LMFDB - Embedded newform 162.4.g.b.7.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,4,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$9.55830942093$
Analytic rank:	$0$
Dimension:	$252$
Relative dimension:	$14$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			7.12
Character	$\chi$	$=$	162.7
Dual form			162.4.g.b.139.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19432 - 1.60425i) q^{2} +(3.85407 - 3.48513i) q^{3} +(-1.14721 + 3.83196i) q^{4} +(-1.04141 + 0.684943i) q^{5} +(-10.1940 - 2.02053i) q^{6} +(3.33832 - 3.53842i) q^{7} +(7.51754 - 2.73616i) q^{8} +(2.70774 - 26.8639i) q^{9} +O(q^{10})$	\(q+(-1.19432 - 1.60425i) q^{2} +(3.85407 - 3.48513i) q^{3} +(-1.14721 + 3.83196i) q^{4} +(-1.04141 + 0.684943i) q^{5} +(-10.1940 - 2.02053i) q^{6} +(3.33832 - 3.53842i) q^{7} +(7.51754 - 2.73616i) q^{8} +(2.70774 - 26.8639i) q^{9} +(2.34259 + 0.852632i) q^{10} +(-10.2108 + 5.12805i) q^{11} +(8.93343 + 18.7668i) q^{12} +(-30.1692 - 69.9401i) q^{13} +(-9.66351 - 1.12950i) q^{14} +(-1.62654 + 6.26926i) q^{15} +(-13.3678 - 8.79214i) q^{16} +(74.2653 - 62.3160i) q^{17} +(-46.3302 + 27.7401i) q^{18} +(-65.1692 - 54.6835i) q^{19} +(-1.42996 - 4.77640i) q^{20} +(0.534300 - 25.2718i) q^{21} +(20.4216 + 10.2561i) q^{22} +(44.6134 + 47.2874i) q^{23} +(19.4373 - 36.7450i) q^{24} +(-48.8946 + 113.350i) q^{25} +(-76.1695 + 131.929i) q^{26} +(-83.1883 - 112.972i) q^{27} +(9.72930 + 16.8516i) q^{28} +(-58.3752 + 6.82309i) q^{29} +(12.0000 - 4.87811i) q^{30} +(-22.5946 + 5.35503i) q^{31} +(1.86063 + 31.9459i) q^{32} +(-21.4812 + 55.3498i) q^{33} +(-188.666 - 44.7148i) q^{34} +(-1.05294 + 5.97149i) q^{35} +(99.8349 + 41.1945i) q^{36} +(-47.6641 - 270.317i) q^{37} +(-9.89304 + 169.857i) q^{38} +(-360.025 - 164.411i) q^{39} +(-5.95470 + 7.99854i) q^{40} +(-62.2071 + 83.5586i) q^{41} +(-41.1803 + 29.3254i) q^{42} +(23.5741 - 404.751i) q^{43} +(-7.93652 - 45.0103i) q^{44} +(15.5804 + 29.8309i) q^{45} +(22.5781 - 128.047i) q^{46} +(54.3350 + 12.8776i) q^{47} +(-82.1622 + 12.7030i) q^{48} +(18.5677 + 318.795i) q^{49} +(240.238 - 56.9374i) q^{50} +(69.0445 - 498.994i) q^{51} +(302.618 - 35.3710i) q^{52} +(191.521 + 331.725i) q^{53} +(-81.8820 + 268.379i) q^{54} +(7.12115 - 12.3342i) q^{55} +(15.4143 - 35.7344i) q^{56} +(-441.746 + 16.3692i) q^{57} +(80.6645 + 85.4993i) q^{58} +(564.087 + 283.295i) q^{59} +(-22.1575 - 13.4250i) q^{60} +(-34.1392 - 114.033i) q^{61} +(35.5760 + 29.8518i) q^{62} +(-86.0163 - 99.2615i) q^{63} +(49.0268 - 41.1384i) q^{64} +(79.3234 + 52.1718i) q^{65} +(114.450 - 31.6441i) q^{66} +(399.710 + 46.7193i) q^{67} +(153.594 + 356.071i) q^{68} +(336.746 + 26.7657i) q^{69} +(10.8373 - 5.44269i) q^{70} +(435.025 + 158.336i) q^{71} +(-53.1483 - 209.359i) q^{72} +(911.306 - 331.688i) q^{73} +(-376.728 + 399.309i) q^{74} +(206.598 + 607.265i) q^{75} +(284.308 - 186.992i) q^{76} +(-15.9417 + 53.2491i) q^{77} +(166.229 + 773.926i) q^{78} +(-73.3298 - 98.4990i) q^{79} +19.9434 q^{80} +(-714.336 - 145.481i) q^{81} +208.343 q^{82} +(75.7267 + 101.719i) q^{83} +(96.2276 + 31.0396i) q^{84} +(-34.6574 + 115.764i) q^{85} +(-677.475 + 445.582i) q^{86} +(-201.203 + 229.742i) q^{87} +(-62.7288 + 66.4887i) q^{88} +(507.149 - 184.587i) q^{89} +(29.2481 - 60.6223i) q^{90} +(-348.192 - 126.731i) q^{91} +(-232.384 + 116.708i) q^{92} +(-68.4184 + 99.3839i) q^{93} +(-44.2344 - 102.547i) q^{94} +(105.323 + 12.3105i) q^{95} +(118.506 + 116.637i) q^{96} +(602.018 + 395.953i) q^{97} +(489.250 - 410.529i) q^{98} +(110.111 + 288.187i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 252 q - 36 q^{6}+O(q^{10}) $ 252 * q - 36 * q^6	$ 252 q - 36 q^{6} + 90 q^{13} - 252 q^{18} - 144 q^{20} + 189 q^{21} + 1512 q^{23} + 846 q^{25} + 702 q^{26} + 702 q^{27} - 504 q^{28} + 540 q^{29} - 342 q^{30} - 2214 q^{31} - 1548 q^{33} - 1242 q^{35} - 576 q^{36} - 882 q^{38} - 927 q^{41} + 774 q^{42} - 900 q^{43} + 2817 q^{45} - 2088 q^{46} + 297 q^{47} - 144 q^{48} + 2151 q^{51} - 720 q^{52} + 1431 q^{53} - 2970 q^{55} + 729 q^{57} + 126 q^{58} + 2628 q^{59} + 261 q^{63} + 3627 q^{65} + 4680 q^{66} + 2538 q^{67} - 936 q^{68} + 4716 q^{69} - 3150 q^{70} + 720 q^{71} - 1440 q^{72} + 3204 q^{73} - 2088 q^{74} + 918 q^{75} + 1764 q^{76} - 9792 q^{77} - 3132 q^{78} + 3897 q^{79} - 1440 q^{80} - 17352 q^{81} + 5904 q^{82} - 1035 q^{83} - 1224 q^{84} + 2421 q^{85} - 3600 q^{86} - 10827 q^{87} + 1224 q^{88} - 4086 q^{89} + 4473 q^{91} + 1872 q^{92} + 8955 q^{93} - 6174 q^{94} + 8037 q^{95} + 1152 q^{96} + 6192 q^{97} + 8136 q^{98} + 2187 q^{99}+O(q^{100}) $ 252 * q - 36 * q^6 + 90 * q^13 - 252 * q^18 - 144 * q^20 + 189 * q^21 + 1512 * q^23 + 846 * q^25 + 702 * q^26 + 702 * q^27 - 504 * q^28 + 540 * q^29 - 342 * q^30 - 2214 * q^31 - 1548 * q^33 - 1242 * q^35 - 576 * q^36 - 882 * q^38 - 927 * q^41 + 774 * q^42 - 900 * q^43 + 2817 * q^45 - 2088 * q^46 + 297 * q^47 - 144 * q^48 + 2151 * q^51 - 720 * q^52 + 1431 * q^53 - 2970 * q^55 + 729 * q^57 + 126 * q^58 + 2628 * q^59 + 261 * q^63 + 3627 * q^65 + 4680 * q^66 + 2538 * q^67 - 936 * q^68 + 4716 * q^69 - 3150 * q^70 + 720 * q^71 - 1440 * q^72 + 3204 * q^73 - 2088 * q^74 + 918 * q^75 + 1764 * q^76 - 9792 * q^77 - 3132 * q^78 + 3897 * q^79 - 1440 * q^80 - 17352 * q^81 + 5904 * q^82 - 1035 * q^83 - 1224 * q^84 + 2421 * q^85 - 3600 * q^86 - 10827 * q^87 + 1224 * q^88 - 4086 * q^89 + 4473 * q^91 + 1872 * q^92 + 8955 * q^93 - 6174 * q^94 + 8037 * q^95 + 1152 * q^96 + 6192 * q^97 + 8136 * q^98 + 2187 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{8}{27}\right)$

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 $

$2$	−1.19432	−	1.60425i	−0.422255	−	0.567187i
$2$	−1.19432	−	1.60425i	−0.422255	−	0.567187i
$3$	3.85407	−	3.48513i	0.741717	−	0.670714i
$3$	3.85407	−	3.48513i	0.741717	−	0.670714i
$4$	−1.14721	+	3.83196i	−0.143402	+	0.478995i
$5$	−1.04141	+	0.684943i	−0.0931462	+	0.0612632i	−0.595228	−	0.803557i	$-0.702938\pi$
$5$	−1.04141	+	0.684943i	−0.0931462	+	0.0612632i	0.502081	+	0.864820i	$0.332568\pi$
$6$	−10.1940	−	2.02053i	−0.693613	−	0.137480i
$7$	3.33832	−	3.53842i	0.180253	−	0.191057i	−0.630947	−	0.775826i	$-0.717333\pi$
$7$	3.33832	−	3.53842i	0.180253	−	0.191057i	0.811200	+	0.584769i	$0.198815\pi$
$8$	7.51754	−	2.73616i	0.332232	−	0.120922i
$9$	2.70774	−	26.8639i	0.100287	−	0.994959i
$10$	2.34259	+	0.852632i	0.0740791	+	0.0269626i
$11$	−10.2108	+	5.12805i	−0.279879	+	0.140560i	−0.583202	−	0.812327i	$-0.698200\pi$
$11$	−10.2108	+	5.12805i	−0.279879	+	0.140560i	0.303323	+	0.952888i	$0.401904\pi$
$12$	8.93343	+	18.7668i	0.214905	+	0.451460i
$13$	−30.1692	−	69.9401i	−0.643649	−	1.49215i	−0.857078	−	0.515187i	$-0.827723\pi$
$13$	−30.1692	−	69.9401i	−0.643649	−	1.49215i	0.213429	−	0.976959i	$-0.431537\pi$
$14$	−9.66351	−	1.12950i	−0.184477	−	0.0215623i
$15$	−1.62654	+	6.26926i	−0.0279980	+	0.107914i
$16$	−13.3678	−	8.79214i	−0.208872	−	0.137377i
$17$	74.2653	−	62.3160i	1.05953	−	0.889050i	0.0654651	−	0.997855i	$-0.479147\pi$
$17$	74.2653	−	62.3160i	1.05953	−	0.889050i	0.994063	+	0.108805i	$0.0347025\pi$
$18$	−46.3302	+	27.7401i	−0.606674	+	0.363245i
$19$	−65.1692	−	54.6835i	−0.786887	−	0.660276i	0.158086	−	0.987425i	$-0.449468\pi$
$19$	−65.1692	−	54.6835i	−0.786887	−	0.660276i	−0.944973	+	0.327149i	$0.893912\pi$
$20$	−1.42996	−	4.77640i	−0.0159874	−	0.0534018i
$21$	0.534300	−	25.2718i	0.00555209	−	0.262608i
$22$	20.4216	+	10.2561i	0.197904	+	0.0993913i
$23$	44.6134	+	47.2874i	0.404458	+	0.428700i	0.897302	−	0.441417i	$-0.145524\pi$
$23$	44.6134	+	47.2874i	0.404458	+	0.428700i	−0.492844	+	0.870118i	$0.664043\pi$
$24$	19.4373	−	36.7450i	0.165317	−	0.312522i
$25$	−48.8946	+	113.350i	−0.391157	+	0.906803i
$26$	−76.1695	+	131.929i	−0.574541	+	0.995135i
$27$	−83.1883	−	112.972i	−0.592948	−	0.805241i
$28$	9.72930	+	16.8516i	0.0656666	+	0.113738i
$29$	−58.3752	+	6.82309i	−0.373793	+	0.0436902i	−0.300916	−	0.953651i	$-0.597292\pi$
$29$	−58.3752	+	6.82309i	−0.373793	+	0.0436902i	−0.0728776	+	0.997341i	$0.523218\pi$
$30$	12.0000	−	4.87811i	0.0730299	−	0.0296873i
$31$	−22.5946	+	5.35503i	−0.130907	+	0.0310255i	−0.295547	−	0.955328i	$-0.595502\pi$
$31$	−22.5946	+	5.35503i	−0.130907	+	0.0310255i	0.164640	+	0.986354i	$0.447354\pi$
$32$	1.86063	+	31.9459i	0.0102787	+	0.176478i
$33$	−21.4812	+	55.3498i	−0.113315	+	0.291975i
$34$	−188.666	−	44.7148i	−0.951648	−	0.225545i
$35$	−1.05294	+	5.97149i	−0.00508510	+	0.0288390i
$36$	99.8349	+	41.1945i	0.462199	+	0.190716i
$37$	−47.6641	−	270.317i	−0.211782	−	1.20107i	−0.886404	−	0.462912i	$-0.846805\pi$
$37$	−47.6641	−	270.317i	−0.211782	−	1.20107i	0.674622	−	0.738163i	$-0.264306\pi$
$38$	−9.89304	+	169.857i	−0.0422332	+	0.725117i
$39$	−360.025	−	164.411i	−1.47821	−	0.675045i
$40$	−5.95470	+	7.99854i	−0.0235380	+	0.0316170i
$41$	−62.2071	+	83.5586i	−0.236954	+	0.318284i	−0.904655	−	0.426145i	$-0.859871\pi$
$41$	−62.2071	+	83.5586i	−0.236954	+	0.318284i	0.667701	+	0.744430i	$0.267279\pi$
$42$	−41.1803	+	29.3254i	−0.151292	+	0.107738i
$43$	23.5741	−	404.751i	0.0836049	−	1.43544i	−0.652097	−	0.758135i	$-0.726111\pi$
$43$	23.5741	−	404.751i	0.0836049	−	1.43544i	0.735702	−	0.677305i	$-0.236852\pi$
$44$	−7.93652	−	45.0103i	−0.0271926	−	0.154217i
$45$	15.5804	+	29.8309i	0.0516130	+	0.0988205i
$46$	22.5781	−	128.047i	0.0723688	−	0.410424i
$47$	54.3350	+	12.8776i	0.168629	+	0.0399659i	0.314063	−	0.949402i	$-0.398310\pi$
$47$	54.3350	+	12.8776i	0.168629	+	0.0399659i	−0.145434	+	0.989368i	$0.546458\pi$
$48$	−82.1622	+	12.7030i	−0.247065	+	0.0381983i
$49$	18.5677	+	318.795i	0.0541332	+	0.929431i
$50$	240.238	−	56.9374i	0.679495	−	0.161043i
$51$	69.0445	−	498.994i	0.189572	−	1.37006i
$52$	302.618	−	35.3710i	0.807030	−	0.0943283i
$53$	191.521	+	331.725i	0.496368	+	0.859734i	0.999991	−	0.00418895i	$-0.00133339\pi$
$53$	191.521	+	331.725i	0.496368	+	0.859734i	−0.503623	+	0.863923i	$0.668000\pi$
