LMFDB - Embedded newform 11.5.d.a.8.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,5,Mod(2,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("11.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	11.d (of order $10$, degree $4$, 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:	$1.13706959392$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 115x^{10} + 5030x^{8} + 102975x^{6} + 953170x^{4} + 2910655x^{2} + 73205 $ x^12 + 115x^10 + 5030x^8 + 102975x^6 + 953170x^4 + 2910655*x^2 + 73205
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			8.1
Root			$-6.10049i$ of defining polynomial
Character	$\chi$	$=$	11.8
Dual form			11.5.d.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.46775 - 3.39656i) q^{2} +(-2.26281 - 6.96422i) q^{3} +(-0.502581 + 1.54679i) q^{4} +(14.7329 + 10.7041i) q^{5} +(-18.0704 + 24.8717i) q^{6} +(47.9990 + 15.5958i) q^{7} +(-57.3923 + 18.6479i) q^{8} +(22.1503 - 16.0931i) q^{9} +O(q^{10})$	\(q+(-2.46775 - 3.39656i) q^{2} +(-2.26281 - 6.96422i) q^{3} +(-0.502581 + 1.54679i) q^{4} +(14.7329 + 10.7041i) q^{5} +(-18.0704 + 24.8717i) q^{6} +(47.9990 + 15.5958i) q^{7} +(-57.3923 + 18.6479i) q^{8} +(22.1503 - 16.0931i) q^{9} -76.4560i q^{10} +(-82.9397 - 88.1022i) q^{11} +11.9094 q^{12} +(125.766 + 173.103i) q^{13} +(-65.4772 - 201.518i) q^{14} +(41.2077 - 126.824i) q^{15} +(226.021 + 164.214i) q^{16} +(-255.614 + 351.822i) q^{17} +(-109.323 - 35.5210i) q^{18} +(-61.3806 + 19.9438i) q^{19} +(-23.9614 + 17.4089i) q^{20} -369.566i q^{21} +(-94.5704 + 499.124i) q^{22} +536.875 q^{23} +(259.736 + 357.496i) q^{24} +(-90.6549 - 279.007i) q^{25} +(277.594 - 854.346i) q^{26} +(-642.052 - 466.478i) q^{27} +(-48.2468 + 66.4060i) q^{28} +(-481.802 - 156.547i) q^{29} +(-532.457 + 173.006i) q^{30} +(192.037 - 139.523i) q^{31} -207.397i q^{32} +(-425.887 + 776.970i) q^{33} +1825.78 q^{34} +(540.225 + 743.556i) q^{35} +(13.7603 + 42.3498i) q^{36} +(-718.836 + 2212.35i) q^{37} +(219.212 + 159.267i) q^{38} +(920.939 - 1267.56i) q^{39} +(-1045.16 - 339.594i) q^{40} +(-100.981 + 32.8108i) q^{41} +(-1255.25 + 911.995i) q^{42} -2058.95i q^{43} +(177.959 - 84.0114i) q^{44} +498.599 q^{45} +(-1324.87 - 1823.53i) q^{46} +(17.8846 + 55.0431i) q^{47} +(632.178 - 1945.64i) q^{48} +(118.225 + 85.8952i) q^{49} +(-723.951 + 996.433i) q^{50} +(3028.58 + 984.044i) q^{51} +(-330.960 + 107.536i) q^{52} +(926.358 - 673.039i) q^{53} +3331.92i q^{54} +(-278.889 - 2185.79i) q^{55} -3045.60 q^{56} +(277.786 + 382.340i) q^{57} +(657.244 + 2022.79i) q^{58} +(-596.473 + 1835.75i) q^{59} +(175.460 + 127.479i) q^{60} +(-375.548 + 516.897i) q^{61} +(-947.795 - 307.957i) q^{62} +(1314.18 - 427.002i) q^{63} +(2911.90 - 2115.62i) q^{64} +3896.51i q^{65} +(3690.00 - 470.814i) q^{66} -8692.22 q^{67} +(-415.727 - 572.199i) q^{68} +(-1214.85 - 3738.92i) q^{69} +(1192.39 - 3669.81i) q^{70} +(1518.36 + 1103.16i) q^{71} +(-971.154 + 1336.68i) q^{72} +(2334.33 + 758.471i) q^{73} +(9288.28 - 3017.94i) q^{74} +(-1737.93 + 1262.68i) q^{75} -104.966i q^{76} +(-2607.00 - 5522.33i) q^{77} -6578.00 q^{78} +(-2255.51 - 3104.44i) q^{79} +(1572.18 + 4838.68i) q^{80} +(-1110.50 + 3417.77i) q^{81} +(360.640 + 262.020i) q^{82} +(4351.57 - 5989.42i) q^{83} +(571.640 + 185.737i) q^{84} +(-7531.86 + 2447.25i) q^{85} +(-6993.34 + 5080.96i) q^{86} +3709.62i q^{87} +(6403.03 + 3509.74i) q^{88} +11104.2 q^{89} +(-1230.42 - 1693.52i) q^{90} +(3336.98 + 10270.2i) q^{91} +(-269.823 + 830.430i) q^{92} +(-1406.21 - 1021.67i) q^{93} +(142.823 - 196.578i) q^{94} +(-1117.79 - 363.193i) q^{95} +(-1444.36 + 469.300i) q^{96} +(9943.57 - 7224.43i) q^{97} -613.524i q^{98} +(-3254.98 - 616.730i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 5 q^{2} - 6 q^{3} + 7 q^{4} - 18 q^{5} + 75 q^{6} - 80 q^{7} - 245 q^{8} + q^{9}+O(q^{10}) $ 12 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 - 18 * q^5 + 75 * q^6 - 80 * q^7 - 245 * q^8 + q^9	\( 12 q - 5 q^{2} - 6 q^{3} + 7 q^{4} - 18 q^{5} + 75 q^{6} - 80 q^{7} - 245 q^{8} + q^{9} - 43 q^{11} + 594 q^{12} + 250 q^{13} + 610 q^{14} + 1134 q^{15} - 633 q^{16} - 1250 q^{17} - 3150 q^{18} - 1025 q^{19} + 752 q^{20} - 35 q^{22} + 1684 q^{23} + 5345 q^{24} + 197 q^{25} + 3490 q^{26} - 687 q^{27} - 3580 q^{28} - 2690 q^{29} - 6740 q^{30} - 1136 q^{31} + 5939 q^{33} + 2370 q^{34} + 3610 q^{35} - 514 q^{36} - 336 q^{37} + 1900 q^{38} - 6880 q^{39} - 2340 q^{40} - 4550 q^{41} + 1310 q^{42} - 6268 q^{44} + 5136 q^{45} + 4150 q^{46} + 24 q^{47} + 344 q^{48} + 827 q^{49} + 8895 q^{50} + 13155 q^{51} + 14070 q^{52} + 414 q^{53} - 2738 q^{55} - 21340 q^{56} - 26925 q^{57} + 2980 q^{58} - 10011 q^{59} - 6856 q^{60} + 9460 q^{61} - 6200 q^{62} + 9150 q^{63} - 2633 q^{64} - 3210 q^{66} + 12154 q^{67} - 9400 q^{68} - 9022 q^{69} - 9380 q^{70} + 17574 q^{71} + 43045 q^{72} + 27950 q^{73} + 43270 q^{74} - 1761 q^{75} + 4090 q^{77} - 42920 q^{78} - 41540 q^{79} - 2308 q^{80} - 21080 q^{81} - 28175 q^{82} - 18665 q^{83} + 26250 q^{84} - 4230 q^{85} - 10125 q^{86} - 15125 q^{88} + 5554 q^{89} + 18400 q^{90} + 7390 q^{91} + 3904 q^{92} + 36898 q^{93} + 18920 q^{94} + 14110 q^{95} - 21140 q^{96} + 20769 q^{97} - 3269 q^{99}+O(q^{100}) \) 12 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 - 18 * q^5 + 75 * q^6 - 80 * q^7 - 245 * q^8 + q^9 - 43 * q^11 + 594 * q^12 + 250 * q^13 + 610 * q^14 + 1134 * q^15 - 633 * q^16 - 1250 * q^17 - 3150 * q^18 - 1025 * q^19 + 752 * q^20 - 35 * q^22 + 1684 * q^23 + 5345 * q^24 + 197 * q^25 + 3490 * q^26 - 687 * q^27 - 3580 * q^28 - 2690 * q^29 - 6740 * q^30 - 1136 * q^31 + 5939 * q^33 + 2370 * q^34 + 3610 * q^35 - 514 * q^36 - 336 * q^37 + 1900 * q^38 - 6880 * q^39 - 2340 * q^40 - 4550 * q^41 + 1310 * q^42 - 6268 * q^44 + 5136 * q^45 + 4150 * q^46 + 24 * q^47 + 344 * q^48 + 827 * q^49 + 8895 * q^50 + 13155 * q^51 + 14070 * q^52 + 414 * q^53 - 2738 * q^55 - 21340 * q^56 - 26925 * q^57 + 2980 * q^58 - 10011 * q^59 - 6856 * q^60 + 9460 * q^61 - 6200 * q^62 + 9150 * q^63 - 2633 * q^64 - 3210 * q^66 + 12154 * q^67 - 9400 * q^68 - 9022 * q^69 - 9380 * q^70 + 17574 * q^71 + 43045 * q^72 + 27950 * q^73 + 43270 * q^74 - 1761 * q^75 + 4090 * q^77 - 42920 * q^78 - 41540 * q^79 - 2308 * q^80 - 21080 * q^81 - 28175 * q^82 - 18665 * q^83 + 26250 * q^84 - 4230 * q^85 - 10125 * q^86 - 15125 * q^88 + 5554 * q^89 + 18400 * q^90 + 7390 * q^91 + 3904 * q^92 + 36898 * q^93 + 18920 * q^94 + 14110 * q^95 - 21140 * q^96 + 20769 * q^97 - 3269 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.46775	−	3.39656i	−0.616936	−	0.849140i	0.380189	−	0.924909i	$-0.375859\pi$
$2$	−2.46775	−	3.39656i	−0.616936	−	0.849140i	−0.997125	+	0.0757688i	$0.975859\pi$
$3$	−2.26281	−	6.96422i	−0.251424	−	0.773803i	−0.994513	−	0.104611i	$-0.966640\pi$
$3$	−2.26281	−	6.96422i	−0.251424	−	0.773803i	0.743090	−	0.669192i	$-0.233360\pi$
$4$	−0.502581	+	1.54679i	−0.0314113	+	0.0966741i
$5$	14.7329	+	10.7041i	0.589315	+	0.428163i	0.842070	−	0.539368i	$-0.181337\pi$
$5$	14.7329	+	10.7041i	0.589315	+	0.428163i	−0.252755	+	0.967530i	$0.581337\pi$
$6$	−18.0704	+	24.8717i	−0.501954	+	0.690881i
$7$	47.9990	+	15.5958i	0.979571	+	0.318282i	0.754674	−	0.656100i	$-0.227795\pi$
$7$	47.9990	+	15.5958i	0.979571	+	0.318282i	0.224898	+	0.974382i	$0.427795\pi$
$8$	−57.3923	+	18.6479i	−0.896755	+	0.291373i
$9$	22.1503	−	16.0931i	0.273460	−	0.198681i
$10$		−	76.4560i		−	0.764560i
$11$	−82.9397	−	88.1022i	−0.685452	−	0.728118i
$11$	−82.9397	−	88.1022i	−0.685452	−	0.728118i
$12$	11.9094			0.0827042
$13$	125.766	+	173.103i	0.744180	+	1.02428i	0.998367	+	0.0571206i	$0.0181919\pi$
$13$	125.766	+	173.103i	0.744180	+	1.02428i	−0.254188	+	0.967155i	$0.581808\pi$
$14$	−65.4772	−	201.518i	−0.334067	−	1.02815i
$15$	41.2077	−	126.824i	0.183146	−	0.563664i
$16$	226.021	+	164.214i	0.882894	+	0.641460i
$17$	−255.614	+	351.822i	−0.884477	+	1.21738i	0.0906838	+	0.995880i	$0.471095\pi$
$17$	−255.614	+	351.822i	−0.884477	+	1.21738i	−0.975161	+	0.221498i	$0.928905\pi$
$18$	−109.323	−	35.5210i	−0.337415	−	0.109633i
$19$	−61.3806	+	19.9438i	−0.170029	+	0.0552459i	−0.392795	−	0.919626i	$-0.628492\pi$
$19$	−61.3806	+	19.9438i	−0.170029	+	0.0552459i	0.222765	+	0.974872i	$0.428492\pi$
$20$	−23.9614	+	17.4089i	−0.0599034	+	0.0435224i
$21$		−	369.566i		−	0.838019i
$22$	−94.5704	+	499.124i	−0.195393	+	1.03125i
$23$	536.875			1.01489			0.507443	−	0.861685i	$-0.330591\pi$
$23$	536.875			1.01489			0.507443	+	0.861685i	$0.330591\pi$
$24$	259.736	+	357.496i	0.450931	+	0.620653i
$25$	−90.6549	−	279.007i	−0.145048	−	0.446411i
$26$	277.594	−	854.346i	0.410642	−	1.26383i
$27$	−642.052	−	466.478i	−0.880730	−	0.639888i
$28$	−48.2468	+	66.4060i	−0.0615393	+	0.0847015i
$29$	−481.802	−	156.547i	−0.572892	−	0.186144i	0.00822167	−	0.999966i	$-0.497383\pi$
$29$	−481.802	−	156.547i	−0.572892	−	0.186144i	−0.581114	+	0.813822i	$0.697383\pi$
$30$	−532.457	+	173.006i	−0.591619	+	0.192229i
$31$	192.037	−	139.523i	0.199830	−	0.145185i	−0.483370	−	0.875416i	$-0.660588\pi$
$31$	192.037	−	139.523i	0.199830	−	0.145185i	0.683200	+	0.730231i	$0.260588\pi$
$32$		−	207.397i		−	0.202536i
$33$	−425.887	+	776.970i	−0.391080	+	0.713471i
$34$	1825.78			1.57939
$35$	540.225	+	743.556i	0.441000	+	0.606984i
$36$	13.7603	+	42.3498i	0.0106175	+	0.0326773i
$37$	−718.836	+	2212.35i	−0.525081	+	1.61603i	0.239075	+	0.971001i	$0.423156\pi$
$37$	−718.836	+	2212.35i	−0.525081	+	1.61603i	−0.764156	+	0.645032i	$0.776844\pi$
$38$	219.212	+	159.267i	0.151809	+	0.110296i
$39$	920.939	−	1267.56i	0.605483	−	0.833375i
$40$	−1045.16	−	339.594i	−0.653227	−	0.212246i
$41$	−100.981	+	32.8108i	−0.0600721	+	0.0195186i	−0.338899	−	0.940823i	$-0.610054\pi$
$41$	−100.981	+	32.8108i	−0.0600721	+	0.0195186i	0.278827	+	0.960341i	$0.410054\pi$
