LMFDB - Embedded newform 177.4.e.a.76.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,4,Mod(4,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("177.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.e (of order $29$, degree $28$, 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:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$420$
Relative dimension:	$15$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			76.5
Character	$\chi$	$=$	177.76
Dual form			177.4.e.a.7.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59837 + 2.35742i) q^{2} +(-0.162417 - 2.99560i) q^{3} +(-0.0415309 - 0.104235i) q^{4} +(14.5110 + 6.71353i) q^{5} +(7.32148 + 4.40519i) q^{6} +(0.937125 + 3.37522i) q^{7} +(-21.9407 - 4.82952i) q^{8} +(-8.94724 + 0.973071i) q^{9} +O(q^{10})$	\(q+(-1.59837 + 2.35742i) q^{2} +(-0.162417 - 2.99560i) q^{3} +(-0.0415309 - 0.104235i) q^{4} +(14.5110 + 6.71353i) q^{5} +(7.32148 + 4.40519i) q^{6} +(0.937125 + 3.37522i) q^{7} +(-21.9407 - 4.82952i) q^{8} +(-8.94724 + 0.973071i) q^{9} +(-39.0206 + 23.4779i) q^{10} +(10.9330 + 10.3563i) q^{11} +(-0.305500 + 0.141340i) q^{12} +(83.7523 + 9.10861i) q^{13} +(-9.45468 - 3.18565i) q^{14} +(17.7542 - 44.5597i) q^{15} +(47.1062 - 44.6214i) q^{16} +(-3.89572 + 14.0311i) q^{17} +(12.0071 - 22.6477i) q^{18} +(-83.9359 - 63.8064i) q^{19} +(0.0971255 - 1.79138i) q^{20} +(9.95860 - 3.35544i) q^{21} +(-41.8892 + 9.22051i) q^{22} +(61.5381 + 116.073i) q^{23} +(-10.9038 + 66.5100i) q^{24} +(84.5758 + 99.5703i) q^{25} +(-155.340 + 182.880i) q^{26} +(4.36811 + 26.6443i) q^{27} +(0.312896 - 0.237857i) q^{28} +(141.278 + 208.369i) q^{29} +(76.6680 + 113.077i) q^{30} +(-220.137 + 167.344i) q^{31} +(0.821431 + 5.01051i) q^{32} +(29.2477 - 34.4330i) q^{33} +(-26.8504 - 31.6107i) q^{34} +(-9.06096 + 55.2694i) q^{35} +(0.473015 + 0.892201i) q^{36} +(-114.804 + 25.2703i) q^{37} +(284.579 - 95.8858i) q^{38} +(13.6830 - 252.368i) q^{39} +(-285.960 - 217.381i) q^{40} +(-100.801 + 190.131i) q^{41} +(-8.00734 + 28.8398i) q^{42} +(-179.351 + 169.890i) q^{43} +(0.625430 - 1.56971i) q^{44} +(-136.367 - 45.9473i) q^{45} +(-371.994 - 40.4567i) q^{46} +(301.937 - 139.691i) q^{47} +(-141.319 - 133.864i) q^{48} +(283.388 - 170.509i) q^{49} +(-369.912 + 40.2304i) q^{50} +(42.6643 + 9.39112i) q^{51} +(-2.52888 - 9.10819i) q^{52} +(-12.7283 - 7.65835i) q^{53} +(-69.7937 - 32.2900i) q^{54} +(89.1224 + 223.680i) q^{55} +(-4.26052 - 78.5806i) q^{56} +(-177.506 + 261.802i) q^{57} -717.028 q^{58} +(441.303 + 103.105i) q^{59} -5.38202 q^{60} +(441.142 - 650.636i) q^{61} +(-42.6391 - 786.432i) q^{62} +(-11.6690 - 29.2870i) q^{63} +(457.980 + 211.884i) q^{64} +(1154.18 + 694.449i) q^{65} +(34.4245 + 123.986i) q^{66} +(-441.588 - 97.2008i) q^{67} +(1.62432 - 0.176656i) q^{68} +(337.714 - 203.196i) q^{69} +(-115.810 - 109.701i) q^{70} +(-128.775 + 59.5778i) q^{71} +(201.008 + 21.8610i) q^{72} +(-650.212 - 219.082i) q^{73} +(123.927 - 311.032i) q^{74} +(284.536 - 269.527i) q^{75} +(-3.16491 + 11.3990i) q^{76} +(-24.7092 + 46.6066i) q^{77} +(573.066 + 435.633i) q^{78} +(38.7863 - 715.371i) q^{79} +(983.128 - 331.254i) q^{80} +(79.1063 - 17.4126i) q^{81} +(-287.102 - 541.531i) q^{82} +(-101.741 + 620.592i) q^{83} +(-0.763344 - 0.898678i) q^{84} +(-150.729 + 177.452i) q^{85} +(-113.833 - 694.353i) q^{86} +(601.246 - 457.055i) q^{87} +(-189.863 - 280.026i) q^{88} +(-83.2418 - 122.772i) q^{89} +(326.281 - 248.032i) q^{90} +(47.7428 + 291.218i) q^{91} +(9.54313 - 11.2350i) q^{92} +(537.049 + 632.263i) q^{93} +(-153.297 + 935.068i) q^{94} +(-789.632 - 1489.40i) q^{95} +(14.8761 - 3.27447i) q^{96} +(889.351 - 299.657i) q^{97} +(-50.9979 + 940.601i) q^{98} +(-107.898 - 82.0219i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9}+O(q^{10}) $ 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9	\( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9} + 854 q^{10} + 32 q^{11} + 192 q^{12} - 22 q^{13} - 884 q^{14} - 42 q^{15} - 268 q^{16} - 56 q^{17} - 18 q^{18} - 112 q^{19} - 250 q^{20} + 243 q^{21} + 108 q^{22} + 16 q^{23} - 54 q^{24} - 197 q^{25} - 328 q^{26} + 405 q^{27} + 236 q^{28} - 54 q^{29} - 126 q^{30} + 66 q^{31} + 857 q^{32} - 96 q^{33} + 112 q^{34} + 532 q^{35} - 576 q^{36} + 110 q^{37} + 56 q^{38} + 66 q^{39} - 6044 q^{40} + 304 q^{41} - 306 q^{42} - 324 q^{43} - 568 q^{44} + 126 q^{45} + 5842 q^{46} + 4082 q^{47} + 804 q^{48} + 739 q^{49} + 576 q^{50} + 168 q^{51} - 1372 q^{52} - 1498 q^{53} + 54 q^{54} - 4422 q^{55} - 12036 q^{56} + 336 q^{57} + 6298 q^{58} - 3305 q^{59} + 750 q^{60} - 1718 q^{61} - 4333 q^{62} + 54 q^{63} - 6250 q^{64} - 5884 q^{65} - 324 q^{66} + 382 q^{67} + 734 q^{68} + 3780 q^{69} + 8082 q^{70} + 8638 q^{71} + 162 q^{72} + 8894 q^{73} + 12428 q^{74} + 243 q^{75} - 15468 q^{76} - 9916 q^{77} + 984 q^{78} - 578 q^{79} + 24570 q^{80} - 1215 q^{81} - 1382 q^{82} - 32 q^{83} + 7557 q^{84} + 708 q^{85} + 2296 q^{86} - 5928 q^{87} - 17646 q^{88} - 2284 q^{89} + 378 q^{90} + 11124 q^{91} + 762 q^{92} - 198 q^{93} - 1232 q^{94} + 24184 q^{95} - 396 q^{96} - 658 q^{97} - 4356 q^{98} + 288 q^{99}+O(q^{100}) \) 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9 + 854 * q^10 + 32 * q^11 + 192 * q^12 - 22 * q^13 - 884 * q^14 - 42 * q^15 - 268 * q^16 - 56 * q^17 - 18 * q^18 - 112 * q^19 - 250 * q^20 + 243 * q^21 + 108 * q^22 + 16 * q^23 - 54 * q^24 - 197 * q^25 - 328 * q^26 + 405 * q^27 + 236 * q^28 - 54 * q^29 - 126 * q^30 + 66 * q^31 + 857 * q^32 - 96 * q^33 + 112 * q^34 + 532 * q^35 - 576 * q^36 + 110 * q^37 + 56 * q^38 + 66 * q^39 - 6044 * q^40 + 304 * q^41 - 306 * q^42 - 324 * q^43 - 568 * q^44 + 126 * q^45 + 5842 * q^46 + 4082 * q^47 + 804 * q^48 + 739 * q^49 + 576 * q^50 + 168 * q^51 - 1372 * q^52 - 1498 * q^53 + 54 * q^54 - 4422 * q^55 - 12036 * q^56 + 336 * q^57 + 6298 * q^58 - 3305 * q^59 + 750 * q^60 - 1718 * q^61 - 4333 * q^62 + 54 * q^63 - 6250 * q^64 - 5884 * q^65 - 324 * q^66 + 382 * q^67 + 734 * q^68 + 3780 * q^69 + 8082 * q^70 + 8638 * q^71 + 162 * q^72 + 8894 * q^73 + 12428 * q^74 + 243 * q^75 - 15468 * q^76 - 9916 * q^77 + 984 * q^78 - 578 * q^79 + 24570 * q^80 - 1215 * q^81 - 1382 * q^82 - 32 * q^83 + 7557 * q^84 + 708 * q^85 + 2296 * q^86 - 5928 * q^87 - 17646 * q^88 - 2284 * q^89 + 378 * q^90 + 11124 * q^91 + 762 * q^92 - 198 * q^93 - 1232 * q^94 + 24184 * q^95 - 396 * q^96 - 658 * q^97 - 4356 * q^98 + 288 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{20}{29}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.59837	+	2.35742i	−0.565109	+	0.833473i	−0.997677	−	0.0681283i	$-0.978297\pi$
$2$	−1.59837	+	2.35742i	−0.565109	+	0.833473i	0.432568	+	0.901601i	$0.357608\pi$
$3$	−0.162417	−	2.99560i	−0.0312571	−	0.576504i
$3$	−0.162417	−	2.99560i	−0.0312571	−	0.576504i
$4$	−0.0415309	−	0.104235i	−0.00519137	−	0.0130293i
$5$	14.5110	+	6.71353i	1.29791	+	0.600476i	0.942491	−	0.334232i	$-0.108477\pi$
$5$	14.5110	+	6.71353i	1.29791	+	0.600476i	0.355417	+	0.934708i	$0.384339\pi$
$6$	7.32148	+	4.40519i	0.498164	+	0.299735i
$7$	0.937125	+	3.37522i	0.0506000	+	0.182245i	0.984532	−	0.175207i	$-0.0560595\pi$
$7$	0.937125	+	3.37522i	0.0506000	+	0.182245i	−0.933932	+	0.357452i	$0.883646\pi$
$8$	−21.9407	−	4.82952i	−0.969652	−	0.213437i
$9$	−8.94724	+	0.973071i	−0.331379	+	0.0360397i
$10$	−39.0206	+	23.4779i	−1.23394	+	0.742437i
$11$	10.9330	+	10.3563i	0.299676	+	0.283868i	0.822731	−	0.568431i	$-0.192449\pi$
$11$	10.9330	+	10.3563i	0.299676	+	0.283868i	−0.523055	+	0.852299i	$0.675208\pi$
$12$	−0.305500	+	0.141340i	−0.00734920	+	0.00340010i
$13$	83.7523	+	9.10861i	1.78682	+	0.194329i	0.940833	−	0.338870i	$-0.110045\pi$
$13$	83.7523	+	9.10861i	1.78682	+	0.194329i	0.845990	+	0.533199i	$0.179010\pi$
$14$	−9.45468	−	3.18565i	−0.180491	−	0.0608144i
$15$	17.7542	−	44.5597i	0.305608	−	0.767017i
$16$	47.1062	−	44.6214i	0.736035	−	0.697209i
$17$	−3.89572	+	14.0311i	−0.0555794	+	0.200179i	−0.986127	−	0.165992i	$-0.946918\pi$
$17$	−3.89572	+	14.0311i	−0.0555794	+	0.200179i	0.930548	+	0.366171i	$0.119331\pi$
$18$	12.0071	−	22.6477i	0.157227	−	0.296562i
$19$	−83.9359	−	63.8064i	−1.01348	−	0.770431i	−0.0400038	−	0.999200i	$-0.512737\pi$
$19$	−83.9359	−	63.8064i	−1.01348	−	0.770431i	−0.973481	+	0.228768i	$0.926530\pi$
$20$	0.0971255	−	1.79138i	0.00108590	−	0.0200282i
$21$	9.95860	−	3.35544i	0.103483	−	0.0348675i
$22$	−41.8892	+	9.22051i	−0.405946	+	0.0893554i
$23$	61.5381	+	116.073i	0.557895	+	1.05230i	0.988707	+	0.149860i	$0.0478822\pi$
$23$	61.5381	+	116.073i	0.557895	+	1.05230i	−0.430812	+	0.902442i	$0.641773\pi$
$24$	−10.9038	+	66.5100i	−0.0927384	+	0.565679i
$25$	84.5758	+	99.5703i	0.676606	+	0.796563i
$26$	−155.340	+	182.880i	−1.17172	+	1.37945i
$27$	4.36811	+	26.6443i	0.0311350	+	0.189915i
$28$	0.312896	−	0.237857i	0.00211185	−	0.00160538i
$29$	141.278	+	208.369i	0.904644	+	1.33425i	0.942234	+	0.334956i	$0.108722\pi$
$29$	141.278	+	208.369i	0.904644	+	1.33425i	−0.0375901	+	0.999293i	$0.511968\pi$
$30$	76.6680	+	113.077i	0.466587	+	0.688164i
$31$	−220.137	+	167.344i	−1.27541	+	0.969542i	−0.275445	+	0.961317i	$0.588825\pi$
$31$	−220.137	+	167.344i	−1.27541	+	0.969542i	−0.999966	+	0.00822562i	$0.997382\pi$
$32$	0.821431	+	5.01051i	0.00453781	+	0.0276794i
$33$	29.2477	−	34.4330i	0.154284	−	0.181637i
$34$	−26.8504	−	31.6107i	−0.135435	−	0.159447i
$35$	−9.06096	+	55.2694i	−0.0437595	+	0.266921i
$36$	0.473015	+	0.892201i	0.00218989	+	0.00413056i
$37$	−114.804	+	25.2703i	−0.510099	+	0.112281i	−0.462560	−	0.886588i	$-0.653069\pi$
$37$	−114.804	+	25.2703i	−0.510099	+	0.112281i	−0.0475391	+	0.998869i	$0.515138\pi$
$38$	284.579	−	95.8858i	1.21486	−	0.409335i
$39$	13.6830	−	252.368i	0.0561803	−	1.03618i
$40$	−285.960	−	217.381i	−1.13036	−	0.859274i
$41$	−100.801	+	190.131i	−0.383964	+	0.724233i	−0.997876	−	0.0651415i	$-0.979250\pi$
$41$	−100.801	+	190.131i	−0.383964	+	0.724233i	0.613912	+	0.789374i	$0.289595\pi$
$42$	−8.00734	+	28.8398i	−0.0294181	+	0.105954i
$43$	−179.351	+	169.890i	−0.636065	+	0.602512i	−0.936236	−	0.351373i	$-0.885715\pi$
$43$	−179.351	+	169.890i	−0.636065	+	0.602512i	0.300171	+	0.953885i	$0.402956\pi$
