LMFDB - Embedded newform 891.2.n.i.379.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(136,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("891.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.n (of order $15$, degree $8$, 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			379.4
Character	$\chi$	$=$	891.379
Dual form			891.2.n.i.757.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.79145 + 0.380785i) q^{2} +(1.23721 + 0.550844i) q^{4} +(-1.63692 + 0.347939i) q^{5} +(-0.432236 - 4.11245i) q^{7} +(-0.956730 - 0.695105i) q^{8} +O(q^{10})$	\(q+(1.79145 + 0.380785i) q^{2} +(1.23721 + 0.550844i) q^{4} +(-1.63692 + 0.347939i) q^{5} +(-0.432236 - 4.11245i) q^{7} +(-0.956730 - 0.695105i) q^{8} -3.06496 q^{10} +(1.92634 - 2.69985i) q^{11} +(-3.54177 + 3.93353i) q^{13} +(0.791630 - 7.53186i) q^{14} +(-3.26166 - 3.62244i) q^{16} +(1.79348 - 5.51975i) q^{17} +(-0.756141 - 0.549369i) q^{19} +(-2.21688 - 0.471213i) q^{20} +(4.47901 - 4.10314i) q^{22} +(0.505016 + 0.874713i) q^{23} +(-2.00927 + 0.894586i) q^{25} +(-7.84274 + 5.69808i) q^{26} +(1.73055 - 5.32608i) q^{28} +(-0.437181 - 4.15950i) q^{29} +(0.863415 - 0.958919i) q^{31} +(-3.28115 - 5.68312i) q^{32} +(5.31477 - 9.20544i) q^{34} +(2.13842 + 6.58138i) q^{35} +(8.02034 - 5.82712i) q^{37} +(-1.14540 - 1.27210i) q^{38} +(1.80795 + 0.804949i) q^{40} +(0.145580 - 1.38510i) q^{41} +(-3.77814 + 6.54393i) q^{43} +(3.87049 - 2.27919i) q^{44} +(0.571634 + 1.75931i) q^{46} +(5.38826 - 2.39901i) q^{47} +(-9.87841 + 2.09972i) q^{49} +(-3.94016 + 0.837508i) q^{50} +(-6.54869 + 2.91566i) q^{52} +(0.303205 + 0.933170i) q^{53} +(-2.21389 + 5.08970i) q^{55} +(-2.44505 + 4.23496i) q^{56} +(0.800686 - 7.61802i) q^{58} +(4.05985 + 1.80756i) q^{59} +(7.41150 + 8.23130i) q^{61} +(1.91191 - 1.38908i) q^{62} +(-0.701393 - 2.15867i) q^{64} +(4.42897 - 7.67120i) q^{65} +(-1.37586 - 2.38307i) q^{67} +(5.25943 - 5.84119i) q^{68} +(1.32479 + 12.6045i) q^{70} +(2.76800 - 8.51901i) q^{71} +(-9.56397 + 6.94863i) q^{73} +(16.5869 - 7.38498i) q^{74} +(-0.632893 - 1.09620i) q^{76} +(-11.9357 - 6.75501i) q^{77} +(10.8992 + 2.31669i) q^{79} +(6.59947 + 4.79479i) q^{80} +(0.788227 - 2.42591i) q^{82} +(9.51417 + 10.5666i) q^{83} +(-1.01525 + 9.65942i) q^{85} +(-9.26019 + 10.2845i) q^{86} +(-3.71967 + 1.24402i) q^{88} -7.12753 q^{89} +(17.7073 + 12.8651i) q^{91} +(0.142983 + 1.36039i) q^{92} +(10.5663 - 2.24594i) q^{94} +(1.42889 + 0.636184i) q^{95} +(3.42861 + 0.728774i) q^{97} -18.4963 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 4 q^{4} + q^{5} + 2 q^{7}+O(q^{10}) $ 32 * q + 2 * q^2 + 4 * q^4 + q^5 + 2 * q^7	$ 32 q + 2 q^{2} + 4 q^{4} + q^{5} + 2 q^{7} + 12 q^{10} + 13 q^{11} + 2 q^{13} - 22 q^{14} + 24 q^{16} + 4 q^{17} - 4 q^{19} - 15 q^{22} + 14 q^{23} + 19 q^{25} - 42 q^{26} + 30 q^{28} + q^{29} - 14 q^{31} - 48 q^{32} - 10 q^{34} + 36 q^{35} + 18 q^{37} + 11 q^{38} - 33 q^{40} + 25 q^{41} - 14 q^{43} - 28 q^{44} + 8 q^{46} - 28 q^{47} + 4 q^{49} - 63 q^{50} - 10 q^{52} - 2 q^{53} - 80 q^{55} + 96 q^{56} + 20 q^{58} + 41 q^{59} + 10 q^{62} - 184 q^{64} - 60 q^{65} + 48 q^{67} + 25 q^{68} + 31 q^{70} - 6 q^{71} - 26 q^{73} + 29 q^{74} + 58 q^{76} - 2 q^{77} + 166 q^{80} + 82 q^{82} - 14 q^{83} + 10 q^{85} - 56 q^{86} - 86 q^{88} - 164 q^{89} + 28 q^{91} + 74 q^{92} + 2 q^{94} - 56 q^{95} - 12 q^{97} - 52 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 4 * q^4 + q^5 + 2 * q^7 + 12 * q^10 + 13 * q^11 + 2 * q^13 - 22 * q^14 + 24 * q^16 + 4 * q^17 - 4 * q^19 - 15 * q^22 + 14 * q^23 + 19 * q^25 - 42 * q^26 + 30 * q^28 + q^29 - 14 * q^31 - 48 * q^32 - 10 * q^34 + 36 * q^35 + 18 * q^37 + 11 * q^38 - 33 * q^40 + 25 * q^41 - 14 * q^43 - 28 * q^44 + 8 * q^46 - 28 * q^47 + 4 * q^49 - 63 * q^50 - 10 * q^52 - 2 * q^53 - 80 * q^55 + 96 * q^56 + 20 * q^58 + 41 * q^59 + 10 * q^62 - 184 * q^64 - 60 * q^65 + 48 * q^67 + 25 * q^68 + 31 * q^70 - 6 * q^71 - 26 * q^73 + 29 * q^74 + 58 * q^76 - 2 * q^77 + 166 * q^80 + 82 * q^82 - 14 * q^83 + 10 * q^85 - 56 * q^86 - 86 * q^88 - 164 * q^89 + 28 * q^91 + 74 * q^92 + 2 * q^94 - 56 * q^95 - 12 * q^97 - 52 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.79145	+	0.380785i	1.26675	+	0.269256i	0.791812	−	0.610765i	$-0.209138\pi$
$2$	1.79145	+	0.380785i	1.26675	+	0.269256i	0.474936	+	0.880020i	$0.342471\pi$
$3$		0			0
$3$		0			0
$4$	1.23721	+	0.550844i	0.618607	+	0.275422i
$5$	−1.63692	+	0.347939i	−0.732054	+	0.155603i	−0.558833	−	0.829280i	$-0.688751\pi$
$5$	−1.63692	+	0.347939i	−0.732054	+	0.155603i	−0.173221	+	0.984883i	$0.555417\pi$
$6$		0			0
$7$	−0.432236	−	4.11245i	−0.163370	−	1.55436i	−0.702220	−	0.711960i	$-0.747808\pi$
$7$	−0.432236	−	4.11245i	−0.163370	−	1.55436i	0.538850	−	0.842402i	$-0.318859\pi$
$8$	−0.956730	−	0.695105i	−0.338255	−	0.245757i
$9$		0			0
$10$	−3.06496			−0.969225
$11$	1.92634	−	2.69985i	0.580813	−	0.814037i
$11$	1.92634	−	2.69985i	0.580813	−	0.814037i
$12$		0			0
$13$	−3.54177	+	3.93353i	−0.982310	+	1.09097i	0.0135361	+	0.999908i	$0.495691\pi$
$13$	−3.54177	+	3.93353i	−0.982310	+	1.09097i	−0.995846	+	0.0910570i	$0.970975\pi$
$14$	0.791630	−	7.53186i	0.211572	−	2.01297i
$15$		0			0
$16$	−3.26166	−	3.62244i	−0.815414	−	0.905610i
$17$	1.79348	−	5.51975i	0.434982	−	1.33874i	−0.458124	−	0.888889i	$-0.651478\pi$
$17$	1.79348	−	5.51975i	0.434982	−	1.33874i	0.893105	−	0.449848i	$-0.148522\pi$
$18$		0			0
$19$	−0.756141	−	0.549369i	−0.173471	−	0.126034i	0.497662	−	0.867371i	$-0.334192\pi$
$19$	−0.756141	−	0.549369i	−0.173471	−	0.126034i	−0.671133	+	0.741337i	$0.734192\pi$
$20$	−2.21688	−	0.471213i	−0.495710	−	0.105367i
$21$		0			0
$22$	4.47901	−	4.10314i	0.954928	−	0.874793i
$23$	0.505016	+	0.874713i	0.105303	+	0.182390i	0.913862	−	0.406025i	$-0.133085\pi$
$23$	0.505016	+	0.874713i	0.105303	+	0.182390i	−0.808559	+	0.588415i	$0.799752\pi$
$24$		0			0
$25$	−2.00927	+	0.894586i	−0.401855	+	0.178917i
$26$	−7.84274	+	5.69808i	−1.53809	+	1.11749i
$27$		0			0
$28$	1.73055	−	5.32608i	0.327043	−	1.00654i
$29$	−0.437181	−	4.15950i	−0.0811825	−	0.772400i	−0.957065	−	0.289875i	$-0.906386\pi$
$29$	−0.437181	−	4.15950i	−0.0811825	−	0.772400i	0.875882	−	0.482525i	$-0.160280\pi$
$30$		0			0
$31$	0.863415	−	0.958919i	0.155074	−	0.172227i	−0.660602	−	0.750737i	$-0.729699\pi$
$31$	0.863415	−	0.958919i	0.155074	−	0.172227i	0.815676	+	0.578510i	$0.196365\pi$
$32$	−3.28115	−	5.68312i	−0.580031	−	1.00464i
$33$		0			0
$34$	5.31477	−	9.20544i	0.911475	−	1.57872i
$35$	2.13842	+	6.58138i	0.361459	+	1.11246i
$36$		0			0
$37$	8.02034	−	5.82712i	1.31854	−	0.957972i	0.318586	−	0.947894i	$-0.396792\pi$
$37$	8.02034	−	5.82712i	1.31854	−	0.957972i	0.999949	−	0.0100784i	$-0.00320810\pi$
$38$	−1.14540	−	1.27210i	−0.185808	−	0.206361i
$39$		0			0
$40$	1.80795	+	0.804949i	0.285861	+	0.127274i
$41$	0.145580	−	1.38510i	0.0227358	−	0.216317i	−0.977255	−	0.212067i	$-0.931981\pi$
$41$	0.145580	−	1.38510i	0.0227358	−	0.216317i	0.999991	−	0.00424999i	$-0.00135282\pi$
$42$		0			0
$43$	−3.77814	+	6.54393i	−0.576161	+	0.997940i	0.419754	+	0.907638i	$0.362116\pi$
$43$	−3.77814	+	6.54393i	−0.576161	+	0.997940i	−0.995914	+	0.0903017i	$0.971217\pi$
$44$	3.87049	−	2.27919i	0.583499	−	0.343601i
$45$		0			0
$46$	0.571634	+	1.75931i	0.0842829	+	0.259396i
$47$	5.38826	−	2.39901i	0.785958	−	0.349931i	0.0257983	−	0.999667i	$-0.491787\pi$
$47$	5.38826	−	2.39901i	0.785958	−	0.349931i	0.760160	+	0.649736i	$0.225121\pi$
$48$		0			0
$49$	−9.87841	+	2.09972i	−1.41120	+	0.299960i
$50$	−3.94016	+	0.837508i	−0.557223	+	0.118441i
$51$		0			0
$52$	−6.54869	+	2.91566i	−0.908140	+	0.404330i
$53$	0.303205	+	0.933170i	0.0416485	+	0.128181i	0.969719	−	0.244224i	$-0.0785333\pi$
$53$	0.303205	+	0.933170i	0.0416485	+	0.128181i	−0.928070	+	0.372405i	$0.878533\pi$
$54$		0			0
$55$	−2.21389	+	5.08970i	−0.298520	+	0.686295i
$56$	−2.44505	+	4.23496i	−0.326734	+	0.565920i
$57$		0			0
$58$	0.800686	−	7.61802i	0.105135	−	1.00030i
$59$	4.05985	+	1.80756i	0.528548	+	0.235325i	0.653620	−	0.756823i	$-0.273250\pi$
$59$	4.05985	+	1.80756i	0.528548	+	0.235325i	−0.125072	+	0.992148i	$0.539916\pi$
