LMFDB - Embedded newform 211.4.o.a.53.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [211,4,Mod(4,211)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(211, base_ring=CyclotomicField(210))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("211.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 211 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	211.o (of order $105$, degree $48$, 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:	$12.4494030112$
Analytic rank:	$0$
Dimension:	$2496$
Relative dimension:	$52$ over $\Q(\zeta_{105})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{105}]$

Embedding invariants

Embedding label			53.13
Character	$\chi$	$=$	211.53
Dual form			211.4.o.a.4.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.97205 + 0.0889500i) q^{2} +(1.11700 - 3.82337i) q^{3} +(0.839479 - 0.0502943i) q^{4} +(9.58614 - 10.0263i) q^{5} +(-2.97968 + 11.4626i) q^{6} +(-5.32177 + 8.61188i) q^{7} +(21.2008 - 1.90810i) q^{8} +(9.38297 + 5.99407i) q^{9} +O(q^{10})$	\(q+(-2.97205 + 0.0889500i) q^{2} +(1.11700 - 3.82337i) q^{3} +(0.839479 - 0.0502943i) q^{4} +(9.58614 - 10.0263i) q^{5} +(-2.97968 + 11.4626i) q^{6} +(-5.32177 + 8.61188i) q^{7} +(21.2008 - 1.90810i) q^{8} +(9.38297 + 5.99407i) q^{9} +(-27.5986 + 30.6514i) q^{10} +(7.03762 + 51.9538i) q^{11} +(0.745402 - 3.26582i) q^{12} +(2.60554 - 6.09597i) q^{13} +(15.0505 - 26.0683i) q^{14} +(-27.6267 - 47.8508i) q^{15} +(-69.5198 + 8.36006i) q^{16} +(74.3546 + 25.3952i) q^{17} +(-28.4198 - 16.9800i) q^{18} +(-2.70945 + 25.7787i) q^{19} +(7.54310 - 8.89901i) q^{20} +(26.9820 + 29.9666i) q^{21} +(-25.5375 - 153.783i) q^{22} +(-49.0310 + 35.6231i) q^{23} +(16.3858 - 83.1898i) q^{24} +(-3.02484 - 67.3533i) q^{25} +(-7.20156 + 18.3493i) q^{26} +(114.388 - 99.9381i) q^{27} +(-4.03439 + 7.49715i) q^{28} +(61.9052 + 82.5785i) q^{29} +(86.3641 + 139.757i) q^{30} +(-4.65272 + 1.43517i) q^{31} +(37.4827 - 5.64961i) q^{32} +(206.500 + 31.1248i) q^{33} +(-223.244 - 68.8618i) q^{34} +(35.3302 + 135.913i) q^{35} +(8.17827 + 4.55998i) q^{36} +(288.985 - 118.437i) q^{37} +(5.75961 - 76.8566i) q^{38} +(-20.3968 - 16.7711i) q^{39} +(184.102 - 230.857i) q^{40} +(131.179 - 73.1419i) q^{41} +(-82.8574 - 86.6621i) q^{42} +(-104.073 - 96.5661i) q^{43} +(8.52092 + 43.2602i) q^{44} +(150.045 - 36.6166i) q^{45} +(142.554 - 110.235i) q^{46} +(330.380 - 211.055i) q^{47} +(-45.6898 + 275.138i) q^{48} +(107.585 + 215.110i) q^{49} +(14.9811 + 199.908i) q^{50} +(180.149 - 255.919i) q^{51} +(1.88070 - 5.24848i) q^{52} +(-23.4222 - 1.40326i) q^{53} +(-331.078 + 307.196i) q^{54} +(588.369 + 427.475i) q^{55} +(-96.3934 + 192.733i) q^{56} +(95.5352 + 39.1540i) q^{57} +(-191.330 - 239.921i) q^{58} +(-0.797016 + 53.2726i) q^{59} +(-25.5986 - 38.7802i) q^{60} +(240.669 + 51.1558i) q^{61} +(13.7005 - 4.67927i) q^{62} +(-101.554 + 48.9059i) q^{63} +(440.265 - 79.8963i) q^{64} +(-36.1430 - 84.5609i) q^{65} +(-616.496 - 74.1364i) q^{66} +(-303.052 - 145.942i) q^{67} +(63.6963 + 17.5791i) q^{68} +(81.4329 + 227.255i) q^{69} +(-117.093 - 400.796i) q^{70} +(-327.581 - 1008.19i) q^{71} +(210.364 + 109.175i) q^{72} +(135.146 + 344.347i) q^{73} +(-848.341 + 377.706i) q^{74} +(-260.896 - 63.6684i) q^{75} +(-0.978004 + 21.7770i) q^{76} +(-484.873 - 215.879i) q^{77} +(62.1120 + 48.0304i) q^{78} +(-1009.68 - 90.8727i) q^{79} +(-582.606 + 777.168i) q^{80} +(-127.961 - 276.209i) q^{81} +(-383.364 + 229.050i) q^{82} +(-645.650 + 137.237i) q^{83} +(24.1580 + 23.7993i) q^{84} +(967.394 - 502.062i) q^{85} +(317.901 + 277.742i) q^{86} +(384.876 - 144.447i) q^{87} +(248.336 + 1088.03i) q^{88} +(-248.905 - 45.1696i) q^{89} +(-442.684 + 122.173i) q^{90} +(38.6317 + 54.8800i) q^{91} +(-39.3688 + 32.3708i) q^{92} +(0.290128 + 19.3922i) q^{93} +(-963.131 + 656.652i) q^{94} +(232.493 + 274.284i) q^{95} +(20.2675 - 149.621i) q^{96} +(593.106 + 222.596i) q^{97} +(-338.882 - 629.749i) q^{98} +(-245.381 + 529.665i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2496 q - 44 q^{2} - 56 q^{3} - 270 q^{4} - 50 q^{5} - 89 q^{6} - 55 q^{7} + 211 q^{8} - 596 q^{9}+O(q^{10}) $ 2496 * q - 44 * q^2 - 56 * q^3 - 270 * q^4 - 50 * q^5 - 89 * q^6 - 55 * q^7 + 211 * q^8 - 596 * q^9	\( 2496 q - 44 q^{2} - 56 q^{3} - 270 q^{4} - 50 q^{5} - 89 q^{6} - 55 q^{7} + 211 q^{8} - 596 q^{9} - 113 q^{10} - 122 q^{11} - 762 q^{12} - 126 q^{13} + 25 q^{14} - 1511 q^{15} - 1994 q^{16} - 92 q^{17} - 717 q^{18} - 177 q^{19} - 238 q^{20} + 456 q^{21} - 1073 q^{22} - 1168 q^{23} - 1104 q^{24} + 2030 q^{25} + 1476 q^{26} + 1066 q^{27} + 1399 q^{28} + 307 q^{29} - 1475 q^{30} - 1544 q^{31} + 4027 q^{32} + 445 q^{33} + 1565 q^{34} - 1350 q^{35} + 3080 q^{36} + 1831 q^{37} + 1812 q^{38} - 794 q^{39} - 5788 q^{40} - 175 q^{41} + 2276 q^{42} - 4278 q^{43} + 4022 q^{44} + 205 q^{45} - 138 q^{46} + 1921 q^{47} - 8817 q^{48} - 2291 q^{49} - 212 q^{50} - 3222 q^{51} - 8923 q^{52} - 3859 q^{53} - 1402 q^{54} - 2984 q^{55} + 3512 q^{56} - 3181 q^{57} + 2194 q^{58} - 4252 q^{59} + 2334 q^{60} - 964 q^{61} + 829 q^{62} + 169 q^{63} + 7061 q^{64} + 1166 q^{65} + 3166 q^{66} - 5721 q^{67} + 3037 q^{68} + 2580 q^{69} + 2878 q^{70} - 3364 q^{71} + 11440 q^{72} + 6320 q^{73} + 9408 q^{74} + 353 q^{75} - 5224 q^{76} - 1509 q^{77} + 6631 q^{78} - 542 q^{79} - 2155 q^{80} - 3451 q^{81} + 21513 q^{82} + 183 q^{83} + 23087 q^{84} - 16600 q^{85} - 134 q^{86} + 11238 q^{87} - 6171 q^{88} - 209 q^{89} - 22438 q^{90} - 19392 q^{91} - 16409 q^{92} + 14536 q^{93} - 26379 q^{94} + 11081 q^{95} - 5408 q^{96} + 5034 q^{97} + 16030 q^{98} - 25788 q^{99}+O(q^{100}) \) 2496 * q - 44 * q^2 - 56 * q^3 - 270 * q^4 - 50 * q^5 - 89 * q^6 - 55 * q^7 + 211 * q^8 - 596 * q^9 - 113 * q^10 - 122 * q^11 - 762 * q^12 - 126 * q^13 + 25 * q^14 - 1511 * q^15 - 1994 * q^16 - 92 * q^17 - 717 * q^18 - 177 * q^19 - 238 * q^20 + 456 * q^21 - 1073 * q^22 - 1168 * q^23 - 1104 * q^24 + 2030 * q^25 + 1476 * q^26 + 1066 * q^27 + 1399 * q^28 + 307 * q^29 - 1475 * q^30 - 1544 * q^31 + 4027 * q^32 + 445 * q^33 + 1565 * q^34 - 1350 * q^35 + 3080 * q^36 + 1831 * q^37 + 1812 * q^38 - 794 * q^39 - 5788 * q^40 - 175 * q^41 + 2276 * q^42 - 4278 * q^43 + 4022 * q^44 + 205 * q^45 - 138 * q^46 + 1921 * q^47 - 8817 * q^48 - 2291 * q^49 - 212 * q^50 - 3222 * q^51 - 8923 * q^52 - 3859 * q^53 - 1402 * q^54 - 2984 * q^55 + 3512 * q^56 - 3181 * q^57 + 2194 * q^58 - 4252 * q^59 + 2334 * q^60 - 964 * q^61 + 829 * q^62 + 169 * q^63 + 7061 * q^64 + 1166 * q^65 + 3166 * q^66 - 5721 * q^67 + 3037 * q^68 + 2580 * q^69 + 2878 * q^70 - 3364 * q^71 + 11440 * q^72 + 6320 * q^73 + 9408 * q^74 + 353 * q^75 - 5224 * q^76 - 1509 * q^77 + 6631 * q^78 - 542 * q^79 - 2155 * q^80 - 3451 * q^81 + 21513 * q^82 + 183 * q^83 + 23087 * q^84 - 16600 * q^85 - 134 * q^86 + 11238 * q^87 - 6171 * q^88 - 209 * q^89 - 22438 * q^90 - 19392 * q^91 - 16409 * q^92 + 14536 * q^93 - 26379 * q^94 + 11081 * q^95 - 5408 * q^96 + 5034 * q^97 + 16030 * q^98 - 25788 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/211\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{104}{105}\right)$

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 $

$2$	−2.97205	+	0.0889500i	−1.05078	+	0.0314486i	−0.550838	−	0.834612i	$-0.685692\pi$
$2$	−2.97205	+	0.0889500i	−1.05078	+	0.0314486i	−0.499939	+	0.866060i	$0.666644\pi$
$3$	1.11700	−	3.82337i	0.214966	−	0.735809i	−0.779087	−	0.626916i	$-0.784317\pi$
$3$	1.11700	−	3.82337i	0.214966	−	0.735809i	0.994053	−	0.108893i	$-0.0347306\pi$
$4$	0.839479	−	0.0502943i	0.104935	−	0.00628679i
$5$	9.58614	−	10.0263i	0.857411	−	0.896781i	−0.138197	−	0.990405i	$-0.544131\pi$
$5$	9.58614	−	10.0263i	0.857411	−	0.896781i	0.995608	+	0.0936234i	$0.0298450\pi$
$6$	−2.97968	+	11.4626i	−0.202742	+	0.779932i
$7$	−5.32177	+	8.61188i	−0.287349	+	0.464998i	−0.961966	−	0.273170i	$-0.911928\pi$
$7$	−5.32177	+	8.61188i	−0.287349	+	0.464998i	0.674617	+	0.738168i	$0.264309\pi$
$8$	21.2008	−	1.90810i	0.936951	−	0.0843271i
$9$	9.38297	+	5.99407i	0.347517	+	0.222003i
$10$	−27.5986	+	30.6514i	−0.872746	+	0.969282i
$11$	7.03762	+	51.9538i	0.192902	+	1.42406i	0.785649	+	0.618672i	$0.212329\pi$
$11$	7.03762	+	51.9538i	0.192902	+	1.42406i	−0.592747	+	0.805389i	$0.701957\pi$
$12$	0.745402	−	3.26582i	0.0179316	−	0.0785634i
$13$	2.60554	−	6.09597i	0.0555883	−	0.130055i	−0.889431	−	0.457069i	$-0.848899\pi$
$13$	2.60554	−	6.09597i	0.0555883	−	0.130055i	0.945020	+	0.327013i	$0.106042\pi$
$14$	15.0505	−	26.0683i	0.287316	−	0.497646i
$15$	−27.6267	−	47.8508i	−0.475545	−	0.823668i
$16$	−69.5198	+	8.36006i	−1.08625	+	0.130626i
$17$	74.3546	+	25.3952i	1.06080	+	0.362308i	0.798072	−	0.602562i	$-0.205853\pi$
$17$	74.3546	+	25.3952i	1.06080	+	0.362308i	0.262730	+	0.964869i	$0.415377\pi$
$18$	−28.4198	−	16.9800i	−0.372145	−	0.222346i
$19$	−2.70945	+	25.7787i	−0.0327153	+	0.311265i	0.965911	+	0.258873i	$0.0833512\pi$
$19$	−2.70945	+	25.7787i	−0.0327153	+	0.311265i	−0.998627	+	0.0523921i	$0.983315\pi$
$20$	7.54310	−	8.89901i	0.0843344	−	0.0994940i
$21$	26.9820	+	29.9666i	0.280379	+	0.311393i
$22$	−25.5375	−	153.783i	−0.247482	−	1.49030i
$23$	−49.0310	+	35.6231i	−0.444507	+	0.322953i	−0.787423	−	0.616413i	$-0.788585\pi$
$23$	−49.0310	+	35.6231i	−0.444507	+	0.322953i	0.342916	+	0.939366i	$0.388585\pi$
$24$	16.3858	−	83.1898i	0.139364	−	0.707544i
$25$	−3.02484	−	67.3533i	−0.0241987	−	0.538827i
$26$	−7.20156	+	18.3493i	−0.0543209	+	0.138407i
$27$	114.388	−	99.9381i	0.815335	−	0.712337i
$28$	−4.03439	+	7.49715i	−0.0272296	+	0.0506010i
$29$	61.9052	+	82.5785i	0.396397	+	0.528774i	0.953389	−	0.301744i	$-0.0975686\pi$
$29$	61.9052	+	82.5785i	0.396397	+	0.528774i	−0.556993	+	0.830517i	$0.688045\pi$
$30$	86.3641	+	139.757i	0.525595	+	0.850537i
$31$	−4.65272	+	1.43517i	−0.0269566	+	0.00831500i	−0.308204	−	0.951320i	$-0.599728\pi$
$31$	−4.65272	+	1.43517i	−0.0269566	+	0.00831500i	0.281248	+	0.959635i	$0.409252\pi$
$32$	37.4827	−	5.64961i	0.207065	−	0.0312100i
$33$	206.500	+	31.1248i	1.08930	+	0.164186i
$34$	−223.244	−	68.8618i	−1.12606	−	0.347344i
$35$	35.3302	+	135.913i	0.170626	+	0.656383i
$36$	8.17827	+	4.55998i	0.0378624	+	0.0211110i
$37$	288.985	−	118.437i	1.28402	−	0.526241i	0.368918	−	0.929462i	$-0.379728\pi$
$37$	288.985	−	118.437i	1.28402	−	0.526241i	0.915103	+	0.403221i	$0.132109\pi$