$44$	0.625430	−	1.56971i	0.00214289	−	0.00537824i
$45$	−136.367	−	45.9473i	−0.451741	−	0.152209i
$46$	−371.994	−	40.4567i	−1.19234	−	0.129674i
$47$	301.937	−	139.691i	0.937064	−	0.433532i	0.108922	−	0.994050i	$-0.465260\pi$
$47$	301.937	−	139.691i	0.937064	−	0.433532i	0.828142	+	0.560519i	$0.189398\pi$
$48$	−141.319	−	133.864i	−0.424950	−	0.402534i
$49$	283.388	−	170.509i	0.826204	−	0.497111i
$50$	−369.912	+	40.2304i	−1.04627	+	0.113789i
$51$	42.6643	+	9.39112i	0.117141	+	0.0257847i
$52$	−2.52888	−	9.10819i	−0.00674408	−	0.0242900i
$53$	−12.7283	−	7.65835i	−0.0329880	−	0.0198482i	0.498964	−	0.866623i	$-0.333714\pi$
$53$	−12.7283	−	7.65835i	−0.0329880	−	0.0198482i	−0.531952	+	0.846774i	$0.678541\pi$
$54$	−69.7937	−	32.2900i	−0.175884	−	0.0813724i
$55$	89.1224	+	223.680i	0.218496	+	0.548383i
$56$	−4.26052	−	78.5806i	−0.0101667	−	0.187514i
$57$	−177.506	+	261.802i	−0.412478	+	0.608359i
$58$	−717.028			−1.62328
$59$	441.303	+	103.105i	0.973776	+	0.227511i
$59$	441.303	+	103.105i	0.973776	+	0.227511i
$60$	−5.38202			−0.0115803
$61$	441.142	−	650.636i	0.925942	−	1.36566i	−0.00480164	−	0.999988i	$-0.501528\pi$
$61$	441.142	−	650.636i	0.925942	−	1.36566i	0.930743	−	0.365673i	$-0.119161\pi$
$62$	−42.6391	−	786.432i	−0.0873414	−	1.61092i
$63$	−11.6690	−	29.2870i	−0.0233358	−	0.0585685i
$64$	457.980	+	211.884i	0.894492	+	0.413836i
$65$	1154.18	+	694.449i	2.20244	+	1.32517i
$66$	34.4245	+	123.986i	0.0642024	+	0.231236i
$67$	−441.588	−	97.2008i	−0.805202	−	0.177238i	−0.206746	−	0.978395i	$-0.566287\pi$
$67$	−441.588	−	97.2008i	−0.805202	−	0.177238i	−0.598455	+	0.801156i	$0.704219\pi$
$68$	1.62432	−	0.176656i	0.00289673	−	0.000315039i
$69$	337.714	−	203.196i	0.589217	−	0.354520i
$70$	−115.810	−	109.701i	−0.197743	−	0.187312i
$71$	−128.775	+	59.5778i	−0.215251	+	0.0995858i	−0.524552	−	0.851379i	$-0.675767\pi$
$71$	−128.775	+	59.5778i	−0.215251	+	0.0995858i	0.309301	+	0.950964i	$0.399905\pi$
$72$	201.008	+	21.8610i	0.329015	+	0.0357825i
$73$	−650.212	−	219.082i	−1.04249	−	0.351255i	−0.254581	−	0.967051i	$-0.581938\pi$
$73$	−650.212	−	219.082i	−1.04249	−	0.351255i	−0.787905	+	0.615797i	$0.788834\pi$
$74$	123.927	−	311.032i	0.194678	−	0.488605i
$75$	284.536	−	269.527i	0.438072	−	0.414964i
$76$	−3.16491	+	11.3990i	−0.00477684	+	0.0172046i
$77$	−24.7092	+	46.6066i	−0.0365699	+	0.0689781i
$78$	573.066	+	435.633i	0.831884	+	0.632382i
$79$	38.7863	−	715.371i	0.0552379	−	1.01880i	−0.831205	−	0.555966i	$-0.812348\pi$
$79$	38.7863	−	715.371i	0.0552379	−	1.01880i	0.886443	−	0.462838i	$-0.153169\pi$
$80$	983.128	−	331.254i	1.37396	−	0.462942i
$81$	79.1063	−	17.4126i	0.108513	−	0.0238856i
$82$	−287.102	−	541.531i	−0.386647	−	0.729294i
$83$	−101.741	+	620.592i	−0.134548	+	0.820708i	0.830187	+	0.557485i	$0.188234\pi$
$83$	−101.741	+	620.592i	−0.134548	+	0.820708i	−0.964735	+	0.263223i	$0.915215\pi$
$84$	−0.763344	−	0.898678i	−0.000991520	−	0.00116731i
$85$	−150.729	+	177.452i	−0.192340	+	0.226440i
$86$	−113.833	−	694.353i	−0.142732	−	0.870628i
$87$	601.246	−	457.055i	0.740923	−	0.563235i
$88$	−189.863	−	280.026i	−0.229993	−	0.339215i
$89$	−83.2418	−	122.772i	−0.0991417	−	0.146223i	0.774883	−	0.632105i	$-0.217809\pi$
$89$	−83.2418	−	122.772i	−0.0991417	−	0.146223i	−0.874024	+	0.485882i	$0.838499\pi$
$90$	326.281	−	248.032i	0.382145	−	0.290499i
$91$	47.7428	+	291.218i	0.0549979	+	0.335472i
$92$	9.54313	−	11.2350i	0.0108146	−	0.0127319i
$93$	537.049	+	632.263i	0.598810	+	0.704974i
$94$	−153.297	+	935.068i	−0.168206	+	1.02601i
$95$	−789.632	−	1489.40i	−0.852784	−	1.60852i
$96$	14.8761	−	3.27447i	0.0158154	−	0.00348124i
$97$	889.351	−	299.657i	0.930927	−	0.313666i	0.187332	−	0.982297i	$-0.440016\pi$
$97$	889.351	−	299.657i	0.930927	−	0.313666i	0.743594	+	0.668631i	$0.233119\pi$
$98$	−50.9979	+	940.601i	−0.0525670	+	0.969541i
$99$	−107.898	−	82.0219i	−0.109537	−	0.0832678i
$100$	6.86618	−	12.9510i	0.00686618	−	0.0129510i
$101$	87.8571	−	316.433i	0.0865556	−	0.311745i	−0.907581	−	0.419877i	$-0.862073\pi$
$101$	87.8571	−	316.433i	0.0865556	−	0.311745i	0.994137	+	0.108132i	$0.0344870\pi$
$102$	−90.3321	+	85.5671i	−0.0876884	+	0.0830628i
$103$	574.480	−	1441.84i	0.549565	−	1.37930i	−0.347614	−	0.937638i	$-0.613008\pi$
$103$	574.480	−	1441.84i	0.549565	−	1.37930i	0.897179	−	0.441667i	$-0.145613\pi$
$104$	−1793.60	−	604.333i	−1.69112	−	0.569805i
$105$	167.037	+	18.1663i	0.155249	+	0.0168843i
$106$	38.3984	−	17.7650i	0.0351848	−	0.0162782i
$107$	−1016.60	−	962.973i	−0.918488	−	0.870039i	0.0733802	−	0.997304i	$-0.476621\pi$
$107$	−1016.60	−	962.973i	−0.918488	−	0.870039i	−0.991869	+	0.127266i	$0.959380\pi$
$108$	2.59585	−	1.56187i	0.00231283	−	0.00139159i
$109$	1015.61	−	110.454i	0.892454	−	0.0970602i	0.349612	−	0.936895i	$-0.386314\pi$
$109$	1015.61	−	110.454i	0.892454	−	0.0970602i	0.542843	+	0.839834i	$0.317348\pi$
$110$	−669.758	−	147.425i	−0.580536	−	0.127786i
$111$	94.3457	+	339.803i	0.0806748	+	0.290564i
$112$	194.752	+	117.178i	0.164306	+	0.0988597i
$113$	635.300	+	293.921i	0.528885	+	0.244688i	0.666112	−	0.745851i	$-0.267957\pi$
$113$	635.300	+	293.921i	0.528885	+	0.244688i	−0.137228	+	0.990540i	$0.543819\pi$
$114$	−333.456	−	836.911i	−0.273956	−	0.687578i
$115$	113.722	+	2097.48i	0.0922143	+	1.70079i
$116$	15.8519	−	23.3799i	0.0126881	−	0.0187135i
$117$	−758.215			−0.599120
$118$	−948.427	+	875.536i	−0.739913	+	0.683047i
$119$	−51.0088			−0.0392939
$120$	−604.742	+	891.928i	−0.460043	+	0.678512i
$121$	−59.7810	−	1102.60i	−0.0449144	−	0.828397i
$122$	828.713	+	2079.91i	0.614985	+	1.54350i
$123$	585.930	+	271.080i	0.429524	+	0.198719i
$124$	26.5855	+	15.9960i	0.0192536	+	0.0115845i
$125$	24.1332	+	86.9200i	0.0172683	+	0.0621949i
$126$	87.6931	+	19.3027i	0.0620026	+	0.0136478i
$127$	−1138.56	+	123.826i	−0.795519	+	0.0865179i	−0.496847	−	0.867838i	$-0.665509\pi$
$127$	−1138.56	+	123.826i	−0.795519	+	0.0865179i	−0.298672	+	0.954356i	$0.596544\pi$
$128$	−1266.32	+	761.922i	−0.874440	+	0.526133i
$129$	538.053	+	509.671i	0.367232	+	0.347861i
$130$	−3481.92	+	1610.91i	−2.34911	+	1.08681i
$131$	1026.81	+	111.673i	0.684833	+	0.0744800i	0.443919	−	0.896067i	$-0.353588\pi$
$131$	1026.81	+	111.673i	0.684833	+	0.0744800i	0.240913	+	0.970547i	$0.422553\pi$
$132$	−4.80380	−	1.61859i	−0.00316756	−	0.00106727i
$133$	136.702	−	343.097i	0.0891247	−	0.223686i
$134$	934.963	−	885.644i	0.602750	−	0.570955i
$135$	−115.491	+	415.962i	−0.0736290	+	0.265188i
$136$	153.238	−	289.038i	0.0966182	−	0.182241i
$137$	−1796.24	−	1365.46i	−1.12017	−	0.851528i	−0.130013	−	0.991512i	$-0.541502\pi$
$137$	−1796.24	−	1365.46i	−1.12017	−	0.851528i	−0.990154	+	0.139984i	$0.955295\pi$
$138$	−60.7742	+	1120.92i	−0.0374887	+	0.691439i
$139$	−2149.46	+	724.238i	−1.31162	+	0.441936i	−0.886301	−	0.463109i	$-0.846734\pi$
$139$	−2149.46	+	724.238i	−1.31162	+	0.441936i	−0.425317	+	0.905044i	$0.639837\pi$
$140$	6.13730	−	1.35092i	0.00370498	−	0.000815527i
$141$	−467.497	−	881.793i	−0.279223	−	0.526670i
$142$	65.3807	−	398.805i	0.0386382	−	0.235683i
$143$	821.335	+	966.950i	0.480304	+	0.565458i
$144$	−378.051	+	445.076i	−0.218780	+	0.257567i
$145$	651.198	+	3972.13i	0.372959	+	2.27495i
$146$	1555.75	−	1182.65i	0.881879	−	0.670387i
$147$	−556.804	−	821.224i	−0.312411	−	0.460772i
$148$	7.40196	+	10.9171i	0.00411106	+	0.00606336i
$149$	2375.94	−	1806.14i	1.30634	−	0.993053i	0.307196	−	0.951646i	$-0.400609\pi$
$149$	2375.94	−	1806.14i	1.30634	−	0.993053i	0.999142	−	0.0414062i	$-0.0131838\pi$
$150$	180.594	+	1101.58i	0.0983030	+	0.599622i
$151$	1630.24	−	1919.27i	0.878591	−	1.03436i	−0.120541	−	0.992708i	$-0.538463\pi$
$151$	1630.24	−	1919.27i	0.878591	−	1.03436i	0.999132	−	0.0416489i	$-0.0132611\pi$
$152$	1533.46	+	1805.33i	0.818289	+	0.963365i
$153$	21.2027	−	129.330i	0.0112035	−	0.0683382i
$154$	−70.3767	−	132.744i	−0.0368254	−	0.0694601i
$155$	−4317.88	+	950.438i	−2.23755	+	0.492523i
$156$	−26.8738	+	9.05483i	−0.0137925	+	0.00464722i
$157$	−83.0570	+	1531.90i	−0.0422208	+	0.778717i	0.898383	+	0.439212i	$0.144742\pi$
$157$	−83.0570	+	1531.90i	−0.0422208	+	0.778717i	−0.940604	+	0.339505i	$0.889740\pi$
$158$	1624.43	+	1234.86i	0.817930	+	0.621774i
$159$	−20.8741	+	39.3727i	−0.0104115	+	0.0196381i
$160$	−21.7184	+	78.2224i	−0.0107312	+	0.0386502i
$161$	−334.104	+	316.480i	−0.163547	+	0.154920i
$162$	−85.3922	+	214.318i	−0.0414139	+	0.103941i
$163$	−2171.32	−	731.601i	−1.04338	−	0.351555i	−0.255126	−	0.966908i	$-0.582117\pi$
$163$	−2171.32	−	731.601i	−1.04338	−	0.351555i	−0.788252	+	0.615353i	$0.789013\pi$
$164$	24.0047	+	2.61067i	0.0114296	+	0.00124304i
$165$	655.582	−	303.304i	0.309315	−	0.143104i
$166$	−1300.37	−	1231.78i	−0.608004	−	0.575932i
$167$	2060.65	−	1239.85i	0.954840	−	0.574508i	0.0493066	−	0.998784i	$-0.484299\pi$
$167$	2060.65	−	1239.85i	0.954840	−	0.574508i	0.905533	+	0.424276i	$0.139471\pi$
$168$	−234.704	+	25.5256i	−0.107785	+	0.0117223i
$169$	4785.84	+	1053.44i	2.17835	+	0.479492i
$170$	−177.408	−	638.965i	−0.0800386	−	0.288273i
$171$	813.083	+	489.216i	0.363614	+	0.218779i
$172$	25.1571	+	11.6389i	0.0111524	+	0.00515965i
$173$	631.925	+	1586.01i	0.277713	+	0.697008i	0.999985	+	0.00539871i	$0.00171847\pi$
$173$	631.925	+	1586.01i	0.277713	+	0.697008i	−0.722272	+	0.691609i	$0.756902\pi$
$174$	116.457	+	2147.93i	0.0507391	+	0.935828i
$175$	−256.814	+	378.772i	−0.110933	+	0.163614i
$176$	977.128			0.418487
$177$	237.187	−	1338.71i	0.100723	−	0.568496i
$178$	422.477			0.177899
$179$	−627.704	+	925.793i	−0.262105	+	0.386576i	−0.935856	−	0.352383i	$-0.885372\pi$
$179$	−627.704	+	925.793i	−0.262105	+	0.386576i	0.673751	+	0.738958i	$0.264682\pi$
$180$	0.874130	+	16.1224i	0.000361966	+	0.00667606i
$181$	452.763	+	1136.35i	0.185931	+	0.466653i	0.992163	−	0.124947i	$-0.0398760\pi$
$181$	452.763	+	1136.35i	0.185931	+	0.466653i	−0.806232	+	0.591600i	$0.798497\pi$
$182$	−762.834	−	352.925i	−0.310687	−	0.143739i
$183$	−2020.69	−	1215.81i	−0.816251	−	0.491122i
$184$	−789.613	−	2843.93i	−0.316364	−	1.13944i
$185$	−1835.58	−	404.041i	−0.729483	−	0.160571i
