LMFDB - Embedded newform 475.2.j.d.349.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(49,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("475.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.j (of order $6$, degree $2$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.3
Character	$\chi$	$=$	475.349
Dual form			475.2.j.d.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.28275 + 0.740597i) q^{2} +(-2.47401 + 1.42837i) q^{3} +(0.0969683 - 0.167954i) q^{4} +(2.11569 - 3.66449i) q^{6} +3.78541i q^{7} -2.67513i q^{8} +(2.58048 - 4.46952i) q^{9} -5.59460 q^{11} +0.554026i q^{12} +(-4.24917 - 2.45326i) q^{13} +(-2.80346 - 4.85574i) q^{14} +(2.17513 + 3.76744i) q^{16} +(1.51571 - 0.875095i) q^{17} +7.64438i q^{18} +(-0.636061 + 4.31224i) q^{19} +(-5.40696 - 9.36514i) q^{21} +(7.17648 - 4.14335i) q^{22} +(-0.503625 - 0.290768i) q^{23} +(3.82107 + 6.61830i) q^{24} +7.26750 q^{26} +6.17328i q^{27} +(0.635775 + 0.367065i) q^{28} +(0.832153 - 1.44133i) q^{29} +7.01680 q^{31} +(-0.946844 - 0.546661i) q^{32} +(13.8411 - 7.99116i) q^{33} +(-1.29619 + 2.24506i) q^{34} +(-0.500449 - 0.866803i) q^{36} -2.36322i q^{37} +(-2.37773 - 6.00260i) q^{38} +14.0166 q^{39} +(-0.417676 - 0.723435i) q^{41} +(13.8716 + 8.00877i) q^{42} +(-0.927797 + 0.535664i) q^{43} +(-0.542499 + 0.939635i) q^{44} +0.861369 q^{46} +(3.34941 + 1.93378i) q^{47} +(-10.7626 - 6.21378i) q^{48} -7.32934 q^{49} +(-2.49992 + 4.32999i) q^{51} +(-0.824069 + 0.475776i) q^{52} +(5.88624 + 3.39842i) q^{53} +(-4.57192 - 7.91879i) q^{54} +10.1265 q^{56} +(-4.58585 - 11.5771i) q^{57} +2.46516i q^{58} +(-0.204282 - 0.353827i) q^{59} +(-6.98016 + 12.0900i) q^{61} +(-9.00081 + 5.19662i) q^{62} +(16.9190 + 9.76817i) q^{63} -7.08110 q^{64} +(-11.8365 + 20.5013i) q^{66} +(0.676717 + 0.390703i) q^{67} -0.339426i q^{68} +1.66130 q^{69} +(-3.18919 - 5.52384i) q^{71} +(-11.9565 - 6.90312i) q^{72} +(2.50208 - 1.44458i) q^{73} +(1.75019 + 3.03142i) q^{74} +(0.662580 + 0.524980i) q^{76} -21.1779i q^{77} +(-17.9799 + 10.3807i) q^{78} +(-6.25135 - 10.8276i) q^{79} +(-1.07630 - 1.86420i) q^{81} +(1.07155 + 0.618659i) q^{82} -10.3903i q^{83} -2.09722 q^{84} +(0.793422 - 1.37425i) q^{86} +4.75449i q^{87} +14.9663i q^{88} +(8.92106 - 15.4517i) q^{89} +(9.28659 - 16.0848i) q^{91} +(-0.0976714 + 0.0563906i) q^{92} +(-17.3596 + 10.0226i) q^{93} -5.72861 q^{94} +3.12333 q^{96} +(-9.52619 + 5.49995i) q^{97} +(9.40172 - 5.42809i) q^{98} +(-14.4367 + 25.0052i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4} + 2 q^{6} + 14 q^{9} - 4 q^{11} - 12 q^{14} + 12 q^{16} + 12 q^{19} - 6 q^{21} + 22 q^{24} + 76 q^{26} + 6 q^{29} - 12 q^{31} - 2 q^{34} - 26 q^{36} - 32 q^{39} - 22 q^{41} + 42 q^{44} - 48 q^{46}+ \cdots - 40 q^{99}+O(q^{100}) $ 24 * q + 4 * q^4 + 2 * q^6 + 14 * q^9 - 4 * q^11 - 12 * q^14 + 12 * q^16 + 12 * q^19 - 6 * q^21 + 22 * q^24 + 76 * q^26 + 6 * q^29 - 12 * q^31 - 2 * q^34 - 26 * q^36 - 32 * q^39 - 22 * q^41 + 42 * q^44 - 48 * q^46 - 16 * q^49 + 34 * q^51 + 36 * q^54 + 16 * q^56 + 8 * q^59 - 50 * q^61 + 88 * q^64 - 68 * q^66 - 52 * q^69 - 36 * q^71 - 12 * q^74 + 48 * q^76 + 6 * q^79 - 4 * q^81 - 148 * q^84 - 18 * q^86 + 24 * q^89 + 22 * q^91 - 32 * q^94 - 52 * q^96 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.28275	+	0.740597i	−0.907043	+	0.523681i	−0.879478	−	0.475939i	$-0.842108\pi$
$2$	−1.28275	+	0.740597i	−0.907043	+	0.523681i	−0.0275641	+	0.999620i	$0.508775\pi$
$3$	−2.47401	+	1.42837i	−1.42837	+	0.824669i	−0.996992	−	0.0775023i	$-0.975305\pi$
$3$	−2.47401	+	1.42837i	−1.42837	+	0.824669i	−0.431377	+	0.902172i	$0.641972\pi$
$4$	0.0969683	−	0.167954i	0.0484841	−	0.0839770i
$5$		0			0
$5$		0			0
$6$	2.11569	−	3.66449i	0.863728	−	1.49602i
$7$			3.78541i			1.43075i	0.698740	+	0.715375i	$0.253744\pi$
$7$			3.78541i			1.43075i	−0.698740	+	0.715375i	$0.746256\pi$
$8$		−	2.67513i		−	0.945802i
$9$	2.58048	−	4.46952i	0.860159	−	1.48984i
$10$		0			0
$11$	−5.59460			−1.68684			−0.843418	−	0.537258i	$-0.819460\pi$
$11$	−5.59460			−1.68684			−0.843418	+	0.537258i	$0.819460\pi$
$12$			0.554026i			0.159934i
$13$	−4.24917	−	2.45326i	−1.17851	−	0.680411i	−0.222838	−	0.974855i	$-0.571532\pi$
$13$	−4.24917	−	2.45326i	−1.17851	−	0.680411i	−0.955669	+	0.294444i	$0.904866\pi$
$14$	−2.80346	−	4.85574i	−0.749257	−	1.29775i
$15$		0			0
$16$	2.17513	+	3.76744i	0.543783	+	0.941859i
$17$	1.51571	−	0.875095i	0.367614	−	0.212242i	−0.304802	−	0.952416i	$-0.598590\pi$
$17$	1.51571	−	0.875095i	0.367614	−	0.212242i	0.672415	+	0.740174i	$0.265257\pi$
$18$			7.64438i			1.80180i
$19$	−0.636061	+	4.31224i	−0.145922	+	0.989296i
$19$	−0.636061	+	4.31224i	−0.145922	+	0.989296i
$20$		0			0
$21$	−5.40696	−	9.36514i	−1.17990	−	2.04364i
$22$	7.17648	−	4.14335i	1.53003	−	0.883364i
$23$	−0.503625	−	0.290768i	−0.105013	−	0.0606294i	0.446574	−	0.894747i	$-0.352644\pi$
$23$	−0.503625	−	0.290768i	−0.105013	−	0.0606294i	−0.551587	+	0.834118i	$0.685977\pi$
$24$	3.82107	+	6.61830i	0.779974	+	1.35095i
$25$		0			0
$26$	7.26750			1.42527
$27$			6.17328i			1.18805i
$28$	0.635775	+	0.367065i	0.120150	+	0.0693687i
$29$	0.832153	−	1.44133i	0.154527	−	0.267649i	−0.778360	−	0.627819i	$-0.783948\pi$
$29$	0.832153	−	1.44133i	0.154527	−	0.267649i	0.932887	+	0.360170i	$0.117281\pi$
$30$		0			0
$31$	7.01680			1.26025			0.630127	−	0.776492i	$-0.283003\pi$
$31$	7.01680			1.26025			0.630127	+	0.776492i	$0.283003\pi$
$32$	−0.946844	−	0.546661i	−0.167380	−	0.0966369i
$33$	13.8411	−	7.99116i	2.40942	−	1.39108i
$34$	−1.29619	+	2.24506i	−0.222294	+	0.385025i
$35$		0			0
$36$	−0.500449	−	0.866803i	−0.0834082	−	0.144467i
$37$		−	2.36322i		−	0.388510i	−0.980951	−	0.194255i	$-0.937771\pi$
$37$		−	2.36322i		−	0.388510i	0.980951	−	0.194255i	$-0.0622290\pi$
$38$	−2.37773	−	6.00260i	−0.385718	−	0.973750i
$39$	14.0166			2.24446
$40$		0			0
$41$	−0.417676	−	0.723435i	−0.0652300	−	0.112982i	0.831566	−	0.555426i	$-0.187445\pi$
$41$	−0.417676	−	0.723435i	−0.0652300	−	0.112982i	−0.896796	+	0.442444i	$0.854111\pi$
$42$	13.8716	+	8.00877i	2.14043	+	1.23578i
$43$	−0.927797	+	0.535664i	−0.141488	+	0.0816880i	−0.569073	−	0.822287i	$-0.692698\pi$
$43$	−0.927797	+	0.535664i	−0.141488	+	0.0816880i	0.427585	+	0.903975i	$0.359364\pi$
$44$	−0.542499	+	0.939635i	−0.0817848	+	0.141655i
$45$		0			0
$46$	0.861369			0.127002
$47$	3.34941	+	1.93378i	0.488561	+	0.282071i	0.723977	−	0.689824i	$-0.242312\pi$
$47$	3.34941	+	1.93378i	0.488561	+	0.282071i	−0.235416	+	0.971895i	$0.575645\pi$
$48$	−10.7626	−	6.21378i	−1.55345	−	0.896882i
$49$	−7.32934			−1.04705
$50$		0			0
$51$	−2.49992	+	4.32999i	−0.350059	+	0.606319i
$52$	−0.824069	+	0.475776i	−0.114278	+	0.0659783i
$53$	5.88624	+	3.39842i	0.808537	+	0.466809i	0.846448	−	0.532472i	$-0.178737\pi$
$53$	5.88624	+	3.39842i	0.808537	+	0.466809i	−0.0379106	+	0.999281i	$0.512070\pi$
$54$	−4.57192	−	7.91879i	−0.622159	−	1.07761i
$55$		0			0
$56$	10.1265			1.35321
$57$	−4.58585	−	11.5771i	−0.607411	−	1.53342i
$58$			2.46516i			0.323691i
$59$	−0.204282	−	0.353827i	−0.0265953	−	0.0460643i	0.852421	−	0.522855i	$-0.175133\pi$
$59$	−0.204282	−	0.353827i	−0.0265953	−	0.0460643i	−0.879017	+	0.476791i	$0.841800\pi$
$60$		0			0
$61$	−6.98016	+	12.0900i	−0.893718	+	1.54796i	−0.0583341	+	0.998297i	$0.518579\pi$
$61$	−6.98016	+	12.0900i	−0.893718	+	1.54796i	−0.835384	+	0.549667i	$0.814754\pi$
$62$	−9.00081	+	5.19662i	−1.14310	+	0.659971i
$63$	16.9190	+	9.76817i	2.13159	+	1.23067i
$64$	−7.08110			−0.885138
$65$		0			0
$66$	−11.8365	+	20.5013i	−1.45697	+	2.52354i
$67$	0.676717	+	0.390703i	0.0826742	+	0.0477319i	0.540767	−	0.841172i	$-0.318134\pi$
$67$	0.676717	+	0.390703i	0.0826742	+	0.0477319i	−0.458093	+	0.888904i	$0.651467\pi$
$68$		−	0.339426i		−	0.0411614i
$69$	1.66130			0.199997
$70$		0			0
