LMFDB - Embedded newform 605.2.e.c.362.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(362,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("605.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.e (of order $4$, degree $2$, 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			362.9
Character	$\chi$	$=$	605.362
Dual form			605.2.e.c.483.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.436764 + 0.436764i) q^{2} +(1.06258 - 1.06258i) q^{3} +1.61847i q^{4} +(-1.07825 + 1.95892i) q^{5} +0.928194i q^{6} +(-1.08812 + 1.08812i) q^{7} +(-1.58042 - 1.58042i) q^{8} +0.741845i q^{9} +O(q^{10})$	\(q+(-0.436764 + 0.436764i) q^{2} +(1.06258 - 1.06258i) q^{3} +1.61847i q^{4} +(-1.07825 + 1.95892i) q^{5} +0.928194i q^{6} +(-1.08812 + 1.08812i) q^{7} +(-1.58042 - 1.58042i) q^{8} +0.741845i q^{9} +(-0.384643 - 1.32653i) q^{10} +(1.71976 + 1.71976i) q^{12} +(-0.147104 - 0.147104i) q^{13} -0.950501i q^{14} +(0.935779 + 3.22724i) q^{15} -1.85641 q^{16} +(2.69584 - 2.69584i) q^{17} +(-0.324011 - 0.324011i) q^{18} -6.52083 q^{19} +(-3.17046 - 1.74513i) q^{20} +2.31242i q^{21} +(-4.95331 + 4.95331i) q^{23} -3.35865 q^{24} +(-2.67474 - 4.22443i) q^{25} +0.128500 q^{26} +(3.97601 + 3.97601i) q^{27} +(-1.76109 - 1.76109i) q^{28} -9.03244 q^{29} +(-1.81826 - 1.00083i) q^{30} +6.06733 q^{31} +(3.97165 - 3.97165i) q^{32} +2.35489i q^{34} +(-0.958268 - 3.30480i) q^{35} -1.20066 q^{36} +(-0.916496 - 0.916496i) q^{37} +(2.84806 - 2.84806i) q^{38} -0.312620 q^{39} +(4.80001 - 1.39182i) q^{40} +5.01676i q^{41} +(-1.00998 - 1.00998i) q^{42} +(7.33931 + 7.33931i) q^{43} +(-1.45322 - 0.799898i) q^{45} -4.32686i q^{46} +(0.236866 + 0.236866i) q^{47} +(-1.97258 + 1.97258i) q^{48} +4.63200i q^{49} +(3.01331 + 0.676849i) q^{50} -5.72909i q^{51} +(0.238085 - 0.238085i) q^{52} +(3.74336 - 3.74336i) q^{53} -3.47316 q^{54} +3.43936 q^{56} +(-6.92891 + 6.92891i) q^{57} +(3.94505 - 3.94505i) q^{58} -5.21163i q^{59} +(-5.22321 + 1.51453i) q^{60} +14.7845i q^{61} +(-2.64999 + 2.64999i) q^{62} +(-0.807215 - 0.807215i) q^{63} -0.243462i q^{64} +(0.446781 - 0.129550i) q^{65} +(-1.11373 - 1.11373i) q^{67} +(4.36314 + 4.36314i) q^{68} +10.5266i q^{69} +(1.86196 + 1.02488i) q^{70} -1.37578 q^{71} +(1.17243 - 1.17243i) q^{72} +(9.27002 + 9.27002i) q^{73} +0.800585 q^{74} +(-7.33092 - 1.64667i) q^{75} -10.5538i q^{76} +(0.136541 - 0.136541i) q^{78} +5.52412 q^{79} +(2.00168 - 3.63655i) q^{80} +6.22413 q^{81} +(-2.19114 - 2.19114i) q^{82} +(-5.84120 - 5.84120i) q^{83} -3.74260 q^{84} +(2.37413 + 8.18773i) q^{85} -6.41110 q^{86} +(-9.59770 + 9.59770i) q^{87} -9.01467i q^{89} +(0.984079 - 0.285346i) q^{90} +0.320133 q^{91} +(-8.01681 - 8.01681i) q^{92} +(6.44703 - 6.44703i) q^{93} -0.206909 q^{94} +(7.03111 - 12.7738i) q^{95} -8.44040i q^{96} +(5.99925 + 5.99925i) q^{97} +(-2.02309 - 2.02309i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{3} - 4 q^{5}+O(q^{10}) $ 40 * q + 8 * q^3 - 4 * q^5	$ 40 q + 8 q^{3} - 4 q^{5} - 32 q^{12} + 32 q^{15} - 24 q^{16} + 32 q^{20} - 24 q^{23} - 52 q^{25} - 8 q^{26} + 32 q^{27} + 16 q^{31} - 40 q^{36} + 36 q^{37} + 32 q^{38} + 32 q^{42} + 64 q^{45} + 32 q^{47} - 16 q^{48} - 68 q^{53} + 80 q^{56} + 132 q^{58} - 64 q^{60} - 88 q^{67} - 8 q^{70} - 16 q^{75} - 248 q^{78} - 164 q^{80} - 40 q^{81} + 100 q^{82} - 80 q^{86} - 96 q^{91} - 56 q^{92} + 24 q^{93} - 68 q^{97}+O(q^{100}) $ 40 * q + 8 * q^3 - 4 * q^5 - 32 * q^12 + 32 * q^15 - 24 * q^16 + 32 * q^20 - 24 * q^23 - 52 * q^25 - 8 * q^26 + 32 * q^27 + 16 * q^31 - 40 * q^36 + 36 * q^37 + 32 * q^38 + 32 * q^42 + 64 * q^45 + 32 * q^47 - 16 * q^48 - 68 * q^53 + 80 * q^56 + 132 * q^58 - 64 * q^60 - 88 * q^67 - 8 * q^70 - 16 * q^75 - 248 * q^78 - 164 * q^80 - 40 * q^81 + 100 * q^82 - 80 * q^86 - 96 * q^91 - 56 * q^92 + 24 * q^93 - 68 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.436764	+	0.436764i	−0.308839	+	0.308839i	−0.844459	−	0.535620i	$-0.820078\pi$
$2$	−0.436764	+	0.436764i	−0.308839	+	0.308839i	0.535620	+	0.844459i	$0.320078\pi$
$3$	1.06258	−	1.06258i	0.613481	−	0.613481i	−0.330370	−	0.943851i	$-0.607174\pi$
$3$	1.06258	−	1.06258i	0.613481	−	0.613481i	0.943851	+	0.330370i	$0.107174\pi$
$4$			1.61847i			0.809237i
$5$	−1.07825	+	1.95892i	−0.482210	+	0.876056i
$5$	−1.07825	+	1.95892i	−0.482210	+	0.876056i
$6$			0.928194i			0.378934i
$7$	−1.08812	+	1.08812i	−0.411270	+	0.411270i	−0.882181	−	0.470911i	$-0.843925\pi$
$7$	−1.08812	+	1.08812i	−0.411270	+	0.411270i	0.470911	+	0.882181i	$0.343925\pi$
$8$	−1.58042	−	1.58042i	−0.558763	−	0.558763i
$9$			0.741845i			0.247282i
$10$	−0.384643	−	1.32653i	−0.121635	−	0.419485i
$11$		0			0
$11$		0			0
$12$	1.71976	+	1.71976i	0.496452	+	0.496452i
$13$	−0.147104	−	0.147104i	−0.0407994	−	0.0407994i	0.686413	−	0.727212i	$-0.259184\pi$
$13$	−0.147104	−	0.147104i	−0.0407994	−	0.0407994i	−0.727212	+	0.686413i	$0.759184\pi$
$14$		−	0.950501i		−	0.254032i
$15$	0.935779	+	3.22724i	0.241617	+	0.833270i
$16$	−1.85641			−0.464102
$17$	2.69584	−	2.69584i	0.653837	−	0.653837i	−0.300078	−	0.953915i	$-0.597013\pi$
$17$	2.69584	−	2.69584i	0.653837	−	0.653837i	0.953915	+	0.300078i	$0.0970127\pi$
$18$	−0.324011	−	0.324011i	−0.0763702	−	0.0763702i
$19$	−6.52083			−1.49598			−0.747990	−	0.663710i	$-0.768981\pi$
$19$	−6.52083			−1.49598			−0.747990	+	0.663710i	$0.768981\pi$
$20$	−3.17046	−	1.74513i	−0.708937	−	0.390222i
$21$			2.31242i			0.504612i
$22$		0			0
$23$	−4.95331	+	4.95331i	−1.03284	+	1.03284i	−0.0333949	+	0.999442i	$0.510632\pi$
$23$	−4.95331	+	4.95331i	−1.03284	+	1.03284i	−0.999442	+	0.0333949i	$0.989368\pi$
$24$	−3.35865			−0.685581
$25$	−2.67474	−	4.22443i	−0.534947	−	0.844885i
$26$	0.128500			0.0252009
$27$	3.97601	+	3.97601i	0.765184	+	0.765184i
$28$	−1.76109	−	1.76109i	−0.332815	−	0.332815i
$29$	−9.03244			−1.67728			−0.838641	−	0.544684i	$-0.816650\pi$
$29$	−9.03244			−1.67728			−0.838641	+	0.544684i	$0.816650\pi$
$30$	−1.81826	−	1.00083i	−0.331967	−	0.182726i
$31$	6.06733			1.08973			0.544863	−	0.838525i	$-0.316582\pi$
$31$	6.06733			1.08973			0.544863	+	0.838525i	$0.316582\pi$
$32$	3.97165	−	3.97165i	0.702095	−	0.702095i
$33$		0			0
$34$			2.35489i			0.403861i
$35$	−0.958268	−	3.30480i	−0.161977	−	0.558613i
$36$	−1.20066			−0.200110
$37$	−0.916496	−	0.916496i	−0.150671	−	0.150671i	0.627747	−	0.778418i	$-0.283977\pi$
$37$	−0.916496	−	0.916496i	−0.150671	−	0.150671i	−0.778418	+	0.627747i	$0.783977\pi$
$38$	2.84806	−	2.84806i	0.462017	−	0.462017i
$39$	−0.312620			−0.0500593
$40$	4.80001	−	1.39182i	0.758948	−	0.220066i
$41$			5.01676i			0.783487i	0.920075	+	0.391743i	$0.128128\pi$
$41$			5.01676i			0.783487i	−0.920075	+	0.391743i	$0.871872\pi$
$42$	−1.00998	−	1.00998i	−0.155844	−	0.155844i
$43$	7.33931	+	7.33931i	1.11923	+	1.11923i	0.991854	+	0.127381i	$0.0406570\pi$
$43$	7.33931	+	7.33931i	1.11923	+	1.11923i	0.127381	+	0.991854i	$0.459343\pi$
$44$		0			0
$45$	−1.45322	−	0.799898i	−0.216633	−	0.119242i
$46$		−	4.32686i		−	0.637961i
$47$	0.236866	+	0.236866i	0.0345504	+	0.0345504i	0.724171	−	0.689621i	$-0.242223\pi$
$47$	0.236866	+	0.236866i	0.0345504	+	0.0345504i	−0.689621	+	0.724171i	$0.742223\pi$
$48$	−1.97258	+	1.97258i	−0.284718	+	0.284718i
$49$			4.63200i			0.661715i
$50$	3.01331	+	0.676849i	0.426146	+	0.0957210i
$51$		−	5.72909i		−	0.802233i
$52$	0.238085	−	0.238085i	0.0330164	−	0.0330164i
$53$	3.74336	−	3.74336i	0.514190	−	0.514190i	−0.401618	−	0.915807i	$-0.631552\pi$
$53$	3.74336	−	3.74336i	0.514190	−	0.514190i	0.915807	+	0.401618i	$0.131552\pi$
$54$	−3.47316			−0.472637
$55$		0			0
$56$	3.43936			0.459604
$57$	−6.92891	+	6.92891i	−0.917756	+	0.917756i
$58$	3.94505	−	3.94505i	0.518010	−	0.518010i
$59$		−	5.21163i		−	0.678497i	−0.940697	−	0.339248i	$-0.889827\pi$
$59$		−	5.21163i		−	0.678497i	0.940697	−	0.339248i	$-0.110173\pi$
$60$	−5.22321	+	1.51453i	−0.674313	+	0.195525i
$61$			14.7845i			1.89296i	0.322770	+	0.946478i	$0.395386\pi$
$61$			14.7845i			1.89296i	−0.322770	+	0.946478i	$0.604614\pi$
$62$	−2.64999	+	2.64999i	−0.336550	+	0.336550i
$63$	−0.807215	−	0.807215i	−0.101699	−	0.101699i
$64$		−	0.243462i		−	0.0304327i
$65$	0.446781	−	0.129550i	0.0554164	−	0.0160687i
$66$		0			0
