LMFDB - Embedded newform 925.2.o.d.174.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(174,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("925.174");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			174.7
Character	$\chi$	$=$	925.174
Dual form			925.2.o.d.824.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20392 + 0.695082i) q^{2} +(-2.14707 - 1.23961i) q^{3} +(-0.0337208 + 0.0584061i) q^{4} +3.44653 q^{6} +(-0.117956 - 0.0681017i) q^{7} -2.87408i q^{8} +(1.57328 + 2.72500i) q^{9} +O(q^{10})$	\(q+(-1.20392 + 0.695082i) q^{2} +(-2.14707 - 1.23961i) q^{3} +(-0.0337208 + 0.0584061i) q^{4} +3.44653 q^{6} +(-0.117956 - 0.0681017i) q^{7} -2.87408i q^{8} +(1.57328 + 2.72500i) q^{9} +1.48686 q^{11} +(0.144802 - 0.0836015i) q^{12} +(-0.00145531 - 0.000840224i) q^{13} +0.189345 q^{14} +(1.93028 + 3.34335i) q^{16} +(-0.902303 + 0.520945i) q^{17} +(-3.78820 - 2.18712i) q^{18} +(-1.74302 + 3.01900i) q^{19} +(0.168839 + 0.292438i) q^{21} +(-1.79005 + 1.03349i) q^{22} +2.30676i q^{23} +(-3.56275 + 6.17087i) q^{24} +0.00233610 q^{26} -0.363355i q^{27} +(0.00795511 - 0.00459289i) q^{28} +2.25018 q^{29} +0.923643 q^{31} +(0.330253 + 0.190671i) q^{32} +(-3.19239 - 1.84313i) q^{33} +(0.724199 - 1.25435i) q^{34} -0.212209 q^{36} +(1.82779 - 5.80165i) q^{37} -4.84618i q^{38} +(0.00208311 + 0.00360805i) q^{39} +(1.89504 - 3.28231i) q^{41} +(-0.406538 - 0.234715i) q^{42} +7.76491i q^{43} +(-0.0501380 + 0.0868416i) q^{44} +(-1.60339 - 2.77715i) q^{46} -5.38040i q^{47} -9.57122i q^{48} +(-3.49072 - 6.04611i) q^{49} +2.58308 q^{51} +(9.81485e-5 - 5.66661e-5i) q^{52} +(-3.40582 + 1.96635i) q^{53} +(0.252561 + 0.437449i) q^{54} +(-0.195730 + 0.339014i) q^{56} +(7.48479 - 4.32134i) q^{57} +(-2.70904 + 1.56406i) q^{58} +(-5.56703 - 9.64239i) q^{59} +(2.01966 - 3.49816i) q^{61} +(-1.11199 + 0.642008i) q^{62} -0.428572i q^{63} -8.25127 q^{64} +5.12450 q^{66} +(-10.8695 - 6.27551i) q^{67} -0.0702667i q^{68} +(2.85949 - 4.95278i) q^{69} +(4.12644 - 7.14720i) q^{71} +(7.83188 - 4.52174i) q^{72} +0.488959i q^{73} +(1.83212 + 8.25518i) q^{74} +(-0.117552 - 0.203606i) q^{76} +(-0.175383 - 0.101257i) q^{77} +(-0.00501578 - 0.00289586i) q^{78} +(-0.658728 + 1.14095i) q^{79} +(4.26942 - 7.39485i) q^{81} +5.26885i q^{82} +(10.6136 - 6.12774i) q^{83} -0.0227736 q^{84} +(-5.39725 - 9.34831i) q^{86} +(-4.83131 - 2.78936i) q^{87} -4.27335i q^{88} +(-4.05665 - 7.02632i) q^{89} +(0.000114441 + 0.000198218i) q^{91} +(-0.134729 - 0.0777857i) q^{92} +(-1.98313 - 1.14496i) q^{93} +(3.73982 + 6.47756i) q^{94} +(-0.472717 - 0.818771i) q^{96} -18.5354i q^{97} +(8.40509 + 4.85268i) q^{98} +(2.33924 + 4.05169i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 22 q^{4} + 20 q^{9}+O(q^{10}) $ 48 * q + 22 * q^4 + 20 * q^9	$ 48 q + 22 q^{4} + 20 q^{9} - 40 q^{14} - 26 q^{16} - 10 q^{19} - 12 q^{21} + 42 q^{24} - 40 q^{26} - 12 q^{29} + 76 q^{31} + 10 q^{34} - 4 q^{36} - 28 q^{39} - 26 q^{41} + 30 q^{44} - 26 q^{46} + 52 q^{49} - 92 q^{51} + 74 q^{54} + 14 q^{59} + 32 q^{61} - 40 q^{64} + 164 q^{66} - 42 q^{69} - 4 q^{71} - 96 q^{74} + 34 q^{76} + 42 q^{79} - 32 q^{81} - 152 q^{84} - 32 q^{86} - 58 q^{89} + 64 q^{91} + 26 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) $ 48 * q + 22 * q^4 + 20 * q^9 - 40 * q^14 - 26 * q^16 - 10 * q^19 - 12 * q^21 + 42 * q^24 - 40 * q^26 - 12 * q^29 + 76 * q^31 + 10 * q^34 - 4 * q^36 - 28 * q^39 - 26 * q^41 + 30 * q^44 - 26 * q^46 + 52 * q^49 - 92 * q^51 + 74 * q^54 + 14 * q^59 + 32 * q^61 - 40 * q^64 + 164 * q^66 - 42 * q^69 - 4 * q^71 - 96 * q^74 + 34 * q^76 + 42 * q^79 - 32 * q^81 - 152 * q^84 - 32 * q^86 - 58 * q^89 + 64 * q^91 + 26 * q^94 + 52 * q^96 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−1.20392	+	0.695082i	−0.851299	+	0.491498i	−0.861089	−	0.508455i	$-0.830217\pi$
$2$	−1.20392	+	0.695082i	−0.851299	+	0.491498i	0.00979016	+	0.999952i	$0.496884\pi$
$3$	−2.14707	−	1.23961i	−1.23961	−	0.715691i	−0.270598	−	0.962692i	$-0.587221\pi$
$3$	−2.14707	−	1.23961i	−1.23961	−	0.715691i	−0.969015	+	0.247002i	$0.920555\pi$
$4$	−0.0337208	+	0.0584061i	−0.0168604	+	0.0292031i
$5$		0			0
$5$		0			0
$6$	3.44653			1.40704
$7$	−0.117956	−	0.0681017i	−0.0445830	−	0.0257400i	0.477543	−	0.878608i	$-0.341528\pi$
$7$	−0.117956	−	0.0681017i	−0.0445830	−	0.0257400i	−0.522126	+	0.852868i	$0.674861\pi$
$8$		−	2.87408i		−	1.01614i
$9$	1.57328	+	2.72500i	0.524427	+	0.908334i
$10$		0			0
$11$	1.48686			0.448304			0.224152	−	0.974554i	$-0.428039\pi$
$11$	1.48686			0.448304			0.224152	+	0.974554i	$0.428039\pi$
$12$	0.144802	−	0.0836015i	0.0418007	−	0.0241337i
$13$	−0.00145531		0.000840224i	−0.000403631		0.000233036i	0.499798	−	0.866142i	$-0.333408\pi$
$13$	−0.00145531		0.000840224i	−0.000403631		0.000233036i	−0.500202	+	0.865909i	$0.666741\pi$
$14$	0.189345			0.0506046
$15$		0			0
$16$	1.93028	+	3.34335i	0.482571	+	0.835838i
$17$	−0.902303	+	0.520945i	−0.218841	+	0.126348i	−0.605413	−	0.795911i	$-0.706992\pi$
$17$	−0.902303	+	0.520945i	−0.218841	+	0.126348i	0.386573	+	0.922259i	$0.373659\pi$
$18$	−3.78820	−	2.18712i	−0.892887	−	0.515509i
$19$	−1.74302	+	3.01900i	−0.399877	+	0.692607i	−0.993710	−	0.111981i	$-0.964280\pi$
$19$	−1.74302	+	3.01900i	−0.399877	+	0.692607i	0.593834	+	0.804588i	$0.297614\pi$
$20$		0			0
$21$	0.168839	+	0.292438i	0.0368438	+	0.0638153i
$22$	−1.79005	+	1.03349i	−0.381641	+	0.220340i
$23$			2.30676i			0.480992i	0.970650	+	0.240496i	$0.0773102\pi$
$23$			2.30676i			0.480992i	−0.970650	+	0.240496i	$0.922690\pi$
$24$	−3.56275	+	6.17087i	−0.727244	+	1.25962i
$25$		0			0
$26$	0.00233610			0.000458147
$27$		−	0.363355i		−	0.0699276i
$28$	0.00795511	−	0.00459289i	0.00150337	−	0.000867974i
$29$	2.25018			0.417849			0.208924	−	0.977932i	$-0.433004\pi$
$29$	2.25018			0.417849			0.208924	+	0.977932i	$0.433004\pi$
$30$		0			0
$31$	0.923643			0.165891			0.0829456	−	0.996554i	$-0.473567\pi$
$31$	0.923643			0.165891			0.0829456	+	0.996554i	$0.473567\pi$
$32$	0.330253	+	0.190671i	0.0583810	+	0.0337063i
$33$	−3.19239	−	1.84313i	−0.555724	−	0.320847i
$34$	0.724199	−	1.25435i	0.124199	−	0.215119i
$35$		0			0
$36$	−0.212209			−0.0353682
$37$	1.82779	−	5.80165i	0.300486	−	0.953786i
$37$	1.82779	−	5.80165i	0.300486	−	0.953786i
$38$		−	4.84618i		−	0.786153i
$39$	0.00208311	+	0.00360805i	0.000333564	+	0.000577750i
$40$		0			0
$41$	1.89504	−	3.28231i	0.295956	−	0.512611i	−0.679251	−	0.733906i	$-0.737695\pi$
$41$	1.89504	−	3.28231i	0.295956	−	0.512611i	0.975207	+	0.221295i	$0.0710284\pi$
$42$	−0.406538	−	0.234715i	−0.0627301	−	0.0362172i
$43$			7.76491i			1.18414i	0.805888	+	0.592069i	$0.201689\pi$
$43$			7.76491i			1.18414i	−0.805888	+	0.592069i	$0.798311\pi$
$44$	−0.0501380	+	0.0868416i	−0.00755859	+	0.0130919i
$45$		0			0
$46$	−1.60339	−	2.77715i	−0.236407	−	0.409468i
$47$		−	5.38040i		−	0.784812i	−0.919792	−	0.392406i	$-0.871643\pi$
$47$		−	5.38040i		−	0.784812i	0.919792	−	0.392406i	$-0.128357\pi$
$48$		−	9.57122i		−	1.38149i
$49$	−3.49072	−	6.04611i	−0.498675	−	0.863730i
$50$		0			0
$51$	2.58308			0.361704
$52$	9.81485e−5	0	5.66661e-5i	1.36108e−5	0	7.85817e-6i
$53$	−3.40582	+	1.96635i	−0.467825	+	0.270099i	−0.715329	−	0.698788i	$-0.753723\pi$
$53$	−3.40582	+	1.96635i	−0.467825	+	0.270099i	0.247504	+	0.968887i	$0.420390\pi$
$54$	0.252561	+	0.437449i	0.0343693	+	0.0595293i
$55$		0			0
$56$	−0.195730	+	0.339014i	−0.0261555	+	0.0453027i
$57$	7.48479	−	4.32134i	0.991384	−	0.572376i
$58$	−2.70904	+	1.56406i	−0.355714	+	0.205372i
$59$	−5.56703	−	9.64239i	−0.724766	−	1.25533i	−0.959070	−	0.283168i	$-0.908615\pi$
$59$	−5.56703	−	9.64239i	−0.724766	−	1.25533i	0.234304	−	0.972163i	$-0.424719\pi$
$60$		0			0
$61$	2.01966	−	3.49816i	0.258591	−	0.447893i	−0.707273	−	0.706940i	$-0.750075\pi$
$61$	2.01966	−	3.49816i	0.258591	−	0.447893i	0.965865	+	0.259047i	$0.0834084\pi$
$62$	−1.11199	+	0.642008i	−0.141223	+	0.0815351i
$63$		−	0.428572i		−	0.0539950i
$64$	−8.25127			−1.03141
$65$		0			0
$66$	5.12450			0.630783
$67$	−10.8695	−	6.27551i	−1.32792	−	0.766676i	−0.342944	−	0.939356i	$-0.611424\pi$