$71$	−3.18919	−	5.52384i	−0.378487	−	0.655559i	0.612355	−	0.790583i	$-0.290222\pi$
$71$	−3.18919	−	5.52384i	−0.378487	−	0.655559i	−0.990842	+	0.135024i	$0.956889\pi$
$72$	−11.9565	−	6.90312i	−1.40909	−	0.813540i
$73$	2.50208	−	1.44458i	0.292846	−	0.169075i	−0.346378	−	0.938095i	$-0.612589\pi$
$73$	2.50208	−	1.44458i	0.292846	−	0.169075i	0.639225	+	0.769020i	$0.279255\pi$
$74$	1.75019	+	3.03142i	0.203456	+	0.352395i
$75$		0			0
$76$	0.662580	+	0.524980i	0.0760032	+	0.0602193i
$77$		−	21.1779i		−	2.41344i
$78$	−17.9799	+	10.3807i	−2.03582	+	1.17538i
$79$	−6.25135	−	10.8276i	−0.703331	−	1.21821i	−0.967290	−	0.253672i	$-0.918362\pi$
$79$	−6.25135	−	10.8276i	−0.703331	−	1.21821i	0.263959	−	0.964534i	$-0.414972\pi$
$80$		0			0
$81$	−1.07630	−	1.86420i	−0.119589	−	0.207133i
$82$	1.07155	+	0.618659i	0.118333	+	0.0683194i
$83$		−	10.3903i		−	1.14048i	−0.821478	−	0.570240i	$-0.806850\pi$
$83$		−	10.3903i		−	1.14048i	0.821478	−	0.570240i	$-0.193150\pi$
$84$	−2.09722			−0.228825
$85$		0			0
$86$	0.793422	−	1.37425i	0.0855569	−	0.148189i
$87$			4.75449i			0.509735i
$88$			14.9663i			1.59541i
$89$	8.92106	−	15.4517i	0.945631	−	1.63788i	0.191148	−	0.981561i	$-0.438779\pi$
$89$	8.92106	−	15.4517i	0.945631	−	1.63788i	0.754483	−	0.656320i	$-0.227888\pi$
$90$		0			0
$91$	9.28659	−	16.0848i	0.973499	−	1.68615i
$92$	−0.0976714	+	0.0563906i	−0.0101829	+	0.00587913i
$93$	−17.3596	+	10.0226i	−1.80011	+	1.03929i
$94$	−5.72861			−0.590861
$95$		0			0
$96$	3.12333			0.318774
$97$	−9.52619	+	5.49995i	−0.967238	+	0.558435i	−0.898393	−	0.439192i	$-0.855265\pi$
$97$	−9.52619	+	5.49995i	−0.967238	+	0.558435i	−0.0688448	+	0.997627i	$0.521931\pi$
$98$	9.40172	−	5.42809i	0.949717	−	0.548319i
$99$	−14.4367	+	25.0052i	−1.45095	+	2.51311i
$100$		0			0
$101$	−2.57944	+	4.46772i	−0.256664	+	0.444555i	−0.965346	−	0.260973i	$-0.915957\pi$
$101$	−2.57944	+	4.46772i	−0.256664	+	0.444555i	0.708682	+	0.705528i	$0.249290\pi$
$102$		−	7.40573i		−	0.733277i
$103$		−	7.75851i		−	0.764469i	−0.924065	−	0.382235i	$-0.875155\pi$
$103$		−	7.75851i		−	0.764469i	0.924065	−	0.382235i	$-0.124845\pi$
$104$	−6.56279	+	11.3671i	−0.643534	+	1.11463i
$105$		0			0
$106$	−10.0674			−0.977837
$107$			12.6521i			1.22313i	0.791195	+	0.611564i	$0.209459\pi$
$107$			12.6521i			1.22313i	−0.791195	+	0.611564i	$0.790541\pi$
$108$	1.03683	+	0.598613i	0.0997688	+	0.0576015i
$109$	−4.09697	−	7.09616i	−0.392418	−	0.679689i	0.600350	−	0.799738i	$-0.295028\pi$
$109$	−4.09697	−	7.09616i	−0.392418	−	0.679689i	−0.992768	+	0.120049i	$0.961695\pi$
$110$		0			0
$111$	3.37554	+	5.84661i	0.320392	+	0.554936i
$112$	−14.2613	+	8.23376i	−1.34757	+	0.778018i
$113$		−	12.5551i		−	1.18108i	−0.807007	−	0.590541i	$-0.798914\pi$
$113$		−	12.5551i		−	1.18108i	0.807007	−	0.590541i	$-0.201086\pi$
$114$	14.4564	+	11.4542i	1.35397	+	1.07279i
$115$		0			0
$116$	−0.161385	−	0.279527i	−0.0149842	−	0.0259534i
$117$	−21.9298	+	12.6612i	−2.02741	+	1.17052i
$118$	0.524086	+	0.302581i	0.0482461	+	0.0278549i
$119$	3.31260	+	5.73758i	0.303665	+	0.525963i
$120$		0			0
$121$	20.2996			1.84541
$122$		−	20.6779i		−	1.87209i
$123$	2.06667	+	1.19319i	0.186345	+	0.107586i
$124$	0.680407	−	1.17850i	0.0611023	−	0.105832i
$125$		0			0
$126$	−28.9371			−2.57792
$127$	−7.06602	−	4.07957i	−0.627007	−	0.362003i	0.152585	−	0.988290i	$-0.451240\pi$
$127$	−7.06602	−	4.07957i	−0.627007	−	0.362003i	−0.779592	+	0.626287i	$0.784574\pi$
$128$	10.9770	−	6.33757i	0.970238	−	0.560167i
$129$	1.53025	−	2.65047i	0.134731	−	0.233361i
$130$		0			0
$131$	−9.62491	−	16.6708i	−0.840932	−	1.45654i	−0.889108	−	0.457698i	$-0.848674\pi$
$131$	−9.62491	−	16.6708i	−0.840932	−	1.45654i	0.0481757	−	0.998839i	$-0.484659\pi$
$132$		−	3.09955i		−	0.269782i
$133$	−16.3236	−	2.40775i	−1.41544	−	0.208779i
$134$	−1.15741			−0.0999853
$135$		0			0
$136$	−2.34099	−	4.05472i	−0.200739	−	0.347689i
$137$	−1.36131	−	0.785955i	−0.116305	−	0.0671487i	0.440719	−	0.897645i	$-0.354724\pi$
$137$	−1.36131	−	0.785955i	−0.116305	−	0.0671487i	−0.557024	+	0.830496i	$0.688057\pi$
$138$	−2.13103	+	1.23035i	−0.181406	+	0.104735i
$139$	−1.02459	+	1.77464i	−0.0869047	+	0.150523i	−0.906201	−	0.422847i	$-0.861031\pi$
$139$	−1.02459	+	1.77464i	−0.0869047	+	0.150523i	0.819297	+	0.573370i	$0.194364\pi$
$140$		0			0
$141$	−11.0486			−0.930461
$142$	8.18188	+	4.72381i	0.686608	+	0.396413i
$143$	23.7724	+	13.7250i	1.98795	+	1.14774i
$144$	22.4515			1.87096
$145$		0			0
$146$	−2.13970	+	3.70607i	−0.177083	+	0.306716i
$147$	18.1328	−	10.4690i	1.49557	−	0.863468i
$148$	−0.396911	−	0.229157i	−0.0326259	−	0.0188366i
$149$	−0.737839	−	1.27797i	−0.0604461	−	0.104696i	0.834219	−	0.551434i	$-0.185919\pi$
$149$	−0.737839	−	1.27797i	−0.0604461	−	0.104696i	−0.894665	+	0.446738i	$0.852586\pi$
$150$		0			0
$151$	6.42543			0.522894			0.261447	−	0.965218i	$-0.415800\pi$
$151$	6.42543			0.522894			0.261447	+	0.965218i	$0.415800\pi$
$152$	11.5358	+	1.70155i	0.935678	+	0.138014i
$153$		−	9.03266i		−	0.730247i
$154$	15.6843	+	27.1659i	1.26387	+	2.18909i
$155$		0			0
$156$	1.35917	−	2.35415i	0.108821	−	0.188483i
$157$	19.3028	−	11.1445i	1.54053	−	0.889425i	0.541724	−	0.840556i	$-0.317772\pi$
$157$	19.3028	−	11.1445i	1.54053	−	0.889425i	0.998805	−	0.0488688i	$-0.0155616\pi$
$158$	16.0379	+	9.25946i	1.27590	+	0.736643i
$159$	−19.4168			−1.53985
$160$		0			0
$161$	1.10068	−	1.90643i	0.0867455	−	0.150248i
$162$	2.76124	+	1.59420i	0.216944	+	0.125253i
$163$			15.0321i			1.17741i	0.808350	+	0.588703i	$0.200361\pi$
$163$			15.0321i			1.17741i	−0.808350	+	0.588703i	$0.799639\pi$
$164$	−0.162005			−0.0126505
$165$		0			0
$166$	7.69500	+	13.3281i	0.597248	+	1.03446i
$167$	−8.31260	−	4.79928i	−0.643249	−	0.371380i	0.142616	−	0.989778i	$-0.454449\pi$
$167$	−8.31260	−	4.79928i	−0.643249	−	0.371380i	−0.785865	+	0.618398i	$0.787782\pi$
$168$	−25.0530	+	14.4643i	−1.93288	+	1.11595i
$169$	5.53695	+	9.59028i	0.425919	+	0.737714i
$170$		0			0
$171$	17.6323	+	13.9705i	1.34838	+	1.06835i
$172$			0.207770i			0.0158423i
$173$	7.64894	−	4.41611i	0.581538	−	0.335751i	−0.180207	−	0.983629i	$-0.557677\pi$
$173$	7.64894	−	4.41611i	0.581538	−	0.335751i	0.761744	+	0.647878i	$0.224343\pi$
$174$	−3.52116	−	6.09883i	−0.266938	−	0.462351i
$175$		0			0
$176$	−12.1690	−	21.0773i	−0.917272	−	1.58876i
$177$	1.01079	+	0.583580i	0.0759757	+	0.0438646i
$178$			26.4277i			1.98084i
$179$	−10.8178			−0.808564			−0.404282	−	0.914634i	$-0.632478\pi$
$179$	−10.8178			−0.808564			−0.404282	+	0.914634i	$0.632478\pi$
$180$		0			0
$181$	−5.37359	+	9.30733i	−0.399416	+	0.691808i	−0.993654	−	0.112481i	$-0.964120\pi$
$181$	−5.37359	+	9.30733i	−0.399416	+	0.691808i	0.594238	+	0.804289i	$0.297454\pi$
$182$			27.5105i			2.03921i
$183$		−	39.8810i		−	2.94809i
$184$	−0.777843	+	1.34726i	−0.0573434	+	0.0993216i
$185$		0			0
$186$	14.8454	−	25.7130i	1.08852	−	1.88537i
$187$	−8.47979	+	4.89581i	−0.620104	+	0.358017i
$188$	0.649573	−	0.375031i	0.0473750	−	0.0273519i
$189$	−23.3684			−1.69980
$190$		0			0
$191$	−6.28362			−0.454667			−0.227334	−	0.973817i	$-0.573001\pi$
$191$	−6.28362			−0.454667			−0.227334	+	0.973817i	$0.573001\pi$
$192$	17.5187	−	10.1144i	1.26430	−	0.729946i
$193$	−15.4405	+	8.91459i	−1.11143	+	0.641686i	−0.939200	−	0.343370i	$-0.888431\pi$
$193$	−15.4405	+	8.91459i	−1.11143	+	0.641686i	−0.172233	+	0.985056i	$0.555098\pi$
$194$	8.14649	−	14.1101i	0.584884	−	1.01305i
$195$		0			0
$196$	−0.710713	+	1.23099i	−0.0507652	+	0.0879279i
$197$		−	16.9925i		−	1.21066i	−0.795973	−	0.605332i	$-0.793041\pi$
$197$		−	16.9925i		−	1.21066i	0.795973	−	0.605332i	$-0.206959\pi$
$198$		−	42.7672i		−	3.03934i
$199$	8.22212	−	14.2411i	0.582850	−	1.00953i	−0.412289	−	0.911053i	$-0.635271\pi$
$199$	8.22212	−	14.2411i	0.582850	−	1.00953i	0.995140	−	0.0984735i	$-0.0313960\pi$
$200$		0			0
$201$	−2.23227			−0.157452
