LMFDB - Embedded newform 975.2.n.q.749.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(749,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("975.749");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.n (of order $4$, 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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			749.5
Character	$\chi$	$=$	975.749
Dual form			975.2.n.q.824.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35176 - 1.35176i) q^{2} +(-0.875587 + 1.49444i) q^{3} +1.65452i q^{4} +(3.20371 - 0.836541i) q^{6} +(3.04341 + 3.04341i) q^{7} +(-0.467005 + 0.467005i) q^{8} +(-1.46670 - 2.61702i) q^{9} +O(q^{10})$	\(q+(-1.35176 - 1.35176i) q^{2} +(-0.875587 + 1.49444i) q^{3} +1.65452i q^{4} +(3.20371 - 0.836541i) q^{6} +(3.04341 + 3.04341i) q^{7} +(-0.467005 + 0.467005i) q^{8} +(-1.46670 - 2.61702i) q^{9} +(1.65064 + 1.65064i) q^{11} +(-2.47258 - 1.44868i) q^{12} +(2.93636 + 2.09231i) q^{13} -8.22793i q^{14} +4.57160 q^{16} +4.34228i q^{17} +(-1.55497 + 5.52021i) q^{18} +(-3.93929 - 3.93929i) q^{19} +(-7.21296 + 1.88342i) q^{21} -4.46254i q^{22} -3.46204i q^{23} +(-0.289007 - 1.10681i) q^{24} +(-1.14095 - 6.79757i) q^{26} +(5.19520 + 0.0995434i) q^{27} +(-5.03538 + 5.03538i) q^{28} +5.82342i q^{29} +(1.77766 + 1.77766i) q^{31} +(-5.24571 - 5.24571i) q^{32} +(-3.91206 + 1.02150i) q^{33} +(5.86973 - 5.86973i) q^{34} +(4.32992 - 2.42668i) q^{36} +(-4.39024 - 4.39024i) q^{37} +10.6500i q^{38} +(-5.69787 + 2.55621i) q^{39} +(5.91144 - 5.91144i) q^{41} +(12.2961 + 7.20427i) q^{42} -8.59781 q^{43} +(-2.73102 + 2.73102i) q^{44} +(-4.67985 + 4.67985i) q^{46} +(-6.54241 + 6.54241i) q^{47} +(-4.00283 + 6.83198i) q^{48} +11.5247i q^{49} +(-6.48927 - 3.80204i) q^{51} +(-3.46178 + 4.85827i) q^{52} +1.40983 q^{53} +(-6.88811 - 7.15723i) q^{54} -2.84257 q^{56} +(9.33623 - 2.43784i) q^{57} +(7.87188 - 7.87188i) q^{58} +(4.52860 + 4.52860i) q^{59} +4.47788 q^{61} -4.80594i q^{62} +(3.50091 - 12.4284i) q^{63} +5.03870i q^{64} +(6.66900 + 3.90734i) q^{66} +(-4.35368 + 4.35368i) q^{67} -7.18440 q^{68} +(5.17380 + 3.03131i) q^{69} +(-6.80223 + 6.80223i) q^{71} +(1.90712 + 0.537208i) q^{72} +(7.30145 + 7.30145i) q^{73} +11.8691i q^{74} +(6.51765 - 6.51765i) q^{76} +10.0471i q^{77} +(11.1576 + 4.24678i) q^{78} +2.67693 q^{79} +(-4.69761 + 7.67675i) q^{81} -15.9817 q^{82} +(4.42241 + 4.42241i) q^{83} +(-3.11616 - 11.9340i) q^{84} +(11.6222 + 11.6222i) q^{86} +(-8.70275 - 5.09891i) q^{87} -1.54171 q^{88} +(2.02174 + 2.02174i) q^{89} +(2.56879 + 15.3043i) q^{91} +5.72801 q^{92} +(-4.21310 + 1.10011i) q^{93} +17.6876 q^{94} +(12.4325 - 3.24632i) q^{96} +(-1.21361 + 1.21361i) q^{97} +(15.5786 - 15.5786i) q^{98} +(1.89877 - 6.74074i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 12 q^{6} - 16 q^{7}+O(q^{10}) $ 40 * q + 12 * q^6 - 16 * q^7	$ 40 q + 12 q^{6} - 16 q^{7} - 24 q^{12} + 24 q^{13} - 64 q^{16} + 4 q^{18} + 16 q^{19} - 12 q^{21} - 8 q^{24} + 32 q^{28} + 32 q^{31} + 4 q^{33} + 16 q^{34} + 32 q^{37} + 8 q^{39} - 32 q^{43} - 40 q^{46} - 8 q^{52} + 32 q^{54} + 36 q^{57} + 24 q^{58} + 8 q^{61} - 8 q^{63} - 48 q^{66} + 32 q^{67} + 132 q^{72} + 64 q^{73} + 16 q^{76} - 108 q^{78} - 40 q^{79} + 72 q^{81} - 128 q^{82} - 124 q^{84} - 80 q^{88} + 8 q^{91} - 108 q^{93} + 32 q^{94} - 76 q^{96} - 24 