$67$	−1.11373	−	1.11373i	−0.136064	−	0.136064i	0.635794	−	0.771859i	$-0.280673\pi$
$67$	−1.11373	−	1.11373i	−0.136064	−	0.136064i	−0.771859	+	0.635794i	$0.780673\pi$
$68$	4.36314	+	4.36314i	0.529109	+	0.529109i
$69$			10.5266i			1.26725i
$70$	1.86196	+	1.02488i	0.222546	+	0.122497i
$71$	−1.37578			−0.163275			−0.0816373	−	0.996662i	$-0.526015\pi$
$71$	−1.37578			−0.163275			−0.0816373	+	0.996662i	$0.526015\pi$
$72$	1.17243	−	1.17243i	0.138172	−	0.138172i
$73$	9.27002	+	9.27002i	1.08497	+	1.08497i	0.996037	+	0.0889359i	$0.0283466\pi$
$73$	9.27002	+	9.27002i	1.08497	+	1.08497i	0.0889359	+	0.996037i	$0.471653\pi$
$74$	0.800585			0.0930661
$75$	−7.33092	−	1.64667i	−0.846501	−	0.190141i
$76$		−	10.5538i		−	1.21060i
$77$		0			0
$78$	0.136541	−	0.136541i	0.0154603	−	0.0154603i
$79$	5.52412			0.621512			0.310756	−	0.950490i	$-0.399418\pi$
$79$	5.52412			0.621512			0.310756	+	0.950490i	$0.399418\pi$
$80$	2.00168	−	3.63655i	0.223794	−	0.406579i
$81$	6.22413			0.691570
$82$	−2.19114	−	2.19114i	−0.241971	−	0.241971i
$83$	−5.84120	−	5.84120i	−0.641155	−	0.641155i	0.309685	−	0.950839i	$-0.399777\pi$
$83$	−5.84120	−	5.84120i	−0.641155	−	0.641155i	−0.950839	+	0.309685i	$0.899777\pi$
$84$	−3.74260			−0.408351
$85$	2.37413	+	8.18773i	0.257511	+	0.888084i
$86$	−6.41110			−0.691327
$87$	−9.59770	+	9.59770i	−1.02898	+	1.02898i
$88$		0			0
$89$		−	9.01467i		−	0.955554i	−0.878481	−	0.477777i	$-0.841443\pi$
$89$		−	9.01467i		−	0.955554i	0.878481	−	0.477777i	$-0.158557\pi$
$90$	0.984079	−	0.285346i	0.103731	−	0.0300781i
$91$	0.320133			0.0335591
$92$	−8.01681	−	8.01681i	−0.835810	−	0.835810i
$93$	6.44703	−	6.44703i	0.668526	−	0.668526i
$94$	−0.206909			−0.0213410
$95$	7.03111	−	12.7738i	0.721377	−	1.31056i
$96$		−	8.44040i		−	0.861445i
$97$	5.99925	+	5.99925i	0.609132	+	0.609132i	0.942719	−	0.333587i	$-0.108259\pi$
$97$	5.99925	+	5.99925i	0.609132	+	0.609132i	−0.333587	+	0.942719i	$0.608259\pi$
$98$	−2.02309	−	2.02309i	−0.204363	−	0.204363i
$99$		0			0
$100$	6.83713	−	4.32899i	0.683713	−	0.432899i
$101$			1.74893i			0.174025i	0.996207	+	0.0870124i	$0.0277320\pi$
$101$			1.74893i			0.174025i	−0.996207	+	0.0870124i	$0.972268\pi$
$102$	2.50226	+	2.50226i	0.247761	+	0.247761i
$103$	−6.26589	+	6.26589i	−0.617397	+	0.617397i	−0.944863	−	0.327466i	$-0.893805\pi$
$103$	−6.26589	+	6.26589i	−0.617397	+	0.617397i	0.327466	+	0.944863i	$0.393805\pi$
$104$			0.464973i			0.0455944i
$105$	−4.52985	−	2.49338i	−0.442069	−	0.243329i
$106$			3.26993i			0.317604i
$107$	9.27089	−	9.27089i	0.896251	−	0.896251i	−0.0988516	−	0.995102i	$-0.531517\pi$
$107$	9.27089	−	9.27089i	0.896251	−	0.896251i	0.995102	+	0.0988516i	$0.0315169\pi$
$108$	−6.43507	+	6.43507i	−0.619215	+	0.619215i
$109$	−9.28469			−0.889312			−0.444656	−	0.895701i	$-0.646674\pi$
$109$	−9.28469			−0.889312			−0.444656	+	0.895701i	$0.646674\pi$
$110$		0			0
$111$	−1.94770			−0.184868
$112$	2.01999	−	2.01999i	0.190871	−	0.190871i
$113$	−1.02983	+	1.02983i	−0.0968786	+	0.0968786i	−0.753885	−	0.657006i	$-0.771822\pi$
$113$	−1.02983	+	1.02983i	−0.0968786	+	0.0968786i	0.657006	+	0.753885i	$0.271822\pi$
$114$		−	6.05260i		−	0.566878i
$115$	−4.36221	−	15.0441i	−0.406779	−	1.40287i
$116$		−	14.6188i		−	1.35732i
$117$	0.109129	−	0.109129i	0.0100889	−	0.0100889i
$118$	2.27625	+	2.27625i	0.209546	+	0.209546i
$119$			5.86678i			0.537806i
$120$	3.62147	−	6.57932i	0.330594	−	0.600607i
$121$		0			0
$122$	−6.45732	−	6.45732i	−0.584618	−	0.584618i
$123$	5.33071	+	5.33071i	0.480654	+	0.480654i
$124$			9.81982i			0.881846i
$125$	11.1594	−	0.684590i	0.998124	−	0.0612316i
$126$	0.705125			0.0628175
$127$	−3.85001	+	3.85001i	−0.341633	+	0.341633i	−0.856981	−	0.515348i	$-0.827663\pi$
$127$	−3.85001	+	3.85001i	−0.341633	+	0.341633i	0.515348	+	0.856981i	$0.327663\pi$
$128$	8.04964	+	8.04964i	0.711494	+	0.711494i
$129$	15.5972			1.37326
$130$	−0.138555	+	0.251721i	−0.0121521	+	0.0220774i
$131$		−	3.43352i		−	0.299988i	−0.988687	−	0.149994i	$-0.952074\pi$
$131$		−	3.43352i		−	0.299988i	0.988687	−	0.149994i	$-0.0479255\pi$
$132$		0			0
$133$	7.09543	−	7.09543i	0.615251	−	0.615251i
$134$	0.972879			0.0840440
$135$	−12.0758	+	3.50154i	−1.03932	+	0.301364i
$136$	−8.52111			−0.730679
$137$	7.22911	+	7.22911i	0.617624	+	0.617624i	0.944922	−	0.327297i	$-0.106138\pi$
$137$	7.22911	+	7.22911i	0.617624	+	0.617624i	−0.327297	+	0.944922i	$0.606138\pi$
$138$	−4.59764	−	4.59764i	−0.391377	−	0.391377i
$139$	−0.798717			−0.0677463			−0.0338732	−	0.999426i	$-0.510784\pi$
$139$	−0.798717			−0.0677463			−0.0338732	+	0.999426i	$0.510784\pi$
$140$	5.34874	−	1.55093i	0.452051	−	0.131078i
$141$	0.503378			0.0423921
$142$	0.600890	−	0.600890i	0.0504256	−	0.0504256i
$143$		0			0
$144$		−	1.37717i		−	0.114764i
$145$	9.73927	−	17.6938i	0.808802	−	1.46939i
$146$	−8.09762			−0.670164
$147$	4.92187	+	4.92187i	0.405949	+	0.405949i
$148$	1.48332	−	1.48332i	0.121929	−	0.121929i
$149$	8.80143			0.721041			0.360521	−	0.932751i	$-0.382599\pi$
$149$	8.80143			0.721041			0.360521	+	0.932751i	$0.382599\pi$
$150$	3.92109	−	2.48268i	0.320156	−	0.202710i
$151$			5.69525i			0.463473i	0.972779	+	0.231737i	$0.0744407\pi$
$151$			5.69525i			0.463473i	−0.972779	+	0.231737i	$0.925559\pi$
$152$	10.3056	+	10.3056i	0.835898	+	0.835898i
$153$	1.99989	+	1.99989i	0.161682	+	0.161682i
$154$		0			0
$155$	−6.54213	+	11.8854i	−0.525476	+	0.954660i
$156$		−	0.505968i		−	0.0405099i
$157$	6.26418	+	6.26418i	0.499936	+	0.499936i	0.911418	−	0.411482i	$-0.134989\pi$
$157$	6.26418	+	6.26418i	0.499936	+	0.499936i	−0.411482	+	0.911418i	$0.634989\pi$
$158$	−2.41274	+	2.41274i	−0.191947	+	0.191947i
$159$		−	7.95524i		−	0.630892i
$160$	3.49770	+	12.0626i	0.276517	+	0.953632i
$161$		−	10.7796i		−	0.849549i
$162$	−2.71848	+	2.71848i	−0.213584	+	0.213584i
$163$	11.1371	−	11.1371i	0.872328	−	0.872328i	−0.120398	−	0.992726i	$-0.538417\pi$
$163$	11.1371	−	11.1371i	0.872328	−	0.872328i	0.992726	+	0.120398i	$0.0384169\pi$
$164$	−8.11950			−0.634026
$165$		0			0
$166$	5.10245			0.396027
$167$	4.85655	−	4.85655i	0.375811	−	0.375811i	−0.493777	−	0.869588i	$-0.664384\pi$
$167$	4.85655	−	4.85655i	0.375811	−	0.375811i	0.869588	+	0.493777i	$0.164384\pi$
$168$	3.65460	−	3.65460i	0.281959	−	0.281959i
$169$		−	12.9567i		−	0.996671i
$170$	−4.61304	−	2.53917i	−0.353804	−	0.194746i
$171$		−	4.83744i		−	0.369929i
$172$	−11.8785	+	11.8785i	−0.905726	+	0.905726i
$173$	7.75549	+	7.75549i	0.589639	+	0.589639i	0.937534	−	0.347895i	$-0.113103\pi$
$173$	7.75549	+	7.75549i	0.589639	+	0.589639i	−0.347895	+	0.937534i	$0.613103\pi$
$174$		−	8.38386i		−	0.635579i
$175$	7.50710	+	1.68625i	0.567483	+	0.127468i
$176$		0			0
$177$	−5.53778	−	5.53778i	−0.416245	−	0.416245i
$178$	3.93729	+	3.93729i	0.295112	+	0.295112i
$179$		−	6.24189i		−	0.466541i	−0.972412	−	0.233270i	$-0.925057\pi$
$179$		−	6.24189i		−	0.466541i	0.972412	−	0.233270i	$-0.0749427\pi$
$180$	1.29461	−	2.35199i	0.0964948	−	0.175307i
$181$	−13.8228			−1.02744			−0.513722	−	0.857957i	$-0.671734\pi$
$181$	−13.8228			−1.02744			−0.513722	+	0.857957i	$0.671734\pi$
$182$	−0.139823	+	0.139823i	−0.0103644	+	0.0103644i
$183$	15.7097	+	15.7097i	1.16129	+	1.16129i
$184$	15.6566			1.15422
$185$	2.78356	−	0.807127i	0.204651	−	0.0593411i
$186$			5.63166i			0.412934i
$187$		0			0
$188$	−0.383361	+	0.383361i	−0.0279595	+	0.0279595i
$189$	−8.65273			−0.629394
$190$	2.50819	+	8.65007i	0.181964	+	0.627542i
$191$	16.5430			1.19701			0.598505	−	0.801119i	$-0.295762\pi$
$191$	16.5430			1.19701			0.598505	+	0.801119i	$0.295762\pi$
$192$	−0.258698	−	0.258698i	−0.0186699	−	0.0186699i
$193$	15.0207	+	15.0207i	1.08122	+	1.08122i	0.996396	+	0.0848209i	$0.0270318\pi$
$193$	15.0207	+	15.0207i	1.08122	+	1.08122i	0.0848209	+	0.996396i	$0.472968\pi$
$194$	−5.24052			−0.376247
$195$	0.337084	−	0.612398i	0.0241391	−	0.0438548i
$196$	−7.49677			−0.535484
$197$	−12.0343	+	12.0343i	−0.857411	+	0.857411i	−0.991032	−	0.133621i	$-0.957339\pi$
$197$	−12.0343	+	12.0343i	−0.857411	+	0.857411i	0.133621	+	0.991032i	$0.457339\pi$
$198$		0			0
$199$		−	3.98992i		−	0.282838i	−0.989950	−	0.141419i	$-0.954834\pi$
$199$		−	3.98992i		−	0.282838i	0.989950	−	0.141419i	$-0.0451664\pi$
$200$	−2.44916	+	10.9036i	−0.173182	+	0.770999i
$201$	−2.36687			−0.166946
