LMFDB - Embedded newform 27.4.e.a.25.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,4,Mod(4,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

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("27.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, degree $6$, 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:	$1.59305157015$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.5
Character	$\chi$	$=$	27.25
Dual form			27.4.e.a.13.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.111911 - 0.634678i) q^{2} +(-0.446524 + 5.17693i) q^{3} +(7.12725 + 2.59411i) q^{4} +(-0.393954 + 0.330567i) q^{5} +(3.23571 + 0.862753i) q^{6} +(9.02395 - 3.28445i) q^{7} +(5.02191 - 8.69820i) q^{8} +(-26.6012 - 4.62325i) q^{9} +O(q^{10})$	\(q+(0.111911 - 0.634678i) q^{2} +(-0.446524 + 5.17693i) q^{3} +(7.12725 + 2.59411i) q^{4} +(-0.393954 + 0.330567i) q^{5} +(3.23571 + 0.862753i) q^{6} +(9.02395 - 3.28445i) q^{7} +(5.02191 - 8.69820i) q^{8} +(-26.6012 - 4.62325i) q^{9} +(0.165716 + 0.287028i) q^{10} +(-31.1376 - 26.1275i) q^{11} +(-16.6120 + 35.7389i) q^{12} +(-0.304384 - 1.72625i) q^{13} +(-1.07469 - 6.09486i) q^{14} +(-1.53541 - 2.18708i) q^{15} +(41.5229 + 34.8419i) q^{16} +(-37.5984 - 65.1223i) q^{17} +(-5.91124 + 16.3658i) q^{18} +(42.1545 - 73.0137i) q^{19} +(-3.66533 + 1.33407i) q^{20} +(12.9740 + 48.1829i) q^{21} +(-20.0672 + 16.8384i) q^{22} +(121.405 + 44.1880i) q^{23} +(42.7876 + 29.8820i) q^{24} +(-21.6601 + 122.841i) q^{25} -1.12968 q^{26} +(35.8123 - 135.648i) q^{27} +72.8361 q^{28} +(-45.3923 + 257.433i) q^{29} +(-1.55992 + 0.729733i) q^{30} +(-284.215 - 103.446i) q^{31} +(88.3123 - 74.1029i) q^{32} +(149.164 - 149.530i) q^{33} +(-45.5393 + 16.5750i) q^{34} +(-2.46929 + 4.27694i) q^{35} +(-177.600 - 101.957i) q^{36} +(-103.323 - 178.961i) q^{37} +(-41.6226 - 34.9255i) q^{38} +(9.07259 - 0.804965i) q^{39} +(0.896935 + 5.08677i) q^{40} +(54.5513 + 309.376i) q^{41} +(32.0325 - 2.84209i) q^{42} +(99.6799 + 83.6413i) q^{43} +(-154.148 - 266.991i) q^{44} +(12.0080 - 6.97214i) q^{45} +(41.6317 - 72.1082i) q^{46} +(-186.753 + 67.9727i) q^{47} +(-198.915 + 199.404i) q^{48} +(-192.109 + 161.199i) q^{49} +(75.5401 + 27.4944i) q^{50} +(353.922 - 165.566i) q^{51} +(2.30865 - 13.0930i) q^{52} +527.620 q^{53} +(-82.0852 - 37.9098i) q^{54} +20.9037 q^{55} +(16.7487 - 94.9863i) q^{56} +(359.164 + 250.833i) q^{57} +(158.307 + 57.6190i) q^{58} +(-59.2219 + 49.6931i) q^{59} +(-5.26974 - 19.5709i) q^{60} +(251.901 - 91.6844i) q^{61} +(-97.4613 + 168.808i) q^{62} +(-255.233 + 45.6504i) q^{63} +(179.669 + 311.196i) q^{64} +(0.690554 + 0.579443i) q^{65} +(-78.2106 - 111.405i) q^{66} +(15.6338 + 88.6636i) q^{67} +(-99.0389 - 561.677i) q^{68} +(-282.968 + 608.776i) q^{69} +(2.43814 + 2.04584i) q^{70} +(-360.735 - 624.811i) q^{71} +(-173.803 + 208.165i) q^{72} +(66.7796 - 115.666i) q^{73} +(-125.145 + 45.5491i) q^{74} +(-626.265 - 166.984i) q^{75} +(489.851 - 411.034i) q^{76} +(-366.798 - 133.504i) q^{77} +(0.504427 - 5.84825i) q^{78} +(21.9986 - 124.760i) q^{79} -27.8757 q^{80} +(686.251 + 245.968i) q^{81} +202.459 q^{82} +(146.748 - 832.248i) q^{83} +(-32.5231 + 377.068i) q^{84} +(36.3393 + 13.2264i) q^{85} +(64.2405 - 53.9042i) q^{86} +(-1312.44 - 349.943i) q^{87} +(-383.633 + 139.631i) q^{88} +(-693.455 + 1201.10i) q^{89} +(-3.08124 - 8.40144i) q^{90} +(-8.41652 - 14.5778i) q^{91} +(750.658 + 629.877i) q^{92} +(662.440 - 1425.17i) q^{93} +(22.2410 + 126.135i) q^{94} +(7.52897 + 42.6989i) q^{95} +(344.192 + 490.276i) q^{96} +(-216.678 - 181.815i) q^{97} +(80.8102 + 139.967i) q^{98} +(707.504 + 838.981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.111911	−	0.634678i	0.0395664	−	0.224392i	−0.958613	−	0.284714i	$-0.908101\pi$
$2$	0.111911	−	0.634678i	0.0395664	−	0.224392i	0.998179	+	0.0603214i	$0.0192126\pi$
$3$	−0.446524	+	5.17693i	−0.0859336	+	0.996301i
$3$	−0.446524	+	5.17693i	−0.0859336	+	0.996301i
$4$	7.12725	+	2.59411i	0.890906	+	0.324263i
$5$	−0.393954	+	0.330567i	−0.0352363	+	0.0295668i	−0.660236	−	0.751058i	$-0.729544\pi$
$5$	−0.393954	+	0.330567i	−0.0352363	+	0.0295668i	0.624999	+	0.780625i	$0.285099\pi$
$6$	3.23571	+	0.862753i	0.220162	+	0.0587029i
$7$	9.02395	−	3.28445i	0.487247	−	0.177344i	−0.0867021	−	0.996234i	$-0.527633\pi$
$7$	9.02395	−	3.28445i	0.487247	−	0.177344i	0.573949	+	0.818891i	$0.305411\pi$
$8$	5.02191	−	8.69820i	0.221939	−	0.384410i
$9$	−26.6012	−	4.62325i	−0.985231	−	0.171231i
$10$	0.165716	+	0.287028i	0.00524039	+	0.00907662i
$11$	−31.1376	−	26.1275i	−0.853484	−	0.716158i	0.107070	−	0.994252i	$-0.465853\pi$
$11$	−31.1376	−	26.1275i	−0.853484	−	0.716158i	−0.960554	+	0.278093i	$0.910298\pi$
$12$	−16.6120	+	35.7389i	−0.399623	+	0.859745i
$13$	−0.304384	−	1.72625i	−0.00649392	−	0.0368289i	0.981389	−	0.192032i	$-0.0615078\pi$
$13$	−0.304384	−	1.72625i	−0.00649392	−	0.0368289i	−0.987883	+	0.155203i	$0.950397\pi$
$14$	−1.07469	−	6.09486i	−0.0205159	−	0.116351i
$15$	−1.53541	−	2.18708i	−0.0264294	−	0.0376468i
$16$	41.5229	+	34.8419i	0.648796	+	0.544405i
$17$	−37.5984	−	65.1223i	−0.536409	−	0.929087i	−0.999094	−	0.0425646i	$-0.986447\pi$
$17$	−37.5984	−	65.1223i	−0.536409	−	0.929087i	0.462685	−	0.886523i	$-0.346886\pi$
$18$	−5.91124	+	16.3658i	−0.0774051	+	0.214303i
$19$	42.1545	−	73.0137i	0.508995	−	0.881605i	−0.490951	−	0.871187i	$-0.663350\pi$
$19$	42.1545	−	73.0137i	0.508995	−	0.881605i	0.999946	−	0.0104179i	$-0.00331617\pi$
$20$	−3.66533	+	1.33407i	−0.0409797	+	0.0149154i
$21$	12.9740	+	48.1829i	0.134817	+	0.500685i
$22$	−20.0672	+	16.8384i	−0.194470	+	0.163180i
$23$	121.405	+	44.1880i	1.10064	+	0.400601i	0.827553	−	0.561388i	$-0.189732\pi$
$23$	121.405	+	44.1880i	1.10064	+	0.400601i	0.273089	+	0.961989i	$0.411954\pi$
$24$	42.7876	+	29.8820i	0.363916	+	0.254152i
$25$	−21.6601	+	122.841i	−0.173281	+	0.982724i
$26$	−1.12968			−0.00852106
$27$	35.8123	−	135.648i	0.255262	−	0.966872i
$28$	72.8361			0.491598
$29$	−45.3923	+	257.433i	−0.290660	+	1.64841i	0.393677	+	0.919249i	$0.371203\pi$
$29$	−45.3923	+	257.433i	−0.290660	+	1.64841i	−0.684337	+	0.729166i	$0.739908\pi$
$30$	−1.55992	+	0.729733i	−0.00949337	+	0.00444102i
$31$	−284.215	−	103.446i	−1.64666	−	0.599335i	−0.658475	−	0.752603i	$-0.728798\pi$
$31$	−284.215	−	103.446i	−1.64666	−	0.599335i	−0.988185	+	0.153267i	$0.951020\pi$
$32$	88.3123	−	74.1029i	0.487861	−	0.409364i
$33$	149.164	−	149.530i	0.786852	−	0.788785i
$34$	−45.5393	+	16.5750i	−0.229704	+	0.0836054i
$35$	−2.46929	+	4.27694i	−0.0119253	+	0.0206553i
$36$	−177.600	−	101.957i	−0.822224	−	0.472025i
$37$	−103.323	−	178.961i	−0.459086	−	0.795161i	0.539827	−	0.841776i	$-0.318490\pi$
$37$	−103.323	−	178.961i	−0.459086	−	0.795161i	−0.998913	+	0.0466154i	$0.985156\pi$
$38$	−41.6226	−	34.9255i	−0.177686	−	0.149097i
$39$	9.07259	−	0.804965i	0.0372507	−	0.00330506i
$40$	0.896935	+	5.08677i	0.00354545	+	0.0201072i
$41$	54.5513	+	309.376i	0.207792	+	1.17845i	0.892985	+	0.450087i	$0.148607\pi$
$41$	54.5513	+	309.376i	0.207792	+	1.17845i	−0.685192	+	0.728362i	$0.740282\pi$
$42$	32.0325	−	2.84209i	0.117684	−	0.0104415i
$43$	99.6799	+	83.6413i	0.353513	+	0.296632i	0.802199	−	0.597057i	$-0.203663\pi$
$43$	99.6799	+	83.6413i	0.353513	+	0.296632i	−0.448686	+	0.893689i	$0.648108\pi$
$44$	−154.148	−	266.991i	−0.528151	−	0.914784i
$45$	12.0080	−	6.97214i	0.0397787	−	0.0230965i
$46$	41.6317	−	72.1082i	0.133440	−	0.231125i
$47$	−186.753	+	67.9727i	−0.579591	+	0.210954i	−0.615145	−	0.788414i	$-0.710903\pi$
$47$	−186.753	+	67.9727i	−0.579591	+	0.210954i	0.0355541	+	0.999368i	$0.488680\pi$
$48$	−198.915	+	199.404i	−0.598144	+	0.599613i
$49$	−192.109	+	161.199i	−0.560085	+	0.469967i
$50$	75.5401	+	27.4944i	0.213660	+	0.0777658i
$51$	353.922	−	165.566i	0.971746	−	0.454585i
$52$	2.30865	−	13.0930i	0.00615677	−	0.0349168i
$53$	527.620			1.36744			0.683719	−	0.729746i	$-0.260362\pi$
$53$	527.620			1.36744			0.683719	+	0.729746i	$0.260362\pi$
$54$	−82.0852	−	37.9098i	−0.206859	−	0.0955346i
$55$	20.9037			0.0512482
$56$	16.7487	−	94.9863i	0.0399667	−	0.226662i
$57$	359.164	+	250.833i	0.834604	+	0.582872i
$58$	158.307	+	57.6190i	0.358391	+	0.130444i
$59$	−59.2219	+	49.6931i	−0.130679	+	0.109652i	−0.705784	−	0.708427i	$-0.749405\pi$
$59$	−59.2219	+	49.6931i	−0.130679	+	0.109652i	0.575106	+	0.818079i	$0.304961\pi$
$60$	−5.26974	−	19.5709i	−0.0113387	−	0.0421098i
$61$	251.901	−	91.6844i	0.528731	−	0.192442i	−0.0638405	−	0.997960i	$-0.520335\pi$
$61$	251.901	−	91.6844i	0.528731	−	0.192442i	0.592572	+	0.805518i	$0.298113\pi$
$62$	−97.4613	+	168.808i	−0.199639	+	0.345784i
$63$	−255.233	+	45.6504i	−0.510418	+	0.0912923i
$64$	179.669	+	311.196i	0.350916	+	0.607805i
$65$	0.690554	+	0.579443i	0.00131773	+	0.00110571i
$66$	−78.2106	−	111.405i	−0.145864	−	0.207773i
$67$	15.6338	+	88.6636i	0.0285070	+	0.161671i	0.995738	−	0.0922265i	$-0.0293984\pi$
$67$	15.6338	+	88.6636i	0.0285070	+	0.161671i	−0.967231	+	0.253898i	$0.918287\pi$
$68$	−99.0389	−	561.677i	−0.176621	−	1.00167i
$69$	−282.968	+	608.776i	−0.493701	+	1.06215i
$70$	2.43814	+	2.04584i	0.00416304	+	0.00349321i
$71$	−360.735	−	624.811i	−0.602977	−	1.04439i	−0.992368	−	0.123314i	$-0.960648\pi$
$71$	−360.735	−	624.811i	−0.602977	−	1.04439i	0.389391	−	0.921073i	$-0.372686\pi$
$72$	−173.803	+	208.165i	−0.284484	+	0.340730i
$73$	66.7796	−	115.666i	0.107068	−	0.185447i	−0.807513	−	0.589849i	$-0.799187\pi$
