LMFDB - Embedded newform 11.5.d.a.7.3

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			7.3
Root			$-5.08417i$ of defining polynomial
Character	$\chi$	$=$	11.7
Dual form			11.5.d.a.8.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.10644 - 5.65202i) q^{2} +(-4.15494 + 12.7876i) q^{3} +(-10.1383 - 31.2024i) q^{4} +(-10.0543 + 7.30486i) q^{5} +(55.2138 + 75.9952i) q^{6} +(23.8119 - 7.73696i) q^{7} +(-111.679 - 36.2869i) q^{8} +(-80.7285 - 58.6527i) q^{9} +O(q^{10})$	\(q+(4.10644 - 5.65202i) q^{2} +(-4.15494 + 12.7876i) q^{3} +(-10.1383 - 31.2024i) q^{4} +(-10.0543 + 7.30486i) q^{5} +(55.2138 + 75.9952i) q^{6} +(23.8119 - 7.73696i) q^{7} +(-111.679 - 36.2869i) q^{8} +(-80.7285 - 58.6527i) q^{9} +86.8239i q^{10} +(16.1882 - 119.912i) q^{11} +441.128 q^{12} +(-110.382 + 151.927i) q^{13} +(54.0526 - 166.357i) q^{14} +(-51.6366 - 158.921i) q^{15} +(-239.021 + 173.659i) q^{16} +(-30.5398 - 42.0345i) q^{17} +(-663.013 + 215.426i) q^{18} +(369.226 + 119.969i) q^{19} +(329.862 + 239.659i) q^{20} +336.644i q^{21} +(-611.271 - 583.908i) q^{22} +164.959 q^{23} +(928.043 - 1277.34i) q^{24} +(-145.408 + 447.520i) q^{25} +(405.422 + 1247.76i) q^{26} +(204.349 - 148.468i) q^{27} +(-482.824 - 664.551i) q^{28} +(596.085 - 193.680i) q^{29} +(-1110.27 - 360.748i) q^{30} +(-974.492 - 708.010i) q^{31} +185.241i q^{32} +(1466.13 + 705.236i) q^{33} -362.990 q^{34} +(-182.894 + 251.732i) q^{35} +(-1011.66 + 3113.56i) q^{36} +(203.784 + 627.181i) q^{37} +(2194.27 - 1594.23i) q^{38} +(-1484.16 - 2042.76i) q^{39} +(1387.93 - 450.965i) q^{40} +(-2188.14 - 710.968i) q^{41} +(1902.72 + 1382.41i) q^{42} +1744.86i q^{43} +(-3905.67 + 710.592i) q^{44} +1240.12 q^{45} +(677.395 - 932.355i) q^{46} +(1141.17 - 3512.17i) q^{47} +(-1227.56 - 3778.04i) q^{48} +(-1435.30 + 1042.81i) q^{49} +(1932.29 + 2659.56i) q^{50} +(664.411 - 215.880i) q^{51} +(5859.58 + 1903.89i) q^{52} +(63.9262 + 46.4451i) q^{53} -1764.66i q^{54} +(713.181 + 1323.88i) q^{55} -2940.05 q^{56} +(-3068.22 + 4223.04i) q^{57} +(1353.10 - 4164.42i) q^{58} +(341.080 + 1049.74i) q^{59} +(-4435.22 + 3222.38i) q^{60} +(137.227 + 188.877i) q^{61} +(-8003.38 + 2600.46i) q^{62} +(-2376.10 - 772.040i) q^{63} +(-2777.35 - 2017.86i) q^{64} -2333.84i q^{65} +(10006.6 - 5390.58i) q^{66} +6390.51 q^{67} +(-1001.96 + 1379.08i) q^{68} +(-685.397 + 2109.43i) q^{69} +(671.753 + 2067.44i) q^{70} +(4467.06 - 3245.51i) q^{71} +(6887.39 + 9479.69i) q^{72} +(2979.95 - 968.246i) q^{73} +(4381.67 + 1423.69i) q^{74} +(-5118.54 - 3718.84i) q^{75} -12737.0i q^{76} +(-542.284 - 2980.59i) q^{77} -17640.3 q^{78} +(-1853.24 + 2550.77i) q^{79} +(1134.63 - 3492.02i) q^{80} +(-1448.19 - 4457.06i) q^{81} +(-13003.8 + 9447.85i) q^{82} +(3663.21 + 5041.98i) q^{83} +(10504.1 - 3412.99i) q^{84} +(614.112 + 199.537i) q^{85} +(9861.99 + 7165.15i) q^{86} +8427.22i q^{87} +(-6159.13 + 12804.3i) q^{88} -1267.14 q^{89} +(5092.46 - 7009.16i) q^{90} +(-1452.94 + 4471.70i) q^{91} +(-1672.41 - 5147.14i) q^{92} +(13102.7 - 9519.67i) q^{93} +(-15164.7 - 20872.4i) q^{94} +(-4588.65 + 1490.94i) q^{95} +(-2368.78 - 769.664i) q^{96} +(4428.29 + 3217.34i) q^{97} +12394.6i q^{98} +(-8340.03 + 8730.85i) 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 $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	4.10644	−	5.65202i	1.02661	−	1.41301i	0.119144	−	0.992877i	$-0.461985\pi$
$2$	4.10644	−	5.65202i	1.02661	−	1.41301i	0.907464	−	0.420129i	$-0.138015\pi$
$3$	−4.15494	+	12.7876i	−0.461660	+	1.42084i	0.401475	+	0.915870i	$0.368498\pi$
$3$	−4.15494	+	12.7876i	−0.461660	+	1.42084i	−0.863135	+	0.504973i	$0.831502\pi$
$4$	−10.1383	−	31.2024i	−0.633643	−	1.95015i
$5$	−10.0543	+	7.30486i	−0.402171	+	0.292194i	−0.770425	−	0.637531i	$-0.779956\pi$
$5$	−10.0543	+	7.30486i	−0.402171	+	0.292194i	0.368254	+	0.929725i	$0.379956\pi$
$6$	55.2138	+	75.9952i	1.53372	+	2.11098i
$7$	23.8119	−	7.73696i	0.485958	−	0.157897i	−0.0557829	−	0.998443i	$-0.517765\pi$
$7$	23.8119	−	7.73696i	0.485958	−	0.157897i	0.541741	+	0.840546i	$0.317765\pi$
$8$	−111.679	−	36.2869i	−1.74499	−	0.566982i
$9$	−80.7285	−	58.6527i	−0.996648	−	0.724107i
$10$			86.8239i			0.868239i
$11$	16.1882	−	119.912i	0.133787	−	0.991010i
$11$	16.1882	−	119.912i	0.133787	−	0.991010i
$12$	441.128			3.06339
$13$	−110.382	+	151.927i	−0.653146	+	0.898978i	−0.999230	−	0.0392250i	$-0.987511\pi$
$13$	−110.382	+	151.927i	−0.653146	+	0.898978i	0.346084	+	0.938203i	$0.387511\pi$
$14$	54.0526	−	166.357i	0.275779	−	0.848760i
$15$	−51.6366	−	158.921i	−0.229496	−	0.706316i
$16$	−239.021	+	173.659i	−0.933674	+	0.678354i
$17$	−30.5398	−	42.0345i	−0.105674	−	0.145448i	0.752905	−	0.658130i	$-0.228652\pi$
$17$	−30.5398	−	42.0345i	−0.105674	−	0.145448i	−0.858579	+	0.512682i	$0.828652\pi$
$18$	−663.013	+	215.426i	−2.04634	+	0.664895i
$19$	369.226	+	119.969i	1.02279	+	0.332323i	0.771934	−	0.635702i	$-0.219289\pi$
$19$	369.226	+	119.969i	1.02279	+	0.332323i	0.250851	+	0.968026i	$0.419289\pi$
$20$	329.862	+	239.659i	0.824656	+	0.599148i
$21$			336.644i			0.763365i
$22$	−611.271	−	583.908i	−1.26296	−	1.20642i
$23$	164.959			0.311833			0.155916	−	0.987770i	$-0.450167\pi$
$23$	164.959			0.311833			0.155916	+	0.987770i	$0.450167\pi$
$24$	928.043	−	1277.34i	1.61119	−	2.21761i
$25$	−145.408	+	447.520i	−0.232653	+	0.716032i
$26$	405.422	+	1247.76i	0.599736	+	1.84580i
$27$	204.349	−	148.468i	0.280314	−	0.203660i
$28$	−482.824	−	664.551i	−0.615847	−	0.847641i
$29$	596.085	−	193.680i	0.708781	−	0.230297i	0.0676290	−	0.997711i	$-0.478457\pi$
$29$	596.085	−	193.680i	0.708781	−	0.230297i	0.641153	+	0.767413i	$0.278457\pi$
$30$	−1110.27	−	360.748i	−1.23363	−	0.400831i
$31$	−974.492	−	708.010i	−1.01404	−	0.736743i	−0.0489874	−	0.998799i	$-0.515599\pi$
$31$	−974.492	−	708.010i	−1.01404	−	0.736743i	−0.965053	+	0.262056i	$0.915599\pi$
$32$			185.241i			0.180899i
$33$	1466.13	+	705.236i	1.34631	+	0.647600i
$34$	−362.990			−0.314005
$35$	−182.894	+	251.732i	−0.149301	+	0.205496i
$36$	−1011.66	+	3113.56i	−0.780600	+	2.40244i
$37$	203.784	+	627.181i	0.148856	+	0.458131i	0.997487	−	0.0708544i	$-0.0225726\pi$
$37$	203.784	+	627.181i	0.148856	+	0.458131i	−0.848631	+	0.528986i	$0.822573\pi$
$38$	2194.27	−	1594.23i	1.51958	−	1.10404i
$39$	−1484.16	−	2042.76i	−0.975776	−	1.34304i
$40$	1387.93	−	450.965i	0.867454	−	0.281853i
$41$	−2188.14	−	710.968i	−1.30169	−	0.422944i	−0.425519	−	0.904950i	$-0.639908\pi$
$41$	−2188.14	−	710.968i	−1.30169	−	0.422944i	−0.876168	+	0.482006i	$0.839908\pi$
$42$	1902.72	+	1382.41i	1.07864	+	0.783677i
$43$			1744.86i			0.943677i	0.881685	+	0.471839i	$0.156410\pi$
$43$			1744.86i			0.943677i	−0.881685	+	0.471839i	$0.843590\pi$
$44$	−3905.67	+	710.592i	−2.01739	+	0.367041i
$45$	1240.12			0.612403
$46$	677.395	−	932.355i	0.320130	−	0.440621i
$47$	1141.17	−	3512.17i	0.516601	−	1.58994i	−0.263748	−	0.964592i	$-0.584959\pi$
$47$	1141.17	−	3512.17i	0.516601	−	1.58994i	0.780349	−	0.625344i	$-0.215041\pi$
$48$	−1227.56	−	3778.04i	−0.532795	−	1.63977i
$49$	−1435.30	+	1042.81i	−0.597794	+	0.434322i
$50$	1932.29	+	2659.56i	0.772914	+	1.06383i
$51$	664.411	−	215.880i	0.255444	−	0.0829989i
$52$	5859.58	+	1903.89i	2.16701	+	0.704103i
$53$	63.9262	+	46.4451i	0.0227576	+	0.0165344i	0.599106	−	0.800670i	$-0.295523\pi$
$53$	63.9262	+	46.4451i	0.0227576	+	0.0165344i	−0.576348	+	0.817204i	$0.695523\pi$
$54$		−	1764.66i		−	0.605165i
$55$	713.181	+	1323.88i	0.235762	+	0.437647i
$56$	−2940.05			−0.937517
$57$	−3068.22	+	4223.04i	−0.944358	+	1.29980i
$58$	1353.10	−	4164.42i	0.402230	−	1.23794i
$59$	341.080	+	1049.74i	0.0979834	+	0.301562i	0.988020	−	0.154328i	$-0.0493212\pi$
$59$	341.080	+	1049.74i	0.0979834	+	0.301562i	−0.890036	+	0.455890i	$0.849321\pi$
$60$	−4435.22	+	3222.38i	−1.23201	+	0.895104i
$61$	137.227	+	188.877i	0.0368791	+	0.0507597i	0.827058	−	0.562116i	$-0.190013\pi$
$61$	137.227	+	188.877i	0.0368791	+	0.0507597i	−0.790179	+	0.612876i	$0.790013\pi$
$62$	−8003.38	+	2600.46i	−2.08204	+	0.676497i
$63$	−2376.10	−	772.040i	−0.598663	−	0.194518i
$64$	−2777.35	−	2017.86i	−0.678063	−	0.492642i
$65$		−	2333.84i		−	0.552388i
$66$	10006.6	−	5390.58i	2.29719	−	1.23751i
$67$	6390.51			1.42359			0.711797	−	0.702385i	$-0.247882\pi$
$67$	6390.51			1.42359			0.711797	+	0.702385i	$0.247882\pi$
$68$	−1001.96	+	1379.08i	−0.216686	+	0.298243i
$69$	−685.397	+	2109.43i	−0.143961	+	0.443065i
$70$	671.753	+	2067.44i	0.137093	+	0.421927i
$71$	4467.06	−	3245.51i	0.886145	−	0.643822i	−0.0487247	−	0.998812i	$-0.515516\pi$
$71$	4467.06	−	3245.51i	0.886145	−	0.643822i	0.934870	+	0.354990i	$0.115516\pi$
$72$	6887.39	+	9479.69i	1.32859	+	1.82864i
$73$	2979.95	−	968.246i	0.559196	−	0.181694i	−0.0157636	−	0.999876i	$-0.505018\pi$
$73$	2979.95	−	968.246i	0.559196	−	0.181694i	0.574959	+	0.818182i	$0.305018\pi$
$74$	4381.67	+	1423.69i	0.800159	+	0.259987i
$75$	−5118.54	−	3718.84i	−0.909963	−	0.661127i
$76$		−	12737.0i		−	2.20516i
