LMFDB - Embedded newform 162.4.e.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,4,Mod(19,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

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("162.19");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	162.e (of order $9$, degree $6$, not 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:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	162.19
Dual form			162.4.e.b.145.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87939 + 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(-2.39299 - 13.5713i) q^{5} +(20.6081 + 17.2922i) q^{7} +(-4.00000 + 6.92820i) q^{8} +O(q^{10})$	\(q+(-1.87939 + 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(-2.39299 - 13.5713i) q^{5} +(20.6081 + 17.2922i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(13.7807 + 23.8688i) q^{10} +(1.76636 - 10.0175i) q^{11} +(-53.7496 - 19.5632i) q^{13} +(-50.5591 - 18.4020i) q^{14} +(2.77837 - 15.7569i) q^{16} +(-15.2393 - 26.3953i) q^{17} +(69.5964 - 120.544i) q^{19} +(-42.2264 - 35.4322i) q^{20} +(3.53272 + 20.0351i) q^{22} +(1.34797 - 1.13108i) q^{23} +(-60.9925 + 22.1995i) q^{25} +114.398 q^{26} +107.608 q^{28} +(57.1815 - 20.8124i) q^{29} +(196.045 - 164.501i) q^{31} +(5.55674 + 31.5138i) q^{32} +(46.6960 + 39.1826i) q^{34} +(185.363 - 321.059i) q^{35} +(-205.579 - 356.073i) q^{37} +(-48.3411 + 274.156i) q^{38} +(103.597 + 37.7061i) q^{40} +(-151.094 - 54.9937i) q^{41} +(-24.3594 + 138.149i) q^{43} +(-20.3441 - 35.2371i) q^{44} +(-1.75966 + 3.04781i) q^{46} +(-450.340 - 377.880i) q^{47} +(66.1103 + 374.930i) q^{49} +(99.4431 - 83.4427i) q^{50} +(-214.998 + 78.2530i) q^{52} +507.593 q^{53} -140.178 q^{55} +(-202.236 + 73.6080i) q^{56} +(-93.2295 + 78.2289i) q^{58} +(-2.03414 - 11.5362i) q^{59} +(26.2010 + 21.9853i) q^{61} +(-255.918 + 443.264i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(-136.877 + 776.267i) q^{65} +(229.762 + 83.6266i) q^{67} +(-114.562 - 41.6973i) q^{68} +(-128.752 + 730.189i) q^{70} +(569.503 + 986.408i) q^{71} +(-139.745 + 242.045i) q^{73} +(629.930 + 528.574i) q^{74} +(-96.6823 - 548.312i) q^{76} +(209.627 - 175.898i) q^{77} +(-935.039 + 340.327i) q^{79} -220.491 q^{80} +321.582 q^{82} +(-303.303 + 110.393i) q^{83} +(-321.751 + 269.981i) q^{85} +(-48.7189 - 276.298i) q^{86} +(62.3380 + 52.3078i) q^{88} +(297.715 - 515.657i) q^{89} +(-769.383 - 1332.61i) q^{91} +(1.22224 - 6.93169i) q^{92} +(1104.85 + 402.131i) q^{94} +(-1802.49 - 656.053i) q^{95} +(75.9826 - 430.919i) q^{97} +(-380.714 - 659.416i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8}+O(q^{10}) $ 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8	$ 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8} - 30 q^{10} + 39 q^{11} - 60 q^{13} + 66 q^{14} - 102 q^{17} - 171 q^{19} - 96 q^{20} + 78 q^{22} - 48 q^{23} - 432 q^{25} + 468 q^{26} + 336 q^{28} + 381 q^{29} - 801 q^{31} - 222 q^{34} - 624 q^{35} - 555 q^{37} - 606 q^{38} + 96 q^{40} - 1401 q^{41} + 648 q^{43} - 132 q^{44} - 348 q^{46} - 540 q^{47} + 15 q^{49} + 828 q^{50} - 240 q^{52} + 1794 q^{53} + 3906 q^{55} + 264 q^{56} - 444 q^{58} + 1500 q^{59} - 378 q^{61} - 744 q^{62} - 960 q^{64} - 3666 q^{65} + 3087 q^{67} + 24 q^{68} + 2118 q^{70} - 120 q^{71} - 2604 q^{73} + 1974 q^{74} - 1212 q^{76} + 6504 q^{77} - 2625 q^{79} + 480 q^{80} + 3408 q^{82} + 5211 q^{83} - 1395 q^{85} + 1296 q^{86} - 912 q^{88} - 2604 q^{89} - 3399 q^{91} - 372 q^{92} + 4500 q^{94} - 7545 q^{95} + 8940 q^{97} - 4002 q^{98}+O(q^{100}) $ 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8 - 30 * q^10 + 39 * q^11 - 60 * q^13 + 66 * q^14 - 102 * q^17 - 171 * q^19 - 96 * q^20 + 78 * q^22 - 48 * q^23 - 432 * q^25 + 468 * q^26 + 336 * q^28 + 381 * q^29 - 801 * q^31 - 222 * q^34 - 624 * q^35 - 555 * q^37 - 606 * q^38 + 96 * q^40 - 1401 * q^41 + 648 * q^43 - 132 * q^44 - 348 * q^46 - 540 * q^47 + 15 * q^49 + 828 * q^50 - 240 * q^52 + 1794 * q^53 + 3906 * q^55 + 264 * q^56 - 444 * q^58 + 1500 * q^59 - 378 * q^61 - 744 * q^62 - 960 * q^64 - 3666 * q^65 + 3087 * q^67 + 24 * q^68 + 2118 * q^70 - 120 * q^71 - 2604 * q^73 + 1974 * q^74 - 1212 * q^76 + 6504 * q^77 - 2625 * q^79 + 480 * q^80 + 3408 * q^82 + 5211 * q^83 - 1395 * q^85 + 1296 * q^86 - 912 * q^88 - 2604 * q^89 - 3399 * q^91 - 372 * q^92 + 4500 * q^94 - 7545 * q^95 + 8940 * q^97 - 4002 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$83$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	−1.87939	+	0.684040i	−0.664463	+	0.241845i
$2$	−1.87939	+	0.684040i	−0.664463	+	0.241845i
$3$		0			0
$3$		0			0
$4$	3.06418	−	2.57115i	0.383022	−	0.321394i
$5$	−2.39299	−	13.5713i	−0.214035	−	1.21386i	−0.882573	−	0.470176i	$-0.844190\pi$
$5$	−2.39299	−	13.5713i	−0.214035	−	1.21386i	0.668537	−	0.743679i	$-0.266921\pi$
$6$		0			0
$7$	20.6081	+	17.2922i	1.11273	+	0.933693i	0.998215	−	0.0597287i	$-0.0190236\pi$
$7$	20.6081	+	17.2922i	1.11273	+	0.933693i	0.114517	+	0.993421i	$0.463468\pi$
$8$	−4.00000	+	6.92820i	−0.176777	+	0.306186i
$9$		0			0
$10$	13.7807	+	23.8688i	0.435783	+	0.754798i
$11$	1.76636	−	10.0175i	0.0484161	−	0.274582i	−0.950983	−	0.309243i	$-0.899924\pi$
$11$	1.76636	−	10.0175i	0.0484161	−	0.274582i	0.999399	+	0.0346617i	$0.0110354\pi$
$12$		0			0
$13$	−53.7496	−	19.5632i	−1.14673	−	0.417375i	−0.302389	−	0.953185i	$-0.597784\pi$
$13$	−53.7496	−	19.5632i	−1.14673	−	0.417375i	−0.844338	+	0.535810i	$0.820006\pi$
$14$	−50.5591	−	18.4020i	−0.965178	−	0.351296i
$15$		0			0
$16$	2.77837	−	15.7569i	0.0434120	−	0.246202i
$17$	−15.2393	−	26.3953i	−0.217416	−	0.376576i	0.736601	−	0.676328i	$-0.236430\pi$
$17$	−15.2393	−	26.3953i	−0.217416	−	0.376576i	−0.954017	+	0.299751i	$0.903096\pi$
$18$		0			0
$19$	69.5964	−	120.544i	0.840342	−	1.45552i	−0.0492635	−	0.998786i	$-0.515687\pi$
$19$	69.5964	−	120.544i	0.840342	−	1.45552i	0.889606	−	0.456729i	$-0.150979\pi$
$20$	−42.2264	−	35.4322i	−0.472106	−	0.396144i
$21$		0			0
$22$	3.53272	+	20.0351i	0.0342354	+	0.194159i
$23$	1.34797	−	1.13108i	0.0122205	−	0.0102542i	−0.636657	−	0.771147i	$-0.719683\pi$
$23$	1.34797	−	1.13108i	0.0122205	−	0.0102542i	0.648877	+	0.760893i	$0.275239\pi$
$24$		0			0
$25$	−60.9925	+	22.1995i	−0.487940	+	0.177596i
$26$	114.398			0.862898
$27$		0			0
$28$	107.608			0.726284
$29$	57.1815	−	20.8124i	0.366149	−	0.133267i	−0.152392	−	0.988320i	$-0.548698\pi$
$29$	57.1815	−	20.8124i	0.366149	−	0.133267i	0.518541	+	0.855053i	$0.326475\pi$
$30$		0			0
$31$	196.045	−	164.501i	1.13583	−	0.953074i	0.136535	−	0.990635i	$-0.456403\pi$
$31$	196.045	−	164.501i	1.13583	−	0.953074i	0.999294	+	0.0375614i	$0.0119590\pi$
$32$	5.55674	+	31.5138i	0.0306970	+	0.174091i
$33$		0			0
$34$	46.6960	+	39.1826i	0.235538	+	0.197640i
$35$	185.363	−	321.059i	0.895204	−	1.55054i
$36$		0			0
$37$	−205.579	−	356.073i	−0.913431	−	1.58211i	−0.809182	−	0.587558i	$-0.800089\pi$
$37$	−205.579	−	356.073i	−0.913431	−	1.58211i	−0.104249	−	0.994551i	$-0.533244\pi$
$38$	−48.3411	+	274.156i	−0.206368	+	1.17037i
$39$		0			0
$40$	103.597	+	37.7061i	0.409502	+	0.149047i
$41$	−151.094	−	54.9937i	−0.575534	−	0.209477i	0.0378209	−	0.999285i	$-0.487958\pi$
$41$	−151.094	−	54.9937i	−0.575534	−	0.209477i	−0.613355	+	0.789807i	$0.710181\pi$
$42$		0			0
$43$	−24.3594	+	138.149i	−0.0863902	+	0.489943i	0.910658	+	0.413162i	$0.135576\pi$
$43$	−24.3594	+	138.149i	−0.0863902	+	0.489943i	−0.997048	+	0.0767817i	$0.975536\pi$
$44$	−20.3441	−	35.2371i	−0.0697044	−	0.120732i
$45$		0			0
$46$	−1.75966	+	3.04781i	−0.00564015	+	0.00976903i
$47$	−450.340	−	377.880i	−1.39763	−	1.17275i	−0.962138	−	0.272563i	$-0.912129\pi$
$47$	−450.340	−	377.880i	−1.39763	−	1.17275i	−0.435496	−	0.900191i	$-0.643427\pi$
$48$		0			0
$49$	66.1103	+	374.930i	0.192741	+	1.09309i
$50$	99.4431	−	83.4427i	0.281268	−	0.236012i
$51$		0			0
$52$	−214.998	+	78.2530i	−0.573364	+	0.208687i
$53$	507.593			1.31553			0.657767	−	0.753222i	$-0.271501\pi$
$53$	507.593			1.31553			0.657767	+	0.753222i	$0.271501\pi$