$60$		0			0
$61$	7.41150	+	8.23130i	0.948945	+	1.05391i	0.998479	+	0.0551379i	$0.0175598\pi$
$61$	7.41150	+	8.23130i	0.948945	+	1.05391i	−0.0495336	+	0.998772i	$0.515774\pi$
$62$	1.91191	−	1.38908i	0.242813	−	0.176414i
$63$		0			0
$64$	−0.701393	−	2.15867i	−0.0876742	−	0.269833i
$65$	4.42897	−	7.67120i	0.549346	−	0.951496i
$66$		0			0
$67$	−1.37586	−	2.38307i	−0.168089	−	0.291138i	0.769659	−	0.638455i	$-0.220426\pi$
$67$	−1.37586	−	2.38307i	−0.168089	−	0.291138i	−0.937748	+	0.347317i	$0.887093\pi$
$68$	5.25943	−	5.84119i	0.637800	−	0.708349i
$69$		0			0
$70$	1.32479	+	12.6045i	0.158342	+	1.50653i
$71$	2.76800	−	8.51901i	0.328501	−	1.01102i	−0.641335	−	0.767261i	$-0.721619\pi$
$71$	2.76800	−	8.51901i	0.328501	−	1.01102i	0.969836	−	0.243760i	$-0.0783809\pi$
$72$		0			0
$73$	−9.56397	+	6.94863i	−1.11938	+	0.813275i	−0.984115	−	0.177534i	$-0.943188\pi$
$73$	−9.56397	+	6.94863i	−1.11938	+	0.813275i	−0.135263	+	0.990810i	$0.543188\pi$
$74$	16.5869	−	7.38498i	1.92819	−	0.858487i
$75$		0			0
$76$	−0.632893	−	1.09620i	−0.0725978	−	0.125743i
$77$	−11.9357	−	6.75501i	−1.36019	−	0.769805i
$78$		0			0
$79$	10.8992	+	2.31669i	1.22625	+	0.260649i	0.775124	−	0.631809i	$-0.217687\pi$
$79$	10.8992	+	2.31669i	1.22625	+	0.260649i	0.451131	+	0.892458i	$0.351021\pi$
$80$	6.59947	+	4.79479i	0.737843	+	0.536074i
$81$		0			0
$82$	0.788227	−	2.42591i	0.0870451	−	0.267897i
$83$	9.51417	+	10.5666i	1.04432	+	1.15983i	0.986876	+	0.161482i	$0.0516272\pi$
$83$	9.51417	+	10.5666i	1.04432	+	1.15983i	0.0574403	+	0.998349i	$0.481706\pi$
$84$		0			0
$85$	−1.01525	+	9.65942i	−0.110119	+	1.04771i
$86$	−9.26019	+	10.2845i	−0.998552	+	1.10900i
$87$		0			0
$88$	−3.71967	+	1.24402i	−0.396518	+	0.132613i
$89$	−7.12753			−0.755517			−0.377758	−	0.925904i	$-0.623305\pi$
$89$	−7.12753			−0.755517			−0.377758	+	0.925904i	$0.623305\pi$
$90$		0			0
$91$	17.7073	+	12.8651i	1.85623	+	1.34863i
$92$	0.142983	+	1.36039i	0.0149070	+	0.141831i
$93$		0			0
$94$	10.5663	−	2.24594i	1.08983	−	0.231651i
$95$	1.42889	+	0.636184i	0.146601	+	0.0652711i
$96$		0			0
$97$	3.42861	+	0.728774i	0.348123	+	0.0739958i	0.378655	−	0.925538i	$-0.376387\pi$
$97$	3.42861	+	0.728774i	0.348123	+	0.0739958i	−0.0305318	+	0.999534i	$0.509720\pi$
$98$	−18.4963			−1.86840
$99$		0			0
$100$	−2.97868			−0.297868
$101$	−15.1392	−	3.21794i	−1.50641	−	0.320197i	−0.620554	−	0.784164i	$-0.713092\pi$
$101$	−15.1392	−	3.21794i	−1.50641	−	0.320197i	−0.885852	+	0.463967i	$0.846426\pi$
$102$		0			0
$103$	−0.700591	−	0.311923i	−0.0690313	−	0.0307347i	0.371931	−	0.928261i	$-0.378696\pi$
$103$	−0.700591	−	0.311923i	−0.0690313	−	0.0307347i	−0.440962	+	0.897526i	$0.645363\pi$
$104$	6.12273	−	1.30143i	0.600383	−	0.127615i
$105$		0			0
$106$	0.187841	+	1.78719i	0.0182447	+	0.173587i
$107$	−1.45829	−	1.05951i	−0.140978	−	0.102427i	0.515061	−	0.857154i	$-0.327769\pi$
$107$	−1.45829	−	1.05951i	−0.140978	−	0.102427i	−0.656039	+	0.754727i	$0.727769\pi$
$108$		0			0
$109$	−15.7233			−1.50602			−0.753009	−	0.658010i	$-0.771399\pi$
$109$	−15.7233			−1.50602			−0.753009	+	0.658010i	$0.771399\pi$
$110$	−5.90415	+	8.27494i	−0.562939	+	0.788985i
$111$		0			0
$112$	−13.4873	+	14.9792i	−1.27443	+	1.41540i
$113$	1.24607	−	11.8555i	0.117220	−	1.11528i	−0.764866	−	0.644189i	$-0.777195\pi$
$113$	1.24607	−	11.8555i	0.117220	−	1.11528i	0.882087	−	0.471087i	$-0.156138\pi$
$114$		0			0
$115$	−1.13102	−	1.25612i	−0.105468	−	0.117134i
$116$	1.75035	−	5.38701i	0.162516	−	0.500172i
$117$		0			0
$118$	6.58474	+	4.78409i	0.606174	+	0.440412i
$119$	−23.4749	−	4.98975i	−2.15194	−	0.457410i
$120$		0			0
$121$	−3.57843	−	10.4017i	−0.325312	−	0.945607i
$122$	10.1430	+	17.5682i	0.918303	+	1.59055i
$123$		0			0
$124$	1.59644	−	0.710783i	0.143365	−	0.0638302i
$125$	9.74718	−	7.08174i	0.871814	−	0.633410i
$126$		0			0
$127$	−3.10481	+	9.55562i	−0.275507	+	0.847924i	0.713577	+	0.700576i	$0.247074\pi$
$127$	−3.10481	+	9.55562i	−0.275507	+	0.847924i	−0.989085	+	0.147348i	$0.952926\pi$
$128$	0.937370	+	8.91848i	0.0828526	+	0.788290i
$129$		0			0
$130$	10.8554	−	12.0561i	0.952079	−	1.05739i
$131$	−2.50914	−	4.34597i	−0.219225	−	0.379709i	0.735346	−	0.677692i	$-0.237020\pi$
$131$	−2.50914	−	4.34597i	−0.219225	−	0.379709i	−0.954571	+	0.297983i	$0.903686\pi$
$132$		0			0
$133$	−1.93242	+	3.34705i	−0.167562	+	0.290226i
$134$	−1.55736	−	4.79306i	−0.134535	−	0.414057i
$135$		0			0
$136$	−5.55268	+	4.03426i	−0.476138	+	0.345935i
$137$	−2.68050	−	2.97700i	−0.229011	−	0.254342i	0.617677	−	0.786432i	$-0.288074\pi$
$137$	−2.68050	−	2.97700i	−0.229011	−	0.254342i	−0.846688	+	0.532089i	$0.821407\pi$
$138$		0			0
$139$	1.08484	+	0.483004i	0.0920153	+	0.0409679i	0.452228	−	0.891902i	$-0.350629\pi$
$139$	1.08484	+	0.483004i	0.0920153	+	0.0409679i	−0.360213	+	0.932870i	$0.617296\pi$
$140$	−0.979625	+	9.32051i	−0.0827934	+	0.787727i
$141$		0			0
$142$	8.20265	−	14.2074i	0.688351	−	1.19226i
$143$	3.79732	+	17.1396i	0.317547	+	1.43328i
$144$		0			0
$145$	2.16288	+	6.65667i	0.179618	+	0.552806i
$146$	−19.7793	+	8.80632i	−1.63695	+	0.728816i
$147$		0			0
$148$	13.1327	−	2.79144i	1.07950	−	0.229455i
$149$	20.0286	−	4.25721i	1.64081	−	0.348764i	0.707187	−	0.707027i	$-0.249964\pi$
$149$	20.0286	−	4.25721i	1.64081	−	0.348764i	0.933621	+	0.358263i	$0.116631\pi$
$150$		0			0
$151$	−0.118840	+	0.0529110i	−0.00967106	+	0.00430583i	−0.411566	−	0.911380i	$-0.635018\pi$
$151$	−0.118840	+	0.0529110i	−0.00967106	+	0.00430583i	0.401895	+	0.915686i	$0.368352\pi$
$152$	0.341554	+	1.05119i	0.0277037	+	0.0852632i
$153$		0			0
$154$	−18.8100	−	16.6462i	−1.51575	−	1.34139i
$155$	−1.07970	+	1.87009i	−0.0867234	+	0.150209i
$156$		0			0
$157$	−0.416822	+	3.96579i	−0.0332660	+	0.316505i	0.965217	+	0.261449i	$0.0842003\pi$
$157$	−0.416822	+	3.96579i	−0.0332660	+	0.316505i	−0.998483	+	0.0550558i	$0.982466\pi$
$158$	18.6432	+	8.30050i	1.48318	+	0.660352i
$159$		0			0
$160$	7.34837	+	8.16119i	0.580940	+	0.645199i
$161$	3.37893	−	2.45494i	0.266297	−	0.193476i
$162$		0			0
$163$	−4.11733	−	12.6718i	−0.322494	−	0.992535i	−0.972559	−	0.232656i	$-0.925258\pi$
$163$	−4.11733	−	12.6718i	−0.322494	−	0.992535i	0.650065	−	0.759879i	$-0.274742\pi$
$164$	0.943090	−	1.63348i	0.0736429	−	0.127553i
$165$		0			0
$166$	13.0206	+	22.5523i	1.01059	+	1.75040i
$167$	−4.22397	+	4.69120i	−0.326861	+	0.363016i	−0.884068	−	0.467358i	$-0.845206\pi$
$167$	−4.22397	+	4.69120i	−0.326861	+	0.363016i	0.557208	+	0.830373i	$0.311873\pi$
$168$		0			0
$169$	−1.56968	−	14.9345i	−0.120745	−	1.14881i
$170$	−5.49693	+	16.9178i	−0.421595	+	1.29754i
$171$		0			0
$172$	−8.27905	+	6.01508i	−0.631272	+	0.458646i
$173$	16.9604	−	7.55127i	1.28948	−	0.574112i	0.356583	−	0.934264i	$-0.383942\pi$
$173$	16.9604	−	7.55127i	1.28948	−	0.574112i	0.932894	+	0.360152i	$0.117275\pi$
$174$		0			0
$175$	4.54742	+	7.87637i	0.343753	+	0.595398i
$176$	−16.0631	+	1.82796i	−1.21080	+	0.137787i
$177$		0			0
$178$	−12.7686	−	2.71406i	−0.957050	−	0.203427i
$179$	−2.70110	−	1.96246i	−0.201890	−	0.146681i	0.482247	−	0.876035i	$-0.339821\pi$
$179$	−2.70110	−	1.96246i	−0.201890	−	0.146681i	−0.684137	+	0.729354i	$0.739821\pi$
$180$		0			0
$181$	6.04906	−	18.6171i	0.449623	−	1.38380i	−0.427710	−	0.903916i	$-0.640679\pi$
$181$	6.04906	−	18.6171i	0.449623	−	1.38380i	0.877333	−	0.479882i	$-0.159321\pi$
$182$	26.8230	+	29.7900i	1.98825	+	2.20818i
$183$		0			0
$184$	0.124854	−	1.18790i	0.00920433	−	0.0875734i
$185$	−11.1012	+	12.3291i	−0.816176	+	0.906455i
$186$		0			0
$187$	−11.4477	−	15.4750i	−0.837137	−	1.13165i
$188$	7.98791			0.582578
$189$		0			0
$190$	2.31754	+	1.68379i	0.168132	+	0.122155i
$191$	−1.91685	−	18.2376i	−0.138698	−	1.31963i	−0.813473	−	0.581603i	$-0.802426\pi$
$191$	−1.91685	−	18.2376i	−0.138698	−	1.31963i	0.674775	−	0.738024i	$-0.264241\pi$
$192$		0			0
$193$	8.23546	−	1.75050i	0.592801	−	0.126004i	0.0982641	−	0.995160i	$-0.468671\pi$
$193$	8.23546	−	1.75050i	0.592801	−	0.126004i	0.494537	+	0.869157i	$0.335338\pi$
$194$	5.86469	+	2.61113i	0.421060	+	0.187468i
$195$		0			0
$196$	−13.3783	−	2.84365i	−0.955596	−	0.203118i