$202$		−	7.64131i		−	0.537641i
$203$	5.45603	+	3.15004i	0.382938	+	0.221090i
$204$	0.484826	+	0.839743i	0.0339446	+	0.0587937i
$205$		0			0
$206$	5.74593	+	9.95225i	0.400338	+	0.693406i
$207$	−2.59919	+	1.50064i	−0.180656	+	0.104302i
$208$		−	21.3446i		−	1.47998i
$209$	3.55851	−	24.1253i	0.246147	−	1.66878i
$210$		0			0
$211$	−7.79632	−	13.5036i	−0.536721	−	0.929628i	−0.999078	−	0.0429343i	$-0.986329\pi$
$211$	−7.79632	−	13.5036i	−0.536721	−	0.929628i	0.462357	−	0.886694i	$-0.347004\pi$
$212$	1.14156	−	0.659078i	0.0784024	−	0.0452657i
$213$	15.7802	+	9.11068i	1.08124	+	0.624253i
$214$	−9.37013	−	16.2295i	−0.640529	−	1.10943i
$215$		0			0
$216$	16.5143			1.12366
$217$			26.5615i			1.80311i
$218$	10.5108	+	6.06841i	0.711880	+	0.411004i
$219$	−4.12678	+	7.14779i	−0.278862	+	0.483003i
$220$		0			0
$221$	−8.58734			−0.577647
$222$	−8.65997	−	4.99984i	−0.581219	−	0.335567i
$223$	−6.76042	+	3.90313i	−0.452711	+	0.261373i	−0.708974	−	0.705234i	$-0.750842\pi$
$223$	−6.76042	+	3.90313i	−0.452711	+	0.261373i	0.256263	+	0.966607i	$0.417509\pi$
$224$	2.06933	−	3.58419i	0.138263	−	0.239479i
$225$		0			0
$226$	9.29826	+	16.1051i	0.618511	+	1.07129i
$227$			16.8511i			1.11845i	0.829017	+	0.559223i	$0.188900\pi$
$227$			16.8511i			1.11845i	−0.829017	+	0.559223i	$0.811100\pi$
$228$	−2.38909	−	0.352394i	−0.158222	−	0.0233379i
$229$	0.251385			0.0166120			0.00830600	−	0.999966i	$-0.497356\pi$
$229$	0.251385			0.0166120			0.00830600	+	0.999966i	$0.497356\pi$
$230$		0			0
$231$	30.2498	+	52.3942i	1.99029	+	3.44729i
$232$	−3.85575	−	2.22612i	−0.253142	−	0.146152i
$233$	−20.0943	+	11.6014i	−1.31642	+	0.760035i	−0.983151	−	0.182797i	$-0.941485\pi$
$233$	−20.0943	+	11.6014i	−1.31642	+	0.760035i	−0.333269	+	0.942832i	$0.608152\pi$
$234$	18.7536	−	32.4822i	1.22596	−	2.12343i
$235$		0			0
$236$	−0.0792355			−0.00515779
$237$	30.9318	+	17.8585i	2.00923	+	1.16003i
$238$	−8.49848	−	4.90660i	−0.550874	−	0.318047i
$239$	7.58778			0.490813			0.245406	−	0.969420i	$-0.421079\pi$
$239$	7.58778			0.490813			0.245406	+	0.969420i	$0.421079\pi$
$240$		0			0
$241$	2.75808	−	4.77714i	0.177664	−	0.307723i	−0.763416	−	0.645907i	$-0.776479\pi$
$241$	2.75808	−	4.77714i	0.177664	−	0.307723i	0.941080	+	0.338184i	$0.109813\pi$
$242$	−26.0393	+	15.0338i	−1.67387	+	0.966409i
$243$	−10.7131	−	6.18523i	−0.687248	−	0.396783i
$244$	1.35371	+	2.34469i	0.0866623	+	0.150103i
$245$		0			0
$246$	−3.53469			−0.225364
$247$	13.2818	−	16.7630i	0.845099	−	1.06661i
$248$		−	18.7708i		−	1.19195i
$249$	14.8411	+	25.7056i	0.940519	+	1.62903i
$250$		0			0
$251$	9.32933	−	16.1589i	0.588862	−	1.01994i	−0.405520	−	0.914086i	$-0.632910\pi$
$251$	9.32933	−	16.1589i	0.588862	−	1.01994i	0.994382	−	0.105852i	$-0.0337571\pi$
$252$	3.28121	−	1.89441i	0.206697	−	0.119336i
$253$	2.81758	+	1.62673i	0.177140	+	0.102272i
$254$	12.0853			0.758297
$255$		0			0
$256$	−2.30606	+	3.99422i	−0.144129	+	0.249639i
$257$	−0.599899	−	0.346352i	−0.0374207	−	0.0216048i	0.481173	−	0.876626i	$-0.340211\pi$
$257$	−0.599899	−	0.346352i	−0.0374207	−	0.0216048i	−0.518594	+	0.855021i	$0.673544\pi$
$258$			4.53320i			0.282225i
$259$	8.94574			0.555861
$260$		0			0
$261$	−4.29470	−	7.43865i	−0.265836	−	0.460441i
$262$	24.6927	+	14.2564i	1.52552	+	0.880761i
$263$	−10.0691	+	5.81338i	−0.620885	+	0.358468i	−0.777214	−	0.629237i	$-0.783368\pi$
$263$	−10.0691	+	5.81338i	−0.620885	+	0.358468i	0.156328	+	0.987705i	$0.450034\pi$
$264$	−21.3774	−	37.0267i	−1.31569	−	2.27884i
$265$		0			0
$266$	22.7223	−	9.00067i	1.39319	−	0.551866i
$267$			50.9703i			3.11933i
$268$	0.131240	−	0.0757716i	0.00801677	−	0.00462849i
$269$	−11.8057	−	20.4481i	−0.719809	−	1.24675i	−0.961075	−	0.276286i	$-0.910896\pi$
$269$	−11.8057	−	20.4481i	−0.719809	−	1.24675i	0.241267	−	0.970459i	$-0.422437\pi$
$270$		0			0
$271$	3.81995	+	6.61635i	0.232046	+	0.401915i	0.958410	−	0.285395i	$-0.0921248\pi$
$271$	3.81995	+	6.61635i	0.232046	+	0.401915i	−0.726364	+	0.687310i	$0.758791\pi$
$272$	6.59373	+	3.80689i	0.399804	+	0.230827i
$273$			53.0587i			3.21126i
$274$	2.32830			0.140658
$275$		0			0
$276$	0.161093	−	0.279022i	0.00969667	−	0.0167951i
$277$		−	18.6537i		−	1.12079i	−0.828224	−	0.560397i	$-0.810648\pi$
$277$		−	18.6537i		−	1.12079i	0.828224	−	0.560397i	$-0.189352\pi$
$278$		−	3.03524i		−	0.182041i
$279$	18.1067	−	31.3617i	1.08402	−	1.87758i
$280$		0			0
$281$	−6.99489	+	12.1155i	−0.417280	+	0.722750i	−0.995665	−	0.0930139i	$-0.970350\pi$
$281$	−6.99489	+	12.1155i	−0.417280	+	0.722750i	0.578385	+	0.815764i	$0.303683\pi$
$282$	14.1726	−	8.18257i	0.843968	−	0.487265i
$283$	21.3620	−	12.3334i	1.26984	−	0.733143i	0.294884	−	0.955533i	$-0.404719\pi$
$283$	21.3620	−	12.3334i	1.26984	−	0.733143i	0.974958	+	0.222390i	$0.0713857\pi$
$284$	−1.23700			−0.0734025
$285$		0			0
$286$	−40.6588			−2.40420
$287$	2.73850	−	1.58107i	0.161649	−	0.0933278i
$288$	−4.88662	+	2.82129i	−0.287947	+	0.166246i
$289$	−6.96842	+	12.0697i	−0.409907	+	0.709979i
$290$		0			0
$291$	15.7119	−	27.2138i	0.921049	−	1.59530i
$292$		−	0.560312i		−	0.0327898i
$293$		−	10.5784i		−	0.617994i	−0.951063	−	0.308997i	$-0.900007\pi$
$293$		−	10.5784i		−	0.617994i	0.951063	−	0.308997i	$-0.0999933\pi$
$294$	−15.5066	+	26.8583i	−0.904365	+	1.56641i
$295$		0			0
$296$	−6.32191			−0.367454
$297$		−	34.5371i		−	2.00404i
$298$	1.89293	+	1.09288i	0.109654	+	0.0633090i
$299$	1.42666	+	2.47105i	0.0825058	+	0.142904i
$300$		0			0
$301$	−2.02771	−	3.51209i	−0.116875	−	0.202434i
$302$	−8.24223	+	4.75866i	−0.474287	+	0.273830i
$303$		−	14.7376i		−	0.846652i
$304$	−17.6296	+	6.98337i	−1.01113	+	0.400524i
$305$		0			0
$306$	6.68956	+	11.5867i	0.382417	+	0.662365i
$307$	−11.1063	+	6.41222i	−0.633870	+	0.365965i	−0.782249	−	0.622966i	$-0.785928\pi$
$307$	−11.1063	+	6.41222i	−0.633870	+	0.365965i	0.148379	+	0.988931i	$0.452594\pi$
$308$	−3.55691	−	2.05358i	−0.202674	−	0.117014i
$309$	11.0820	+	19.1946i	0.630434	+	1.09194i
$310$		0			0
$311$	3.42706			0.194331			0.0971655	−	0.995268i	$-0.469022\pi$
$311$	3.42706			0.194331			0.0971655	+	0.995268i	$0.469022\pi$
$312$		−	37.4963i		−	2.12281i
$313$	2.46339	+	1.42224i	0.139239	+	0.0803896i	0.568001	−	0.823028i	$-0.307717\pi$
$313$	2.46339	+	1.42224i	0.139239	+	0.0803896i	−0.428762	+	0.903417i	$0.641050\pi$
$314$	−16.5071	+	28.5912i	−0.931551	+	1.61349i
$315$		0			0
$316$	−2.42473			−0.136402
$317$	−4.03693	−	2.33072i	−0.226737	−	0.130907i	0.382329	−	0.924026i	$-0.375122\pi$
$317$	−4.03693	−	2.33072i	−0.226737	−	0.130907i	−0.609066	+	0.793120i	$0.708455\pi$
$318$	24.9069	−	14.3800i	1.39671	−	0.806392i
$319$	−4.65556	+	8.06367i	−0.260662	+	0.451479i
$320$		0			0
$321$	−18.0719	−	31.3015i	−1.00868	−	1.74708i
$322$			3.26063i			0.181708i
$323$	2.80954	+	7.09272i	0.156327	+	0.394649i
$324$	−0.417467			−0.0231926
$325$		0			0
$326$	−11.1327	−	19.2825i	−0.616585	−	1.06796i
$327$	20.2719	+	11.7040i	1.12104	+	0.647231i
$328$	−1.93528	+	1.11734i	−0.106858	+	0.0616946i
$329$	−7.32016	+	12.6789i	−0.403573	+	0.699010i
$330$		0			0
$331$	−7.00260			−0.384898			−0.192449	−	0.981307i	$-0.561643\pi$
$331$	−7.00260			−0.384898			−0.192449	+	0.981307i	$0.561643\pi$
$332$	−1.74509	−	1.00753i	−0.0957741	−	0.0552952i
$333$	−10.5624	−	6.09822i	−0.578818	−	0.334181i
$334$	14.2173			0.777938
$335$		0			0
$336$	23.5217	−	40.7408i	1.28321	−	2.22259i
$337$	11.7239	−	6.76881i	0.638643	−	0.368721i	−0.145449	−	0.989366i	$-0.546463\pi$
$337$	11.7239	−	6.76881i	0.638643	−	0.368721i	0.784092	+	0.620645i	$0.213129\pi$
$338$	−14.2051	−	8.20130i	−0.772654	−	0.446092i
$339$	17.9333	+	31.0614i	0.974003	+	1.68702i
$340$		0			0
$341$	−39.2562			−2.12584
$342$	−32.9644	−	4.86229i	−1.78251	−	0.262923i
$343$		−	1.24667i		−	0.0673140i
$344$	1.43297	+	2.48198i	0.0772606	+	0.133819i
$345$		0			0
$346$	−6.54112	+	11.3296i	−0.351653	+	0.609081i