q^{97} + 20 q^{99}+O(q^{100}) $ 40 * q + 12 * q^6 - 16 * q^7 - 24 * q^12 + 24 * q^13 - 64 * q^16 + 4 * q^18 + 16 * q^19 - 12 * q^21 - 8 * q^24 + 32 * q^28 + 32 * q^31 + 4 * q^33 + 16 * q^34 + 32 * q^37 + 8 * q^39 - 32 * q^43 - 40 * q^46 - 8 * q^52 + 32 * q^54 + 36 * q^57 + 24 * q^58 + 8 * q^61 - 8 * q^63 - 48 * q^66 + 32 * q^67 + 132 * q^72 + 64 * q^73 + 16 * q^76 - 108 * q^78 - 40 * q^79 + 72 * q^81 - 128 * q^82 - 124 * q^84 - 80 * q^88 + 8 * q^91 - 108 * q^93 + 32 * q^94 - 76 * q^96 - 24 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

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 $

$2$	−1.35176	−	1.35176i	−0.955840	−	0.955840i	0.0432252	−	0.999065i	$-0.486237\pi$
$2$	−1.35176	−	1.35176i	−0.955840	−	0.955840i	−0.999065	+	0.0432252i	$0.986237\pi$
$3$	−0.875587	+	1.49444i	−0.505520	+	0.862815i
$3$	−0.875587	+	1.49444i	−0.505520	+	0.862815i
$4$			1.65452i			0.827261i
$5$		0			0
$5$		0			0
$6$	3.20371	−	0.836541i	1.30791	−	0.341516i
$7$	3.04341	+	3.04341i	1.15030	+	1.15030i	0.986492	+	0.163808i	$0.0523778\pi$
$7$	3.04341	+	3.04341i	1.15030	+	1.15030i	0.163808	+	0.986492i	$0.447622\pi$
$8$	−0.467005	+	0.467005i	−0.165111	+	0.165111i
$9$	−1.46670	−	2.61702i	−0.488898	−	0.872341i
$10$		0			0
$11$	1.65064	+	1.65064i	0.497686	+	0.497686i	0.910717	−	0.413031i	$-0.135530\pi$
$11$	1.65064	+	1.65064i	0.497686	+	0.497686i	−0.413031	+	0.910717i	$0.635530\pi$
$12$	−2.47258	−	1.44868i	−0.713773	−	0.418197i
$13$	2.93636	+	2.09231i	0.814400	+	0.580303i
$13$	2.93636	+	2.09231i	0.814400	+	0.580303i
$14$		−	8.22793i		−	2.19901i
$15$		0			0
$16$	4.57160			1.14290
$17$			4.34228i			1.05316i	0.850126	+	0.526579i	$0.176525\pi$
$17$			4.34228i			1.05316i	−0.850126	+	0.526579i	$0.823475\pi$
$18$	−1.55497	+	5.52021i	−0.366509	+	1.30113i
$19$	−3.93929	−	3.93929i	−0.903736	−	0.903736i	0.0920208	−	0.995757i	$-0.470667\pi$
$19$	−3.93929	−	3.93929i	−0.903736	−	0.903736i	−0.995757	+	0.0920208i	$0.970667\pi$
$20$		0			0
$21$	−7.21296	+	1.88342i	−1.57400	+	0.410996i
$22$		−	4.46254i		−	0.951417i
$23$		−	3.46204i		−	0.721884i	−0.932588	−	0.360942i	$-0.882455\pi$
$23$		−	3.46204i		−	0.721884i	0.932588	−	0.360942i	$-0.117545\pi$
$24$	−0.289007	−	1.10681i	−0.0589933	−	0.225927i
$25$		0			0
$26$	−1.14095	−	6.79757i	−0.223759	−	1.33311i
$27$	5.19520	+	0.0995434i	0.999816	+	0.0191571i
$28$	−5.03538	+	5.03538i	−0.951598	+	0.951598i
$29$			5.82342i			1.08138i	0.841221	+	0.540691i	$0.181837\pi$
$29$			5.82342i			1.08138i	−0.841221	+	0.540691i	$0.818163\pi$
$30$		0			0
$31$	1.77766	+	1.77766i	0.319277	+	0.319277i	0.848489	−	0.529212i	$-0.177513\pi$
$31$	1.77766	+	1.77766i	0.319277	+	0.319277i	−0.529212	+	0.848489i	$0.677513\pi$
$32$	−5.24571	−	5.24571i	−0.927319	−	0.927319i
$33$	−3.91206	+	1.02150i	−0.681002	+	0.177821i
$34$	5.86973	−	5.86973i	1.00665	−	1.00665i
$35$		0			0
$36$	4.32992	−	2.42668i	0.721653	−	0.404447i
$37$	−4.39024	−	4.39024i	−0.721750	−	0.721750i	0.247211	−	0.968962i	$-0.420486\pi$
$37$	−4.39024	−	4.39024i	−0.721750	−	0.721750i	−0.968962	+	0.247211i	$0.920486\pi$
$38$			10.6500i			1.72765i
$39$	−5.69787	+	2.55621i	−0.912390	+	0.409322i
$40$		0			0
$41$	5.91144	−	5.91144i	0.923212	−	0.923212i	−0.0740434	−	0.997255i	$-0.523590\pi$
$41$	5.91144	−	5.91144i	0.923212	−	0.923212i	0.997255	+	0.0740434i	$0.0235903\pi$