$38$	5.75961	−	76.8566i	0.0245877	−	0.328100i
$39$	−20.3968	−	16.7711i	−0.0837461	−	0.0688598i
$40$	184.102	−	230.857i	0.727729	−	0.912543i
$41$	131.179	−	73.1419i	0.499676	−	0.278606i	−0.216802	−	0.976216i	$-0.569563\pi$
$41$	131.179	−	73.1419i	0.499676	−	0.278606i	0.716478	+	0.697610i	$0.245753\pi$
$42$	−82.8574	−	86.6621i	−0.304409	−	0.318387i
$43$	−104.073	−	96.5661i	−0.369094	−	0.342470i	0.473718	−	0.880676i	$-0.342911\pi$
$43$	−104.073	−	96.5661i	−0.369094	−	0.342470i	−0.842813	+	0.538207i	$0.819102\pi$
$44$	8.52092	+	43.2602i	0.0291949	+	0.148221i
$45$	150.045	−	36.6166i	0.497053	−	0.121300i
$46$	142.554	−	110.235i	0.456922	−	0.353331i
$47$	330.380	−	211.055i	1.02534	−	0.655010i	0.0853960	−	0.996347i	$-0.472784\pi$
$47$	330.380	−	211.055i	1.02534	−	0.655010i	0.939941	+	0.341337i	$0.110880\pi$
$48$	−45.6898	+	275.138i	−0.137391	+	0.827349i
$49$	107.585	+	215.110i	0.313659	+	0.627144i
$50$	14.9811	+	199.908i	0.0423728	+	0.565426i
$51$	180.149	−	255.919i	0.494626	−	0.702664i
$52$	1.88070	−	5.24848i	0.00501552	−	0.0139968i
$53$	−23.4222	−	1.40326i	−0.0607036	−	0.00363684i	0.0294247	−	0.999567i	$-0.490632\pi$
$53$	−23.4222	−	1.40326i	−0.0607036	−	0.00363684i	−0.0901283	+	0.995930i	$0.528728\pi$
$54$	−331.078	+	307.196i	−0.834334	+	0.774149i
$55$	588.369	+	427.475i	1.44247	+	1.04801i
$56$	−96.3934	+	192.733i	−0.230020	+	0.459912i
$57$	95.5352	+	39.1540i	0.221999	+	0.0909838i
$58$	−191.330	−	239.921i	−0.433154	−	0.543158i
$59$	−0.797016	+	53.2726i	−0.00175869	+	0.117551i	0.997280	+	0.0737090i	$0.0234836\pi$
$59$	−0.797016	+	53.2726i	−0.00175869	+	0.117551i	−0.999038	+	0.0438419i	$0.986040\pi$
$60$	−25.5986	−	38.7802i	−0.0550795	−	0.0834418i
$61$	240.669	+	51.1558i	0.505156	+	0.107374i	0.453439	−	0.891288i	$-0.350197\pi$
$61$	240.669	+	51.1558i	0.505156	+	0.107374i	0.0517175	+	0.998662i	$0.483530\pi$
$62$	13.7005	−	4.67927i	0.0280639	−	0.00958496i
$63$	−101.554	+	48.9059i	−0.203089	+	0.0978027i
$64$	440.265	−	79.8963i	0.859892	−	0.156047i
$65$	−36.1430	−	84.5609i	−0.0689691	−	0.161361i
$66$	−616.496	−	74.1364i	−1.14978	−	0.138266i
$67$	−303.052	−	145.942i	−0.552593	−	0.266115i	0.136681	−	0.990615i	$-0.456356\pi$
$67$	−303.052	−	145.942i	−0.552593	−	0.266115i	−0.689275	+	0.724500i	$0.742071\pi$
$68$	63.6963	+	17.5791i	0.113593	+	0.0313496i
$69$	81.4329	+	227.255i	0.142078	+	0.396496i
$70$	−117.093	−	400.796i	−0.199932	−	0.684347i
$71$	−327.581	−	1008.19i	−0.547560	−	1.68522i	−0.714824	−	0.699305i	$-0.753493\pi$
$71$	−327.581	−	1008.19i	−0.547560	−	1.68522i	0.167264	−	0.985912i	$-0.446507\pi$
$72$	210.364	+	109.175i	0.344327	+	0.178700i
$73$	135.146	+	344.347i	0.216680	+	0.552093i	0.997342	−	0.0728611i	$-0.0232130\pi$
$73$	135.146	+	344.347i	0.216680	+	0.552093i	−0.780662	+	0.624954i	$0.785118\pi$
$74$	−848.341	+	377.706i	−1.33267	+	0.593343i
$75$	−260.896	−	63.6684i	−0.401675	−	0.0980240i
$76$	−0.978004	+	21.7770i	−0.00147612	+	0.0328683i
$77$	−484.873	−	215.879i	−0.717616	−	0.319503i
$78$	62.1120	+	48.0304i	0.0901641	+	0.0697227i
$79$	−1009.68	−	90.8727i	−1.43794	−	0.129417i	−0.656940	−	0.753943i	$-0.728150\pi$
$79$	−1009.68	−	90.8727i	−1.43794	−	0.129417i	−0.781005	+	0.624525i	$0.785293\pi$
$80$	−582.606	+	777.168i	−0.814216	+	1.08613i
$81$	−127.961	−	276.209i	−0.175529	−	0.378887i
$82$	−383.364	+	229.050i	−0.516287	+	0.308467i
$83$	−645.650	+	137.237i	−0.853848	+	0.181491i	−0.613987	−	0.789316i	$-0.710435\pi$
$83$	−645.650	+	137.237i	−0.853848	+	0.181491i	−0.239861	+	0.970807i	$0.577102\pi$
$84$	24.1580	+	23.7993i	0.0313792	+	0.0309132i
$85$	967.394	−	502.062i	1.23445	−	0.640661i
$86$	317.901	+	277.742i	0.398606	+	0.348252i
$87$	384.876	−	144.447i	0.474288	−	0.178003i
$88$	248.336	+	1088.03i	0.300827	+	1.31801i
$89$	−248.905	−	45.1696i	−0.296448	−	0.0537974i	0.0282951	−	0.999600i	$-0.490992\pi$
$89$	−248.905	−	45.1696i	−0.296448	−	0.0537974i	−0.324743	+	0.945802i	$0.605278\pi$
$90$	−442.684	+	122.173i	−0.518477	+	0.143091i
$91$	38.6317	+	54.8800i	0.0445022	+	0.0632196i
$92$	−39.3688	+	32.3708i	−0.0446140	+	0.0366836i
$93$	0.290128	+	19.3922i	0.000323493	+	0.0216223i
$94$	−963.131	+	656.652i	−1.05680	+	0.720516i
$95$	232.493	+	274.284i	0.251087	+	0.296221i
$96$	20.2675	−	149.621i	0.0215474	−	0.159069i
$97$	593.106	+	222.596i	0.620833	+	0.233002i	0.641916	−	0.766775i	$-0.278140\pi$
$97$	593.106	+	222.596i	0.620833	+	0.233002i	−0.0210828	+	0.999778i	$0.506711\pi$
$98$	−338.882	−	629.749i	−0.349309	−	0.649125i
$99$	−245.381	+	529.665i	−0.249108	+	0.537710i
$100$	−5.92678	−	56.3896i	−0.00592678	−	0.0563896i
$101$	−102.727	−	70.0378i	−0.101205	−	0.0690003i	0.511660	−	0.859188i	$-0.329031\pi$
$101$	−102.727	−	70.0378i	−0.101205	−	0.0690003i	−0.612865	+	0.790188i	$0.709983\pi$
$102$	−512.648	+	776.628i	−0.497644	+	0.753899i
$103$	849.334	−	836.723i	0.812499	−	0.800434i	−0.170246	−	0.985402i	$-0.554456\pi$
$103$	849.334	−	836.723i	0.812499	−	0.800434i	0.982745	+	0.184967i	$0.0592180\pi$
$104$	43.6078	−	134.211i	0.0411163	−	0.126543i
$105$	559.108	+	16.7335i	0.519651	+	0.0155526i
$106$	69.7369	+	2.08714i	0.0639004	+	0.00191247i
$107$	−450.423	+	1386.26i	−0.406954	+	1.25248i	0.512299	+	0.858807i	$0.328794\pi$
$107$	−450.423	+	1386.26i	−0.406954	+	1.25248i	−0.919253	+	0.393668i	$0.871206\pi$
$108$	91.0003	−	89.6490i	0.0810788	−	0.0798748i
$109$	−471.851	+	714.824i	−0.414634	+	0.628144i	−0.980538	−	0.196327i	$-0.937099\pi$
$109$	−471.851	+	714.824i	−0.414634	+	0.628144i	0.565904	+	0.824471i	$0.308527\pi$
$110$	−1786.69	−	1218.14i	−1.54867	−	1.05587i
$111$	−130.034	−	1237.19i	−0.111192	−	1.05792i
$112$	297.973	−	643.186i	0.251391	−	0.542637i
$113$	−730.646	−	1357.77i	−0.608260	−	1.13034i	−0.979432	−	0.201772i	$-0.935330\pi$
$113$	−730.646	−	1357.77i	−0.608260	−	1.13034i	0.371173	−	0.928564i	$-0.378956\pi$
$114$	−287.418	−	107.870i	−0.236133	−	0.0886222i
$115$	−112.850	+	833.089i	−0.0915067	+	0.675530i
$116$	56.1213	+	66.2094i	0.0449201	+	0.0529947i
$117$	60.9874	−	41.5805i	0.0481905	−	0.0328557i
$118$	−2.36983	−	158.400i	−0.00184882	−	0.123575i
$119$	−614.399	+	505.186i	−0.473293	+	0.389162i
$120$	−677.011	−	961.759i	−0.515020	−	0.731635i
$121$	−1366.64	+	377.168i	−1.02677	+	0.283372i
$122$	−719.831	−	130.630i	−0.534184	−	0.0969400i
$123$	−133.122	−	583.246i	−0.0975870	−	0.427557i
$124$	−3.83368	+	1.43880i	−0.00277641	+	0.00104200i
$125$	601.485	+	525.502i	0.430388	+	0.376019i
$126$	297.474	−	154.384i	0.210326	−	0.109156i
$127$	180.712	+	178.029i	0.126265	+	0.124390i	0.762169	−	0.647378i	$-0.224135\pi$
$127$	180.712	+	178.029i	0.126265	+	0.124390i	−0.635904	+	0.771768i	$0.719373\pi$
$128$	−1598.00	+	339.666i	−1.10348	+	0.234551i
$129$	−485.458	+	290.048i	−0.331335	+	0.197963i
$130$	114.941	+	248.104i	0.0775458	+	0.167386i
$131$	23.7985	−	31.7460i	0.0158724	−	0.0211730i	−0.792127	−	0.610356i	$-0.791026\pi$
$131$	23.7985	−	31.7460i	0.0158724	−	0.0211730i	0.808000	+	0.589183i	$0.200550\pi$
$132$	174.918	+	15.7429i	0.115338	+	0.0103806i
$133$	−207.584	−	160.522i	−0.135337	−	0.104654i
$134$	913.668	+	406.791i	0.589021	+	0.262249i
$135$	94.5319	−	2104.92i	0.0602667	−	1.34194i
$136$	1624.83	+	396.521i	1.02447	+	0.250010i
$137$	593.825	−	264.388i	0.370320	−	0.164877i	−0.213134	−	0.977023i	$-0.568367\pi$
$137$	593.825	−	264.388i	0.370320	−	0.164877i	0.583455	+	0.812146i	$0.301701\pi$
$138$	−262.237	−	668.169i	−0.161761	−	0.412161i
$139$	2218.67	+	1151.46i	1.35385	+	0.702627i	0.974870	−	0.222776i	$-0.0715119\pi$
$139$	2218.67	+	1151.46i	1.35385	+	0.702627i	0.378983	+	0.925404i	$0.376274\pi$
$140$	36.4946	+	112.319i	0.0220311	+	0.0678048i
$141$	−437.907	−	1498.91i	−0.261549	−	0.895257i
$142$	1063.27	+	2967.26i	0.628362	+	1.75357i
$143$	335.046	+	92.4668i	0.195930	+	0.0540731i
$144$	−702.412	−	338.264i	−0.406489	−	0.195755i
$145$	1421.39	+	170.928i	0.814069	+	0.0978954i
$146$	−432.291	−	1011.40i	−0.245046	−	0.573313i
$147$	942.620	−	171.060i	0.528884	−	0.0959783i
$148$	236.640	−	113.960i	0.131430	−	0.0632934i
$149$	328.456	−	112.181i	0.180592	−	0.0616795i	−0.231439	−	0.972849i	$-0.574343\pi$
$149$	328.456	−	112.181i	0.180592	−	0.0616795i	0.412031	+	0.911170i	$0.364820\pi$
$150$	781.058	+	166.019i	0.425154	+	0.0903693i
$151$	1317.69	+	1996.22i	0.710149	+	1.07583i	0.993166	+	0.116714i	$0.0372362\pi$
$151$	1317.69	+	1996.22i	0.710149	+	1.07583i	−0.283017	+	0.959115i	$0.591335\pi$
$152$	−8.25401	+	551.699i	−0.00440453	+	0.294399i
$153$	545.447	+	683.968i	0.288214	+	0.361409i
$154$	1460.27	+	598.474i	0.764102	+	0.313159i
$155$	−30.2121	+	60.4075i	−0.0156561	+	0.0313035i
$156$	−17.9662	−	13.0532i	−0.00922079	−	0.00669930i
$157$	1832.92	−	1700.70i	0.931740	−	0.864529i	−0.0592798	−	0.998241i	$-0.518880\pi$
$157$	1832.92	−	1700.70i	0.931740	−	0.864529i	0.991020	+	0.133713i	$0.0426899\pi$
$158$	3008.90	+	180.267i	1.51503	+	0.0907676i
$159$	−31.5278	+	87.9845i	−0.0157253	+	0.0438845i
$160$	302.670	−	429.972i	0.149551	−	0.212452i
$161$	−45.8501	−	611.827i	−0.0224441	−	0.299495i
$162$	404.874	+	809.523i	0.196358	+	0.392606i
$163$	−153.143	+	922.208i	−0.0735895	+	0.443147i	0.924490	+	0.381206i	$0.124491\pi$
$163$	−153.143	+	922.208i	−0.0735895	+	0.443147i	−0.998080	+	0.0619410i	$0.980271\pi$
$164$	106.443	−	67.9986i	0.0506819	−	0.0323768i
$165$	2291.60	−	1772.07i	1.08122	−	0.836092i
$166$	1906.70	−	465.306i	0.891496	−	0.217559i
$167$	31.9822	+	162.372i	0.0148195	+	0.0752377i	0.987837	−	0.155495i	$-0.0496972\pi$
$167$	31.9822	+	162.372i	0.0148195	+	0.0752377i	−0.973017	+	0.230733i	$0.925888\pi$
$168$	629.219	+	583.830i	0.288960	+	0.268116i
$169$	1487.89	+	1556.21i	0.677238	+	0.708336i
$170$	−2830.48	+	1578.20i	−1.27699	+	0.712015i
$171$	−179.942	+	225.640i	−0.0804709	+	0.100907i
$172$	−92.2242	−	75.8309i	−0.0408839	−	0.0336166i
$173$	76.1956	−	1016.76i	0.0334858	−	0.446837i	−0.955111	−	0.296249i	$-0.904264\pi$
$173$	76.1956	−	1016.76i	0.0334858	−	0.446837i	0.988597	−	0.150588i	$-0.0481168\pi$
$174$	−1131.02	+	463.537i	−0.492774	+	0.201958i
$175$	596.137	+	332.390i	0.257507	+	0.143579i
$176$	−923.591	−	3552.98i	−0.395558	−	1.52168i
$177$	202.791	+	62.5527i	0.0861169	+	0.0265636i
$178$	743.776	+	112.106i	0.313193	+	0.0472063i
$179$	−793.006	+	119.526i	−0.331129	+	0.0499096i	−0.312503	−	0.949917i	$-0.601167\pi$
