-0.225846\pi$
$457$	−38605.7	−	66867.0i	−0.184850	−	0.320169i	−0.943526	+	0.331299i	$0.892513\pi$
$458$	−50191.6	−	28978.1i	−0.239277	−	0.138146i
$459$	−8023.13	+	114986.i	−0.0380819	+	0.545784i
$460$	167856.	+	290734.i	0.793268	+	1.37398i
$461$		−	282417.i		−	1.32889i	−0.747338	−	0.664444i	$-0.768668\pi$
$461$		−	282417.i		−	1.32889i	0.747338	−	0.664444i	$-0.231332\pi$
$462$	21788.9	+	100562.i	0.102083	+	0.471141i
$463$	258151.			1.20424			0.602119	−	0.798406i	$-0.294323\pi$
$463$	258151.			1.20424			0.602119	+	0.798406i	$0.294323\pi$
$464$	22399.7	−	12932.4i	0.104041	−	0.0600682i
$465$	−23862.4	+	61108.0i	−0.110359	+	0.282613i
$466$	−43733.5	+	75748.7i	−0.201392	+	0.348822i
$467$	−150689.	+	87000.2i	−0.690951	+	0.398921i	−0.803968	−	0.594672i	$-0.797282\pi$
$467$	−150689.	+	87000.2i	−0.690951	+	0.398921i	0.113017	+	0.993593i	$0.463948\pi$
$468$	198930.	−	62108.9i	0.908257	−	0.283571i
$469$	−98017.0	+	6090.83i	−0.445611	+	0.0276905i
$470$			10248.6i			0.0463947i
$471$	−213693.	+	171014.i	−0.963271	+	0.770886i
$472$	32430.1	−	56170.6i	0.145568	−	0.252131i
$473$	−105563.	−	60946.9i	−0.471835	−	0.272414i
$474$	−86188.9	−	107699.i	−0.383614	−	0.479350i
$475$	14305.8			0.0634050
$476$	94271.9	+	46887.6i	0.416072	+	0.206940i
$477$	52004.3	+	166566.i	0.228561	+	0.732065i
$478$	25883.2	+	44831.1i	0.113282	+	0.196211i
$479$	−184584.	−	106569.i	−0.804493	−	0.464474i	0.0405469	−	0.999178i	$-0.487090\pi$
$479$	−184584.	−	106569.i	−0.804493	−	0.464474i	−0.845040	+	0.534704i	$0.820423\pi$
$480$	−218014.	−	85133.4i	−0.946240	−	0.369503i
$481$	−38973.7	−	67504.4i	−0.168454	−	0.291771i
$482$			35347.2i			0.152146i
$483$	−270797.	−	298382.i	−1.16078	−	1.27902i
$484$	−107981.			−0.460952
$485$	−170259.	+	98299.0i	−0.723813	+	0.417894i
$486$	21163.9	+	89197.1i	0.0896030	+	0.377640i
$487$	−145909.	+	252722.i	−0.615212	+	1.06558i	0.375135	+	0.926970i	$0.377596\pi$
$487$	−145909.	+	252722.i	−0.615212	+	1.06558i	−0.990347	+	0.138609i	$0.955737\pi$
$488$	74698.8	−	43127.4i	0.313671	−	0.181098i
$489$	−47742.6	−	313112.i	−0.199659	−	1.30943i
$490$	60807.4	+	80367.9i	0.253259	+	0.334727i
$491$		−	354762.i		−	1.47155i	−0.677227	−	0.735774i	$-0.736818\pi$
$491$		−	354762.i		−	1.47155i	0.677227	−	0.735774i	$-0.263182\pi$
$492$	−131877.	−	164789.i	−0.544802	−	0.680765i
$493$	−13994.3	+	24238.9i	−0.0575783	+	0.0997285i
$494$	−34363.7	−	19839.9i	−0.140814	−	0.0812990i
$495$	−242031.	−	223034.i	−0.987782	−	0.910251i
$496$	39393.6			0.160126
$497$	−217894.	+	144526.i	−0.882128	+	0.585104i
$498$	−18982.5	−	124494.i	−0.0765412	−	0.501982i
$499$	85605.9	+	148274.i	0.343797	+	0.595474i	0.985135	−	0.171785i	$-0.0549533\pi$
$499$	85605.9	+	148274.i	0.343797	+	0.595474i	−0.641337	+	0.767259i	$0.721620\pi$
$500$	−165153.	−	95350.9i	−0.660610	−	0.381403i
$501$	−73768.7	+	188910.i	−0.293898	+	0.752627i
$502$	6019.31	+	10425.8i	0.0238858	+	0.0413714i
$503$			269550.i			1.06538i	0.846312	+	0.532688i	$0.178818\pi$
$503$			269550.i			1.06538i	−0.846312	+	0.532688i	$0.821182\pi$
$504$	180031.	+	28852.6i	0.708738	+	0.113586i
$505$	101832.			0.399302
$506$	−184627.	+	106594.i	−0.721096	+	0.416325i
$507$	61048.4	+	23839.2i	0.237497	+	0.0927417i
$508$	42772.3	−	74083.8i	0.165743	−	0.287075i
$509$	228152.	−	131724.i	0.880622	−	0.508427i	0.00975830	−	0.999952i	$-0.496894\pi$
$509$	228152.	−	131724.i	0.880622	−	0.508427i	0.870863	+	0.491525i	$0.163560\pi$
$510$	59048.0	−	9003.51i	0.227020	−	0.0346156i
$511$	254333.	−	15804.4i	0.974005	−	0.0605252i
$512$			247941.i			0.945820i
$513$	−55020.9	+	81598.4i	−0.209071	+	0.310061i
$514$	60941.7	−	105554.i	0.230668	−	0.399529i
$515$	429173.	+	247783.i	1.61815	+	0.934237i
$516$	−77451.1	+	61982.5i	−0.290890	+	0.232793i
$517$	36695.3			0.137287
$518$	−1942.52	−	31260.1i	−0.00723946	−	0.116501i
$519$	1008.04	−	153.703i	0.00374233	−	0.000570623i
$520$	−117569.	−	203636.i	−0.434798	−	0.753092i
$521$	−116816.	−	67443.9i	−0.430356	−	0.248466i	0.269142	−	0.963100i	$-0.413260\pi$
$521$	−116816.	−	67443.9i	−0.430356	−	0.248466i	−0.699498	+	0.714634i	$0.746593\pi$
$522$	−4878.96	+	21718.8i	−0.0179055	+	0.0797066i
$523$	209471.	+	362815.i	0.765810	+	1.32642i	0.939817	+	0.341677i	$0.110995\pi$
$523$	209471.	+	362815.i	0.765810	+	1.32642i	−0.174008	+	0.984744i	$0.555672\pi$
$524$		−	131640.i		−	0.479429i
$525$	−44501.2	−	14266.0i	−0.161455	−	0.0517588i
$526$	141583.			0.511728
$527$	−36917.2	+	21314.1i	−0.132925	+	0.0767444i
$528$	−71890.1	+	184099.i	−0.257870	+	0.660366i
$529$	277506.	−	480655.i	0.991658	−	1.71760i
$530$	78308.7	−	45211.6i	0.278778	−	0.160953i
$531$	−34083.7	−	109167.i	−0.120881	−	0.387172i
$532$	49690.3	+	74915.1i	0.175569	+	0.264695i
$533$		−	326706.i		−	1.15001i
$534$	142900.	−	114360.i	0.501128	−	0.401042i
$535$	−256393.	+	444086.i	−0.895774	+	1.55153i
$536$	79734.3	+	46034.6i	0.277534	+	0.160234i
$537$	52798.7	+	65975.3i	0.183094	+	0.228788i
$538$	−58420.7			−0.201838