$67$	−10.8695	−	6.27551i	−1.32792	−	0.766676i	−0.984978	+	0.172680i	$0.944757\pi$
$68$		−	0.0702667i		−	0.00852109i
$69$	2.85949	−	4.95278i	0.344242	−	0.596244i
$70$		0			0
$71$	4.12644	−	7.14720i	0.489718	−	0.848216i	−0.510212	−	0.860049i	$-0.670433\pi$
$71$	4.12644	−	7.14720i	0.489718	−	0.848216i	0.999930	+	0.0118323i	$0.00376644\pi$
$72$	7.83188	−	4.52174i	0.922996	−	0.532892i
$73$			0.488959i			0.0572283i	0.999591	+	0.0286141i	$0.00910941\pi$
$73$			0.488959i			0.0572283i	−0.999591	+	0.0286141i	$0.990891\pi$
$74$	1.83212	+	8.25518i	0.212980	+	0.959645i
$75$		0			0
$76$	−0.117552	−	0.203606i	−0.0134842	−	0.0233552i
$77$	−0.175383	−	0.101257i	−0.0199868	−	0.0115394i
$78$	−0.00501578	−	0.00289586i	−0.000567925	−	0.000327892i
$79$	−0.658728	+	1.14095i	−0.0741126	+	0.128367i	−0.900700	−	0.434442i	$-0.856946\pi$
$79$	−0.658728	+	1.14095i	−0.0741126	+	0.128367i	0.826587	+	0.562808i	$0.190279\pi$
$80$		0			0
$81$	4.26942	−	7.39485i	0.474380	−	0.821650i
$82$			5.26885i			0.581847i
$83$	10.6136	−	6.12774i	1.16499	−	0.672607i	0.212495	−	0.977162i	$-0.431841\pi$
$83$	10.6136	−	6.12774i	1.16499	−	0.672607i	0.952495	+	0.304555i	$0.0985078\pi$
$84$	−0.0227736			−0.00248480
$85$		0			0
$86$	−5.39725	−	9.34831i	−0.582001	−	1.00805i
$87$	−4.83131	−	2.78936i	−0.517970	−	0.299050i
$88$		−	4.27335i		−	0.455541i
$89$	−4.05665	−	7.02632i	−0.430004	−	0.744789i	0.566869	−	0.823808i	$-0.308154\pi$
$89$	−4.05665	−	7.02632i	−0.430004	−	0.744789i	−0.996873	+	0.0790192i	$0.974821\pi$
$90$		0			0
$91$	0.000114441	0	0.000198218i	1.19967e−5	0	2.07789e-5i
$92$	−0.134729	−	0.0777857i	−0.0140465	−	0.00810973i
$93$	−1.98313	−	1.14496i	−0.205641	−	0.118727i
$94$	3.73982	+	6.47756i	0.385733	+	0.668109i
$95$		0			0
$96$	−0.472717	−	0.818771i	−0.0482465	−	0.0835654i
$97$		−	18.5354i		−	1.88199i	−0.338423	−	0.940994i	$-0.609894\pi$
$97$		−	18.5354i		−	1.88199i	0.338423	−	0.940994i	$-0.390106\pi$
$98$	8.40509	+	4.85268i	0.849043	+	0.490195i
$99$	2.33924	+	4.05169i	0.235103	+	0.407210i
$100$		0			0
$101$	0.0716103			0.00712549			0.00356275	−	0.999994i	$-0.498866\pi$
$101$	0.0716103			0.00712549			0.00356275	+	0.999994i	$0.498866\pi$
$102$	−3.10982	+	1.79545i	−0.307918	+	0.177776i
$103$			9.39559i			0.925775i	0.886417	+	0.462887i	$0.153187\pi$
$103$			9.39559i			0.925775i	−0.886417	+	0.462887i	$0.846813\pi$
$104$	−0.00241488	+	0.00418269i	−0.000236798	+	0.000410146i
$105$		0			0
$106$	2.73355	−	4.73465i	0.265506	−	0.459870i
$107$	6.96265	+	4.01989i	0.673105	+	0.388617i	0.797252	−	0.603647i	$-0.206286\pi$
$107$	6.96265	+	4.01989i	0.673105	+	0.388617i	−0.124147	+	0.992264i	$0.539619\pi$
$108$	0.0212221	+	0.0122526i	0.00204210	+	0.00117901i
$109$	−8.91402	−	15.4395i	−0.853808	−	1.47884i	−0.877746	−	0.479126i	$-0.840954\pi$
$109$	−8.91402	−	15.4395i	−0.853808	−	1.47884i	0.0239381	−	0.999713i	$-0.492380\pi$
$110$		0			0
$111$	−11.1162	+	10.1908i	−1.05510	+	0.967270i
$112$		−	0.525822i		−	0.0496855i
$113$	7.13107	−	4.11713i	0.670835	−	0.387307i	−0.125558	−	0.992086i	$-0.540072\pi$
$113$	7.13107	−	4.11713i	0.670835	−	0.387307i	0.796393	+	0.604780i	$0.206739\pi$
$114$	−6.00738	+	10.4051i	−0.562643	+	0.974526i
$115$		0			0
$116$	−0.0758780	+	0.131425i	−0.00704509	+	0.0122025i
$117$		−	0.00528763i		−	0.000488842i
$118$	13.4045	+	7.73909i	1.23398	+	0.712441i
$119$	0.141909			0.0130088
$120$		0			0
$121$	−8.78926			−0.799023
$122$			5.61533i			0.508388i
$123$	−8.13759	+	4.69824i	−0.733742	+	0.423626i
$124$	−0.0311460	+	0.0539464i	−0.00279699	+	0.00484453i
$125$		0			0
$126$	0.297893	+	0.515965i	0.0265384	+	0.0459659i
$127$	−14.9653	+	8.64024i	−1.32796	+	0.766697i	−0.984984	−	0.172647i	$-0.944768\pi$
$127$	−14.9653	+	8.64024i	−1.32796	+	0.766697i	−0.342975	+	0.939345i	$0.611435\pi$
$128$	9.27334	−	5.35397i	0.819656	−	0.473228i
$129$	9.62548	−	16.6718i	0.847476	−	1.46787i
$130$		0			0
$131$	3.74545	+	6.48732i	0.327242	+	0.566800i	0.981964	−	0.189071i	$-0.0605475\pi$
$131$	3.74545	+	6.48732i	0.327242	+	0.566800i	−0.654722	+	0.755870i	$0.727214\pi$
$132$	0.215300	−	0.124303i	0.0187395	−	0.0108192i
$133$	0.411198	−	0.237405i	0.0356554	−	0.0205857i
$134$	17.4480			1.50728
$135$		0			0
$136$	1.49724	+	2.59330i	0.128387	+	0.222373i
$137$			8.65593i			0.739526i	0.929126	+	0.369763i	$0.120561\pi$
$137$			8.65593i			0.739526i	−0.929126	+	0.369763i	$0.879439\pi$
$138$			7.95032i			0.676776i
$139$	−0.600304	−	1.03976i	−0.0509171	−	0.0881911i	0.839443	−	0.543447i	$-0.182881\pi$
$139$	−0.600304	−	1.03976i	−0.0509171	−	0.0881911i	−0.890361	+	0.455256i	$0.849548\pi$
$140$		0			0
$141$	−6.66961	+	11.5521i	−0.561683	+	0.972863i
$142$			11.4729i			0.962780i
$143$	−0.00216384	−	0.00124929i	−0.000180949	−	0.000104471i
$144$	−6.07375	+	10.5201i	−0.506146	+	0.876671i
$145$		0			0
$146$	−0.339867	−	0.588666i	−0.0281276	−	0.0487184i
$147$			17.3086i			1.42759i
$148$	0.277218	+	0.302390i	0.0227872	+	0.0248563i
$149$	19.0499			1.56063			0.780316	−	0.625385i	$-0.215058\pi$
$149$	19.0499			1.56063			0.780316	+	0.625385i	$0.215058\pi$
$150$		0			0
$151$	−3.21837	+	5.57437i	−0.261907	+	0.453636i	−0.966749	−	0.255729i	$-0.917685\pi$
$151$	−3.21837	+	5.57437i	−0.261907	+	0.453636i	0.704842	+	0.709365i	$0.251018\pi$
$152$	8.67687	+	5.00959i	0.703787	+	0.406332i
$153$	−2.83915	−	1.63918i	−0.229532	−	0.132520i
$154$	0.281529			0.0226863
$155$		0			0
$156$	−0.000280976	0		−2.24961e−5	0
$157$	−1.76269	+	1.01769i	−0.140678	+	0.0812204i	−0.568687	−	0.822554i	$-0.692548\pi$
$157$	−1.76269	+	1.01769i	−0.140678	+	0.0812204i	0.428009	+	0.903774i	$0.359215\pi$
$158$		−	1.83148i		−	0.145705i
$159$	9.75006			0.773230
$160$		0			0
$161$	0.157094	−	0.272095i	0.0123807	−	0.0214441i
$162$			11.8704i			0.932626i
$163$	5.99002	−	3.45834i	0.469174	−	0.270878i	−0.246720	−	0.969087i	$-0.579353\pi$
$163$	5.99002	−	3.45834i	0.469174	−	0.270878i	0.715894	+	0.698209i	$0.246019\pi$
$164$	0.127805	+	0.221364i	0.00997988	+	0.0172857i
$165$		0			0
$166$	−8.51857	+	14.7546i	−0.661169	+	1.14518i
$167$	−15.7433	−	9.08938i	−1.21825	−	0.703358i	−0.253707	−	0.967281i	$-0.581650\pi$
$167$	−15.7433	−	9.08938i	−1.21825	−	0.703358i	−0.964544	+	0.263924i	$0.914983\pi$
$168$	0.840493	−	0.485259i	0.0648454	−	0.0374385i
$169$	−6.50000	−	11.2583i	−0.500000	−	0.866025i
$170$		0			0
$171$	−10.9690			−0.838824
$172$	−0.453518	−	0.261839i	−0.0345804	−	0.0199650i
$173$	−12.2353	+	7.06407i	−0.930235	+	0.537071i	−0.886886	−	0.461989i	$-0.847136\pi$
$173$	−12.2353	+	7.06407i	−0.930235	+	0.537071i	−0.0433491	+	0.999060i	$0.513803\pi$
$174$	7.75533			0.587930
$175$		0			0
$176$	2.87006	+	4.97108i	0.216339	+	0.374710i
$177$			27.6039i			2.07483i
$178$	9.76775	+	5.63941i	0.732123	+	0.422692i
$179$	5.01933			0.375163			0.187581	−	0.982249i	$-0.439935\pi$
$179$	5.01933			0.375163			0.187581	+	0.982249i	$0.439935\pi$
$180$		0			0
$181$	6.45366	−	11.1781i	0.479697	−	0.830860i	−0.520032	−	0.854147i	$-0.674080\pi$
$181$	6.45366	−	11.1781i	0.479697	−	0.830860i	0.999729	+	0.0232872i	$0.00741322\pi$
$182$	−0.000275556	0	0.000159092i	−2.04256e−5	0	1.17927e-5i
$183$	−8.67272	+	5.00720i	−0.641106	+	0.370143i
$184$	6.62982			0.488757
$185$		0			0
$186$	3.18336			0.233416
$187$	−1.34160	+	0.774571i	−0.0981072	+	0.0566422i
$188$	0.314248	+	0.181431i	0.0229189	+	0.0132322i
$189$	−0.0247451	+	0.0428597i	−0.00179994	+	0.00311758i
$190$		0			0
$191$	−10.1152			−0.731908			−0.365954	−	0.930633i	$-0.619257\pi$
$191$	−10.1152			−0.731908			−0.365954	+	0.930633i	$0.619257\pi$
$192$	17.7161	+	10.2284i	1.27855	+	0.738169i
$193$		−	3.51475i		−	0.252998i	−0.991967	−	0.126499i	$-0.959626\pi$
$193$		−	3.51475i		−	0.252998i	0.991967	−	0.126499i	$-0.0403740\pi$
$194$	12.8837	+	22.3151i	0.924992	+	1.60213i
$195$		0			0
$196$	0.470840			0.0336314
$197$	18.1546	−	10.4815i	1.29346	−	0.746779i	0.314193	−	0.949359i	$-0.398266\pi$
$197$	18.1546	−	10.4815i	1.29346	−	0.746779i	0.979266	+	0.202580i	$0.0649327\pi$
$198$	−5.63251	−	3.25193i	−0.400285	−	0.231105i
$199$	−13.6891			−0.970398			−0.485199	−	0.874404i	$-0.661253\pi$