$202$	−0.763869	−	0.763869i	−0.0537456	−	0.0537456i
$203$	9.82836	−	9.82836i	0.689816	−	0.689816i
$204$	9.27238			0.649197
$205$	−9.82744	−	5.40934i	−0.686378	−	0.377805i
$206$		−	5.47343i		−	0.381352i
$207$	−3.67459	−	3.67459i	−0.255402	−	0.255402i
$208$	0.273085	+	0.273085i	0.0189351	+	0.0189351i
$209$		0			0
$210$	3.06750	−	0.889459i	0.211677	−	0.0613785i
$211$			1.13158i			0.0779012i	0.999241	+	0.0389506i	$0.0124015\pi$
$211$			1.13158i			0.0779012i	−0.999241	+	0.0389506i	$0.987599\pi$
$212$	6.05853	+	6.05853i	0.416101	+	0.416101i
$213$	−1.46187	+	1.46187i	−0.100166	+	0.100166i
$214$			8.09838i			0.553594i
$215$	−22.2908	+	6.46348i	−1.52022	+	0.440806i
$216$		−	12.5675i		−	0.855113i
$217$	−6.60197	+	6.60197i	−0.448171	+	0.448171i
$218$	4.05522	−	4.05522i	0.274654	−	0.274654i
$219$	19.7003			1.33122
$220$		0			0
$221$	−0.793139			−0.0533523
$222$	0.850686	−	0.850686i	0.0570943	−	0.0570943i
$223$	14.9750	−	14.9750i	1.00280	−	1.00280i	0.00280356	−	0.999996i	$-0.499108\pi$
$223$	14.9750	−	14.9750i	1.00280	−	1.00280i	0.999996	−	0.00280356i	$-0.000892403\pi$
$224$			8.64325i			0.577501i
$225$	3.13387	−	1.98424i	0.208925	−	0.132283i
$226$		−	0.899589i		−	0.0598398i
$227$	7.40106	−	7.40106i	0.491226	−	0.491226i	−0.417466	−	0.908692i	$-0.637082\pi$
$227$	7.40106	−	7.40106i	0.491226	−	0.491226i	0.908692	+	0.417466i	$0.137082\pi$
$228$	−11.2143	−	11.2143i	−0.742682	−	0.742682i
$229$			15.2542i			1.00802i	0.863696	+	0.504012i	$0.168143\pi$
$229$			15.2542i			1.00802i	−0.863696	+	0.504012i	$0.831857\pi$
$230$	8.47597	+	4.66545i	0.558889	+	0.307631i
$231$		0			0
$232$	14.2751	+	14.2751i	0.937203	+	0.937203i
$233$	−3.55430	−	3.55430i	−0.232850	−	0.232850i	0.581031	−	0.813881i	$-0.302649\pi$
$233$	−3.55430	−	3.55430i	−0.232850	−	0.232850i	−0.813881	+	0.581031i	$0.802649\pi$
$234$			0.0953270i			0.00623172i
$235$	−0.719403	+	0.208600i	−0.0469286	+	0.0136075i
$236$	8.43489			0.549065
$237$	5.86982	−	5.86982i	0.381286	−	0.381286i
$238$	−2.56240	−	2.56240i	−0.166096	−	0.166096i
$239$	−21.5697			−1.39523			−0.697615	−	0.716473i	$-0.745755\pi$
$239$	−21.5697			−1.39523			−0.697615	+	0.716473i	$0.745755\pi$
$240$	−1.73719	−	5.99107i	−0.112135	−	0.386722i
$241$		−	0.880312i		−	0.0567059i	−0.999598	−	0.0283529i	$-0.990974\pi$
$241$		−	0.880312i		−	0.0567059i	0.999598	−	0.0283529i	$-0.00902623\pi$
$242$		0			0
$243$	−5.31440	+	5.31440i	−0.340919	+	0.340919i
$244$	−23.9283			−1.53185
$245$	−9.07372	−	4.99447i	−0.579699	−	0.319085i
$246$	−4.65653			−0.296890
$247$	0.959242	+	0.959242i	0.0610351	+	0.0610351i
$248$	−9.58894	−	9.58894i	−0.608898	−	0.608898i
$249$	−12.4135			−0.786673
$250$	−4.57501	+	5.17301i	−0.289349	+	0.327170i
$251$	−20.5234			−1.29543			−0.647713	−	0.761884i	$-0.724274\pi$
$251$	−20.5234			−1.29543			−0.647713	+	0.761884i	$0.724274\pi$
$252$	1.30646	−	1.30646i	0.0822990	−	0.0822990i
$253$		0			0
$254$		−	3.36309i		−	0.211019i
$255$	11.2228	+	6.17741i	0.702801	+	0.386845i
$256$	−6.54467			−0.409042
$257$	−3.71243	−	3.71243i	−0.231575	−	0.231575i	0.581775	−	0.813350i	$-0.302358\pi$
$257$	−3.71243	−	3.71243i	−0.231575	−	0.231575i	−0.813350	+	0.581775i	$0.802358\pi$
$258$	−6.81231	+	6.81231i	−0.424116	+	0.424116i
$259$	1.99451			0.123933
$260$	0.209673	+	0.723104i	0.0130034	+	0.0448450i
$261$		−	6.70068i		−	0.414761i
$262$	1.49964	+	1.49964i	0.0926481	+	0.0926481i
$263$	−3.74008	−	3.74008i	−0.230623	−	0.230623i	0.582330	−	0.812953i	$-0.302141\pi$
$263$	−3.74008	−	3.74008i	−0.230623	−	0.230623i	−0.812953	+	0.582330i	$0.802141\pi$
$264$		0			0
$265$	3.29665	+	11.3692i	0.202512	+	0.698406i
$266$			6.19806i			0.380027i
$267$	−9.57882	−	9.57882i	−0.586214	−	0.586214i
$268$	1.80255	−	1.80255i	0.110108	−	0.110108i
$269$			23.3113i			1.42132i	0.703538	+	0.710658i	$0.251603\pi$
$269$			23.3113i			1.42132i	−0.703538	+	0.710658i	$0.748397\pi$
$270$	3.74495	−	6.80364i	0.227910	−	0.414056i
$271$			4.10899i			0.249603i	0.992182	+	0.124802i	$0.0398294\pi$
$271$			4.10899i			0.249603i	−0.992182	+	0.124802i	$0.960171\pi$
$272$	−5.00457	+	5.00457i	−0.303447	+	0.303447i
$273$	0.340168	−	0.340168i	0.0205879	−	0.0205879i
$274$	−6.31483			−0.381493
$275$		0			0
$276$	−17.0370			−1.02551
$277$	−13.3585	+	13.3585i	−0.802632	+	0.802632i	−0.983506	−	0.180875i	$-0.942107\pi$
$277$	−13.3585	+	13.3585i	−0.802632	+	0.802632i	0.180875	+	0.983506i	$0.442107\pi$
$278$	0.348851	−	0.348851i	0.0209227	−	0.0209227i
$279$			4.50102i			0.269469i
$280$	−3.70851	+	6.73744i	−0.221626	+	0.402639i
$281$		−	8.23856i		−	0.491471i	−0.969337	−	0.245736i	$-0.920970\pi$
$281$		−	8.23856i		−	0.491471i	0.969337	−	0.245736i	$-0.0790295\pi$
$282$	−0.219857	+	0.219857i	−0.0130923	+	0.0130923i
$283$	−7.91581	−	7.91581i	−0.470546	−	0.470546i	0.431545	−	0.902091i	$-0.357969\pi$
$283$	−7.91581	−	7.91581i	−0.470546	−	0.470546i	−0.902091	+	0.431545i	$0.857969\pi$
$284$		−	2.22666i		−	0.132128i
$285$	−6.10205	−	21.0443i	−0.361454	−	1.24656i
$286$		0			0
$287$	−5.45883	−	5.45883i	−0.322224	−	0.322224i
$288$	2.94635	+	2.94635i	0.173615	+	0.173615i
$289$			2.46491i			0.144995i
$290$	3.47427	+	11.9818i	0.204016	+	0.703596i
$291$	12.7494			0.747382
$292$	−15.0033	+	15.0033i	−0.878001	+	0.878001i
$293$	−6.89888	−	6.89888i	−0.403037	−	0.403037i	0.476265	−	0.879302i	$-0.341990\pi$
$293$	−6.89888	−	6.89888i	−0.403037	−	0.403037i	−0.879302	+	0.476265i	$0.841990\pi$
$294$	−4.29940			−0.250746
$295$	10.2092	+	5.61946i	0.594401	+	0.327178i
$296$			2.89690i			0.168379i
$297$		0			0
$298$	−3.84415	+	3.84415i	−0.222686	+	0.222686i
$299$	1.45731			0.0842783
$300$	2.66509	−	11.8649i	0.153869	−	0.685020i
$301$	−15.9721			−0.920615
$302$	−2.48748	−	2.48748i	−0.143139	−	0.143139i
$303$	1.85838	+	1.85838i	0.106761	+	0.106761i
$304$	12.1053			0.694287
$305$	−28.9616	−	15.9414i	−1.65833	−	0.912802i
$306$	−1.74696			−0.0998673
$307$	14.8788	−	14.8788i	0.849179	−	0.849179i	−0.140852	−	0.990031i	$-0.544984\pi$
$307$	14.8788	−	14.8788i	0.849179	−	0.849179i	0.990031	+	0.140852i	$0.0449842\pi$
$308$		0			0
$309$			13.3160i			0.757522i
$310$	−2.33376	−	8.04849i	−0.132549	−	0.457124i
$311$	8.79912			0.498952			0.249476	−	0.968381i	$-0.419742\pi$
$311$	8.79912			0.498952			0.249476	+	0.968381i	$0.419742\pi$
$312$	0.494071	+	0.494071i	0.0279713	+	0.0279713i
$313$	−19.4540	+	19.4540i	−1.09961	+	1.09961i	−0.105149	+	0.994456i	$0.533532\pi$
$313$	−19.4540	+	19.4540i	−1.09961	+	1.09961i	−0.994456	+	0.105149i	$0.966468\pi$
$314$	−5.47194			−0.308799
$315$	2.45165	−	0.710887i	0.138135	−	0.0400539i
$316$			8.94065i			0.502951i
$317$	−19.7562	−	19.7562i	−1.10962	−	1.10962i	−0.993201	−	0.116416i	$-0.962859\pi$
$317$	−19.7562	−	19.7562i	−1.10962	−	1.10962i	−0.116416	−	0.993201i	$-0.537141\pi$
$318$	3.47456	+	3.47456i	0.194844	+	0.194844i
$319$		0			0
$320$	0.476922	+	0.262514i	0.0266608	+	0.0146750i
$321$		−	19.7021i		−	1.09967i
$322$	4.70813	+	4.70813i	0.262374	+	0.262374i
$323$	−17.5791	+	17.5791i	−0.978127	+	0.978127i
$324$			10.0736i			0.559644i
$325$	−0.227966	+	1.01490i	−0.0126453	+	0.0562963i
$326$			9.72861i			0.538818i
$327$	−9.86573	+	9.86573i	−0.545576	+	0.545576i
$328$	7.92859	−	7.92859i	0.437783	−	0.437783i
$329$	−0.515475			−0.0284191
$330$		0			0
$331$	9.55622			0.525258			0.262629	−	0.964897i	$-0.415411\pi$
$331$	9.55622			0.525258			0.262629	+	0.964897i	$0.415411\pi$
$332$	9.45383	−	9.45383i	0.518846	−	0.518846i
$333$	0.679898	−	0.679898i	0.0372582	−	0.0372582i
$334$			4.24234i			0.232130i
$335$	3.38261	−	0.980829i	0.184812	−	0.0535884i
$336$		−	4.29280i		−	0.234191i
$337$	−23.3958	+	23.3958i	−1.27445	+	1.27445i	−0.330725	+	0.943727i	$0.607293\pi$
$337$	−23.3958	+	23.3958i	−1.27445	+	1.27445i	−0.943727	+	0.330725i	$0.892707\pi$
$338$	5.65903	+	5.65903i	0.307811	+	0.307811i
$339$			2.18856i			0.118866i
$340$	−13.2516	+	3.84247i	−0.718670	+	0.208387i
$341$		0			0
$342$	2.11282	+	2.11282i	0.114248	+	0.114248i
$343$	−12.6570	−	12.6570i	−0.683413	−	0.683413i
$344$		−	23.1984i		−	1.25077i
$345$	−20.6207	−	11.3503i	−1.11018	−	0.611082i
$346$	−6.77464			−0.364207
$347$	17.1691	−	17.1691i	0.921686	−	0.921686i	−0.0754631	−	0.997149i	$-0.524043\pi$
$347$	17.1691	−	17.1691i	0.921686	−	0.921686i	0.997149	+	0.0754631i	$0.0240435\pi$