$197$	26.5949			1.89481			0.947404	−	0.320040i	$-0.103696\pi$
$197$	26.5949			1.89481			0.947404	+	0.320040i	$0.103696\pi$
$198$		0			0
$199$	15.2454			1.08072			0.540361	−	0.841434i	$-0.318288\pi$
$199$	15.2454			1.08072			0.540361	+	0.841434i	$0.318288\pi$
$200$	2.54416	+	0.540778i	0.179899	+	0.0382388i
$201$		0			0
$202$	−25.8958	−	11.5296i	−1.82202	−	0.811217i
$203$	−16.9168	+	3.59577i	−1.18733	+	0.252374i
$204$		0			0
$205$	0.243628	+	2.31796i	0.0170157	+	0.161893i
$206$	−1.13630	−	0.825570i	−0.0791697	−	0.0575202i
$207$		0			0
$208$	25.8010			1.78898
$209$	−2.93980	+	0.983201i	−0.203350	+	0.0680094i
$210$		0			0
$211$	12.0394	−	13.3711i	0.828826	−	0.920504i	−0.169053	−	0.985607i	$-0.554071\pi$
$211$	12.0394	−	13.3711i	0.828826	−	0.920504i	0.997879	+	0.0651027i	$0.0207375\pi$
$212$	−0.138901	+	1.32155i	−0.00953973	+	0.0907645i
$213$		0			0
$214$	−2.20901	−	2.45335i	−0.151005	−	0.167708i
$215$	3.90764	−	12.0265i	0.266499	−	0.820198i
$216$		0			0
$217$	−4.31671	−	3.13627i	−0.293037	−	0.212904i
$218$	−28.1675	−	5.98720i	−1.90775	−	0.405504i
$219$		0			0
$220$	−5.54268	+	5.07755i	−0.373687	+	0.342328i
$221$	15.3600	+	26.6044i	1.03323	+	1.78960i
$222$		0			0
$223$	11.4219	−	5.08537i	0.764869	−	0.340541i	0.0130529	−	0.999915i	$-0.495845\pi$
$223$	11.4219	−	5.08537i	0.764869	−	0.340541i	0.751816	+	0.659373i	$0.229178\pi$
$224$	−21.9534	+	15.9500i	−1.46682	+	1.06571i
$225$		0			0
$226$	6.74669	−	20.7642i	0.448783	−	1.38121i
$227$	2.70963	+	25.7804i	0.179844	+	1.71110i	0.596977	+	0.802258i	$0.296368\pi$
$227$	2.70963	+	25.7804i	0.179844	+	1.71110i	−0.417133	+	0.908845i	$0.636965\pi$
$228$		0			0
$229$	−2.04988	+	2.27662i	−0.135460	+	0.150444i	−0.807058	−	0.590472i	$-0.798942\pi$
$229$	−2.04988	+	2.27662i	−0.135460	+	0.150444i	0.671598	+	0.740916i	$0.265608\pi$
$230$	−1.54785	−	2.68096i	−0.102062	−	0.176777i
$231$		0			0
$232$	−2.47302	+	4.28340i	−0.162362	+	0.281219i
$233$	0.0550372	+	0.169387i	0.00360561	+	0.0110969i	0.952843	−	0.303463i	$-0.0981430\pi$
$233$	0.0550372	+	0.169387i	0.00360561	+	0.0110969i	−0.949238	+	0.314560i	$0.898143\pi$
$234$		0			0
$235$	−7.98545	+	5.80177i	−0.520914	+	0.378466i
$236$	4.02722	+	4.47269i	0.262150	+	0.291147i
$237$		0			0
$238$	−40.1542	−	17.8778i	−2.60281	−	1.15885i
$239$	−0.670676	+	6.38106i	−0.0433824	+	0.412756i	0.951182	+	0.308631i	$0.0998709\pi$
$239$	−0.670676	+	6.38106i	−0.0433824	+	0.412756i	−0.994564	+	0.104125i	$0.966796\pi$
$240$		0			0
$241$	−7.44251	+	12.8908i	−0.479415	+	0.830370i	−0.999721	−	0.0236091i	$-0.992484\pi$
$241$	−7.44251	+	12.8908i	−0.479415	+	0.830370i	0.520307	+	0.853979i	$0.325818\pi$
$242$	−2.44979	−	19.9967i	−0.157478	−	1.28544i
$243$		0			0
$244$	4.63546	+	14.2665i	0.296755	+	0.913317i
$245$	15.4396	−	6.87416i	0.986401	−	0.439174i
$246$		0			0
$247$	4.83904	−	1.02857i	0.307901	−	0.0654463i
$248$	−1.49260	+	0.317263i	−0.0947804	+	0.0201462i
$249$		0			0
$250$	20.1582	−	8.97503i	1.27492	−	0.567630i
$251$	3.45988	+	10.6484i	0.218386	+	0.672123i	0.998896	+	0.0469795i	$0.0149595\pi$
$251$	3.45988	+	10.6484i	0.218386	+	0.672123i	−0.780510	+	0.625143i	$0.785040\pi$
$252$		0			0
$253$	3.33443	+	0.321525i	0.209634	+	0.0202141i
$254$	−9.20076	+	15.9362i	−0.577307	+	0.999925i
$255$		0			0
$256$	−2.19128	+	20.8486i	−0.136955	+	1.30304i
$257$	4.84328	+	2.15637i	0.302115	+	0.134510i	0.552195	−	0.833715i	$-0.313790\pi$
$257$	4.84328	+	2.15637i	0.302115	+	0.134510i	−0.250080	+	0.968225i	$0.580457\pi$
$258$		0			0
$259$	−27.4304	−	30.4646i	−1.70444	−	1.89298i
$260$	9.70522	−	7.05126i	0.601892	−	0.437300i
$261$		0			0
$262$	−2.84013	−	8.74104i	−0.175464	−	0.540023i
$263$	3.48315	−	6.03300i	0.214780	−	0.372011i	−0.738424	−	0.674336i	$-0.764430\pi$
$263$	3.48315	−	6.03300i	0.214780	−	0.372011i	0.953205	+	0.302326i	$0.0977631\pi$
$264$		0			0
$265$	−0.821010	−	1.42203i	−0.0504342	−	0.0873546i
$266$	−4.73635	+	5.26025i	−0.290404	+	0.322527i
$267$		0			0
$268$	−0.389543	−	3.70625i	−0.0237951	−	0.226395i
$269$	4.00525	−	12.3269i	0.244204	−	0.751583i	−0.751562	−	0.659662i	$-0.770699\pi$
$269$	4.00525	−	12.3269i	0.244204	−	0.751583i	0.995766	−	0.0919210i	$-0.0293007\pi$
$270$		0			0
$271$	−2.10547	+	1.52971i	−0.127898	+	0.0929235i	−0.649895	−	0.760024i	$-0.725187\pi$
$271$	−2.10547	+	1.52971i	−0.127898	+	0.0929235i	0.521997	+	0.852947i	$0.325187\pi$
$272$	−25.8447	+	11.5068i	−1.56706	+	0.697701i
$273$		0			0
$274$	−3.66840	−	6.35385i	−0.221616	−	0.383850i
$275$	−1.45529	+	7.14802i	−0.0877573	+	0.431042i
$276$		0			0
$277$	12.2080	+	2.59489i	0.733509	+	0.155912i	0.559498	−	0.828832i	$-0.310994\pi$
$277$	12.2080	+	2.59489i	0.733509	+	0.155912i	0.174011	+	0.984744i	$0.444327\pi$
$278$	1.75953	+	1.27837i	0.105529	+	0.0766716i
$279$		0			0
$280$	2.52886	−	7.78302i	0.151128	−	0.465125i
$281$	−12.2260	−	13.5784i	−0.729342	−	0.810017i	0.258412	−	0.966035i	$-0.416801\pi$
$281$	−12.2260	−	13.5784i	−0.729342	−	0.810017i	−0.987754	+	0.156018i	$0.950134\pi$
$282$		0			0
$283$	1.14478	−	10.8918i	0.0680499	−	0.647452i	−0.906334	−	0.422562i	$-0.861131\pi$
$283$	1.14478	−	10.8918i	0.0680499	−	0.647452i	0.974384	−	0.224890i	$-0.0722023\pi$
$284$	8.11725	−	9.01512i	0.481670	−	0.534949i
$285$		0			0
$286$	0.276217	+	32.1507i	0.0163330	+	1.90111i
$287$	−5.75910			−0.339949
$288$		0			0
$289$	−13.4978	−	9.80673i	−0.793988	−	0.576866i
$290$	1.33994	+	12.7487i	0.0786841	+	0.748629i
$291$		0			0
$292$	−15.6603	+	3.32870i	−0.916449	+	0.194797i
$293$	19.8909	+	8.85598i	1.16204	+	0.517372i	0.894891	−	0.446284i	$-0.147253\pi$
$293$	19.8909	+	8.85598i	1.16204	+	0.517372i	0.267145	+	0.963656i	$0.413920\pi$
$294$		0			0
$295$	−7.27458	−	1.54626i	−0.423543	−	0.0900268i
$296$	−11.7238			−0.681429
$297$		0			0
$298$	37.5014			2.17240
$299$	−5.22936	−	1.11154i	−0.302422	−	0.0642817i
$300$		0			0
$301$	28.5447	+	12.7089i	1.64529	+	0.732529i
$302$	−0.233044	+	0.0495350i	−0.0134102	+	0.00285042i
$303$		0			0
$304$	0.476220	+	4.53093i	0.0273131	+	0.259867i
$305$	−14.9960	−	10.8953i	−0.858671	−	0.623861i
$306$		0			0
$307$	2.26858			0.129475			0.0647374	−	0.997902i	$-0.479379\pi$
$307$	2.26858			0.129475			0.0647374	+	0.997902i	$0.479379\pi$
$308$	−11.0460	−	14.9321i	−0.629406	−	0.850834i
$309$		0			0
$310$	−2.64633	+	2.93905i	−0.150302	+	0.166927i
$311$	2.88807	−	27.4782i	0.163768	−	1.55814i	−0.536275	−	0.844043i	$-0.680169\pi$
$311$	2.88807	−	27.4782i	0.163768	−	1.55814i	0.700042	−	0.714101i	$-0.253164\pi$
$312$		0			0
$313$	6.15423	+	6.83497i	0.347858	+	0.386335i	0.891529	−	0.452963i	$-0.149633\pi$
$313$	6.15423	+	6.83497i	0.347858	+	0.386335i	−0.543672	+	0.839298i	$0.682966\pi$
$314$	−2.25683	+	6.94581i	−0.127360	+	0.391975i
$315$		0			0
$316$	12.2085	+	8.87000i	0.686782	+	0.498976i
$317$	11.9564	+	2.54141i	0.671539	+	0.142740i	0.531048	−	0.847342i	$-0.321799\pi$
$317$	11.9564	+	2.54141i	0.671539	+	0.142740i	0.140491	+	0.990082i	$0.455132\pi$
$318$		0			0
$319$	−12.0722	−	6.83229i	−0.675914	−	0.382535i
$320$	1.89921	+	3.28953i	0.106169	+	0.183890i
$321$		0			0
$322$	6.98800	−	3.11126i	0.389426	−	0.173384i
$323$	−4.38850	+	3.18843i	−0.244183	+	0.177409i
$324$		0			0
$325$	3.59750	−	11.0720i	0.199553	−	0.614162i
$326$	−2.55076	−	24.2688i	−0.141273	−	1.34413i
$327$		0			0
$328$	−1.10207	+	1.22398i	−0.0608518	+	0.0675828i
$329$	−12.1948	−	21.1220i	−0.672321	−	1.16449i
$330$		0			0
$331$	−15.6995	+	27.1924i	−0.862924	+	1.49463i	0.00616924	+	0.999981i	$0.498036\pi$
$331$	−15.6995	+	27.1924i	−0.862924	+	1.49463i	−0.869094	+	0.494648i	$0.835297\pi$
$332$	5.95055	+	18.3139i	0.326579	+	1.00511i
$333$		0			0
$334$	−9.35338	+	6.79563i	−0.511794	+	0.371840i
$335$	3.08135	+	3.42218i	0.168352	+	0.186974i
$336$		0			0
$337$	−18.8368	−	8.38666i	−1.02610	−	0.456851i	−0.176515	−	0.984298i	$-0.556483\pi$
$337$	−18.8368	−	8.38666i	−1.02610	−	0.456851i	−0.849588	+	0.527447i	$0.823149\pi$
$338$	2.87483	−	27.3522i	0.156370	−	1.48776i
$339$		0			0
$340$	−6.57691	+	11.3915i	−0.356683	+	0.617793i
$341$	−0.925712	−	4.17830i	−0.0501301	−	0.226268i
$342$		0			0
$343$	3.96009	+	12.1879i	0.213825	+	0.658085i
$344$	8.16337	−	3.63457i	0.440140	−	0.195963i