$77$	−542.284	−	2980.59i	−0.0914629	−	0.502714i
$78$	−17640.3			−2.89946
$79$	−1853.24	+	2550.77i	−0.296946	+	0.408711i	−0.931255	−	0.364368i	$-0.881285\pi$
$79$	−1853.24	+	2550.77i	−0.296946	+	0.408711i	0.634309	+	0.773080i	$0.281285\pi$
$80$	1134.63	−	3492.02i	0.177285	−	0.545629i
$81$	−1448.19	−	4457.06i	−0.220726	−	0.679326i
$82$	−13003.8	+	9447.85i	−1.93395	+	1.40509i
$83$	3663.21	+	5041.98i	0.531748	+	0.731889i	0.987396	−	0.158272i	$-0.0505922\pi$
$83$	3663.21	+	5041.98i	0.531748	+	0.731889i	−0.455647	+	0.890160i	$0.650592\pi$
$84$	10504.1	−	3412.99i	1.48868	−	0.483700i
$85$	614.112	+	199.537i	0.0849982	+	0.0276176i
$86$	9861.99	+	7165.15i	1.33342	+	0.968788i
$87$			8427.22i			1.11339i
$88$	−6159.13	+	12804.3i	−0.795342	+	1.65345i
$89$	−1267.14			−0.159972			−0.0799859	−	0.996796i	$-0.525488\pi$
$89$	−1267.14			−0.159972			−0.0799859	+	0.996796i	$0.525488\pi$
$90$	5092.46	−	7009.16i	0.628698	−	0.865329i
$91$	−1452.94	+	4471.70i	−0.175455	+	0.539995i
$92$	−1672.41	−	5147.14i	−0.197591	−	0.608121i
$93$	13102.7	−	9519.67i	1.51494	−	1.10067i
$94$	−15164.7	−	20872.4i	−1.71624	−	2.36220i
$95$	−4588.65	+	1490.94i	−0.508438	+	0.165201i
$96$	−2368.78	−	769.664i	−0.257029	−	0.0835139i
$97$	4428.29	+	3217.34i	0.470644	+	0.341943i	0.797692	−	0.603065i	$-0.206054\pi$
$97$	4428.29	+	3217.34i	0.470644	+	0.341943i	−0.327048	+	0.945008i	$0.606054\pi$
$98$			12394.6i			1.29057i
$99$	−8340.03	+	8730.85i	−0.850936	+	0.890812i
$100$	15437.9			1.54379
$101$	−6193.29	+	8524.33i	−0.607125	+	0.835636i	−0.996337	−	0.0855119i	$-0.972747\pi$
$101$	−6193.29	+	8524.33i	−0.607125	+	0.835636i	0.389212	+	0.921148i	$0.372747\pi$
$102$	1508.20	−	4641.76i	0.144964	−	0.446152i
$103$	−1070.41	−	3294.38i	−0.100896	−	0.310527i	0.887849	−	0.460135i	$-0.152199\pi$
$103$	−1070.41	−	3294.38i	−0.100896	−	0.310527i	−0.988745	+	0.149608i	$0.952199\pi$
$104$	17840.3	−	12961.8i	1.64944	−	1.19839i
$105$	−2459.13	−	3384.71i	−0.223051	−	0.307003i
$106$	525.017	−	170.589i	0.0467264	−	0.0151823i
$107$	−7796.18	−	2533.13i	−0.680949	−	0.221254i	−0.0519380	−	0.998650i	$-0.516540\pi$
$107$	−7796.18	−	2533.13i	−0.680949	−	0.221254i	−0.629011	+	0.777397i	$0.716540\pi$
$108$	−6704.32	−	4870.97i	−0.574787	−	0.417607i
$109$		−	13677.7i		−	1.15123i	−0.817722	−	0.575613i	$-0.804763\pi$
$109$		−	13677.7i		−	1.15123i	0.817722	−	0.575613i	$-0.195237\pi$
$110$	10411.2	+	1405.53i	0.860434	+	0.116159i
$111$	−8866.85			−0.719653
$112$	−4347.95	+	5984.44i	−0.346616	+	0.477076i
$113$	885.702	−	2725.91i	0.0693635	−	0.213479i	−0.910366	−	0.413804i	$-0.864200\pi$
$113$	885.702	−	2725.91i	0.0693635	−	0.213479i	0.979729	+	0.200325i	$0.0641999\pi$
$114$	11269.3	+	34683.3i	0.867135	+	2.66877i
$115$	−1658.55	+	1205.01i	−0.125410	+	0.0911157i
$116$	−12086.6	−	16635.7i	−0.898229	−	1.23631i
$117$	17821.9	−	5790.69i	1.30191	−	0.423017i
$118$	7333.76	+	2382.88i	0.526699	+	0.171135i
$119$	−1052.43	−	764.637i	−0.0743190	−	0.0539959i
$120$			19622.0i			1.36264i
$121$	−14116.9	−	3882.33i	−0.964202	−	0.265169i
$122$	1631.05			0.109584
$123$	18183.1	−	25026.9i	1.20187	−	1.65424i
$124$	−12212.0	+	37584.5i	−0.794222	+	2.44436i
$125$	−4207.34	−	12948.9i	−0.269270	−	0.828728i
$126$	−14120.9	+	10259.4i	−0.889448	+	0.646222i
$127$	16460.3	+	22655.7i	1.02054	+	1.40465i	0.911824	+	0.410582i	$0.134674\pi$
$127$	16460.3	+	22655.7i	1.02054	+	1.40465i	0.108718	+	0.994073i	$0.465326\pi$
$128$	−25628.8	+	8327.29i	−1.56426	+	0.508258i
$129$	−22312.5	−	7249.79i	−1.34082	−	0.435658i
$130$	−13190.9	−	9583.77i	−0.780528	−	0.567087i
$131$			12108.6i			0.705586i	0.935701	+	0.352793i	$0.114768\pi$
$131$			12108.6i			0.705586i	−0.935701	+	0.352793i	$0.885232\pi$
$132$	7141.08	−	52896.6i	0.409842	−	3.03585i
$133$	9720.17			0.549504
$134$	26242.2	−	36119.3i	1.46147	−	2.01155i
$135$	−970.041	+	2985.48i	−0.0532259	+	0.163812i
$136$	1885.37	+	5802.58i	0.101934	+	0.313721i
$137$	−30186.6	+	21931.8i	−1.60832	+	1.16851i	−0.739850	+	0.672772i	$0.765103\pi$
$137$	−30186.6	+	21931.8i	−1.60832	+	1.16851i	−0.868470	+	0.495741i	$0.834897\pi$
$138$	9108.03	+	12536.1i	0.478263	+	0.658272i
$139$	−3774.88	+	1226.53i	−0.195377	+	0.0634819i	−0.405071	−	0.914285i	$-0.632753\pi$
$139$	−3774.88	+	1226.53i	−0.195377	+	0.0634819i	0.209694	+	0.977767i	$0.432753\pi$
$140$	9708.89	+	3154.61i	0.495352	+	0.160950i
$141$	40170.7	+	29185.7i	2.02056	+	1.46802i
$142$		−	38575.4i		−	1.91308i
$143$	16431.1	+	15695.5i	0.803514	+	0.767546i
$144$	29481.3			1.42175
$145$	−4578.40	+	6301.63i	−0.217760	+	0.299721i
$146$	6764.44	−	20818.8i	0.317341	−	0.976675i
$147$	−7371.41	−	22686.9i	−0.341127	−	1.04988i
$148$	17503.6	−	12717.1i	0.799104	−	0.580583i
$149$	1533.16	+	2110.22i	0.0690583	+	0.0950506i	0.842149	−	0.539245i	$-0.181290\pi$
$149$	1533.16	+	2110.22i	0.0690583	+	0.0950506i	−0.773091	+	0.634295i	$0.781290\pi$
$150$	−42037.9	+	13659.0i	−1.86835	+	0.607065i
$151$	20848.6	+	6774.10i	0.914370	+	0.297097i	0.728155	−	0.685412i	$-0.240378\pi$
$151$	20848.6	+	6774.10i	0.914370	+	0.297097i	0.186215	+	0.982509i	$0.440378\pi$
$152$	−36881.6	−	26796.1i	−1.59633	−	1.15980i
$153$			5184.63i			0.221480i
$154$	−19073.2	−	9174.60i	−0.804234	−	0.386853i
$155$	14969.7			0.623089
$156$	−48692.4	+	67019.4i	−2.00084	+	2.75392i
$157$	5242.72	−	16135.4i	0.212695	−	0.654608i	−0.786614	−	0.617445i	$-0.788168\pi$
$157$	5242.72	−	16135.4i	0.212695	−	0.654608i	0.999309	−	0.0371634i	$-0.0118322\pi$
$158$	6806.79	+	20949.1i	0.272664	+	0.839174i
$159$	−859.530	+	624.485i	−0.0339991	+	0.0247018i
$160$	−1353.16	−	1862.46i	−0.0528577	−	0.0727524i
$161$	3928.00	−	1276.29i	0.151537	−	0.0492375i
$162$	−31138.3	−	10117.4i	−1.18649	−	0.385514i
$163$	−31471.1	−	22865.1i	−1.18450	−	0.860593i	−0.191832	−	0.981428i	$-0.561443\pi$
$163$	−31471.1	−	22865.1i	−1.18450	−	0.860593i	−0.992673	+	0.120835i	$0.961443\pi$
$164$			75483.2i			2.80648i
$165$	−19892.5	+	3619.21i	−0.730670	+	0.132937i
$166$	43540.1			1.58006
$167$	10485.2	−	14431.7i	0.375963	−	0.517468i	−0.578547	−	0.815649i	$-0.696380\pi$
$167$	10485.2	−	14431.7i	0.375963	−	0.517468i	0.954509	+	0.298181i	$0.0963800\pi$
$168$	12215.7	−	37596.2i	0.432814	−	1.33206i
$169$	−2071.97	−	6376.87i	−0.0725454	−	0.223272i
$170$	3649.60	−	2651.59i	0.126284	−	0.0917505i
$171$	−22770.5	−	31341.0i	−0.778720	−	1.07182i
$172$	54443.9	−	17689.9i	1.84031	−	0.597954i
$173$	19714.8	+	6405.71i	0.658718	+	0.214030i	0.619254	−	0.785191i	$-0.287435\pi$
$173$	19714.8	+	6405.71i	0.658718	+	0.214030i	0.0394636	+	0.999221i	$0.487435\pi$
$174$	47630.8	+	34605.8i	1.57322	+	1.14301i
$175$			11781.3i			0.384697i
$176$	16954.5	+	31472.7i	0.547342	+	1.01604i
$177$	−14840.8			−0.473707
$178$	−5203.42	+	7161.89i	−0.164229	+	0.226041i
$179$	−2401.43	+	7390.85i	−0.0749487	+	0.230668i	−0.981512	−	0.191402i	$-0.938697\pi$
$179$	−2401.43	+	7390.85i	−0.0749487	+	0.230668i	0.906563	+	0.422071i	$0.138697\pi$
$180$	−12572.6	−	38694.6i	−0.388045	−	1.19428i
$181$	−4026.47	+	2925.40i	−0.122904	+	0.0892952i	−0.647539	−	0.762032i	$-0.724202\pi$
$181$	−4026.47	+	2925.40i	−0.122904	+	0.0892952i	0.524635	+	0.851327i	$0.324202\pi$
$182$	19307.7	+	26574.8i	0.582893	+	0.802283i
$183$	−2985.45	+	970.032i	−0.0891472	+	0.0289657i
$184$	−18422.6	−	5985.86i	−0.544145	−	0.176804i
$185$	−6630.37	−	4817.24i	−0.193729	−	0.140752i
$186$		−	113149.i		−	3.27057i
$187$	−5534.84	+	2981.64i	−0.158278	+	0.0852651i
$188$	−121158.			−3.42796
$189$	3717.25	−	5116.36i	0.104063	−	0.143231i
$190$	−10416.1	+	32057.6i	−0.288536	+	0.888022i
$191$	−14758.2	−	45421.1i	−0.404545	−	1.24506i	−0.921274	−	0.388914i	$-0.872850\pi$
$191$	−14758.2	−	45421.1i	−0.404545	−	1.24506i	0.516729	−	0.856149i	$-0.327150\pi$
$192$	37343.3	−	27131.5i	1.01300	−	0.735988i
$193$	12311.9	+	16945.8i	0.330528	+	0.454933i	0.941645	−	0.336607i	$-0.109279\pi$
$193$	12311.9	+	16945.8i	0.330528	+	0.454933i	−0.611117	+	0.791540i	$0.709279\pi$
$194$	36368.9	−	11817.0i	0.966334	−	0.313981i
$195$	29844.2	+	9696.97i	0.784857	+	0.255016i
$196$	47089.7	+	34212.6i	1.22578	+	0.890583i
$197$			1957.53i			0.0504400i	0.999682	+	0.0252200i	$0.00802862\pi$
$197$			1957.53i			0.0504400i	−0.999682	+	0.0252200i	$0.991971\pi$
$198$	15099.2	+	82990.7i	0.385144	+	2.11689i
$199$	−50821.6			−1.28334			−0.641670	−	0.766980i	$-0.721758\pi$
$199$	−50821.6			−1.28334			−0.641670	+	0.766980i	$0.721758\pi$
$200$	32478.2	−	44702.4i	0.811955	−	1.11756i
$201$	−26552.2	+	81719.2i	−0.657216	+	2.02270i
$202$	22747.4	+	70009.2i	0.557479	+	1.71574i
$203$	12695.4	−	9223.78i	0.308075	−	0.223829i
$204$	−13472.0	−	18542.6i	−0.323721	−	0.445564i
$205$	27193.6	−	8835.75i	0.647082	−	0.210250i
$206$	−23015.5	−	7478.19i	−0.542358	−	0.176223i
$207$	−13316.9	−	9675.32i	−0.310787	−	0.225800i
$208$		−	55482.5i		−	1.28242i
$209$	20362.8	−	42332.6i	0.466171	−	0.969130i
$210$	−29228.7			−0.662783
$211$	−6534.60	+	8994.10i	−0.146776	+	0.202019i	−0.876074	−	0.482176i	$-0.839847\pi$