$199$	−13.6891			−0.970398			−0.485199	+	0.874404i	$0.661253\pi$
$200$		0			0
$201$	15.5584	+	26.9480i	1.09741	+	1.90076i
$202$	−0.0862130	+	0.0497751i	−0.00606592	+	0.00350216i
$203$	−0.265422	−	0.153241i	−0.0186289	−	0.0107554i
$204$	−0.0871035	+	0.150868i	−0.00609847	+	0.0105629i
$205$		0			0
$206$	−6.53071	−	11.3115i	−0.455016	−	0.788111i
$207$	−6.28592	+	3.62918i	−0.436902	+	0.252245i
$208$		−	0.00648749i		−	0.000449826i
$209$	−2.59162	+	4.48883i	−0.179266	+	0.310499i
$210$		0			0
$211$	−16.7664			−1.15425			−0.577123	−	0.816657i	$-0.695825\pi$
$211$	−16.7664			−1.15425			−0.577123	+	0.816657i	$0.695825\pi$
$212$		−	0.265228i		−	0.0182159i
$213$	−17.7195	+	10.2304i	−1.21412	+	0.700973i
$214$	−11.1766			−0.764018
$215$		0			0
$216$	−1.04431			−0.0710564
$217$	−0.108949	−	0.0629016i	−0.00739593	−	0.00427004i
$218$	21.4635	+	12.3920i	1.45369	+	0.839289i
$219$	0.606119	−	1.04983i	0.0409577	−	0.0709409i
$220$		0			0
$221$	0.00175084			0.000117774
$222$	6.29953	−	19.9956i	0.422797	−	1.34202i
$223$		−	10.3727i		−	0.694606i	−0.937753	−	0.347303i	$-0.887098\pi$
$223$		−	10.3727i		−	0.694606i	0.937753	−	0.347303i	$-0.112902\pi$
$224$	−0.0259701	−	0.0449815i	−0.00173520	−	0.00300545i
$225$		0			0
$226$	−5.72349	+	9.91337i	−0.380721	+	0.659427i
$227$	−3.96789	−	2.29086i	−0.263358	−	0.152050i	0.362507	−	0.931981i	$-0.381921\pi$
$227$	−3.96789	−	2.29086i	−0.263358	−	0.152050i	−0.625865	+	0.779931i	$0.715254\pi$
$228$			0.582877i			0.0386020i
$229$	−4.12581	+	7.14610i	−0.272641	+	0.472228i	−0.969537	−	0.244944i	$-0.921230\pi$
$229$	−4.12581	+	7.14610i	−0.272641	+	0.472228i	0.696896	+	0.717172i	$0.254564\pi$
$230$		0			0
$231$	0.251040	+	0.434814i	0.0165172	+	0.0286087i
$232$		−	6.46722i		−	0.424594i
$233$		−	23.0003i		−	1.50680i	−0.657563	−	0.753399i	$-0.728413\pi$
$233$		−	23.0003i		−	1.50680i	0.657563	−	0.753399i	$-0.271587\pi$
$234$	0.00367534	+	0.00636588i	0.000240265	+	0.000416150i
$235$		0			0
$236$	0.750899			0.0488794
$237$	2.82867	−	1.63313i	0.183742	−	0.106083i
$238$	−0.170847	+	0.0986384i	−0.0110743	+	0.00639378i
$239$	11.7827	+	20.4082i	0.762158	+	1.32010i	0.941736	+	0.336353i	$0.109194\pi$
$239$	11.7827	+	20.4082i	0.762158	+	1.32010i	−0.179578	+	0.983744i	$0.557473\pi$
$240$		0			0
$241$	−7.17508	+	12.4276i	−0.462188	+	0.800532i	−0.999070	−	0.0431249i	$-0.986269\pi$
$241$	−7.17508	+	12.4276i	−0.462188	+	0.800532i	0.536882	+	0.843657i	$0.319602\pi$
$242$	10.5815	−	6.10926i	0.680207	−	0.392718i
$243$	−19.2775	+	11.1299i	−1.23665	+	0.713983i
$244$	0.136209	+	0.235921i	0.00871991	+	0.0151033i
$245$		0			0
$246$	6.53133	−	11.3126i	0.416423	−	0.721265i
$247$	0.00507328	−	0.00292906i	0.000322805	−	0.000186372i
$248$		−	2.65463i		−	0.168569i
$249$	−30.3841			−1.92551
$250$		0			0
$251$	1.32879			0.0838724			0.0419362	−	0.999120i	$-0.486647\pi$
$251$	1.32879			0.0838724			0.0419362	+	0.999120i	$0.486647\pi$
$252$	0.0250312	+	0.0144518i	0.00157682	+	0.000910377i
$253$			3.42982i			0.215631i
$254$	12.0114	−	20.8043i	0.753659	−	1.30538i
$255$		0			0
$256$	0.808369	−	1.40014i	0.0505230	−	0.0875085i
$257$	15.7458	−	9.09085i	0.982197	−	0.567072i	0.0792641	−	0.996854i	$-0.474743\pi$
$257$	15.7458	−	9.09085i	0.982197	−	0.567072i	0.902933	+	0.429782i	$0.141410\pi$
$258$			26.7620i			1.66613i
$259$	−0.610700	+	0.559862i	−0.0379470	+	0.0347881i
$260$		0			0
$261$	3.54017	+	6.13175i	0.219131	+	0.379546i
$262$	−9.01844	−	5.20680i	−0.557161	−	0.321677i
$263$	−21.5604	−	12.4479i	−1.32947	−	0.767570i	−0.344253	−	0.938877i	$-0.611868\pi$
$263$	−21.5604	−	12.4479i	−1.32947	−	0.767570i	−0.985218	+	0.171307i	$0.945201\pi$
$264$	−5.29730	+	9.17520i	−0.326027	+	0.564695i
$265$		0			0
$266$	−0.330033	+	0.571633i	−0.0202356	+	0.0350491i
$267$			20.1147i			1.23100i
$268$	0.733057	−	0.423231i	0.0447786	−	0.0258529i
$269$	6.50676			0.396724			0.198362	−	0.980129i	$-0.436438\pi$
$269$	6.50676			0.396724			0.198362	+	0.980129i	$0.436438\pi$
$270$		0			0
$271$	−9.92346	−	17.1879i	−0.602807	−	1.04409i	−0.992394	−	0.123103i	$-0.960715\pi$
$271$	−9.92346	−	17.1879i	−0.602807	−	1.04409i	0.389586	−	0.920990i	$-0.372618\pi$
$272$	−3.48340	−	2.01114i	−0.211212	−	0.121944i
$273$		0	0.000567452i		0	3.43438e-5i
$274$	−6.01659	−	10.4210i	−0.363475	−	0.629558i
$275$		0			0
$276$	0.192848	+	0.334023i	0.0116081	+	0.0201058i
$277$	5.14949	+	2.97306i	0.309403	+	0.178634i	0.646659	−	0.762779i	$-0.276166\pi$
$277$	5.14949	+	2.97306i	0.309403	+	0.178634i	−0.337256	+	0.941413i	$0.609499\pi$
$278$	1.44543	+	0.834522i	0.0866914	+	0.0500513i
$279$	1.45315	+	2.51693i	0.0869977	+	0.150684i
$280$		0			0
$281$	−6.54607	−	11.3381i	−0.390506	−	0.676376i	0.602010	−	0.798488i	$-0.294367\pi$
$281$	−6.54607	−	11.3381i	−0.390506	−	0.676376i	−0.992516	+	0.122112i	$0.961033\pi$
$282$		−	18.5437i		−	1.10426i
$283$	17.9692	+	10.3745i	1.06816	+	0.616702i	0.927678	−	0.373381i	$-0.121802\pi$
$283$	17.9692	+	10.3745i	1.06816	+	0.616702i	0.140481	+	0.990083i	$0.455135\pi$
$284$	0.278293	+	0.482018i	0.0165137	+	0.0286025i
$285$		0			0
$286$	0.00347345			0.000205389
$287$	−0.447062	+	0.258111i	−0.0263892	+	0.0152358i
$288$			1.19992i			0.0707058i
$289$	−7.95723	+	13.7823i	−0.468073	+	0.810725i
$290$		0			0
$291$	−22.9768	+	39.7969i	−1.34692	+	2.33294i
$292$	−0.0285582	−	0.0164881i	−0.00167124	−	0.000964892i
$293$	−11.8087	−	6.81776i	−0.689872	−	0.398298i	0.113692	−	0.993516i	$-0.463732\pi$
$293$	−11.8087	−	6.81776i	−0.689872	−	0.398298i	−0.803564	+	0.595218i	$0.797066\pi$
$294$	−12.0309	−	20.8381i	−0.701656	−	1.21530i
$295$		0			0
$296$	−16.6744	−	5.25322i	−0.969182	−	0.305337i
$297$		−	0.540257i		−	0.0313489i
$298$	−22.9346	+	13.2413i	−1.32856	+	0.767047i
$299$	0.00193820	−	0.00335705i	0.000112089	−	0.000194143i
$300$		0			0
$301$	0.528803	−	0.915914i	0.0304797	−	0.0527924i
$302$		−	8.94812i		−	0.514906i
$303$	−0.153753	−	0.0887691i	−0.00883285	−	0.00509965i
$304$	−13.4581			−0.771875
$305$		0			0
$306$	4.55747			0.260533
$307$		−	25.9933i		−	1.48352i	−0.670667	−	0.741759i	$-0.733992\pi$
$307$		−	25.9933i		−	1.48352i	0.670667	−	0.741759i	$-0.266008\pi$
$308$	0.0118281	−	0.00682897i	0.000673969	−	0.000389116i
$309$	11.6469	−	20.1730i	0.662569	−	1.14760i
$310$		0			0
$311$	−3.27682	−	5.67561i	−0.185811	−	0.321835i	0.758038	−	0.652210i	$-0.226158\pi$
$311$	−3.27682	−	5.67561i	−0.185811	−	0.321835i	−0.943850	+	0.330375i	$0.892825\pi$
$312$	0.0103698	−	0.00598702i	0.000587076	−	0.000338948i
$313$	−2.29061	+	1.32248i	−0.129473	+	0.0747511i	−0.563337	−	0.826227i	$-0.690483\pi$
$313$	−2.29061	+	1.32248i	−0.129473	+	0.0747511i	0.433865	+	0.900978i	$0.357150\pi$
$314$	1.41476	−	2.45043i	0.0798392	−	0.138286i
$315$		0			0
$316$	−0.0444256	−	0.0769475i	−0.00249914	−	0.00432863i
$317$	15.4376	−	8.91292i	0.867064	−	0.500599i	0.000692314	−	1.00000i	$-0.499780\pi$
$317$	15.4376	−	8.91292i	0.867064	−	0.500599i	0.866371	+	0.499400i	$0.166446\pi$
$318$	−11.7383	+	6.77709i	−0.658250	+	0.380041i
$319$	3.34570			0.187323
$320$		0			0
$321$	−9.96621	−	17.2620i	−0.556260	−	0.963470i
$322$			0.436773i			0.0243404i
$323$		−	3.63207i		−	0.202094i
$324$	0.287937	+	0.498721i	0.0159965	+	0.0277067i
$325$		0			0
$326$	−4.80766	+	8.32711i	−0.266272	+	0.461196i
$327$			44.1997i			2.44425i
$328$	−9.43365	−	5.44652i	−0.520886	−	0.300734i
$329$	−0.366414	+	0.634648i	−0.0202011	+	0.0349893i
$330$		0			0
$331$	3.87967	+	6.71978i	0.213246	+	0.369353i	0.952729	−	0.303823i	$-0.0982631\pi$
$331$	3.87967	+	6.71978i	0.213246	+	0.369353i	−0.739483	+	0.673176i	$0.764930\pi$
$332$			0.826529i			0.0453617i
$333$	18.6851	−	4.14690i	1.02394	−	0.227249i
$334$	25.2715			1.38279
$335$		0			0
$336$	−0.651816	+	1.12898i	−0.0355595	+	0.0615908i
$337$	13.7268	+	7.92518i	0.747747	+	0.431712i	0.824879	−	0.565309i	$-0.191243\pi$
$337$	13.7268	+	7.92518i	0.747747	+	0.431712i	−0.0771320	+	0.997021i	$0.524576\pi$
$338$	15.6509	+	9.03607i	0.851298	+	0.491497i
$339$	−20.4146			−1.10877
$340$		0			0
$341$	1.37332			0.0743697
$342$	13.2058	−	7.62439i	0.714090	−	0.412280i