$186$	−2348.91	+	255.459i	−0.925970	+	0.100705i
$187$	−187.903	+	113.057i	−0.0734802	+	0.0442116i
$188$	−27.1004	−	25.6708i	−0.0105133	−	0.00995871i
$189$	−85.8370	+	39.7124i	−0.0330356	+	0.0152839i
$190$	4773.27	+	519.124i	1.82258	+	0.198217i
$191$	−1208.63	−	407.235i	−0.457872	−	0.154275i	0.0809082	−	0.996722i	$-0.474218\pi$
$191$	−1208.63	−	407.235i	−0.457872	−	0.154275i	−0.538780	+	0.842447i	$0.681114\pi$
$192$	560.336	−	1406.34i	0.210619	−	0.528613i
$193$	−31.7016	+	30.0293i	−0.0118235	+	0.0111998i	−0.693588	−	0.720372i	$-0.743971\pi$
$193$	−31.7016	+	30.0293i	−0.0118235	+	0.0111998i	0.681765	+	0.731571i	$0.261213\pi$
$194$	−715.093	+	2575.53i	−0.264643	+	0.953157i
$195$	1892.83	−	3570.26i	0.695121	−	1.31114i
$196$	−29.5423	−	22.4575i	−0.0107662	−	0.00818422i
$197$	82.8211	−	1527.55i	0.0299531	−	0.552452i	−0.944590	−	0.328252i	$-0.893540\pi$
$197$	82.8211	−	1527.55i	0.0299531	−	0.552452i	0.974543	−	0.224200i	$-0.0719769\pi$
$198$	365.821	−	123.259i	0.131302	−	0.0442407i
$199$	4847.01	−	1066.91i	1.72661	−	0.380056i	0.762799	−	0.646636i	$-0.223825\pi$
$199$	4847.01	−	1066.91i	1.72661	−	0.380056i	0.963813	+	0.266580i	$0.0858936\pi$
$200$	−1374.78	−	2593.11i	−0.486057	−	0.916801i
$201$	−219.453	+	1338.61i	−0.0770102	+	0.469741i
$202$	605.536	+	712.892i	0.210918	+	0.248312i
$203$	−570.898	+	672.113i	−0.197385	+	0.232380i
$204$	−0.793007	−	4.83713i	−0.000272165	−	0.00166013i
$205$	−2739.19	+	2082.27i	−0.933234	+	0.709426i
$206$	2480.78	+	3658.88i	0.839049	+	1.23750i
$207$	−663.544	−	978.654i	−0.222799	−	0.328605i
$208$	4351.69	−	3308.07i	1.45065	−	1.10276i
$209$	−256.874	−	1566.86i	−0.0850161	−	0.518575i
$210$	−309.812	+	364.739i	−0.101805	+	0.119854i
$211$	1473.62	+	1734.88i	0.480797	+	0.566038i	0.948064	−	0.318078i	$-0.103037\pi$
$211$	1473.62	+	1734.88i	0.480797	+	0.566038i	−0.467268	+	0.884116i	$0.654762\pi$
$212$	−0.269649	+	1.64479i	−8.73565e−5	+	0.000532851i
$213$	199.387	+	376.083i	0.0641397	+	0.120980i
$214$	3895.03	−	857.361i	1.24420	−	0.273869i
$215$	−3743.14	+	1261.21i	−1.18735	+	0.400064i
$216$	32.8396	−	605.691i	0.0103447	−	0.190797i
$217$	−771.118	−	586.188i	−0.241230	−	0.183378i
$218$	−1362.93	+	2570.76i	−0.423437	+	0.798686i
$219$	−550.676	+	1983.36i	−0.169914	+	0.611976i
$220$	19.6139	−	18.5793i	0.00601078	−	0.00569371i
$221$	−454.079	+	1139.65i	−0.138211	+	0.346884i
$222$	−951.856	−	320.718i	−0.287767	−	0.0969602i
$223$	−138.096	−	15.0188i	−0.0414690	−	0.00451003i	0.0873610	−	0.996177i	$-0.472157\pi$
$223$	−138.096	−	15.0188i	−0.0414690	−	0.00451003i	−0.128830	+	0.991667i	$0.541122\pi$
$224$	−16.1418	+	7.46798i	−0.00481481	+	0.00222757i
$225$	−853.609	−	808.582i	−0.252921	−	0.239580i
$226$	−1708.34	+	1027.87i	−0.502818	+	0.302536i
$227$	−1843.66	+	200.510i	−0.539066	+	0.0586269i	−0.373602	−	0.927589i	$-0.621878\pi$
$227$	−1843.66	+	200.510i	−0.539066	+	0.0586269i	−0.165463	+	0.986216i	$0.552912\pi$
$228$	34.6608	+	7.62942i	0.0100678	+	0.00221610i
$229$	788.983	+	2841.66i	0.227675	+	0.820010i	0.985803	+	0.167905i	$0.0537001\pi$
$229$	788.983	+	2841.66i	0.227675	+	0.820010i	−0.758129	+	0.652105i	$0.773886\pi$
$230$	−5126.41	−	3084.46i	−1.46968	−	0.884275i
$231$	143.628	+	66.4493i	0.0409092	+	0.0189266i
$232$	−2093.42	−	5254.08i	−0.592412	−	1.48684i
$233$	−32.5013	−	599.451i	−0.00913832	−	0.168546i	−0.999540	−	0.0303275i	$-0.990345\pi$
$233$	−32.5013	−	599.451i	−0.00913832	−	0.168546i	0.990402	−	0.138219i	$-0.0441378\pi$
$234$	1211.91	−	1787.43i	0.338568	−	0.499350i
$235$	5319.24			1.47655
$236$	−7.58059	−	50.2812i	−0.00209091	−	0.0138688i
$237$	−2149.26			−0.589071
$238$	81.5309	−	120.249i	0.0222053	−	0.0327504i
$239$	−25.9319	−	478.286i	−0.00701839	−	0.129447i	−0.999943	−	0.0106982i	$-0.996595\pi$
$239$	−25.9319	−	478.286i	−0.00701839	−	0.129447i	0.992924	−	0.118748i	$-0.0378882\pi$
$240$	−1151.98	−	2891.26i	−0.309834	−	0.777624i
$241$	−5074.49	−	2347.71i	−1.35633	−	0.627507i	−0.399122	−	0.916898i	$-0.630685\pi$
$241$	−5074.49	−	2347.71i	−1.35633	−	0.627507i	−0.957211	+	0.289391i	$0.906547\pi$
$242$	2694.83	+	1621.43i	0.715828	+	0.430699i
$243$	−65.0094	−	234.143i	−0.0171620	−	0.0618118i
$244$	−86.1399	−	18.9608i	−0.0226006	−	0.00497477i
$245$	5256.97	−	571.730i	1.37084	−	0.149088i
$246$	−1575.58	+	947.996i	−0.408355	+	0.245699i
$247$	−6448.63	−	6108.47i	−1.66120	−	1.57357i
$248$	5638.15	−	2608.49i	1.44364	−	0.667900i
$249$	1875.57	+	203.980i	0.477347	+	0.0519146i
$250$	−243.481	−	82.0382i	−0.0615963	−	0.0207542i
$251$	−1162.18	+	2916.85i	−0.292255	+	0.733505i	0.707389	+	0.706825i	$0.249873\pi$
$251$	−1162.18	+	2916.85i	−0.292255	+	0.733505i	−0.999644	+	0.0266806i	$0.991506\pi$
$252$	−2.56810	+	2.43263i	−0.000641965	+	0.000608102i
$253$	−529.293	+	1906.34i	−0.131527	+	0.473718i
$254$	1527.93	−	2881.98i	0.377444	−	0.711935i
$255$	556.056	+	422.703i	0.136555	+	0.103807i
$256$	9.32875	−	172.059i	0.00227753	−	0.0420065i
$257$	−5436.51	+	1831.77i	−1.31953	+	0.444603i	−0.888974	−	0.457959i	$-0.848581\pi$
$257$	−5436.51	+	1831.77i	−1.31953	+	0.444603i	−0.430561	+	0.902562i	$0.641684\pi$
$258$	−2061.52	+	453.774i	−0.497459	+	0.109499i
$259$	−192.878	−	363.807i	−0.0462737	−	0.0872814i
$260$	24.4514	−	149.147i	0.00583236	−	0.0355758i
$261$	−1466.81	−	1726.86i	−0.347866	−	0.409540i
$262$	−1904.49	+	2242.13i	−0.449082	+	0.528700i
$263$	307.296	+	1874.42i	0.0720482	+	0.439474i	0.998075	+	0.0620169i	$0.0197533\pi$
$263$	307.296	+	1874.42i	0.0720482	+	0.439474i	−0.926027	+	0.377457i	$0.876798\pi$
$264$	−808.010	+	614.234i	−0.188370	+	0.143195i
$265$	−133.286	−	196.582i	−0.0308970	−	0.0455696i
$266$	590.322	+	870.659i	0.136071	+	0.200690i
$267$	−354.257	+	269.299i	−0.0811992	+	0.0617261i
$268$	8.20784	+	50.0656i	0.00187080	+	0.0114114i
$269$	1685.14	−	1983.90i	0.381951	−	0.449667i	−0.537270	−	0.843410i	$-0.680544\pi$
$269$	1685.14	−	1983.90i	0.381951	−	0.449667i	0.919220	+	0.393743i	$0.128820\pi$
$270$	−795.999	−	937.123i	−0.179418	−	0.211228i
$271$	706.191	−	4307.57i	0.158295	−	0.965559i	−0.781521	−	0.623879i	$-0.785556\pi$
$271$	706.191	−	4307.57i	0.158295	−	0.965559i	0.939816	−	0.341680i	$-0.110996\pi$
$272$	442.575	+	834.785i	0.0986583	+	0.186089i
$273$	864.619	−	190.317i	0.191682	−	0.0421924i
$274$	6090.02	−	2051.97i	1.34274	−	0.452422i
$275$	−106.512	+	1964.50i	−0.0233561	+	0.430777i
$276$	−35.2057	−	26.7626i	−0.00767801	−	0.00583667i
$277$	835.028	−	1575.03i	0.181126	−	0.341640i	−0.776278	−	0.630390i	$-0.782895\pi$
$277$	835.028	−	1575.03i	0.181126	−	0.341640i	0.957405	+	0.288750i	$0.0932396\pi$
$278$	1728.30	−	6224.78i	0.372866	−	1.34294i
$279$	1806.78	−	1711.47i	0.387703	−	0.367252i
$280$	465.729	−	1168.89i	0.0994022	−	0.249481i
$281$	−6080.70	−	2048.83i	−1.29090	−	0.434956i	−0.411664	−	0.911336i	$-0.635052\pi$
$281$	−6080.70	−	2048.83i	−1.29090	−	0.434956i	−0.879240	+	0.476379i	$0.841949\pi$
$282$	2825.99	+	307.345i	0.596756	+	0.0649011i
$283$	3685.59	−	1705.13i	0.774153	−	0.358161i	0.00729117	−	0.999973i	$-0.497679\pi$
$283$	3685.59	−	1705.13i	0.774153	−	0.358161i	0.766862	+	0.641812i	$0.221817\pi$
$284$	11.5582	+	10.9486i	0.00241499	+	0.00228760i
$285$	−4333.41	+	2607.32i	−0.900663	+	0.541911i
$286$	−3592.30	+	390.686i	−0.742718	+	0.0807754i
$287$	−736.199	−	162.050i	−0.151416	−	0.0333292i
$288$	−12.2251	−	44.0309i	−0.00250129	−	0.00900884i
$289$	4028.04	+	2423.59i	0.819875	+	0.493302i
$290$	−10404.8	−	4813.79i	−2.10687	−	0.974743i
$291$	−1042.10	−	2615.47i	−0.209927	−	0.526878i
$292$	4.16795	+	76.8733i	0.000835311	+	0.0154064i
$293$	−216.994	+	320.042i	−0.0432659	+	0.0638124i	−0.848707	−	0.528864i	$-0.822618\pi$
$293$	−216.994	+	320.042i	−0.0432659	+	0.0638124i	0.805441	+	0.592676i	$0.201929\pi$
$294$	2825.95			0.560587
$295$	5711.57	+	4458.86i	1.12726	+	0.880017i
$296$	2640.93			0.518583
$297$	−228.180	+	336.541i	−0.0445804	+	0.0657511i
$298$	460.204	+	8487.96i	0.0894594	+	1.64998i
$299$	4096.69	+	10281.9i	0.792367	+	1.98869i
$300$	−39.9112	−	18.4649i	−0.00768091	−	0.00355357i
$301$	−741.492	−	446.141i	−0.141990	−	0.0854323i
$302$	1918.79	+	6910.86i	0.365609	+	1.31681i
$303$	−962.176	−	211.791i	−0.182428	−	0.0401553i
$304$	−6801.03	+	739.657i	−1.28311	+	0.139547i
$305$	10769.5	−	6479.79i	2.02183	−	1.21650i
$306$	270.996	+	256.701i	0.0506269	+	0.0479563i
$307$	172.701	−	79.8999i	0.0321061	−	0.0148538i	−0.403770	−	0.914860i	$-0.632301\pi$
$307$	172.701	−	79.8999i	0.0321061	−	0.0148538i	0.435876	+	0.900007i	$0.356438\pi$
$308$	5.88422	+	0.639948i	0.00108859	+	0.000118391i
$309$	−4412.47	−	1486.73i	−0.812352	−	0.273713i
$310$	4660.99	−	11698.2i	0.853957	−	2.14327i
$311$	4810.63	−	4556.87i	0.877124	−	0.830856i	−0.109480	−	0.993989i	$-0.534919\pi$
$311$	4810.63	−	4556.87i	0.877124	−	0.830856i	0.986604	+	0.163133i	$0.0521599\pi$
$312$	−1519.03	+	5471.05i	−0.275635	+	0.992747i
$313$	−1149.26	+	2167.73i	−0.207540	+	0.391462i	−0.965328	−	0.261038i	$-0.915935\pi$
$313$	−1149.26	+	2167.73i	−0.207540	+	0.391462i	0.757788	+	0.652500i	$0.226280\pi$
$314$	−3478.56	−	2644.34i	−0.625181	−	0.475250i
$315$	27.2895	−	503.326i	0.00488124	−	0.0900292i
$316$	−76.1774	+	25.6671i	−0.0135611	+	0.00456927i
$317$	−7215.45	+	1588.24i	−1.27842	+	0.281402i	−0.801740	−	0.597673i	$-0.796092\pi$
$317$	−7215.45	+	1588.24i	−1.27842	+	0.281402i	−0.476683	+	0.879075i	$0.658161\pi$
$318$	−59.4534	−	112.141i	−0.0104842	−	0.0197753i
$319$	−613.344	+	3741.23i	−0.107651	+	0.656642i
$320$	5223.28	+	6149.32i	0.912469	+	1.07424i
$321$	−2719.57	+	3201.73i	−0.472871	+	0.556707i
$322$	−212.054	−	1293.47i	−0.0366997	−	0.223859i
$323$	1222.26	−	929.141i	0.210553	−	0.160058i
$324$	−5.10036	−	7.52246i	−0.000874547	−	0.00128986i
$325$	6176.47	+	9109.61i	1.05418	+	1.55480i
$326$	5195.25	−	3949.33i	0.882633	−	0.670960i
$327$	−495.827	−	3024.41i	−0.0838511	−	0.511469i
$328$	3129.90	−	3684.80i	0.526889	−	0.620302i
$329$	754.440	+	888.195i	0.126424	+	0.148838i
$330$	−332.846	+	2030.27i	−0.0555230	+	0.338675i
$331$	3830.19	+	7224.50i	0.636031	+	1.19968i	0.966695	+	0.255933i	$0.0823826\pi$
$331$	3830.19	+	7224.50i	0.636031	+	1.19968i	−0.330664	+	0.943749i	$0.607273\pi$