$539$	287759.	−	217722.i	0.990493	−	0.749420i
$540$	−240722.	+	117453.i	−0.825522	+	0.402789i
$541$	−97872.3	−	169520.i	−0.334399	−	0.579197i	0.648970	−	0.760814i	$-0.275200\pi$
$541$	−97872.3	−	169520.i	−0.334399	−	0.579197i	−0.983369	+	0.181617i	$0.941867\pi$
$542$	−104302.	−	60219.1i	−0.355055	−	0.204991i
$543$	429511.	+	167722.i	1.45672	+	0.568842i
$544$	−76041.9	−	131708.i	−0.256954	−	0.445057i
$545$		−	75310.7i		−	0.253550i
$546$	87111.0	+	95984.5i	0.292205	+	0.321970i
$547$	−252143.			−0.842698			−0.421349	−	0.906898i	$-0.638443\pi$
$547$	−252143.			−0.842698			−0.421349	+	0.906898i	$0.638443\pi$
$548$	70333.7	−	40607.2i	0.234208	−	0.135220i
$549$	33334.7	−	148390.i	0.110599	−	0.492334i
$550$	−12362.4	+	21412.3i	−0.0408675	+	0.0707846i
$551$	−20695.5	+	11948.6i	−0.0681668	+	0.0393561i
$552$	56942.5	+	373448.i	0.186878	+	1.22561i
$553$	−215422.	+	433127.i	−0.704434	+	1.41633i
$554$			227264.i			0.740478i
$555$	62596.7	+	78218.6i	0.203220	+	0.253936i
$556$	87211.1	−	151054.i	0.282112	−	0.488633i
$557$	−300457.	−	173469.i	−0.968437	−	0.559127i	−0.0696774	−	0.997570i	$-0.522197\pi$
$557$	−300457.	−	173469.i	−0.968437	−	0.559127i	−0.898759	+	0.438442i	$0.855530\pi$
$558$	−22974.8	+	24931.7i	−0.0737876	+	0.0800724i
$559$	−153553.			−0.491398
$560$	12005.6	+	193201.i	0.0382832	+	0.616075i
$561$	−32237.3	−	211423.i	−0.102431	−	0.671778i
$562$	20046.8	+	34722.0i	0.0634705	+	0.109934i
$563$	420857.	+	242982.i	1.32775	+	0.766579i	0.984952	−	0.172829i	$-0.0552907\pi$
$563$	420857.	+	242982.i	1.32775	+	0.766579i	0.342802	+	0.939408i	$0.388624\pi$
$564$	10862.6	−	27817.5i	0.0341489	−	0.0874502i
$565$	−126144.	−	218487.i	−0.395156	−	0.684430i
$566$			4692.22i			0.0146469i
$567$	252526.	−	198962.i	0.785489	−	0.618875i
$568$	245129.			0.759798
$569$	528706.	−	305249.i	1.63301	−	0.942821i	0.649857	−	0.760057i	$-0.274829\pi$
$569$	528706.	−	305249.i	1.63301	−	0.942821i	0.983157	−	0.182764i	$-0.0585045\pi$
$570$	47505.2	+	18550.6i	0.146215	+	0.0570963i
$571$	−81677.6	+	141470.i	−0.250513	+	0.433902i	−0.963667	−	0.267106i	$-0.913933\pi$
$571$	−81677.6	+	141470.i	−0.250513	+	0.433902i	0.713154	+	0.701008i	$0.247266\pi$
$572$	−334866.	+	193335.i	−1.02348	+	0.590906i
$573$	271031.	−	41326.2i	0.825487	−	0.125868i
$574$	58460.2	−	117540.i	0.177434	−	0.356747i
$575$		−	96823.4i		−	0.292850i
$576$	50308.7	+	46360.0i	0.151635	+	0.139733i
$577$	88878.9	−	153943.i	0.266961	−	0.462389i	−0.701115	−	0.713048i	$-0.747314\pi$
$577$	88878.9	−	153943.i	0.266961	−	0.462389i	0.968075	+	0.250659i	$0.0806473\pi$
$578$	−78681.3	−	45426.6i	−0.235513	−	0.135974i
$579$	−126462.	+	101205.i	−0.377226	+	0.301886i
$580$	−65038.4			−0.193337
$581$	−368033.	+	244111.i	−1.09027	+	0.723162i
$582$	−100442.	+	15315.1i	−0.296529	+	0.0452141i
$583$	−161881.	−	280386.i	−0.476276	−	0.824934i
$584$	−206894.	−	119450.i	−0.606626	−	0.350236i
$585$	−404525.	−	90873.6i	−1.18204	−	0.265537i
$586$	5023.44	+	8700.85i	0.0146287	+	0.0253376i
$587$			423908.i			1.23026i	0.788427	+	0.615128i	$0.210896\pi$
$587$			423908.i			1.23026i	−0.788427	+	0.615128i	$0.789104\pi$
$588$	−79865.3	−	282592.i	−0.230996	−	0.817344i
$589$	−36396.6			−0.104913
$590$	−51323.6	+	29631.7i	−0.147439	+	0.0851241i
$591$	86942.7	−	222647.i	0.248919	−	0.637443i
$592$	30079.5	−	52099.2i	0.0858276	−	0.148658i
$593$	184085.	−	106282.i	0.523491	−	0.302238i	−0.214871	−	0.976642i	$-0.568933\pi$
$593$	184085.	−	106282.i	0.523491	−	0.302238i	0.738362	+	0.674405i	$0.235600\pi$
$594$	−74586.9	−	152867.i	−0.211393	−	0.433253i
$595$	−115783.	−	174560.i	−0.327049	−	0.493072i
$596$			201847.i			0.568236i
$597$	−251166.	+	201003.i	−0.704712	+	0.563966i
$598$	−134279.	+	232578.i	−0.375497	+	0.650380i
$599$	−425386.	−	245597.i	−1.18558	−	0.684493i	−0.228279	−	0.973596i	$-0.573310\pi$
$599$	−425386.	−	245597.i	−1.18558	−	0.684493i	−0.957298	+	0.289102i	$0.906643\pi$
$600$	27374.8	+	34206.5i	0.0760411	+	0.0950182i
$601$	77227.2			0.213807			0.106903	−	0.994269i	$-0.465906\pi$
$601$	77227.2			0.213807			0.106903	+	0.994269i	$0.465906\pi$
$602$	−55243.9	−	27476.4i	−0.152437	−	0.0758171i
$603$	154963.	−	48381.8i	0.426181	−	0.133060i
$604$	224613.	+	389041.i	0.615688	+	1.06640i
$605$	186044.	+	107412.i	0.508282	+	0.293456i
$606$	49022.0	+	19142.9i	0.133489	+	0.0521270i
$607$	−166602.	−	288563.i	−0.452171	−	0.783183i	0.546350	−	0.837557i	$-0.316017\pi$
$607$	−166602.	−	288563.i	−0.452171	−	0.783183i	−0.998521	+	0.0543744i	$0.982684\pi$
$608$		−	129851.i		−	0.351268i
$609$	76293.2	−	16530.6i	0.205708	−	0.0445710i
$610$	−78811.7			−0.211803
$611$	40032.8	−	23112.9i	0.107234	−	0.0619117i
$612$	−169816.	−	38147.9i	−0.453394	−	0.101852i
$613$	−43879.5	+	76001.5i	−0.116772	+	0.202256i	−0.918487	−	0.395451i	$-0.870588\pi$
$613$	−43879.5	+	76001.5i	−0.116772	+	0.202256i	0.801714	+	0.597707i	$0.203921\pi$
$614$	−3928.87	+	2268.33i	−0.0104215	+	0.00601686i