$179$	−793.006	+	119.526i	−0.331129	+	0.0499096i	−0.0186262	+	0.999827i	$0.505929\pi$
$180$	124.118	−	38.2853i	0.0513956	−	0.0158534i
$181$	−1135.47	−	1837.46i	−0.466292	−	0.754571i	0.529292	−	0.848440i	$-0.322458\pi$
$181$	−1135.47	−	1837.46i	−0.466292	−	0.754571i	−0.995585	+	0.0938689i	$0.970077\pi$
$182$	−119.697	−	159.670i	−0.0487501	−	0.0650303i
$183$	464.415	−	863.027i	0.187598	−	0.348616i
$184$	−971.523	+	848.794i	−0.389248	+	0.340076i
$185$	1582.76	−	4032.81i	0.629010	−	1.60269i
$186$	−2.58721	−	57.6087i	−0.00101991	−	0.0227101i
$187$	−796.096	+	4041.73i	−0.311317	+	1.58054i
$188$	266.732	−	193.792i	0.103476	−	0.0751795i
$189$	251.906	+	1516.95i	0.0969497	+	0.583819i
$190$	−715.377	−	794.506i	−0.273152	−	0.303366i
$191$	−895.501	+	1056.47i	−0.339247	+	0.400228i	−0.905737	−	0.423840i	$-0.860682\pi$
$191$	−895.501	+	1056.47i	−0.339247	+	0.400228i	0.566490	+	0.824068i	$0.308301\pi$
$192$	186.302	−	1772.54i	0.0700269	−	0.666261i
$193$	2268.27	+	1355.23i	0.845977	+	0.505448i	0.869303	−	0.494280i	$-0.164568\pi$
$193$	2268.27	+	1355.23i	0.845977	+	0.505448i	−0.0233257	+	0.999728i	$0.507425\pi$
$194$	−1782.54	−	608.810i	−0.659685	−	0.225309i
$195$	−363.679	+	43.7341i	−0.133557	+	0.0160608i
$196$	101.134	+	175.170i	0.0368565	+	0.0638374i
$197$	13.1663	−	22.8047i	0.00476172	−	0.00824754i	−0.863635	−	0.504118i	$-0.831818\pi$
$197$	13.1663	−	22.8047i	0.00476172	−	0.00824754i	0.868396	+	0.495871i	$0.165151\pi$
$198$	682.170	−	1596.02i	0.244847	−	0.572848i
$199$	432.609	−	1895.39i	0.154105	−	0.675177i	−0.837561	−	0.546343i	$-0.816019\pi$
$199$	432.609	−	1895.39i	0.154105	−	0.675177i	0.991666	−	0.128834i	$-0.0411235\pi$
$200$	−192.646	−	1422.17i	−0.0681107	−	0.502814i
$201$	−896.501	+	995.665i	−0.314598	+	0.349397i
$202$	311.538	+	199.018i	0.108514	+	0.0693212i
$203$	−1040.60	+	93.6559i	−0.359783	+	0.0323810i
$204$	138.360	−	223.899i	0.0474860	−	0.0768435i
$205$	524.157	−	2016.39i	0.178579	−	0.686980i
$206$	−2449.84	+	2562.33i	−0.828584	+	0.866630i
$207$	−673.584	+	40.3553i	−0.226170	+	0.0135502i
$208$	−130.174	+	445.573i	−0.0433940	+	0.148533i
$209$	−1358.37	+	40.6545i	−0.449572	+	0.0134552i
$210$	−1663.19			−0.546527
$211$	−440.132	−	3033.19i	−0.143602	−	0.989636i
$211$	−440.132	−	3033.19i	−0.143602	−	0.989636i
$212$	−19.7331			−0.00639279
$213$	−4220.60	+	126.318i	−1.35770	+	0.0406345i
$214$	1215.37	−	4160.10i	0.388230	−	1.32887i
$215$	−1965.87	+	117.778i	−0.623586	+	0.0373599i
$216$	2234.43	−	2337.03i	0.703860	−	0.736180i
$217$	12.4012	−	47.7064i	0.00387948	−	0.0149241i
$218$	1338.78	−	2166.46i	0.415934	−	0.673079i
$219$	1467.53	−	132.080i	0.452814	−	0.0407540i
$220$	515.423	+	329.265i	0.157954	+	0.100905i
$221$	348.542	−	387.095i	0.106088	−	0.117823i
$222$	496.515	+	3665.42i	0.150108	+	1.10814i
$223$	−1158.46	+	5075.53i	−0.347874	+	1.52414i	0.434122	+	0.900854i	$0.357059\pi$
$223$	−1158.46	+	5075.53i	−0.347874	+	1.52414i	−0.781996	+	0.623283i	$0.785798\pi$
$224$	−150.821	+	352.863i	−0.0449872	+	0.105253i
$225$	375.339	−	650.105i	0.111211	−	0.192624i
$226$	2292.29	+	3970.36i	0.674693	+	1.16860i
$227$	−854.182	+	102.719i	−0.249753	+	0.0300340i	−0.243323	−	0.969945i	$-0.578237\pi$
$227$	−854.182	+	102.719i	−0.249753	+	0.0300340i	−0.00643064	+	0.999979i	$0.502047\pi$
$228$	82.1690	+	28.0641i	0.0238674	+	0.00815171i
$229$	−5273.13	−	3150.55i	−1.52165	−	0.909145i	−0.998375	−	0.0569817i	$-0.981852\pi$
$229$	−5273.13	−	3150.55i	−1.52165	−	0.909145i	−0.523277	−	0.852163i	$-0.675291\pi$
$230$	261.291	−	2486.02i	0.0749088	−	0.712709i
$231$	−1366.99	+	1612.71i	−0.389356	+	0.459345i
$232$	1470.01	+	1632.61i	0.415994	+	0.462008i
$233$	911.211	+	5487.19i	0.256203	+	1.54282i	0.742990	+	0.669303i	$0.233407\pi$
$233$	911.211	+	5487.19i	0.256203	+	1.54282i	−0.486786	+	0.873521i	$0.661831\pi$
$234$	−177.559	+	129.004i	−0.0496042	+	0.0360396i
$235$	1050.97	−	5335.69i	0.291734	−	1.48112i
$236$	2.01023	+	44.7613i	0.000554471	+	0.0123462i
$237$	−1475.25	+	3758.87i	−0.404336	+	1.03023i
$238$	1781.09	−	1556.09i	0.485087	−	0.423808i
$239$	653.952	−	1215.25i	0.176990	−	0.328903i	−0.776609	−	0.629983i	$-0.783062\pi$
$239$	653.952	−	1215.25i	0.176990	−	0.328903i	0.953599	+	0.301081i	$0.0973474\pi$
$240$	2320.63	+	3095.61i	0.624151	+	0.832588i
$241$	−3758.56	−	6082.24i	−1.00461	−	1.62569i	−0.753179	−	0.657815i	$-0.771481\pi$
$241$	−3758.56	−	6082.24i	−1.00461	−	1.62569i	−0.251428	−	0.967876i	$-0.580900\pi$
$242$	4028.16	−	1242.52i	1.07000	−	0.330051i
$243$	2856.40	−	430.533i	0.754066	−	0.113657i
$244$	204.609	+	30.8399i	0.0536835	+	0.00809149i
$245$	3188.09	+	983.396i	0.831346	+	0.256436i
$246$	447.525	+	1721.59i	0.115988	+	0.446198i
$247$	150.087	+	83.6843i	0.0386631	+	0.0215575i
$248$	−95.9028	+	39.3047i	−0.0245558	+	0.0100639i
$249$	−196.481	+	2621.86i	−0.0500059	+	0.667283i
$250$	−1834.39	−	1508.31i	−0.464067	−	0.381577i
$251$	−4593.00	+	5759.44i	−1.15501	+	1.44834i	−0.282820	+	0.959173i	$0.591270\pi$
$251$	−4593.00	+	5759.44i	−1.15501	+	1.44834i	−0.872191	+	0.489165i	$0.837302\pi$
$252$	−82.7929	+	46.1631i	−0.0206963	+	0.0115397i
$253$	−2195.82	−	2296.65i	−0.545652	−	0.570707i
$254$	−552.922	−	513.036i	−0.136588	−	0.126735i
$255$	−838.992	−	4259.51i	−0.206038	−	1.04604i
$256$	1241.54	−	302.983i	0.303111	−	0.0739705i
$257$	−5158.55	+	3989.04i	−1.25207	+	0.968208i	−0.252069	+	0.967709i	$0.581111\pi$
$257$	−5158.55	+	3989.04i	−1.25207	+	0.968208i	−1.00000		0.000498218i	$0.999841\pi$
$258$	1417.01	−	905.217i	0.341934	−	0.218436i
$259$	−517.945	+	3119.00i	−0.124261	+	0.748282i
$260$	−34.5942	−	69.1692i	−0.00825171	−	0.0164988i
$261$	85.8730	+	1145.90i	0.0203655	+	0.271759i
$262$	−67.9064	+	96.4675i	−0.0160125	+	0.0227473i
$263$	−680.457	+	1898.95i	−0.159539	+	0.445225i	−0.994456	−	0.105150i	$-0.966468\pi$
$263$	−680.457	+	1898.95i	−0.159539	+	0.445225i	0.834917	+	0.550375i	$0.185515\pi$
$264$	4437.35	+	265.848i	1.03447	+	0.0619765i
$265$	−238.599	+	221.387i	−0.0553094	+	0.0513196i
$266$	631.229	+	458.615i	0.145500	+	0.105712i
$267$	−450.727	+	901.203i	−0.103311	+	0.206564i
$268$	−261.746	−	107.274i	−0.0596593	−	0.0244507i
$269$	−624.581	−	783.200i	−0.141566	−	0.177519i	0.705994	−	0.708218i	$-0.250501\pi$
$269$	−624.581	−	783.200i	−0.141566	−	0.177519i	−0.847560	+	0.530700i	$0.821929\pi$
$270$	−93.7210	+	6264.32i	−0.0211247	+	1.41198i
$271$	1837.46	+	2783.63i	0.411873	+	0.623961i	0.980004	−	0.198977i	$-0.0637618\pi$
$271$	1837.46	+	2783.63i	0.411873	+	0.623961i	−0.568131	+	0.822938i	$0.692333\pi$
$272$	−5381.42	−	1143.86i	−1.19962	−	0.254987i
$273$	252.978	−	86.4025i	0.0560840	−	0.0191550i
$274$	−1741.36	+	838.594i	−0.383939	+	0.184895i
$275$	3477.98	−	631.160i	0.762654	−	0.138401i
$276$	79.7908	+	186.680i	0.0174016	+	0.0407131i
$277$	−1752.27	−	210.718i	−0.380085	−	0.0457070i	−0.0728561	−	0.997342i	$-0.523211\pi$
$277$	−1752.27	−	210.718i	−0.380085	−	0.0457070i	−0.307229	+	0.951636i	$0.599402\pi$
$278$	−6696.43	−	3224.83i	−1.44470	−	0.695729i
$279$	−52.2589	−	14.4225i	−0.0112138	−	0.00309482i
$280$	1008.36	+	2814.04i	0.215219	+	0.600610i
$281$	−1170.78	−	4007.48i	−0.248552	−	0.850770i	−0.984746	−	0.173999i	$-0.944331\pi$
$281$	−1170.78	−	4007.48i	−0.248552	−	0.850770i	0.736194	−	0.676771i	$-0.236621\pi$
$282$	1434.81	+	4415.89i	0.302985	+	0.932491i
$283$	5032.44	+	2611.75i	1.05706	+	0.548596i	0.898599	−	0.438770i	$-0.144586\pi$
$283$	5032.44	+	2611.75i	1.05706	+	0.548596i	0.158458	+	0.987366i	$0.449348\pi$
$284$	−325.704	−	829.880i	−0.0680527	−	0.173396i
$285$	1308.39	−	582.531i	0.271937	−	0.121074i
$286$	−1004.00	−	245.013i	−0.207579	−	0.0506571i
$287$	−68.2158	+	1518.94i	−0.0140301	+	0.312405i
$288$	385.563	+	171.664i	0.0788873	+	0.0351229i
$289$	997.163	+	771.092i	0.202964	+	0.156949i
$290$	−4239.64	−	381.575i	−0.858485	−	0.0772650i
$291$	1513.57	−	2019.03i	0.304903	−	0.406726i
$292$	130.771	+	282.275i	0.0262082	+	0.0565716i
$293$	−241.883	+	144.518i	−0.0482284	+	0.0288152i	−0.536811	−	0.843702i	$-0.680371\pi$
$293$	−241.883	+	144.518i	−0.0482284	+	0.0288152i	0.488583	+	0.872518i	$0.337514\pi$
$294$	−2786.30	+	592.246i	−0.552721	+	0.117485i
$295$	526.488	+	518.670i	0.103910	+	0.102367i
$296$	5900.71	−	3062.37i	1.15869	−	0.601340i
$297$	5997.19	+	5239.59i	1.17169	+	1.02368i
$298$	−966.209	+	362.624i	−0.187822	+	0.0704908i
$299$	89.4050	+	391.709i	0.0172924	+	0.0757629i
$300$	−222.219	−	40.3267i	−0.0427660	−	0.00776088i
$301$	1385.47	−	382.366i	0.265306	−	0.0732199i
$302$	−4093.82	−	5815.66i	−0.780042	−	1.10812i
$303$	−382.526	+	314.530i	−0.0725266	+	0.0596346i
$304$	−27.1511	−	1814.78i	−0.00512244	−	0.342384i
$305$	2819.99	−	1922.64i	0.529417	−	0.360951i
$306$	−1681.93	−	1984.27i	−0.314215	−	0.370697i
$307$	1162.00	−	8578.23i	0.216022	−	1.59474i	−0.480360	−	0.877071i	$-0.659494\pi$
$307$	1162.00	−	8578.23i	0.216022	−	1.59474i	0.696383	−	0.717670i	$-0.254792\pi$
$308$	−417.898	−	156.840i	−0.0773115	−	0.0290155i
$309$	−2250.40	−	4181.94i	−0.414306	−	0.769910i
$310$	84.4187	−	182.221i	0.0154666	−	0.0333854i
$311$	−580.187	−	5520.11i	−0.105786	−	1.00648i	−0.910693	−	0.413084i	$-0.864452\pi$
$311$	−580.187	−	5520.11i	−0.105786	−	1.00648i	0.804907	−	0.593401i	$-0.202215\pi$
$312$	−464.429	−	316.642i	−0.0842728	−	0.0574562i
$313$	3908.43	−	5921.02i	0.705807	−	1.06925i	−0.287945	−	0.957647i	$-0.592972\pi$
$313$	3908.43	−	5921.02i	0.705807	−	1.06925i	0.993753	−	0.111606i	$-0.0355993\pi$
$314$	−5296.26	+	5217.62i	−0.951864	+	0.937729i
$315$	−483.167	+	1487.03i	−0.0864234	+	0.265984i
$316$	−852.174	−	25.5046i	−0.151704	−	0.00454033i
$317$	−7403.89	−	221.590i	−1.31181	−	0.0392610i	−0.633332	−	0.773881i	$-0.718313\pi$
$317$	−7403.89	−	221.590i	−1.31181	−	0.0392610i	−0.678479	+	0.734620i	$0.737361\pi$
$318$	85.8759	−	264.299i	0.0151436	−	0.0466073i
$319$	−3854.60	+	3797.37i	−0.676540	+	0.666494i
$320$	3419.38	−	5180.13i	0.597341	−	0.904932i
$321$	4797.07	+	3270.59i	0.834101	+	0.568680i
$322$	190.691	+	1814.30i	0.0330024	+	0.313997i
$323$	−856.115	+	1847.96i	−0.147478	+	0.318338i
$324$	−121.312	−	225.436i	−0.0208011	−	0.0386549i
$325$	−418.465	−	157.053i	−0.0714224	−	0.0268053i
$326$	373.118	−	2754.47i	0.0633899	−	0.467963i
$327$	2205.98	+	2602.52i	0.373061	+	0.440121i
$328$	2641.53	−	1800.97i	0.444678	−	0.303176i
$329$	59.3712	+	3968.38i	0.00994906	+	0.664996i
$330$	−6653.14	+	5470.51i	−1.10983	+	0.912550i
