LMFDB - Embedded newform 441.2.u.c.190.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(64,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("441.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.u (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			190.2
Character	$\chi$	$=$	441.190
Dual form			441.2.u.c.253.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.159899 + 0.200507i) q^{2} +(0.430406 + 1.88573i) q^{4} +(1.50958 + 0.726973i) q^{5} +(2.63685 - 0.216906i) q^{7} +(-0.909048 - 0.437774i) q^{8} +O(q^{10})$	\(q+(-0.159899 + 0.200507i) q^{2} +(0.430406 + 1.88573i) q^{4} +(1.50958 + 0.726973i) q^{5} +(2.63685 - 0.216906i) q^{7} +(-0.909048 - 0.437774i) q^{8} +(-0.387144 + 0.186439i) q^{10} +(2.04337 - 2.56231i) q^{11} +(1.69439 - 2.12470i) q^{13} +(-0.378139 + 0.563390i) q^{14} +(-3.25223 + 1.56619i) q^{16} +(-0.947383 + 4.15076i) q^{17} -2.59506 q^{19} +(-0.721147 + 3.15955i) q^{20} +(0.187028 + 0.819422i) q^{22} +(1.32984 + 5.82640i) q^{23} +(-1.36712 - 1.71431i) q^{25} +(0.155086 + 0.679476i) q^{26} +(1.54394 + 4.87903i) q^{28} +(0.403151 - 1.76632i) q^{29} +1.19212 q^{31} +(0.655029 - 2.86987i) q^{32} +(-0.680771 - 0.853660i) q^{34} +(4.13820 + 1.58948i) q^{35} +(0.755841 - 3.31155i) q^{37} +(0.414948 - 0.520328i) q^{38} +(-1.05403 - 1.32171i) q^{40} +(5.05633 + 2.43500i) q^{41} +(-9.10344 + 4.38399i) q^{43} +(5.71131 + 2.75042i) q^{44} +(-1.38088 - 0.664995i) q^{46} +(-0.656516 + 0.823245i) q^{47} +(6.90590 - 1.14389i) q^{49} +0.562334 q^{50} +(4.73589 + 2.28069i) q^{52} +(-2.01380 - 8.82301i) q^{53} +(4.94735 - 2.38252i) q^{55} +(-2.49197 - 0.957165i) q^{56} +(0.289696 + 0.363268i) q^{58} +(-10.7625 + 5.18294i) q^{59} +(-1.71060 + 7.49462i) q^{61} +(-0.190620 + 0.239029i) q^{62} +(-4.03053 - 5.05413i) q^{64} +(4.10241 - 1.97562i) q^{65} +11.8842 q^{67} -8.23498 q^{68} +(-0.980398 + 0.575583i) q^{70} +(-3.66683 - 16.0655i) q^{71} +(-4.59351 - 5.76008i) q^{73} +(0.543133 + 0.681067i) q^{74} +(-1.11693 - 4.89359i) q^{76} +(4.83227 - 7.19962i) q^{77} -0.219320 q^{79} -6.04806 q^{80} +(-1.29674 + 0.624477i) q^{82} +(-10.0647 - 12.6208i) q^{83} +(-4.44764 + 5.57716i) q^{85} +(0.576612 - 2.52630i) q^{86} +(-2.97923 + 1.43472i) q^{88} +(10.7698 + 13.5050i) q^{89} +(4.00699 - 5.97003i) q^{91} +(-10.4147 + 5.01544i) q^{92} +(-0.0600903 - 0.263273i) q^{94} +(-3.91744 - 1.88654i) q^{95} -5.31289 q^{97} +(-0.874890 + 1.56759i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} - 3 q^{4} - 3 q^{8}+O(q^{10}) $ 24 * q - q^2 - 3 * q^4 - 3 * q^8	$ 24 q - q^{2} - 3 q^{4} - 3 q^{8} - 30 q^{10} - 9 q^{11} + 21 q^{14} - 29 q^{16} - 5 q^{17} + 26 q^{19} + 13 q^{20} + 11 q^{22} - 4 q^{23} - 28 q^{25} + 22 q^{26} - 7 q^{28} - 6 q^{29} + 36 q^{31} - 14 q^{32} + 46 q^{34} + 7 q^{35} - 22 q^{37} + 45 q^{38} + 35 q^{40} + 11 q^{41} + 6 q^{43} - 82 q^{44} - 16 q^{46} - 29 q^{47} - 42 q^{49} + 48 q^{50} - 50 q^{52} - 28 q^{53} + 23 q^{55} - 21 q^{56} + 39 q^{58} + 15 q^{59} - 32 q^{61} + 8 q^{62} + 29 q^{64} + 21 q^{65} - 34 q^{67} + 22 q^{68} - 24 q^{71} - 15 q^{73} - 6 q^{74} + 7 q^{76} + 21 q^{77} - 34 q^{79} - 8 q^{80} + 14 q^{82} - 14 q^{83} + 20 q^{85} + 100 q^{86} - 108 q^{88} - 10 q^{89} + 84 q^{91} + 21 q^{92} + 99 q^{94} - 18 q^{95} - 64 q^{97} - 91 q^{98}+O(q^{100}) $ 24 * q - q^2 - 3 * q^4 - 3 * q^8 - 30 * q^10 - 9 * q^11 + 21 * q^14 - 29 * q^16 - 5 * q^17 + 26 * q^19 + 13 * q^20 + 11 * q^22 - 4 * q^23 - 28 * q^25 + 22 * q^26 - 7 * q^28 - 6 * q^29 + 36 * q^31 - 14 * q^32 + 46 * q^34 + 7 * q^35 - 22 * q^37 + 45 * q^38 + 35 * q^40 + 11 * q^41 + 6 * q^43 - 82 * q^44 - 16 * q^46 - 29 * q^47 - 42 * q^49 + 48 * q^50 - 50 * q^52 - 28 * q^53 + 23 * q^55 - 21 * q^56 + 39 * q^58 + 15 * q^59 - 32 * q^61 + 8 * q^62 + 29 * q^64 + 21 * q^65 - 34 * q^67 + 22 * q^68 - 24 * q^71 - 15 * q^73 - 6 * q^74 + 7 * q^76 + 21 * q^77 - 34 * q^79 - 8 * q^80 + 14 * q^82 - 14 * q^83 + 20 * q^85 + 100 * q^86 - 108 * q^88 - 10 * q^89 + 84 * q^91 + 21 * q^92 + 99 * q^94 - 18 * q^95 - 64 * q^97 - 91 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.159899	+	0.200507i	−0.113066	+	0.141780i	−0.835144	−	0.550031i	$-0.814616\pi$
$2$	−0.159899	+	0.200507i	−0.113066	+	0.141780i	0.722078	+	0.691812i	$0.243187\pi$
$3$		0			0
$3$		0			0
$4$	0.430406	+	1.88573i	0.215203	+	0.942867i
$5$	1.50958	+	0.726973i	0.675103	+	0.325112i	0.739833	−	0.672790i	$-0.234904\pi$
$5$	1.50958	+	0.726973i	0.675103	+	0.325112i	−0.0647303	+	0.997903i	$0.520619\pi$
$6$		0			0
$7$	2.63685	−	0.216906i	0.996634	−	0.0819826i
$7$	2.63685	−	0.216906i	0.996634	−	0.0819826i
$8$	−0.909048	−	0.437774i	−0.321397	−	0.154777i
$9$		0			0
$10$	−0.387144	+	0.186439i	−0.122426	+	0.0589571i
$11$	2.04337	−	2.56231i	0.616100	−	0.772564i	−0.371690	−	0.928357i	$-0.621222\pi$
$11$	2.04337	−	2.56231i	0.616100	−	0.772564i	0.987790	+	0.155792i	$0.0497931\pi$
$12$		0			0
$13$	1.69439	−	2.12470i	0.469939	−	0.589285i	−0.489217	−	0.872162i	$-0.662717\pi$
$13$	1.69439	−	2.12470i	0.469939	−	0.589285i	0.959156	+	0.282877i	$0.0912887\pi$
$14$	−0.378139	+	0.563390i	−0.101062	+	0.150572i
$15$		0			0
$16$	−3.25223	+	1.56619i	−0.813057	+	0.391547i
$17$	−0.947383	+	4.15076i	−0.229774	+	1.00671i	0.720050	+	0.693922i	$0.244119\pi$
$17$	−0.947383	+	4.15076i	−0.229774	+	1.00671i	−0.949824	+	0.312784i	$0.898738\pi$
$18$		0			0
$19$	−2.59506			−0.595347			−0.297674	−	0.954668i	$-0.596211\pi$
$19$	−2.59506			−0.595347			−0.297674	+	0.954668i	$0.596211\pi$
$20$	−0.721147	+	3.15955i	−0.161253	+	0.706497i
$21$		0			0
$22$	0.187028	+	0.819422i	0.0398745	+	0.174701i
$23$	1.32984	+	5.82640i	0.277290	+	1.21489i	0.901204	+	0.433395i	$0.142685\pi$
$23$	1.32984	+	5.82640i	0.277290	+	1.21489i	−0.623914	+	0.781493i	$0.714458\pi$
$24$		0			0
$25$	−1.36712	−	1.71431i	−0.273424	−	0.342863i
$26$	0.155086	+	0.679476i	0.0304149	+	0.133256i
$27$		0			0
$28$	1.54394	+	4.87903i	0.291778	+	0.922050i
$29$	0.403151	−	1.76632i	0.0748632	−	0.327997i	−0.923604	−	0.383349i	$-0.874771\pi$
$29$	0.403151	−	1.76632i	0.0748632	−	0.327997i	0.998467	+	0.0553515i	$0.0176279\pi$
$30$		0			0
$31$	1.19212			0.214112			0.107056	−	0.994253i	$-0.465858\pi$
$31$	1.19212			0.214112			0.107056	+	0.994253i	$0.465858\pi$
$32$	0.655029	−	2.86987i	0.115794	−	0.507326i
$33$		0			0
$34$	−0.680771	−	0.853660i	−0.116751	−	0.146402i
$35$	4.13820	+	1.58948i	0.699484	+	0.268671i
$36$		0			0
$37$	0.755841	−	3.31155i	0.124259	−	0.544416i	−0.874026	−	0.485880i	$-0.838499\pi$
$37$	0.755841	−	3.31155i	0.124259	−	0.544416i	0.998285	−	0.0585367i	$-0.0186435\pi$
$38$	0.414948	−	0.520328i	0.0673135	−	0.0844084i
$39$		0			0
$40$	−1.05403	−	1.32171i	−0.166656	−	0.208980i
$41$	5.05633	+	2.43500i	0.789666	+	0.380283i	0.784835	−	0.619705i	$-0.212748\pi$
$41$	5.05633	+	2.43500i	0.789666	+	0.380283i	0.00483134	+	0.999988i	$0.498462\pi$
$42$		0			0
$43$	−9.10344	+	4.38399i	−1.38826	+	0.668552i	−0.970744	−	0.240117i	$-0.922814\pi$
$43$	−9.10344	+	4.38399i	−1.38826	+	0.668552i	−0.417518	+	0.908669i	$0.637100\pi$
$44$	5.71131	+	2.75042i	0.861012	+	0.414642i
$45$		0			0
$46$	−1.38088	−	0.664995i	−0.203599	−	0.0980482i
$47$	−0.656516	+	0.823245i	−0.0957627	+	0.120083i	−0.827404	−	0.561607i	$-0.810183\pi$
$47$	−0.656516	+	0.823245i	−0.0957627	+	0.120083i	0.731641	+	0.681690i	$0.238755\pi$
$48$		0			0
$49$	6.90590	−	1.14389i	0.986558	−	0.163413i
$50$	0.562334			0.0795261
$51$		0			0
$52$	4.73589	+	2.28069i	0.656750	+	0.316274i
$53$	−2.01380	−	8.82301i	−0.276616	−	1.21193i	−0.902041	−	0.431650i	$-0.857932\pi$
$53$	−2.01380	−	8.82301i	−0.276616	−	1.21193i	0.625425	−	0.780284i	$-0.284926\pi$
$54$		0			0
$55$	4.94735	−	2.38252i	0.667101	−	0.321259i
$56$	−2.49197	−	0.957165i	−0.333004	−	0.127907i
$57$		0			0
$58$	0.289696	+	0.363268i	0.0380390	+	0.0476994i
$59$	−10.7625	+	5.18294i	−1.40116	+	0.674761i	−0.973396	−	0.229131i	$-0.926412\pi$