$345$		0			0
$346$	33.2592	−	7.06946i	1.78803	−	0.380057i
$347$	−8.80923	+	1.87246i	−0.472904	+	0.100519i	−0.438198	−	0.898879i	$-0.644383\pi$
$347$	−8.80923	+	1.87246i	−0.472904	+	0.100519i	−0.0347067	+	0.999398i	$0.511050\pi$
$348$		0			0
$349$	5.69178	−	2.53414i	0.304674	−	0.135650i	−0.248705	−	0.968579i	$-0.580005\pi$
$349$	5.69178	−	2.53414i	0.304674	−	0.135650i	0.553379	+	0.832930i	$0.313338\pi$
$350$	5.14729	+	15.8417i	0.275134	+	0.846777i
$351$		0			0
$352$	−21.6642	−	2.08899i	−1.15471	−	0.111344i
$353$	−5.04457	+	8.73745i	−0.268495	+	0.465047i	−0.968473	−	0.249117i	$-0.919860\pi$
$353$	−5.04457	+	8.73745i	−0.268495	+	0.465047i	0.699978	+	0.714164i	$0.253193\pi$
$354$		0			0
$355$	−1.56690	+	14.9081i	−0.0831624	+	0.791238i
$356$	−8.81829	−	3.92615i	−0.467368	−	0.208086i
$357$		0			0
$358$	−4.09162	−	4.54420i	−0.216249	−	0.240168i
$359$	−10.0638	+	7.31180i	−0.531148	+	0.385902i	−0.820787	−	0.571234i	$-0.806465\pi$
$359$	−10.0638	+	7.31180i	−0.531148	+	0.385902i	0.289639	+	0.957136i	$0.406465\pi$
$360$		0			0
$361$	−5.60138	−	17.2393i	−0.294809	−	0.907330i
$362$	17.9257	−	31.0483i	0.942155	−	1.63186i
$363$		0			0
$364$	14.8211	+	25.6709i	0.776837	+	1.34552i
$365$	13.2378	−	14.7020i	0.692897	−	0.769540i
$366$		0			0
$367$	−1.76626	−	16.8048i	−0.0921979	−	0.877204i	−0.938681	−	0.344788i	$-0.887951\pi$
$367$	−1.76626	−	16.8048i	−0.0921979	−	0.877204i	0.846483	−	0.532416i	$-0.178716\pi$
$368$	1.52141	−	4.68240i	0.0793087	−	0.244087i
$369$		0			0
$370$	−24.5820	+	17.8599i	−1.27796	+	0.928491i
$371$	3.70656	−	1.65027i	0.192435	−	0.0856777i
$372$		0			0
$373$	−4.76122	−	8.24668i	−0.246527	−	0.426997i	0.716033	−	0.698067i	$-0.245956\pi$
$373$	−4.76122	−	8.24668i	−0.246527	−	0.426997i	−0.962560	+	0.271069i	$0.912623\pi$
$374$	−14.6153	−	32.0819i	−0.755740	−	1.65892i
$375$		0			0
$376$	−6.82267	−	1.45020i	−0.351852	−	0.0747885i
$377$	17.9099	+	13.0123i	0.922408	+	0.670168i
$378$		0			0
$379$	−7.67585	+	23.6238i	−0.394282	+	1.21348i	0.535237	+	0.844702i	$0.320222\pi$
$379$	−7.67585	+	23.6238i	−0.394282	+	1.21348i	−0.929519	+	0.368774i	$0.879778\pi$
$380$	1.41741	+	1.57419i	0.0727115	+	0.0807543i
$381$		0			0
$382$	3.51066	−	33.4017i	0.179621	−	1.70898i
$383$	−19.8218	+	22.0143i	−1.01284	+	1.12488i	−0.0206991	+	0.999786i	$0.506589\pi$
$383$	−19.8218	+	22.0143i	−1.01284	+	1.12488i	−0.992145	+	0.125092i	$0.960077\pi$
$384$		0			0
$385$	21.8881	+	6.90455i	1.11552	+	0.351888i
$386$	15.4200			0.784857
$387$		0			0
$388$	3.84049	+	2.79028i	0.194971	+	0.141655i
$389$	1.42659	+	13.5731i	0.0723312	+	0.688186i	0.969265	+	0.246020i	$0.0791229\pi$
$389$	1.42659	+	13.5731i	0.0723312	+	0.688186i	−0.896933	+	0.442165i	$0.854210\pi$
$390$		0			0
$391$	5.73393	−	1.21879i	0.289977	−	0.0616366i
$392$	10.9105	+	4.85767i	0.551063	+	0.245349i
$393$		0			0
$394$	47.6435	+	10.1269i	2.40024	+	0.510188i
$395$	−18.6472			−0.938242
$396$		0			0
$397$	24.1728			1.21320			0.606599	−	0.795008i	$-0.292533\pi$
$397$	24.1728			1.21320			0.606599	+	0.795008i	$0.292533\pi$
$398$	27.3115	+	5.80524i	1.36900	+	0.290990i
$399$		0			0
$400$	9.79415	+	4.36063i	0.489707	+	0.218032i
$401$	7.33275	−	1.55862i	0.366180	−	0.0778339i	−0.0211470	−	0.999776i	$-0.506732\pi$
$401$	7.33275	−	1.55862i	0.366180	−	0.0778339i	0.387327	+	0.921942i	$0.373398\pi$
$402$		0			0
$403$	0.713925	+	6.79254i	0.0355631	+	0.338360i
$404$	−16.9579	−	12.3206i	−0.843685	−	0.612973i
$405$		0			0
$406$	−31.6748			−1.57200
$407$	−0.282472	−	32.8788i	−0.0140016	−	1.62974i
$408$		0			0
$409$	−4.58844	+	5.09598i	−0.226884	+	0.251980i	−0.845829	−	0.533454i	$-0.820894\pi$
$409$	−4.58844	+	5.09598i	−0.226884	+	0.251980i	0.618945	+	0.785434i	$0.287560\pi$
$410$	−0.446198	+	4.24529i	−0.0220361	+	0.209660i
$411$		0			0
$412$	−0.694960	−	0.771832i	−0.0342382	−	0.0380254i
$413$	5.67870	−	17.4772i	0.279431	−	0.859999i
$414$		0			0
$415$	−19.2505	−	13.9863i	−0.944969	−	0.686560i
$416$	33.9758	+	7.22179i	1.66580	+	0.354077i
$417$		0			0
$418$	−5.64090	+	0.641925i	−0.275906	+	0.0313976i
$419$	−2.37899	−	4.12054i	−0.116221	−	0.201301i	0.802046	−	0.597262i	$-0.203745\pi$
$419$	−2.37899	−	4.12054i	−0.116221	−	0.201301i	−0.918267	+	0.395961i	$0.870412\pi$
$420$		0			0
$421$	−2.22415	+	0.990257i	−0.108399	+	0.0482622i	−0.460219	−	0.887805i	$-0.652229\pi$
$421$	−2.22415	+	0.990257i	−0.108399	+	0.0482622i	0.351821	+	0.936067i	$0.385563\pi$
$422$	26.6595	−	19.3693i	1.29776	−	0.942881i
$423$		0			0
$424$	0.358565	−	1.10355i	0.0174135	−	0.0535932i
$425$	1.33431	+	12.6951i	0.0647235	+	0.615803i
$426$		0			0
$427$	30.6473	−	34.0373i	1.48313	−	1.64718i
$428$	−1.22059	−	2.11413i	−0.0589996	−	0.102190i
$429$		0			0
$430$	11.5798	−	20.0569i	0.558430	−	0.967228i
$431$	−0.292969	−	0.901665i	−0.0141118	−	0.0434317i	0.943753	−	0.330652i	$-0.107269\pi$
$431$	−0.292969	−	0.901665i	−0.0141118	−	0.0434317i	−0.957864	+	0.287221i	$0.907269\pi$
$432$		0			0
$433$	−7.63117	+	5.54437i	−0.366731	+	0.266446i	−0.755854	−	0.654740i	$-0.772778\pi$
$433$	−7.63117	+	5.54437i	−0.366731	+	0.266446i	0.389123	+	0.921186i	$0.372778\pi$
$434$	−6.53894	−	7.26223i	−0.313879	−	0.348598i
$435$		0			0
$436$	−19.4531	−	8.66108i	−0.931634	−	0.414790i
$437$	0.0986768	−	0.938847i	0.00472035	−	0.0449111i
$438$		0			0
$439$	−4.66424	+	8.07871i	−0.222612	+	0.385576i	−0.955600	−	0.294666i	$-0.904792\pi$
$439$	−4.66424	+	8.07871i	−0.222612	+	0.385576i	0.732988	+	0.680241i	$0.238125\pi$
$440$	5.65596	−	3.33058i	0.269638	−	0.158779i
$441$		0			0
$442$	17.3862	+	53.5093i	0.826979	+	2.54518i
$443$	28.5290	−	12.7020i	1.35546	−	0.603488i	0.404991	−	0.914321i	$-0.367275\pi$
$443$	28.5290	−	12.7020i	1.35546	−	0.603488i	0.950465	+	0.310833i	$0.100608\pi$
$444$		0			0
$445$	11.6672	−	2.47994i	0.553079	−	0.117561i
$446$	22.3983	−	4.76090i	1.06059	−	0.225435i
$447$		0			0
$448$	−8.57425	+	3.81750i	−0.405095	+	0.180360i
$449$	−7.64865	−	23.5401i	−0.360962	−	1.11093i	−0.952471	−	0.304629i	$-0.901468\pi$
$449$	−7.64865	−	23.5401i	−0.360962	−	1.11093i	0.591509	−	0.806298i	$-0.298532\pi$
$450$		0			0
$451$	−3.45914	−	3.06123i	−0.162885	−	0.144148i
$452$	8.07221	−	13.9815i	0.379685	−	0.657633i
$453$		0			0
$454$	−4.96261	+	47.2161i	−0.232907	+	2.21596i
$455$	−33.4618	−	14.8982i	−1.56871	−	0.698437i
$456$		0			0
$457$	−9.57031	−	10.6289i	−0.447680	−	0.497199i	0.476490	−	0.879180i	$-0.341909\pi$
$457$	−9.57031	−	10.6289i	−0.447680	−	0.497199i	−0.924170	+	0.381981i	$0.875242\pi$
$458$	−4.53917	+	3.29790i	−0.212101	+	0.154101i
$459$		0			0
$460$	−0.707386	−	2.17711i	−0.0329820	−	0.101508i
$461$	−11.4337	+	19.8038i	−0.532522	+	0.922355i	0.466757	+	0.884386i	$0.345422\pi$
$461$	−11.4337	+	19.8038i	−0.532522	+	0.922355i	−0.999279	+	0.0379694i	$0.987911\pi$
$462$		0			0
$463$	13.3111	+	23.0556i	0.618621	+	1.07148i	0.989738	+	0.142897i	$0.0456418\pi$
$463$	13.3111	+	23.0556i	0.618621	+	1.07148i	−0.371116	+	0.928586i	$0.621025\pi$
$464$	−13.6416	+	15.1505i	−0.633295	+	0.703346i
$465$		0			0
$466$	0.0340965	+	0.324406i	0.00157949	+	0.0150278i
$467$	−11.5834	+	35.6500i	−0.536015	+	1.64968i	0.205430	+	0.978672i	$0.434141\pi$
$467$	−11.5834	+	35.6500i	−0.536015	+	1.64968i	−0.741445	+	0.671013i	$0.765859\pi$
$468$		0			0
$469$	−9.20556	+	6.68823i	−0.425073	+	0.308834i
$470$	−16.5148	+	7.35286i	−0.761770	+	0.339162i
$471$		0			0
$472$	−2.62773	−	4.55137i	−0.120951	−	0.209494i
$473$	10.3897	+	22.8063i	0.477718	+	1.04863i
$474$		0			0
$475$	2.01075	+	0.427399i	0.0922597	+	0.0196104i
$476$	−26.2950	−	19.1044i	−1.20523	−	0.875649i
$477$		0			0
$478$	−3.63130	+	11.1760i	−0.166092	+	0.511178i
$479$	−1.67119	−	1.85605i	−0.0763588	−	0.0848051i	0.703755	−	0.710443i	$-0.251505\pi$
$479$	−1.67119	−	1.85605i	−0.0763588	−	0.0848051i	−0.780114	+	0.625638i	$0.784839\pi$
$480$		0			0
$481$	−5.48503	+	52.1866i	−0.250096	+	2.37950i
$482$	−18.2415	+	20.2593i	−0.830880	+	0.922785i
$483$		0			0
$484$	1.30241	−	14.8403i	0.0592004	−	0.674557i
$485$	−5.86594			−0.266359
$486$		0			0
$487$	−28.4544	−	20.6733i	−1.28939	−	0.936797i	−0.289597	−	0.957149i	$-0.593521\pi$