$211$	−6534.60	+	8994.10i	−0.146776	+	0.202019i	0.729299	+	0.684196i	$0.239847\pi$
$212$	801.098	−	2465.53i	0.0178244	−	0.0548577i
$213$	22941.9	+	70607.8i	0.505673	+	1.55630i
$214$	−46331.8	+	33662.1i	−1.01170	+	0.735044i
$215$	−12745.9	−	17543.3i	−0.275737	−	0.379520i
$216$	−28209.0	+	9165.67i	−0.604617	+	0.196452i
$217$	−28682.4	−	9319.47i	−0.609110	−	0.197912i
$218$	−77306.8	−	56166.7i	−1.62669	−	1.18186i
$219$			42129.4i			0.878410i
$220$	34077.9	−	35674.9i	0.704090	−	0.737084i
$221$	9757.23			0.199775
$222$	−36411.1	+	50115.6i	−0.738802	+	1.01687i
$223$	24854.2	−	76493.4i	0.499793	−	1.53820i	−0.309559	−	0.950880i	$-0.600181\pi$
$223$	24854.2	−	76493.4i	0.499793	−	1.53820i	0.809352	−	0.587324i	$-0.199819\pi$
$224$	1433.20	+	4410.94i	0.0285635	+	0.0879094i
$225$	37986.9	−	27599.1i	0.750358	−	0.545167i
$226$	−11769.8	−	16199.8i	−0.230438	−	0.317170i
$227$	−5169.69	+	1679.73i	−0.100326	+	0.0325978i	−0.358750	−	0.933434i	$-0.616797\pi$
$227$	−5169.69	+	1679.73i	−0.100326	+	0.0325978i	0.258424	+	0.966032i	$0.416797\pi$
$228$	162876.	+	52921.5i	3.13319	+	1.01803i
$229$	10375.1	+	7537.98i	0.197844	+	0.143742i	0.682297	−	0.731075i	$-0.260981\pi$
$229$	10375.1	+	7537.98i	0.197844	+	0.143742i	−0.484453	+	0.874817i	$0.660981\pi$
$230$			14322.4i			0.270745i
$231$	40367.7	+	5449.67i	0.756502	+	0.102128i
$232$	−73598.5			−1.36739
$233$	−29361.6	+	40412.7i	−0.540838	+	0.744400i	−0.988734	−	0.149686i	$-0.952174\pi$
$233$	−29361.6	+	40412.7i	−0.540838	+	0.744400i	0.447896	+	0.894086i	$0.352174\pi$
$234$	40455.4	−	124509.i	0.738830	−	2.27389i
$235$	14182.2	+	43648.4i	0.256808	+	0.790374i
$236$	29296.4	−	21285.1i	0.526005	−	0.382165i
$237$	−24918.1	−	34296.8i	−0.443627	−	0.610600i
$238$	−8643.49	+	2808.44i	−0.152593	+	0.0495805i
$239$	19061.2	+	6193.36i	0.333699	+	0.108425i	0.471074	−	0.882094i	$-0.343867\pi$
$239$	19061.2	+	6193.36i	0.333699	+	0.108425i	−0.137375	+	0.990519i	$0.543867\pi$
$240$	39940.2	+	29018.3i	0.693407	+	0.503790i
$241$		−	67743.9i		−	1.16637i	−0.812340	−	0.583185i	$-0.801806\pi$
$241$		−	67743.9i		−	1.16637i	0.812340	−	0.583185i	$-0.198194\pi$
$242$	−79913.1	+	63846.4i	−1.36454	+	1.09020i
$243$	83471.9			1.41360
$244$	4502.17	−	6196.71i	0.0756210	−	0.104083i
$245$	6813.36	−	20969.4i	0.113509	−	0.349344i
$246$	−66785.0	−	205543.i	−1.10359	−	3.39651i
$247$	−58982.3	+	42853.1i	−0.966780	+	0.702407i
$248$	83139.3	+	114431.i	1.35177	+	1.86055i
$249$	−79695.2	+	25894.5i	−1.28539	+	0.417647i
$250$	−90464.5	−	29393.7i	−1.44743	−	0.470299i
$251$	14482.2	+	10522.0i	0.229873	+	0.167013i	0.696760	−	0.717305i	$-0.254624\pi$
$251$	14482.2	+	10522.0i	0.229873	+	0.167013i	−0.466887	+	0.884317i	$0.654624\pi$
$252$			81967.1i			1.29074i
$253$	2670.40	−	19780.7i	0.0417192	−	0.309029i
$254$	195644.			3.03248
$255$	−5103.19	+	7023.94i	−0.0784805	+	0.108019i
$256$	−41203.2	+	126810.i	−0.628711	+	1.93497i
$257$	21254.3	+	65413.9i	0.321796	+	0.990385i	0.972866	+	0.231368i	$0.0743201\pi$
$257$	21254.3	+	65413.9i	0.321796	+	0.990385i	−0.651071	+	0.759017i	$0.725680\pi$
$258$	−132601.	+	96340.3i	−1.99208	+	1.44733i
$259$	9704.96	+	13357.7i	0.144675	+	0.199128i
$260$	−72821.5	+	23661.1i	−1.07724	+	0.350017i
$261$	−59480.9	−	19326.5i	−0.873166	−	0.283709i
$262$	68437.9	+	49723.0i	0.996997	+	0.724361i
$263$		−	89436.3i		−	1.29301i	−0.762909	−	0.646506i	$-0.776230\pi$
$263$		−	89436.3i		−	1.29301i	0.762909	−	0.646506i	$-0.223770\pi$
$264$	−138145.	−	131962.i	−1.98211	−	1.89339i
$265$	−982.006			−0.0139837
$266$	39915.2	−	54938.6i	0.564125	−	0.776452i
$267$	5264.88	−	16203.6i	0.0738526	−	0.227295i
$268$	−64788.8	−	199400.i	−0.902050	−	2.77622i
$269$	68994.6	−	50127.5i	0.953478	−	0.692742i	0.00185080	−	0.999998i	$-0.499411\pi$
$269$	68994.6	−	50127.5i	0.953478	−	0.692742i	0.951627	+	0.307256i	$0.0994109\pi$
$270$	12890.6	+	17742.4i	0.176826	+	0.243380i
$271$	−1142.71	+	371.287i	−0.0155595	+	0.00505559i	−0.316786	−	0.948497i	$-0.602604\pi$
$271$	−1142.71	+	371.287i	−0.0155595	+	0.00505559i	0.301227	+	0.953552i	$0.402604\pi$
$272$	14599.3	+	4743.60i	0.197331	+	0.0641166i
$273$	−51145.4	−	37159.3i	−0.686248	−	0.498588i
$274$			260677.i			3.47217i
$275$	51309.3	+	24680.8i	0.678469	+	0.326357i
$276$	72768.2			0.955264
$277$	1919.07	−	2641.37i	0.0250110	−	0.0344247i	−0.796328	−	0.604865i	$-0.793227\pi$
$277$	1919.07	−	2641.37i	0.0250110	−	0.0344247i	0.821339	+	0.570440i	$0.193227\pi$
$278$	−8568.92	+	26372.4i	−0.110876	+	0.341240i
$279$	37142.6	+	114313.i	0.477160	+	1.46855i
$280$	29560.1	−	21476.7i	0.377042	−	0.273937i
$281$	75056.5	+	103306.i	0.950551	+	1.30832i	0.951282	+	0.308322i	$0.0997673\pi$
$281$	75056.5	+	103306.i	0.950551	+	1.30832i	−0.000731006		1.00000i	$0.500233\pi$
$282$	329916.	−	107196.i	4.14864	−	1.34797i
$283$	−48541.1	−	15771.9i	−0.606089	−	0.196930i	−0.0101347	−	0.999949i	$-0.503226\pi$
$283$	−48541.1	−	15771.9i	−0.606089	−	0.196930i	−0.595954	+	0.803018i	$0.703226\pi$
$284$	−146556.	−	106479.i	−1.81705	−	1.32016i
$285$		−	64872.5i		−	0.798677i
$286$	156185.	−	28416.0i	1.90944	−	0.347401i
$287$	−57604.5			−0.699346
$288$	10864.9	−	14954.2i	0.130990	−	0.180293i
$289$	24975.2	−	76865.7i	0.299029	−	0.920316i
$290$	16816.0	+	51754.4i	0.199953	+	0.615392i
$291$	−59541.3	+	43259.3i	−0.703124	+	0.510850i
$292$	−60423.2	−	83165.4i	−0.708661	−	0.975388i
$293$	−131095.	+	42595.4i	−1.52704	+	0.496167i	−0.947767	−	0.318964i	$-0.896665\pi$
$293$	−131095.	+	42595.4i	−1.52704	+	0.496167i	−0.579277	+	0.815130i	$0.696665\pi$
$294$	−158497.	−	51498.8i	−1.83369	−	0.595802i
$295$	−11097.5	−	8062.80i	−0.127521	−	0.0926492i
$296$		−	77438.0i		−	0.883833i
$297$	−14495.1	−	26907.4i	−0.164327	−	0.305041i
$298$	18222.8			0.205203
$299$	−18208.5	+	25061.9i	−0.203672	+	0.280331i
$300$	−64143.6	+	197414.i	−0.712706	+	2.19348i
$301$	13499.9	+	41548.5i	0.149004	+	0.458587i
$302$	123901.	−	90019.1i	1.35850	−	0.987008i
$303$	−83272.9	−	114615.i	−0.907023	−	1.24841i
$304$	−109086.	+	35444.2i	−1.18038	+	0.383529i
$305$	−2759.44	−	896.596i	−0.0296634	−	0.00963823i
$306$	29303.6	+	21290.3i	0.312953	+	0.227373i
$307$			118248.i			1.25464i	0.778762	+	0.627320i	$0.215848\pi$
$307$			118248.i			1.25464i	−0.778762	+	0.627320i	$0.784152\pi$
$308$	−87503.8	+	47138.6i	−0.922413	+	0.496907i
$309$	46574.7			0.487790
$310$	61472.2	−	84609.2i	0.639669	−	0.880429i
$311$	−37325.6	+	114876.i	−0.385910	+	1.18771i	0.549909	+	0.835225i	$0.314663\pi$
$311$	−37325.6	+	114876.i	−0.385910	+	1.18771i	−0.935818	+	0.352483i	$0.885337\pi$
$312$	91624.2	+	281990.i	0.941241	+	2.89684i
$313$	128376.	−	93270.3i	1.31037	−	0.952039i	0.310370	−	0.950616i	$-0.399547\pi$
$313$	128376.	−	93270.3i	1.31037	−	0.952039i	0.999999	−	0.00142300i	$-0.000452956\pi$
$314$	−69669.0	−	95891.2i	−0.706611	−	0.972566i
$315$	29529.6	−	9594.73i	0.297602	−	0.0966967i
$316$	98378.9	+	31965.2i	0.985207	+	0.320113i
$317$	−2127.69	−	1545.86i	−0.0211734	−	0.0153834i	0.577148	−	0.816639i	$-0.304165\pi$
$317$	−2127.69	−	1545.86i	−0.0211734	−	0.0153834i	−0.598322	+	0.801256i	$0.704165\pi$
$318$			7422.49i			0.0733999i
$319$	−13575.0	−	74613.2i	−0.133401	−	0.733220i
$320$	42664.4			0.416644
$321$	64785.3	−	89169.3i	0.628733	−	0.865377i
$322$	8916.49	−	27442.1i	0.0859968	−	0.264671i
$323$	−6233.27	−	19184.0i	−0.0597463	−	0.183880i
$324$	−124389.	+	90373.9i	−1.18493	+	0.860900i
$325$	−51940.2	−	71489.5i	−0.491741	−	0.676824i
$326$	−258468.	+	83981.4i	−2.43205	+	0.790219i
$327$	174905.	+	56830.1i	1.63571	+	0.531475i
$328$	218571.	+	158801.i	2.03163	+	1.47607i
$329$		−	92460.7i		−	0.854212i
$330$	−61231.4	+	127295.i	−0.562272	+	1.16892i
$331$	−140188.			−1.27954			−0.639772	−	0.768565i	$-0.720971\pi$
$331$	−140188.			−1.27954			−0.639772	+	0.768565i	$0.720971\pi$
$332$	120183.	−	165418.i	1.09036	−	1.50075i
$333$	20334.7	−	62583.9i	0.183379	−	0.564383i
$334$	−38511.2	−	118525.i	−0.345219	−	1.06247i
$335$	−64252.0	+	46681.8i	−0.572528	+	0.415966i
$336$	−58461.1	−	80464.8i	−0.517832	−	0.712734i
$337$	63862.6	−	20750.2i	0.562324	−	0.182710i	−0.0140424	−	0.999901i	$-0.504470\pi$
$337$	63862.6	−	20750.2i	0.562324	−	0.182710i	0.576367	+	0.817191i	$0.304470\pi$
$338$	−44550.6	−	14475.4i	−0.389960	−	0.126706i
$339$	31177.8	+	22652.0i	0.271298	+	0.197109i
$340$		−	21184.7i		−	0.183259i
$341$	−100674.	+	105392.i	−0.865785	+	0.906357i
$342$	−270646.			−2.31392
$343$	−61443.7	+	84569.9i	−0.522262	+	0.718833i
$344$	63315.5	−	194865.i	0.535048	−	1.64671i
$345$	−8517.95	−	26215.5i	−0.0715643	−	0.220252i
$346$	117163.	−	85123.6i	0.978671	−	0.711046i
$347$	−45007.6	−	61947.6i	−0.373789	−	0.514477i	0.580137	−	0.814519i	$-0.302999\pi$
$347$	−45007.6	−	61947.6i	−0.373789	−	0.514477i	−0.953926	+	0.300043i	$0.902999\pi$
$348$	262950.	−	85437.6i	2.17127	−	0.705489i
$349$	192023.	+	62392.0i	1.57653	+	0.512246i	0.961160	−	0.275993i	$-0.0890066\pi$
$349$	192023.	+	62392.0i	1.57653	+	0.512246i	0.615370	+	0.788238i	$0.289007\pi$