$348$	−15.5336	−	15.5336i	−0.832690	−	0.832690i
$349$	−12.3942			−0.663447			−0.331724	−	0.943377i	$-0.607630\pi$
$349$	−12.3942			−0.663447			−0.331724	+	0.943377i	$0.607630\pi$
$350$	−4.01532	+	2.54234i	−0.214628	+	0.135894i
$351$		−	1.16978i		−	0.0624381i
$352$		0			0
$353$	4.53224	−	4.53224i	0.241227	−	0.241227i	−0.576131	−	0.817358i	$-0.695438\pi$
$353$	4.53224	−	4.53224i	0.241227	−	0.241227i	0.817358	+	0.576131i	$0.195438\pi$
$354$	4.83741			0.257105
$355$	1.48344	−	2.69504i	0.0787326	−	0.143038i
$356$	14.5900			0.773269
$357$	6.23392	+	6.23392i	0.329934	+	0.329934i
$358$	2.72623	+	2.72623i	0.144086	+	0.144086i
$359$	10.8781			0.574123			0.287062	−	0.957912i	$-0.407322\pi$
$359$	10.8781			0.574123			0.287062	+	0.957912i	$0.407322\pi$
$360$	1.03252	+	3.56086i	0.0544184	+	0.187674i
$361$	23.5212			1.23796
$362$	6.03732	−	6.03732i	0.317315	−	0.317315i
$363$		0			0
$364$			0.518128i			0.0271573i
$365$	−28.1547	+	8.16379i	−1.47368	+	0.427312i
$366$	−13.7228			−0.717305
$367$	3.77393	+	3.77393i	0.196998	+	0.196998i	0.798712	−	0.601714i	$-0.205515\pi$
$367$	3.77393	+	3.77393i	0.196998	+	0.196998i	−0.601714	+	0.798712i	$0.705515\pi$
$368$	9.19536	−	9.19536i	0.479341	−	0.479341i
$369$	−3.72166			−0.193742
$370$	−0.863234	+	1.56828i	−0.0448774	+	0.0815311i
$371$			8.14643i			0.422941i
$372$	10.4344	+	10.4344i	0.540996	+	0.540996i
$373$	3.06257	+	3.06257i	0.158574	+	0.158574i	0.781934	−	0.623361i	$-0.214233\pi$
$373$	3.06257	+	3.06257i	0.158574	+	0.158574i	−0.623361	+	0.781934i	$0.714233\pi$
$374$		0			0
$375$	11.1303	−	12.5852i	0.574766	−	0.649894i
$376$		−	0.748695i		−	0.0386110i
$377$	1.32871	+	1.32871i	0.0684321	+	0.0684321i
$378$	3.77920	−	3.77920i	0.194381	−	0.194381i
$379$		−	3.57034i		−	0.183396i	−0.995787	−	0.0916981i	$-0.970771\pi$
$379$		−	3.57034i		−	0.183396i	0.995787	−	0.0916981i	$-0.0292295\pi$
$380$	20.6740	+	11.3797i	1.06056	+	0.583765i
$381$			8.18189i			0.419171i
$382$	−7.22539	+	7.22539i	−0.369683	+	0.369683i
$383$	5.00566	−	5.00566i	0.255777	−	0.255777i	−0.567557	−	0.823334i	$-0.692111\pi$
$383$	5.00566	−	5.00566i	0.255777	−	0.255777i	0.823334	+	0.567557i	$0.192111\pi$
$384$	17.1068			0.872977
$385$		0			0
$386$	−13.1211			−0.667844
$387$	−5.44463	+	5.44463i	−0.276766	+	0.276766i
$388$	−9.70964	+	9.70964i	−0.492932	+	0.492932i
$389$			12.9384i			0.656001i	0.944678	+	0.328000i	$0.106375\pi$
$389$			12.9384i			0.656001i	−0.944678	+	0.328000i	$0.893625\pi$
$390$	0.120247	+	0.414700i	0.00608896	+	0.0209992i
$391$			26.7067i			1.35061i
$392$	7.32051	−	7.32051i	0.369741	−	0.369741i
$393$	−3.64840	−	3.64840i	−0.184037	−	0.184037i
$394$		−	10.5123i		−	0.529604i
$395$	−5.95641	+	10.8213i	−0.299699	+	0.544479i
$396$		0			0
$397$	9.28740	+	9.28740i	0.466121	+	0.466121i	0.900655	−	0.434534i	$-0.143087\pi$
$397$	9.28740	+	9.28740i	0.466121	+	0.466121i	−0.434534	+	0.900655i	$0.643087\pi$
$398$	1.74265	+	1.74265i	0.0873513	+	0.0873513i
$399$		−	15.0789i		−	0.754890i
$400$	4.96540	+	7.84225i	0.248270	+	0.392113i
$401$	−7.59340			−0.379196			−0.189598	−	0.981862i	$-0.560719\pi$
$401$	−7.59340			−0.379196			−0.189598	+	0.981862i	$0.560719\pi$
$402$	1.03376	−	1.03376i	0.0515594	−	0.0515594i
$403$	−0.892531	−	0.892531i	−0.0444601	−	0.0444601i
$404$	−2.83059			−0.140827
$405$	−6.71119	+	12.1926i	−0.333482	+	0.605854i
$406$			8.58535i			0.426084i
$407$		0			0
$408$	−9.05437	+	9.05437i	−0.448258	+	0.448258i
$409$	4.98518			0.246501			0.123251	−	0.992376i	$-0.460668\pi$
$409$	4.98518			0.246501			0.123251	+	0.992376i	$0.460668\pi$
$410$	6.65488	−	1.92966i	0.328661	−	0.0952994i
$411$	15.3630			0.757802
$412$	−10.1412	−	10.1412i	−0.499620	−	0.499620i
$413$	5.67087	+	5.67087i	0.279045	+	0.279045i
$414$	3.20986			0.157756
$415$	17.7407	−	5.14415i	0.870859	−	0.252516i
$416$	−1.16849			−0.0572901
$417$	−0.848701	+	0.848701i	−0.0415611	+	0.0415611i
$418$		0			0
$419$			31.6286i			1.54516i	0.634917	+	0.772580i	$0.281034\pi$
$419$			31.6286i			1.54516i	−0.634917	+	0.772580i	$0.718966\pi$
$420$	4.03547	−	7.33145i	0.196911	−	0.357738i
$421$	38.8972			1.89573			0.947866	−	0.318670i	$-0.103236\pi$
$421$	38.8972			1.89573			0.947866	+	0.318670i	$0.103236\pi$
$422$	−0.494234	−	0.494234i	−0.0240589	−	0.0240589i
$423$	−0.175718	+	0.175718i	−0.00854369	+	0.00854369i
$424$	−11.8322			−0.574620
$425$	−18.5990	−	4.17772i	−0.902185	−	0.202649i
$426$		−	1.27699i		−	0.0618703i
$427$	−16.0872	−	16.0872i	−0.778515	−	0.778515i
$428$	15.0047	+	15.0047i	0.725279	+	0.725279i
$429$		0			0
$430$	6.91279	−	12.5588i	0.333364	−	0.605641i
$431$			14.8188i			0.713799i	0.934143	+	0.356899i	$0.116166\pi$
$431$			14.8188i			0.713799i	−0.934143	+	0.356899i	$0.883834\pi$
$432$	−7.38109	−	7.38109i	−0.355123	−	0.355123i
$433$	24.4210	−	24.4210i	1.17360	−	1.17360i	0.192253	−	0.981345i	$-0.438421\pi$
$433$	24.4210	−	24.4210i	1.17360	−	1.17360i	0.981345	−	0.192253i	$-0.0615793\pi$
$434$		−	5.76701i		−	0.276825i
$435$	−8.45237	−	29.1499i	−0.405260	−	1.39763i
$436$		−	15.0270i		−	0.719664i
$437$	32.2997	−	32.2997i	1.54510	−	1.54510i
$438$	−8.60438	+	8.60438i	−0.411133	+	0.411133i
$439$	−5.16472			−0.246499			−0.123249	−	0.992376i	$-0.539332\pi$
$439$	−5.16472			−0.246499			−0.123249	+	0.992376i	$0.539332\pi$
$440$		0			0
$441$	−3.43623			−0.163630
$442$	0.346415	−	0.346415i	0.0164773	−	0.0164773i
$443$	−24.3973	+	24.3973i	−1.15915	+	1.15915i	−0.174492	+	0.984659i	$0.555828\pi$
$443$	−24.3973	+	24.3973i	−1.15915	+	1.15915i	−0.984659	+	0.174492i	$0.944172\pi$
$444$		−	3.15230i		−	0.149602i
$445$	17.6590	+	9.72011i	0.837118	+	0.460777i
$446$			13.0811i			0.619407i
$447$	9.35223	−	9.35223i	0.442345	−	0.442345i
$448$	0.264915	+	0.264915i	0.0125161	+	0.0125161i
$449$			13.5203i			0.638060i	0.947745	+	0.319030i	$0.103357\pi$
$449$			13.5203i			0.638060i	−0.947745	+	0.319030i	$0.896643\pi$
$450$	−0.502117	+	2.23541i	−0.0236700	+	0.105378i
$451$		0			0
$452$	−1.66676	−	1.66676i	−0.0783978	−	0.0783978i
$453$	6.05166	+	6.05166i	0.284332	+	0.284332i
$454$			6.46504i			0.303419i
$455$	−0.345185	+	0.627116i	−0.0161825	+	0.0293996i
$456$	21.9012			1.02562
$457$	10.7421	−	10.7421i	0.502494	−	0.502494i	−0.409718	−	0.912212i	$-0.634373\pi$
$457$	10.7421	−	10.7421i	0.502494	−	0.502494i	0.912212	+	0.409718i	$0.134373\pi$
$458$	−6.66248	−	6.66248i	−0.311317	−	0.311317i
$459$	21.4374			1.00061
$460$	24.3484	−	7.06013i	1.13525	−	0.329180i
$461$			4.03102i			0.187744i	0.995584	+	0.0938718i	$0.0299244\pi$
$461$			4.03102i			0.187744i	−0.995584	+	0.0938718i	$0.970076\pi$
$462$		0			0
$463$	8.70734	−	8.70734i	0.404665	−	0.404665i	−0.475209	−	0.879873i	$-0.657627\pi$
$463$	8.70734	−	8.70734i	0.404665	−	0.404665i	0.879873	+	0.475209i	$0.157627\pi$
$464$	16.7679			0.778430
$465$	5.67768	+	19.5808i	0.263296	+	0.908036i
$466$	3.10478			0.143826
$467$	−21.2968	−	21.2968i	−0.985496	−	0.985496i	0.0144001	−	0.999896i	$-0.495416\pi$
$467$	−21.2968	−	21.2968i	−0.985496	−	0.985496i	−0.999896	+	0.0144001i	$0.995416\pi$
$468$	0.176622	+	0.176622i	0.00816435	+	0.00816435i
$469$	2.42375			0.111918
$470$	0.223100	−	0.405318i	0.0102909	−	0.0186959i
$471$	13.3124			0.613403
$472$	−8.23657	+	8.23657i	−0.379119	+	0.379119i
$473$		0			0
$474$			5.12746i			0.235512i
$475$	17.4415	+	27.5468i	0.800271	+	1.26393i
$476$	−9.49522			−0.435213
$477$	2.77699	+	2.77699i	0.127150	+	0.127150i
$478$	9.42088	−	9.42088i	0.430901	−	0.430901i
$479$	−11.0337			−0.504141			−0.252071	−	0.967709i	$-0.581112\pi$
$479$	−11.0337			−0.504141			−0.252071	+	0.967709i	$0.581112\pi$
$480$	16.5341	+	9.10090i	0.754674	+	0.415397i
$481$			0.269641i			0.0122946i
$482$	0.384489	+	0.384489i	0.0175130	+	0.0175130i
$483$	−11.4542	−	11.4542i	−0.521182	−	0.521182i
$484$		0			0
$485$	−18.2208	+	5.28334i	−0.827363	+	0.239904i
$486$		−	4.64228i		−	0.210578i
$487$	−12.1632	−	12.1632i	−0.551166	−	0.551166i	0.375611	−	0.926777i	$-0.377433\pi$
$487$	−12.1632	−	12.1632i	−0.551166	−	0.551166i	−0.926777	+	0.375611i	$0.877433\pi$
$488$	23.3656	−	23.3656i	1.05771	−	1.05771i
$489$		−	23.6682i		−	1.07031i
$490$	6.14448	−	1.78167i	0.277580	−	0.0804876i
$491$			43.3958i			1.95842i	0.202838	+	0.979212i	$0.434983\pi$
$491$			43.3958i			1.95842i	−0.202838	+	0.979212i	$0.565017\pi$