$487$	−28.4544	−	20.6733i	−1.28939	−	0.936797i	−0.999793	+	0.0203519i	$0.993521\pi$
$488$	−1.36918	−	13.0269i	−0.0619800	−	0.589700i
$489$		0			0
$490$	30.2769	−	6.43556i	1.36777	−	0.290729i
$491$	−32.5003	−	14.4701i	−1.46672	−	0.653026i	−0.490823	−	0.871259i	$-0.663304\pi$
$491$	−32.5003	−	14.4701i	−1.46672	−	0.653026i	−0.975897	+	0.218234i	$0.929970\pi$
$492$		0			0
$493$	−23.7435	−	5.04683i	−1.06935	−	0.227298i
$494$	9.06057			0.407654
$495$		0			0
$496$	−6.28979			−0.282420
$497$	−36.2305	−	7.70103i	−1.62516	−	0.345438i
$498$		0			0
$499$	−5.54396	−	2.46833i	−0.248182	−	0.110498i	0.278876	−	0.960327i	$-0.410038\pi$
$499$	−5.54396	−	2.46833i	−0.248182	−	0.110498i	−0.527058	+	0.849829i	$0.676705\pi$
$500$	15.9603	−	3.39246i	0.713766	−	0.151716i
$501$		0			0
$502$	2.14346	+	20.3936i	0.0956672	+	0.910212i
$503$	4.89369	+	3.55547i	0.218199	+	0.158531i	0.691515	−	0.722362i	$-0.256943\pi$
$503$	4.89369	+	3.55547i	0.218199	+	0.158531i	−0.473317	+	0.880892i	$0.656943\pi$
$504$		0			0
$505$	25.9013			1.15259
$506$	5.85104	+	1.84570i	0.260111	+	0.0820513i
$507$		0			0
$508$	−9.10497	+	10.1121i	−0.403968	+	0.448652i
$509$	−0.508398	+	4.83708i	−0.0225343	+	0.214400i	0.977460	+	0.211119i	$0.0677109\pi$
$509$	−0.508398	+	4.83708i	−0.0225343	+	0.214400i	−0.999995	+	0.00328056i	$0.998956\pi$
$510$		0			0
$511$	32.7098	+	36.3279i	1.44700	+	1.60705i
$512$	−6.32213	+	19.4575i	−0.279401	+	0.859909i
$513$		0			0
$514$	7.85539	+	5.70728i	0.346487	+	0.251737i
$515$	1.25534	+	0.266831i	0.0553170	+	0.0117580i
$516$		0			0
$517$	3.90265	−	19.1688i	0.171638	−	0.843044i
$518$	−37.5399	−	65.0210i	−1.64941	−	2.85686i
$519$		0			0
$520$	−9.56962	+	4.26067i	−0.419656	+	0.186843i
$521$	20.5110	−	14.9021i	0.898602	−	0.652873i	−0.0395043	−	0.999219i	$-0.512578\pi$
$521$	20.5110	−	14.9021i	0.898602	−	0.652873i	0.938107	+	0.346347i	$0.112578\pi$
$522$		0			0
$523$	−0.108444	+	0.333757i	−0.00474193	+	0.0145942i	−0.953399	−	0.301711i	$-0.902442\pi$
$523$	−0.108444	+	0.333757i	−0.00474193	+	0.0145942i	0.948658	+	0.316305i	$0.102442\pi$
$524$	−0.710404	−	6.75904i	−0.0310341	−	0.295270i
$525$		0			0
$526$	8.53718	−	9.48150i	0.372239	−	0.413413i
$527$	−3.74448	−	6.48563i	−0.163112	−	0.282519i
$528$		0			0
$529$	10.9899	−	19.0351i	0.477823	−	0.827613i
$530$	−0.929312	−	2.86013i	−0.0403667	−	0.124236i
$531$		0			0
$532$	−4.23453	+	3.07656i	−0.183590	+	0.133386i
$533$	4.93274	+	5.47836i	0.213661	+	0.237294i
$534$		0			0
$535$	2.75575	+	1.22694i	0.119141	+	0.0530452i
$536$	−0.340151	+	3.23632i	−0.0146923	+	0.139788i
$537$		0			0
$538$	11.8691	−	20.5579i	0.511714	−	0.886314i
$539$	−13.3602	+	30.7151i	−0.575466	+	1.32299i
$540$		0			0
$541$	4.14825	+	12.7670i	0.178347	+	0.548896i	0.999771	−	0.0214230i	$-0.00681967\pi$
$541$	4.14825	+	12.7670i	0.178347	+	0.548896i	−0.821423	+	0.570319i	$0.806820\pi$
$542$	−4.35434	+	1.93868i	−0.187035	+	0.0832733i
$543$		0			0
$544$	−37.2541	+	7.91860i	−1.59726	+	0.339507i
$545$	25.7378	−	5.47074i	1.10249	−	0.234341i
$546$		0			0
$547$	−3.58250	+	1.59503i	−0.153177	+	0.0681987i	−0.481893	−	0.876230i	$-0.660051\pi$
$547$	−3.58250	+	1.59503i	−0.153177	+	0.0681987i	0.328716	+	0.944429i	$0.393384\pi$
$548$	−1.67650	−	5.15973i	−0.0716164	−	0.220413i
$549$		0			0
$550$	−5.32894	+	12.2512i	−0.227227	+	0.522393i
$551$	−1.95453	+	3.38534i	−0.0832658	+	0.144221i
$552$		0			0
$553$	4.81627	−	45.8238i	0.204809	−	1.94863i
$554$	20.8820	+	9.29726i	0.887191	+	0.395003i
$555$		0			0
$556$	1.07613	+	1.19516i	0.0456379	+	0.0506860i
$557$	−26.0314	+	18.9129i	−1.10299	+	0.801366i	−0.981545	−	0.191232i	$-0.938752\pi$
$557$	−26.0314	+	18.9129i	−1.10299	+	0.801366i	−0.121441	+	0.992599i	$0.538752\pi$
$558$		0			0
$559$	−12.3595	−	38.0385i	−0.522749	−	1.60886i
$560$	16.8658	−	29.2125i	0.712712	−	1.23445i
$561$		0			0
$562$	−16.7319	−	28.9805i	−0.705792	−	1.22247i
$563$	30.5760	−	33.9581i	1.28863	−	1.43116i	0.443797	−	0.896127i	$-0.353631\pi$
$563$	30.5760	−	33.9581i	1.28863	−	1.43116i	0.844829	−	0.535037i	$-0.179702\pi$
$564$		0			0
$565$	2.08529	+	19.8402i	0.0877286	+	0.834682i
$566$	6.19826	−	19.0763i	0.260532	−	0.801836i
$567$		0			0
$568$	−8.56983	+	6.22635i	−0.359582	+	0.261252i
$569$	8.04097	−	3.58007i	0.337095	−	0.150084i	−0.231207	−	0.972905i	$-0.574267\pi$
$569$	8.04097	−	3.58007i	0.337095	−	0.150084i	0.568302	+	0.822820i	$0.307601\pi$
$570$		0			0
$571$	−6.51717	−	11.2881i	−0.272735	−	0.472391i	0.696826	−	0.717240i	$-0.254595\pi$
$571$	−6.51717	−	11.2881i	−0.272735	−	0.472391i	−0.969561	+	0.244849i	$0.921262\pi$
$572$	−4.74313	+	23.2971i	−0.198320	+	0.974099i
$573$		0			0
$574$	−10.3172	−	2.19298i	−0.430630	−	0.0915332i
$575$	−1.79722	−	1.30576i	−0.0749493	−	0.0544539i
$576$		0			0
$577$	5.05362	−	15.5534i	0.210385	−	0.647498i	−0.789064	−	0.614311i	$-0.789434\pi$
$577$	5.05362	−	15.5534i	0.210385	−	0.647498i	0.999449	−	0.0331875i	$-0.0105659\pi$
$578$	−20.4464	−	22.7081i	−0.850459	−	0.944530i
$579$		0			0
$580$	−0.990832	+	9.42714i	−0.0411421	+	0.391441i
$581$	39.3421	−	43.6938i	1.63219	−	1.81273i
$582$		0			0
$583$	3.10350	+	0.978992i	0.128534	+	0.0405457i
$584$	13.9802			0.578503
$585$		0			0
$586$	32.2613	+	23.4392i	1.33270	+	0.968265i
$587$	−1.99081	−	18.9413i	−0.0821695	−	0.781790i	−0.955565	−	0.294779i	$-0.904754\pi$
$587$	−1.99081	−	18.9413i	−0.0821695	−	0.781790i	0.873396	−	0.487011i	$-0.161913\pi$
$588$		0			0
$589$	−1.17966	+	0.250745i	−0.0486072	+	0.0103318i
$590$	−12.4433	−	5.54010i	−0.512282	−	0.228083i
$591$		0			0
$592$	−47.2680	−	10.0471i	−1.94270	−	0.412934i
$593$	25.8883			1.06311			0.531553	−	0.847025i	$-0.321609\pi$
$593$	25.8883			1.06311			0.531553	+	0.847025i	$0.321609\pi$
$594$		0			0
$595$	40.1628			1.64651
$596$	27.1248	+	5.76554i	1.11107	+	0.236166i
$597$		0			0
$598$	−8.94490	−	3.98253i	−0.365784	−	0.162858i
$599$	−24.1766	+	5.13890i	−0.987831	+	0.209970i	−0.673374	−	0.739302i	$-0.735156\pi$
$599$	−24.1766	+	5.13890i	−0.987831	+	0.209970i	−0.314457	+	0.949272i	$0.601822\pi$
$600$		0			0
$601$	2.06709	+	19.6670i	0.0843183	+	0.802235i	0.952202	+	0.305468i	$0.0988130\pi$
$601$	2.06709	+	19.6670i	0.0843183	+	0.802235i	−0.867884	+	0.496767i	$0.834520\pi$
$602$	46.2970	+	33.6368i	1.88693	+	1.37093i
$603$		0			0
$604$	−0.176176			−0.00716851
$605$	9.47676	+	15.7817i	0.385285	+	0.641616i
$606$		0			0
$607$	−28.0709	+	31.1759i	−1.13936	+	1.26539i	−0.179861	+	0.983692i	$0.557565\pi$
$607$	−28.0709	+	31.1759i	−1.13936	+	1.26539i	−0.959503	+	0.281699i	$0.909102\pi$
$608$	−0.641116	+	6.09981i	−0.0260007	+	0.247380i
$609$		0			0
$610$	−22.7159	−	25.2286i	−0.919742	−	1.02148i
$611$	−9.64739	+	29.6916i	−0.390292	+	1.20119i
$612$		0			0
$613$	8.69282	+	6.31570i	0.351100	+	0.255089i	0.749330	−	0.662197i	$-0.230376\pi$
$613$	8.69282	+	6.31570i	0.351100	+	0.255089i	−0.398231	+	0.917285i	$0.630376\pi$
$614$	4.06406	+	0.863842i	0.164012	+	0.0348618i
$615$		0			0
$616$	6.72376	+	14.7592i	0.270908	+	0.594667i
$617$	13.4507	+	23.2974i	0.541507	+	0.937917i	0.998818	+	0.0486102i	$0.0154792\pi$
$617$	13.4507	+	23.2974i	0.541507	+	0.937917i	−0.457311	+	0.889307i	$0.651187\pi$
$618$		0			0
$619$	−6.57449	+	2.92715i	−0.264251	+	0.117652i	−0.534586	−	0.845114i	$-0.679532\pi$
$619$	−6.57449	+	2.92715i	−0.264251	+	0.117652i	0.270335	+	0.962766i	$0.412866\pi$
$620$	−2.36595	+	1.71896i	−0.0950187	+	0.0690351i
$621$		0			0
$622$	15.6371	−	48.1261i	0.626992	−	1.92968i
$623$	3.08078	+	29.3116i	0.123429	+	1.17435i
$624$		0			0
$625$	−6.13286	+	6.81123i	−0.245314	+	0.272449i
$626$	8.42236	+	14.5880i	0.336625	+	0.583052i
$627$		0			0
$628$	−2.70023	+	4.67694i	−0.107751	+	0.186630i
$629$	−17.7800	−	54.7211i	−0.708933	−	2.18187i
$630$		0			0
$631$	22.2414	−	16.1594i	0.885418	−	0.643294i	−0.0492612	−	0.998786i	$-0.515687\pi$
$631$	22.2414	−	16.1594i	0.885418	−	0.643294i	0.934679	+	0.355492i	$0.115687\pi$
$632$	−8.81723	−	9.79253i	−0.350731	−	0.389526i
$633$		0			0
$634$	20.4516	+	9.10564i	0.812237	+	0.361631i
$635$	1.75756	−	16.7221i	0.0697468	−	0.663596i
$636$		0			0
$637$	26.7277	−	46.2938i	1.05899	−	1.83423i
$638$	−19.0252	−	16.8366i	−0.753213	−	0.666569i