$54$	−81.8820	+	268.379i	−0.206347	+	0.676329i
$55$	7.12115	−	12.3342i	0.0174585	−	0.0302389i
$56$	15.4143	−	35.7344i	0.0367826	−	0.0852716i
$57$	−441.746	+	16.3692i	−1.02650	+	0.0380377i
$58$	80.6645	+	85.4993i	0.182617	+	0.193562i
$59$	564.087	+	283.295i	1.24471	+	0.625116i	0.944423	−	0.328733i	$-0.106622\pi$
$59$	564.087	+	283.295i	1.24471	+	0.625116i	0.300286	+	0.953849i	$0.402918\pi$
$60$	−22.1575	−	13.4250i	−0.0476754	−	0.0288860i
$61$	−34.1392	−	114.033i	−0.0716570	−	0.239351i	0.914656	−	0.404232i	$-0.132461\pi$
$61$	−34.1392	−	114.033i	−0.0716570	−	0.239351i	−0.986313	+	0.164881i	$0.947276\pi$
$62$	35.5760	+	29.8518i	0.0728734	+	0.0611480i
$63$	−86.0163	−	99.2615i	−0.172016	−	0.198504i
$64$	49.0268	−	41.1384i	0.0957556	−	0.0803485i
$65$	79.3234	+	52.1718i	0.151367	+	0.0995556i
$66$	114.450	−	31.6441i	0.213452	−	0.0590169i
$67$	399.710	+	46.7193i	0.728840	+	0.0851892i	0.472417	−	0.881375i	$-0.343382\pi$
$67$	399.710	+	46.7193i	0.728840	+	0.0851892i	0.256424	+	0.966565i	$0.417456\pi$
$68$	153.594	+	356.071i	0.273912	+	0.635000i
$69$	336.746	+	26.7657i	0.587528	+	0.0466987i
$70$	10.8373	−	5.44269i	0.0185043	−	0.00929322i
$71$	435.025	+	158.336i	0.727155	+	0.264663i	0.678960	−	0.734175i	$-0.262431\pi$
$71$	435.025	+	158.336i	0.727155	+	0.264663i	0.0481949	+	0.998838i	$0.484653\pi$
$72$	−53.1483	−	209.359i	−0.0869943	−	0.342684i
$73$	911.306	−	331.688i	1.46110	−	0.531797i	0.515432	−	0.856930i	$-0.327631\pi$
$73$	911.306	−	331.688i	1.46110	−	0.531797i	0.945668	+	0.325133i	$0.105409\pi$
$74$	−376.728	+	399.309i	−0.591808	+	0.627280i
$75$	206.598	+	607.265i	0.318078	+	0.934945i
$76$	284.308	−	186.992i	0.429110	−	0.282230i
$77$	−15.9417	+	53.2491i	−0.0235939	+	0.0788091i
$78$	166.229	+	773.926i	0.241304	+	1.12346i
$79$	−73.3298	−	98.4990i	−0.104433	−	0.140279i	0.746834	−	0.665010i	$-0.231573\pi$
$79$	−73.3298	−	98.4990i	−0.104433	−	0.140279i	−0.851267	+	0.524732i	$0.824166\pi$
$80$	19.9434			0.0278718
$81$	−714.336	−	145.481i	−0.979885	−	0.199562i
$82$	208.343			0.280582
$83$	75.7267	+	101.719i	0.100146	+	0.134519i	0.849371	−	0.527796i	$-0.176981\pi$
$83$	75.7267	+	101.719i	0.100146	+	0.134519i	−0.749225	+	0.662315i	$0.769574\pi$
$84$	96.2276	+	31.0396i	0.124992	+	0.0403178i
$85$	−34.6574	+	115.764i	−0.0442250	+	0.147722i
$86$	−677.475	+	445.582i	−0.849465	+	0.558702i
$87$	−201.203	+	229.742i	−0.247945	+	0.283114i
$88$	−62.7288	+	66.4887i	−0.0759877	+	0.0805422i
$89$	507.149	−	184.587i	0.604019	−	0.219845i	−0.0218651	−	0.999761i	$-0.506960\pi$
$89$	507.149	−	184.587i	0.604019	−	0.219845i	0.625884	+	0.779916i	$0.284738\pi$
$90$	29.2481	−	60.6223i	0.0342558	−	0.0710016i
$91$	−348.192	−	126.731i	−0.401104	−	0.145990i
$92$	−232.384	+	116.708i	−0.263345	+	0.132257i
$93$	−68.4184	+	99.3839i	−0.0762866	+	0.110813i
$94$	−44.2344	−	102.547i	−0.0485365	−	0.112520i
$95$	105.323	+	12.3105i	0.113746	+	0.0132950i
$96$	118.506	+	116.637i	0.125990	+	0.124002i
$97$	602.018	+	395.953i	0.630162	+	0.414464i	0.824016	−	0.566567i	$-0.191729\pi$
$97$	602.018	+	395.953i	0.630162	+	0.414464i	−0.193854	+	0.981030i	$0.562099\pi$
$98$	489.250	−	410.529i	0.504303	−	0.423161i
$99$	110.111	+	288.187i	0.111784	+	0.292564i
$100$	−378.261	−	317.399i	−0.378261	−	0.317399i
$101$	429.485	+	1434.58i	0.423122	+	1.41333i	0.858377	+	0.513019i	$0.171473\pi$
$101$	429.485	+	1434.58i	0.423122	+	1.41333i	−0.435255	+	0.900307i	$0.643342\pi$
$102$	−882.971	+	485.193i	−0.857129	+	0.470993i
$103$	776.469	+	389.957i	0.742794	+	0.373045i	0.779600	−	0.626277i	$-0.215422\pi$
$103$	776.469	+	389.957i	0.742794	+	0.373045i	−0.0368067	+	0.999322i	$0.511719\pi$
$104$	−418.166	−	443.230i	−0.394274	−	0.417906i
$105$	16.7533	+	26.6842i	0.0155710	+	0.0248010i
$106$	303.431	−	703.432i	0.278036	−	0.644560i
$107$	694.795	−	1203.42i	0.627742	−	1.08728i	−0.360262	−	0.932851i	$-0.617313\pi$
$107$	694.795	−	1203.42i	0.627742	−	1.08728i	0.988004	−	0.154429i	$-0.0493539\pi$
$108$	528.339	−	189.171i	0.470736	−	0.168546i
$109$	−911.264	−	1578.36i	−0.800764	−	1.38696i	−0.919114	−	0.393992i	$-0.871094\pi$
$109$	−911.264	−	1578.36i	−0.800764	−	1.38696i	0.118350	−	0.992972i	$-0.462240\pi$
$110$	−28.2920	+	3.30686i	−0.0245231	+	0.00286633i
$111$	−1125.79	−	875.704i	−0.962659	−	0.748812i
$112$	−75.7364	+	17.9498i	−0.0638965	+	0.0151438i
$113$	−105.568	−	1812.54i	−0.0878852	−	1.50893i	−0.697702	−	0.716388i	$-0.745794\pi$
$113$	−105.568	−	1812.54i	−0.0878852	−	1.50893i	0.609817	−	0.792542i	$-0.291243\pi$
$114$	553.845	+	689.119i	0.455020	+	0.566157i
$115$	−78.8498	−	18.6878i	−0.0639372	−	0.0151534i
$116$	40.8230	−	231.519i	0.0326752	−	0.185310i
$117$	−1960.55	+	621.082i	−1.54917	+	0.490761i
$118$	−219.223	−	1243.28i	−0.171027	−	0.969941i
$119$	27.4217	−	470.813i	0.0211239	−	0.362683i
$120$	4.92614	+	51.5799i	0.00374744	+	0.0392381i
$121$	−716.855	+	962.903i	−0.538584	+	0.723443i
$122$	−142.164	+	190.959i	−0.105499	+	0.141710i
$123$	51.4620	+	538.840i	0.0377250	+	0.395005i
$124$	5.40062	−	92.7251i	0.00391121	−	0.0671529i
$125$	−53.7753	−	304.975i	−0.0384785	−	0.218222i
$126$	−56.5091	+	256.541i	−0.0399542	+	0.181385i
$127$	−247.383	+	1402.98i	−0.172848	+	0.980269i	0.767751	+	0.640749i	$0.221376\pi$
$127$	−247.383	+	1402.98i	−0.172848	+	0.980269i	−0.940599	+	0.339521i	$0.889735\pi$
$128$	−124.550	−	29.5188i	−0.0860058	−	0.0203838i
$129$	−1319.75	−	1642.10i	−0.900758	−	1.12076i
$130$	−11.0408	−	189.564i	−0.00744882	−	0.127891i
$131$	−1713.80	+	406.178i	−1.14302	+	0.270900i	−0.758156	−	0.652073i	$-0.773899\pi$
$131$	−1713.80	+	406.178i	−1.14302	+	0.270900i	−0.384863	+	0.922974i	$0.625751\pi$
$132$	−187.455	−	145.813i	−0.123605	−	0.0961469i
$133$	−411.049	+	48.0447i	−0.267989	+	0.0313234i
$134$	−402.431	−	697.030i	−0.259438	−	0.449360i
$135$	164.012	+	60.6706i	0.104562	+	0.0386792i
$136$	387.786	−	671.665i	0.244503	−	0.423491i
$137$	−533.601	+	1237.03i	−0.332764	+	0.771433i	0.666891	+	0.745155i	$0.267625\pi$
$137$	−533.601	+	1237.03i	−0.332764	+	0.771433i	−0.999655	+	0.0262778i	$0.991635\pi$
$138$	−359.243	−	572.190i	−0.221600	−	0.352957i
$139$	933.875	+	989.850i	0.569858	+	0.604014i	0.946642	−	0.322287i	$-0.104452\pi$
$139$	933.875	+	989.850i	0.569858	+	0.604014i	−0.376784	+	0.926301i	$0.622970\pi$
$140$	−21.6746	−	10.8854i	−0.0130845	−	0.00657130i
$141$	254.291	−	139.733i	0.151881	−	0.0834586i
$142$	−265.548	−	886.991i	−0.156932	−	0.524188i
$143$	666.708	+	559.434i	0.389880	+	0.327148i
$144$	−272.388	+	335.304i	−0.157632	+	0.194042i
$145$	56.1189	−	47.0893i	0.0321408	−	0.0269694i
$146$	−1620.50	−	1065.82i	−0.918585	−	0.604163i
$147$	1182.60	+	1163.95i	0.663534	+	0.653067i
$148$	1090.52	+	127.464i	0.605678	+	0.0707937i
$149$	202.368	+	469.142i	0.111266	+	0.257944i	0.964746	−	0.263181i	$-0.0847717\pi$
$149$	202.368	+	469.142i	0.111266	+	0.257944i	−0.853480	+	0.521125i	$0.825512\pi$
$150$	727.459	−	1056.70i	0.395979	−	0.575195i
$151$	418.259	−	210.057i	0.225413	−	0.113207i	−0.332509	−	0.943100i	$-0.607895\pi$
$151$	418.259	−	210.057i	0.225413	−	0.113207i	0.557922	+	0.829893i	$0.311599\pi$
$152$	−639.535	−	232.772i	−0.341271	−	0.124212i
$153$	−1472.96	−	2163.79i	−0.778311	−	1.14335i
$154$	104.464	−	38.0219i	0.0546621	−	0.0198954i
$155$	19.8623	−	21.0528i	0.0102928	−	0.0109097i
$156$	1043.04	−	1190.99i	0.535320	−	0.611251i
$157$	−2418.25	+	1590.51i	−1.22928	+	0.808511i	−0.986847	−	0.161657i	$-0.948316\pi$
$157$	−2418.25	+	1590.51i	−1.22928	+	0.808511i	−0.242434	+	0.970168i	$0.577946\pi$
$158$	−70.4376	+	235.278i	−0.0354666	+	0.118467i
$159$	1894.24	+	611.015i	0.944800	+	0.304759i
$160$	−23.8188	−	31.9942i	−0.0117690	−	0.0158085i
$161$	316.257			0.154811
$162$	619.757	+	1319.72i	0.300572	+	0.640044i
$163$	2260.23			1.08610			0.543051	−	0.839700i	$-0.317269\pi$
$163$	2260.23			1.08610			0.543051	+	0.839700i	$0.317269\pi$
$164$	−248.828	−	334.234i	−0.118477	−	0.159142i
$165$	−15.5408	−	72.3550i	−0.00733244	−	0.0341384i
$166$	72.7400	−	242.969i	0.0340104	−	0.113603i
$167$	−438.153	+	288.178i	−0.203026	+	0.133532i	−0.646951	−	0.762532i	$-0.723956\pi$
$167$	−438.153	+	288.178i	−0.203026	+	0.133532i	0.443925	+	0.896064i	$0.353586\pi$
$168$	−65.1311	−	191.444i	−0.0299106	−	0.0879179i
$169$	−2473.76	+	2622.03i	−1.12597	+	1.19346i
$170$	227.105	−	82.6596i	0.102460	−	0.0372924i
$171$	−1645.47	+	1602.63i	−0.735862	+	0.716703i
$172$	1523.94	+	554.670i	0.675579	+	0.245891i
$173$	−434.601	+	218.265i	−0.190995	+	0.0959211i	−0.541727	−	0.840555i	$-0.682229\pi$
$173$	−434.601	+	218.265i	−0.190995	+	0.0959211i	0.350732	+	0.936476i	$0.385933\pi$
$174$	608.863	+	48.3945i	0.265275	+	0.0210849i
$175$	237.855	+	551.410i	0.102744	+	0.238187i
$176$	181.582	+	21.2239i	0.0777687	+	0.00908985i
$177$	3161.35	−	874.076i	1.34249	−	0.371184i
$178$	−901.820	−	593.137i	−0.379743	−	0.249761i
$179$	2234.60	−	1875.05i	0.933082	−	0.782949i	−0.0432861	−	0.999063i	$-0.513783\pi$
$179$	2234.60	−	1875.05i	0.933082	−	0.782949i	0.976368	+	0.216114i	$0.0693382\pi$
$180$	−132.185	+	25.4810i	−0.0547359	+	0.0105513i
$181$	−2419.88	−	2030.52i	−0.993747	−	0.833853i	−0.00764113	−	0.999971i	$-0.502432\pi$
$181$	−2419.88	−	2030.52i	−0.993747	−	0.833853i	−0.986106	+	0.166118i	$0.946877\pi$
$182$	212.543	+	709.943i	0.0865645	+	0.289146i
$183$	−528.994	−	320.511i	−0.213685	−	0.129469i
$184$	464.769	+	233.416i	0.186213	+	0.0935197i
$185$	234.789	+	248.862i	0.0933084	+	0.0989011i
$186$	241.150	−	8.93594i	0.0950642	−	0.00352266i
$187$	−438.748	+	1017.13i	−0.171574	+	0.397754i
$188$	−111.680	+	193.436i	−0.0433252	+	0.0750414i
$189$	−677.452	−	82.7829i	−0.260727	−	0.0318602i
$190$	−106.040	−	183.666i	−0.0404891	−	0.0701292i
$191$	240.458	−	28.1056i	0.0910941	−	0.0106474i	−0.0704238	−	0.997517i	$-0.522435\pi$
$191$	240.458	−	28.1056i	0.0910941	−	0.0106474i	0.161518	+	0.986870i	$0.448361\pi$
$192$	45.5803	−	329.415i	0.0171327	−	0.123820i