$73$	66.7796	−	115.666i	0.107068	−	0.185447i	0.914581	+	0.404402i	$0.132520\pi$
$74$	−125.145	+	45.5491i	−0.196592	+	0.0715538i
$75$	−626.265	−	166.984i	−0.964198	−	0.257089i
$76$	489.851	−	411.034i	0.739339	−	0.620379i
$77$	−366.798	−	133.504i	−0.542864	−	0.197586i
$78$	0.504427	−	5.84825i	0.000732245	−	0.00848954i
$79$	21.9986	−	124.760i	0.0313296	−	0.177679i	−0.965128	−	0.261780i	$-0.915691\pi$
$79$	21.9986	−	124.760i	0.0313296	−	0.177679i	0.996457	+	0.0841006i	$0.0268017\pi$
$80$	−27.8757			−0.0389575
$81$	686.251	+	245.968i	0.941360	+	0.337405i
$82$	202.459			0.272657
$83$	146.748	−	832.248i	0.194068	−	1.10062i	−0.719671	−	0.694315i	$-0.755708\pi$
$83$	146.748	−	832.248i	0.194068	−	1.10062i	0.913740	−	0.406300i	$-0.133181\pi$
$84$	−32.5231	+	377.068i	−0.0422447	+	0.489779i
$85$	36.3393	+	13.2264i	0.0463712	+	0.0168777i
$86$	64.2405	−	53.9042i	0.0805492	−	0.0675888i
$87$	−1312.44	−	349.943i	−1.61734	−	0.431239i
$88$	−383.633	+	139.631i	−0.464720	+	0.169144i
$89$	−693.455	+	1201.10i	−0.825912	+	1.43052i	0.0753091	+	0.997160i	$0.476006\pi$
$89$	−693.455	+	1201.10i	−0.825912	+	1.43052i	−0.901221	+	0.433361i	$0.857328\pi$
$90$	−3.08124	−	8.40144i	−0.00360879	−	0.00983988i
$91$	−8.41652	−	14.5778i	−0.00969551	−	0.0167931i
$92$	750.658	+	629.877i	0.850669	+	0.713796i
$93$	662.440	−	1425.17i	0.738621	−	1.58907i
$94$	22.2410	+	126.135i	0.0244041	+	0.138403i
$95$	7.52897	+	42.6989i	0.00813112	+	0.0461139i
$96$	344.192	+	490.276i	0.365926	+	0.521235i
$97$	−216.678	−	181.815i	−0.226808	−	0.190314i	0.522301	−	0.852761i	$-0.325074\pi$
$97$	−216.678	−	181.815i	−0.226808	−	0.190314i	−0.749109	+	0.662447i	$0.769518\pi$
$98$	80.8102	+	139.967i	0.0832965	+	0.144274i
$99$	707.504	+	838.981i	0.718250	+	0.851725i
$100$	−473.038	+	819.326i	−0.473038	+	0.819326i
$101$	436.501	−	158.873i	0.430034	−	0.156520i	−0.117929	−	0.993022i	$-0.537626\pi$
$101$	436.501	−	158.873i	0.430034	−	0.156520i	0.547963	+	0.836502i	$0.315403\pi$
$102$	−65.4731	−	243.155i	−0.0635568	−	0.236039i
$103$	248.422	−	208.451i	0.237648	−	0.199410i	−0.516184	−	0.856478i	$-0.672648\pi$
$103$	248.422	−	208.451i	0.237648	−	0.199410i	0.753832	+	0.657068i	$0.228203\pi$
$104$	−16.5439	−	6.02147i	−0.0155986	−	0.00567744i
$105$	−21.0388	−	14.6931i	−0.0195541	−	0.0136562i
$106$	59.0464	−	334.869i	0.0541046	−	0.306843i
$107$	2130.35			1.92475			0.962376	−	0.271722i	$-0.0875932\pi$
$107$	2130.35			1.92475			0.962376	+	0.271722i	$0.0875932\pi$
$108$	607.130	−	873.899i	0.540936	−	0.778620i
$109$	−1208.72			−1.06215			−0.531077	−	0.847323i	$-0.678213\pi$
$109$	−1208.72			−1.06215			−0.531077	+	0.847323i	$0.678213\pi$
$110$	2.33934	−	13.2671i	0.00202771	−	0.0114997i
$111$	972.603	−	454.986i	0.831670	−	0.389057i
$112$	489.137	+	178.031i	0.412671	+	0.150200i
$113$	−737.089	+	618.491i	−0.613624	+	0.514892i	−0.895792	−	0.444473i	$-0.853391\pi$
$113$	−737.089	+	618.491i	−0.613624	+	0.514892i	0.282168	+	0.959365i	$0.408946\pi$
$114$	199.393	−	199.882i	0.163814	−	0.164217i
$115$	−62.4352	+	22.7246i	−0.0506271	+	0.0184268i
$116$	−991.330	+	1717.03i	−0.793471	+	1.37433i
$117$	0.116120	+	47.3276i	9.17550e−5	+	0.0373969i
$118$	24.9115	+	43.1480i	0.0194347	+	0.0336618i
$119$	−553.177	−	464.170i	−0.426131	−	0.357567i
$120$	−26.7344	+	2.37201i	−0.0203375	+	0.00180445i
$121$	55.7749	+	316.315i	0.0419045	+	0.237652i
$122$	−29.9996	−	170.136i	−0.0222626	−	0.126258i
$123$	−1625.98	+	144.265i	−1.19195	+	0.105755i
$124$	−1757.32	−	1474.57i	−1.27268	−	1.06790i
$125$	−64.2158	−	111.225i	−0.0459491	−	0.0795862i
$126$	0.409986	+	167.099i	0.000289876	+	0.118146i
$127$	−408.496	+	707.535i	−0.285418	+	0.494359i	−0.972711	−	0.232022i	$-0.925466\pi$
$127$	−408.496	+	707.535i	−0.285418	+	0.494359i	0.687292	+	0.726381i	$0.258799\pi$
$128$	1084.27	−	394.640i	0.748722	−	0.272512i
$129$	−477.515	+	478.688i	−0.325914	+	0.326714i
$130$	0.445040	−	0.373433i	0.000300251	−	0.000251940i
$131$	−867.673	−	315.807i	−0.578694	−	0.210627i	0.0360555	−	0.999350i	$-0.488521\pi$
$131$	−867.673	−	315.807i	−0.578694	−	0.210627i	−0.614750	+	0.788722i	$0.710743\pi$
$132$	1451.03	−	678.793i	0.956786	−	0.447586i
$133$	140.590	−	797.326i	0.0916595	−	0.519827i
$134$	58.0224			0.0374058
$135$	30.7324	+	65.2776i	0.0195928	+	0.0416163i
$136$	−755.263			−0.476201
$137$	89.6988	−	508.707i	0.0559378	−	0.317239i	−0.943981	−	0.330001i	$-0.892951\pi$
$137$	89.6988	−	508.707i	0.0559378	−	0.317239i	0.999919	+	0.0127613i	$0.00406217\pi$
$138$	354.710	+	247.722i	0.218803	+	0.152808i
$139$	1482.07	+	539.428i	0.904369	+	0.329163i	0.752002	−	0.659161i	$-0.229088\pi$
$139$	1482.07	+	539.428i	0.904369	+	0.329163i	0.152367	+	0.988324i	$0.451311\pi$
$140$	−28.6941	+	24.0772i	−0.0173221	+	0.0145350i
$141$	−268.500	−	997.161i	−0.160367	−	0.595575i
$142$	−436.924	+	159.027i	−0.258210	+	0.0939808i
$143$	−35.6248	+	61.7040i	−0.0208328	+	0.0360835i
$144$	−943.479	−	1118.81i	−0.545995	−	0.647458i
$145$	−67.2162	−	116.422i	−0.0384965	−	0.0666780i
$146$	−65.9370	−	55.3277i	−0.0373766	−	0.0313627i
$147$	−748.734	−	1066.52i	−0.420099	−	0.598399i
$148$	−272.166	−	1543.53i	−0.151161	−	0.857279i
$149$	151.290	+	858.006i	0.0831820	+	0.471749i	0.997734	+	0.0672805i	$0.0214322\pi$
$149$	151.290	+	858.006i	0.0831820	+	0.471749i	−0.914552	+	0.404468i	$0.867457\pi$
$150$	−176.067	+	378.789i	−0.0958386	+	0.206187i
$151$	1827.75	+	1533.66i	0.985033	+	0.826541i	0.984841	−	0.173459i	$-0.0554945\pi$
$151$	1827.75	+	1533.66i	0.985033	+	0.826541i	0.000191679		1.00000i	$0.499939\pi$
$152$	−423.392	−	733.337i	−0.225932	−	0.391326i
$153$	699.087	+	1906.16i	0.369398	+	1.00722i
$154$	−125.780	+	217.858i	−0.0658161	+	0.113997i
$155$	146.163	−	53.1991i	0.0757427	−	0.0275681i
$156$	66.7507	+	17.7981i	0.0342586	+	0.00913453i
$157$	−947.000	+	794.627i	−0.481394	+	0.403937i	−0.850930	−	0.525279i	$-0.823961\pi$
$157$	−947.000	+	794.627i	−0.481394	+	0.403937i	0.369536	+	0.929216i	$0.379517\pi$
$158$	−76.7208	−	27.9241i	−0.0386302	−	0.0140603i
$159$	−235.595	+	2731.45i	−0.117509	+	1.36238i
$160$	−10.2951	+	58.3862i	−0.00508685	+	0.0288490i
$161$	1240.69			0.607329
$162$	232.909	−	408.022i	0.112957	−	0.197884i
$163$	3274.82			1.57364			0.786822	−	0.617180i	$-0.211725\pi$
$163$	3274.82			1.57364			0.786822	+	0.617180i	$0.211725\pi$
$164$	−413.753	+	2346.51i	−0.197004	+	1.11727i
$165$	−9.33398	+	108.217i	−0.00440394	+	0.0510586i
$166$	−511.786	−	186.275i	−0.239291	−	0.0870948i
$167$	1454.32	−	1220.32i	0.673883	−	0.565455i	−0.240329	−	0.970692i	$-0.577255\pi$
$167$	1454.32	−	1220.32i	0.673883	−	0.565455i	0.914212	+	0.405236i	$0.132811\pi$
$168$	484.259	+	129.120i	0.222389	+	0.0592967i
$169$	2061.62	−	750.367i	0.938378	−	0.341542i
$170$	12.4613	−	21.5836i	0.00562198	−	0.00973755i
$171$	−1458.92	+	1747.36i	−0.652436	+	0.781429i
$172$	493.469	+	854.713i	0.218760	+	0.378903i
$173$	−1643.25	−	1378.85i	−0.722160	−	0.605964i	0.205822	−	0.978589i	$-0.434013\pi$
$173$	−1643.25	−	1378.85i	−0.722160	−	0.605964i	−0.927982	+	0.372626i	$0.878458\pi$
$174$	−368.977	+	793.815i	−0.160759	+	0.345856i
$175$	208.004	+	1179.65i	0.0898492	+	0.509560i
$176$	−382.591	−	2169.78i	−0.163857	−	0.929282i
$177$	−230.814	−	328.777i	−0.0980171	−	0.139618i
$178$	684.706	+	574.537i	0.288320	+	0.241929i
$179$	−1780.29	−	3083.56i	−0.743382	−	1.28757i	−0.950947	−	0.309354i	$-0.899887\pi$
$179$	−1780.29	−	3083.56i	−0.743382	−	1.28757i	0.207565	−	0.978221i	$-0.433446\pi$
$180$	103.670	−	18.5422i	0.0429284	−	0.00767809i
$181$	1888.78	−	3271.46i	0.775645	−	1.34346i	−0.158787	−	0.987313i	$-0.550758\pi$
$181$	1888.78	−	3271.46i	0.775645	−	1.34346i	0.934431	−	0.356143i	$-0.115908\pi$
$182$	−10.1941	+	3.71036i	−0.00415186	+	0.00151115i
$183$	362.164	+	1345.01i	0.146295	+	0.543313i
$184$	994.043	−	834.101i	0.398271	−	0.334189i
$185$	99.8630	+	36.3471i	0.0396869	+	0.0144448i
$186$	−830.388	−	579.927i	−0.327350	−	0.228615i
$187$	−530.762	+	3010.10i	−0.207557	+	1.17712i
$188$	−1507.37			−0.584766
$189$	−122.361	−	1341.71i	−0.0470925	−	0.516375i
$190$	27.9426			0.0106693
$191$	−84.2917	+	478.042i	−0.0319326	+	0.181099i	−0.996602	−	0.0823631i	$-0.973753\pi$
$191$	−84.2917	+	478.042i	−0.0319326	+	0.181099i	0.964670	+	0.263462i	$0.0848644\pi$
$192$	−1691.27	+	791.178i	−0.635712	+	0.297387i
$193$	−3259.23	−	1186.26i	−1.21557	−	0.442431i	−0.346936	−	0.937889i	$-0.612778\pi$
$193$	−3259.23	−	1186.26i	−1.21557	−	0.442431i	−0.868632	+	0.495458i	$0.835000\pi$
$194$	−139.642	+	117.174i	−0.0516790	+	0.0433639i
$195$	−3.30809	+	3.31621i	−0.00121486	+	0.00121784i
$196$	−1787.38	+	650.552i	−0.651377	+	0.237082i
$197$	977.466	−	1693.02i	0.353511	−	0.612298i	−0.633351	−	0.773864i	$-0.718321\pi$
$197$	977.466	−	1693.02i	0.353511	−	0.612298i	0.986862	+	0.161566i	$0.0516545\pi$
$198$	611.660	−	355.146i	0.219539	−	0.127470i
$199$	−665.106	−	1152.00i	−0.236925	−	0.410367i	0.722905	−	0.690947i	$-0.242806\pi$
$199$	−665.106	−	1152.00i	−0.236925	−	0.410367i	−0.959830	+	0.280581i	$0.909473\pi$
$200$	959.717	+	805.298i	0.339311	+	0.284716i
$201$	−465.986	+	41.3446i	−0.163523	+	0.0145086i
$202$	−51.9841	−	294.817i	−0.0181069	−	0.102689i
$203$	435.906	+	2472.15i	0.150712	+	0.854732i
$204$	2951.99	−	261.915i	1.01314	−	0.0898908i
$205$	−123.760	−	103.847i	−0.0421648	−	0.0353805i
$206$	−104.498	−	180.996i	−0.0353432	−	0.0612163i
$207$	−3025.24	−	1736.74i	−1.01579	−	0.583149i