$350$	66588.4	+	48379.3i	0.543579	+	0.394933i
$351$			47434.4i			0.385016i
$352$	22212.6	+	2998.72i	0.179273	+	0.0242020i
$353$	−52506.0			−0.421366			−0.210683	−	0.977554i	$-0.567569\pi$
$353$	−52506.0			−0.421366			−0.210683	+	0.977554i	$0.567569\pi$
$354$	−60942.7	+	83880.4i	−0.486312	+	0.669351i
$355$	−21205.1	+	65262.5i	−0.168261	+	0.517853i
$356$	12846.6	+	39537.8i	0.101365	+	0.311969i
$357$	14150.6	−	10281.0i	0.111030	−	0.0806679i
$358$	31911.9	+	43923.0i	0.248993	+	0.342709i
$359$	181110.	−	58846.2i	1.40525	−	0.456594i	0.494366	−	0.869254i	$-0.335400\pi$
$359$	181110.	−	58846.2i	1.40525	−	0.456594i	0.910885	+	0.412660i	$0.135400\pi$
$360$	−138495.	−	44999.9i	−1.06864	−	0.347222i
$361$	16503.2	+	11990.3i	0.126635	+	0.0920056i
$362$			34770.7i			0.265336i
$363$	108300.	−	164390.i	0.821896	−	1.24756i
$364$	154258.			1.16425
$365$	−22888.4	+	31503.1i	−0.171802	+	0.236466i
$366$	−6776.92	+	20857.2i	−0.0505907	+	0.155702i
$367$	−12757.1	−	39262.2i	−0.0947149	−	0.291502i	0.892464	−	0.451118i	$-0.148975\pi$
$367$	−12757.1	−	39262.2i	−0.0947149	−	0.291502i	−0.987179	+	0.159615i	$0.948975\pi$
$368$	−39428.7	+	28646.6i	−0.291150	+	0.211533i
$369$	134945.	+	185735.i	0.991067	+	1.36409i
$370$	−54454.3	+	17693.3i	−0.397767	+	0.129242i
$371$	1881.55	+	611.353i	0.0136700	+	0.00444165i
$372$	−429876.	−	312323.i	−3.10640	−	2.25693i
$373$			135550.i			0.974278i	0.873325	+	0.487139i	$0.161959\pi$
$373$			135550.i			0.974278i	−0.873325	+	0.487139i	$0.838041\pi$
$374$	−5876.16	+	43526.9i	−0.0420098	+	0.311182i
$375$	183066.			1.30180
$376$	−254891.	+	350828.i	−1.80293	+	2.48152i
$377$	−36371.6	+	111940.i	−0.255906	+	0.787597i
$378$	−13653.1	−	42020.0i	−0.0955538	−	0.294085i
$379$	−116364.	+	84543.6i	−0.810105	+	0.588576i	−0.913861	−	0.406027i	$-0.866914\pi$
$379$	−116364.	+	84543.6i	−0.810105	+	0.588576i	0.103756	+	0.994603i	$0.466914\pi$
$380$	93042.1	+	128061.i	0.644336	+	0.886852i
$381$	−358103.	+	116355.i	−2.46694	+	0.801556i
$382$	−317325.	−	103105.i	−2.17459	−	0.706567i
$383$	35217.9	+	25587.3i	0.240086	+	0.174432i	0.701321	−	0.712845i	$-0.252594\pi$
$383$	35217.9	+	25587.3i	0.240086	+	0.174432i	−0.461236	+	0.887278i	$0.652594\pi$
$384$		−	362330.i		−	2.45720i
$385$	27225.0	+	26006.4i	0.183674	+	0.175452i
$386$	146336.			0.982147
$387$	102341.	−	140860.i	0.683324	−	0.940515i
$388$	55493.6	−	170792.i	0.368620	−	1.13450i
$389$	−25941.4	−	79839.4i	−0.171433	−	0.527616i	0.828020	−	0.560699i	$-0.189467\pi$
$389$	−25941.4	−	79839.4i	−0.171433	−	0.527616i	−0.999453	+	0.0330828i	$0.989467\pi$
$390$	177361.	−	128860.i	1.16608	−	0.847207i
$391$	−5037.84	−	6933.99i	−0.0329527	−	0.0453554i
$392$	198134.	−	64377.7i	1.28940	−	0.418951i
$393$	−154839.	−	50310.3i	−1.00253	−	0.325741i
$394$	11064.0	+	8038.45i	0.0712720	+	0.0517821i
$395$		−	39183.8i		−	0.251138i
$396$	356977.	+	171713.i	2.27641	+	1.09500i
$397$	−203508.			−1.29122			−0.645609	−	0.763668i	$-0.723396\pi$
$397$	−203508.			−1.29122			−0.645609	+	0.763668i	$0.723396\pi$
$398$	−208696.	+	287245.i	−1.31749	+	1.81337i
$399$	−40386.7	+	124297.i	−0.253684	+	0.780758i
$400$	−42960.2	−	132218.i	−0.268501	−	0.826362i
$401$	−40878.6	+	29700.0i	−0.254218	+	0.184701i	−0.707594	−	0.706619i	$-0.750220\pi$
$401$	−40878.6	+	29700.0i	−0.254218	+	0.184701i	0.453376	+	0.891319i	$0.350220\pi$
$402$	352844.	+	485648.i	2.18339	+	3.00518i
$403$	215132.	−	69900.7i	1.32463	−	0.430399i
$404$	328769.	+	106824.i	2.01432	+	0.654492i
$405$	47118.6	+	34233.7i	0.287265	+	0.208710i
$406$		−	109632.i		−	0.665096i
$407$	78505.6	−	14283.2i	0.473928	−	0.0862256i
$408$	−82034.7			−0.492807
$409$	145408.	−	200136.i	0.869241	−	1.19641i	−0.110045	−	0.993927i	$-0.535099\pi$
$409$	145408.	−	200136.i	0.869241	−	1.19641i	0.979286	−	0.202482i	$-0.0649006\pi$
$410$	61729.0	−	189982.i	0.367216	−	1.13018i
$411$	−155032.	−	477139.i	−0.917777	−	2.82463i
$412$	−91940.6	+	66798.8i	−0.541643	+	0.393527i
$413$	16243.6	+	22357.3i	0.0952316	+	0.131075i
$414$	−109370.	+	35536.5i	−0.638114	+	0.207336i
$415$	−73661.9	−	23934.2i	−0.427707	−	0.138971i
$416$	−28143.1	−	20447.2i	−0.162624	−	0.118154i
$417$		−	53367.8i		−	0.306907i
$418$	−155646.	−	288927.i	−0.890812	−	1.65362i
$419$	−82331.5			−0.468962			−0.234481	−	0.972121i	$-0.575339\pi$
$419$	−82331.5			−0.468962			−0.234481	+	0.972121i	$0.575339\pi$
$420$	−80679.7	+	111046.i	−0.457368	+	0.629513i
$421$	104696.	−	322221.i	0.590698	−	1.81798i	0.0156269	−	0.999878i	$-0.495026\pi$
$421$	104696.	−	322221.i	0.590698	−	1.81798i	0.575071	−	0.818103i	$-0.304974\pi$
$422$	24001.0	+	73867.4i	0.134773	+	0.414790i
$423$	−298123.	+	216599.i	−1.66615	+	1.21053i
$424$	−5453.90	−	7506.64i	−0.0303372	−	0.0417555i
$425$	23252.0	−	7555.04i	0.128731	−	0.0418272i
$426$	493286.	+	160278.i	2.71819	+	0.883193i
$427$	4728.98	+	3435.80i	0.0259365	+	0.0188440i
$428$			268941.i			1.46815i
$429$	−268978.	+	144900.i	−1.46151	+	0.787322i
$430$	−151496.			−0.819338
$431$	187263.	−	257746.i	1.00809	−	1.38751i	0.0878574	−	0.996133i	$-0.471998\pi$
$431$	187263.	−	257746.i	1.00809	−	1.38751i	0.920229	−	0.391379i	$-0.128002\pi$
$432$	−23060.8	+	70974.0i	−0.123568	+	0.380305i
$433$	94321.8	+	290293.i	0.503079	+	1.54832i	0.803976	+	0.594662i	$0.202714\pi$
$433$	94321.8	+	290293.i	0.503079	+	1.54832i	−0.300897	+	0.953657i	$0.597286\pi$
$434$	−170456.	+	123844.i	−0.904969	+	0.657498i
$435$	−61559.6	−	84729.6i	−0.325325	−	0.447772i
$436$	−426778.	+	138669.i	−2.24507	+	0.729467i
$437$	60907.3	+	19790.0i	0.318938	+	0.103629i
$438$	238116.	+	173002.i	1.24120	+	0.901783i
$439$			109029.i			0.565735i	0.959159	+	0.282868i	$0.0912857\pi$
$439$			109029.i			0.565735i	−0.959159	+	0.282868i	$0.908714\pi$
$440$	−31608.1	−	173730.i	−0.163265	−	0.897364i
$441$	177033.			0.910286
$442$	40067.4	−	55148.1i	0.205091	−	0.282284i
$443$	22834.7	−	70277.9i	0.116356	−	0.358106i	−0.875872	−	0.482544i	$-0.839713\pi$
$443$	22834.7	−	70277.9i	0.116356	−	0.358106i	0.992227	+	0.124438i	$0.0397128\pi$
$444$	89894.6	+	276667.i	0.456003	+	1.40343i
$445$	12740.1	−	9256.26i	0.0643360	−	0.0467429i
$446$	−330280.	−	454592.i	−1.66040	−	2.28535i
$447$	−33354.8	+	10837.6i	−0.166933	+	0.0542400i
$448$	−81746.1	−	26560.9i	−0.407297	−	0.132339i
$449$	−59594.1	−	43297.7i	−0.295604	−	0.214769i	0.430091	−	0.902786i	$-0.358482\pi$
$449$	−59594.1	−	43297.7i	−0.295604	−	0.214769i	−0.725695	+	0.688017i	$0.758482\pi$
$450$		−	328036.i		−	1.61993i
$451$	−120676.	+	250875.i	−0.593290	+	1.23340i
$452$	−94034.6			−0.460268
$453$	−173249.	+	238457.i	−0.844256	+	1.16202i
$454$	−11735.1	+	36116.9i	−0.0569344	+	0.175226i
$455$	−18056.8	−	55573.3i	−0.0872206	−	0.268437i
$456$	495898.	−	360291.i	2.38486	−	1.73270i
$457$	203868.	+	280600.i	0.976149	+	1.34355i	0.938878	+	0.344249i	$0.111867\pi$
$457$	203868.	+	280600.i	0.976149	+	1.34355i	0.0372711	+	0.999305i	$0.488133\pi$
$458$	85209.7	−	27686.3i	0.406217	−	0.131988i
$459$	−12481.6	−	4055.51i	−0.0592439	−	0.0192495i
$460$	54413.9	+	39534.0i	0.257155	+	0.186834i
$461$		−	45865.9i		−	0.215818i	−0.994161	−	0.107909i	$-0.965584\pi$
$461$		−	45865.9i		−	0.215818i	0.994161	−	0.107909i	$-0.0344156\pi$
$462$	196569.	−	205780.i	0.920939	−	0.964096i
$463$	100968.			0.471003			0.235501	−	0.971874i	$-0.424327\pi$
$463$	100968.			0.471003			0.235501	+	0.971874i	$0.424327\pi$
$464$	−108843.	+	149809.i	−0.505548	+	0.695827i
$465$	−62198.3	+	191427.i	−0.287655	+	0.885312i
$466$	107842.	+	331904.i	0.496612	+	1.52841i
$467$	−3773.53	+	2741.63i	−0.0173027	+	0.0125711i	−0.596403	−	0.802685i	$-0.703404\pi$
$467$	−3773.53	+	2741.63i	−0.0173027	+	0.0125711i	0.579100	+	0.815256i	$0.303404\pi$
$468$	−361367.	−	497379.i	−1.64990	−	2.27089i
$469$	152170.	−	49443.2i	0.691806	−	0.224782i
$470$	304940.	+	99081.1i	1.38044	+	0.448534i
$471$	184550.	+	134084.i	0.831903	+	0.604413i
$472$		−	129611.i		−	0.581778i
$473$	209230.	+	28246.2i	0.935194	+	0.126252i
$474$	−296171.			−1.31821
$475$	−107377.	+	147792.i	−0.475908	+	0.655032i
$476$	−13188.7	+	40590.5i	−0.0582086	+	0.179148i
$477$	−2436.54	−	7498.89i	−0.0107087	−	0.0329579i
$478$	113279.	−	82301.7i	0.495784	−	0.360208i
$479$	−191734.	−	263900.i	−0.835659	−	1.15019i	−0.986843	−	0.161680i	$-0.948309\pi$
$479$	−191734.	−	263900.i	−0.835659	−	1.15019i	0.151184	−	0.988506i	$-0.451691\pi$
$480$	29438.7	−	9565.20i	0.127772	−	0.0415156i
$481$	−117780.	−	38269.0i	−0.509075	−	0.165408i
$482$	−382890.	−	278186.i	−1.64809	−	1.19740i
$483$			55532.6i			0.238042i
$484$	21982.7	+	479841.i	0.0938405	+	2.04836i
$485$	−68025.4			−0.289193
$486$	342772.	−	471785.i	1.45122	−	1.99743i
$487$	6638.87	−	20432.3i	0.0279922	−	0.0861510i	−0.936084	−	0.351775i	$-0.885578\pi$
$487$	6638.87	−	20432.3i	0.0279922	−	0.0861510i	0.964077	+	0.265624i	$0.0855781\pi$
$488$	−8471.71	−	26073.2i	−0.0355739	−	0.109485i
$489$	423150.	−	307436.i	1.76961	−	1.28569i
$490$	−90540.7	−	124619.i	−0.377096	−	0.519028i