$343$			1.90432i			0.102824i
$344$	22.3170			1.20325
$345$		0			0
$346$	9.82022	−	17.0091i	0.527939	−	0.914416i
$347$			0.0849270i			0.00455912i	0.999997	+	0.00227956i	$0.000725607\pi$
$347$			0.0849270i			0.00455912i	−0.999997	+	0.00227956i	$0.999274\pi$
$348$	0.325831	−	0.188119i	0.0174664	−	0.0100842i
$349$	0.518987	+	0.898913i	0.0277808	+	0.0481177i	0.879582	−	0.475748i	$-0.157823\pi$
$349$	0.518987	+	0.898913i	0.0277808	+	0.0481177i	−0.851801	+	0.523866i	$0.824489\pi$
$350$		0			0
$351$	−0.000305300	0	0.000528794i	−1.62957e−5	0	2.82250e-5i
$352$	0.491038	+	0.283501i	0.0261724	+	0.0151107i
$353$	30.0942	−	17.3749i	1.60175	−	0.924772i	0.610615	−	0.791927i	$-0.290922\pi$
$353$	30.0942	−	17.3749i	1.60175	−	0.924772i	0.991137	−	0.132845i	$-0.0424111\pi$
$354$	−19.1870	−	33.2328i	−1.01978	−	1.76630i
$355$		0			0
$356$	0.547174			0.0290002
$357$	−0.304689	−	0.175912i	−0.0161258	−	0.00931025i
$358$	−6.04287	+	3.48885i	−0.319375	+	0.184391i
$359$	24.1679			1.27553			0.637766	−	0.770230i	$-0.279859\pi$
$359$	24.1679			1.27553			0.637766	+	0.770230i	$0.279859\pi$
$360$		0			0
$361$	3.42375	+	5.93011i	0.180197	+	0.312111i
$362$			17.9433i			0.943080i
$363$	18.8712	+	10.8953i	0.990479	+	0.571854i
$364$	−1.54362e−5	0		−8.09078e−7	0
$365$		0			0
$366$	6.96083	−	12.0565i	0.363849	−	0.630204i
$367$	−20.3027	−	11.7218i	−1.05979	−	0.611871i	−0.134417	−	0.990925i	$-0.542916\pi$
$367$	−20.3027	−	11.7218i	−1.05979	−	0.611871i	−0.925375	+	0.379054i	$0.876250\pi$
$368$	−7.71230	+	4.45270i	−0.402032	+	0.232113i
$369$	11.9257			0.620829
$370$		0			0
$371$	0.535647			0.0278094
$372$	0.133745	−	0.0772179i	0.00693437	−	0.00400356i
$373$	5.51890	+	3.18634i	0.285758	+	0.164982i	0.636027	−	0.771667i	$-0.280577\pi$
$373$	5.51890	+	3.18634i	0.285758	+	0.164982i	−0.350269	+	0.936649i	$0.613910\pi$
$374$	1.07678	−	1.86504i	0.0556790	−	0.0964389i
$375$		0			0
$376$	−15.4637			−0.797481
$377$	−0.00327472	−	0.00189066i	−0.000168657	−	9.73739e-5i
$378$		−	0.0687994i		−	0.00353866i
$379$	4.85735	+	8.41318i	0.249505	+	0.432156i	0.963389	−	0.268109i	$-0.0863986\pi$
$379$	4.85735	+	8.41318i	0.249505	+	0.432156i	−0.713883	+	0.700265i	$0.753065\pi$
$380$		0			0
$381$	42.8422			2.19487
$382$	12.1778	−	7.03087i	0.623072	−	0.359731i
$383$	−15.5312	−	8.96696i	−0.793609	−	0.458190i	0.0476225	−	0.998865i	$-0.484836\pi$
$383$	−15.5312	−	8.96696i	−0.793609	−	0.458190i	−0.841232	+	0.540675i	$0.818169\pi$
$384$	−26.5474			−1.35474
$385$		0			0
$386$	2.44304	+	4.23148i	0.124348	+	0.215376i
$387$	−21.1594	+	12.2164i	−1.07559	+	0.620993i
$388$	1.08258	+	0.625030i	0.0549598	+	0.0317311i
$389$	−14.9907	+	25.9646i	−0.760057	+	1.31646i	0.182764	+	0.983157i	$0.441496\pi$
$389$	−14.9907	+	25.9646i	−0.760057	+	1.31646i	−0.942821	+	0.333300i	$0.891838\pi$
$390$		0			0
$391$	−1.20169	−	2.08140i	−0.0607723	−	0.105261i
$392$	−17.3770	+	10.0326i	−0.877673	+	0.506725i
$393$		−	18.5717i		−	0.936816i
$394$	−14.5711	+	25.2378i	−0.734080	+	1.27146i
$395$		0			0
$396$	−0.315525			−0.0158557
$397$			10.0944i			0.506623i	0.967385	+	0.253312i	$0.0815198\pi$
$397$			10.0944i			0.506623i	−0.967385	+	0.253312i	$0.918480\pi$
$398$	16.4806	−	9.51509i	0.826099	−	0.476948i
$399$	−1.17716			−0.0589319
$400$		0			0
$401$	16.0927			0.803630			0.401815	−	0.915721i	$-0.368379\pi$
$401$	16.0927			0.803630			0.401815	+	0.915721i	$0.368379\pi$
$402$	−37.4621	−	21.6288i	−1.86844	−	1.07874i
$403$	−0.00134419		0.000776067i	−6.69588e−5		3.86587e-5i
$404$	−0.00241476	+	0.00418248i	−0.000120139	+	0.000208086i
$405$		0			0
$406$	0.426061			0.0211451
$407$	2.71766	−	8.62623i	0.134709	−	0.427586i
$408$		−	7.42399i		−	0.367542i
$409$	−17.5127	−	30.3329i	−0.865947	−	1.49986i	−0.866104	−	0.499864i	$-0.833383\pi$
$409$	−17.5127	−	30.3329i	−0.865947	−	1.49986i	0.000157567	−	1.00000i	$-0.499950\pi$
$410$		0			0
$411$	10.7300	−	18.5849i	0.529272	−	0.916726i
$412$	−0.548760	−	0.316827i	−0.0270355	−	0.0156089i
$413$			1.51650i			0.0746219i
$414$	5.04515	−	8.73846i	0.247956	−	0.429472i
$415$		0			0
$416$	−0.000320414	0	0.000554973i	−1.57096e−5	0	2.72098e-5i
$417$			2.97658i			0.145764i
$418$		−	7.20557i		−	0.352436i
$419$	19.0623	+	33.0168i	0.931253	+	1.61298i	0.781184	+	0.624301i	$0.214616\pi$
$419$	19.0623	+	33.0168i	0.931253	+	1.61298i	0.150069	+	0.988676i	$0.452050\pi$
$420$		0			0
$421$	26.7199			1.30225			0.651125	−	0.758971i	$-0.274297\pi$
$421$	26.7199			1.30225			0.651125	+	0.758971i	$0.274297\pi$
$422$	20.1854	−	11.6540i	0.982609	−	0.567309i
$423$	14.6616	−	8.46488i	0.712871	−	0.411576i
$424$	5.65146	+	9.78862i	0.274459	+	0.475377i
$425$		0			0
$426$	14.2219	−	24.6330i	0.689053	−	1.19348i
$427$	−0.476461	+	0.275085i	−0.0230576	+	0.0133123i
$428$	−0.469572	+	0.271108i	−0.0226976	+	0.0131045i
$429$	0.00309728	+	0.00536465i	0.000149538	+	0.000259008i
$430$		0			0
$431$	13.4904	−	23.3660i	0.649808	−	1.12550i	−0.333361	−	0.942799i	$-0.608183\pi$
$431$	13.4904	−	23.3660i	0.649808	−	1.12550i	0.983169	−	0.182701i	$-0.0584839\pi$
$432$	1.21482	−	0.701378i	0.0584482	−	0.0337451i
$433$		−	11.1569i		−	0.536165i	−0.963396	−	0.268082i	$-0.913610\pi$
$433$		−	11.1569i		−	0.536165i	0.963396	−	0.268082i	$-0.0863899\pi$
$434$	0.174887			0.00839485
$435$		0			0
$436$	1.20235			0.0575822
$437$	−6.96411	−	4.02073i	−0.333139	−	0.192338i
$438$			1.68521i			0.0805225i
$439$	9.33988	−	16.1771i	0.445768	−	0.772093i	−0.552337	−	0.833621i	$-0.686264\pi$
$439$	9.33988	−	16.1771i	0.445768	−	0.772093i	0.998105	+	0.0615278i	$0.0195973\pi$
$440$		0			0
$441$	10.9838	−	19.0245i	0.523037	−	0.905926i
$442$	−0.00210787	+	0.00121698i	−0.000100261	+	5.78858e-5i
$443$		−	12.4211i		−	0.590145i	−0.955475	−	0.295073i	$-0.904656\pi$
$443$		−	12.4211i		−	0.590145i	0.955475	−	0.295073i	$-0.0953438\pi$
$444$	−0.220360	−	0.992897i	−0.0104578	−	0.0471208i
$445$		0			0
$446$	7.20987	+	12.4879i	0.341397	+	0.591317i
$447$	−40.9016	−	23.6146i	−1.93458	−	1.11693i
$448$	0.973283	+	0.561925i	0.0459833	+	0.0265485i
$449$	−10.7899	+	18.6886i	−0.509206	+	0.881971i	0.490737	+	0.871308i	$0.336728\pi$
$449$	−10.7899	+	18.6886i	−0.509206	+	0.881971i	−0.999943	+	0.0106635i	$0.996606\pi$
$450$		0			0
$451$	2.81766	−	4.88033i	0.132678	−	0.229806i
$452$			0.555331i			0.0261206i
$453$	13.8201	−	7.97905i	0.649326	−	0.374889i
$454$	6.36935			0.298928
$455$		0			0
$456$	−12.4199	−	21.5119i	−0.581616	−	1.00739i
$457$	−8.63053	−	4.98284i	−0.403719	−	0.233087i	0.284368	−	0.958715i	$-0.408216\pi$
$457$	−8.63053	−	4.98284i	−0.403719	−	0.233087i	−0.688088	+	0.725628i	$0.741550\pi$
$458$		−	11.4711i		−	0.536009i
$459$	0.189288	+	0.327856i	0.00883520	+	0.0153030i
$460$		0			0
$461$	3.28999	+	5.69843i	0.153230	+	0.265403i	0.932413	−	0.361394i	$-0.117699\pi$
$461$	3.28999	+	5.69843i	0.153230	+	0.265403i	−0.779183	+	0.626797i	$0.784366\pi$
$462$	−0.604463	−	0.348987i	−0.0281222	−	0.0162363i
$463$	5.67947	+	3.27904i	0.263947	+	0.152390i	0.626134	−	0.779716i	$-0.284636\pi$
$463$	5.67947	+	3.27904i	0.263947	+	0.152390i	−0.362187	+	0.932106i	$0.617970\pi$
$464$	4.34349	+	7.52315i	0.201642	+	0.349254i
$465$		0			0
$466$	15.9871	+	27.6905i	0.740588	+	1.28274i
$467$		−	27.0874i		−	1.25345i	−0.779239	−	0.626727i	$-0.784394\pi$
$467$		−	27.0874i		−	1.25345i	0.779239	−	0.626727i	$-0.215606\pi$
$468$	0.000308830	0	0.000178303i	1.42757e−5	0	8.24207e-6i
$469$	0.854746	+	1.48046i	0.0394685	+	0.0683614i
$470$		0			0
$471$	5.04616			0.232515
$472$	−27.7130	+	16.0001i	−1.27560	+	0.736465i
$473$			11.5453i			0.530854i
$474$	−2.27033	+	3.93232i	−0.104280	+	0.180617i
$475$		0			0
$476$	−0.00478528	+	0.00828835i	−0.000219333	+	0.000379896i
$477$	−10.7166	−	6.18724i	−0.490680	−	0.283294i
$478$	−28.3708	−	16.3799i	−1.29765	−	0.749198i
$479$	−15.2625	−	26.4355i	−0.697363	−	1.20787i	−0.969378	−	0.245575i	$-0.921023\pi$
$479$	−15.2625	−	26.4355i	−0.697363	−	1.20787i	0.272015	−	0.962293i	$-0.412310\pi$
$480$		0			0
$481$	−0.00753469	+	0.00690746i	−0.000343552	+	0.000314953i
$482$		−	19.9491i		−	0.908656i
$483$	−0.674585	+	0.389472i	−0.0306947	+	0.0177216i