$193$	−200.410	+	47.4980i	−0.0747451	+	0.0177149i	−0.267818	−	0.963469i	$-0.586303\pi$
$193$	−200.410	+	47.4980i	−0.0747451	+	0.0177149i	0.193073	+	0.981184i	$0.438155\pi$
$194$	−83.7935	−	1438.68i	−0.0310104	−	0.532429i
$195$	487.544	−	75.3784i	0.179045	−	0.0276818i
$196$	−1242.91	−	294.575i	−0.452955	−	0.107352i
$197$	265.794	−	1507.40i	0.0961273	−	0.545165i	−0.898269	−	0.439446i	$-0.855175\pi$
$197$	265.794	−	1507.40i	0.0961273	−	0.545165i	0.994396	−	0.105718i	$-0.0337142\pi$
$198$	330.815	−	520.832i	0.118737	−	0.186939i
$199$	−281.047	−	1593.89i	−0.100115	−	0.567780i	−0.993059	−	0.117613i	$-0.962476\pi$
$199$	−281.047	−	1593.89i	−0.100115	−	0.567780i	0.892945	−	0.450167i	$-0.148635\pi$
$200$	−57.4221	+	985.900i	−0.0203018	+	0.348568i
$201$	1703.33	−	1212.98i	0.597730	−	0.425657i
$202$	1788.48	−	2402.34i	0.622954	−	0.836773i
$203$	−170.733	+	229.334i	−0.0590299	+	0.0792910i
$204$	1832.92	+	837.029i	0.629068	+	0.287273i
$205$	7.54990	−	129.627i	0.00257223	−	0.0441635i
$206$	−301.762	−	1711.38i	−0.102062	−	0.578823i
$207$	1391.12	−	1070.45i	0.467101	−	0.359426i
$208$	−211.627	+	1200.20i	−0.0705467	+	0.400090i
$209$	945.849	+	224.170i	0.313042	+	0.0741923i
$210$	22.7992	−	58.7459i	0.00749188	−	0.0193040i
$211$	245.730	+	4219.03i	0.0801743	+	1.37654i	0.763208	+	0.646152i	$0.223623\pi$
$211$	245.730	+	4219.03i	0.0801743	+	1.37654i	−0.683034	+	0.730386i	$0.739340\pi$
$212$	−1490.87	+	353.343i	−0.482988	+	0.114470i
$213$	2228.44	−	905.880i	0.716856	−	0.291408i
$214$	−2760.39	+	322.643i	−0.881758	+	0.103063i
$215$	252.681	+	437.657i	0.0801522	+	0.138828i
$216$	−934.481	−	621.656i	−0.294368	−	0.195826i
$217$	−56.4799	+	97.8261i	−0.0176687	+	0.0306031i
$218$	−1443.73	+	3346.95i	−0.448541	+	1.03984i
$219$	2356.26	−	4454.37i	0.727039	−	1.37442i
$220$	39.0946	+	41.4379i	0.0119807	+	0.0126988i
$221$	−6598.91	−	3314.10i	−2.00856	−	1.00873i
$222$	−60.2955	+	2851.91i	−0.0182287	+	0.862197i
$223$	1226.56	+	4097.00i	0.368325	+	1.23029i	0.918560	+	0.395282i	$0.129353\pi$
$223$	1226.56	+	4097.00i	0.368325	+	1.23029i	−0.550235	+	0.835010i	$0.685462\pi$
$224$	119.249	+	100.062i	0.0355700	+	0.0298467i
$225$	2912.64	+	1620.42i	0.863004	+	0.480125i
$226$	−2781.67	+	2334.10i	−0.818735	+	0.687000i
$227$	2999.15	+	1972.57i	0.876920	+	0.576759i	0.906218	−	0.422811i	$-0.138957\pi$
$227$	2999.15	+	1972.57i	0.876920	+	0.576759i	−0.0292976	+	0.999571i	$0.509327\pi$
$228$	444.051	−	1711.53i	0.128982	−	0.497144i
$229$	1655.35	+	193.482i	0.477679	+	0.0558327i	0.351526	−	0.936178i	$-0.385663\pi$
$229$	1655.35	+	193.482i	0.477679	+	0.0558327i	0.126153	+	0.992011i	$0.459737\pi$
$230$	64.1919	+	148.814i	0.0184030	+	0.0426630i
$231$	124.139	+	260.785i	0.0353583	+	0.0742788i
$232$	−420.169	+	211.017i	−0.118903	+	0.0597152i
$233$	312.384	+	113.698i	0.0878324	+	0.0319684i	0.385563	−	0.922682i	$-0.374007\pi$
$233$	312.384	+	113.698i	0.0878324	+	0.0319684i	−0.297730	+	0.954650i	$0.596230\pi$
$234$	3337.89	+	2403.44i	0.932499	+	0.671444i
$235$	−65.4053	+	23.8056i	−0.0181556	+	0.00660811i
$236$	−1732.70	+	1836.56i	−0.477921	+	0.506566i
$237$	−625.900	−	124.058i	−0.171547	−	0.0340019i
$238$	−788.050	+	518.308i	−0.214629	+	0.141164i
$239$	1611.45	−	5382.63i	0.436135	−	1.45679i	−0.404174	−	0.914682i	$-0.632441\pi$
$239$	1611.45	−	5382.63i	0.436135	−	1.45679i	0.840308	−	0.542109i	$-0.182374\pi$
$240$	76.8634	−	69.5054i	0.0206730	−	0.0186940i
$241$	355.128	+	477.019i	0.0949203	+	0.127500i	0.847046	−	0.531520i	$-0.178379\pi$
$241$	355.128	+	477.019i	0.0949203	+	0.127500i	−0.752126	+	0.659020i	$0.770971\pi$
$242$	2400.89			0.637747
$243$	−3260.12	+	1928.86i	−0.860646	+	0.509203i
$244$	476.134			0.124924
$245$	−237.693	−	319.277i	−0.0619822	−	0.0832566i
$246$	802.971	−	726.104i	0.208112	−	0.188190i
$247$	−1858.46	+	6207.70i	−0.478750	+	1.59914i
$248$	−155.204	+	102.079i	−0.0397398	+	0.0261372i
$249$	646.359	+	128.114i	0.164503	+	0.0326059i
$250$	−425.030	+	450.505i	−0.107525	+	0.113970i
$251$	3813.91	−	1388.15i	0.959091	−	0.349080i	0.185414	−	0.982661i	$-0.440638\pi$
$251$	3813.91	−	1388.15i	0.959091	−	0.349080i	0.773677	+	0.633580i	$0.218415\pi$
$252$	479.045	−	215.737i	0.119750	−	0.0539291i
$253$	−698.030	−	254.062i	−0.173458	−	0.0631334i
$254$	2546.18	−	1278.74i	0.628982	−	0.315886i
$255$	269.880	+	566.947i	0.0662765	+	0.139230i
$256$	101.396	+	235.063i	0.0247550	+	0.0573885i
$257$	−1575.91	−	184.197i	−0.382500	−	0.0447079i	−0.0773297	−	0.997006i	$-0.524639\pi$
$257$	−1575.91	−	184.197i	−0.382500	−	0.0447079i	−0.305171	+	0.952298i	$0.598713\pi$
$258$	−1058.13	+	4078.40i	−0.255333	+	0.984147i
$259$	−1115.61	−	733.749i	−0.267648	−	0.176035i
$260$	−290.921	+	244.112i	−0.0693929	+	0.0582276i
$261$	25.2295	+	1586.66i	0.00598339	+	0.376290i
$262$	2698.43	+	2264.25i	0.636296	+	0.533916i
$263$	1846.70	+	6168.39i	0.432974	+	1.44623i	0.844855	+	0.534996i	$0.179687\pi$
$263$	1846.70	+	6168.39i	0.432974	+	1.44623i	−0.411881	+	0.911238i	$0.635128\pi$
$264$	−10.0398	+	474.870i	−0.00234055	+	0.110705i
$265$	−426.664	−	214.279i	−0.0989048	−	0.0496719i
$266$	567.999	+	602.043i	0.130926	+	0.138773i
$267$	1311.28	−	2478.89i	0.300558	−	0.568187i
$268$	−637.579	+	1478.07i	−0.145322	+	0.336894i
$269$	−3246.92	+	5623.83i	−0.735942	+	1.27469i	0.218367	+	0.975867i	$0.429927\pi$
$269$	−3246.92	+	5623.83i	−0.735942	+	1.27469i	−0.954309	+	0.298822i	$0.903406\pi$
$270$	−98.5521	−	335.576i	−0.0222137	−	0.0756389i
$271$	−406.834	−	704.657i	−0.0911933	−	0.157951i	0.816820	−	0.576892i	$-0.195735\pi$
$271$	−406.834	−	704.657i	−0.0911933	−	0.157951i	−0.908014	+	0.418941i	$0.862401\pi$
$272$	−1540.65	+	180.077i	−0.343441	+	0.0401425i
$273$	−1783.63	+	725.062i	−0.395422	+	0.160743i
$274$	2621.79	−	621.375i	0.578058	−	0.137002i
$275$	−82.0143	−	1408.13i	−0.0179842	−	0.308776i
$276$	−488.884	+	1259.69i	−0.106621	+	0.274726i
$277$	−7861.65	−	1863.25i	−1.70527	−	0.404157i	−0.741516	−	0.670935i	$-0.765893\pi$
$277$	−7861.65	−	1863.25i	−1.70527	−	0.404157i	−0.963758	+	0.266778i	$0.914041\pi$
$278$	472.620	−	2680.36i	0.101964	−	0.578264i
$279$	82.6764	+	621.480i	0.0177409	+	0.133359i
$280$	8.42348	+	47.7719i	0.00179785	+	0.0101961i
$281$	417.606	−	7170.01i	0.0886557	−	1.52216i	−0.601719	−	0.798708i	$-0.705517\pi$
$281$	417.606	−	7170.01i	0.0886557	−	1.52216i	0.690374	−	0.723452i	$-0.257446\pi$
$282$	−527.871	−	241.060i	−0.111469	−	0.0509040i
$283$	3409.10	−	4579.22i	0.716079	−	0.961860i	−0.283917	−	0.958849i	$-0.591634\pi$
$283$	3409.10	−	4579.22i	0.716079	−	0.961860i	0.999995	−	0.00301158i	$-0.000958616\pi$
$284$	−1105.80	+	1485.35i	−0.231047	+	0.310350i
$285$	448.825	−	319.618i	0.0932845	−	0.0664299i
$286$	101.210	−	1737.70i	0.0209254	−	0.359275i
$287$	87.9978	+	499.060i	0.0180988	+	0.102643i
$288$	863.228	+	36.5173i	0.176619	+	0.00747154i
$289$	778.919	−	4417.47i	0.158542	−	0.899139i
$290$	−142.567	−	33.7889i	−0.0288683	−	0.00684191i
$291$	3700.17	−	572.078i	0.745388	−	0.115243i
$292$	225.553	+	3872.60i	0.0452038	+	0.776120i
$293$	551.339	−	130.670i	0.109930	−	0.0260539i	−0.175283	−	0.984518i	$-0.556084\pi$
$293$	551.339	−	130.670i	0.109930	−	0.0260539i	0.285213	+	0.958464i	$0.407936\pi$
$294$	454.856	−	3287.31i	0.0902304	−	0.652108i
$295$	−781.484	+	91.3424i	−0.154236	+	0.0180277i
$296$	−1097.95	−	1901.70i	−0.215597	−	0.373426i
$297$	1428.74	+	726.941i	0.279139	+	0.142025i
$298$	510.928	−	884.953i	0.0993196	−	0.172027i
$299$	1961.34	−	4546.89i	0.379354	−	0.879442i
$300$	−2564.02	+	95.0114i	−0.493447	+	0.0182850i
$301$	−1353.48	−	1434.61i	−0.259180	−	0.274715i
$302$	−836.517	−	420.115i	−0.159391	−	0.0800493i
$303$	6654.96	+	4032.16i	1.26177	+	0.764494i
$304$	390.385	+	1303.98i	0.0736516	+	0.246014i
$305$	113.659	+	95.3711i	0.0213380	+	0.0179047i
$306$	−1712.07	+	4947.24i	−0.319845	+	0.924231i
$307$	3551.93	−	2980.43i	0.660324	−	0.554078i	−0.249860	−	0.968282i	$-0.580385\pi$
$307$	3551.93	−	2980.43i	0.660324	−	0.554078i	0.910184	+	0.414204i	$0.135940\pi$
$308$	−185.760	−	122.176i	−0.0343657	−	0.0226027i
$309$	4351.62	−	1203.17i	0.801149	−	0.221508i
$310$	−57.4958	−	6.72029i	−0.0105340	−	0.00123125i
$311$	−2114.61	−	4902.21i	−0.385557	−	0.893822i	−0.994895	−	0.100912i	$-0.967824\pi$
$311$	−2114.61	−	4902.21i	−0.385557	−	0.893822i	0.609338	−	0.792910i	$-0.291435\pi$
$312$	−3156.35	−	250.878i	−0.572735	−	0.0455229i
$313$	−200.820	+	100.856i	−0.0362652	+	0.0182131i	−0.466839	−	0.884342i	$-0.654607\pi$
$313$	−200.820	+	100.856i	−0.0362652	+	0.0182131i	0.430574	+	0.902555i	$0.358311\pi$
$314$	5439.72	+	1979.89i	0.977646	+	0.355834i
$315$	157.566	+	44.4552i	0.0281837	+	0.00795164i
$316$	461.569	−	167.997i	0.0821686	−	0.0299069i
$317$	−5307.43	+	5625.54i	−0.940362	+	0.996726i	−0.999999	−	0.00149451i	$-0.999524\pi$
$317$	−5307.43	+	5625.54i	−0.940362	+	0.996726i	0.0596367	+	0.998220i	$0.481006\pi$
$318$	−1282.11	−	3768.58i	−0.226091	−	0.664564i
$319$	561.068	−	369.020i	0.0984758	−	0.0647685i
$320$	−22.8794	+	76.4224i	−0.00399686	+	0.0133504i
$321$	−1516.29	−	7059.52i	−0.263647	−	1.22749i
$322$	−377.711	−	507.353i	−0.0653695	−	0.0878065i
$323$	−8247.47			−1.42075
$324$	1376.97	−	2570.41i	0.236106	−	0.440742i
$325$	9402.85			1.60485
$326$	−2699.43	−	3625.96i	−0.458612	−	0.616022i
$327$	−9012.85	−	2907.22i	−1.52420	−	0.491651i
$328$	−239.014	+	798.364i	−0.0402359	+	0.134397i
$329$	226.955	−	149.270i	0.0380316	−	0.0250138i
$330$	−97.5145	+	111.346i	−0.0162667	+	0.0185739i
$331$	−3091.99	+	3277.32i	−0.513448	+	0.544223i	−0.931281	−	0.364301i	$-0.881308\pi$
$331$	−3091.99	+	3277.32i	−0.513448	+	0.544223i	0.417833	+	0.908524i	$0.362790\pi$
$332$	−476.656	+	173.489i	−0.0787949	+	0.0286790i
$333$	−7390.81	+	548.495i	−1.21626	+	0.0902623i
$334$	985.602	+	358.730i	0.161466	+	0.0587689i
$335$	−448.260	+	225.125i	−0.0731076	+	0.0367160i
$336$	−229.336	+	333.131i	−0.0372360	+	0.0540886i
$337$	−584.385	−	1354.76i	−0.0944614	−	0.218986i	0.864434	−	0.502747i	$-0.167677\pi$