$331$	−897.022	−	1274.31i	−0.148957	−	0.211608i	0.736367	−	0.676582i	$-0.236540\pi$
$331$	−897.022	−	1274.31i	−0.148957	−	0.211608i	−0.885324	+	0.464975i	$0.846063\pi$
$332$	−535.108	+	147.680i	−0.0884574	+	0.0244127i
$333$	3421.45	+	620.902i	0.563046	+	0.102178i
$334$	−109.496	−	479.732i	−0.0179381	−	0.0785921i
$335$	−4368.37	+	1639.48i	−0.712446	+	0.267385i
$336$	−2126.31	−	1857.70i	−0.345237	−	0.301624i
$337$	229.424	−	119.067i	0.0370846	−	0.0192463i	−0.442000	−	0.897015i	$-0.645731\pi$
$337$	229.424	−	119.067i	0.0370846	−	0.0192463i	0.479084	+	0.877769i	$0.340969\pi$
$338$	−4560.51	−	4492.79i	−0.733903	−	0.723005i
$339$	−6007.38	+	1276.91i	−0.962466	+	0.204579i
$340$	786.856	−	470.124i	0.125510	−	0.0749885i
$341$	−107.307	−	231.626i	−0.0170410	−	0.0367838i
$342$	514.726	−	686.620i	0.0813836	−	0.108562i
$343$	−5883.44	−	529.519i	−0.926169	−	0.0833567i
$344$	−2390.70	−	1848.69i	−0.374703	−	0.289752i
$345$	3059.16	+	1362.02i	0.477390	+	0.212548i
$346$	−136.016	+	3028.64i	−0.0211338	+	0.470580i
$347$	−1977.41	−	482.562i	−0.305916	−	0.0746550i	0.0811655	−	0.996701i	$-0.474136\pi$
$347$	−1977.41	−	482.562i	−0.305916	−	0.0746550i	−0.387081	+	0.922046i	$0.626517\pi$
$348$	315.831	−	140.617i	0.0486503	−	0.0216605i
$349$	1188.87	+	3029.19i	0.182346	+	0.464610i	0.992594	−	0.121477i	$-0.0387631\pi$
$349$	1188.87	+	3029.19i	0.182346	+	0.464610i	−0.810248	+	0.586087i	$0.800668\pi$
$350$	−1801.31	−	934.852i	−0.275098	−	0.142771i
$351$	−311.176	−	957.701i	−0.0473201	−	0.145636i
$352$	557.308	+	1907.61i	0.0843881	+	0.288852i
$353$	2732.17	+	7624.66i	0.411951	+	1.14963i	0.951492	+	0.307672i	$0.0995500\pi$
$353$	2732.17	+	7624.66i	0.411951	+	1.14963i	−0.539541	+	0.841959i	$0.681402\pi$
$354$	−608.268	−	167.871i	−0.0913252	−	0.0252041i
$355$	−13248.7	−	6380.24i	−1.98075	−	0.953881i
$356$	−211.222	−	25.4004i	−0.0314460	−	0.00378152i
$357$	1245.23	+	2913.37i	0.184607	+	0.431910i
$358$	2346.22	−	425.776i	0.346373	−	0.0628575i
$359$	10615.9	−	5112.37i	1.56069	−	0.751589i	0.563474	−	0.826134i	$-0.309465\pi$
$359$	10615.9	−	5112.37i	1.56069	−	0.751589i	0.997218	+	0.0745447i	$0.0237503\pi$
$360$	3111.20	−	1062.60i	0.455485	−	0.155567i
$361$	6051.91	+	1286.37i	0.882332	+	0.187545i
$362$	3538.12	+	5360.02i	0.513700	+	0.778222i
$363$	−84.4771	+	5646.46i	−0.0122146	+	0.816425i
$364$	35.1906	+	44.1276i	0.00506728	+	0.00635417i
$365$	4748.07	+	1945.94i	0.680891	+	0.279055i
$366$	−1303.50	+	2606.27i	−0.186161	+	0.372218i
$367$	10084.6	+	7326.92i	1.43437	+	1.04213i	0.989182	+	0.146695i	$0.0468637\pi$
$367$	10084.6	+	7326.92i	1.43437	+	1.04213i	0.445190	+	0.895436i	$0.353136\pi$
$368$	3110.81	−	2886.41i	0.440658	−	0.408871i
$369$	1669.27	+	100.008i	0.235497	+	0.0141090i
$370$	−4345.32	+	12126.5i	−0.610547	+	1.70385i
$371$	136.733	−	194.242i	0.0191342	−	0.0271820i
$372$	1.21887	+	16.2647i	0.000169881	+	0.00226690i
$373$	−4526.04	−	9049.56i	−0.628282	−	1.25622i	−0.950845	−	0.309667i	$-0.899782\pi$
$373$	−4526.04	−	9049.56i	−0.628282	−	1.25622i	0.322563	−	0.946548i	$-0.395456\pi$
$374$	2006.52	−	12083.0i	0.277419	−	1.67058i
$375$	2681.05	−	1712.72i	0.369197	−	0.235852i
$376$	6601.59	−	5104.92i	0.905455	−	0.700176i
$377$	664.693	−	162.210i	0.0908048	−	0.0221598i
$378$	−883.610	−	4486.03i	−0.120233	−	0.610415i
$379$	−8949.81	−	8304.21i	−1.21298	−	1.12548i	−0.988534	−	0.150998i	$-0.951751\pi$
$379$	−8949.81	−	8304.21i	−1.21298	−	1.12548i	−0.224449	−	0.974486i	$-0.572058\pi$
$380$	208.967	+	218.563i	0.0282100	+	0.0295054i
$381$	882.527	−	492.073i	0.118670	−	0.0661671i
$382$	2567.50	−	3219.54i	0.343886	−	0.431220i
$383$	327.571	+	269.343i	0.0437025	+	0.0359342i	0.656713	−	0.754141i	$-0.271946\pi$
$383$	327.571	+	269.343i	0.0437025	+	0.0359342i	−0.613010	+	0.790075i	$0.710042\pi$
$384$	−486.296	+	6489.17i	−0.0646255	+	0.862368i
$385$	−6812.54	+	2792.04i	−0.901816	+	0.369599i
$386$	−6861.95	−	3826.04i	−0.904829	−	0.504508i
$387$	−397.695	−	1529.90i	−0.0522376	−	0.200954i
$388$	509.095	+	157.035i	0.0666118	+	0.0205470i
$389$	8305.82	+	1251.90i	1.08258	+	0.163172i	0.666017	−	0.745937i	$-0.267998\pi$
$389$	8305.82	+	1251.90i	1.08258	+	0.163172i	0.416559	+	0.909109i	$0.363236\pi$
$390$	1076.98	−	162.329i	0.139834	−	0.0210765i
$391$	−4550.33	+	1403.59i	−0.588543	+	0.181541i
$392$	2691.34	+	4355.22i	0.346769	+	0.561153i
$393$	−94.7940	−	126.451i	−0.0121672	−	0.0162305i
$394$	−37.1024	+	68.9477i	−0.00474414	+	0.00881608i
$395$	−10590.0	+	9252.24i	−1.34897	+	1.17856i
$396$	−179.353	+	456.984i	−0.0227597	+	0.0579907i
$397$	5.64704	+	125.741i	0.000713897	+	0.0158961i	0.999318	−	0.0369153i	$-0.0117532\pi$
$397$	5.64704	+	125.741i	0.000713897	+	0.0158961i	−0.998604	+	0.0528115i	$0.983182\pi$
$398$	−1117.14	+	5671.66i	−0.140697	+	0.714308i
$399$	−845.607	+	614.369i	−0.106098	+	0.0770850i
$400$	773.364	+	4657.10i	0.0966705	+	0.582138i
$401$	−9722.21	−	10797.6i	−1.21073	−	1.34466i	−0.921973	−	0.387254i	$-0.873424\pi$
$401$	−9722.21	−	10797.6i	−1.21073	−	1.34466i	−0.288760	−	0.957402i	$-0.593243\pi$
$402$	2575.88	−	3038.91i	0.319585	−	0.377032i
$403$	−3.37408	+	32.1023i	−0.000417060	+	0.00396806i
$404$	−89.7593	−	53.6287i	−0.0110537	−	0.00660428i
$405$	−3996.01	−	1364.80i	−0.490279	−	0.167450i
$406$	3084.39	−	370.911i	0.377034	−	0.0453399i
$407$	8187.02	+	14180.3i	0.997090	+	1.72701i
$408$	3330.98	−	5769.43i	0.404186	−	0.700072i
$409$	3916.88	−	9164.00i	0.473539	−	1.10790i	−0.497173	−	0.867652i	$-0.665628\pi$
$409$	3916.88	−	9164.00i	0.473539	−	1.10790i	0.970712	−	0.240248i	$-0.0772286\pi$
$410$	−1378.46	+	6039.44i	−0.166042	+	0.727479i
$411$	−347.552	−	2565.73i	−0.0417117	−	0.307928i
$412$	670.916	−	745.127i	0.0802273	−	0.0891014i
$413$	−454.536	−	290.369i	−0.0541556	−	0.0345959i
$414$	1998.33	−	179.853i	0.237229	−	0.0213510i
$415$	−4813.31	+	7789.07i	−0.569340	+	0.921327i
$416$	63.2230	−	243.214i	0.00745135	−	0.0286648i
$417$	6880.70	−	7196.65i	0.808032	−	0.845135i
$418$	4033.53	−	241.654i	0.471977	−	0.0282768i
$419$	−2634.98	+	9019.29i	−0.307225	+	1.05160i	0.649440	+	0.760413i	$0.275003\pi$
$419$	−2634.98	+	9019.29i	−0.307225	+	1.05160i	−0.956666	+	0.291189i	$0.905949\pi$
$420$	470.201	−	14.0726i	0.0546273	−	0.00163493i
$421$	−11836.5			−1.37025			−0.685127	−	0.728423i	$-0.740253\pi$
$421$	−11836.5			−1.37025			−0.685127	+	0.728423i	$0.740253\pi$
$422$	1577.90	+	8975.62i	0.182016	+	1.03537i
$423$	4365.02			0.501736
$424$	−499.247	+	14.9419i	−0.0571830	+	0.00171142i
$425$	1485.54	−	5084.85i	0.169551	−	0.580356i
$426$	12532.6	−	750.845i	1.42537	−	0.0853957i
$427$	−1721.33	+	1800.37i	−0.195085	+	0.204043i
$428$	−308.400	+	1186.39i	−0.0348296	+	0.133987i
$429$	727.780	−	1177.72i	0.0819057	−	0.132543i
$430$	5832.17	−	524.905i	0.654075	−	0.0588678i
$431$	−7872.61	−	5029.21i	−0.879838	−	0.562062i	0.0192575	−	0.999815i	$-0.493870\pi$
$431$	−7872.61	−	5029.21i	−0.879838	−	0.562062i	−0.899095	+	0.437753i	$0.855775\pi$
$432$	−7116.76	+	7903.97i	−0.792605	+	0.880277i
$433$	−1309.81	−	9669.37i	−0.145370	−	1.07316i	−0.905788	−	0.423731i	$-0.860720\pi$
$433$	−1309.81	−	9669.37i	−0.145370	−	1.07316i	0.760418	−	0.649434i	$-0.224994\pi$
$434$	−32.6134	+	142.889i	−0.00360713	+	0.0158039i
$435$	2241.21	−	5243.58i	0.247030	−	0.577955i
$436$	−360.157	+	623.811i	−0.0395606	+	0.0685209i
$437$	−785.471	−	1360.48i	−0.0859821	−	0.148925i
$438$	−4349.81	+	523.084i	−0.474525	+	0.0570637i
$439$	−4624.86	−	1579.58i	−0.502808	−	0.171729i	0.0601916	−	0.998187i	$-0.480829\pi$
$439$	−4624.86	−	1579.58i	−0.502808	−	0.171729i	−0.562999	+	0.826457i	$0.690353\pi$
$440$	13289.6	+	7940.14i	1.43990	+	0.860298i
$441$	−279.919	+	2663.25i	−0.0302255	+	0.287577i
$442$	−1001.45	+	1181.47i	−0.107770	+	0.127142i
$443$	−8822.68	−	9798.58i	−0.946226	−	1.05089i	−0.998633	−	0.0522646i	$-0.983356\pi$
$443$	−8822.68	−	9798.58i	−0.946226	−	1.05089i	0.0524073	−	0.998626i	$-0.483311\pi$
$444$	−171.384	−	1032.05i	−0.0183188	−	0.110313i
$445$	−2838.93	+	2062.60i	−0.302422	+	0.219723i
$446$	2991.52	−	15187.8i	0.317607	−	1.61247i
$447$	−62.0260	−	1381.12i	−0.00656316	−	0.146140i
$448$	−1654.93	+	4216.70i	−0.174527	+	0.444688i
$449$	4260.82	−	3722.57i	0.447841	−	0.391267i	−0.404260	−	0.914644i	$-0.632471\pi$
$449$	4260.82	−	3722.57i	0.447841	−	0.391267i	0.852101	+	0.523377i	$0.175328\pi$
$450$	−1057.70	+	1965.53i	−0.110801	+	0.205902i
$451$	4723.19	+	6300.50i	0.493140	+	0.657825i
$452$	−681.649	−	1103.07i	−0.0709338	−	0.114788i
$453$	9104.16	−	2808.26i	0.944262	−	0.291266i
$454$	2529.53	−	381.266i	0.261491	−	0.0394134i
$455$	920.573	+	138.754i	0.0948509	+	0.0142965i
$456$	2100.13	+	647.805i	0.215675	+	0.0665268i
$457$	1569.56	+	6037.98i	0.160659	+	0.618041i	0.997505	+	0.0706028i	$0.0224923\pi$
$457$	1569.56	+	6037.98i	0.160659	+	0.618041i	−0.836846	+	0.547439i	$0.815603\pi$
$458$	15952.2	+	8894.54i	1.62751	+	0.907455i
$459$	11043.2	−	4525.95i	1.12300	−	0.460247i
$460$	−52.8351	+	705.036i	−0.00535533	+	0.0714619i
$461$	209.048	+	171.889i	0.0211201	+	0.0173659i	0.645616	−	0.763662i	$-0.276600\pi$
$461$	209.048	+	171.889i	0.0211201	+	0.0173659i	−0.624496	+	0.781028i	$0.714696\pi$
$462$	3919.31	−	4914.66i	0.394681	−	0.494914i
$463$	−4068.29	+	2268.37i	−0.408357	+	0.227689i	−0.677674	−	0.735363i	$-0.737012\pi$
$463$	−4068.29	+	2268.37i	−0.408357	+	0.227689i	0.269317	+	0.963052i	$0.413202\pi$
$464$	−4993.99	−	5223.31i	−0.499656	−	0.522599i
$465$	197.213	+	182.987i	0.0196679	+	0.0182491i
$466$	−3196.25	−	16227.2i	−0.317732	−	1.61311i
$467$	−9999.81	+	2440.33i	−0.990869	+	0.241810i	−0.699369	−	0.714761i	$-0.746535\pi$
$467$	−9999.81	+	2440.33i	−0.990869	+	0.241810i	−0.291500	+	0.956571i	$0.594154\pi$
$468$	49.1063	−	37.9733i	0.00485030	−	0.00375067i
$469$	2869.61	−	1833.18i	0.282530	−	0.180487i
$470$	−2648.91	+	15951.4i	−0.259969	+	1.56550i
$471$	−4455.06	−	8907.63i	−0.435835	−	0.871427i
$472$	84.7524	+	1130.94i	0.00826493	+	0.110288i
$473$	4284.55	−	6086.61i	0.416498	−	0.591676i
$474$	4050.16	−	11302.8i	0.392468	−	1.09526i
$475$	1744.48	+	104.514i	0.168510	+	0.0100957i
$476$	−490.367	+	454.994i	−0.0472183	+	0.0438122i
$477$	−211.359	−	153.561i	−0.0202882	−	0.0147402i
$478$	−1835.48	+	3669.94i	−0.175634	+	0.351170i
$479$	−1972.84	−	808.545i	−0.188186	−	0.0771261i	0.283166	−	0.959071i	$-0.408615\pi$
$479$	−1972.84	−	808.545i	−0.188186	−	0.0771261i	−0.471353	+	0.881945i	$0.656234\pi$