$491$	98398.4	−	31971.6i	0.408155	−	0.132618i	−0.0977415	−	0.995212i	$-0.531162\pi$
$491$	98398.4	−	31971.6i	0.408155	−	0.132618i	0.505896	+	0.862594i	$0.331162\pi$
$492$	−965247.	−	313628.i	−3.98757	−	1.29564i
$493$	−26345.6	−	19141.2i	−0.108396	−	0.0787544i
$494$			509343.i			2.08716i
$495$	20075.3	−	148705.i	0.0819316	−	0.606898i
$496$	355876.			1.44656
$497$	81258.9	−	111843.i	0.328971	−	0.452790i
$498$	−180907.	+	556773.i	−0.729451	+	2.24502i
$499$	38922.4	+	119791.i	0.156314	+	0.481086i	0.998292	−	0.0584271i	$-0.0186085\pi$
$499$	38922.4	+	119791.i	0.156314	+	0.481086i	−0.841978	+	0.539513i	$0.818609\pi$
$500$	−361381.	+	262559.i	−1.44552	+	1.05023i
$501$	140981.	+	194043.i	0.561674	+	0.773078i
$502$	118941.	−	38646.2i	0.471979	−	0.153355i
$503$	−180440.	−	58628.6i	−0.713177	−	0.231725i	−0.0701146	−	0.997539i	$-0.522337\pi$
$503$	−180440.	−	58628.6i	−0.713177	−	0.231725i	−0.643063	+	0.765814i	$0.722337\pi$
$504$	237346.	+	172442.i	0.934375	+	0.678863i
$505$		−	130947.i		−	0.513467i
$506$	−100835.	−	96321.2i	−0.393831	−	0.376202i
$507$	90153.6			0.350725
$508$	540033.	−	743292.i	2.09263	−	2.88026i
$509$	−57036.6	+	175541.i	−0.220150	+	0.677551i	0.778598	+	0.627523i	$0.215931\pi$
$509$	−57036.6	+	175541.i	−0.220150	+	0.677551i	−0.998748	+	0.0500282i	$0.984069\pi$
$510$	18743.6	+	57686.8i	0.0720629	+	0.221787i
$511$	63467.2	−	46111.6i	0.243056	−	0.176591i
$512$	294106.	+	404802.i	1.12193	+	1.54420i
$513$	93262.4	−	30302.8i	0.354382	−	0.115146i
$514$	457000.	+	148488.i	1.72978	+	0.562039i
$515$	34827.2	+	25303.4i	0.131312	+	0.0954036i
$516$			769706.i			2.89085i
$517$	−402678.	−	193696.i	−1.50653	−	0.724670i
$518$	115351.			0.429895
$519$	−163827.	+	225489.i	−0.608207	+	0.837125i
$520$	−84687.8	+	260642.i	−0.313194	+	0.963913i
$521$	−98896.3	−	304371.i	−0.364338	−	1.12132i	−0.950395	−	0.311047i	$-0.899320\pi$
$521$	−98896.3	−	304371.i	−0.364338	−	1.12132i	0.586057	−	0.810270i	$-0.300680\pi$
$522$	−353488.	+	256824.i	−1.29728	+	0.942530i
$523$	−23706.2	−	32628.8i	−0.0866681	−	0.119288i	0.763481	−	0.645830i	$-0.223488\pi$
$523$	−23706.2	−	32628.8i	−0.0866681	−	0.119288i	−0.850149	+	0.526542i	$0.823488\pi$
$524$	377817.	−	122760.i	1.37600	−	0.447090i
$525$	−150655.	−	48950.7i	−0.546594	−	0.177599i
$526$	−505496.	−	367265.i	−1.82703	−	1.32742i
$527$			62584.8i			0.225345i
$528$	−472905.	+	86039.6i	−1.69631	+	0.308625i
$529$	−252629.			−0.902760
$530$	−4032.54	+	5550.32i	−0.0143558	+	0.0197591i
$531$	34035.0	−	104749.i	0.120708	−	0.371502i
$532$	−98545.8	−	303293.i	−0.348189	−	1.07162i
$533$	349546.	−	253960.i	1.23041	−	0.893944i
$534$	−69963.4	−	96296.4i	−0.245351	−	0.337697i
$535$	96889.1	−	31481.2i	0.338507	−	0.109988i
$536$	−713689.	−	231892.i	−2.48416	−	0.807152i
$537$	−84533.3	−	61417.0i	−0.293143	−	0.212981i
$538$		−	595804.i		−	2.05844i
$539$	101810.	+	188992.i	0.350441	+	0.650526i
$540$	102989.			0.353185
$541$	−216936.	+	298587.i	−0.741204	+	1.02018i	0.257344	+	0.966320i	$0.417153\pi$
$541$	−216936.	+	298587.i	−0.741204	+	1.02018i	−0.998548	+	0.0538605i	$0.982847\pi$
$542$	−2593.92	+	7983.27i	−0.00882995	+	0.0271758i
$543$	−20679.1	−	63643.7i	−0.0701345	−	0.215852i
$544$	7786.50	−	5657.22i	0.0263114	−	0.0191164i
$545$	99913.8	+	137520.i	0.336382	+	0.462990i
$546$	−420050.	+	136483.i	−1.40902	+	0.457817i
$547$	465924.	+	151388.i	1.55718	+	0.505960i	0.956054	−	0.293191i	$-0.0947171\pi$
$547$	465924.	+	151388.i	1.55718	+	0.505960i	0.601131	+	0.799151i	$0.294717\pi$
$548$	990366.	+	719543.i	3.29788	+	2.39605i
$549$		−	23296.5i		−	0.0772940i
$550$	350194.	−	188651.i	1.15767	−	0.623640i
$551$	243325.			0.801465
$552$	153089.	−	210710.i	0.502420	−	0.691522i
$553$	−24394.1	+	75077.2i	−0.0797689	+	0.245503i
$554$	−7048.56	−	21693.3i	−0.0229658	−	0.0706814i
$555$	89149.7	−	64771.0i	0.289424	−	0.210279i
$556$	76541.7	+	105351.i	0.247599	+	0.340790i
$557$	−438618.	+	142515.i	−1.41376	+	0.459358i	−0.913614	−	0.406583i	$-0.866720\pi$
$557$	−438618.	+	142515.i	−1.41376	+	0.459358i	−0.500146	+	0.865941i	$0.666720\pi$
$558$	798625.	+	259489.i	2.56492	+	0.833394i
$559$	−265092.	−	192601.i	−0.848346	−	0.616359i
$560$		−	91930.4i		−	0.293145i
$561$	−15131.0	−	83165.7i	−0.0480776	−	0.264252i
$562$	892105.			2.82451
$563$	−250537.	+	344834.i	−0.790414	+	1.08791i	0.203642	+	0.979045i	$0.434722\pi$
$563$	−250537.	+	344834.i	−0.790414	+	1.08791i	−0.994056	+	0.108867i	$0.965278\pi$
$564$	503403.	−	1.54932e6i	1.58255	−	4.87059i
$565$	11007.3	+	33877.0i	0.0344813	+	0.106123i
$566$	−288474.	+	209589.i	−0.900480	+	0.654237i
$567$	−68968.2	−	94926.6i	−0.214527	−	0.295272i
$568$	−616648.	+	200361.i	−1.91135	+	0.621036i
$569$	−472778.	−	153615.i	−1.46027	−	0.474470i	−0.532117	−	0.846671i	$-0.678603\pi$
$569$	−472778.	−	153615.i	−1.46027	−	0.474470i	−0.928152	+	0.372201i	$0.878603\pi$
$570$	−366661.	−	266395.i	−1.12854	−	0.819929i
$571$			310454.i			0.952192i	0.879393	+	0.476096i	$0.157948\pi$
$571$			310454.i			0.952192i	−0.879393	+	0.476096i	$0.842052\pi$
$572$	323156.	−	671815.i	0.987690	−	2.05332i
$573$	642146.			1.95580
$574$	−236549.	+	325582.i	−0.717955	+	0.988181i
$575$	−23986.4	+	73822.7i	−0.0725488	+	0.223282i
$576$	105858.	+	325798.i	0.319065	+	0.981981i
$577$	−120971.	+	87890.3i	−0.363353	+	0.263991i	−0.754449	−	0.656359i	$-0.772096\pi$
$577$	−120971.	+	87890.3i	−0.363353	+	0.263991i	0.391096	+	0.920350i	$0.372096\pi$
$578$	−331888.	−	456805.i	−0.993427	−	1.36733i
$579$	−267851.	+	87030.1i	−0.798981	+	0.259605i
$580$	243043.	+	78969.5i	0.722483	+	0.234749i
$581$	126238.	+	91717.1i	0.373970	+	0.271705i
$582$			514170.i			1.51796i
$583$	6604.19	−	6913.67i	0.0194304	−	0.0203410i
$584$	−367934.			−1.07881
$585$	−136886.	+	188408.i	−0.399989	+	0.550537i
$586$	−297584.	+	915869.i	−0.866591	+	2.66709i
$587$	44466.6	+	136854.i	0.129050	+	0.397174i	0.994617	−	0.103618i	$-0.0330420\pi$
$587$	44466.6	+	136854.i	0.129050	+	0.397174i	−0.865567	+	0.500793i	$0.833042\pi$
$588$	−633152.	+	460012.i	−1.83127	+	1.33050i
$589$	−274869.	−	378324.i	−0.792309	−	1.09052i
$590$	−91142.2	+	29613.9i	−0.261828	+	0.0850730i
$591$	−25032.0	−	8133.40i	−0.0716673	−	0.0232861i
$592$	−157624.	−	114521.i	−0.449758	−	0.326768i
$593$		−	251778.i		−	0.715992i	−0.933723	−	0.357996i	$-0.883460\pi$
$593$		−	251778.i		−	0.715992i	0.933723	−	0.357996i	$-0.116540\pi$
$594$	−211604.	−	28566.7i	−0.599724	−	0.0809632i
$595$	16167.0			0.0456663
$596$	50300.3	−	69232.4i	0.141605	−	0.194902i
$597$	211161.	−	649885.i	0.592467	−	1.82343i
$598$	66878.1	+	205830.i	0.187017	+	0.575580i
$599$	78951.7	−	57361.8i	0.220043	−	0.159871i	−0.472303	−	0.881436i	$-0.656577\pi$
$599$	78951.7	−	57361.8i	0.220043	−	0.159871i	0.692346	+	0.721566i	$0.256577\pi$
$600$	436691.	+	601054.i	1.21303	+	1.66959i
$601$	579164.	−	188182.i	1.60344	−	0.520989i	0.635485	−	0.772113i	$-0.280800\pi$
$601$	579164.	−	188182.i	1.60344	−	0.520989i	0.967955	+	0.251124i	$0.0808003\pi$
$602$	290269.	+	94314.3i	0.800956	+	0.260246i
$603$	−515897.	−	374821.i	−1.41882	−	1.03083i
$604$		−	719203.i		−	1.97141i
$605$	170295.	−	64087.8i	0.465255	−	0.175091i
$606$	−989763.			−2.69517
$607$	115572.	−	159071.i	0.313671	−	0.431731i	−0.622851	−	0.782341i	$-0.714026\pi$
$607$	115572.	−	159071.i	0.313671	−	0.431731i	0.936522	+	0.350609i	$0.114026\pi$
$608$	−22223.1	+	68395.6i	−0.0601170	+	0.185021i
$609$	65201.1	+	200668.i	0.175801	+	0.541059i
$610$	−16399.0	+	11914.6i	−0.0440716	+	0.0320199i
$611$	407630.	+	561054.i	1.09190	+	1.50287i
$612$	161773.	−	52563.2i	0.431920	−	0.140339i
$613$	−172252.	−	55967.9i	−0.458398	−	0.148942i	0.0707104	−	0.997497i	$-0.477473\pi$
$613$	−172252.	−	55967.9i	−0.458398	−	0.148942i	−0.529108	+	0.848554i	$0.677473\pi$
$614$	668343.	+	485580.i	1.77281	+	1.28802i
$615$			384453.i			1.01647i
$616$	−47594.3	+	352548.i	−0.125428	+	0.929089i
$617$	−110226.			−0.289543			−0.144772	−	0.989465i	$-0.546245\pi$
$617$	−110226.			−0.289543			−0.144772	+	0.989465i	$0.546245\pi$
$618$	191256.	−	263241.i	0.500770	−	0.689250i
$619$	92714.6	−	285346.i	0.241973	−	0.744716i	−0.754147	−	0.656706i	$-0.771949\pi$
$619$	92714.6	−	285346.i	0.241973	−	0.744716i	0.996120	−	0.0880101i	$-0.0280508\pi$
$620$	−151767.	−	467092.i	−0.394816	−	1.21512i
$621$	33709.3	−	24491.2i	0.0874111	−	0.0635079i
$622$	496008.	+	682697.i	1.28206	+	1.76460i
$623$	−30173.0	+	9803.80i	−0.0777396	+	0.0252591i
$624$	709488.	+	230526.i	1.82211	+	0.592041i
$625$	−101036.	−	73406.8i	−0.258652	−	0.187921i
$626$		−	1.10859e6i		−	2.82893i
$627$	456725.	+	436281.i	1.16177	+	1.10976i
$628$	−556617.			−1.41136
$629$	20139.7	−	27720.0i	0.0509041	−	0.0700634i
$630$	67031.5	−	206302.i	0.168888	−	0.519783i
$631$	−31706.3	−	97581.9i	−0.0796318	−	0.245082i	0.903313	−	0.428982i	$-0.141128\pi$
$631$	−31706.3	−	97581.9i	−0.0796318	−	0.245082i	−0.982945	+	0.183900i	$0.941128\pi$
$632$	299528.	−	217620.i	0.749901	−	0.544835i
$633$	−87862.0	−	120932.i	−0.219277	−	0.301809i