$337$	−584.385	−	1354.76i	−0.0944614	−	0.218986i	−0.958895	+	0.283761i	$0.908418\pi$
$338$	7160.84	+	836.983i	1.15236	+	0.134692i
$339$	−6723.79	−	6617.73i	−1.07725	−	1.06025i
$340$	−403.842	−	265.611i	−0.0644160	−	0.0423671i
$341$	203.248	−	170.545i	0.0322771	−	0.0270837i
$342$	4536.23	+	725.694i	0.717226	+	0.114740i
$343$	2468.22	+	2071.08i	0.388546	+	0.326029i
$344$	−930.245	−	3107.23i	−0.145801	−	0.487008i
$345$	−369.022	+	202.778i	−0.0575869	+	0.0316440i
$346$	869.201	+	436.529i	0.135054	+	0.0678265i
$347$	−6930.32	−	7345.71i	−1.07216	−	1.13642i	−0.990182	−	0.139787i	$-0.955358\pi$
$347$	−6930.32	−	7345.71i	−1.07216	−	1.13642i	−0.0819769	−	0.996634i	$-0.526123\pi$
$348$	−649.539	−	1034.56i	−0.100054	−	0.159363i
$349$	1661.89	−	3852.70i	0.254897	−	0.590918i	−0.741933	−	0.670474i	$-0.766091\pi$
$349$	1661.89	−	3852.70i	0.254897	−	0.590918i	0.996830	+	0.0795559i	$0.0253502\pi$
$350$	600.523	−	1040.14i	0.0917123	−	0.158850i
$351$	−5391.56	+	9226.48i	−0.819886	+	1.40306i
$352$	−182.819	−	316.651i	−0.0276826	−	0.0479476i
$353$	7254.30	−	847.906i	1.09379	−	0.127846i	0.449985	−	0.893036i	$-0.351429\pi$
$353$	7254.30	−	847.906i	1.09379	−	0.127846i	0.643804	+	0.765191i	$0.277355\pi$
$354$	−5177.89	−	4027.66i	−0.777406	−	0.604711i
$355$	−561.489	+	133.075i	−0.0839458	+	0.0198955i
$356$	125.522	+	2155.14i	0.0186873	+	0.320848i
$357$	−1535.16	−	1910.11i	−0.227589	−	0.283176i
$358$	−5676.86	−	1345.44i	−0.838077	−	0.198628i
$359$	−389.350	+	2208.11i	−0.0572398	+	0.324623i	−0.999960	−	0.00896197i	$-0.997147\pi$
$359$	−389.350	+	2208.11i	−0.0572398	+	0.324623i	0.942720	+	0.333585i	$0.108258\pi$
$360$	198.748	+	181.624i	0.0290971	+	0.0265901i
$361$	65.6933	+	372.565i	0.00957768	+	0.0543177i
$362$	−367.351	+	6307.17i	−0.0533357	+	0.915739i
$363$	593.032	+	6209.43i	0.0857469	+	0.897825i
$364$	885.080	−	1188.87i	0.127447	−	0.171191i
$365$	−721.852	+	969.615i	−0.103516	+	0.139047i
$366$	117.608	+	1231.43i	0.0167963	+	0.175868i
$367$	386.985	−	6644.27i	0.0550421	−	0.945036i	−0.851880	−	0.523737i	$-0.824537\pi$
$367$	386.985	−	6644.27i	0.0550421	−	0.945036i	0.906922	−	0.421299i	$-0.138426\pi$
$368$	−180.625	−	1024.38i	−0.0255862	−	0.145107i
$369$	2076.27	+	1897.38i	0.292916	+	0.267679i
$370$	118.823	−	673.880i	0.0166955	−	0.0946847i
$371$	1813.14	+	429.723i	0.253730	+	0.0601350i
$372$	−302.345	−	376.191i	−0.0421393	−	0.0524317i
$373$	0.806008	+	13.8386i	0.000111886	+	0.00192101i	0.998364	−	0.0571843i	$-0.0182123\pi$
$373$	0.806008	+	13.8386i	0.000111886	+	0.00192101i	−0.998252	+	0.0591053i	$0.981175\pi$
$374$	2155.73	−	510.918i	0.298049	−	0.0706389i
$375$	−1270.13	−	987.981i	−0.174905	−	0.136051i
$376$	443.701	−	51.8612i	0.0608568	−	0.00711314i
$377$	2238.34	+	3876.92i	0.305784	+	0.529633i
$378$	676.289	+	1185.67i	0.0920226	+	0.161334i
$379$	6317.59	−	10942.4i	0.856234	−	1.48304i	−0.0192615	−	0.999814i	$-0.506132\pi$
$379$	6317.59	−	10942.4i	0.856234	−	1.48304i	0.875495	−	0.483226i	$-0.160535\pi$
$380$	−168.001	+	389.470i	−0.0226796	+	0.0525773i
$381$	3936.13	+	6269.34i	0.529276	+	0.843013i
$382$	−332.272	−	352.188i	−0.0445040	−	0.0471714i
$383$	−9802.09	−	4922.80i	−1.30774	−	0.656771i	−0.347954	−	0.937511i	$-0.613124\pi$
$383$	−9802.09	−	4922.80i	−1.30774	−	0.656771i	−0.959784	+	0.280741i	$0.909420\pi$
$384$	−582.901	+	320.304i	−0.0774636	+	0.0425663i
$385$	−19.8708	−	66.3731i	−0.00263042	−	0.00878620i
$386$	315.551	+	264.779i	0.0416092	+	0.0349142i
$387$	−10809.3	−	1729.25i	−1.41982	−	0.227139i
$388$	−2207.92	+	1852.66i	−0.288892	+	0.242409i
$389$	132.428	+	87.0992i	0.0172606	+	0.0113525i	0.558110	−	0.829767i	$-0.311527\pi$
$389$	132.428	+	87.0992i	0.0172606	+	0.0113525i	−0.540849	+	0.841119i	$0.681897\pi$
$390$	−703.207	−	692.114i	−0.0913033	−	0.0898630i
$391$	6259.99	+	731.687i	0.809670	+	0.0946369i
$392$	1011.86	+	2345.75i	0.130374	+	0.302240i
$393$	−5189.53	+	7538.26i	−0.666099	+	0.967569i
$394$	−2735.68	+	1373.91i	−0.349800	+	0.175676i
$395$	143.832	+	52.3507i	0.0183215	+	0.00666848i
$396$	−1230.64	+	91.3296i	−0.156167	+	0.0115896i
$397$	−10907.4	+	3969.95i	−1.37890	+	0.501880i	−0.921845	−	0.387558i	$-0.873319\pi$
$397$	−10907.4	+	3969.95i	−1.37890	+	0.501880i	−0.457057	+	0.889437i	$0.651097\pi$
$398$	−2221.34	+	2354.48i	−0.279763	+	0.296532i
$399$	−1416.77	+	1617.73i	−0.177763	+	0.202977i
$400$	1650.21	−	1085.36i	0.206276	−	0.135670i
$401$	−4094.33	+	13676.0i	−0.509878	+	1.70311i	0.183919	+	0.982941i	$0.441122\pi$
$401$	−4094.33	+	13676.0i	−0.509878	+	1.70311i	−0.693797	+	0.720170i	$0.744064\pi$
$402$	−3980.24	−	1283.88i	−0.493821	−	0.159289i
$403$	1056.19	+	1418.71i	0.130553	+	0.175363i
$404$	−5989.96			−0.737652
$405$	843.560	−	337.775i	0.103498	−	0.0414424i
$406$	571.816			0.0698985
$407$	1872.88	+	2515.72i	0.228097	+	0.306387i
$408$	−846.284	−	3940.13i	−0.102689	−	0.478101i
$409$	3021.46	−	10092.4i	0.365285	−	1.22014i	−0.555979	−	0.831196i	$-0.687656\pi$
$409$	3021.46	−	10092.4i	0.365285	−	1.22014i	0.921263	−	0.388939i	$-0.127158\pi$
$410$	−216.970	+	142.704i	−0.0261351	+	0.0171893i
$411$	2254.66	+	6627.26i	0.270594	+	0.795374i
$412$	−2385.07	+	2528.03i	−0.285204	+	0.302299i
$413$	2885.52	−	1050.24i	0.343795	−	0.125131i
$414$	−3378.70	−	953.255i	−0.401097	−	0.113164i
$415$	−148.534	−	54.0619i	−0.0175692	−	0.00639468i
$416$	2178.16	−	1093.91i	0.256714	−	0.128927i
$417$	7048.98	+	560.277i	0.827794	+	0.0657958i
$418$	−770.019	−	1785.10i	−0.0901025	−	0.208881i
$419$	11882.7	+	1388.89i	1.38546	+	0.161938i	0.775928	−	0.630821i	$-0.217282\pi$
$419$	11882.7	+	1388.89i	1.38546	+	0.161938i	0.609536	+	0.792759i	$0.291356\pi$
$420$	−121.472	+	33.5857i	−0.0141125	+	0.00390193i
$421$	5913.50	+	3889.37i	0.684576	+	0.450252i	0.843564	−	0.537028i	$-0.180453\pi$
$421$	5913.50	+	3889.37i	0.684576	+	0.450252i	−0.158989	+	0.987280i	$0.550823\pi$
$422$	6474.88	−	5433.07i	0.746901	−	0.626724i
$423$	493.069	−	1424.78i	0.0566757	−	0.163771i
$424$	2347.42	+	1969.72i	0.268870	+	0.225609i
$425$	3432.37	+	11464.9i	0.391752	+	1.30854i
$426$	−4114.72	−	2493.06i	−0.467979	−	0.283543i
$427$	−517.464	−	259.880i	−0.0586459	−	0.0294531i
$428$	3814.38	+	4043.00i	0.430782	+	0.456603i
$429$	4519.24	−	167.463i	0.508604	−	0.0188466i
$430$	400.328	−	928.064i	0.0448966	−	0.104082i
$431$	−5003.55	+	8666.41i	−0.559194	+	0.968553i	0.438370	+	0.898795i	$0.355556\pi$
$431$	−5003.55	+	8666.41i	−0.559194	+	0.968553i	−0.997564	+	0.0697582i	$0.977777\pi$
$432$	118.777	+	2241.59i	0.0132284	+	0.249650i
$433$	−6719.11	−	11637.8i	−0.745727	−	1.29164i	−0.949854	−	0.312693i	$-0.898769\pi$
$433$	−6719.11	−	11637.8i	−0.745727	−	1.29164i	0.204127	−	0.978944i	$-0.434565\pi$
$434$	224.392	−	26.2277i	0.0248184	−	0.00290085i
$435$	52.1738	−	377.067i	0.00575067	−	0.0415609i
$436$	7093.61	−	1681.22i	0.779179	−	0.184669i
$437$	−321.579	−	5521.30i	−0.0352019	−	0.604393i
$438$	−9960.03	+	1539.91i	−1.08655	+	0.167990i
$439$	11266.1	+	2670.11i	1.22483	+	0.290290i	0.791626	−	0.611006i	$-0.209235\pi$
$439$	11266.1	+	2670.11i	1.22483	+	0.290290i	0.433204	+	0.901296i	$0.357383\pi$
$440$	19.7852	−	112.207i	0.00214369	−	0.0121575i
$441$	8614.35	+	364.414i	0.930174	+	0.0393494i
$442$	2564.56	+	14544.4i	0.275982	+	1.56517i
$443$	801.409	−	13759.7i	0.0859505	−	1.47571i	−0.629473	−	0.777022i	$-0.716729\pi$
$443$	801.409	−	13759.7i	0.0859505	−	1.47571i	0.715424	−	0.698691i	$-0.246234\pi$
$444$	4647.18	−	3309.36i	0.496724	−	0.353728i
$445$	−401.716	+	539.599i	−0.0427937	+	0.0574819i
$446$	5107.69	−	6860.82i	0.542278	−	0.728406i
$447$	2414.96	+	1102.83i	0.255534	+	0.116693i
$448$	18.1027	−	310.811i	0.00190909	−	0.0327777i
$449$	2569.89	+	14574.6i	0.270113	+	1.53188i	0.754071	+	0.656793i	$0.228088\pi$
$449$	2569.89	+	14574.6i	0.270113	+	1.53188i	−0.483958	+	0.875091i	$0.660801\pi$
$450$	−879.057	−	6607.89i	−0.0920870	−	0.692220i
$451$	206.690	−	1172.20i	0.0215802	−	0.122387i
$452$	7066.67	+	1674.83i	0.735373	+	0.174286i
$453$	879.922	−	2267.26i	0.0912634	−	0.235155i
$454$	−417.446	−	7167.26i	−0.0431535	−	0.740917i
$455$	449.413	−	106.513i	0.0463051	−	0.0109745i
$456$	−3276.05	+	1331.74i	−0.336437	+	0.136765i
$457$	9815.92	−	1147.32i	1.00475	−	0.117438i	0.402225	−	0.915541i	$-0.368237\pi$
$457$	9815.92	−	1147.32i	1.00475	−	0.117438i	0.602521	+	0.798103i	$0.294163\pi$
$458$	−1666.62	−	2886.67i	−0.170035	−	0.294509i
$459$	−13218.0	−	3205.95i	−1.34414	−	0.326015i
$460$	162.068	−	280.710i	0.0164271	−	0.0284526i
$461$	−3816.76	+	8848.25i	−0.385606	+	0.893935i	0.609282	+	0.792953i	$0.291458\pi$
$461$	−3816.76	+	8848.25i	−0.385606	+	0.893935i	−0.994888	+	0.100982i	$0.967802\pi$
$462$	270.101	−	510.610i	0.0271997	−	0.0514194i
$463$	−10971.1	−	11628.7i	−1.10123	−	1.16724i	−0.984737	−	0.174047i	$-0.944315\pi$
$463$	−10971.1	−	11628.7i	−1.10123	−	1.16724i	−0.116495	−	0.993191i	$-0.537166\pi$
$464$	840.338	+	422.034i	0.0840770	+	0.0422251i
$465$	3.17897	−	150.362i	0.000317035	−	0.0149954i
$466$	−190.685	−	636.933i	−0.0189556	−	0.0633162i
$467$	3924.79	+	3293.29i	0.388903	+	0.326328i	0.816186	−	0.577790i	$-0.196085\pi$
$467$	3924.79	+	3293.29i	0.388903	+	0.326328i	−0.427283	+	0.904118i	$0.640529\pi$
$468$	−130.790	−	8225.27i	−0.0129183	−	0.812421i
$469$	1499.67	−	1258.38i	0.147651	−	0.123894i
$470$	116.305	+	76.4948i	0.0114143	+	0.00750732i
$471$	−3776.98	+	14557.8i	−0.369499	+	1.42418i
$472$	5015.68	+	586.249i	0.489122	+	0.0571702i
$473$	1834.87	+	4253.71i	0.178367	+	0.413501i
$474$	548.503	+	1152.26i	0.0531510	+	0.111657i
$475$	9384.82	−	4713.23i	0.906537	−	0.455280i
$476$	1772.68	+	645.201i	0.170694	+	0.0621276i
$477$	9430.01	−	4246.78i	0.905179	−	0.407645i
$478$	−10559.6	+	3843.40i	−1.01043	+	0.367767i
$479$	4238.04	−	4492.06i	0.404261	−	0.428491i	−0.492975	−	0.870044i	$-0.664091\pi$
$479$	4238.04	−	4492.06i	0.404261	−	0.428491i	0.897236	+	0.441552i	$0.145572\pi$
$480$	−203.303	−	40.2963i	−0.0193322	−	0.00383181i