$484$	0.296381	−	0.513347i	0.0134719	−	0.0233339i
$485$		0			0
$486$	15.4724	−	26.7989i	0.701841	−	1.21563i
$487$			11.0247i			0.499579i	0.968300	+	0.249789i	$0.0803614\pi$
$487$			11.0247i			0.499579i	−0.968300	+	0.249789i	$0.919639\pi$
$488$	−10.0540	−	5.80468i	−0.455123	−	0.262766i
$489$	−17.1480			−0.775459
$490$		0			0
$491$	−1.47901			−0.0667468			−0.0333734	−	0.999443i	$-0.510625\pi$
$491$	−1.47901			−0.0667468			−0.0333734	+	0.999443i	$0.510625\pi$
$492$		−	0.633714i		−	0.0285700i
$493$	−2.03035	+	1.17222i	−0.0914423	+	0.0527942i
$494$	−0.00407187	+	0.00705269i	−0.000183202	+	0.000317316i
$495$		0			0
$496$	1.78289	+	3.08806i	0.0800543	+	0.138658i
$497$	−0.973472	+	0.562034i	−0.0436662	+	0.0252107i
$498$	36.5800	−	21.1195i	1.63919	−	0.946386i
$499$	6.10143	−	10.5680i	0.273138	−	0.473088i	−0.696526	−	0.717532i	$-0.745272\pi$
$499$	6.10143	−	10.5680i	0.273138	−	0.473088i	0.969664	+	0.244443i	$0.0786053\pi$
$500$		0			0
$501$	22.5346	+	39.0311i	1.00677	+	1.74378i
$502$	−1.59975	+	0.923618i	−0.0714005	+	0.0412231i
$503$	10.1732	−	5.87352i	0.453602	−	0.261887i	−0.255748	−	0.966743i	$-0.582322\pi$
$503$	10.1732	−	5.87352i	0.453602	−	0.261887i	0.709350	+	0.704856i	$0.248988\pi$
$504$	−1.23175			−0.0548666
$505$		0			0
$506$	−2.38401	−	4.12922i	−0.105982	−	0.183566i
$507$			32.2299i			1.43138i
$508$		−	1.16542i		−	0.0517073i
$509$	−6.90974	−	11.9680i	−0.306269	−	0.530473i	0.671274	−	0.741209i	$-0.265747\pi$
$509$	−6.90974	−	11.9680i	−0.306269	−	0.530473i	−0.977543	+	0.210736i	$0.932414\pi$
$510$		0			0
$511$	0.0332989	−	0.0576754i	0.00147306	−	0.00255141i
$512$			23.6634i			1.04578i
$513$	1.09697	+	0.633335i	0.0484323	+	0.0279624i
$514$	−12.6378	+	21.8893i	−0.557429	+	0.965494i
$515$		0			0
$516$	0.649158	+	1.12437i	0.0285776	+	0.0494978i
$517$		−	7.99989i		−	0.351835i
$518$	0.346083	−	1.09851i	0.0152060	−	0.0482660i
$519$	35.0269			1.53751
$520$		0			0
$521$	6.28810	−	10.8913i	0.275487	−	0.477157i	−0.694771	−	0.719231i	$-0.744494\pi$
$521$	6.28810	−	10.8913i	0.275487	−	0.477157i	0.970258	+	0.242074i	$0.0778277\pi$
$522$	−8.52414	−	4.92142i	−0.373092	−	0.215405i
$523$	−0.386530	−	0.223163i	−0.0169018	−	0.00975824i	0.491525	−	0.870863i	$-0.336440\pi$
$523$	−0.386530	−	0.223163i	−0.0169018	−	0.00975824i	−0.508427	+	0.861105i	$0.669773\pi$
$524$	−0.505199			−0.0220697
$525$		0			0
$526$	34.6093			1.50904
$527$	−0.833406	+	0.481167i	−0.0363037	+	0.0209600i
$528$		−	14.2310i		−	0.619326i
$529$	17.6789			0.768646
$530$		0			0
$531$	17.5170	−	30.3403i	0.760173	−	1.31666i
$532$			0.0320220i			0.00138833i
$533$	−0.00551576	+	0.00318453i	−0.000238914	+	0.000137937i
$534$	−13.9814	−	24.2164i	−0.605033	−	1.04795i
$535$		0			0
$536$	−18.0364	+	31.2399i	−0.779052	+	1.34936i
$537$	−10.7769	−	6.22203i	−0.465056	−	0.268500i
$538$	−7.83361	+	4.52273i	−0.337731	+	0.194989i
$539$	−5.19021	−	8.98971i	−0.223558	−	0.387214i
$540$		0			0
$541$	−1.04194			−0.0447965			−0.0223982	−	0.999749i	$-0.507130\pi$
$541$	−1.04194			−0.0447965			−0.0223982	+	0.999749i	$0.507130\pi$
$542$	23.8941	+	13.7952i	1.02634	+	0.592557i
$543$	−27.7130	+	16.0001i	−1.18928	+	0.686630i
$544$	−0.397317			−0.0170348
$545$		0			0
$546$	0.000394426	0	0.000683166i	1.68799e−5	0	2.92368e-5i
$547$			34.4307i			1.47215i	0.676899	+	0.736076i	$0.263323\pi$
$547$			34.4307i			1.47215i	−0.676899	+	0.736076i	$0.736677\pi$
$548$	−0.505560	−	0.291885i	−0.0215964	−	0.0124687i
$549$	12.7100			0.542449
$550$		0			0
$551$	−3.92212	+	6.79331i	−0.167088	+	0.289405i
$552$	−14.2347	−	8.21841i	−0.605869	−	0.349799i
$553$	0.155401	−	0.0897209i	0.00660833	−	0.00381532i
$554$	−8.26609			−0.351192
$555$		0			0
$556$	0.0809710			0.00343393
$557$	0.591491	−	0.341497i	0.0250623	−	0.0144697i	−0.487417	−	0.873170i	$-0.662061\pi$
$557$	0.591491	−	0.341497i	0.0250623	−	0.0144697i	0.512479	+	0.858700i	$0.328727\pi$
$558$	−3.49894	−	2.02012i	−0.148122	−	0.0855183i
$559$	0.00652427	−	0.0113004i	0.000275947	−	0.000477954i
$560$		0			0
$561$	3.84067			0.162153
$562$	15.7619	+	9.10012i	0.664874	+	0.383865i
$563$			46.6535i			1.96621i	0.183044	+	0.983105i	$0.441405\pi$
$563$			46.6535i			1.96621i	−0.183044	+	0.983105i	$0.558595\pi$
$564$	−0.449809	−	0.779093i	−0.0189404	−	0.0328057i
$565$		0			0
$566$	−28.8446			−1.21243
$567$	−1.00720	+	0.581509i	−0.0422986	+	0.0244211i
$568$	−20.5417	−	11.8597i	−0.861909	−	0.497623i
$569$	10.5614			0.442758			0.221379	−	0.975188i	$-0.428944\pi$
$569$	10.5614			0.442758			0.221379	+	0.975188i	$0.428944\pi$
$570$		0			0
$571$	8.15701	+	14.1283i	0.341360	+	0.591253i	0.984686	−	0.174340i	$-0.0557791\pi$
$571$	8.15701	+	14.1283i	0.341360	+	0.591253i	−0.643325	+	0.765593i	$0.722446\pi$
$572$	0.000145933	0	8.42544e-5i	6.10176e−6	0	3.52285e-6i
$573$	21.7180	+	12.5389i	0.907282	+	0.523820i
$574$	0.358817	−	0.621490i	0.0149767	−	0.0259405i
$575$		0			0
$576$	−12.9816	−	22.4847i	−0.540898	−	0.936863i
$577$	0.404882	−	0.233758i	0.0168554	−	0.00973149i	−0.491549	−	0.870850i	$-0.663569\pi$
$577$	0.404882	−	0.233758i	0.0168554	−	0.00973149i	0.508404	+	0.861119i	$0.330236\pi$
$578$		−	22.1237i		−	0.920226i
$579$	−4.35693	+	7.54643i	−0.181068	+	0.313619i
$580$		0			0
$581$	−1.66924			−0.0692516
$582$		−	63.8830i		−	2.64803i
$583$	−5.06397	+	2.92368i	−0.209728	+	0.121087i
$584$	1.40531			0.0581521
$585$		0			0
$586$	18.9556			0.783050
$587$	−14.4467	−	8.34083i	−0.596281	−	0.344263i	0.171296	−	0.985220i	$-0.445204\pi$
$587$	−14.4467	−	8.34083i	−0.596281	−	0.344263i	−0.767577	+	0.640957i	$0.778538\pi$
$588$	−1.01093	−	0.583659i	−0.0416900	−	0.0240697i
$589$	−1.60993	+	2.78848i	−0.0663360	+	0.114897i
$590$		0			0
$591$	−51.9722			−2.13785
$592$	22.9251	−	5.08791i	0.942216	−	0.209112i
$593$		−	31.6518i		−	1.29978i	−0.760027	−	0.649892i	$-0.774814\pi$
$593$		−	31.6518i		−	1.29978i	0.760027	−	0.649892i	$-0.225186\pi$
$594$	0.375523	+	0.650425i	0.0154079	+	0.0266872i
$595$		0			0
$596$	−0.642380	+	1.11263i	−0.0263129	+	0.0455753i
$597$	29.3916	+	16.9692i	1.20292	+	0.694505i
$598$			0.00538882i			0.000220365i
$599$	−21.3347	+	36.9528i	−0.871712	+	1.50985i	−0.0114877	+	0.999934i	$0.503657\pi$
$599$	−21.3347	+	36.9528i	−0.871712	+	1.50985i	−0.860224	+	0.509916i	$0.829677\pi$
$600$		0			0
$601$	−5.36011	−	9.28398i	−0.218643	−	0.378702i	0.735750	−	0.677253i	$-0.236830\pi$
$601$	−5.36011	−	9.28398i	−0.218643	−	0.378702i	−0.954393	+	0.298552i	$0.903496\pi$
$602$			1.47025i			0.0599228i
$603$		−	39.4926i		−	1.60826i
$604$	−0.217052	−	0.375945i	−0.00883171	−	0.0152970i
$605$		0			0
$606$	0.246807			0.0100259
$607$	33.5001	−	19.3413i	1.35973	−	0.785038i	0.370140	−	0.928976i	$-0.379310\pi$
$607$	33.5001	−	19.3413i	1.35973	−	0.785038i	0.989587	+	0.143938i	$0.0459765\pi$
$608$	−1.15127	+	0.664689i	−0.0466904	+	0.0269567i
$609$	0.379920	+	0.658040i	0.0153951	+	0.0266651i
$610$		0			0
$611$	−0.00452074	+	0.00783016i	−0.000182890	+	0.000316774i
$612$	0.191477	−	0.110549i	0.00773999	−	0.00446869i
$613$	−40.0988	+	23.1511i	−1.61958	+	0.935063i	−0.632547	+	0.774522i	$0.717990\pi$
$613$	−40.0988	+	23.1511i	−1.61958	+	0.935063i	−0.987029	+	0.160540i	$0.948676\pi$
$614$	18.0675	+	31.2938i	0.729145	+	1.26292i
$615$		0			0
$616$	−0.291022	+	0.504066i	−0.0117256	+	0.0203094i
$617$	−1.00646	+	0.581081i	−0.0405186	+	0.0233934i	−0.520122	−	0.854092i	$-0.674114\pi$
$617$	−1.00646	+	0.581081i	−0.0405186	+	0.0233934i	0.479604	+	0.877485i	$0.340780\pi$
$618$			32.3822i			1.30260i
$619$	4.57548			0.183904			0.0919520	−	0.995763i	$-0.470689\pi$
$619$	4.57548			0.183904			0.0919520	+	0.995763i	$0.470689\pi$
$620$		0			0
$621$	0.838172			0.0336347
$622$	7.89004	+	4.55532i	0.316362	+	0.182652i
$623$			1.10506i			0.0442732i
$624$	−0.00804197	+	0.0139291i	−0.000321937	+	0.000557611i
$625$		0			0
$626$	1.83847	−	3.18432i	0.0734800	−	0.127271i
$627$	11.1288	−	6.42522i	0.444442	−	0.256599i
$628$		−	0.137269i		−	0.00547763i
$629$	1.37312	+	6.18703i	0.0547501	+	0.246693i
$630$		0			0
$631$	−9.29368	−	16.0971i	−0.369976	−	0.640817i	0.619586	−	0.784929i	$-0.287301\pi$