$42$	−1255.25	+	911.995i	−0.711595	+	0.517004i
$43$		−	2058.95i		−	1.11355i	−0.830664	−	0.556773i	$-0.812039\pi$
$43$		−	2058.95i		−	1.11355i	0.830664	−	0.556773i	$-0.187961\pi$
$44$	177.959	−	84.0114i	0.0919211	−	0.0433943i
$45$	498.599			0.246222
$46$	−1324.87	−	1823.53i	−0.626120	−	0.861780i
$47$	17.8846	+	55.0431i	0.00809624	+	0.0249177i	0.955023	−	0.296532i	$-0.0958300\pi$
$47$	17.8846	+	55.0431i	0.00809624	+	0.0249177i	−0.946927	+	0.321449i	$0.895830\pi$
$48$	632.178	−	1945.64i	0.274383	−	0.844464i
$49$	118.225	+	85.8952i	0.0492397	+	0.0357748i
$50$	−723.951	+	996.433i	−0.289580	+	0.398573i
$51$	3028.58	+	984.044i	1.16439	+	0.378333i
$52$	−330.960	+	107.536i	−0.122397	+	0.0397691i
$53$	926.358	−	673.039i	0.329782	−	0.239601i	−0.410556	−	0.911835i	$-0.634665\pi$
$53$	926.358	−	673.039i	0.329782	−	0.239601i	0.740338	+	0.672235i	$0.234665\pi$
$54$			3331.92i			1.14263i
$55$	−278.889	−	2185.79i	−0.0921948	−	0.722576i
$56$	−3045.60			−0.971175
$57$	277.786	+	382.340i	0.0854989	+	0.117679i
$58$	657.244	+	2022.79i	0.195376	+	0.601305i
$59$	−596.473	+	1835.75i	−0.171351	+	0.527364i	−0.999448	−	0.0332206i	$-0.989424\pi$
$59$	−596.473	+	1835.75i	−0.171351	+	0.527364i	0.828097	+	0.560585i	$0.189424\pi$
$60$	175.460	+	127.479i	0.0487389	+	0.0354108i
$61$	−375.548	+	516.897i	−0.100927	+	0.138913i	−0.856493	−	0.516158i	$-0.827362\pi$
$61$	−375.548	+	516.897i	−0.100927	+	0.138913i	0.755567	+	0.655072i	$0.227362\pi$
$62$	−947.795	−	307.957i	−0.246565	−	0.0801138i
$63$	1314.18	−	427.002i	0.331110	−	0.107584i
$64$	2911.90	−	2115.62i	0.710912	−	0.516508i
$65$			3896.51i			0.922251i
$66$	3690.00	−	470.814i	0.847108	−	0.108084i
$67$	−8692.22			−1.93634			−0.968169	−	0.250298i	$-0.919471\pi$
$67$	−8692.22			−1.93634			−0.968169	+	0.250298i	$0.919471\pi$
$68$	−415.727	−	572.199i	−0.0899063	−	0.123745i
$69$	−1214.85	−	3738.92i	−0.255166	−	0.785322i
$70$	1192.39	−	3669.81i	0.243346	−	0.748941i
$71$	1518.36	+	1103.16i	0.301203	+	0.218837i	0.728113	−	0.685457i	$-0.240398\pi$
$71$	1518.36	+	1103.16i	0.301203	+	0.218837i	−0.426910	+	0.904294i	$0.640398\pi$
$72$	−971.154	+	1336.68i	−0.187337	+	0.257847i
$73$	2334.33	+	758.471i	0.438043	+	0.142329i	0.519733	−	0.854329i	$-0.326032\pi$
$73$	2334.33	+	758.471i	0.438043	+	0.142329i	−0.0816893	+	0.996658i	$0.526032\pi$
$74$	9288.28	−	3017.94i	1.69618	−	0.551122i
$75$	−1737.93	+	1262.68i	−0.308966	+	0.224477i
$76$		−	104.966i		−	0.0181728i
$77$	−2607.00	−	5522.33i	−0.439703	−	0.931410i
$78$	−6578.00			−1.08120
$79$	−2255.51	−	3104.44i	−0.361401	−	0.497426i	0.589137	−	0.808033i	$-0.299468\pi$
$79$	−2255.51	−	3104.44i	−0.361401	−	0.497426i	−0.950539	+	0.310607i	$0.899468\pi$
$80$	1572.18	+	4838.68i	0.245654	+	0.756044i
$81$	−1110.50	+	3417.77i	−0.169258	+	0.520922i
$82$	360.640	+	262.020i	0.0536347	+	0.0389679i
$83$	4351.57	−	5989.42i	0.631669	−	0.869418i	−0.366468	−	0.930431i	$-0.619433\pi$
$83$	4351.57	−	5989.42i	0.631669	−	0.869418i	0.998137	+	0.0610127i	$0.0194330\pi$
$84$	571.640	+	185.737i	0.0810147	+	0.0263233i
$85$	−7531.86	+	2447.25i	−1.04247	+	0.338720i
$86$	−6993.34	+	5080.96i	−0.945557	+	0.686987i
$87$			3709.62i			0.490107i
$88$	6403.03	+	3509.74i	0.826837	+	0.453221i
$89$	11104.2			1.40187			0.700937	−	0.713223i	$-0.252765\pi$
$89$	11104.2			1.40187			0.700937	+	0.713223i	$0.252765\pi$
$90$	−1230.42	−	1693.52i	−0.151903	−	0.209077i
$91$	3336.98	+	10270.2i	0.402969	+	1.24021i
$92$	−269.823	+	830.430i	−0.0318789	+	0.0981132i
$93$	−1406.21	−	1021.67i	−0.162587	−	0.118126i
$94$	142.823	−	196.578i	0.0161637	−	0.0222475i
$95$	−1117.79	−	363.193i	−0.123855	−	0.0402430i
$96$	−1444.36	+	469.300i	−0.156723	+	0.0509223i
$97$	9943.57	−	7224.43i	1.05682	−	0.767821i	0.0833186	−	0.996523i	$-0.473448\pi$
$97$	9943.57	−	7224.43i	1.05682	−	0.767821i	0.973497	+	0.228702i	$0.0734481\pi$
$98$		−	613.524i		−	0.0638822i
$99$	−3254.98	−	616.730i	−0.332107	−	0.0629252i
$100$	477.125			0.0477125
$101$	−4980.55	−	6855.14i	−0.488241	−	0.672006i	0.491821	−	0.870696i	$-0.336331\pi$
$101$	−4980.55	−	6855.14i	−0.488241	−	0.672006i	−0.980062	+	0.198690i	$0.936331\pi$
$102$	−4131.39	−	12715.1i	−0.397096	−	1.22214i
$103$	−3982.66	+	12257.4i	−0.375404	+	1.15537i	0.567802	+	0.823165i	$0.307794\pi$
$103$	−3982.66	+	12257.4i	−0.375404	+	1.15537i	−0.943206	+	0.332209i	$0.892206\pi$
$104$	−10446.0	−	7589.48i	−0.965794	−	0.701690i
$105$	3955.86	−	5444.77i	0.358808	−	0.493857i
$106$	−4572.03	−	1485.54i	−0.406909	−	0.132213i
$107$	−3063.72	+	995.464i	−0.267597	+	0.0869477i	−0.439742	−	0.898124i	$-0.644930\pi$
$107$	−3063.72	+	995.464i	−0.267597	+	0.0869477i	0.172145	+	0.985072i	$0.444930\pi$
$108$	1044.22	−	758.674i	0.0895254	−	0.0650440i
$109$		−	14090.5i		−	1.18597i	−0.805215	−	0.592983i	$-0.797950\pi$
$109$		−	14090.5i		−	1.18597i	0.805215	−	0.592983i	$-0.202050\pi$
$110$	−6735.94	+	6341.24i	−0.556690	+	0.524069i
$111$	17033.9			1.38251
$112$	8287.72	+	11407.1i	0.660692	+	0.909365i
$113$	461.161	+	1419.31i	0.0361157	+	0.111153i	0.967489	−	0.252913i	$-0.0813885\pi$
$113$	461.161	+	1419.31i	0.0361157	+	0.111153i	−0.931373	+	0.364065i	$0.881389\pi$
$114$	613.134	−	1887.03i	0.0471787	−	0.145201i
$115$	7909.71	+	5746.74i	0.598088	+	0.434536i
$116$	484.289	−	666.567i	0.0359906	−	0.0495368i
$117$	5571.52	+	1810.30i	0.407007	+	0.132245i
$118$	7707.19	−	2504.22i	0.553519	−	0.179849i
$119$	−17756.2	+	12900.6i	−1.25388	+	0.910996i
$120$			8047.19i			0.558832i
$121$	−883.004	+	14614.3i	−0.0603104	+	0.998180i
$122$	2682.43			0.180222
$123$	457.003	+	629.011i	0.0302071	+	0.0415765i
$124$	119.298	+	367.161i	0.00775871	+	0.0238788i
$125$	5168.06	−	15905.7i	0.330756	−	1.01796i
$126$	−4693.39	−	3409.95i	−0.295628	−	0.214786i
$127$	−10211.8	+	14055.4i	−0.633134	+	0.871435i	−0.998226	−	0.0595368i	$-0.981038\pi$
$127$	−10211.8	+	14055.4i	−0.633134	+	0.871435i	0.365092	+	0.930972i	$0.381038\pi$
$128$	−17527.6	−	5695.05i	−1.06980	−	0.347599i
$129$	−14339.0	+	4659.02i	−0.861665	+	0.279972i
$130$	13234.7	−	9615.60i	0.783120	−	0.568970i
$131$		−	18372.1i		−	1.07057i	−0.844671	−	0.535285i	$-0.820204\pi$
$131$		−	18372.1i		−	1.07057i	0.844671	−	0.535285i	$-0.179796\pi$
$132$	−987.763	−	1049.25i	−0.0566898	−	0.0602184i
$133$	−3257.25			−0.184140
$134$	21450.2	+	29523.6i	1.19460	+	1.64422i
$135$	−4466.06	−	13745.1i	−0.245052	−	0.754191i
$136$	8109.53	−	24958.6i	0.438448	−	1.34940i
$137$	17181.8	+	12483.3i	0.915434	+	0.665102i	0.942383	−	0.334535i	$-0.108579\pi$
$137$	17181.8	+	12483.3i	0.915434	+	0.665102i	−0.0269489	+	0.999637i	$0.508579\pi$
$138$	−9701.52	+	13353.0i	−0.509427	+	0.701165i
$139$	−3870.52	−	1257.61i	−0.200327	−	0.0650901i	0.207135	−	0.978312i	$-0.433586\pi$
$139$	−3870.52	−	1257.61i	−0.200327	−	0.0650901i	−0.407462	+	0.913222i	$0.633586\pi$
$140$	−1421.63	+	461.915i	−0.0725320	+	0.0235671i
$141$	342.863	−	249.105i	0.0172458	−	0.0125298i
$142$		−	7879.53i		−	0.390772i
$143$	4819.69	−	25437.4i	0.235693	−	1.24394i
$144$	7649.14			0.368882
$145$	−5422.65	−	7463.63i	−0.257914	−	0.354988i
$146$	−3184.35	−	9800.42i	−0.149388	−	0.459768i
$147$	330.673	−	1017.71i	0.0153026	−	0.0470965i
$148$	−3060.76	−	2223.77i	−0.139735	−	0.101523i
$149$	−10578.8	+	14560.5i	−0.476503	+	0.655850i	−0.977828	−	0.209409i	$-0.932846\pi$
$149$	−10578.8	+	14560.5i	−0.476503	+	0.655850i	0.501325	+	0.865259i	$0.332846\pi$
$150$	8577.55	+	2787.01i	0.381224	+	0.123867i
$151$	−8398.18	+	2728.73i	−0.368325	+	0.119676i	−0.487331	−	0.873218i	$-0.662029\pi$
$151$	−8398.18	+	2728.73i	−0.368325	+	0.119676i	0.119006	+	0.992894i	$0.462029\pi$
$152$	3150.87	−	2289.24i	0.136378	−	0.0990842i
$153$			11906.6i			0.508633i
$154$	−12323.5	+	22482.5i	−0.519629	+	0.947990i
$155$	4322.71			0.179926
$156$	1497.80	+	2061.55i	0.0615468	+	0.0847119i
$157$	−5990.27	−	18436.1i	−0.243023	−	0.747947i	−0.995955	−	0.0898493i	$-0.971361\pi$
$157$	−5990.27	−	18436.1i	−0.243023	−	0.747947i	0.752933	−	0.658098i	$-0.228639\pi$
$158$	−4978.39	+	15321.9i	−0.199423	+	0.613761i
$159$	−6783.37	−	4928.40i	−0.268319	−	0.194945i
$160$	2219.99	−	3055.55i	0.0867183	−	0.119357i
$161$	25769.5	+	8373.00i	0.994153	+	0.323020i
$162$	14349.1	−	4662.30i	0.546757	−	0.177652i
$163$	3687.37	−	2679.03i	0.138785	−	0.100833i	−0.516227	−	0.856452i	$-0.672664\pi$
$163$	3687.37	−	2679.03i	0.138785	−	0.100833i	0.655011	+	0.755619i	$0.272664\pi$
$164$		−	172.686i		−	0.00642052i
$165$	−14591.3	+	6888.29i	−0.535951	+	0.253013i
$166$	−31082.0			−1.12796
$167$	7251.30	+	9980.56i	0.260006	+	0.357867i	0.918984	−	0.394295i	$-0.129011\pi$
$167$	7251.30	+	9980.56i	0.260006	+	0.357867i	−0.658978	+	0.752162i	$0.729011\pi$
$168$	6891.63	+	21210.3i	0.244176	+	0.751498i
$169$	−5321.48	+	16377.8i	−0.186320	+	0.573434i
$170$	26898.9	+	19543.2i	0.930759	+	0.676236i
$171$	−1038.64	+	1429.57i	−0.0355200	+	0.0488891i
$172$	3184.75	+	1034.79i	0.107651	+	0.0349780i
$173$	653.072	−	212.196i	0.0218207	−	0.00708998i	−0.298086	−	0.954539i	$-0.596348\pi$
$173$	653.072	−	212.196i	0.0218207	−	0.00708998i	0.319907	+	0.947449i	$0.396348\pi$
$174$	12599.9	−	9154.39i	0.416169	−	0.302365i
$175$		−	14805.9i		−	0.483458i
$176$	−4278.51	−	33532.8i	−0.138123	−	1.08254i
$177$	14134.3			0.451158
$178$	−27402.4	−	37716.2i	−0.864867	−	1.19039i
$179$	4275.10	+	13157.4i	0.133426	+	0.410643i	0.995342	−	0.0964086i	$-0.0307355\pi$
$179$	4275.10	+	13157.4i	0.133426	+	0.410643i	−0.861916	+	0.507051i	$0.830736\pi$
$180$	−250.587	+	771.226i	−0.00773415	+	0.0238033i
$181$	−16520.5	−	12002.8i	−0.504272	−	0.366375i	0.306374	−	0.951911i	$-0.400884\pi$
$181$	−16520.5	−	12002.8i	−0.504272	−	0.366375i	−0.810647	+	0.585536i	$0.800884\pi$
$182$	26648.5	−	36678.5i	0.804506	−	1.10731i
$183$	4449.58	+	1445.76i	0.132867	+	0.0431711i