$347$	−19.0208	+	10.9817i	−1.02109	+	0.589527i	−0.914420	−	0.404768i	$-0.867352\pi$
$347$	−19.0208	+	10.9817i	−1.02109	+	0.589527i	−0.106671	+	0.994294i	$0.534019\pi$
$348$	0.798535	+	0.461034i	0.0428060	+	0.0247140i
$349$	22.1930			1.18796			0.593981	−	0.804479i	$-0.297555\pi$
$349$	22.1930			1.18796			0.593981	+	0.804479i	$0.297555\pi$
$350$		0			0
$351$	15.1447	−	26.2313i	0.808362	−	1.40012i
$352$	5.29721	+	3.05835i	0.282342	+	0.163010i
$353$		−	0.679013i		−	0.0361402i	−0.999837	−	0.0180701i	$-0.994248\pi$
$353$		−	0.679013i		−	0.0361402i	0.999837	−	0.0180701i	$-0.00575221\pi$
$354$	−1.72879			−0.0918843
$355$		0			0
$356$	−1.73012	−	2.99666i	−0.0916962	−	0.158822i
$357$	−16.3908	−	9.46322i	−0.867492	−	0.500847i
$358$	13.8766	−	8.01166i	0.733402	−	0.423430i
$359$	−12.6627	−	21.9325i	−0.668314	−	1.15755i	−0.978375	−	0.206837i	$-0.933683\pi$
$359$	−12.6627	−	21.9325i	−0.668314	−	1.15755i	0.310062	−	0.950716i	$-0.399650\pi$
$360$		0			0
$361$	−18.1909	−	5.48570i	−0.957413	−	0.288721i
$362$		−	15.9187i		−	0.836666i
$363$	−50.2213	+	28.9953i	−2.63593	+	1.52186i
$364$	−1.80101	−	3.11944i	−0.0943985	−	0.163503i
$365$		0			0
$366$	29.5357	+	51.1574i	1.54386	+	2.67404i
$367$	10.1005	+	5.83153i	0.527243	+	0.304404i	0.739893	−	0.672725i	$-0.234876\pi$
$367$	10.1005	+	5.83153i	0.527243	+	0.304404i	−0.212650	+	0.977128i	$0.568210\pi$
$368$		−	2.52984i		−	0.131877i
$369$	−4.31121			−0.224433
$370$		0			0
$371$	−12.8644	+	22.2818i	−0.667887	+	1.15681i
$372$			3.88749i			0.201557i
$373$		−	13.0913i		−	0.677843i	−0.940815	−	0.338921i	$-0.889938\pi$
$373$		−	13.0913i		−	0.677843i	0.940815	−	0.338921i	$-0.110062\pi$
$374$	7.25164	−	12.5602i	0.374974	−	0.649473i
$375$		0			0
$376$	5.17312	−	8.96010i	0.266783	−	0.462082i
$377$	−7.07192	+	4.08297i	−0.364222	+	0.210284i
$378$	29.9759	−	17.3066i	1.54179	−	0.890155i
$379$	32.7566			1.68259			0.841297	−	0.540573i	$-0.181792\pi$
$379$	32.7566			1.68259			0.841297	+	0.540573i	$0.181792\pi$
$380$		0			0
$381$	23.3085			1.19413
$382$	8.06033	−	4.65363i	0.412402	−	0.238101i
$383$	−22.2096	+	12.8227i	−1.13486	+	0.655211i	−0.945152	−	0.326630i	$-0.894087\pi$
$383$	−22.2096	+	12.8227i	−1.13486	+	0.655211i	−0.189707	+	0.981841i	$0.560754\pi$
$384$	−18.1048	+	31.3584i	−0.923905	+	1.60025i
$385$		0			0
$386$	13.2042	−	22.8704i	0.672078	−	1.16407i
$387$			5.52907i			0.281059i
$388$			2.13328i			0.108301i
$389$	−9.27329	+	16.0618i	−0.470174	+	0.814366i	−0.999418	−	0.0341039i	$-0.989142\pi$
$389$	−9.27329	+	16.0618i	−0.470174	+	0.814366i	0.529244	+	0.848470i	$0.322476\pi$
$390$		0			0
$391$	−1.01780			−0.0514723
$392$			19.6069i			0.990300i
$393$	47.6242	+	27.4958i	2.40232	+	1.38698i
$394$	12.5846	+	21.7971i	0.634002	+	1.09812i
$395$		0			0
$396$	2.79981	+	4.84942i	0.140696	+	0.243692i
$397$	−13.3334	+	7.69806i	−0.669186	+	0.386355i	−0.795768	−	0.605601i	$-0.792933\pi$
$397$	−13.3334	+	7.69806i	−0.669186	+	0.386355i	0.126582	+	0.991956i	$0.459599\pi$
$398$			24.3571i			1.22091i
$399$	43.8239	−	17.3593i	2.19394	−	0.869054i
$400$		0			0
$401$	10.2956	+	17.8326i	0.514140	+	0.890517i	0.999865	+	0.0164054i	$0.00522222\pi$
$401$	10.2956	+	17.8326i	0.514140	+	0.890517i	−0.485725	+	0.874112i	$0.661444\pi$
$402$	2.86345	−	1.65321i	0.142816	−	0.0824548i
$403$	−29.8155	−	17.2140i	−1.48522	−	0.857491i
$404$	0.500248	+	0.866455i	0.0248883	+	0.0431078i
$405$		0			0
$406$	−9.33165			−0.463122
$407$			13.2212i			0.655353i
$408$	11.5833	+	6.68761i	0.573458	+	0.331086i
$409$	−0.811919	+	1.40629i	−0.0401468	+	0.0695363i	−0.885401	−	0.464829i	$-0.846116\pi$
$409$	−0.811919	+	1.40629i	−0.0401468	+	0.0695363i	0.845254	+	0.534365i	$0.179449\pi$
$410$		0			0
$411$	4.49054			0.221502
$412$	−1.30307	−	0.752330i	−0.0641978	−	0.0370646i
$413$	1.33938	−	0.773292i	0.0659066	−	0.0380512i
$414$	2.22274	−	3.84990i	0.109242	−	0.189212i
$415$		0			0
$416$	2.68220	+	4.64570i	0.131506	+	0.227774i
$417$		−	5.85398i		−	0.286671i
$418$	13.3024	+	33.5822i	0.650643	+	1.64256i
$419$	−16.8087			−0.821161			−0.410580	−	0.911824i	$-0.634674\pi$
$419$	−16.8087			−0.821161			−0.410580	+	0.911824i	$0.634674\pi$
$420$		0			0
$421$	−10.4718	−	18.1377i	−0.510365	−	0.883977i	−0.999928	−	0.0120096i	$-0.996177\pi$
$421$	−10.4718	−	18.1377i	−0.510365	−	0.883977i	0.489563	−	0.871968i	$-0.337156\pi$
$422$	20.0015	+	11.5479i	0.973658	+	0.562142i
$423$	17.2861	−	9.98016i	0.840481	−	0.485252i
$424$	9.09122	−	15.7465i	0.441509	−	0.764716i
$425$		0			0
$426$	−26.9894			−1.30764
$427$	−45.7656	−	26.4228i	−2.21475	−	1.27869i
$428$	2.12498	+	1.22686i	0.102715	+	0.0593023i
$429$	−78.4175			−3.78603
$430$		0			0
$431$	−16.8908	+	29.2557i	−0.813600	+	1.40920i	0.0967292	+	0.995311i	$0.469162\pi$
$431$	−16.8908	+	29.2557i	−0.813600	+	1.40920i	−0.910329	+	0.413885i	$0.864171\pi$
$432$	−23.2575	+	13.4277i	−1.11898	+	0.646041i
$433$	−13.0154	−	7.51443i	−0.625479	−	0.361120i	0.153520	−	0.988146i	$-0.450939\pi$
$433$	−13.0154	−	7.51443i	−0.625479	−	0.361120i	−0.778999	+	0.627025i	$0.784272\pi$
$434$	−19.6713	−	34.0718i	−0.944254	−	1.63550i
$435$		0			0
$436$	−1.58910			−0.0761043
$437$	1.57420	−	1.98681i	0.0753042	−	0.0950419i
$438$		−	12.2251i		−	0.584139i
$439$	18.8607	+	32.6677i	0.900173	+	1.55915i	0.827269	+	0.561807i	$0.189894\pi$
$439$	18.8607	+	32.6677i	0.900173	+	1.55915i	0.0729045	+	0.997339i	$0.476773\pi$
$440$		0			0
$441$	−18.9132	+	32.7586i	−0.900628	+	1.55993i
$442$	11.0154	−	6.35976i	0.523950	−	0.302503i
$443$	11.3574	+	6.55722i	0.539608	+	0.311543i	0.744920	−	0.667154i	$-0.232488\pi$
$443$	11.3574	+	6.55722i	0.539608	+	0.311543i	−0.205312	+	0.978697i	$0.565821\pi$
$444$	1.30928			0.0621358
$445$		0			0
$446$	5.78129	−	10.0135i	0.273752	−	0.474153i
$447$	3.65084	+	2.10781i	0.172679	+	0.0996961i
$448$		−	26.8049i		−	1.26641i
$449$	−11.6905			−0.551711			−0.275855	−	0.961199i	$-0.588961\pi$
$449$	−11.6905			−0.551711			−0.275855	+	0.961199i	$0.588961\pi$
$450$		0			0
$451$	2.33673	+	4.04733i	0.110032	+	0.190581i
$452$	−2.10868	−	1.21744i	−0.0991838	−	0.0572638i
$453$	−15.8966	+	9.17789i	−0.746886	+	0.431215i
$454$	−12.4799	−	21.6158i	−0.585709	−	1.01448i
$455$		0			0
$456$	−30.9701	+	12.2678i	−1.45031	+	0.574490i
$457$		−	21.4290i		−	1.00240i	−0.865330	−	0.501202i	$-0.832891\pi$
$457$		−	21.4290i		−	1.00240i	0.865330	−	0.501202i	$-0.167109\pi$
$458$	−0.322465	+	0.186175i	−0.0150678	+	0.00869939i
$459$	5.40221	+	9.35691i	0.252154	+	0.436743i
$460$		0			0
$461$	4.82920	+	8.36442i	0.224918	+	0.389570i	0.956295	−	0.292404i	$-0.0944551\pi$
$461$	4.82920	+	8.36442i	0.224918	+	0.389570i	−0.731377	+	0.681974i	$0.761122\pi$
$462$	−77.6060	−	44.8058i	−3.61056	−	2.08456i
$463$		−	1.24981i		−	0.0580838i	−0.999578	−	0.0290419i	$-0.990754\pi$
$463$		−	1.24981i		−	0.0580838i	0.999578	−	0.0290419i	$-0.00924562\pi$
$464$	7.24017			0.336116
$465$		0			0
$466$	17.1840	−	29.7635i	0.796032	−	1.37877i
$467$		−	31.3476i		−	1.45059i	−0.688437	−	0.725296i	$-0.741703\pi$
$467$		−	31.3476i		−	1.45059i	0.688437	−	0.725296i	$-0.258297\pi$
$468$			4.91092i			0.227007i
$469$	−1.47897	+	2.56165i	−0.0682925	+	0.118286i
$470$		0			0
$471$	−31.8368	+	55.1430i	−1.46696	+	2.54085i
$472$	−0.946533	+	0.546481i	−0.0435677	+	0.0251538i
$473$	5.19065	−	2.99682i	0.238666	−	0.137794i
$474$	−52.9037			−2.42995
$475$		0			0
$476$	1.28487			0.0588918
$477$	30.3786	−	17.5391i	1.39094	−	0.803060i
$478$	−9.73324	+	5.61949i	−0.445188	+	0.257029i
$479$	2.37730	−	4.11760i	0.108622	−	0.188138i	−0.806591	−	0.591111i	$-0.798690\pi$
$479$	2.37730	−	4.11760i	0.108622	−	0.188138i	0.915212	+	0.402973i	$0.132023\pi$
$480$		0			0
$481$	−5.79758	+	10.0417i	−0.264347	+	0.457862i
$482$			8.17052i			0.372157i
$483$			6.28870i			0.286146i
$484$	1.96841	−	3.40939i	0.0894733	−	0.154972i
$485$		0			0
$486$	18.3230			0.831150