$208$	47.5068	−	82.2842i	0.0158366	−	0.0274297i
$209$	−3220.26	+	1172.08i	−1.06579	+	0.387915i
$210$	−11.6799	+	11.7085i	−0.00383803	+	0.00384746i
$211$	−2707.90	+	2272.19i	−0.883504	+	0.741348i	−0.966896	−	0.255169i	$-0.917869\pi$
$211$	−2707.90	+	2272.19i	−0.883504	+	0.741348i	0.0833927	+	0.996517i	$0.473424\pi$
$212$	3760.48	+	1368.70i	1.21826	+	0.443410i
$213$	3395.68	−	1588.51i	1.09234	−	0.510999i
$214$	238.409	−	1352.08i	0.0761555	−	0.431900i
$215$	−66.9183			−0.0212269
$216$	−1000.05	−	992.717i	−0.315022	−	0.312712i
$217$	−2904.50			−0.908619
$218$	−135.269	+	767.151i	−0.0420257	+	0.238339i
$219$	568.974	+	397.361i	0.175560	+	0.122608i
$220$	148.986	+	54.2263i	0.0456573	+	0.0166179i
$221$	−100.973	+	84.7264i	−0.0307338	+	0.0257888i
$222$	−179.924	−	668.207i	−0.0543952	−	0.202014i
$223$	736.550	−	268.082i	0.221180	−	0.0805028i	−0.229054	−	0.973414i	$-0.573563\pi$
$223$	736.550	−	268.082i	0.221180	−	0.0805028i	0.450233	+	0.892911i	$0.351341\pi$
$224$	553.539	−	958.757i	0.165111	−	0.285981i
$225$	1144.11	−	3167.57i	0.338995	−	0.938539i
$226$	310.054	+	537.030i	0.0912589	+	0.158065i
$227$	459.784	+	385.805i	0.134436	+	0.112805i	0.707526	−	0.706687i	$-0.249811\pi$
$227$	459.784	+	385.805i	0.134436	+	0.112805i	−0.573090	+	0.819492i	$0.694256\pi$
$228$	1909.16	+	2719.46i	0.554550	+	0.789916i
$229$	−357.830	−	2029.35i	−0.103258	−	0.585605i	−0.991902	−	0.127007i	$-0.959463\pi$
$229$	−357.830	−	2029.35i	−0.103258	−	0.585605i	0.888644	−	0.458598i	$-0.151648\pi$
$230$	7.43560	+	42.1694i	0.00213169	+	0.0120894i
$231$	854.923	−	1839.28i	0.243506	−	0.523877i
$232$	2011.25	+	1687.64i	0.569158	+	0.477580i
$233$	2198.44	+	3807.80i	0.618130	+	1.07063i	0.989827	+	0.142279i	$0.0454429\pi$
$233$	2198.44	+	3807.80i	0.618130	+	1.07063i	−0.371696	+	0.928354i	$0.621224\pi$
$234$	30.0507	+	5.22277i	0.00839521	+	0.00145907i
$235$	51.1028	−	88.5126i	0.0141854	−	0.0245699i
$236$	−550.999	+	200.547i	−0.151979	+	0.0553157i
$237$	636.053	+	169.594i	0.174330	+	0.0464823i
$238$	−356.505	+	299.143i	−0.0970957	+	0.0814730i
$239$	2485.16	+	904.525i	0.672601	+	0.244807i	0.655667	−	0.755050i	$-0.272387\pi$
$239$	2485.16	+	904.525i	0.672601	+	0.244807i	0.0169337	+	0.999857i	$0.494610\pi$
$240$	12.4472	−	144.311i	0.00334776	−	0.0388134i
$241$	−223.747	+	1268.93i	−0.0598043	+	0.339167i	−0.999999	−	0.00147066i	$-0.999532\pi$
$241$	−223.747	+	1268.93i	−0.0598043	+	0.339167i	0.940195	+	0.340638i	$0.110643\pi$
$242$	207.000			0.0549854
$243$	−1579.79	+	3442.84i	−0.417051	+	0.908883i
$244$	2033.20			0.533452
$245$	22.3953	−	127.010i	0.00583992	−	0.0331198i
$246$	−90.4028	+	1048.12i	−0.0234304	+	0.271648i
$247$	−138.871	−	50.5449i	−0.0357739	−	0.0130206i
$248$	−2327.09	+	1952.66i	−0.595849	+	0.499976i
$249$	4242.96	+	1131.32i	1.07987	+	0.287930i
$250$	−77.7785	+	28.3091i	−0.0196766	+	0.00716169i
$251$	1567.41	−	2714.84i	0.394161	−	0.682706i	−0.598833	−	0.800874i	$-0.704369\pi$
$251$	1567.41	−	2714.84i	0.394161	−	0.682706i	0.992994	+	0.118168i	$0.0377020\pi$
$252$	−1937.53	−	336.739i	−0.484337	−	0.0841769i
$253$	−2625.75	−	4547.93i	−0.652487	−	1.13014i
$254$	403.342	+	338.444i	0.0996374	+	0.0836057i
$255$	−84.6987	+	182.220i	−0.0208002	+	0.0447493i
$256$	370.059	+	2098.71i	0.0903465	+	0.512380i
$257$	825.159	+	4679.71i	0.200280	+	1.13584i	0.904696	+	0.426057i	$0.140098\pi$
$257$	825.159	+	4679.71i	0.200280	+	1.13584i	−0.704416	+	0.709787i	$0.748791\pi$
$258$	250.373	+	356.638i	0.0604169	+	0.0860594i
$259$	−1520.17	−	1275.57i	−0.364705	−	0.306024i
$260$	3.41861	+	5.92121i	0.000815436	+	0.00141238i
$261$	2397.67	−	6638.16i	0.568628	−	1.57430i
$262$	−297.538	+	515.350i	−0.0701600	+	0.121521i
$263$	−2784.08	+	1013.32i	−0.652753	+	0.237583i	−0.647104	−	0.762401i	$-0.724020\pi$
$263$	−2784.08	+	1013.32i	−0.652753	+	0.237583i	−0.00564853	+	0.999984i	$0.501798\pi$
$264$	−551.558	−	2048.39i	−0.128584	−	0.477536i
$265$	−207.858	+	174.414i	−0.0481835	+	0.0404307i
$266$	−490.311	−	178.459i	−0.113019	−	0.0411354i
$267$	−5908.37	−	4126.29i	−1.35426	−	0.945786i
$268$	−118.577	+	672.484i	−0.0270270	+	0.153278i
$269$	−5521.68			−1.25154			−0.625768	−	0.780010i	$-0.715214\pi$
$269$	−5521.68			−1.25154			−0.625768	+	0.780010i	$0.715214\pi$
$270$	44.8695	−	12.1999i	0.0101136	−	0.00274986i
$271$	601.325			0.134789			0.0673946	−	0.997726i	$-0.478531\pi$
$271$	601.325			0.134789			0.0673946	+	0.997726i	$0.478531\pi$
$272$	707.789	−	4014.07i	0.157779	−	0.894812i
$273$	79.2267	−	37.0624i	0.0175642	−	0.00821655i
$274$	−312.827	−	113.860i	−0.0689728	−	0.0251040i
$275$	3883.96	−	3259.03i	0.851679	−	0.714643i
$276$	−3596.02	+	3604.85i	−0.784257	+	0.786183i
$277$	−2510.79	+	913.853i	−0.544617	+	0.198224i	−0.599653	−	0.800260i	$-0.704695\pi$
$277$	−2510.79	+	913.853i	−0.544617	+	0.198224i	0.0550364	+	0.998484i	$0.482473\pi$
$278$	508.222	−	880.266i	0.109644	−	0.189910i
$279$	7082.20	+	4065.78i	1.51971	+	0.872443i
$280$	24.8011	+	42.9568i	0.00529339	+	0.00916843i
$281$	2846.11	+	2388.17i	0.604216	+	0.506998i	0.892798	−	0.450458i	$-0.148739\pi$
$281$	2846.11	+	2388.17i	0.604216	+	0.506998i	−0.288582	+	0.957455i	$0.593184\pi$
$282$	−662.924	+	58.8179i	−0.139988	+	0.0124204i
$283$	−304.681	−	1727.93i	−0.0639979	−	0.362950i	−0.999942	−	0.0108007i	$-0.996562\pi$
$283$	−304.681	−	1727.93i	−0.0639979	−	0.362950i	0.935944	−	0.352150i	$-0.114549\pi$
$284$	−950.221	−	5388.97i	−0.198540	−	1.12597i
$285$	−224.411	+	19.9109i	−0.0466420	+	0.00413831i
$286$	35.1753	+	29.5156i	0.00727259	+	0.00610243i
$287$	1508.40	+	2612.62i	0.310237	+	0.537346i
$288$	−2691.81	+	1562.94i	−0.550752	+	0.319781i
$289$	−370.779	+	642.208i	−0.0754690	+	0.130716i
$290$	−81.4125	+	29.6317i	−0.0164852	+	0.00600012i
$291$	1037.99	−	1040.54i	0.209101	−	0.209614i
$292$	776.004	−	651.144i	0.155521	−	0.130498i
$293$	−6974.36	−	2538.46i	−1.39060	−	0.506138i	−0.465227	−	0.885191i	$-0.654027\pi$
$293$	−6974.36	−	2538.46i	−1.39060	−	0.506138i	−0.925375	+	0.379053i	$0.876250\pi$
$294$	−760.685	+	355.850i	−0.150898	+	0.0705904i
$295$	6.90384	−	39.1536i	0.00136257	−	0.00772749i
$296$	−2075.52			−0.407557
$297$	−4659.26	+	3288.07i	−0.910296	+	0.642402i
$298$	561.488			0.109148
$299$	39.3255	−	223.026i	0.00760620	−	0.0431369i
$300$	−4030.37	−	2814.74i	−0.775646	−	0.541696i
$301$	1174.22	+	427.382i	0.224854	+	0.0818401i
$302$	1177.93	−	988.397i	0.224444	−	0.188331i
$303$	627.568	+	2330.67i	0.118986	+	0.441894i
$304$	4294.32	−	1563.00i	0.810184	−	0.294883i
$305$	−68.9296	+	119.390i	−0.0129406	+	0.0224139i
$306$	1288.03	−	230.375i	0.240627	−	0.0430381i
$307$	4911.87	+	8507.61i	0.913144	+	1.58161i	0.809597	+	0.586987i	$0.199686\pi$
$307$	4911.87	+	8507.61i	0.913144	+	1.58161i	0.103547	+	0.994625i	$0.466981\pi$
$308$	−2267.94	−	1903.03i	−0.419571	−	0.352062i
$309$	968.208	+	1379.14i	0.178251	+	0.253905i
$310$	−17.4070	−	98.7201i	−0.00318920	−	0.0180868i
$311$	−388.151	−	2201.31i	−0.0707718	−	0.401367i	−0.999529	−	0.0306789i	$-0.990233\pi$
$311$	−388.151	−	2201.31i	−0.0707718	−	0.401367i	0.928758	−	0.370688i	$-0.120878\pi$
$312$	38.5600	−	82.9577i	0.00699689	−	0.0150531i
$313$	−221.336	−	185.723i	−0.0399702	−	0.0335390i	0.622584	−	0.782553i	$-0.286083\pi$
$313$	−221.336	−	185.723i	−0.0399702	−	0.0335390i	−0.662554	+	0.749014i	$0.730527\pi$
$314$	398.352	+	689.967i	0.0715934	+	0.124003i
$315$	85.4595	−	102.356i	0.0152860	−	0.0183082i
$316$	480.432	−	832.132i	0.0855266	−	0.148136i
$317$	7046.46	−	2564.70i	1.24848	−	0.454410i	0.368594	−	0.929591i	$-0.379839\pi$
$317$	7046.46	−	2564.70i	1.24848	−	0.454410i	0.879889	+	0.475180i	$0.157617\pi$
$318$	1707.23	+	455.206i	0.301058	+	0.0802726i
$319$	8139.48	−	6829.83i	1.42860	−	1.19874i
$320$	−173.652	−	63.2043i	−0.0303358	−	0.0110413i
$321$	−951.251	+	11028.7i	−0.165401	+	1.91763i
$322$	138.846	−	787.437i	0.0240298	−	0.136280i
$323$	−6339.77			−1.09212
$324$	4253.02	+	3533.29i	0.729255	+	0.605845i
$325$	218.646			0.0373179
$326$	366.488	−	2078.46i	0.0622635	−	0.353114i
$327$	539.725	−	6257.49i	0.0912747	−	1.05823i
$328$	2964.97	+	1079.16i	0.499125	+	0.181667i
$329$	−1462.00	+	1226.76i	−0.244993	+	0.205573i
$330$	67.6382	+	18.0347i	0.0112829	+	0.00300842i
$331$	−601.688	+	218.996i	−0.0999147	+	0.0363660i	−0.391494	−	0.920181i	$-0.628042\pi$
$331$	−601.688	+	218.996i	−0.0999147	+	0.0363660i	0.291579	+	0.956547i	$0.405819\pi$
$332$	3204.85	−	5550.96i	0.529786	−	0.917616i
$333$	1921.14	+	5238.26i	0.316149	+	0.862027i
$334$	−611.754	−	1059.59i	−0.100221	−	0.173587i
$335$	−35.4682	−	29.7614i	−0.00578459	−	0.00485385i
$336$	−1140.07	+	2452.73i	−0.185107	+	0.398237i
$337$	1656.56	+	9394.81i	0.267770	+	1.51860i	0.761029	+	0.648717i	$0.224694\pi$
$337$	1656.56	+	9394.81i	0.267770	+	1.51860i	−0.493259	+	0.869882i	$0.664195\pi$
$338$	−245.524	−	1392.44i	−0.0395111	−	0.224079i
$339$	−2872.76	−	4092.03i	−0.460256	−	0.655601i
$340$	224.689	+	188.536i	0.0358396	+	0.0300730i
$341$	6146.97	+	10646.9i	0.976179	+	1.69079i
$342$	945.744	+	1121.49i	0.149532	+	0.177320i
$343$	−2851.06	+	4938.19i	−0.448813	+	0.777367i
$344$	1228.11	−	446.997i	0.192487	−	0.0700594i
$345$	−89.7647	−	333.370i	−0.0140080	−	0.0520233i
$346$	−1059.02	+	888.623i	−0.164547	+	0.138071i
$347$	−3480.35	−	1266.74i	−0.538429	−	0.195972i	0.0584689	−	0.998289i	$-0.481378\pi$
$347$	−3480.35	−	1266.74i	−0.538429	−	0.195972i	−0.596898	+	0.802317i	$0.703600\pi$
$348$	−8446.31	−	5898.74i	−1.30106	−	0.908637i