$332$	68.9126	−	15.1688i	0.0113918	−	0.00250752i
$333$	1002.59	−	337.812i	0.164990	−	0.0555915i
$334$	−370.831	+	6839.57i	−0.0607513	+	1.12049i
$335$	−5755.34	−	4375.09i	−0.938650	−	0.713543i
$336$	319.388	−	602.429i	0.0518572	−	0.0978131i
$337$	268.627	−	967.505i	0.0434214	−	0.156390i	−0.938661	−	0.344841i	$-0.887933\pi$
$337$	268.627	−	967.505i	0.0434214	−	0.156390i	0.982083	+	0.188451i	$0.0603467\pi$
$338$	−10133.0	+	9598.44i	−1.63065	+	1.54463i
$339$	777.286	−	1950.84i	0.124532	−	0.312552i
$340$	24.7566	+	8.34147i	0.00394887	+	0.00133053i
$341$	−4139.83	−	450.233i	−0.657432	−	0.0715000i
$342$	−2452.89	+	1134.83i	−0.387828	+	0.179428i
$343$	1713.36	+	1622.98i	0.269716	+	0.255488i
$344$	4755.58	−	2861.34i	0.745360	−	0.448468i
$345$	6264.74	−	681.332i	0.977630	−	0.106324i
$346$	−4748.94	−	1045.32i	−0.737875	−	0.162419i
$347$	−3403.90	−	12259.8i	−0.526603	−	1.89665i	−0.433908	−	0.900957i	$-0.642866\pi$
$347$	−3403.90	−	12259.8i	−0.526603	−	1.89665i	−0.0926947	−	0.995695i	$-0.529548\pi$
$348$	−72.6113	−	43.6888i	−0.0111850	−	0.00672978i
$349$	−3345.47	−	1547.78i	−0.513121	−	0.237395i	0.146202	−	0.989255i	$-0.453295\pi$
$349$	−3345.47	−	1547.78i	−0.513121	−	0.237395i	−0.659323	+	0.751860i	$0.729157\pi$
$350$	−482.441	−	1210.83i	−0.0736787	−	0.184919i
$351$	123.147	+	2271.31i	0.0187268	+	0.345395i
$352$	−42.9097	+	63.2871i	−0.00649743	+	0.00958299i
$353$	12969.3			1.95548			0.977742	−	0.209812i	$-0.0672851\pi$
$353$	12969.3			1.95548			0.977742	+	0.209812i	$0.0672851\pi$
$354$	2776.80	+	2698.91i	0.416907	+	0.405213i
$355$	−2268.64			−0.339175
$356$	−9.34005	+	13.7755i	−0.00139051	+	0.00205085i
$357$	8.28469	+	152.802i	0.00122821	+	0.0226531i
$358$	−1179.18	−	2959.52i	−0.174083	−	0.436915i
$359$	−7462.73	−	3452.63i	−1.09713	−	0.507584i	−0.214053	−	0.976822i	$-0.568667\pi$
$359$	−7462.73	−	3452.63i	−1.09713	−	0.507584i	−0.883072	+	0.469238i	$0.844529\pi$
$360$	2770.08	+	1666.70i	0.405544	+	0.244008i
$361$	1139.00	+	4102.30i	0.166059	+	0.598090i
$362$	−3402.53	−	748.954i	−0.494014	−	0.108741i
$363$	−3293.23	+	358.160i	−0.476170	+	0.0517866i
$364$	28.3723	−	17.0710i	0.00408547	−	0.00245815i
$365$	−7964.44	−	7544.32i	−1.14213	−	1.08188i
$366$	6095.99	−	2820.30i	0.870608	−	0.402786i
$367$	−940.149	−	102.247i	−0.133720	−	0.0145430i	0.0410140	−	0.999159i	$-0.486941\pi$
$367$	−940.149	−	102.247i	−0.133720	−	0.0145430i	−0.174734	+	0.984616i	$0.555907\pi$
$368$	8078.18	+	2721.85i	1.14430	+	0.385561i
$369$	716.882	−	1799.24i	0.101137	−	0.253834i
$370$	3886.43	−	3681.42i	0.546069	−	0.517265i
$371$	13.9206	−	50.1376i	0.00194804	−	0.00701621i
$372$	43.5996	−	82.2376i	0.00607671	−	0.0114619i
$373$	−3977.48	−	3023.60i	−0.552134	−	0.419722i	0.291554	−	0.956554i	$-0.405828\pi$
$373$	−3977.48	−	3023.60i	−0.552134	−	0.419722i	−0.843689	+	0.536833i	$0.819621\pi$
$374$	33.8145	−	623.672i	0.00467515	−	0.0862281i
$375$	256.458	−	86.4108i	0.0353158	−	0.0118993i
$376$	−7299.35	+	1606.71i	−1.00116	+	0.220371i
$377$	9934.40	+	18738.3i	1.35716	+	2.55987i
$378$	43.5804	−	265.829i	0.00592998	−	0.0361713i
$379$	−8843.65	−	10411.5i	−1.19860	−	1.41110i	−0.887557	−	0.460699i	$-0.847599\pi$
$379$	−8843.65	−	10411.5i	−1.19860	−	1.41110i	−0.311039	−	0.950397i	$-0.600677\pi$
$380$	−122.453	+	144.163i	−0.0165309	+	0.0194616i
$381$	555.854	+	3390.56i	0.0747435	+	0.455915i
$382$	2891.86	−	2198.34i	0.387331	−	0.294442i
$383$	−1496.35	−	2206.95i	−0.199634	−	0.294438i	0.714674	−	0.699458i	$-0.246575\pi$
$383$	−1496.35	−	2206.95i	−0.199634	−	0.294438i	−0.914308	+	0.405019i	$0.867265\pi$
$384$	2488.09	+	3669.65i	0.330650	+	0.487672i
$385$	−671.451	+	510.424i	−0.0888840	+	0.0675678i
$386$	−20.1209	−	122.732i	−0.00265317	−	0.0161836i
$387$	1439.38	−	1694.57i	0.189064	−	0.222584i
$388$	−68.1703	−	80.2562i	−0.00891964	−	0.0105010i
$389$	−1299.76	+	7928.20i	−0.169410	+	1.03336i	0.756051	+	0.654513i	$0.227126\pi$
$389$	−1299.76	+	7928.20i	−0.169410	+	1.03336i	−0.925461	+	0.378843i	$0.876322\pi$
$390$	5391.15	+	10168.8i	0.699978	+	1.32030i
$391$	−1868.37	+	411.259i	−0.241656	+	0.0531925i
$392$	−7041.22	+	2372.46i	−0.907233	+	0.305682i
$393$	167.755	−	3094.06i	0.0215321	−	0.397136i
$394$	3468.68	+	2636.82i	0.443527	+	0.337161i
$395$	5365.49	−	10120.4i	0.683461	−	1.28914i
$396$	−4.06843	+	14.6532i	−0.000516279	+	0.00185947i
$397$	−8761.70	+	8299.52i	−1.10765	+	1.04922i	−0.109175	+	0.994023i	$0.534821\pi$
$397$	−8761.70	+	8299.52i	−1.10765	+	1.04922i	−0.998475	+	0.0551991i	$0.982421\pi$
$398$	−5232.17	+	13131.8i	−0.658957	+	1.65386i
$399$	−1049.98	−	353.780i	−0.131742	−	0.0443889i
$400$	8427.02	+	916.493i	1.05338	+	0.114562i
$401$	−4731.60	+	2189.07i	−0.589239	+	0.272611i	−0.691769	−	0.722119i	$-0.743168\pi$
$401$	−4731.60	+	2189.07i	−0.589239	+	0.272611i	0.102530	+	0.994730i	$0.467306\pi$
$402$	−2804.89	−	2656.93i	−0.347998	−	0.329641i
$403$	−19961.2	+	12010.3i	−2.46734	+	1.48455i
$404$	−36.6321	+	3.98398i	−0.00451118	+	0.000490620i
$405$	1264.81	+	278.407i	0.155183	+	0.0341584i
$406$	−671.945	−	2420.13i	−0.0821381	−	0.295835i
$407$	−1516.86	−	912.666i	−0.184737	−	0.111153i
$408$	−890.731	−	412.096i	−0.108083	−	0.0500044i
$409$	19.3098	+	48.4640i	0.00233450	+	0.00585914i	0.930139	−	0.367207i	$-0.119686\pi$
$409$	19.3098	+	48.4640i	0.00233450	+	0.00585914i	−0.927805	+	0.373066i	$0.878307\pi$
$410$	−530.563	−	9785.65i	−0.0639088	−	1.17873i
$411$	−3798.64	+	5602.58i	−0.455896	+	0.672396i
$412$	−174.148			−0.0208244
$413$	65.5537	+	1586.12i	0.00781038	+	0.188978i
$414$	3367.68			0.399789
$415$	−5642.72	+	8322.39i	−0.667447	+	0.984410i
$416$	23.1580	+	427.124i	0.00272936	+	0.0503400i
$417$	2518.64	+	6321.30i	0.295775	+	0.742339i
$418$	4104.33	+	1898.87i	0.480262	+	0.222193i
$419$	11088.3	+	6671.59i	1.29283	+	0.777873i	0.984832	−	0.173513i	$-0.0555119\pi$
$419$	11088.3	+	6671.59i	1.29283	+	0.777873i	0.308003	+	0.951386i	$0.400339\pi$
$420$	−5.04363	−	18.1655i	−0.000585961	−	0.00211044i
$421$	11350.7	+	2498.48i	1.31401	+	0.289236i	0.816060	−	0.577967i	$-0.196154\pi$
$421$	11350.7	+	2498.48i	1.31401	+	0.289236i	0.497954	+	0.867203i	$0.334085\pi$
$422$	−6445.22	+	700.960i	−0.743480	+	0.0808583i
$423$	−2565.57	+	1543.65i	−0.294899	+	0.177435i
$424$	242.281	+	229.501i	0.0277505	+	0.0262867i
$425$	−1726.57	+	798.794i	−0.197060	+	0.0911699i
$426$	−1205.28	−	131.082i	−0.137080	−	0.0149083i
$427$	2609.44	+	879.224i	0.295737	+	0.0996455i
$428$	−58.1550	+	145.958i	−0.00656782	+	0.0164840i
$429$	2763.20	−	2617.44i	0.310975	−	0.294572i
$430$	3009.71	−	10840.0i	0.337538	−	1.21570i
$431$	−4542.77	+	8568.58i	−0.507698	+	0.957619i	0.488670	+	0.872468i	$0.337482\pi$
$431$	−4542.77	+	8568.58i	−0.507698	+	0.957619i	−0.996368	+	0.0851509i	$0.972863\pi$
$432$	1394.67	+	1060.20i	0.155327	+	0.118076i
$433$	−390.560	+	7203.45i	−0.0433467	+	0.799482i	0.893355	+	0.449352i	$0.148345\pi$
$433$	−390.560	+	7203.45i	−0.0433467	+	0.799482i	−0.936701	+	0.350130i	$0.886138\pi$
$434$	2614.42	−	880.901i	0.289162	−	0.0974300i
$435$	11793.2	−	2595.87i	1.29986	−	0.286121i
$436$	−53.6923	−	101.274i	−0.00589769	−	0.0111242i
$437$	2240.96	−	13669.2i	0.245308	−	1.49631i
$438$	−3795.42	−	4468.31i	−0.414046	−	0.487452i
$439$	4552.39	−	5359.49i	0.494929	−	0.582675i	−0.456818	−	0.889560i	$-0.651011\pi$
$439$	4552.39	−	5359.49i	0.494929	−	0.582675i	0.951747	+	0.306885i	$0.0992867\pi$
$440$	−875.141	−	5338.12i	−0.0948198	−	0.578375i
$441$	−2369.62	+	1801.34i	−0.255871	+	0.194508i
$442$	−1960.85	−	2892.04i	−0.211014	−	0.311222i
$443$	−6168.62	−	9098.03i	−0.661580	−	0.975757i	−0.999403	−	0.0345474i	$-0.989001\pi$
$443$	−6168.62	−	9098.03i	−0.661580	−	0.975757i	0.337823	−	0.941209i	$-0.390309\pi$
$444$	31.5010	−	23.9464i	0.00336705	−	0.00255957i
$445$	−383.690	−	2340.40i	−0.0408733	−	0.249316i
$446$	256.134	−	301.544i	0.0271935	−	0.0320147i
$447$	−5796.37	−	6824.01i	−0.613331	−	0.722069i
$448$	−285.971	+	1744.34i	−0.0301581	+	0.183957i
$449$	4153.42	+	7834.17i	0.436552	+	0.823424i	0.999996	−	0.00272969i	$-0.000868889\pi$
$449$	4153.42	+	7834.17i	0.436552	+	0.823424i	−0.563444	+	0.826154i	$0.690524\pi$
$450$	3270.55	−	719.902i	0.342611	−	0.0754145i
$451$	−3071.13	+	1034.78i	−0.320651	+	0.108040i
$452$	4.25220	−	78.4271i	0.000442492	−	0.00816129i
$453$	−6014.14	−	4571.83i	−0.623773	−	0.474180i
$454$	2474.16	−	4666.76i	0.255767	−	0.482427i
$455$	−1262.30	+	4546.41i	−0.130061	+	0.468437i
$456$	5158.98	−	4886.85i	0.529806	−	0.501859i
$457$	−1801.96	+	4522.59i	−0.184447	+	0.462927i	−0.991903	−	0.127001i	$-0.959465\pi$
$457$	−1801.96	+	4522.59i	−0.184447	+	0.462927i	0.807456	+	0.589928i	$0.200844\pi$
$458$	−7960.07	−	2682.06i	−0.812117	−	0.273634i
$459$	−390.866	−	42.5092i	−0.0397474	−	0.00432279i
$460$	213.908	−	98.9642i	0.0216815	−	0.0100309i
$461$	−3740.37	−	3543.07i	−0.377888	−	0.357955i	0.475057	−	0.879955i	$-0.342427\pi$
$461$	−3740.37	−	3543.07i	−0.377888	−	0.357955i	−0.852945	+	0.522000i	$0.825186\pi$
$462$	−386.219	+	232.380i	−0.0388929	+	0.0234011i
$463$	−4006.57	+	435.740i	−0.402162	+	0.0437377i	−0.306965	−	0.951721i	$-0.599314\pi$
$463$	−4006.57	+	435.740i	−0.402162	+	0.0437377i	−0.0951967	+	0.995458i	$0.530348\pi$
$464$	15952.8	+	3511.48i	1.59610	+	0.351328i
$465$	3548.43	+	12780.3i	0.353880	+	1.27456i
$466$	1465.10	+	881.524i	0.145643	+	0.0876305i
$467$	−6940.37	−	3210.96i	−0.687713	−	0.318170i	0.0447294	−	0.998999i	$-0.485757\pi$
$467$	−6940.37	−	3210.96i	−0.687713	−	0.318170i	−0.732442	+	0.680829i	$0.761620\pi$
$468$	31.4894	+	79.0324i	0.00311025	+	0.00780614i
$469$	−85.7488	−	1581.54i	−0.00844246	−	0.155712i
$470$	−8502.10	+	12539.7i	−0.834410	+	1.23066i
$471$	4602.44			0.450253
$472$	−9184.56	−	4393.48i	−0.895664	−	0.428446i
$473$	−3720.29			−0.361647
$474$	3435.32	−	5066.72i	0.332889	−	0.490975i
$475$	−745.720	−	13754.0i	−0.0720337	−	1.32858i
$476$	2.11844	+	5.31689i	0.000203989	+	0.000511974i
$477$	121.335	+	56.1356i	0.0116469	+	0.00538841i
$478$	1168.97	+	703.345i	0.111856	+	0.0673017i
$479$	−2553.62	−	9197.31i	−0.243586	−	0.877319i	−0.979701	−	0.200463i	$-0.935755\pi$
$479$	−2553.62	−	9197.31i	−0.243586	−	0.877319i	0.736115	−	0.676857i	$-0.236658\pi$