$42$	12.2961	+	7.20427i	1.89733	+	1.11164i
$43$	−8.59781			−1.31115			−0.655576	−	0.755129i	$-0.727574\pi$
$43$	−8.59781			−1.31115			−0.655576	+	0.755129i	$0.727574\pi$
$44$	−2.73102	+	2.73102i	−0.411716	+	0.411716i
$45$		0			0
$46$	−4.67985	+	4.67985i	−0.690006	+	0.690006i
$47$	−6.54241	+	6.54241i	−0.954309	+	0.954309i	−0.999001	−	0.0446917i	$-0.985769\pi$
$47$	−6.54241	+	6.54241i	−0.954309	+	0.954309i	0.0446917	+	0.999001i	$0.485769\pi$
$48$	−4.00283	+	6.83198i	−0.577759	+	0.986111i
$49$			11.5247i			1.64638i
$50$		0			0
$51$	−6.48927	−	3.80204i	−0.908680	−	0.532393i
$52$	−3.46178	+	4.85827i	−0.480062	+	0.673722i
$53$	1.40983			0.193655			0.0968277	−	0.995301i	$-0.469130\pi$
$53$	1.40983			0.193655			0.0968277	+	0.995301i	$0.469130\pi$
$54$	−6.88811	−	7.15723i	−0.937354	−	0.973976i
$55$		0			0
$56$	−2.84257			−0.379855
$57$	9.33623	−	2.43784i	1.23661	−	0.322900i
$58$	7.87188	−	7.87188i	1.03363	−	1.03363i
$59$	4.52860	+	4.52860i	0.589573	+	0.589573i	0.937516	−	0.347943i	$-0.113120\pi$
$59$	4.52860	+	4.52860i	0.589573	+	0.589573i	−0.347943	+	0.937516i	$0.613120\pi$
$60$		0			0
$61$	4.47788			0.573334			0.286667	−	0.958030i	$-0.407453\pi$
$61$	4.47788			0.573334			0.286667	+	0.958030i	$0.407453\pi$
$62$		−	4.80594i		−	0.610355i
$63$	3.50091	−	12.4284i	0.441074	−	1.56583i
$64$			5.03870i			0.629837i
$65$		0			0
$66$	6.66900	+	3.90734i	0.820897	+	0.480961i
$67$	−4.35368	+	4.35368i	−0.531886	+	0.531886i	−0.921133	−	0.389247i	$-0.872735\pi$
$67$	−4.35368	+	4.35368i	−0.531886	+	0.531886i	0.389247	+	0.921133i	$0.372735\pi$
$68$	−7.18440			−0.871236
$69$	5.17380	+	3.03131i	0.622852	+	0.364927i
$70$		0			0
$71$	−6.80223	+	6.80223i	−0.807276	+	0.807276i	−0.984221	−	0.176945i	$-0.943378\pi$
$71$	−6.80223	+	6.80223i	−0.807276	+	0.807276i	0.176945	+	0.984221i	$0.443378\pi$
$72$	1.90712	+	0.537208i	0.224756	+	0.0633106i
$73$	7.30145	+	7.30145i	0.854571	+	0.854571i	0.990692	−	0.136121i	$-0.0434637\pi$
$73$	7.30145	+	7.30145i	0.854571	+	0.854571i	−0.136121	+	0.990692i	$0.543464\pi$
$74$			11.8691i			1.37976i
$75$		0			0
$76$	6.51765	−	6.51765i	0.747626	−	0.747626i
$77$			10.0471i			1.14498i
$78$	11.1576	+	4.24678i	1.26335	+	0.480853i
$79$	2.67693			0.301178			0.150589	−	0.988596i	$-0.451883\pi$
$79$	2.67693			0.301178			0.150589	+	0.988596i	$0.451883\pi$
$80$		0			0
$81$	−4.69761	+	7.67675i	−0.521957	+	0.852972i
$82$	−15.9817			−1.76489
$83$	4.42241	+	4.42241i	0.485423	+	0.485423i	0.906858	−	0.421436i	$-0.138474\pi$
$83$	4.42241	+	4.42241i	0.485423	+	0.485423i	−0.421436	+	0.906858i	$0.638474\pi$
$84$	−3.11616	−	11.9340i	−0.340001	−	1.30211i
$85$		0			0
$86$	11.6222	+	11.6222i	1.25325	+	1.25325i
$87$	−8.70275	−	5.09891i	−0.933033	−	0.546661i
$88$	−1.54171			−0.164347
$89$	2.02174	+	2.02174i	0.214304	+	0.214304i	0.806093	−	0.591789i	$-0.201578\pi$
$89$	2.02174	+	2.02174i	0.214304	+	0.214304i	−0.591789	+	0.806093i	$0.701578\pi$
$90$		0			0
$91$	2.56879	+	15.3043i	0.269282	+	1.60433i
$92$	5.72801			0.597187
$93$	−4.21310	+	1.10011i	−0.436878	+	0.114076i
$94$	17.6876			1.82433
$95$		0			0
$96$	12.4325	−	3.24632i	1.26888	−	0.331326i
$97$	−1.21361	+	1.21361i	−0.123224	+	0.123224i	−0.766029	−	0.642806i	$-0.777770\pi$
$97$	−1.21361	+	1.21361i	−0.123224	+	0.123224i	0.642806	+	0.766029i	$0.277770\pi$
$98$	15.5786	−	15.5786i	1.57368	−	1.57368i