$634$	−17474.5	+	5677.80i	−0.0434736	+	0.0141254i
$635$	−330993.	−	107546.i	−0.820864	−	0.266715i
$636$	28199.6	+	20488.2i	0.0697154	+	0.0506512i
$637$		−	333169.i		−	0.821080i
$638$	−477461.	−	229668.i	−1.17300	−	0.564234i
$639$	−550977.			−1.34937
$640$	196849.	−	270939.i	0.480588	−	0.661473i
$641$	−201254.	+	619395.i	−0.489810	+	1.50748i	0.335082	+	0.942189i	$0.391236\pi$
$641$	−201254.	+	619395.i	−0.489810	+	1.50748i	−0.824892	+	0.565291i	$0.808764\pi$
$642$	−237950.	−	732336.i	−0.577320	−	1.77681i
$643$	−192555.	+	139900.i	−0.465730	+	0.338372i	−0.795775	−	0.605593i	$-0.792936\pi$
$643$	−192555.	+	139900.i	−0.465730	+	0.338372i	0.330045	+	0.943965i	$0.392936\pi$
$644$	−79646.4	−	109624.i	−0.192041	−	0.264322i
$645$	277295.	−	90098.6i	0.666535	−	0.216570i
$646$	−134025.	−	43547.4i	−0.321160	−	0.104351i
$647$	64434.0	+	46814.1i	0.153924	+	0.111832i	0.662082	−	0.749432i	$-0.269673\pi$
$647$	64434.0	+	46814.1i	0.153924	+	0.111832i	−0.508157	+	0.861264i	$0.669673\pi$
$648$			550312.i			1.31057i
$649$	131398.	−	23906.3i	0.311960	−	0.0567574i
$650$	−617349.			−1.46118
$651$	238347.	−	328057.i	0.562404	−	0.774082i
$652$	−394384.	+	1.21379e6i	−0.927734	+	2.85527i
$653$	162023.	+	498656.i	0.379971	+	1.16943i	0.940063	+	0.341001i	$0.110766\pi$
$653$	162023.	+	498656.i	0.379971	+	1.16943i	−0.560092	+	0.828431i	$0.689234\pi$
$654$	1.03944e6	−	755199.i	2.43021	−	1.76565i
$655$	−88451.3	−	121743.i	−0.206168	−	0.283766i
$656$	646475.	−	210053.i	1.50226	−	0.488113i
$657$	−297357.	−	96617.3i	−0.688887	−	0.223833i
$658$	−522590.	−	379684.i	−1.20701	−	0.876941i
$659$			35482.4i			0.0817038i	0.999165	+	0.0408519i	$0.0130072\pi$
$659$			35482.4i			0.0817038i	−0.999165	+	0.0408519i	$0.986993\pi$
$660$	314604.	+	584002.i	0.722231	+	1.34068i
$661$	706789.			1.61766			0.808829	−	0.588043i	$-0.200102\pi$
$661$	706789.			1.61766			0.808829	+	0.588043i	$0.200102\pi$
$662$	−575673.	+	792346.i	−1.31359	+	1.80800i
$663$	−40540.7	+	124771.i	−0.0922283	+	0.283849i
$664$	−226148.	−	696012.i	−0.512928	−	1.57863i
$665$	−97729.2	+	71004.4i	−0.220994	+	0.160562i
$666$	−270222.	−	371929.i	−0.609218	−	0.838517i
$667$	98329.9	−	31949.3i	0.221021	−	0.0718141i
$668$	−556605.	−	180852.i	−1.24737	−	0.405294i
$669$	874898.	+	635651.i	1.95481	+	1.42025i
$670$			554849.i			1.23602i
$671$	24870.1	−	13397.6i	0.0552374	−	0.0297566i
$672$	−62360.1			−0.138092
$673$	8421.04	−	11590.6i	0.0185924	−	0.0255903i	−0.799620	−	0.600507i	$-0.794966\pi$
$673$	8421.04	−	11590.6i	0.0185924	−	0.0255903i	0.818212	+	0.574917i	$0.194966\pi$
$674$	144967.	−	446162.i	0.319116	−	0.982139i
$675$	36728.5	+	113039.i	0.0806113	+	0.248096i
$676$	−177967.	+	129301.i	−0.389446	+	0.282949i
$677$	−263209.	−	362276.i	−0.574280	−	0.790429i	0.418773	−	0.908091i	$-0.362460\pi$
$677$	−263209.	−	362276.i	−0.574280	−	0.790429i	−0.993054	+	0.117662i	$0.962460\pi$
$678$	256059.	−	83198.7i	0.557033	−	0.180991i
$679$	130338.	+	42349.5i	0.282705	+	0.0918563i
$680$	−61343.1	−	44568.4i	−0.132662	−	0.0963849i
$681$		−	73087.0i		−	0.157596i
$682$	182266.	+	1.00180e6i	0.391865	+	2.15383i
$683$	281044.			0.602466			0.301233	−	0.953551i	$-0.402602\pi$
$683$	281044.			0.602466			0.301233	+	0.953551i	$0.402602\pi$
$684$	−747060.	+	1.02824e6i	−1.59677	+	2.19777i
$685$	143295.	−	441017.i	0.305387	−	0.939884i
$686$	225677.	+	694562.i	0.479555	+	1.47592i
$687$	−139501.	+	101353.i	−0.295572	+	0.214745i
$688$	−303010.	−	417058.i	−0.640148	−	0.881088i
$689$	−14112.6	+	4585.45i	−0.0297281	+	0.00965925i
$690$	−183149.	−	59508.8i	−0.384687	−	0.124992i
$691$	−533286.	−	387455.i	−1.11687	−	0.811457i	−0.133142	−	0.991097i	$-0.542507\pi$
$691$	−533286.	−	387455.i	−1.11687	−	0.811457i	−0.983732	+	0.179640i	$0.942507\pi$
$692$		−	680091.i		−	1.42022i
$693$	−131042.	+	272425.i	−0.272862	+	0.567258i
$694$	−534950.			−1.11069
$695$	28994.0	−	39906.9i	0.0600260	−	0.0826187i
$696$	305797.	−	941147.i	0.631270	−	1.94285i
$697$	36940.1	+	113690.i	0.0760384	+	0.234022i
$698$	1.14117e6	−	829109.i	2.34229	−	1.70177i
$699$	−394786.	−	543376.i	−0.807992	−	1.11211i
$700$	367606.	−	119443.i	0.750217	−	0.243760i
$701$	633231.	+	205749.i	1.28862	+	0.418700i	0.871610	−	0.490200i	$-0.163076\pi$
$701$	633231.	+	205749.i	1.28862	+	0.418700i	0.417015	+	0.908900i	$0.363076\pi$
$702$	268100.	+	194786.i	0.544030	+	0.395261i
$703$			256019.i			0.518038i
$704$	−286926.	+	300372.i	−0.578929	+	0.606058i
$705$	−617084.			−1.24156
$706$	−215613.	+	296765.i	−0.432578	+	0.595393i
$707$	−81521.7	+	250898.i	−0.163093	+	0.501947i
$708$	150460.	+	463068.i	0.300161	+	0.923801i
$709$	−611367.	+	444184.i	−1.21621	+	0.883630i	−0.995780	−	0.0917725i	$-0.970747\pi$
$709$	−611367.	+	444184.i	−1.21621	+	0.883630i	−0.220432	+	0.975402i	$0.570747\pi$
$710$	281788.	+	387848.i	0.558992	+	0.769386i
$711$	299219.	−	97222.1i	0.591902	−	0.192321i
$712$	141513.	+	45980.4i	0.279150	+	0.0907012i
$713$	−160752.	−	116793.i	−0.316211	−	0.229741i
$714$		−	122198.i		−	0.239700i
$715$	−279856.	−	37780.8i	−0.547423	−	0.0739024i
$716$	254959.			0.497329
$717$	−158396.	+	218014.i	−0.308111	+	0.424078i
$718$	411117.	−	1.26529e6i	0.797473	−	2.45437i
$719$	−178748.	−	550130.i	−0.345767	−	1.06416i	−0.961172	−	0.275950i	$-0.911008\pi$
$719$	−178748.	−	550130.i	−0.345767	−	1.06416i	0.615405	−	0.788211i	$-0.288992\pi$
$720$	−296413.	+	215357.i	−0.571785	+	0.415426i
$721$	−50977.0	−	70163.9i	−0.0980627	−	0.134972i
$722$	135538.	−	44039.1i	0.260009	−	0.0844820i
$723$	866281.	+	281472.i	1.65723	+	0.538466i
$724$	132101.	+	95977.1i	0.252017	+	0.183101i
$725$			294923.i			0.561090i
$726$	−484407.	−	1.28717e6i	−0.919046	−	2.44210i
$727$	−205506.			−0.388825			−0.194413	−	0.980920i	$-0.562280\pi$
$727$	−205506.			−0.388825			−0.194413	+	0.980920i	$0.562280\pi$
$728$	324528.	−	446675.i	0.612336	−	0.842808i
$729$	−229518.	+	706382.i	−0.431878	+	1.32918i
$730$	84066.9	+	258731.i	0.157754	+	0.485515i
$731$	73344.3	−	53287.7i	0.137256	−	0.0997224i
$732$	60534.7	+	83318.9i	0.112975	+	0.155497i
$733$	−819407.	+	266241.i	−1.52508	+	0.495527i	−0.947213	−	0.320606i	$-0.896113\pi$
$733$	−819407.	+	266241.i	−1.52508	+	0.495527i	−0.577863	+	0.816134i	$0.696113\pi$
$734$	−274297.	−	89124.4i	−0.509130	−	0.165426i
$735$	239838.	+	174253.i	0.443960	+	0.322556i
$736$			30557.2i			0.0564103i
$737$	103451.	−	766301.i	0.190458	−	1.41080i
$738$	1.60392e6			2.94490
$739$	573905.	−	789913.i	1.05088	−	1.44641i	0.162828	−	0.986655i	$-0.447939\pi$
$739$	573905.	−	789913.i	1.05088	−	1.44641i	0.888048	−	0.459751i	$-0.152061\pi$
$740$	−83089.2	+	255722.i	−0.151733	+	0.466987i
$741$	−302920.	−	932293.i	−0.551686	−	1.69792i
$742$	11181.8	−	8124.08i	0.0203098	−	0.0147559i
$743$	417262.	+	574311.i	0.755842	+	1.04033i	0.997549	+	0.0699776i	$0.0222928\pi$
$743$	417262.	+	574311.i	0.755842	+	1.04033i	−0.241707	+	0.970349i	$0.577707\pi$
$744$	−1.80874e6	+	587696.i	−3.26761	+	1.06171i
$745$	−30829.7	−	10017.2i	−0.0555465	−	0.0180481i
$746$	766133.	+	556628.i	1.37666	+	1.00020i
$747$		−	621889.i		−	1.11448i
$748$	149148.	+	142472.i	0.266572	+	0.254639i
$749$	−205241.			−0.365848
$750$	751749.	−	1.03469e6i	1.33644	−	1.83946i
$751$	187442.	−	576888.i	0.332344	−	1.02285i	−0.635672	−	0.771960i	$-0.719277\pi$
$751$	187442.	−	576888.i	0.332344	−	1.02285i	0.968016	−	0.250890i	$-0.0807233\pi$
$752$	337155.	+	1.03766e6i	0.596202	+	1.83492i
$753$	−194723.	+	141475.i	−0.343422	+	0.249510i
$754$	483332.	+	665249.i	0.850164	+	1.17015i
$755$	−259101.	+	84187.0i	−0.454543	+	0.147690i
$756$	−197329.	−	64116.2i	−0.345261	−	0.112182i
$757$	444331.	+	322825.i	0.775380	+	0.563346i	0.903589	−	0.428401i	$-0.140923\pi$
$757$	444331.	+	322825.i	0.775380	+	0.563346i	−0.128209	+	0.991747i	$0.540923\pi$
$758$			1.00487e6i			1.74892i
$759$	241852.	+	116335.i	0.419822	+	0.201943i
$760$	566559.			0.980886
$761$	−165158.	+	227320.i	−0.285187	+	0.392527i	−0.927443	−	0.373963i	$-0.877999\pi$
$761$	−165158.	+	227320.i	−0.285187	+	0.392527i	0.642256	+	0.766490i	$0.277999\pi$
$762$	−812887.	+	2.50181e6i	−1.39998	+	4.30868i
$763$	−105824.	−	325693.i	−0.181776	−	0.559448i
$764$	−1.26763e6	+	920985.i	−2.17172	+	1.57785i
$765$	−37872.9	−	52127.6i	−0.0647152	−	0.0890728i
$766$	289240.	−	93979.9i	0.492948	−	0.160169i
$767$	−197133.	−	64052.3i	−0.335095	−	0.108879i
$768$	−1.45040e6	−	1.05378e6i	−2.45904	−	1.78660i
$769$			427381.i			0.722708i	0.932429	+	0.361354i	$0.117685\pi$
$769$			427381.i			0.722708i	−0.932429	+	0.361354i	$0.882315\pi$
$770$	258786.	−	47083.2i	0.436476	−	0.0794117i
$771$	−924797.			−1.55574
$772$	403929.	−	555961.i	0.677752	−	0.932846i
$773$	−6642.23	+	20442.7i	−0.0111162	+	0.0342121i	−0.956461	−	0.291861i	$-0.905726\pi$
$773$	−6642.23	+	20442.7i	−0.0111162	+	0.0342121i	0.945345	+	0.326073i	$0.105726\pi$
$774$	−375888.	−	1.15686e6i	−0.627446	−	1.93108i
$775$	458548.	−	333155.i	0.763451	−	0.554680i
$776$	−377802.	−	519999.i	−0.627394	−	0.863534i