$349$	1791.57	−	10160.5i	0.274787	−	1.55839i	−0.464850	−	0.885389i	$-0.653892\pi$
$349$	1791.57	−	10160.5i	0.274787	−	1.55839i	0.739637	−	0.673006i	$-0.234997\pi$
$350$	771.974			0.117896
$351$	−245.063	−	20.5318i	−0.0372664	−	0.00312223i
$352$	−4685.95			−0.709552
$353$	−9.58591	+	54.3644i	−0.00144534	+	0.00819695i	−0.985522	−	0.169548i	$-0.945769\pi$
$353$	−9.58591	+	54.3644i	−0.00144534	+	0.00819695i	0.984077	+	0.177745i	$0.0568803\pi$
$354$	−234.498	+	109.699i	−0.0352074	+	0.0164701i
$355$	348.655	+	126.900i	0.0521259	+	0.0189723i
$356$	−8058.21	+	6761.64i	−1.19968	+	1.00665i
$357$	2649.99	−	2656.50i	0.392863	−	0.393828i
$358$	−2156.30	+	784.828i	−0.318335	+	0.115864i
$359$	502.399	−	870.181i	0.0738597	−	0.127929i	−0.826730	−	0.562599i	$-0.809802\pi$
$359$	502.399	−	870.181i	0.0738597	−	0.127929i	0.900590	+	0.434670i	$0.143135\pi$
$360$	−0.342174	−	139.461i	−5.00949e−5	−	0.0204174i
$361$	−124.503	−	215.646i	−0.0181518	−	0.0314399i
$362$	−1864.95	−	1564.88i	−0.270772	−	0.227204i
$363$	−1662.45	+	147.501i	−0.240374	+	0.0213272i
$364$	−22.1702	−	125.733i	−0.00319240	−	0.0181050i
$365$	11.9271	+	67.6421i	0.00171039	+	0.00970013i
$366$	894.180	−	79.3360i	0.127704	−	0.0113305i
$367$	−9113.56	−	7647.18i	−1.29625	−	1.08768i	−0.990780	−	0.135481i	$-0.956742\pi$
$367$	−9113.56	−	7647.18i	−1.29625	−	1.08768i	−0.305470	−	0.952202i	$-0.598814\pi$
$368$	3501.52	+	6064.81i	0.496003	+	0.859103i
$369$	−20.8109	−	8481.99i	−0.00293597	−	1.19663i
$370$	34.2445	−	59.3131i	0.00481158	−	0.00833390i
$371$	4761.21	−	1732.94i	0.666280	−	0.242506i
$372$	8418.41	−	8439.09i	1.17332	−	1.17620i
$373$	−349.502	+	293.267i	−0.0485161	+	0.0407098i	−0.666723	−	0.745305i	$-0.732304\pi$
$373$	−349.502	+	293.267i	−0.0485161	+	0.0407098i	0.618207	+	0.786015i	$0.287859\pi$
$374$	1851.05	+	673.726i	0.255923	+	0.0931485i
$375$	604.478	−	282.776i	0.0832403	−	0.0389400i
$376$	−346.619	+	1965.77i	−0.0475412	+	0.269620i
$377$	458.209			0.0625968
$378$	−865.245	−	72.4914i	−0.117734	−	0.00986390i
$379$	−5244.85			−0.710845			−0.355422	−	0.934706i	$-0.615663\pi$
$379$	−5244.85			−0.710845			−0.355422	+	0.934706i	$0.615663\pi$
$380$	−57.1047	+	323.857i	−0.00770897	+	0.0437198i
$381$	−3480.46	−	2430.69i	−0.468003	−	0.326845i
$382$	293.969	+	106.996i	0.0393738	+	0.0143309i
$383$	1794.93	−	1506.12i	0.239469	−	0.200938i	−0.515153	−	0.857098i	$-0.672265\pi$
$383$	1794.93	−	1506.12i	0.239469	−	0.200938i	0.754622	+	0.656160i	$0.227820\pi$
$384$	1558.87	+	5789.38i	0.207164	+	0.769370i
$385$	188.633	−	68.6570i	0.0249705	−	0.00908853i
$386$	−1117.64	+	1935.81i	−0.147374	+	0.255259i
$387$	−2264.91	−	2685.81i	−0.297499	−	0.352784i
$388$	−1072.67	−	1857.92i	−0.140352	−	0.243098i
$389$	−765.582	−	642.400i	−0.0997855	−	0.0837299i	0.591530	−	0.806283i	$-0.298524\pi$
$389$	−765.582	−	642.400i	−0.0997855	−	0.0837299i	−0.691316	+	0.722553i	$0.742969\pi$
$390$	1.73452	+	2.47069i	0.000225207	+	0.000320790i
$391$	−1687.03	−	9567.60i	−0.218201	−	1.23748i
$392$	437.385	+	2480.53i	0.0563553	+	0.319607i
$393$	2022.35	−	4350.87i	0.259577	−	0.558453i
$394$	−965.134	−	809.843i	−0.123408	−	0.103552i
$395$	32.5752	+	56.4219i	0.00414946	+	0.00718707i
$396$	2866.15	+	7814.97i	0.363711	+	0.991709i
$397$	−5258.34	+	9107.72i	−0.664758	+	1.15139i	0.314593	+	0.949227i	$0.398132\pi$
$397$	−5258.34	+	9107.72i	−0.664758	+	1.15139i	−0.979351	+	0.202167i	$0.935201\pi$
$398$	−805.579	+	293.207i	−0.101457	+	0.0369275i
$399$	4064.93	+	1083.85i	0.510027	+	0.135991i
$400$	−5179.39	+	4346.02i	−0.647423	+	0.543253i
$401$	−8244.37	−	3000.71i	−1.02669	−	0.373686i	−0.226873	−	0.973924i	$-0.572850\pi$
$401$	−8244.37	−	3000.71i	−1.02669	−	0.373686i	−0.799821	+	0.600238i	$0.795072\pi$
$402$	−25.9084	+	300.378i	−0.00321441	+	0.0372674i
$403$	−92.0625	+	522.112i	−0.0113796	+	0.0645366i
$404$	3523.18			0.433874
$405$	−351.660	+	129.952i	−0.0431460	+	0.0159441i
$406$	1617.80			0.197759
$407$	−1458.57	+	8271.97i	−0.177638	+	1.00744i
$408$	337.243	−	3909.95i	0.0409216	−	0.474439i
$409$	6620.19	+	2409.55i	0.800360	+	0.291307i	0.709636	−	0.704569i	$-0.248860\pi$
$409$	6620.19	+	2409.55i	0.800360	+	0.291307i	0.0907243	+	0.995876i	$0.471082\pi$
$410$	−79.7595	+	66.9262i	−0.00960742	+	0.00806158i
$411$	2593.49	+	691.514i	0.311259	+	0.0829924i
$412$	2311.31	−	841.247i	0.276383	−	0.100595i
$413$	−371.201	+	642.939i	−0.0442267	+	0.0766028i
$414$	−1440.83	+	1725.69i	−0.171045	+	0.204863i
$415$	217.302	+	376.377i	0.0257034	+	0.0445196i
$416$	−154.801	−	129.893i	−0.0182446	−	0.0153090i
$417$	−3454.36	+	7431.69i	−0.405661	+	0.872737i
$418$	383.510	+	2174.99i	0.0448758	+	0.254503i
$419$	111.525	+	632.491i	0.0130032	+	0.0737451i	0.990619	−	0.136654i	$-0.0436348\pi$
$419$	111.525	+	632.491i	0.0130032	+	0.0737451i	−0.977616	+	0.210399i	$0.932524\pi$
$420$	−111.833	−	159.298i	−0.0129926	−	0.0185071i
$421$	4569.59	+	3834.34i	0.528998	+	0.443882i	0.867755	−	0.496992i	$-0.165562\pi$
$421$	4569.59	+	3834.34i	0.528998	+	0.443882i	−0.338757	+	0.940874i	$0.610006\pi$
$422$	1139.07	+	1972.92i	0.131396	+	0.227584i
$423$	5282.13	−	944.750i	0.607153	−	0.108594i
$424$	2649.66	−	4589.35i	0.303488	−	0.525657i
$425$	8814.05	−	3208.05i	1.00599	−	0.366149i
$426$	−628.176	−	2332.93i	−0.0714442	−	0.265331i
$427$	1972.01	−	1654.71i	0.223494	−	0.187534i
$428$	15183.5	+	5526.35i	1.71477	+	0.624126i
$429$	−303.530	−	211.979i	−0.0341598	−	0.0238566i
$430$	−7.48888	+	42.4716i	−0.000839875	+	0.00476317i
$431$	−11815.6			−1.32051			−0.660253	−	0.751043i	$-0.729551\pi$
$431$	−11815.6			−1.32051			−0.660253	+	0.751043i	$0.729551\pi$
$432$	6213.28	−	4384.75i	0.691983	−	0.488337i
$433$	3726.80			0.413623			0.206811	−	0.978381i	$-0.433691\pi$
$433$	3726.80			0.413623			0.206811	+	0.978381i	$0.433691\pi$
$434$	−325.045	+	1843.42i	−0.0359508	+	0.203887i
$435$	632.721	−	295.988i	0.0697395	−	0.0326243i
$436$	−8614.88	−	3135.56i	−0.946280	−	0.344418i
$437$	8344.11	−	7001.54i	0.913394	−	0.766428i
$438$	315.870	−	316.646i	0.0344586	−	0.0345432i
$439$	−11389.9	+	4145.60i	−1.23830	+	0.450703i	−0.876431	−	0.481527i	$-0.840082\pi$
$439$	−11389.9	+	4145.60i	−1.23830	+	0.450703i	−0.361865	+	0.932230i	$0.617860\pi$
$440$	104.976	−	181.824i	0.0113740	−	0.0197003i
$441$	5855.60	−	3399.92i	0.632286	−	0.367122i
$442$	42.4740	+	73.5671i	0.00457077	+	0.00791681i
$443$	2944.32	+	2470.58i	0.315776	+	0.264968i	0.786875	−	0.617113i	$-0.211698\pi$
$443$	2944.32	+	2470.58i	0.315776	+	0.264968i	−0.471098	+	0.882081i	$0.656142\pi$
$444$	8112.27	−	719.761i	0.867097	−	0.0769332i
$445$	−123.854	−	702.412i	−0.0131938	−	0.0748259i
$446$	−87.7180	−	497.473i	−0.00931293	−	0.0528162i
$447$	−4509.39	+	400.095i	−0.477152	+	0.0423353i
$448$	2643.43	+	2218.10i	0.278773	+	0.233919i
$449$	−2582.64	−	4473.26i	−0.271453	−	0.470170i	0.697781	−	0.716311i	$-0.254171\pi$
$449$	−2582.64	−	4473.26i	−0.271453	−	0.470170i	−0.969234	+	0.246141i	$0.920837\pi$
$450$	−1882.35	−	1080.62i	−0.197188	−	0.113202i
$451$	6384.63	−	11058.5i	0.666609	−	1.15460i
$452$	−6857.85	+	2496.05i	−0.713642	+	0.259745i
$453$	−8755.79	+	8777.30i	−0.908130	+	0.910361i
$454$	296.317	−	248.639i	0.0306318	−	0.0257031i
$455$	8.13467	+	2.96078i	0.000838152	+	0.000305062i
$456$	3985.49	−	1864.42i	0.409293	−	0.191468i
$457$	−1788.70	+	10144.2i	−0.183089	+	1.03835i	0.745297	+	0.666733i	$0.232308\pi$
$457$	−1788.70	+	10144.2i	−0.183089	+	1.03835i	−0.928386	+	0.371617i	$0.878803\pi$
$458$	−1328.03			−0.135491
$459$	−10180.2	+	2767.98i	−1.03523	+	0.281478i
$460$	−503.941			−0.0510791
$461$	850.417	−	4822.95i	0.0859172	−	0.487261i	−0.911238	−	0.411881i	$-0.864872\pi$
$461$	850.417	−	4822.95i	0.0859172	−	0.487261i	0.997155	−	0.0753799i	$-0.0240169\pi$
$462$	−1071.67	−	748.435i	−0.107919	−	0.0753687i
$463$	−5384.34	−	1959.74i	−0.540457	−	0.196710i	0.0573444	−	0.998354i	$-0.481737\pi$
$463$	−5384.34	−	1959.74i	−0.540457	−	0.196710i	−0.597802	+	0.801644i	$0.703959\pi$
$464$	−10854.3	+	9107.81i	−1.08598	+	0.911248i
$465$	210.142	+	780.432i	0.0209573	+	0.0778315i
$466$	2662.76	−	969.164i	0.264699	−	0.0963426i
$467$	5051.03	−	8748.64i	0.500501	−	0.866893i	−0.499499	−	0.866314i	$-0.666483\pi$
$467$	5051.03	−	8748.64i	0.500501	−	0.866893i	1.00000		0.000578251i	$-0.000184063\pi$
$468$	−121.945	+	337.617i	−0.0120447	+	0.0333469i
$469$	432.290	+	748.747i	0.0425614	+	0.0737184i
$470$	−50.4580	−	42.3393i	−0.00495203	−	0.00415525i
$471$	−3690.87	−	5257.37i	−0.361075	−	0.514325i
$472$	134.833	+	764.679i	0.0131488	+	0.0745703i
$473$	−918.448	−	5208.78i	−0.0892817	−	0.506342i
$474$	178.819	−	384.709i	0.0173279	−	0.0372791i
$475$	8055.97	+	6759.76i	0.778176	+	0.652967i
$476$	−2738.52	−	4743.26i	−0.263697	−	0.456737i
$477$	−14035.3	−	2439.32i	−1.34724	−	0.234148i
$478$	852.198	−	1476.05i	0.0815452	−	0.141240i
$479$	−17351.2	+	6315.33i	−1.65511	+	0.602411i	−0.989583	−	0.143962i	$-0.954016\pi$
$479$	−17351.2	+	6315.33i	−1.65511	+	0.602411i	−0.665528	+	0.746373i	$0.731793\pi$
$480$	−297.665	−	79.3677i	−0.0283051	−	0.00754713i
$481$	−277.481	+	232.834i	−0.0263036	+	0.0220713i
$482$	780.325	+	284.015i	0.0737403	+	0.0268393i
$483$	−553.997	+	6422.96i	−0.0521900	+	0.605083i
$484$	−423.034	+	2399.14i	−0.0397289	+	0.225314i
$485$	145.463			0.0136188
$486$	2008.30	+	1387.95i	0.187445	+	0.129544i
$487$	12918.0			1.20199			0.600996	−	0.799252i	$-0.294771\pi$
$487$	12918.0			1.20199			0.600996	+	0.799252i	$0.294771\pi$