$184$	−30812.5	+	10011.6i	−0.910105	+	0.295711i
$185$	−34271.6	+	24899.8i	−1.00136	+	0.727533i
$186$			7297.51i			0.210935i
$187$	52196.9	−	6659.89i	1.49266	−	0.190451i
$188$	−94.1283			−0.00266321
$189$	−23542.7	−	32403.8i	−0.659073	−	0.907136i
$190$	1524.82	+	4692.92i	0.0422388	+	0.129998i
$191$	−2265.94	+	6973.85i	−0.0621130	+	0.191164i	−0.977298	−	0.211870i	$-0.932045\pi$
$191$	−2265.94	+	6973.85i	−0.0621130	+	0.191164i	0.915185	+	0.403034i	$0.132045\pi$
$192$	−21322.7	−	15491.9i	−0.578416	−	0.420244i
$193$	21150.0	−	29110.5i	0.567801	−	0.781511i	−0.424491	−	0.905432i	$-0.639547\pi$
$193$	21150.0	−	29110.5i	0.567801	−	0.781511i	0.992292	+	0.123921i	$0.0395470\pi$
$194$	−49076.4	−	15945.9i	−1.30398	−	0.423687i
$195$	27136.2	−	8817.08i	0.713640	−	0.231876i
$196$	−192.279	+	139.699i	−0.00500518	+	0.00363647i
$197$			39661.5i			1.02197i	0.859591	+	0.510983i	$0.170718\pi$
$197$			39661.5i			1.02197i	−0.859591	+	0.510983i	$0.829282\pi$
$198$	5937.70	+	12577.7i	0.151456	+	0.320826i
$199$	8985.83			0.226909			0.113455	−	0.993543i	$-0.463808\pi$
$199$	8985.83			0.226909			0.113455	+	0.993543i	$0.463808\pi$
$200$	10405.8	+	14322.3i	0.260145	+	0.358058i
$201$	19668.9	+	60534.6i	0.486841	+	1.49834i
$202$	−10993.2	+	33833.5i	−0.269414	+	0.829170i
$203$	−20684.6	−	15028.2i	−0.501943	−	0.364683i
$204$	−3044.21	+	4189.99i	−0.0731500	+	0.100682i
$205$	−1838.95	−	597.512i	−0.0437586	−	0.0142180i
$206$	51461.1	−	16720.7i	1.21267	−	0.394022i
$207$	11891.9	−	8639.99i	0.277531	−	0.201638i
$208$			59777.3i			1.38169i
$209$	6847.99	+	3753.64i	0.156773	+	0.0859330i
$210$	−28255.6			−0.640716
$211$	4141.35	+	5700.08i	0.0930202	+	0.128031i	0.852990	−	0.521927i	$-0.174787\pi$
$211$	4141.35	+	5700.08i	0.0930202	+	0.128031i	−0.759970	+	0.649958i	$0.774787\pi$
$212$	575.476	+	1771.13i	0.0128043	+	0.0394076i
$213$	4246.85	−	13070.5i	0.0936069	−	0.288093i
$214$	10941.6	+	7949.57i	0.238921	+	0.173586i
$215$	22039.1	−	30334.2i	0.476779	−	0.656230i
$216$	45547.7	+	14799.3i	0.976245	+	0.317201i
$217$	11393.5	−	3701.99i	0.241958	−	0.0786168i
$218$	−47859.1	+	34771.7i	−1.00705	+	0.731665i
$219$		−	17973.1i		−	0.374744i
$220$	3521.11	+	667.156i	0.0727503	+	0.0137842i
$221$	−93049.0			−1.90514
$222$	−42035.3	−	57856.6i	−0.852920	−	1.17394i
$223$	−3954.30	−	12170.1i	−0.0795170	−	0.244728i	0.903393	−	0.428813i	$-0.141068\pi$
$223$	−3954.30	−	12170.1i	−0.0795170	−	0.244728i	−0.982910	+	0.184085i	$0.941068\pi$
$224$	3234.52	−	9954.83i	0.0644635	−	0.198398i
$225$	−6498.12	−	4721.16i	−0.128358	−	0.0932575i
$226$	3682.74	−	5068.85i	0.0721031	−	0.0992414i
$227$	−53534.9	−	17394.5i	−1.03893	−	0.337568i	−0.260613	−	0.965443i	$-0.583925\pi$
$227$	−53534.9	−	17394.5i	−1.03893	−	0.337568i	−0.778314	+	0.627876i	$0.783925\pi$
$228$	−731.007	+	237.519i	−0.0140622	+	0.00456907i
$229$	72710.1	−	52827.0i	1.38651	−	1.00736i	0.390275	−	0.920698i	$-0.372380\pi$
$229$	72710.1	−	52827.0i	1.38651	−	1.00736i	0.996238	−	0.0866626i	$-0.0276202\pi$
$230$		−	41047.3i		−	0.775941i
$231$	−32559.6	+	30651.7i	−0.610176	+	0.574422i
$232$	30571.0			0.567982
$233$	14585.7	+	20075.5i	0.268668	+	0.369790i	0.921939	−	0.387334i	$-0.126604\pi$
$233$	14585.7	+	20075.5i	0.268668	+	0.369790i	−0.653272	+	0.757124i	$0.726604\pi$
$234$	−7600.31	−	23391.4i	−0.138803	−	0.427193i
$235$	−325.693	+	1002.38i	−0.00589757	+	0.0181509i
$236$	−2539.74	−	1845.23i	−0.0456001	−	0.0331304i
$237$	−16516.2	+	22732.6i	−0.294045	+	0.404718i
$238$	87635.4	+	28474.5i	1.54713	+	0.502692i
$239$	31899.0	−	10364.6i	0.558445	−	0.181450i	−0.0161762	−	0.999869i	$-0.505149\pi$
$239$	31899.0	−	10364.6i	0.558445	−	0.181450i	0.574622	+	0.818419i	$0.305149\pi$
$240$	30140.1	−	21898.1i	0.523266	−	0.380175i
$241$			71818.0i			1.23651i	0.785976	+	0.618257i	$0.212161\pi$
$241$			71818.0i			1.23651i	−0.785976	+	0.618257i	$0.787839\pi$
$242$	51817.5	−	33065.3i	0.884802	−	0.564601i
$243$	−37968.2			−0.642996
$244$	−610.786	−	840.674i	−0.0102591	−	0.0141204i
$245$	822.361	+	2530.97i	0.0137003	+	0.0421652i
$246$	1008.71	−	3104.48i	0.0166684	−	0.0513001i
$247$	−11171.9	−	8116.89i	−0.183120	−	0.133044i
$248$	−8419.63	+	11588.6i	−0.136896	+	0.188421i
$249$	−51558.5	−	16752.4i	−0.831575	−	0.270195i
$250$	−66778.0	+	21697.5i	−1.06845	+	0.347160i
$251$	−38944.7	+	28295.0i	−0.618160	+	0.449120i	−0.852278	−	0.523089i	$-0.824780\pi$
$251$	−38944.7	+	28295.0i	−0.618160	+	0.449120i	0.234118	+	0.972208i	$0.424780\pi$
$252$			2247.35i			0.0353892i
$253$	−44528.2	−	47299.9i	−0.695656	−	0.738956i
$254$	72940.1			1.13057
$255$	34086.4	+	46915.9i	0.524204	+	0.721505i
$256$	6114.07	+	18817.2i	0.0932933	+	0.287127i
$257$	7798.62	−	24001.7i	0.118073	−	0.363392i	−0.874502	−	0.485021i	$-0.838812\pi$
$257$	7798.62	−	24001.7i	0.118073	−	0.363392i	0.992576	+	0.121629i	$0.0388119\pi$
$258$	51209.6	+	37205.9i	0.769328	+	0.558950i
$259$	−69006.8	+	94979.7i	−1.02871	+	1.41590i
$260$	−6027.07	−	1958.31i	−0.0891578	−	0.0289691i
$261$	−13191.4	+	4286.14i	−0.193646	+	0.0629196i
$262$	−62401.8	+	45337.6i	−0.909064	+	0.660474i
$263$		−	73780.1i		−	1.06666i	−0.845906	−	0.533332i	$-0.820940\pi$
$263$		−	73780.1i		−	1.06666i	0.845906	−	0.533332i	$-0.179060\pi$
$264$	9953.77	−	52534.0i	0.142817	−	0.753759i
$265$	20852.2			0.296934
$266$	8038.06	+	11063.4i	0.113603	+	0.156360i
$267$	−25126.8	−	77332.4i	−0.352464	−	1.08477i
$268$	4368.54	−	13445.0i	0.0608229	−	0.187194i
$269$	114414.	+	83127.0i	1.58116	+	1.14878i	0.915348	+	0.402663i	$0.131915\pi$
$269$	114414.	+	83127.0i	1.58116	+	1.14878i	0.665813	+	0.746119i	$0.268085\pi$
$270$	−35665.1	+	49088.7i	−0.489233	+	0.673371i
$271$	96839.3	+	31465.0i	1.31860	+	0.428439i	0.882014	−	0.471223i	$-0.156187\pi$
$271$	96839.3	+	31465.0i	1.31860	+	0.428439i	0.436586	+	0.899663i	$0.356187\pi$
$272$	−115548.	+	37543.8i	−1.56180	+	0.507459i
$273$	63972.9	−	46479.0i	0.858362	−	0.623636i
$274$		−	89164.6i		−	1.18766i
$275$	−17062.2	+	31127.7i	−0.225616	+	0.411605i
$276$	6393.86			0.0839354
$277$	15920.1	+	21912.2i	0.207485	+	0.285579i	0.900059	−	0.435768i	$-0.143523\pi$
$277$	15920.1	+	21912.2i	0.207485	+	0.285579i	−0.692574	+	0.721347i	$0.743523\pi$
$278$	5279.91	+	16249.9i	0.0683183	+	0.210262i
$279$	2008.31	−	6180.94i	0.0258001	−	0.0794047i
$280$	−44870.5	−	32600.3i	−0.572328	−	0.415821i
$281$	77971.9	−	107319.i	0.987474	−	1.35914i	0.0547693	−	0.998499i	$-0.482558\pi$
$281$	77971.9	−	107319.i	0.987474	−	1.35914i	0.932704	−	0.360642i	$-0.117442\pi$
$282$	−1692.20	−	549.828i	−0.0212791	−	0.00691399i
$283$	80080.5	−	26019.7i	0.999894	−	0.324885i	0.237071	−	0.971492i	$-0.423813\pi$
$283$	80080.5	−	26019.7i	0.999894	−	0.324885i	0.762823	+	0.646607i	$0.223813\pi$
$284$	−2469.45	+	1794.16i	−0.0306170	+	0.0222446i
$285$			8606.40i			0.105958i
$286$	−98293.3	+	46402.6i	−1.20169	+	0.567297i
$287$	−5358.71			−0.0650574
$288$	−3337.66	−	4593.90i	−0.0402399	−	0.0553855i
$289$	−32631.1	−	100428.i	−0.390693	−	1.20243i
$290$	−11969.0	+	36836.7i	−0.142318	+	0.438011i
$291$	−72813.0	−	52901.7i	−0.859850	−	0.624718i
$292$	−2346.38	+	3229.52i	−0.0275190	+	0.0378767i
$293$	−114757.	−	37286.9i	−1.33673	−	0.434331i	−0.448524	−	0.893771i	$-0.648050\pi$
$293$	−114757.	−	37286.9i	−1.33673	−	0.434331i	−0.888209	+	0.459440i	$0.848050\pi$
$294$	−4272.72	+	1388.29i	−0.0494322	+	0.0160615i
$295$	−28437.8	+	20661.3i	−0.326777	+	0.237418i
$296$		−	140377.i		−	1.60218i
$297$	12153.9	+	95255.8i	0.137785	+	1.07989i
$298$	75561.6			0.850880
$299$	67520.8	+	92934.4i	0.755258	+	1.03952i
$300$	−1079.65	−	3322.81i	−0.0119961	−	0.0369201i
$301$	32111.0	−	98827.4i	0.354422	−	1.09080i
$302$	29992.9	+	21791.1i	0.328855	+	0.238927i
$303$	−36470.7	+	50197.5i	−0.397245	+	0.546761i
$304$	−17148.3	−	5571.83i	−0.185556	−	0.0602908i
$305$	−11065.8	+	3595.50i	−0.118955	+	0.0386508i
$306$	40441.4	−	29382.4i	0.431901	−	0.313794i
$307$			130584.i			1.38553i	0.721166	+	0.692763i	$0.243607\pi$
$307$			130584.i			1.38553i	−0.721166	+	0.692763i	$0.756393\pi$
$308$	9852.09	−	1257.05i	0.103855	−	0.0132510i
$309$	94375.0			0.988417
$310$	−10667.4	−	14682.4i	−0.111003	−	0.152782i
$311$	30522.3	+	93937.9i	0.315570	+	0.971225i	0.975519	+	0.219915i	$0.0705780\pi$
$311$	30522.3	+	93937.9i	0.315570	+	0.971225i	−0.659949	+	0.751311i	$0.729422\pi$
$312$	−29217.4	+	89922.0i	−0.300146	+	0.923755i
$313$	−50811.9	−	36917.0i	−0.518653	−	0.376823i	0.297443	−	0.954739i	$-0.403866\pi$
$313$	−50811.9	−	36917.0i	−0.518653	−	0.376823i	−0.816096	+	0.577916i	$0.803866\pi$
$314$	−47837.0	+	65842.0i	−0.485182	+	0.667796i
$315$	23932.3	+	7776.07i	0.241192	+	0.0783680i
$316$	5935.47	−	1928.55i	0.0594403	−	0.0193133i
$317$	−15918.3	+	11565.4i	−0.158409	+	0.115091i	−0.664166	−	0.747585i	$-0.731213\pi$
$317$	−15918.3	+	11565.4i	−0.158409	+	0.115091i	0.505757	+	0.862676i	$0.331213\pi$
$318$			35202.2i			0.348109i
$319$	26168.4	+	55431.8i	0.257156	+	0.544726i
$320$	65546.3			0.640101
$321$	13865.3	+	19083.9i	0.134561	+	0.185207i
$322$	−35153.0	−	108190.i	−0.339040	−	1.04346i
$323$	8673.08	−	26693.0i	0.0831320	−	0.255854i
$324$	−4728.44	−	3435.41i	−0.0450431	−	0.0327257i
$325$	36895.5	−	50782.3i	0.349306	−	0.480779i
$326$	−18199.0	−	5913.21i	−0.171243	−	0.0556401i
$327$	−98129.1	+	31884.1i	−0.917704	+	0.298180i
$328$	5183.70	−	3766.18i	0.0481828	−	0.0350068i
$329$			2920.94i			0.0269855i
$330$	59404.0	+	32561.6i	0.545491	+	0.299004i
$331$	28807.4			0.262935			0.131468	−	0.991320i	$-0.458031\pi$
$331$	28807.4			0.262935			0.131468	+	0.991320i	$0.458031\pi$
$332$	7077.33	+	9741.11i	0.0642086	+	0.0883756i
$333$	19681.2	+	60572.5i	0.177485	+	0.546244i
$334$	16005.2	−	49259.0i	0.143472	−	0.441563i
$335$	−128061.	−	93042.1i	−1.14111	−	0.829067i
$336$	60687.8	−	83529.6i	0.537555	−	0.739881i