$631$	−9.29368	−	16.0971i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$632$	3.27919	+	1.89324i	0.130439	+	0.0753090i
$633$	35.9987	+	20.7838i	1.43082	+	0.826084i
$634$	−12.3904	+	21.4609i	−0.492087	+	0.852319i
$635$		0			0
$636$	−0.328780	+	0.569463i	−0.0130370	+	0.0225807i
$637$			0.0117320i			0.000464838i
$638$	−4.02795	+	2.32554i	−0.159468	+	0.0920689i
$639$	25.9682			1.02728
$640$		0			0
$641$	−11.0580	−	19.1531i	−0.436766	−	0.756501i	0.560672	−	0.828038i	$-0.310543\pi$
$641$	−11.0580	−	19.1531i	−0.436766	−	0.756501i	−0.997438	+	0.0715369i	$0.977210\pi$
$642$	23.9970	+	13.8547i	0.947086	+	0.546800i
$643$			33.4057i			1.31739i	0.752410	+	0.658695i	$0.228891\pi$
$643$			33.4057i			1.31739i	−0.752410	+	0.658695i	$0.771109\pi$
$644$	0.0105947	+	0.0183505i	0.000417489	+	0.000723112i
$645$		0			0
$646$	2.52459	+	4.37272i	0.0993287	+	0.172042i
$647$	5.13406	+	2.96415i	0.201841	+	0.116533i	0.597514	−	0.801859i	$-0.296155\pi$
$647$	5.13406	+	2.96415i	0.201841	+	0.116533i	−0.395673	+	0.918391i	$0.629489\pi$
$648$	−21.2534	−	12.2707i	−0.834914	−	0.482038i
$649$	−8.27738	−	14.3369i	−0.324916	−	0.562771i
$650$		0			0
$651$	0.155947	+	0.270109i	0.00611206	+	0.0105864i
$652$			0.466472i			0.0182684i
$653$	−22.2052	−	12.8202i	−0.868955	−	0.501692i	−0.00195430	−	0.999998i	$-0.500622\pi$
$653$	−22.2052	−	12.8202i	−0.868955	−	0.501692i	−0.867001	+	0.498307i	$0.833955\pi$
$654$	−30.7225	−	53.2129i	−1.20134	−	2.08079i
$655$		0			0
$656$	14.6319			0.571280
$657$	−1.33241	+	0.769269i	−0.0519824	+	0.0300120i
$658$		−	1.01875i		−	0.0397151i
$659$	5.85082	−	10.1339i	0.227916	−	0.394762i	−0.729274	−	0.684221i	$-0.760142\pi$
$659$	5.85082	−	10.1339i	0.227916	−	0.394762i	0.957190	+	0.289460i	$0.0934756\pi$
$660$		0			0
$661$	−22.8299	+	39.5425i	−0.887979	+	1.53802i	−0.0457184	+	0.998954i	$0.514558\pi$
$661$	−22.8299	+	39.5425i	−0.887979	+	1.53802i	−0.842261	+	0.539070i	$0.818776\pi$
$662$	−9.34161	−	5.39338i	−0.363072	−	0.209620i
$663$	−0.00375919	−	0.00217037i	−0.000145995	−	8.42901e-5i
$664$	−17.6116	−	30.5043i	−0.683464	−	1.18380i
$665$		0			0
$666$	−19.6129	+	17.9802i	−0.759986	+	0.696720i
$667$			5.19063i			0.200982i
$668$	1.06175	−	0.613003i	0.0410804	−	0.0237178i
$669$	−12.8581	+	22.2709i	−0.497123	+	0.861043i
$670$		0			0
$671$	3.00295	−	5.20126i	0.115928	−	0.200792i
$672$			0.128771i			0.00496746i
$673$	13.6180	+	7.86237i	0.524936	+	0.303072i	0.738952	−	0.673758i	$-0.235321\pi$
$673$	13.6180	+	7.86237i	0.524936	+	0.303072i	−0.214016	+	0.976830i	$0.568654\pi$
$674$	−22.0346			−0.848742
$675$		0			0
$676$	0.876741			0.0337208
$677$		−	44.7603i		−	1.72028i	−0.510059	−	0.860140i	$-0.670376\pi$
$677$		−	44.7603i		−	1.72028i	0.510059	−	0.860140i	$-0.329624\pi$
$678$	24.5775	−	14.1898i	0.943892	−	0.544956i
$679$	−1.26229	+	2.18636i	−0.0484424	+	0.0839047i
$680$		0			0
$681$	5.67956	+	9.83729i	0.217641	+	0.376966i
$682$	−1.65337	+	0.954574i	−0.0633108	+	0.0365525i
$683$	−42.9089	+	24.7735i	−1.64186	+	0.947930i	−0.661692	+	0.749775i	$0.730162\pi$
$683$	−42.9089	+	24.7735i	−1.64186	+	0.947930i	−0.980171	+	0.198155i	$0.936505\pi$
$684$	0.369885	−	0.640660i	0.0141429	−	0.0244962i
$685$		0			0
$686$	−1.32366	−	2.29265i	−0.0505375	−	0.0875336i
$687$	17.7168	−	10.2288i	0.675938	−	0.390253i
$688$	−25.9608	+	14.9885i	−0.989747	+	0.571430i
$689$	0.00660871			0.000251772
$690$		0			0
$691$	−17.8530	−	30.9222i	−0.679159	−	1.17634i	−0.975235	−	0.221173i	$-0.929011\pi$
$691$	−17.8530	−	30.9222i	−0.679159	−	1.17634i	0.296076	−	0.955164i	$-0.404322\pi$
$692$		−	0.952825i		−	0.0362210i
$693$		−	0.637225i		−	0.0242062i
$694$	−0.0590313	−	0.102245i	−0.00224080	−	0.00388117i
$695$		0			0
$696$	−8.01685	+	13.8856i	−0.303878	+	0.526332i
$697$			3.94886i			0.149574i
$698$	−1.24964	−	0.721478i	−0.0472994	−	0.0273083i
$699$	−28.5114	+	49.3833i	−1.07840	+	1.86785i
$700$		0			0
$701$	14.8246	+	25.6769i	0.559916	+	0.969803i	0.997503	+	0.0706270i	$0.0225000\pi$
$701$	14.8246	+	25.6769i	0.559916	+	0.969803i	−0.437587	+	0.899176i	$0.644167\pi$
$702$		0	0.000848833i		0	3.20372e-5i
$703$	14.3293	+	15.6305i	0.540441	+	0.589516i
$704$	−12.2685			−0.462385
$705$		0			0
$706$	−24.1540	+	41.8359i	−0.909046	+	1.57451i
$707$	−0.00844684	−	0.00487678i	−0.000317676	−	0.000183410i
$708$	−1.61224	−	0.930824i	−0.0605915	−	0.0349825i
$709$	20.0890			0.754458			0.377229	−	0.926120i	$-0.376877\pi$
$709$	20.0890			0.754458			0.377229	+	0.926120i	$0.376877\pi$
$710$		0			0
$711$	−4.14545			−0.155467
$712$	−20.1942	+	11.6592i	−0.756811	+	0.436945i
$713$			2.13062i			0.0797924i
$714$	0.489094			0.0183039
$715$		0			0
$716$	−0.169256	+	0.293160i	−0.00632539	+	0.0109559i
$717$		−	58.4239i		−	2.18188i
$718$	−29.0962	+	16.7987i	−1.08586	+	0.626921i
$719$	−7.55435	−	13.0845i	−0.281730	−	0.487970i	0.690081	−	0.723732i	$-0.257575\pi$
$719$	−7.55435	−	13.0845i	−0.281730	−	0.487970i	−0.971811	+	0.235762i	$0.924241\pi$
$720$		0			0
$721$	0.639855	−	1.10826i	0.0238295	−	0.0412738i
$722$	−8.24383	−	4.75958i	−0.306804	−	0.177133i
$723$	30.8108	−	17.7886i	1.14587	−	0.661567i
$724$	0.435245	+	0.753867i	0.0161758	+	0.0280173i
$725$		0			0
$726$	−30.2925			−1.12426
$727$	28.7640	+	16.6069i	1.06680	+	0.615916i	0.927305	−	0.374307i	$-0.122119\pi$
$727$	28.7640	+	16.6069i	1.06680	+	0.615916i	0.139493	+	0.990223i	$0.455453\pi$
$728$	0.000569696	0	0.000328914i	2.11143e−5	0	1.21904e-5i
$729$	29.5705			1.09520
$730$		0			0
$731$	−4.04509	−	7.00630i	−0.149613	−	0.259137i
$732$		−	0.675387i		−	0.0249630i
$733$	−14.9906	−	8.65483i	−0.553691	−	0.319673i	0.196919	−	0.980420i	$-0.436907\pi$
$733$	−14.9906	−	8.65483i	−0.553691	−	0.319673i	−0.750609	+	0.660746i	$0.770240\pi$
$734$	32.5904			1.20293
$735$		0			0
$736$	−0.439833	+	0.761813i	−0.0162125	+	0.0280808i
$737$	−16.1614	−	9.33079i	−0.595313	−	0.343704i
$738$	−14.3576	+	8.28937i	−0.528511	+	0.305136i
$739$	−35.4609			−1.30445			−0.652226	−	0.758025i	$-0.726165\pi$
$739$	−35.4609			−1.30445			−0.652226	+	0.758025i	$0.726165\pi$
$740$		0			0
$741$	−0.0145236			−0.000533538
$742$	−0.644875	+	0.372319i	−0.0236741	+	0.0136683i
$743$	−2.49668	−	1.44146i	−0.0915945	−	0.0528821i	0.453503	−	0.891255i	$-0.350174\pi$
$743$	−2.49668	−	1.44146i	−0.0915945	−	0.0528821i	−0.545098	+	0.838373i	$0.683507\pi$
$744$	−3.29071	+	5.69968i	−0.120643	+	0.208960i
$745$		0			0
$746$	−8.85907			−0.324354
$747$	33.3962	+	19.2813i	1.22190	+	0.705466i
$748$		−	0.104477i		−	0.00382004i
$749$	−0.547522	−	0.948336i	−0.0200060	−	0.0346515i
$750$		0			0
$751$	48.6875			1.77663			0.888316	−	0.459233i	$-0.151876\pi$
$751$	48.6875			1.77663			0.888316	+	0.459233i	$0.151876\pi$
$752$	17.9886	−	10.3857i	0.655975	−	0.378728i
$753$	−2.85301	−	1.64718i	−0.103969	−	0.0600267i
$754$	0.00525666			0.000191436
$755$		0			0
$756$	−0.00166885	−	0.00289053i	−6.06954e−5	−	0.000105127i
$757$	3.38343	−	1.95342i	0.122973	−	0.0709984i	−0.437252	−	0.899339i	$-0.644048\pi$
$757$	3.38343	−	1.95342i	0.122973	−	0.0709984i	0.560225	+	0.828341i	$0.310715\pi$
$758$	−11.6957	−	6.75252i	−0.424807	−	0.245263i
$759$	4.25165	−	7.36407i	0.154325	−	0.267299i
$760$		0			0
$761$	8.72821	+	15.1177i	0.316398	+	0.548017i	0.979734	−	0.200305i	$-0.0641933\pi$
$761$	8.72821	+	15.1177i	0.316398	+	0.548017i	−0.663336	+	0.748322i	$0.730860\pi$
$762$	−51.5785	+	29.7789i	−1.86849	+	1.07877i
$763$			2.42824i			0.0879081i
$764$	0.341091	−	0.590788i	0.0123403	−	0.0213740i
$765$		0			0
$766$	24.9311			0.900798
$767$			0.0187102i			0.000675587i
$768$	−3.47125	+	2.00413i	−0.125258	+	0.0723178i
$769$	−13.5564			−0.488855			−0.244427	−	0.969668i	$-0.578600\pi$
$769$	−13.5564			−0.488855			−0.244427	+	0.969668i	$0.578600\pi$
$770$		0			0
$771$	−45.0765			−1.62339
$772$	0.205283	+	0.118520i	0.00738831	+	0.00426564i
$773$	−13.7092	−	7.91500i	−0.493085	−	0.284683i	0.232768	−	0.972532i	$-0.425222\pi$
$773$	−13.7092	−	7.91500i	−0.493085	−	0.284683i	−0.725853	+	0.687849i	$0.758555\pi$
$774$	16.9828	−	29.4150i	0.610433	−	1.05730i
$775$		0			0
$776$	−53.2724			−1.91237
$777$	2.00523	−	0.445033i	0.0719372	−	0.0159655i