$54$		0			0
$55$	−140.178			−0.343665
$56$	−202.236	+	73.6080i	−0.482589	+	0.175648i
$57$		0			0
$58$	−93.2295	+	78.2289i	−0.211063	+	0.177103i
$59$	−2.03414	−	11.5362i	−0.00448851	−	0.0254556i	0.982481	−	0.186361i	$-0.0596696\pi$
$59$	−2.03414	−	11.5362i	−0.00448851	−	0.0254556i	−0.986970	+	0.160906i	$0.948558\pi$
$60$		0			0
$61$	26.2010	+	21.9853i	0.0549951	+	0.0461463i	0.669871	−	0.742478i	$-0.266349\pi$
$61$	26.2010	+	21.9853i	0.0549951	+	0.0461463i	−0.614876	+	0.788624i	$0.710794\pi$
$62$	−255.918	+	443.264i	−0.524221	+	0.907977i
$63$		0			0
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	−136.877	+	776.267i	−0.261192	+	1.48129i
$66$		0			0
$67$	229.762	+	83.6266i	0.418954	+	0.152487i	0.542891	−	0.839803i	$-0.317330\pi$
$67$	229.762	+	83.6266i	0.418954	+	0.152487i	−0.123937	+	0.992290i	$0.539552\pi$
$68$	−114.562	−	41.6973i	−0.204305	−	0.0743608i
$69$		0			0
$70$	−128.752	+	730.189i	−0.219840	+	1.24678i
$71$	569.503	+	986.408i	0.951937	+	1.64880i	0.741227	+	0.671255i	$0.234244\pi$
$71$	569.503	+	986.408i	0.951937	+	1.64880i	0.210710	+	0.977549i	$0.432422\pi$
$72$		0			0
$73$	−139.745	+	242.045i	−0.224054	+	0.388072i	−0.956035	−	0.293252i	$-0.905262\pi$
$73$	−139.745	+	242.045i	−0.224054	+	0.388072i	0.731982	+	0.681324i	$0.238596\pi$
$74$	629.930	+	528.574i	0.989566	+	0.830345i
$75$		0			0
$76$	−96.6823	−	548.312i	−0.145924	−	0.827575i
$77$	209.627	−	175.898i	0.310249	−	0.260330i
$78$		0			0
$79$	−935.039	+	340.327i	−1.33165	+	0.484680i	−0.907172	−	0.420759i	$-0.861764\pi$
$79$	−935.039	+	340.327i	−1.33165	+	0.484680i	−0.424475	+	0.905440i	$0.639541\pi$
$80$	−220.491			−0.308145
$81$		0			0
$82$	321.582			0.433082
$83$	−303.303	+	110.393i	−0.401106	+	0.145991i	−0.534693	−	0.845047i	$-0.679573\pi$
$83$	−303.303	+	110.393i	−0.401106	+	0.145991i	0.133587	+	0.991037i	$0.457350\pi$
$84$		0			0
$85$	−321.751	+	269.981i	−0.410574	+	0.344513i
$86$	−48.7189	−	276.298i	−0.0610871	−	0.346442i
$87$		0			0
$88$	62.3380	+	52.3078i	0.0755143	+	0.0633640i
$89$	297.715	−	515.657i	0.354581	−	0.614152i	−0.632465	−	0.774589i	$-0.717957\pi$
$89$	297.715	−	515.657i	0.354581	−	0.614152i	0.987046	+	0.160437i	$0.0512903\pi$
$90$		0			0
$91$	−769.383	−	1332.61i	−0.886300	−	1.53512i
$92$	1.22224	−	6.93169i	0.00138508	−	0.00785520i
$93$		0			0
$94$	1104.85	+	402.131i	1.21230	+	0.441241i
$95$	−1802.49	−	656.053i	−1.94665	−	0.708522i
$96$		0			0
$97$	75.9826	−	430.919i	0.0795347	−	0.451063i	−0.918868	−	0.394565i	$-0.870895\pi$
$97$	75.9826	−	430.919i	0.0795347	−	0.451063i	0.998403	−	0.0564985i	$-0.0179936\pi$
$98$	−380.714	−	659.416i	−0.392428	−	0.679705i
$99$		0			0
$100$	−129.814	+	224.844i	−0.129814	+	0.224844i
$101$	1153.21	+	967.660i	1.13613	+	0.953325i	0.999305	−	0.0372708i	$-0.0118664\pi$
$101$	1153.21	+	967.660i	1.13613	+	0.953325i	0.136823	+	0.990596i	$0.456311\pi$
$102$		0			0
$103$	134.393	+	762.180i	0.128564	+	0.729125i	0.979127	+	0.203251i	$0.0651506\pi$
$103$	134.393	+	762.180i	0.128564	+	0.729125i	−0.850562	+	0.525874i	$0.823738\pi$
$104$	350.537	−	294.135i	0.330509	−	0.277330i
$105$		0			0
$106$	−953.963	+	347.214i	−0.874124	+	0.318155i
$107$	399.510			0.360954			0.180477	−	0.983579i	$-0.442236\pi$
$107$	399.510			0.360954			0.180477	+	0.983579i	$0.442236\pi$
$108$		0			0
$109$	718.708			0.631557			0.315779	−	0.948833i	$-0.397734\pi$
$109$	718.708			0.631557			0.315779	+	0.948833i	$0.397734\pi$
$110$	263.448	−	95.8873i	0.228353	−	0.0831136i
$111$		0			0
$112$	329.729	−	276.676i	0.278183	−	0.233423i
$113$	109.352	+	620.164i	0.0910349	+	0.516284i	0.995890	+	0.0905658i	$0.0288676\pi$
$113$	109.352	+	620.164i	0.0910349	+	0.516284i	−0.904856	+	0.425719i	$0.860021\pi$
$114$		0			0
$115$	−18.5760	−	15.5871i	−0.0150628	−	0.0126392i
$116$	121.703	−	210.795i	0.0974120	−	0.168723i
$117$		0			0
$118$	11.7141	+	20.2895i	0.00913875	+	0.0158288i
$119$	142.380	−	807.478i	0.109680	−	0.622028i
$120$		0			0
$121$	1153.50	+	419.840i	0.866642	+	0.315432i
$122$	−64.2807	−	23.3962i	−0.0477024	−	0.0173623i
$123$		0			0
$124$	177.759	−	1008.12i	0.128736	−	0.730097i
$125$	−414.062	−	717.176i	−0.296278	−	0.513169i
$126$		0			0
$127$	−566.422	+	981.072i	−0.395763	+	0.685481i	−0.993198	−	0.116436i	$-0.962853\pi$
$127$	−566.422	+	981.072i	−0.395763	+	0.685481i	0.597436	+	0.801917i	$0.296186\pi$
$128$	98.0537	+	82.2768i	0.0677094	+	0.0568149i
$129$		0			0
$130$	−273.754	−	1552.53i	−0.184691	−	1.04743i
$131$	1029.26	−	863.648i	0.686462	−	0.576010i	−0.231425	−	0.972853i	$-0.574339\pi$
$131$	1029.26	−	863.648i	0.686462	−	0.576010i	0.917887	+	0.396843i	$0.129894\pi$
$132$		0			0
$133$	3518.73	−	1280.71i	2.29408	−	0.834976i
$134$	−489.016			−0.315258
$135$		0			0
$136$	243.829			0.153737
$137$	−1543.11	+	561.646i	−0.962313	+	0.350253i	−0.774939	−	0.632036i	$-0.782220\pi$
$137$	−1543.11	+	561.646i	−0.962313	+	0.350253i	−0.187373	+	0.982289i	$0.559997\pi$
$138$		0			0
$139$	627.220	−	526.300i	0.382735	−	0.321153i	−0.431040	−	0.902333i	$-0.641853\pi$
$139$	627.220	−	526.300i	0.382735	−	0.321153i	0.813775	+	0.581180i	$0.197409\pi$
$140$	−257.504	−	1460.38i	−0.155450	−	0.881603i
$141$		0			0
$142$	−1745.06	−	1464.28i	−1.03128	−	0.865348i
$143$	−290.916	+	503.882i	−0.170123	+	0.294663i
$144$		0			0
$145$	−419.286	−	726.224i	−0.240136	−	0.415928i
$146$	97.0658	−	550.488i	0.0550221	−	0.312046i
$147$		0			0
$148$	−1545.45	−	562.497i	−0.858345	−	0.312412i
$149$	801.612	+	291.763i	0.440742	+	0.160417i	0.552853	−	0.833279i	$-0.313539\pi$
$149$	801.612	+	291.763i	0.440742	+	0.160417i	−0.112111	+	0.993696i	$0.535761\pi$
$150$		0			0
$151$	1.74243	−	9.88179i	0.000939050	−	0.00532562i	−0.984335	−	0.176310i	$-0.943584\pi$
$151$	1.74243	−	9.88179i	0.000939050	−	0.00532562i	0.985274	+	0.170985i	$0.0546949\pi$
$152$	556.771	+	964.356i	0.297106	+	0.514602i
$153$		0			0
$154$	−273.648	+	473.972i	−0.143190	+	0.248012i
$155$	−2701.63	−	2266.94i	−1.40000	−	1.17474i
$156$		0			0
$157$	322.652	+	1829.85i	0.164016	+	0.930179i	0.950073	+	0.312026i	$0.101008\pi$
$157$	322.652	+	1829.85i	0.164016	+	0.930179i	−0.786058	+	0.618153i	$0.787881\pi$
$158$	1524.50	−	1279.21i	0.767613	−	0.644104i
$159$		0			0
$160$	414.387	−	150.825i	0.204751	−	0.0745233i
$161$	47.3381			0.0231725
$162$		0			0
$163$	491.591			0.236223			0.118112	−	0.993000i	$-0.462316\pi$
$163$	491.591			0.236223			0.118112	+	0.993000i	$0.462316\pi$
$164$	−604.376	+	219.975i	−0.287767	+	0.104739i
$165$		0			0
$166$	494.509	−	414.942i	0.231213	−	0.194011i
$167$	533.075	+	3023.22i	0.247009	+	1.40086i	0.815780	+	0.578363i	$0.196308\pi$
$167$	533.075	+	3023.22i	0.247009	+	1.40086i	−0.568770	+	0.822496i	$0.692581\pi$
$168$		0			0
$169$	823.297	+	690.829i	0.374737	+	0.314442i
$170$	420.016	−	727.490i	0.189493	−	0.328211i
$171$		0			0
$172$	280.561	+	485.946i	0.124375	+	0.215424i
$173$	328.157	−	1861.07i	0.144216	−	0.817889i	−0.823778	−	0.566913i	$-0.808138\pi$
$173$	328.157	−	1861.07i	0.144216	−	0.817889i	0.967993	−	0.250976i	$-0.0807514\pi$
$174$		0			0
$175$	−1640.82	−	597.208i	−0.708766	−	0.257970i
$176$	−152.938	−	55.6648i	−0.0655007	−	0.0238403i
$177$		0			0
$178$	−206.790	+	1172.77i	−0.0870764	+	0.493835i
$179$	−905.798	−	1568.89i	−0.378226	−	0.655107i	0.612578	−	0.790410i	$-0.290133\pi$
$179$	−905.798	−	1568.89i	−0.378226	−	0.655107i	−0.990804	+	0.135303i	$0.956799\pi$
$180$		0			0
$181$	−1184.56	+	2051.72i	−0.486453	+	0.842561i	−0.999879	−	0.0155730i	$-0.995043\pi$
$181$	−1184.56	+	2051.72i	−0.486453	+	0.842561i	0.513426	+	0.858134i	$0.328376\pi$
$182$	2357.53	+	1978.20i	0.960173	+	0.805681i
$183$		0			0
$184$	2.44449	+	13.8634i	0.000979402	+	0.00555447i
$185$	−4340.43	+	3642.05i	−1.72494	+	1.44740i
$186$		0			0
$187$	−291.334	+	106.037i	−0.113927	+	0.0414662i
$188$	−2351.51			−0.912240
$189$		0			0
$190$	3836.34			1.46483
$191$	3972.67	−	1445.94i	1.50499	−	0.547771i	0.547641	−	0.836713i	$-0.315526\pi$
$191$	3972.67	−	1445.94i	1.50499	−	0.547771i	0.957346	+	0.288943i	$0.0933037\pi$