$480$	−1305.86	−	1637.50i	−0.124175	−	0.155711i
$481$	30.9729	−	2070.23i	0.00293606	−	0.196246i
$482$	11711.6	+	17742.4i	1.10674	+	1.67665i
$483$	−2390.46	−	508.108i	−0.225196	−	0.0478669i
$484$	−1128.29	+	385.358i	−0.105963	+	0.0361907i
$485$	7917.42	−	3812.83i	0.741261	−	0.356972i
$486$	−8451.06	+	1533.64i	−0.788782	+	0.143143i
$487$	7489.79	+	17523.2i	0.696909	+	1.63050i	0.773777	+	0.633458i	$0.218365\pi$
$487$	7489.79	+	17523.2i	0.696909	+	1.63050i	−0.0768676	+	0.997041i	$0.524492\pi$
$488$	5199.98	+	625.321i	0.482361	+	0.0580060i
$489$	3354.88	+	1615.63i	0.310252	+	0.149409i
$490$	−9562.64	−	2639.12i	−0.881625	−	0.243313i
$491$	−4469.52	−	12473.1i	−0.410808	−	1.14644i	−0.952148	−	0.305637i	$-0.901131\pi$
$491$	−4469.52	−	12473.1i	−0.410808	−	1.14644i	0.541340	−	0.840804i	$-0.317917\pi$
$492$	−141.087	−	482.927i	−0.0129282	−	0.0442521i
$493$	2505.84	+	7712.18i	0.228920	+	0.704542i
$494$	−453.509	−	235.364i	−0.0413043	−	0.0214363i
$495$	2958.33	+	7537.71i	0.268621	+	0.684434i
$496$	311.458	−	138.670i	0.0281953	−	0.0125534i
$497$	10425.7	+	2544.28i	0.940963	+	0.229631i
$498$	350.737	−	7809.76i	0.0315600	−	0.702739i
$499$	−12788.9	−	5693.99i	−1.14732	−	0.510818i	−0.257113	−	0.966381i	$-0.582771\pi$
$499$	−12788.9	−	5693.99i	−1.14732	−	0.510818i	−0.890203	+	0.455564i	$0.849438\pi$
$500$	531.364	+	410.896i	0.0475266	+	0.0367517i
$501$	656.532	+	59.0889i	0.0585463	+	0.00526926i
$502$	13138.3	−	17525.9i	1.16811	−	1.55820i
$503$	3863.03	+	8338.51i	0.342433	+	0.739157i	0.999897	−	0.0143291i	$-0.00456124\pi$
$503$	3863.03	+	8338.51i	0.342433	+	0.739157i	−0.657464	+	0.753486i	$0.728371\pi$
$504$	−2059.71	+	1230.62i	−0.182037	+	0.108762i
$505$	−1686.97	+	358.577i	−0.148652	+	0.0315970i
$506$	6730.36	+	6630.42i	0.591307	+	0.582526i
$507$	7611.96	−	3950.48i	0.666783	−	0.346049i
$508$	160.658	+	140.363i	0.0140316	+	0.0122590i
$509$	923.118	−	346.452i	0.0803860	−	0.0301694i	−0.310858	−	0.950456i	$-0.600616\pi$
$509$	923.118	−	346.452i	0.0803860	−	0.0301694i	0.391244	+	0.920287i	$0.372045\pi$
$510$	2872.41	+	12584.8i	0.249397	+	1.09268i
$511$	−3684.70	−	668.674i	−0.318985	−	0.0578872i
$512$	8935.67	−	2466.09i	0.771298	−	0.212865i
$513$	2266.35	+	3219.56i	0.195052	+	0.277090i
$514$	14976.6	−	12314.5i	1.28520	−	1.05675i
$515$	−247.406	−	16536.6i	−0.0211690	−	1.41493i
$516$	−392.944	+	267.905i	−0.0335240	+	0.0228563i
$517$	13290.2	+	15679.2i	1.13056	+	1.33379i
$518$	1261.92	−	9315.88i	0.107038	−	0.790186i
$519$	−3802.34	−	1427.04i	−0.321588	−	0.120694i
$520$	−927.611	−	1723.79i	−0.0782278	−	0.145372i
$521$	−1753.96	+	3785.99i	−0.147490	+	0.318363i	−0.967032	−	0.254656i	$-0.918038\pi$
$521$	−1753.96	+	3785.99i	−0.147490	+	0.318363i	0.819542	+	0.573020i	$0.194228\pi$
$522$	−357.146	−	3398.02i	−0.0299461	−	0.284918i
$523$	−5027.37	−	3427.60i	−0.420328	−	0.286575i	0.334628	−	0.942350i	$-0.391389\pi$
$523$	−5027.37	−	3427.60i	−0.420328	−	0.286575i	−0.754956	+	0.655775i	$0.772342\pi$
$524$	18.3817	−	27.8470i	0.00153246	−	0.00232157i
$525$	1936.73	−	1907.97i	0.161002	−	0.158611i
$526$	1853.44	−	5704.30i	0.153638	−	0.472850i
$527$	−382.398	−	11.4447i	−0.0316082	−	0.000945997i
$528$	−14616.0	−	437.441i	−1.20470	−	0.0360553i
$529$	−2624.78	+	8078.23i	−0.215729	+	0.663946i
$530$	689.434	−	679.196i	0.0565040	−	0.0556649i
$531$	−326.798	+	495.078i	−0.0267078	+	0.0404606i
$532$	−182.336	−	124.315i	−0.0148595	−	0.0101310i
$533$	−104.078	−	990.237i	−0.00845802	−	0.0804727i
$534$	1259.42	−	2718.51i	0.102061	−	0.220302i
$535$	9581.27	+	17805.0i	0.774270	+	1.43883i
$536$	−6703.42	−	2515.83i	−0.540193	−	0.202738i
$537$	−428.792	+	3165.47i	−0.0344576	+	0.254376i
$538$	1925.95	+	2272.15i	0.154338	+	0.182081i
$539$	−10418.7	+	7103.33i	−0.832586	+	0.567647i
$540$	−26.5078	−	1771.79i	−0.00211244	−	0.141195i
$541$	9231.76	−	7590.77i	0.733650	−	0.603240i	−0.192100	−	0.981375i	$-0.561530\pi$
$541$	9231.76	−	7590.77i	0.733650	−	0.603240i	0.925750	+	0.378136i	$0.123435\pi$
$542$	−5708.62	−	8109.64i	−0.452410	−	0.642692i
$543$	−8293.61	+	2288.89i	−0.655457	+	0.180895i
$544$	2930.49	+	531.805i	0.230962	+	0.0419135i
$545$	2643.82	+	11583.3i	0.207796	+	0.910414i
$546$	−744.178	+	279.295i	−0.0583295	+	0.0218914i
$547$	−4600.71	−	4019.52i	−0.359620	−	0.314191i	0.459099	−	0.888385i	$-0.348172\pi$
$547$	−4600.71	−	4019.52i	−0.359620	−	0.314191i	−0.818719	+	0.574195i	$0.805315\pi$
$548$	485.206	−	251.814i	0.0378229	−	0.0196295i
$549$	1951.56	+	1922.58i	0.151713	+	0.149460i
$550$	−10280.6	+	2185.20i	−0.797027	+	0.169413i
$551$	−2296.50	+	1372.09i	−0.177557	+	0.106086i
$552$	2160.07	+	4662.59i	0.166555	+	0.359517i
$553$	6155.86	−	8211.63i	0.473371	−	0.631454i
$554$	5226.57	+	470.400i	0.400823	+	0.0360747i
$555$	−13651.0	−	10556.1i	−1.04406	−	0.807355i
$556$	1920.44	+	855.036i	0.146484	+	0.0652187i
$557$	−266.294	+	5929.50i	−0.0202572	+	0.451061i	0.963074	+	0.269237i	$0.0867716\pi$
$557$	−266.294	+	5929.50i	−0.0202572	+	0.451061i	−0.983331	+	0.181824i	$0.941800\pi$
$558$	156.599	+	38.2160i	0.0118806	+	0.00289931i
$559$	−859.832	+	382.822i	−0.0650573	+	0.0289654i
$560$	−3592.38	−	9153.25i	−0.271082	−	0.690706i
$561$	14563.8	+	7558.37i	1.09605	+	0.568832i
$562$	3836.10	+	11806.3i	0.287929	+	0.886153i
$563$	−6619.20	−	22656.9i	−0.495499	−	1.69604i	−0.697438	−	0.716645i	$-0.745677\pi$
$563$	−6619.20	−	22656.9i	−0.495499	−	1.69604i	0.201939	−	0.979398i	$-0.435276\pi$
$564$	−443.000	−	1236.28i	−0.0330739	−	0.0922993i
$565$	−20617.5	−	5690.06i	−1.53519	−	0.423686i
$566$	−15189.0	−	7314.62i	−1.12799	−	0.543209i
$567$	3059.65	+	367.937i	0.226620	+	0.0272520i
$568$	−8868.72	−	20749.4i	−0.655146	−	1.53279i
$569$	−10640.7	+	1931.01i	−0.783976	+	0.142271i	−0.555763	−	0.831341i	$-0.687574\pi$
$569$	−10640.7	+	1931.01i	−0.783976	+	0.142271i	−0.228213	+	0.973611i	$0.573288\pi$
$570$	−3836.77	+	1847.69i	−0.281938	+	0.135774i
$571$	−3740.83	+	1277.65i	−0.274166	+	0.0936390i	−0.456884	−	0.889526i	$-0.651034\pi$
$571$	−3740.83	+	1277.65i	−0.274166	+	0.0936390i	0.182718	+	0.983165i	$0.441511\pi$
$572$	285.914	+	60.7730i	0.0208998	+	0.00444239i
$573$	3039.01	+	4603.91i	0.221565	+	0.335656i
$574$	67.6306	−	4520.44i	0.00491786	−	0.328710i
$575$	2547.65	+	3194.65i	0.184773	+	0.231697i
$576$	4609.90	+	1889.31i	0.333470	+	0.136669i
$577$	−8690.85	+	17376.9i	−0.627045	+	1.25374i	0.324399	+	0.945920i	$0.394838\pi$
$577$	−8690.85	+	17376.9i	−0.627045	+	1.25374i	−0.951444	+	0.307821i	$0.900400\pi$
$578$	−3032.20	−	2203.03i	−0.218206	−	0.158536i
$579$	7715.19	−	7158.65i	0.553769	−	0.513823i
$580$	1201.82	+	72.0029i	0.0860397	+	0.00515476i
$581$	2254.13	−	6290.61i	0.160959	−	0.449189i
$582$	−4318.80	+	6135.27i	−0.307595	+	0.436968i
$583$	−91.9323	−	1226.75i	−0.00653078	−	0.0871472i
$584$	3522.26	+	7042.55i	0.249575	+	0.499012i
$585$	167.734	−	1010.08i	0.0118546	−	0.0713872i
$586$	706.032	−	451.030i	0.0497712	−	0.0317950i
$587$	2792.14	−	2159.13i	0.196327	−	0.151817i	−0.508833	−	0.860865i	$-0.669923\pi$
$587$	2792.14	−	2159.13i	0.196327	−	0.151817i	0.705160	+	0.709048i	$0.250875\pi$
$588$	782.706	−	191.010i	0.0548950	−	0.0133965i
$589$	−24.3906	−	123.830i	−0.00170628	−	0.00866267i
$590$	−1610.88	−	1494.68i	−0.112405	−	0.104297i
$591$	−72.4841	−	75.8124i	−0.00504500	−	0.00527666i
$592$	−19100.0	+	10649.6i	−1.32602	+	0.739354i
$593$	−3516.05	+	4408.98i	−0.243485	+	0.305321i	−0.888525	−	0.458828i	$-0.848269\pi$
$593$	−3516.05	+	4408.98i	−0.243485	+	0.305321i	0.645040	+	0.764149i	$0.276841\pi$
$594$	−18290.0	−	15038.9i	−1.26338	−	1.03881i
$595$	−824.556	+	11002.9i	−0.0568126	+	0.758112i
$596$	270.090	−	110.693i	0.0185626	−	0.00760767i
$597$	−6763.54	−	3771.17i	−0.463674	−	0.258532i
$598$	−300.559	−	1156.23i	−0.0205531	−	0.0790662i
$599$	−14593.7	−	4501.55i	−0.995460	−	0.307059i	−0.246116	−	0.969240i	$-0.579155\pi$
$599$	−14593.7	−	4501.55i	−0.995460	−	0.307059i	−0.749343	+	0.662182i	$0.769631\pi$
$600$	−5652.68	−	852.004i	−0.384616	−	0.0579715i
$601$	19334.4	−	2914.19i	1.31226	−	0.197791i	0.544624	−	0.838680i	$-0.316672\pi$
$601$	19334.4	−	2914.19i	1.31226	−	0.197791i	0.767634	+	0.640889i	$0.221434\pi$
$602$	−4083.68	+	1259.65i	−0.276475	+	0.0852814i
$603$	−1968.74	−	3185.89i	−0.132958	−	0.215157i
$604$	1206.58	+	1609.51i	0.0812829	+	0.108427i
$605$	−9319.17	+	17317.9i	−0.626245	+	1.16376i
$606$	1108.91	−	968.825i	0.0743339	−	0.0649436i
$607$	−5856.64	+	14922.5i	−0.391621	+	0.997833i	0.590070	+	0.807352i	$0.299100\pi$
$607$	−5856.64	+	14922.5i	−0.391621	+	0.997833i	−0.981691	+	0.190481i	$0.938995\pi$
$608$	44.0821	+	981.564i	0.00294040	+	0.0654731i
$609$	−804.269	+	4083.22i	−0.0535150	+	0.271692i
$610$	−8210.14	+	5965.01i	−0.544949	+	0.395928i
$611$	−425.764	−	2563.90i	−0.0281908	−	0.169761i
$612$	492.291	+	546.744i	0.0325158	+	0.0361125i
$613$	16153.2	−	19056.8i	1.06431	−	1.25562i	0.0988385	−	0.995103i	$-0.468487\pi$
$613$	16153.2	−	19056.8i	1.06431	−	1.25562i	0.965469	−	0.260519i	$-0.0838937\pi$
$614$	−2690.49	+	25598.3i	−0.176839	+	1.68251i
$615$	−7123.93	−	4256.35i	−0.467097	−	0.279077i
$616$	−10691.6	−	3651.62i	−0.699313	−	0.238844i
$617$	−12442.0	+	1496.21i	−0.811827	+	0.0976258i	−0.514874	−	0.857266i	$-0.672161\pi$
$617$	−12442.0	+	1496.21i	−0.811827	+	0.0976258i	−0.296954	+	0.954892i	$0.595971\pi$
$618$	7060.27	+	12228.8i	0.459556	+	0.795975i
$619$	−4345.58	+	7526.77i	−0.282171	+	0.488734i	−0.971919	−	0.235315i	$-0.924388\pi$
$619$	−4345.58	+	7526.77i	−0.282171	+	0.488734i	0.689748	+	0.724049i	$0.257721\pi$
$620$	−22.3243	+	52.2303i	−0.00144607	+	0.00338326i
$621$	−2048.47	+	8974.94i	−0.132371	+	0.579955i
$622$	2215.36	+	16354.4i	0.142810	+	1.05426i
$623$	1713.61	−	1903.16i	0.110200	−	0.122389i
$624$	1558.19	+	995.408i	0.0999638	+	0.0638593i
$625$	19428.5	−	1748.60i	1.24342	−	0.111910i
$626$	−11089.4	+	17945.2i	−0.708020	+	1.14574i
$627$	−1361.86	+	5238.97i	−0.0867424	+	0.333691i
$628$	1453.16	−	1519.89i	0.0923369	−	0.0965768i
$629$	24495.1	−	1467.53i	1.55275	−	0.0930276i
$630$	1303.72	−	4462.52i	0.0824470	−	0.282208i
$631$	−23618.7	+	706.879i	−1.49009	+	0.0445966i	−0.764986	−	0.644047i	$-0.777254\pi$
$631$	−23618.7	+	706.879i	−1.49009	+	0.0445966i	−0.725100	+	0.688644i	$0.758206\pi$
$632$	−21579.4			−1.35820
$633$	−12088.6	−	1705.27i	−0.759052	−	0.107075i
$634$	22024.4			1.37966