$481$	−17468.0	+	11488.9i	−1.65587	+	1.08908i
$482$	341.121	−	1139.42i	0.0322358	−	0.107675i
$483$	1218.88	−	1102.19i	0.114826	−	0.103834i
$484$	−2867.42	−	3851.61i	−0.269292	−	0.361722i
$485$	−898.151			−0.0840885
$486$	6987.99	+	2926.37i	0.652226	+	0.273133i
$487$	6939.94			0.645747			0.322873	−	0.946442i	$-0.395351\pi$
$487$	6939.94			0.645747			0.322873	+	0.946442i	$0.395351\pi$
$488$	−568.655	−	763.836i	−0.0527496	−	0.0708550i
$489$	8711.07	−	7877.18i	0.805579	−	0.728463i
$490$	−228.318	+	762.636i	−0.0210497	+	0.0703110i
$491$	−3527.12	+	2319.82i	−0.324189	+	0.213222i	−0.701162	−	0.713002i	$-0.747335\pi$
$491$	−3527.12	+	2319.82i	−0.324189	+	0.213222i	0.376974	+	0.926224i	$0.376965\pi$
$492$	−2123.85	−	420.964i	−0.194615	−	0.0385743i
$493$	−3910.07	+	4144.43i	−0.357202	+	0.378612i
$494$	12178.3	−	4432.53i	1.10916	−	0.403702i
$495$	−312.062	−	224.700i	−0.0283356	−	0.0204030i
$496$	349.123	+	127.070i	0.0316050	+	0.0115033i
$497$	2012.52	−	1010.72i	0.181637	−	0.0912216i
$498$	−566.432	−	1189.93i	−0.0509687	−	0.107072i
$499$	1713.95	+	3973.39i	0.153762	+	0.356460i	0.977633	−	0.210317i	$-0.0674495\pi$
$499$	1713.95	+	3973.39i	0.153762	+	0.356460i	−0.823872	+	0.566777i	$0.808190\pi$
$500$	1230.34	+	143.806i	0.110045	+	0.0128624i
$501$	−684.336	+	2637.68i	−0.0610257	+	0.235215i
$502$	−6781.95	−	4460.56i	−0.602975	−	0.396583i
$503$	−8800.62	+	7384.60i	−0.780120	+	0.654598i	−0.943279	−	0.332001i	$-0.892276\pi$
$503$	−8800.62	+	7384.60i	−0.780120	+	0.654598i	0.163159	+	0.986600i	$0.447832\pi$
$504$	−918.227	−	510.848i	−0.0811529	−	0.0451488i
$505$	−1429.87	−	1199.81i	−0.125997	−	0.105724i
$506$	426.091	+	1423.24i	0.0374349	+	0.125041i
$507$	−395.927	+	18726.9i	−0.0346819	+	1.64041i
$508$	−5092.35	−	2557.48i	−0.444757	−	0.223365i
$509$	12647.5	+	13405.6i	1.10136	+	1.16737i	0.984711	+	0.174197i	$0.0557331\pi$
$509$	12647.5	+	13405.6i	1.10136	+	1.16737i	0.116647	+	0.993173i	$0.462785\pi$
$510$	587.201	−	1110.07i	0.0509838	−	0.0963817i
$511$	1868.58	−	4331.86i	0.161764	−	0.375011i
$512$	256.000	−	443.405i	0.0220971	−	0.0382733i
$513$	−756.395	+	11911.3i	−0.0650988	+	1.02514i
$514$	1586.64	+	2748.14i	0.136155	+	0.235827i
$515$	−1075.72	+	125.733i	−0.0920423	+	0.0107582i
$516$	7806.49	−	3173.40i	0.666011	−	0.270739i
$517$	−620.841	+	147.142i	−0.0528134	+	0.0125170i
$518$	155.279	+	2666.04i	0.0131710	+	0.226138i
$519$	−914.302	+	2355.85i	−0.0773283	+	0.199249i
$520$	739.067	+	175.162i	0.0623274	+	0.0147719i
$521$	1590.43	−	9019.79i	0.133739	−	0.758472i	−0.841990	−	0.539493i	$-0.818616\pi$
$521$	1590.43	−	9019.79i	0.133739	−	0.758472i	0.975729	−	0.218980i	$-0.0702728\pi$
$522$	2515.26	−	1935.45i	0.210900	−	0.162284i
$523$	1323.29	+	7504.74i	0.110637	+	0.627455i	0.988818	+	0.149127i	$0.0476462\pi$
$523$	1323.29	+	7504.74i	0.110637	+	0.627455i	−0.878181	+	0.478329i	$0.841243\pi$
$524$	409.636	−	7033.18i	0.0341509	−	0.586347i
$525$	2838.45	+	1296.22i	0.235962	+	0.107755i
$526$	7690.08	−	10329.6i	0.637459	−	0.856256i
$527$	−1344.29	+	1805.70i	−0.111116	+	0.149255i
$528$	773.800	−	551.039i	0.0637790	−	0.0454184i
$529$	461.702	−	7927.11i	0.0379471	−	0.651526i
$530$	165.816	+	940.392i	0.0135898	+	0.0770717i
$531$	9137.80	−	14386.5i	0.746793	−	1.17574i
$532$	287.455	−	1630.24i	0.0234263	−	0.132857i
$533$	7720.83	+	1829.87i	0.627442	+	0.148706i
$534$	−5542.84	+	856.970i	−0.449180	+	0.0694470i
$535$	100.711	+	1729.14i	0.00813855	+	0.139733i
$536$	3132.66	−	742.455i	0.252445	−	0.0598306i
$537$	2077.51	−	15014.4i	0.166948	−	1.20656i
$538$	12899.9	−	1507.78i	1.03374	−	0.120827i
$539$	−1824.39	−	3159.93i	−0.145792	−	0.252519i
$540$	−420.644	+	558.886i	−0.0335216	+	0.0445382i
$541$	5425.12	−	9396.58i	0.431135	−	0.746747i	−0.565836	−	0.824517i	$-0.691447\pi$
$541$	5425.12	−	9396.58i	0.431135	−	0.746747i	0.996971	+	0.0777700i	$0.0247800\pi$
$542$	−644.554	+	1494.24i	−0.0510811	+	0.118419i
$543$	−16403.0	+	607.823i	−1.29635	+	0.0480372i
$544$	2128.92	+	2256.52i	0.167788	+	0.177845i
$545$	2030.08	+	1019.54i	0.159558	+	0.0801330i
$546$	3293.40	+	1995.43i	0.258140	+	0.156404i
$547$	2951.25	+	9857.85i	0.230688	+	0.770550i	0.992445	+	0.122688i	$0.0391515\pi$
$547$	2951.25	+	9857.85i	0.230688	+	0.770550i	−0.761758	+	0.647862i	$0.775663\pi$
$548$	−4128.08	−	3463.87i	−0.321794	−	0.270017i
$549$	−3155.81	+	608.340i	−0.245331	+	0.0472920i
$550$	−2161.04	+	1813.33i	−0.167540	+	0.140583i
$551$	4177.38	+	2747.51i	0.322981	+	0.212428i
$552$	2604.74	−	720.179i	0.200842	−	0.0555305i
$553$	−593.329	−	69.3502i	−0.0456255	−	0.00533286i
$554$	6400.20	+	14837.3i	0.490828	+	1.13787i
$555$	1772.21	+	140.861i	0.135543	+	0.0107734i
$556$	−4864.42	+	2443.00i	−0.371038	+	0.186342i
$557$	3098.12	+	1127.62i	0.235676	+	0.0857791i	0.457158	−	0.889385i	$-0.348867\pi$
$557$	3098.12	+	1127.62i	0.235676	+	0.0857791i	−0.221482	+	0.975164i	$0.571089\pi$
$558$	898.265	−	874.877i	0.0681480	−	0.0663737i
$559$	−29019.5	+	10562.2i	−2.19570	+	0.799169i
$560$	66.5777	−	70.5682i	0.00502396	−	0.00532509i
$561$	1853.87	+	5449.19i	0.139519	+	0.410098i
$562$	−12001.2	+	7893.33i	−0.900784	+	0.592455i
$563$	−4721.39	+	15770.6i	−0.353433	+	1.18055i	0.577816	+	0.816167i	$0.303905\pi$
$563$	−4721.39	+	15770.6i	−0.353433	+	1.18055i	−0.931249	+	0.364383i	$0.881280\pi$
$564$	243.726	+	1134.74i	0.0181963	+	0.0847182i
$565$	1351.42	+	1815.28i	0.100628	+	0.135167i
$566$	−11417.8			−0.847922
$567$	−2899.46	+	2041.96i	−0.214755	+	0.151242i
$568$	3703.55			0.273587
$569$	−12962.1	−	17411.1i	−0.955007	−	1.28280i	−0.959177	−	0.282806i	$-0.908735\pi$
$569$	−12962.1	−	17411.1i	−0.955007	−	1.28280i	0.00417037	−	0.999991i	$-0.498673\pi$
$570$	−1048.79	−	338.301i	−0.0770680	−	0.0248594i
$571$	1376.28	−	4597.09i	0.100868	−	0.336921i	−0.892628	−	0.450795i	$-0.851141\pi$
$571$	1376.28	−	4597.09i	0.100868	−	0.336921i	0.993495	+	0.113873i	$0.0363258\pi$
$572$	−2908.58	+	1913.01i	−0.212612	+	0.139837i
$573$	828.793	−	946.350i	0.0604246	−	0.0689953i
$574$	695.518	−	737.206i	0.0505756	−	0.0536070i
$575$	−7541.40	+	2744.84i	−0.546953	+	0.199075i
$576$	−972.385	−	1428.44i	−0.0703404	−	0.103331i
$577$	6464.48	+	2352.88i	0.466412	+	0.169760i	0.564526	−	0.825415i	$-0.309059\pi$
$577$	6464.48	+	2352.88i	0.466412	+	0.169760i	−0.0981144	+	0.995175i	$0.531281\pi$
$578$	−8016.98	+	4026.28i	−0.576925	+	0.289743i
$579$	−606.857	+	881.514i	−0.0435581	+	0.0632720i
$580$	116.064	+	269.067i	0.00830913	+	0.0192627i
$581$	612.724	+	71.6171i	0.0437522	+	0.00511390i
$582$	−5336.93	−	5252.74i	−0.380108	−	0.374112i
$583$	−3656.69	−	2405.04i	−0.259768	−	0.170852i
$584$	5943.23	−	4986.96i	0.421117	−	0.353359i
$585$	1616.32	−	1989.67i	0.114234	−	0.140620i
$586$	−868.099	−	728.422i	−0.0611960	−	0.0513495i
$587$	−4841.46	−	16171.6i	−0.340424	−	1.13709i	−0.941249	−	0.337714i	$-0.890346\pi$
$587$	−4841.46	−	16171.6i	−0.340424	−	1.13709i	0.600825	−	0.799380i	$-0.294839\pi$
$588$	−5816.90	+	3196.39i	−0.407967	+	0.224178i
$589$	1765.31	+	886.571i	0.123494	+	0.0620212i
$590$	1079.88	+	1144.60i	0.0753522	+	0.0798686i
$591$	−4229.08	−	6735.94i	−0.294350	−	0.468832i
$592$	−1739.50	+	4032.61i	−0.120765	+	0.279965i
$593$	−6708.49	+	11619.5i	−0.464561	+	0.804644i	−0.999182	−	0.0404487i	$-0.987121\pi$
$593$	−6708.49	+	11619.5i	−0.464561	+	0.804644i	0.534620	+	0.845092i	$0.320455\pi$
$594$	−540.182	−	3160.26i	−0.0373130	−	0.218294i
$595$	293.923	+	509.089i	0.0202515	+	0.0350767i
$596$	−2029.89	+	237.260i	−0.139509	+	0.0163063i
$597$	−6638.10	−	5163.50i	−0.455074	−	0.353983i
$598$	−9636.78	+	2283.96i	−0.658992	+	0.156184i
$599$	−1346.80	−	23123.7i	−0.0918679	−	1.57731i	−0.658014	−	0.753005i	$-0.728603\pi$
$599$	−1346.80	−	23123.7i	−0.0918679	−	1.57731i	0.566146	−	0.824305i	$-0.308434\pi$
$600$	3214.68	+	3999.85i	0.218731	+	0.272155i
$601$	−1618.53	−	383.600i	−0.109853	−	0.0260355i	0.175322	−	0.984511i	$-0.443903\pi$
$601$	−1618.53	−	383.600i	−0.109853	−	0.0260355i	−0.285174	+	0.958476i	$0.592052\pi$
$602$	−684.976	+	3884.69i	−0.0463746	+	0.263004i
$603$	2337.37	−	10611.2i	0.157853	−	0.716622i
$604$	325.099	+	1843.73i	0.0219008	+	0.124206i
$605$	87.0027	−	1493.78i	0.00584655	−	0.100381i
$606$	−1479.55	−	15491.9i	−0.0991794	−	1.03847i
$607$	−6119.55	+	8219.98i	−0.409201	+	0.549652i	−0.958173	−	0.286188i	$-0.907612\pi$
$607$	−6119.55	+	8219.98i	−0.409201	+	0.549652i	0.548973	+	0.835840i	$0.315019\pi$
$608$	1625.65	−	2183.63i	0.108436	−	0.145655i
$609$	141.242	+	1478.89i	0.00939804	+	0.0984036i
$610$	17.2540	−	296.240i	0.00114524	−	0.0196630i
$611$	−738.582	−	4188.71i	−0.0489032	−	0.277344i
$612$	9981.35	−	3161.98i	0.659268	−	0.208849i
$613$	212.490	−	1205.09i	0.0140006	−	0.0794014i	−0.977007	−	0.213208i	$-0.931609\pi$
$613$	212.490	−	1205.09i	0.0140006	−	0.0794014i	0.991008	+	0.133806i	$0.0427200\pi$
$614$	−9023.47	−	2138.60i	−0.593091	−	0.140565i
$615$	−422.668	−	525.903i	−0.0277132	−	0.0344820i
$616$	25.8555	+	443.922i	0.00169115	+	0.0290359i
$617$	−13444.6	+	3186.43i	−0.877245	+	0.207911i	−0.644479	−	0.764622i	$-0.722926\pi$
$617$	−13444.6	+	3186.43i	−0.877245	+	0.207911i	−0.232766	+	0.972533i	$0.574778\pi$
$618$	−7127.39	−	5544.10i	−0.463925	−	0.360868i
$619$	16006.8	−	1870.93i	1.03937	−	0.121485i	0.420750	−	0.907177i	$-0.361767\pi$
$619$	16006.8	−	1870.93i	1.03937	−	0.121485i	0.618618	+	0.785692i	$0.287693\pi$
$620$	57.8872	+	100.264i	0.00374969	+	0.00649465i
$621$	1630.85	−	8973.83i	0.105385	−	0.579883i
$622$	−5338.84	+	9247.14i	−0.344161	+	0.596104i
$623$	1039.88	−	2410.72i	0.0668732	−	0.155029i
$624$	3367.22	+	5363.20i	0.216020	+	0.344070i
$625$	−10324.4	−	10943.2i	−0.660759	−	0.700364i
$626$	401.640	+	201.711i	0.0256434	+	0.0128786i
$627$	4426.63	−	2432.44i	0.281950	−	0.154932i
$628$	−3320.51	−	11091.3i	−0.210992	−	0.704761i
$629$	−20384.8	−	17104.9i	−1.29220	−	1.08429i
$630$	−116.867	−	305.869i	−0.00739063	−	0.0193430i
$631$	−15466.3	+	12977.8i	−0.975758	+	0.818758i	−0.983444	−	0.181213i	$-0.941998\pi$