$488$	467.534	−	2651.52i	0.0433694	−	0.245960i
$489$	−1462.29	+	16953.5i	−0.135229	+	1.56782i
$490$	−78.1040	−	28.4275i	−0.00720078	−	0.00262087i
$491$	14094.2	−	11826.4i	1.29544	−	1.08701i	0.304531	−	0.952502i	$-0.401500\pi$
$491$	14094.2	−	11826.4i	1.29544	−	1.08701i	0.990913	−	0.134504i	$-0.0429441\pi$
$492$	−11963.0	−	3189.75i	−1.09621	−	0.292286i
$493$	18471.3	−	6723.00i	1.68743	−	0.614176i
$494$	−47.6209	+	82.4818i	−0.00433718	+	0.00751221i
$495$	−556.063	−	96.6428i	−0.0504913	−	0.00877529i
$496$	−8197.19	−	14197.9i	−0.742066	−	1.28530i
$497$	−5307.41	−	4453.45i	−0.479014	−	0.401941i
$498$	1192.86	−	2566.31i	0.107336	−	0.230922i
$499$	−269.926	−	1530.83i	−0.0242155	−	0.137333i	0.970303	−	0.241892i	$-0.0777680\pi$
$499$	−269.926	−	1530.83i	−0.0242155	−	0.137333i	−0.994519	+	0.104559i	$0.966657\pi$
$500$	−169.152	−	959.311i	−0.0151295	−	0.0858034i
$501$	5668.11	+	8073.80i	0.505454	+	0.719982i
$502$	−1547.64	−	1298.62i	−0.137599	−	0.115459i
$503$	−10145.3	−	17572.2i	−0.899317	−	1.55766i	−0.828370	−	0.560182i	$-0.810731\pi$
$503$	−10145.3	−	17572.2i	−0.899317	−	1.55766i	−0.0709470	−	0.997480i	$-0.522602\pi$
$504$	−884.680	+	2449.32i	−0.0781881	+	0.216471i
$505$	−119.443	+	206.881i	−0.0105250	+	0.0182299i
$506$	−3180.32	+	1157.54i	−0.279412	+	0.101698i
$507$	2964.04	+	11007.9i	0.259640	+	0.964257i
$508$	−4746.87	+	3983.10i	−0.414583	+	0.347877i
$509$	−1546.10	−	562.735i	−0.134636	−	0.0490035i	0.273823	−	0.961780i	$-0.411712\pi$
$509$	−1546.10	−	562.735i	−0.134636	−	0.0490035i	−0.408459	+	0.912776i	$0.633934\pi$
$510$	106.172	+	74.1488i	0.00921842	+	0.00643797i
$511$	222.718	−	1263.09i	0.0192807	−	0.109346i
$512$	10604.2			0.915322
$513$	−8394.54	−	8332.98i	−0.722472	−	0.717174i
$514$	3062.45			0.262799
$515$	−28.9599	+	164.240i	−0.00247792	+	0.0140530i
$516$	−4645.14	+	2173.00i	−0.396300	+	0.185390i
$517$	7591.00	+	2762.90i	0.645748	+	0.235033i
$518$	−979.700	+	822.066i	−0.0830995	+	0.0697288i
$519$	7871.94	−	7891.28i	0.665780	−	0.667416i
$520$	8.50802	−	3.09667i	0.000717502	−	0.000261150i
$521$	−3156.83	+	5467.80i	−0.265458	+	0.459786i	−0.967683	−	0.252168i	$-0.918856\pi$
$521$	−3156.83	+	5467.80i	−0.265458	+	0.459786i	0.702226	+	0.711954i	$0.252190\pi$
$522$	−3944.77	−	2264.63i	−0.330762	−	0.189885i
$523$	7633.72	+	13222.0i	0.638240	+	1.10546i	0.985819	+	0.167813i	$0.0536704\pi$
$523$	7633.72	+	13222.0i	0.638240	+	1.10546i	−0.347579	+	0.937651i	$0.612996\pi$
$524$	−5364.88	−	4501.67i	−0.447263	−	0.375298i
$525$	−6199.83	+	550.080i	−0.515396	+	0.0457285i
$526$	331.565	+	1880.40i	0.0274846	+	0.155873i
$527$	3949.39	+	22398.1i	0.326448	+	1.85138i
$528$	11403.7	−	1011.79i	0.939925	−	0.0833948i
$529$	3466.24	+	2908.52i	0.284888	+	0.239050i
$530$	87.4349	+	151.442i	0.00716590	+	0.0124117i
$531$	1805.12	−	1048.10i	0.147525	−	0.0856566i
$532$	3070.37	−	5318.04i	0.250221	−	0.433395i
$533$	517.455	−	188.338i	0.0420516	−	0.0153055i
$534$	−3280.07	+	3288.13i	−0.265810	+	0.266463i
$535$	−839.259	+	704.222i	−0.0678212	+	0.0569087i
$536$	849.726	+	309.275i	0.0684749	+	0.0249228i
$537$	16758.3	−	7839.57i	1.34669	−	0.629986i
$538$	−617.936	+	3504.49i	−0.0495188	+	0.280835i
$539$	10193.5			0.814595
$540$	49.7006	+	544.973i	0.00396069	+	0.0434294i
$541$	−7691.12			−0.611215			−0.305607	−	0.952158i	$-0.598859\pi$
$541$	−7691.12			−0.611215			−0.305607	+	0.952158i	$0.598859\pi$
$542$	67.2947	−	381.647i	0.00533313	−	0.0302457i
$543$	16092.7	+	11238.9i	1.27183	+	0.888223i
$544$	−8146.15	−	2964.96i	−0.642028	−	0.233679i
$545$	476.182	−	399.564i	0.0374264	−	0.0314045i
$546$	−14.6563	−	54.4311i	−0.00114878	−	0.00426636i
$547$	−15250.8	+	5550.83i	−1.19209	+	0.433887i	−0.860459	−	0.509520i	$-0.829823\pi$
$547$	−15250.8	+	5550.83i	−1.19209	+	0.433887i	−0.331636	+	0.943407i	$0.607601\pi$
$548$	1958.95	−	3392.99i	0.152704	−	0.264492i
$549$	−7124.76	+	1274.32i	−0.553875	+	0.0990648i
$550$	−1633.78	−	2829.78i	−0.126663	−	0.219386i
$551$	16882.6	+	14166.2i	1.30531	+	1.09528i
$552$	3874.22	+	5518.54i	0.298728	+	0.425516i
$553$	−211.255	−	1198.08i	−0.0162450	−	0.0921298i
$554$	299.018	+	1695.81i	0.0229315	+	0.130051i
$555$	−232.758	+	500.754i	−0.0178018	+	0.0382988i
$556$	9163.72	+	7689.28i	0.698972	+	0.586507i
$557$	−4337.76	−	7513.21i	−0.329976	−	0.571535i	0.652531	−	0.757762i	$-0.273707\pi$
$557$	−4337.76	−	7513.21i	−0.329976	−	0.571535i	−0.982507	+	0.186227i	$0.940374\pi$
$558$	3373.03	−	4039.91i	0.255899	−	0.306493i
$559$	114.045	−	197.531i	0.00862894	−	0.0149458i
$560$	−251.549	+	91.5563i	−0.0189819	+	0.00690886i
$561$	−15346.1	−	4091.80i	−1.15492	−	0.307943i
$562$	1834.23	−	1539.10i	0.137673	−	0.115521i
$563$	9900.05	+	3603.32i	0.741096	+	0.269737i	0.684854	−	0.728680i	$-0.259866\pi$
$563$	9900.05	+	3603.32i	0.741096	+	0.269737i	0.0562422	+	0.998417i	$0.482088\pi$
$564$	673.075	−	7803.53i	0.0502510	−	0.582603i
$565$	85.9267	−	487.314i	0.00639816	−	0.0362858i
$566$	−1130.78			−0.0839754
$567$	7000.56	−	34.3526i	0.518511	−	0.00254440i
$568$	−7246.32			−0.535297
$569$	659.397	−	3739.63i	0.0485824	−	0.275524i	−0.950833	−	0.309703i	$-0.899770\pi$
$569$	659.397	−	3739.63i	0.0485824	−	0.275524i	0.999416	+	0.0341786i	$0.0108815\pi$
$570$	−12.4771	+	144.657i	−0.000916853	+	0.0106299i
$571$	242.799	+	88.3714i	0.0177948	+	0.00647676i	0.350902	−	0.936412i	$-0.385875\pi$
$571$	242.799	+	88.3714i	0.0177948	+	0.00647676i	−0.333107	+	0.942889i	$0.608097\pi$
$572$	−413.974	+	347.365i	−0.0302607	+	0.0253917i
$573$	−2437.15	−	649.830i	−0.177685	−	0.0473770i
$574$	1826.98	−	664.966i	0.132851	−	0.0483539i
$575$	−8057.72	+	13956.4i	−0.584401	+	1.01221i
$576$	−3340.68	−	9108.85i	−0.241658	−	0.658916i
$577$	−5430.30	−	9405.55i	−0.391796	−	0.678611i	0.600890	−	0.799331i	$-0.294813\pi$
$577$	−5430.30	−	9405.55i	−0.391796	−	0.678611i	−0.992687	+	0.120721i	$0.961479\pi$
$578$	366.101	+	307.195i	0.0263457	+	0.0221066i
$579$	7596.53	−	16343.1i	0.545252	−	1.17305i
$580$	−177.056	−	1004.13i	−0.0126756	−	0.0718868i
$581$	−1409.23	−	7992.14i	−0.100628	−	0.570688i
$582$	−544.247	−	775.239i	−0.0387625	−	0.0552143i
$583$	−16428.8	−	13785.4i	−1.16709	−	0.979302i
$584$	−670.722	−	1161.72i	−0.0475251	−	0.0823160i
$585$	−15.6907	−	18.6065i	−0.00110894	−	0.00131502i
$586$	−2391.61	+	4142.39i	−0.168595	+	0.292014i
$587$	−19177.0	+	6979.86i	−1.34842	+	0.490783i	−0.912453	−	0.409182i	$-0.865814\pi$
$587$	−19177.0	+	6979.86i	−1.34842	+	0.490783i	−0.435963	+	0.899965i	$0.643592\pi$
$588$	−2569.76	−	9543.62i	−0.180230	−	0.669340i
$589$	−19533.9	+	16390.9i	−1.36652	+	1.14665i
$590$	−24.0773	−	8.76342i	−0.00168008	−	0.000611499i
$591$	8328.19	+	5816.25i	0.579655	+	0.404820i
$592$	1945.05	−	11030.9i	0.135036	−	0.765826i
$593$	15542.4			1.07631			0.538153	−	0.842847i	$-0.319122\pi$
$593$	15542.4			1.07631			0.538153	+	0.842847i	$0.319122\pi$
$594$	1565.44	+	3325.10i	0.108133	+	0.229681i
$595$	371.366			0.0255874
$596$	−1147.48	+	6507.68i	−0.0788634	+	0.447257i
$597$	6260.80	−	2928.81i	0.429208	−	0.200785i
$598$	−137.149	−	49.9180i	−0.00937864	−	0.00341355i
$599$	−6110.15	+	5127.02i	−0.416784	+	0.349724i	−0.826938	−	0.562293i	$-0.809919\pi$
$599$	−6110.15	+	5127.02i	−0.416784	+	0.349724i	0.410154	+	0.912016i	$0.365475\pi$
$600$	−4597.51	+	4608.80i	−0.312821	+	0.313589i
$601$	5695.33	−	2072.93i	0.386551	−	0.140693i	−0.141432	−	0.989948i	$-0.545171\pi$
$601$	5695.33	−	2072.93i	0.386551	−	0.140693i	0.527983	+	0.849255i	$0.322948\pi$
$602$	402.658	−	697.423i	0.0272610	−	0.0472174i
$603$	−5.96418	−	2430.84i	−0.000402786	−	0.164165i
$604$	9048.33	+	15672.2i	0.609555	+	1.05578i
$605$	−126.536	−	106.176i	−0.00850318	−	0.00713501i
$606$	1549.46	−	137.476i	0.103865	−	0.00921545i
$607$	−3020.71	−	17131.3i	−0.201988	−	1.14553i	−0.902109	−	0.431508i	$-0.857982\pi$
$607$	−3020.71	−	17131.3i	−0.201988	−	1.14553i	0.700121	−	0.714025i	$-0.253130\pi$
$608$	−1687.76	−	9571.78i	−0.112579	−	0.638465i
$609$	−12992.8	+	1152.78i	−0.864522	+	0.0767047i
$610$	68.0599	+	57.1090i	0.00451748	+	0.00379062i
$611$	174.183	+	301.693i	0.0115330	+	0.0199758i
$612$	37.7826	+	15399.2i	0.00249554	+	1.01712i
$613$	5434.53	−	9412.88i	0.358073	−	0.620200i	−0.629566	−	0.776947i	$-0.716767\pi$
$613$	5434.53	−	9412.88i	0.358073	−	0.620200i	0.987639	+	0.156747i	$0.0501007\pi$
$614$	5949.28	−	2165.36i	0.391031	−	0.142324i
$615$	592.871	−	594.328i	0.0388730	−	0.0389685i
$616$	−3003.27	+	2520.04i	−0.196437	+	0.164830i
$617$	−7517.47	−	2736.13i	−0.490505	−	0.178529i	0.0849133	−	0.996388i	$-0.472939\pi$
$617$	−7517.47	−	2736.13i	−0.490505	−	0.178529i	−0.575419	+	0.817859i	$0.695161\pi$
$618$	983.662	−	460.159i	0.0640270	−	0.0299520i
$619$	−2625.45	+	14889.6i	−0.170478	+	0.966826i	0.772758	+	0.634701i	$0.218877\pi$
$619$	−2625.45	+	14889.6i	−0.170478	+	0.966826i	−0.943235	+	0.332125i	$0.892234\pi$
$620$	1179.75			0.0764189
$621$	10341.8	−	14886.0i	0.668283	−	0.961922i
$622$	−1440.56			−0.0928638
$623$	−2312.75	+	13116.3i	−0.148730	+	0.843487i
$624$	404.767	+	282.681i	0.0259674	+	0.0181351i
$625$	−14589.6	−	5310.17i	−0.933732	−	0.339851i
$626$	−142.644	+	119.693i	−0.00910737	+	0.00764199i
$627$	−4629.84	−	17194.4i	−0.294893	−	1.09518i
$628$	−8810.85	+	3206.89i	−0.559859	+	0.203772i
$629$	−7769.56	+	13457.3i	−0.492516	+	0.853063i
$630$	−55.3990	−	65.6940i	−0.00350341	−	0.00415446i
$631$	−5114.69	−	8858.89i	−0.322682	−	0.558902i	0.658358	−	0.752705i	$-0.271251\pi$