$635$	3517.31	−	105.269i	0.219811	−	0.00657870i
$636$	−22.0418	+	75.4468i	−0.00137423	+	0.00470387i
$637$	1591.62	−	95.3564i	0.0989992	−	0.00593118i
$638$	11118.3	−	11628.8i	0.689933	−	0.721614i
$639$	2969.49	−	11423.4i	0.183836	−	0.707202i
$640$	−11913.1	+	19278.2i	−0.735791	+	1.19068i
$641$	28326.7	−	2549.45i	1.74546	−	0.157094i	0.829535	−	0.558454i	$-0.188605\pi$
$641$	28326.7	−	2549.45i	1.74546	−	0.157094i	0.915920	+	0.401360i	$0.131462\pi$
$642$	−14548.0	−	9293.64i	−0.894339	−	0.571325i
$643$	−13543.8	+	15041.9i	−0.830661	+	0.922543i	−0.997991	−	0.0633584i	$-0.979819\pi$
$643$	−13543.8	+	15041.9i	−0.830661	+	0.922543i	0.167330	+	0.985901i	$0.446486\pi$
$644$	−69.2616	−	511.310i	−0.00423803	−	0.0312864i
$645$	−1745.56	+	7647.80i	−0.106560	+	0.466871i
$646$	2380.04	−	5568.38i	0.144956	−	0.339141i
$647$	9909.88	−	17164.4i	0.602160	−	1.04297i	−0.390333	−	0.920674i	$-0.627640\pi$
$647$	9909.88	−	17164.4i	0.602160	−	1.04297i	0.992493	−	0.122298i	$-0.0390264\pi$
$648$	−3239.90	−	5611.67i	−0.196413	−	0.340197i
$649$	−2773.33	+	333.505i	−0.167739	+	0.0201714i
$650$	1257.67	+	429.546i	0.0758921	+	0.0259203i
$651$	−168.547	−	100.702i	−0.0101473	−	0.00606272i
$652$	−82.1785	+	781.876i	−0.00493613	+	0.0469642i
$653$	−13575.1	+	16015.3i	−0.813531	+	0.959768i	−0.999741	−	0.0227420i	$-0.992760\pi$
$653$	−13575.1	+	16015.3i	−0.813531	+	0.959768i	0.186210	+	0.982510i	$0.440379\pi$
$654$	−6787.78	−	7538.59i	−0.405846	−	0.450737i
$655$	−90.1601	−	542.933i	−0.00537839	−	0.0323880i
$656$	−8508.06	+	6181.47i	−0.506378	+	0.367905i
$657$	−795.967	+	4041.07i	−0.0472658	+	0.239965i
$658$	−529.441	−	11788.9i	−0.0313674	−	0.698450i
$659$	−3388.98	+	8634.97i	−0.200328	+	0.510426i	−0.995369	−	0.0961290i	$-0.969354\pi$
$659$	−3388.98	+	8634.97i	−0.200328	+	0.510426i	0.795041	+	0.606555i	$0.207449\pi$
$660$	1834.63	−	1602.87i	0.108201	−	0.0945326i
$661$	−4197.73	+	7800.69i	−0.247009	+	0.459019i	−0.973665	−	0.227982i	$-0.926787\pi$
$661$	−4197.73	+	7800.69i	−0.247009	+	0.459019i	0.726657	+	0.687001i	$0.241073\pi$
$662$	2779.34	+	3707.51i	0.163175	+	0.217668i
$663$	−1090.69	−	1764.99i	−0.0638897	−	0.103389i
$664$	−13426.4	+	4141.50i	−0.784709	+	0.242051i
$665$	−3599.38	+	542.519i	−0.209892	+	0.0316361i
$666$	−10224.0	−	1541.01i	−0.594850	−	0.0896592i
$667$	−5976.97	−	1843.65i	−0.346971	−	0.107026i
$668$	35.0148	+	134.699i	0.00202809	+	0.00780189i
$669$	18111.7	+	10098.6i	1.04669	+	0.583607i
$670$	12837.2	−	5261.17i	0.740214	−	0.303368i
$671$	−964.001	+	12863.7i	−0.0554617	+	0.740086i
$672$	1180.66	+	970.791i	0.0677752	+	0.0557278i
$673$	−9946.66	+	12472.7i	−0.569711	+	0.714395i	−0.980320	−	0.197417i	$-0.936745\pi$
$673$	−9946.66	+	12472.7i	−0.569711	+	0.714395i	0.410609	+	0.911812i	$0.365316\pi$
$674$	−671.268	+	374.281i	−0.0383624	+	0.0213898i
$675$	−7077.17	−	7402.14i	−0.403556	−	0.422087i
$676$	1327.32	+	1231.58i	0.0755191	+	0.0700714i
$677$	−1962.06	−	9961.25i	−0.111386	−	0.565497i	−0.995217	−	0.0976915i	$-0.968854\pi$
$677$	−1962.06	−	9961.25i	−0.111386	−	0.565497i	0.883831	−	0.467806i	$-0.154955\pi$
$678$	17740.6	−	4329.39i	1.00490	−	0.245235i
$679$	−5073.35	+	3923.15i	−0.286741	+	0.221733i
$680$	19551.5	−	12490.0i	1.10260	−	0.704366i
$681$	−561.386	+	3380.59i	−0.0315893	+	0.190227i
$682$	339.524	+	678.860i	0.0190631	+	0.0381157i
$683$	−261.265	−	3486.34i	−0.0146369	−	0.195316i	−0.999729	−	0.0232873i	$-0.992587\pi$
$683$	−261.265	−	3486.34i	−0.0146369	−	0.195316i	0.985092	−	0.172029i	$-0.0550323\pi$
$684$	−139.709	+	198.470i	−0.00780981	+	0.0110946i
$685$	3041.65	−	8488.34i	0.169658	−	0.473464i
$686$	17533.0	+	1050.42i	0.975819	+	0.0584627i
$687$	−17935.8	+	16642.0i	−0.996060	+	0.924209i
$688$	8042.46	+	5843.19i	0.445663	+	0.323793i
$689$	−69.5819	+	139.125i	−0.00384740	+	0.00769266i
$690$	−9213.11	−	3775.89i	−0.508315	−	0.208327i
$691$	−3854.74	−	4833.70i	−0.212216	−	0.266111i	0.664318	−	0.747450i	$-0.268722\pi$
$691$	−3854.74	−	4833.70i	−0.212216	−	0.266111i	−0.876534	+	0.481339i	$0.840151\pi$
$692$	12.8273	−	857.381i	0.000704657	−	0.0470993i
$693$	−3255.55	−	4931.95i	−0.178453	−	0.270345i
$694$	5919.87	+	1258.31i	0.323797	+	0.0688252i
$695$	32813.4	−	11207.1i	1.79091	−	0.611670i
$696$	7884.06	−	3796.76i	0.429374	−	0.206776i
$697$	11611.2	−	2107.12i	0.630999	−	0.114509i
$698$	−3802.82	−	8897.15i	−0.206216	−	0.482467i
$699$	21997.4	+	2645.29i	1.19030	+	0.143139i
$700$	517.161	+	249.052i	0.0279241	+	0.0134475i
$701$	−1686.13	−	465.342i	−0.0908477	−	0.0250724i	0.220317	−	0.975428i	$-0.429291\pi$
$701$	−1686.13	−	465.342i	−0.0908477	−	0.0250724i	−0.311165	+	0.950356i	$0.600719\pi$
$702$	1010.02	+	2818.66i	0.0543029	+	0.151543i
$703$	2270.17	+	7770.55i	0.121794	+	0.416888i
$704$	7249.34	+	22311.2i	0.388096	+	1.19444i
$705$	−19226.4	−	9978.19i	−1.02710	−	0.533050i
$706$	−8798.35	−	22417.8i	−0.469023	−	1.19505i
$707$	1149.85	−	511.944i	0.0611661	−	0.0272329i
$708$	173.385	+	42.3124i	0.00920367	+	0.00224604i
$709$	1547.55	−	34458.8i	0.0819736	−	1.82528i	−0.365303	−	0.930888i	$-0.619035\pi$
$709$	1547.55	−	34458.8i	0.0819736	−	1.82528i	0.447277	−	0.894395i	$-0.352394\pi$
$710$	39943.3	+	17783.9i	2.11133	+	0.940025i
$711$	−8929.08	−	6904.73i	−0.470980	−	0.364202i
$712$	−5363.17	−	482.694i	−0.282294	−	0.0254069i
$713$	177.002	−	236.112i	0.00929703	−	0.0124018i
$714$	−3960.04	−	8547.90i	−0.207564	−	0.448035i
$715$	4138.90	−	2472.88i	0.216484	−	0.129343i
$716$	−659.700	+	140.224i	−0.0344332	+	0.00731900i
$717$	−3915.88	−	3857.73i	−0.203962	−	0.200934i
$718$	−31096.4	+	16138.5i	−1.61630	+	0.838835i
$719$	−17943.0	−	15676.3i	−0.930682	−	0.813112i	0.0519553	−	0.998649i	$-0.483455\pi$
$719$	−17943.0	−	15676.3i	−0.930682	−	0.813112i	−0.982637	+	0.185537i	$0.940598\pi$
$720$	−10125.0	+	3799.96i	−0.524077	+	0.196689i
$721$	2685.79	+	11767.2i	0.138730	+	0.607814i
$722$	−18101.0	−	3284.85i	−0.933033	−	0.169320i
$723$	−27453.0	+	7576.54i	−1.41215	+	0.389730i
$724$	−1045.62	−	1485.40i	−0.0536741	−	0.0762493i
$725$	5374.69	−	4419.31i	0.275325	−	0.226385i
$726$	−251.183	−	16789.1i	−0.0128406	−	0.858265i
$727$	3593.02	−	2449.68i	0.183298	−	0.124970i	−0.468195	−	0.883625i	$-0.655095\pi$
$727$	3593.02	−	2449.68i	0.183298	−	0.124970i	0.651493	+	0.758655i	$0.274143\pi$
$728$	923.738	+	1089.79i	0.0470275	+	0.0554810i
$729$	2647.77	−	19546.7i	0.134521	−	0.993073i
$730$	−14284.6	−	5361.09i	−0.724241	−	0.271812i
$731$	−5286.03	−	9823.10i	−0.267457	−	0.497018i
$732$	346.461	−	747.850i	0.0174939	−	0.0377614i
$733$	1326.25	+	12618.4i	0.0668295	+	0.635841i	0.975753	+	0.218877i	$0.0702392\pi$
$733$	1326.25	+	12618.4i	0.0668295	+	0.635841i	−0.908923	+	0.416964i	$0.863094\pi$
$734$	−30623.8	−	20878.9i	−1.53998	−	1.04994i
$735$	7320.98	−	11090.8i	0.367399	−	0.556586i
$736$	−1636.56	+	1612.26i	−0.0819624	+	0.0807453i
$737$	5449.49	−	16771.8i	0.272367	−	0.838260i
$738$	−4970.03	−	148.747i	−0.247899	−	0.00741933i
$739$	16837.1	+	503.915i	0.838110	+	0.0250837i	0.446214	−	0.894926i	$-0.352772\pi$
$739$	16837.1	+	503.915i	0.838110	+	0.0250837i	0.391895	+	0.920010i	$0.371820\pi$
$740$	1125.87	−	3465.06i	0.0559293	−	0.172133i
$741$	487.603	−	480.362i	0.0241735	−	0.0238145i
$742$	−389.098	+	589.458i	−0.0192510	+	0.0291640i
$743$	13759.2	+	9380.88i	0.679377	+	0.463191i	0.853199	−	0.521586i	$-0.174659\pi$
$743$	13759.2	+	9380.88i	0.679377	+	0.463191i	−0.173822	+	0.984777i	$0.555612\pi$
$744$	43.1532	+	410.576i	0.00212644	+	0.0202318i
$745$	2023.86	−	4368.59i	0.0995283	−	0.214836i
$746$	14256.6	+	26493.1i	0.699691	+	1.30024i
$747$	−6880.73	−	2582.38i	−0.337018	−	0.126485i
$748$	−465.029	+	3432.98i	−0.0227315	+	0.167811i
$749$	−9541.27	−	11256.4i	−0.465461	−	0.549130i
$750$	−7815.86	+	5328.76i	−0.380526	+	0.259438i
$751$	−542.867	−	36285.3i	−0.0263775	−	1.76307i	−0.485067	−	0.874477i	$-0.661205\pi$
$751$	−542.867	−	36285.3i	−0.0263775	−	1.76307i	0.458689	−	0.888597i	$-0.348319\pi$
$752$	−21203.5	+	17434.5i	−1.02821	+	0.845438i
$753$	16890.1	+	23994.0i	0.817411	+	1.16121i
$754$	−1961.07	+	541.221i	−0.0947188	+	0.0261407i
$755$	32646.4	+	5924.44i	1.57367	+	0.285579i
$756$	287.764	+	1260.78i	0.0138437	+	0.0606534i
$757$	4691.85	−	1760.88i	0.225268	−	0.0845446i	−0.236189	−	0.971707i	$-0.575898\pi$
$757$	4691.85	−	1760.88i	0.225268	−	0.0845446i	0.461457	+	0.887163i	$0.347327\pi$
$758$	27337.9	+	23884.4i	1.30997	+	1.14449i
$759$	−11233.7	+	5830.08i	−0.537228	+	0.278812i
$760$	5452.38	+	5371.42i	0.260235	+	0.256371i
$761$	−29970.0	+	6370.31i	−1.42761	+	0.303447i	−0.855956	−	0.517049i	$-0.827031\pi$
$761$	−29970.0	+	6370.31i	−1.42761	+	0.303447i	−0.571652	+	0.820496i	$0.693697\pi$
$762$	−2579.14	+	1540.97i	−0.122615	+	0.0732589i
$763$	−3644.89	−	7867.66i	−0.172941	−	0.373301i
$764$	−698.619	+	931.924i	−0.0330827	+	0.0441307i
$765$	12086.4	+	1087.80i	0.571223	+	0.0514110i
$766$	−997.514	−	771.363i	−0.0470517	−	0.0363845i
$767$	322.672	+	143.663i	0.0151904	+	0.00676318i
$768$	228.381	−	5085.31i	0.0107305	−	0.238933i
$769$	−2300.90	−	561.506i	−0.107897	−	0.0263309i	0.182766	−	0.983156i	$-0.441495\pi$
$769$	−2300.90	−	561.506i	−0.107897	−	0.0263309i	−0.290663	+	0.956826i	$0.593876\pi$
$770$	19998.8	−	8904.06i	0.935984	−	0.416727i
$771$	9489.49	+	24178.8i	0.443263	+	1.12941i
$772$	1972.32	+	1023.60i	0.0919501	+	0.0477206i
$773$	−7646.11	−	23532.3i	−0.355772	−	1.09495i	−0.955561	−	0.294794i	$-0.904749\pi$
$773$	−7646.11	−	23532.3i	−0.355772	−	1.09495i	0.599789	−	0.800158i	$-0.295251\pi$
$774$	1318.05	+	4511.56i	0.0612098	+	0.209515i
$775$	110.738	+	309.035i	0.00513266	+	0.0143237i
$776$	12999.0	+	3587.51i	0.601338	+	0.165959i
$777$	11346.5	+	5464.21i	0.523880	+	0.252287i
$778$	−24796.7	−	2981.91i	−1.14268	−	0.137412i
$779$	1530.08	+	3579.80i	0.0703733	+	0.164647i
$780$	−303.102	+	55.0048i	−0.0139138	+	0.00252499i
$781$	50074.0	−	24114.4i	2.29423	−	1.10484i
$782$	13399.0	−	4576.30i	0.612719	−	0.209269i
$783$	15334.0	+	3259.34i	0.699861	+	0.148760i
$784$	−9277.63	−	14055.0i	−0.422633	−	0.640261i
$785$	518.860	−	34680.7i	0.0235910	−	1.57682i
$786$	292.980	+	367.385i	0.0132955	+	0.0166720i
$787$	33090.8	+	13561.9i	1.49880	+	0.614268i	0.971845	−	0.235623i	$-0.0757129\pi$
$787$	33090.8	+	13561.9i	1.49880	+	0.614268i	0.526959	+	0.849890i	$0.323332\pi$
$788$	9.90587	−	19.8062i	0.000447820	−	0.000895391i