$631$	−15466.3	+	12977.8i	−0.975758	+	0.818758i	0.00768637	+	0.999970i	$0.497553\pi$
$632$	−820.769	−	539.828i	−0.0516589	−	0.0339766i
$633$	15650.9	+	15404.0i	0.982730	+	0.967228i
$634$	15363.5	+	1795.74i	0.962402	+	0.112489i
$635$	−703.335	−	1630.51i	−0.0439543	−	0.101898i
$636$	−4514.48	+	6557.69i	−0.281464	+	0.408851i
$637$	21736.4	−	10916.4i	1.35200	−	0.679002i
$638$	−1262.09	−	459.364i	−0.0783177	−	0.0285053i
$639$	5431.46	−	11257.7i	0.336252	−	0.696947i
$640$	149.926	−	54.5684i	0.00925989	−	0.00337032i
$641$	−16851.7	+	17861.8i	−1.03838	+	1.10062i	−0.0435555	+	0.999051i	$0.513869\pi$
$641$	−16851.7	+	17861.8i	−1.03838	+	1.10062i	−0.994828	+	0.101571i	$0.967613\pi$
$642$	−9514.28	+	10863.8i	−0.584889	+	0.667850i
$643$	−5788.45	+	3807.12i	−0.355014	+	0.233496i	−0.714471	−	0.699665i	$-0.753332\pi$
$643$	−5788.45	+	3807.12i	−0.355014	+	0.233496i	0.359457	+	0.933162i	$0.382962\pi$
$644$	−362.814	+	1211.88i	−0.0222001	+	0.0741535i
$645$	2499.14	+	806.134i	0.152564	+	0.0492116i
$646$	9850.09	+	13231.0i	0.599917	+	0.805829i
$647$	−20764.3			−1.26171			−0.630856	−	0.775900i	$-0.717296\pi$
$647$	−20764.3			−1.26171			−0.630856	+	0.775900i	$0.717296\pi$
$648$	−5768.11	+	860.880i	−0.349680	+	0.0521891i
$649$	−7212.52			−0.436234
$650$	−11230.0	−	15084.5i	−0.677656	−	0.910249i
$651$	123.259	+	573.869i	0.00742074	+	0.0345494i
$652$	−2592.96	+	8661.09i	−0.155749	+	0.520237i
$653$	12928.2	−	8503.04i	0.774764	−	0.509571i	−0.0994900	−	0.995039i	$-0.531721\pi$
$653$	12928.2	−	8503.04i	0.774764	−	0.509571i	0.874254	+	0.485468i	$0.161351\pi$
$654$	6100.30	+	17931.0i	0.364741	+	1.07211i
$655$	1506.55	−	1596.85i	0.0898716	−	0.0952583i
$656$	1566.23	−	570.061i	0.0932180	−	0.0339286i
$657$	−6442.85	−	25379.3i	−0.382587	−	1.50707i
$658$	−510.522	−	185.815i	−0.0302465	−	0.0110088i
$659$	15461.1	−	7764.85i	0.913928	−	0.458992i	0.0712797	−	0.997456i	$-0.477292\pi$
$659$	15461.1	−	7764.85i	0.913928	−	0.458992i	0.842648	+	0.538465i	$0.180995\pi$
$660$	295.090	+	23.4547i	0.0174036	+	0.00138330i
$661$	−12757.0	−	29574.1i	−0.750668	−	1.74024i	−0.668607	−	0.743616i	$-0.733109\pi$
$661$	−12757.0	−	29574.1i	−0.750668	−	1.74024i	−0.0820607	−	0.996627i	$-0.526150\pi$
$662$	8950.45	+	1046.16i	0.525482	+	0.0614201i
$663$	−36982.7	+	10225.3i	−2.16635	+	0.598970i
$664$	847.597	+	557.474i	0.0495379	+	0.0325816i
$665$	395.161	−	331.579i	0.0230431	−	0.0193355i
$666$	9706.90	+	11201.6i	0.564767	+	0.651732i
$667$	−2926.96	−	2456.01i	−0.169914	−	0.142574i
$668$	−601.630	−	2009.58i	−0.0348470	−	0.116397i
$669$	19005.8	+	11515.4i	1.09837	+	0.665487i
$670$	896.520	+	450.249i	0.0516949	+	0.0259622i
$671$	933.354	+	989.298i	0.0536986	+	0.0569172i
$672$	808.324	−	29.9529i	0.0464014	−	0.00171943i
$673$	888.268	−	2059.24i	0.0508770	−	0.117946i	−0.890882	−	0.454235i	$-0.849913\pi$
$673$	888.268	−	2059.24i	0.0508770	−	0.117946i	0.941759	+	0.336289i	$0.109172\pi$
$674$	−1475.42	+	2555.51i	−0.0843192	+	0.146045i
$675$	16872.9	−	3905.70i	0.962131	−	0.222712i
$676$	−7209.59	−	12487.4i	−0.410195	−	0.710479i
$677$	7364.31	−	860.765i	0.418070	−	0.0488654i	0.0955424	−	0.995425i	$-0.469541\pi$
$677$	7364.31	−	860.765i	0.418070	−	0.0488654i	0.322528	+	0.946560i	$0.395467\pi$
$678$	−2586.12	+	18690.3i	−0.146489	+	1.05870i
$679$	3410.78	−	808.370i	0.192774	−	0.0456883i
$680$	56.2099	+	965.087i	0.00316993	+	0.0544256i
$681$	18433.6	−	2850.00i	1.03727	−	0.160370i
$682$	−516.340	−	122.375i	−0.0289907	−	0.00687093i
$683$	5877.70	−	33334.1i	0.329289	−	1.86749i	−0.148355	−	0.988934i	$-0.547398\pi$
$683$	5877.70	−	33334.1i	0.329289	−	1.86749i	0.477644	−	0.878554i	$-0.341491\pi$
$684$	−4253.50	−	8143.94i	−0.237773	−	0.455250i
$685$	−291.598	−	1653.73i	−0.0162648	−	0.0922422i
$686$	374.689	−	6433.15i	0.0208538	−	0.358045i
$687$	7054.14	−	5023.41i	0.391750	−	0.278974i
$688$	−3873.76	+	5203.37i	−0.214660	+	0.288338i
$689$	17422.8	−	23402.9i	0.963362	−	1.29402i
$690$	766.035	+	349.821i	0.0422644	+	0.0193007i
$691$	317.020	−	5443.03i	0.0174530	−	0.299656i	−0.978274	−	0.207314i	$-0.933528\pi$
$691$	317.020	−	5443.03i	0.0174530	−	0.299656i	0.995727	−	0.0923419i	$-0.0294353\pi$
$692$	−337.802	−	1915.77i	−0.0185568	−	0.105241i
$693$	1387.31	+	572.442i	0.0760456	+	0.0313785i
$694$	−3507.33	+	19891.0i	−0.191839	+	1.08797i
$695$	−1650.53	−	391.184i	−0.0900839	−	0.0213503i
$696$	−883.941	+	2277.62i	−0.0481404	+	0.124042i
$697$	587.209	+	10082.0i	0.0319112	+	0.547895i
$698$	−8165.51	+	1935.26i	−0.442792	+	0.104944i
$699$	1600.20	−	650.497i	0.0865884	−	0.0351989i
$700$	−2385.85	+	278.866i	−0.128824	+	0.0150573i
$701$	−4985.25	−	8634.71i	−0.268602	−	0.465233i	0.699899	−	0.714242i	$-0.253228\pi$
$701$	−4985.25	−	8634.71i	−0.268602	−	0.465233i	−0.968501	+	0.249009i	$0.919895\pi$
$702$	21240.8	−	2369.95i	1.14200	−	0.127419i
$703$	−11675.6	+	20222.8i	−0.626393	+	1.08494i
$704$	−289.643	+	671.468i	−0.0155061	+	0.0359473i
$705$	−169.111	+	319.694i	−0.00903418	+	0.0170786i
$706$	−10024.2	−	10625.0i	−0.534370	−	0.566399i
$707$	6509.90	+	3269.39i	0.346294	+	0.173915i
$708$	−277.320	+	13116.9i	−0.0147208	+	0.696276i
$709$	7257.17	+	24240.6i	0.384413	+	1.28403i	0.903235	+	0.429146i	$0.141186\pi$
$709$	7257.17	+	24240.6i	0.384413	+	1.28403i	−0.518822	+	0.854882i	$0.673629\pi$
$710$	884.082	+	741.833i	0.0467310	+	0.0392120i
$711$	−2844.62	+	1703.21i	−0.150045	+	0.0898389i
$712$	3307.45	−	2775.28i	0.174090	−	0.146079i
$713$	−1261.25	−	829.536i	−0.0662470	−	0.0435713i
$714$	−1230.83	+	4744.05i	−0.0645134	+	0.248658i
$715$	−1077.49	−	125.941i	−0.0563580	−	0.00658731i
$716$	4621.55	+	10714.0i	0.241223	+	0.559218i
$717$	−12548.5	−	26361.1i	−0.653601	−	1.37305i
$718$	4007.36	−	2012.57i	0.208292	−	0.104608i
$719$	26149.6	+	9517.67i	1.35635	+	0.493671i	0.914924	−	0.403627i	$-0.132251\pi$
$719$	26149.6	+	9517.67i	1.35635	+	0.493671i	0.441425	+	0.897298i	$0.354473\pi$
$720$	54.0017	−	535.758i	0.00279517	−	0.0277313i
$721$	3971.94	−	1445.67i	0.205163	−	0.0746733i
$722$	519.228	−	550.349i	0.0267641	−	0.0283683i
$723$	3031.16	+	600.801i	0.155920	+	0.0309046i
$724$	10557.0	−	6943.44i	0.541916	−	0.356424i
$725$	2080.83	−	6950.47i	0.106593	−	0.356047i
$726$	9253.19	−	8367.40i	0.473028	−	0.427746i
$727$	18355.4	+	24655.6i	0.936402	+	1.25781i	0.966079	+	0.258247i	$0.0831448\pi$
$727$	18355.4	+	24655.6i	0.936402	+	1.25781i	−0.0296768	+	0.999560i	$0.509448\pi$
$728$	−2964.30			−0.150913
$729$	−5842.42	+	18795.9i	−0.296826	+	0.954932i
$730$	2417.62			0.122576
$731$	−23471.7	−	31528.0i	−1.18760	−	1.59522i
$732$	1835.05	−	1659.39i	0.0926579	−	0.0837879i
$733$	−5681.26	+	18976.7i	−0.286279	+	0.956238i	0.687009	+	0.726649i	$0.258923\pi$
$733$	−5681.26	+	18976.7i	−0.286279	+	0.956238i	−0.973288	+	0.229589i	$0.926262\pi$
$734$	−11121.2	+	7314.55i	−0.559254	+	0.367827i
$735$	−2028.81	−	402.126i	−0.101815	−	0.0201805i
$736$	−1427.63	+	1513.20i	−0.0714987	+	0.0757842i
$737$	−4320.93	+	1572.69i	−0.215961	+	0.0786035i
$738$	564.141	−	5596.91i	0.0281386	−	0.279167i
$739$	15147.1	+	5513.09i	0.753985	+	0.274428i	0.690281	−	0.723541i	$-0.257487\pi$
$739$	15147.1	+	5513.09i	0.753985	+	0.274428i	0.0637031	+	0.997969i	$0.479709\pi$
$740$	−1222.98	+	614.205i	−0.0607537	+	0.0305116i
$741$	14472.0	+	30401.9i	0.717465	+	1.50721i
$742$	−1476.09	−	3421.95i	−0.0730308	−	0.169304i
$743$	−2527.04	−	295.368i	−0.124775	−	0.0145841i	0.0534761	−	0.998569i	$-0.482970\pi$
$743$	−2527.04	−	295.368i	−0.124775	−	0.0145841i	−0.178251	+	0.983985i	$0.557044\pi$
$744$	−242.408	+	934.326i	−0.0119450	+	0.0460404i
$745$	−532.083	−	349.957i	−0.0261665	−	0.0172100i
$746$	21.2379	−	17.8207i	0.00104233	−	0.000874616i
$747$	2937.61	−	1758.89i	0.143884	−	0.0861503i
$748$	−3394.27	−	2848.13i	−0.165918	−	0.139222i
$749$	−1938.75	−	6475.88i	−0.0945800	−	0.315919i
$750$	−68.0262	+	3217.56i	−0.00331196	+	0.156652i
$751$	29709.0	+	14920.4i	1.44354	+	0.724972i	0.986391	−	0.164419i	$-0.0525748\pi$
$751$	29709.0	+	14920.4i	1.44354	+	0.724972i	0.457148	+	0.889391i	$0.348871\pi$
$752$	−613.118	−	649.867i	−0.0297315	−	0.0315136i
$753$	9861.20	−	18642.0i	0.477240	−	0.902194i
$754$	3546.25	−	8221.13i	0.171282	−	0.397077i
$755$	−291.700	+	505.239i	−0.0140610	+	0.0243543i
$756$	1094.40	−	2501.00i	0.0526495	−	0.120318i
$757$	7036.32	+	12187.3i	0.337833	+	0.585144i	0.984025	−	0.178031i	$-0.0569728\pi$
$757$	7036.32	+	12187.3i	0.337833	+	0.585144i	−0.646192	+	0.763175i	$0.723639\pi$
$758$	−25099.5	+	2933.71i	−1.20271	+	0.140577i
$759$	−3575.70	+	1453.55i	−0.171001	+	0.0695132i
$760$	825.451	−	195.636i	0.0393977	−	0.00933743i
$761$	1291.46	+	22173.4i	0.0615181	+	1.05622i	0.877941	+	0.478770i	$0.158917\pi$
$761$	1291.46	+	22173.4i	0.0615181	+	1.05622i	−0.816423	+	0.577455i	$0.804046\pi$
$762$	5356.58	−	13802.1i	0.254657	−	0.656165i
$763$	−8626.98	−	2044.63i	−0.409328	−	0.0970126i
$764$	−168.158	+	953.670i	−0.00796300	+	0.0451604i
$765$	3016.02	+	1244.49i	0.142542	+	0.0588165i
$766$	3809.43	+	21604.4i	0.179687	+	1.01906i
$767$	2795.63	−	47999.0i	0.131609	−	2.25964i
$768$	1210.02	+	552.571i	0.0568524	+	0.0259625i
$769$	−10983.7	+	14753.7i	−0.515063	+	0.691849i	−0.981229	−	0.192848i	$-0.938228\pi$
$769$	−10983.7	+	14753.7i	−0.515063	+	0.691849i	0.466166	+	0.884697i	$0.345635\pi$
$770$	−82.7468	+	111.148i	−0.00387271	+	0.00520195i
$771$	−6715.62	+	4782.34i	−0.313693	+	0.223388i
$772$	47.9024	−	822.452i	0.00223322	−	0.0383429i
$773$	6148.28	+	34868.6i	0.286078	+	1.62243i	0.701410	+	0.712758i	$0.252554\pi$
$773$	6148.28	+	34868.6i	0.286078	+	1.62243i	−0.415332	+	0.909670i	$0.636334\pi$
$774$	10135.6	+	19406.1i	0.470695	+	0.901213i
$775$	497.761	−	2822.94i	0.0230711	−	0.130843i
$776$	5609.09	+	1329.38i	0.259477	+	0.0614973i
$777$	−6856.86	+	1060.13i	−0.316587	+	0.0489471i
$778$	−18.4323	−	316.471i	−0.000849397	−	0.0145836i
$779$	8623.26	−	2043.75i	0.396611	−	0.0939987i