$192$		0			0
$193$	−403.539	+	338.609i	−0.150505	+	0.126288i	−0.714931	−	0.699195i	$-0.753542\pi$
$193$	−403.539	+	338.609i	−0.150505	+	0.126288i	0.564426	+	0.825483i	$0.309097\pi$
$194$	151.965	+	861.837i	0.0562395	+	0.318950i
$195$		0			0
$196$	1166.58	+	978.873i	0.425137	+	0.356732i
$197$	−1717.86	+	2975.42i	−0.621282	+	1.07609i	0.367965	+	0.929840i	$0.380054\pi$
$197$	−1717.86	+	2975.42i	−0.621282	+	1.07609i	−0.989247	+	0.146252i	$0.953279\pi$
$198$		0			0
$199$	−1803.67	−	3124.05i	−0.642506	−	1.11285i	−0.984871	−	0.173287i	$-0.944561\pi$
$199$	−1803.67	−	3124.05i	−0.642506	−	1.11285i	0.342365	−	0.939567i	$-0.388772\pi$
$200$	90.1677	−	511.366i	0.0318791	−	0.180795i
$201$		0			0
$202$	−2829.25	−	1029.76i	−0.985472	−	0.358682i
$203$	1538.29	+	559.893i	0.531857	+	0.193580i
$204$		0			0
$205$	−384.771	+	2182.14i	−0.131090	+	0.743451i
$206$	−773.938	−	1340.50i	−0.261761	−	0.453384i
$207$		0			0
$208$	−457.593	+	792.574i	−0.152540	+	0.264207i
$209$	−1084.62	−	910.108i	−0.358972	−	0.301213i
$210$		0			0
$211$	−164.252	−	931.522i	−0.0535905	−	0.303927i	0.946217	−	0.323532i	$-0.104870\pi$
$211$	−164.252	−	931.522i	−0.0535905	−	0.303927i	−0.999808	+	0.0196049i	$0.993759\pi$
$212$	1555.36	−	1305.10i	0.503879	−	0.422804i
$213$		0			0
$214$	−750.834	+	273.281i	−0.239841	+	0.0872949i
$215$	1933.16			0.613211
$216$		0			0
$217$	6884.70			2.15375
$218$	−1350.73	+	491.625i	−0.419647	+	0.152739i
$219$		0			0
$220$	−429.530	+	360.418i	−0.131631	+	0.110452i
$221$	302.730	+	1716.87i	0.0921440	+	0.522574i
$222$		0			0
$223$	−120.255	−	100.906i	−0.0361114	−	0.0303011i	0.624553	−	0.780982i	$-0.285281\pi$
$223$	−120.255	−	100.906i	−0.0361114	−	0.0303011i	−0.660665	+	0.750681i	$0.729725\pi$
$224$	−430.431	+	745.528i	−0.128390	+	0.222378i
$225$		0			0
$226$	−629.731	−	1090.73i	−0.185350	−	0.321036i
$227$	−14.1015	+	79.9735i	−0.00412312	+	0.0233834i	−0.986800	−	0.161944i	$-0.948224\pi$
$227$	−14.1015	+	79.9735i	−0.00412312	+	0.0233834i	0.982677	+	0.185328i	$0.0593346\pi$
$228$		0			0
$229$	−4651.51	−	1693.01i	−1.34227	−	0.488547i	−0.431745	−	0.901996i	$-0.642102\pi$
$229$	−4651.51	−	1693.01i	−1.34227	−	0.488547i	−0.910527	+	0.413449i	$0.864324\pi$
$230$	45.5736	+	16.5875i	0.0130654	+	0.00475541i
$231$		0			0
$232$	−84.5337	+	479.414i	−0.0239220	+	0.135668i
$233$	1647.07	+	2852.82i	0.463105	+	0.802121i	0.999114	−	0.0420911i	$-0.0134020\pi$
$233$	1647.07	+	2852.82i	0.463105	+	0.802121i	−0.536009	+	0.844212i	$0.680069\pi$
$234$		0			0
$235$	−4050.67	+	7015.96i	−1.12441	+	1.94754i
$236$	−35.8942	−	30.1188i	−0.00990047	−	0.00830748i
$237$		0			0
$238$	284.760	+	1614.96i	0.0775558	+	0.439841i
$239$	802.343	−	673.246i	0.217152	−	0.182212i	−0.527723	−	0.849417i	$-0.676954\pi$
$239$	802.343	−	673.246i	0.217152	−	0.182212i	0.744874	+	0.667205i	$0.232509\pi$
$240$		0			0
$241$	1797.85	−	654.363i	0.480537	−	0.174901i	−0.0903825	−	0.995907i	$-0.528809\pi$
$241$	1797.85	−	654.363i	0.480537	−	0.174901i	0.570920	+	0.821006i	$0.306587\pi$
$242$	−2455.06			−0.652137
$243$		0			0
$244$	136.812			0.0358955
$245$	4930.09	−	1794.41i	1.28560	−	0.467920i
$246$		0			0
$247$	−6099.02	+	5117.68i	−1.57114	+	1.31834i
$248$	355.518	+	2016.24i	0.0910300	+	0.516257i
$249$		0			0
$250$	1268.76	+	1064.61i	0.320973	+	0.269329i
$251$	2116.15	−	3665.28i	0.532152	−	0.921714i	−0.467144	−	0.884181i	$-0.654717\pi$
$251$	2116.15	−	3665.28i	0.532152	−	0.921714i	0.999295	−	0.0375325i	$-0.0119498\pi$
$252$		0			0
$253$	−8.94966	−	15.5013i	−0.00222395	−	0.00385200i
$254$	393.433	−	2231.27i	0.0971896	−	0.551190i
$255$		0			0
$256$	−240.561	−	87.5572i	−0.0587308	−	0.0213763i
$257$	6312.13	+	2297.43i	1.53206	+	0.557625i	0.964125	−	0.265448i	$-0.0855198\pi$
$257$	6312.13	+	2297.43i	1.53206	+	0.557625i	0.567936	+	0.823073i	$0.307742\pi$
$258$		0			0
$259$	1920.71	−	10892.9i	0.460800	−	2.61333i
$260$	1576.48	+	2730.55i	0.376036	+	0.651314i
$261$		0			0
$262$	−1343.60	+	2327.18i	−0.316824	+	0.548755i
$263$	−4258.30	−	3573.14i	−0.998395	−	0.837753i	−0.0116336	−	0.999932i	$-0.503703\pi$
$263$	−4258.30	−	3573.14i	−0.998395	−	0.837753i	−0.986761	+	0.162180i	$0.948148\pi$
$264$		0			0
$265$	−1214.66	−	6888.71i	−0.281571	−	1.59687i
$266$	−5736.99	+	4813.90i	−1.32240	+	1.10962i
$267$		0			0
$268$	919.049	−	334.506i	0.209477	−	0.0762434i
$269$	−2591.71			−0.587432			−0.293716	−	0.955893i	$-0.594892\pi$
$269$	−2591.71			−0.587432			−0.293716	+	0.955893i	$0.594892\pi$
$270$		0			0
$271$	−2987.39			−0.669636			−0.334818	−	0.942283i	$-0.608675\pi$
$271$	−2987.39			−0.669636			−0.334818	+	0.942283i	$0.608675\pi$
$272$	−458.249	+	166.789i	−0.102152	+	0.0371804i
$273$		0			0
$274$	2515.91	−	2111.10i	0.554714	−	0.465461i
$275$	114.649	+	650.206i	0.0251403	+	0.142578i
$276$		0			0
$277$	733.702	+	615.649i	0.159147	+	0.133541i	0.718884	−	0.695130i	$-0.244653\pi$
$277$	733.702	+	615.649i	0.159147	+	0.133541i	−0.559737	+	0.828671i	$0.689098\pi$
$278$	−818.778	+	1418.17i	−0.176644	+	0.305956i
$279$		0			0
$280$	1482.91	+	2568.47i	0.316502	+	0.548198i
$281$	−1594.63	+	9043.59i	−0.338532	+	1.91991i	0.0505761	+	0.998720i	$0.483894\pi$
$281$	−1594.63	+	9043.59i	−0.338532	+	1.91991i	−0.389108	+	0.921192i	$0.627217\pi$
$282$		0			0
$283$	3722.53	+	1354.89i	0.781913	+	0.284593i	0.701970	−	0.712206i	$-0.252304\pi$
$283$	3722.53	+	1354.89i	0.781913	+	0.284593i	0.0799430	+	0.996799i	$0.474526\pi$
$284$	4281.26	+	1558.25i	0.894528	+	0.325582i
$285$		0			0
$286$	202.068	−	1145.99i	0.0417782	−	0.236936i
$287$	−2162.79	−	3746.06i	−0.444828	−	0.770464i
$288$		0			0
$289$	1992.03	−	3450.29i	0.405460	−	0.702278i
$290$	1284.77	+	1078.05i	0.260152	+	0.218293i
$291$		0			0
$292$	194.132	+	1100.98i	0.0389065	+	0.220650i
$293$	2657.44	−	2229.86i	0.529862	−	0.444607i	−0.338192	−	0.941077i	$-0.609815\pi$
$293$	2657.44	−	2229.86i	0.529862	−	0.444607i	0.868054	+	0.496470i	$0.165371\pi$
$294$		0			0
$295$	−151.693	+	55.2118i	−0.0299387	+	0.0108968i
$296$	3289.26			0.645893
$297$		0			0
$298$	−1706.11			−0.331653
$299$	−94.5807	+	34.4246i	−0.0182935	+	0.00665828i
$300$		0			0
$301$	−2890.91	+	2425.76i	−0.553586	+	0.464513i
$302$	3.48485	+	19.7636i	0.000664009	+	0.00376578i
$303$		0			0
$304$	−1706.05	−	1431.54i	−0.321870	−	0.270081i
$305$	235.670	−	408.193i	0.0442441	−	0.0766330i
$306$		0			0
$307$	1230.80	+	2131.80i	0.228812	+	0.396314i	0.957456	−	0.288578i	$-0.0931825\pi$
$307$	1230.80	+	2131.80i	0.228812	+	0.396314i	−0.728644	+	0.684892i	$0.759849\pi$
$308$	190.074	−	1077.96i	0.0351639	−	0.199424i
$309$		0			0
$310$	6628.08	+	2412.42i	1.21435	+	0.441989i
$311$	−7334.30	−	2669.47i	−1.33727	−	0.486725i	−0.428316	−	0.903629i	$-0.640893\pi$
$311$	−7334.30	−	2669.47i	−1.33727	−	0.486725i	−0.908951	+	0.416904i	$0.863115\pi$
$312$		0			0
$313$	−1268.22	+	7192.43i	−0.229022	+	1.29885i	0.625822	+	0.779966i	$0.284763\pi$
$313$	−1268.22	+	7192.43i	−0.229022	+	1.29885i	−0.854845	+	0.518884i	$0.826348\pi$
$314$	−1858.08	−	3218.29i	−0.333941	−	0.578404i
$315$		0			0
$316$	−1990.10	+	3446.95i	−0.354277	+	0.613626i
$317$	−2895.87	−	2429.92i	−0.513086	−	0.430530i	0.349128	−	0.937075i	$-0.386478\pi$
$317$	−2895.87	−	2429.92i	−0.513086	−	0.430530i	−0.862213	+	0.506545i	$0.830922\pi$
$318$		0			0
$319$	−107.485	−	609.579i	−0.0188653	−	0.106990i
$320$	−675.623	+	566.915i	−0.118026	+	0.0990359i
$321$		0			0
$322$	−88.9666	+	32.3812i	−0.0153972	+	0.00560414i
$323$	−4242.41			−0.730817
$324$		0			0
$325$	3712.62			0.633658
$326$	−923.889	+	336.268i	−0.156962	+	0.0571293i
$327$		0			0
$328$	985.383	−	826.835i	0.165880	−	0.139190i
$329$	−2746.25	−	15574.7i	−0.460199	−	2.60992i
$330$		0			0
$331$	−2464.36	−	2067.84i	−0.409225	−	0.343381i	0.414821	−	0.909903i	$-0.363844\pi$
$331$	−2464.36	−	2067.84i	−0.409225	−	0.343381i	−0.824046	+	0.566522i	$0.808288\pi$
$332$	−645.536	+	1118.10i	−0.106712	+	0.184831i
$333$		0			0
$334$	−3069.85	−	5317.14i	−0.502919	−	0.871081i