$631$	−5114.69	−	8858.89i	−0.322682	−	0.558902i	−0.981041	+	0.193803i	$0.937918\pi$
$632$	−974.717	−	817.884i	−0.0613483	−	0.0514774i
$633$	−10553.9	−	15033.2i	−0.662683	−	0.943942i
$634$	−839.184	−	4759.25i	−0.0525682	−	0.298129i
$635$	−72.9591	−	413.771i	−0.00455952	−	0.0258583i
$636$	−8764.82	+	18856.6i	−0.546459	+	1.17565i
$637$	336.744	+	282.562i	0.0209455	+	0.0175754i
$638$	−3423.85	−	5930.28i	−0.212463	−	0.367997i
$639$	6707.34	+	18288.5i	0.415240	+	1.13221i
$640$	−296.696	+	513.892i	−0.0183249	+	0.0317396i
$641$	28204.7	−	10265.7i	1.73794	−	0.632558i	0.738795	−	0.673930i	$-0.235395\pi$
$641$	28204.7	−	10265.7i	1.73794	−	0.632558i	0.999144	+	0.0413721i	$0.0131729\pi$
$642$	6893.19	+	1837.96i	0.423758	+	0.112989i
$643$	21277.9	−	17854.3i	1.30501	−	1.09503i	0.315751	−	0.948842i	$-0.397744\pi$
$643$	21277.9	−	17854.3i	1.30501	−	1.09503i	0.989257	−	0.146189i	$-0.0467007\pi$
$644$	8842.70	+	3218.48i	0.541073	+	0.196935i
$645$	29.8806	−	346.432i	0.00182411	−	0.0211484i
$646$	−709.488	+	4023.71i	−0.0432112	+	0.245063i
$647$	6120.46			0.371901			0.185951	−	0.982559i	$-0.440464\pi$
$647$	6120.46			0.371901			0.185951	+	0.982559i	$0.440464\pi$
$648$	5585.77	−	4733.92i	0.338626	−	0.286985i
$649$	3142.38			0.190061
$650$	24.4689	−	138.770i	0.00147654	−	0.00837385i
$651$	1296.93	−	15036.4i	0.0780809	−	0.905258i
$652$	23340.5	+	8495.24i	1.40197	+	0.510275i
$653$	−4140.87	+	3474.60i	−0.248154	+	0.208226i	−0.758377	−	0.651816i	$-0.774007\pi$
$653$	−4140.87	+	3474.60i	−0.248154	+	0.208226i	0.510223	+	0.860042i	$0.329563\pi$
$654$	−3911.08	−	1042.83i	−0.233846	−	0.0623516i
$655$	446.219	−	162.410i	0.0266186	−	0.00968839i
$656$	−8514.11	+	14746.9i	−0.506738	+	0.877696i
$657$	−2311.17	+	2768.11i	−0.137241	+	0.164375i
$658$	614.986	+	1065.19i	0.0364356	+	0.0631084i
$659$	−191.173	−	160.413i	−0.0113005	−	0.00948225i	0.637120	−	0.770765i	$-0.280126\pi$
$659$	−191.173	−	160.413i	−0.0113005	−	0.00948225i	−0.648420	+	0.761282i	$0.724570\pi$
$660$	−347.252	+	747.075i	−0.0204799	+	0.0440604i
$661$	5019.50	+	28467.0i	0.295364	+	1.67509i	0.665718	+	0.746203i	$0.268125\pi$
$661$	5019.50	+	28467.0i	0.295364	+	1.67509i	−0.370354	+	0.928891i	$0.620764\pi$
$662$	71.6568	+	406.386i	0.00420698	+	0.0238590i
$663$	−393.536	−	560.563i	−0.0230523	−	0.0328363i
$664$	−6502.11	−	5455.92i	−0.380016	−	0.318871i
$665$	208.183	+	360.584i	0.0121399	+	0.0210269i
$666$	3539.60	−	633.086i	0.205941	−	0.0368342i
$667$	−16886.3	+	29247.9i	−0.980270	+	1.69788i
$668$	13530.9	−	4924.85i	0.783723	−	0.285252i
$669$	1058.96	+	3932.78i	0.0611983	+	0.227279i
$670$	−22.8582	+	19.1803i	−0.00131804	+	0.00110597i
$671$	−10239.1	−	3726.72i	−0.589083	−	0.214409i
$672$	4716.25	+	3293.74i	0.270734	+	0.189076i
$673$	4614.50	−	26170.1i	0.264303	−	1.49894i	−0.506710	−	0.862116i	$-0.669139\pi$
$673$	4614.50	−	26170.1i	0.264303	−	1.49894i	0.771013	−	0.636819i	$-0.219750\pi$
$674$	6148.06			0.351357
$675$	15887.4	+	7337.36i	0.905936	+	0.418393i
$676$	16640.2			0.946757
$677$	1596.16	−	9052.28i	0.0906137	−	0.513896i	−0.905390	−	0.424581i	$-0.860421\pi$
$677$	1596.16	−	9052.28i	0.0906137	−	0.513896i	0.996003	−	0.0893144i	$-0.0284676\pi$
$678$	−2918.61	+	1365.33i	−0.165323	+	0.0773382i
$679$	−2552.45	−	929.017i	−0.144262	−	0.0525072i
$680$	297.539	−	249.665i	0.0167796	−	0.0140797i
$681$	−2202.59	+	2208.00i	−0.123940	+	0.124245i
$682$	7445.24	−	2709.85i	0.418025	−	0.152149i
$683$	−9472.69	+	16407.2i	−0.530692	+	0.919185i	0.468667	+	0.883375i	$0.344734\pi$
$683$	−9472.69	+	16407.2i	−0.530692	+	0.919185i	−0.999359	+	0.0358099i	$0.988599\pi$
$684$	−14931.0	+	8669.30i	−0.834648	+	0.484619i
$685$	132.824	+	230.059i	0.00740870	+	0.0128322i
$686$	2815.09	+	2362.14i	0.156677	+	0.131468i
$687$	10665.6	−	946.306i	0.592312	−	0.0525529i
$688$	1224.78	+	6946.07i	0.0678696	+	0.384908i
$689$	−160.599	−	910.803i	−0.00888003	−	0.0503612i
$690$	−221.628	+	19.6639i	−0.0122279	+	0.00108492i
$691$	1303.09	+	1093.42i	0.0717393	+	0.0601964i	0.677952	−	0.735106i	$-0.262868\pi$
$691$	1303.09	+	1093.42i	0.0717393	+	0.0601964i	−0.606213	+	0.795302i	$0.707312\pi$
$692$	−8134.94	−	14090.1i	−0.446885	−	0.774027i
$693$	9140.06	+	5247.16i	0.501013	+	0.287624i
$694$	−1193.46	+	2067.14i	−0.0652784	+	0.113065i
$695$	−762.183	+	277.412i	−0.0415989	+	0.0151408i
$696$	−9634.84	+	9658.51i	−0.524724	+	0.526013i
$697$	18096.2	−	15184.6i	0.983421	−	0.825188i
$698$	−6248.15	−	2274.14i	−0.338820	−	0.123320i
$699$	−20694.4	+	9680.88i	−1.11979	+	0.523840i
$700$	−1577.64	+	8947.23i	−0.0851844	+	0.483105i
$701$	16364.5			0.881710			0.440855	−	0.897578i	$-0.354675\pi$
$701$	16364.5			0.881710			0.440855	+	0.897578i	$0.354675\pi$
$702$	−40.4563	+	153.239i	−0.00217511	+	0.00823877i
$703$	−17422.1			−0.934691
$704$	2536.32	−	14384.2i	0.135783	−	0.770064i
$705$	435.405	+	304.078i	0.0232600	+	0.0162443i
$706$	33.4311	+	12.1679i	0.00178215	+	0.000648649i
$707$	3417.15	−	2867.33i	0.181775	−	0.152527i
$708$	−792.184	−	2942.03i	−0.0420510	−	0.156170i
$709$	−7531.07	+	2741.09i	−0.398922	+	0.145196i	−0.533687	−	0.845682i	$-0.679194\pi$
$709$	−7531.07	+	2741.09i	−0.398922	+	0.145196i	0.134766	+	0.990877i	$0.456972\pi$
$710$	119.559	−	207.082i	0.00631967	−	0.0109460i
$711$	−1161.99	+	3217.08i	−0.0612911	+	0.169690i
$712$	6964.94	+	12063.6i	0.366604	+	0.634977i
$713$	−29934.1	−	25117.7i	−1.57229	−	1.31931i
$714$	−1389.46	−	1979.18i	−0.0728278	−	0.103738i
$715$	−6.36274	−	36.0849i	−0.000332802	−	0.00188741i
$716$	−4689.51	−	26595.5i	−0.244770	−	1.38816i
$717$	−5792.34	+	12461.6i	−0.301700	+	0.649076i
$718$	−496.061	−	416.244i	−0.0257839	−	0.0216352i
$719$	3033.06	+	5253.42i	0.157322	+	0.272489i	0.933902	−	0.357529i	$-0.116381\pi$
$719$	3033.06	+	5253.42i	0.157322	+	0.272489i	−0.776580	+	0.630018i	$0.783047\pi$
$720$	741.528	+	128.876i	0.0383821	+	0.00667074i
$721$	1557.10	−	2696.98i	0.0804291	−	0.139307i
$722$	−150.799	+	54.8864i	−0.00777308	+	0.00282917i
$723$	−6469.28	−	1724.93i	−0.332773	−	0.0887289i
$724$	21948.3	−	18416.8i	1.12666	−	0.945380i
$725$	−30639.9	−	11152.0i	−1.56957	−	0.571277i
$726$	−92.4304	+	1071.62i	−0.00472509	+	0.0547820i
$727$	5392.55	−	30582.7i	0.275101	−	1.56018i	−0.463539	−	0.886077i	$-0.653421\pi$
$727$	5392.55	−	30582.7i	0.275101	−	1.56018i	0.738640	−	0.674100i	$-0.235468\pi$
$728$	−169.068			−0.00860725
$729$	−17118.0	−	9715.77i	−0.869682	−	0.493612i
$730$	44.2657			0.00224431
$731$	1699.12	−	9636.17i	0.0859700	−	0.487560i
$732$	−907.873	+	10525.7i	−0.0458414	+	0.531479i
$733$	30594.3	+	11135.4i	1.54165	+	0.561113i	0.966439	−	0.256896i	$-0.0826997\pi$
$733$	30594.3	+	11135.4i	1.54165	+	0.561113i	0.575206	+	0.818009i	$0.304922\pi$
$734$	−5873.40	+	4928.37i	−0.295356	+	0.247833i
$735$	647.521	+	172.652i	0.0324955	+	0.00866443i
$736$	13996.0	−	5094.15i	0.700953	−	0.255126i
$737$	1829.76	−	3169.24i	0.0914520	−	0.158400i
$738$	−5385.66	−	936.018i	−0.268630	−	0.0466874i
$739$	603.349	+	1045.03i	0.0300332	+	0.0520191i	0.880651	−	0.473765i	$-0.157105\pi$
$739$	603.349	+	1045.03i	0.0300332	+	0.0520191i	−0.850618	+	0.525784i	$0.823772\pi$
$740$	617.460	+	518.110i	0.0306733	+	0.0257380i
$741$	323.677	−	696.356i	0.0160466	−	0.0345226i
$742$	−567.027	−	3215.77i	−0.0280542	−	0.159103i
$743$	2498.60	+	14170.3i	0.123371	+	0.699672i	0.982262	+	0.187513i	$0.0600428\pi$
$743$	2498.60	+	14170.3i	0.123371	+	0.699672i	−0.858891	+	0.512158i	$0.828846\pi$
$744$	−9069.69	−	12919.1i	−0.446924	−	0.636609i
$745$	−343.229	−	288.004i	−0.0168791	−	0.0141633i
$746$	147.017	+	254.641i	0.00721537	+	0.0124974i
$747$	−7751.36	+	21460.4i	−0.379662	+	1.05113i
$748$	−11591.4	+	20076.9i	−0.566609	+	0.981396i
$749$	19224.1	−	6997.01i	0.937830	−	0.341342i
$750$	−111.824	−	415.295i	−0.00544432	−	0.0202192i
$751$	−23807.3	+	19976.7i	−1.15678	+	0.970652i	−0.999856	−	0.0169589i	$-0.994602\pi$
$751$	−23807.3	+	19976.7i	−1.15678	+	0.970652i	−0.156922	+	0.987611i	$0.550157\pi$
$752$	−10122.8	−	3684.42i	−0.490881	−	0.178666i
$753$	13354.7	+	9326.64i	0.646309	+	0.451370i
$754$	51.2786	−	290.815i	0.00247673	−	0.0140462i
$755$	−1227.03			−0.0591471
$756$	2608.43	−	9880.10i	0.125486	−	0.475312i
$757$	−18020.9			−0.865231			−0.432616	−	0.901578i	$-0.642409\pi$
$757$	−18020.9			−0.865231			−0.432616	+	0.901578i	$0.642409\pi$
$758$	−586.956	+	3328.79i	−0.0281256	+	0.159508i
$759$	24716.8	−	11562.6i	1.18203	−	0.552957i
$760$	409.214	+	148.942i	0.0195312	+	0.00710879i
$761$	−6118.25	+	5133.82i	−0.291441	+	0.244548i	−0.776771	−	0.629783i	$-0.783144\pi$
$761$	−6118.25	+	5133.82i	−0.291441	+	0.244548i	0.485330	+	0.874331i	$0.338699\pi$
$762$	−1932.20	+	1936.95i	−0.0918586	+	0.0920843i
$763$	−10907.5	+	3969.99i	−0.517532	+	0.188366i
$764$	−1840.86	+	3188.46i	−0.0871727	+	0.150988i
$765$	−905.522	−	519.845i	−0.0427963	−	0.0245687i
$766$	−755.031	−	1307.75i	−0.0356141	−	0.0616854i
$767$	103.809	+	87.1060i	0.00488699	+	0.00410067i
$768$	−11030.1	+	978.646i	−0.518249	+	0.0459816i
$769$	1924.09	+	10912.1i	0.0902268	+	0.511702i	0.996106	+	0.0881653i	$0.0281004\pi$
$769$	1924.09	+	10912.1i	0.0902268	+	0.511702i	−0.905879	+	0.423537i	$0.860789\pi$
$770$	−22.4649	−	127.405i	−0.00105140	−	0.00596280i
$771$	−24595.0	+	2182.19i	−1.14885	+	0.101932i
$772$	−20152.1	−	16909.6i	−0.939493	−	0.788328i
$773$	5237.99	+	9072.46i	0.243722	+	0.422139i	0.961772	−	0.273853i	$-0.0882981\pi$