$780$	−270.470	+	1954.72i	−0.0124159	+	0.0897311i
$781$	−5253.91	+	614.094i	−0.240716	+	0.0281357i
$782$	−6302.60	−	10916.4i	−0.288210	−	0.499195i
$783$	5626.95	+	6027.18i	0.256821	+	0.275088i
$784$	2554.68	−	4424.84i	0.116376	−	0.201569i
$785$	1428.97	−	3312.72i	0.0649708	−	0.150619i
$786$	18291.2	−	677.790i	0.830056	−	0.0307582i
$787$	−27037.5	−	28658.0i	−1.22463	−	1.29803i	−0.940723	−	0.339177i	$-0.889851\pi$
$787$	−27037.5	−	28658.0i	−1.22463	−	1.29803i	−0.283905	−	0.958852i	$-0.591630\pi$
$788$	5471.35	+	2747.82i	0.247346	+	0.124222i
$789$	28614.9	+	17337.5i	1.29115	+	0.782294i
$790$	−87.7980	−	293.266i	−0.00395407	−	0.0132075i
$791$	−6765.93	−	5677.29i	−0.304133	−	0.255198i
$792$	1616.29	+	1865.17i	0.0725156	+	0.0836819i
$793$	−6945.51	+	5827.98i	−0.311025	+	0.260981i
$794$	19395.6	+	12756.7i	0.866908	+	0.570174i
$795$	−2391.19	+	661.134i	−0.106675	+	0.0294944i
$796$	6430.16	+	751.577i	0.286320	+	0.0334660i
$797$	7788.20	+	18055.1i	0.346138	+	0.802439i	0.998989	+	0.0449521i	$0.0143135\pi$
$797$	7788.20	+	18055.1i	0.346138	+	0.802439i	−0.652851	+	0.757486i	$0.726427\pi$
$798$	4287.31	+	340.770i	0.190187	+	0.0151167i
$799$	4837.69	−	2429.58i	0.214199	−	0.107575i
$800$	−3712.05	−	1351.08i	−0.164051	−	0.0597097i
$801$	−3585.50	−	14123.8i	−0.158162	−	0.623022i
$802$	26829.6	−	9765.19i	1.18128	−	0.429951i
$803$	−7604.24	+	8060.02i	−0.334181	+	0.354212i
$804$	2694.00	+	7918.64i	0.118172	+	0.347350i
$805$	−329.351	+	216.618i	−0.0144200	+	0.00948419i
$806$	1014.54	−	3388.79i	0.0443369	−	0.148096i
$807$	7085.92	+	32990.6i	0.309091	+	1.43906i
$808$	7153.91	+	9609.36i	0.311477	+	0.418386i
$809$	9425.55			0.409623			0.204811	−	0.978801i	$-0.434342\pi$
$809$	9425.55			0.409623			0.204811	+	0.978801i	$0.434342\pi$
$810$	−1549.35	−	949.868i	−0.0672083	−	0.0412036i
$811$	20200.3			0.874636			0.437318	−	0.899307i	$-0.355929\pi$
$811$	20200.3			0.874636			0.437318	+	0.899307i	$0.355929\pi$
$812$	−682.930	−	917.335i	−0.0295150	−	0.0396455i
$813$	−4023.79	−	1297.93i	−0.173580	−	0.0559906i
$814$	1799.02	−	6009.14i	0.0774638	−	0.258747i
$815$	−2353.81	+	1548.13i	−0.101166	+	0.0665380i
$816$	−5310.20	+	6063.41i	−0.227812	+	0.260125i
$817$	−23669.5	+	25088.2i	−1.01358	+	1.07433i
$818$	−19799.2	+	7206.33i	−0.846288	+	0.308024i
$819$	−4347.31	+	9010.63i	−0.185479	+	0.384441i
$820$	488.063	+	177.640i	0.0207852	+	0.00756521i
$821$	10885.2	−	5466.76i	0.462724	−	0.232389i	−0.202135	−	0.979358i	$-0.564788\pi$
$821$	10885.2	−	5466.76i	0.462724	−	0.232389i	0.664859	+	0.746969i	$0.268492\pi$
$822$	7938.98	−	11532.1i	0.336866	−	0.489328i
$823$	15518.4	+	35975.7i	0.657274	+	1.52373i	0.841160	+	0.540786i	$0.181873\pi$
$823$	15518.4	+	35975.7i	0.657274	+	1.52373i	−0.183886	+	0.982948i	$0.558868\pi$
$824$	6904.12	+	806.976i	0.291889	+	0.0341169i
$825$	−5223.61	−	5141.21i	−0.220440	−	0.216962i
$826$	−5131.08	−	3374.76i	−0.216142	−	0.142159i
$827$	−16799.6	+	14096.5i	−0.706384	+	0.592726i	−0.923582	−	0.383401i	$-0.874753\pi$
$827$	−16799.6	+	14096.5i	−0.706384	+	0.592726i	0.217198	+	0.976128i	$0.430308\pi$
$828$	2505.99	+	6558.76i	0.105180	+	0.275281i
$829$	−36418.7	−	30558.9i	−1.52578	−	1.28028i	−0.821153	−	0.570708i	$-0.806669\pi$
$829$	−36418.7	−	30558.9i	−1.52578	−	1.28028i	−0.704629	−	0.709576i	$-0.748887\pi$
$830$	90.6679	+	302.852i	0.00379172	+	0.0126652i
$831$	−36793.0	+	20217.8i	−1.53590	+	0.843980i
$832$	−4356.32	−	2187.83i	−0.181525	−	0.0911650i
$833$	21245.0	+	22518.3i	0.883666	+	0.936631i
$834$	−7519.89	−	11977.4i	−0.312221	−	0.497296i
$835$	258.910	−	600.220i	0.0107305	−	0.0248760i
$836$	−1944.10	+	3367.28i	−0.0804284	+	0.139306i
$837$	2484.58	+	2107.09i	0.102604	+	0.0870152i
$838$	−11963.6	−	20721.6i	−0.493170	−	0.854196i
$839$	12990.3	−	1518.34i	0.534533	−	0.0624780i	0.155456	−	0.987843i	$-0.450315\pi$
$839$	12990.3	−	1518.34i	0.534533	−	0.0624780i	0.379078	+	0.925365i	$0.376241\pi$
$840$	198.956	+	154.760i	0.00817219	+	0.00635680i
$841$	−20370.5	+	4827.89i	−0.835232	+	0.197954i
$842$	−823.087	−	14131.9i	−0.0336882	−	0.578404i
$843$	−23378.9	−	29089.2i	−0.955176	−	1.18847i
$844$	−16449.0	−	3898.49i	−0.670852	−	0.158995i
$845$	780.245	−	4424.99i	0.0317648	−	0.180147i
$846$	−2874.58	+	910.637i	−0.116820	+	0.0370075i
$847$	1014.06	+	5751.02i	0.0411375	+	0.233303i
$848$	356.351	−	6118.32i	0.0144306	−	0.247764i
$849$	−2820.25	−	29529.8i	−0.114006	−	1.19371i
$850$	14293.2	−	19199.1i	0.576768	−	0.774734i
$851$	10656.1	−	14313.6i	0.429244	−	0.576575i
$852$	914.798	+	9578.53i	0.0367846	+	0.385158i
$853$	1238.14	−	21258.1i	0.0496989	−	0.853297i	−0.877697	−	0.479216i	$-0.840921\pi$
$853$	1238.14	−	21258.1i	0.0496989	−	0.853297i	0.927396	−	0.374081i	$-0.122042\pi$
$854$	201.104	+	1140.52i	0.00805813	+	0.0456999i
$855$	615.894	−	2796.04i	0.0246352	−	0.111839i
$856$	1930.40	−	10947.8i	0.0770790	−	0.437137i
$857$	16109.4	+	3817.99i	0.642108	+	0.152182i	0.538755	−	0.842462i	$-0.318895\pi$
$857$	16109.4	+	3817.99i	0.642108	+	0.152182i	0.103353	+	0.994645i	$0.467043\pi$
$858$	−5666.06	−	7049.97i	−0.225450	−	0.280515i
$859$	610.694	+	10485.2i	0.0242568	+	0.416474i	0.988477	+	0.151371i	$0.0483688\pi$
$859$	610.694	+	10485.2i	0.0242568	+	0.416474i	−0.964220	+	0.265103i	$0.914594\pi$
$860$	−1966.96	+	466.179i	−0.0779917	+	0.0184844i
$861$	2078.44	+	1616.73i	0.0822683	+	0.0639931i
$862$	19878.9	−	2323.51i	0.785473	−	0.0918086i
$863$	19722.7	+	34160.8i	0.777949	+	1.34745i	0.933122	+	0.359560i	$0.117073\pi$
$863$	19722.7	+	34160.8i	0.777949	+	1.34745i	−0.155173	+	0.987887i	$0.549594\pi$
$864$	3454.21	−	2867.72i	0.136012	−	0.112919i
$865$	303.097	−	524.979i	0.0119140	−	0.0206356i
$866$	−10645.2	+	24678.4i	−0.417713	+	0.968367i
$867$	−12393.4	−	19739.9i	−0.485471	−	0.773243i
$868$	−310.071	−	328.656i	−0.0121250	−	0.0128517i
$869$	1253.86	+	629.713i	0.0489463	+	0.0245818i
$870$	−667.221	+	366.638i	−0.0260010	+	0.0142876i
$871$	−8791.37	−	29365.2i	−0.342002	−	1.14237i
$872$	−11169.1	−	9371.99i	−0.433754	−	0.363963i
$873$	12267.0	−	15100.4i	0.475571	−	0.585419i
$874$	−8473.46	+	7110.07i	−0.327939	+	0.275174i
$875$	−1258.65	−	827.826i	−0.0486286	−	0.0319836i
$876$	14365.8	+	14139.2i	0.554083	+	0.545342i
$877$	25395.9	+	2968.36i	0.977834	+	0.114292i	0.589971	−	0.807425i	$-0.299139\pi$
$877$	25395.9	+	2968.36i	0.977834	+	0.114292i	0.387863	+	0.921717i	$0.373213\pi$
$878$	−9171.76	−	21262.5i	−0.352542	−	0.817284i
$879$	1669.50	−	2425.10i	0.0640623	−	0.0930563i
$880$	−203.638	+	102.271i	−0.00780073	+	0.00391767i
$881$	−36112.6	−	13143.9i	−1.38100	−	0.502644i	−0.458521	−	0.888684i	$-0.651621\pi$
$881$	−36112.6	−	13143.9i	−1.38100	−	0.502644i	−0.922482	+	0.386039i	$0.873843\pi$
$882$	−9703.65	−	14254.8i	−0.370452	−	0.544198i
$883$	−12423.1	+	4521.63i	−0.473466	+	0.172327i	−0.567722	−	0.823221i	$-0.692175\pi$
$883$	−12423.1	+	4521.63i	−0.473466	+	0.172327i	0.0942560	+	0.995548i	$0.469953\pi$
$884$	20269.8	−	21484.8i	0.771209	−	0.817433i
$885$	−2693.56	+	3075.61i	−0.102308	+	0.116820i
$886$	−23031.0	+	15147.7i	−0.873298	+	0.574377i
$887$	−9365.78	+	31283.9i	−0.354535	+	1.18423i	0.575823	+	0.817574i	$0.304682\pi$
$887$	−9365.78	+	31283.9i	−0.354535	+	1.18423i	−0.930358	+	0.366654i	$0.880503\pi$
$888$	−10859.2	−	3502.80i	−0.410374	−	0.132372i
$889$	4138.48	+	5558.94i	0.156131	+	0.209720i
$890$	1345.43			0.0506728
$891$	8039.97	−	2177.68i	0.302300	−	0.0818798i
$892$	−17106.6			−0.642122
$893$	−2836.78	−	3810.46i	−0.106304	−	0.142791i
$894$	−1115.02	−	5191.32i	−0.0417136	−	0.194210i
$895$	−1042.82	+	3483.26i	−0.0389471	+	0.130092i
$896$	−520.237	+	342.166i	−0.0193972	+	0.0127578i
$897$	−8287.36	−	24359.5i	−0.308480	−	0.906735i
$898$	20311.9	−	21529.4i	0.754808	−	0.800050i
$899$	1282.43	−	466.766i	0.0475767	−	0.0173165i
$900$	−9550.81	+	9302.14i	−0.353734	+	0.344524i
$901$	34895.2	+	12700.8i	1.29026	+	0.469617i
$902$	−2127.35	+	1068.40i	−0.0785289	+	0.0394387i
$903$	−10216.2	−	812.018i	−0.376494	−	0.0299250i
$904$	−5753.01	−	13337.0i	−0.211662	−	0.490687i
$905$	3910.87	+	457.115i	0.143648	+	0.0167901i
$906$	−4688.15	+	1296.22i	−0.171913	+	0.0475320i
$907$	−9713.01	−	6388.35i	−0.355585	−	0.233872i	0.359130	−	0.933287i	$-0.383073\pi$
$907$	−9713.01	−	6388.35i	−0.355585	−	0.233872i	−0.714715	+	0.699416i	$0.753444\pi$
$908$	−10999.5	+	9229.67i	−0.402017	+	0.337332i
$909$	39701.3	−	7653.16i	1.44863	−	0.279251i
$910$	−707.614	−	593.759i	−0.0257771	−	0.0216296i
$911$	9970.87	+	33305.0i	0.362623	+	1.21125i	0.923582	+	0.383402i	$0.125248\pi$
$911$	9970.87	+	33305.0i	0.362623	+	1.21125i	−0.560958	+	0.827844i	$0.689567\pi$
$912$	6049.09	+	3665.07i	0.219633	+	0.133073i
$913$	−1294.85	−	650.297i	−0.0469367	−	0.0235725i
$914$	−13563.9	−	14376.9i	−0.490869	−	0.520290i
$915$	770.430	−	28.5487i	0.0278357	−	0.00103147i
$916$	−2640.45	+	6121.26i	−0.0952435	+	0.220799i
$917$	−4283.99	+	7420.10i	−0.154275	+	0.267212i
$918$	10643.3	+	25033.8i	0.382660	+	0.900042i
$919$	7027.94	+	12172.7i	0.252264	+	0.436934i	0.964149	−	0.265362i	$-0.0854916\pi$
$919$	7027.94	+	12172.7i	0.252264	+	0.436934i	−0.711885	+	0.702296i	$0.752158\pi$
$920$	−643.889	+	75.2599i	−0.0230744	+	0.00269701i
$921$	3302.24	−	23865.7i	0.118146	−	0.853857i
$922$	18753.2	−	4444.59i	0.669852	−	0.158758i
$923$	−2050.32	−	35202.6i	−0.0731170	−	1.25537i
$924$	−1141.73	+	176.521i	−0.0406496	+	0.00628477i
$925$	32971.0	+	7814.27i	1.17198	+	0.277764i
$926$	−5552.31	+	31488.7i	−0.197041	+	1.11748i
$927$	12578.2	−	19803.1i	0.445657	−	0.701637i
$928$	−326.584	−	1852.15i	−0.0115524	−	0.0655171i
$929$	−1531.66	+	26297.6i	−0.0540928	+	0.928737i	0.856685	+	0.515840i	$0.172520\pi$
$929$	−1531.66	+	26297.6i	−0.0540928	+	0.928737i	−0.910778	+	0.412897i	$0.864517\pi$
$930$	−245.014	+	174.480i	−0.00863906	+	0.00615206i
$931$	16222.8	−	21791.0i	0.571085	−	0.767100i
$932$	−794.059	+	1066.61i	−0.0279080	+	0.0374870i
$933$	−25234.7	−	11523.8i	−0.885473	−	0.404364i