$492$	−8.62762	+	8.62762i	−0.388963	+	0.388963i
$493$	−24.3500	+	24.3500i	−1.09667	+	1.09667i
$494$	−0.837925			−0.0377000
$495$		0			0
$496$	−11.2634			−0.505743
$497$	1.49701	−	1.49701i	0.0671499	−	0.0671499i
$498$	5.42177	−	5.42177i	0.242955	−	0.242955i
$499$			3.45460i			0.154649i	0.997006	+	0.0773246i	$0.0246378\pi$
$499$			3.45460i			0.154649i	−0.997006	+	0.0773246i	$0.975362\pi$
$500$	1.10799	+	18.0611i	0.0495508	+	0.807719i
$501$		−	10.3210i		−	0.461106i
$502$	8.96389	−	8.96389i	0.400078	−	0.400078i
$503$	13.3908	+	13.3908i	0.597067	+	0.597067i	0.939531	−	0.342464i	$-0.111261\pi$
$503$	13.3908	+	13.3908i	0.597067	+	0.597067i	−0.342464	+	0.939531i	$0.611261\pi$
$504$			2.55148i			0.113652i
$505$	−3.42601	−	1.88579i	−0.152455	−	0.0839165i
$506$		0			0
$507$	−13.7676	−	13.7676i	−0.611439	−	0.611439i
$508$	−6.23114	−	6.23114i	−0.276462	−	0.276462i
$509$			35.2464i			1.56227i	0.624361	+	0.781136i	$0.285359\pi$
$509$			35.2464i			1.56227i	−0.624361	+	0.781136i	$0.714641\pi$
$510$	−7.59980	+	2.20366i	−0.336525	+	0.0975796i
$511$	−20.1737			−0.892433
$512$	−13.2408	+	13.2408i	−0.585166	+	0.585166i
$513$	−25.9269	−	25.9269i	−1.14470	−	1.14470i
$514$	3.24291			0.143039
$515$	−5.51816	−	19.0306i	−0.243159	−	0.838589i
$516$			25.2437i			1.11129i
$517$		0			0
$518$	−0.871130	+	0.871130i	−0.0382753	+	0.0382753i
$519$	16.4817			0.723465
$520$	−0.910845	−	0.501359i	−0.0399432	−	0.0219861i
$521$	−26.7758			−1.17307			−0.586534	−	0.809925i	$-0.699508\pi$
$521$	−26.7758			−1.17307			−0.586534	+	0.809925i	$0.699508\pi$
$522$	2.92662	+	2.92662i	0.128094	+	0.128094i
$523$	−2.88246	−	2.88246i	−0.126041	−	0.126041i	0.641272	−	0.767314i	$-0.278407\pi$
$523$	−2.88246	−	2.88246i	−0.126041	−	0.126041i	−0.767314	+	0.641272i	$0.778407\pi$
$524$	5.55707			0.242762
$525$	9.76867	−	6.18513i	0.426340	−	0.269941i
$526$	3.26706			0.142451
$527$	16.3565	−	16.3565i	0.712502	−	0.712502i
$528$		0			0
$529$		−	26.0706i		−	1.13351i
$530$	−6.40553	−	3.52582i	−0.278239	−	0.153152i
$531$	3.86622			0.167780
$532$	11.4838	+	11.4838i	0.497884	+	0.497884i
$533$	0.737987	−	0.737987i	0.0319658	−	0.0319658i
$534$	8.36737			0.362091
$535$	8.16456	+	28.1573i	0.352985	+	1.21735i
$536$			3.52034i			0.152055i
$537$	−6.63251	−	6.63251i	−0.286214	−	0.286214i
$538$	−10.1815	−	10.1815i	−0.438958	−	0.438958i
$539$		0			0
$540$	−5.66715	−	19.5444i	−0.243875	−	0.841059i
$541$		−	7.86922i		−	0.338324i	−0.985588	−	0.169162i	$-0.945894\pi$
$541$		−	7.86922i		−	0.338324i	0.985588	−	0.169162i	$-0.0541061\pi$
$542$	−1.79466	−	1.79466i	−0.0770872	−	0.0770872i
$543$	−14.6879	+	14.6879i	−0.630317	+	0.630317i
$544$		−	21.4139i		−	0.918112i
$545$	10.0113	−	18.1880i	0.428835	−	0.779087i
$546$			0.297146i			0.0127167i
$547$	11.4338	−	11.4338i	0.488872	−	0.488872i	−0.419078	−	0.907950i	$-0.637647\pi$
$547$	11.4338	−	11.4338i	0.488872	−	0.488872i	0.907950	+	0.419078i	$0.137647\pi$
$548$	−11.7001	+	11.7001i	−0.499805	+	0.499805i
$549$	−10.9678			−0.468093
$550$		0			0
$551$	58.8990			2.50918
$552$	16.6364	−	16.6364i	0.708093	−	0.708093i
$553$	−6.01089	+	6.01089i	−0.255609	+	0.255609i
$554$		−	11.6690i		−	0.495768i
$555$	2.10012	−	3.81539i	0.0891450	−	0.161954i
$556$		−	1.29270i		−	0.0548228i
$557$	22.0004	−	22.0004i	0.932187	−	0.932187i	−0.0656557	−	0.997842i	$-0.520914\pi$
$557$	22.0004	−	22.0004i	0.932187	−	0.932187i	0.997842	+	0.0656557i	$0.0209139\pi$
$558$	−1.96589	−	1.96589i	−0.0832226	−	0.0832226i
$559$		−	2.15929i		−	0.0913282i
$560$	1.77893	+	6.13505i	0.0751737	+	0.259253i
$561$		0			0
$562$	3.59831	+	3.59831i	0.151786	+	0.151786i
$563$	−9.01316	−	9.01316i	−0.379859	−	0.379859i	0.491192	−	0.871051i	$-0.336561\pi$
$563$	−9.01316	−	9.01316i	−0.379859	−	0.379859i	−0.871051	+	0.491192i	$0.836561\pi$
$564$			0.814704i			0.0343052i
$565$	−0.906940	−	3.12779i	−0.0381553	−	0.131587i
$566$	6.91469			0.290646
$567$	−6.77258	+	6.77258i	−0.284422	+	0.284422i
$568$	2.17430	+	2.17430i	0.0912318	+	0.0912318i
$569$	9.93860			0.416648			0.208324	−	0.978060i	$-0.433199\pi$
$569$	9.93860			0.416648			0.208324	+	0.978060i	$0.433199\pi$
$570$	11.8566	+	6.52624i	0.496616	+	0.273354i
$571$		−	21.5089i		−	0.900120i	−0.892998	−	0.450060i	$-0.851403\pi$
$571$		−	21.5089i		−	0.900120i	0.892998	−	0.450060i	$-0.148597\pi$
$572$		0			0
$573$	17.5783	−	17.5783i	0.734343	−	0.734343i
$574$	4.76844			0.199031
$575$	34.1737	+	7.67610i	1.42514	+	0.320116i
$576$	0.180611			0.00752545
$577$	7.59993	+	7.59993i	0.316389	+	0.316389i	0.847379	−	0.530989i	$-0.178180\pi$
$577$	7.59993	+	7.59993i	0.316389	+	0.316389i	−0.530989	+	0.847379i	$0.678180\pi$
$578$	−1.07659	−	1.07659i	−0.0447801	−	0.0447801i
$579$	31.9215			1.32661
$580$	28.6370	+	15.7628i	1.18909	+	0.654513i
$581$	12.7118			0.527375
$582$	−5.56847	+	5.56847i	−0.230821	+	0.230821i
$583$		0			0
$584$		−	29.3010i		−	1.21249i
$585$	0.0961059	+	0.331443i	0.00397349	+	0.0137035i
$586$	6.02637			0.248947
$587$	−16.7593	−	16.7593i	−0.691729	−	0.691729i	0.270883	−	0.962612i	$-0.412684\pi$
$587$	−16.7593	−	16.7593i	−0.691729	−	0.691729i	−0.962612	+	0.270883i	$0.912684\pi$
$588$	−7.96593	+	7.96593i	−0.328509	+	0.328509i
$589$	−39.5640			−1.63021
$590$	−6.91338	+	2.00462i	−0.284619	+	0.0825289i
$591$			25.5749i			1.05201i
$592$	1.70139	+	1.70139i	0.0699266	+	0.0699266i
$593$	−31.7567	−	31.7567i	−1.30409	−	1.30409i	−0.925608	−	0.378485i	$-0.876445\pi$
$593$	−31.7567	−	31.7567i	−1.30409	−	1.30409i	−0.378485	−	0.925608i	$-0.623555\pi$
$594$		0			0
$595$	−11.4925	−	6.32587i	−0.471148	−	0.259336i
$596$			14.2449i			0.583493i
$597$	−4.23961	−	4.23961i	−0.173516	−	0.173516i
$598$	−0.636500	+	0.636500i	−0.0260284	+	0.0260284i
$599$		−	29.3394i		−	1.19878i	−0.800459	−	0.599388i	$-0.795411\pi$
$599$		−	29.3394i		−	1.19878i	0.800459	−	0.599388i	$-0.204589\pi$
$600$	8.98350	+	14.1884i	0.366750	+	0.579237i
$601$			4.56165i			0.186074i	0.995663	+	0.0930368i	$0.0296574\pi$
$601$			4.56165i			0.186074i	−0.995663	+	0.0930368i	$0.970343\pi$
$602$	6.97603	−	6.97603i	0.284322	−	0.284322i
$603$	0.826219	−	0.826219i	0.0336462	−	0.0336462i
$604$	−9.21762			−0.375060
$605$		0			0
$606$	−1.62334			−0.0659439
$607$	28.5816	−	28.5816i	1.16009	−	1.16009i	0.175639	−	0.984455i	$-0.443801\pi$
$607$	28.5816	−	28.5816i	1.16009	−	1.16009i	0.984455	−	0.175639i	$-0.0561990\pi$
$608$	−25.8985	+	25.8985i	−1.05032	+	1.05032i
$609$		−	20.8868i		−	0.846378i
$610$	19.6120	−	5.68674i	0.794067	−	0.230249i
$611$		−	0.0696879i		−	0.00281927i
$612$	−3.23678	+	3.23678i	−0.130839	+	0.130839i
$613$	3.07151	+	3.07151i	0.124057	+	0.124057i	0.766409	−	0.642352i	$-0.222041\pi$
$613$	3.07151	+	3.07151i	0.124057	+	0.124057i	−0.642352	+	0.766409i	$0.722041\pi$
$614$			12.9971i			0.524519i
$615$	−16.1903	+	4.69458i	−0.652856	+	0.189304i
$616$		0			0
$617$	−12.4130	−	12.4130i	−0.499729	−	0.499729i	0.411624	−	0.911354i	$-0.364962\pi$
$617$	−12.4130	−	12.4130i	−0.499729	−	0.499729i	−0.911354	+	0.411624i	$0.864962\pi$
$618$	−5.81596	−	5.81596i	−0.233952	−	0.233952i
$619$		−	30.1600i		−	1.21223i	−0.795376	−	0.606117i	$-0.792726\pi$
$619$		−	30.1600i		−	1.21223i	0.795376	−	0.606117i	$-0.207274\pi$
$620$	−19.2362	−	10.5883i	−0.772546	−	0.425235i
$621$	−39.3889			−1.58062
$622$	−3.84314	+	3.84314i	−0.154096	+	0.154096i
$623$	9.80902	+	9.80902i	0.392990	+	0.392990i
$624$	0.580350			0.0232326
$625$	−10.6916	+	22.5985i	−0.427663	+	0.903938i
$626$		−	16.9936i		−	0.679202i
$627$		0			0
$628$	−10.1384	+	10.1384i	−0.404567	+	0.404567i
$629$	−4.94145			−0.197028
$630$	−0.760304	+	1.38128i	−0.0302912	+	0.0550316i
$631$	−47.7205			−1.89972			−0.949862	−	0.312669i	$-0.898777\pi$
$631$	−47.7205			−1.89972			−0.949862	+	0.312669i	$0.898777\pi$
$632$	−8.73043	−	8.73043i	−0.347278	−	0.347278i
$633$	1.20240	+	1.20240i	0.0477909	+	0.0477909i
$634$	17.2576			0.685386
$635$	−3.39057	−	11.6932i	−0.134551	−	0.464029i
$636$	12.8753			0.510541
$637$	0.681387	−	0.681387i	0.0269976	−	0.0269976i
$638$		0			0
$639$		−	1.02061i		−	0.0403748i
$640$	−24.4482	+	7.08904i	−0.966398	+	0.280219i
$641$	−16.3102			−0.644216			−0.322108	−	0.946703i	$-0.604391\pi$
$641$	−16.3102			−0.644216			−0.322108	+	0.946703i	$0.604391\pi$