$789$	6500.32	+	4722.76i	0.293305	+	0.213099i
$790$	30651.1	−	28440.1i	1.38040	−	1.28083i
$791$	15581.3	+	933.495i	0.700387	+	0.0419611i
$792$	−4191.61	+	11697.5i	−0.188059	+	0.524815i
$793$	938.918	−	1333.82i	0.0420453	−	0.0597294i
$794$	−27.9680	−	373.207i	−0.00125006	−	0.0166809i
$795$	579.931	+	1159.54i	0.0258718	+	0.0517291i
$796$	267.839	−	1612.89i	0.0119263	−	0.0718185i
$797$	17440.2	−	11141.2i	0.775109	−	0.495158i	−0.0904894	−	0.995897i	$-0.528843\pi$
$797$	17440.2	−	11141.2i	0.775109	−	0.495158i	0.865598	+	0.500739i	$0.166938\pi$
$798$	2458.54	−	1901.15i	0.109062	−	0.0843359i
$799$	29925.0	−	7302.84i	1.32500	−	0.323349i
$800$	−493.899	−	2507.50i	−0.0218275	−	0.110817i
$801$	−2064.72	−	1915.78i	−0.0910777	−	0.0845078i
$802$	29855.3	+	31226.2i	1.31450	+	1.37486i
$803$	−16939.0	+	9444.75i	−0.744416	+	0.415066i
$804$	−702.517	+	880.928i	−0.0308158	+	0.0386417i
$805$	−6573.90	−	5405.36i	−0.287826	−	0.236663i
$806$	7.17244	−	95.7096i	0.000313447	−	0.00418266i
$807$	−3692.12	+	1513.17i	−0.161052	+	0.0660052i
$808$	−2311.52	−	1288.84i	−0.100642	−	0.0561155i
$809$	−28.2708	−	108.756i	−0.00122861	−	0.00472638i	0.967218	−	0.253949i	$-0.0817296\pi$
$809$	−28.2708	−	108.756i	−0.00122861	−	0.00472638i	−0.968446	+	0.249223i	$0.919825\pi$
$810$	11997.7	+	3700.81i	0.520441	+	0.160535i
$811$	20812.2	+	3136.94i	0.901129	+	0.135823i	0.583236	−	0.812303i	$-0.301786\pi$
$811$	20812.2	+	3136.94i	0.901129	+	0.135823i	0.317894	+	0.948126i	$0.397025\pi$
$812$	−868.853	+	130.958i	−0.0375502	+	0.00565978i
$813$	12695.3	−	3915.98i	0.547655	−	0.168929i
$814$	−25593.6	−	41416.4i	−1.10203	−	1.78335i
$815$	7778.30	+	10375.9i	0.334309	+	0.445952i
$816$	−10384.4	+	19297.5i	−0.445499	+	0.827877i
$817$	2771.33	−	2421.24i	0.118674	−	0.103682i
$818$	−10826.0	+	27584.3i	−0.462742	+	1.17905i
$819$	33.5253	+	746.498i	0.00143036	+	0.0318495i
$820$	338.606	−	1719.08i	0.0144203	−	0.0732108i
$821$	−4263.44	+	3097.57i	−0.181236	+	0.131676i	−0.674704	−	0.738088i	$-0.735729\pi$
$821$	−4263.44	+	3097.57i	−0.181236	+	0.131676i	0.493468	+	0.869764i	$0.335729\pi$
$822$	1261.16	+	7594.57i	0.0535136	+	0.322252i
$823$	−11500.8	−	12772.9i	−0.487111	−	0.540992i	0.448612	−	0.893727i	$-0.351918\pi$
$823$	−11500.8	−	12772.9i	−0.487111	−	0.540992i	−0.935723	+	0.352735i	$0.885252\pi$
$824$	16410.0	−	19359.8i	0.693773	−	0.818483i
$825$	1471.73	−	14002.6i	0.0621081	−	0.590919i
$826$	1376.73	+	822.559i	0.0579935	+	0.0346495i
$827$	38263.7	+	13068.6i	1.60890	+	0.549504i	0.974671	−	0.223643i	$-0.0717951\pi$
$827$	38263.7	+	13068.6i	1.60890	+	0.549504i	0.634226	+	0.773148i	$0.281319\pi$
$828$	−563.429	+	67.7549i	−0.0236480	+	0.00284377i
$829$	22677.5	+	39278.6i	0.950088	+	1.64560i	0.745229	+	0.666809i	$0.232340\pi$
$829$	22677.5	+	39278.6i	0.950088	+	1.64560i	0.204859	+	0.978792i	$0.434327\pi$
$830$	13612.6	−	23577.7i	0.569276	−	0.986015i
$831$	−2762.94	+	6464.21i	−0.115337	+	0.269845i
$832$	660.084	−	2892.02i	0.0275051	−	0.120508i
$833$	2536.69	+	18726.6i	0.105512	+	0.778917i
$834$	−19809.6	+	22000.8i	−0.822484	+	0.913461i
$835$	1934.58	+	1235.85i	0.0801782	+	0.0512198i
$836$	−1138.28	+	102.447i	−0.0470912	+	0.00423828i
$837$	−388.789	+	629.152i	−0.0160556	+	0.0259817i
$838$	7029.03	−	27040.1i	0.289754	−	1.11466i
$839$	−25677.5	+	26856.6i	−1.05660	+	1.10511i	−0.0623453	+	0.998055i	$0.519858\pi$
$839$	−25677.5	+	26856.6i	−1.05660	+	1.10511i	−0.994253	+	0.107060i	$0.965856\pi$
$840$	11885.5	−	712.074i	0.488199	−	0.0292487i
$841$	3852.38	−	13186.3i	0.157956	−	0.540667i
$842$	35178.7	−	1052.86i	1.43983	−	0.0430926i
$843$	−16629.9			−0.679434
$844$	−522.033	−	2524.16i	−0.0212904	−	0.102944i
$845$	29866.2			1.21589
$846$	−12973.0	+	388.268i	−0.527213	+	0.0157789i
$847$	4024.81	−	13776.5i	0.163275	−	0.558875i
$848$	1640.04	−	98.2571i	0.0664142	−	0.00397896i
$849$	15606.9	−	16323.6i	0.630893	−	0.659863i
$850$	−3962.79	+	15244.6i	−0.159909	+	0.615158i
$851$	−9950.11	+	16101.6i	−0.400805	+	0.648597i
$852$	−3536.75	+	318.314i	−0.142215	+	0.0127996i
$853$	−26968.3	−	17228.0i	−1.08250	−	0.691530i	−0.128616	−	0.991694i	$-0.541054\pi$
$853$	−26968.3	−	17228.0i	−1.08250	−	0.691530i	−0.953887	+	0.300165i	$0.902958\pi$
$854$	4955.75	−	5503.91i	0.198574	−	0.220539i
$855$	537.391	+	3967.18i	0.0214952	+	0.158684i
$856$	−6904.20	+	30249.3i	−0.275678	+	1.20783i
$857$	−17632.2	+	41252.7i	−0.702808	+	1.64430i	0.0604221	+	0.998173i	$0.480755\pi$
$857$	−17632.2	+	41252.7i	−0.702808	+	1.64430i	−0.763230	+	0.646127i	$0.776388\pi$
$858$	−2058.24	+	3564.98i	−0.0818965	+	0.141849i
$859$	4469.82	+	7741.95i	0.177541	+	0.307511i	0.941038	−	0.338301i	$-0.109852\pi$
$859$	4469.82	+	7741.95i	0.177541	+	0.307511i	−0.763496	+	0.645812i	$0.776519\pi$
$860$	−1644.38	+	197.744i	−0.0652010	+	0.00784071i
$861$	5731.29	+	1957.47i	0.226855	+	0.0774801i
$862$	23845.1	+	14246.8i	0.942190	+	0.562932i
$863$	1361.75	−	12956.2i	0.0537131	−	0.511046i	−0.934279	−	0.356542i	$-0.883955\pi$
$863$	1361.75	−	12956.2i	0.0537131	−	0.511046i	0.987992	−	0.154504i	$-0.0493778\pi$
$864$	3722.98	−	4392.20i	0.146595	−	0.172946i
$865$	−9463.94	−	10510.8i	−0.372004	−	0.413152i
$866$	4752.89	+	28621.3i	0.186501	+	1.12309i
$867$	4062.00	−	2951.22i	0.159115	−	0.115604i
$868$	8.01116	−	40.6722i	0.000313268	−	0.00159044i
$869$	−2384.55	−	53096.2i	−0.0930844	−	2.07269i
$870$	−6194.58	+	15783.5i	−0.241398	+	0.615071i
$871$	−1679.28	+	1467.14i	−0.0653273	+	0.0570748i
$872$	−8639.65	+	16055.2i	−0.335522	+	0.623505i
$873$	4230.84	+	5643.73i	0.164023	+	0.218799i
$874$	2455.47	+	3973.53i	0.0950315	+	0.153783i
$875$	−7726.53	+	2383.32i	−0.298519	+	0.0920810i
$876$	1225.31	−	184.686i	0.0472597	−	0.00712326i
$877$	−1323.07	−	199.421i	−0.0509429	−	0.00767841i	0.123521	−	0.992342i	$-0.460581\pi$
$877$	−1323.07	−	199.421i	−0.0509429	−	0.00767841i	−0.174464	+	0.984664i	$0.555819\pi$
$878$	13885.8	+	4283.21i	0.533740	+	0.164637i
$879$	282.364	+	1086.23i	0.0108349	+	0.0416812i
$880$	−44477.0	−	24799.2i	−1.70377	−	0.949977i
$881$	−27223.4	+	11157.2i	−1.04107	+	0.426669i	−0.834062	−	0.551671i	$-0.813991\pi$
$881$	−27223.4	+	11157.2i	−1.04107	+	0.426669i	−0.207005	+	0.978340i	$0.566371\pi$
$882$	595.036	−	7940.20i	0.0227164	−	0.303130i
$883$	3593.83	+	2955.01i	0.136967	+	0.112621i	0.701098	−	0.713065i	$-0.252693\pi$
$883$	3593.83	+	2955.01i	0.136967	+	0.112621i	−0.564131	+	0.825685i	$0.690789\pi$
$884$	273.125	−	342.488i	0.0103916	−	0.0130307i
$885$	2571.16	−	1433.61i	0.0976593	−	0.0544522i
$886$	27093.0	+	28337.1i	1.02732	+	1.07449i
$887$	−20839.0	−	19335.7i	−0.788844	−	0.731940i	0.178903	−	0.983867i	$-0.442745\pi$
$887$	−20839.0	−	19335.7i	−0.788844	−	0.731940i	−0.967746	+	0.251927i	$0.918936\pi$
$888$	−5117.51	−	25981.3i	−0.193392	−	0.981840i
$889$	−2494.88	+	608.844i	−0.0941231	+	0.0229696i
$890$	8253.96	−	6382.67i	0.310869	−	0.240391i
$891$	13449.6	−	8591.90i	0.505698	−	0.323052i
$892$	−717.229	+	4319.06i	−0.0269222	+	0.162122i
$893$	4545.57	+	9088.61i	0.170338	+	0.340581i
$894$	307.195	+	4099.23i	0.0114923	+	0.153354i
$895$	−6403.46	+	9096.73i	−0.239155	+	0.339743i
$896$	5579.05	−	15569.5i	0.208017	−	0.580512i
$897$	1597.51	+	95.7093i	0.0594643	+	0.00356259i
$898$	−12332.2	+	11442.7i	−0.458277	+	0.425218i
$899$	−406.542	−	295.370i	−0.0150822	−	0.0109579i
$900$	282.392	−	564.627i	0.0104590	−	0.0209121i
$901$	−1705.92	−	699.150i	−0.0630769	−	0.0258514i
$902$	−14598.0	−	18305.3i	−0.538868	−	0.675720i
$903$	85.6414	−	5724.28i	0.00315611	−	0.210955i
$904$	−18081.0	−	27391.6i	−0.665227	−	1.00778i
$905$	−29307.7	−	6229.55i	−1.07649	−	0.228815i
$906$	−26808.2	+	9156.11i	−0.983050	+	0.335752i
$907$	−13544.3	+	6522.60i	−0.495845	+	0.238786i	−0.665056	−	0.746793i	$-0.731592\pi$
$907$	−13544.3	+	6522.60i	−0.495845	+	0.238786i	0.169211	+	0.985580i	$0.445878\pi$
$908$	−711.901	+	129.191i	−0.0260190	+	0.00472176i
$909$	−544.069	−	1272.91i	−0.0198522	−	0.0464465i
$910$	−2748.33	−	330.499i	−0.100117	−	0.0120395i
$911$	−3445.24	−	1659.14i	−0.125297	−	0.0603401i	0.370185	−	0.928958i	$-0.379294\pi$
$911$	−3445.24	−	1659.14i	−0.125297	−	0.0603401i	−0.495482	+	0.868618i	$0.665009\pi$
$912$	−6968.91	−	1923.30i	−0.253031	−	0.0698320i
$913$	−11673.8	−	32578.2i	−0.423163	−	1.18092i
$914$	−5201.89	−	17805.6i	−0.188253	−	0.644372i
$915$	−4201.04	−	12929.5i	−0.151784	−	0.467142i
$916$	−4585.14	−	2379.61i	−0.165390	−	0.0858346i
$917$	146.743	+	373.895i	0.00528449	+	0.0134647i
$918$	−32418.5	+	14433.6i	−1.16554	+	0.518934i
$919$	29035.1	+	7085.66i	1.04220	+	0.254335i	0.721187	−	0.692740i	$-0.243597\pi$
$919$	29035.1	+	7085.66i	1.04220	+	0.254335i	0.321010	+	0.947076i	$0.395978\pi$
$920$	−802.877	+	17877.5i	−0.0287718	+	0.640655i
$921$	−31499.8	−	14024.6i	−1.12699	−	0.501767i
$922$	−636.591	−	492.267i	−0.0227386	−	0.0175835i
$923$	−6999.44	−	629.961i	−0.249609	−	0.0224652i
$924$	−1066.45	+	1422.59i	−0.0379692	+	0.0506491i
$925$	−8851.27	−	19105.8i	−0.314625	−	0.679131i
$926$	11889.4	−	7103.57i	0.421932	−	0.252093i
$927$	12984.6	−	2759.97i	0.460056	−	0.0977879i
$928$	2786.91	+	2745.53i	0.0985828	+	0.0971189i
$929$	−13153.6	+	6826.51i	−0.464538	+	0.241088i	−0.676860	−	0.736112i	$-0.736660\pi$
$929$	−13153.6	+	6826.51i	−0.464538	+	0.241088i	0.212321	+	0.977200i	$0.431898\pi$
$930$	−602.404	−	526.305i	−0.0212405	−	0.0185572i
$931$	−5836.77	+	2190.58i	−0.205470	+	0.0771141i
$932$	1040.92	+	4560.55i	0.0365841	+	0.160285i
$933$	−21753.5	−	3947.68i	−0.763320	−	0.138522i
$934$	29502.8	−	8142.27i	1.03358	−	0.285250i
$935$	32892.2	+	46726.5i	1.15047	+	1.63435i
$936$	1213.64	−	997.909i	0.0423815	−	0.0348479i
$937$	−600.453	−	40134.3i	−0.0209348	−	1.39929i	−0.724803	−	0.688956i	$-0.758069\pi$
$937$	−600.453	−	40134.3i	−0.0209348	−	1.39929i	0.703868	−	0.710330i	$-0.251454\pi$
$938$	−8365.57	+	5703.55i	−0.291200	+	0.198537i
$939$	−18272.6	−	21557.2i	−0.635040	−	0.749192i
$940$	613.909	−	4532.06i	0.0213016	−	0.157255i
$941$	−30676.0	−	11512.9i	−1.06271	−	0.398842i	−0.242053	−	0.970263i	$-0.577821\pi$
$941$	−30676.0	−	11512.9i	−1.06271	−	0.398842i	−0.820657	+	0.571421i	$0.806392\pi$
$942$	14033.0	+	26077.6i	0.485371	+	0.901970i
$943$	−3826.30	+	8259.22i	−0.132133	+	0.285214i
$944$	−389.954	−	3710.16i	−0.0134448	−	0.127919i
$945$	17624.2	+	12016.0i	0.606683	+	0.413630i
$946$	−12192.5	+	18470.8i	−0.419040	+	0.634818i