$934$	595.804	−	10229.6i	0.0208729	−	0.358374i
$935$	−239.763	−	1359.76i	−0.00838619	−	0.0475605i
$936$	−13039.2	+	10033.4i	−0.455340	+	0.350376i
$937$	−6534.86	+	37061.0i	−0.227838	+	1.29214i	0.629345	+	0.777126i	$0.283323\pi$
$937$	−6534.86	+	37061.0i	−0.227838	+	1.29214i	−0.857184	+	0.515010i	$0.827788\pi$
$938$	−3809.83	−	902.946i	−0.132618	−	0.0314310i
$939$	−422.480	+	1088.59i	−0.0146827	+	0.0378325i
$940$	−16.1882	−	277.940i	−0.000561703	−	0.00964406i
$941$	−20110.3	+	4766.23i	−0.696681	+	0.165117i	−0.563673	−	0.825998i	$-0.690612\pi$
$941$	−20110.3	+	4766.23i	−0.696681	+	0.165117i	−0.133009	+	0.991115i	$0.542464\pi$
$942$	27865.3	−	11327.5i	0.963799	−	0.391793i
$943$	−6726.53	+	786.219i	−0.232286	+	0.0271504i
$944$	−5049.83	−	8746.56i	−0.174108	−	0.301564i
$945$	762.204	−	377.806i	0.0262376	−	0.0130053i
$946$	4632.59	−	8023.87i	0.159216	−	0.275770i
$947$	−17443.7	+	40438.9i	−0.598567	+	1.38763i	0.302164	+	0.953256i	$0.402291\pi$
$947$	−17443.7	+	40438.9i	−0.598567	+	1.38763i	−0.900731	+	0.434378i	$0.856968\pi$
$948$	1193.43	−	2256.10i	0.0408868	−	0.0772940i
$949$	−50691.7	−	53730.1i	−1.73395	−	1.83788i
$950$	−18769.6	−	9426.47i	−0.641018	−	0.321932i
$951$	−849.456	+	40178.3i	−0.0289648	+	1.37000i
$952$	−1082.08	−	3614.38i	−0.0368385	−	0.123049i
$953$	22184.2	+	18614.8i	0.754059	+	0.632730i	0.936573	−	0.350473i	$-0.113979\pi$
$953$	22184.2	+	18614.8i	0.754059	+	0.632730i	−0.182514	+	0.983203i	$0.558424\pi$
$954$	−18075.3	−	10056.1i	−0.613427	−	0.341275i
$955$	−231.164	+	193.970i	−0.00783277	+	0.00657248i
$956$	18777.3	+	12350.0i	0.635253	+	0.417812i
$957$	876.313	−	3377.62i	0.0296000	−	0.114089i
$958$	−12267.9	−	1433.92i	−0.413736	−	0.0483588i
$959$	2595.78	+	6017.70i	0.0874059	+	0.202630i
$960$	178.163	+	374.275i	0.00598979	+	0.0125830i
$961$	−26140.4	+	13128.2i	−0.877459	+	0.440676i
$962$	39293.3	+	14301.6i	1.31691	+	0.479316i
$963$	−30447.2	−	21923.4i	−1.01884	−	0.733617i
$964$	−2235.33	+	813.592i	−0.0746836	+	0.0271826i
$965$	176.174	−	186.734i	0.00587695	−	0.00622920i
$966$	−3223.92	−	639.006i	−0.107379	−	0.0212833i
$967$	3643.92	−	2396.64i	0.121179	−	0.0797009i	−0.487472	−	0.873138i	$-0.662081\pi$
$967$	3643.92	−	2396.64i	0.121179	−	0.0797009i	0.608652	+	0.793437i	$0.291711\pi$
$968$	−2754.33	+	9200.09i	−0.0914540	+	0.305478i
$969$	−31786.3	+	28743.5i	−1.05379	+	0.952914i
$970$	1072.68	+	1440.86i	0.0355068	+	0.0476939i
$971$	39330.4			1.29987			0.649935	−	0.759990i	$-0.274796\pi$
$971$	39330.4			1.29987			0.649935	+	0.759990i	$0.274796\pi$
$972$	−3651.26	−	14705.5i	−0.120488	−	0.485266i
$973$	6620.08			0.218119
$974$	−8288.49	−	11133.4i	−0.272670	−	0.366259i
$975$	36239.3	−	32770.1i	1.19034	−	1.07639i
$976$	−546.227	+	1824.53i	−0.0179142	+	0.0598377i
$977$	45079.8	−	29649.4i	1.47618	−	0.970900i	0.480606	−	0.876937i	$-0.340417\pi$
$977$	45079.8	−	29649.4i	1.47618	−	0.970900i	0.995576	−	0.0939635i	$-0.0299537\pi$
$978$	−23040.7	−	4566.86i	−0.753334	−	0.149317i
$979$	−4231.82	+	4485.47i	−0.138151	+	0.146431i
$980$	1496.14	−	544.551i	0.0487678	−	0.0177500i
$981$	−44868.2	+	20206.3i	−1.46028	+	0.657633i
$982$	7934.06	+	2887.76i	0.257827	+	0.0938413i
$983$	8176.36	−	4106.32i	0.265295	−	0.133236i	−0.311180	−	0.950351i	$-0.600724\pi$
$983$	8176.36	−	4106.32i	0.265295	−	0.133236i	0.576475	+	0.817115i	$0.304428\pi$
$984$	1861.22	+	3909.95i	0.0602984	+	0.126671i
$985$	755.681	+	1751.86i	0.0244447	+	0.0566691i
$986$	11318.5	+	1322.95i	0.365574	+	0.0427295i
$987$	354.473	−	1366.26i	0.0114316	−	0.0440615i
$988$	−21655.6	−	14243.1i	−0.697324	−	0.458637i
$989$	20191.3	−	16942.5i	0.649188	−	0.544734i
$990$	12.2276	+	768.987i	0.000392546	+	0.0246869i
$991$	−20299.7	−	17033.5i	−0.650698	−	0.546000i	0.256585	−	0.966522i	$-0.417403\pi$
$991$	−20299.7	−	17033.5i	−0.650698	−	0.546000i	−0.907283	+	0.420521i	$0.861847\pi$
$992$	−213.111	−	711.842i	−0.00682086	−	0.0227833i
$993$	−494.875	+	23407.0i	−0.0158151	+	0.748036i
$994$	−4025.03	−	2021.45i	−0.128437	−	0.0645034i
$995$	1384.41	+	1467.39i	0.0441093	+	0.0467532i
$996$	−1232.44	+	2329.85i	−0.0392081	+	0.0741205i
$997$	−14245.2	+	33024.0i	−0.452507	+	1.04903i	0.527408	+	0.849612i	$0.323164\pi$
$997$	−14245.2	+	33024.0i	−0.452507	+	1.04903i	−0.979915	+	0.199417i	$0.936095\pi$
$998$	4327.30	−	7495.10i	0.137253	−	0.237729i
$999$	−26573.2	+	27871.9i	−0.841579	+	0.882710i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.g.b.7.12	✓	252
81.58	even	27	inner	162.4.g.b.139.12	yes	252

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.4.g.b.7.12	✓	252	1.1	even	1	trivial
162.4.g.b.139.12	yes	252	81.58	even	27	inner

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19432 - 1.60425i) q^{2} +(3.85407 - 3.48513i) q^{3} +(-1.14721 + 3.83196i) q^{4} +(-1.04141 + 0.684943i) q^{5} +(-10.1940 - 2.02053i) q^{6} +(3.33832 - 3.53842i) q^{7} +(7.51754 - 2.73616i) q^{8} +(2.70774 - 26.8639i) q^{9} +O(q^{10})\)	\(q+(-1.19432 - 1.60425i) q^{2} +(3.85407 - 3.48513i) q^{3} +(-1.14721 + 3.83196i) q^{4} +(-1.04141 + 0.684943i) q^{5} +(-10.1940 - 2.02053i) q^{6} +(3.33832 - 3.53842i) q^{7} +(7.51754 - 2.73616i) q^{8} +(2.70774 - 26.8639i) q^{9} +(2.34259 + 0.852632i) q^{10} +(-10.2108 + 5.12805i) q^{11} +(8.93343 + 18.7668i) q^{12} +(-30.1692 - 69.9401i) q^{13} +(-9.66351 - 1.12950i) q^{14} +(-1.62654 + 6.26926i) q^{15} +(-13.3678 - 8.79214i) q^{16} +(74.2653 - 62.3160i) q^{17} +(-46.3302 + 27.7401i) q^{18} +(-65.1692 - 54.6835i) q^{19} +(-1.42996 - 4.77640i) q^{20} +(0.534300 - 25.2718i) q^{21} +(20.4216 + 10.2561i) q^{22} +(44.6134 + 47.2874i) q^{23} +(19.4373 - 36.7450i) q^{24} +(-48.8946 + 113.350i) q^{25} +(-76.1695 + 131.929i) q^{26} +(-83.1883 - 112.972i) q^{27} +(9.72930 + 16.8516i) q^{28} +(-58.3752 + 6.82309i) q^{29} +(12.0000 - 4.87811i) q^{30} +(-22.5946 + 5.35503i) q^{31} +(1.86063 + 31.9459i) q^{32} +(-21.4812 + 55.3498i) q^{33} +(-188.666 - 44.7148i) q^{34} +(-1.05294 + 5.97149i) q^{35} +(99.8349 + 41.1945i) q^{36} +(-47.6641 - 270.317i) q^{37} +(-9.89304 + 169.857i) q^{38} +(-360.025 - 164.411i) q^{39} +(-5.95470 + 7.99854i) q^{40} +(-62.2071 + 83.5586i) q^{41} +(-41.1803 + 29.3254i) q^{42} +(23.5741 - 404.751i) q^{43} +(-7.93652 - 45.0103i) q^{44} +(15.5804 + 29.8309i) q^{45} +(22.5781 - 128.047i) q^{46} +(54.3350 + 12.8776i) q^{47} +(-82.1622 + 12.7030i) q^{48} +(18.5677 + 318.795i) q^{49} +(240.238 - 56.9374i) q^{50} +(69.0445 - 498.994i) q^{51} +(302.618 - 35.3710i) q^{52} +(191.521 + 331.725i) q^{53} +(-81.8820 + 268.379i) q^{54} +(7.12115 - 12.3342i) q^{55} +(15.4143 - 35.7344i) q^{56} +(-441.746 + 16.3692i) q^{57} +(80.6645 + 85.4993i) q^{58} +(564.087 + 283.295i) q^{59} +(-22.1575 - 13.4250i) q^{60} +(-34.1392 - 114.033i) q^{61} +(35.5760 + 29.8518i) q^{62} +(-86.0163 - 99.2615i) q^{63} +(49.0268 - 41.1384i) q^{64} +(79.3234 + 52.1718i) q^{65} +(114.450 - 31.6441i) q^{66} +(399.710 + 46.7193i) q^{67} +(153.594 + 356.071i) q^{68} +(336.746 + 26.7657i) q^{69} +(10.8373 - 5.44269i) q^{70} +(435.025 + 158.336i) q^{71} +(-53.1483 - 209.359i) q^{72} +(911.306 - 331.688i) q^{73} +(-376.728 + 399.309i) q^{74} +(206.598 + 607.265i) q^{75} +(284.308 - 186.992i) q^{76} +(-15.9417 + 53.2491i) q^{77} +(166.229 + 773.926i) q^{78} +(-73.3298 - 98.4990i) q^{79} +19.9434 q^{80} +(-714.336 - 145.481i) q^{81} +208.343 q^{82} +(75.7267 + 101.719i) q^{83} +(96.2276 + 31.0396i) q^{84} +(-34.6574 + 115.764i) q^{85} +(-677.475 + 445.582i) q^{86} +(-201.203 + 229.742i) q^{87} +(-62.7288 + 66.4887i) q^{88} +(507.149 - 184.587i) q^{89} +(29.2481 - 60.6223i) q^{90} +(-348.192 - 126.731i) q^{91} +(-232.384 + 116.708i) q^{92} +(-68.4184 + 99.3839i) q^{93} +(-44.2344 - 102.547i) q^{94} +(105.323 + 12.3105i) q^{95} +(118.506 + 116.637i) q^{96} +(602.018 + 395.953i) q^{97} +(489.250 - 410.529i) q^{98} +(110.111 + 288.187i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 252 q - 36 q^{6}+O(q^{10}) \) 252 * q - 36 * q^6	\( 252 q - 36 q^{6} + 90 q^{13} - 252 q^{18} - 144 q^{20} + 189 q^{21} + 1512 q^{23} + 846 q^{25} + 702 q^{26} + 702 q^{27} - 504 q^{28} + 540 q^{29} - 342 q^{30} - 2214 q^{31} - 1548 q^{33} - 1242 q^{35} - 576 q^{36} - 882 q^{38} - 927 q^{41} + 774 q^{42} - 900 q^{43} + 2817 q^{45} - 2088 q^{46} + 297 q^{47} - 144 q^{48} + 2151 q^{51} - 720 q^{52} + 1431 q^{53} - 2970 q^{55} + 729 q^{57} + 126 q^{58} + 2628 q^{59} + 261 q^{63} + 3627 q^{65} + 4680 q^{66} + 2538 q^{67} - 936 q^{68} + 4716 q^{69} - 3150 q^{70} + 720 q^{71} - 1440 q^{72} + 3204 q^{73} - 2088 q^{74} + 918 q^{75} + 1764 q^{76} - 9792 q^{77} - 3132 q^{78} + 3897 q^{79} - 1440 q^{80} - 17352 q^{81} + 5904 q^{82} - 1035 q^{83} - 1224 q^{84} + 2421 q^{85} - 3600 q^{86} - 10827 q^{87} + 1224 q^{88} - 4086 q^{89} + 4473 q^{91} + 1872 q^{92} + 8955 q^{93} - 6174 q^{94} + 8037 q^{95} + 1152 q^{96} + 6192 q^{97} + 8136 q^{98} + 2187 q^{99}+O(q^{100}) \) 252 * q - 36 * q^6 + 90 * q^13 - 252 * q^18 - 144 * q^20 + 189 * q^21 + 1512 * q^23 + 846 * q^25 + 702 * q^26 + 702 * q^27 - 504 * q^28 + 540 * q^29 - 342 * q^30 - 2214 * q^31 - 1548 * q^33 - 1242 * q^35 - 576 * q^36 - 882 * q^38 - 927 * q^41 + 774 * q^42 - 900 * q^43 + 2817 * q^45 - 2088 * q^46 + 297 * q^47 - 144 * q^48 + 2151 * q^51 - 720 * q^52 + 1431 * q^53 - 2970 * q^55 + 729 * q^57 + 126 * q^58 + 2628 * q^59 + 261 * q^63 + 3627 * q^65 + 4680 * q^66 + 2538 * q^67 - 936 * q^68 + 4716 * q^69 - 3150 * q^70 + 720 * q^71 - 1440 * q^72 + 3204 * q^73 - 2088 * q^74 + 918 * q^75 + 1764 * q^76 - 9792 * q^77 - 3132 * q^78 + 3897 * q^79 - 1440 * q^80 - 17352 * q^81 + 5904 * q^82 - 1035 * q^83 - 1224 * q^84 + 2421 * q^85 - 3600 * q^86 - 10827 * q^87 + 1224 * q^88 - 4086 * q^89 + 4473 * q^91 + 1872 * q^92 + 8955 * q^93 - 6174 * q^94 + 8037 * q^95 + 1152 * q^96 + 6192 * q^97 + 8136 * q^98 + 2187 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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