$59$	−10.7625	+	5.18294i	−1.40116	+	0.674761i	−0.427761	+	0.903892i	$0.640697\pi$
$60$		0			0
$61$	−1.71060	+	7.49462i	−0.219020	+	0.959588i	0.739184	+	0.673503i	$0.235211\pi$
$61$	−1.71060	+	7.49462i	−0.219020	+	0.959588i	−0.958204	+	0.286085i	$0.907646\pi$
$62$	−0.190620	+	0.239029i	−0.0242087	+	0.0303568i
$63$		0			0
$64$	−4.03053	−	5.05413i	−0.503816	−	0.631766i
$65$	4.10241	−	1.97562i	0.508842	−	0.245045i
$66$		0			0
$67$	11.8842			1.45188			0.725941	−	0.687757i	$-0.241404\pi$
$67$	11.8842			1.45188			0.725941	+	0.687757i	$0.241404\pi$
$68$	−8.23498			−0.998638
$69$		0			0
$70$	−0.980398	+	0.575583i	−0.117180	+	0.0687954i
$71$	−3.66683	−	16.0655i	−0.435173	−	1.90662i	−0.421758	−	0.906709i	$-0.638587\pi$
$71$	−3.66683	−	16.0655i	−0.435173	−	1.90662i	−0.0134155	−	0.999910i	$-0.504270\pi$
$72$		0			0
$73$	−4.59351	−	5.76008i	−0.537630	−	0.674167i	0.436618	−	0.899647i	$-0.356176\pi$
$73$	−4.59351	−	5.76008i	−0.537630	−	0.674167i	−0.974248	+	0.225480i	$0.927605\pi$
$74$	0.543133	+	0.681067i	0.0631379	+	0.0791724i
$75$		0			0
$76$	−1.11693	−	4.89359i	−0.128121	−	0.561333i
$77$	4.83227	−	7.19962i	0.550689	−	0.820473i
$78$		0			0
$79$	−0.219320			−0.0246754			−0.0123377	−	0.999924i	$-0.503927\pi$
$79$	−0.219320			−0.0246754			−0.0123377	+	0.999924i	$0.503927\pi$
$80$	−6.04806			−0.676194
$81$		0			0
$82$	−1.29674	+	0.624477i	−0.143201	+	0.0689619i
$83$	−10.0647	−	12.6208i	−1.10475	−	1.38531i	−0.914990	−	0.403476i	$-0.867802\pi$
$83$	−10.0647	−	12.6208i	−1.10475	−	1.38531i	−0.189756	−	0.981831i	$-0.560770\pi$
$84$		0			0
$85$	−4.44764	+	5.57716i	−0.482414	+	0.604928i
$86$	0.576612	−	2.52630i	0.0621777	−	0.272418i
$87$		0			0
$88$	−2.97923	+	1.43472i	−0.317587	+	0.152942i
$89$	10.7698	+	13.5050i	1.14160	+	1.43152i	0.885358	+	0.464910i	$0.153913\pi$
$89$	10.7698	+	13.5050i	1.14160	+	1.43152i	0.256243	+	0.966613i	$0.417515\pi$
$90$		0			0
$91$	4.00699	−	5.97003i	0.420046	−	0.625829i
$92$	−10.4147	+	5.01544i	−1.08580	+	0.522896i
$93$		0			0
$94$	−0.0600903	−	0.263273i	−0.00619784	−	0.0271545i
$95$	−3.91744	−	1.88654i	−0.401920	−	0.193555i
$96$		0			0
$97$	−5.31289			−0.539443			−0.269721	−	0.962938i	$-0.586932\pi$
$97$	−5.31289			−0.539443			−0.269721	+	0.962938i	$0.586932\pi$
$98$	−0.874890	+	1.56759i	−0.0883773	+	0.158351i
$99$		0			0
$100$	2.64432	−	3.31588i	0.264432	−	0.331588i
$101$	1.53692	+	0.740143i	0.152929	+	0.0736469i	0.508783	−	0.860895i	$-0.330096\pi$
$101$	1.53692	+	0.740143i	0.152929	+	0.0736469i	−0.355854	+	0.934542i	$0.615810\pi$
$102$		0			0
$103$	−1.39443	−	0.671520i	−0.137397	−	0.0661669i	0.363922	−	0.931429i	$-0.381437\pi$
$103$	−1.39443	−	0.671520i	−0.137397	−	0.0661669i	−0.501319	+	0.865262i	$0.667152\pi$
$104$	−2.47042	+	1.18969i	−0.242245	+	0.116659i
$105$		0			0
$106$	2.09108	+	1.00701i	0.203104	+	0.0978098i
$107$	−4.05487	−	5.08464i	−0.391999	−	0.491551i	0.546197	−	0.837657i	$-0.316075\pi$
$107$	−4.05487	−	5.08464i	−0.391999	−	0.491551i	−0.938195	+	0.346106i	$0.887504\pi$
$108$		0			0
$109$	2.33450	−	2.92737i	0.223604	−	0.280391i	−0.657357	−	0.753579i	$-0.728326\pi$
$109$	2.33450	−	2.92737i	0.223604	−	0.280391i	0.880961	+	0.473188i	$0.156897\pi$
$110$	−0.313366	+	1.37294i	−0.0298782	+	0.130905i
$111$		0			0
$112$	−8.23590	+	4.83523i	−0.778220	+	0.456886i
$113$	−2.54602	−	3.19261i	−0.239510	−	0.300335i	0.647520	−	0.762049i	$-0.275806\pi$
$113$	−2.54602	−	3.19261i	−0.239510	−	0.300335i	−0.887029	+	0.461713i	$0.847235\pi$
$114$		0			0
$115$	−2.22815	+	9.76215i	−0.207776	+	0.910325i
$116$	3.50432			0.325368
$117$		0			0
$118$	0.681696	−	2.98671i	0.0627552	−	0.274949i
$119$	−1.59778	+	11.1504i	−0.146468	+	1.02215i
$120$		0			0
$121$	0.0576819	+	0.252721i	0.00524381	+	0.0229746i
$122$	−1.22920	−	1.54137i	−0.111287	−	0.139549i
$123$		0			0
$124$	0.513097	+	2.24803i	0.0460775	+	0.201879i
$125$	−2.68168	−	11.7492i	−0.239857	−	1.05088i
$126$		0			0
$127$	4.37360	−	19.1620i	0.388095	−	1.70035i	−0.283115	−	0.959086i	$-0.591368\pi$
$127$	4.37360	−	19.1620i	0.388095	−	1.70035i	0.671210	−	0.741268i	$-0.265775\pi$
$128$	7.54521			0.666909
$129$		0			0
$130$	−0.259847	+	1.13846i	−0.0227901	+	0.0998499i
$131$	1.39191	−	0.670310i	0.121612	−	0.0585653i	−0.372088	−	0.928197i	$-0.621358\pi$
$131$	1.39191	−	0.670310i	0.121612	−	0.0585653i	0.493700	+	0.869632i	$0.335644\pi$
$132$		0			0
$133$	−6.84276	+	0.562883i	−0.593343	+	0.0488081i
$134$	−1.90027	+	2.38286i	−0.164158	+	0.205848i
$135$		0			0
$136$	2.67831	−	3.35850i	0.229663	−	0.287989i
$137$	17.5395	−	8.44660i	1.49850	−	0.721641i	0.508288	−	0.861187i	$-0.330279\pi$
$137$	17.5395	−	8.44660i	1.49850	−	0.721641i	0.990216	+	0.139546i	$0.0445642\pi$
$138$		0			0
$139$	−16.3626	−	7.87982i	−1.38786	−	0.668358i	−0.417200	−	0.908815i	$-0.636988\pi$
$139$	−16.3626	−	7.87982i	−1.38786	−	0.668358i	−0.970660	+	0.240457i	$0.922703\pi$
$140$	−1.21623	+	8.48767i	−0.102790	+	0.717339i
$141$		0			0
$142$	3.80757	+	1.83363i	0.319524	+	0.153875i
$143$	−1.98186	−	8.68310i	−0.165731	−	0.726117i
$144$		0			0
$145$	1.89265	−	2.37331i	0.157176	−	0.197093i
$146$	1.88944			0.156371
$147$		0			0
$148$	6.57003			0.540053
$149$	5.94663	−	7.45684i	0.487167	−	0.610888i	−0.476114	−	0.879384i	$-0.657955\pi$
$149$	5.94663	−	7.45684i	0.487167	−	0.610888i	0.963281	+	0.268495i	$0.0865264\pi$
$150$		0			0
$151$	1.97637	+	8.65906i	0.160835	+	0.704664i	0.989454	+	0.144851i	$0.0462702\pi$
$151$	1.97637	+	8.65906i	0.160835	+	0.704664i	−0.828618	+	0.559814i	$0.810873\pi$
$152$	2.35903	+	1.13605i	0.191343	+	0.0921458i
$153$		0			0
$154$	0.670901	+	2.12012i	0.0540627	+	0.170844i
$155$	1.79960	+	0.866642i	0.144547	+	0.0696103i
$156$		0			0
$157$	−15.4870	+	7.45815i	−1.23600	+	0.595225i	−0.933723	−	0.357996i	$-0.883460\pi$
$157$	−15.4870	+	7.45815i	−1.23600	+	0.595225i	−0.302274	+	0.953221i	$0.597746\pi$
$158$	0.0350691	−	0.0439752i	0.00278995	−	0.00349848i
$159$		0			0
$160$	3.07513	−	3.85610i	0.243111	−	0.304851i
$161$	4.77036	+	15.0749i	0.375957	+	1.18807i
$162$		0			0
$163$	13.7162	−	6.60538i	1.07434	−	0.517373i	0.188834	−	0.982009i	$-0.439529\pi$
$163$	13.7162	−	6.60538i	1.07434	−	0.517373i	0.885502	+	0.464636i	$0.153815\pi$
$164$	−2.41548	+	10.5829i	−0.188618	+	0.826388i
$165$		0			0
$166$	4.13990			0.321318
$167$	4.31049	−	18.8855i	0.333555	−	1.46140i	−0.478637	−	0.878013i	$-0.658869\pi$
$167$	4.31049	−	18.8855i	0.333555	−	1.46140i	0.812193	−	0.583389i	$-0.198274\pi$
$168$		0			0
$169$	1.24939	+	5.47392i	0.0961067	+	0.421071i
$170$	−0.407088	−	1.78357i	−0.0312222	−	0.136793i
$171$		0			0
$172$	−12.1852	−	15.2798i	−0.929113	−	1.16507i
$173$	1.96924	+	8.62781i	0.149719	+	0.655960i	0.992963	+	0.118429i	$0.0377858\pi$
$173$	1.96924	+	8.62781i	0.149719	+	0.655960i	−0.843244	+	0.537531i	$0.819357\pi$
$174$		0			0
$175$	−3.97673	−	4.22385i	−0.300612	−	0.319293i
$176$	−2.63245	+	11.5335i	−0.198428	+	0.869371i
$177$		0			0
$178$	−4.42993			−0.332038
$179$	−4.45240	+	19.5072i	−0.332788	+	1.45804i	0.480919	+	0.876765i	$0.340303\pi$
$179$	−4.45240	+	19.5072i	−0.332788	+	1.45804i	−0.813707	+	0.581275i	$0.802554\pi$
$180$		0			0
$181$	11.0159	+	13.8135i	0.818808	+	1.02675i	0.999069	+	0.0431337i	$0.0137342\pi$
$181$	11.0159	+	13.8135i	0.818808	+	1.02675i	−0.180262	+	0.983619i	$0.557694\pi$
$182$	0.556320	+	1.75803i	0.0412372	+	0.130314i
$183$		0			0
$184$	1.34176	−	5.87865i	0.0989161	−	0.433380i
$185$	3.54841	−	4.44957i	0.260884	−	0.327139i
$186$		0			0
$187$	8.69965	+	10.9090i	0.636182	+	0.797747i
$188$	−1.83499	−	0.883685i	−0.133830	−	0.0644493i
$189$		0			0
$190$	1.00466	−	0.483819i	0.0728857	−	0.0350999i
$191$	−1.04098	−	0.501308i	−0.0753225	−	0.0362734i	0.395843	−	0.918318i	$-0.370452\pi$
$191$	−1.04098	−	0.501308i	−0.0753225	−	0.0362734i	−0.471166	+	0.882045i	$0.656167\pi$
$192$		0			0
$193$	4.86065	+	2.34077i	0.349877	+	0.168492i	0.600565	−	0.799576i	$-0.294942\pi$
$193$	4.86065	+	2.34077i	0.349877	+	0.168492i	−0.250688	+	0.968068i	$0.580657\pi$