$639$		0			0
$640$	−4.63749	−	14.2727i	−0.183313	−	0.564179i
$641$	−12.4687	+	5.55141i	−0.492483	+	0.219267i	−0.637924	−	0.770099i	$-0.720207\pi$
$641$	−12.4687	+	5.55141i	−0.492483	+	0.219267i	0.145441	+	0.989367i	$0.453540\pi$
$642$		0			0
$643$	−20.3560	+	4.32680i	−0.802762	+	0.170632i	−0.590982	−	0.806685i	$-0.701260\pi$
$643$	−20.3560	+	4.32680i	−0.802762	+	0.170632i	−0.211781	+	0.977317i	$0.567926\pi$
$644$	5.53275	−	1.17602i	0.218021	−	0.0463418i
$645$		0			0
$646$	−9.07590	+	4.04085i	−0.357086	+	0.158985i
$647$	4.99597	+	15.3760i	0.196412	+	0.604494i	0.999957	+	0.00925026i	$0.00294449\pi$
$647$	4.99597	+	15.3760i	0.196412	+	0.604494i	−0.803545	+	0.595244i	$0.797056\pi$
$648$		0			0
$649$	12.7008	−	7.47903i	0.498550	−	0.293578i
$650$	10.6608	−	18.4650i	0.418150	−	0.724257i
$651$		0			0
$652$	1.88618	−	17.9458i	0.0738685	−	0.702812i
$653$	−15.4314	−	6.87052i	−0.603879	−	0.268864i	0.0819391	−	0.996637i	$-0.473889\pi$
$653$	−15.4314	−	6.87052i	−0.603879	−	0.268864i	−0.685818	+	0.727773i	$0.740555\pi$
$654$		0			0
$655$	5.61940	+	6.24098i	0.219568	+	0.243855i
$656$	−5.49229	+	3.99038i	−0.214438	+	0.155798i
$657$		0			0
$658$	−13.8035	−	42.4827i	−0.538115	−	1.65615i
$659$	−15.1724	+	26.2794i	−0.591033	+	1.02370i	0.403060	+	0.915173i	$0.367946\pi$
$659$	−15.1724	+	26.2794i	−0.591033	+	1.02370i	−0.994094	+	0.108526i	$0.965387\pi$
$660$		0			0
$661$	−7.79563	−	13.5024i	−0.303215	−	0.525183i	0.673648	−	0.739053i	$-0.264727\pi$
$661$	−7.79563	−	13.5024i	−0.303215	−	0.525183i	−0.976862	+	0.213869i	$0.931393\pi$
$662$	−38.4794	+	42.7357i	−1.49555	+	1.66097i
$663$		0			0
$664$	−1.75762	−	16.7227i	−0.0682091	−	0.648966i
$665$	1.99866	−	6.15123i	0.0775046	−	0.238535i
$666$		0			0
$667$	3.41759	−	2.48302i	0.132329	−	0.0961430i
$668$	−7.81007	+	3.47727i	−0.302181	+	0.134540i
$669$		0			0
$670$	4.21697	+	7.30401i	0.162916	+	0.282178i
$671$	36.5004	−	4.15368i	1.40908	−	0.160351i
$672$		0			0
$673$	2.52790	+	0.537322i	0.0974435	+	0.0207122i	0.256375	−	0.966577i	$-0.417472\pi$
$673$	2.52790	+	0.537322i	0.0974435	+	0.0207122i	−0.158932	+	0.987290i	$0.550805\pi$
$674$	−30.5516	−	22.1971i	−1.17681	−	0.854999i
$675$		0			0
$676$	6.28455	−	19.3419i	0.241714	−	0.743918i
$677$	1.95756	+	2.17409i	0.0752351	+	0.0835571i	0.779587	−	0.626294i	$-0.215429\pi$
$677$	1.95756	+	2.17409i	0.0752351	+	0.0835571i	−0.704352	+	0.709851i	$0.748762\pi$
$678$		0			0
$679$	1.51508	−	14.4150i	0.0581434	−	0.553198i
$680$	7.68563	−	8.53575i	0.294730	−	0.327331i
$681$		0			0
$682$	−0.0673363	−	7.83772i	−0.00257844	−	0.300122i
$683$	−12.4096			−0.474841			−0.237420	−	0.971407i	$-0.576302\pi$
$683$	−12.4096			−0.474841			−0.237420	+	0.971407i	$0.576302\pi$
$684$		0			0
$685$	5.42359	+	3.94047i	0.207225	+	0.150558i
$686$	2.45334	+	23.3420i	0.0936691	+	0.891202i
$687$		0			0
$688$	36.0280	−	7.65798i	1.37355	−	0.291958i
$689$	−4.74454	−	2.11240i	−0.180752	−	0.0804762i
$690$		0			0
$691$	3.89426	+	0.827751i	0.148145	+	0.0314891i	0.281387	−	0.959594i	$-0.409206\pi$
$691$	3.89426	+	0.827751i	0.148145	+	0.0314891i	−0.133242	+	0.991083i	$0.542539\pi$
$692$	25.1432			0.955803
$693$		0			0
$694$	−16.4943			−0.626116
$695$	−1.94386	−	0.413181i	−0.0737349	−	0.0156728i
$696$		0			0
$697$	−7.38433	−	3.28772i	−0.279702	−	0.124531i
$698$	11.1615	−	2.37245i	0.422470	−	0.0897987i
$699$		0			0
$700$	1.28749	+	12.2497i	0.0486627	+	0.462995i
$701$	20.6731	+	15.0199i	0.780814	+	0.567295i	0.905223	−	0.424936i	$-0.139704\pi$
$701$	20.6731	+	15.0199i	0.780814	+	0.567295i	−0.124409	+	0.992231i	$0.539704\pi$
$702$		0			0
$703$	−9.26575			−0.349464
$704$	−7.17921	−	2.26467i	−0.270577	−	0.0853528i
$705$		0			0
$706$	−12.3642	+	13.7318i	−0.465333	+	0.516804i
$707$	−6.68990	+	63.6501i	−0.251600	+	2.39381i
$708$		0			0
$709$	−32.9303	−	36.5728i	−1.23672	−	1.37352i	−0.902308	−	0.431093i	$-0.858128\pi$
$709$	−32.9303	−	36.5728i	−1.23672	−	1.37352i	−0.334414	−	0.942426i	$-0.608538\pi$
$710$	−8.48379	+	26.1104i	−0.318391	+	0.979907i
$711$		0			0
$712$	6.81912	+	4.95438i	0.255557	+	0.185673i
$713$	1.27482	+	0.270971i	0.0477423	+	0.0101479i
$714$		0			0
$715$	−12.1794	−	26.7349i	−0.455485	−	0.999830i
$716$	−2.26083	−	3.91587i	−0.0844912	−	0.146343i
$717$		0			0
$718$	−20.8131	+	9.26658i	−0.776738	+	0.345826i
$719$	22.4358	−	16.3006i	0.836716	−	0.607910i	−0.0847354	−	0.996403i	$-0.527005\pi$
$719$	22.4358	−	16.3006i	0.836716	−	0.607910i	0.921451	+	0.388494i	$0.127005\pi$
$720$		0			0
$721$	−0.979948	+	3.01597i	−0.0364952	+	0.112321i
$722$	−3.47015	−	33.0163i	−0.129146	−	1.22874i
$723$		0			0
$724$	17.7391	−	19.7013i	0.659268	−	0.732192i
$725$	4.59945	+	7.96648i	0.170819	+	0.295868i
$726$		0			0
$727$	9.95086	−	17.2354i	0.369057	−	0.639225i	−0.620361	−	0.784316i	$-0.713014\pi$
$727$	9.95086	−	17.2354i	0.369057	−	0.639225i	0.989418	+	0.145091i	$0.0463474\pi$
$728$	−7.99852	−	24.6169i	−0.296445	−	0.912364i
$729$		0			0
$730$	29.3132	−	21.2973i	1.08493	−	0.788247i
$731$	29.3449	+	32.5908i	1.08536	+	1.20541i
$732$		0			0
$733$	−17.3269	−	7.71441i	−0.639982	−	0.284938i	0.0609779	−	0.998139i	$-0.480578\pi$
$733$	−17.3269	−	7.71441i	−0.639982	−	0.284938i	−0.700960	+	0.713201i	$0.747245\pi$
$734$	3.23486	−	30.7776i	0.119401	−	1.13602i
$735$		0			0
$736$	3.31407	−	5.74014i	0.122158	−	0.211584i
$737$	−9.08432	−	0.875963i	−0.334625	−	0.0322665i
$738$		0			0
$739$	−11.0601	−	34.0394i	−0.406851	−	1.25216i	−0.919339	−	0.393465i	$-0.871276\pi$
$739$	−11.0601	−	34.0394i	−0.406851	−	1.25216i	0.512488	−	0.858694i	$-0.328724\pi$
$740$	−20.5260	+	9.13876i	−0.754550	+	0.335947i
$741$		0			0
$742$	7.26853	−	1.54497i	0.266836	−	0.0567178i
$743$	−35.3547	+	7.51487i	−1.29704	+	0.275694i	−0.804165	−	0.594407i	$-0.797387\pi$
$743$	−35.3547	+	7.51487i	−1.29704	+	0.275694i	−0.492874	+	0.870101i	$0.664054\pi$
$744$		0			0
$745$	−31.3040	+	13.9375i	−1.14689	+	0.510629i
$746$	−5.38930	−	16.5865i	−0.197316	−	0.607277i
$747$		0			0
$748$	−5.63892	−	25.4518i	−0.206179	−	0.930611i
$749$	−3.72685	+	6.45510i	−0.136176	+	0.235864i
$750$		0			0
$751$	−0.910960	+	8.66720i	−0.0332414	+	0.316271i	0.965248	+	0.261334i	$0.0841624\pi$
$751$	−0.910960	+	8.66720i	−0.0332414	+	0.316271i	−0.998490	+	0.0549368i	$0.982504\pi$
$752$	−26.2649	−	11.6939i	−0.957783	−	0.426432i
$753$		0			0
$754$	27.1299	+	30.1308i	0.988012	+	1.09730i
$755$	0.176122	−	0.127960i	0.00640974	−	0.00465695i
$756$		0			0
$757$	10.0628	+	30.9702i	0.365740	+	1.12563i	0.949516	+	0.313717i	$0.101574\pi$
$757$	10.0628	+	30.9702i	0.365740	+	1.12563i	−0.583777	+	0.811914i	$0.698426\pi$
$758$	−22.7465	+	39.3981i	−0.826191	+	1.43101i
$759$		0			0
$760$	−0.924849	−	1.60188i	−0.0335478	−	0.0581065i
$761$	−28.6218	+	31.7878i	−1.03754	+	1.15231i	−0.0493962	+	0.998779i	$0.515730\pi$
$761$	−28.6218	+	31.7878i	−1.03754	+	1.15231i	−0.988145	+	0.153526i	$0.950937\pi$
$762$		0			0
$763$	6.79618	+	64.6613i	0.246038	+	2.34090i
$764$	7.67451	−	23.6197i	0.277654	−	0.854531i
$765$		0			0
$766$	−43.8924	+	31.8897i	−1.58590	+	1.15222i
$767$	−21.4892	+	9.56759i	−0.775928	+	0.345466i
$768$		0			0
$769$	2.00465	+	3.47215i	0.0722894	+	0.125209i	0.899904	−	0.436087i	$-0.143636\pi$
$769$	2.00465	+	3.47215i	0.0722894	+	0.125209i	−0.827615	+	0.561296i	$0.810303\pi$
$770$	36.5823	+	20.7038i	1.31834	+	0.746114i
$771$		0			0
$772$	11.1533	+	2.37070i	0.401415	+	0.0853235i
$773$	−16.5649	−	12.0351i	−0.595798	−	0.432872i	0.248587	−	0.968610i	$-0.420034\pi$
$773$	−16.5649	−	12.0351i	−0.595798	−	0.432872i	−0.844385	+	0.535737i	$0.820034\pi$
$774$		0			0
$775$	−0.877001	+	2.69913i	−0.0315028	+	0.0969556i
$776$	−2.77368	−	3.08049i	−0.0995694	−	0.110583i
$777$		0			0
$778$	−2.61277	+	24.8589i	−0.0936724	+	0.891234i
$779$	−0.871012	+	0.967357i	−0.0312073	+	0.0346592i
$780$		0			0
$781$	−17.6680	−	23.8837i	−0.632211	−	0.854626i
$782$	10.7362			0.383924
$783$		0			0
$784$	39.8261	+	28.9354i	1.42236	+	1.03341i
$785$	−0.697548	−	6.63672i	−0.0248966	−	0.236875i
$786$		0			0
$787$	−30.8381	+	6.55485i	−1.09926	+	0.233655i	−0.721615	−	0.692295i	$-0.756600\pi$