$337$	−178804.	−	58096.9i	−1.57441	−	0.511556i	−0.613800	−	0.789462i	$-0.710360\pi$
$337$	−178804.	−	58096.9i	−1.57441	−	0.511556i	−0.960608	+	0.277906i	$0.910360\pi$
$338$	68760.4	−	22341.6i	0.601873	−	0.195560i
$339$	8840.86	−	6423.26i	0.0769299	−	0.0558928i
$340$		−	12880.1i		−	0.111420i
$341$	−28219.7	−	5346.88i	−0.242686	−	0.0459824i
$342$	7418.71			0.0634273
$343$	−66890.6	−	92067.1i	−0.568561	−	0.782557i
$344$	38395.1	+	118168.i	0.324458	+	0.998579i
$345$	22123.4	−	68088.8i	0.185872	−	0.572055i
$346$	−2332.35	−	1694.55i	−0.0194824	−	0.0141548i
$347$	17060.3	−	23481.5i	0.141687	−	0.195015i	−0.732276	−	0.681008i	$-0.761542\pi$
$347$	17060.3	−	23481.5i	0.141687	−	0.195015i	0.873963	+	0.485993i	$0.161542\pi$
$348$	−5737.98	−	1864.38i	−0.0473806	−	0.0153949i
$349$	90136.3	−	29287.0i	0.740029	−	0.240450i	0.0853437	−	0.996352i	$-0.472801\pi$
$349$	90136.3	−	29287.0i	0.740029	−	0.240450i	0.654685	+	0.755902i	$0.272801\pi$
$350$	−50289.1	+	36537.2i	−0.410523	+	0.298263i
$351$		−	169808.i		−	1.37830i
$352$	−18272.1	+	17201.4i	−0.147470	+	0.138829i
$353$	−107013.			−0.858793			−0.429397	−	0.903116i	$-0.641274\pi$
$353$	−107013.			−0.858793			−0.429397	+	0.903116i	$0.641274\pi$
$354$	−34879.9	−	48008.0i	−0.278335	−	0.383096i
$355$	10561.6	+	32505.3i	0.0838058	+	0.257928i
$356$	−5580.78	+	17175.9i	−0.0440347	+	0.135525i
$357$	130022.	+	94466.2i	1.02019	+	0.741208i
$358$	34140.0	−	46989.7i	0.266378	−	0.366638i
$359$	64156.8	+	20845.8i	0.497799	+	0.161745i	0.547146	−	0.837037i	$-0.315714\pi$
$359$	64156.8	+	20845.8i	0.497799	+	0.161745i	−0.0493475	+	0.998782i	$0.515714\pi$
$360$	−28615.8	+	9297.83i	−0.220801	+	0.0717425i
$361$	−102062.	+	74152.4i	−0.783159	+	0.568998i
$362$			85732.7i			0.654228i
$363$	103776.	−	26920.1i	0.787558	−	0.204298i
$364$	−17562.9			−0.132554
$365$	26272.7	+	36161.3i	0.197206	+	0.271430i
$366$	−6069.83	−	18681.0i	−0.0453121	−	0.139456i
$367$	−50426.9	+	155198.i	−0.374395	+	1.15227i	0.569491	+	0.821998i	$0.307141\pi$
$367$	−50426.9	+	155198.i	−0.374395	+	1.15227i	−0.943886	+	0.330272i	$0.892859\pi$
$368$	121345.	+	88162.2i	0.896037	+	0.651009i
$369$	−1708.74	+	2351.87i	−0.0125494	+	0.0172727i
$370$	169147.	+	54959.3i	1.23555	+	0.401456i
$371$	54960.9	−	17857.9i	0.399306	−	0.129742i
$372$	2287.04	−	1661.63i	0.0165268	−	0.0120074i
$373$			125734.i			0.903719i	0.892089	+	0.451860i	$0.149239\pi$
$373$			125734.i			0.903719i	−0.892089	+	0.451860i	$0.850761\pi$
$374$	−151429.	−	160855.i	−1.08260	−	1.14998i
$375$	−122465.			−0.870862
$376$	−2052.88	−	2825.54i	−0.0145207	−	0.0199860i
$377$	−33495.8	−	103090.i	−0.235672	−	0.725324i
$378$	−51964.0	+	159929.i	−0.363680	+	1.11929i
$379$	−78050.7	−	56707.2i	−0.543373	−	0.394784i	0.281963	−	0.959425i	$-0.409014\pi$
$379$	−78050.7	−	56707.2i	−0.543373	−	0.394784i	−0.825336	+	0.564641i	$0.809014\pi$
$380$	1123.56	−	1546.45i	0.00778091	−	0.0107095i
$381$	120992.	+	39312.8i	0.833504	+	0.270822i
$382$	29278.9	−	9513.29i	0.200645	−	0.0651934i
$383$	123692.	−	89867.7i	0.843228	−	0.612641i	−0.0800426	−	0.996791i	$-0.525506\pi$
$383$	123692.	−	89867.7i	0.843228	−	0.612641i	0.923270	+	0.384151i	$0.125506\pi$
$384$			134953.i			0.915207i
$385$	20702.8	−	109265.i	0.139672	−	0.737158i
$386$	−151068.			−1.01391
$387$	−33134.9	−	45606.3i	−0.221240	−	0.304511i
$388$	6177.19	+	19011.4i	0.0410325	+	0.126285i
$389$	−10802.6	+	33246.9i	−0.0713884	+	0.219711i	−0.980385	−	0.197093i	$-0.936850\pi$
$389$	−10802.6	+	33246.9i	−0.0713884	+	0.219711i	0.908996	+	0.416804i	$0.136850\pi$
$390$	−96912.9	−	70411.3i	−0.637166	−	0.462928i
$391$	−137233.	+	188884.i	−0.897643	+	1.23550i
$392$	−8386.95	−	2725.09i	−0.0545798	−	0.0177341i
$393$	−127947.	+	41572.5i	−0.828410	+	0.269167i
$394$	134713.	−	97874.4i	0.867792	−	0.630488i
$395$		−	69880.4i		−	0.447879i
$396$	2589.84	−	4724.80i	0.0165151	−	0.0301296i
$397$	20457.2			0.129797			0.0648986	−	0.997892i	$-0.479328\pi$
$397$	20457.2			0.129797			0.0648986	+	0.997892i	$0.479328\pi$
$398$	−22174.7	−	30520.9i	−0.139989	−	0.192678i
$399$	7370.55	+	22684.2i	0.0462971	+	0.142488i
$400$	25326.9	−	77948.1i	0.158293	−	0.487176i
$401$	153780.	+	111728.i	0.956338	+	0.694820i	0.952297	−	0.305171i	$-0.0987137\pi$
$401$	153780.	+	111728.i	0.956338	+	0.694820i	0.00404091	+	0.999992i	$0.498714\pi$
$402$	157072.	−	216190.i	0.971953	−	1.33778i
$403$	48303.5	+	15694.8i	0.297419	+	0.0966373i
$404$	13106.6	−	4258.58i	0.0803019	−	0.0260917i
$405$	−52944.9	+	38466.7i	−0.322786	+	0.234517i
$406$			107342.i			0.651205i
$407$	254533.	−	120161.i	1.53658	−	0.725393i
$408$	−192167.			−1.15441
$409$	−110780.	−	152476.i	−0.662240	−	0.911495i	0.337313	−	0.941392i	$-0.390482\pi$
$409$	−110780.	−	152476.i	−0.662240	−	0.911495i	−0.999553	+	0.0298979i	$0.990482\pi$
$410$	2508.58	+	7720.62i	0.0149232	+	0.0459288i
$411$	48057.3	−	147905.i	0.284496	−	0.875588i
$412$	−16957.9	−	12320.6i	−0.0999028	−	0.0725836i
$413$	−57260.2	+	78811.9i	−0.335701	+	0.462053i
$414$	−58692.5	−	19070.3i	−0.342438	−	0.111265i
$415$	128222.	−	41661.9i	0.744504	−	0.241904i
$416$	35900.9	−	26083.5i	0.207452	−	0.150723i
$417$			29800.9i			0.171379i
$418$	−4149.62	−	32522.6i	−0.0237496	−	0.186137i
$419$	−34335.6			−0.195577			−0.0977883	−	0.995207i	$-0.531177\pi$
$419$	−34335.6			−0.195577			−0.0977883	+	0.995207i	$0.531177\pi$
$420$	6433.76	+	8855.31i	0.0364725	+	0.0502002i
$421$	81293.7	+	250196.i	0.458662	+	1.41162i	0.866781	+	0.498688i	$0.166185\pi$
$421$	81293.7	+	250196.i	0.458662	+	1.41162i	−0.408119	+	0.912929i	$0.633815\pi$
$422$	9140.87	−	28132.7i	0.0513290	−	0.157974i
$423$	1281.96	+	931.402i	0.00716465	+	0.00520543i
$424$	−40615.1	+	55901.9i	−0.225921	+	0.310953i
$425$	121333.	+	39423.6i	0.671743	+	0.218262i
$426$	−54874.8	+	17829.9i	−0.302380	+	0.0982493i
$427$	−26087.3	+	18953.6i	−0.143078	+	0.103953i
$428$		−	5239.22i		−	0.0286009i
$429$	−188058.	+	23994.6i	−1.02182	+	0.130376i
$430$	−157419.			−0.851373
$431$	−128666.	−	177094.i	−0.692643	−	0.953341i	−0.999998	−	0.00174659i	$-0.999444\pi$
$431$	−128666.	−	177094.i	−0.692643	−	0.953341i	0.307355	−	0.951595i	$-0.400556\pi$
$432$	−68515.0	−	210867.i	−0.367129	−	1.12991i
$433$	21470.6	−	66079.8i	0.114517	−	0.352446i	−0.877329	−	0.479889i	$-0.840677\pi$
$433$	21470.6	−	66079.8i	0.114517	−	0.352446i	0.991846	+	0.127443i	$0.0406769\pi$
$434$	−40690.4	−	29563.3i	−0.216029	−	0.156954i
$435$	−39708.0	+	54653.3i	−0.209845	+	0.288827i
$436$	21794.9	+	7081.60i	0.114652	+	0.0372527i
$437$	−32953.7	+	10707.3i	−0.172561	+	0.0560683i
$438$	−61046.7	+	44353.0i	−0.318210	+	0.231193i
$439$			72005.3i			0.373625i	0.982396	+	0.186812i	$0.0598156\pi$
$439$			72005.3i			0.373625i	−0.982396	+	0.186812i	$0.940184\pi$
$440$	56766.5	+	120247.i	0.293216	+	0.621111i
$441$	4001.03			0.0205729
$442$	229621.	+	316046.i	1.17535	+	1.61773i
$443$	−13800.0	−	42472.2i	−0.0703190	−	0.216420i	0.909721	−	0.415220i	$-0.136295\pi$
$443$	−13800.0	−	42472.2i	−0.0703190	−	0.216420i	−0.980040	+	0.198800i	$0.936295\pi$
$444$	−8560.91	+	26347.8i	−0.0434264	+	0.133653i
$445$	163597.	+	118861.i	0.826146	+	0.600230i
$446$	−31578.2	+	43463.7i	−0.158752	+	0.218503i
$447$	125341.	+	40725.7i	0.627303	+	0.203823i
$448$	172763.	−	56134.1i	0.860785	−	0.279686i
$449$	−104641.	+	76026.2i	−0.519050	+	0.377112i	−0.816246	−	0.577704i	$-0.803949\pi$
$449$	−104641.	+	76026.2i	−0.519050	+	0.377112i	0.297196	+	0.954817i	$0.403949\pi$
$450$			33721.9i			0.166528i
$451$	11266.1	+	6175.35i	0.0553884	+	0.0303605i
$452$	−2427.14			−0.0118800
$453$	38007.0	+	52312.2i	0.185211	+	0.254922i
$454$	73028.8	+	224760.i	0.354309	+	1.09045i
$455$	−60769.3	+	187029.i	−0.293536	+	0.903411i
$456$	−23072.6	−	16763.2i	−0.110960	−	0.0806173i
$457$	180382.	−	248275.i	0.863697	−	1.18878i	−0.116979	−	0.993134i	$-0.537321\pi$
$457$	180382.	−	248275.i	0.863697	−	1.18878i	0.980675	−	0.195642i	$-0.0626791\pi$
$458$	−358860.	−	116601.i	−1.71078	−	0.555866i
$459$	328235.	−	106650.i	1.55797	−	0.506215i
$460$	−12864.2	+	9346.42i	−0.0607951	+	0.0441702i
$461$		−	22814.7i		−	0.107353i	−0.998558	−	0.0536764i	$-0.982906\pi$
$461$		−	22814.7i		−	0.107353i	0.998558	−	0.0536764i	$-0.0170940\pi$
$462$	184459.	+	34950.0i	0.864204	+	0.163743i
$463$	247942.			1.15661			0.578307	−	0.815819i	$-0.303713\pi$
$463$	247942.			1.15661			0.578307	+	0.815819i	$0.303713\pi$
$464$	−83190.2	−	114501.i	−0.386399	−	0.531833i
$465$	−9781.50	−	30104.4i	−0.0452376	−	0.139227i
$466$	32193.8	−	99082.5i	0.148252	−	0.456273i
$467$	−261318.	−	189859.i	−1.19822	−	0.870557i	−0.204111	−	0.978948i	$-0.565430\pi$
$467$	−261318.	−	189859.i	−1.19822	−	0.870557i	−0.994108	+	0.108390i	$0.965430\pi$
$468$	−5600.28	+	7708.13i	−0.0255693	+	0.0351931i
$469$	−417218.	−	135562.i	−1.89678	−	0.616301i
$470$	4208.38	−	1367.38i	0.0190511	−	0.00619006i
$471$	−114839.	+	83435.1i	−0.517662	+	0.376103i
$472$		−	116481.i		−	0.522844i
$473$	−181398.	+	170769.i	−0.810793	+	0.763283i
$474$	117970.			0.525069
$475$	11128.9	+	15317.6i	0.0493248	+	0.0678898i
$476$	−11030.6	−	33948.6i	−0.0486837	−	0.149833i
$477$	9687.80	−	29816.0i	0.0425783	−	0.131043i
$478$	−113922.	−	82769.5i	−0.498602	−	0.362255i
$479$	58964.1	−	81157.2i	0.256990	−	0.353717i	−0.660954	−	0.750427i	$-0.729848\pi$
$479$	58964.1	−	81157.2i	0.256990	−	0.353717i	0.917944	+	0.396710i	$0.129848\pi$
$480$	−26303.0	−	8546.35i	−0.114162	−	0.0370935i
$481$	−473369.	+	153807.i	−2.04602	+	0.664791i
$482$	243934.	−	177229.i	1.04997	−	0.762851i
$483$		−	198411.i		−	0.850493i
$484$	−22161.5	−	8710.71i	−0.0946037	−	0.0371846i
$485$	223828.			0.951549
$486$	93695.9	+	128961.i	0.396687	+	0.545993i
$487$	−113517.	−	349368.i	−0.478632	−	1.47308i	−0.840997	−	0.541040i	$-0.818031\pi$