$194$	0.849528	−	1.06527i	0.0609926	−	0.0764823i
$195$		0			0
$196$	5.12942	+	12.5304i	0.366387	+	0.895026i
$197$	5.72299			0.407746			0.203873	−	0.978997i	$-0.434647\pi$
$197$	5.72299			0.407746			0.203873	+	0.978997i	$0.434647\pi$
$198$		0			0
$199$	−9.22567	−	4.44285i	−0.653990	−	0.314945i	0.0773037	−	0.997008i	$-0.475369\pi$
$199$	−9.22567	−	4.44285i	−0.653990	−	0.314945i	−0.731294	+	0.682062i	$0.761083\pi$
$200$	0.492295	+	2.15688i	0.0348105	+	0.152515i
$201$		0			0
$202$	−0.394157	+	0.189816i	−0.0277328	+	0.0133554i
$203$	0.679921	−	4.74495i	0.0477211	−	0.333030i
$204$		0			0
$205$	5.86273	+	7.35163i	0.409471	+	0.513460i
$206$	0.357613	−	0.172217i	0.0249161	−	0.0119989i
$207$		0			0
$208$	−2.18286	+	9.56374i	−0.151354	+	0.663126i
$209$	−5.30267	+	6.64933i	−0.366793	+	0.459944i
$210$		0			0
$211$	−9.39160	−	11.7767i	−0.646544	−	0.810741i	0.345260	−	0.938507i	$-0.387791\pi$
$211$	−9.39160	−	11.7767i	−0.646544	−	0.810741i	−0.991804	+	0.127766i	$0.959219\pi$
$212$	15.7711	−	7.59496i	1.08316	−	0.521624i
$213$		0			0
$214$	1.66788			0.114014
$215$	−16.9294			−1.15457
$216$		0			0
$217$	3.14344	−	0.258578i	0.213391	−	0.0175534i
$218$	0.213674	+	0.936169i	0.0144719	+	0.0634053i
$219$		0			0
$220$	6.62217	+	8.30394i	0.446467	+	0.559851i
$221$	7.21387	+	9.04591i	0.485257	+	0.608494i
$222$		0			0
$223$	6.49936	+	28.4756i	0.435230	+	1.90687i	0.421208	+	0.906964i	$0.361606\pi$
$223$	6.49936	+	28.4756i	0.435230	+	1.90687i	0.0140213	+	0.999902i	$0.495537\pi$
$224$	1.10472	−	7.70948i	0.0738121	−	0.515111i
$225$		0			0
$226$	1.04725			0.0696620
$227$	−4.81003			−0.319253			−0.159627	−	0.987177i	$-0.551029\pi$
$227$	−4.81003			−0.319253			−0.159627	+	0.987177i	$0.551029\pi$
$228$		0			0
$229$	14.0047	−	6.74431i	0.925457	−	0.445677i	0.0904407	−	0.995902i	$-0.471172\pi$
$229$	14.0047	−	6.74431i	0.925457	−	0.445677i	0.835016	+	0.550225i	$0.185458\pi$
$230$	−1.60110	−	2.00772i	−0.105574	−	0.132385i
$231$		0			0
$232$	−1.13973	+	1.42918i	−0.0748271	+	0.0938302i
$233$	−2.06413	+	9.04354i	−0.135226	+	0.592462i	0.861221	+	0.508231i	$0.169700\pi$
$233$	−2.06413	+	9.04354i	−0.135226	+	0.592462i	−0.996446	+	0.0842309i	$0.973157\pi$
$234$		0			0
$235$	−1.58954	+	0.765481i	−0.103690	+	0.0499345i
$236$	−14.4059	−	18.0644i	−0.937743	−	1.17589i
$237$		0			0
$238$	−1.98025	−	2.10331i	−0.128361	−	0.136337i
$239$	−20.2040	+	9.72972i	−1.30689	+	0.629363i	−0.952158	−	0.305606i	$-0.901141\pi$
$239$	−20.2040	+	9.72972i	−1.30689	+	0.629363i	−0.354728	+	0.934969i	$0.615427\pi$
$240$		0			0
$241$	−1.32632	−	5.81097i	−0.0854355	−	0.374318i	0.914077	−	0.405541i	$-0.132917\pi$
$241$	−1.32632	−	5.81097i	−0.0854355	−	0.374318i	−0.999512	+	0.0312234i	$0.990060\pi$
$242$	−0.0598958	−	0.0288443i	−0.00385024	−	0.00185418i
$243$		0			0
$244$	−14.8691			−0.951898
$245$	11.2566	+	3.29361i	0.719156	+	0.210421i
$246$		0			0
$247$	−4.39704	+	5.51372i	−0.279777	+	0.350829i
$248$	−1.08370	−	0.521881i	−0.0688148	−	0.0331395i
$249$		0			0
$250$	2.78461	+	1.34100i	0.176114	+	0.0848120i
$251$	7.17225	−	3.45397i	0.452708	−	0.218013i	−0.193613	−	0.981078i	$-0.562021\pi$
$251$	7.17225	−	3.45397i	0.452708	−	0.218013i	0.646322	+	0.763065i	$0.276306\pi$
$252$		0			0
$253$	17.6464	+	8.49805i	1.10942	+	0.534268i
$254$	3.14279	+	3.94093i	0.197196	+	0.247276i
$255$		0			0
$256$	6.85459	−	8.59538i	0.428412	−	0.537211i
$257$	−6.79093	+	29.7530i	−0.423606	+	1.85594i	0.0871208	+	0.996198i	$0.472233\pi$
$257$	−6.79093	+	29.7530i	−0.423606	+	1.85594i	−0.510727	+	0.859743i	$0.670624\pi$
$258$		0			0
$259$	1.27474	−	8.89600i	0.0792085	−	0.552771i
$260$	5.49119	+	6.88574i	0.340549	+	0.427035i
$261$		0			0
$262$	−0.0881638	+	0.386271i	−0.00544678	+	0.0238639i
$263$	−13.6768			−0.843346			−0.421673	−	0.906748i	$-0.638557\pi$
$263$	−13.6768			−0.843346			−0.421673	+	0.906748i	$0.638557\pi$
$264$		0			0
$265$	3.37412	−	14.7830i	0.207271	−	0.908112i
$266$	0.981291	−	1.46203i	0.0601668	−	0.0896428i
$267$		0			0
$268$	5.11502	+	22.4104i	0.312450	+	1.36893i
$269$	6.44065	+	8.07631i	0.392693	+	0.492422i	0.938398	−	0.345556i	$-0.112310\pi$
$269$	6.44065	+	8.07631i	0.392693	+	0.492422i	−0.545705	+	0.837977i	$0.683738\pi$
$270$		0			0
$271$	0.684131	+	2.99737i	0.0415580	+	0.182077i	0.991447	−	0.130510i	$-0.0416614\pi$
$271$	0.684131	+	2.99737i	0.0415580	+	0.182077i	−0.949889	+	0.312587i	$0.898804\pi$
$272$	−3.41977	−	14.9830i	−0.207354	−	0.908477i
$273$		0			0
$274$	−1.11096	+	4.86741i	−0.0671153	+	0.294051i
$275$	−7.18613			−0.433340
$276$		0			0
$277$	4.07414	−	17.8500i	0.244791	−	1.07250i	−0.691803	−	0.722086i	$-0.743184\pi$
$277$	4.07414	−	17.8500i	0.244791	−	1.07250i	0.936595	−	0.350415i	$-0.113959\pi$
$278$	4.19634	−	2.02085i	0.251679	−	0.121202i
$279$		0			0
$280$	−3.06599	−	3.25651i	−0.183228	−	0.194614i
$281$	−3.68754	+	4.62402i	−0.219980	+	0.275846i	−0.879560	−	0.475788i	$-0.842163\pi$
$281$	−3.68754	+	4.62402i	−0.219980	+	0.275846i	0.659580	+	0.751635i	$0.270734\pi$
$282$		0			0
$283$	−0.320125	+	0.401424i	−0.0190294	+	0.0238622i	−0.791255	−	0.611486i	$-0.790572\pi$
$283$	−0.320125	+	0.401424i	−0.0190294	+	0.0238622i	0.772226	+	0.635348i	$0.219143\pi$
$284$	28.7169	−	13.8293i	1.70404	−	0.820621i
$285$		0			0
$286$	2.05792	+	0.991044i	0.121688	+	0.0586016i
$287$	13.8609	+	5.32397i	0.818184	+	0.314264i
$288$		0			0
$289$	−1.01477	−	0.488687i	−0.0596922	−	0.0287463i
$290$	0.173233	+	0.758982i	0.0101726	+	0.0445690i
$291$		0			0
$292$	8.88491	−	11.1413i	0.519950	−	0.651996i
$293$	12.3237			0.719957			0.359978	−	0.932961i	$-0.382784\pi$
$293$	12.3237			0.719957			0.359978	+	0.932961i	$0.382784\pi$
$294$		0			0
$295$	−20.0146			−1.16530
$296$	−2.13681	+	2.67947i	−0.124200	+	0.155741i
$297$		0			0
$298$	0.544290	+	2.38469i	0.0315299	+	0.138141i
$299$	14.6326	+	7.04670i	0.846226	+	0.407521i
$300$		0			0
$301$	−23.0534	+	13.5345i	−1.32878	+	0.780114i
$302$	−2.05223	−	0.988300i	−0.118092	−	0.0568703i
$303$		0			0
$304$	8.43972	−	4.06435i	0.484051	−	0.233107i
$305$	−8.03067	+	10.0701i	−0.459835	+	0.576615i
$306$		0			0
$307$	2.55303	−	3.20139i	0.145709	−	0.182713i	−0.703621	−	0.710575i	$-0.748435\pi$
$307$	2.55303	−	3.20139i	0.145709	−	0.182713i	0.849330	+	0.527862i	$0.177006\pi$
$308$	15.6564	+	6.01362i	0.892107	+	0.342658i
$309$		0			0
$310$	−0.461523	+	0.222258i	−0.0262127	+	0.0126234i
$311$	−3.76986	+	16.5168i	−0.213769	+	0.936583i	0.748210	+	0.663461i	$0.230913\pi$
$311$	−3.76986	+	16.5168i	−0.213769	+	0.936583i	−0.961979	+	0.273122i	$0.911944\pi$
$312$		0			0
$313$	−33.8439			−1.91297			−0.956487	−	0.291776i	$-0.905754\pi$
$313$	−33.8439			−1.91297			−0.956487	+	0.291776i	$0.905754\pi$
$314$	0.980948	−	4.29781i	0.0553581	−	0.242540i
$315$		0			0
$316$	−0.0943966	−	0.413579i	−0.00531023	−	0.0232656i
$317$	−2.56091	−	11.2201i	−0.143835	−	0.630183i	−0.994524	−	0.104513i	$-0.966672\pi$
$317$	−2.56091	−	11.2201i	−0.143835	−	0.630183i	0.850688	−	0.525670i	$-0.176185\pi$
$318$		0			0
$319$	−3.70206	−	4.64224i	−0.207276	−	0.259915i
$320$	−2.41018	−	10.5597i	−0.134733	−	0.590304i
$321$		0			0
$322$	−3.78540	−	1.45397i	−0.210952	−	0.0810265i
$323$	2.45851	−	10.7715i	0.136795	−	0.599340i
$324$		0			0
$325$	−5.95884			−0.330537
$326$	−0.868785	+	3.80640i	−0.0481176	+	0.210817i
$327$		0			0
$328$	−3.53046	−	4.42706i	−0.194937	−	0.244444i
$329$	−1.55257	+	2.31317i	−0.0855957	+	0.127529i
$330$		0			0
$331$	−3.44857	+	15.1092i	−0.189551	+	0.830476i	0.787303	+	0.616567i	$0.211477\pi$
$331$	−3.44857	+	15.1092i	−0.189551	+	0.830476i	−0.976853	+	0.213910i	$0.931380\pi$
$332$	19.4675	−	24.4114i	1.06842	−	1.33975i
$333$		0			0
$334$	3.09743	+	3.88406i	0.169484	+	0.212526i
$335$	17.9401	+	8.63948i	0.980170	+	0.472025i
$336$		0			0
$337$	17.9871	−	8.66214i	0.979821	−	0.471857i	0.125777	−	0.992059i	$-0.459858\pi$
$337$	17.9871	−	8.66214i	0.979821	−	0.471857i	0.854043	+	0.520202i	$0.174143\pi$