$335$	585.104	−	3318.29i	0.0954259	−	0.541187i
$336$		0			0
$337$	8275.33	+	3011.97i	1.33764	+	0.486862i	0.909070	−	0.416644i	$-0.136794\pi$
$337$	8275.33	+	3011.97i	1.33764	+	0.486862i	0.428574	+	0.903507i	$0.359016\pi$
$338$	−2019.85	−	735.164i	−0.325045	−	0.118307i
$339$		0			0
$340$	−291.740	+	1654.54i	−0.0465348	+	0.263912i
$341$	−1301.61	−	2254.45i	−0.206704	−	0.358022i
$342$		0			0
$343$	−507.289	+	878.650i	−0.0798572	+	0.138317i
$344$	−859.688	−	721.364i	−0.134742	−	0.113062i
$345$		0			0
$346$	656.315	+	3722.15i	0.101976	+	0.578335i
$347$	−1675.54	+	1405.94i	−0.259215	+	0.217507i	−0.763128	−	0.646247i	$-0.776338\pi$
$347$	−1675.54	+	1405.94i	−0.259215	+	0.217507i	0.503913	+	0.863754i	$0.331893\pi$
$348$		0			0
$349$	−2990.01	+	1088.28i	−0.458601	+	0.166917i	−0.560982	−	0.827828i	$-0.689576\pi$
$349$	−2990.01	+	1088.28i	−0.458601	+	0.166917i	0.102381	+	0.994745i	$0.467354\pi$
$350$	3492.24			0.533338
$351$		0			0
$352$	325.506			0.0492884
$353$	4906.13	−	1785.68i	0.739736	−	0.269242i	0.0554559	−	0.998461i	$-0.482339\pi$
$353$	4906.13	−	1785.68i	0.739736	−	0.269242i	0.684280	+	0.729219i	$0.260117\pi$
$354$		0			0
$355$	12024.0	−	10089.4i	1.79766	−	1.50842i
$356$	−413.581	−	2345.53i	−0.0615723	−	0.349194i
$357$		0			0
$358$	2775.53	+	2328.94i	0.409752	+	0.343822i
$359$	−903.145	+	1564.29i	−0.132775	+	0.229973i	−0.924745	−	0.380587i	$-0.875722\pi$
$359$	−903.145	+	1564.29i	−0.132775	+	0.229973i	0.791970	+	0.610559i	$0.209055\pi$
$360$		0			0
$361$	−6257.81	−	10838.8i	−0.912350	−	1.58024i
$362$	822.789	−	4666.27i	0.119461	−	0.677497i
$363$		0			0
$364$	−5783.87	−	2105.16i	−0.832849	−	0.303132i
$365$	3619.28	+	1317.31i	0.519019	+	0.188907i
$366$		0			0
$367$	453.766	−	2573.43i	0.0645405	−	0.366027i	−0.935383	−	0.353637i	$-0.884945\pi$
$367$	453.766	−	2573.43i	0.0645405	−	0.366027i	0.999923	−	0.0123904i	$-0.00394408\pi$
$368$	−14.0772	−	24.3825i	−0.00199410	−	0.00345387i
$369$		0			0
$370$	5666.03	−	9813.85i	0.796116	−	1.37891i
$371$	10460.5	+	8777.42i	1.46384	+	1.22830i
$372$		0			0
$373$	25.2234	+	143.049i	0.00350140	+	0.0198574i	0.986508	−	0.163711i	$-0.0523463\pi$
$373$	25.2234	+	143.049i	0.00350140	+	0.0198574i	−0.983007	+	0.183568i	$0.941235\pi$
$374$	474.995	−	398.568i	0.0656722	−	0.0551055i
$375$		0			0
$376$	4419.39	−	1608.52i	0.606150	−	0.220621i
$377$	−3480.64			−0.475496
$378$		0			0
$379$	9238.34			1.25209			0.626044	−	0.779787i	$-0.284673\pi$
$379$	9238.34			1.25209			0.626044	+	0.779787i	$0.284673\pi$
$380$	−7209.96	+	2624.21i	−0.973324	+	0.354261i
$381$		0			0
$382$	−6477.11	+	5434.94i	−0.867533	+	0.727947i
$383$	−864.219	−	4901.23i	−0.115299	−	0.653893i	−0.986602	−	0.163147i	$-0.947835\pi$
$383$	−864.219	−	4901.23i	−0.115299	−	0.653893i	0.871303	−	0.490746i	$-0.163276\pi$
$384$		0			0
$385$	−2888.80	−	2423.99i	−0.382407	−	0.320877i
$386$	526.783	−	912.415i	0.0694625	−	0.120313i
$387$		0			0
$388$	−875.132	−	1515.77i	−0.114505	−	0.198329i
$389$	−598.380	+	3393.58i	−0.0779925	+	0.442317i	0.920657	+	0.390371i	$0.127653\pi$
$389$	−598.380	+	3393.58i	−0.0779925	+	0.442317i	−0.998650	+	0.0519458i	$0.983458\pi$
$390$		0			0
$391$	−50.3975	−	18.3432i	−0.00651845	−	0.00237252i
$392$	−2862.03	−	1041.69i	−0.368761	−	0.134218i
$393$		0			0
$394$	1193.21	−	6767.05i	0.152572	−	0.865277i
$395$	6856.22	+	11875.3i	0.873351	+	1.51269i
$396$		0			0
$397$	−588.400	+	1019.14i	−0.0743852	+	0.128839i	−0.900819	−	0.434195i	$-0.857033\pi$
$397$	−588.400	+	1019.14i	−0.0743852	+	0.128839i	0.826434	+	0.563034i	$0.190366\pi$
$398$	5526.76	+	4637.51i	0.696060	+	0.584063i
$399$		0			0
$400$	180.335	+	1022.73i	0.0225419	+	0.127842i
$401$	6328.88	−	5310.56i	0.788152	−	0.661338i	−0.157135	−	0.987577i	$-0.550226\pi$
$401$	6328.88	−	5310.56i	0.788152	−	0.661338i	0.945287	+	0.326239i	$0.105781\pi$
$402$		0			0
$403$	−13755.5	+	5006.60i	−1.70027	+	0.618849i
$404$	6021.65			0.741555
$405$		0			0
$406$	−3274.03			−0.400216
$407$	−3930.10	+	1430.44i	−0.478643	+	0.174212i
$408$		0			0
$409$	5891.08	−	4943.20i	0.712213	−	0.597618i	−0.213006	−	0.977051i	$-0.568325\pi$
$409$	5891.08	−	4943.20i	0.712213	−	0.597618i	0.925219	+	0.379433i	$0.123881\pi$
$410$	−769.541	−	4364.28i	−0.0926949	−	0.525699i
$411$		0			0
$412$	2371.48	+	1989.91i	0.283579	+	0.237951i
$413$	157.566	−	272.913i	0.0187732	−	0.0325161i
$414$		0			0
$415$	2223.98	+	3852.04i	0.263062	+	0.455637i
$416$	317.841	−	1802.56i	0.0374601	−	0.212447i
$417$		0			0
$418$	2660.98	+	968.517i	0.311370	+	0.113329i
$419$	−506.294	−	184.276i	−0.0590312	−	0.0214856i	0.312336	−	0.949972i	$-0.398889\pi$
$419$	−506.294	−	184.276i	−0.0590312	−	0.0214856i	−0.371367	+	0.928486i	$0.621111\pi$
$420$		0			0
$421$	−1842.80	+	10451.0i	−0.213331	+	1.20986i	0.670447	+	0.741957i	$0.266102\pi$
$421$	−1842.80	+	10451.0i	−0.213331	+	1.20986i	−0.883779	+	0.467905i	$0.845009\pi$
$422$	945.892	+	1638.33i	0.109112	+	0.188988i
$423$		0			0
$424$	−2030.37	+	3516.71i	−0.232556	+	0.402798i
$425$	1515.45	+	1271.61i	0.172965	+	0.145135i
$426$		0			0
$427$	159.778	+	906.149i	0.0181082	+	0.102697i
$428$	1224.17	−	1027.20i	0.138254	−	0.116009i
$429$		0			0
$430$	−3633.15	+	1322.36i	−0.407456	+	0.148302i
$431$	9434.05			1.05434			0.527172	−	0.849759i	$-0.323252\pi$
$431$	9434.05			1.05434			0.527172	+	0.849759i	$0.323252\pi$
$432$		0			0
$433$	−15555.1			−1.72640			−0.863199	−	0.504864i	$-0.831543\pi$
$433$	−15555.1			−1.72640			−0.863199	+	0.504864i	$0.831543\pi$
$434$	−12939.0	+	4709.41i	−1.43109	+	0.520873i
$435$		0			0
$436$	2202.25	−	1847.91i	0.241901	−	0.202979i
$437$	−42.5319	−	241.210i	−0.00465578	−	0.0264042i
$438$		0			0
$439$	5470.90	+	4590.63i	0.594788	+	0.499086i	0.889766	−	0.456418i	$-0.150868\pi$
$439$	5470.90	+	4590.63i	0.594788	+	0.499086i	−0.294978	+	0.955504i	$0.595312\pi$
$440$	560.711	−	971.181i	0.0607520	−	0.105225i
$441$		0			0
$442$	−1743.35	−	3019.57i	−0.187608	−	0.324947i
$443$	−1999.57	+	11340.1i	−0.214452	+	1.21622i	0.667403	+	0.744697i	$0.267406\pi$
$443$	−1999.57	+	11340.1i	−0.214452	+	1.21622i	−0.881855	+	0.471521i	$0.843705\pi$
$444$		0			0
$445$	−7710.56	−	2806.42i	−0.821384	−	0.298959i
$446$	295.028	+	107.382i	0.0313229	+	0.0114006i
$447$		0			0
$448$	298.974	−	1695.57i	0.0315295	−	0.178813i
$449$	−2556.93	−	4428.73i	−0.268750	−	0.465489i	0.699789	−	0.714349i	$-0.253277\pi$
$449$	−2556.93	−	4428.73i	−0.268750	−	0.465489i	−0.968539	+	0.248860i	$0.919944\pi$
$450$		0			0
$451$	−817.787	+	1416.45i	−0.0853838	+	0.147889i
$452$	1929.61	+	1619.13i	0.200799	+	0.168490i
$453$		0			0
$454$	−28.2030	−	159.947i	−0.00291549	−	0.0165346i
$455$	−16244.2	+	13630.5i	−1.67371	+	1.40441i
$456$		0			0
$457$	379.505	−	138.129i	0.0388457	−	0.0141387i	−0.322524	−	0.946561i	$-0.604531\pi$
$457$	379.505	−	138.129i	0.0388457	−	0.0141387i	0.361370	+	0.932423i	$0.382309\pi$
$458$	9900.06			1.01004
$459$		0			0
$460$	−96.9969			−0.00983153
$461$	−6952.08	+	2530.35i	−0.702366	+	0.255640i	−0.668421	−	0.743783i	$-0.733029\pi$
$461$	−6952.08	+	2530.35i	−0.702366	+	0.255640i	−0.0339453	+	0.999424i	$0.510807\pi$
$462$		0			0
$463$	2874.14	−	2411.69i	0.288494	−	0.242075i	−0.487042	−	0.873378i	$-0.661924\pi$
$463$	2874.14	−	2411.69i	0.288494	−	0.242075i	0.775536	+	0.631304i	$0.217480\pi$
$464$	−169.067	−	958.829i	−0.0169154	−	0.0959321i
$465$		0			0
$466$	−5046.93	−	4234.88i	−0.501705	−	0.420980i
$467$	3375.01	−	5845.69i	0.334426	−	0.579242i	−0.648949	−	0.760832i	$-0.724791\pi$
$467$	3375.01	−	5845.69i	0.334426	−	0.579242i	0.983374	+	0.181590i	$0.0581244\pi$
$468$		0			0
$469$	3288.87	+	5696.48i	0.323808	+	0.560851i
$470$	2813.56	−	15956.5i	0.276128	−	1.56600i
$471$		0			0
$472$	88.0615	+	32.0517i	0.00858762	+	0.00312564i
$473$	1340.89	+	488.043i	0.130347	+	0.0474423i
$474$		0			0
$475$	−1568.84	+	8897.31i	−0.151543	+	0.859446i
$476$	−1639.87	−	2840.34i	−0.157906	−	0.273501i
$477$		0			0
$478$	−1047.38	+	1814.12i	−0.100222	+	0.173590i
$479$	−10684.4	−	8965.27i	−1.01917	−	0.855186i	−0.0296473	−	0.999560i	$-0.509438\pi$