$99$	1.89877	−	6.74074i	0.190834	−	0.677470i
$100$		0			0
$101$	−5.82645			−0.579754			−0.289877	−	0.957064i	$-0.593614\pi$
$101$	−5.82645			−0.579754			−0.289877	+	0.957064i	$0.593614\pi$
$102$	3.63249	+	13.9114i	0.359671	+	1.37743i
$103$	0.655146			0.0645535			0.0322767	−	0.999479i	$-0.489724\pi$
$103$	0.655146			0.0645535			0.0322767	+	0.999479i	$0.489724\pi$
$104$	−2.34842	+	0.394175i	−0.230281	+	0.0386520i
$105$		0			0
$106$	−1.90576	−	1.90576i	−0.185104	−	0.185104i
$107$	−0.228933			−0.0221318			−0.0110659	−	0.999939i	$-0.503522\pi$
$107$	−0.228933			−0.0221318			−0.0110659	+	0.999939i	$0.503522\pi$
$108$	−0.164697	+	8.59557i	−0.0158480	+	0.827109i
$109$	9.83957	+	9.83957i	0.942459	+	0.942459i	0.998432	−	0.0559728i	$-0.0178260\pi$
$109$	9.83957	+	9.83957i	0.942459	+	0.942459i	−0.0559728	+	0.998432i	$0.517826\pi$
$110$		0			0
$111$	10.4050	−	2.71691i	0.987596	−	0.257877i
$112$	13.9133	+	13.9133i	1.31468	+	1.31468i
$113$	−6.58296			−0.619273			−0.309636	−	0.950855i	$-0.600207\pi$
$113$	−6.58296			−0.619273			−0.309636	+	0.950855i	$0.600207\pi$
$114$	−15.9157	−	9.32498i	−1.49065	−	0.873365i
$115$		0			0
$116$	−9.63498			−0.894585
$117$	1.16888	−	10.7533i	0.108063	−	0.994144i
$118$		−	12.2432i		−	1.12708i
$119$	−13.2153	+	13.2153i	−1.21145	+	1.21145i
$120$		0			0
$121$		−	5.55078i		−	0.504616i
$122$	−6.05303	−	6.05303i	−0.548016	−	0.548016i
$123$	3.65831	+	14.0103i	0.329858	+	1.26326i
$124$	−2.94117	+	2.94117i	−0.264125	+	0.264125i
$125$		0			0
$126$	−21.5327	+	12.0679i	−1.91828	+	1.07509i
$127$	8.21272			0.728761			0.364381	−	0.931250i	$-0.381281\pi$
$127$	8.21272			0.728761			0.364381	+	0.931250i	$0.381281\pi$
$128$	−3.68030	+	3.68030i	−0.325296	+	0.325296i
$129$	7.52812	−	12.8489i	0.662814	−	1.13128i
$130$		0			0
$131$			7.36853i			0.643791i	0.946775	+	0.321896i	$0.104320\pi$
$131$			7.36853i			0.643791i	−0.946775	+	0.321896i	$0.895680\pi$
$132$	−1.69010	−	6.47258i	−0.147104	−	0.563366i
$133$		−	23.9778i		−	2.07914i
$134$	11.7703			1.01680
$135$		0			0
$136$	−2.02787	−	2.02787i	−0.173888	−	0.173888i
$137$	1.95599	−	1.95599i	0.167112	−	0.167112i	−0.618597	−	0.785709i	$-0.712299\pi$
$137$	1.95599	−	1.95599i	0.167112	−	0.167112i	0.785709	+	0.618597i	$0.212299\pi$
$138$	−2.89613	−	11.0914i	−0.246535	−	0.944159i
$139$	−14.3848			−1.22010			−0.610052	−	0.792361i	$-0.708852\pi$
$139$	−14.3848			−1.22010			−0.610052	+	0.792361i	$0.708852\pi$
$140$		0			0
$141$	−4.04879	−	15.5057i	−0.340969	−	1.30581i
$142$	18.3900			1.54325
$143$	1.39322	+	8.30053i	0.116507	+	0.694125i
$144$	−6.70515	−	11.9640i	−0.558762	−	0.996999i
$145$		0			0
$146$		−	19.7397i		−	1.63367i
$147$	−17.2229	−	10.0908i	−1.42052	−	0.832279i
$148$	7.26374	−	7.26374i	0.597076	−	0.597076i
$149$	4.35495	−	4.35495i	0.356772	−	0.356772i	−0.505850	−	0.862622i	$-0.668821\pi$
$149$	4.35495	−	4.35495i	0.356772	−	0.356772i	0.862622	+	0.505850i	$0.168821\pi$
$150$		0			0
$151$	4.31495	−	4.31495i	0.351145	−	0.351145i	−0.509390	−	0.860536i	$-0.670129\pi$
$151$	4.31495	−	4.31495i	0.351145	−	0.351145i	0.860536	+	0.509390i	$0.170129\pi$
$152$	3.67934			0.298434
$153$	11.3638	−	6.36880i	0.918712	−	0.514887i
$154$	13.5813	−	13.5813i	1.09442	−	1.09442i
$155$		0			0
$156$	−4.22931	−	9.42726i	−0.338616	−	0.754785i
$157$		−	17.4089i		−	1.38938i	−0.719308	−	0.694691i	$-0.755541\pi$