$480$	237.851	+	52.3549i	0.0226174	+	0.00497846i
$481$	−9845.27	+	1070.74i	−0.933276	+	0.101500i
$482$	13645.4	−	8210.18i	1.28949	−	0.775858i
$483$	1002.31	+	949.439i	0.0944238	+	0.0894430i
$484$	−112.446	+	52.0231i	−0.0105603	+	0.00488572i
$485$	14917.2	+	1622.34i	1.39661	+	0.151890i
$486$	655.881	+	220.992i	0.0612168	+	0.0206263i
$487$	155.565	−	390.438i	0.0144750	−	0.0363294i	−0.921562	−	0.388232i	$-0.873086\pi$
$487$	155.565	−	390.438i	0.0144750	−	0.0363294i	0.936037	+	0.351903i	$0.114465\pi$
$488$	−12821.2	+	12144.9i	−1.18932	+	1.12659i
$489$	−1838.93	+	6623.22i	−0.170060	+	0.612499i
$490$	−7054.78	+	13306.7i	−0.650413	+	1.22681i
$491$	1041.67	+	791.860i	0.0957436	+	0.0727824i	0.651951	−	0.758261i	$-0.273951\pi$
$491$	1041.67	+	791.860i	0.0957436	+	0.0727824i	−0.556207	+	0.831044i	$0.687744\pi$
$492$	3.92175	−	72.3325i	0.000359362	−	0.00662805i
$493$	−3474.03	+	1170.54i	−0.317368	+	0.106934i
$494$	24707.5	−	5438.53i	2.25029	−	0.495326i
$495$	−1015.06	−	1914.60i	−0.0921684	−	0.173848i
$496$	−2902.71	+	17705.8i	−0.262773	+	1.60285i
$497$	−321.767	−	378.813i	−0.0290407	−	0.0341893i
$498$	−3478.72	+	4095.46i	−0.313022	+	0.368518i
$499$	−2093.06	−	12767.1i	−0.187772	−	1.14536i	−0.897544	−	0.440926i	$-0.854650\pi$
$499$	−2093.06	−	12767.1i	−0.187772	−	1.14536i	0.709772	−	0.704432i	$-0.248798\pi$
$500$	8.05782	−	6.12539i	0.000720713	−	0.000547872i
$501$	−4048.79	−	5971.52i	−0.361051	−	0.532511i
$502$	−5018.64	−	7401.94i	−0.446201	−	0.658097i
$503$	8276.05	−	6291.29i	0.733620	−	0.557683i	−0.170297	−	0.985393i	$-0.554473\pi$
$503$	8276.05	−	6291.29i	0.733620	−	0.557683i	0.903916	+	0.427710i	$0.140679\pi$
$504$	114.584	+	698.934i	0.0101270	+	0.0617718i
$505$	3399.28	−	4001.94i	0.299536	−	0.352642i
$506$	−3648.04	−	4294.80i	−0.320504	−	0.377326i
$507$	2378.40	−	14507.6i	0.208340	−	1.27082i
$508$	60.1924	+	113.535i	0.00525710	+	0.00991594i
$509$	10327.2	−	2273.19i	0.899305	−	0.197952i	0.258823	−	0.965925i	$-0.416665\pi$
$509$	10327.2	−	2273.19i	0.899305	−	0.197952i	0.640482	+	0.767973i	$0.278734\pi$
$510$	−1885.27	+	635.222i	−0.163689	+	0.0551531i
$511$	130.120	−	2399.91i	0.0112645	−	0.207761i
$512$	−9021.48	−	6857.95i	−0.778705	−	0.591956i
$513$	1333.44	−	2515.13i	0.114761	−	0.216463i
$514$	4371.30	−	15744.0i	0.375116	−	1.35105i
$515$	18016.1	−	17065.8i	1.54152	−	1.46021i
$516$	30.7796	−	77.2510i	0.00262596	−	0.00659067i
$517$	4747.77	+	1599.71i	0.403881	+	0.136083i
$518$	1165.94	+	126.803i	0.0988964	+	0.0107556i
$519$	4648.42	−	2150.59i	0.393147	−	0.181889i
$520$	−21969.7	−	20810.9i	−1.85276	−	1.75503i
$521$	8913.73	−	5363.21i	0.749554	−	0.450991i	−0.0888475	−	0.996045i	$-0.528318\pi$
$521$	8913.73	−	5363.21i	0.749554	−	0.450991i	0.838401	+	0.545054i	$0.183491\pi$
$522$	6415.43	−	697.720i	0.537922	−	0.0585026i
$523$	−9531.99	−	2098.15i	−0.796950	−	0.175422i	−0.202212	−	0.979342i	$-0.564813\pi$
$523$	−9531.99	−	2098.15i	−0.796950	−	0.175422i	−0.594738	+	0.803920i	$0.702744\pi$
$524$	−31.0043	−	111.668i	−0.00258479	−	0.00930958i
$525$	1176.36	+	707.792i	0.0977915	+	0.0588392i
$526$	−4909.97	−	2271.59i	−0.407005	−	0.188301i
$527$	−1490.43	−	3740.69i	−0.123195	−	0.309197i
$528$	−158.702	−	2927.08i	−0.0130807	−	0.241259i
$529$	−2858.08	+	4215.35i	−0.234904	+	0.346458i
$530$	676.467			0.0554412
$531$	−4048.77	−	493.087i	−0.330888	−	0.0402979i
$532$	−41.4400			−0.00337716
$533$	−10174.2	+	15005.8i	−0.826815	+	1.21946i
$534$	−68.6174	−	1265.57i	−0.00556061	−	0.102559i
$535$	−8286.96	−	20798.7i	−0.669676	−	1.68076i
$536$	9219.32	+	4265.31i	0.742936	+	0.343719i
$537$	2875.26	+	1729.98i	0.231055	+	0.139021i
$538$	1983.40	+	7143.58i	0.158942	+	0.572456i
$539$	4864.14	+	1070.68i	0.388707	+	0.0855609i
$540$	48.1542	−	5.23709i	0.00383746	−	0.000417349i
$541$	20877.8	−	12561.7i	1.65916	−	0.998283i	0.700530	−	0.713623i	$-0.252947\pi$
$541$	20877.8	−	12561.7i	1.65916	−	0.998283i	0.958629	−	0.284660i	$-0.0918807\pi$
$542$	9026.00	+	8549.88i	0.715313	+	0.677581i
$543$	3330.51	−	1540.86i	0.263215	−	0.121776i
$544$	−73.5030	−	7.99394i	−0.00579304	−	0.000630032i
$545$	15479.1	+	5215.50i	1.21661	+	0.409922i
$546$	−933.324	+	2342.47i	−0.0731549	+	0.183605i
$547$	3989.11	−	3778.68i	0.311814	−	0.295365i	−0.515748	−	0.856740i	$-0.672486\pi$
$547$	3989.11	−	3778.68i	0.311814	−	0.295365i	0.827562	+	0.561375i	$0.189727\pi$
$548$	−67.7294	+	243.939i	−0.00527967	+	0.0190156i
$549$	−3313.89	+	6250.66i	−0.257620	+	0.485923i
$550$	−4460.90	−	3391.09i	−0.345843	−	0.262903i
$551$	1437.01	−	26504.1i	0.111105	−	2.04921i
$552$	−8391.03	+	2827.27i	−0.647003	+	0.218001i
$553$	2450.88	−	539.480i	0.188467	−	0.0414847i
$554$	2378.32	+	4485.99i	0.182392	+	0.344028i
$555$	−912.218	+	5564.28i	−0.0697685	+	0.425569i
$556$	164.760	+	193.970i	0.0125672	+	0.0147953i
$557$	−3496.86	+	4116.82i	−0.266008	+	0.313169i	−0.878908	−	0.476992i	$-0.841727\pi$
$557$	−3496.86	+	4116.82i	−0.266008	+	0.313169i	0.612900	+	0.790161i	$0.290003\pi$
$558$	1146.76	+	6994.90i	0.0870001	+	0.530677i
$559$	−16568.5	+	12595.1i	−1.25362	+	0.952978i
$560$	2039.37	+	3007.85i	0.153891	+	0.226973i
$561$	369.193	+	544.519i	0.0277849	+	0.0409797i
$562$	14549.1	−	11060.0i	1.09203	−	0.830136i
$563$	2543.02	+	15511.7i	0.190365	+	1.16118i	0.893145	+	0.449769i	$0.148494\pi$
$563$	2543.02	+	15511.7i	0.190365	+	1.16118i	−0.702780	+	0.711407i	$0.748058\pi$
$564$	−72.4980	+	85.3512i	−0.00541261	+	0.00637222i
$565$	7245.62	+	8530.20i	0.539514	+	0.635165i
$566$	−1871.21	+	11413.9i	−0.138963	+	0.847636i
$567$	132.904	+	250.683i	0.00984380	+	0.0185674i
$568$	3113.16	−	685.258i	0.229974	−	0.0506211i
$569$	−16525.3	+	5568.01i	−1.21753	+	0.410234i	−0.853471	−	0.521141i	$-0.825507\pi$
$569$	−16525.3	+	5568.01i	−1.21753	+	0.410234i	−0.364061	+	0.931375i	$0.618610\pi$
$570$	779.830	−	14383.1i	0.0573044	−	1.05692i
$571$	8003.80	+	6084.33i	0.586600	+	0.445922i	0.855905	−	0.517133i	$-0.173001\pi$
$571$	8003.80	+	6084.33i	0.586600	+	0.445922i	−0.269305	+	0.963055i	$0.586794\pi$
$572$	66.6790	−	125.770i	0.00487411	−	0.00919355i
$573$	−1023.61	+	3686.72i	−0.0746283	+	0.268787i
$574$	1558.74	−	1476.51i	0.113346	−	0.107367i
$575$	−6352.81	+	15944.4i	−0.460749	+	1.15639i
$576$	−4303.83	−	1450.13i	−0.311331	−	0.104899i
$577$	11695.6	+	1271.97i	0.843835	+	0.0917726i	0.519816	−	0.854278i	$-0.326000\pi$
$577$	11695.6	+	1271.97i	0.843835	+	0.0917726i	0.324019	+	0.946051i	$0.394966\pi$
$578$	−12151.7	+	5621.99i	−0.874473	+	0.404574i
$579$	95.1047	+	90.0880i	0.00682628	+	0.00646620i
$580$	386.990	−	232.844i	0.0277049	−	0.0166695i
$581$	−2189.98	+	238.174i	−0.156378	+	0.0170071i
$582$	7831.41	+	1723.82i	0.557771	+	0.122775i
$583$	−59.8464	−	215.547i	−0.00425143	−	0.0153123i
$584$	13208.1	+	7947.02i	0.935879	+	0.563099i
$585$	−11002.5	−	5090.30i	−0.777602	−	0.359757i
$586$	−407.636	−	1023.09i	−0.0287360	−	0.0721219i
$587$	−401.097	−	7397.80i	−0.0282028	−	0.520170i	−0.978168	−	0.207815i	$-0.933365\pi$
$587$	−401.097	−	7397.80i	−0.0282028	−	0.520170i	0.949965	−	0.312355i	$-0.101118\pi$
$588$	−62.4755	+	92.1445i	−0.00438171	+	0.00646254i
$589$	29155.0			2.03958
$590$	−19640.6	+	6337.65i	−1.37049	+	0.442232i
$591$	−4589.37			−0.319427
$592$	−4280.39	+	6313.10i	−0.297167	+	0.438289i
$593$	−452.148	−	8339.38i	−0.0313111	−	0.577499i	−0.971528	−	0.236924i	$-0.923861\pi$
$593$	−452.148	−	8339.38i	−0.0313111	−	0.577499i	0.940217	−	0.340576i	$-0.110622\pi$
$594$	−428.651	−	1075.83i	−0.0296090	−	0.0743131i
$595$	−740.192	−	342.449i	−0.0509998	−	0.0235950i
$596$	−286.938	−	172.645i	−0.0197205	−	0.0118654i
$597$	−3983.27	−	14346.4i	−0.273072	−	0.983518i
$598$	−30786.8	−	6776.69i	−2.10529	−	0.463410i
$599$	15717.0	−	1709.32i	1.07208	−	0.116596i	0.444986	−	0.895538i	$-0.353209\pi$
$599$	15717.0	−	1709.32i	1.07208	−	0.116596i	0.627096	+	0.778942i	$0.284243\pi$
$600$	−7544.62	+	4539.45i	−0.513346	+	0.308870i
$601$	−220.709	−	209.066i	−0.0149799	−	0.0141897i	0.680173	−	0.733052i	$-0.261905\pi$
$601$	−220.709	−	209.066i	−0.0149799	−	0.0141897i	−0.695153	+	0.718862i	$0.744663\pi$
$602$	2236.92	−	1034.91i	0.151445	−	0.0700660i
$603$	4045.57	+	439.983i	0.273215	+	0.0297139i
$604$	−267.760	−	90.2189i	−0.0180381	−	0.00607774i
$605$	6534.82	−	16401.2i	0.439138	−	1.10215i
$606$	2037.19	−	1929.73i	0.136560	−	0.129356i
$607$	−6063.80	+	21839.8i	−0.405473	+	1.46038i	0.425953	+	0.904745i	$0.359939\pi$
$607$	−6063.80	+	21839.8i	−0.405473	+	1.46038i	−0.831426	+	0.555636i	$0.812475\pi$
$608$	250.755	−	472.974i	0.0167261	−	0.0315487i
$609$	2106.10	+	1601.02i	0.140137	+	0.106530i
$610$	−1938.05	+	35745.3i	−0.128638	+	2.37260i
$611$	26560.3	−	8949.20i	1.75861	−	0.592546i
$612$	−14.3613	+	3.16116i	−0.000948564	+	0.000208795i
$613$	−3781.70	−	7133.05i	−0.249171	−	0.469986i	0.727102	−	0.686529i	$-0.240867\pi$
$613$	−3781.70	−	7133.05i	−0.249171	−	0.469986i	−0.976273	+	0.216543i	$0.930522\pi$
$614$	−87.6822	+	534.838i	−0.00576314	+	0.0351536i
$615$	6682.55	+	7867.31i	0.438157	+	0.515838i
$616$	767.226	−	903.248i	0.0501825	−	0.0590794i
$617$	3659.82	+	22323.9i	0.238799	+	1.45661i	0.785282	+	0.619139i	$0.212518\pi$
$617$	3659.82	+	22323.9i	0.238799	+	1.45661i	−0.546483	+	0.837471i	$0.684034\pi$
$618$	10557.6	−	8025.69i	0.687200	−	0.522396i
$619$	−11965.4	−	17647.7i	−0.776949	−	1.14591i	−0.985793	−	0.167966i	$-0.946280\pi$
$619$	−11965.4	−	17647.7i	−0.776949	−	1.14591i	0.208843	−	0.977949i	$-0.433030\pi$
$620$	278.394	+	410.601i	0.0180332	+	0.0265970i
$621$	−2823.88	+	2146.66i	−0.182478	+	0.138716i
$622$	3053.28	+	18624.2i	0.196826	+	1.20058i
$623$	336.376	−	396.013i	0.0216318	−	0.0254669i
$624$	−10616.5	−	12498.7i	−0.681087	−	0.801837i
$625$	2408.60	−	14691.8i	0.154150	−	0.940275i
$626$	−3273.31	−	6174.12i	−0.208990	−	0.394198i
$627$	−4651.98	+	1023.98i	−0.296303	+	0.0652213i
$628$	163.126	−	54.9637i	0.0103654	−	0.00349250i
$629$	92.6740	−	1709.27i	0.00587465	−	0.108352i
$630$	1142.93	+	868.833i	0.0722784	+	0.0549446i
$631$	−1722.57	+	3249.12i	−0.108676	+	0.204985i	−0.931885	−	0.362754i	$-0.881837\pi$
$631$	−1722.57	+	3249.12i	−0.108676	+	0.204985i	0.823209	+	0.567738i	$0.192181\pi$