$777$	−211137.	+	68602.5i	−0.349721	+	0.113631i
$778$	−557781.	−	181234.i	−0.921519	−	0.299420i
$779$	−722622.	−	525015.i	−1.19079	−	0.865161i
$780$		−	1.02952e6i		−	1.69218i
$781$	−316862.	−	588194.i	−0.519480	−	0.964314i
$782$	−59878.6			−0.0979170
$783$	93054.1	−	128078.i	0.151779	−	0.208906i
$784$	161974.	−	498505.i	0.263520	−	0.811032i
$785$	65155.3	+	200528.i	0.105733	+	0.325413i
$786$	−920193.	+	668559.i	−1.48948	+	1.08217i
$787$	405961.	+	558757.i	0.655443	+	0.902140i	0.999320	−	0.0368749i	$-0.0117403\pi$
$787$	405961.	+	558757.i	0.655443	+	0.902140i	−0.343877	+	0.939015i	$0.611740\pi$
$788$	61079.5	−	19845.9i	0.0983656	−	0.0319609i
$789$	1.14368e6	+	371603.i	1.83717	+	0.596932i
$790$	−221468.	−	160906.i	−0.354859	−	0.257820i
$791$		−	71761.9i		−	0.114694i
$792$	1.24822e6	−	672423.i	1.98995	−	1.07199i
$793$	−43843.0			−0.0697194
$794$	−835691.	+	1.15023e6i	−1.32558	+	1.82450i
$795$	4080.18	−	12557.5i	0.00645572	−	0.0198687i
$796$	515244.	+	1.58576e6i	0.813180	+	2.50271i
$797$	−33788.9	+	24549.1i	−0.0531934	+	0.0386473i	−0.614064	−	0.789256i	$-0.710466\pi$
$797$	−33788.9	+	24549.1i	−0.0531934	+	0.0386473i	0.560871	+	0.827903i	$0.310466\pi$
$798$	536687.	+	738686.i	0.842782	+	1.15999i
$799$	−182483.	+	59292.5i	−0.285845	+	0.0928765i
$800$	−82899.0	−	26935.5i	−0.129530	−	0.0420867i
$801$	102294.	+	74321.0i	0.159436	+	0.115837i
$802$			353008.i			0.548827i
$803$	−67864.3	−	373007.i	−0.105247	−	0.578477i
$804$	2.81903e6			4.36102
$805$	−30170.1	+	41525.6i	−0.0465570	+	0.0640803i
$806$	488346.	−	1.50297e6i	0.751723	−	2.31356i
$807$	354342.	+	1.09055e6i	0.544095	+	1.67455i
$808$	1.00098e6	−	727257.i	1.53322	−	1.11395i
$809$	239793.	+	330047.i	0.366387	+	0.504288i	0.951914	−	0.306365i	$-0.0991127\pi$
$809$	239793.	+	330047.i	0.366387	+	0.504288i	−0.585528	+	0.810652i	$0.699113\pi$
$810$	386979.	−	125737.i	0.589818	−	0.191643i
$811$	−234792.	−	76288.6i	−0.356978	−	0.115989i	0.125037	−	0.992152i	$-0.460095\pi$
$811$	−234792.	−	76288.6i	−0.356978	−	0.115989i	−0.482015	+	0.876163i	$0.660095\pi$
$812$	−416514.	−	302615.i	−0.631710	−	0.458964i
$813$		−	16155.1i		−	0.0244416i
$814$	241649.	−	502369.i	0.364701	−	0.758182i
$815$	483445.			0.727834
$816$	−121318.	+	166981.i	−0.182199	+	0.250776i
$817$	−209329.	+	644247.i	−0.313606	+	0.965180i
$818$	−534069.	−	1.64369e6i	−0.798161	−	2.45649i
$819$	379571.	−	275775.i	0.565882	−	0.411137i
$820$	−551394.	−	758928.i	−0.820038	−	1.12869i
$821$	1.08412e6	−	352254.i	1.60840	−	0.522600i	0.639232	−	0.769014i	$-0.279253\pi$
$821$	1.08412e6	−	352254.i	1.60840	−	0.522600i	0.969164	+	0.246415i	$0.0792526\pi$
$822$	−3.33343e6	−	1.08310e6i	−4.93341	−	1.60296i
$823$	613174.	+	445497.i	0.905282	+	0.657726i	0.939817	−	0.341678i	$-0.110995\pi$
$823$	613174.	+	445497.i	0.905282	+	0.657726i	−0.0345354	+	0.999403i	$0.510995\pi$
$824$			406757.i			0.599074i
$825$	−528794.	+	553574.i	−0.776925	+	0.813332i
$826$	193067.			0.282975
$827$	617263.	−	849589.i	0.902524	−	1.24222i	−0.0671316	−	0.997744i	$-0.521385\pi$
$827$	617263.	−	849589.i	0.902524	−	1.24222i	0.969656	−	0.244474i	$-0.0786153\pi$
$828$	−166883.	+	513612.i	−0.243417	+	0.749159i
$829$	173323.	+	533435.i	0.252202	+	0.776198i	0.994368	+	0.105982i	$0.0337985\pi$
$829$	173323.	+	533435.i	0.252202	+	0.776198i	−0.742166	+	0.670216i	$0.766201\pi$
$830$	−437765.	+	318055.i	−0.635454	+	0.461685i
$831$	25803.2	+	35515.0i	0.0373655	+	0.0514292i
$832$	613136.	−	199220.i	0.885748	−	0.287797i
$833$	87667.8	+	28485.0i	0.126343	+	0.0410512i
$834$	−301636.	−	219152.i	−0.433662	−	0.315074i
$835$			221693.i			0.317965i
$836$	−1.52732e6	−	206190.i	−2.18534	−	0.295022i
$837$	−304254.			−0.434295
$838$	−338089.	+	465339.i	−0.481441	+	0.662646i
$839$	−33674.1	+	103638.i	−0.0478379	+	0.147230i	−0.972122	−	0.234475i	$-0.924663\pi$
$839$	−33674.1	+	103638.i	−0.0478379	+	0.147230i	0.924284	+	0.381705i	$0.124663\pi$
$840$	151814.	+	467237.i	0.215156	+	0.662183i
$841$	−254397.	+	184830.i	−0.359683	+	0.261325i
$842$	−1.39127e6	−	1.91492e6i	−1.96240	−	2.70102i
$843$	−1.63289e6	+	530560.i	−2.29775	+	0.746584i
$844$	346888.	+	112711.i	0.486972	+	0.158227i
$845$	67414.2	+	48979.3i	0.0944144	+	0.0685961i
$846$			2.57445e6i			3.59703i
$847$	−366188.	+	16776.0i	−0.510431	+	0.0233841i
$848$	−23345.3			−0.0324644
$849$	403370.	−	555192.i	0.559614	−	0.770243i
$850$	52781.7	−	162445.i	0.0730542	−	0.224838i
$851$	33616.0	+	103460.i	0.0464181	+	0.142860i
$852$	1.97054e6	−	1.43168e6i	2.71461	−	1.97228i
$853$	163026.	+	224386.i	0.224057	+	0.308388i	0.906215	−	0.422817i	$-0.138959\pi$
$853$	163026.	+	224386.i	0.224057	+	0.308388i	−0.682158	+	0.731204i	$0.738959\pi$
$854$	38838.5	−	12619.4i	0.0532533	−	0.0173030i
$855$	457883.	+	148775.i	0.626357	+	0.203516i
$856$	778754.	+	565798.i	1.06280	+	0.772171i
$857$		−	1.05897e6i		−	1.44186i	−0.693009	−	0.720929i	$-0.743715\pi$
$857$		−	1.05897e6i		−	1.44186i	0.693009	−	0.720929i	$-0.256285\pi$
$858$	−285566.	+	2.11529e6i	−0.387911	+	2.87340i
$859$	358536.			0.485899			0.242949	−	0.970039i	$-0.421885\pi$
$859$	358536.			0.485899			0.242949	+	0.970039i	$0.421885\pi$
$860$	−418171.	+	575564.i	−0.565402	+	0.778209i
$861$	239343.	−	736622.i	0.322860	−	0.993662i
$862$	−687800.	−	2.11683e6i	−0.925652	−	2.84887i
$863$	−1.00600e6	+	730905.i	−1.35076	+	0.981385i	−0.351787	+	0.936080i	$0.614426\pi$
$863$	−1.00600e6	+	730905.i	−1.35076	+	0.981385i	−0.998973	+	0.0453045i	$0.985574\pi$
$864$	27502.4	+	37853.8i	0.0368420	+	0.0507086i
$865$	−245010.	+	79608.7i	−0.327456	+	0.106397i
$866$	2.02807e6	+	658959.i	2.70425	+	0.878663i
$867$	879157.	+	638745.i	1.16958	+	0.849746i
$868$			989444.i			1.31326i
$869$	275868.	+	263519.i	0.365310	+	0.348957i
$870$	−731684.			−0.966685
$871$	−705396.	+	970894.i	−0.929815	+	1.27978i
$872$	−496322.	+	1.52752e6i	−0.652725	+	2.00888i
$873$	−168783.	−	519462.i	−0.221463	−	0.681593i
$874$	361965.	−	262983.i	0.473853	−	0.344274i
$875$	−200370.	−	275785.i	−0.261708	−	0.360210i
$876$	1.31454e6	−	427120.i	1.71303	−	0.556598i
$877$	−49773.4	−	16172.3i	−0.0647139	−	0.0210268i	0.276481	−	0.961019i	$-0.410832\pi$
$877$	−49773.4	−	16172.3i	−0.0647139	−	0.0210268i	−0.341195	+	0.939993i	$0.610832\pi$
$878$	616235.	+	447721.i	0.799387	+	0.580789i
$879$		−	1.85337e6i		−	2.39875i
$880$	−400369.	−	192585.i	−0.517005	−	0.248690i
$881$	−506638.			−0.652748			−0.326374	−	0.945241i	$-0.605827\pi$
$881$	−506638.			−0.652748			−0.326374	+	0.945241i	$0.605827\pi$
$882$	726976.	−	1.00060e6i	0.934508	−	1.28624i
$883$	100048.	−	307915.i	0.128317	−	0.394921i	−0.866173	−	0.499744i	$-0.833428\pi$
$883$	100048.	−	307915.i	0.128317	−	0.394921i	0.994491	+	0.104823i	$0.0334276\pi$
$884$	−98921.6	−	304449.i	−0.126586	−	0.389592i
$885$	149213.	−	108410.i	0.190511	−	0.138414i
$886$	−303443.	−	417654.i	−0.386554	−	0.532046i
$887$	−38371.0	+	12467.5i	−0.0487703	+	0.0158464i	−0.333301	−	0.942821i	$-0.608162\pi$
$887$	−38371.0	+	12467.5i	−0.0487703	+	0.0158464i	0.284530	+	0.958667i	$0.408162\pi$
$888$	990245.	+	321750.i	1.25579	+	0.408030i
$889$	567238.	+	412123.i	0.717731	+	0.521462i
$890$		−	110018.i		−	0.138894i
$891$	−557899.	+	101503.i	−0.702749	+	0.127857i
$892$	−2.63876e6			−3.31642
$893$	842700.	−	1.15988e6i	1.05675	−	1.45448i
$894$	−75714.8	+	233026.i	−0.0947340	+	0.291561i
$895$	−29844.4	−	91851.7i	−0.0372578	−	0.114668i
$896$	−545843.	+	396578.i	−0.679910	+	0.493983i
$897$	−244825.	−	336973.i	−0.304279	−	0.418804i
$898$	−489439.	+	159028.i	−0.606940	+	0.197207i
$899$	−718008.	−	233295.i	−0.888403	−	0.288659i
$900$	−1.24628e6	−	905475.i	−1.53862	−	1.11787i
$901$		−	4105.53i		−	0.00505731i
$902$	922403.	+	1.71226e6i	1.13372	+	2.10454i
$903$	−587396.			−0.720370
$904$	−197830.	+	272289.i	−0.242077	+	0.333191i
$905$	19113.6	−	58825.5i	0.0233370	−	0.0718239i
$906$	636327.	+	1.95841e6i	0.775219	+	2.38588i
$907$	695735.	−	505481.i	0.845725	−	0.614455i	−0.0782389	−	0.996935i	$-0.524930\pi$
$907$	695735.	−	505481.i	0.845725	−	0.614455i	0.923964	+	0.382479i	$0.124930\pi$
$908$	104824.	+	144277.i	0.127141	+	0.174995i
$909$	999950.	−	324903.i	1.21018	−	0.393212i
$910$	−388251.	−	126150.i	−0.468845	−	0.152337i
$911$	86967.3	+	63185.4i	0.104790	+	0.0761342i	0.638946	−	0.769251i	$-0.279371\pi$
$911$	86967.3	+	63185.4i	0.104790	+	0.0761342i	−0.534156	+	0.845386i	$0.679371\pi$
$912$		−	1.54222e6i		−	1.85420i
$913$	663896.	−	357643.i	0.796450	−	0.429051i
$914$	2.42313e6			2.90057
$915$	22930.6	−	31561.3i	0.0273888	−	0.0376975i
$916$	130017.	−	400152.i	0.154957	−	0.476907i
$917$	93683.5	+	288328.i	0.111410	+	0.342885i
$918$	−74176.6	+	53892.5i	−0.0880200	+	0.0639503i
$919$	−330184.	−	454460.i	−0.390954	−	0.538102i	0.567491	−	0.823380i	$-0.307914\pi$
$919$	−330184.	−	454460.i	−0.390954	−	0.538102i	−0.958445	+	0.285278i	$0.907914\pi$
$920$	228952.	−	74390.9i	0.270500	−	0.0878909i
$921$	−1.51211e6	−	491315.i	−1.78265	−	0.579217i