$615$	63294.0	+	415103.i	0.167345	+	1.09750i
$616$	−337644.	+	20981.4i	−0.889810	+	0.0552933i
$617$			176448.i			0.463497i	0.972776	+	0.231749i	$0.0744447\pi$
$617$			176448.i			0.463497i	−0.972776	+	0.231749i	$0.925555\pi$
$618$	160025.	+	199961.i	0.418996	+	0.523562i
$619$	75679.9	−	131081.i	0.197514	−	0.342105i	−0.750207	−	0.661203i	$-0.770046\pi$
$619$	75679.9	−	131081.i	0.197514	−	0.342105i	0.947722	+	0.319097i	$0.103380\pi$
$620$	−85785.9	−	49528.5i	−0.223168	−	0.128846i
$621$	552270.	+	372389.i	1.43208	+	0.965637i
$622$	−86766.9			−0.224271
$623$	−574693.	−	285833.i	−1.48068	−	0.736438i
$624$	37528.5	+	246125.i	0.0963812	+	0.632100i
$625$	222813.	+	385923.i	0.570401	+	0.987964i
$626$	193531.	+	111735.i	0.493858	+	0.285129i
$627$	66420.7	−	170093.i	0.168954	−	0.432665i
$628$	−206638.	−	357907.i	−0.523951	−	0.907510i
$629$			65098.7i			0.164540i
$630$	−129276.	−	105079.i	−0.325715	−	0.264749i
$631$	−609711.			−1.53132			−0.765658	−	0.643248i	$-0.777587\pi$
$631$	−609711.			−1.53132			−0.765658	+	0.643248i	$0.777587\pi$
$632$	392754.	−	226756.i	0.983300	−	0.567708i
$633$	316881.	+	123741.i	0.790841	+	0.308820i
$634$	54087.3	−	93681.9i	0.134560	−	0.233065i
$635$	−147388.	+	85094.4i	−0.365522	+	0.211034i
$636$	−260473.	+	39716.3i	−0.643944	+	0.0981871i
$637$	176796.	−	418773.i	0.435707	−	1.03205i
$638$		−	41301.7i		−	0.101467i
$639$	292899.	−	317846.i	0.717325	−	0.778423i
$640$	225767.	−	391039.i	0.551188	−	0.954686i
$641$	−174468.	−	100729.i	−0.424620	−	0.245154i	0.272432	−	0.962175i	$-0.412172\pi$
$641$	−174468.	−	100729.i	−0.424620	−	0.245154i	−0.697052	+	0.717021i	$0.745505\pi$
$642$	−206909.	+	165585.i	−0.502007	+	0.401746i
$643$	45865.0			0.110933			0.0554663	−	0.998461i	$-0.482335\pi$
$643$	45865.0			0.110933			0.0554663	+	0.998461i	$0.482335\pi$
$644$	507036.	−	336311.i	1.22255	−	0.810903i
$645$	195099.	−	29748.3i	0.468961	−	0.0715061i
$646$	16569.5	+	28699.3i	0.0397050	+	0.0687711i
$647$	454897.	+	262635.i	1.08669	+	0.627400i	0.932693	−	0.360672i	$-0.117453\pi$
$647$	454897.	+	262635.i	1.08669	+	0.627400i	0.153995	+	0.988072i	$0.450786\pi$
$648$	−300395.	+	24582.1i	−0.715391	+	0.0585422i
$649$	106097.	+	183765.i	0.251892	+	0.436289i
$650$			31146.5i			0.0737194i
$651$	113219.	+	36295.5i	0.267152	+	0.0856427i
$652$	478254.			1.12503
$653$	−18109.6	+	10455.6i	−0.0424700	+	0.0245201i	−0.521085	−	0.853505i	$-0.674472\pi$
$653$	−18109.6	+	10455.6i	−0.0424700	+	0.0245201i	0.478615	+	0.878025i	$0.341139\pi$
$654$	14157.3	−	36254.6i	0.0330997	−	0.0847633i
$655$	−130947.	+	226807.i	−0.305220	+	0.528656i
$656$	218367.	−	126074.i	0.507433	−	0.292967i
$657$	−402097.	+	125540.i	−0.931537	+	0.290839i
$658$	18538.5	−	1151.99i	0.0428175	−	0.00266071i
$659$			109922.i			0.253112i	0.991959	+	0.126556i	$0.0403923\pi$
$659$			109922.i			0.253112i	−0.991959	+	0.126556i	$0.959608\pi$
$660$	388015.	−	310521.i	0.890761	−	0.712857i
$661$	−272262.	+	471571.i	−0.623137	+	1.07931i	0.365761	+	0.930709i	$0.380809\pi$
$661$	−272262.	+	471571.i	−0.623137	+	1.07931i	−0.988898	+	0.148596i	$0.952524\pi$
$662$	139177.	+	80353.9i	0.317579	+	0.183354i
$663$	−168336.	−	210347.i	−0.382958	−	0.478530i
$664$	414035.			0.939075
$665$	−11092.2	−	178502.i	−0.0250828	−	0.403646i
$666$	15430.2	+	49421.7i	0.0347874	+	0.111422i
$667$	80869.5	+	140070.i	0.181775	+	0.314843i
$668$	−265200.	−	153113.i	−0.594320	−	0.343131i
$669$	165872.	+	64772.3i	0.370613	+	0.144723i
$670$	−42062.3	−	72854.0i	−0.0937008	−	0.162294i
$671$			282187.i			0.626747i
$672$	−129490.	+	403930.i	−0.286747	+	0.894474i
$673$	142497.			0.314611			0.157306	−	0.987550i	$-0.449719\pi$
$673$	142497.			0.314611			0.157306	+	0.987550i	$0.449719\pi$
$674$	123555.	−	71334.4i	0.271982	−	0.157029i
$675$	77063.4	+	5377.07i	0.169138	+	0.0118015i
$676$	−49480.2	+	85702.2i	−0.108277	+	0.187542i
$677$	−288321.	+	166462.i	−0.629071	+	0.363194i	−0.780392	−	0.625290i	$-0.784980\pi$
$677$	−288321.	+	166462.i	−0.629071	+	0.363194i	0.151321	+	0.988485i	$0.451647\pi$
$678$	−19653.3	−	128893.i	−0.0427540	−	0.280395i
$679$	196949.	+	296929.i	0.427184	+	0.644040i
$680$			196379.i			0.424695i
$681$	−351706.	−	439479.i	−0.758377	−	0.947640i
$682$	31452.3	−	54477.1i	0.0676214	−	0.117124i
$683$	490015.	+	282910.i	1.05043	+	0.606467i	0.922770	−	0.385351i	$-0.125920\pi$
$683$	490015.	+	282910.i	1.05043	+	0.606467i	0.127661	+	0.991818i	$0.459253\pi$
$684$	−109280.	−	100703.i	−0.233577	−	0.215244i
$685$	−161574.			−0.344341
$686$	138541.	−	119027.i	0.294394	−	0.252928i
$687$	−50643.9	−	332140.i	−0.107303	−	0.703732i
$688$	−59255.2	−	102633.i	−0.125184	−	0.216825i
$689$	−353209.	−	203925.i	−0.744035	−	0.429569i
$690$	125553.	−	321522.i	0.263711	−	0.675324i
$691$	265530.	+	459911.i	0.556105	+	0.963203i	0.997817	+	0.0660456i	$0.0210383\pi$
$691$	265530.	+	459911.i	0.556105	+	0.963203i	−0.441711	+	0.897157i	$0.645628\pi$
$692$			1539.70i			0.00321532i