$157$		−	17.4089i		−	1.38938i	0.719308	−	0.694691i	$-0.244459\pi$
$158$	−3.61858	−	3.61858i	−0.287878	−	0.287878i
$159$	−1.23443	+	2.10691i	−0.0978967	+	0.167089i
$160$		0			0
$161$	10.5364	−	10.5364i	0.830384	−	0.830384i
$162$	16.7272	−	4.02709i	1.31421	−	0.316398i
$163$	−2.05453	−	2.05453i	−0.160923	−	0.160923i	0.622052	−	0.782976i	$-0.286299\pi$
$163$	−2.05453	−	2.05453i	−0.160923	−	0.160923i	−0.782976	+	0.622052i	$0.786299\pi$
$164$	9.78060	+	9.78060i	0.763737	+	0.763737i
$165$		0			0
$166$		−	11.9561i		−	0.927973i
$167$	−13.6508	+	13.6508i	−1.05633	+	1.05633i	−0.0580142	+	0.998316i	$0.518477\pi$
$167$	−13.6508	+	13.6508i	−1.05633	+	1.05633i	−0.998316	+	0.0580142i	$0.981523\pi$
$168$	2.48892	−	4.24805i	0.192024	−	0.327744i
$169$	4.24445	+	12.2876i	0.326496	+	0.945199i
$170$		0			0
$171$	−4.53148	+	16.0870i	−0.346531	+	1.23020i
$172$		−	14.2253i		−	1.08467i
$173$		−	7.23751i		−	0.550257i	−0.961407	−	0.275129i	$-0.911280\pi$
$173$		−	7.23751i		−	0.550257i	0.961407	−	0.275129i	$-0.0887205\pi$
$174$	4.87153	+	18.6566i	0.369310	+	1.41435i
$175$		0			0
$176$	7.54606	+	7.54606i	0.568806	+	0.568806i
$177$	−10.7329	+	2.80253i	−0.806734	+	0.210651i
$178$		−	5.46583i		−	0.409681i
$179$	−10.1878			−0.761474			−0.380737	−	0.924683i	$-0.624330\pi$
$179$	−10.1878			−0.761474			−0.380737	+	0.924683i	$0.624330\pi$
$180$		0			0
$181$			20.8159i			1.54723i	0.633655	+	0.773616i	$0.281554\pi$
$181$			20.8159i			1.54723i	−0.633655	+	0.773616i	$0.718446\pi$
$182$	17.2154	−	24.1602i	1.27609	−	1.79087i
$183$	−3.92077	+	6.69192i	−0.289832	+	0.494681i
$184$	1.61679	+	1.61679i	0.119191	+	0.119191i
$185$		0			0
$186$	7.18219	+	4.20802i	0.526624	+	0.308547i
$187$	−7.16754	+	7.16754i	−0.524142	+	0.524142i
$188$	−10.8246	−	10.8246i	−0.789462	−	0.789462i
$189$	15.5082	+	16.1141i	1.12805	+	1.17213i
$190$		0			0
$191$		−	20.6575i		−	1.49472i	−0.664417	−	0.747362i	$-0.731320\pi$
$191$		−	20.6575i		−	1.49472i	0.664417	−	0.747362i	$-0.268680\pi$
$192$	−7.53002	−	4.41182i	−0.543433	−	0.318395i
$193$	2.66617	+	2.66617i	0.191915	+	0.191915i	0.796523	−	0.604608i	$-0.206670\pi$
$193$	2.66617	+	2.66617i	0.191915	+	0.191915i	−0.604608	+	0.796523i	$0.706670\pi$
$194$	3.28104			0.235565
$195$		0			0
$196$	−19.0678			−1.36199
$197$	−16.8317	−	16.8317i	−1.19921	−	1.19921i	−0.974404	−	0.224804i	$-0.927826\pi$
$197$	−16.8317	−	16.8317i	−1.19921	−	1.19921i	−0.224804	−	0.974404i	$-0.572174\pi$
$198$	−11.6786	+	6.54519i	−0.829960	+	0.465146i
$199$			6.70679i			0.475432i	0.971335	+	0.237716i	$0.0763987\pi$
$199$			6.70679i			0.475432i	−0.971335	+	0.237716i	$0.923601\pi$
$200$		0			0
$201$	−2.69428	−	10.3183i	−0.190040	−	0.727799i
$202$	7.87598	+	7.87598i	0.554152	+	0.554152i
$203$	−17.7231	+	17.7231i	−1.24391	+	1.24391i
$204$	6.29056	−	10.7366i	0.440427	−	0.751715i
$205$		0			0
$206$	−0.885602	−	0.885602i	−0.0617028	−	0.0617028i
$207$	−9.06022	+	5.07775i	−0.629729	+	0.352928i
$208$	13.4239	+	9.56522i	0.930779	+	0.663229i
$209$		−	13.0047i		−	0.899555i
$210$		0			0
$211$	−25.4362			−1.75110			−0.875549	−	0.483129i	$-0.839500\pi$
$211$	−25.4362			−1.75110			−0.875549	+	0.483129i	$0.839500\pi$
$212$			2.33260i			0.160203i
$213$	−4.20957	−	16.1214i	−0.288435	−	1.10462i
$214$	0.309463	+	0.309463i	0.0211544	+	0.0211544i