$487$			17.0491i			0.772569i	0.922380	+	0.386285i	$0.126242\pi$
$487$			17.0491i			0.772569i	−0.922380	+	0.386285i	$0.873758\pi$
$488$	32.3423	+	18.6728i	1.46407	+	0.845280i
$489$	−21.4714	−	37.1896i	−0.970970	−	1.68177i
$490$		0			0
$491$	2.14031	+	3.70713i	0.0965910	+	0.167301i	0.910272	−	0.414012i	$-0.135873\pi$
$491$	2.14031	+	3.70713i	0.0965910	+	0.167301i	−0.813680	+	0.581312i	$0.802539\pi$
$492$	0.400802	−	0.231403i	0.0180696	−	0.0104325i
$493$		−	2.91285i		−	0.131188i
$494$	−4.62258	+	31.3392i	−0.207980	+	1.41002i
$495$		0			0
$496$	15.2624	+	26.4353i	0.685304	+	1.18698i
$497$	20.9100	−	12.0724i	0.937942	−	0.541521i
$498$	−38.0750	−	21.9826i	−1.70618	−	0.985064i
$499$	−2.41284	−	4.17916i	−0.108013	−	0.187085i	0.806952	−	0.590617i	$-0.201116\pi$
$499$	−2.41284	−	4.17916i	−0.108013	−	0.187085i	−0.914965	+	0.403532i	$0.867782\pi$
$500$		0			0
$501$	27.4206			1.22506
$502$			27.6371i			1.23350i
$503$	−21.0215	−	12.1368i	−0.937304	−	0.541153i	−0.0481900	−	0.998838i	$-0.515345\pi$
$503$	−21.0215	−	12.1368i	−0.937304	−	0.541153i	−0.889114	+	0.457685i	$0.848679\pi$
$504$	26.1311	−	45.2604i	1.16397	−	2.01606i
$505$		0			0
$506$	−4.81901			−0.214231
$507$	−27.3969	−	15.8176i	−1.21674	−	0.702485i
$508$	−1.37036	+	0.791177i	−0.0607998	+	0.0351028i
$509$	−5.05690	+	8.75880i	−0.224143	+	0.388227i	−0.956062	−	0.293165i	$-0.905292\pi$
$509$	−5.05690	+	8.75880i	−0.224143	+	0.388227i	0.731919	+	0.681392i	$0.238625\pi$
$510$		0			0
$511$	5.46831	+	9.47140i	0.241904	+	0.418990i
$512$			18.5188i			0.818423i
$513$	−26.6207	−	3.92659i	−1.17533	−	0.173363i
$514$	1.02603			0.0452562
$515$		0			0
$516$	−0.296772	−	0.514024i	−0.0130646	−	0.0226286i
$517$	−18.7386	−	10.8187i	−0.824123	−	0.475807i
$518$	−11.4752	+	6.62519i	−0.504190	+	0.291094i
$519$	−12.6157	+	21.8510i	−0.553767	+	0.959153i
$520$		0			0
$521$	29.3729			1.28685			0.643426	−	0.765508i	$-0.277513\pi$
$521$	29.3729			1.28685			0.643426	+	0.765508i	$0.277513\pi$
$522$	11.0181	+	6.36129i	0.482248	+	0.278426i
$523$	−9.69944	−	5.59998i	−0.424127	−	0.244870i	0.272714	−	0.962095i	$-0.412079\pi$
$523$	−9.69944	−	5.59998i	−0.424127	−	0.244870i	−0.696842	+	0.717225i	$0.745412\pi$
$524$	−3.73324			−0.163087
$525$		0			0
$526$	8.61074	−	14.9142i	0.375446	−	0.650292i
$527$	10.6354	−	6.14037i	0.463286	−	0.267479i
$528$	60.2124	+	34.7636i	2.62041	+	1.51289i
$529$	−11.3309	−	19.6257i	−0.492648	−	0.853292i
$530$		0			0
$531$	−2.10858			−0.0915046
$532$	−1.98726	+	2.50814i	−0.0861588	+	0.108742i
$533$			4.09866i			0.177533i
$534$	−37.7485	−	65.3822i	−1.63354	−	2.82937i
$535$		0			0
$536$	1.04518	−	1.81031i	0.0451450	−	0.0781934i
$537$	26.7634	−	15.4519i	1.15493	−	0.666798i
$538$	30.2877	+	17.4866i	1.30579	+	0.753901i
$539$	41.0047			1.76620
$540$		0			0
$541$	−2.84691	+	4.93100i	−0.122398	+	0.212000i	−0.920713	−	0.390241i	$-0.872392\pi$
$541$	−2.84691	+	4.93100i	−0.122398	+	0.212000i	0.798315	+	0.602241i	$0.205725\pi$
$542$	−9.80010	−	5.65809i	−0.420950	−	0.243036i
$543$		−	30.7019i		−	1.31754i
$544$	−1.91352			−0.0820415
$545$		0			0
$546$	−39.2951	−	68.0612i	−1.68168	−	2.91275i
$547$	−10.3765	−	5.99088i	−0.443667	−	0.256151i	0.261485	−	0.965208i	$-0.415788\pi$
$547$	−10.3765	−	5.99088i	−0.443667	−	0.256151i	−0.705152	+	0.709056i	$0.749121\pi$
$548$	−0.264009	+	0.152425i	−0.0112779	+	0.00651129i
$549$	36.0243	+	62.3959i	1.53748	+	2.66299i
$550$		0			0
$551$	5.68607	+	4.50522i	0.242235	+	0.191929i
$552$		−	4.44419i		−	0.189157i
$553$	40.9871	−	23.6639i	1.74295	−	1.00629i
$554$	13.8149	+	23.9281i	0.586939	+	1.01661i
$555$		0			0
$556$	0.198706	+	0.344168i	0.00842700	+	0.0145960i
$557$	29.9275	+	17.2786i	1.26807	+	0.732119i	0.974622	−	0.223857i	$-0.0718647\pi$
$557$	29.9275	+	17.2786i	1.26807	+	0.732119i	0.293446	+	0.955976i	$0.405198\pi$
$558$			53.6390i			2.27072i
$559$	5.25649			0.222326
$560$		0			0
$561$	13.9860	−	24.2245i	0.590491	−	1.02276i
$562$		−	20.7216i		−	0.874087i
$563$		−	24.8817i		−	1.04864i	−0.851522	−	0.524318i	$-0.824320\pi$
$563$		−	24.8817i		−	1.04864i	0.851522	−	0.524318i	$-0.175680\pi$
$564$	−1.07137	+	1.85566i	−0.0451126	+	0.0781374i
$565$		0			0
$566$	−18.2681	+	31.6413i	−0.767867	+	1.32998i
$567$	7.05676	−	4.07422i	0.296356	−	0.171101i
$568$	−14.7770	+	8.53150i	−0.620029	+	0.357974i
$569$	38.7345			1.62384			0.811918	−	0.583771i	$-0.198423\pi$
$569$	38.7345			1.62384			0.811918	+	0.583771i	$0.198423\pi$
$570$		0			0
$571$	−4.53514			−0.189790			−0.0948948	−	0.995487i	$-0.530251\pi$
$571$	−4.53514			−0.189790			−0.0948948	+	0.995487i	$0.530251\pi$
$572$	4.61034	−	2.66178i	0.192768	−	0.111295i
$573$	15.5457	−	8.97534i	0.649433	−	0.374950i
$574$	−2.34188	+	4.05625i	−0.0977481	+	0.169305i
$575$		0			0
$576$	−18.2726	+	31.6491i	−0.761359	+	1.31871i
$577$			21.9514i			0.913847i	0.889506	+	0.456923i	$0.151049\pi$
$577$			21.9514i			0.913847i	−0.889506	+	0.456923i	$0.848951\pi$
$578$		−	20.6432i		−	0.858642i
$579$	25.4666	−	44.1095i	1.05836	−	1.83313i
$580$		0			0
$581$	39.3314			1.63174
$582$			46.5448i			1.92934i
$583$	−32.9311	−	19.0128i	−1.36387	−	0.787430i
$584$	−3.86443	−	6.69339i	−0.159911	−	0.276974i
$585$		0			0
$586$	7.83430	+	13.5694i	0.323632	+	0.560547i
$587$	35.5472	−	20.5232i	1.46719	−	0.847084i	0.467866	−	0.883799i	$-0.345023\pi$
$587$	35.5472	−	20.5232i	1.46719	−	0.847084i	0.999326	+	0.0367158i	$0.0116896\pi$
$588$		−	4.06064i		−	0.167458i
$589$	−4.46311	+	30.2581i	−0.183899	+	1.24676i
$590$		0			0
$591$	24.2715	+	42.0395i	0.998397	+	1.72927i
$592$	8.90327	−	5.14030i	0.365922	−	0.211265i
$593$	8.41745	+	4.85982i	0.345663	+	0.199569i	0.662774	−	0.748820i	$-0.269379\pi$
$593$	8.41745	+	4.85982i	0.345663	+	0.199569i	−0.317110	+	0.948389i	$0.602713\pi$
$594$	25.5780	+	44.3025i	1.04948	+	1.81775i
$595$		0			0
$596$	−0.286188			−0.0117227
$597$			46.9769i			1.92264i
$598$	−3.66010	−	2.11316i	−0.149673	−	0.0864135i
$599$	−15.2247	+	26.3700i	−0.622065	+	1.07745i	0.367036	+	0.930207i	$0.380373\pi$
$599$	−15.2247	+	26.3700i	−0.622065	+	1.07745i	−0.989101	+	0.147241i	$0.952961\pi$
$600$		0			0
$601$	24.5483			1.00135			0.500673	−	0.865637i	$-0.333086\pi$
$601$	24.5483			1.00135			0.500673	+	0.865637i	$0.333086\pi$
$602$	5.20209	+	3.00343i	0.212021	+	0.122411i
$603$	3.49251	−	2.01640i	0.142226	−	0.0821142i
$604$	0.623063	−	1.07918i	0.0253521	−	0.0439111i
$605$		0			0
$606$	10.9146	+	18.9047i	0.443376	+	0.767949i
$607$		−	39.0162i		−	1.58362i	−0.610767	−	0.791810i	$-0.709139\pi$
$607$		−	39.0162i		−	1.58362i	0.610767	−	0.791810i	$-0.290861\pi$
$608$	2.95958	−	3.73531i	0.120027	−	0.151487i
$609$	−17.9977			−0.729303
$610$		0			0
$611$	−9.48813	−	16.4339i	−0.383849	−	0.664845i
$612$	−1.51707	−	0.875881i	−0.0613239	−	0.0354054i
$613$	4.30775	−	2.48708i	0.173988	−	0.100452i	−0.410477	−	0.911871i	$-0.634638\pi$
$613$	4.30775	−	2.48708i	0.173988	−	0.100452i	0.584465	+	0.811419i	$0.301304\pi$
$614$	9.49775	−	16.4506i	0.383298	−	0.663891i
$615$		0			0
$616$	−56.6536			−2.28264
$617$	−33.4649	−	19.3210i	−1.34725	−	0.777834i	−0.359389	−	0.933188i	$-0.617015\pi$
$617$	−33.4649	−	19.3210i	−1.34725	−	0.777834i	−0.987859	+	0.155354i	$0.950348\pi$
$618$	−28.4310	−	16.4146i	−1.14366	−	0.660293i
$619$	27.9053			1.12161			0.560804	−	0.827949i	$-0.310492\pi$
$619$	27.9053			1.12161			0.560804	+	0.827949i	$0.310492\pi$
$620$		0			0
$621$	1.79500	−	3.10902i	0.0720307	−	0.124761i
$622$	−4.39607	+	2.53807i	−0.176266	+	0.101767i
$623$	58.4912	+	33.7699i	2.34340	+	1.35296i
$624$	30.4880	+	52.8068i	1.22050	+	2.11396i
$625$		0			0
$626$	−4.21322			−0.168394
$627$	25.6560	+	64.7690i	1.02460	+	2.58662i
$628$		−	4.32264i		−	0.172492i
$629$	−2.06804	−	3.58195i	−0.0824581	−	0.142822i
$630$		0			0
$631$	6.62012	−	11.4664i	0.263543	−	0.456469i	−0.703638	−	0.710559i	$-0.748442\pi$