$693$	−376237.	+	462876.i	−0.783421	+	0.963825i
$694$	−142021.			−0.294871
$695$	−300518.	+	173504.i	−0.622158	+	0.359203i
$696$	−68172.1	−	26620.9i	−0.140730	−	0.0549547i
$697$	−136426.	+	236297.i	−0.280823	+	0.486399i
$698$	70463.6	−	40682.2i	0.144629	−	0.0835013i
$699$	−501262.	+	76431.4i	−1.02591	+	0.156429i
$700$	31423.9	−	63180.7i	0.0641304	−	0.128940i
$701$		−	492091.i		−	1.00140i	−0.865620	−	0.500702i	$-0.833075\pi$
$701$		−	492091.i		−	1.00140i	0.865620	−	0.500702i	$-0.166925\pi$
$702$	−177656.	−	119791.i	−0.360500	−	0.243081i
$703$	−27791.1	+	48135.6i	−0.0562334	+	0.0973992i
$704$	−109927.	−	63466.5i	−0.221799	−	0.128056i
$705$	−46386.7	+	37122.3i	−0.0933287	+	0.0746890i
$706$	339247.			0.680623
$707$	−11446.4	−	184202.i	−0.0228998	−	0.368515i
$708$	170714.	−	26030.1i	0.340567	−	0.0519289i
$709$	−279225.	−	483632.i	−0.555472	−	0.962106i	−0.997867	−	0.0652854i	$-0.979204\pi$
$709$	−279225.	−	483632.i	−0.555472	−	0.962106i	0.442395	−	0.896821i	$-0.354129\pi$
$710$	−193969.	−	111988.i	−0.384784	−	0.222155i
$711$	175268.	−	780209.i	0.346708	−	1.54338i
$712$	300871.	+	521125.i	0.593500	+	1.02797i
$713$			246337.i			0.484564i
$714$	−22923.6	−	105799.i	−0.0449662	−	0.207532i
$715$	769269.			1.50476
$716$	−110500.	+	63797.2i	−0.215544	+	0.124444i
$717$	−109159.	+	279538.i	−0.212334	+	0.543755i
$718$	149364.	−	258706.i	0.289732	−	0.501830i
$719$	−546654.	+	315611.i	−1.05744	+	0.610512i	−0.924722	−	0.380642i	$-0.875703\pi$
$719$	−546654.	+	315611.i	−1.05744	+	0.610512i	−0.132715	+	0.991154i	$0.542370\pi$
$720$	−95365.3	−	305448.i	−0.183961	−	0.589213i
$721$	399969.	−	804175.i	0.769406	−	1.54696i
$722$		−	174029.i		−	0.333846i
$723$	−159987.	+	128035.i	−0.306062	+	0.244935i
$724$	−348122.	+	602965.i	−0.664132	+	1.15031i
$725$	16244.8	+	9378.96i	0.0309058	+	0.0178434i
$726$	69369.7	+	86681.8i	0.131612	+	0.164458i
$727$	415516.			0.786175			0.393088	−	0.919501i	$-0.371407\pi$
$727$	415516.			0.786175			0.393088	+	0.919501i	$0.371407\pi$
$728$	−355138.	+	235559.i	−0.670092	+	0.444464i
$729$	−327061.	+	418880.i	−0.615423	+	0.788197i
$730$	109143.	+	189041.i	0.204809	+	0.354739i
$731$	111060.	+	64120.7i	0.207837	+	0.119995i
$732$	213917.	+	83533.8i	0.399231	+	0.155898i
$733$	−510930.	−	884957.i	−0.950941	−	1.64708i	−0.743394	−	0.668853i	$-0.766785\pi$
$733$	−510930.	−	884957.i	−0.950941	−	1.64708i	−0.207547	−	0.978225i	$-0.566548\pi$
$734$			142888.i			0.265219i
$735$	−143502.	+	566332.i	−0.265633	+	1.04833i
$736$	−878851.			−1.62241
$737$	−260855.	+	150605.i	−0.480247	+	0.277271i
$738$	−47563.4	+	211729.i	−0.0873293	+	0.388748i
$739$	−330262.	+	572031.i	−0.604742	+	1.04744i	0.387350	+	0.921933i	$0.373390\pi$
$739$	−330262.	+	572031.i	−0.604742	+	1.04744i	−0.992092	+	0.125511i	$0.959943\pi$
$740$	−131006.	+	75636.3i	−0.239236	+	0.138123i
$741$	−34673.4	−	227400.i	−0.0631480	−	0.414146i
$742$	−90584.6	−	136569.i	−0.164531	−	0.248053i
$743$		−	462747.i		−	0.838235i	−0.907932	−	0.419118i	$-0.862340\pi$
$743$		−	462747.i		−	0.838235i	0.907932	−	0.419118i	$-0.137660\pi$
$744$	−69646.7	−	87028.0i	−0.125821	−	0.157222i
$745$	200784.	−	347768.i	0.361757	−	0.626581i
$746$	−114167.	−	65914.3i	−0.205146	−	0.118441i
$747$	494720.	−	536858.i	0.886581	−	0.962095i
$748$	322932.			0.577176
$749$	832118.	+	413867.i	1.48327	+	0.737730i
$750$	29555.1	+	193832.i	0.0525425	+	0.344591i
$751$	154413.	+	267452.i	0.273782	+	0.474205i	0.969827	−	0.243794i	$-0.0783919\pi$
$751$	154413.	+	267452.i	0.273782	+	0.474205i	−0.696045	+	0.717998i	$0.745059\pi$
$752$	30896.9	+	17838.3i	0.0546360	+	0.0315441i
$753$	−25385.5	+	65008.4i	−0.0447710	+	0.114652i
$754$	−26014.4	−	45058.2i	−0.0457584	−	0.0792558i
$755$		−	893722.i		−	1.56786i
$756$	239517.	+	422236.i	0.419076	+	0.738773i
$757$	−525069.			−0.916273			−0.458137	−	0.888882i	$-0.651483\pi$
$757$	−525069.			−0.916273			−0.458137	+	0.888882i	$0.651483\pi$
$758$	−246225.	+	142158.i	−0.428542	+	0.247419i
$759$	−1.15122e6	−	449545.i	−1.99836	−	0.780350i
$760$	−83835.5	+	145207.i	−0.145144	+	0.251398i
$761$	753264.	−	434897.i	1.30070	−	0.750961i	0.320178	−	0.947357i	$-0.396257\pi$
$761$	753264.	−	434897.i	1.30070	−	0.750961i	0.980525	+	0.196396i	$0.0629239\pi$
$762$	−86949.0	+	13257.8i	−0.149746	+	0.0228329i
$763$	−136228.	+	8465.30i	−0.234001	+	0.0145410i
$764$			413980.i			0.709238i
$765$	254635.	+	234648.i	0.435106	+	0.400954i
$766$	−29379.9	+	50887.5i	−0.0500718	+	0.0867269i
$767$	231494.	+	133653.i	0.393503	+	0.227189i
$768$	87236.2	−	69813.3i	0.147902	−	0.118363i
$769$	973772.			1.64666			0.823331	−	0.567562i	$-0.192113\pi$
$769$	973772.			1.64666			0.823331	+	0.567562i	$0.192113\pi$
$770$	276761.	+	137652.i	0.466793	+	0.232167i
$771$	698497.	−	106505.i	1.17505	−	0.179169i
$772$	−122287.	−	211807.i	−0.205184	−	0.355390i
$773$	611492.	+	353045.i	1.02337	+	0.590842i	0.915078	−	0.403277i	$-0.132129\pi$
$773$	611492.	+	353045.i	1.02337	+	0.590842i	0.108291	+	0.994119i	$0.465462\pi$