$479$	−10684.4	−	8965.27i	−1.01917	−	0.855186i	−0.989523	+	0.144375i	$0.953883\pi$
$480$		0			0
$481$	4083.83	+	23160.6i	0.387124	+	2.19549i
$482$	−2931.24	+	2459.60i	−0.277000	+	0.232431i
$483$		0			0
$484$	4614.00	−	1679.36i	0.433321	−	0.157716i
$485$	−6029.96			−0.564549
$486$		0			0
$487$	3227.46			0.300308			0.150154	−	0.988663i	$-0.452023\pi$
$487$	3227.46			0.300308			0.150154	+	0.988663i	$0.452023\pi$
$488$	−257.123	+	93.5850i	−0.0238512	+	0.00868113i
$489$		0			0
$490$	−8038.09	+	6744.76i	−0.741070	+	0.621831i
$491$	2316.31	+	13136.4i	0.212899	+	1.20741i	0.884515	+	0.466512i	$0.154490\pi$
$491$	2316.31	+	13136.4i	0.212899	+	1.20741i	−0.671615	+	0.740900i	$0.734399\pi$
$492$		0			0
$493$	−1420.76	−	1192.16i	−0.129792	−	0.108909i
$494$	7961.70	−	13790.1i	0.725129	−	1.25596i
$495$		0			0
$496$	−2047.35	−	3546.11i	−0.185340	−	0.321018i
$497$	−5320.83	+	30175.9i	−0.480225	+	2.72349i
$498$		0			0
$499$	8134.10	+	2960.57i	0.729724	+	0.265598i	0.680048	−	0.733167i	$-0.261959\pi$
$499$	8134.10	+	2960.57i	0.729724	+	0.265598i	0.0496762	+	0.998765i	$0.484181\pi$
$500$	−3112.73	−	1132.94i	−0.278411	−	0.101333i
$501$		0			0
$502$	−1469.86	+	8336.00i	−0.130684	+	0.741143i
$503$	2596.61	+	4497.45i	0.230173	+	0.398671i	0.957859	−	0.287239i	$-0.0927375\pi$
$503$	2596.61	+	4497.45i	0.230173	+	0.398671i	−0.727686	+	0.685910i	$0.759404\pi$
$504$		0			0
$505$	10372.8	−	17966.2i	0.914026	−	1.58314i
$506$	27.4234	+	23.0109i	0.00240932	+	0.00202166i
$507$		0			0
$508$	786.865	+	4462.54i	0.0687234	+	0.389750i
$509$	10201.5	−	8560.07i	0.888356	−	0.745419i	−0.0795235	−	0.996833i	$-0.525340\pi$
$509$	10201.5	−	8560.07i	0.888356	−	0.745419i	0.967880	+	0.251414i	$0.0808954\pi$
$510$		0			0
$511$	−7065.38	+	2571.59i	−0.611652	+	0.222623i
$512$	512.000			0.0441942
$513$		0			0
$514$	−13434.5			−1.15286
$515$	10022.2	−	3647.78i	0.857534	−	0.312117i
$516$		0			0
$517$	−4580.88	+	3843.82i	−0.389685	+	0.326984i
$518$	3841.42	+	21785.8i	0.325835	+	1.84790i
$519$		0			0
$520$	−4830.63	−	4053.38i	−0.407379	−	0.341832i
$521$	−5378.71	+	9316.20i	−0.452295	+	0.783398i	−0.998528	−	0.0542354i	$-0.982728\pi$
$521$	−5378.71	+	9316.20i	−0.452295	+	0.783398i	0.546233	+	0.837633i	$0.316061\pi$
$522$		0			0
$523$	9388.78	+	16261.8i	0.784976	+	1.35962i	0.929013	+	0.370046i	$0.120658\pi$
$523$	9388.78	+	16261.8i	0.784976	+	1.35962i	−0.144037	+	0.989572i	$0.546009\pi$
$524$	933.254	−	5292.74i	0.0778042	−	0.441249i
$525$		0			0
$526$	10447.1	+	3802.45i	0.866003	+	0.315199i
$527$	−7329.65	−	2667.77i	−0.605853	−	0.220512i
$528$		0			0
$529$	−2112.24	+	11979.1i	−0.173604	+	0.984557i
$530$	6994.98	+	12115.7i	0.573287	+	0.992963i
$531$		0			0
$532$	7489.11	−	12971.5i	0.610327	−	1.05712i
$533$	7045.38	+	5911.78i	0.572550	+	0.480427i
$534$		0			0
$535$	−956.024	−	5421.88i	−0.0772570	−	0.438146i
$536$	−1498.43	+	1257.33i	−0.120751	+	0.101322i
$537$		0			0
$538$	4870.82	−	1772.83i	0.390327	−	0.142067i
$539$	3872.65			0.309474
$540$		0			0
$541$	3383.92			0.268921			0.134460	−	0.990919i	$-0.457070\pi$
$541$	3383.92			0.268921			0.134460	+	0.990919i	$0.457070\pi$
$542$	5614.46	−	2043.50i	0.444948	−	0.161948i
$543$		0			0
$544$	747.136	−	626.922i	0.0588845	−	0.0494100i
$545$	−1719.86	−	9753.81i	−0.135176	−	0.766619i
$546$		0			0
$547$	−5495.82	−	4611.54i	−0.429587	−	0.360467i	0.402209	−	0.915548i	$-0.368243\pi$
$547$	−5495.82	−	4611.54i	−0.429587	−	0.360467i	−0.831796	+	0.555081i	$0.812687\pi$
$548$	−3284.29	+	5688.55i	−0.256018	+	0.443436i
$549$		0			0
$550$	−660.237	−	1143.56i	−0.0511865	−	0.0886577i
$551$	1470.81	−	8341.37i	0.113718	−	0.644926i
$552$		0			0
$553$	−25154.4	−	9155.44i	−1.93431	−	0.704031i
$554$	−1800.04	−	655.160i	−0.138044	−	0.0502438i
$555$		0			0
$556$	568.717	−	3225.36i	0.0433795	−	0.246017i
$557$	−11939.9	−	20680.4i	−0.908273	−	1.57317i	−0.816463	−	0.577398i	$-0.804068\pi$
$557$	−11939.9	−	20680.4i	−0.908273	−	1.57317i	−0.0918105	−	0.995776i	$-0.529265\pi$
$558$		0			0
$559$	4011.96	−	6948.91i	0.303556	−	0.525774i
$560$	−4543.89	−	3812.78i	−0.342883	−	0.287713i
$561$		0			0
$562$	−3189.26	−	18087.2i	−0.239378	−	1.35758i
$563$	7653.84	−	6422.33i	0.572950	−	0.480762i	−0.309673	−	0.950843i	$-0.600220\pi$
$563$	7653.84	−	6422.33i	0.572950	−	0.480762i	0.882623	+	0.470081i	$0.155775\pi$
$564$		0			0
$565$	8154.77	−	2968.09i	0.607210	−	0.221006i
$566$	−7922.87			−0.588380
$567$		0			0
$568$	−9112.04			−0.673121
$569$	2763.29	−	1005.76i	0.203591	−	0.0741010i	−0.238212	−	0.971213i	$-0.576561\pi$
$569$	2763.29	−	1005.76i	0.203591	−	0.0741010i	0.441803	+	0.897112i	$0.354339\pi$
$570$		0			0
$571$	4391.79	−	3685.15i	0.321875	−	0.270085i	−0.467504	−	0.883991i	$-0.654847\pi$
$571$	4391.79	−	3685.15i	0.321875	−	0.270085i	0.789380	+	0.613905i	$0.210402\pi$
$572$	404.137	+	2291.97i	0.0295416	+	0.167539i
$573$		0			0
$574$	6627.18	+	5560.86i	0.481904	+	0.404366i
$575$	−57.1069	+	98.9120i	−0.00414178	+	0.00717377i
$576$		0			0
$577$	−723.163	−	1252.55i	−0.0521762	−	0.0903718i	0.838758	−	0.544505i	$-0.183282\pi$
$577$	−723.163	−	1252.55i	−0.0521762	−	0.0903718i	−0.890934	+	0.454133i	$0.849949\pi$
$578$	−1383.65	+	7847.05i	−0.0995711	+	0.564696i
$579$		0			0
$580$	−3152.00	−	1147.23i	−0.225654	−	0.0821315i
$581$	−8159.42	−	2969.79i	−0.582633	−	0.212061i
$582$		0			0
$583$	896.592	−	5084.83i	0.0636931	−	0.361221i
$584$	−1117.96	−	1936.36i	−0.0792149	−	0.137204i
$585$		0			0
$586$	−3469.05	+	6008.57i	−0.244548	+	0.423569i
$587$	−13424.8	−	11264.7i	−0.943954	−	0.792071i	0.0343152	−	0.999411i	$-0.489075\pi$
$587$	−13424.8	−	11264.7i	−0.943954	−	0.792071i	−0.978269	+	0.207340i	$0.933519\pi$
$588$		0			0
$589$	−6185.69	−	35080.8i	−0.432728	−	2.45412i
$590$	247.323	−	207.529i	0.0172578	−	0.0144810i
$591$		0			0
$592$	−6181.79	+	2249.99i	−0.429172	+	0.156206i
$593$	6852.33			0.474522			0.237261	−	0.971446i	$-0.423750\pi$
$593$	6852.33			0.474522			0.237261	+	0.971446i	$0.423750\pi$
$594$		0			0
$595$	−11299.2			−0.778528
$596$	3206.45	−	1167.05i	0.220371	−	0.0802085i
$597$		0			0
$598$	154.206	−	129.394i	0.0105451	−	0.00884836i
$599$	−1720.88	−	9759.60i	−0.117384	−	0.665720i	−0.985542	−	0.169432i	$-0.945807\pi$
$599$	−1720.88	−	9759.60i	−0.117384	−	0.665720i	0.868157	−	0.496289i	$-0.165304\pi$
$600$		0			0
$601$	7800.33	+	6545.25i	0.529421	+	0.444237i	0.867901	−	0.496736i	$-0.165468\pi$
$601$	7800.33	+	6545.25i	0.529421	+	0.444237i	−0.338480	+	0.940973i	$0.609913\pi$
$602$	3773.81	−	6536.44i	0.255497	−	0.442534i
$603$		0			0
$604$	−20.0685	−	34.7596i	−0.00135194	−	0.00234164i
$605$	2937.46	−	16659.2i	0.197396	−	1.11949i
$606$		0			0
$607$	16806.1	+	6116.91i	1.12378	+	0.409024i	0.836032	−	0.548681i	$-0.184870\pi$
$607$	16806.1	+	6116.91i	1.12378	+	0.409024i	0.287753	+	0.957705i	$0.407092\pi$
$608$	4185.55	+	1523.41i	0.279188	+	0.101616i
$609$		0			0
$610$	−163.695	+	928.360i	−0.0108653	+	0.0616200i
$611$	16813.0	+	29121.0i	1.11323	+	1.92817i
$612$		0			0
$613$	6907.19	−	11963.6i	0.455104	−	0.788263i	−0.543590	−	0.839351i	$-0.682936\pi$
$613$	6907.19	−	11963.6i	0.455104	−	0.788263i	0.998694	+	0.0510878i	$0.0162688\pi$
$614$	−3771.38	−	3164.57i	−0.247884	−	0.207999i
$615$		0			0
$616$	380.148	+	2155.93i	0.0248646	+	0.141014i
$617$	13558.4	−	11376.8i	0.884668	−	0.742325i	−0.0824654	−	0.996594i	$-0.526279\pi$
$617$	13558.4	−	11376.8i	0.884668	−	0.742325i	0.967133	+	0.254269i	$0.0818350\pi$
$618$		0			0
$619$	23983.6	−	8729.32i	1.55732	−	0.566819i	0.587202	−	0.809440i	$-0.300229\pi$
$619$	23983.6	−	8729.32i	1.55732	−	0.566819i	0.970121	+	0.242621i	$0.0780071\pi$
$620$	−14106.9			−0.913786
$621$		0			0
$622$	15610.0			1.00628
$623$	15052.2	−	5478.54i	0.967982	−	0.352317i
$624$		0			0
$625$	−14957.4	+	12550.7i	−0.957272	+	0.803246i
$626$	−2536.44	−	14384.9i	−0.161943	−	0.918425i
$627$		0			0
$628$	5693.49	+	4777.41i	0.361776	+	0.303566i
$629$	−6265.77	+	10852.6i	−0.397190	+	0.687953i
$630$		0			0