$338$	−1.29734	−	0.624765i	−0.0705659	−	0.0339827i
$339$		0			0
$340$	−12.4313	−	5.98661i	−0.674183	−	0.324670i
$341$	2.43595	−	3.05458i	0.131914	−	0.165415i
$342$		0			0
$343$	17.9617	−	4.51420i	0.969840	−	0.243744i
$344$	10.1947			0.549659
$345$		0			0
$346$	−2.04482	−	0.984733i	−0.109930	−	0.0529396i
$347$	−2.97561	−	13.0370i	−0.159739	−	0.699863i	−0.989832	−	0.142238i	$-0.954570\pi$
$347$	−2.97561	−	13.0370i	−0.159739	−	0.699863i	0.830093	−	0.557625i	$-0.188287\pi$
$348$		0			0
$349$	16.6371	−	8.01201i	0.890564	−	0.428873i	0.0680921	−	0.997679i	$-0.478309\pi$
$349$	16.6371	−	8.01201i	0.890564	−	0.428873i	0.822472	+	0.568806i	$0.192595\pi$
$350$	1.48279	−	0.121974i	0.0792584	−	0.00651976i
$351$		0			0
$352$	−6.01502	−	7.54259i	−0.320601	−	0.402021i
$353$	−0.532918	+	0.256640i	−0.0283644	+	0.0136596i	−0.448012	−	0.894027i	$-0.647868\pi$
$353$	−0.532918	+	0.256640i	−0.0283644	+	0.0136596i	0.419648	+	0.907687i	$0.362154\pi$
$354$		0			0
$355$	6.14379	−	26.9177i	0.326079	−	1.42864i
$356$	−20.8313	+	26.1217i	−1.10406	+	1.38445i
$357$		0			0
$358$	−3.19941	−	4.01193i	−0.169094	−	0.212037i
$359$	−19.9810	+	9.62233i	−1.05456	+	0.507847i	−0.879098	−	0.476640i	$-0.841854\pi$
$359$	−19.9810	+	9.62233i	−1.05456	+	0.507847i	−0.175457	+	0.984487i	$0.556140\pi$
$360$		0			0
$361$	−12.2657			−0.645562
$362$	−4.53116			−0.238152
$363$		0			0
$364$	12.9825	+	4.98657i	0.680469	+	0.261367i
$365$	−2.74683	−	12.0346i	−0.143776	−	0.629922i
$366$		0			0
$367$	4.49285	+	5.63385i	0.234525	+	0.294085i	0.885142	−	0.465321i	$-0.154061\pi$
$367$	4.49285	+	5.63385i	0.234525	+	0.294085i	−0.650617	+	0.759406i	$0.725490\pi$
$368$	−13.4502	−	16.8660i	−0.701139	−	0.879201i
$369$		0			0
$370$	0.324783	+	1.42297i	0.0168846	+	0.0739765i
$371$	−7.22383	−	22.8281i	−0.375042	−	1.18518i
$372$		0			0
$373$	−6.27122			−0.324711			−0.162356	−	0.986732i	$-0.551909\pi$
$373$	−6.27122			−0.324711			−0.162356	+	0.986732i	$0.551909\pi$
$374$	−3.57841			−0.185035
$375$		0			0
$376$	0.957200	−	0.460963i	0.0493638	−	0.0237724i
$377$	−3.06980	−	3.84941i	−0.158103	−	0.198255i
$378$		0			0
$379$	−5.46460	+	6.85239i	−0.280698	+	0.351984i	−0.902115	−	0.431496i	$-0.857986\pi$
$379$	−5.46460	+	6.85239i	−0.280698	+	0.351984i	0.621417	+	0.783480i	$0.286557\pi$
$380$	1.87142	−	8.19922i	0.0960017	−	0.420611i
$381$		0			0
$382$	0.266968	−	0.128565i	0.0136592	−	0.00657795i
$383$	−5.48419	−	6.87696i	−0.280229	−	0.351396i	0.621719	−	0.783240i	$-0.286435\pi$
$383$	−5.48419	−	6.87696i	−0.280229	−	0.351396i	−0.901948	+	0.431844i	$0.857863\pi$
$384$		0			0
$385$	12.5286	−	7.35544i	0.638518	−	0.374868i
$386$	−1.24656	+	0.600309i	−0.0634480	+	0.0305549i
$387$		0			0
$388$	−2.28670	−	10.0187i	−0.116090	−	0.508623i
$389$	−23.8499	−	11.4855i	−1.20924	−	0.582339i	−0.282944	−	0.959137i	$-0.591311\pi$
$389$	−23.8499	−	11.4855i	−1.20924	−	0.582339i	−0.926296	+	0.376798i	$0.877025\pi$
$390$		0			0
$391$	−25.4438			−1.28675
$392$	−6.77856	−	1.98337i	−0.342369	−	0.100176i
$393$		0			0
$394$	−0.915102	+	1.14750i	−0.0461022	+	0.0578103i
$395$	−0.331080	−	0.159440i	−0.0166584	−	0.00802228i
$396$		0			0
$397$	0.00498532	+	0.00240080i	0.000250206	+	0.000120493i	0.434009	−	0.900909i	$-0.357099\pi$
$397$	0.00498532	+	0.00240080i	0.000250206	+	0.000120493i	−0.433759	+	0.901029i	$0.642813\pi$
$398$	2.36600	−	1.13941i	0.118597	−	0.0571133i
$399$		0			0
$400$	7.13113	+	3.43417i	0.356556	+	0.171708i
$401$	−2.11708	−	2.65474i	−0.105722	−	0.132571i	0.726155	−	0.687531i	$-0.241305\pi$
$401$	−2.11708	−	2.65474i	−0.105722	−	0.132571i	−0.831878	+	0.554959i	$0.812734\pi$
$402$		0			0
$403$	2.01992	−	2.53290i	0.100619	−	0.126173i
$404$	−0.734211	+	3.21679i	−0.0365284	+	0.160041i
$405$		0			0
$406$	0.842679	+	0.895044i	0.0418215	+	0.0444203i
$407$	−6.94075	−	8.70343i	−0.344040	−	0.431413i
$408$		0			0
$409$	−5.73225	+	25.1146i	−0.283442	+	1.24184i	0.609906	+	0.792473i	$0.291207\pi$
$409$	−5.73225	+	25.1146i	−0.283442	+	1.24184i	−0.893348	+	0.449365i	$0.851650\pi$
$410$	−2.41150			−0.119096
$411$		0			0
$412$	0.666139	−	2.91854i	0.0328183	−	0.143786i
$413$	−27.2548	+	16.0011i	−1.34112	+	0.787360i
$414$		0			0
$415$	−6.01850	−	26.3688i	−0.295436	−	1.29439i
$416$	−4.98773	−	6.25442i	−0.244544	−	0.306648i
$417$		0			0
$418$	−0.485348	−	2.12645i	−0.0237391	−	0.104008i
$419$	3.15269	+	13.8128i	0.154019	+	0.674800i	0.991693	+	0.128630i	$0.0410579\pi$
$419$	3.15269	+	13.8128i	0.154019	+	0.674800i	−0.837674	+	0.546171i	$0.816085\pi$
$420$		0			0
$421$	−0.559549	+	2.45155i	−0.0272708	+	0.119481i	−0.986731	−	0.162362i	$-0.948089\pi$
$421$	−0.559549	+	2.45155i	−0.0272708	+	0.119481i	0.959460	+	0.281843i	$0.0909458\pi$
$422$	3.86302			0.188049
$423$		0			0
$424$	−2.03185	+	8.90213i	−0.0986755	+	0.432326i
$425$	8.41089	−	4.05047i	0.407988	−	0.196477i
$426$		0			0
$427$	−2.88496	+	20.1332i	−0.139613	+	0.974314i
$428$	7.84304	−	9.83486i	0.379108	−	0.475386i
$429$		0			0
$430$	2.70700	−	3.39447i	0.130543	−	0.163696i
$431$	21.0248	−	10.1250i	1.01273	−	0.487704i	0.147489	−	0.989064i	$-0.452881\pi$
$431$	21.0248	−	10.1250i	1.01273	−	0.487704i	0.865239	+	0.501359i	$0.167167\pi$
$432$		0			0
$433$	7.12961	+	3.43344i	0.342627	+	0.165001i	0.597282	−	0.802032i	$-0.296247\pi$
$433$	7.12961	+	3.43344i	0.342627	+	0.165001i	−0.254655	+	0.967032i	$0.581962\pi$
$434$	−0.450788	+	0.671630i	−0.0216385	+	0.0322393i
$435$		0			0
$436$	6.52502	+	3.14228i	0.312492	+	0.150488i
$437$	−3.45101	−	15.1198i	−0.165084	−	0.723280i
$438$		0			0
$439$	−9.41179	+	11.8020i	−0.449200	+	0.563279i	−0.953942	−	0.299991i	$-0.903016\pi$
$439$	−9.41179	+	11.8020i	−0.449200	+	0.563279i	0.504742	+	0.863270i	$0.331588\pi$
$440$	−5.54039			−0.264128
$441$		0			0
$442$	−2.96726			−0.141138
$443$	−13.9535	+	17.4971i	−0.662950	+	0.831312i	−0.993661	−	0.112420i	$-0.964140\pi$
$443$	−13.9535	+	17.4971i	−0.662950	+	0.831312i	0.330711	+	0.943732i	$0.392711\pi$
$444$		0			0
$445$	6.44015	+	28.2161i	0.305292	+	1.33757i
$446$	−6.74881	−	3.25005i	−0.319565	−	0.153895i
$447$		0			0
$448$	−11.7242	−	12.4527i	−0.553914	−	0.588335i
$449$	−15.4624	−	7.44629i	−0.729714	−	0.351412i	0.0318574	−	0.999492i	$-0.489858\pi$
$449$	−15.4624	−	7.44629i	−0.729714	−	0.351412i	−0.761572	+	0.648080i	$0.775572\pi$
$450$		0			0
$451$	16.5712	−	7.98026i	0.780306	−	0.375776i
$452$	4.92459	−	6.17524i	0.231633	−	0.290459i
$453$		0			0
$454$	0.769121	−	0.964447i	0.0360966	−	0.0452637i
$455$	10.3889	−	6.09923i	0.487039	−	0.285936i
$456$		0			0
$457$	14.2078	−	6.84213i	0.664615	−	0.320061i	−0.0709858	−	0.997477i	$-0.522614\pi$
$457$	14.2078	−	6.84213i	0.664615	−	0.320061i	0.735600	+	0.677416i	$0.236900\pi$
$458$	−0.887059	+	3.88646i	−0.0414495	+	0.181602i
$459$		0			0
$460$	−19.3678			−0.903030
$461$	−5.32105	+	23.3131i	−0.247826	+	1.08580i	0.685868	+	0.727726i	$0.259423\pi$
$461$	−5.32105	+	23.3131i	−0.247826	+	1.08580i	−0.933694	+	0.358071i	$0.883434\pi$
$462$		0			0
$463$	3.38309	+	14.8223i	0.157226	+	0.688850i	0.990674	+	0.136253i	$0.0435061\pi$
$463$	3.38309	+	14.8223i	0.157226	+	0.688850i	−0.833448	+	0.552597i	$0.813637\pi$
$464$	1.45525	+	6.37588i	0.0675584	+	0.295993i
$465$		0			0
$466$	−1.48324	−	1.85993i	−0.0687100	−	0.0861596i
$467$	−8.58347	−	37.6066i	−0.397195	−	1.74023i	−0.638355	−	0.769742i	$-0.720385\pi$
$467$	−8.58347	−	37.6066i	−0.397195	−	1.74023i	0.241160	−	0.970485i	$-0.422472\pi$
$468$		0			0
$469$	31.3367	−	2.57774i	1.44700	−	0.119029i
$470$	0.100681	−	0.441114i	0.00464409	−	0.0203471i
$471$		0			0
$472$	12.0526			0.554765
$473$	−7.36859	+	32.2839i	−0.338808	+	1.48442i
$474$		0			0
$475$	3.54776	+	4.44874i	0.162782	+	0.204122i
$476$	−21.7144	+	1.78621i	−0.995276	+	0.0818710i
$477$		0			0
$478$	1.27972	−	5.60682i	0.0585331	−	0.256450i
$479$	−11.4590	+	14.3692i	−0.523577	+	0.656545i	−0.971364	−	0.237595i	$-0.923641\pi$