$631$	6.62012	−	11.4664i	0.263543	−	0.456469i	0.967181	+	0.254089i	$0.0817757\pi$
$632$	−28.9654	+	16.7232i	−1.15218	+	0.665212i
$633$	38.5763	+	22.2721i	1.53327	+	0.885235i
$634$	6.90451			0.274213
$635$		0			0
$636$	−1.88281	+	3.26113i	−0.0746584	+	0.129312i
$637$	31.1436	+	17.9808i	1.23395	+	0.712423i
$638$		−	13.7916i		−	0.546014i
$639$	−32.9185			−1.30224
$640$		0			0
$641$	−18.7555	−	32.4854i	−0.740796	−	1.28310i	−0.952133	−	0.305684i	$-0.901115\pi$
$641$	−18.7555	−	32.4854i	−0.740796	−	1.28310i	0.211337	−	0.977413i	$-0.432218\pi$
$642$	46.3636	+	26.7680i	1.82982	+	1.05645i
$643$	−21.1257	+	12.1969i	−0.833117	+	0.481000i	−0.854919	−	0.518762i	$-0.826393\pi$
$643$	−21.1257	+	12.1969i	−0.833117	+	0.481000i	0.0218020	+	0.999762i	$0.493060\pi$
$644$	−0.213462	−	0.369726i	−0.00841157	−	0.0145693i
$645$		0			0
$646$	−8.85679	−	7.01746i	−0.348466	−	0.276098i
$647$		−	8.05266i		−	0.316583i	−0.987392	−	0.158291i	$-0.949401\pi$
$647$		−	8.05266i		−	0.316583i	0.987392	−	0.158291i	$-0.0505985\pi$
$648$	−4.98698	+	2.87923i	−0.195907	+	0.113107i
$649$	1.14288	+	1.97952i	0.0448618	+	0.0777030i
$650$		0			0
$651$	−37.9396	−	65.7133i	−1.48697	−	2.57551i
$652$	2.52470	+	1.45764i	0.0988750	+	0.0570855i
$653$		−	19.9890i		−	0.782228i	−0.920342	−	0.391114i	$-0.872090\pi$
$653$		−	19.9890i		−	0.782228i	0.920342	−	0.391114i	$-0.127910\pi$
$654$	−34.6717			−1.35577
$655$		0			0
$656$	1.81700	−	3.14713i	0.0709419	−	0.122875i
$657$		−	14.9108i		−	0.581725i
$658$		−	21.6852i		−	0.845375i
$659$	−16.2197	+	28.0933i	−0.631829	+	1.09436i	0.355349	+	0.934734i	$0.384362\pi$
$659$	−16.2197	+	28.0933i	−0.631829	+	1.09436i	−0.987178	+	0.159626i	$0.948971\pi$
$660$		0			0
$661$	17.7771	−	30.7908i	0.691448	−	1.19762i	−0.279915	−	0.960025i	$-0.590306\pi$
$661$	17.7771	−	30.7908i	0.691448	−	1.19762i	0.971363	−	0.237599i	$-0.0763603\pi$
$662$	8.98260	−	5.18610i	0.349118	−	0.201564i
$663$	21.2451	−	12.2659i	0.825093	−	0.476368i
$664$	−27.7953			−1.07867
$665$		0			0
$666$	18.0653			0.700017
$667$	−0.838187	+	0.483927i	−0.0324547	+	0.0187377i
$668$	−1.61212	+	0.930757i	−0.0623747	+	0.0360121i
$669$	11.1502	−	19.3127i	0.431092	−	0.746674i
$670$		0			0
$671$	39.0512	−	67.6387i	1.50755	−	2.61116i
$672$			11.8231i			0.456086i
$673$			27.5963i			1.06376i	0.846820	+	0.531880i	$0.178514\pi$
$673$			27.5963i			1.06376i	−0.846820	+	0.531880i	$0.821486\pi$
$674$	−10.0259	+	17.3654i	−0.386184	+	0.668891i
$675$		0			0
$676$	2.14763			0.0826013
$677$		−	21.2114i		−	0.815221i	−0.913156	−	0.407610i	$-0.866362\pi$
$677$		−	21.2114i		−	0.815221i	0.913156	−	0.407610i	$-0.133638\pi$
$678$	−46.0079	−	26.5627i	−1.76692	−	1.02013i
$679$	−20.8196	−	36.0605i	−0.798981	−	1.38388i
$680$		0			0
$681$	−24.0696	−	41.6897i	−0.922348	−	1.59755i
$682$	50.3559	−	29.0730i	1.92823	−	1.11326i
$683$			19.3626i			0.740891i	0.928854	+	0.370446i	$0.120795\pi$
$683$			19.3626i			0.740891i	−0.928854	+	0.370446i	$0.879205\pi$
$684$	4.05618	−	1.60672i	0.155092	−	0.0614344i
$685$		0			0
$686$	0.923282	+	1.59917i	0.0352511	+	0.0610567i
$687$	−0.621929	+	0.359071i	−0.0237281	+	0.0136994i
$688$	−4.03616	−	2.33028i	−0.153877	−	0.0888410i
$689$	−16.6744	−	28.8809i	−0.635244	−	1.10028i
$690$		0			0
$691$	−1.28081			−0.0487241			−0.0243621	−	0.999703i	$-0.507755\pi$
$691$	−1.28081			−0.0487241			−0.0243621	+	0.999703i	$0.507755\pi$
$692$		−	1.71289i		−	0.0651144i
$693$	−94.6548	−	54.6490i	−3.59564	−	2.07594i
$694$	16.2660	−	28.1735i	0.617448	−	1.06945i
$695$		0			0
$696$	12.7189			0.482108
$697$	−1.26615	−	0.731012i	−0.0479588	−	0.0276891i
$698$	−28.4681	+	16.4361i	−1.07753	+	0.622114i
$699$	33.1423	−	57.4041i	1.25356	−	2.17122i
$700$		0			0
$701$	18.5649	+	32.1553i	0.701185	+	1.21449i	0.968051	+	0.250754i	$0.0806787\pi$
$701$	18.5649	+	32.1553i	0.701185	+	1.21449i	−0.266866	+	0.963734i	$0.585988\pi$
$702$			44.8644i			1.69330i
$703$	10.1908	+	1.50315i	0.384352	+	0.0566924i
$704$	39.6159			1.49308
$705$		0			0
$706$	0.502875	+	0.871005i	0.0189260	+	0.0327807i
$707$	−16.9122	−	9.76425i	−0.636048	−	0.367222i
$708$	0.196029	−	0.113178i	0.00736723	−	0.00425347i
$709$	6.57886	−	11.3949i	0.247074	−	0.427945i	−0.715638	−	0.698471i	$-0.753864\pi$
$709$	6.57886	−	11.3949i	0.247074	−	0.427945i	0.962713	+	0.270526i	$0.0871975\pi$
$710$		0			0
$711$	−64.5258			−2.41991
$712$	−41.3354	−	23.8650i	−1.54911	−	0.894379i
$713$	−3.53384	−	2.04026i	−0.132343	−	0.0764084i
$714$	28.0337			1.04914
$715$		0			0
$716$	−1.04899	+	1.81690i	−0.0392025	+	0.0679007i
$717$	−18.7722	+	10.8382i	−0.701062	+	0.404758i
$718$	32.4863	+	18.7560i	1.21238	+	0.699967i
$719$	7.27853	+	12.6068i	0.271443	+	0.470153i	0.969232	−	0.246150i	$-0.0791657\pi$
$719$	7.27853	+	12.6068i	0.271443	+	0.470153i	−0.697788	+	0.716304i	$0.745832\pi$
$720$		0			0
$721$	29.3692			1.09376
$722$	27.3970	−	6.43530i	1.01961	−	0.239497i
$723$			15.7583i			0.586056i
$724$	1.04214	+	1.80503i	0.0387306	+	0.0670834i
$725$		0			0
$726$	42.9476	−	74.3874i	1.59394	−	2.76078i
$727$	−7.76966	+	4.48581i	−0.288161	+	0.166370i	−0.637112	−	0.770771i	$-0.719871\pi$
$727$	−7.76966	+	4.48581i	−0.288161	+	0.166370i	0.348951	+	0.937141i	$0.386538\pi$
$728$	−43.0291	−	24.8428i	−1.59476	−	0.920737i
$729$	41.7969			1.54803
$730$		0			0
$731$	−0.937514	+	1.62382i	−0.0346752	+	0.0600592i
$732$	−6.69817	−	3.86719i	−0.247571	−	0.142935i
$733$			24.7325i			0.913516i	0.889591	+	0.456758i	$0.150990\pi$
$733$			24.7325i			0.913516i	−0.889591	+	0.456758i	$0.849010\pi$
$734$	−17.2753			−0.637642
$735$		0			0
$736$	0.317903	+	0.550624i	0.0117181	+	0.0202963i
$737$	−3.78596	−	2.18583i	−0.139458	−	0.0805159i
$738$	5.53021	−	3.19287i	0.203570	−	0.117531i
$739$	−0.784588	−	1.35895i	−0.0288615	−	0.0499896i	0.851234	−	0.524787i	$-0.175855\pi$
$739$	−0.784588	−	1.35895i	−0.0288615	−	0.0499896i	−0.880095	+	0.474797i	$0.842522\pi$
$740$		0			0
$741$	−8.91543	+	60.4431i	−0.327517	+	2.22043i
$742$		−	38.1094i		−	1.39904i
$743$	−21.0380	+	12.1463i	−0.771808	+	0.445604i	−0.833519	−	0.552490i	$-0.813678\pi$
$743$	−21.0380	+	12.1463i	−0.771808	+	0.445604i	0.0617109	+	0.998094i	$0.480344\pi$
$744$	26.8117	+	46.4392i	0.982965	+	1.70254i
$745$		0			0
$746$	9.69539	+	16.7929i	0.354974	+	0.614832i
$747$	−46.4395	−	26.8119i	−1.69913	−	0.980994i
$748$			1.89895i			0.0694326i
$749$	−47.8935			−1.74999
$750$		0			0
$751$	−17.4771	+	30.2712i	−0.637748	+	1.10461i	0.348178	+	0.937429i	$0.386801\pi$
$751$	−17.4771	+	30.2712i	−0.637748	+	1.10461i	−0.985926	+	0.167184i	$0.946533\pi$
$752$			16.8249i			0.613541i
$753$			53.3029i			1.94247i
$754$	6.04768	−	10.4749i	0.220243	−	0.381473i
$755$		0			0
$756$	−2.26600	+	3.92482i	−0.0824135	+	0.142744i
$757$	2.78935	−	1.61043i	0.101381	−	0.0585321i	−0.448452	−	0.893807i	$-0.648025\pi$
$757$	2.78935	−	1.61043i	0.101381	−	0.0585321i	0.549833	+	0.835275i	$0.314691\pi$
$758$	−42.0186	+	24.2595i	−1.52619	+	0.881143i
$759$	−9.29430			−0.337362
$760$		0			0
$761$	3.72402			0.134996			0.0674979	−	0.997719i	$-0.478498\pi$
$761$	3.72402			0.134996			0.0674979	+	0.997719i	$0.478498\pi$
$762$	−29.8990	+	17.2622i	−1.08313	+	0.625344i
$763$	26.8619	−	15.5087i	0.972465	−	0.561453i
$764$	−0.609312	+	1.05536i	−0.0220441	+	0.0381816i
$765$		0			0
$766$	18.9930	−	32.8968i	0.686244	−	1.18861i
$767$			2.00463i			0.0723829i
$768$		−	13.1756i		−	0.475435i
$769$	−16.1032	+	27.8915i	−0.580695	+	1.00579i	0.414702	+	0.909957i	$0.363886\pi$
$769$	−16.1032	+	27.8915i	−0.580695	+	1.00579i	−0.995397	+	0.0958365i	$0.969447\pi$
$770$		0			0
$771$	1.97887			0.0712674
$772$			3.45773i			0.124446i
$773$	−17.9122	−	10.3416i	−0.644259	−	0.371963i	0.141994	−	0.989867i	$-0.454649\pi$
$773$	−17.9122	−	10.3416i	−0.644259	−	0.371963i	−0.786253	+	0.617904i	$0.787982\pi$
$774$	−4.09482	−	7.09243i	−0.147185	−	0.254932i
$775$		0			0