$774$	99513.2	+	22354.9i	0.166111	+	0.0373156i
$775$	14284.7	+	24741.8i	0.0237830	+	0.0411933i
$776$		−	334043.i		−	0.554727i
$777$	134452.	−	122022.i	0.222703	−	0.202114i
$778$	−160210.			−0.264686
$779$	−201754.	+	116482.i	−0.332465	+	0.191949i
$780$	227721.	−	583159.i	0.374295	−	0.958513i
$781$	−400977.	+	694512.i	−0.657381	+	1.13862i
$782$	194241.	−	112145.i	0.317634	−	0.183386i
$783$	−115975.	+	56586.6i	−0.189165	+	0.0922976i
$784$	348128.	−	43433.5i	0.566379	−	0.0706631i
$785$			822201.i			1.33425i
$786$	−105674.	+	84568.8i	−0.171050	+	0.136888i
$787$	306916.	−	531593.i	0.495529	−	0.858282i	−0.504457	−	0.863437i	$-0.668307\pi$
$787$	306916.	−	531593.i	0.495529	−	0.858282i	0.999987	+	0.00515455i	$0.00164075\pi$
$788$	312560.	+	180457.i	0.503363	+	0.290617i
$789$	512840.	+	640826.i	0.823812	+	1.02941i
$790$	−414379.			−0.663962
$791$	−381038.	+	252738.i	−0.608997	+	0.403940i
$792$	533810.	−	166663.i	0.851013	−	0.265699i
$793$	177739.	+	307853.i	0.282641	+	0.489549i
$794$	−67198.4	−	38797.0i	−0.106590	−	0.0615400i
$795$	488284.	+	190673.i	0.772571	+	0.301686i
$796$	−242873.	−	420669.i	−0.383313	−	0.663918i
$797$		−	766545.i		−	1.20676i	−0.797454	−	0.603380i	$-0.793820\pi$
$797$		−	766545.i		−	1.20676i	0.797454	−	0.603380i	$-0.206180\pi$
$798$	28216.0	−	88016.4i	0.0443087	−	0.138216i
$799$	−38606.1			−0.0604731
$800$	−88270.5	+	50963.0i	−0.137923	+	0.0796297i
$801$	1.03522e6	+	232554.i	1.61349	+	0.362459i
$802$	−30639.6	+	53069.3i	−0.0476358	+	0.0825077i
$803$	676864.	−	390788.i	1.04971	−	0.606052i
$804$	36949.8	+	242329.i	0.0571610	+	0.374881i
$805$	−1.20813e6	+	75073.9i	−1.86433	+	0.115850i
$806$		−	79242.5i		−	0.121980i
$807$	−211611.	−	264422.i	−0.324931	−	0.406022i
$808$	−86512.3	+	149844.i	−0.132512	+	0.229517i
$809$	−13527.2	−	7809.93i	−0.0206686	−	0.0119330i	0.489630	−	0.871930i	$-0.337132\pi$
$809$	−13527.2	−	7809.93i	−0.0206686	−	0.0119330i	−0.510299	+	0.859997i	$0.670465\pi$
$810$	248932.	+	117785.i	0.379412	+	0.179523i
$811$	−619953.			−0.942577			−0.471288	−	0.881979i	$-0.656211\pi$
$811$	−619953.			−0.942577			−0.471288	+	0.881979i	$0.656211\pi$
$812$	7310.64	+	117647.i	0.0110877	+	0.178430i
$813$	−105242.	−	690215.i	−0.159224	−	1.04425i
$814$	−48031.7	−	83193.3i	−0.0724902	−	0.125557i
$815$	−824000.	−	475737.i	−1.24054	−	0.716228i
$816$	75633.6	−	193686.i	0.113589	−	0.290883i
$817$	54747.1	+	94824.7i	0.0820194	+	0.142062i
$818$			195709.i			0.292486i
$819$	−118909.	+	741953.i	−0.177275	+	1.10614i
$820$	−634038.			−0.942948
$821$	−503201.	+	290523.i	−0.746544	+	0.431017i	−0.824444	−	0.565944i	$-0.808512\pi$
$821$	−503201.	+	290523.i	−0.746544	+	0.431017i	0.0778998	+	0.996961i	$0.475179\pi$
$822$	−77781.6	−	30373.4i	−0.115115	−	0.0449521i
$823$	596607.	−	1.03335e6i	0.880824	−	1.52563i	0.0303966	−	0.999538i	$-0.490323\pi$
$823$	596607.	−	1.03335e6i	0.880824	−	1.52563i	0.850427	−	0.526093i	$-0.176344\pi$
$824$	−729215.	+	421013.i	−1.07399	+	0.620070i
$825$	−141695.	+	21605.3i	−0.208183	+	0.0317433i
$826$	59369.3	+	89507.6i	0.0870165	+	0.131190i
$827$		−	850652.i		−	1.24377i	−0.783108	−	0.621886i	$-0.786367\pi$
$827$		−	850652.i		−	1.24377i	0.783108	−	0.621886i	$-0.213633\pi$
$828$	−681572.	+	739625.i	−0.994149	+	1.07883i
$829$	278806.	−	482907.i	0.405689	−	0.702674i	−0.588712	−	0.808343i	$-0.700365\pi$
$829$	278806.	−	482907.i	0.405689	−	0.702674i	0.994401	+	0.105668i	$0.0336982\pi$
$830$	−327624.	−	189154.i	−0.475575	−	0.274573i
$831$	−1.02864e6	+	823195.i	−1.48956	+	1.19207i
$832$	−159901.			−0.230995
$833$	−302743.	+	229060.i	−0.436300	+	0.330110i
$834$	−177286.	+	27032.1i	−0.254883	+	0.0388641i
$835$	304614.	+	527607.i	0.436895	+	0.756725i
$836$	238784.	+	137862.i	0.341658	+	0.197257i
$837$	−196064.	−	13680.3i	−0.279864	−	0.0195274i
$838$	9395.01	+	16272.6i	0.0133786	+	0.0231723i
$839$		−	914591.i		−	1.29928i	−0.760242	−	0.649640i	$-0.774920\pi$
$839$		−	914591.i		−	1.29928i	0.760242	−	0.649640i	$-0.225080\pi$
$840$	405592.	−	368096.i	0.574819	−	0.521678i
$841$	675947.			0.955698
$842$	81947.5	−	47312.4i	0.115588	−	0.0667345i
$843$	−84544.2	+	216505.i	−0.118968	+	0.304658i
$844$	−256834.	+	444850.i	−0.360552	+	0.624495i
$845$	170502.	−	98439.4i	0.238790	−	0.137866i
$846$	−29309.0	+	9150.70i	−0.0409507	+	0.0127854i
$847$	173384.	−	348605.i	0.241681	−	0.485922i
$848$		−	314775.i		−	0.437732i
$849$	−21237.7	+	16996.1i	−0.0294641	+	0.0235795i
$850$	13006.2	−	22527.4i	0.0180016	−	0.0311797i
$851$	325788.	+	188094.i	0.449859	+	0.259726i
$852$	407790.	+	509559.i	0.561768	+	0.701965i
$853$	−49816.1			−0.0684655			−0.0342328	−	0.999414i	$-0.510899\pi$
$853$	−49816.1			−0.0684655			−0.0342328	+	0.999414i	$0.510899\pi$
$854$	8858.82	+	142561.i	0.0121468	+	0.195472i
$855$	88110.0	+	282210.i	0.120529	+	0.386047i
$856$	−435642.	−	754554.i	−0.594541	−	1.02978i
$857$	−534102.	−	308364.i	−0.727215	−	0.419858i	0.0901876	−	0.995925i	$-0.471253\pi$