$479$	−11.4590	+	14.3692i	−0.523577	+	0.656545i	0.447787	+	0.894140i	$0.352212\pi$
$480$		0			0
$481$	−5.75537	−	7.21700i	−0.262422	−	0.329067i
$482$	1.37722	+	0.663234i	0.0627306	+	0.0302095i
$483$		0			0
$484$	−0.451738	+	0.217546i	−0.0205335	+	0.00988843i
$485$	−8.02021	−	3.86233i	−0.364179	−	0.175379i
$486$		0			0
$487$	−2.96773	−	1.42918i	−0.134481	−	0.0647624i	0.365433	−	0.930837i	$-0.380921\pi$
$487$	−2.96773	−	1.42918i	−0.134481	−	0.0647624i	−0.499914	+	0.866075i	$0.666635\pi$
$488$	4.83597	−	6.06411i	0.218914	−	0.274510i
$489$		0			0
$490$	−2.46031	+	1.73038i	−0.111146	+	0.0781705i
$491$	36.0201			1.62556			0.812782	−	0.582567i	$-0.197952\pi$
$491$	36.0201			1.62556			0.812782	+	0.582567i	$0.197952\pi$
$492$		0			0
$493$	6.94962	+	3.34676i	0.312995	+	0.150730i
$494$	−0.402457	−	1.76328i	−0.0181074	−	0.0793337i
$495$		0			0
$496$	−3.87705	+	1.86709i	−0.174085	+	0.0838349i
$497$	−13.1536	−	41.5668i	−0.590018	−	1.86452i
$498$		0			0
$499$	−19.2267	−	24.1095i	−0.860704	−	1.07929i	−0.996077	−	0.0884944i	$-0.971794\pi$
$499$	−19.2267	−	24.1095i	−0.860704	−	1.07929i	0.135372	−	0.990795i	$-0.456777\pi$
$500$	21.0017	−	10.1139i	0.939224	−	0.452306i
$501$		0			0
$502$	−0.454291	+	1.99038i	−0.0202760	+	0.0888349i
$503$	−15.2391	+	19.1092i	−0.679476	+	0.852036i	−0.995306	−	0.0967800i	$-0.969146\pi$
$503$	−15.2391	+	19.1092i	−0.679476	+	0.852036i	0.315830	+	0.948816i	$0.397717\pi$
$504$		0			0
$505$	1.78204	+	2.23460i	0.0792996	+	0.0994385i
$506$	−4.52557	+	2.17940i	−0.201186	+	0.0968860i
$507$		0			0
$508$	38.0169			1.68673
$509$	6.30258			0.279357			0.139679	−	0.990197i	$-0.455393\pi$
$509$	6.30258			0.279357			0.139679	+	0.990197i	$0.455393\pi$
$510$		0			0
$511$	−13.3618	−	14.1921i	−0.591090	−	0.627821i
$512$	3.98533	+	17.4609i	0.176128	+	0.771669i
$513$		0			0
$514$	−4.87983	−	6.11911i	−0.215240	−	0.269903i
$515$	−1.61682	−	2.02742i	−0.0712454	−	0.0893389i
$516$		0			0
$517$	0.767900	+	3.36439i	0.0337722	+	0.147966i
$518$	1.57988	+	1.67806i	0.0694161	+	0.0737297i
$519$		0			0
$520$	−4.59416			−0.201467
$521$	16.4157			0.719186			0.359593	−	0.933109i	$-0.382916\pi$
$521$	16.4157			0.719186			0.359593	+	0.933109i	$0.382916\pi$
$522$		0			0
$523$	−9.49011	+	4.57019i	−0.414973	+	0.199841i	−0.629708	−	0.776832i	$-0.716826\pi$
$523$	−9.49011	+	4.57019i	−0.414973	+	0.199841i	0.214735	+	0.976672i	$0.431111\pi$
$524$	1.86311	+	2.33627i	0.0813905	+	0.102061i
$525$		0			0
$526$	2.18691	−	2.74230i	0.0953537	−	0.119570i
$527$	−1.12940	+	4.94821i	−0.0491973	+	0.215547i
$528$		0			0
$529$	−11.4562	+	5.51701i	−0.498095	+	0.239870i
$530$	2.42458	+	3.04033i	0.105317	+	0.132063i
$531$		0			0
$532$	−4.00662	−	12.6614i	−0.173709	−	0.548940i
$533$	13.7410	−	6.61734i	0.595191	−	0.286629i
$534$		0			0
$535$	−2.42473	−	10.6234i	−0.104830	−	0.459291i
$536$	−10.8033	−	5.20258i	−0.466631	−	0.224717i
$537$		0			0
$538$	−2.64922			−0.114216
$539$	11.1803	−	20.0324i	0.481570	−	0.862858i
$540$		0			0
$541$	−17.1969	+	21.5643i	−0.739353	+	0.927120i	−0.999258	−	0.0385145i	$-0.987737\pi$
$541$	−17.1969	+	21.5643i	−0.739353	+	0.927120i	0.259905	+	0.965634i	$0.416309\pi$
$542$	−0.710387	−	0.342105i	−0.0305138	−	0.0146946i
$543$		0			0
$544$	11.2916	+	5.43773i	0.484122	+	0.233141i
$545$	5.65222	−	2.72197i	0.242115	−	0.116596i
$546$		0			0
$547$	−23.0799	−	11.1147i	−0.986824	−	0.475229i	−0.130377	−	0.991464i	$-0.541619\pi$
$547$	−23.0799	−	11.1147i	−0.986824	−	0.475229i	−0.856447	+	0.516235i	$0.827333\pi$
$548$	23.4772	+	29.4394i	1.00289	+	1.25759i
$549$		0			0
$550$	1.14906	−	1.44087i	0.0489960	−	0.0614390i
$551$	−1.04620	+	4.58370i	−0.0445696	+	0.195272i
$552$		0			0
$553$	−0.578312	+	0.0475717i	−0.0245923	+	0.00202295i
$554$	2.92760	+	3.67109i	0.124382	+	0.155970i
$555$		0			0
$556$	7.81667	−	34.2471i	0.331501	−	1.45240i
$557$	3.89939			0.165222			0.0826112	−	0.996582i	$-0.473674\pi$
$557$	3.89939			0.165222			0.0826112	+	0.996582i	$0.473674\pi$
$558$		0			0
$559$	−6.11014	+	26.7703i	−0.258431	+	1.13226i
$560$	−15.9478	+	1.31186i	−0.673918	+	0.0554362i
$561$		0			0
$562$	−0.337517	−	1.47876i	−0.0142373	−	0.0623776i
$563$	13.4442	+	16.8585i	0.566604	+	0.710499i	0.979763	−	0.200160i	$-0.0641461\pi$
$563$	13.4442	+	16.8585i	0.566604	+	0.710499i	−0.413159	+	0.910659i	$0.635575\pi$
$564$		0			0
$565$	−1.52247	−	6.67038i	−0.0640508	−	0.280625i
$566$	−0.0293007	−	0.128375i	−0.00123160	−	0.00539599i
$567$		0			0
$568$	−3.69972	+	16.2095i	−0.155237	+	0.680136i
$569$	1.84530			0.0773591			0.0386795	−	0.999252i	$-0.487685\pi$
$569$	1.84530			0.0773591			0.0386795	+	0.999252i	$0.487685\pi$
$570$		0			0
$571$	−8.13901	+	35.6594i	−0.340607	+	1.49230i	0.457189	+	0.889370i	$0.348856\pi$
$571$	−8.13901	+	35.6594i	−0.340607	+	1.49230i	−0.797796	+	0.602928i	$0.794001\pi$
$572$	15.5210	−	7.47452i	0.648966	−	0.312525i
$573$		0			0
$574$	−3.28385	+	1.92792i	−0.137065	+	0.0804698i
$575$	8.17024	−	10.2452i	0.340722	−	0.427252i
$576$		0			0
$577$	16.8516	−	21.1313i	0.701542	−	0.879706i	−0.295595	−	0.955313i	$-0.595518\pi$
$577$	16.8516	−	21.1313i	0.701542	−	0.879706i	0.997138	+	0.0756071i	$0.0240895\pi$
$578$	0.260246	−	0.125328i	0.0108248	−	0.00521295i
$579$		0			0
$580$	5.29004	+	2.54755i	0.219657	+	0.105781i
$581$	−29.2766	−	31.0959i	−1.21460	−	1.29007i
$582$		0			0
$583$	−26.7222	−	12.8687i	−1.10672	−	0.532968i
$584$	1.65411	+	7.24711i	0.0684474	+	0.299888i
$585$		0			0
$586$	−1.97055	+	2.47099i	−0.0814025	+	0.102076i
$587$	11.6610			0.481299			0.240650	−	0.970612i	$-0.422640\pi$
$587$	11.6610			0.481299			0.240650	+	0.970612i	$0.422640\pi$
$588$		0			0
$589$	−3.09363			−0.127471
$590$	3.20033	−	4.01309i	0.131755	−	0.165216i
$591$		0			0
$592$	2.72836	+	11.9537i	0.112135	+	0.491295i
$593$	29.9529	+	14.4245i	1.23002	+	0.592345i	0.932084	−	0.362242i	$-0.117989\pi$
$593$	29.9529	+	14.4245i	1.23002	+	0.592345i	0.297933	+	0.954587i	$0.403703\pi$
$594$		0			0
$595$	−10.5180	+	15.6708i	−0.431196	+	0.642441i
$596$	16.6211	+	8.00430i	0.680827	+	0.327869i
$597$		0			0
$598$	−3.75266	+	1.80719i	−0.153458	+	0.0739013i
$599$	−10.1191	+	12.6889i	−0.413455	+	0.518456i	−0.944333	−	0.328993i	$-0.893291\pi$
$599$	−10.1191	+	12.6889i	−0.413455	+	0.518456i	0.530878	+	0.847448i	$0.321862\pi$
$600$		0			0
$601$	25.3906	−	31.8388i	1.03570	−	1.29873i	0.0824381	−	0.996596i	$-0.473729\pi$
$601$	25.3906	−	31.8388i	1.03570	−	1.29873i	0.953265	−	0.302135i	$-0.0976992\pi$
$602$	0.972468	−	6.78654i	0.0396348	−	0.276599i
$603$		0			0
$604$	−15.4780	+	7.45383i	−0.629793	+	0.303292i
$605$	−0.0966462	+	0.423435i	−0.00392923	+	0.0172151i
$606$		0			0
$607$	14.9927			0.608537			0.304268	−	0.952586i	$-0.401588\pi$
$607$	14.9927			0.608537			0.304268	+	0.952586i	$0.401588\pi$
$608$	−1.69984	+	7.44747i	−0.0689375	+	0.302035i
$609$		0			0
$610$	−0.735039	−	3.22042i	−0.0297609	−	0.130391i
$611$	0.636753	+	2.78980i	0.0257603	+	0.112863i
$612$		0			0
$613$	−3.16086	−	3.96360i	−0.127666	−	0.160088i	0.713890	−	0.700258i	$-0.246932\pi$
$613$	−3.16086	−	3.96360i	−0.127666	−	0.160088i	−0.841556	+	0.540169i	$0.818360\pi$
$614$	0.233676	+	1.02380i	0.00943040	+	0.0413173i
$615$		0			0
$616$	−7.54458	+	4.42936i	−0.303980	+	0.178464i
$617$	−2.86318	+	12.5444i	−0.115267	+	0.505018i	0.884026	+	0.467437i	$0.154823\pi$
$617$	−2.86318	+	12.5444i	−0.115267	+	0.505018i	−0.999294	+	0.0375815i	$0.988035\pi$
$618$		0			0
$619$	25.1525			1.01096			0.505481	−	0.862838i	$-0.331315\pi$
$619$	25.1525			1.01096			0.505481	+	0.862838i	$0.331315\pi$
$620$	−0.859696	+	3.76657i	−0.0345262	+	0.151269i
$621$		0			0
$622$	−2.70895	−	3.39691i	−0.108619	−	0.136204i
$623$	31.3277	+	33.2744i	1.25512	+	1.33311i
$624$		0			0
$625$	2.05357	−	8.99727i	0.0821428	−	0.359891i
$626$	5.41162	−	6.78596i	0.216292	−	0.271222i
$627$		0			0
$628$	−20.7298	−	25.9943i	−0.827209	−	1.03729i
$629$	13.0294	+	6.27462i	0.519516	+	0.250186i
$630$		0			0