$631$	10546.5	+	18267.2i	0.665375	+	1.15246i	0.979184	+	0.202976i	$0.0650615\pi$
$631$	10546.5	+	18267.2i	0.665375	+	1.15246i	−0.313809	+	0.949486i	$0.601605\pi$
$632$	1382.31	−	7839.45i	0.0870019	−	0.493412i
$633$		0			0
$634$	7104.61	+	2585.87i	0.445048	+	0.161984i
$635$	14669.9	+	5339.40i	0.916781	+	0.333681i
$636$		0			0
$637$	3781.45	−	21445.7i	0.235206	−	1.33392i
$638$	618.983	+	1072.11i	0.0384103	+	0.0665286i
$639$		0			0
$640$	881.963	−	1527.60i	0.0544729	−	0.0943498i
$641$	−11013.8	−	9241.67i	−0.678656	−	0.569460i	0.236957	−	0.971520i	$-0.423850\pi$
$641$	−11013.8	−	9241.67i	−0.678656	−	0.569460i	−0.915613	+	0.402060i	$0.868294\pi$
$642$		0			0
$643$	491.866	+	2789.51i	0.0301668	+	0.171085i	0.996169	−	0.0874495i	$-0.0278716\pi$
$643$	491.866	+	2789.51i	0.0301668	+	0.171085i	−0.966002	+	0.258534i	$0.916761\pi$
$644$	145.052	−	121.713i	0.00887557	−	0.00744749i
$645$		0			0
$646$	7973.12	−	2901.98i	0.485601	−	0.176744i
$647$	−7731.84			−0.469814			−0.234907	−	0.972018i	$-0.575479\pi$
$647$	−7731.84			−0.469814			−0.234907	+	0.972018i	$0.575479\pi$
$648$		0			0
$649$	−119.157			−0.00720696
$650$	−6977.44	+	2539.58i	−0.421042	+	0.153247i
$651$		0			0
$652$	1506.32	−	1263.95i	0.0904787	−	0.0759206i
$653$	4227.92	+	23977.7i	0.253371	+	1.43694i	0.800220	+	0.599707i	$0.204716\pi$
$653$	4227.92	+	23977.7i	0.253371	+	1.43694i	−0.546848	+	0.837232i	$0.684173\pi$
$654$		0			0
$655$	−14183.8	−	11901.7i	−0.846120	−	0.709979i
$656$	−1286.33	+	2227.98i	−0.0765589	+	0.132604i
$657$		0			0
$658$	15815.0	+	27392.4i	0.936981	+	1.62290i
$659$	569.244	−	3228.34i	0.0336489	−	0.190832i	−0.963350	−	0.268247i	$-0.913556\pi$
$659$	569.244	−	3228.34i	0.0336489	−	0.190832i	0.996999	+	0.0774151i	$0.0246667\pi$
$660$		0			0
$661$	−9754.90	−	3550.49i	−0.574011	−	0.208923i	0.0386714	−	0.999252i	$-0.487687\pi$
$661$	−9754.90	−	3550.49i	−0.574011	−	0.208923i	−0.612683	+	0.790329i	$0.709910\pi$
$662$	6045.97	+	2200.55i	0.354960	+	0.129195i
$663$		0			0
$664$	448.384	−	2542.91i	0.0262059	−	0.148621i
$665$	−25801.2	−	44689.0i	−1.50455	−	2.60596i
$666$		0			0
$667$	53.5386	−	92.7316i	0.00310798	−	0.00538318i
$668$	9406.58	+	7893.06i	0.544838	+	0.457173i
$669$		0			0
$670$	1170.21	+	6636.58i	0.0674763	+	0.382677i
$671$	266.519	−	223.636i	0.0153336	−	0.0128664i
$672$		0			0
$673$	421.451	−	153.396i	0.0241393	−	0.00878599i	−0.329922	−	0.944008i	$-0.607023\pi$
$673$	421.451	−	153.396i	0.0241393	−	0.00878599i	0.354062	+	0.935222i	$0.384800\pi$
$674$	−17612.8			−1.00656
$675$		0			0
$676$	4298.95			0.244592
$677$	19005.3	−	6917.35i	1.07892	−	0.392696i	0.259417	−	0.965765i	$-0.416470\pi$
$677$	19005.3	−	6917.35i	1.07892	−	0.392696i	0.819507	+	0.573069i	$0.194247\pi$
$678$		0			0
$679$	9017.40	−	7566.50i	0.509655	−	0.427652i
$680$	−583.480	−	3309.08i	−0.0329051	−	0.186614i
$681$		0			0
$682$	3988.36	+	3346.63i	0.223933	+	0.187902i
$683$	4472.00	−	7745.73i	0.250536	−	0.433942i	−0.713137	−	0.701024i	$-0.752726\pi$
$683$	4472.00	−	7745.73i	0.250536	−	0.433942i	0.963674	+	0.267083i	$0.0860597\pi$
$684$		0			0
$685$	11314.9	+	19598.0i	0.631126	+	1.09314i
$686$	352.359	−	1998.33i	0.0196110	−	0.111219i
$687$		0			0
$688$	2109.13	+	767.660i	0.116875	+	0.0425389i
$689$	−27282.9	−	9930.17i	−1.50856	−	0.549070i
$690$		0			0
$691$	5796.44	−	32873.2i	0.319113	−	1.80978i	−0.229058	−	0.973413i	$-0.573565\pi$
$691$	5796.44	−	32873.2i	0.319113	−	1.80978i	0.548171	−	0.836366i	$-0.315324\pi$
$692$	−3779.57	−	6546.40i	−0.207626	−	0.359620i
$693$		0			0
$694$	2187.26	−	3788.44i	0.119636	−	0.207215i
$695$	−8643.52	−	7252.77i	−0.471751	−	0.395846i
$696$		0			0
$697$	850.995	+	4826.23i	0.0462464	+	0.262276i
$698$	4874.96	−	4090.58i	0.264355	−	0.221821i
$699$		0			0
$700$	−6563.27	+	2388.83i	−0.354383	+	0.128985i
$701$	−13867.6			−0.747177			−0.373588	−	0.927595i	$-0.621873\pi$
$701$	−13867.6			−0.747177			−0.373588	+	0.927595i	$0.621873\pi$
$702$		0			0
$703$	−57230.2			−3.07038
$704$	−611.751	+	222.659i	−0.0327503	+	0.0119201i
$705$		0			0
$706$	−7999.02	+	6711.98i	−0.426413	+	0.357803i
$707$	7032.49	+	39883.2i	0.374093	+	2.12159i
$708$		0			0
$709$	−1738.83	−	1459.05i	−0.0921060	−	0.0772861i	0.595572	−	0.803302i	$-0.296925\pi$
$709$	−1738.83	−	1459.05i	−0.0921060	−	0.0772861i	−0.687678	+	0.726016i	$0.741370\pi$
$710$	−15696.3	+	27186.7i	−0.829676	+	1.43704i
$711$		0			0
$712$	2381.72	+	4125.25i	0.125363	+	0.217135i
$713$	78.1987	−	443.487i	0.00410738	−	0.0232941i
$714$		0			0
$715$	7534.50	+	2742.33i	0.394090	+	0.143437i
$716$	−6809.37	−	2478.41i	−0.355417	−	0.129361i
$717$		0			0
$718$	627.318	−	3557.70i	0.0326063	−	0.184919i
$719$	−2188.43	−	3790.48i	−0.113512	−	0.196608i	0.803672	−	0.595072i	$-0.202877\pi$
$719$	−2188.43	−	3790.48i	−0.113512	−	0.196608i	−0.917184	+	0.398464i	$0.869543\pi$
$720$		0			0
$721$	−10410.2	+	18031.0i	−0.537721	+	0.931360i
$722$	19175.0	+	16089.8i	0.988395	+	0.829362i
$723$		0			0
$724$	1645.58	+	9332.54i	0.0844716	+	0.479062i
$725$	−3025.62	+	2538.80i	−0.154991	+	0.130053i
$726$		0			0
$727$	−20612.7	+	7502.42i	−1.05156	+	0.382736i	−0.809251	−	0.587463i	$-0.800127\pi$
$727$	−20612.7	+	7502.42i	−1.05156	+	0.382736i	−0.242309	+	0.970199i	$0.577905\pi$
$728$	12310.1			0.626709
$729$		0			0
$730$	−7703.12			−0.390555
$731$	4017.71	−	1462.33i	0.203284	−	0.0739892i
$732$		0			0
$733$	−8801.52	+	7385.35i	−0.443508	+	0.372148i	−0.837020	−	0.547172i	$-0.815704\pi$
$733$	−8801.52	+	7385.35i	−0.443508	+	0.372148i	0.393512	+	0.919320i	$0.371260\pi$
$734$	907.531	+	5146.86i	0.0456370	+	0.258820i
$735$		0			0
$736$	43.1352	+	36.1947i	0.00216030	+	0.00181271i
$737$	1243.57	−	2153.93i	0.0621542	−	0.107654i
$738$		0			0
$739$	−9287.58	−	16086.6i	−0.462313	−	0.800749i	0.536763	−	0.843733i	$-0.319647\pi$
$739$	−9287.58	−	16086.6i	−0.462313	−	0.800749i	−0.999076	+	0.0429838i	$0.986314\pi$
$740$	−3935.58	+	22319.8i	−0.195507	+	1.10877i
$741$		0			0
$742$	−25663.5	−	9340.73i	−1.26972	−	0.462142i
$743$	27121.4	+	9871.39i	1.33915	+	0.487411i	0.909545	−	0.415606i	$-0.136430\pi$
$743$	27121.4	+	9871.39i	1.33915	+	0.487411i	0.429606	+	0.903017i	$0.358653\pi$
$744$		0			0
$745$	2041.36	−	11577.1i	0.100389	−	0.569332i
$746$	−145.256	−	251.591i	−0.00712896	−	0.0123477i
$747$		0			0
$748$	−620.062	+	1073.98i	−0.0303098	+	0.0524980i
$749$	8233.14	+	6908.42i	0.401645	+	0.337021i
$750$		0			0
$751$	3496.86	+	19831.7i	0.169910	+	0.963606i	0.943857	+	0.330355i	$0.107169\pi$
$751$	3496.86	+	19831.7i	0.169910	+	0.963606i	−0.773947	+	0.633251i	$0.781720\pi$
$752$	−7205.43	+	6046.08i	−0.349408	+	0.293188i
$753$		0			0
$754$	6541.46	−	2380.90i	0.315949	−	0.114996i
$755$	−138.278			−0.00666552
$756$		0			0
$757$	1095.53			0.0525991			0.0262996	−	0.999654i	$-0.491628\pi$
$757$	1095.53			0.0525991			0.0262996	+	0.999654i	$0.491628\pi$
$758$	−17362.4	+	6319.40i	−0.831967	+	0.302811i
$759$		0			0
$760$	11755.2	−	9863.80i	0.561062	−	0.470787i
$761$	−525.691	−	2981.34i	−0.0250411	−	0.142015i	0.969724	−	0.244204i	$-0.0785266\pi$
$761$	−525.691	−	2981.34i	−0.0250411	−	0.142015i	−0.994765	+	0.102189i	$0.967415\pi$
$762$		0			0
$763$	14811.2	+	12428.1i	0.702754	+	0.589681i
$764$	8455.26	−	14644.9i	0.400394	−	0.693502i
$765$		0			0
$766$	4976.84	+	8620.14i	0.234753	+	0.406603i
$767$	−116.351	+	659.858i	−0.00547743	+	0.0310640i
$768$		0			0
$769$	−62.0651	−	22.5899i	−0.00291044	−	0.00105931i	0.340565	−	0.940221i	$-0.389382\pi$
$769$	−62.0651	−	22.5899i	−0.00291044	−	0.00105931i	−0.343475	+	0.939162i	$0.611604\pi$
$770$	7087.26	+	2579.55i	0.331698	+	0.120728i
$771$		0			0
$772$	−365.900	+	2075.12i	−0.0170583	+	0.0967425i
$773$	15748.4	+	27277.0i	0.732768	+	1.26919i	0.955696	+	0.294356i	$0.0951051\pi$
$773$	15748.4	+	27277.0i	0.732768	+	1.26919i	−0.222928	+	0.974835i	$0.571562\pi$
$774$		0			0
$775$	−8305.44	+	14385.4i	−0.384955	+	0.666761i
$776$	2681.56	+	2250.10i	0.124050	+	0.104090i
$777$		0			0
$778$	−1196.76	−	6787.16i	−0.0551490	−	0.312765i