$778$		−	41.6790i		−	1.49426i
$779$	6.60621	+	11.4423i	0.236692	+	0.409962i
$780$		0			0
$781$	6.13542	−	10.6269i	0.219543	−	0.380259i
$782$	2.89348	+	1.67055i	0.103471	+	0.0597389i
$783$		−	0.817615i		−	0.0292192i
$784$	13.4762	−	23.3414i	0.481292	−	0.833622i
$785$		0			0
$786$	12.9088	+	22.3587i	0.460443	+	0.797510i
$787$			22.9418i			0.817787i	0.912582	+	0.408893i	$0.134085\pi$
$787$			22.9418i			0.817787i	−0.912582	+	0.408893i	$0.865915\pi$
$788$			1.41378i			0.0503640i
$789$	30.8612	+	53.4531i	1.09869	+	1.90298i
$790$		0			0
$791$	−1.12153			−0.0398771
$792$	11.6449	−	6.72318i	0.413783	−	0.238898i
$793$	−0.00587848	+	0.00339394i	−0.000208751	+	0.000120522i
$794$	−7.01644	−	12.1528i	−0.249004	−	0.431288i
$795$		0			0
$796$	0.461609	−	0.799530i	0.0163613	−	0.0283386i
$797$	30.3699	−	17.5341i	1.07576	−	0.621089i	0.146009	−	0.989283i	$-0.453357\pi$
$797$	30.3699	−	17.5341i	1.07576	−	0.621089i	0.929749	+	0.368194i	$0.120024\pi$
$798$	1.41721	−	0.818225i	0.0501686	−	0.0289649i
$799$	2.80289	+	4.85475i	0.0991592	+	0.171749i
$800$		0			0
$801$	12.7645	−	22.1087i	0.451011	−	0.781174i
$802$	−19.3743	+	11.1857i	−0.684129	+	0.394982i
$803$			0.727012i			0.0256557i
$804$	−2.09857			−0.0740108
$805$		0			0
$806$	0.00215772			7.60025e−5
$807$	−13.9705	−	8.06586i	−0.491784	−	0.283932i
$808$		−	0.205814i		−	0.00724052i
$809$	−2.29848	+	3.98109i	−0.0808103	+	0.139968i	−0.903598	−	0.428381i	$-0.859084\pi$
$809$	−2.29848	+	3.98109i	−0.0808103	+	0.139968i	0.822788	+	0.568349i	$0.192417\pi$
$810$		0			0
$811$	6.82428	−	11.8200i	0.239633	−	0.415056i	−0.720976	−	0.692960i	$-0.756306\pi$
$811$	6.82428	−	11.8200i	0.239633	−	0.415056i	0.960609	+	0.277904i	$0.0896396\pi$
$812$	0.0179005	−	0.0103348i	0.000628183	−	0.000362682i
$813$			49.2050i			1.72569i
$814$	2.72410	+	12.2743i	0.0954798	+	0.430213i
$815$		0			0
$816$	4.98608	+	8.63614i	0.174548	+	0.302325i
$817$	−23.4423	−	13.5344i	−0.820141	−	0.473509i
$818$	42.1677	+	24.3455i	1.47436	+	0.851221i
$819$	−0.000360097	0	0.000623706i	−1.25828e−5	0	2.17940e-5i
$820$		0			0
$821$	2.12640	−	3.68304i	0.0742120	−	0.128539i	−0.826531	−	0.562891i	$-0.809689\pi$
$821$	2.12640	−	3.68304i	0.0742120	−	0.128539i	0.900743	+	0.434352i	$0.143023\pi$
$822$			29.8329i			1.04054i
$823$	3.22008	−	1.85911i	0.112245	−	0.0648046i	−0.442827	−	0.896607i	$-0.646024\pi$
$823$	3.22008	−	1.85911i	0.112245	−	0.0648046i	0.555071	+	0.831803i	$0.312691\pi$
$824$	27.0037			0.940719
$825$		0			0
$826$	−1.05409	−	1.82574i	−0.0366765	−	0.0635256i
$827$	30.4865	+	17.6014i	1.06012	+	0.612060i	0.925465	−	0.378833i	$-0.123674\pi$
$827$	30.4865	+	17.6014i	1.06012	+	0.612060i	0.134654	+	0.990893i	$0.457008\pi$
$828$		−	0.489515i		−	0.0170118i
$829$	−4.55756	−	7.89393i	−0.158291	−	0.274167i	0.775962	−	0.630780i	$-0.217265\pi$
$829$	−4.55756	−	7.89393i	−0.158291	−	0.274167i	−0.934252	+	0.356613i	$0.883932\pi$
$830$		0			0
$831$	−7.37089	−	12.7668i	−0.255693	−	0.442874i
$832$	0.0120082	+	0.00693292i	0.000416308	+	0.000240356i
$833$	6.29938	+	3.63695i	0.218261	+	0.126013i
$834$	−2.06897	−	3.58356i	−0.0716425	−	0.124088i
$835$		0			0
$836$	−0.174783	−	0.302734i	−0.00604501	−	0.0104703i
$837$		−	0.335610i		−	0.0116004i
$838$	−45.8988	−	26.4997i	−1.58555	−	0.915417i
$839$	−7.94040	−	13.7532i	−0.274133	−	0.474813i	0.695783	−	0.718252i	$-0.255058\pi$
$839$	−7.94040	−	13.7532i	−0.274133	−	0.474813i	−0.969916	+	0.243440i	$0.921724\pi$
$840$		0			0
$841$	−23.9367			−0.825403
$842$	−32.1686	+	18.5726i	−1.10860	+	0.640053i
$843$			32.4584i			1.11793i
$844$	0.565377	−	0.979261i	0.0194611	−	0.0337076i
$845$		0			0
$846$	−11.7676	+	20.3820i	−0.404577	+	0.700749i
$847$	1.03674	+	0.598563i	0.0356229	+	0.0205669i
$848$	−13.1484	−	7.59124i	−0.451518	−	0.260684i
$849$	−25.7208	−	44.5498i	−0.882736	−	1.52894i
$850$		0			0
$851$	13.3830	+	4.21626i	0.458764	+	0.144532i
$852$		−	1.37990i		−	0.0472748i
$853$	45.2510	−	26.1257i	1.54937	−	0.894526i	0.551175	−	0.834390i	$-0.314180\pi$
$853$	45.2510	−	26.1257i	1.54937	−	0.894526i	0.998190	−	0.0601369i	$-0.0191537\pi$
$854$	0.382413	−	0.662359i	0.0130859	−	0.0226655i
$855$		0			0
$856$	11.5535	−	20.0112i	0.394891	−	0.683970i
$857$			31.7419i			1.08428i	0.840287	+	0.542141i	$0.182386\pi$
$857$			31.7419i			1.08428i	−0.840287	+	0.542141i	$0.817614\pi$
$858$	−0.00745775	−	0.00430573i	−0.000254603	−	0.000146995i
$859$	1.67935			0.0572988			0.0286494	−	0.999590i	$-0.490879\pi$
$859$	1.67935			0.0572988			0.0286494	+	0.999590i	$0.490879\pi$
$860$		0			0
$861$	1.27983			0.0436166
$862$			37.5076i			1.27752i
$863$	−12.1508	+	7.01529i	−0.413620	+	0.238803i	−0.692344	−	0.721568i	$-0.743422\pi$
$863$	−12.1508	+	7.01529i	−0.413620	+	0.238803i	0.278724	+	0.960371i	$0.410088\pi$
$864$	0.0692814	−	0.119999i	0.00235700	−	0.00408244i
$865$		0			0
$866$	7.75494	+	13.4320i	0.263524	+	0.456436i
$867$	34.1695	−	19.7278i	1.16046	−	0.669990i
$868$	0.00734768	−	0.00424219i	0.000249397	−	0.000143989i
$869$	−0.979434	+	1.69643i	−0.0332250	+	0.0575474i
$870$		0			0
$871$	0.0105457	+	0.0182657i	0.000357327	+	0.000618908i
$872$	−44.3745	+	25.6196i	−1.50271	+	0.867591i
$873$	50.5091	−	29.1614i	1.70947	−	0.986965i
$874$	11.1790			0.378134
$875$		0			0
$876$	0.0408777	+	0.0708022i	0.00138113	+	0.00239218i
$877$			47.1523i			1.59222i	0.605151	+	0.796111i	$0.293113\pi$
$877$			47.1523i			1.59222i	−0.605151	+	0.796111i	$0.706887\pi$
$878$			25.9679i			0.876376i
$879$	16.9028	+	29.2765i	0.570116	+	0.987471i
$880$		0			0
$881$	−19.1419	+	33.1547i	−0.644906	+	1.11701i	0.339417	+	0.940636i	$0.389770\pi$
$881$	−19.1419	+	33.1547i	−0.644906	+	1.11701i	−0.984323	+	0.176374i	$0.943563\pi$
$882$			30.5385i			1.02829i
$883$	24.6163	+	14.2122i	0.828405	+	0.478280i	0.853306	−	0.521410i	$-0.174594\pi$
$883$	24.6163	+	14.2122i	0.828405	+	0.478280i	−0.0249010	+	0.999690i	$0.507927\pi$
$884$	−5.90398e−5	0	0.000102260i	−1.98572e−6	0	3.43938e-6i
$885$		0			0
$886$	8.63370	+	14.9540i	0.290055	+	0.502390i
$887$		−	17.0648i		−	0.572980i	−0.958083	−	0.286490i	$-0.907512\pi$
$887$		−	17.0648i		−	0.572980i	0.958083	−	0.286490i	$-0.0924885\pi$
$888$	29.2893	+	31.9489i	0.982884	+	1.07213i
$889$	2.35366			0.0789392
$890$		0			0
$891$	6.34802	−	10.9951i	0.212667	−	0.368349i
$892$	0.605828	+	0.349775i	0.0202846	+	0.0117113i
$893$	16.2434	+	9.37815i	0.543566	+	0.313828i
$894$	65.6563			2.19587
$895$		0			0
$896$	−1.45846			−0.0487236
$897$	−0.00832289	+	0.00480522i	−0.000277893	+	0.000160442i
$898$		−	29.9995i		−	1.00109i
$899$	2.07837			0.0693174
$900$		0			0
$901$	2.04872	−	3.54849i	0.0682528	−	0.118217i
$902$			7.83403i			0.260845i
$903$	−2.27076	+	1.31102i	−0.0755661	+	0.0436281i
$904$	−11.8330	−	20.4953i	−0.393559	−	0.681664i
$905$		0			0
$906$	−11.0922	+	19.2123i	−0.368514	+	0.638284i
$907$	42.7341	+	24.6726i	1.41896	+	0.819239i	0.996208	−	0.0870050i	$-0.0277296\pi$
$907$	42.7341	+	24.6726i	1.41896	+	0.819239i	0.422755	+	0.906244i	$0.361063\pi$
$908$	0.267601	−	0.154499i	0.00888064	−	0.00512724i
$909$	0.112663	+	0.195138i	0.00373680	+	0.00647233i
$910$		0			0
$911$	−4.77518			−0.158209			−0.0791043	−	0.996866i	$-0.525206\pi$
$911$	−4.77518			−0.158209			−0.0791043	+	0.996866i	$0.525206\pi$
$912$	28.8955	+	16.6828i	0.956827	+	0.552424i
$913$	15.7808	−	9.11108i	0.522270	−	0.301533i
$914$	13.8539			0.458248
$915$		0			0
$916$	−0.278251	−	0.481945i	−0.00919367	−	0.0159239i
$917$		−	1.02029i		−	0.0336928i
$918$	−0.455774	−	0.263141i	−0.0150428	−	0.00868496i
$919$	43.7642			1.44365			0.721823	−	0.692078i	$-0.243304\pi$
$919$	43.7642			1.44365			0.721823	+	0.692078i	$0.243304\pi$
$920$		0			0
$921$	−32.2217	+	55.8096i	−1.06174	+	1.83899i
$922$	−7.92176	−	4.57363i	−0.260889	−	0.150625i
$923$	−0.0120105	+	0.00693427i	−0.000395330	+	0.000228244i
$924$	−0.0338611			−0.00111395
$925$		0			0
$926$	−9.11682			−0.299597
$927$	−25.6030	+	14.7819i	−0.840912	+	0.485501i
$928$	0.743129	+	0.429046i	0.0243944	+	0.0140841i
$929$	−28.0032	+	48.5029i	−0.918754	+	1.59133i	−0.117444	+	0.993079i	$0.537470\pi$