$632$	−4305.90	+	15508.4i	−0.271012	+	0.976096i
$633$	4957.66	−	4696.15i	0.311294	−	0.294874i
$634$	7788.80	−	19548.4i	0.487907	−	1.22455i
$635$	−17353.0	−	5846.91i	−1.08446	−	0.365398i
$636$	4.97092	+	0.540620i	0.000309921	+	3.37060e-5i
$637$	25287.5	−	11699.2i	1.57288	−	0.727694i
$638$	−7839.29	−	7425.77i	−0.486459	−	0.460798i
$639$	1094.21	−	658.365i	0.0677407	−	0.0407582i
$640$	−23490.9	+	2554.79i	−1.45087	+	0.157792i
$641$	−15269.2	−	3361.01i	−0.940869	−	0.207101i	−0.282048	−	0.959400i	$-0.591014\pi$
$641$	−15269.2	−	3361.01i	−0.940869	−	0.207101i	−0.658821	+	0.752299i	$0.728945\pi$
$642$	−3200.93	−	11528.7i	−0.196777	−	0.708725i
$643$	3394.38	+	2042.33i	0.208183	+	0.125259i	0.615827	−	0.787882i	$-0.288822\pi$
$643$	3394.38	+	2042.33i	0.208183	+	0.125259i	−0.407644	+	0.913141i	$0.633650\pi$
$644$	46.8638	+	21.6815i	0.00286754	+	0.00132666i
$645$	4386.03	+	11008.1i	0.267751	+	0.672005i
$646$	236.745	+	4366.50i	0.0144189	+	0.265941i
$647$	−9271.97	+	13675.1i	−0.563398	+	0.830950i	−0.997555	−	0.0698871i	$-0.977736\pi$
$647$	−9271.97	+	13675.1i	−0.563398	+	0.830950i	0.434157	+	0.900837i	$0.357046\pi$
$648$	−1819.74			−0.110318
$649$	3756.99	+	5697.53i	0.227234	+	0.344603i
$650$	−31347.4			−1.89161
$651$	−1630.74	+	2405.17i	−0.0981780	+	0.144802i
$652$	13.9185	+	256.711i	0.000836025	+	0.0154196i
$653$	683.470	+	1715.38i	0.0409590	+	0.102799i	0.948033	−	0.318171i	$-0.103069\pi$
$653$	683.470	+	1715.38i	0.0409590	+	0.102799i	−0.907074	+	0.420971i	$0.861689\pi$
$654$	7922.32	+	3665.26i	0.473681	+	0.219148i
$655$	14150.4	+	8514.02i	0.844126	+	0.507894i
$656$	3735.56	+	13454.3i	0.222331	+	0.800764i
$657$	6030.78	+	1327.48i	0.358118	+	0.0788276i
$658$	−3299.72	+	358.866i	−0.195496	+	0.0212615i
$659$	−15504.5	+	9328.75i	−0.916494	+	0.551436i	−0.893879	−	0.448308i	$-0.852027\pi$
$659$	−15504.5	+	9328.75i	−0.916494	+	0.551436i	−0.0226151	+	0.999744i	$0.507199\pi$
$660$	−58.8418	−	55.7379i	−0.00347032	−	0.00328727i
$661$	−17156.3	+	7937.35i	−1.00954	+	0.467061i	−0.853724	−	0.520726i	$-0.825661\pi$
$661$	−17156.3	+	7937.35i	−1.00954	+	0.467061i	−0.155811	+	0.987787i	$0.549799\pi$
$662$	−23153.2	−	2518.07i	−1.35933	−	0.147836i
$663$	3487.69	+	1175.14i	0.204300	+	0.0688366i
$664$	5229.43	−	13124.9i	0.305634	−	0.767084i
$665$	4287.08	−	4060.94i	0.249994	−	0.236807i
$666$	−806.144	+	2903.47i	−0.0469031	+	0.168930i
$667$	−15492.1	+	29221.2i	−0.899336	+	1.69633i
$668$	−214.817	−	163.300i	−0.0124424	−	0.00945846i
$669$	−22.5613	+	416.120i	−0.00130384	+	0.0240480i
$670$	19513.1	−	6574.72i	1.12516	−	0.379110i
$671$	11561.2	−	2544.82i	0.665150	−	0.146411i
$672$	24.9928	+	47.1414i	0.00143470	+	0.00270613i
$673$	−2546.28	+	15531.6i	−0.145842	+	0.889598i	0.807976	+	0.589215i	$0.200563\pi$
$673$	−2546.28	+	15531.6i	−0.145842	+	0.889598i	−0.953819	+	0.300383i	$0.902885\pi$
$674$	1851.45	+	2179.70i	0.105809	+	0.124568i
$675$	−2283.55	+	2688.40i	−0.130213	+	0.153299i
$676$	−88.9551	−	542.602i	−0.00506117	−	0.0308717i
$677$	−8074.95	+	6138.42i	−0.458413	+	0.348476i	−0.808755	−	0.588145i	$-0.799858\pi$
$677$	−8074.95	+	6138.42i	−0.458413	+	0.348476i	0.350342	+	0.936622i	$0.386065\pi$
$678$	3356.56	+	4950.55i	0.190130	+	0.280420i
$679$	1844.84	+	2720.94i	0.104269	+	0.153785i
$680$	4164.11	−	3165.48i	0.234833	−	0.178515i
$681$	900.089	+	5490.30i	0.0506483	+	0.308941i
$682$	7678.36	−	9039.67i	0.431114	−	0.507547i
$683$	−8975.32	−	10566.6i	−0.502828	−	0.591974i	0.450927	−	0.892561i	$-0.351093\pi$
$683$	−8975.32	−	10566.6i	−0.502828	−	0.591974i	−0.953755	+	0.300587i	$0.902818\pi$
$684$	17.2252	−	105.069i	0.000962898	−	0.00587342i
$685$	−16898.2	−	31873.4i	−0.942550	−	1.77784i
$686$	−6564.61	+	1444.98i	−0.365361	+	0.0804221i
$687$	8384.34	−	2825.01i	0.465622	−	0.156886i
$688$	−867.809	+	16005.8i	−0.0480885	+	0.886941i
$689$	−996.265	−	757.341i	−0.0550866	−	0.0418758i
$690$	−8407.19	+	15857.6i	−0.463850	+	0.874913i
$691$	−3939.86	+	14190.1i	−0.216902	+	0.781210i	0.772376	+	0.635165i	$0.219068\pi$
$691$	−3939.86	+	14190.1i	−0.216902	+	0.781210i	−0.989278	+	0.146044i	$0.953346\pi$
$692$	139.073	−	131.737i	0.00763984	−	0.00723684i
$693$	175.728	−	441.044i	0.00963255	−	0.0241759i
$694$	34342.1	+	11571.2i	1.87840	+	0.632905i
$695$	−36053.1	−	3921.01i	−1.96773	−	0.214004i
$696$	−15399.1	+	7124.39i	−0.838653	+	0.388002i
$697$	−2275.06	−	2155.05i	−0.123636	−	0.117114i
$698$	8996.07	−	5412.76i	0.487831	−	0.293518i
$699$	−1790.44	+	194.722i	−0.0968820	+	0.0105365i
$700$	50.1469	+	11.0382i	0.00270768	+	0.000596005i
$701$	9236.04	+	33265.2i	0.497632	+	1.79231i	0.602843	+	0.797860i	$0.294034\pi$
$701$	9236.04	+	33265.2i	0.497632	+	1.79231i	−0.105211	+	0.994450i	$0.533552\pi$
$702$	−5551.26	−	3340.08i	−0.298460	−	0.179577i
$703$	11248.6	+	5204.15i	0.603482	+	0.279201i
$704$	2812.77	+	7059.52i	0.150583	+	0.377934i
$705$	−863.933	−	15934.3i	−0.0461526	−	0.851235i
$706$	−20729.7	+	30574.0i	−1.10506	+	1.62984i
$707$	1150.36			0.0611936
$708$	−149.391	+	30.8749i	−0.00793003	+	0.00163891i
$709$	2956.94			0.156629			0.0783146	−	0.996929i	$-0.475046\pi$
$709$	2956.94			0.156629			0.0783146	+	0.996929i	$0.475046\pi$
$710$	3626.13	−	5348.14i	0.191671	−	0.282693i
$711$	349.077	+	6438.34i	0.0184126	+	0.339601i
$712$	1233.45	+	3095.73i	0.0649236	+	0.162946i
$713$	−32970.9	−	15254.0i	−1.73180	−	0.801214i
$714$	−373.460	−	224.704i	−0.0195748	−	0.0117778i
$715$	5426.78	+	19545.5i	0.283847	+	1.02232i
$716$	122.569	+	26.9795i	0.00639751	+	0.00140820i
$717$	−1428.54	+	155.363i	−0.0744070	+	0.00809225i
$718$	20067.5	−	12074.2i	1.04305	−	0.627584i
$719$	15641.6	+	14816.5i	0.811310	+	0.768514i	0.975986	−	0.217834i	$-0.0698992\pi$
$719$	15641.6	+	14816.5i	0.811310	+	0.768514i	−0.164676	+	0.986348i	$0.552658\pi$
$720$	−8473.95	+	3920.47i	−0.438619	+	0.202927i
$721$	5404.87	+	587.816i	0.279179	+	0.0303625i
$722$	−11491.4	−	3871.90i	−0.592333	−	0.199580i
$723$	−6208.61	+	15582.4i	−0.319365	+	0.801545i
$724$	99.6434	−	94.3873i	0.00511494	−	0.00484513i
$725$	−8798.72	+	31690.1i	−0.450726	+	1.62337i
$726$	4419.46	−	8335.99i	0.225925	−	0.426140i
$727$	11694.4	+	8889.82i	0.596589	+	0.453515i	0.859380	−	0.511338i	$-0.170850\pi$
$727$	11694.4	+	8889.82i	0.596589	+	0.453515i	−0.262791	+	0.964853i	$0.584643\pi$
$728$	358.932	−	6620.11i	0.0182732	−	0.337030i
$729$	−690.839	+	232.771i	−0.0350983	+	0.0118260i
$730$	30515.2	−	6716.91i	1.54715	−	0.340553i
$731$	−1685.05	−	3178.34i	−0.0852582	−	0.160814i
$732$	−42.8085	+	261.120i	−0.00216154	+	0.0131848i
$733$	−6632.04	−	7807.84i	−0.334188	−	0.393437i	0.569243	−	0.822169i	$-0.307236\pi$
$733$	−6632.04	−	7807.84i	−0.334188	−	0.393437i	−0.903432	+	0.428732i	$0.858960\pi$
$734$	1743.74	−	2052.90i	0.0876877	−	0.103234i
$735$	−2566.50	−	15654.9i	−0.128798	−	0.785634i
$736$	−531.036	+	403.683i	−0.0265955	+	0.0202173i
$737$	−3821.25	−	5635.92i	−0.190987	−	0.281685i
$738$	3095.72	+	4565.84i	0.154410	+	0.227738i
$739$	29879.7	−	22714.0i	1.48734	−	1.13064i	0.527691	−	0.849437i	$-0.323058\pi$
$739$	29879.7	−	22714.0i	1.48734	−	1.13064i	0.959647	−	0.281208i	$-0.0907351\pi$
$740$	34.1181	+	208.111i	0.00169487	+	0.0103383i
$741$	−17251.2	+	20309.6i	−0.855246	+	1.00687i
$742$	95.9449	+	112.955i	0.00474697	+	0.00558856i
$743$	1660.14	−	10126.4i	0.0819714	−	0.500004i	−0.913648	−	0.406506i	$-0.866747\pi$
$743$	1660.14	−	10126.4i	0.0819714	−	0.500004i	0.995620	−	0.0934976i	$-0.0298047\pi$
$744$	−8729.71	−	16466.0i	−0.430170	−	0.811388i
$745$	46602.9	−	10258.1i	2.29181	−	0.504466i
$746$	13485.4	−	4543.75i	0.661843	−	0.223001i
$747$	306.420	−	5651.58i	0.0150085	−	0.276815i
$748$	19.5883	+	14.8906i	0.000957511	+	0.000727881i
$749$	2297.57	−	4333.67i	0.112084	−	0.211414i
$750$	−206.208	+	742.695i	−0.0100396	+	0.0361592i
$751$	−6450.26	+	6110.01i	−0.313413	+	0.296881i	−0.828194	−	0.560441i	$-0.810632\pi$
$751$	−6450.26	+	6110.01i	−0.313413	+	0.296881i	0.514781	+	0.857322i	$0.327873\pi$
$752$	7989.90	−	20053.1i	0.387449	−	0.972424i
$753$	8926.47	+	3007.68i	0.432003	+	0.145559i
$754$	−60052.8	−	6531.13i	−2.90052	−	0.315451i
$755$	36541.6	−	16905.9i	1.76144	−	0.814927i
$756$	7.70430	+	7.29790i	0.000370639	+	0.000351088i
$757$	−24189.5	+	14554.3i	−1.16140	+	0.698793i	−0.959803	−	0.280675i	$-0.909442\pi$
$757$	−24189.5	+	14554.3i	−1.16140	+	0.698793i	−0.201600	+	0.979468i	$0.564614\pi$
$758$	38679.8	−	4206.68i	1.85345	−	0.201575i
$759$	5796.60	+	1275.93i	0.277211	+	0.0610188i
$760$	10132.0	+	36492.1i	0.483587	+	1.74172i
$761$	−26660.4	−	16041.0i	−1.26996	−	0.764109i	−0.288815	−	0.957385i	$-0.593261\pi$
$761$	−26660.4	−	16041.0i	−1.26996	−	0.764109i	−0.981144	+	0.193276i	$0.938089\pi$
$762$	−8881.43	−	4108.99i	−0.422231	−	0.195345i
$763$	1324.56	+	3324.39i	0.0628469	+	0.157734i
$764$	7.74750	+	142.894i	0.000366878	+	0.00676667i
$765$	1175.94	−	1734.38i	0.0555766	−	0.0819693i
$766$	7594.42			0.358221
$767$	36021.0	+	12654.9i	1.69575	+	0.595754i
$768$	−516.934			−0.0242881
$769$	2983.33	−	4400.08i	0.139898	−	0.206334i	−0.751285	−	0.659978i	$-0.770566\pi$
$769$	2983.33	−	4400.08i	0.139898	−	0.206334i	0.891183	+	0.453644i	$0.149876\pi$
$770$	−130.056	−	2398.74i	−0.00608686	−	0.112266i
$771$	6370.24	+	15988.1i	0.297560	+	0.746819i
$772$	4.44670	+	2.05726i	0.000207306	+	9.59099e-5i
$773$	−15675.9	−	9431.86i	−0.729394	−	0.438862i	0.101828	−	0.994802i	$-0.467531\pi$
$773$	−15675.9	−	9431.86i	−0.729394	−	0.438862i	−0.831222	+	0.555940i	$0.812358\pi$
$774$	1694.15	+	6101.78i	0.0786756	+	0.283364i
$775$	−35280.7	−	7765.87i	−1.63525	−	0.359946i
$776$	−20960.2	+	2279.56i	−0.969623	+	0.105453i
$777$	−1058.49	+	636.875i	−0.0488717	+	0.0294051i
$778$	−16612.6	−	15736.3i	−0.765540	−	0.725158i
$779$	20592.5	−	9527.08i	0.947113	−	0.438181i
$780$	−450.756	−	49.0227i	−0.0206919	−	0.00225038i
$781$	−2024.91	−	682.273i	−0.0927748	−	0.0312595i
$782$	2016.83	−	5061.87i	0.0922274	−	0.231473i
$783$	−4934.74	+	4674.44i	−0.225228	+	0.213347i
$784$	5741.00	−	20677.2i	0.261525	−	0.941928i
$785$	−11489.7	+	21671.8i	−0.522400	+	0.985351i
$786$	7025.86	+	5340.92i	0.318835	+	0.242372i