$776$	14.7131	+	25.4838i	0.528169	+	0.914815i
$777$	−22.1318	+	12.7778i	−0.793975	+	0.458402i
$778$		−	27.4711i		−	0.984886i
$779$	3.38530	−	1.34097i	0.121291	−	0.0480452i
$780$		0			0
$781$	17.8422	+	30.9037i	0.638446	+	1.10582i
$782$	1.30558	−	0.753780i	0.0466876	−	0.0269551i
$783$	8.89775	+	5.13712i	0.317980	+	0.183586i
$784$	−15.9423	−	27.6128i	−0.569367	−	0.986172i
$785$		0			0
$786$	−81.4534			−2.90535
$787$			46.0227i			1.64053i	0.571982	+	0.820266i	$0.306175\pi$
$787$			46.0227i			1.64053i	−0.571982	+	0.820266i	$0.693825\pi$
$788$	−2.85395	−	1.64773i	−0.101668	−	0.0586980i
$789$	16.6073	−	28.7647i	0.591236	−	1.02405i
$790$		0			0
$791$	47.5261			1.68983
$792$	66.8921	+	38.6202i	2.37691	+	1.37231i
$793$	59.3197	−	34.2483i	2.10651	−	1.21619i
$794$	11.4023	−	19.7494i	0.404654	−	0.700880i
$795$		0			0
$796$	−1.59457	−	2.76187i	−0.0565180	−	0.0978920i
$797$			25.0847i			0.888546i	0.895891	+	0.444273i	$0.146538\pi$
$797$			25.0847i			0.888546i	−0.895891	+	0.444273i	$0.853462\pi$
$798$	−43.3589	+	54.7236i	−1.53489	+	1.93719i
$799$	6.76897			0.239469
$800$		0			0
$801$	−46.0412	−	79.7457i	−1.62679	−	2.81768i
$802$	−26.4135	−	15.2499i	−0.932694	−	0.538491i
$803$	−13.9981	+	8.08183i	−0.493983	+	0.285201i
$804$	−0.216460	+	0.374919i	−0.00763394	+	0.0132224i
$805$		0			0
$806$	50.9946			1.79621
$807$	58.4150	+	33.7259i	2.05631	+	1.18721i
$808$	11.9517	+	6.90034i	0.420461	+	0.242753i
$809$	−27.6272			−0.971319			−0.485660	−	0.874148i	$-0.661421\pi$
$809$	−27.6272			−0.971319			−0.485660	+	0.874148i	$0.661421\pi$
$810$		0			0
$811$	19.2254	−	33.2993i	0.675094	−	1.16930i	−0.301347	−	0.953514i	$-0.597436\pi$
$811$	19.2254	−	33.2993i	0.675094	−	1.16930i	0.976441	−	0.215783i	$-0.0692304\pi$
$812$	1.05812	−	0.610908i	0.0371329	−	0.0214387i
$813$	−18.9012	−	10.9126i	−0.662893	−	0.382722i
$814$	−9.79162	−	16.9596i	−0.343196	−	0.594433i
$815$		0			0
$816$	−21.7506			−0.761423
$817$	−1.71978	−	4.34160i	−0.0601674	−	0.151893i
$818$		−	2.40522i		−	0.0840966i
$819$	−47.9277	−	83.0132i	−1.67473	−	2.90071i
$820$		0			0
$821$	−26.3339	+	45.6117i	−0.919060	+	1.59186i	−0.118215	+	0.992988i	$0.537717\pi$
$821$	−26.3339	+	45.6117i	−0.919060	+	1.59186i	−0.800845	+	0.598871i	$0.795616\pi$
$822$	−5.76024	+	3.32568i	−0.200912	+	0.115996i
$823$	4.04602	+	2.33597i	0.141035	+	0.0814269i	0.568857	−	0.822436i	$-0.307386\pi$
$823$	4.04602	+	2.33597i	0.141035	+	0.0814269i	−0.427822	+	0.903863i	$0.640719\pi$
$824$	−20.7550			−0.723036
$825$		0			0
$826$	−1.14540	+	1.98388i	−0.0398534	+	0.0690281i
$827$	−23.7506	−	13.7124i	−0.825888	−	0.476827i	0.0265546	−	0.999647i	$-0.491546\pi$
$827$	−23.7506	−	13.7124i	−0.825888	−	0.476827i	−0.852443	+	0.522821i	$0.824880\pi$
$828$			0.582059i			0.0202279i
$829$	−0.156181			−0.00542438			−0.00271219	−	0.999996i	$-0.500863\pi$
$829$	−0.156181			−0.00542438			−0.00271219	+	0.999996i	$0.500863\pi$
$830$		0			0
$831$	26.6444	+	46.1495i	0.924285	+	1.60091i
$832$	30.0888	+	17.3718i	1.04314	+	0.602258i
$833$	−11.1091	+	6.41387i	−0.384909	+	0.222227i
$834$	4.33544	+	7.50920i	0.150124	+	0.260022i
$835$		0			0
$836$	−3.70687	−	2.93705i	−0.128205	−	0.101580i
$837$			43.3167i			1.49724i
$838$	21.5615	−	12.4485i	0.744828	−	0.430027i
$839$	−14.5946	−	25.2786i	−0.503862	−	0.872715i	−0.999990	−	0.00446519i	$-0.998579\pi$
$839$	−14.5946	−	25.2786i	−0.503862	−	0.872715i	0.496128	−	0.868249i	$-0.334755\pi$
$840$		0			0
$841$	13.1150	+	22.7159i	0.452243	+	0.783308i
$842$	26.8655	+	15.5108i	0.925845	+	0.534537i
$843$		−	39.9651i		−	1.37647i
$844$	−3.02398			−0.104090
$845$		0			0
$846$	−14.7826	+	25.6041i	−0.508235	+	0.880288i
$847$			76.8421i			2.64033i
$848$			29.5680i			1.01537i
$849$	−35.2332	+	61.0258i	−1.20920	+	2.09440i
$850$		0			0
$851$	−0.687148	+	1.19018i	−0.0235551	+	0.0407987i
$852$	3.06035	−	1.76689i	0.104846	−	0.0605328i
$853$	39.6348	−	22.8832i	1.35707	−	0.783505i	0.367842	−	0.929888i	$-0.380097\pi$
$853$	39.6348	−	22.8832i	1.35707	−	0.783505i	0.989228	+	0.146384i	$0.0467634\pi$
$854$	78.2745			2.67850
$855$		0			0
$856$	33.8461			1.15684
$857$	12.9177	−	7.45807i	0.441262	−	0.254763i	−0.262871	−	0.964831i	$-0.584669\pi$
$857$	12.9177	−	7.45807i	0.441262	−	0.254763i	0.704133	+	0.710068i	$0.251336\pi$
$858$	100.590	−	58.0757i	3.43409	−	1.98267i
$859$	24.6100	−	42.6258i	0.839682	−	1.45437i	−0.0504787	−	0.998725i	$-0.516075\pi$
$859$	24.6100	−	42.6258i	0.839682	−	1.45437i	0.890161	−	0.455647i	$-0.150592\pi$
$860$		0			0
$861$	−4.51671	+	7.82318i	−0.153929	+	0.266613i
$862$		−	50.0370i		−	1.70427i
$863$		−	20.9577i		−	0.713407i	−0.934218	−	0.356704i	$-0.883901\pi$
$863$		−	20.9577i		−	0.713407i	0.934218	−	0.356704i	$-0.116099\pi$
$864$	3.37469	−	5.84514i	0.114809	−	0.198856i
$865$		0			0
$866$	22.2607			0.756448
$867$		−	39.8139i		−	1.35215i
$868$	4.46110	+	2.57562i	0.151420	+	0.0874222i
$869$	34.9738	+	60.5764i	1.18640	+	2.05491i
$870$		0			0
$871$	−1.91699	−	3.32032i	−0.0649547	−	0.112505i
$872$	−18.9831	+	10.9599i	−0.642851	+	0.371150i
$873$			56.7700i			1.92137i
$874$	−0.547883	+	3.71443i	−0.0185324	+	0.125642i
$875$		0			0
$876$	0.800333	+	1.38622i	0.0270407	+	0.0468359i
$877$	−22.6914	+	13.1009i	−0.766233	+	0.442385i	−0.831529	−	0.555481i	$-0.812534\pi$
$877$	−22.6914	+	13.1009i	−0.766233	+	0.442385i	0.0652963	+	0.997866i	$0.479201\pi$
$878$	−48.3873	−	27.9364i	−1.63299	−	0.942808i
$879$	15.1098	+	26.1709i	0.509641	+	0.882724i
$880$		0			0
$881$	−45.3499			−1.52788			−0.763938	−	0.645289i	$-0.776737\pi$
$881$	−45.3499			−1.52788			−0.763938	+	0.645289i	$0.776737\pi$
$882$		−	56.0282i		−	1.88657i
$883$	−37.5136	−	21.6585i	−1.26243	−	0.728867i	−0.288890	−	0.957362i	$-0.593286\pi$
$883$	−37.5136	−	21.6585i	−1.26243	−	0.728867i	−0.973545	+	0.228495i	$0.926619\pi$
$884$	−0.832699	+	1.44228i	−0.0280067	+	0.0485090i
$885$		0			0
$886$	−19.4250			−0.652597
$887$	−33.7877	−	19.5073i	−1.13448	−	0.654992i	−0.189422	−	0.981896i	$-0.560661\pi$
$887$	−33.7877	−	19.5073i	−1.13448	−	0.654992i	−0.945058	+	0.326904i	$0.893995\pi$
$888$	15.6405	−	9.03002i	0.524859	−	0.303028i
$889$	15.4428	−	26.7478i	0.517936	−	0.897091i
$890$		0			0
$891$	6.02145	+	10.4295i	0.201726	+	0.349400i
$892$			1.51392i			0.0506898i
$893$	−10.4694	+	13.2135i	−0.350344	+	0.442171i
$894$	−6.24416			−0.208836
$895$		0			0
$896$	23.9903	+	41.5524i	0.801459	+	1.38817i
$897$	−7.05913	−	4.07559i	−0.235698	−	0.136080i
$898$	14.9961	−	8.65798i	0.500425	−	0.288921i
$899$	5.83905	−	10.1135i	0.194743	−	0.337305i
$900$		0			0
$901$	11.8958			0.396306
$902$	−5.99488	−	3.46115i	−0.199608	−	0.115244i
$903$	10.0331	+	5.79263i	0.333882	+	0.192767i
$904$	−33.5865			−1.11707
$905$		0			0
$906$	13.5942	−	23.5459i	0.451638	−	0.782260i
$907$	−43.4405	+	25.0804i	−1.44242	+	0.832780i	−0.998011	−	0.0630443i	$-0.979919\pi$
$907$	−43.4405	+	25.0804i	−1.44242	+	0.832780i	−0.444407	+	0.895825i	$0.646586\pi$
$908$	2.83021	+	1.63402i	0.0939237	+	0.0542269i
$909$	13.3124	+	23.0577i	0.441544	+	0.764776i
$910$		0			0
$911$	−50.4028			−1.66992			−0.834959	−	0.550312i	$-0.814509\pi$
$911$	−50.4028			−1.66992			−0.834959	+	0.550312i	$0.814509\pi$
$912$	33.6410	−	42.4585i	1.11396	−	1.40594i
$913$			58.1294i			1.92380i
$914$	15.8702	+	27.4880i	0.524940	+	0.909223i
$915$		0			0
$916$	0.0243764	−	0.0422211i	0.000805418	−	0.00139503i
$917$	63.1059	−	36.4342i	2.08394	−	1.20316i
$918$	−13.8594	−	8.00173i	−0.457428	−	0.264096i
$919$	−48.7246			−1.60728			−0.803638	−	0.595118i	$-0.797105\pi$
$919$	−48.7246			−1.60728			−0.803638	+	0.595118i	$0.797105\pi$
$920$		0			0
$921$	18.3180	−	31.7278i	0.603600	−	1.04547i
$922$	−12.3893	−	7.15299i	−0.408021	−	0.235571i
$923$			31.2956i			1.03011i
$924$	11.7331			0.385990
$925$		0			0
$926$	0.925608	+	1.60320i	0.0304174	+	0.0526844i
$927$	−34.6768	−	20.0207i	−1.13894	−	0.657565i