$215$		0			0
$216$	−2.47267	+	2.37970i	−0.168244	+	0.161918i
$217$			10.8203i			0.734529i
$218$		−	26.6015i		−	1.80168i
$219$	−17.3046	+	4.51852i	−1.16934	+	0.305333i
$220$		0			0
$221$	−9.08541	+	12.7505i	−0.611151	+	0.857692i
$222$	−17.7377	−	10.3924i	−1.19047	−	0.697495i
$223$	−5.17991	+	5.17991i	−0.346872	+	0.346872i	−0.858943	−	0.512071i	$-0.828878\pi$
$223$	−5.17991	+	5.17991i	−0.346872	+	0.346872i	0.512071	+	0.858943i	$0.328878\pi$
$224$		−	31.9297i		−	2.13339i
$225$		0			0
$226$	8.89859	+	8.89859i	0.591926	+	0.591926i
$227$	20.0123	+	20.0123i	1.32827	+	1.32827i	0.906883	+	0.421383i	$0.138455\pi$
$227$	20.0123	+	20.0123i	1.32827	+	1.32827i	0.421383	+	0.906883i	$0.361545\pi$
$228$	4.03346	+	15.4470i	0.267122	+	1.02300i
$229$	−11.2696	+	11.2696i	−0.744713	+	0.744713i	−0.973481	−	0.228768i	$-0.926530\pi$
$229$	−11.2696	+	11.2696i	−0.744713	+	0.744713i	0.228768	+	0.973481i	$0.426530\pi$
$230$		0			0
$231$	−15.0148	−	8.79714i	−0.987904	−	0.578809i
$232$	−2.71957	−	2.71957i	−0.178548	−	0.178548i
$233$			10.0133i			0.655994i	0.944679	+	0.327997i	$0.106374\pi$
$233$			10.0133i			0.655994i	−0.944679	+	0.327997i	$0.893626\pi$
$234$	−16.1160	+	12.9559i	−1.05353	+	0.846952i
$235$		0			0
$236$	−7.49266	+	7.49266i	−0.487731	+	0.487731i
$237$	−2.34389	+	4.00051i	−0.152252	+	0.259861i
$238$	35.7280			2.31590
$239$	12.6708	−	12.6708i	0.819603	−	0.819603i	−0.166448	−	0.986050i	$-0.553230\pi$
$239$	12.6708	−	12.6708i	0.819603	−	0.819603i	0.986050	+	0.166448i	$0.0532296\pi$
$240$		0			0
$241$	−6.25390	+	6.25390i	−0.402849	+	0.402849i	−0.879236	−	0.476387i	$-0.841946\pi$
$241$	−6.25390	+	6.25390i	−0.402849	+	0.402849i	0.476387	+	0.879236i	$0.341946\pi$
$242$	−7.50333	+	7.50333i	−0.482333	+	0.482333i
$243$	−7.35927	−	13.7420i	−0.472097	−	0.881547i
$244$			7.40875i			0.474297i
$245$		0			0
$246$	13.9934	−	23.8837i	0.892185	−	1.52277i
$247$	−3.32496	−	19.8094i	−0.211562	−	1.26044i
$248$	−1.66035			−0.105432
$249$	−10.4812	+	2.73682i	−0.664221	+	0.173439i
$250$		0			0
$251$	14.2440			0.899071			0.449535	−	0.893263i	$-0.351590\pi$
$251$	14.2440			0.899071			0.449535	+	0.893263i	$0.351590\pi$
$252$	20.5631	+	5.79234i	1.29535	+	0.364883i
$253$	5.71457	−	5.71457i	0.359272	−	0.359272i
$254$	−11.1016	−	11.1016i	−0.696579	−	0.696579i
$255$		0			0
$256$	20.0272			1.25170
$257$		−	24.9676i		−	1.55743i	−0.627376	−	0.778717i	$-0.715871\pi$
$257$		−	24.9676i		−	1.55743i	0.627376	−	0.778717i	$-0.284129\pi$
$258$	−27.5449	+	7.19241i	−1.71487	+	0.447780i
$259$		−	26.7226i		−	1.66046i
$260$		0			0
$261$	15.2400	−	8.54119i	0.943334	−	0.528686i
$262$	9.96050	−	9.96050i	0.615361	−	0.615361i
$263$	−4.70892			−0.290364			−0.145182	−	0.989405i	$-0.546377\pi$
$263$	−4.70892			−0.290364			−0.145182	+	0.989405i	$0.546377\pi$
$264$	1.34990	−	2.30400i	0.0830808	−	0.141801i
$265$		0			0
$266$	−32.4122	+	32.4122i	−1.98732	+	1.98732i
$267$	−4.79158	+	1.25116i	−0.293240	+	0.0765697i
$268$	−7.20325	−	7.20325i	−0.440009	−	0.440009i
$269$		−	18.3605i		−	1.11946i	−0.828675	−	0.559730i	$-0.810905\pi$
$269$		−	18.3605i		−	1.11946i	0.828675	−	0.559730i	$-0.189095\pi$
$270$		0			0
$271$	7.79066	−	7.79066i	0.473249	−	0.473249i	−0.429715	−	0.902964i	$-0.641386\pi$
$271$	7.79066	−	7.79066i	0.473249	−	0.473249i	0.902964	+	0.429715i	$0.141386\pi$
$272$			19.8512i			1.20365i