$642$	8.60519	+	8.60519i	0.339620	+	0.339620i
$643$	−19.2380	+	19.2380i	−0.758672	+	0.758672i	−0.976081	−	0.217409i	$-0.930240\pi$
$643$	−19.2380	+	19.2380i	−0.758672	+	0.758672i	0.217409	+	0.976081i	$0.430240\pi$
$644$	17.4465			0.687487
$645$	−16.8178	+	30.5537i	−0.662199	+	1.20305i
$646$		−	15.3558i		−	0.604168i
$647$	7.40310	+	7.40310i	0.291046	+	0.291046i	0.837493	−	0.546448i	$-0.184020\pi$
$647$	7.40310	+	7.40310i	0.291046	+	0.291046i	−0.546448	+	0.837493i	$0.684020\pi$
$648$	−9.83674	−	9.83674i	−0.386424	−	0.386424i
$649$		0			0
$650$	−0.343703	−	0.542838i	−0.0134811	−	0.0212919i
$651$			14.0303i			0.549889i
$652$	18.0252	+	18.0252i	0.705920	+	0.705920i
$653$	17.1609	−	17.1609i	0.671558	−	0.671558i	−0.286517	−	0.958075i	$-0.592498\pi$
$653$	17.1609	−	17.1609i	0.671558	−	0.671558i	0.958075	+	0.286517i	$0.0924976\pi$
$654$		−	8.61800i		−	0.336990i
$655$	6.72600	+	3.70221i	0.262807	+	0.144657i
$656$		−	9.31315i		−	0.363617i
$657$	−6.87692	+	6.87692i	−0.268294	+	0.268294i
$658$	0.225141	−	0.225141i	0.00877692	−	0.00877692i
$659$	34.3924			1.33974			0.669870	−	0.742479i	$-0.266350\pi$
$659$	34.3924			1.33974			0.669870	+	0.742479i	$0.266350\pi$
$660$		0			0
$661$	−22.5208			−0.875958			−0.437979	−	0.898985i	$-0.644306\pi$
$661$	−22.5208			−0.875958			−0.437979	+	0.898985i	$0.644306\pi$
$662$	−4.17382	+	4.17382i	−0.162220	+	0.162220i
$663$	−0.842774	+	0.842774i	−0.0327306	+	0.0327306i
$664$			18.4631i			0.716507i
$665$	6.24870	+	21.5500i	0.242314	+	0.835675i
$666$			0.593910i			0.0230136i
$667$	44.7405	−	44.7405i	1.73236	−	1.73236i
$668$	7.86020	+	7.86020i	0.304120	+	0.304120i
$669$		−	31.8243i		−	1.23040i
$670$	−1.04901	+	1.90579i	−0.0405268	+	0.0736272i
$671$		0			0
$672$	9.18414	+	9.18414i	0.354286	+	0.354286i
$673$	17.9542	+	17.9542i	0.692082	+	0.692082i	0.962690	−	0.270608i	$-0.0872246\pi$
$673$	17.9542	+	17.9542i	0.692082	+	0.692082i	−0.270608	+	0.962690i	$0.587225\pi$
$674$		−	20.4369i		−	0.787201i
$675$	6.16159	−	27.4312i	0.237160	−	1.05583i
$676$	20.9701			0.806543
$677$	−1.62324	+	1.62324i	−0.0623860	+	0.0623860i	−0.737611	−	0.675225i	$-0.764046\pi$
$677$	−1.62324	+	1.62324i	−0.0623860	+	0.0623860i	0.675225	+	0.737611i	$0.264046\pi$
$678$	−0.955886	−	0.955886i	−0.0367106	−	0.0367106i
$679$	−13.0558			−0.501035
$680$	9.18792	−	16.6922i	0.352341	−	0.640116i
$681$		−	15.7285i		−	0.602716i
$682$		0			0
$683$	10.2462	−	10.2462i	0.392058	−	0.392058i	−0.483362	−	0.875420i	$-0.660585\pi$
$683$	10.2462	−	10.2462i	0.392058	−	0.392058i	0.875420	+	0.483362i	$0.160585\pi$
$684$	7.82928			0.299360
$685$	−21.9561	+	6.36643i	−0.838898	+	0.243249i
$686$	11.0562			0.422129
$687$	16.2088	+	16.2088i	0.618404	+	0.618404i
$688$	−13.6247	−	13.6247i	−0.519439	−	0.519439i
$689$	−1.10133			−0.0419573
$690$	13.9638	−	4.04898i	0.531594	−	0.154142i
$691$	−18.2583			−0.694580			−0.347290	−	0.937758i	$-0.612898\pi$
$691$	−18.2583			−0.694580			−0.347290	+	0.937758i	$0.612898\pi$
$692$	−12.5521	+	12.5521i	−0.477158	+	0.477158i
$693$		0			0
$694$			14.9977i			0.569305i
$695$	0.861220	−	1.56462i	0.0326679	−	0.0593495i
$696$	30.3368			1.14991
$697$	13.5244	+	13.5244i	0.512272	+	0.512272i
$698$	5.41335	−	5.41335i	0.204898	−	0.204898i
$699$	−7.55345			−0.285698
$700$	−2.72914	+	12.1500i	−0.103152	+	0.459229i
$701$		−	14.9531i		−	0.564771i	−0.959301	−	0.282386i	$-0.908874\pi$
$701$		−	14.9531i		−	0.564771i	0.959301	−	0.282386i	$-0.0911258\pi$
$702$	0.510917	+	0.510917i	0.0192833	+	0.0192833i
$703$	5.97631	+	5.97631i	0.225401	+	0.225401i
$704$		0			0
$705$	−0.542769	+	0.986077i	−0.0204419	+	0.0371378i
$706$			3.95904i			0.149001i
$707$	−1.90304	−	1.90304i	−0.0715711	−	0.0715711i
$708$	8.96275	−	8.96275i	0.336841	−	0.336841i
$709$		−	27.0118i		−	1.01445i	−0.861814	−	0.507224i	$-0.830672\pi$
$709$		−	27.0118i		−	1.01445i	0.861814	−	0.507224i	$-0.169328\pi$
$710$	0.529183	+	1.82501i	0.0198599	+	0.0684913i
$711$			4.09804i			0.153689i
$712$	−14.2470	+	14.2470i	−0.533928	+	0.533928i
$713$	−30.0534	+	30.0534i	−1.12551	+	1.12551i
$714$	−5.44551			−0.203793
$715$		0			0
$716$	10.1023			0.377542
$717$	−22.9196	+	22.9196i	−0.855947	+	0.855947i
$718$	−4.75116	+	4.75116i	−0.177312	+	0.177312i
$719$			33.7792i			1.25975i	0.776696	+	0.629876i	$0.216894\pi$
$719$			33.7792i			1.25975i	−0.776696	+	0.629876i	$0.783106\pi$
$720$	2.69776	+	1.48493i	0.100540	+	0.0553403i
$721$		−	13.6360i		−	0.507833i
$722$	−10.2732	+	10.2732i	−0.382330	+	0.382330i
$723$	−0.935402	−	0.935402i	−0.0347880	−	0.0347880i
$724$		−	22.3719i		−	0.831446i
$725$	24.1594	+	38.1569i	0.897258	+	1.41711i
$726$		0			0
$727$	3.25083	+	3.25083i	0.120567	+	0.120567i	0.764816	−	0.644249i	$-0.222830\pi$
$727$	3.25083	+	3.25083i	0.120567	+	0.120567i	−0.644249	+	0.764816i	$0.722830\pi$
$728$	−0.505945	−	0.505945i	−0.0187516	−	0.0187516i
$729$			29.9663i			1.10986i
$730$	8.73129	−	15.8626i	0.323160	−	0.587101i
$731$	39.5712			1.46359
$732$	−25.4257	+	25.4257i	−0.939761	+	0.939761i
$733$	−28.4959	−	28.4959i	−1.05252	−	1.05252i	−0.998542	−	0.0539794i	$-0.982809\pi$
$733$	−28.4959	−	28.4959i	−1.05252	−	1.05252i	−0.0539794	−	0.998542i	$-0.517191\pi$
$734$	−3.29664			−0.121681
$735$	−14.9486	+	4.33453i	−0.551387	+	0.159881i
$736$			39.3457i			1.45030i
$737$		0			0
$738$	1.62549	−	1.62549i	0.0598351	−	0.0598351i
$739$	33.4190			1.22934			0.614670	−	0.788785i	$-0.289289\pi$
$739$	33.4190			1.22934			0.614670	+	0.788785i	$0.289289\pi$
$740$	1.30631	+	4.50512i	0.0480210	+	0.165611i
$741$	2.03854			0.0748878
$742$	−3.55807	−	3.55807i	−0.130621	−	0.130621i
$743$	16.0525	+	16.0525i	0.588907	+	0.588907i	0.937335	−	0.348428i	$-0.113284\pi$
$743$	16.0525	+	16.0525i	0.588907	+	0.588907i	−0.348428	+	0.937335i	$0.613284\pi$
$744$	−20.3780			−0.747095
$745$	−9.49018	+	17.2413i	−0.347693	+	0.631672i
$746$	−2.67524			−0.0979476
$747$	4.33327	−	4.33327i	0.158546	−	0.158546i
$748$		0			0
$749$			20.1756i			0.737201i
$750$	0.635432	+	10.3581i	0.0232027	+	0.378223i
$751$	10.7712			0.393045			0.196523	−	0.980499i	$-0.437035\pi$
$751$	10.7712			0.393045			0.196523	+	0.980499i	$0.437035\pi$
$752$	−0.439719	−	0.439719i	−0.0160349	−	0.0160349i
$753$	−21.8078	+	21.8078i	−0.794720	+	0.794720i
$754$	−1.16067			−0.0422690
$755$	−11.1565	−	6.14093i	−0.406028	−	0.223491i
$756$		−	14.0042i		−	0.509329i
$757$	0.254678	+	0.254678i	0.00925643	+	0.00925643i	0.711720	−	0.702463i	$-0.247917\pi$
$757$	0.254678	+	0.254678i	0.00925643	+	0.00925643i	−0.702463	+	0.711720i	$0.747917\pi$
$758$	1.55940	+	1.55940i	0.0566399	+	0.0566399i
$759$		0			0
$760$	−31.3000	+	9.07583i	−1.13537	+	0.329215i
$761$		−	9.07482i		−	0.328962i	−0.986380	−	0.164481i	$-0.947405\pi$
$761$		−	9.07482i		−	0.328962i	0.986380	−	0.164481i	$-0.0525949\pi$
$762$	−3.57356	−	3.57356i	−0.129456	−	0.129456i
$763$	10.1028	−	10.1028i	0.365747	−	0.365747i
$764$			26.7744i			0.968665i
$765$	−6.07403	+	1.76124i	−0.219607	+	0.0636777i
$766$			4.37258i			0.157988i
$767$	−0.766653	+	0.766653i	−0.0276823	+	0.0276823i
$768$	−6.95423	+	6.95423i	−0.250939	+	0.250939i
$769$	31.3668			1.13112			0.565559	−	0.824708i	$-0.308661\pi$
$769$	31.3668			1.13112			0.565559	+	0.824708i	$0.308661\pi$
$770$		0			0
$771$	−7.88951			−0.284134
$772$	−24.3107	+	24.3107i	−0.874961	+	0.874961i
$773$	6.08786	−	6.08786i	0.218965	−	0.218965i	−0.589097	−	0.808062i	$-0.700516\pi$
$773$	6.08786	−	6.08786i	0.218965	−	0.218965i	0.808062	+	0.589097i	$0.200516\pi$
$774$		−	4.75604i		−	0.170952i
$775$	−16.2285	−	25.6310i	−0.582946	−	0.920693i
$776$		−	18.9627i		−	0.680721i
$777$	2.11933	−	2.11933i	0.0760304	−	0.0760304i
$778$	−5.65101	−	5.65101i	−0.202599	−	0.202599i
$779$		−	32.7134i		−	1.17208i
$780$	0.991151	+	0.545562i	0.0354889	+	0.0195343i
$781$		0			0
$782$	−11.6645	−	11.6645i	−0.417122	−	0.417122i
$783$	−35.9131	−	35.9131i	−1.28343	−	1.28343i
$784$		−	8.59888i		−	0.307103i
$785$	−19.0254	+	5.51665i	−0.679046	+	0.196898i
$786$	3.18698			0.113676
$787$	28.9216	−	28.9216i	1.03094	−	1.03094i	0.0314393	−	0.999506i	$-0.489991\pi$
$787$	28.9216	−	28.9216i	1.03094	−	1.03094i	0.999506	−	0.0314393i	$-0.0100091\pi$
$788$	−19.4773	−	19.4773i	−0.693849	−	0.693849i
$789$	−7.94826			−0.282966
$790$	−2.12482	−	7.32791i	−0.0755976	−	0.260715i