$487$	−113517.	−	349368.i	−0.478632	−	1.47308i	0.362365	−	0.932036i	$-0.381969\pi$
$488$	11914.5	−	36669.1i	0.0500307	−	0.153979i
$489$	−27001.2	−	19617.5i	−0.112919	−	0.0820402i
$490$	6567.20	−	9038.98i	0.0273520	−	0.0376467i
$491$	212925.	+	69183.6i	0.883210	+	0.286972i	0.715290	−	0.698828i	$-0.246295\pi$
$491$	212925.	+	69183.6i	0.883210	+	0.286972i	0.167921	+	0.985801i	$0.446295\pi$
$492$	−1202.63	+	390.757i	−0.00496822	+	0.00161427i
$493$	178232.	−	129493.i	0.733318	−	0.532786i
$494$			57976.6i			0.237574i
$495$	−41353.7	−	43927.7i	−0.168773	−	0.179278i
$496$	66315.8			0.269559
$497$	55675.4	+	76630.5i	0.225398	+	0.310234i
$498$	70332.8	+	216462.i	0.283595	+	0.872816i
$499$	−128358.	+	395046.i	−0.515492	+	1.58652i	0.266892	+	0.963726i	$0.414003\pi$
$499$	−128358.	+	395046.i	−0.515492	+	1.58652i	−0.782384	+	0.622796i	$0.785997\pi$
$500$	22005.3	+	15987.8i	0.0880211	+	0.0639511i
$501$	53098.5	−	73083.9i	0.211547	−	0.291170i
$502$	192211.	+	62453.2i	0.762731	+	0.247826i
$503$	−319477.	+	103805.i	−1.26271	+	0.410280i	−0.862460	−	0.506125i	$-0.831077\pi$
$503$	−319477.	+	103805.i	−1.26271	+	0.410280i	−0.400252	+	0.916405i	$0.631077\pi$
$504$	−67461.0	+	49013.3i	−0.265578	+	0.192954i
$505$		−	154308.i		−	0.605070i
$506$	−50772.4	+	267967.i	−0.198302	+	1.04660i
$507$	126100.			0.490570
$508$	−16608.4	−	22859.5i	−0.0643576	−	0.0885806i
$509$	69443.4	+	213725.i	0.268038	+	0.824935i	0.990978	+	0.134024i	$0.0427901\pi$
$509$	69443.4	+	213725.i	0.268038	+	0.824935i	−0.722940	+	0.690910i	$0.757210\pi$
$510$	75236.1	−	231553.i	0.289258	−	0.890245i
$511$	100217.	+	72811.7i	0.383794	+	0.278843i
$512$	−124497.	+	171355.i	−0.474917	+	0.653667i
$513$	48712.9	+	15827.8i	0.185101	+	0.0601430i
$514$	−100768.	+	32741.5i	−0.381414	+	0.123929i
$515$	−189880.	+	137956.i	−0.715919	+	0.520146i
$516$		−	24520.8i		−	0.0920950i
$517$	3366.08	−	6140.93i	0.0125934	−	0.0229749i
$518$	492895.			1.83694
$519$	−2955.56	−	4067.98i	−0.0109725	−	0.0151023i
$520$	−72661.7	−	223630.i	−0.268719	−	0.827033i
$521$	65350.4	−	201128.i	0.240754	−	0.740964i	−0.755552	−	0.655088i	$-0.772631\pi$
$521$	65350.4	−	201128.i	0.240754	−	0.740964i	0.996306	−	0.0858752i	$-0.0273686\pi$
$522$	47111.1	+	34228.2i	0.172895	+	0.125616i
$523$	−79321.4	+	109177.i	−0.289993	+	0.399141i	−0.929012	−	0.370050i	$-0.879340\pi$
$523$	−79321.4	+	109177.i	−0.289993	+	0.399141i	0.639019	+	0.769191i	$0.279340\pi$
$524$	28417.6	+	9233.45i	0.103496	+	0.0336280i
$525$	−103112.	+	33503.0i	−0.374101	+	0.121553i
$526$	−250599.	+	182071.i	−0.905748	+	0.658064i
$527$			103227.i			0.371682i
$528$	−223848.	+	105675.i	−0.802945	+	0.379057i
$529$	8393.49			0.0299938
$530$	−51457.8	−	70825.7i	−0.183189	−	0.252138i
$531$	16331.0	+	50261.6i	0.0579193	+	0.178257i
$532$	1637.03	−	5038.27i	0.00578407	−	0.0178015i
$533$	−18379.7	−	13353.6i	−0.0646969	−	0.0470050i
$534$	−200658.	+	276182.i	−0.703677	+	0.968528i
$535$	−55793.0	−	18128.2i	−0.194927	−	0.0633356i
$536$	498867.	−	162092.i	1.73642	−	0.564197i
$537$	81957.3	−	59545.5i	0.284210	−	0.206491i
$538$		−	593752.i		−	2.05135i
$539$	−2237.96	−	17540.0i	−0.00770325	−	0.0603742i
$540$	23505.3			0.0806081
$541$	−36527.6	−	50275.9i	−0.124803	−	0.171777i	0.742043	−	0.670352i	$-0.233857\pi$
$541$	−36527.6	−	50275.9i	−0.124803	−	0.171777i	−0.866847	+	0.498575i	$0.833857\pi$
$542$	−132102.	−	406568.i	−0.449687	−	1.38400i
$543$	−46207.6	+	142212.i	−0.156716	+	0.482323i
$544$	72966.8	+	53013.5i	0.246563	+	0.179138i
$545$	150825.	−	207593.i	0.507786	−	0.698908i
$546$	−315737.	−	102589.i	−1.05911	−	0.344125i
$547$	−338850.	+	110099.i	−1.13249	+	0.367967i	−0.814520	−	0.580135i	$-0.803000\pi$
$547$	−338850.	+	110099.i	−1.13249	+	0.367967i	−0.317966	+	0.948102i	$0.603000\pi$
$548$	−27944.2	+	20302.7i	−0.0930531	+	0.0676071i
$549$			17493.1i			0.0580395i
$550$	147832.	−	18862.2i	0.488702	−	0.0623543i
$551$	32695.5			0.107692
$552$	139446.	+	191931.i	0.457644	+	0.629893i
$553$	−59845.8	−	184186.i	−0.195697	−	0.602292i
$554$	35139.2	−	108147.i	0.114491	−	0.352368i
$555$	250958.	+	182332.i	0.814733	+	0.591938i
$556$	3890.50	−	5354.81i	0.0125851	−	0.0173218i
$557$	376433.	+	122311.i	1.21333	+	0.394234i	0.844647	−	0.535323i	$-0.179810\pi$
$557$	376433.	+	122311.i	1.21333	+	0.394234i	0.368679	+	0.929557i	$0.379810\pi$
$558$	−25949.9	+	8431.64i	−0.0833427	+	0.0270797i
$559$	356409.	−	258946.i	1.14058	−	0.828679i
$560$			256771.i			0.818786i
$561$	−164493.	−	348441.i	−0.522662	−	1.10714i
$562$	−556931.			−1.76331
$563$	254804.	+	350707.i	0.803876	+	1.10644i	0.992240	+	0.124341i	$0.0396817\pi$
$563$	254804.	+	350707.i	0.803876	+	1.10644i	−0.188363	+	0.982099i	$0.560318\pi$
$564$	212.995	+	655.531i	0.000669593	+	0.00206080i
$565$	−8398.14	+	25846.8i	−0.0263079	+	0.0809674i
$566$	−285996.	−	207788.i	−0.892744	−	0.648617i
$567$	−106606.	+	146730.i	−0.331600	+	0.456409i
$568$	−107714.	−	34998.4i	−0.333869	−	0.108481i
$569$	81414.7	−	26453.2i	0.251466	−	0.0817061i	−0.180572	−	0.983562i	$-0.557795\pi$
$569$	81414.7	−	26453.2i	0.251466	−	0.0817061i	0.432037	+	0.901856i	$0.357795\pi$
$570$	29232.2	−	21238.4i	0.0899728	−	0.0653691i
$571$		−	474437.i		−	1.45514i	−0.686031	−	0.727572i	$-0.740649\pi$
$571$		−	474437.i		−	1.45514i	0.686031	−	0.727572i	$-0.259351\pi$
$572$	36923.9	+	20239.4i	0.112854	+	0.0618593i
$573$	53694.9			0.163540
$574$	13223.9	+	18201.2i	0.0401362	+	0.0552428i
$575$	−48670.3	−	149792.i	−0.147207	−	0.453056i
$576$	30452.5	−	93723.0i	0.0917862	−	0.282489i
$577$	499816.	+	363138.i	1.50127	+	1.09074i	0.969873	+	0.243612i	$0.0783325\pi$
$577$	499816.	+	363138.i	1.50127	+	1.09074i	0.531396	+	0.847123i	$0.321668\pi$
$578$	−260585.	+	358664.i	−0.779998	+	1.07358i
$579$	−250591.	−	81421.8i	−0.747494	−	0.242875i
$580$	14270.0	−	4636.59i	0.0424196	−	0.0137830i
$581$	302281.	−	219620.i	0.895485	−	0.650608i
$582$			377862.i			1.11554i
$583$	−136128.	−	25792.6i	−0.400507	−	0.0758853i
$584$	−148117.			−0.434289
$585$	62707.0	+	86308.8i	0.183233	+	0.252199i
$586$	156544.	+	481794.i	0.455871	+	1.40303i
$587$	52321.6	−	161029.i	0.151846	−	0.467335i	−0.845981	−	0.533213i	$-0.820985\pi$
$587$	52321.6	−	161029.i	0.151846	−	0.467335i	0.997828	+	0.0658772i	$0.0209846\pi$
$588$	1407.98	+	1022.96i	0.00407233	+	0.00295872i
$589$	−9004.72	+	12393.9i	−0.0259561	+	0.0357255i
$590$	140354.	+	45603.9i	0.403202	+	0.131008i
$591$	276211.	−	89746.5i	0.790800	−	0.256946i
$592$	−525770.	+	381994.i	−1.50021	+	1.08997i
$593$			519770.i			1.47809i	0.673654	+	0.739047i	$0.264724\pi$
$593$			519770.i			1.47809i	−0.673654	+	0.739047i	$0.735276\pi$
$594$	293549.	−	276348.i	0.831971	−	0.783220i
$595$	−399688.			−1.12898
$596$	−17205.3	−	23681.0i	−0.0484361	−	0.0666666i
$597$	−20333.3	−	62579.4i	−0.0570504	−	0.175583i
$598$	149033.	−	458677.i	0.416755	−	1.28264i
$599$	−364603.	−	264899.i	−1.01617	−	0.738291i	−0.0506757	−	0.998715i	$-0.516137\pi$
$599$	−364603.	−	264899.i	−1.01617	−	0.738291i	−0.965494	+	0.260425i	$0.916137\pi$
$600$	76197.6	−	104877.i	0.211660	−	0.291325i
$601$	18199.0	+	5913.22i	0.0503848	+	0.0163710i	0.334101	−	0.942537i	$-0.391567\pi$
$601$	18199.0	+	5913.22i	0.0503848	+	0.0163710i	−0.283716	+	0.958908i	$0.591567\pi$
$602$	−414915.	+	134814.i	−1.14490	+	0.371999i
$603$	−192535.	+	139885.i	−0.529511	+	0.384713i
$604$		−	14361.6i		−	0.0393667i
$605$	−169442.	+	205860.i	−0.462925	+	0.562420i
$606$	260499.			0.709351
$607$	179595.	+	247192.i	0.487436	+	0.670898i	0.979913	−	0.199428i	$-0.0639083\pi$
$607$	179595.	+	247192.i	0.487436	+	0.670898i	−0.492477	+	0.870326i	$0.663908\pi$
$608$	4136.27	+	12730.1i	0.0111893	+	0.0344371i
$609$	−57854.5	+	178058.i	−0.155992	+	0.480094i
$610$	39519.9	+	28712.9i	0.106208	+	0.0771644i
$611$	−7278.82	+	10018.4i	−0.0194975	+	0.0268360i
$612$	−18416.9	−	5984.03i	−0.0491716	−	0.0159768i
$613$	471453.	−	153184.i	1.25463	−	0.407656i	0.395055	−	0.918657i	$-0.370725\pi$
$613$	471453.	−	153184.i	1.25463	−	0.407656i	0.859580	+	0.511002i	$0.170725\pi$
$614$	443538.	−	322249.i	1.17650	−	0.854781i
$615$			14158.9i			0.0374352i
$616$	252602.	+	268325.i	0.665694	+	0.707129i
$617$	−481904.			−1.26587			−0.632937	−	0.774203i	$-0.718151\pi$
$617$	−481904.			−1.26587			−0.632937	+	0.774203i	$0.718151\pi$
$618$	−232894.	−	320550.i	−0.609790	−	0.839304i
$619$	172028.	+	529448.i	0.448971	+	1.38179i	0.878070	+	0.478532i	$0.158831\pi$
$619$	172028.	+	529448.i	0.448971	+	1.38179i	−0.429099	+	0.903257i	$0.641169\pi$
$620$	−2172.51	+	6686.31i	−0.00565170	+	0.0173942i
$621$	−344702.	−	250440.i	−0.893840	−	0.649413i
$622$	243745.	−	335486.i	0.630020	−	0.867148i
$623$	532993.	+	173180.i	1.37324	+	0.446191i
$624$	416303.	−	135265.i	1.06915	−	0.347389i
$625$	98059.8	−	71244.6i	0.251033	−	0.182386i
$626$			263687.i			0.672885i
$627$	10645.5	−	56184.7i	0.0270788	−	0.142917i
$628$	31527.3			0.0799407
$629$	−594609.	−	818409.i	−1.50290	−	2.06857i
$630$	−32646.9	−	100477.i	−0.0822546	−	0.253154i
$631$	−122608.	+	377349.i	−0.307936	+	0.947730i	0.670629	+	0.741793i	$0.266024\pi$
$631$	−122608.	+	377349.i	−0.307936	+	0.947730i	−0.978565	+	0.205937i	$0.933976\pi$
$632$	187340.	+	136110.i	0.469025	+	0.340767i
$633$	30325.5	−	41739.5i	0.0756835	−	0.104169i
$634$	78564.8	+	25527.3i	0.195456	+	0.0635076i
$635$	−300899.	+	97768.1i	−0.746232	+	0.242465i
$636$	11032.4	−	8015.49i	0.0272744	−	0.0198160i
$637$			31267.7i			0.0770579i
$638$	123701.	−	225674.i	0.303900	−	0.554422i
$639$	51385.4			0.125846
$640$	−197271.	−	271521.i	−0.481620	−	0.662893i
$641$	−220138.	−	677516.i	−0.535771	−	1.64893i	−0.741976	−	0.670426i	$-0.766111\pi$
$641$	−220138.	−	677516.i	−0.535771	−	1.64893i	0.206205	−	0.978509i	$-0.433889\pi$
$642$	30603.7	−	94188.4i	0.0742512	−	0.228522i