$787$	−1422.00	+	26227.3i	−0.0644077	+	1.18793i	0.770463	+	0.637485i	$0.220025\pi$
$787$	−1422.00	+	26227.3i	−0.0644077	+	1.18793i	−0.834871	+	0.550446i	$0.814458\pi$
$788$	−162.663	+	54.8075i	−0.00735359	+	0.00247771i
$789$	5565.11	−	1224.97i	0.251106	−	0.0552727i
$790$	15282.0	+	28824.8i	0.688237	+	1.29815i
$791$	−396.692	+	2419.72i	−0.0178316	+	0.108768i
$792$	1971.23	+	2320.71i	0.0884403	+	0.104120i
$793$	42873.0	−	50474.0i	1.91988	−	2.26026i
$794$	−5561.01	−	33920.7i	−0.248555	−	1.51612i
$795$	−567.234	+	431.200i	−0.0253053	+	0.0192366i
$796$	−312.510	−	460.918i	−0.0139154	−	0.0205236i
$797$	8538.75	+	12593.7i	0.379496	+	0.559715i	0.968689	−	0.248278i	$-0.0798646\pi$
$797$	8538.75	+	12593.7i	0.379496	+	0.559715i	−0.589193	+	0.807992i	$0.700554\pi$
$798$	2512.27	−	1909.78i	0.111445	−	0.0847185i
$799$	783.756	+	4780.70i	0.0347025	+	0.211676i
$800$	−429.425	+	505.558i	−0.0189781	+	0.0223427i
$801$	864.251	+	1017.47i	0.0381233	+	0.0448823i
$802$	2402.29	−	14653.3i	0.105770	−	0.645170i
$803$	−4839.90	−	9129.03i	−0.212698	−	0.401191i
$804$	148.644	−	32.7189i	0.00652021	−	0.00143521i
$805$	−6972.89	+	2349.44i	−0.305294	+	0.102866i
$806$	3592.18	−	66253.8i	0.156984	−	2.89540i
$807$	−6216.66	−	4725.78i	−0.271173	−	0.206141i
$808$	−3455.87	+	6518.46i	−0.150467	+	0.283810i
$809$	10534.9	−	37943.3i	0.457834	−	1.64897i	−0.269734	−	0.962935i	$-0.586936\pi$
$809$	10534.9	−	37943.3i	0.457834	−	1.64897i	0.727569	−	0.686035i	$-0.240650\pi$
$810$	−2677.96	+	2536.70i	−0.116165	+	0.110038i
$811$	7482.98	−	18780.9i	0.323999	−	0.813175i	−0.673276	−	0.739392i	$-0.735113\pi$
$811$	7482.98	−	18780.9i	0.323999	−	0.813175i	0.997274	−	0.0737835i	$-0.0235074\pi$
$812$	93.7674	+	31.5939i	0.00405245	+	0.00136543i
$813$	−13018.5	−	1415.84i	−0.561596	−	0.0610772i
$814$	4576.04	−	2117.10i	0.197040	−	0.0911602i
$815$	−26596.4	−	25193.5i	−1.14311	−	1.08281i
$816$	2428.80	−	1461.36i	0.104197	−	0.0626935i
$817$	25894.1	−	2816.15i	1.10884	−	0.120593i
$818$	−145.114	−	31.9420i	−0.00620268	−	0.00136531i
$819$	−710.543	−	2559.14i	−0.0303155	−	0.109186i
$820$	330.806	+	199.040i	0.0140881	+	0.00847654i
$821$	25661.3	+	11872.2i	1.09085	+	0.504680i	0.881030	−	0.473061i	$-0.156851\pi$
$821$	25661.3	+	11872.2i	1.09085	+	0.504680i	0.209818	+	0.977741i	$0.432713\pi$
$822$	−7135.99	−	17910.0i	−0.302793	−	0.759954i
$823$	−1847.03	−	34066.4i	−0.0782301	−	1.44287i	−0.729478	−	0.684004i	$-0.760237\pi$
$823$	−1847.03	−	34066.4i	−0.0782301	−	1.44287i	0.651248	−	0.758865i	$-0.274246\pi$
$824$	−19567.9	+	28860.5i	−0.827281	+	1.22015i
$825$	5902.16			0.249075
$826$	−3843.92	−	2380.66i	−0.161921	−	0.100283i
$827$	21887.5			0.920317			0.460158	−	0.887837i	$-0.347793\pi$
$827$	21887.5			0.920317			0.460158	+	0.887837i	$0.347793\pi$
$828$	−74.4522	+	109.809i	−0.00312487	+	0.00460884i
$829$	−1350.28	−	24904.4i	−0.0565707	−	1.04338i	−0.879700	−	0.475530i	$-0.842256\pi$
$829$	−1350.28	−	24904.4i	−0.0565707	−	1.04338i	0.823129	−	0.567855i	$-0.192226\pi$
$830$	−10600.2	−	26604.5i	−0.443300	−	1.11260i
$831$	−4853.78	−	2245.60i	−0.202618	−	0.0937413i
$832$	36426.9	+	21917.3i	1.51788	+	0.913277i
$833$	1288.43	+	4640.50i	0.0535911	+	0.193018i
$834$	−18927.7	−	4166.29i	−0.785865	−	0.172982i
$835$	38226.0	−	4157.33i	1.58427	−	0.172300i
$836$	−152.654	+	91.8486i	−0.00631535	+	0.00379982i
$837$	−5420.34	−	5134.42i	−0.223840	−	0.212033i
$838$	−33450.9	+	15476.0i	−1.37893	+	0.637960i
$839$	5144.55	+	559.503i	0.211692	+	0.0230229i	0.213350	−	0.976976i	$-0.431562\pi$
$839$	5144.55	+	559.503i	0.211692	+	0.0230229i	−0.00165855	+	0.999999i	$0.500528\pi$
$840$	−3577.17	−	1205.29i	−0.146933	−	0.0495076i
$841$	−14431.1	+	36219.2i	−0.591703	+	1.48506i
$842$	−24032.6	+	22764.9i	−0.983632	+	0.931745i
$843$	−5149.86	+	18548.1i	−0.210404	+	0.757806i
$844$	119.634	−	225.654i	0.00487911	−	0.00920298i
$845$	62375.3	+	47416.5i	2.53938	+	1.93039i
$846$	461.694	−	8515.45i	0.0187629	−	0.346061i
$847$	3665.48	−	1235.04i	0.148698	−	0.0501023i
$848$	−941.308	+	207.197i	−0.0381187	+	0.00839056i
$849$	−5706.50	−	10763.6i	−0.230679	−	0.435107i
$850$	876.597	−	5347.00i	0.0353730	−	0.215766i
$851$	−9998.02	−	11770.6i	−0.402735	−	0.474137i
$852$	30.9202	−	36.4021i	0.00124332	−	0.00146375i
$853$	−3883.33	−	23687.3i	−0.155877	−	0.950805i	−0.942704	−	0.333632i	$-0.891726\pi$
$853$	−3883.33	−	23687.3i	−0.155877	−	0.950805i	0.786827	−	0.617174i	$-0.211722\pi$
$854$	−6243.55	+	4746.23i	−0.250176	+	0.190179i
$855$	8514.32	+	12557.7i	0.340566	+	0.502297i
$856$	17654.2	+	26038.0i	0.704916	+	1.03967i
$857$	−1033.49	+	785.637i	−0.0411940	+	0.0313149i	−0.625569	−	0.780169i	$-0.715133\pi$
$857$	−1033.49	+	785.637i	−0.0411940	+	0.0313149i	0.584375	+	0.811484i	$0.301340\pi$
$858$	1753.79	+	10697.6i	0.0697825	+	0.425655i
$859$	1395.68	−	1643.13i	0.0554367	−	0.0652651i	−0.733745	−	0.679425i	$-0.762229\pi$
$859$	1395.68	−	1643.13i	0.0554367	−	0.0652651i	0.789181	+	0.614160i	$0.210505\pi$
$860$	286.918	+	337.786i	0.0113765	+	0.0133935i
$861$	−365.865	+	2231.68i	−0.0144816	+	0.0883338i
$862$	−12938.7	−	24405.0i	−0.511246	−	0.964312i
$863$	17321.0	−	3812.65i	0.683215	−	0.150387i	0.140217	−	0.990121i	$-0.455220\pi$
$863$	17321.0	−	3812.65i	0.683215	−	0.150387i	0.542998	+	0.839734i	$0.317289\pi$
$864$	−129.913	+	43.7729i	−0.00511545	+	0.00172359i
$865$	−1477.84	+	27257.2i	−0.0580902	+	1.07141i
$866$	−16357.3	−	12434.5i	−0.641851	−	0.487923i
$867$	6605.90	−	12460.0i	0.258764	−	0.488080i
$868$	−29.0760	+	104.722i	−0.00113699	+	0.00409505i
$869$	7832.66	−	7419.49i	0.305759	−	0.289631i
$870$	−12730.3	+	31950.6i	−0.496088	+	1.24509i
$871$	−36098.6	−	12163.0i	−1.40431	−	0.473167i
$872$	−22816.6	−	2481.45i	−0.886086	−	0.0963677i
$873$	−7665.65	+	3546.51i	−0.297185	+	0.137493i
$874$	28642.2	+	27131.3i	1.10851	+	1.05004i
$875$	−270.758	+	162.910i	−0.0104609	+	0.00629413i
$876$	229.605	−	24.9710i	0.00885574	−	0.000963120i
$877$	17340.5	+	3816.93i	0.667671	+	0.146965i	0.535857	−	0.844309i	$-0.319989\pi$
$877$	17340.5	+	3816.93i	0.667671	+	0.146965i	0.131814	+	0.991274i	$0.457920\pi$
$878$	5358.16	+	19298.3i	0.205956	+	0.741785i
$879$	993.961	+	598.046i	0.0381405	+	0.0229483i
$880$	14179.1	+	6559.97i	0.543158	+	0.251292i
$881$	−1966.79	−	4936.26i	−0.0752131	−	0.188771i	0.886563	−	0.462608i	$-0.153086\pi$
$881$	−1966.79	−	4936.26i	−0.0752131	−	0.188771i	−0.961776	+	0.273837i	$0.911707\pi$
$882$	−458.981	−	8465.40i	−0.0175223	−	0.323180i
$883$	−11769.0	+	17358.0i	−0.448539	+	0.661545i	−0.982991	−	0.183654i	$-0.941208\pi$
$883$	−11769.0	+	17358.0i	−0.448539	+	0.661545i	0.534452	+	0.845199i	$0.320518\pi$
$884$	137.650			0.00523717
$885$	12429.3	−	17833.8i	0.472098	−	0.677374i
$886$	31307.6			1.18713
$887$	−19170.3	+	28274.0i	−0.725675	+	1.07029i	0.268580	+	0.963257i	$0.413446\pi$
$887$	−19170.3	+	28274.0i	−0.725675	+	1.07029i	−0.994255	+	0.107034i	$0.965865\pi$
$888$	−428.931	−	7911.16i	−0.0162094	−	0.298965i
$889$	−1484.91	−	3726.85i	−0.0560207	−	0.140601i
$890$	6130.59	+	2836.31i	0.230896	+	0.106824i
$891$	1045.20	+	628.877i	0.0392992	+	0.0236455i
$892$	4.16977	+	15.0181i	0.000156518	+	0.000563727i
$893$	−34256.5	−	7540.42i	−1.28371	−	0.282565i
$894$	25351.8	−	2757.17i	0.948423	−	0.103147i
$895$	−15324.0	+	9220.13i	−0.572317	+	0.344352i
$896$	−3758.36	−	3560.11i	−0.140132	−	0.132740i
$897$	30135.2	−	13942.0i	1.12172	−	0.518963i
$898$	−25107.1	−	2730.56i	−0.933001	−	0.101470i
$899$	−65969.8	−	22227.8i	−2.44740	−	0.824626i
$900$	−48.8311	+	122.557i	−0.00180856	+	0.00453915i
$901$	157.041	−	148.757i	0.00580665	−	0.00550035i
$902$	2469.38	−	8893.90i	0.0911544	−	0.328309i
$903$	−1216.03	+	2293.67i	−0.0448138	+	0.0845279i
$904$	−12519.4	−	9517.03i	−0.460609	−	0.350146i
$905$	−1058.85	+	19529.3i	−0.0388919	+	0.717320i
$906$	20390.5	−	6870.37i	0.747716	−	0.251935i
$907$	33757.6	−	7430.60i	1.23583	−	0.272028i	0.451446	−	0.892298i	$-0.350908\pi$
$907$	33757.6	−	7430.60i	1.23583	−	0.272028i	0.784388	+	0.620270i	$0.212977\pi$
$908$	97.4690	+	183.846i	0.00356236	+	0.00671932i
$909$	−478.167	+	2916.69i	−0.0174475	+	0.106425i
$910$	−8700.15	−	10242.6i	−0.316931	−	0.373120i
$911$	−14735.5	+	17348.0i	−0.535905	+	0.630916i	−0.961766	−	0.273872i	$-0.911695\pi$
$911$	−14735.5	+	17348.0i	−0.535905	+	0.630916i	0.425861	+	0.904789i	$0.359971\pi$
$912$	3320.32	+	20253.0i	0.120556	+	0.735357i
$913$	−7539.38	+	5731.29i	−0.273294	+	0.207752i
$914$	−7781.42	−	11476.7i	−0.281605	−	0.415336i
$915$	−21160.0	−	31208.7i	−0.764512	−	1.12757i
$916$	263.433	−	200.256i	0.00950225	−	0.00722342i
$917$	585.333	+	3570.37i	0.0210789	+	0.128576i
$918$	724.960	−	853.489i	0.0260645	−	0.0306856i
$919$	16756.8	+	19727.6i	0.601476	+	0.708112i	0.975671	−	0.219238i	$-0.0703570\pi$
$919$	16756.8	+	19727.6i	0.601476	+	0.708112i	−0.374196	+	0.927350i	$0.622081\pi$
$920$	7634.68	−	46569.5i	0.273596	−	1.66886i
$921$	−267.398	−	504.366i	−0.00956684	−	0.0180450i
$922$	14331.0	−	3154.49i	0.511894	−	0.112676i
$923$	−11327.9	+	3816.82i	−0.403968	+	0.136113i
$924$	0.961332	−	17.7307i	3.42267e−5	−	0.000631275i
$925$	−12225.8	−	9293.82i	−0.434575	−	0.330356i
$926$	5376.75	−	10141.6i	0.190811	−	0.359908i
$927$	−3737.00	+	13459.5i	−0.132405	+	0.476879i
$928$	−927.987	+	879.036i	−0.0328261	+	0.0310946i
$929$	−20548.4	+	51572.5i	−0.725695	+	1.82136i	−0.179371	+	0.983781i	$0.557406\pi$
$929$	−20548.4	+	51572.5i	−0.725695	+	1.82136i	−0.546323	+	0.837574i	$0.683973\pi$
$930$	−35800.2	−	12062.5i	−1.26229	−	0.425317i
$931$	−34666.0	−	3770.15i	−1.22034	−	0.132719i
$932$	−61.1338	+	28.2835i	−0.00214861	+	0.000994053i
$933$	−14431.9	−	13670.6i	−0.506408	−	0.479695i
$934$	18662.8	−	11229.1i	0.653818	−	0.393390i
$935$	−3485.68	+	379.090i	−0.121919	+	0.0132594i
$936$	16635.8	+	3661.81i	0.580938	+	0.127874i
$937$	−12755.6	−	45941.5i	−0.444725	−	1.60176i	−0.758108	−	0.652129i	$-0.773876\pi$
$937$	−12755.6	−	45941.5i	−0.444725	−	1.60176i	0.313383	−	0.949627i	$-0.398538\pi$
$938$	3865.42	+	2325.75i	0.134553	+	0.0809577i
$939$	6680.32	+	3090.65i	0.232166	+	0.107412i
$940$	−220.913	−	554.449i	−0.00766530	−	0.0192385i