$791$		−	2.24116i		−	0.0796865i
$792$		0			0
$793$	2.17486	−	2.17486i	0.0772314	−	0.0772314i
$794$	−8.11281			−0.287913
$795$	15.5837	+	8.57777i	0.552696	+	0.304222i
$796$	6.45758			0.228883
$797$	−19.7206	−	19.7206i	−0.698539	−	0.698539i	0.265557	−	0.964095i	$-0.414444\pi$
$797$	−19.7206	−	19.7206i	−0.698539	−	0.698539i	−0.964095	+	0.265557i	$0.914444\pi$
$798$	6.58593	+	6.58593i	0.233140	+	0.233140i
$799$	1.27710			0.0451807
$800$	−27.4011	−	6.15483i	−0.968774	−	0.217606i
$801$	6.68749			0.236291
$802$	3.31653	−	3.31653i	0.117111	−	0.117111i
$803$		0			0
$804$		−	3.83071i		−	0.135099i
$805$	21.1163	+	11.6231i	0.744252	+	0.409661i
$806$	0.779651			0.0274620
$807$	24.7701	+	24.7701i	0.871951	+	0.871951i
$808$	2.76404	−	2.76404i	0.0972386	−	0.0972386i
$809$	1.64968			0.0579996			0.0289998	−	0.999579i	$-0.490768\pi$
$809$	1.64968			0.0579996			0.0289998	+	0.999579i	$0.490768\pi$
$810$	−2.39407	−	8.25649i	−0.0841191	−	0.290103i
$811$		−	24.5319i		−	0.861430i	−0.902488	−	0.430715i	$-0.858261\pi$
$811$		−	24.5319i		−	0.861430i	0.902488	−	0.430715i	$-0.141739\pi$
$812$	15.9069	+	15.9069i	0.558224	+	0.558224i
$813$	4.36613	+	4.36613i	0.153127	+	0.153127i
$814$		0			0
$815$	9.80810	+	33.8254i	0.343563	+	1.18485i
$816$			10.6355i			0.372318i
$817$	−47.8584	−	47.8584i	−1.67435	−	1.67435i
$818$	−2.17735	+	2.17735i	−0.0761292	+	0.0761292i
$819$			0.237489i			0.00829855i
$820$	8.75488	−	15.9055i	0.305734	−	0.555442i
$821$			11.4601i			0.399961i	0.979800	+	0.199980i	$0.0640878\pi$
$821$			11.4601i			0.399961i	−0.979800	+	0.199980i	$0.935912\pi$
$822$	−6.71002	+	6.71002i	−0.234039	+	0.234039i
$823$	30.0347	−	30.0347i	1.04694	−	1.04694i	0.0481019	−	0.998842i	$-0.484683\pi$
$823$	30.0347	−	30.0347i	1.04694	−	1.04694i	0.998842	−	0.0481019i	$-0.0153172\pi$
$824$	19.8055			0.689957
$825$		0			0
$826$	−4.95366			−0.172360
$827$	19.5793	−	19.5793i	0.680839	−	0.680839i	−0.279350	−	0.960189i	$-0.590119\pi$
$827$	19.5793	−	19.5793i	0.680839	−	0.680839i	0.960189	+	0.279350i	$0.0901190\pi$
$828$	5.94723	−	5.94723i	0.206681	−	0.206681i
$829$			10.0754i			0.349933i	0.984574	+	0.174966i	$0.0559817\pi$
$829$			10.0754i			0.349933i	−0.984574	+	0.174966i	$0.944018\pi$
$830$	−5.50174	+	9.99530i	−0.190968	+	0.346942i
$831$			28.3889i			0.984799i
$832$	−0.0358143	+	0.0358143i	−0.00124164	+	0.00124164i
$833$	12.4871	+	12.4871i	0.432653	+	0.432653i
$834$		−	0.741365i		−	0.0256714i
$835$	4.27700	+	14.7502i	0.148012	+	0.510451i
$836$		0			0
$837$	24.1238	+	24.1238i	0.833840	+	0.833840i
$838$	−13.8143	−	13.8143i	−0.477206	−	0.477206i
$839$		−	25.7110i		−	0.887642i	−0.896115	−	0.443821i	$-0.853623\pi$
$839$		−	25.7110i		−	0.887642i	0.896115	−	0.443821i	$-0.146377\pi$
$840$	3.21848	+	11.0997i	0.111048	+	0.382975i
$841$	52.5851			1.81328
$842$	−16.9889	+	16.9889i	−0.585476	+	0.585476i
$843$	−8.75414	−	8.75414i	−0.301508	−	0.301508i
$844$	−1.83143			−0.0630405
$845$	25.3812	+	13.9706i	0.873139	+	0.480605i
$846$		−	0.153494i		−	0.00527725i
$847$		0			0
$848$	−6.94919	+	6.94919i	−0.238636	+	0.238636i
$849$	−16.8224			−0.577343
$850$	9.94807	−	6.29871i	0.341216	−	0.216044i
$851$	9.07938			0.311237
$852$	−2.36600	−	2.36600i	−0.0810580	−	0.0810580i
$853$	7.46693	+	7.46693i	0.255663	+	0.255663i	0.823287	−	0.567625i	$-0.192138\pi$
$853$	7.46693	+	7.46693i	0.255663	+	0.255663i	−0.567625	+	0.823287i	$0.692138\pi$
$854$	14.0526			0.480871
$855$	9.47617	+	5.21599i	0.324078	+	0.178383i
$856$	−29.3038			−1.00158
$857$	−2.51091	+	2.51091i	−0.0857710	+	0.0857710i	−0.748691	−	0.662920i	$-0.769317\pi$
$857$	−2.51091	+	2.51091i	−0.0857710	+	0.0857710i	0.662920	+	0.748691i	$0.269317\pi$
$858$		0			0
$859$		−	7.36630i		−	0.251335i	−0.992072	−	0.125667i	$-0.959893\pi$
$859$		−	7.36630i		−	0.251335i	0.992072	−	0.125667i	$-0.0401072\pi$
$860$	−10.4610	−	36.0770i	−0.356717	−	1.23022i
$861$	−11.6009			−0.395357
$862$	−6.47234	−	6.47234i	−0.220449	−	0.220449i
$863$	−38.9993	+	38.9993i	−1.32755	+	1.32755i	−0.420050	+	0.907501i	$0.637987\pi$
$863$	−38.9993	+	38.9993i	−1.32755	+	1.32755i	−0.907501	+	0.420050i	$0.862013\pi$
$864$	31.5827			1.07446
$865$	−23.5548	+	6.83000i	−0.800887	+	0.232227i
$866$			21.3324i			0.724906i
$867$	2.61917	+	2.61917i	0.0889517	+	0.0889517i
$868$	−10.6851	−	10.6851i	−0.362677	−	0.362677i
$869$		0			0
$870$	16.4233	+	9.03994i	0.556803	+	0.306483i
$871$			0.327670i			0.0111027i
$872$	14.6737	+	14.6737i	0.496914	+	0.496914i
$873$	−4.45052	+	4.45052i	−0.150627	+	0.150627i
$874$			28.2147i			0.954377i
$875$	−11.3978	+	12.8876i	−0.385315	+	0.435681i
$876$			31.8844i			1.07727i
$877$	−20.1542	+	20.1542i	−0.680558	+	0.680558i	−0.960126	−	0.279568i	$-0.909809\pi$
$877$	−20.1542	+	20.1542i	−0.680558	+	0.680558i	0.279568	+	0.960126i	$0.409809\pi$
$878$	2.25577	−	2.25577i	0.0761284	−	0.0761284i
$879$	−14.6612			−0.494511
$880$		0			0
$881$	−3.27148			−0.110219			−0.0551095	−	0.998480i	$-0.517551\pi$
$881$	−3.27148			−0.110219			−0.0551095	+	0.998480i	$0.517551\pi$
$882$	1.50082	−	1.50082i	0.0505353	−	0.0505353i
$883$	14.5555	−	14.5555i	0.489833	−	0.489833i	−0.418421	−	0.908253i	$-0.637416\pi$
$883$	14.5555	−	14.5555i	0.489833	−	0.489833i	0.908253	+	0.418421i	$0.137416\pi$
$884$		−	1.28367i		−	0.0431746i
$885$	16.8192	−	4.87693i	0.565371	−	0.163936i
$886$		−	21.3117i		−	0.715982i
$887$	−8.66544	+	8.66544i	−0.290957	+	0.290957i	−0.837458	−	0.546501i	$-0.815959\pi$
$887$	−8.66544	+	8.66544i	−0.290957	+	0.290957i	0.546501	+	0.837458i	$0.315959\pi$
$888$	3.07819	+	3.07819i	0.103297	+	0.103297i
$889$		−	8.37853i		−	0.281007i
$890$	−11.9582	+	3.46744i	−0.400841	+	0.116229i
$891$		0			0
$892$	24.2366	+	24.2366i	0.811503	+	0.811503i
$893$	−1.54456	−	1.54456i	−0.0516868	−	0.0516868i
$894$			8.16944i			0.273227i
$895$	12.2274	+	6.73034i	0.408715	+	0.224970i
$896$	−17.5179			−0.585232
$897$	1.54851	−	1.54851i	0.0517031	−	0.0517031i
$898$	−5.90516	−	5.90516i	−0.197058	−	0.197058i
$899$	−54.8029			−1.82778
$900$	3.21144	+	5.07209i	0.107048	+	0.169070i
$901$		−	20.1830i		−	0.672392i
$902$		0			0
$903$	−16.9716	+	16.9716i	−0.564780	+	0.564780i
$904$	3.25514			0.108264
$905$	14.9045	−	27.0778i	0.495444	−	0.900098i
$906$	−5.28630			−0.175626
$907$	18.1910	+	18.1910i	0.604022	+	0.604022i	0.941377	−	0.337355i	$-0.109532\pi$
$907$	18.1910	+	18.1910i	0.604022	+	0.604022i	−0.337355	+	0.941377i	$0.609532\pi$
$908$	11.9784	+	11.9784i	0.397518	+	0.397518i
$909$	−1.29743			−0.0430332
$910$	−0.123137	−	0.424666i	−0.00408196	−	0.0140776i
$911$	44.7681			1.48323			0.741617	−	0.670824i	$-0.234059\pi$
$911$	44.7681			1.48323			0.741617	+	0.670824i	$0.234059\pi$
$912$	12.8629	−	12.8629i	0.425932	−	0.425932i
$913$		0			0
$914$			9.38353i			0.310380i
$915$	−47.7130	+	13.8350i	−1.57734	+	0.457370i
$916$	−24.6885			−0.815731
$917$	3.73608	+	3.73608i	0.123376	+	0.123376i
$918$	−9.36308	+	9.36308i	−0.309028	+	0.309028i
$919$	28.1431			0.928356			0.464178	−	0.885742i	$-0.346350\pi$
$919$	28.1431			0.928356			0.464178	+	0.885742i	$0.346350\pi$
$920$	−16.8818	+	30.6701i	−0.556577	+	1.01116i
$921$		−	31.6199i		−	1.04191i
$922$	−1.76061	−	1.76061i	−0.0579825	−	0.0579825i
$923$	0.202383	+	0.202383i	0.00666151	+	0.00666151i
$924$		0			0
$925$	−1.42028	+	6.32305i	−0.0466987	+	0.207901i
$926$			7.60611i			0.249952i
$927$	−4.64832	−	4.64832i	−0.152671	−	0.152671i
$928$	−35.8737	+	35.8737i	−1.17761	+	1.17761i
$929$			14.1451i			0.464086i	0.972706	+	0.232043i	$0.0745410\pi$
$929$			14.1451i			0.464086i	−0.972706	+	0.232043i	$0.925459\pi$
$930$	−11.0320	−	6.07237i	−0.361753	−	0.199121i
$931$		−	30.2045i		−	0.989912i
$932$	5.75254	−	5.75254i	0.188431	−	0.188431i
$933$	9.34977	−	9.34977i	0.306098	−	0.306098i
$934$	18.6033			0.608719
$935$		0			0
$936$	−0.344938			−0.0112747
$937$	0.973273	−	0.973273i	0.0317954	−	0.0317954i	−0.691030	−	0.722826i	$-0.742843\pi$
$937$	0.973273	−	0.973273i	0.0317954	−	0.0317954i	0.722826	+	0.691030i	$0.242843\pi$
$938$	−1.05861	+	1.05861i	−0.0345647	+	0.0345647i
$939$			41.3429i			1.34917i
$940$	−0.337613	−	1.16433i	−0.0110117	−	0.0379764i
$941$			3.30248i			0.107658i	0.998550	+	0.0538288i	$0.0171425\pi$
$941$			3.30248i			0.107658i	−0.998550	+	0.0538288i	$0.982857\pi$