$787$	−30.8381	+	6.55485i	−1.09926	+	0.233655i	−0.377646	+	0.925950i	$0.623266\pi$
$788$	32.9036	+	14.6496i	1.17214	+	0.521871i
$789$		0			0
$790$	−33.4056	−	7.10057i	−1.18852	−	0.252627i
$791$	−49.2940			−1.75269
$792$		0			0
$793$	−58.6279			−2.08194
$794$	43.3045	+	9.20465i	1.53682	+	0.326661i
$795$		0			0
$796$	18.8619	+	8.39786i	0.668542	+	0.297654i
$797$	7.26346	−	1.54390i	0.257285	−	0.0546876i	−0.0774634	−	0.996995i	$-0.524682\pi$
$797$	7.26346	−	1.54390i	0.257285	−	0.0546876i	0.334748	+	0.942308i	$0.391349\pi$
$798$		0			0
$799$	−3.57821	−	34.0444i	−0.126588	−	1.20440i
$800$	11.6768	+	8.48368i	0.412836	+	0.299943i
$801$		0			0
$802$	13.7298			0.484815
$803$	0.336837	+	39.2067i	0.0118867	+	1.38358i
$804$		0			0
$805$	−4.67688	+	5.19420i	−0.164838	+	0.183072i
$806$	−1.30754	+	12.4404i	−0.0460560	+	0.438193i
$807$		0			0
$808$	12.2473	+	13.6020i	0.430859	+	0.478517i
$809$	−2.53499	+	7.80189i	−0.0891254	+	0.274300i	−0.985678	−	0.168637i	$-0.946063\pi$
$809$	−2.53499	+	7.80189i	−0.0891254	+	0.274300i	0.896553	+	0.442937i	$0.146063\pi$
$810$		0			0
$811$	33.7432	+	24.5159i	1.18488	+	0.860868i	0.992714	−	0.120494i	$-0.0384477\pi$
$811$	33.7432	+	24.5159i	1.18488	+	0.860868i	0.192169	+	0.981362i	$0.438448\pi$
$812$	−22.9104	−	4.86976i	−0.803998	−	0.170895i
$813$		0			0
$814$	12.0137	−	59.0083i	0.421080	−	2.06824i
$815$	11.1488	+	19.3102i	0.390525	+	0.676408i
$816$		0			0
$817$	6.45184	−	2.87254i	0.225721	−	0.100498i
$818$	−10.1605	+	7.38200i	−0.355252	+	0.258106i
$819$		0			0
$820$	−0.975414	+	3.00202i	−0.0340629	+	0.104835i
$821$	−2.33650	−	22.2303i	−0.0815443	−	0.775842i	−0.956518	−	0.291672i	$-0.905788\pi$
$821$	−2.33650	−	22.2303i	−0.0815443	−	0.775842i	0.874974	−	0.484170i	$-0.160878\pi$
$822$		0			0
$823$	−16.1253	+	17.9090i	−0.562094	+	0.624269i	−0.955463	−	0.295112i	$-0.904643\pi$
$823$	−16.1253	+	17.9090i	−0.562094	+	0.624269i	0.393368	+	0.919381i	$0.371310\pi$
$824$	0.453457	+	0.785410i	0.0157969	+	0.0273611i
$825$		0			0
$826$	16.8282	−	29.1473i	0.585528	−	1.01416i
$827$	9.19763	+	28.3074i	0.319833	+	0.984344i	0.973719	+	0.227752i	$0.0731374\pi$
$827$	9.19763	+	28.3074i	0.319833	+	0.984344i	−0.653886	+	0.756593i	$0.726863\pi$
$828$		0			0
$829$	−9.13755	+	6.63882i	−0.317360	+	0.230576i	−0.735048	−	0.678015i	$-0.762841\pi$
$829$	−9.13755	+	6.63882i	−0.317360	+	0.230576i	0.417688	+	0.908591i	$0.362841\pi$
$830$	−29.1605	−	32.3861i	−1.01218	−	1.12414i
$831$		0			0
$832$	10.9754	+	4.88654i	0.380502	+	0.169410i
$833$	−6.12676	+	58.2922i	−0.212279	+	2.01970i
$834$		0			0
$835$	5.28207	−	9.14881i	0.182793	−	0.316607i
$836$	−4.17876	−	0.402940i	−0.144525	−	0.0139360i
$837$		0			0
$838$	−2.69282	−	8.28763i	−0.0930218	−	0.286292i
$839$	4.36415	−	1.94305i	0.150667	−	0.0670814i	−0.330018	−	0.943975i	$-0.607055\pi$
$839$	4.36415	−	1.94305i	0.150667	−	0.0670814i	0.480685	+	0.876893i	$0.340388\pi$
$840$		0			0
$841$	11.2560	−	2.39253i	0.388137	−	0.0825010i
$842$	−4.36154	+	0.927074i	−0.150309	+	0.0319491i
$843$		0			0
$844$	22.2607	−	9.91110i	0.766245	−	0.341154i
$845$	7.76575	+	23.9005i	0.267150	+	0.822202i
$846$		0			0
$847$	−41.2297	+	19.2121i	−1.41667	+	0.660136i
$848$	2.39140	−	4.14202i	0.0821210	−	0.142238i
$849$		0			0
$850$	−2.44375	+	23.2508i	−0.0838201	+	0.797495i
$851$	9.14746	+	4.07271i	0.313571	+	0.139611i
$852$		0			0
$853$	−0.443703	−	0.492782i	−0.0151921	−	0.0168725i	0.735501	−	0.677524i	$-0.236947\pi$
$853$	−0.443703	−	0.492782i	−0.0151921	−	0.0168725i	−0.750693	+	0.660651i	$0.770280\pi$
$854$	67.8641	−	49.3062i	2.32226	−	1.68722i
$855$		0			0
$856$	0.658718	+	2.02733i	0.0225145	+	0.0692926i
$857$	−21.3432	+	36.9675i	−0.729069	+	1.26279i	0.228207	+	0.973613i	$0.426714\pi$
$857$	−21.3432	+	36.9675i	−0.729069	+	1.26279i	−0.957277	+	0.289173i	$0.906620\pi$
$858$		0			0
$859$	28.8694	+	50.0032i	0.985010	+	1.70609i	0.641891	+	0.766796i	$0.278150\pi$
$859$	28.8694	+	50.0032i	0.985010	+	1.70609i	0.343119	+	0.939292i	$0.388517\pi$
$860$	11.4593	−	12.7268i	0.390758	−	0.433981i
$861$		0			0
$862$	−0.181499	−	1.72685i	−0.00618188	−	0.0588167i
$863$	4.56726	−	14.0566i	0.155471	−	0.478492i	−0.842737	−	0.538326i	$-0.819057\pi$
$863$	4.56726	−	14.0566i	0.155471	−	0.478492i	0.998208	+	0.0598337i	$0.0190570\pi$
$864$		0			0
$865$	−25.1355	+	18.2620i	−0.854633	+	0.620927i
$866$	−15.7821	+	7.02664i	−0.536298	+	0.238775i
$867$		0			0
$868$	−3.61310	−	6.25808i	−0.122637	−	0.212413i
$869$	27.2503	−	24.9635i	0.924403	−	0.846828i
$870$		0			0
$871$	14.2469	+	3.02826i	0.482737	+	0.102609i
$872$	15.0429	+	10.9293i	0.509418	+	0.370114i
$873$		0			0
$874$	0.534274	−	1.64433i	0.0180721	−	0.0556201i
$875$	−33.3364	−	37.0238i	−1.12698	−	1.25163i
$876$		0			0
$877$	−4.69287	+	44.6497i	−0.158467	+	1.50771i	0.569438	+	0.822034i	$0.307161\pi$
$877$	−4.69287	+	44.6497i	−0.158467	+	1.50771i	−0.727905	+	0.685678i	$0.759506\pi$
$878$	−11.4320	+	12.6965i	−0.385812	+	0.428488i
$879$		0			0
$880$	25.6581	−	8.58120i	0.864933	−	0.289272i
$881$	6.57023			0.221357			0.110678	−	0.993856i	$-0.464698\pi$
$881$	6.57023			0.221357			0.110678	+	0.993856i	$0.464698\pi$
$882$		0			0
$883$	28.4843	+	20.6950i	0.958572	+	0.696443i	0.952819	−	0.303540i	$-0.0981686\pi$
$883$	28.4843	+	20.6950i	0.958572	+	0.696443i	0.00575336	+	0.999983i	$0.498169\pi$
$884$	4.34882	+	41.3763i	0.146267	+	1.39164i
$885$		0			0
$886$	55.9452	−	11.8915i	1.87951	−	0.399503i
$887$	−1.01093	−	0.450094i	−0.0339437	−	0.0151127i	0.389695	−	0.920944i	$-0.372581\pi$
$887$	−1.01093	−	0.450094i	−0.0339437	−	0.0151127i	−0.423638	+	0.905831i	$0.639247\pi$
$888$		0			0
$889$	40.6391	+	8.63810i	1.36299	+	0.289713i
$890$	21.8456			0.732266
$891$		0			0
$892$	16.9326			0.566946
$893$	−5.39223	−	1.14615i	−0.180444	−	0.0383545i
$894$		0			0
$895$	5.10431	+	2.27258i	0.170618	+	0.0759641i
$896$	36.2717	−	7.70979i	1.21175	−	0.257566i
$897$		0			0
$898$	−4.73847	−	45.0835i	−0.158125	−	1.50446i
$899$	−4.36609	−	3.17215i	−0.145617	−	0.105797i
$900$		0			0
$901$	5.69466			0.189717
$902$	−5.03122	−	6.80123i	−0.167521	−	0.226456i
$903$		0			0
$904$	−9.43300	+	10.4764i	−0.313737	+	0.348440i
$905$	−3.42424	+	32.5795i	−0.113826	+	1.08298i
$906$		0			0
$907$	9.46799	+	10.5153i	0.314379	+	0.349154i	0.879538	−	0.475829i	$-0.157852\pi$
$907$	9.46799	+	10.5153i	0.314379	+	0.349154i	−0.565159	+	0.824982i	$0.691185\pi$
$908$	−10.8486	+	33.3884i	−0.360022	+	1.10803i
$909$		0			0
$910$	−54.2723	−	39.4311i	−1.79911	−	1.30713i
$911$	44.0310	+	9.35908i	1.45881	+	0.310080i	0.867933	−	0.496681i	$-0.165448\pi$
$911$	44.0310	+	9.35908i	1.45881	+	0.310080i	0.590878	+	0.806761i	$0.298781\pi$
$912$		0			0
$913$	46.8557	−	5.33210i	1.55070	−	0.176467i
$914$	−13.0974	−	22.6854i	−0.433224	−	0.750367i
$915$		0			0
$916$	−3.79021	+	1.68751i	−0.125232	+	0.0557569i
$917$	−16.7880	+	12.1972i	−0.554390	+	0.402788i
$918$		0			0
$919$	0.438782	−	1.35043i	0.0144741	−	0.0445466i	−0.943559	−	0.331206i	$-0.892545\pi$
$919$	0.438782	−	1.35043i	0.0144741	−	0.0445466i	0.958033	+	0.286659i	$0.0925446\pi$
$920$	0.208942	+	1.98795i	0.00688860	+	0.0655407i
$921$		0			0
$922$	−28.0240	+	31.1238i	−0.922921	+	1.02501i
$923$	23.7062	+	41.0604i	0.780300	+	1.35152i
$924$		0			0
$925$	−10.9022	+	18.8832i	−0.358462	+	0.620874i
$926$	15.0671	+	46.3717i	0.495135	+	1.52387i
$927$		0			0
$928$	−22.2045	+	16.1325i	−0.728898	+	0.529576i
$929$	−5.15429	−	5.72442i	−0.169107	−	0.187812i	0.652634	−	0.757673i	$-0.273664\pi$
$929$	−5.15429	−	5.72442i	−0.169107	−	0.187812i	−0.821741	+	0.569861i	$0.806997\pi$
$930$		0			0
$931$	8.62300	+	3.83921i	0.282607	+	0.125825i
$932$	−0.0252129	+	0.239885i	−0.000825877	+	0.00785770i
$933$		0			0
$934$	−34.3261	+	59.4545i	−1.12318	+	1.94541i
$935$	24.1233	+	21.3483i	0.788917	+	0.698166i
$936$		0			0
$937$	15.9680	+	49.1445i	0.521652	+	1.60548i	0.770843	+	0.637025i	$0.219835\pi$
$937$	15.9680	+	49.1445i	0.521652	+	1.60548i	−0.249191	+	0.968454i	$0.580165\pi$
$938$	−19.0381	+	8.47631i	−0.621616	+	0.276761i
$939$		0			0
$940$	−13.0756	+	2.77930i	−0.426479	+	0.0906509i
$941$	9.91567	−	2.10764i	0.323242	−	0.0687072i	−0.0434330	−	0.999056i	$-0.513830\pi$