$928$	−1.57584	+	0.909811i	−0.0517294	+	0.0298660i
$929$	4.01832	+	6.95993i	0.131837	+	0.228348i	0.924385	−	0.381462i	$-0.124579\pi$
$929$	4.01832	+	6.95993i	0.131837	+	0.228348i	−0.792548	+	0.609810i	$0.791246\pi$
$930$		0			0
$931$	4.66191	−	31.6059i	0.152788	−	1.03584i
$932$			4.49989i			0.147399i
$933$	−8.47858	+	4.89511i	−0.277576	+	0.160259i
$934$	23.2159	+	40.2111i	0.759648	+	1.31575i
$935$		0			0
$936$	33.8702	+	58.6650i	1.10708	+	1.91752i
$937$	22.1206	+	12.7713i	0.722647	+	0.417221i	0.815726	−	0.578438i	$-0.196338\pi$
$937$	22.1206	+	12.7713i	0.722647	+	0.417221i	−0.0930789	+	0.995659i	$0.529671\pi$
$938$		−	4.38129i		−	0.143054i
$939$	−8.12592			−0.265179
$940$		0			0
$941$	−4.30747	+	7.46075i	−0.140419	+	0.243214i	−0.927655	−	0.373439i	$-0.878178\pi$
$941$	−4.30747	+	7.46075i	−0.140419	+	0.243214i	0.787235	+	0.616653i	$0.211512\pi$
$942$		−	94.3130i		−	3.07288i
$943$			0.485787i			0.0158194i
$944$	0.888680	−	1.53924i	0.0289241	−	0.0500980i
$945$		0			0
$946$	−4.43888	+	7.68837i	−0.144320	+	0.249970i
$947$	33.2793	−	19.2138i	1.08143	−	0.624364i	0.150149	−	0.988663i	$-0.452025\pi$
$947$	33.2793	−	19.2138i	1.08143	−	0.624364i	0.931282	+	0.364299i	$0.118691\pi$
$948$	5.99880	−	3.46341i	0.194832	−	0.112486i
$949$	−14.1757			−0.460162
$950$		0			0
$951$	13.3165			0.431819
$952$	15.3488	−	8.86163i	0.497457	−	0.287207i
$953$	7.69932	−	4.44520i	0.249405	−	0.143994i	−0.370087	−	0.928997i	$-0.620672\pi$
$953$	7.69932	−	4.44520i	0.249405	−	0.143994i	0.619492	+	0.785003i	$0.287339\pi$
$954$	−25.9788	+	44.9966i	−0.841095	+	1.45682i
$955$		0			0
$956$	0.735774	−	1.27440i	0.0237966	−	0.0412170i
$957$		−	26.5995i		−	0.859838i
$958$			7.04248i			0.227532i
$959$	2.97516	−	5.15313i	0.0960730	−	0.166403i
$960$		0			0
$961$	18.2354			0.588239
$962$		−	17.1747i		−	0.553734i
$963$	56.5489	+	32.6485i	1.82226	+	1.05208i
$964$	−0.534893	−	0.926463i	−0.0172278	−	0.0298394i
$965$		0			0
$966$	−4.65739	−	8.06684i	−0.149849	−	0.259546i
$967$	53.3729	−	30.8149i	1.71636	−	0.990939i	0.791021	−	0.611789i	$-0.209550\pi$
$967$	53.3729	−	30.8149i	1.71636	−	0.990939i	0.925335	−	0.379150i	$-0.123784\pi$
$968$		−	54.3040i		−	1.74540i
$969$	−17.0818	−	13.5344i	−0.548748	−	0.434787i
$970$		0			0
$971$	−2.92998	−	5.07488i	−0.0940277	−	0.162861i	0.815175	−	0.579215i	$-0.196641\pi$
$971$	−2.92998	−	5.07488i	−0.0940277	−	0.162861i	−0.909202	+	0.416354i	$0.863308\pi$
$972$	−2.07767	+	1.19954i	−0.0666412	+	0.0384753i
$973$	−6.71776	−	3.87850i	−0.215361	−	0.124339i
$974$	−12.6265	−	21.8698i	−0.404580	−	0.700753i
$975$		0			0
$976$	−60.7310			−1.94395
$977$		−	2.40082i		−	0.0768089i	−0.999262	−	0.0384044i	$-0.987772\pi$
$977$		−	2.40082i		−	0.0768089i	0.999262	−	0.0384044i	$-0.0122275\pi$
$978$	55.0850	+	31.8033i	1.76142	+	1.01696i
$979$	−49.9098	+	86.4463i	−1.59512	+	2.76284i
$980$		0			0
$981$	−42.2885			−1.35017
$982$	−5.49098	−	3.17022i	−0.175224	−	0.101166i
$983$	−15.9076	+	9.18425i	−0.507373	+	0.292932i	−0.731753	−	0.681570i	$-0.761298\pi$
$983$	−15.9076	+	9.18425i	−0.507373	+	0.292932i	0.224380	+	0.974502i	$0.427964\pi$
$984$	3.19194	−	5.52860i	0.101755	−	0.176245i
$985$		0			0
$986$	2.15725	+	3.73647i	0.0687009	+	0.118993i
$987$		−	41.8236i		−	1.33126i
$988$	−1.52750	−	3.85621i	−0.0485964	−	0.122682i
$989$	0.623016			0.0198108
$990$		0			0
$991$	−5.14734	−	8.91546i	−0.163511	−	0.283209i	0.772615	−	0.634875i	$-0.218948\pi$
$991$	−5.14734	−	8.91546i	−0.163511	−	0.283209i	−0.936125	+	0.351666i	$0.885615\pi$
$992$	−6.64381	−	3.83581i	−0.210941	−	0.121787i
$993$	17.3245	−	10.0023i	0.549776	−	0.317413i
$994$	−17.8816	+	30.9718i	−0.567169	+	0.982365i
$995$		0			0
$996$	5.75648			0.182401
$997$	−1.99385	−	1.15115i	−0.0631459	−	0.0364573i	0.468095	−	0.883678i	$-0.344941\pi$
$997$	−1.99385	−	1.15115i	−0.0631459	−	0.0364573i	−0.531241	+	0.847221i	$0.678274\pi$
$998$	6.19014	+	3.57388i	0.195946	+	0.113129i
$999$	14.5888			0.461569

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.j.d.349.3		24
5.2	odd	4		475.2.e.h.26.2	yes	12
5.3	odd	4		475.2.e.f.26.5	✓	12
5.4	even	2	inner	475.2.j.d.349.10		24
19.11	even	3	inner	475.2.j.d.49.10		24
95.7	odd	12		9025.2.a.br.1.5		6
95.12	even	12		9025.2.a.by.1.2		6
95.49	even	6	inner	475.2.j.d.49.3		24
95.68	odd	12		475.2.e.f.201.5	yes	12
95.83	odd	12		9025.2.a.bz.1.2		6
95.87	odd	12		475.2.e.h.201.2	yes	12
95.88	even	12		9025.2.a.bs.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.e.f.26.5	✓	12	5.3	odd	4
475.2.e.f.201.5	yes	12	95.68	odd	12
475.2.e.h.26.2	yes	12	5.2	odd	4
475.2.e.h.201.2	yes	12	95.87	odd	12
475.2.j.d.49.3		24	95.49	even	6	inner
475.2.j.d.49.10		24	19.11	even	3	inner
475.2.j.d.349.3		24	1.1	even	1	trivial
475.2.j.d.349.10		24	5.4	even	2	inner
9025.2.a.br.1.5		6	95.7	odd	12
9025.2.a.bs.1.5		6	95.88	even	12
9025.2.a.by.1.2		6	95.12	even	12
9025.2.a.bz.1.2		6	95.83	odd	12

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.28275 + 0.740597i) q^{2} +(-2.47401 + 1.42837i) q^{3} +(0.0969683 - 0.167954i) q^{4} +(2.11569 - 3.66449i) q^{6} +3.78541i q^{7} -2.67513i q^{8} +(2.58048 - 4.46952i) q^{9} -5.59460 q^{11} +0.554026i q^{12} +(-4.24917 - 2.45326i) q^{13} +(-2.80346 - 4.85574i) q^{14} +(2.17513 + 3.76744i) q^{16} +(1.51571 - 0.875095i) q^{17} +7.64438i q^{18} +(-0.636061 + 4.31224i) q^{19} +(-5.40696 - 9.36514i) q^{21} +(7.17648 - 4.14335i) q^{22} +(-0.503625 - 0.290768i) q^{23} +(3.82107 + 6.61830i) q^{24} +7.26750 q^{26} +6.17328i q^{27} +(0.635775 + 0.367065i) q^{28} +(0.832153 - 1.44133i) q^{29} +7.01680 q^{31} +(-0.946844 - 0.546661i) q^{32} +(13.8411 - 7.99116i) q^{33} +(-1.29619 + 2.24506i) q^{34} +(-0.500449 - 0.866803i) q^{36} -2.36322i q^{37} +(-2.37773 - 6.00260i) q^{38} +14.0166 q^{39} +(-0.417676 - 0.723435i) q^{41} +(13.8716 + 8.00877i) q^{42} +(-0.927797 + 0.535664i) q^{43} +(-0.542499 + 0.939635i) q^{44} +0.861369 q^{46} +(3.34941 + 1.93378i) q^{47} +(-10.7626 - 6.21378i) q^{48} -7.32934 q^{49} +(-2.49992 + 4.32999i) q^{51} +(-0.824069 + 0.475776i) q^{52} +(5.88624 + 3.39842i) q^{53} +(-4.57192 - 7.91879i) q^{54} +10.1265 q^{56} +(-4.58585 - 11.5771i) q^{57} +2.46516i q^{58} +(-0.204282 - 0.353827i) q^{59} +(-6.98016 + 12.0900i) q^{61} +(-9.00081 + 5.19662i) q^{62} +(16.9190 + 9.76817i) q^{63} -7.08110 q^{64} +(-11.8365 + 20.5013i) q^{66} +(0.676717 + 0.390703i) q^{67} -0.339426i q^{68} +1.66130 q^{69} +(-3.18919 - 5.52384i) q^{71} +(-11.9565 - 6.90312i) q^{72} +(2.50208 - 1.44458i) q^{73} +(1.75019 + 3.03142i) q^{74} +(0.662580 + 0.524980i) q^{76} -21.1779i q^{77} +(-17.9799 + 10.3807i) q^{78} +(-6.25135 - 10.8276i) q^{79} +(-1.07630 - 1.86420i) q^{81} +(1.07155 + 0.618659i) q^{82} -10.3903i q^{83} -2.09722 q^{84} +(0.793422 - 1.37425i) q^{86} +4.75449i q^{87} +14.9663i q^{88} +(8.92106 - 15.4517i) q^{89} +(9.28659 - 16.0848i) q^{91} +(-0.0976714 + 0.0563906i) q^{92} +(-17.3596 + 10.0226i) q^{93} -5.72861 q^{94} +3.12333 q^{96} +(-9.52619 + 5.49995i) q^{97} +(9.40172 - 5.42809i) q^{98} +(-14.4367 + 25.0052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} + 2 q^{6} + 14 q^{9} - 4 q^{11} - 12 q^{14} + 12 q^{16} + 12 q^{19} - 6 q^{21} + 22 q^{24} + 76 q^{26} + 6 q^{29} - 12 q^{31} - 2 q^{34} - 26 q^{36} - 32 q^{39} - 22 q^{41} + 42 q^{44} - 48 q^{46}+ \cdots - 40 q^{99}+O(q^{100}) \) 24 * q + 4 * q^4 + 2 * q^6 + 14 * q^9 - 4 * q^11 - 12 * q^14 + 12 * q^16 + 12 * q^19 - 6 * q^21 + 22 * q^24 + 76 * q^26 + 6 * q^29 - 12 * q^31 - 2 * q^34 - 26 * q^36 - 32 * q^39 - 22 * q^41 + 42 * q^44 - 48 * q^46 - 16 * q^49 + 34 * q^51 + 36 * q^54 + 16 * q^56 + 8 * q^59 - 50 * q^61 + 88 * q^64 - 68 * q^66 - 52 * q^69 - 36 * q^71 - 12 * q^74 + 48 * q^76 + 6 * q^79 - 4 * q^81 - 148 * q^84 - 18 * q^86 + 24 * q^89 + 22 * q^91 - 32 * q^94 - 52 * q^96 - 40 * q^99

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