$922$	−259235.	−	188345.i	−0.304953	−	0.221561i
$923$			1.03691e6i			1.21714i
$924$	−239216.	−	1.31482e6i	−0.280186	−	1.54001i
$925$	−310308.			−0.362668
$926$	414620.	−	570676.i	0.483536	−	0.665530i
$927$	−106812.	+	328733.i	−0.124297	+	0.382546i
$928$	35877.4	+	110419.i	0.0416605	+	0.128218i
$929$	−120738.	+	87721.2i	−0.139898	+	0.101642i	−0.655533	−	0.755166i	$-0.727556\pi$
$929$	−120738.	+	87721.2i	−0.139898	+	0.101642i	0.515635	+	0.856808i	$0.327556\pi$
$930$	826535.	+	1.13763e6i	0.955642	+	1.31533i
$931$	−655055.	+	212840.i	−0.755750	+	0.245558i
$932$	1.55865e6	+	506436.i	1.79439	+	0.583033i
$933$	−1.31391e6	−	954608.i	−1.50939	−	1.09663i
$934$			32586.4i			0.0373545i
$935$	33868.3	−	70409.4i	0.0387410	−	0.0805392i
$936$	−2.20047e6			−2.51167
$937$	−135239.	+	186140.i	−0.154036	+	0.212012i	−0.879060	−	0.476711i	$-0.841829\pi$
$937$	−135239.	+	186140.i	−0.154036	+	0.212012i	0.725024	+	0.688724i	$0.241829\pi$
$938$	345424.	−	1.06311e6i	0.392597	−	1.20829i
$939$	659309.	+	2.02915e6i	0.747753	+	2.30135i
$940$	1.21815e6	−	885040.i	1.37862	−	1.00163i
$941$	88227.4	+	121435.i	0.0996378	+	0.137140i	0.855925	−	0.517100i	$-0.172989\pi$
$941$	88227.4	+	121435.i	0.0996378	+	0.137140i	−0.756287	+	0.654240i	$0.772989\pi$
$942$	1.51569e6	−	492477.i	1.70808	−	0.554988i
$943$	−360954.	−	117281.i	−0.405908	−	0.131888i
$944$	−263821.	−	191677.i	−0.296050	−	0.215093i
$945$			78595.2i			0.0880101i
$946$	1.01884e6	−	1.06658e6i	1.13847	−	1.19182i
$947$	404416.			0.450950			0.225475	−	0.974249i	$-0.427607\pi$
$947$	404416.			0.450950			0.225475	+	0.974249i	$0.427607\pi$
$948$	−817516.	+	1.12521e6i	−0.909662	+	1.25204i
$949$	−181829.	+	559613.i	−0.201898	+	0.621377i
$950$	394385.	+	1.21379e6i	0.436992	+	1.34492i
$951$	28608.2	−	20785.1i	0.0316323	−	0.0229822i
$952$	89788.8	+	123584.i	0.0990714	+	0.136360i
$953$	−189347.	+	61522.7i	−0.208484	+	0.0677407i	−0.411397	−	0.911456i	$-0.634959\pi$
$953$	−189347.	+	61522.7i	−0.208484	+	0.0677407i	0.202913	+	0.979197i	$0.434959\pi$
$954$	−52389.4	−	17022.3i	−0.0575634	−	0.0187035i
$955$	480178.	+	348870.i	0.526497	+	0.382522i
$956$		−	657546.i		−	0.719466i
$957$	1.01053e6	+	136422.i	1.10338	+	0.148957i
$958$	−2.27891e6			−2.48311
$959$	−549115.	+	755791.i	−0.597071	+	0.821797i
$960$	−177268.	+	545574.i	−0.192348	+	0.591986i
$961$	162973.	+	501580.i	0.176470	+	0.543117i
$962$	−699953.	+	508546.i	−0.756343	+	0.549516i
$963$	480799.	+	661763.i	0.518455	+	0.713592i
$964$	−2.11377e6	+	686807.i	−2.27460	+	0.739061i
$965$	−247573.	−	80441.5i	−0.265858	−	0.0863824i
$966$	313871.	+	228041.i	0.336355	+	0.244376i
$967$		−	708306.i		−	0.757475i	−0.925504	−	0.378737i	$-0.876358\pi$
$967$		−	708306.i		−	0.757475i	0.925504	−	0.378737i	$-0.123642\pi$
$968$	1.43569e6	+	945834.i	1.53218	+	1.00940i
$969$	271216.			0.288847
$970$	−279342.	+	384481.i	−0.296888	+	0.408631i
$971$	−225987.	+	695515.i	−0.239687	+	0.737680i	0.756778	+	0.653672i	$0.226772\pi$
$971$	−225987.	+	695515.i	−0.239687	+	0.737680i	−0.996465	+	0.0840083i	$0.973228\pi$
$972$	−846262.	−	2.60453e6i	−0.895720	−	2.75674i
$973$	−80397.6	+	58412.3i	−0.0849214	+	0.0616990i
$974$	−88222.0	−	121427.i	−0.0929949	−	0.127996i
$975$	1.12999e6	−	367155.i	1.18868	−	0.386225i
$976$	−65600.3	−	21314.8i	−0.0688662	−	0.0223760i
$977$	−1.39678e6	−	1.01482e6i	−1.46331	−	1.06316i	−0.982484	−	0.186347i	$-0.940335\pi$
$977$	−1.39678e6	−	1.01482e6i	−1.46331	−	1.06316i	−0.480831	−	0.876813i	$-0.659665\pi$
$978$		−	3.65412e6i		−	3.82037i
$979$	−20512.7	+	151945.i	−0.0214022	+	0.158534i
$980$	−723371.			−0.753197
$981$	−802235.	+	1.10418e6i	−0.833612	+	1.14737i
$982$	223363.	−	687439.i	0.231626	−	0.712872i
$983$	−309481.	−	952483.i	−0.320277	−	0.985713i	−0.973527	−	0.228570i	$-0.926595\pi$
$983$	−309481.	−	952483.i	−0.320277	−	0.985713i	0.653250	−	0.757142i	$-0.273405\pi$
$984$	−2.93883e6	+	2.13519e6i	−3.03518	+	2.20519i
$985$	−14299.4	−	19681.5i	−0.0147383	−	0.0202855i
$986$	−216373.	+	70303.8i	−0.222561	+	0.0723144i
$987$	1.18235e6	+	384169.i	1.21370	+	0.394355i
$988$	1.93510e6	+	1.40593e6i	1.98239	+	1.44029i
$989$			287831.i			0.294269i
$990$	−758047.	−	724114.i	−0.773438	−	0.738816i
$991$	1.19823e6			1.22009			0.610047	−	0.792366i	$-0.291151\pi$
$991$	1.19823e6			1.22009			0.610047	+	0.792366i	$0.291151\pi$
$992$	131152.	−	180516.i	0.133276	−	0.183439i
$993$	582473.	−	1.79267e6i	0.590714	−	1.81803i
$994$	−298456.	−	918554.i	−0.302070	−	0.929677i
$995$	510974.	−	371244.i	0.516122	−	0.374985i
$996$	1.61595e6	+	2.22416e6i	1.62895	+	2.24206i
$997$	−1.72764e6	+	561344.i	−1.73805	+	0.564727i	−0.994574	−	0.104035i	$-0.966825\pi$
$997$	−1.72764e6	+	561344.i	−1.73805	+	0.564727i	−0.743477	+	0.668762i	$0.766825\pi$
$998$	836893.	+	271923.i	0.840250	+	0.273014i
$999$	134760.	+	97908.5i	0.135029	+	0.0981046i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.5.d.a.7.3	✓	12
3.2	odd	2		99.5.k.a.73.1		12
4.3	odd	2		176.5.n.a.161.3		12
11.2	odd	10		121.5.d.e.94.3		12
11.3	even	5		121.5.d.d.118.1		12
11.4	even	5		121.5.d.e.112.3		12
11.5	even	5		121.5.b.b.120.12		12
11.6	odd	10		121.5.b.b.120.1		12
11.7	odd	10		121.5.d.c.112.1		12
11.8	odd	10	inner	11.5.d.a.8.3	yes	12
11.9	even	5		121.5.d.c.94.1		12
11.10	odd	2		121.5.d.d.40.1		12
33.8	even	10		99.5.k.a.19.1		12
44.19	even	10		176.5.n.a.129.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.5.d.a.7.3	✓	12	1.1	even	1	trivial
11.5.d.a.8.3	yes	12	11.8	odd	10	inner
99.5.k.a.19.1		12	33.8	even	10
99.5.k.a.73.1		12	3.2	odd	2
121.5.b.b.120.1		12	11.6	odd	10
121.5.b.b.120.12		12	11.5	even	5
121.5.d.c.94.1		12	11.9	even	5
121.5.d.c.112.1		12	11.7	odd	10
121.5.d.d.40.1		12	11.10	odd	2
121.5.d.d.118.1		12	11.3	even	5
121.5.d.e.94.3		12	11.2	odd	10
121.5.d.e.112.3		12	11.4	even	5
176.5.n.a.129.3		12	44.19	even	10
176.5.n.a.161.3		12	4.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+(4.10644 - 5.65202i) q^{2} +(-4.15494 + 12.7876i) q^{3} +(-10.1383 - 31.2024i) q^{4} +(-10.0543 + 7.30486i) q^{5} +(55.2138 + 75.9952i) q^{6} +(23.8119 - 7.73696i) q^{7} +(-111.679 - 36.2869i) q^{8} +(-80.7285 - 58.6527i) q^{9} +O(q^{10})\)	\(q+(4.10644 - 5.65202i) q^{2} +(-4.15494 + 12.7876i) q^{3} +(-10.1383 - 31.2024i) q^{4} +(-10.0543 + 7.30486i) q^{5} +(55.2138 + 75.9952i) q^{6} +(23.8119 - 7.73696i) q^{7} +(-111.679 - 36.2869i) q^{8} +(-80.7285 - 58.6527i) q^{9} +86.8239i q^{10} +(16.1882 - 119.912i) q^{11} +441.128 q^{12} +(-110.382 + 151.927i) q^{13} +(54.0526 - 166.357i) q^{14} +(-51.6366 - 158.921i) q^{15} +(-239.021 + 173.659i) q^{16} +(-30.5398 - 42.0345i) q^{17} +(-663.013 + 215.426i) q^{18} +(369.226 + 119.969i) q^{19} +(329.862 + 239.659i) q^{20} +336.644i q^{21} +(-611.271 - 583.908i) q^{22} +164.959 q^{23} +(928.043 - 1277.34i) q^{24} +(-145.408 + 447.520i) q^{25} +(405.422 + 1247.76i) q^{26} +(204.349 - 148.468i) q^{27} +(-482.824 - 664.551i) q^{28} +(596.085 - 193.680i) q^{29} +(-1110.27 - 360.748i) q^{30} +(-974.492 - 708.010i) q^{31} +185.241i q^{32} +(1466.13 + 705.236i) q^{33} -362.990 q^{34} +(-182.894 + 251.732i) q^{35} +(-1011.66 + 3113.56i) q^{36} +(203.784 + 627.181i) q^{37} +(2194.27 - 1594.23i) q^{38} +(-1484.16 - 2042.76i) q^{39} +(1387.93 - 450.965i) q^{40} +(-2188.14 - 710.968i) q^{41} +(1902.72 + 1382.41i) q^{42} +1744.86i q^{43} +(-3905.67 + 710.592i) q^{44} +1240.12 q^{45} +(677.395 - 932.355i) q^{46} +(1141.17 - 3512.17i) q^{47} +(-1227.56 - 3778.04i) q^{48} +(-1435.30 + 1042.81i) q^{49} +(1932.29 + 2659.56i) q^{50} +(664.411 - 215.880i) q^{51} +(5859.58 + 1903.89i) q^{52} +(63.9262 + 46.4451i) q^{53} -1764.66i q^{54} +(713.181 + 1323.88i) q^{55} -2940.05 q^{56} +(-3068.22 + 4223.04i) q^{57} +(1353.10 - 4164.42i) q^{58} +(341.080 + 1049.74i) q^{59} +(-4435.22 + 3222.38i) q^{60} +(137.227 + 188.877i) q^{61} +(-8003.38 + 2600.46i) q^{62} +(-2376.10 - 772.040i) q^{63} +(-2777.35 - 2017.86i) q^{64} -2333.84i q^{65} +(10006.6 - 5390.58i) q^{66} +6390.51 q^{67} +(-1001.96 + 1379.08i) q^{68} +(-685.397 + 2109.43i) q^{69} +(671.753 + 2067.44i) q^{70} +(4467.06 - 3245.51i) q^{71} +(6887.39 + 9479.69i) q^{72} +(2979.95 - 968.246i) q^{73} +(4381.67 + 1423.69i) q^{74} +(-5118.54 - 3718.84i) q^{75} -12737.0i q^{76} +(-542.284 - 2980.59i) q^{77} -17640.3 q^{78} +(-1853.24 + 2550.77i) q^{79} +(1134.63 - 3492.02i) q^{80} +(-1448.19 - 4457.06i) q^{81} +(-13003.8 + 9447.85i) q^{82} +(3663.21 + 5041.98i) q^{83} +(10504.1 - 3412.99i) q^{84} +(614.112 + 199.537i) q^{85} +(9861.99 + 7165.15i) q^{86} +8427.22i q^{87} +(-6159.13 + 12804.3i) q^{88} -1267.14 q^{89} +(5092.46 - 7009.16i) q^{90} +(-1452.94 + 4471.70i) q^{91} +(-1672.41 - 5147.14i) q^{92} +(13102.7 - 9519.67i) q^{93} +(-15164.7 - 20872.4i) q^{94} +(-4588.65 + 1490.94i) q^{95} +(-2368.78 - 769.664i) q^{96} +(4428.29 + 3217.34i) q^{97} +12394.6i q^{98} +(-8340.03 + 8730.85i) 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

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