$273$	−25.1206	−	9.56136i	−1.52037	−	0.578680i
$274$	−5.28807			−0.319464
$275$		0			0
$276$	−5.01537	+	8.56016i	−0.301890	+	0.515261i
$277$	5.90222			0.354630			0.177315	−	0.984154i	$-0.443259\pi$
$277$	5.90222			0.354630			0.177315	+	0.984154i	$0.443259\pi$
$278$	19.4448	+	19.4448i	1.16622	+	1.16622i
$279$	2.04489	−	7.25945i	0.122424	−	0.434612i
$280$		0			0
$281$	3.71699	+	3.71699i	0.221737	+	0.221737i	0.809230	−	0.587492i	$-0.199885\pi$
$281$	3.71699	+	3.71699i	0.221737	+	0.221737i	−0.587492	+	0.809230i	$0.699885\pi$
$282$	−15.4870	+	26.4330i	−0.922238	+	1.57406i
$283$	−2.46580			−0.146577			−0.0732884	−	0.997311i	$-0.523349\pi$
$283$	−2.46580			−0.146577			−0.0732884	+	0.997311i	$0.523349\pi$
$284$	−11.2544	−	11.2544i	−0.667827	−	0.667827i
$285$		0			0
$286$	9.33704	−	13.1036i	0.552111	−	0.774835i
$287$	35.9818			2.12394
$288$	−6.03428	+	21.4220i	−0.355573	+	1.26230i
$289$	−1.85540			−0.109141
$290$		0			0
$291$	−0.751048	−	2.87630i	−0.0440272	−	0.168612i
$292$	−12.0804	+	12.0804i	−0.706953	+	0.706953i
$293$	−2.46556	+	2.46556i	−0.144039	+	0.144039i	−0.775449	−	0.631410i	$-0.782477\pi$
$293$	−2.46556	+	2.46556i	−0.144039	+	0.144039i	0.631410	+	0.775449i	$0.282477\pi$
$294$	9.64086	+	36.9217i	0.562266	+	2.15332i
$295$		0			0
$296$	4.10052			0.238338
$297$	8.41109	+	8.73971i	0.488061	+	0.507129i
$298$	−11.7737			−0.682033
$299$	7.24366	−	10.1658i	0.418912	−	0.587903i
$300$		0			0
$301$	−26.1666	−	26.1666i	−1.50822	−	1.50822i
$302$	−11.6656			−0.671278
$303$	5.10156	−	8.70728i	0.293077	−	0.500220i
$304$	−18.0089	−	18.0089i	−1.03288	−	1.03288i
$305$		0			0
$306$	−23.9703	−	6.75211i	−1.37029	−	0.385992i
$307$	7.33272	+	7.33272i	0.418500	+	0.418500i	0.884687	−	0.466186i	$-0.154372\pi$
$307$	7.33272	+	7.33272i	0.418500	+	0.418500i	−0.466186	+	0.884687i	$0.654372\pi$
$308$	−16.6232			−0.947195
$309$	−0.573637	+	0.979076i	−0.0326331	+	0.0556977i
$310$		0			0
$311$	−4.15959			−0.235869			−0.117934	−	0.993021i	$-0.537627\pi$
$311$	−4.15959			−0.235869			−0.117934	+	0.993021i	$0.537627\pi$
$312$	1.46717	−	3.85470i	0.0830622	−	0.218229i
$313$		−	15.3278i		−	0.866380i	−0.901303	−	0.433190i	$-0.857388\pi$
$313$		−	15.3278i		−	0.866380i	0.901303	−	0.433190i	$-0.142612\pi$
$314$	−23.5327	+	23.5327i	−1.32803	+	1.32803i
$315$		0			0
$316$			4.42904i			0.249153i
$317$	6.41472	+	6.41472i	0.360287	+	0.360287i	0.863918	−	0.503632i	$-0.168003\pi$
$317$	6.41472	+	6.41472i	0.360287	+	0.360287i	−0.503632	+	0.863918i	$0.668003\pi$
$318$	4.51669	−	1.17938i	0.253284	−	0.0661365i
$319$	−9.61237	+	9.61237i	−0.538189	+	0.538189i
$320$		0			0
$321$	0.200451	−	0.342126i	0.0111881	−	0.0190956i
$322$	−28.4854			−1.58743
$323$	17.1055	−	17.1055i	0.951777	−	0.951777i
$324$	−12.7013	−	7.77230i	−0.705630	−	0.431794i
$325$		0			0
$326$			5.55447i			0.307634i
$327$	−23.3200	+	6.08924i	−1.28960	+	0.336736i
$328$			5.52134i			0.304865i
$329$	−39.8225			−2.19548
$330$		0			0
$331$	−11.7642	−	11.7642i	−0.646616	−	0.646616i	0.305557	−	0.952174i	$-0.401157\pi$
$331$	−11.7642	−	11.7642i	−0.646616	−	0.646616i	−0.952174	+	0.305557i	$0.901157\pi$
$332$	−7.31697	+	7.31697i	−0.401571	+	0.401571i
$333$	−5.05021	+	17.9285i	−0.276750	+	0.982475i
$334$	36.9052			2.01937
$335$		0			0
$336$	−32.9748	+	8.61024i	−1.79892	+	0.469727i