$857$	−534102.	−	308364.i	−0.727215	−	0.419858i	−0.817402	+	0.576067i	$0.804587\pi$
$858$	370327.	+	144611.i	0.503049	+	0.196439i
$859$	−618179.	−	1.07072e6i	−0.837776	−	1.45107i	−0.891750	−	0.452528i	$-0.850522\pi$
$859$	−618179.	−	1.07072e6i	−0.837776	−	1.45107i	0.0539740	−	0.998542i	$-0.482811\pi$
$860$			298000.i			0.402920i
$861$	743757.	−	161151.i	1.00329	−	0.217383i
$862$	377401.			0.507912
$863$	−601860.	+	347484.i	−0.808116	+	0.466566i	−0.846301	−	0.532705i	$-0.821176\pi$
$863$	−601860.	+	347484.i	−0.808116	+	0.466566i	0.0381854	+	0.999271i	$0.487842\pi$
$864$	48806.9	−	699492.i	0.0653813	−	0.937034i
$865$	1531.60	−	2652.80i	0.00204697	−	0.00354546i
$866$	−369352.	+	213246.i	−0.492499	+	0.284344i
$867$	−79390.3	−	520668.i	−0.105616	−	0.692664i
$868$	−79948.4	+	160744.i	−0.106113	+	0.213351i
$869$			1.48369e6i			1.96474i
$870$	41782.4	+	52209.8i	0.0552020	+	0.0689784i
$871$	−189720.	+	328605.i	−0.250079	+	0.433150i
$872$	110818.	+	63980.9i	0.145740	+	0.0841429i
$873$	−433137.	−	399140.i	−0.568325	−	0.523717i
$874$	191502.			0.250697
$875$	573014.	−	380073.i	0.748427	−	0.496422i
$876$	−95876.8	−	628792.i	−0.124941	−	0.819405i
$877$	389898.	+	675323.i	0.506934	+	0.878036i	0.999968	+	0.00802556i	$0.00255464\pi$
$877$	389898.	+	675323.i	0.506934	+	0.878036i	−0.493034	+	0.870010i	$0.664112\pi$
$878$	285453.	+	164806.i	0.370293	+	0.213789i
$879$	−21185.6	+	54253.0i	−0.0274197	+	0.0702176i
$880$	296857.	+	514171.i	0.383338	+	0.663961i
$881$			1.33859e6i			1.72463i	0.506371	+	0.862316i	$0.330987\pi$
$881$			1.33859e6i			1.72463i	−0.506371	+	0.862316i	$0.669013\pi$
$882$	−175544.	+	245656.i	−0.225657	+	0.315785i
$883$	174007.			0.223175			0.111587	−	0.993755i	$-0.464406\pi$
$883$	174007.			0.223175			0.111587	+	0.993755i	$0.464406\pi$
$884$	352304.	−	203403.i	0.450830	−	0.260287i
$885$	−320022.	−	124967.i	−0.408595	−	0.159555i
$886$	−168503.	+	291856.i	−0.214655	+	0.371793i
$887$	505345.	−	291761.i	0.642305	−	0.370835i	−0.143197	−	0.989694i	$-0.545738\pi$
$887$	505345.	−	291761.i	0.642305	−	0.370835i	0.785502	+	0.618859i	$0.212405\pi$
$888$	−168277.	+	25658.5i	−0.213402	+	0.0325390i
$889$	170493.	+	257042.i	0.215726	+	0.325237i
$890$		−	549818.i		−	0.694127i
$891$	421733.	−	891306.i	0.531229	−	1.12272i
$892$	−134440.	+	232857.i	−0.168966	+	0.292658i
$893$	−28546.3	−	16481.2i	−0.0357970	−	0.0206674i
$894$	162033.	−	129672.i	0.202735	−	0.162244i
$895$	253845.			0.316901
$896$	−732721.	−	364430.i	−0.912688	−	0.453940i
$897$	−1.53907e6	+	234674.i	−1.91282	+	0.291663i
$898$	210867.	+	365232.i	0.261490	+	0.452914i
$899$	−41330.0	−	23861.9i	−0.0511382	−	0.0295247i
$900$	−25566.6	+	113810.i	−0.0315637	+	0.140506i
$901$	170311.	+	294987.i	0.209794	+	0.363373i
$902$		−	402637.i		−	0.494880i
$903$	−75741.3	−	349568.i	−0.0928875	−	0.428702i
$904$	428666.			0.524544
$905$	1.19958e6	−	692579.i	1.46465	−	0.845614i
$906$	168006.	−	430238.i	0.204677	−	0.524146i
$907$	84915.6	−	147078.i	0.103222	−	0.178786i	−0.809788	−	0.586722i	$-0.800418\pi$
$907$	84915.6	−	147078.i	0.103222	−	0.178786i	0.913010	+	0.407936i	$0.133751\pi$
$908$	736069.	−	424969.i	0.892784	−	0.515449i
$909$	90923.3	+	291221.i	0.110039	+	0.352448i
$910$	388635.	−	24150.0i	0.469309	−	0.0291632i
$911$			181589.i			0.218803i	0.993998	+	0.109402i	$0.0348934\pi$
$911$			181589.i			0.218803i	−0.993998	+	0.109402i	$0.965107\pi$
$912$	138611.	−	110928.i	0.166651	−	0.133368i
$913$	−677269.	+	1.17306e6i	−0.812492	+	1.40728i
$914$	−103811.	−	59935.3i	−0.124266	−	0.0717447i
$915$	−285471.	−	356715.i	−0.340973	−	0.426068i
$916$	507318.			0.604630
$917$	424985.	+	211373.i	0.505400	+	0.251369i
$918$	78470.9	+	160827.i	0.0931158	+	0.190842i
$919$	−620186.	−	1.07419e6i	−0.734330	−	1.27190i	−0.955017	−	0.296552i	$-0.904163\pi$
$919$	−620186.	−	1.07419e6i	−0.734330	−	1.27190i	0.220687	−	0.975345i	$-0.429170\pi$
$920$	982783.	+	567410.i	1.16113	+	0.670381i
$921$	−24497.9	−	9566.35i	−0.0288809	−	0.0112779i
$922$	−219226.	−	379710.i	−0.257887	−	0.446674i
$923$			1.01024e6i			1.18583i
$924$	−605310.	−	666970.i	−0.708979	−	0.781200i
$925$	43628.9			0.0509907
$926$	347086.	−	200390.i	0.404776	−	0.233697i
$927$	−325416.	+	1.44859e6i	−0.378686	+	1.68573i
$928$	85131.3	−	147452.i	0.0988538	−	0.171220i
$929$	−901222.	+	520321.i	−1.04424	+	0.602892i	−0.921031	−	0.389489i	$-0.872652\pi$
$929$	−901222.	+	520321.i	−1.04424	+	0.602892i	−0.123209	+	0.992381i	$0.539318\pi$
$930$	15352.0	+	100683.i	0.0177500	+	0.116410i
$931$	−321643.	+	40129.1i	−0.371086	+	0.0462978i
$932$		−	765640.i		−	0.881440i
$933$	−314287.	−	392721.i	−0.361046	−	0.451150i
$934$	−135068.	+	233944.i	−0.154831	+	0.268175i
$935$	−556391.	−	321232.i	−0.636439	−	0.367448i
$936$	477387.	−	518048.i	0.544902	−	0.591314i
$937$	1.19663e6			1.36295			0.681477	−	0.731840i	$-0.261338\pi$
$937$	1.19663e6			1.36295			0.681477	+	0.731840i	$0.261338\pi$