$643$	−93657.4	−	68046.1i	−0.226527	−	0.164582i	0.468733	−	0.883340i	$-0.344711\pi$
$643$	−93657.4	−	68046.1i	−0.226527	−	0.164582i	−0.695260	+	0.718758i	$0.744711\pi$
$644$	−25902.5	+	35651.7i	−0.0624553	+	0.0859624i
$645$	−261125.	−	84844.6i	−0.627666	−	0.203941i
$646$	−112067.	+	36412.9i	−0.268543	+	0.0872549i
$647$	−453337.	+	329369.i	−1.08296	+	0.786817i	−0.978197	−	0.207680i	$-0.933409\pi$
$647$	−453337.	+	329369.i	−1.08296	+	0.786817i	−0.104764	+	0.994497i	$0.533409\pi$
$648$		−	216862.i		−	0.516457i
$649$	211205.	−	99706.4i	0.501436	−	0.236719i
$650$	−263534.			−0.623748
$651$	−51562.9	−	70970.3i	−0.121668	−	0.167461i
$652$	2290.69	+	7050.01i	0.00538853	+	0.0165842i
$653$	−125501.	+	386251.i	−0.294320	+	0.905823i	0.689129	+	0.724638i	$0.257993\pi$
$653$	−125501.	+	386251.i	−0.294320	+	0.905823i	−0.983449	+	0.181184i	$0.942007\pi$
$654$	350454.	+	254620.i	0.819361	+	0.595301i
$655$	196656.	−	270673.i	0.458378	−	0.630903i
$656$	−28211.8	−	9166.58i	−0.0655577	−	0.0213010i
$657$	63912.3	−	20766.4i	0.148065	−	0.0481094i
$658$	9921.15	−	7208.13i	0.0229145	−	0.0166483i
$659$		−	237251.i		−	0.546307i	−0.961970	−	0.273154i	$-0.911933\pi$
$659$		−	237251.i		−	0.546307i	0.961970	−	0.273154i	$-0.0880667\pi$
$660$	−3321.40	−	26031.5i	−0.00762490	−	0.0597601i
$661$	202580.			0.463655			0.231827	−	0.972757i	$-0.425530\pi$
$661$	202580.			0.463655			0.231827	+	0.972757i	$0.425530\pi$
$662$	−71089.4	−	97846.2i	−0.162214	−	0.223269i
$663$	210552.	+	648014.i	0.478998	+	1.47420i
$664$	−138057.	+	424895.i	−0.313127	+	0.963707i
$665$	−47988.7	−	34865.8i	−0.108516	−	0.0788418i
$666$	157170.	−	216326.i	0.354341	−	0.487708i
$667$	−258668.	−	84046.2i	−0.581420	−	0.188915i
$668$	−19082.2	+	6200.17i	−0.0427636	+	0.0138947i
$669$	−75807.4	+	55077.3i	−0.169379	+	0.123061i
$670$			664572.i			1.48045i
$671$	76687.6	−	9784.71i	0.170326	−	0.0217322i
$672$	−76646.8			−0.169729
$673$	122108.	+	168067.i	0.269596	+	0.371066i	0.922253	−	0.386587i	$-0.126346\pi$
$673$	122108.	+	168067.i	0.269596	+	0.371066i	−0.652658	+	0.757653i	$0.726346\pi$
$674$	243913.	+	750687.i	0.536927	+	1.65249i
$675$	−71945.5	+	221425.i	−0.157905	+	0.485982i
$676$	−22658.5	−	16462.4i	−0.0495836	−	0.0360246i
$677$	212149.	−	291998.i	0.462875	−	0.637093i	−0.512227	−	0.858850i	$-0.671179\pi$
$677$	212149.	−	291998.i	0.462875	−	0.637093i	0.975102	+	0.221758i	$0.0711794\pi$
$678$	−43634.0	−	14177.5i	−0.0949217	−	0.0308419i
$679$	589952.	−	191687.i	1.27961	−	0.415770i
$680$	386635.	−	280907.i	0.836148	−	0.607497i
$681$			412189.i			0.888797i
$682$	51478.2	+	109045.i	0.110676	+	0.234442i
$683$	310133.			0.664824			0.332412	−	0.943134i	$-0.392138\pi$
$683$	310133.			0.664824			0.332412	+	0.943134i	$0.392138\pi$
$684$	−1689.23	−	2325.03i	−0.00361058	−	0.00496954i
$685$	119515.	+	367830.i	0.254708	+	0.783910i
$686$	−147642.	+	454396.i	−0.313735	+	0.965576i
$687$	−532429.	−	386832.i	−1.12810	−	0.819613i
$688$	338107.	−	465365.i	0.714295	−	0.983143i
$689$	233009.	+	75709.3i	0.490834	+	0.159482i
$690$	−285863.	+	92882.4i	−0.600426	+	0.195090i
$691$	27576.4	−	20035.5i	0.0577540	−	0.0419607i	−0.558534	−	0.829482i	$-0.688636\pi$
$691$	27576.4	−	20035.5i	0.0577540	−	0.0419607i	0.616288	+	0.787521i	$0.288636\pi$
$692$			1116.81i			0.00233220i
$693$	−146617.	−	80366.5i	−0.305294	−	0.167343i
$694$	−121857.			−0.253006
$695$	−43562.3	−	59958.4i	−0.0901865	−	0.124131i
$696$	−69176.6	−	212904.i	−0.142804	−	0.439506i
$697$	14268.6	−	43914.3i	0.0293709	−	0.0903943i
$698$	−321909.	−	233880.i	−0.660726	−	0.480046i
$699$	106806.	−	147005.i	0.218595	−	0.300870i
$700$	22901.5	+	7441.16i	0.0467378	+	0.0151860i
$701$	−154914.	+	50334.5i	−0.315249	+	0.102431i	−0.462368	−	0.886688i	$-0.653000\pi$
$701$	−154914.	+	50334.5i	−0.315249	+	0.102431i	0.147119	+	0.989119i	$0.453000\pi$
$702$	−576763.	+	419043.i	−1.17037	+	0.850324i
$703$		−	150132.i		−	0.303782i
$704$	−427903.	−	81075.9i	−0.863375	−	0.163586i
$705$	7717.79			0.0155280
$706$	264082.	+	363477.i	0.529821	+	0.729236i
$707$	−132150.	−	406715.i	−0.264380	−	0.813677i
$708$	−7103.64	+	21862.8i	−0.0141715	+	0.0436152i
$709$	−42019.7	−	30529.1i	−0.0835912	−	0.0607326i	0.545205	−	0.838303i	$-0.316452\pi$
$709$	−42019.7	−	30529.1i	−0.0835912	−	0.0607326i	−0.628796	+	0.777570i	$0.716452\pi$
$710$	84342.9	−	116088.i	0.167314	−	0.230288i
$711$	−99920.2	−	32466.0i	−0.197658	−	0.0642229i
$712$	−637299.	+	207071.i	−1.25714	+	0.408469i
$713$	103100.	−	74906.3i	0.202805	−	0.147346i
$714$		−	674745.i		−	1.32356i
$715$	343291.	−	323176.i	0.671507	−	0.632159i
$716$	−22500.3			−0.0438896
$717$	−144363.	−	198698.i	−0.280813	−	0.386506i
$718$	−87518.6	−	269354.i	−0.169766	−	0.522487i
$719$	298239.	−	917885.i	0.576908	−	1.77554i	−0.0526809	−	0.998611i	$-0.516777\pi$
$719$	298239.	−	917885.i	0.576908	−	1.77554i	0.629589	−	0.776929i	$-0.283223\pi$
$720$	112694.	+	81876.8i	0.217388	+	0.157941i
$721$	−382327.	+	526228.i	−0.735470	+	1.01229i
$722$	503726.	+	163671.i	0.966319	+	0.313976i
$723$	500157.	−	162511.i	0.956818	−	0.310889i
$724$	26868.7	−	19521.2i	0.0512589	−	0.0372417i
$725$			148618.i			0.282745i
$726$	−347528.	−	286048.i	−0.659350	−	0.542708i
$727$	−138074.			−0.261241			−0.130621	−	0.991432i	$-0.541697\pi$
$727$	−138074.			−0.261241			−0.130621	+	0.991432i	$0.541697\pi$
$728$	−383035.	−	527202.i	−0.722729	−	0.994751i
$729$	175866.	+	541259.i	0.330922	+	1.01847i
$730$	57989.7	−	178474.i	0.108819	−	0.334911i
$731$	724384.	+	526296.i	1.35561	+	0.984906i
$732$	−4472.55	+	6155.94i	−0.00834705	+	0.0114887i
$733$	−512975.	−	166676.i	−0.954746	−	0.310216i	−0.210104	−	0.977679i	$-0.567380\pi$
$733$	−512975.	−	166676.i	−0.954746	−	0.310216i	−0.744643	+	0.667463i	$0.767380\pi$
$734$	651580.	−	211711.i	1.20942	−	0.392963i
$735$	15765.4	−	11454.2i	0.0291830	−	0.0212027i
$736$		−	111346.i		−	0.205551i
$737$	720930.	+	765804.i	1.32727	+	1.40988i
$738$	12205.0			0.0224091
$739$	115460.	+	158917.i	0.211419	+	0.290993i	0.901536	−	0.432705i	$-0.142441\pi$
$739$	115460.	+	158917.i	0.211419	+	0.290993i	−0.690117	+	0.723698i	$0.742441\pi$
$740$	−21290.4	−	65525.0i	−0.0388794	−	0.119659i
$741$	−31247.8	+	96170.9i	−0.0569093	+	0.175149i
$742$	−196285.	−	142609.i	−0.356516	−	0.259024i
$743$	−510591.	+	702769.i	−0.924902	+	1.27302i	0.0369131	+	0.999318i	$0.488248\pi$
$743$	−510591.	+	702769.i	−0.924902	+	1.27302i	−0.961815	+	0.273700i	$0.911752\pi$
$744$	99757.8	+	32413.3i	0.180219	+	0.0585568i
$745$	−311714.	+	101282.i	−0.561621	+	0.182482i
$746$	427062.	−	310278.i	0.767384	−	0.557537i
$747$		−	202698.i		−	0.363252i
$748$	−15931.7	+	84084.5i	−0.0284747	+	0.150284i
$749$	−162581.			−0.289805
$750$	302212.	+	415960.i	0.537266	+	0.739484i
$751$	−213891.	−	658290.i	−0.379239	−	1.16718i	−0.940574	−	0.339589i	$-0.889712\pi$
$751$	−213891.	−	658290.i	−0.379239	−	1.16718i	0.561335	−	0.827589i	$-0.310288\pi$
$752$	−4996.54	+	15377.8i	−0.00883556	+	0.0271931i
$753$	285177.	+	207193.i	0.502950	+	0.365415i
$754$	−267491.	+	368169.i	−0.470507	+	0.647597i
$755$	−152938.	−	49692.5i	−0.268300	−	0.0871761i
$756$	61953.9	−	20130.0i	0.108399	−	0.0352209i
$757$	−61422.9	+	44626.4i	−0.107186	+	0.0778753i	−0.640087	−	0.768302i	$-0.721102\pi$
$757$	−61422.9	+	44626.4i	−0.107186	+	0.0778753i	0.532901	+	0.846178i	$0.321102\pi$
$758$			405043.i			0.704957i
$759$	−228648.	+	417135.i	−0.396902	+	0.724092i
$760$	70925.6			0.122794
$761$	327846.	+	451241.i	0.566109	+	0.779182i	0.992087	−	0.125551i	$-0.0400700\pi$
$761$	327846.	+	451241.i	0.566109	+	0.779182i	−0.425978	+	0.904733i	$0.640070\pi$
$762$	−165050.	−	507971.i	−0.284253	−	0.874841i
$763$	219752.	−	676328.i	0.377472	−	1.16174i
$764$	−9648.24	−	7009.85i	−0.0165296	−	0.0120094i
$765$	−127449.	+	175418.i	−0.217778	+	0.299745i
$766$	−610482.	−	198358.i	−1.04044	−	0.338058i
$767$	−392790.	+	127625.i	−0.667682	+	0.216943i
$768$	117212.	−	85159.5i	0.198724	−	0.144381i
$769$			113451.i			0.191848i	0.995389	+	0.0959239i	$0.0305805\pi$
$769$			113451.i			0.191848i	−0.995389	+	0.0959239i	$0.969419\pi$
$770$	−422215.	+	199321.i	−0.712119	+	0.336179i
$771$	−184800.			−0.310880
$772$	34398.1	+	47344.9i	0.0577165	+	0.0794399i
$773$	−120125.	−	369706.i	−0.201036	−	0.618724i	−0.999853	−	0.0171505i	$-0.994541\pi$
$773$	−120125.	−	369706.i	−0.201036	−	0.618724i	0.798817	−	0.601574i	$-0.205459\pi$
$774$	−73136.0	+	225089.i	−0.122081	+	0.375728i
$775$	−56336.9	−	40931.2i	−0.0937971	−	0.0681476i
$776$	−435965.	+	600054.i	−0.723982	+	0.996476i
$777$	817609.	+	265657.i	1.35427	+	0.440028i
$778$	139583.	−	45353.2i	0.230607	−	0.0749289i
$779$	5543.92	−	4027.90i	0.00913571	−	0.00663748i
$780$			46405.1i			0.0762740i
$781$	−28742.2	−	225267.i	−0.0471214	−	0.369313i
$782$	980213.			1.60290
$783$	236316.	+	325262.i	0.385452	+	0.530529i
$784$	12616.0	+	38828.2i	0.0205254	+	0.0631706i
$785$	109088.	−	335738.i	0.177026	−	0.544830i
$786$	456945.	+	331990.i	0.739637	+	0.537377i
$787$	190393.	−	262053.i	0.307398	−	0.423097i	−0.627169	−	0.778883i	$-0.715787\pi$
$787$	190393.	−	262053.i	0.307398	−	0.423097i	0.934568	+	0.355786i	$0.115787\pi$
$788$	−61347.8	−	19933.1i	−0.0987976	−	0.0321013i
$789$	−513821.	+	166951.i	−0.825388	+	0.268185i
$790$	−237353.	+	172447.i	−0.380312	+	0.276313i
$791$			75317.6i			0.120377i
$792$	198312.	−	25302.9i	0.316153	−	0.0403386i
$793$	−136707.			−0.217393
$794$	−50483.2	−	69484.2i	−0.0800767	−	0.110216i
$795$	−47184.6	−	145219.i	−0.0746562	−	0.229768i
$796$	−4516.11	+	13899.2i	−0.00712752	+	0.0219362i
$797$	−561981.	−	408303.i	−0.884718	−	0.642785i	0.0497774	−	0.998760i	$-0.484149\pi$
$797$	−561981.	−	408303.i	−0.884718	−	0.642785i	−0.934495	+	0.355975i	$0.884149\pi$
$798$	58859.7	−	81013.4i	0.0924298	−	0.127219i