$773$	5237.99	+	9072.46i	0.243722	+	0.422139i	−0.718049	+	0.695992i	$0.754965\pi$
$774$	−1958.09	+	1136.92i	−0.0909329	+	0.0527981i
$775$	18863.4	−	32672.4i	0.874316	−	1.51436i
$776$	−2669.60	+	971.655i	−0.123496	+	0.0449489i
$777$	7282.34	−	7300.23i	0.336232	−	0.337058i
$778$	−493.393	+	414.006i	−0.0227365	+	0.0190782i
$779$	24888.3	+	9058.60i	1.14469	+	0.416634i
$780$	−32.1802	+	15.0540i	−0.00147722	+	0.000691049i
$781$	−5092.36	+	28880.2i	−0.233315	+	1.32320i
$782$	−6261.14			−0.286314
$783$	33294.7	+	15376.7i	1.51961	+	0.701809i
$784$	−13593.4			−0.619233
$785$	110.397	−	626.093i	0.00501942	−	0.0284665i
$786$	−2535.07	−	1770.45i	−0.115042	−	0.0803432i
$787$	−6491.88	−	2362.85i	−0.294041	−	0.107022i	0.190787	−	0.981631i	$-0.438896\pi$
$787$	−6491.88	−	2362.85i	−0.294041	−	0.107022i	−0.484829	+	0.874609i	$0.661118\pi$
$788$	11358.5	−	9530.93i	0.513491	−	0.430870i
$789$	−4002.75	−	14865.5i	−0.180610	−	0.670755i
$790$	39.4552	−	14.3605i	0.00177690	−	0.000646740i
$791$	−4620.05	+	8002.16i	−0.207674	+	0.359702i
$792$	10850.6	−	1940.72i	0.486819	−	0.0870715i
$793$	−234.945	−	406.936i	−0.0105210	−	0.0182229i
$794$	5192.00	+	4356.61i	0.232062	+	0.194723i
$795$	−810.114	−	1153.95i	−0.0361406	−	0.0514796i
$796$	−1751.97	−	9935.93i	−0.0780113	−	0.442424i
$797$	5001.03	+	28362.2i	0.222265	+	1.26053i	0.867844	+	0.496836i	$0.165505\pi$
$797$	5001.03	+	28362.2i	0.222265	+	1.26053i	−0.645579	+	0.763694i	$0.723384\pi$
$798$	1142.80	−	2458.62i	0.0506953	−	0.109066i
$799$	11448.2	+	9606.15i	0.506893	+	0.425333i
$800$	7189.98	+	12453.4i	0.317755	+	0.550368i
$801$	23999.8	−	28744.7i	1.05866	−	1.26797i
$802$	−2827.11	+	4896.71i	−0.124475	+	0.215597i
$803$	−5101.41	+	1856.76i	−0.224190	+	0.0815986i
$804$	−3428.45	−	914.145i	−0.150388	−	0.0400988i
$805$	−488.775	+	410.131i	−0.0214000	+	0.0179568i
$806$	321.070	+	116.860i	0.0140313	+	0.00510697i
$807$	2465.56	−	28585.4i	0.107549	−	1.24691i
$808$	810.155	−	4594.62i	0.0352737	−	0.200047i
$809$	22480.1			0.976957			0.488478	−	0.872576i	$-0.337552\pi$
$809$	22480.1			0.976957			0.488478	+	0.872576i	$0.337552\pi$
$810$	43.1228	+	237.734i	0.00187059	+	0.0103125i
$811$	24023.6			1.04017			0.520087	−	0.854113i	$-0.325899\pi$
$811$	24023.6			1.04017			0.520087	+	0.854113i	$0.325899\pi$
$812$	−3306.20	+	18750.4i	−0.142888	+	0.810357i
$813$	−268.506	+	3113.02i	−0.0115829	+	0.134291i
$814$	5086.80	+	1851.45i	0.219032	+	0.0797213i
$815$	−1290.13	+	1082.55i	−0.0554494	+	0.0465276i
$816$	20464.5	+	5456.55i	0.877943	+	0.234090i
$817$	10308.9	−	3752.14i	0.441449	−	0.160674i
$818$	2270.16	−	3932.03i	0.0970345	−	0.168069i
$819$	156.493	+	426.700i	0.00667680	+	0.0182053i
$820$	−612.679	−	1061.19i	−0.0260923	−	0.0451932i
$821$	19460.6	+	16329.4i	0.827261	+	0.694154i	0.954660	−	0.297697i	$-0.0962186\pi$
$821$	19460.6	+	16329.4i	0.827261	+	0.694154i	−0.127400	+	0.991851i	$0.540663\pi$
$822$	729.128	−	1568.64i	0.0309383	−	0.0665604i
$823$	−1750.88	−	9929.75i	−0.0741579	−	0.420570i	−0.999174	−	0.0406419i	$-0.987060\pi$
$823$	−1750.88	−	9929.75i	−0.0741579	−	0.420570i	0.925016	−	0.379928i	$-0.124051\pi$
$824$	−565.594	−	3207.64i	−0.0239119	−	0.135611i
$825$	15137.5	+	21562.2i	0.638812	+	0.909940i
$826$	366.518	+	307.545i	0.0154392	+	0.0129550i
$827$	−8458.54	−	14650.6i	−0.355662	−	0.616024i	0.631569	−	0.775320i	$-0.282411\pi$
$827$	−8458.54	−	14650.6i	−0.355662	−	0.616024i	−0.987231	+	0.159295i	$0.949078\pi$
$828$	−17056.4	−	20226.0i	−0.715881	−	0.848915i
$829$	−7037.59	+	12189.5i	−0.294844	+	0.510684i	−0.974949	−	0.222431i	$-0.928601\pi$
$829$	−7037.59	+	12189.5i	−0.294844	+	0.510684i	0.680105	+	0.733115i	$0.261934\pi$
$830$	263.197	−	95.7957i	0.0110069	−	0.00400617i
$831$	−3609.83	−	13406.3i	−0.150690	−	0.559636i
$832$	482.513	−	404.877i	0.0201059	−	0.0168709i
$833$	17720.6	+	6449.79i	0.737075	+	0.268274i
$834$	4330.15	+	3024.09i	0.179785	+	0.125558i
$835$	−169.538	+	961.498i	−0.00702648	+	0.0398491i
$836$	−25992.1			−1.07530
$837$	−24210.6	+	34848.6i	−0.999811	+	1.43912i
$838$	413.908			0.0170623
$839$	511.993	−	2903.65i	0.0210679	−	0.119482i	−0.972460	−	0.233069i	$-0.925123\pi$
$839$	511.993	−	2903.65i	0.0210679	−	0.119482i	0.993528	+	0.113587i	$0.0362342\pi$
$840$	−233.459	+	109.212i	−0.00958939	+	0.00448594i
$841$	−41292.9	−	15029.4i	−1.69310	−	0.616236i
$842$	2944.96	−	2471.11i	0.120534	−	0.101140i
$843$	−13634.3	+	13667.7i	−0.557045	+	0.558413i
$844$	−25194.2	+	9169.93i	−1.02751	+	0.373983i
$845$	−564.136	+	977.112i	−0.0229667	+	0.0397795i
$846$	−8.48478	−	3458.17i	−0.000344814	−	0.140537i
$847$	1542.23	+	2671.22i	0.0625640	+	0.108364i
$848$	21908.3	+	18383.3i	0.887188	+	0.744439i
$849$	9081.44	−	805.750i	0.367107	−	0.0325716i
$850$	−1049.69	−	5953.09i	−0.0423578	−	0.240223i
$851$	−4636.06	−	26292.4i	−0.186748	−	1.05910i
$852$	28322.6	−	2512.92i	1.13887	−	0.101046i
$853$	12605.1	+	10576.9i	0.505968	+	0.424557i	0.859708	−	0.510787i	$-0.170646\pi$
$853$	12605.1	+	10576.9i	0.505968	+	0.424557i	−0.353740	+	0.935344i	$0.615090\pi$
$854$	−829.519	−	1436.77i	−0.0332384	−	0.0575705i
$855$	−2.87225	−	1170.65i	−0.000114888	−	0.0468251i
$856$	10698.4	−	18530.2i	0.427178	−	0.739894i
$857$	−37503.3	+	13650.1i	−1.49485	+	0.544082i	−0.954722	−	0.297500i	$-0.903847\pi$
$857$	−37503.3	+	13650.1i	−1.49485	+	0.544082i	−0.540130	+	0.841582i	$0.681625\pi$
$858$	−168.507	+	168.921i	−0.00670481	+	0.00672128i
$859$	−10850.4	+	9104.56i	−0.430979	+	0.361634i	−0.832321	−	0.554294i	$-0.812988\pi$
$859$	−10850.4	+	9104.56i	−0.430979	+	0.361634i	0.401342	+	0.915928i	$0.368544\pi$
$860$	−476.944	−	173.593i	−0.0189112	−	0.00688312i
$861$	−14198.9	+	6642.27i	−0.562018	+	0.262913i
$862$	−1322.30	+	7499.11i	−0.0522477	+	0.296312i
$863$	−13515.4			−0.533104			−0.266552	−	0.963821i	$-0.585884\pi$
$863$	−13515.4			−0.533104			−0.266552	+	0.963821i	$0.585884\pi$
$864$	−6889.26	−	14633.2i	−0.271270	−	0.576195i
$865$	1103.16			0.0433627
$866$	417.069	−	2365.32i	0.0163656	−	0.0928138i
$867$	−3159.11	−	2206.26i	−0.123747	−	0.0864227i
$868$	−20701.1	−	7534.58i	−0.809494	−	0.294632i
$869$	−3944.66	+	3309.97i	−0.153986	+	0.129209i
$870$	−117.049	−	434.698i	−0.00456129	−	0.0169398i
$871$	148.297	−	53.9756i	0.00576905	−	0.00209976i
$872$	−6070.11	+	10513.7i	−0.235734	+	0.408303i
$873$	4923.33	+	5838.25i	0.190870	+	0.226340i
$874$	−3509.92	−	6079.37i	−0.135841	−	0.235283i
$875$	−944.793	−	792.775i	−0.0365027	−	0.0306294i
$876$	3024.43	+	4308.07i	0.116651	+	0.166160i
$877$	−1315.98	−	7463.30i	−0.0506699	−	0.287363i	0.948935	−	0.315472i	$-0.102163\pi$
$877$	−1315.98	−	7463.30i	−0.0506699	−	0.287363i	−0.999605	+	0.0281084i	$0.991052\pi$
$878$	1356.46	+	7692.88i	0.0521394	+	0.295697i
$879$	16255.6	−	34972.3i	0.623765	−	1.34196i
$880$	867.982	+	728.323i	0.0332496	+	0.0278997i
$881$	428.600	+	742.357i	0.0163904	+	0.0283889i	0.874104	−	0.485738i	$-0.161449\pi$
$881$	428.600	+	742.357i	0.0163904	+	0.0283889i	−0.857714	+	0.514127i	$0.828116\pi$
$882$	−1502.55	−	4096.91i	−0.0573621	−	0.156406i
$883$	−2788.53	+	4829.87i	−0.106276	+	0.184075i	−0.914259	−	0.405131i	$-0.867226\pi$
$883$	−2788.53	+	4829.87i	−0.106276	+	0.184075i	0.807983	+	0.589206i	$0.200559\pi$
$884$	−939.449	+	341.931i	−0.0357433	+	0.0130095i
$885$	199.613	+	53.2237i	0.00758182	+	0.00202158i
$886$	1897.52	−	1592.21i	0.0719509	−	0.0603740i
$887$	11301.4	+	4113.38i	0.427807	+	0.155709i	0.546945	−	0.837169i	$-0.315791\pi$
$887$	11301.4	+	4113.38i	0.427807	+	0.155709i	−0.119138	+	0.992878i	$0.538013\pi$
$888$	926.767	−	10744.8i	0.0350228	−	0.406049i
$889$	−1362.38	+	7726.44i	−0.0513979	+	0.291492i
$890$	−459.665			−0.0173124
$891$	−14941.7	−	25588.9i	−0.561800	−	0.962132i
$892$	5945.01			0.223154
$893$	−2909.56	+	16500.9i	−0.109031	+	0.618345i
$894$	−250.718	+	2906.78i	−0.00937948	+	0.108744i
$895$	1720.67	+	626.274i	0.0642635	+	0.0233900i
$896$	8488.17	−	7122.42i	0.316484	−	0.265562i
$897$	1137.03	+	303.172i	0.0423237	+	0.0112850i
$898$	−3128.10	+	1138.54i	−0.116243	+	0.0423090i
$899$	39531.4	−	68470.5i	1.46657	−	2.54018i
$900$	16371.4	−	19608.1i	0.606346	−	0.726227i
$901$	−19837.7	−	34359.8i	−0.733506	−	1.27047i
$902$	−6304.08	−	5289.75i	−0.232708	−	0.195265i
$903$	−2736.84	+	5888.03i	−0.100860	+	0.216989i
$904$	1678.17	+	9517.36i	0.0617423	+	0.350158i
$905$	337.344	+	1913.17i	0.0123908	+	0.0702718i
$906$	4590.89	+	6539.38i	0.168347	+	0.239797i
$907$	−4767.61	−	4000.50i	−0.174538	−	0.146455i	0.551334	−	0.834285i	$-0.314119\pi$
$907$	−4767.61	−	4000.50i	−0.174538	−	0.146455i	−0.725872	+	0.687830i	$0.758563\pi$
$908$	2276.18	+	3942.46i	0.0831913	+	0.144091i
$909$	−12346.0	+	2208.17i	−0.450484	+	0.0805726i
$910$	2.78950	−	4.83155i	0.000101616	−	0.000176005i
$911$	−26015.0	+	9468.69i	−0.946121	+	0.344360i	−0.768580	−	0.639754i	$-0.779036\pi$
$911$	−26015.0	+	9468.69i	−0.946121	+	0.344360i	−0.177541	+	0.984113i	$0.556814\pi$
$912$	6174.04	+	22929.3i	0.224170	+	0.832527i
$913$	−26313.9	+	22080.0i	−0.953849	+	0.800374i
$914$	6238.13	+	2270.49i	0.225754	+	0.0821676i
$915$	−587.293	−	410.154i	−0.0212189	−	0.0148189i
$916$	2714.02	−	15392.0i	0.0978971	−	0.555202i
$917$	−8867.08			−0.319320
$918$	617.497	+	6770.93i	0.0222009	+	0.243436i
$919$	15537.6			0.557711			0.278856	−	0.960333i	$-0.410045\pi$
$919$	15537.6			0.557711			0.278856	+	0.960333i	$0.410045\pi$
$920$	−115.881	+	657.195i	−0.00415271	+	0.0235512i
$921$	−46236.6	+	21629.6i	−1.65423	+	0.773852i