$631$	12.3974	−	5.97026i	0.493531	−	0.237672i	−0.170527	−	0.985353i	$-0.554547\pi$
$631$	12.3974	−	5.97026i	0.493531	−	0.237672i	0.664058	+	0.747681i	$0.268833\pi$
$632$	0.199372	+	0.0960126i	0.00793060	+	0.00381917i
$633$		0			0
$634$	2.65920	+	1.28060i	0.105610	+	0.0508593i
$635$	20.5326	−	25.7470i	0.814810	−	1.02174i
$636$		0			0
$637$	9.27087	−	16.6112i	0.367325	−	0.658159i
$638$	1.52276			0.0602867
$639$		0			0
$640$	11.3901	+	5.48517i	0.450232	+	0.216820i
$641$	10.3244	+	45.2340i	0.407788	+	1.78664i	0.594364	+	0.804196i	$0.297404\pi$
$641$	10.3244	+	45.2340i	0.407788	+	1.78664i	−0.186576	+	0.982441i	$0.559739\pi$
$642$		0			0
$643$	−4.77039	+	2.29730i	−0.188126	+	0.0905967i	−0.525576	−	0.850747i	$-0.676150\pi$
$643$	−4.77039	+	2.29730i	−0.188126	+	0.0905967i	0.337450	+	0.941344i	$0.390436\pi$
$644$	−26.3740	+	15.4839i	−1.03928	+	0.610153i
$645$		0			0
$646$	1.76664	+	2.21530i	0.0695076	+	0.0871597i
$647$	−33.5159	+	16.1404i	−1.31765	+	0.634545i	−0.954785	−	0.297297i	$-0.903915\pi$
$647$	−33.5159	+	16.1404i	−1.31765	+	0.634545i	−0.362862	+	0.931843i	$0.618200\pi$
$648$		0			0
$649$	−8.71147	+	38.1675i	−0.341955	+	1.49820i
$650$	0.952814	−	1.19479i	0.0373725	−	0.0468636i
$651$		0			0
$652$	18.3595	+	23.0221i	0.719015	+	0.901616i
$653$	−5.86470	+	2.82429i	−0.229504	+	0.110523i	−0.545102	−	0.838370i	$-0.683509\pi$
$653$	−5.86470	+	2.82429i	−0.229504	+	0.110523i	0.315598	+	0.948893i	$0.397795\pi$
$654$		0			0
$655$	2.58850			0.101141
$656$	−20.2580			−0.790942
$657$		0			0
$658$	−0.215554	−	0.681176i	−0.00840318	−	0.0265550i
$659$	−1.29949	−	5.69345i	−0.0506211	−	0.221785i	0.943290	−	0.331970i	$-0.107713\pi$
$659$	−1.29949	−	5.69345i	−0.0506211	−	0.221785i	−0.993911	+	0.110184i	$0.964856\pi$
$660$		0			0
$661$	12.9269	+	16.2098i	0.502796	+	0.630487i	0.966858	−	0.255316i	$-0.0821796\pi$
$661$	12.9269	+	16.2098i	0.502796	+	0.630487i	−0.464061	+	0.885803i	$0.653608\pi$
$662$	−2.47808	−	3.10742i	−0.0963133	−	0.120773i
$663$		0			0
$664$	3.62426	+	15.8789i	0.140649	+	0.616222i
$665$	−10.7389	−	4.12479i	−0.416436	−	0.159953i
$666$		0			0
$667$	10.8274			0.419239
$668$	37.4682			1.44969
$669$		0			0
$670$	−4.60088	+	2.21567i	−0.177748	+	0.0855987i
$671$	15.7081	+	19.6974i	0.606406	+	0.760409i
$672$		0			0
$673$	−3.50105	+	4.39018i	−0.134956	+	0.169229i	−0.844717	−	0.535213i	$-0.820231\pi$
$673$	−3.50105	+	4.39018i	−0.134956	+	0.169229i	0.709761	+	0.704442i	$0.248803\pi$
$674$	−1.13930	+	4.99162i	−0.0438844	+	0.192270i
$675$		0			0
$676$	−9.78461	+	4.71202i	−0.376331	+	0.181232i
$677$	16.5410	+	20.7418i	0.635722	+	0.797170i	0.990461	−	0.137795i	$-0.0440016\pi$
$677$	16.5410	+	20.7418i	0.635722	+	0.797170i	−0.354739	+	0.934966i	$0.615430\pi$
$678$		0			0
$679$	−14.0093	+	1.15240i	−0.537627	+	0.0442249i
$680$	6.48465	−	3.12284i	0.248675	−	0.119756i
$681$		0			0
$682$	0.222960	+	0.976852i	0.00853758	+	0.0374056i
$683$	−22.3177	−	10.7477i	−0.853964	−	0.411247i	−0.0449167	−	0.998991i	$-0.514302\pi$
$683$	−22.3177	−	10.7477i	−0.853964	−	0.411247i	−0.809048	+	0.587743i	$0.800017\pi$
$684$		0			0
$685$	32.6177			1.24626
$686$	−1.96693	+	4.32327i	−0.0750978	+	0.165063i
$687$		0			0
$688$	22.7403	−	28.5154i	0.866966	−	1.08714i
$689$	−22.1584	−	10.6709i	−0.844168	−	0.406530i
$690$		0			0
$691$	31.7350	+	15.2828i	1.20726	+	0.581385i	0.925736	−	0.378170i	$-0.123447\pi$
$691$	31.7350	+	15.2828i	1.20726	+	0.581385i	0.281521	+	0.959555i	$0.409161\pi$
$692$	−15.4222	+	7.42693i	−0.586263	+	0.282329i
$693$		0			0
$694$	3.08981	+	1.48798i	0.117288	+	0.0564828i
$695$	−18.9722	−	23.7904i	−0.719656	−	0.902421i
$696$		0			0
$697$	−14.8974	+	18.6807i	−0.564278	+	0.707582i
$698$	−1.05380	+	4.61698i	−0.0398867	+	0.174755i
$699$		0			0
$700$	6.25344	−	9.31702i	0.236358	−	0.352150i
$701$	20.3319	+	25.4954i	0.767925	+	0.962948i	0.999952	−	0.00976148i	$-0.00310722\pi$
$701$	20.3319	+	25.4954i	0.767925	+	0.962948i	−0.232027	+	0.972709i	$0.574536\pi$
$702$		0			0
$703$	−1.96145	+	8.59368i	−0.0739775	+	0.324117i
$704$	−21.1861			−0.798481
$705$		0			0
$706$	0.0337551	−	0.147891i	0.00127039	−	0.00556594i
$707$	4.21317	+	1.61827i	0.158452	+	0.0608615i
$708$		0			0
$709$	6.70819	+	29.3905i	0.251931	+	1.10378i	0.929645	+	0.368457i	$0.120114\pi$
$709$	6.70819	+	29.3905i	0.251931	+	1.10378i	−0.677713	+	0.735326i	$0.737029\pi$
$710$	4.41481	+	5.53600i	0.165685	+	0.207762i
$711$		0			0
$712$	−3.87818	−	16.9914i	−0.145341	−	0.636780i
$713$	1.58533	+	6.94579i	0.0593711	+	0.260122i
$714$		0			0
$715$	3.32061	−	14.5486i	0.124184	−	0.544085i
$716$	−38.7018			−1.44635
$717$		0			0
$718$	1.26560	−	5.54494i	0.0472316	−	0.206935i
$719$	9.64285	−	4.64375i	0.359618	−	0.173183i	−0.245346	−	0.969435i	$-0.578902\pi$
$719$	9.64285	−	4.64375i	0.359618	−	0.173183i	0.604964	+	0.796253i	$0.293187\pi$
$720$		0			0
$721$	−3.82254	−	1.46824i	−0.142359	−	0.0546800i
$722$	1.96127	−	2.45936i	0.0729910	−	0.0915279i
$723$		0			0
$724$	−21.3073	+	26.7186i	−0.791881	+	0.992987i
$725$	−3.57918	+	1.72364i	−0.132927	+	0.0640145i
$726$		0			0
$727$	−10.4401	−	5.02768i	−0.387201	−	0.186466i	0.230148	−	0.973156i	$-0.426079\pi$
$727$	−10.4401	−	5.02768i	−0.387201	−	0.186466i	−0.617349	+	0.786689i	$0.711793\pi$
$728$	−6.25607	+	3.67288i	−0.231865	+	0.136126i
$729$		0			0
$730$	2.85225	+	1.37357i	0.105567	+	0.0508382i
$731$	−9.57241	−	41.9395i	−0.354048	−	1.55119i
$732$		0			0
$733$	21.4791	−	26.9340i	0.793350	−	0.994830i	−0.206515	−	0.978443i	$-0.566212\pi$
$733$	21.4791	−	26.9340i	0.793350	−	0.994830i	0.999866	−	0.0163866i	$-0.00521625\pi$
$734$	−1.84803			−0.0682121
$735$		0			0
$736$	17.5921			0.648453
$737$	24.2838	−	30.4509i	0.894504	−	1.12167i
$738$		0			0
$739$	6.81192	+	29.8450i	0.250580	+	1.09786i	0.930994	+	0.365036i	$0.118943\pi$
$739$	6.81192	+	29.8450i	0.250580	+	1.09786i	−0.680413	+	0.732829i	$0.738200\pi$
$740$	9.91796	+	4.77624i	0.364591	+	0.175578i
$741$		0			0
$742$	5.73229	+	2.20177i	0.210439	+	0.0808295i
$743$	21.4683	+	10.3386i	0.787597	+	0.379287i	0.784043	−	0.620707i	$-0.213154\pi$
$743$	21.4683	+	10.3386i	0.787597	+	0.379287i	0.00355456	+	0.999994i	$0.498869\pi$
$744$		0			0
$745$	14.3978	−	6.93363i	0.527495	−	0.254028i
$746$	1.00276	−	1.25743i	0.0367138	−	0.0460376i
$747$		0			0
$748$	−16.8271	+	21.1005i	−0.615260	+	0.771512i
$749$	−11.7949	−	12.5279i	−0.430978	−	0.457759i
$750$		0			0
$751$	−16.2039	+	7.80340i	−0.591290	+	0.284750i	−0.705504	−	0.708706i	$-0.749279\pi$
$751$	−16.2039	+	7.80340i	−0.591290	+	0.284750i	0.114214	+	0.993456i	$0.463565\pi$
$752$	0.845781	−	3.70561i	0.0308425	−	0.135130i
$753$		0			0
$754$	1.26269			0.0459846
$755$	−3.31142	+	14.5083i	−0.120515	+	0.528010i
$756$		0			0
$757$	−1.16242	−	5.09291i	−0.0422490	−	0.185105i	0.949400	−	0.314068i	$-0.101692\pi$
$757$	−1.16242	−	5.09291i	−0.0422490	−	0.185105i	−0.991649	+	0.128964i	$0.958835\pi$
$758$	−0.500169	−	2.19139i	−0.0181670	−	0.0795947i
$759$		0			0
$760$	2.73526	+	3.42991i	0.0992183	+	0.124416i
$761$	−10.4877	−	45.9495i	−0.380178	−	1.66567i	−0.696914	−	0.717155i	$-0.745444\pi$
$761$	−10.4877	−	45.9495i	−0.380178	−	1.66567i	0.316735	−	0.948514i	$-0.397413\pi$
$762$		0			0
$763$	5.52075	−	8.22538i	0.199865	−	0.297779i
$764$	0.497291	−	2.17877i	0.0179913	−	0.0788252i
$765$		0			0
$766$	2.25580			0.0815054
$767$	−7.22367	+	31.6490i	−0.260832	+	1.14278i
$768$		0			0
$769$	−16.0308	−	20.1019i	−0.578084	−	0.724894i	0.403701	−	0.914891i	$-0.367724\pi$
$769$	−16.0308	−	20.1019i	−0.578084	−	0.724894i	−0.981785	+	0.189997i	$0.939152\pi$
$770$	−0.528497	+	3.68821i	−0.0190457	+	0.132914i
$771$		0			0
$772$	−2.32201	+	10.1734i	−0.0835708	+	0.366148i
$773$	18.3635	−	23.0271i	0.660489	−	0.828227i	−0.332907	−	0.942960i	$-0.608030\pi$
$773$	18.3635	−	23.0271i	0.660489	−	0.828227i	0.993396	+	0.114732i	$0.0366010\pi$
$774$		0			0
$775$	−1.62978	−	2.04367i	−0.0585432	−	0.0734109i
$776$	4.82967	+	2.32585i	0.173375	+	0.0834931i