$938$	−127056.	+	84274.8i	−0.144408	+	0.0957838i
$939$	195275.	+	1.28068e6i	0.221471	+	1.45248i
$940$	−44855.3	−	77691.6i	−0.0507642	−	0.0879262i
$941$	−575750.	−	332410.i	−0.650212	−	0.375400i	0.138325	−	0.990387i	$-0.455828\pi$
$941$	−575750.	−	332410.i	−0.650212	−	0.375400i	−0.788537	+	0.614987i	$0.789161\pi$
$942$	−154561.	+	395808.i	−0.174180	+	0.446049i
$943$	788370.	+	1.36550e6i	0.886557	+	1.53556i
$944$			206304.i			0.231507i
$945$	7340.76	−	965740.i	0.00822010	−	1.08143i
$946$	−189240.			−0.211461
$947$	643813.	−	371705.i	0.717893	−	0.414476i	−0.0960839	−	0.995373i	$-0.530632\pi$
$947$	643813.	−	371705.i	0.717893	−	0.414476i	0.813977	+	0.580898i	$0.197298\pi$
$948$	1.12474e6	+	439207.i	1.25151	+	0.488711i
$949$	492284.	−	852661.i	0.546617	−	0.946769i
$950$	19234.2	−	11104.8i	0.0213121	−	0.0123045i
$951$	619934.	−	94526.1i	0.685463	−	0.104518i
$952$	355226.	−	22074.0i	0.391950	−	0.0243560i
$953$		−	635715.i		−	0.699965i	−0.936756	−	0.349983i	$-0.886187\pi$
$953$		−	635715.i		−	0.699965i	0.936756	−	0.349983i	$-0.113813\pi$
$954$	199217.	+	183580.i	0.218892	+	0.201711i
$955$	411800.	−	713259.i	0.451523	−	0.782061i
$956$	−392427.	−	226568.i	−0.429381	−	0.247903i
$957$	186938.	−	149603.i	0.204115	−	0.163349i
$958$	−330898.			−0.360548
$959$	18161.7	+	292267.i	0.0197478	+	0.317792i
$960$	203165.	−	30978.1i	0.220448	−	0.0336134i
$961$	425418.	+	736845.i	0.460647	+	0.797865i
$962$	−104801.	−	60506.6i	−0.113244	−	0.0653812i
$963$	−1.49893e6	−	336723.i	−1.61633	−	0.363095i
$964$	−154705.	−	267958.i	−0.166476	−	0.288345i
$965$			486572.i			0.522507i
$966$	−595707.	−	190970.i	−0.638379	−	0.204649i
$967$	138299.			0.147900			0.0739498	−	0.997262i	$-0.476440\pi$
$967$	138299.			0.147900			0.0739498	+	0.997262i	$0.476440\pi$
$968$	−316110.	+	182506.i	−0.337356	+	0.194772i
$969$	−69879.5	+	178951.i	−0.0744221	+	0.190584i
$970$	−152609.	+	264327.i	−0.162195	+	0.280930i
$971$	−1.06757e6	+	616363.i	−1.13229	+	0.653730i	−0.944511	−	0.328481i	$-0.893463\pi$
$971$	−1.06757e6	+	616363.i	−1.13229	+	0.653730i	−0.187782	+	0.982211i	$0.560130\pi$
$972$	−550829.	−	583550.i	−0.583021	−	0.617654i
$973$	347628.	+	524098.i	0.367188	+	0.553589i
$974$			453048.i			0.477558i
$975$	−140974.	+	112818.i	−0.148296	+	0.118678i
$976$	−137177.	+	237598.i	−0.144006	+	0.249426i
$977$	−377959.	−	218215.i	−0.395964	−	0.228610i	0.288777	−	0.957396i	$-0.406751\pi$
$977$	−377959.	−	218215.i	−0.395964	−	0.228610i	−0.684741	+	0.728786i	$0.740085\pi$
$978$	−307243.	−	383920.i	−0.321221	−	0.401386i
$979$	−1.96863e6			−2.05400
$980$	−812713.	−	343109.i	−0.846223	−	0.357256i
$981$	215375.	−	67243.1i	0.223798	−	0.0698730i
$982$	−275384.	−	476980.i	−0.285572	−	0.494626i
$983$	−296367.	−	171107.i	−0.306706	−	0.177077i	0.338745	−	0.940878i	$-0.389997\pi$
$983$	−296367.	−	171107.i	−0.306706	−	0.177077i	−0.645452	+	0.763801i	$0.723331\pi$
$984$	−664587.	−	259519.i	−0.686375	−	0.268027i
$985$	−359014.	−	621830.i	−0.370032	−	0.640914i
$986$			43452.4i			0.0446951i
$987$	72364.0	+	79735.3i	0.0742828	+	0.0818496i
$988$	347336.			0.355824
$989$	641787.	−	370536.i	0.656143	−	0.378824i
$990$	−498542.	−	111994.i	−0.508665	−	0.114268i
$991$	34385.0	−	59556.6i	0.0350124	−	0.0606433i	−0.847988	−	0.530015i	$-0.822186\pi$
$991$	34385.0	−	59556.6i	0.0350124	−	0.0606433i	0.883001	+	0.469372i	$0.155520\pi$
$992$	224577.	−	129660.i	0.228214	−	0.131759i
$993$	140431.	+	920995.i	0.142418	+	0.934025i
$994$	−180770.	+	363456.i	−0.182959	+	0.367857i
$995$			966380.i			0.976116i
$996$	688776.	+	860670.i	0.694320	+	0.867597i
$997$	468013.	−	810623.i	0.470834	−	0.815508i	−0.528610	−	0.848865i	$-0.677286\pi$
$997$	468013.	−	810623.i	0.470834	−	0.815508i	0.999444	+	0.0333568i	$0.0106198\pi$
$998$	230195.	+	132903.i	0.231118	+	0.133436i
$999$	−167800.	+	248855.i	−0.168136	+	0.249353i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.5.h.b.11.5	yes	16
3.2	odd	2	inner	21.5.h.b.11.4	yes	16
7.2	even	3	inner	21.5.h.b.2.4	✓	16
7.3	odd	6		147.5.b.f.50.5		8
7.4	even	3		147.5.b.c.50.5		8
7.5	odd	6		147.5.h.b.128.4		16
7.6	odd	2		147.5.h.b.116.5		16
21.2	odd	6	inner	21.5.h.b.2.5	yes	16
21.5	even	6		147.5.h.b.128.5		16
21.11	odd	6		147.5.b.c.50.4		8
21.17	even	6		147.5.b.f.50.4		8
21.20	even	2		147.5.h.b.116.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.5.h.b.2.4	✓	16	7.2	even	3	inner
21.5.h.b.2.5	yes	16	21.2	odd	6	inner
21.5.h.b.11.4	yes	16	3.2	odd	2	inner
21.5.h.b.11.5	yes	16	1.1	even	1	trivial
147.5.b.c.50.4		8	21.11	odd	6
147.5.b.c.50.5		8	7.4	even	3
147.5.b.f.50.4		8	21.17	even	6
147.5.b.f.50.5		8	7.3	odd	6
147.5.h.b.116.4		16	21.20	even	2
147.5.h.b.116.5		16	7.6	odd	2
147.5.h.b.128.4		16	7.5	odd	6