$922$	−2965.85	−	1079.48i	−0.105938	−	0.0385583i
$923$	−968.778	+	812.901i	−0.0345479	+	0.0289891i
$924$	10864.5	−	10891.2i	0.386815	−	0.387765i
$925$	24221.6	−	8815.94i	0.860975	−	0.313369i
$926$	−1846.37	+	3198.01i	−0.0655243	+	0.113491i
$927$	−7572.04	+	4396.53i	−0.268283	+	0.155772i
$928$	15067.8	+	26098.2i	0.533000	+	0.923184i
$929$	−20230.4	−	16975.3i	−0.714465	−	0.599508i	0.211383	−	0.977403i	$-0.432203\pi$
$929$	−20230.4	−	16975.3i	−0.714465	−	0.599508i	−0.925848	+	0.377896i	$0.876648\pi$
$930$	518.840	−	46.0340i	0.0182940	−	0.00162313i
$931$	3671.46	+	20821.9i	0.129245	+	0.732985i
$932$	5790.96	+	32842.1i	0.203529	+	1.15427i
$933$	11569.4	−	1026.49i	0.405964	−	0.0360191i
$934$	−4987.30	−	4184.84i	−0.174721	−	0.146608i
$935$	−785.944	−	1361.30i	−0.0274900	−	0.0476140i
$936$	412.248	+	236.665i	0.0143961	+	0.00826457i
$937$	22520.4	−	39006.5i	0.785176	−	1.35997i	−0.143717	−	0.989619i	$-0.545906\pi$
$937$	22520.4	−	39006.5i	0.785176	−	1.35997i	0.928894	−	0.370347i	$-0.120761\pi$
$938$	523.591	−	190.572i	0.0182259	−	0.00663367i
$939$	1060.31	−	1062.91i	0.0368497	−	0.0369402i
$940$	593.833	−	498.285i	0.0206050	−	0.0172897i
$941$	2547.96	+	927.382i	0.0882690	+	0.0321273i	0.385777	−	0.922592i	$-0.373933\pi$
$941$	2547.96	+	927.382i	0.0882690	+	0.0321273i	−0.297508	+	0.954719i	$0.596156\pi$
$942$	−3749.78	+	1754.16i	−0.129697	+	0.0606725i
$943$	−7047.87	+	39970.4i	−0.243383	+	1.38029i
$944$	−4190.47			−0.144479
$945$	491.729	+	488.122i	0.0169269	+	0.0168028i
$946$	−3408.68			−0.117152
$947$	4493.52	−	25484.0i	0.154192	−	0.874466i	−0.805329	−	0.592828i	$-0.798011\pi$
$947$	4493.52	−	25484.0i	0.154192	−	0.874466i	0.959521	−	0.281638i	$-0.0908777\pi$
$948$	4093.37	+	2858.73i	0.140239	+	0.0979401i
$949$	−219.994	−	80.0714i	−0.00752510	−	0.00273891i
$950$	5191.82	−	4356.45i	0.177310	−	0.148781i
$951$	10130.9	+	37624.3i	0.345443	+	1.28291i
$952$	−6815.45	+	2480.62i	−0.232027	+	0.0844511i
$953$	21304.4	−	36900.3i	0.724152	−	1.25427i	−0.235170	−	0.971954i	$-0.575565\pi$
$953$	21304.4	−	36900.3i	0.724152	−	1.25427i	0.959322	−	0.282314i	$-0.0911021\pi$
$954$	−3118.89	+	8634.93i	−0.105847	+	0.293046i
$955$	−124.818	−	216.191i	−0.00422933	−	0.00732541i
$956$	15365.9	+	12893.5i	0.519843	+	0.436200i
$957$	31723.1	+	45187.2i	1.07154	+	1.52633i
$958$	2066.41	+	11719.2i	0.0696896	+	0.395230i
$959$	−861.385	−	4885.16i	−0.0290048	−	0.164494i
$960$	404.744	−	870.765i	0.0136074	−	0.0292748i
$961$	47255.7	+	39652.3i	1.58624	+	1.33101i
$962$	116.721	+	202.167i	0.00391190	+	0.00677561i
$963$	−56669.9	−	9849.12i	−1.89632	−	0.329578i
$964$	−4886.46	+	8463.59i	−0.163260	+	0.282774i
$965$	1676.13	−	610.060i	0.0559134	−	0.0203508i
$966$	4014.51	+	1070.41i	0.133711	+	0.0356520i
$967$	33864.2	−	28415.4i	1.12616	−	0.944962i	0.127263	−	0.991869i	$-0.459381\pi$
$967$	33864.2	−	28415.4i	1.12616	−	0.944962i	0.998899	+	0.0469069i	$0.0149364\pi$
$968$	3031.47	+	1103.37i	0.100656	+	0.0366359i
$969$	2830.86	−	32820.5i	0.0938496	−	1.08808i
$970$	16.2789	−	92.3222i	0.000538849	−	0.00305597i
$971$	−23241.5			−0.768132			−0.384066	−	0.923306i	$-0.625476\pi$
$971$	−23241.5			−0.768132			−0.384066	+	0.923306i	$0.625476\pi$
$972$	−20190.6	+	20439.9i	−0.666271	+	0.674495i
$973$	15145.8			0.499026
$974$	1445.66	−	8198.76i	0.0475585	−	0.269718i
$975$	−97.6308	+	1131.92i	−0.00320686	+	0.0371798i
$976$	13654.1	+	4969.70i	0.447805	+	0.162988i
$977$	−18242.9	+	15307.6i	−0.597383	+	0.501263i	−0.890603	−	0.454781i	$-0.849717\pi$
$977$	−18242.9	+	15307.6i	−0.597383	+	0.501263i	0.293221	+	0.956045i	$0.405273\pi$
$978$	10596.4	+	2825.36i	0.346457	+	0.0923775i
$979$	52974.3	−	19281.1i	1.72938	−	0.629444i
$980$	489.094	−	847.135i	0.0159424	−	0.0276130i
$981$	32153.6	+	5588.23i	1.04647	+	0.181874i
$982$	−5928.69	−	10268.8i	−0.192660	−	0.333697i
$983$	−17952.9	−	15064.2i	−0.582510	−	0.488784i	0.303260	−	0.952908i	$-0.401925\pi$
$983$	−17952.9	−	15064.2i	−0.582510	−	0.488784i	−0.885770	+	0.464124i	$0.846369\pi$
$984$	−6910.67	+	14867.6i	−0.223886	+	0.481667i
$985$	174.580	+	990.091i	0.00564728	+	0.0320273i
$986$	−2199.80	−	12475.7i	−0.0710506	−	0.402948i
$987$	−5698.05	−	8116.45i	−0.183760	−	0.261752i
$988$	−858.649	−	720.492i	−0.0276491	−	0.0232003i
$989$	8405.74	+	14559.2i	0.270260	+	0.468104i
$990$	−123.566	+	342.105i	−0.00396687	+	0.0109826i
$991$	29.3251	−	50.7926i	0.000940004	−	0.00162813i	−0.865555	−	0.500814i	$-0.833034\pi$
$991$	29.3251	−	50.7926i	0.000940004	−	0.00162813i	0.866495	+	0.499186i	$0.166367\pi$
$992$	−32765.3	+	11925.6i	−1.04869	+	0.381691i
$993$	−865.062	−	3212.68i	−0.0276454	−	0.102670i
$994$	−3420.46	+	2870.11i	−0.109145	+	0.0915838i
$995$	642.833	+	233.972i	0.0204816	+	0.00745469i
$996$	27305.9	+	19069.9i	0.868695	+	0.606680i
$997$	6906.86	−	39170.8i	0.219401	−	1.24428i	−0.653704	−	0.756750i	$-0.726786\pi$
$997$	6906.86	−	39170.8i	0.219401	−	1.24428i	0.873105	−	0.487533i	$-0.162103\pi$
$998$	−1001.79			−0.0317746
$999$	−27976.0	+	7606.60i	−0.886006	+	0.240903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.4.e.a.25.5	yes	48
3.2	odd	2		81.4.e.a.73.4		48
9.2	odd	6		243.4.e.a.55.5		48
9.4	even	3		243.4.e.c.136.5		48
9.5	odd	6		243.4.e.b.136.4		48
9.7	even	3		243.4.e.d.55.4		48
27.4	even	9		243.4.e.c.109.5		48
27.5	odd	18		243.4.e.a.190.5		48
27.11	odd	18		729.4.a.c.1.13		24
27.13	even	9	inner	27.4.e.a.13.5	✓	48
27.14	odd	18		81.4.e.a.10.4		48
27.16	even	9		729.4.a.d.1.12		24
27.22	even	9		243.4.e.d.190.4		48
27.23	odd	18		243.4.e.b.109.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.13.5	✓	48	27.13	even	9	inner
27.4.e.a.25.5	yes	48	1.1	even	1	trivial
81.4.e.a.10.4		48	27.14	odd	18
81.4.e.a.73.4		48	3.2	odd	2
243.4.e.a.55.5		48	9.2	odd	6
243.4.e.a.190.5		48	27.5	odd	18
243.4.e.b.109.4		48	27.23	odd	18
243.4.e.b.136.4		48	9.5	odd	6
243.4.e.c.109.5		48	27.4	even	9
243.4.e.c.136.5		48	9.4	even	3
243.4.e.d.55.4		48	9.7	even	3
243.4.e.d.190.4		48	27.22	even	9
729.4.a.c.1.13		24	27.11	odd	18
729.4.a.d.1.12		24	27.16	even	9

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.111911 - 0.634678i) q^{2} +(-0.446524 + 5.17693i) q^{3} +(7.12725 + 2.59411i) q^{4} +(-0.393954 + 0.330567i) q^{5} +(3.23571 + 0.862753i) q^{6} +(9.02395 - 3.28445i) q^{7} +(5.02191 - 8.69820i) q^{8} +(-26.6012 - 4.62325i) q^{9} +O(q^{10})\)	\(q+(0.111911 - 0.634678i) q^{2} +(-0.446524 + 5.17693i) q^{3} +(7.12725 + 2.59411i) q^{4} +(-0.393954 + 0.330567i) q^{5} +(3.23571 + 0.862753i) q^{6} +(9.02395 - 3.28445i) q^{7} +(5.02191 - 8.69820i) q^{8} +(-26.6012 - 4.62325i) q^{9} +(0.165716 + 0.287028i) q^{10} +(-31.1376 - 26.1275i) q^{11} +(-16.6120 + 35.7389i) q^{12} +(-0.304384 - 1.72625i) q^{13} +(-1.07469 - 6.09486i) q^{14} +(-1.53541 - 2.18708i) q^{15} +(41.5229 + 34.8419i) q^{16} +(-37.5984 - 65.1223i) q^{17} +(-5.91124 + 16.3658i) q^{18} +(42.1545 - 73.0137i) q^{19} +(-3.66533 + 1.33407i) q^{20} +(12.9740 + 48.1829i) q^{21} +(-20.0672 + 16.8384i) q^{22} +(121.405 + 44.1880i) q^{23} +(42.7876 + 29.8820i) q^{24} +(-21.6601 + 122.841i) q^{25} -1.12968 q^{26} +(35.8123 - 135.648i) q^{27} +72.8361 q^{28} +(-45.3923 + 257.433i) q^{29} +(-1.55992 + 0.729733i) q^{30} +(-284.215 - 103.446i) q^{31} +(88.3123 - 74.1029i) q^{32} +(149.164 - 149.530i) q^{33} +(-45.5393 + 16.5750i) q^{34} +(-2.46929 + 4.27694i) q^{35} +(-177.600 - 101.957i) q^{36} +(-103.323 - 178.961i) q^{37} +(-41.6226 - 34.9255i) q^{38} +(9.07259 - 0.804965i) q^{39} +(0.896935 + 5.08677i) q^{40} +(54.5513 + 309.376i) q^{41} +(32.0325 - 2.84209i) q^{42} +(99.6799 + 83.6413i) q^{43} +(-154.148 - 266.991i) q^{44} +(12.0080 - 6.97214i) q^{45} +(41.6317 - 72.1082i) q^{46} +(-186.753 + 67.9727i) q^{47} +(-198.915 + 199.404i) q^{48} +(-192.109 + 161.199i) q^{49} +(75.5401 + 27.4944i) q^{50} +(353.922 - 165.566i) q^{51} +(2.30865 - 13.0930i) q^{52} +527.620 q^{53} +(-82.0852 - 37.9098i) q^{54} +20.9037 q^{55} +(16.7487 - 94.9863i) q^{56} +(359.164 + 250.833i) q^{57} +(158.307 + 57.6190i) q^{58} +(-59.2219 + 49.6931i) q^{59} +(-5.26974 - 19.5709i) q^{60} +(251.901 - 91.6844i) q^{61} +(-97.4613 + 168.808i) q^{62} +(-255.233 + 45.6504i) q^{63} +(179.669 + 311.196i) q^{64} +(0.690554 + 0.579443i) q^{65} +(-78.2106 - 111.405i) q^{66} +(15.6338 + 88.6636i) q^{67} +(-99.0389 - 561.677i) q^{68} +(-282.968 + 608.776i) q^{69} +(2.43814 + 2.04584i) q^{70} +(-360.735 - 624.811i) q^{71} +(-173.803 + 208.165i) q^{72} +(66.7796 - 115.666i) q^{73} +(-125.145 + 45.5491i) q^{74} +(-626.265 - 166.984i) q^{75} +(489.851 - 411.034i) q^{76} +(-366.798 - 133.504i) q^{77} +(0.504427 - 5.84825i) q^{78} +(21.9986 - 124.760i) q^{79} -27.8757 q^{80} +(686.251 + 245.968i) q^{81} +202.459 q^{82} +(146.748 - 832.248i) q^{83} +(-32.5231 + 377.068i) q^{84} +(36.3393 + 13.2264i) q^{85} +(64.2405 - 53.9042i) q^{86} +(-1312.44 - 349.943i) q^{87} +(-383.633 + 139.631i) q^{88} +(-693.455 + 1201.10i) q^{89} +(-3.08124 - 8.40144i) q^{90} +(-8.41652 - 14.5778i) q^{91} +(750.658 + 629.877i) q^{92} +(662.440 - 1425.17i) q^{93} +(22.2410 + 126.135i) q^{94} +(7.52897 + 42.6989i) q^{95} +(344.192 + 490.276i) q^{96} +(-216.678 - 181.815i) q^{97} +(80.8102 + 139.967i) q^{98} +(707.504 + 838.981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Introduction

L-functions

Modular forms

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Database

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