$799$	−23936.9	−	7777.58i	−0.0374952	−	0.0121829i
$800$	−57865.1	+	18801.5i	−0.0904142	+	0.0293774i
$801$	245962.	−	178702.i	0.383357	−	0.278525i
$802$		−	798039.i		−	1.24073i
$803$	−126786.	−	268567.i	−0.196626	−	0.416507i
$804$	−103519.			−0.160143
$805$	290033.	+	399196.i	0.447565	+	0.616020i
$806$	−65892.6	−	202796.i	−0.101430	−	0.312169i
$807$	320016.	−	984909.i	0.491388	−	1.51234i
$808$	413679.	+	300556.i	0.633638	+	0.460365i
$809$	−334920.	+	460978.i	−0.511734	+	0.704341i	−0.984211	−	0.177002i	$-0.943360\pi$
$809$	−334920.	+	460978.i	−0.511734	+	0.704341i	0.472477	+	0.881343i	$0.343360\pi$
$810$	261309.	+	84904.5i	0.398276	+	0.129408i
$811$	115629.	−	37570.0i	0.175802	−	0.0571215i	−0.219793	−	0.975546i	$-0.570538\pi$
$811$	115629.	−	37570.0i	0.175802	−	0.0571215i	0.395595	+	0.918425i	$0.370538\pi$
$812$	33641.1	−	24441.7i	0.0510220	−	0.0370697i
$813$		−	745610.i		−	1.12806i
$814$	−1.03625e6	−	568011.i	−1.56393	−	0.857250i
$815$	83002.2			0.124961
$816$	522928.	+	719748.i	0.785346	+	1.08094i
$817$	41063.2	+	126380.i	0.0615189	+	0.189336i
$818$	−244516.	+	752542.i	−0.365427	+	1.12467i
$819$	239194.	+	173785.i	0.356602	+	0.259086i
$820$	1848.45	−	2544.17i	0.00274903	−	0.00378371i
$821$	−603167.	−	195981.i	−0.894853	−	0.290755i	−0.174742	−	0.984614i	$-0.555909\pi$
$821$	−603167.	−	195981.i	−0.894853	−	0.290755i	−0.720111	+	0.693859i	$0.755909\pi$
$822$	−620962.	+	201763.i	−0.919013	+	0.298605i
$823$	−87568.3	+	63622.1i	−0.129285	+	0.0939309i	−0.650548	−	0.759465i	$-0.725461\pi$
$823$	−87568.3	+	63622.1i	−0.129285	+	0.0939309i	0.521264	+	0.853396i	$0.325461\pi$
$824$		−	777747.i		−	1.14547i
$825$	255389.	+	48389.2i	0.375227	+	0.0710953i
$826$	408993.			0.599454
$827$	186226.	+	256318.i	0.272288	+	0.374773i	0.923161	−	0.384414i	$-0.125597\pi$
$827$	186226.	+	256318.i	0.272288	+	0.374773i	−0.650872	+	0.759187i	$0.725597\pi$
$828$	7387.55	+	22736.6i	0.0107756	+	0.0331638i
$829$	251882.	−	775214.i	0.366512	−	1.12801i	−0.582516	−	0.812819i	$-0.697932\pi$
$829$	251882.	−	775214.i	0.366512	−	1.12801i	0.949029	−	0.315190i	$-0.102068\pi$
$830$	−457927.	−	332704.i	−0.664722	−	0.482949i
$831$	116577.	−	160454.i	0.168815	−	0.232354i
$832$	732437.	+	237983.i	1.05809	+	0.343795i
$833$	−60439.7	+	19638.0i	−0.0871028	+	0.0283014i
$834$	101220.	−	73540.9i	0.145524	−	0.105730i
$835$			224661.i			0.322222i
$836$	−9247.74	+	8705.86i	−0.0132319	+	0.0124566i
$837$	−188382.			−0.268898
$838$	84731.6	+	116623.i	0.120658	+	0.166072i
$839$	80718.2	+	248425.i	0.114669	+	0.352916i	0.991878	−	0.127193i	$-0.0405969\pi$
$839$	80718.2	+	248425.i	0.114669	+	0.352916i	−0.877208	+	0.480110i	$0.840597\pi$
$840$	−125502.	+	386257.i	−0.177866	+	0.547416i
$841$	−364576.	−	264880.i	−0.515461	−	0.374504i
$842$	649195.	−	893540.i	0.915695	−	1.26035i
$843$	−923830.	−	300171.i	−1.29998	−	0.422389i
$844$	−10898.2	+	3541.03i	−0.0152992	+	0.00497101i
$845$	−253710.	+	184331.i	−0.355324	+	0.258158i
$846$		−	6652.73i		−	0.00929521i
$847$	−270306.	+	687703.i	−0.376781	+	0.958593i
$848$	319898.			0.444857
$849$	−362415.	−	498821.i	−0.502794	−	0.692037i
$850$	−165515.	−	509404.i	−0.229087	−	0.705057i
$851$	−385925.	+	1.18775e6i	−0.532897	+	1.64009i
$852$	18082.8	+	13137.9i	0.0249108	+	0.0180987i
$853$	−494677.	+	680864.i	−0.679866	+	0.935756i	−0.999932	−	0.0116396i	$-0.996295\pi$
$853$	−494677.	+	680864.i	−0.679866	+	0.935756i	0.320066	+	0.947395i	$0.396295\pi$
$854$	128754.	+	41834.7i	0.176541	+	0.0573615i
$855$	−30604.3	+	9943.96i	−0.0418650	+	0.0136028i
$856$	157271.	−	114264.i	0.214635	−	0.155942i
$857$			93389.0i			0.127155i	0.997977	+	0.0635776i	$0.0202510\pi$
$857$			93389.0i			0.127155i	−0.997977	+	0.0635776i	$0.979749\pi$
$858$	545578.	+	579536.i	0.741109	+	0.787238i
$859$	1.16761e6			1.58238			0.791190	−	0.611571i	$-0.209462\pi$
$859$	1.16761e6			1.58238			0.791190	+	0.611571i	$0.209462\pi$
$860$	35844.1	+	49335.2i	0.0484642	+	0.0667052i
$861$	12125.8	+	37319.3i	0.0163570	+	0.0503416i
$862$	−283994.	+	874044.i	−0.382204	+	1.17630i
$863$	763401.	+	554643.i	1.02502	+	0.744718i	0.967305	−	0.253615i	$-0.0816197\pi$
$863$	763401.	+	554643.i	1.02502	+	0.744718i	0.0577115	+	0.998333i	$0.481620\pi$
$864$	−96746.0	+	133159.i	−0.129600	+	0.178379i
$865$	11893.0	+	3864.27i	0.0158949	+	0.00516458i
$866$	−277428.	+	90141.8i	−0.369926	+	0.120196i
$867$	−625566.	+	454500.i	−0.832214	+	0.604639i
$868$			19483.9i			0.0258605i
$869$	−86436.8	+	456196.i	−0.114461	+	0.604105i
$870$	283622.			0.374716
$871$	−1.09319e6	−	1.50465e6i	−1.44098	−	1.98334i
$872$	262758.	+	808684.i	0.345559	+	1.06352i
$873$	103989.	−	320046.i	0.136446	−	0.419937i
$874$	117689.	+	85506.4i	0.154069	+	0.111937i
$875$	496124.	−	682856.i	0.647998	−	0.891893i
$876$	27800.5	+	9032.94i	0.0362280	+	0.0117712i
$877$	982991.	−	319393.i	1.27806	−	0.415266i	0.410162	−	0.912013i	$-0.365472\pi$
$877$	982991.	−	319393.i	1.27806	−	0.415266i	0.867895	+	0.496747i	$0.165472\pi$
$878$	244570.	−	177691.i	0.317260	−	0.230503i
$879$			883568.i			1.14357i
$880$	295902.	−	539832.i	0.382105	−	0.697097i
$881$	609739.			0.785584			0.392792	−	0.919627i	$-0.371509\pi$
$881$	609739.			0.785584			0.392792	+	0.919627i	$0.371509\pi$
$882$	−9873.52	−	13589.7i	−0.0126921	−	0.0174692i
$883$	96058.9	+	295639.i	0.123202	+	0.379175i	0.993569	−	0.113227i	$-0.0361188\pi$
$883$	96058.9	+	295639.i	0.123202	+	0.379175i	−0.870368	+	0.492403i	$0.836119\pi$
$884$	46764.6	−	143927.i	0.0598430	−	0.184178i
$885$	208239.	+	151295.i	0.265874	+	0.193169i
$886$	−110204.	+	151683.i	−0.140388	+	0.193228i
$887$	−249889.	−	81194.0i	−0.317615	−	0.103199i	0.145871	−	0.989304i	$-0.453402\pi$
$887$	−249889.	−	81194.0i	−0.317615	−	0.103199i	−0.463486	+	0.886104i	$0.653402\pi$
$888$	−977614.	+	317646.i	−1.23977	+	0.402826i
$889$	−709362.	+	515382.i	−0.897562	+	0.652117i
$890$		−	848986.i		−	1.07182i
$891$	393218.	−	185631.i	0.495311	−	0.233828i
$892$	20811.9			0.0261566
$893$	−2195.54	−	3021.90i	−0.00275320	−	0.00378945i
$894$	−170982.	−	526228.i	−0.213932	−	0.658413i
$895$	−77853.1	+	239607.i	−0.0971919	+	0.299126i
$896$	−752487.	−	546714.i	−0.937310	−	0.680995i
$897$	494429.	−	680523.i	0.614496	−	0.845781i
$898$	516455.	+	167806.i	0.640442	+	0.208092i
$899$	−114366.	+	37159.6i	−0.141506	+	0.0459782i
$900$	10568.5	−	7678.44i	0.0130475	−	0.00947955i
$901$			497951.i			0.613391i
$902$	−6826.81	−	53505.1i	−0.00839082	−	0.0657630i
$903$	−760918.			−0.933173
$904$	−52934.3	−	72857.8i	−0.0647739	−	0.0891536i
$905$	−114915.	−	353672.i	−0.140307	−	0.431821i
$906$	83889.8	−	258186.i	0.102200	−	0.314541i
$907$	−228786.	−	166222.i	−0.278108	−	0.202058i	0.439984	−	0.898006i	$-0.354984\pi$
$907$	−228786.	−	166222.i	−0.278108	−	0.202058i	−0.718092	+	0.695948i	$0.754984\pi$
$908$	53811.2	−	74064.8i	0.0652681	−	0.0898338i
$909$	−220641.	−	71690.6i	−0.267029	−	0.0867630i
$910$	785217.	−	255132.i	0.948215	−	0.308094i
$911$	1.12857e6	−	819956.i	1.35985	−	0.987992i	0.361401	−	0.932411i	$-0.382299\pi$
$911$	1.12857e6	−	819956.i	1.35985	−	0.987992i	0.998454	−	0.0555816i	$-0.0177013\pi$
$912$			132033.i			0.158742i
$913$	−888599.	+	113378.i	−1.06602	+	0.136015i
$914$	−1.28842e6			−1.54228
$915$	50079.7	+	68928.7i	0.0598163	+	0.0823300i
$916$	45169.3	+	139017.i	0.0538335	+	0.165682i
$917$	286527.	−	881840.i	0.340743	−	1.04870i
$918$	−1.17224e6	−	851684.i	−1.39102	−	1.01063i
$919$	−85147.5	+	117196.i	−0.100819	+	0.138765i	−0.856446	−	0.516237i	$-0.827332\pi$
$919$	−85147.5	+	117196.i	−0.100819	+	0.138765i	0.755627	+	0.655002i	$0.227332\pi$
$920$	−561122.	−	182319.i	−0.662951	−	0.215406i
$921$	909419.	−	295488.i	1.07212	−	0.348354i
$922$	−77491.6	+	56301.0i	−0.0911576	+	0.0662299i
$923$			401573.i			0.471369i
$924$	−31047.8	−	65767.7i	−0.0363653	−	0.0770316i
$925$	682427.			0.797577
$926$	−611859.	−	842151.i	−0.713558	−	0.982128i
$927$	109042.	+	335597.i	0.126892	+	0.390534i
$928$	−32467.3	+	99924.2i	−0.0377008	+	0.116031i
$929$	−562289.	−	408527.i	−0.651521	−	0.473358i	0.212268	−	0.977211i	$-0.431915\pi$
$929$	−562289.	−	408527.i	−0.651521	−	0.473358i	−0.863789	+	0.503854i	$0.831915\pi$
$930$	−78113.0	+	107513.i	−0.0903145	+	0.124307i
$931$	−8969.78	−	2914.46i	−0.0103486	−	0.00336247i
$932$	−38383.0	+	12471.4i	−0.0441883	+	0.0143576i
$933$	585138.	−	425128.i	0.672195	−	0.488378i
$934$			1.35611e6i			1.55453i
$935$	840298.	+	460599.i	0.961192	+	0.526866i
$936$	−353521.			−0.403518
$937$	647243.	+	890854.i	0.737205	+	1.01468i	0.998775	+	0.0494911i	$0.0157599\pi$
$937$	647243.	+	890854.i	0.737205	+	1.01468i	−0.261569	+	0.965185i	$0.584240\pi$
$938$	569142.	+	1.75164e6i	0.646867	+	1.99085i
$939$	−142120.	+	437402.i	−0.161185	+	0.496077i
$940$	−1386.78	−	1007.56i	−0.00156947	−	0.00114028i
$941$	497946.	−	685364.i	0.562345	−	0.774002i	−0.429277	−	0.903173i	$-0.641232\pi$
$941$	497946.	−	685364.i	0.562345	−	0.774002i	0.991622	+	0.129171i	$0.0412316\pi$
$942$	566785.	+	184160.i	0.638728	+	0.207535i
$943$	−54214.3	+	17615.3i	−0.0609664	+	0.0198092i
$944$	−436271.	+	316970.i	−0.489568	+	0.355692i
$945$		−	729405.i		−	0.816780i
$946$	1.02767e6	+	194715.i	1.14834	+	0.217580i
$947$	−1.75534e6			−1.95732			−0.978660	−	0.205486i	$-0.934122\pi$
$947$	−1.75534e6			−1.95732			−0.978660	+	0.205486i	$0.934122\pi$
$948$	−26861.7	−	36972.0i	−0.0298894	−	0.0411393i
$949$	162287.	+	499469.i	0.180199	+	0.554595i
$950$	24563.9	−	75600.0i	0.0272177	−	0.0837673i
$951$	116564.	+	84688.7i	0.128885	+	0.0936406i
$952$	778499.	−	1.07151e6i	0.858982	−	1.18229i
$953$	363486.	+	118104.i	0.400222	+	0.130040i	0.502210	−	0.864746i	$-0.332520\pi$
$953$	363486.	+	118104.i	0.400222	+	0.130040i	−0.101988	+	0.994786i	$0.532520\pi$
$954$	−125179.	+	40673.1i	−0.137542	+	0.0446900i