$777$		0			0
$778$	6.11652	−	2.94556i	0.219288	−	0.105603i
$779$	−13.1215	−	6.31897i	−0.470125	−	0.226400i
$780$		0			0
$781$	−48.6573	−	23.4321i	−1.74110	−	0.838468i
$782$	4.06845	−	5.10168i	0.145488	−	0.182436i
$783$		0			0
$784$	−20.6680	+	14.5362i	−0.738143	+	0.519149i
$785$	−28.8007			−1.02794
$786$		0			0
$787$	−36.5974	−	17.6244i	−1.30456	−	0.628242i	−0.352974	−	0.935633i	$-0.614830\pi$
$787$	−36.5974	−	17.6244i	−1.30456	−	0.628242i	−0.951583	+	0.307392i	$0.900544\pi$
$788$	2.46321	+	10.7920i	0.0877482	+	0.384450i
$789$		0			0
$790$	0.0849083	−	0.0408897i	0.00302090	−	0.00145479i
$791$	−7.40596	−	7.86617i	−0.263326	−	0.279689i
$792$		0			0
$793$	13.0254	+	16.3333i	0.462545	+	0.580014i
$794$	−0.00127853		0.000615707i	−4.53733e−5		2.18506e-5i
$795$		0			0
$796$	4.40724	−	19.3094i	0.156211	−	0.684403i
$797$	7.55690	−	9.47606i	0.267679	−	0.335659i	−0.629766	−	0.776785i	$-0.716849\pi$
$797$	7.55690	−	9.47606i	0.267679	−	0.335659i	0.897445	+	0.441126i	$0.145421\pi$
$798$		0			0
$799$	−2.79512	−	3.50497i	−0.0988842	−	0.123997i
$800$	−5.81536	+	2.80053i	−0.205604	+	0.0990137i
$801$		0			0
$802$	0.870815			0.0307496
$803$	−24.1454			−0.852071
$804$		0			0
$805$	−3.75781	+	26.2246i	−0.132446	+	0.924295i
$806$	0.184881	+	0.810019i	0.00651217	+	0.0285317i
$807$		0			0
$808$	−1.07312	−	1.34565i	−0.0377522	−	0.0473398i
$809$	20.0202	+	25.1046i	0.703874	+	0.882629i	0.997306	−	0.0733503i	$-0.0233691\pi$
$809$	20.0202	+	25.1046i	0.703874	+	0.882629i	−0.293433	+	0.955980i	$0.594798\pi$
$810$		0			0
$811$	−6.70771	−	29.3884i	−0.235540	−	1.03197i	−0.944961	−	0.327182i	$-0.893901\pi$
$811$	−6.70771	−	29.3884i	−0.235540	−	1.03197i	0.709422	−	0.704784i	$-0.248956\pi$
$812$	9.24036	−	0.760108i	0.324273	−	0.0266746i
$813$		0			0
$814$	2.85492			0.100065
$815$	25.5076			0.893492
$816$		0			0
$817$	23.6240	−	11.3767i	0.826497	−	0.398020i
$818$	−4.11909	−	5.16517i	−0.144021	−	0.180596i
$819$		0			0
$820$	−11.3399	+	14.2197i	−0.396005	+	0.496575i
$821$	7.30571	−	32.0084i	0.254971	−	1.11710i	−0.671580	−	0.740932i	$-0.734384\pi$
$821$	7.30571	−	32.0084i	0.254971	−	1.11710i	0.926551	−	0.376169i	$-0.122759\pi$
$822$		0			0
$823$	40.5926	−	19.5483i	1.41497	−	0.681412i	0.438831	−	0.898570i	$-0.355393\pi$
$823$	40.5926	−	19.5483i	1.41497	−	0.681412i	0.976137	+	0.217157i	$0.0696785\pi$
$824$	0.973626	+	1.22089i	0.0339179	+	0.0425317i
$825$		0			0
$826$	1.14969	−	8.02335i	0.0400030	−	0.279168i
$827$	17.4941	−	8.42473i	0.608331	−	0.292957i	−0.104245	−	0.994552i	$-0.533243\pi$
$827$	17.4941	−	8.42473i	0.608331	−	0.292957i	0.712576	+	0.701595i	$0.247528\pi$
$828$		0			0
$829$	7.38639	+	32.3619i	0.256540	+	1.12398i	0.924922	+	0.380157i	$0.124130\pi$
$829$	7.38639	+	32.3619i	0.256540	+	1.12398i	−0.668382	+	0.743818i	$0.733013\pi$
$830$	6.24949	+	3.00959i	0.216923	+	0.104465i
$831$		0			0
$832$	−17.5678			−0.609054
$833$	−1.79451	+	29.7484i	−0.0621762	+	1.03072i
$834$		0			0
$835$	20.2362	−	25.3754i	0.700304	−	0.878154i
$836$	−14.8212	−	7.13750i	−0.512601	−	0.246856i
$837$		0			0
$838$	−3.27369	−	1.57652i	−0.113088	−	0.0544601i
$839$	−3.47261	+	1.67232i	−0.119888	+	0.0577349i	−0.492866	−	0.870105i	$-0.664051\pi$
$839$	−3.47261	+	1.67232i	−0.119888	+	0.0577349i	0.372978	+	0.927840i	$0.378337\pi$
$840$		0			0
$841$	23.1707	+	11.1584i	0.798991	+	0.384774i
$842$	−0.402081	−	0.504194i	−0.0138566	−	0.0173757i
$843$		0			0
$844$	18.1655	−	22.7788i	0.625282	−	0.784079i
$845$	−2.09335	+	9.17157i	−0.0720135	+	0.315512i
$846$		0			0
$847$	0.206915	+	0.653875i	0.00710968	+	0.0224674i
$848$	20.3678	+	25.5405i	0.699434	+	0.877063i
$849$		0			0
$850$	−0.532746	+	2.33411i	−0.0182730	+	0.0800594i
$851$	20.2996			0.695861
$852$		0			0
$853$	−0.423044	+	1.85348i	−0.0144847	+	0.0634618i	−0.981654	−	0.190672i	$-0.938933\pi$
$853$	−0.423044	+	1.85348i	−0.0144847	+	0.0634618i	0.967169	+	0.254134i	$0.0817904\pi$
$854$	−3.57555	−	3.79774i	−0.122353	−	0.129956i
$855$		0			0
$856$	1.46014	+	6.39730i	0.0499066	+	0.218655i
$857$	8.23348	+	10.3245i	0.281250	+	0.352677i	0.902311	−	0.431086i	$-0.141869\pi$
$857$	8.23348	+	10.3245i	0.281250	+	0.352677i	−0.621061	+	0.783762i	$0.713298\pi$
$858$		0			0
$859$	−4.81753	−	21.1070i	−0.164372	−	0.720161i	−0.988181	−	0.153293i	$-0.951012\pi$
$859$	−4.81753	−	21.1070i	−0.164372	−	0.720161i	0.823809	−	0.566868i	$-0.191845\pi$
$860$	−7.28651	−	31.9243i	−0.248468	−	1.08861i
$861$		0			0
$862$	−1.33171	+	5.83461i	−0.0453583	+	0.198728i
$863$	−5.47281			−0.186297			−0.0931483	−	0.995652i	$-0.529693\pi$
$863$	−5.47281			−0.186297			−0.0931483	+	0.995652i	$0.529693\pi$
$864$		0			0
$865$	−3.29947	+	14.4559i	−0.112185	+	0.491516i
$866$	−1.82845	+	0.880535i	−0.0621332	+	0.0299218i
$867$		0			0
$868$	1.84057	+	5.81640i	0.0624729	+	0.197422i
$869$	−0.448152	+	0.561964i	−0.0152025	+	0.0190633i
$870$		0			0
$871$	20.1364	−	25.2503i	0.682297	−	0.855573i
$872$	−3.40370	+	1.63913i	−0.115264	+	0.0555081i
$873$		0			0
$874$	3.58346	+	1.72570i	0.121212	+	0.0583727i
$875$	−9.61965	−	30.3992i	−0.325204	−	1.02768i
$876$		0			0
$877$	−30.5120	−	14.6938i	−1.03032	−	0.496174i	−0.159198	−	0.987247i	$-0.550891\pi$
$877$	−30.5120	−	14.6938i	−1.03032	−	0.496174i	−0.871119	+	0.491072i	$0.836605\pi$
$878$	−0.861452	−	3.77427i	−0.0290726	−	0.127375i
$879$		0			0
$880$	−12.3584	+	15.4970i	−0.416603	+	0.522403i
$881$	43.6737			1.47140			0.735702	−	0.677306i	$-0.236853\pi$
$881$	43.6737			1.47140			0.735702	+	0.677306i	$0.236853\pi$
$882$		0			0
$883$	6.92448			0.233027			0.116514	−	0.993189i	$-0.462828\pi$
$883$	6.92448			0.233027			0.116514	+	0.993189i	$0.462828\pi$
$884$	−13.9533	+	17.4969i	−0.469299	+	0.588483i
$885$		0			0
$886$	−1.27715	−	5.59555i	−0.0429066	−	0.187986i
$887$	−4.90228	−	2.36081i	−0.164602	−	0.0792683i	0.349769	−	0.936836i	$-0.386260\pi$
$887$	−4.90228	−	2.36081i	−0.164602	−	0.0792683i	−0.514371	+	0.857568i	$0.671975\pi$
$888$		0			0
$889$	7.37617	−	51.4759i	0.247389	−	1.72645i
$890$	−6.68732	−	3.22044i	−0.224159	−	0.107950i
$891$		0			0
$892$	−50.9000	+	24.5121i	−1.70426	+	0.820727i
$893$	1.70370	−	2.13637i	0.0570121	−	0.0714909i
$894$		0			0
$895$	−20.9025	+	26.2109i	−0.698693	+	0.876133i
$896$	19.8956	−	1.63660i	0.664664	−	0.0546750i
$897$		0			0
$898$	3.96546	−	1.90966i	0.132329	−	0.0637263i
$899$	0.480605	−	2.10567i	0.0160291	−	0.0702280i
$900$		0			0
$901$	38.5300			1.28362
$902$	−1.04962	+	4.59868i	−0.0349485	+	0.153119i
$903$		0			0
$904$	0.916812	+	4.01682i	0.0304927	+	0.133597i
$905$	6.58731	+	28.8609i	0.218969	+	0.959368i
$906$		0			0
$907$	−20.9009	−	26.2090i	−0.694005	−	0.870254i	0.302555	−	0.953132i	$-0.402160\pi$
$907$	−20.9009	−	26.2090i	−0.694005	−	0.870254i	−0.996560	+	0.0828776i	$0.973589\pi$
$908$	−2.07027	−	9.07044i	−0.0687043	−	0.301013i
$909$		0			0
$910$	−0.438237	+	3.05831i	−0.0145274	+	0.101382i
$911$	−6.31547	+	27.6699i	−0.209241	+	0.916744i	0.755833	+	0.654765i	$0.227232\pi$
$911$	−6.31547	+	27.6699i	−0.209241	+	0.916744i	−0.965073	+	0.261979i	$0.915625\pi$
$912$		0			0
$913$	−52.9042			−1.75087
$914$	−0.899925	+	3.94283i	−0.0297669	+	0.130417i
$915$		0			0
$916$	18.7457	+	23.5063i	0.619375	+	0.776672i
$917$	3.52487	−	2.06942i	0.116401	−	0.0683382i
$918$		0			0
$919$	−11.9317	+	52.2760i	−0.393589	+	1.72443i	0.258258	+	0.966076i	$0.416851\pi$
$919$	−11.9317	+	52.2760i	−0.393589	+	1.72443i	−0.651847	+	0.758350i	$0.726006\pi$
$920$	6.29911	−	7.89884i	0.207676	−	0.260417i
$921$		0			0
$922$	−3.82361	−	4.79465i	−0.125924	−	0.157903i
$923$	−40.3473	−	19.4302i	−1.32805	−	0.639554i
$924$		0			0
$925$	−6.71037	+	3.23154i	−0.220636	+	0.106253i
$926$	−3.51293	−	1.69174i	−0.115442	−	0.0555940i
$927$		0			0
$928$	−4.80503	−	2.31398i	−0.157733	−	0.0759601i
$929$	1.83960	−	2.30678i	0.0603553	−	0.0756831i	−0.750738	−	0.660601i	$-0.770302\pi$
$929$	1.83960	−	2.30678i	0.0603553	−	0.0756831i	0.811093	+	0.584918i	$0.198873\pi$