$929$	−28.0032	+	48.5029i	−0.918754	+	1.59133i	−0.801310	+	0.598250i	$0.795863\pi$
$930$		0			0
$931$	24.3376			0.797634
$932$	1.34336	+	0.775588i	0.0440031	+	0.0254052i
$933$			16.2479i			0.531934i
$934$	18.8280	+	32.6110i	0.616070	+	1.06706i
$935$		0			0
$936$	−0.0151971			−0.000496733
$937$	−28.1397	+	16.2465i	−0.919284	+	0.530749i	−0.883406	−	0.468608i	$-0.844756\pi$
$937$	−28.1397	+	16.2465i	−0.919284	+	0.530749i	−0.0358771	+	0.999356i	$0.511422\pi$
$938$	−2.05809	−	1.18824i	−0.0671990	−	0.0387973i
$939$	6.55746			0.213995
$940$		0			0
$941$	7.65935	+	13.2664i	0.249688	+	0.432472i	0.963439	−	0.267927i	$-0.0863387\pi$
$941$	7.65935	+	13.2664i	0.249688	+	0.432472i	−0.713751	+	0.700399i	$0.753005\pi$
$942$	−6.07516	+	3.50750i	−0.197940	+	0.114280i
$943$	7.57150	+	4.37141i	0.246562	+	0.142353i
$944$	21.4919	−	37.2251i	0.699502	−	1.21157i
$945$		0			0
$946$	−8.02494	−	13.8996i	−0.260913	−	0.451915i
$947$	−30.9950	+	17.8950i	−1.00720	+	0.581509i	−0.910371	−	0.413792i	$-0.864204\pi$
$947$	−30.9950	+	17.8950i	−1.00720	+	0.581509i	−0.0968310	+	0.995301i	$0.530871\pi$
$948$			0.220282i			0.00715444i
$949$	0.000410835	0	0.000711587i	1.33363e−5	0	2.30991e-5i
$950$		0			0
$951$	−44.1943			−1.43310
$952$		−	0.407858i		−	0.0132188i
$953$	40.8349	−	23.5761i	1.32277	−	0.763704i	0.338603	−	0.940929i	$-0.390046\pi$
$953$	40.8349	−	23.5761i	1.32277	−	0.763704i	0.984170	+	0.177225i	$0.0567122\pi$
$954$	17.2026			0.556954
$955$		0			0
$956$	−1.58929			−0.0514012
$957$	−7.18346	−	4.14737i	−0.232208	−	0.134066i
$958$	36.7497	+	21.2174i	1.18733	+	0.685504i
$959$	0.589483	−	1.02102i	0.0190354	−	0.0329703i
$960$		0			0
$961$	−30.1469			−0.972480
$962$	0.00426990	−	0.0135533i	0.000137667	−	0.000436974i
$963$			25.2976i			0.815205i
$964$	−0.483899	−	0.838138i	−0.0155853	−	0.0269946i
$965$		0			0
$966$	0.541430	−	0.937784i	0.0174202	−	0.0301727i
$967$	41.9245	+	24.2051i	1.34820	+	0.778384i	0.987995	−	0.154489i	$-0.0493731\pi$
$967$	41.9245	+	24.2051i	1.34820	+	0.778384i	0.360206	+	0.932873i	$0.382706\pi$
$968$			25.2611i			0.811921i
$969$	−4.50237	+	7.79833i	−0.144637	+	0.250518i
$970$		0			0
$971$	−11.5319	−	19.9739i	−0.370078	−	0.640993i	0.619500	−	0.784997i	$-0.287336\pi$
$971$	−11.5319	−	19.9739i	−0.370078	−	0.640993i	−0.989577	+	0.144004i	$0.954002\pi$
$972$		−	1.50124i		−	0.0481521i
$973$			0.163527i			0.00524243i
$974$	−7.66310	−	13.2729i	−0.245542	−	0.425291i
$975$		0			0
$976$	15.5941			0.499155
$977$	23.4504	−	13.5391i	0.750244	−	0.433154i	−0.0755378	−	0.997143i	$-0.524067\pi$
$977$	23.4504	−	13.5391i	0.750244	−	0.433154i	0.825782	+	0.563989i	$0.190734\pi$
$978$	20.6448	−	11.9193i	0.660147	−	0.381136i
$979$	−6.03166	−	10.4471i	−0.192773	−	0.333892i
$980$		0			0
$981$	28.0485	−	48.5814i	0.895519	−	1.55109i
$982$	1.78061	−	1.02803i	0.0568215	−	0.0328059i
$983$	18.1024	−	10.4515i	0.577378	−	0.333350i	−0.182712	−	0.983166i	$-0.558488\pi$
$983$	18.1024	−	10.4515i	0.577378	−	0.333350i	0.760091	+	0.649817i	$0.225154\pi$
$984$	13.5031	+	23.3881i	0.430465	+	0.745587i
$985$		0			0
$986$	1.62958	−	2.82252i	0.0518964	−	0.0898873i
$987$	1.57344	−	0.908423i	0.0500830	−	0.0289154i
$988$		0	0.000395081i		0	1.25692e-5i
$989$	−17.9118			−0.569561
$990$		0			0
$991$	−58.6900			−1.86435			−0.932175	−	0.362008i	$-0.882091\pi$
$991$	−58.6900			−1.86435			−0.932175	+	0.362008i	$0.882091\pi$
$992$	0.305035	+	0.176112i	0.00968488	+	0.00559157i
$993$		−	19.2371i		−	0.610472i
$994$	0.781320	−	1.35329i	0.0247820	−	0.0429236i
$995$		0			0
$996$	1.02458	−	1.77462i	0.0324649	−	0.0562309i
$997$	−2.24033	+	1.29346i	−0.0709521	+	0.0409642i	−0.535056	−	0.844816i	$-0.679710\pi$
$997$	−2.24033	+	1.29346i	−0.0709521	+	0.0409642i	0.464104	+	0.885781i	$0.346376\pi$
$998$			16.9640i			0.536986i
$999$	−2.10806	−	0.664135i	−0.0666960	−	0.0210123i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.o.d.174.7		48
5.2	odd	4		925.2.e.e.26.3	yes	24
5.3	odd	4		925.2.e.d.26.10	✓	24
5.4	even	2	inner	925.2.o.d.174.18		48
37.10	even	3	inner	925.2.o.d.824.18		48
185.47	odd	12		925.2.e.e.676.3	yes	24
185.84	even	6	inner	925.2.o.d.824.7		48
185.158	odd	12		925.2.e.d.676.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.e.d.26.10	✓	24	5.3	odd	4
925.2.e.d.676.10	yes	24	185.158	odd	12
925.2.e.e.26.3	yes	24	5.2	odd	4
925.2.e.e.676.3	yes	24	185.47	odd	12
925.2.o.d.174.7		48	1.1	even	1	trivial
925.2.o.d.174.18		48	5.4	even	2	inner
925.2.o.d.824.7		48	185.84	even	6	inner
925.2.o.d.824.18		48	37.10	even	3	inner

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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.20392 + 0.695082i) q^{2} +(-2.14707 - 1.23961i) q^{3} +(-0.0337208 + 0.0584061i) q^{4} +3.44653 q^{6} +(-0.117956 - 0.0681017i) q^{7} -2.87408i q^{8} +(1.57328 + 2.72500i) q^{9} +O(q^{10})\)	\(q+(-1.20392 + 0.695082i) q^{2} +(-2.14707 - 1.23961i) q^{3} +(-0.0337208 + 0.0584061i) q^{4} +3.44653 q^{6} +(-0.117956 - 0.0681017i) q^{7} -2.87408i q^{8} +(1.57328 + 2.72500i) q^{9} +1.48686 q^{11} +(0.144802 - 0.0836015i) q^{12} +(-0.00145531 - 0.000840224i) q^{13} +0.189345 q^{14} +(1.93028 + 3.34335i) q^{16} +(-0.902303 + 0.520945i) q^{17} +(-3.78820 - 2.18712i) q^{18} +(-1.74302 + 3.01900i) q^{19} +(0.168839 + 0.292438i) q^{21} +(-1.79005 + 1.03349i) q^{22} +2.30676i q^{23} +(-3.56275 + 6.17087i) q^{24} +0.00233610 q^{26} -0.363355i q^{27} +(0.00795511 - 0.00459289i) q^{28} +2.25018 q^{29} +0.923643 q^{31} +(0.330253 + 0.190671i) q^{32} +(-3.19239 - 1.84313i) q^{33} +(0.724199 - 1.25435i) q^{34} -0.212209 q^{36} +(1.82779 - 5.80165i) q^{37} -4.84618i q^{38} +(0.00208311 + 0.00360805i) q^{39} +(1.89504 - 3.28231i) q^{41} +(-0.406538 - 0.234715i) q^{42} +7.76491i q^{43} +(-0.0501380 + 0.0868416i) q^{44} +(-1.60339 - 2.77715i) q^{46} -5.38040i q^{47} -9.57122i q^{48} +(-3.49072 - 6.04611i) q^{49} +2.58308 q^{51} +(9.81485e-5 - 5.66661e-5i) q^{52} +(-3.40582 + 1.96635i) q^{53} +(0.252561 + 0.437449i) q^{54} +(-0.195730 + 0.339014i) q^{56} +(7.48479 - 4.32134i) q^{57} +(-2.70904 + 1.56406i) q^{58} +(-5.56703 - 9.64239i) q^{59} +(2.01966 - 3.49816i) q^{61} +(-1.11199 + 0.642008i) q^{62} -0.428572i q^{63} -8.25127 q^{64} +5.12450 q^{66} +(-10.8695 - 6.27551i) q^{67} -0.0702667i q^{68} +(2.85949 - 4.95278i) q^{69} +(4.12644 - 7.14720i) q^{71} +(7.83188 - 4.52174i) q^{72} +0.488959i q^{73} +(1.83212 + 8.25518i) q^{74} +(-0.117552 - 0.203606i) q^{76} +(-0.175383 - 0.101257i) q^{77} +(-0.00501578 - 0.00289586i) q^{78} +(-0.658728 + 1.14095i) q^{79} +(4.26942 - 7.39485i) q^{81} +5.26885i q^{82} +(10.6136 - 6.12774i) q^{83} -0.0227736 q^{84} +(-5.39725 - 9.34831i) q^{86} +(-4.83131 - 2.78936i) q^{87} -4.27335i q^{88} +(-4.05665 - 7.02632i) q^{89} +(0.000114441 + 0.000198218i) q^{91} +(-0.134729 - 0.0777857i) q^{92} +(-1.98313 - 1.14496i) q^{93} +(3.73982 + 6.47756i) q^{94} +(-0.472717 - 0.818771i) q^{96} -18.5354i q^{97} +(8.40509 + 4.85268i) q^{98} +(2.33924 + 4.05169i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 22 q^{4} + 20 q^{9}+O(q^{10}) \) 48 * q + 22 * q^4 + 20 * q^9	\( 48 q + 22 q^{4} + 20 q^{9} - 40 q^{14} - 26 q^{16} - 10 q^{19} - 12 q^{21} + 42 q^{24} - 40 q^{26} - 12 q^{29} + 76 q^{31} + 10 q^{34} - 4 q^{36} - 28 q^{39} - 26 q^{41} + 30 q^{44} - 26 q^{46} + 52 q^{49} - 92 q^{51} + 74 q^{54} + 14 q^{59} + 32 q^{61} - 40 q^{64} + 164 q^{66} - 42 q^{69} - 4 q^{71} - 96 q^{74} + 34 q^{76} + 42 q^{79} - 32 q^{81} - 152 q^{84} - 32 q^{86} - 58 q^{89} + 64 q^{91} + 26 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) \) 48 * q + 22 * q^4 + 20 * q^9 - 40 * q^14 - 26 * q^16 - 10 * q^19 - 12 * q^21 + 42 * q^24 - 40 * q^26 - 12 * q^29 + 76 * q^31 + 10 * q^34 - 4 * q^36 - 28 * q^39 - 26 * q^41 + 30 * q^44 - 26 * q^46 + 52 * q^49 - 92 * q^51 + 74 * q^54 + 14 * q^59 + 32 * q^61 - 40 * q^64 + 164 * q^66 - 42 * q^69 - 4 * q^71 - 96 * q^74 + 34 * q^76 + 42 * q^79 - 32 * q^81 - 152 * q^84 - 32 * q^86 - 58 * q^89 + 64 * q^91 + 26 * q^94 + 52 * q^96 + 30 * q^99

Introduction

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