147.5.h.b.128.5		16	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	21.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34450 - 0.776250i) q^{2} +(8.38348 + 3.27372i) q^{3} +(-6.79487 + 11.7691i) q^{4} +(23.4142 - 13.5182i) q^{5} +(13.8128 - 2.10615i) q^{6} +(-27.0847 - 40.8340i) q^{7} +45.9381i q^{8} +(59.5656 + 54.8903i) q^{9} +O(q^{10})\)	\(q+(1.34450 - 0.776250i) q^{2} +(8.38348 + 3.27372i) q^{3} +(-6.79487 + 11.7691i) q^{4} +(23.4142 - 13.5182i) q^{5} +(13.8128 - 2.10615i) q^{6} +(-27.0847 - 40.8340i) q^{7} +45.9381i q^{8} +(59.5656 + 54.8903i) q^{9} +(20.9870 - 36.3506i) q^{10} +(-130.154 - 75.1445i) q^{11} +(-95.4933 + 76.4213i) q^{12} -189.322 q^{13} +(-68.1129 - 33.8770i) q^{14} +(240.548 - 36.6782i) q^{15} +(-73.0586 - 126.541i) q^{16} +(136.932 + 79.0575i) q^{17} +(122.695 + 27.5624i) q^{18} +(67.5003 + 116.914i) q^{19} +367.418i q^{20} +(-93.3851 - 430.999i) q^{21} -233.323 q^{22} +(791.290 - 456.852i) q^{23} +(-150.388 + 385.121i) q^{24} +(52.9840 - 91.7711i) q^{25} +(-254.545 + 146.961i) q^{26} +(319.672 + 655.172i) q^{27} +(664.616 - 41.2996i) q^{28} +177.015i q^{29} +(294.946 - 236.039i) q^{30} +(-134.801 + 233.483i) q^{31} +(-832.991 - 480.928i) q^{32} +(-845.142 - 1056.06i) q^{33} +245.473 q^{34} +(-1186.17 - 589.961i) q^{35} +(-1050.75 + 328.059i) q^{36} +(205.859 + 356.558i) q^{37} +(181.509 + 104.794i) q^{38} +(-1587.18 - 619.788i) q^{39} +(621.000 + 1075.60i) q^{40} +1725.66i q^{41} +(-460.120 - 506.990i) q^{42} +811.064 q^{43} +(1768.76 - 1021.19i) q^{44} +(2136.70 + 479.994i) q^{45} +(709.262 - 1228.48i) q^{46} +(-211.453 + 122.082i) q^{47} +(-198.225 - 1300.03i) q^{48} +(-933.837 + 2211.96i) q^{49} -164.515i q^{50} +(889.152 + 1111.05i) q^{51} +(1286.42 - 2228.15i) q^{52} +(1865.65 + 1077.13i) q^{53} +(938.377 + 632.737i) q^{54} -4063.27 q^{55} +(1875.84 - 1244.22i) q^{56} +(183.145 + 1201.12i) q^{57} +(137.408 + 237.997i) q^{58} +(-1222.75 - 705.954i) q^{59} +(-1202.82 + 3080.24i) q^{60} +(-938.815 - 1626.08i) q^{61} +418.558i q^{62} +(628.076 - 3918.99i) q^{63} +844.594 q^{64} +(-4432.84 + 2559.30i) q^{65} +(-1956.06 - 763.835i) q^{66} +(1002.10 - 1735.69i) q^{67} +(-1860.87 + 1074.37i) q^{68} +(8129.37 - 1239.55i) q^{69} +(-2052.77 + 127.560i) q^{70} -5336.08i q^{71} +(-2521.55 + 2736.33i) q^{72} +(-2600.24 + 4503.75i) q^{73} +(553.556 + 319.596i) q^{74} +(744.623 - 595.906i) q^{75} -1834.62 q^{76} +(456.732 + 7349.98i) q^{77} +(-2615.08 + 398.742i) q^{78} +(-4936.13 - 8549.63i) q^{79} +(-3421.22 - 1975.24i) q^{80} +(535.114 + 6539.14i) q^{81} +(1339.54 + 2320.15i) q^{82} -9012.89i q^{83} +(5707.00 + 1829.53i) q^{84} +4274.86 q^{85} +(1090.48 - 629.588i) q^{86} +(-579.496 + 1484.00i) q^{87} +(3451.99 - 5979.02i) q^{88} +(11344.1 - 6549.50i) q^{89} +(3245.40 - 1013.26i) q^{90} +(5127.74 + 7730.80i) q^{91} +12417.0i q^{92} +(-1894.46 + 1516.10i) q^{93} +(-189.533 + 328.280i) q^{94} +(3160.94 + 1824.97i) q^{95} +(-5408.95 - 6758.83i) q^{96} -7271.60 q^{97} +(461.482 + 3698.87i) q^{98} +(-3628.00 - 11620.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 78 q^{4} + 28 q^{6} - 168 q^{7} + 62 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 78 * q^4 + 28 * q^6 - 168 * q^7 + 62 * q^9	\( 16 q + 8 q^{3} + 78 q^{4} + 28 q^{6} - 168 q^{7} + 62 q^{9} - 98 q^{10} + 436 q^{12} - 492 q^{13} - 856 q^{15} + 150 q^{16} - 884 q^{18} - 1326 q^{19} + 2170 q^{21} + 3244 q^{22} + 630 q^{24} + 2094 q^{25} + 1028 q^{27} - 854 q^{28} + 340 q^{30} - 2504 q^{31} - 616 q^{33} - 7728 q^{34} - 9644 q^{36} + 1342 q^{37} - 2626 q^{39} + 5754 q^{40} - 1582 q^{42} + 1460 q^{43} - 1330 q^{45} + 8844 q^{46} + 25864 q^{48} + 5572 q^{49} + 7794 q^{51} + 9536 q^{52} - 18578 q^{54} - 35140 q^{55} + 11696 q^{57} - 12446 q^{58} - 18890 q^{60} + 15012 q^{61} - 13076 q^{63} + 7660 q^{64} - 17192 q^{66} + 8658 q^{67} + 53676 q^{69} + 13790 q^{70} + 21312 q^{72} + 12322 q^{73} - 19514 q^{75} - 84520 q^{76} - 32120 q^{78} - 40168 q^{79} - 23986 q^{81} + 47348 q^{82} - 5992 q^{84} + 22536 q^{85} - 1162 q^{87} + 56430 q^{88} + 139636 q^{90} - 17878 q^{91} + 8556 q^{93} + 6468 q^{94} - 40894 q^{96} - 28268 q^{97} - 47812 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 + 78 * q^4 + 28 * q^6 - 168 * q^7 + 62 * q^9 - 98 * q^10 + 436 * q^12 - 492 * q^13 - 856 * q^15 + 150 * q^16 - 884 * q^18 - 1326 * q^19 + 2170 * q^21 + 3244 * q^22 + 630 * q^24 + 2094 * q^25 + 1028 * q^27 - 854 * q^28 + 340 * q^30 - 2504 * q^31 - 616 * q^33 - 7728 * q^34 - 9644 * q^36 + 1342 * q^37 - 2626 * q^39 + 5754 * q^40 - 1582 * q^42 + 1460 * q^43 - 1330 * q^45 + 8844 * q^46 + 25864 * q^48 + 5572 * q^49 + 7794 * q^51 + 9536 * q^52 - 18578 * q^54 - 35140 * q^55 + 11696 * q^57 - 12446 * q^58 - 18890 * q^60 + 15012 * q^61 - 13076 * q^63 + 7660 * q^64 - 17192 * q^66 + 8658 * q^67 + 53676 * q^69 + 13790 * q^70 + 21312 * q^72 + 12322 * q^73 - 19514 * q^75 - 84520 * q^76 - 32120 * q^78 - 40168 * q^79 - 23986 * q^81 + 47348 * q^82 - 5992 * q^84 + 22536 * q^85 - 1162 * q^87 + 56430 * q^88 + 139636 * q^90 - 17878 * q^91 + 8556 * q^93 + 6468 * q^94 - 40894 * q^96 - 28268 * q^97 - 47812 * q^99

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