$930$		0			0
$931$	−17.9212	+	2.96847i	−0.587344	+	0.0972877i
$932$	−17.9421			−0.587714
$933$		0			0
$934$	8.91290	+	4.29223i	0.291639	+	0.140446i
$935$	5.20222	+	22.7924i	0.170131	+	0.745391i
$936$		0			0
$937$	5.31747	−	2.56076i	0.173714	−	0.0836564i	−0.345006	−	0.938601i	$-0.612123\pi$
$937$	5.31747	−	2.56076i	0.173714	−	0.0836564i	0.518720	+	0.854944i	$0.326409\pi$
$938$	−4.49386	+	6.69542i	−0.146730	+	0.218613i
$939$		0			0
$940$	−2.12764	−	2.66798i	−0.0693960	−	0.0870199i
$941$	−29.7135	+	14.3093i	−0.968632	+	0.466469i	−0.850181	−	0.526491i	$-0.823507\pi$
$941$	−29.7135	+	14.3093i	−0.968632	+	0.466469i	−0.118452	+	0.992960i	$0.537793\pi$
$942$		0			0
$943$	−7.46319	+	32.6984i	−0.243035	+	1.06481i
$944$	26.8846	−	33.7122i	0.875018	−	1.09724i
$945$		0			0
$946$	−5.29493	−	6.63963i	−0.172153	−	0.215873i
$947$	−10.3704	+	4.99411i	−0.336992	+	0.162287i	−0.594725	−	0.803929i	$-0.702739\pi$
$947$	−10.3704	+	4.99411i	−0.336992	+	0.162287i	0.257733	+	0.966216i	$0.417025\pi$
$948$		0			0
$949$	−20.0217			−0.649930
$950$	−1.45929			−0.0473456
$951$		0			0
$952$	6.33381	−	9.43677i	0.205280	−	0.305848i
$953$	3.68387	+	16.1401i	0.119332	+	0.522829i	0.998893	+	0.0470419i	$0.0149794\pi$
$953$	3.68387	+	16.1401i	0.119332	+	0.522829i	−0.879561	+	0.475787i	$0.842163\pi$
$954$		0			0
$955$	−1.20700	−	1.51353i	−0.0390575	−	0.0489765i
$956$	−27.0436	−	33.9116i	−0.874652	−	1.09678i
$957$		0			0
$958$	−1.04884	−	4.59525i	−0.0338863	−	0.148466i
$959$	44.4169	−	26.0768i	1.43430	−	0.842063i
$960$		0			0
$961$	−29.5788			−0.954156
$962$	2.36734			0.0763262
$963$		0			0
$964$	10.3871	−	5.00216i	0.334546	−	0.161109i
$965$	5.63584	+	7.06712i	0.181424	+	0.227499i
$966$		0			0
$967$	32.7914	−	41.1191i	1.05450	−	1.32230i	0.109949	−	0.993937i	$-0.464931\pi$
$967$	32.7914	−	41.1191i	1.05450	−	1.32230i	0.944551	−	0.328364i	$-0.106497\pi$
$968$	0.0581992	−	0.254987i	0.00187059	−	0.00819560i
$969$		0			0
$970$	2.05685	−	0.990528i	0.0660416	−	0.0318039i
$971$	−23.1173	−	28.9882i	−0.741870	−	0.930276i	0.257482	−	0.966283i	$-0.417107\pi$
$971$	−23.1173	−	28.9882i	−0.741870	−	0.930276i	−0.999352	+	0.0360077i	$0.988536\pi$
$972$		0			0
$973$	−44.8549	−	17.2287i	−1.43798	−	0.552328i
$974$	0.761100	−	0.366526i	0.0243872	−	0.0117443i
$975$		0			0
$976$	−6.17475	−	27.0533i	−0.197649	−	0.865956i
$977$	−23.1787	−	11.1623i	−0.741553	−	0.357113i	0.0246630	−	0.999696i	$-0.492149\pi$
$977$	−23.1787	−	11.1623i	−0.741553	−	0.357113i	−0.766217	+	0.642582i	$0.777863\pi$
$978$		0			0
$979$	56.6106			1.80928
$980$	−1.36598	+	22.6445i	−0.0436347	+	0.723351i
$981$		0			0
$982$	−5.75959	+	7.22230i	−0.183796	+	0.230473i
$983$	10.9250	+	5.26119i	0.348452	+	0.167806i	0.599920	−	0.800060i	$-0.295199\pi$
$983$	10.9250	+	5.26119i	0.348452	+	0.167806i	−0.251468	+	0.967866i	$0.580913\pi$
$984$		0			0
$985$	8.63928	+	4.16046i	0.275270	+	0.132563i
$986$	−1.78229	+	0.858305i	−0.0567597	+	0.0273340i
$987$		0			0
$988$	−12.2899	−	5.91851i	−0.390994	−	0.188293i
$989$	−37.6490	−	47.2103i	−1.19717	−	1.50120i
$990$		0			0
$991$	0.776129	−	0.973234i	0.0246545	−	0.0309158i	−0.769351	−	0.638826i	$-0.779420\pi$
$991$	0.776129	−	0.973234i	0.0246545	−	0.0309158i	0.794006	+	0.607910i	$0.207992\pi$
$992$	0.780875	−	3.42124i	0.0247928	−	0.108624i
$993$		0			0
$994$	10.4377	+	4.00911i	0.331063	+	0.127161i
$995$	−10.6970	−	13.4136i	−0.339118	−	0.425241i
$996$		0			0
$997$	3.84303	−	16.8374i	0.121710	−	0.533246i	−0.876907	−	0.480661i	$-0.840397\pi$
$997$	3.84303	−	16.8374i	0.121710	−	0.533246i	0.998616	−	0.0525851i	$-0.0167461\pi$
$998$	7.90847			0.250338
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.c.190.2		24
3.2	odd	2		147.2.i.a.43.3	✓	24
49.8	even	7	inner	441.2.u.c.253.2		24
147.8	odd	14		147.2.i.a.106.3	yes	24
147.20	even	14		7203.2.a.b.1.8		12
147.29	odd	14		7203.2.a.a.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.a.43.3	✓	24	3.2	odd	2
147.2.i.a.106.3	yes	24	147.8	odd	14
441.2.u.c.190.2		24	1.1	even	1	trivial
441.2.u.c.253.2		24	49.8	even	7	inner
7203.2.a.a.1.8		12	147.29	odd	14
7203.2.a.b.1.8		12	147.20	even	14

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.159899 + 0.200507i) q^{2} +(0.430406 + 1.88573i) q^{4} +(1.50958 + 0.726973i) q^{5} +(2.63685 - 0.216906i) q^{7} +(-0.909048 - 0.437774i) q^{8} +O(q^{10})\)	\(q+(-0.159899 + 0.200507i) q^{2} +(0.430406 + 1.88573i) q^{4} +(1.50958 + 0.726973i) q^{5} +(2.63685 - 0.216906i) q^{7} +(-0.909048 - 0.437774i) q^{8} +(-0.387144 + 0.186439i) q^{10} +(2.04337 - 2.56231i) q^{11} +(1.69439 - 2.12470i) q^{13} +(-0.378139 + 0.563390i) q^{14} +(-3.25223 + 1.56619i) q^{16} +(-0.947383 + 4.15076i) q^{17} -2.59506 q^{19} +(-0.721147 + 3.15955i) q^{20} +(0.187028 + 0.819422i) q^{22} +(1.32984 + 5.82640i) q^{23} +(-1.36712 - 1.71431i) q^{25} +(0.155086 + 0.679476i) q^{26} +(1.54394 + 4.87903i) q^{28} +(0.403151 - 1.76632i) q^{29} +1.19212 q^{31} +(0.655029 - 2.86987i) q^{32} +(-0.680771 - 0.853660i) q^{34} +(4.13820 + 1.58948i) q^{35} +(0.755841 - 3.31155i) q^{37} +(0.414948 - 0.520328i) q^{38} +(-1.05403 - 1.32171i) q^{40} +(5.05633 + 2.43500i) q^{41} +(-9.10344 + 4.38399i) q^{43} +(5.71131 + 2.75042i) q^{44} +(-1.38088 - 0.664995i) q^{46} +(-0.656516 + 0.823245i) q^{47} +(6.90590 - 1.14389i) q^{49} +0.562334 q^{50} +(4.73589 + 2.28069i) q^{52} +(-2.01380 - 8.82301i) q^{53} +(4.94735 - 2.38252i) q^{55} +(-2.49197 - 0.957165i) q^{56} +(0.289696 + 0.363268i) q^{58} +(-10.7625 + 5.18294i) q^{59} +(-1.71060 + 7.49462i) q^{61} +(-0.190620 + 0.239029i) q^{62} +(-4.03053 - 5.05413i) q^{64} +(4.10241 - 1.97562i) q^{65} +11.8842 q^{67} -8.23498 q^{68} +(-0.980398 + 0.575583i) q^{70} +(-3.66683 - 16.0655i) q^{71} +(-4.59351 - 5.76008i) q^{73} +(0.543133 + 0.681067i) q^{74} +(-1.11693 - 4.89359i) q^{76} +(4.83227 - 7.19962i) q^{77} -0.219320 q^{79} -6.04806 q^{80} +(-1.29674 + 0.624477i) q^{82} +(-10.0647 - 12.6208i) q^{83} +(-4.44764 + 5.57716i) q^{85} +(0.576612 - 2.52630i) q^{86} +(-2.97923 + 1.43472i) q^{88} +(10.7698 + 13.5050i) q^{89} +(4.00699 - 5.97003i) q^{91} +(-10.4147 + 5.01544i) q^{92} +(-0.0600903 - 0.263273i) q^{94} +(-3.91744 - 1.88654i) q^{95} -5.31289 q^{97} +(-0.874890 + 1.56759i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} - 3 q^{4} - 3 q^{8}+O(q^{10}) \) 24 * q - q^2 - 3 * q^4 - 3 * q^8	\( 24 q - q^{2} - 3 q^{4} - 3 q^{8} - 30 q^{10} - 9 q^{11} + 21 q^{14} - 29 q^{16} - 5 q^{17} + 26 q^{19} + 13 q^{20} + 11 q^{22} - 4 q^{23} - 28 q^{25} + 22 q^{26} - 7 q^{28} - 6 q^{29} + 36 q^{31} - 14 q^{32} + 46 q^{34} + 7 q^{35} - 22 q^{37} + 45 q^{38} + 35 q^{40} + 11 q^{41} + 6 q^{43} - 82 q^{44} - 16 q^{46} - 29 q^{47} - 42 q^{49} + 48 q^{50} - 50 q^{52} - 28 q^{53} + 23 q^{55} - 21 q^{56} + 39 q^{58} + 15 q^{59} - 32 q^{61} + 8 q^{62} + 29 q^{64} + 21 q^{65} - 34 q^{67} + 22 q^{68} - 24 q^{71} - 15 q^{73} - 6 q^{74} + 7 q^{76} + 21 q^{77} - 34 q^{79} - 8 q^{80} + 14 q^{82} - 14 q^{83} + 20 q^{85} + 100 q^{86} - 108 q^{88} - 10 q^{89} + 84 q^{91} + 21 q^{92} + 99 q^{94} - 18 q^{95} - 64 q^{97} - 91 q^{98}+O(q^{100}) \) 24 * q - q^2 - 3 * q^4 - 3 * q^8 - 30 * q^10 - 9 * q^11 + 21 * q^14 - 29 * q^16 - 5 * q^17 + 26 * q^19 + 13 * q^20 + 11 * q^22 - 4 * q^23 - 28 * q^25 + 22 * q^26 - 7 * q^28 - 6 * q^29 + 36 * q^31 - 14 * q^32 + 46 * q^34 + 7 * q^35 - 22 * q^37 + 45 * q^38 + 35 * q^40 + 11 * q^41 + 6 * q^43 - 82 * q^44 - 16 * q^46 - 29 * q^47 - 42 * q^49 + 48 * q^50 - 50 * q^52 - 28 * q^53 + 23 * q^55 - 21 * q^56 + 39 * q^58 + 15 * q^59 - 32 * q^61 + 8 * q^62 + 29 * q^64 + 21 * q^65 - 34 * q^67 + 22 * q^68 - 24 * q^71 - 15 * q^73 - 6 * q^74 + 7 * q^76 + 21 * q^77 - 34 * q^79 - 8 * q^80 + 14 * q^82 - 14 * q^83 + 20 * q^85 + 100 * q^86 - 108 * q^88 - 10 * q^89 + 84 * q^91 + 21 * q^92 + 99 * q^94 - 18 * q^95 - 64 * q^97 - 91 * q^98

Introduction

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