$955$	−108032.	+	78490.2i	−0.118453	+	0.0860614i
$956$			54549.9i			0.0596868i
$957$	326825.	−	307675.i	0.356855	−	0.335945i
$958$	−421164.			−0.458902
$959$	630021.	+	867150.i	0.685043	+	0.942881i
$960$	−148319.	−	456479.i	−0.160937	−	0.495312i
$961$	−267972.	+	824734.i	−0.290164	+	0.893032i
$962$	1.69057e6	+	1.22827e6i	1.82676	+	1.32722i
$963$	−51842.2	+	71354.7i	−0.0559024	+	0.0769431i
$964$	−111087.	−	36094.4i	−0.119539	−	0.0388405i
$965$	623201.	−	202490.i	0.669227	−	0.217445i
$966$	−673914.	+	489627.i	−0.722188	+	0.524700i
$967$			1.17380e6i			1.25528i	0.778505	+	0.627639i	$0.215979\pi$
$967$			1.17380e6i			1.25528i	−0.778505	+	0.627639i	$0.784021\pi$
$968$	−221849.	−	855218.i	−0.236759	−	0.912696i
$969$	−205521.			−0.218882
$970$	−552351.	−	760246.i	−0.587045	−	0.807999i
$971$	38552.4	+	118652.i	0.0408897	+	0.125845i	0.969418	−	0.245417i	$-0.0789250\pi$
$971$	38552.4	+	118652.i	0.0408897	+	0.125845i	−0.928528	+	0.371263i	$0.878925\pi$
$972$	19082.1	−	58728.7i	0.0201973	−	0.0621610i
$973$	−166167.	−	120728.i	−0.175517	−	0.127521i
$974$	−906520.	+	1.24772e6i	−0.955563	+	1.31522i
$975$	−437147.	−	142038.i	−0.459852	−	0.149415i
$976$	−169763.	+	55159.4i	−0.178215	+	0.0579055i
$977$	−326932.	+	237530.i	−0.342506	+	0.248845i	−0.745718	−	0.666261i	$-0.767894\pi$
$977$	−326932.	+	237530.i	−0.342506	+	0.248845i	0.403213	+	0.915106i	$0.367894\pi$
$978$			140122.i			0.146497i
$979$	−920983.	−	978309.i	−0.960918	−	1.02073i
$980$	−4328.17			−0.00450663
$981$	−226760.	−	312108.i	−0.235628	−	0.324315i
$982$	−290459.	−	893941.i	−0.301205	−	0.927013i
$983$	136988.	−	421605.i	0.141767	−	0.436314i	−0.854814	−	0.518934i	$-0.826329\pi$
$983$	136988.	−	421605.i	0.141767	−	0.436314i	0.996581	+	0.0826204i	$0.0263289\pi$
$984$	−37958.2	−	27578.3i	−0.0392027	−	0.0284824i
$985$	−424539.	+	584328.i	−0.437567	+	0.602260i
$986$	−879663.	−	285820.i	−0.904821	−	0.293994i
$987$	20342.1	−	6609.54i	0.0208815	−	0.00678480i
$988$	18169.9	−	13201.2i	0.0186139	−	0.0135238i
$989$		−	1.10540e6i		−	1.13012i
$990$	−47152.7	+	248863.i	−0.0481101	+	0.253916i
$991$	−790967.			−0.805399			−0.402699	−	0.915332i	$-0.631928\pi$
$991$	−790967.			−0.805399			−0.402699	+	0.915332i	$0.631928\pi$
$992$	−28936.6	−	39827.8i	−0.0294052	−	0.0404728i
$993$	−65185.9	−	200621.i	−0.0661081	−	0.203460i
$994$	122888.	−	378209.i	0.124376	−	0.382789i
$995$	132387.	+	96184.9i	0.133721	+	0.0971541i
$996$	51824.6	−	71330.4i	0.0522417	−	0.0719045i
$997$	1.29408e6	+	420473.i	1.30188	+	0.423007i	0.876236	−	0.481883i	$-0.160047\pi$
$997$	1.29408e6	+	420473.i	1.30188	+	0.423007i	0.425646	+	0.904890i	$0.360047\pi$
$998$	1.65855e6	−	538896.i	1.66521	−	0.541058i
$999$	1.49354e6	−	1.08512e6i	1.49653	−	1.08730i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.5.d.a.8.1	yes	12
3.2	odd	2		99.5.k.a.19.3		12
4.3	odd	2		176.5.n.a.129.2		12
11.2	odd	10		121.5.b.b.120.3		12
11.3	even	5		121.5.d.e.94.1		12
11.4	even	5		121.5.d.d.40.3		12
11.5	even	5		121.5.d.c.112.3		12
11.6	odd	10		121.5.d.e.112.1		12
11.7	odd	10	inner	11.5.d.a.7.1	✓	12
11.8	odd	10		121.5.d.c.94.3		12
11.9	even	5		121.5.b.b.120.10		12
11.10	odd	2		121.5.d.d.118.3		12
33.29	even	10		99.5.k.a.73.3		12
44.7	even	10		176.5.n.a.161.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.5.d.a.7.1	✓	12	11.7	odd	10	inner
11.5.d.a.8.1	yes	12	1.1	even	1	trivial
99.5.k.a.19.3		12	3.2	odd	2
99.5.k.a.73.3		12	33.29	even	10
121.5.b.b.120.3		12	11.2	odd	10
121.5.b.b.120.10		12	11.9	even	5
121.5.d.c.94.3		12	11.8	odd	10
121.5.d.c.112.3		12	11.5	even	5
121.5.d.d.40.3		12	11.4	even	5
121.5.d.d.118.3		12	11.10	odd	2
121.5.d.e.94.1		12	11.3	even	5
121.5.d.e.112.1		12	11.6	odd	10
176.5.n.a.129.2		12	4.3	odd	2
176.5.n.a.161.2		12	44.7	even	10

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:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	11.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.46775 - 3.39656i) q^{2} +(-2.26281 - 6.96422i) q^{3} +(-0.502581 + 1.54679i) q^{4} +(14.7329 + 10.7041i) q^{5} +(-18.0704 + 24.8717i) q^{6} +(47.9990 + 15.5958i) q^{7} +(-57.3923 + 18.6479i) q^{8} +(22.1503 - 16.0931i) q^{9} +O(q^{10})\)	\(q+(-2.46775 - 3.39656i) q^{2} +(-2.26281 - 6.96422i) q^{3} +(-0.502581 + 1.54679i) q^{4} +(14.7329 + 10.7041i) q^{5} +(-18.0704 + 24.8717i) q^{6} +(47.9990 + 15.5958i) q^{7} +(-57.3923 + 18.6479i) q^{8} +(22.1503 - 16.0931i) q^{9} -76.4560i q^{10} +(-82.9397 - 88.1022i) q^{11} +11.9094 q^{12} +(125.766 + 173.103i) q^{13} +(-65.4772 - 201.518i) q^{14} +(41.2077 - 126.824i) q^{15} +(226.021 + 164.214i) q^{16} +(-255.614 + 351.822i) q^{17} +(-109.323 - 35.5210i) q^{18} +(-61.3806 + 19.9438i) q^{19} +(-23.9614 + 17.4089i) q^{20} -369.566i q^{21} +(-94.5704 + 499.124i) q^{22} +536.875 q^{23} +(259.736 + 357.496i) q^{24} +(-90.6549 - 279.007i) q^{25} +(277.594 - 854.346i) q^{26} +(-642.052 - 466.478i) q^{27} +(-48.2468 + 66.4060i) q^{28} +(-481.802 - 156.547i) q^{29} +(-532.457 + 173.006i) q^{30} +(192.037 - 139.523i) q^{31} -207.397i q^{32} +(-425.887 + 776.970i) q^{33} +1825.78 q^{34} +(540.225 + 743.556i) q^{35} +(13.7603 + 42.3498i) q^{36} +(-718.836 + 2212.35i) q^{37} +(219.212 + 159.267i) q^{38} +(920.939 - 1267.56i) q^{39} +(-1045.16 - 339.594i) q^{40} +(-100.981 + 32.8108i) q^{41} +(-1255.25 + 911.995i) q^{42} -2058.95i q^{43} +(177.959 - 84.0114i) q^{44} +498.599 q^{45} +(-1324.87 - 1823.53i) q^{46} +(17.8846 + 55.0431i) q^{47} +(632.178 - 1945.64i) q^{48} +(118.225 + 85.8952i) q^{49} +(-723.951 + 996.433i) q^{50} +(3028.58 + 984.044i) q^{51} +(-330.960 + 107.536i) q^{52} +(926.358 - 673.039i) q^{53} +3331.92i q^{54} +(-278.889 - 2185.79i) q^{55} -3045.60 q^{56} +(277.786 + 382.340i) q^{57} +(657.244 + 2022.79i) q^{58} +(-596.473 + 1835.75i) q^{59} +(175.460 + 127.479i) q^{60} +(-375.548 + 516.897i) q^{61} +(-947.795 - 307.957i) q^{62} +(1314.18 - 427.002i) q^{63} +(2911.90 - 2115.62i) q^{64} +3896.51i q^{65} +(3690.00 - 470.814i) q^{66} -8692.22 q^{67} +(-415.727 - 572.199i) q^{68} +(-1214.85 - 3738.92i) q^{69} +(1192.39 - 3669.81i) q^{70} +(1518.36 + 1103.16i) q^{71} +(-971.154 + 1336.68i) q^{72} +(2334.33 + 758.471i) q^{73} +(9288.28 - 3017.94i) q^{74} +(-1737.93 + 1262.68i) q^{75} -104.966i q^{76} +(-2607.00 - 5522.33i) q^{77} -6578.00 q^{78} +(-2255.51 - 3104.44i) q^{79} +(1572.18 + 4838.68i) q^{80} +(-1110.50 + 3417.77i) q^{81} +(360.640 + 262.020i) q^{82} +(4351.57 - 5989.42i) q^{83} +(571.640 + 185.737i) q^{84} +(-7531.86 + 2447.25i) q^{85} +(-6993.34 + 5080.96i) q^{86} +3709.62i q^{87} +(6403.03 + 3509.74i) q^{88} +11104.2 q^{89} +(-1230.42 - 1693.52i) q^{90} +(3336.98 + 10270.2i) q^{91} +(-269.823 + 830.430i) q^{92} +(-1406.21 - 1021.67i) q^{93} +(142.823 - 196.578i) q^{94} +(-1117.79 - 363.193i) q^{95} +(-1444.36 + 469.300i) q^{96} +(9943.57 - 7224.43i) q^{97} -613.524i q^{98} +(-3254.98 - 616.730i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 5 q^{2} - 6 q^{3} + 7 q^{4} - 18 q^{5} + 75 q^{6} - 80 q^{7} - 245 q^{8} + q^{9}+O(q^{10}) \) 12 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 - 18 * q^5 + 75 * q^6 - 80 * q^7 - 245 * q^8 + q^9	\( 12 q - 5 q^{2} - 6 q^{3} + 7 q^{4} - 18 q^{5} + 75 q^{6} - 80 q^{7} - 245 q^{8} + q^{9} - 43 q^{11} + 594 q^{12} + 250 q^{13} + 610 q^{14} + 1134 q^{15} - 633 q^{16} - 1250 q^{17} - 3150 q^{18} - 1025 q^{19} + 752 q^{20} - 35 q^{22} + 1684 q^{23} + 5345 q^{24} + 197 q^{25} + 3490 q^{26} - 687 q^{27} - 3580 q^{28} - 2690 q^{29} - 6740 q^{30} - 1136 q^{31} + 5939 q^{33} + 2370 q^{34} + 3610 q^{35} - 514 q^{36} - 336 q^{37} + 1900 q^{38} - 6880 q^{39} - 2340 q^{40} - 4550 q^{41} + 1310 q^{42} - 6268 q^{44} + 5136 q^{45} + 4150 q^{46} + 24 q^{47} + 344 q^{48} + 827 q^{49} + 8895 q^{50} + 13155 q^{51} + 14070 q^{52} + 414 q^{53} - 2738 q^{55} - 21340 q^{56} - 26925 q^{57} + 2980 q^{58} - 10011 q^{59} - 6856 q^{60} + 9460 q^{61} - 6200 q^{62} + 9150 q^{63} - 2633 q^{64} - 3210 q^{66} + 12154 q^{67} - 9400 q^{68} - 9022 q^{69} - 9380 q^{70} + 17574 q^{71} + 43045 q^{72} + 27950 q^{73} + 43270 q^{74} - 1761 q^{75} + 4090 q^{77} - 42920 q^{78} - 41540 q^{79} - 2308 q^{80} - 21080 q^{81} - 28175 q^{82} - 18665 q^{83} + 26250 q^{84} - 4230 q^{85} - 10125 q^{86} - 15125 q^{88} + 5554 q^{89} + 18400 q^{90} + 7390 q^{91} + 3904 q^{92} + 36898 q^{93} + 18920 q^{94} + 14110 q^{95} - 21140 q^{96} + 20769 q^{97} - 3269 q^{99}+O(q^{100}) \) 12 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 - 18 * q^5 + 75 * q^6 - 80 * q^7 - 245 * q^8 + q^9 - 43 * q^11 + 594 * q^12 + 250 * q^13 + 610 * q^14 + 1134 * q^15 - 633 * q^16 - 1250 * q^17 - 3150 * q^18 - 1025 * q^19 + 752 * q^20 - 35 * q^22 + 1684 * q^23 + 5345 * q^24 + 197 * q^25 + 3490 * q^26 - 687 * q^27 - 3580 * q^28 - 2690 * q^29 - 6740 * q^30 - 1136 * q^31 + 5939 * q^33 + 2370 * q^34 + 3610 * q^35 - 514 * q^36 - 336 * q^37 + 1900 * q^38 - 6880 * q^39 - 2340 * q^40 - 4550 * q^41 + 1310 * q^42 - 6268 * q^44 + 5136 * q^45 + 4150 * q^46 + 24 * q^47 + 344 * q^48 + 827 * q^49 + 8895 * q^50 + 13155 * q^51 + 14070 * q^52 + 414 * q^53 - 2738 * q^55 - 21340 * q^56 - 26925 * q^57 + 2980 * q^58 - 10011 * q^59 - 6856 * q^60 + 9460 * q^61 - 6200 * q^62 + 9150 * q^63 - 2633 * q^64 - 3210 * q^66 + 12154 * q^67 - 9400 * q^68 - 9022 * q^69 - 9380 * q^70 + 17574 * q^71 + 43045 * q^72 + 27950 * q^73 + 43270 * q^74 - 1761 * q^75 + 4090 * q^77 - 42920 * q^78 - 41540 * q^79 - 2308 * q^80 - 21080 * q^81 - 28175 * q^82 - 18665 * q^83 + 26250 * q^84 - 4230 * q^85 - 10125 * q^86 - 15125 * q^88 + 5554 * q^89 + 18400 * q^90 + 7390 * q^91 + 3904 * q^92 + 36898 * q^93 + 18920 * q^94 + 14110 * q^95 - 21140 * q^96 + 20769 * q^97 - 3269 * q^99

Introduction

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