$947$	14939.3	−	14717.5i	0.512633	−	0.505021i	−0.398480	−	0.917177i	$-0.630462\pi$
$947$	14939.3	−	14717.5i	0.512633	−	0.505021i	0.911113	+	0.412156i	$0.135224\pi$
$948$	−1049.39	+	3229.69i	−0.0359521	+	0.110649i
$949$	2451.26	+	73.3634i	0.0838475	+	0.00250946i
$950$	−5193.97	−	155.450i	−0.177384	−	0.00530890i
$951$	−9117.35	+	28060.3i	−0.310884	+	0.956802i
$952$	−12061.8	+	11882.7i	−0.410635	+	0.404537i
$953$	4004.72	−	6066.89i	0.136123	−	0.206218i	−0.760118	−	0.649785i	$-0.774859\pi$
$953$	4004.72	−	6066.89i	0.136123	−	0.206218i	0.896241	+	0.443567i	$0.146287\pi$
$954$	641.828	+	437.591i	0.0217819	+	0.0148507i
$955$	2008.13	+	19106.1i	0.0680435	+	0.647390i
$956$	487.859	−	1053.06i	0.0165047	−	0.0356261i
$957$	10213.2	+	18979.2i	0.344979	+	0.641078i
$958$	5935.29	+	2227.55i	0.200168	+	0.0751242i
$959$	−883.324	+	6520.96i	−0.0297435	+	0.219575i
$960$	−15986.2	−	18859.8i	−0.537449	−	0.634058i
$961$	−24594.9	+	16768.5i	−0.825581	+	0.562872i
$962$	92.0943	+	6155.59i	0.00308653	+	0.206304i
$963$	−12535.7	+	10307.4i	−0.419476	+	0.344912i
$964$	−3461.14	−	4916.88i	−0.115639	−	0.164276i
$965$	35331.9	−	9750.98i	1.17863	−	0.325280i
$966$	7149.75	+	1297.49i	0.238136	+	0.0432154i
$967$	5603.94	+	24552.5i	0.186361	+	0.816499i	0.978515	+	0.206178i	$0.0661025\pi$
$967$	5603.94	+	24552.5i	0.186361	+	0.816499i	−0.792154	+	0.610321i	$0.791040\pi$
$968$	−28254.1	+	10603.9i	−0.938141	+	0.352090i
$969$	6109.16	+	5337.41i	0.202533	+	0.176948i
$970$	−23191.8	+	12036.2i	−0.767674	+	0.398410i
$971$	−7802.86	−	7686.99i	−0.257884	−	0.254055i	0.561264	−	0.827637i	$-0.310315\pi$
$971$	−7802.86	−	7686.99i	−0.257884	−	0.254055i	−0.819148	+	0.573582i	$0.805553\pi$
$972$	2376.23	−	505.084i	0.0784133	−	0.0166673i
$973$	−21723.5	+	12979.2i	−0.715748	+	0.427640i
$974$	−23818.7	−	51413.7i	−0.783573	−	1.69138i
$975$	−1067.90	+	1424.52i	−0.0350770	+	0.0467910i
$976$	−17158.9	−	1544.33i	−0.562750	−	0.0506484i
$977$	18849.6	+	14576.1i	0.617248	+	0.477309i	0.871874	−	0.489731i	$-0.162905\pi$
$977$	18849.6	+	14576.1i	0.617248	+	0.477309i	−0.254626	+	0.967040i	$0.581952\pi$
$978$	−10114.6	−	4503.30i	−0.330704	−	0.147239i
$979$	595.034	−	13249.5i	0.0194253	−	0.432538i
$980$	2725.80	+	665.197i	0.0888493	+	0.0216826i
$981$	−8712.07	+	3878.86i	−0.283542	+	0.126241i
$982$	14393.1	+	36673.0i	0.467722	+	1.19174i
$983$	7531.73	+	3908.85i	0.244379	+	0.126829i	0.578446	−	0.815720i	$-0.303659\pi$
$983$	7531.73	+	3908.85i	0.244379	+	0.126829i	−0.334067	+	0.942549i	$0.608421\pi$
$984$	−3935.18	−	12111.2i	−0.127489	−	0.392370i
$985$	−102.433	−	350.618i	−0.00331349	−	0.0113418i
$986$	−8133.48	−	22698.1i	−0.262701	−	0.733118i
$987$	15238.9	+	4205.67i	0.491448	+	0.135631i
$988$	130.203	+	62.7027i	0.00419264	+	0.00201907i
$989$	8542.81	+	1027.31i	0.274667	+	0.0330299i
$990$	−9462.79	−	22139.3i	−0.303785	−	0.710741i
$991$	24789.2	−	4498.57i	0.794606	−	0.144200i	0.233950	−	0.972249i	$-0.424835\pi$
$991$	24789.2	−	4498.57i	0.794606	−	0.144200i	0.560656	+	0.828049i	$0.310549\pi$
$992$	−166.288	+	80.0803i	−0.00532224	+	0.00256306i
$993$	−5874.12	+	2006.25i	−0.187724	+	0.0641153i
$994$	−31212.1	−	6634.34i	−0.995965	−	0.211699i
$995$	−14856.7	−	22506.9i	−0.473355	−	0.717103i
$996$	−33.0771	+	2210.87i	−0.00105230	+	0.0703356i
$997$	−14067.3	−	17639.9i	−0.446857	−	0.560341i	0.506479	−	0.862252i	$-0.330947\pi$
$997$	−14067.3	−	17639.9i	−0.446857	−	0.560341i	−0.953336	+	0.301911i	$0.902375\pi$
$998$	38515.8	+	15785.2i	1.22164	+	0.500675i
$999$	21220.1	−	42428.4i	0.672047	−	1.34372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	211.4.o.a.53.13	yes	2496
211.4	even	105	inner	211.4.o.a.4.13	✓	2496

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
211.4.o.a.4.13	✓	2496	211.4	even	105	inner
211.4.o.a.53.13	yes	2496	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 211 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	211.o (of order \(105\), degree \(48\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.97205 + 0.0889500i) q^{2} +(1.11700 - 3.82337i) q^{3} +(0.839479 - 0.0502943i) q^{4} +(9.58614 - 10.0263i) q^{5} +(-2.97968 + 11.4626i) q^{6} +(-5.32177 + 8.61188i) q^{7} +(21.2008 - 1.90810i) q^{8} +(9.38297 + 5.99407i) q^{9} +O(q^{10})\)	\(q+(-2.97205 + 0.0889500i) q^{2} +(1.11700 - 3.82337i) q^{3} +(0.839479 - 0.0502943i) q^{4} +(9.58614 - 10.0263i) q^{5} +(-2.97968 + 11.4626i) q^{6} +(-5.32177 + 8.61188i) q^{7} +(21.2008 - 1.90810i) q^{8} +(9.38297 + 5.99407i) q^{9} +(-27.5986 + 30.6514i) q^{10} +(7.03762 + 51.9538i) q^{11} +(0.745402 - 3.26582i) q^{12} +(2.60554 - 6.09597i) q^{13} +(15.0505 - 26.0683i) q^{14} +(-27.6267 - 47.8508i) q^{15} +(-69.5198 + 8.36006i) q^{16} +(74.3546 + 25.3952i) q^{17} +(-28.4198 - 16.9800i) q^{18} +(-2.70945 + 25.7787i) q^{19} +(7.54310 - 8.89901i) q^{20} +(26.9820 + 29.9666i) q^{21} +(-25.5375 - 153.783i) q^{22} +(-49.0310 + 35.6231i) q^{23} +(16.3858 - 83.1898i) q^{24} +(-3.02484 - 67.3533i) q^{25} +(-7.20156 + 18.3493i) q^{26} +(114.388 - 99.9381i) q^{27} +(-4.03439 + 7.49715i) q^{28} +(61.9052 + 82.5785i) q^{29} +(86.3641 + 139.757i) q^{30} +(-4.65272 + 1.43517i) q^{31} +(37.4827 - 5.64961i) q^{32} +(206.500 + 31.1248i) q^{33} +(-223.244 - 68.8618i) q^{34} +(35.3302 + 135.913i) q^{35} +(8.17827 + 4.55998i) q^{36} +(288.985 - 118.437i) q^{37} +(5.75961 - 76.8566i) q^{38} +(-20.3968 - 16.7711i) q^{39} +(184.102 - 230.857i) q^{40} +(131.179 - 73.1419i) q^{41} +(-82.8574 - 86.6621i) q^{42} +(-104.073 - 96.5661i) q^{43} +(8.52092 + 43.2602i) q^{44} +(150.045 - 36.6166i) q^{45} +(142.554 - 110.235i) q^{46} +(330.380 - 211.055i) q^{47} +(-45.6898 + 275.138i) q^{48} +(107.585 + 215.110i) q^{49} +(14.9811 + 199.908i) q^{50} +(180.149 - 255.919i) q^{51} +(1.88070 - 5.24848i) q^{52} +(-23.4222 - 1.40326i) q^{53} +(-331.078 + 307.196i) q^{54} +(588.369 + 427.475i) q^{55} +(-96.3934 + 192.733i) q^{56} +(95.5352 + 39.1540i) q^{57} +(-191.330 - 239.921i) q^{58} +(-0.797016 + 53.2726i) q^{59} +(-25.5986 - 38.7802i) q^{60} +(240.669 + 51.1558i) q^{61} +(13.7005 - 4.67927i) q^{62} +(-101.554 + 48.9059i) q^{63} +(440.265 - 79.8963i) q^{64} +(-36.1430 - 84.5609i) q^{65} +(-616.496 - 74.1364i) q^{66} +(-303.052 - 145.942i) q^{67} +(63.6963 + 17.5791i) q^{68} +(81.4329 + 227.255i) q^{69} +(-117.093 - 400.796i) q^{70} +(-327.581 - 1008.19i) q^{71} +(210.364 + 109.175i) q^{72} +(135.146 + 344.347i) q^{73} +(-848.341 + 377.706i) q^{74} +(-260.896 - 63.6684i) q^{75} +(-0.978004 + 21.7770i) q^{76} +(-484.873 - 215.879i) q^{77} +(62.1120 + 48.0304i) q^{78} +(-1009.68 - 90.8727i) q^{79} +(-582.606 + 777.168i) q^{80} +(-127.961 - 276.209i) q^{81} +(-383.364 + 229.050i) q^{82} +(-645.650 + 137.237i) q^{83} +(24.1580 + 23.7993i) q^{84} +(967.394 - 502.062i) q^{85} +(317.901 + 277.742i) q^{86} +(384.876 - 144.447i) q^{87} +(248.336 + 1088.03i) q^{88} +(-248.905 - 45.1696i) q^{89} +(-442.684 + 122.173i) q^{90} +(38.6317 + 54.8800i) q^{91} +(-39.3688 + 32.3708i) q^{92} +(0.290128 + 19.3922i) q^{93} +(-963.131 + 656.652i) q^{94} +(232.493 + 274.284i) q^{95} +(20.2675 - 149.621i) q^{96} +(593.106 + 222.596i) q^{97} +(-338.882 - 629.749i) q^{98} +(-245.381 + 529.665i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2496 q - 44 q^{2} - 56 q^{3} - 270 q^{4} - 50 q^{5} - 89 q^{6} - 55 q^{7} + 211 q^{8} - 596 q^{9}+O(q^{10}) \) 2496 * q - 44 * q^2 - 56 * q^3 - 270 * q^4 - 50 * q^5 - 89 * q^6 - 55 * q^7 + 211 * q^8 - 596 * q^9	\( 2496 q - 44 q^{2} - 56 q^{3} - 270 q^{4} - 50 q^{5} - 89 q^{6} - 55 q^{7} + 211 q^{8} - 596 q^{9} - 113 q^{10} - 122 q^{11} - 762 q^{12} - 126 q^{13} + 25 q^{14} - 1511 q^{15} - 1994 q^{16} - 92 q^{17} - 717 q^{18} - 177 q^{19} - 238 q^{20} + 456 q^{21} - 1073 q^{22} - 1168 q^{23} - 1104 q^{24} + 2030 q^{25} + 1476 q^{26} + 1066 q^{27} + 1399 q^{28} + 307 q^{29} - 1475 q^{30} - 1544 q^{31} + 4027 q^{32} + 445 q^{33} + 1565 q^{34} - 1350 q^{35} + 3080 q^{36} + 1831 q^{37} + 1812 q^{38} - 794 q^{39} - 5788 q^{40} - 175 q^{41} + 2276 q^{42} - 4278 q^{43} + 4022 q^{44} + 205 q^{45} - 138 q^{46} + 1921 q^{47} - 8817 q^{48} - 2291 q^{49} - 212 q^{50} - 3222 q^{51} - 8923 q^{52} - 3859 q^{53} - 1402 q^{54} - 2984 q^{55} + 3512 q^{56} - 3181 q^{57} + 2194 q^{58} - 4252 q^{59} + 2334 q^{60} - 964 q^{61} + 829 q^{62} + 169 q^{63} + 7061 q^{64} + 1166 q^{65} + 3166 q^{66} - 5721 q^{67} + 3037 q^{68} + 2580 q^{69} + 2878 q^{70} - 3364 q^{71} + 11440 q^{72} + 6320 q^{73} + 9408 q^{74} + 353 q^{75} - 5224 q^{76} - 1509 q^{77} + 6631 q^{78} - 542 q^{79} - 2155 q^{80} - 3451 q^{81} + 21513 q^{82} + 183 q^{83} + 23087 q^{84} - 16600 q^{85} - 134 q^{86} + 11238 q^{87} - 6171 q^{88} - 209 q^{89} - 22438 q^{90} - 19392 q^{91} - 16409 q^{92} + 14536 q^{93} - 26379 q^{94} + 11081 q^{95} - 5408 q^{96} + 5034 q^{97} + 16030 q^{98} - 25788 q^{99}+O(q^{100}) \) 2496 * q - 44 * q^2 - 56 * q^3 - 270 * q^4 - 50 * q^5 - 89 * q^6 - 55 * q^7 + 211 * q^8 - 596 * q^9 - 113 * q^10 - 122 * q^11 - 762 * q^12 - 126 * q^13 + 25 * q^14 - 1511 * q^15 - 1994 * q^16 - 92 * q^17 - 717 * q^18 - 177 * q^19 - 238 * q^20 + 456 * q^21 - 1073 * q^22 - 1168 * q^23 - 1104 * q^24 + 2030 * q^25 + 1476 * q^26 + 1066 * q^27 + 1399 * q^28 + 307 * q^29 - 1475 * q^30 - 1544 * q^31 + 4027 * q^32 + 445 * q^33 + 1565 * q^34 - 1350 * q^35 + 3080 * q^36 + 1831 * q^37 + 1812 * q^38 - 794 * q^39 - 5788 * q^40 - 175 * q^41 + 2276 * q^42 - 4278 * q^43 + 4022 * q^44 + 205 * q^45 - 138 * q^46 + 1921 * q^47 - 8817 * q^48 - 2291 * q^49 - 212 * q^50 - 3222 * q^51 - 8923 * q^52 - 3859 * q^53 - 1402 * q^54 - 2984 * q^55 + 3512 * q^56 - 3181 * q^57 + 2194 * q^58 - 4252 * q^59 + 2334 * q^60 - 964 * q^61 + 829 * q^62 + 169 * q^63 + 7061 * q^64 + 1166 * q^65 + 3166 * q^66 - 5721 * q^67 + 3037 * q^68 + 2580 * q^69 + 2878 * q^70 - 3364 * q^71 + 11440 * q^72 + 6320 * q^73 + 9408 * q^74 + 353 * q^75 - 5224 * q^76 - 1509 * q^77 + 6631 * q^78 - 542 * q^79 - 2155 * q^80 - 3451 * q^81 + 21513 * q^82 + 183 * q^83 + 23087 * q^84 - 16600 * q^85 - 134 * q^86 + 11238 * q^87 - 6171 * q^88 - 209 * q^89 - 22438 * q^90 - 19392 * q^91 - 16409 * q^92 + 14536 * q^93 - 26379 * q^94 + 11081 * q^95 - 5408 * q^96 + 5034 * q^97 + 16030 * q^98 - 25788 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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