$941$	9.91567	−	2.10764i	0.323242	−	0.0687072i	0.366675	+	0.930349i	$0.380496\pi$
$942$		0			0
$943$	1.28509	−	0.572159i	0.0418483	−	0.0186320i
$944$	−6.69406	−	20.6022i	−0.217873	−	0.670545i
$945$		0			0
$946$	9.92833	+	44.8126i	0.322798	+	1.45698i
$947$	−0.504393	+	0.873634i	−0.0163906	+	0.0283893i	−0.874104	−	0.485738i	$-0.838551\pi$
$947$	−0.504393	+	0.873634i	−0.0163906	+	0.0283893i	0.857714	+	0.514127i	$0.171884\pi$
$948$		0			0
$949$	6.54070	−	62.2306i	0.212320	−	2.02009i
$950$	3.43942	+	1.53133i	0.111590	+	0.0496829i
$951$		0			0
$952$	18.9908	+	21.0914i	0.615494	+	0.683575i
$953$	−7.67300	+	5.57476i	−0.248553	+	0.180584i	−0.705085	−	0.709123i	$-0.749091\pi$
$953$	−7.67300	+	5.57476i	−0.248553	+	0.180584i	0.456532	+	0.889707i	$0.349091\pi$
$954$		0			0
$955$	9.48330	+	29.1866i	0.306872	+	0.944456i
$956$	−4.34474	+	7.52530i	−0.140519	+	0.243386i
$957$		0			0
$958$	−2.28711	−	3.96139i	−0.0738932	−	0.127987i
$959$	−11.0842	+	12.3102i	−0.357926	+	0.397517i
$960$		0			0
$961$	3.06634	+	29.1743i	0.0989142	+	0.941106i
$962$	−29.6980	+	91.4011i	−0.957503	+	2.94689i
$963$		0			0
$964$	−16.3088	+	11.8490i	−0.525271	+	0.381632i
$965$	−12.8717	+	5.73087i	−0.414356	+	0.184483i
$966$		0			0
$967$	22.0451	+	38.1833i	0.708923	+	1.22789i	0.965257	+	0.261303i	$0.0841521\pi$
$967$	22.0451	+	38.1833i	0.708923	+	1.22789i	−0.256334	+	0.966588i	$0.582515\pi$
$968$	−3.80666	+	12.4390i	−0.122351	+	0.399804i
$969$		0			0
$970$	−10.5086	−	2.23366i	−0.337410	−	0.0717186i
$971$	12.7768	+	9.28287i	0.410026	+	0.297902i	0.773612	−	0.633659i	$-0.218448\pi$
$971$	12.7768	+	9.28287i	0.410026	+	0.297902i	−0.363586	+	0.931561i	$0.618448\pi$
$972$		0			0
$973$	1.51742	−	4.67014i	0.0486463	−	0.149718i
$974$	−43.1026	−	47.8702i	−1.38110	−	1.53386i
$975$		0			0
$976$	5.64361	−	53.6954i	0.180648	−	1.71875i
$977$	40.2067	−	44.6541i	1.28633	−	1.42861i	0.438144	−	0.898905i	$-0.355636\pi$
$977$	40.2067	−	44.6541i	1.28633	−	1.42861i	0.848182	−	0.529705i	$-0.177697\pi$
$978$		0			0
$979$	−13.7300	+	19.2433i	−0.438814	+	0.615018i
$980$	22.8887			0.731153
$981$		0			0
$982$	−52.7128	−	38.2981i	−1.68213	−	1.22214i
$983$	4.26622	+	40.5904i	0.136071	+	1.29463i	0.823056	+	0.567960i	$0.192267\pi$
$983$	4.26622	+	40.5904i	0.136071	+	1.29463i	−0.686985	+	0.726672i	$0.741066\pi$
$984$		0			0
$985$	−43.5338	+	9.25339i	−1.38710	+	0.294838i
$986$	−40.6136	−	18.0823i	−1.29340	−	0.575858i
$987$		0			0
$988$	6.55351	+	1.39299i	0.208495	+	0.0443170i
$989$	−7.63208			−0.242686
$990$		0			0
$991$	−12.3336			−0.391791			−0.195895	−	0.980625i	$-0.562761\pi$
$991$	−12.3336			−0.391791			−0.195895	+	0.980625i	$0.562761\pi$
$992$	−8.28265	−	1.76053i	−0.262975	−	0.0558970i
$993$		0			0
$994$	−61.9728	−	27.5920i	−1.96566	−	0.875167i
$995$	−24.9556	+	5.30448i	−0.791146	+	0.168163i
$996$		0			0
$997$	0.335377	+	3.19090i	0.0106215	+	0.101057i	0.998548	−	0.0538651i	$-0.0171541\pi$
$997$	0.335377	+	3.19090i	0.0106215	+	0.101057i	−0.987927	+	0.154922i	$0.950487\pi$
$998$	−8.99185	−	6.53296i	−0.284632	−	0.206797i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.i.379.4		32
3.2	odd	2		891.2.n.f.379.1		32
9.2	odd	6		297.2.f.d.82.4	yes	16
9.4	even	3	inner	891.2.n.i.676.1		32
9.5	odd	6		891.2.n.f.676.4		32
9.7	even	3		297.2.f.a.82.1	✓	16
11.9	even	5	inner	891.2.n.i.460.1		32
33.20	odd	10		891.2.n.f.460.4		32
99.20	odd	30		297.2.f.d.163.4	yes	16
99.25	even	15		3267.2.a.bm.1.1		8
99.31	even	15	inner	891.2.n.i.757.4		32
99.47	odd	30		3267.2.a.be.1.8		8
99.52	odd	30		3267.2.a.bf.1.8		8
99.74	even	30		3267.2.a.bl.1.1		8
99.86	odd	30		891.2.n.f.757.1		32
99.97	even	15		297.2.f.a.163.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.a.82.1	✓	16	9.7	even	3
297.2.f.a.163.1	yes	16	99.97	even	15
297.2.f.d.82.4	yes	16	9.2	odd	6
297.2.f.d.163.4	yes	16	99.20	odd	30
891.2.n.f.379.1		32	3.2	odd	2
891.2.n.f.460.4		32	33.20	odd	10
891.2.n.f.676.4		32	9.5	odd	6
891.2.n.f.757.1		32	99.86	odd	30
891.2.n.i.379.4		32	1.1	even	1	trivial
891.2.n.i.460.1		32	11.9	even	5	inner
891.2.n.i.676.1		32	9.4	even	3	inner
891.2.n.i.757.4		32	99.31	even	15	inner
3267.2.a.be.1.8		8	99.47	odd	30
3267.2.a.bf.1.8		8	99.52	odd	30
3267.2.a.bl.1.1		8	99.74	even	30
3267.2.a.bm.1.1		8	99.25	even	15

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.79145 + 0.380785i) q^{2} +(1.23721 + 0.550844i) q^{4} +(-1.63692 + 0.347939i) q^{5} +(-0.432236 - 4.11245i) q^{7} +(-0.956730 - 0.695105i) q^{8} +O(q^{10})\)	\(q+(1.79145 + 0.380785i) q^{2} +(1.23721 + 0.550844i) q^{4} +(-1.63692 + 0.347939i) q^{5} +(-0.432236 - 4.11245i) q^{7} +(-0.956730 - 0.695105i) q^{8} -3.06496 q^{10} +(1.92634 - 2.69985i) q^{11} +(-3.54177 + 3.93353i) q^{13} +(0.791630 - 7.53186i) q^{14} +(-3.26166 - 3.62244i) q^{16} +(1.79348 - 5.51975i) q^{17} +(-0.756141 - 0.549369i) q^{19} +(-2.21688 - 0.471213i) q^{20} +(4.47901 - 4.10314i) q^{22} +(0.505016 + 0.874713i) q^{23} +(-2.00927 + 0.894586i) q^{25} +(-7.84274 + 5.69808i) q^{26} +(1.73055 - 5.32608i) q^{28} +(-0.437181 - 4.15950i) q^{29} +(0.863415 - 0.958919i) q^{31} +(-3.28115 - 5.68312i) q^{32} +(5.31477 - 9.20544i) q^{34} +(2.13842 + 6.58138i) q^{35} +(8.02034 - 5.82712i) q^{37} +(-1.14540 - 1.27210i) q^{38} +(1.80795 + 0.804949i) q^{40} +(0.145580 - 1.38510i) q^{41} +(-3.77814 + 6.54393i) q^{43} +(3.87049 - 2.27919i) q^{44} +(0.571634 + 1.75931i) q^{46} +(5.38826 - 2.39901i) q^{47} +(-9.87841 + 2.09972i) q^{49} +(-3.94016 + 0.837508i) q^{50} +(-6.54869 + 2.91566i) q^{52} +(0.303205 + 0.933170i) q^{53} +(-2.21389 + 5.08970i) q^{55} +(-2.44505 + 4.23496i) q^{56} +(0.800686 - 7.61802i) q^{58} +(4.05985 + 1.80756i) q^{59} +(7.41150 + 8.23130i) q^{61} +(1.91191 - 1.38908i) q^{62} +(-0.701393 - 2.15867i) q^{64} +(4.42897 - 7.67120i) q^{65} +(-1.37586 - 2.38307i) q^{67} +(5.25943 - 5.84119i) q^{68} +(1.32479 + 12.6045i) q^{70} +(2.76800 - 8.51901i) q^{71} +(-9.56397 + 6.94863i) q^{73} +(16.5869 - 7.38498i) q^{74} +(-0.632893 - 1.09620i) q^{76} +(-11.9357 - 6.75501i) q^{77} +(10.8992 + 2.31669i) q^{79} +(6.59947 + 4.79479i) q^{80} +(0.788227 - 2.42591i) q^{82} +(9.51417 + 10.5666i) q^{83} +(-1.01525 + 9.65942i) q^{85} +(-9.26019 + 10.2845i) q^{86} +(-3.71967 + 1.24402i) q^{88} -7.12753 q^{89} +(17.7073 + 12.8651i) q^{91} +(0.142983 + 1.36039i) q^{92} +(10.5663 - 2.24594i) q^{94} +(1.42889 + 0.636184i) q^{95} +(3.42861 + 0.728774i) q^{97} -18.4963 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 4 q^{4} + q^{5} + 2 q^{7}+O(q^{10}) \) 32 * q + 2 * q^2 + 4 * q^4 + q^5 + 2 * q^7	\( 32 q + 2 q^{2} + 4 q^{4} + q^{5} + 2 q^{7} + 12 q^{10} + 13 q^{11} + 2 q^{13} - 22 q^{14} + 24 q^{16} + 4 q^{17} - 4 q^{19} - 15 q^{22} + 14 q^{23} + 19 q^{25} - 42 q^{26} + 30 q^{28} + q^{29} - 14 q^{31} - 48 q^{32} - 10 q^{34} + 36 q^{35} + 18 q^{37} + 11 q^{38} - 33 q^{40} + 25 q^{41} - 14 q^{43} - 28 q^{44} + 8 q^{46} - 28 q^{47} + 4 q^{49} - 63 q^{50} - 10 q^{52} - 2 q^{53} - 80 q^{55} + 96 q^{56} + 20 q^{58} + 41 q^{59} + 10 q^{62} - 184 q^{64} - 60 q^{65} + 48 q^{67} + 25 q^{68} + 31 q^{70} - 6 q^{71} - 26 q^{73} + 29 q^{74} + 58 q^{76} - 2 q^{77} + 166 q^{80} + 82 q^{82} - 14 q^{83} + 10 q^{85} - 56 q^{86} - 86 q^{88} - 164 q^{89} + 28 q^{91} + 74 q^{92} + 2 q^{94} - 56 q^{95} - 12 q^{97} - 52 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 4 * q^4 + q^5 + 2 * q^7 + 12 * q^10 + 13 * q^11 + 2 * q^13 - 22 * q^14 + 24 * q^16 + 4 * q^17 - 4 * q^19 - 15 * q^22 + 14 * q^23 + 19 * q^25 - 42 * q^26 + 30 * q^28 + q^29 - 14 * q^31 - 48 * q^32 - 10 * q^34 + 36 * q^35 + 18 * q^37 + 11 * q^38 - 33 * q^40 + 25 * q^41 - 14 * q^43 - 28 * q^44 + 8 * q^46 - 28 * q^47 + 4 * q^49 - 63 * q^50 - 10 * q^52 - 2 * q^53 - 80 * q^55 + 96 * q^56 + 20 * q^58 + 41 * q^59 + 10 * q^62 - 184 * q^64 - 60 * q^65 + 48 * q^67 + 25 * q^68 + 31 * q^70 - 6 * q^71 - 26 * q^73 + 29 * q^74 + 58 * q^76 - 2 * q^77 + 166 * q^80 + 82 * q^82 - 14 * q^83 + 10 * q^85 - 56 * q^86 - 86 * q^88 - 164 * q^89 + 28 * q^91 + 74 * q^92 + 2 * q^94 - 56 * q^95 - 12 * q^97 - 52 * q^98

Introduction

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