$779$	−17144.8	+	14386.2i	−0.788543	+	0.661666i
$780$		0			0
$781$	10887.3	−	3962.66i	0.498820	−	0.181556i
$782$	107.264			0.00490505
$783$		0			0
$784$	6091.42			0.277488
$785$	24061.4	−	8757.63i	1.09400	−	0.398183i
$786$		0			0
$787$	1492.69	−	1252.52i	0.0676096	−	0.0567312i	−0.608357	−	0.793664i	$-0.708171\pi$
$787$	1492.69	−	1252.52i	0.0676096	−	0.0567312i	0.675966	+	0.736933i	$0.263727\pi$
$788$	2386.43	+	13534.1i	0.107884	+	0.611843i
$789$		0			0
$790$	−21008.7	−	17628.4i	−0.946145	−	0.793910i
$791$	−8470.49	+	14671.3i	−0.380754	+	0.659485i
$792$		0			0
$793$	−978.191	−	1694.28i	−0.0438040	−	0.0758708i
$794$	408.698	−	2317.84i	0.0182672	−	0.103598i
$795$		0			0
$796$	−13559.2	−	4935.13i	−0.603758	−	0.219750i
$797$	−147.577	−	53.7136i	−0.00655890	−	0.00238724i	0.338739	−	0.940881i	$-0.390000\pi$
$797$	−147.577	−	53.7136i	−0.00655890	−	0.00238724i	−0.345298	+	0.938493i	$0.612222\pi$
$798$		0			0
$799$	−3111.37	+	17645.5i	−0.137763	+	0.781292i
$800$	−1038.51	−	1798.75i	−0.0458961	−	0.0794944i
$801$		0			0
$802$	−8261.76	+	14309.8i	−0.363757	+	0.630045i
$803$	2177.86	+	1827.44i	0.0957097	+	0.0803099i
$804$		0			0
$805$	−113.280	−	642.441i	−0.00495973	−	0.0281280i
$806$	22427.2	−	18818.6i	0.980104	−	0.822405i
$807$		0			0
$808$	−11317.0	+	4119.05i	−0.492736	+	0.179341i
$809$	5591.20			0.242987			0.121493	−	0.992592i	$-0.461232\pi$
$809$	5591.20			0.242987			0.121493	+	0.992592i	$0.461232\pi$
$810$		0			0
$811$	28258.0			1.22352			0.611760	−	0.791044i	$-0.290462\pi$
$811$	28258.0			1.22352			0.611760	+	0.791044i	$0.290462\pi$
$812$	6153.17	−	2239.57i	0.265928	−	0.0967900i
$813$		0			0
$814$	6407.69	−	5376.69i	0.275908	−	0.231515i
$815$	−1176.37	−	6671.53i	−0.0505601	−	0.286741i
$816$		0			0
$817$	14957.8	+	12551.1i	0.640523	+	0.537462i
$818$	−7690.26	+	13319.9i	−0.328709	+	0.569340i
$819$		0			0
$820$	4431.61	+	7675.77i	0.188730	+	0.326890i
$821$	5041.37	−	28591.0i	0.214306	−	1.21539i	−0.667802	−	0.744339i	$-0.732765\pi$
$821$	5041.37	−	28591.0i	0.214306	−	1.21539i	0.882107	−	0.471049i	$-0.156124\pi$
$822$		0			0
$823$	−23370.6	−	8506.20i	−0.989851	−	0.360276i	−0.204189	−	0.978932i	$-0.565456\pi$
$823$	−23370.6	−	8506.20i	−0.989851	−	0.360276i	−0.785663	+	0.618655i	$0.787678\pi$
$824$	−5818.11	−	2117.62i	−0.245975	−	0.0895276i
$825$		0			0
$826$	−109.444	+	620.690i	−0.00461024	+	0.0261460i
$827$	2780.85	+	4816.58i	0.116928	+	0.202526i	0.918549	−	0.395307i	$-0.129362\pi$
$827$	2780.85	+	4816.58i	0.116928	+	0.202526i	−0.801621	+	0.597833i	$0.796029\pi$
$828$		0			0
$829$	16211.7	−	28079.5i	0.679199	−	1.17641i	−0.296023	−	0.955181i	$-0.595661\pi$
$829$	16211.7	−	28079.5i	0.679199	−	1.17641i	0.975222	−	0.221227i	$-0.0710061\pi$
$830$	−6814.67	−	5718.18i	−0.284989	−	0.239134i
$831$		0			0
$832$	635.681	+	3605.13i	0.0264883	+	0.150223i
$833$	8888.91	−	7458.68i	0.369727	−	0.310238i
$834$		0			0
$835$	39753.4	−	14469.0i	1.64757	−	0.599667i
$836$	−5663.51			−0.234302
$837$		0			0
$838$	1077.57			0.0444203
$839$	−38538.3	+	14026.8i	−1.58581	+	0.577186i	−0.976456	−	0.215715i	$-0.930792\pi$
$839$	−38538.3	+	14026.8i	−1.58581	+	0.577186i	−0.609350	+	0.792901i	$0.708570\pi$
$840$		0			0
$841$	−15846.5	+	13296.8i	−0.649739	+	0.545196i
$842$	−3685.60	−	20902.1i	−0.150848	−	0.855502i
$843$		0			0
$844$	−2898.38	−	2432.03i	−0.118207	−	0.0991871i
$845$	7405.31	−	12826.4i	0.301480	−	0.522178i
$846$		0			0
$847$	16511.5	+	28598.7i	0.669823	+	1.16017i
$848$	1410.28	−	7998.11i	0.0571100	−	0.323887i
$849$		0			0
$850$	−3717.94	−	1353.22i	−0.150029	−	0.0546059i
$851$	−679.864	−	247.450i	−0.0273859	−	0.00996766i
$852$		0			0
$853$	−3918.92	+	22225.3i	−0.157305	+	0.892121i	0.799343	+	0.600875i	$0.205181\pi$
$853$	−3918.92	+	22225.3i	−0.157305	+	0.892121i	−0.956648	+	0.291246i	$0.905930\pi$
$854$	−920.127	−	1593.71i	−0.0368690	−	0.0638590i
$855$		0			0
$856$	−1598.04	+	2767.89i	−0.0638083	+	0.110519i
$857$	13916.9	+	11677.7i	0.554717	+	0.465463i	0.876535	−	0.481339i	$-0.159849\pi$
$857$	13916.9	+	11677.7i	0.554717	+	0.465463i	−0.321818	+	0.946802i	$0.604294\pi$
$858$		0			0
$859$	87.2399	+	494.762i	0.00346518	+	0.0196520i	0.986491	−	0.163814i	$-0.0523795\pi$
$859$	87.2399	+	494.762i	0.00346518	+	0.0196520i	−0.983026	+	0.183466i	$0.941268\pi$
$860$	5923.54	−	4970.44i	0.234873	−	0.197082i
$861$		0			0
$862$	−17730.2	+	6453.27i	−0.700572	+	0.254988i
$863$	−22894.8			−0.903067			−0.451534	−	0.892254i	$-0.649123\pi$
$863$	−22894.8			−0.903067			−0.451534	+	0.892254i	$0.649123\pi$
$864$		0			0
$865$	−26042.5			−1.02367
$866$	29234.0	−	10640.3i	1.14713	−	0.417520i
$867$		0			0
$868$	21095.9	−	17701.6i	0.824934	−	0.692202i
$869$	1757.61	+	9967.92i	0.0686110	+	0.389112i
$870$		0			0
$871$	−10713.6	−	8989.79i	−0.416782	−	0.349722i
$872$	−2874.83	+	4979.36i	−0.111645	+	0.193374i
$873$		0			0
$874$	244.931	+	424.233i	0.00947932	+	0.0164187i
$875$	3868.55	−	21939.7i	0.149464	−	0.847653i
$876$		0			0
$877$	−12101.6	−	4404.62i	−0.465954	−	0.169594i	0.0983644	−	0.995150i	$-0.468639\pi$
$877$	−12101.6	−	4404.62i	−0.465954	−	0.169594i	−0.564319	+	0.825557i	$0.690861\pi$
$878$	−13422.1	−	4885.25i	−0.515916	−	0.187778i
$879$		0			0
$880$	−389.466	+	2208.77i	−0.0149192	+	0.0846110i
$881$	14923.0	+	25847.4i	0.570679	+	0.988445i	0.996496	+	0.0836356i	$0.0266532\pi$
$881$	14923.0	+	25847.4i	0.570679	+	0.988445i	−0.425818	+	0.904809i	$0.640013\pi$
$882$		0			0
$883$	17302.9	−	29969.5i	0.659444	−	1.14219i	−0.321316	−	0.946972i	$-0.604125\pi$
$883$	17302.9	−	29969.5i	0.659444	−	1.14219i	0.980760	−	0.195218i	$-0.0625415\pi$
$884$	5341.94	+	4482.42i	0.203245	+	0.170543i
$885$		0			0
$886$	−3999.13	−	22680.2i	−0.151640	−	0.859996i
$887$	−10835.6	+	9092.16i	−0.410174	+	0.344177i	−0.824410	−	0.565993i	$-0.808493\pi$
$887$	−10835.6	+	9092.16i	−0.410174	+	0.344177i	0.414237	+	0.910169i	$0.364049\pi$
$888$		0			0
$889$	−28637.8	+	10423.3i	−1.08041	+	0.393236i
$890$	16410.8			0.618081
$891$		0			0
$892$	−627.925			−0.0235701
$893$	−76893.3	+	27986.9i	−2.88145	+	1.04876i
$894$		0			0
$895$	−19124.3	+	16047.2i	−0.714251	+	0.599328i
$896$	597.948	+	3391.13i	0.0222947	+	0.126440i
$897$		0			0
$898$	7834.88	+	6574.24i	0.291151	+	0.244304i
$899$	7786.48	−	13486.6i	0.288869	−	0.500337i
$900$		0			0
$901$	−7735.38	−	13398.1i	−0.286019	−	0.495399i
$902$	568.029	−	3221.45i	0.0209682	−	0.118916i
$903$		0			0
$904$	−4734.03	−	1723.05i	−0.174172	−	0.0633934i
$905$	30679.2	+	11166.3i	1.12686	+	0.410145i
$906$		0			0
$907$	−4343.53	+	24633.4i	−0.159013	+	0.901806i	0.796012	+	0.605281i	$0.206939\pi$
$907$	−4343.53	+	24633.4i	−0.159013	+	0.901806i	−0.955025	+	0.296525i	$0.904172\pi$
$908$	162.414	+	281.310i	0.00593603	+	0.0102815i
$909$		0			0
$910$	21205.2	−	36728.5i	0.772469	−	1.33796i
$911$	−2541.32	−	2132.42i	−0.0924234	−	0.0775524i	0.595405	−	0.803426i	$-0.296992\pi$
$911$	−2541.32	−	2132.42i	−0.0924234	−	0.0775524i	−0.687829	+	0.725873i	$0.741436\pi$
$912$		0			0
$913$	570.124	+	3233.34i	0.0206663	+	0.117205i
$914$	−618.751	+	519.194i	−0.0223922	+	0.0187893i
$915$		0			0
$916$	−18606.0	+	6772.04i	−0.671136	+	0.244274i
$917$	36145.4			1.30166
$918$		0			0
$919$	−25932.6			−0.930837			−0.465418	−	0.885091i	$-0.654096\pi$
$919$	−25932.6			−0.930837			−0.465418	+	0.885091i	$0.654096\pi$
$920$	182.295	−	66.3498i	0.00653269	−	0.00237770i
$921$		0			0
$922$	11334.8	−	9511.01i	0.404871	−	0.339727i
$923$	−11313.2	−	64160.3i	−0.403444	−	2.28804i
$924$		0			0
$925$	20443.4	+	17154.1i	0.726676	+	0.609753i
$926$	−3751.92	+	6498.52i	−0.133149	+	0.230620i
$927$		0			0
$928$	973.620	+	1686.36i	0.0344403	+	0.0596524i
$929$	−3361.00	+	19061.2i	−0.118698	+	0.673173i	0.866154	+	0.499777i	$0.166585\pi$
$929$	−3361.00	+	19061.2i	−0.118698	+	0.673173i	−0.984852	+	0.173395i	$0.944526\pi$
$930$		0			0
$931$	49796.8	+	18124.5i	1.75298	+	0.638032i
$932$	12382.0	+	4506.66i	0.435176	+	0.158391i
$933$		0			0
$934$	−2344.26	+	13294.9i	−0.0821268	+	0.465764i
$935$	2136.22	+	3700.03i	0.0747184	+	0.129416i