$941$	−1448.74	−	26720.5i	−0.0501889	−	0.925679i	−0.909882	−	0.414868i	$-0.863828\pi$
$941$	−1448.74	−	26720.5i	−0.0501889	−	0.925679i	0.859693	−	0.510811i	$-0.170655\pi$
$942$	−7356.40	+	10849.9i	−0.254442	+	0.375274i
$943$	−28272.3			−0.976323
$944$	25388.8	−	14834.7i	0.875356	−	0.511470i
$945$	−1512.19			−0.0520547
$946$	5946.40	−	8770.28i	0.204370	−	0.301423i
$947$	−836.636	−	15430.8i	−0.0287086	−	0.529499i	−0.977151	−	0.212548i	$-0.931824\pi$
$947$	−836.636	−	15430.8i	−0.0287086	−	0.529499i	0.948442	−	0.316951i	$-0.102659\pi$
$948$	89.2610	+	224.028i	0.00305808	+	0.00767521i
$949$	−52461.2	−	24271.1i	−1.79448	−	0.830215i
$950$	33615.9	+	20226.0i	1.14804	+	0.690756i
$951$	5929.64	+	21356.6i	0.202189	+	0.728219i
$952$	1119.17	+	246.348i	0.0381014	+	0.00838675i
$953$	−49932.0	+	5430.44i	−1.69723	+	0.184585i	−0.904933	−	0.425555i	$-0.860079\pi$
$953$	−49932.0	+	5430.44i	−1.69723	+	0.184585i	−0.792294	+	0.610139i	$0.791114\pi$
$954$	−326.273	+	196.312i	−0.0110728	+	0.00666231i
$955$	−14804.5	−	14023.6i	−0.501637	−	0.475175i
$956$	−48.7770	+	22.5667i	−0.00165017	+	0.000763450i
$957$	11306.8	+	1229.69i	0.381921	+	0.0415364i
$958$	25763.5	+	8680.75i	0.868875	+	0.292758i
$959$	2925.44	−	7342.30i	0.0985061	−	0.247232i
$960$	17572.5	−	16645.6i	0.590783	−	0.559619i
$961$	12486.4	−	44971.9i	0.419133	−	1.50958i
$962$	13212.2	−	24920.9i	0.442805	−	0.835219i
$963$	10032.8	+	7626.73i	0.335724	+	0.255211i
$964$	−33.9646	+	626.440i	−0.00113478	+	0.0209298i
$965$	−661.626	+	222.928i	−0.0220710	+	0.00743657i
$966$	−3840.29	+	845.311i	−0.127908	+	0.0281547i
$967$	13204.2	+	24905.8i	0.439109	+	0.828248i	1.00000		0.000358195i	$0.000114017\pi$
$967$	13204.2	+	24905.8i	0.439109	+	0.828248i	−0.560891	+	0.827890i	$0.689541\pi$
$968$	−4013.37	+	24480.5i	−0.133259	+	0.812843i
$969$	−2981.85	−	3510.51i	−0.0988554	−	0.116382i
$970$	−27667.7	+	32572.9i	−0.915830	+	1.07820i
$971$	6853.08	+	41802.0i	0.226494	+	1.38155i	0.817984	+	0.575241i	$0.195092\pi$
$971$	6853.08	+	41802.0i	0.226494	+	1.38155i	−0.591490	+	0.806313i	$0.701460\pi$
$972$	−21.7059	+	16.5004i	−0.000716273	+	0.000544497i
$973$	−4458.78	−	6576.20i	−0.146908	−	0.216674i
$974$	671.775	+	990.794i	0.0220996	+	0.0325945i
$975$	26285.6	−	19981.8i	0.863398	−	0.656338i
$976$	−8251.74	−	50333.4i	−0.270627	−	1.65075i
$977$	−34632.2	+	40772.2i	−1.13407	+	1.33513i	−0.199269	+	0.979945i	$0.563857\pi$
$977$	−34632.2	+	40772.2i	−1.13407	+	1.33513i	−0.934797	+	0.355181i	$0.884419\pi$
$978$	−12674.4	−	14921.5i	−0.414400	−	0.487869i
$979$	361.386	−	2204.35i	0.0117977	−	0.0719627i
$980$	−277.921	−	524.215i	−0.00905905	−	0.0170872i
$981$	−8979.40	+	1976.52i	−0.292243	+	0.0643275i
$982$	−3531.72	+	1189.98i	−0.114768	+	0.0386697i
$983$	−3123.46	+	57608.9i	−0.101346	+	1.86922i	0.300863	+	0.953667i	$0.402725\pi$
$983$	−3123.46	+	57608.9i	−0.101346	+	1.86922i	−0.402209	+	0.915548i	$0.631758\pi$
$984$	−11546.5	−	8777.45i	−0.374075	−	0.284365i
$985$	11457.0	−	21610.3i	0.370611	−	0.699046i
$986$	2793.34	−	10060.7i	0.0902211	−	0.324947i
$987$	2538.14	−	2404.26i	0.0818541	−	0.0775363i
$988$	−368.897	+	925.862i	−0.0118787	+	0.0298134i
$989$	−30756.6	−	10363.1i	−0.988882	−	0.333193i
$990$	6135.94	+	667.324i	0.196983	+	0.0214232i
$991$	−9384.87	+	4341.90i	−0.300828	+	0.139178i	−0.564496	−	0.825436i	$-0.690930\pi$
$991$	−9384.87	+	4341.90i	−0.300828	+	0.139178i	0.263669	+	0.964613i	$0.415067\pi$
$992$	−1019.30	−	965.536i	−0.0326239	−	0.0309030i
$993$	21019.6	−	12647.1i	0.671740	−	0.404173i
$994$	1407.32	−	153.056i	0.0449070	−	0.00488394i
$995$	77498.0	+	17058.6i	2.46920	+	0.543511i
$996$	−56.6323	−	203.971i	−0.00180167	−	0.00648902i
$997$	−19037.9	−	11454.7i	−0.604750	−	0.363866i	0.180011	−	0.983665i	$-0.442387\pi$
$997$	−19037.9	−	11454.7i	−0.604750	−	0.363866i	−0.784761	+	0.619799i	$0.787214\pi$
$998$	33442.8	+	15472.3i	1.06074	+	0.490749i
$999$	−1174.79	−	2948.49i	−0.0372058	−	0.0933795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.e.a.76.5	yes	420
59.7	even	29	inner	177.4.e.a.7.5	✓	420

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.e.a.7.5	✓	420	59.7	even	29	inner
177.4.e.a.76.5	yes	420	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.59837 + 2.35742i) q^{2} +(-0.162417 - 2.99560i) q^{3} +(-0.0415309 - 0.104235i) q^{4} +(14.5110 + 6.71353i) q^{5} +(7.32148 + 4.40519i) q^{6} +(0.937125 + 3.37522i) q^{7} +(-21.9407 - 4.82952i) q^{8} +(-8.94724 + 0.973071i) q^{9} +O(q^{10})\)	\(q+(-1.59837 + 2.35742i) q^{2} +(-0.162417 - 2.99560i) q^{3} +(-0.0415309 - 0.104235i) q^{4} +(14.5110 + 6.71353i) q^{5} +(7.32148 + 4.40519i) q^{6} +(0.937125 + 3.37522i) q^{7} +(-21.9407 - 4.82952i) q^{8} +(-8.94724 + 0.973071i) q^{9} +(-39.0206 + 23.4779i) q^{10} +(10.9330 + 10.3563i) q^{11} +(-0.305500 + 0.141340i) q^{12} +(83.7523 + 9.10861i) q^{13} +(-9.45468 - 3.18565i) q^{14} +(17.7542 - 44.5597i) q^{15} +(47.1062 - 44.6214i) q^{16} +(-3.89572 + 14.0311i) q^{17} +(12.0071 - 22.6477i) q^{18} +(-83.9359 - 63.8064i) q^{19} +(0.0971255 - 1.79138i) q^{20} +(9.95860 - 3.35544i) q^{21} +(-41.8892 + 9.22051i) q^{22} +(61.5381 + 116.073i) q^{23} +(-10.9038 + 66.5100i) q^{24} +(84.5758 + 99.5703i) q^{25} +(-155.340 + 182.880i) q^{26} +(4.36811 + 26.6443i) q^{27} +(0.312896 - 0.237857i) q^{28} +(141.278 + 208.369i) q^{29} +(76.6680 + 113.077i) q^{30} +(-220.137 + 167.344i) q^{31} +(0.821431 + 5.01051i) q^{32} +(29.2477 - 34.4330i) q^{33} +(-26.8504 - 31.6107i) q^{34} +(-9.06096 + 55.2694i) q^{35} +(0.473015 + 0.892201i) q^{36} +(-114.804 + 25.2703i) q^{37} +(284.579 - 95.8858i) q^{38} +(13.6830 - 252.368i) q^{39} +(-285.960 - 217.381i) q^{40} +(-100.801 + 190.131i) q^{41} +(-8.00734 + 28.8398i) q^{42} +(-179.351 + 169.890i) q^{43} +(0.625430 - 1.56971i) q^{44} +(-136.367 - 45.9473i) q^{45} +(-371.994 - 40.4567i) q^{46} +(301.937 - 139.691i) q^{47} +(-141.319 - 133.864i) q^{48} +(283.388 - 170.509i) q^{49} +(-369.912 + 40.2304i) q^{50} +(42.6643 + 9.39112i) q^{51} +(-2.52888 - 9.10819i) q^{52} +(-12.7283 - 7.65835i) q^{53} +(-69.7937 - 32.2900i) q^{54} +(89.1224 + 223.680i) q^{55} +(-4.26052 - 78.5806i) q^{56} +(-177.506 + 261.802i) q^{57} -717.028 q^{58} +(441.303 + 103.105i) q^{59} -5.38202 q^{60} +(441.142 - 650.636i) q^{61} +(-42.6391 - 786.432i) q^{62} +(-11.6690 - 29.2870i) q^{63} +(457.980 + 211.884i) q^{64} +(1154.18 + 694.449i) q^{65} +(34.4245 + 123.986i) q^{66} +(-441.588 - 97.2008i) q^{67} +(1.62432 - 0.176656i) q^{68} +(337.714 - 203.196i) q^{69} +(-115.810 - 109.701i) q^{70} +(-128.775 + 59.5778i) q^{71} +(201.008 + 21.8610i) q^{72} +(-650.212 - 219.082i) q^{73} +(123.927 - 311.032i) q^{74} +(284.536 - 269.527i) q^{75} +(-3.16491 + 11.3990i) q^{76} +(-24.7092 + 46.6066i) q^{77} +(573.066 + 435.633i) q^{78} +(38.7863 - 715.371i) q^{79} +(983.128 - 331.254i) q^{80} +(79.1063 - 17.4126i) q^{81} +(-287.102 - 541.531i) q^{82} +(-101.741 + 620.592i) q^{83} +(-0.763344 - 0.898678i) q^{84} +(-150.729 + 177.452i) q^{85} +(-113.833 - 694.353i) q^{86} +(601.246 - 457.055i) q^{87} +(-189.863 - 280.026i) q^{88} +(-83.2418 - 122.772i) q^{89} +(326.281 - 248.032i) q^{90} +(47.7428 + 291.218i) q^{91} +(9.54313 - 11.2350i) q^{92} +(537.049 + 632.263i) q^{93} +(-153.297 + 935.068i) q^{94} +(-789.632 - 1489.40i) q^{95} +(14.8761 - 3.27447i) q^{96} +(889.351 - 299.657i) q^{97} +(-50.9979 + 940.601i) q^{98} +(-107.898 - 82.0219i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9}+O(q^{10}) \) 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9	\( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9} + 854 q^{10} + 32 q^{11} + 192 q^{12} - 22 q^{13} - 884 q^{14} - 42 q^{15} - 268 q^{16} - 56 q^{17} - 18 q^{18} - 112 q^{19} - 250 q^{20} + 243 q^{21} + 108 q^{22} + 16 q^{23} - 54 q^{24} - 197 q^{25} - 328 q^{26} + 405 q^{27} + 236 q^{28} - 54 q^{29} - 126 q^{30} + 66 q^{31} + 857 q^{32} - 96 q^{33} + 112 q^{34} + 532 q^{35} - 576 q^{36} + 110 q^{37} + 56 q^{38} + 66 q^{39} - 6044 q^{40} + 304 q^{41} - 306 q^{42} - 324 q^{43} - 568 q^{44} + 126 q^{45} + 5842 q^{46} + 4082 q^{47} + 804 q^{48} + 739 q^{49} + 576 q^{50} + 168 q^{51} - 1372 q^{52} - 1498 q^{53} + 54 q^{54} - 4422 q^{55} - 12036 q^{56} + 336 q^{57} + 6298 q^{58} - 3305 q^{59} + 750 q^{60} - 1718 q^{61} - 4333 q^{62} + 54 q^{63} - 6250 q^{64} - 5884 q^{65} - 324 q^{66} + 382 q^{67} + 734 q^{68} + 3780 q^{69} + 8082 q^{70} + 8638 q^{71} + 162 q^{72} + 8894 q^{73} + 12428 q^{74} + 243 q^{75} - 15468 q^{76} - 9916 q^{77} + 984 q^{78} - 578 q^{79} + 24570 q^{80} - 1215 q^{81} - 1382 q^{82} - 32 q^{83} + 7557 q^{84} + 708 q^{85} + 2296 q^{86} - 5928 q^{87} - 17646 q^{88} - 2284 q^{89} + 378 q^{90} + 11124 q^{91} + 762 q^{92} - 198 q^{93} - 1232 q^{94} + 24184 q^{95} - 396 q^{96} - 658 q^{97} - 4356 q^{98} + 288 q^{99}+O(q^{100}) \) 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9 + 854 * q^10 + 32 * q^11 + 192 * q^12 - 22 * q^13 - 884 * q^14 - 42 * q^15 - 268 * q^16 - 56 * q^17 - 18 * q^18 - 112 * q^19 - 250 * q^20 + 243 * q^21 + 108 * q^22 + 16 * q^23 - 54 * q^24 - 197 * q^25 - 328 * q^26 + 405 * q^27 + 236 * q^28 - 54 * q^29 - 126 * q^30 + 66 * q^31 + 857 * q^32 - 96 * q^33 + 112 * q^34 + 532 * q^35 - 576 * q^36 + 110 * q^37 + 56 * q^38 + 66 * q^39 - 6044 * q^40 + 304 * q^41 - 306 * q^42 - 324 * q^43 - 568 * q^44 + 126 * q^45 + 5842 * q^46 + 4082 * q^47 + 804 * q^48 + 739 * q^49 + 576 * q^50 + 168 * q^51 - 1372 * q^52 - 1498 * q^53 + 54 * q^54 - 4422 * q^55 - 12036 * q^56 + 336 * q^57 + 6298 * q^58 - 3305 * q^59 + 750 * q^60 - 1718 * q^61 - 4333 * q^62 + 54 * q^63 - 6250 * q^64 - 5884 * q^65 - 324 * q^66 + 382 * q^67 + 734 * q^68 + 3780 * q^69 + 8082 * q^70 + 8638 * q^71 + 162 * q^72 + 8894 * q^73 + 12428 * q^74 + 243 * q^75 - 15468 * q^76 - 9916 * q^77 + 984 * q^78 - 578 * q^79 + 24570 * q^80 - 1215 * q^81 - 1382 * q^82 - 32 * q^83 + 7557 * q^84 + 708 * q^85 + 2296 * q^86 - 5928 * q^87 - 17646 * q^88 - 2284 * q^89 + 378 * q^90 + 11124 * q^91 + 762 * q^92 - 198 * q^93 - 1232 * q^94 + 24184 * q^95 - 396 * q^96 - 658 * q^97 - 4356 * q^98 + 288 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more