$942$	−5.81438	+	5.81438i	−0.189443	+	0.189443i
$943$	−24.8496	−	24.8496i	−0.809214	−	0.809214i
$944$			9.67491i			0.314891i
$945$	9.32985	−	16.9500i	0.303500	−	0.551384i
$946$		0			0
$947$	−11.9624	−	11.9624i	−0.388727	−	0.388727i	0.485506	−	0.874233i	$-0.338635\pi$
$947$	−11.9624	−	11.9624i	−0.388727	−	0.388727i	−0.874233	+	0.485506i	$0.838635\pi$
$948$	9.50016	+	9.50016i	0.308551	+	0.308551i
$949$		−	2.72732i		−	0.0885325i
$950$	−19.6493	−	4.41362i	−0.637506	−	0.143197i
$951$	−41.9850			−1.36146
$952$	9.27197	−	9.27197i	0.300506	−	0.300506i
$953$	36.0339	+	36.0339i	1.16725	+	1.16725i	0.982851	+	0.184402i	$0.0590348\pi$
$953$	36.0339	+	36.0339i	1.16725	+	1.16725i	0.184402	+	0.982851i	$0.440965\pi$
$954$	−2.42578			−0.0785376
$955$	−17.8376	+	32.4064i	−0.577210	+	1.04865i
$956$		−	34.9100i		−	1.12907i
$957$		0			0
$958$	4.81911	−	4.81911i	0.155698	−	0.155698i
$959$	−15.7322			−0.508020
$960$	0.785710	−	0.227826i	0.0253587	−	0.00735306i
$961$	5.81254			0.187501
$962$	−0.117770	−	0.117770i	−0.00379704	−	0.00379704i
$963$	6.87756	+	6.87756i	0.221626	+	0.221626i
$964$	1.42476			0.0458885
$965$	−45.6206	+	13.2283i	−1.46858	+	0.425833i
$966$	10.0055			0.321923
$967$	16.1521	−	16.1521i	0.519418	−	0.519418i	−0.397977	−	0.917395i	$-0.630288\pi$
$967$	16.1521	−	16.1521i	0.519418	−	0.519418i	0.917395	+	0.397977i	$0.130288\pi$
$968$		0			0
$969$			37.3584i			1.20013i
$970$	5.65061	−	10.2658i	0.181430	−	0.329614i
$971$	−31.9474			−1.02524			−0.512620	−	0.858615i	$-0.671325\pi$
$971$	−31.9474			−1.02524			−0.512620	+	0.858615i	$0.671325\pi$
$972$	−8.60121	−	8.60121i	−0.275884	−	0.275884i
$973$	0.869098	−	0.869098i	0.0278620	−	0.0278620i
$974$	10.6249			0.340443
$975$	0.836177	+	1.32064i	0.0267791	+	0.0422944i
$976$		−	27.4459i		−	0.878523i
$977$	−1.55095	−	1.55095i	−0.0496192	−	0.0496192i	0.681862	−	0.731481i	$-0.261171\pi$
$977$	−1.55095	−	1.55095i	−0.0496192	−	0.0496192i	−0.731481	+	0.681862i	$0.761171\pi$
$978$	10.3374	+	10.3374i	0.330555	+	0.330555i
$979$		0			0
$980$	8.08343	−	14.6856i	0.258216	−	0.469114i
$981$		−	6.88780i		−	0.219911i
$982$	−18.9537	−	18.9537i	−0.604838	−	0.604838i
$983$	−1.77885	+	1.77885i	−0.0567365	+	0.0567365i	−0.734906	−	0.678169i	$-0.762774\pi$
$983$	−1.77885	+	1.77885i	−0.0567365	+	0.0567365i	0.678169	+	0.734906i	$0.262774\pi$
$984$		−	16.8495i		−	0.537144i
$985$	−10.5982	−	36.5504i	−0.337688	−	1.16459i
$986$		−	21.2704i		−	0.677388i
$987$	−0.547734	+	0.547734i	−0.0174346	+	0.0174346i
$988$	−1.55251	+	1.55251i	−0.0493919	+	0.0493919i
$989$	−72.7078			−2.31197
$990$		0			0
$991$	−31.9224			−1.01405			−0.507025	−	0.861932i	$-0.669255\pi$
$991$	−31.9224			−1.01405			−0.507025	+	0.861932i	$0.669255\pi$
$992$	24.0973	−	24.0973i	0.765091	−	0.765091i
$993$	10.1543	−	10.1543i	0.322236	−	0.322236i
$994$			1.30768i			0.0414770i
$995$	7.81593	+	4.30214i	0.247782	+	0.136387i
$996$		−	20.0909i		−	0.636605i
$997$	−17.9694	+	17.9694i	−0.569097	+	0.569097i	−0.931875	−	0.362778i	$-0.881828\pi$
$997$	−17.9694	+	17.9694i	−0.569097	+	0.569097i	0.362778	+	0.931875i	$0.381828\pi$
$998$	−1.50885	−	1.50885i	−0.0477617	−	0.0477617i
$999$		−	7.28800i		−	0.230582i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.e.c.362.9	✓	40
5.3	odd	4	inner	605.2.e.c.483.12	yes	40
11.2	odd	10		605.2.m.g.282.9		160
11.3	even	5		605.2.m.g.112.12		160
11.4	even	5		605.2.m.g.457.9		160
11.5	even	5		605.2.m.g.602.12		160
11.6	odd	10		605.2.m.g.602.9		160
11.7	odd	10		605.2.m.g.457.12		160
11.8	odd	10		605.2.m.g.112.9		160
11.9	even	5		605.2.m.g.282.12		160
11.10	odd	2	inner	605.2.e.c.362.12	yes	40
55.3	odd	20		605.2.m.g.233.12		160
55.8	even	20		605.2.m.g.233.9		160
55.13	even	20		605.2.m.g.403.12		160
55.18	even	20		605.2.m.g.578.12		160
55.28	even	20		605.2.m.g.118.12		160
55.38	odd	20		605.2.m.g.118.9		160
55.43	even	4	inner	605.2.e.c.483.9	yes	40
55.48	odd	20		605.2.m.g.578.9		160
55.53	odd	20		605.2.m.g.403.9		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.e.c.362.9	✓	40	1.1	even	1	trivial
605.2.e.c.362.12	yes	40	11.10	odd	2	inner
605.2.e.c.483.9	yes	40	55.43	even	4	inner
605.2.e.c.483.12	yes	40	5.3	odd	4	inner
605.2.m.g.112.9		160	11.8	odd	10
605.2.m.g.112.12		160	11.3	even	5
605.2.m.g.118.9		160	55.38	odd	20
605.2.m.g.118.12		160	55.28	even	20
605.2.m.g.233.9		160	55.8	even	20
605.2.m.g.233.12		160	55.3	odd	20
605.2.m.g.282.9		160	11.2	odd	10
605.2.m.g.282.12		160	11.9	even	5
605.2.m.g.403.9		160	55.53	odd	20
605.2.m.g.403.12		160	55.13	even	20
605.2.m.g.457.9		160	11.4	even	5
605.2.m.g.457.12		160	11.7	odd	10
605.2.m.g.578.9		160	55.48	odd	20
605.2.m.g.578.12		160	55.18	even	20
605.2.m.g.602.9		160	11.6	odd	10
605.2.m.g.602.12		160	11.5	even	5

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.436764 + 0.436764i) q^{2} +(1.06258 - 1.06258i) q^{3} +1.61847i q^{4} +(-1.07825 + 1.95892i) q^{5} +0.928194i q^{6} +(-1.08812 + 1.08812i) q^{7} +(-1.58042 - 1.58042i) q^{8} +0.741845i q^{9} +O(q^{10})\)	\(q+(-0.436764 + 0.436764i) q^{2} +(1.06258 - 1.06258i) q^{3} +1.61847i q^{4} +(-1.07825 + 1.95892i) q^{5} +0.928194i q^{6} +(-1.08812 + 1.08812i) q^{7} +(-1.58042 - 1.58042i) q^{8} +0.741845i q^{9} +(-0.384643 - 1.32653i) q^{10} +(1.71976 + 1.71976i) q^{12} +(-0.147104 - 0.147104i) q^{13} -0.950501i q^{14} +(0.935779 + 3.22724i) q^{15} -1.85641 q^{16} +(2.69584 - 2.69584i) q^{17} +(-0.324011 - 0.324011i) q^{18} -6.52083 q^{19} +(-3.17046 - 1.74513i) q^{20} +2.31242i q^{21} +(-4.95331 + 4.95331i) q^{23} -3.35865 q^{24} +(-2.67474 - 4.22443i) q^{25} +0.128500 q^{26} +(3.97601 + 3.97601i) q^{27} +(-1.76109 - 1.76109i) q^{28} -9.03244 q^{29} +(-1.81826 - 1.00083i) q^{30} +6.06733 q^{31} +(3.97165 - 3.97165i) q^{32} +2.35489i q^{34} +(-0.958268 - 3.30480i) q^{35} -1.20066 q^{36} +(-0.916496 - 0.916496i) q^{37} +(2.84806 - 2.84806i) q^{38} -0.312620 q^{39} +(4.80001 - 1.39182i) q^{40} +5.01676i q^{41} +(-1.00998 - 1.00998i) q^{42} +(7.33931 + 7.33931i) q^{43} +(-1.45322 - 0.799898i) q^{45} -4.32686i q^{46} +(0.236866 + 0.236866i) q^{47} +(-1.97258 + 1.97258i) q^{48} +4.63200i q^{49} +(3.01331 + 0.676849i) q^{50} -5.72909i q^{51} +(0.238085 - 0.238085i) q^{52} +(3.74336 - 3.74336i) q^{53} -3.47316 q^{54} +3.43936 q^{56} +(-6.92891 + 6.92891i) q^{57} +(3.94505 - 3.94505i) q^{58} -5.21163i q^{59} +(-5.22321 + 1.51453i) q^{60} +14.7845i q^{61} +(-2.64999 + 2.64999i) q^{62} +(-0.807215 - 0.807215i) q^{63} -0.243462i q^{64} +(0.446781 - 0.129550i) q^{65} +(-1.11373 - 1.11373i) q^{67} +(4.36314 + 4.36314i) q^{68} +10.5266i q^{69} +(1.86196 + 1.02488i) q^{70} -1.37578 q^{71} +(1.17243 - 1.17243i) q^{72} +(9.27002 + 9.27002i) q^{73} +0.800585 q^{74} +(-7.33092 - 1.64667i) q^{75} -10.5538i q^{76} +(0.136541 - 0.136541i) q^{78} +5.52412 q^{79} +(2.00168 - 3.63655i) q^{80} +6.22413 q^{81} +(-2.19114 - 2.19114i) q^{82} +(-5.84120 - 5.84120i) q^{83} -3.74260 q^{84} +(2.37413 + 8.18773i) q^{85} -6.41110 q^{86} +(-9.59770 + 9.59770i) q^{87} -9.01467i q^{89} +(0.984079 - 0.285346i) q^{90} +0.320133 q^{91} +(-8.01681 - 8.01681i) q^{92} +(6.44703 - 6.44703i) q^{93} -0.206909 q^{94} +(7.03111 - 12.7738i) q^{95} -8.44040i q^{96} +(5.99925 + 5.99925i) q^{97} +(-2.02309 - 2.02309i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{3} - 4 q^{5}+O(q^{10}) \) 40 * q + 8 * q^3 - 4 * q^5	\( 40 q + 8 q^{3} - 4 q^{5} - 32 q^{12} + 32 q^{15} - 24 q^{16} + 32 q^{20} - 24 q^{23} - 52 q^{25} - 8 q^{26} + 32 q^{27} + 16 q^{31} - 40 q^{36} + 36 q^{37} + 32 q^{38} + 32 q^{42} + 64 q^{45} + 32 q^{47} - 16 q^{48} - 68 q^{53} + 80 q^{56} + 132 q^{58} - 64 q^{60} - 88 q^{67} - 8 q^{70} - 16 q^{75} - 248 q^{78} - 164 q^{80} - 40 q^{81} + 100 q^{82} - 80 q^{86} - 96 q^{91} - 56 q^{92} + 24 q^{93} - 68 q^{97}+O(q^{100}) \) 40 * q + 8 * q^3 - 4 * q^5 - 32 * q^12 + 32 * q^15 - 24 * q^16 + 32 * q^20 - 24 * q^23 - 52 * q^25 - 8 * q^26 + 32 * q^27 + 16 * q^31 - 40 * q^36 + 36 * q^37 + 32 * q^38 + 32 * q^42 + 64 * q^45 + 32 * q^47 - 16 * q^48 - 68 * q^53 + 80 * q^56 + 132 * q^58 - 64 * q^60 - 88 * q^67 - 8 * q^70 - 16 * q^75 - 248 * q^78 - 164 * q^80 - 40 * q^81 + 100 * q^82 - 80 * q^86 - 96 * q^91 - 56 * q^92 + 24 * q^93 - 68 * q^97

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