$936$		0			0
$937$	13665.9	−	23670.1i	0.476463	−	0.825259i	−0.523173	−	0.852227i	$-0.675252\pi$
$937$	13665.9	−	23670.1i	0.476463	−	0.825259i	0.999636	+	0.0269676i	$0.00858510\pi$
$938$	−10077.7	−	8456.17i	−0.350797	−	0.294354i
$939$		0			0
$940$	5627.13	+	31913.0i	0.195252	+	1.10733i
$941$	−30868.0	+	25901.3i	−1.06936	+	0.897299i	−0.994994	−	0.0999322i	$-0.968137\pi$
$941$	−30868.0	+	25901.3i	−1.06936	+	0.897299i	−0.0743649	+	0.997231i	$0.523693\pi$
$942$		0			0
$943$	−265.873	+	96.7699i	−0.00918136	+	0.00334174i
$944$	−187.426			−0.00646208
$945$		0			0
$946$	−2853.88			−0.0980843
$947$	12422.3	−	4521.35i	0.426263	−	0.155147i	−0.119975	−	0.992777i	$-0.538282\pi$
$947$	12422.3	−	4521.35i	0.426263	−	0.155147i	0.546238	+	0.837630i	$0.316059\pi$
$948$		0			0
$949$	12246.4	−	10276.0i	0.418900	−	0.351499i
$950$	−3137.67	−	17794.6i	−0.107157	−	0.607720i
$951$		0			0
$952$	5024.85	+	4216.35i	0.171068	+	0.143543i
$953$	10527.0	−	18233.3i	0.357820	−	0.619763i	−0.629776	−	0.776777i	$-0.716853\pi$
$953$	10527.0	−	18233.3i	0.357820	−	0.619763i	0.987596	+	0.157014i	$0.0501867\pi$
$954$		0			0
$955$	−29129.8	−	50454.3i	−0.987035	−	1.70959i
$956$	727.506	−	4125.89i	0.0246121	−	0.139582i
$957$		0			0
$958$	26212.7	+	9540.65i	0.884023	+	0.321758i
$959$	−41512.7	−	15109.4i	−1.39782	−	0.508766i
$960$		0			0
$961$	6199.81	−	35160.8i	0.208110	−	1.18025i
$962$	−23517.9	−	40734.1i	−0.788198	−	1.36520i
$963$		0			0
$964$	3826.46	−	6627.62i	0.127844	−	0.221433i
$965$	5561.04	+	4666.27i	0.185509	+	0.155661i
$966$		0			0
$967$	−1038.40	−	5889.05i	−0.0345322	−	0.195842i	0.962661	−	0.270709i	$-0.0872580\pi$
$967$	−1038.40	−	5889.05i	−0.0345322	−	0.195842i	−0.997194	+	0.0748667i	$0.976147\pi$
$968$	−7522.74	+	6312.32i	−0.249783	+	0.209593i
$969$		0			0
$970$	11332.6	−	4124.73i	0.375122	−	0.136533i
$971$	37318.8			1.23338			0.616692	−	0.787204i	$-0.288472\pi$
$971$	37318.8			1.23338			0.616692	+	0.787204i	$0.288472\pi$
$972$		0			0
$973$	22026.7			0.725739
$974$	−6065.64	+	2207.71i	−0.199544	+	0.0726280i
$975$		0			0
$976$	419.217	−	351.764i	0.0137488	−	0.0115366i
$977$	8053.08	+	45671.3i	0.263706	+	1.49555i	0.772695	+	0.634778i	$0.218908\pi$
$977$	8053.08	+	45671.3i	0.263706	+	1.49555i	−0.508989	+	0.860773i	$0.669981\pi$
$978$		0			0
$979$	−4639.73	−	3893.20i	−0.151467	−	0.127096i
$980$	10493.0	−	18174.4i	0.342027	−	0.592408i
$981$		0			0
$982$	−13339.1	−	23104.0i	−0.433470	−	0.750792i
$983$	−1189.65	+	6746.83i	−0.0386001	+	0.218912i	−0.998006	−	0.0631163i	$-0.979896\pi$
$983$	−1189.65	+	6746.83i	−0.0386001	+	0.218912i	0.959406	+	0.282028i	$0.0910072\pi$
$984$		0			0
$985$	44491.2	+	16193.5i	1.43920	+	0.523824i
$986$	3485.63	+	1268.67i	0.112581	+	0.0409762i
$987$		0			0
$988$	−5530.14	+	31363.0i	−0.178074	+	1.00991i
$989$	123.423	+	213.774i	0.00396826	+	0.00687323i
$990$		0			0
$991$	−13275.8	+	22994.4i	−0.425551	+	0.737076i	−0.996472	−	0.0839292i	$-0.973253\pi$
$991$	−13275.8	+	22994.4i	−0.425551	+	0.737076i	0.570921	+	0.821005i	$0.306586\pi$
$992$	6273.44	+	5264.04i	0.200788	+	0.168481i
$993$		0			0
$994$	−10641.7	−	60351.9i	−0.339570	−	1.92580i
$995$	−38081.3	+	31954.0i	−1.21332	+	1.01810i
$996$		0			0
$997$	−13752.3	+	5005.42i	−0.436850	+	0.159000i	−0.551077	−	0.834454i	$-0.685783\pi$
$997$	−13752.3	+	5005.42i	−0.436850	+	0.159000i	0.114227	+	0.993455i	$0.463561\pi$
$998$	−17312.3			−0.549108
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.b.19.2		30
3.2	odd	2		54.4.e.b.7.2	✓	30
27.2	odd	18		1458.4.a.i.1.13		15
27.4	even	9	inner	162.4.e.b.145.2		30
27.23	odd	18		54.4.e.b.31.2	yes	30
27.25	even	9		1458.4.a.j.1.3		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.b.7.2	✓	30	3.2	odd	2
54.4.e.b.31.2	yes	30	27.23	odd	18
162.4.e.b.19.2		30	1.1	even	1	trivial
162.4.e.b.145.2		30	27.4	even	9	inner
1458.4.a.i.1.13		15	27.2	odd	18
1458.4.a.j.1.3		15	27.25	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	162.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.87939 + 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(-2.39299 - 13.5713i) q^{5} +(20.6081 + 17.2922i) q^{7} +(-4.00000 + 6.92820i) q^{8} +O(q^{10})\)	\(q+(-1.87939 + 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(-2.39299 - 13.5713i) q^{5} +(20.6081 + 17.2922i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(13.7807 + 23.8688i) q^{10} +(1.76636 - 10.0175i) q^{11} +(-53.7496 - 19.5632i) q^{13} +(-50.5591 - 18.4020i) q^{14} +(2.77837 - 15.7569i) q^{16} +(-15.2393 - 26.3953i) q^{17} +(69.5964 - 120.544i) q^{19} +(-42.2264 - 35.4322i) q^{20} +(3.53272 + 20.0351i) q^{22} +(1.34797 - 1.13108i) q^{23} +(-60.9925 + 22.1995i) q^{25} +114.398 q^{26} +107.608 q^{28} +(57.1815 - 20.8124i) q^{29} +(196.045 - 164.501i) q^{31} +(5.55674 + 31.5138i) q^{32} +(46.6960 + 39.1826i) q^{34} +(185.363 - 321.059i) q^{35} +(-205.579 - 356.073i) q^{37} +(-48.3411 + 274.156i) q^{38} +(103.597 + 37.7061i) q^{40} +(-151.094 - 54.9937i) q^{41} +(-24.3594 + 138.149i) q^{43} +(-20.3441 - 35.2371i) q^{44} +(-1.75966 + 3.04781i) q^{46} +(-450.340 - 377.880i) q^{47} +(66.1103 + 374.930i) q^{49} +(99.4431 - 83.4427i) q^{50} +(-214.998 + 78.2530i) q^{52} +507.593 q^{53} -140.178 q^{55} +(-202.236 + 73.6080i) q^{56} +(-93.2295 + 78.2289i) q^{58} +(-2.03414 - 11.5362i) q^{59} +(26.2010 + 21.9853i) q^{61} +(-255.918 + 443.264i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(-136.877 + 776.267i) q^{65} +(229.762 + 83.6266i) q^{67} +(-114.562 - 41.6973i) q^{68} +(-128.752 + 730.189i) q^{70} +(569.503 + 986.408i) q^{71} +(-139.745 + 242.045i) q^{73} +(629.930 + 528.574i) q^{74} +(-96.6823 - 548.312i) q^{76} +(209.627 - 175.898i) q^{77} +(-935.039 + 340.327i) q^{79} -220.491 q^{80} +321.582 q^{82} +(-303.303 + 110.393i) q^{83} +(-321.751 + 269.981i) q^{85} +(-48.7189 - 276.298i) q^{86} +(62.3380 + 52.3078i) q^{88} +(297.715 - 515.657i) q^{89} +(-769.383 - 1332.61i) q^{91} +(1.22224 - 6.93169i) q^{92} +(1104.85 + 402.131i) q^{94} +(-1802.49 - 656.053i) q^{95} +(75.9826 - 430.919i) q^{97} +(-380.714 - 659.416i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8}+O(q^{10}) \) 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8	\( 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8} - 30 q^{10} + 39 q^{11} - 60 q^{13} + 66 q^{14} - 102 q^{17} - 171 q^{19} - 96 q^{20} + 78 q^{22} - 48 q^{23} - 432 q^{25} + 468 q^{26} + 336 q^{28} + 381 q^{29} - 801 q^{31} - 222 q^{34} - 624 q^{35} - 555 q^{37} - 606 q^{38} + 96 q^{40} - 1401 q^{41} + 648 q^{43} - 132 q^{44} - 348 q^{46} - 540 q^{47} + 15 q^{49} + 828 q^{50} - 240 q^{52} + 1794 q^{53} + 3906 q^{55} + 264 q^{56} - 444 q^{58} + 1500 q^{59} - 378 q^{61} - 744 q^{62} - 960 q^{64} - 3666 q^{65} + 3087 q^{67} + 24 q^{68} + 2118 q^{70} - 120 q^{71} - 2604 q^{73} + 1974 q^{74} - 1212 q^{76} + 6504 q^{77} - 2625 q^{79} + 480 q^{80} + 3408 q^{82} + 5211 q^{83} - 1395 q^{85} + 1296 q^{86} - 912 q^{88} - 2604 q^{89} - 3399 q^{91} - 372 q^{92} + 4500 q^{94} - 7545 q^{95} + 8940 q^{97} - 4002 q^{98}+O(q^{100}) \) 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8 - 30 * q^10 + 39 * q^11 - 60 * q^13 + 66 * q^14 - 102 * q^17 - 171 * q^19 - 96 * q^20 + 78 * q^22 - 48 * q^23 - 432 * q^25 + 468 * q^26 + 336 * q^28 + 381 * q^29 - 801 * q^31 - 222 * q^34 - 624 * q^35 - 555 * q^37 - 606 * q^38 + 96 * q^40 - 1401 * q^41 + 648 * q^43 - 132 * q^44 - 348 * q^46 - 540 * q^47 + 15 * q^49 + 828 * q^50 - 240 * q^52 + 1794 * q^53 + 3906 * q^55 + 264 * q^56 - 444 * q^58 + 1500 * q^59 - 378 * q^61 - 744 * q^62 - 960 * q^64 - 3666 * q^65 + 3087 * q^67 + 24 * q^68 + 2118 * q^70 - 120 * q^71 - 2604 * q^73 + 1974 * q^74 - 1212 * q^76 + 6504 * q^77 - 2625 * q^79 + 480 * q^80 + 3408 * q^82 + 5211 * q^83 - 1395 * q^85 + 1296 * q^86 - 912 * q^88 - 2604 * q^89 - 3399 * q^91 - 372 * q^92 + 4500 * q^94 - 7545 * q^95 + 8940 * q^97 - 4002 * q^98

Introduction

L-functions

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