$337$	10.8474			0.590894			0.295447	−	0.955359i	$-0.404532\pi$
$337$	10.8474			0.590894			0.295447	+	0.955359i	$0.404532\pi$
$338$	10.8724	−	22.3474i	0.591381	−	1.21554i
$339$	5.76395	−	9.83783i	0.313055	−	0.534318i
$340$		0			0
$341$			5.86855i			0.317800i
$342$	27.8712	−	15.6203i	1.50710	−	0.844648i
$343$	−13.7704	+	13.7704i	−0.743533	+	0.743533i
$344$	4.01522	−	4.01522i	0.216486	−	0.216486i
$345$		0			0
$346$	−9.78339	+	9.78339i	−0.525958	+	0.525958i
$347$	8.70464			0.467289			0.233645	−	0.972322i	$-0.424935\pi$
$347$	8.70464			0.467289			0.233645	+	0.972322i	$0.424935\pi$
$348$	8.43626	−	14.3989i	0.452231	−	0.771861i
$349$	23.6983	−	23.6983i	1.26854	−	1.26854i	0.321700	−	0.946842i	$-0.395746\pi$
$349$	23.6983	−	23.6983i	1.26854	−	1.26854i	0.946842	−	0.321700i	$-0.104254\pi$
$350$		0			0
$351$	15.0467	+	11.1623i	0.803134	+	0.595798i
$352$		−	17.3175i		−	0.923028i
$353$	10.1103	+	10.1103i	0.538119	+	0.538119i	0.922976	−	0.384857i	$-0.125749\pi$
$353$	10.1103	+	10.1103i	0.538119	+	0.538119i	−0.384857	+	0.922976i	$0.625749\pi$
$354$	18.2967	+	10.7200i	0.972457	+	0.569759i
$355$		0			0
$356$	−3.34501	+	3.34501i	−0.177285	+	0.177285i
$357$	−8.17834	−	31.3207i	−0.432843	−	1.65767i
$358$	13.7715	+	13.7715i	0.727847	+	0.727847i
$359$	14.1823	+	14.1823i	0.748515	+	0.748515i	0.974200	−	0.225686i	$-0.0724622\pi$
$359$	14.1823	+	14.1823i	0.748515	+	0.748515i	−0.225686	+	0.974200i	$0.572462\pi$
$360$		0			0
$361$			12.0361i			0.633478i
$362$	28.1381	−	28.1381i	1.47891	−	1.47891i
$363$	8.29530	+	4.86019i	0.435390	+	0.255094i
$364$	−25.3213	+	4.25011i	−1.32720	+	0.222766i
$365$		0			0
$366$	14.3458	−	3.74593i	0.749869	−	0.195803i
$367$		−	3.99669i		−	0.208625i	−0.994545	−	0.104313i	$-0.966736\pi$
$367$		−	3.99669i		−	0.208625i	0.994545	−	0.104313i	$-0.0332643\pi$
$368$		−	15.8270i		−	0.825042i
$369$	−24.1406	−	6.80009i	−1.25671	−	0.353998i
$370$		0			0
$371$	4.29069	+	4.29069i	0.222762	+	0.222762i
$372$	−1.82015	−	6.97066i	−0.0943705	−	0.361412i
$373$		−	13.2904i		−	0.688150i	−0.938942	−	0.344075i	$-0.888193\pi$
$373$		−	13.2904i		−	0.688150i	0.938942	−	0.344075i	$-0.111807\pi$
$374$	19.3776			1.00199
$375$		0			0
$376$		−	6.11068i		−	0.315134i
$377$	−12.1844	+	17.0997i	−0.627530	+	0.880678i
$378$	0.819036	−	42.7457i	0.0421267	−	2.19860i
$379$	−3.56862	−	3.56862i	−0.183308	−	0.183308i	0.609488	−	0.792795i	$-0.291375\pi$
$379$	−3.56862	−	3.56862i	−0.183308	−	0.183308i	−0.792795	+	0.609488i	$0.791375\pi$
$380$		0			0
$381$	−7.19095	+	12.2734i	−0.368404	+	0.628786i
$382$	−27.9240	+	27.9240i	−1.42872	+	1.42872i
$383$	22.1631	+	22.1631i	1.13248	+	1.13248i	0.989763	+	0.142718i	$0.0455843\pi$
$383$	22.1631	+	22.1631i	1.13248	+	1.13248i	0.142718	+	0.989763i	$0.454416\pi$
$384$	−2.27756	−	8.72240i	−0.116226	−	0.445113i
$385$		0			0
$386$		−	7.20806i		−	0.366881i
$387$	12.6104	+	22.5006i	0.641021	+	1.14377i
$388$	−2.00795	−	2.00795i	−0.101938	−	0.101938i
$389$	20.9424			1.06182			0.530910	−	0.847428i	$-0.321850\pi$
$389$	20.9424			1.06182			0.530910	+	0.847428i	$0.321850\pi$
$390$		0			0
$391$	15.0331			0.760258
$392$	−5.38208	−	5.38208i	−0.271836	−	0.271836i
$393$	−11.0118	−	6.45179i	−0.555473	−	0.325450i
$394$			45.5049i			2.29250i
$395$		0			0
$396$	11.1527	+	3.14156i	0.560445	+	0.157869i
$397$	−13.9072	−	13.9072i	−0.697984	−	0.697984i	0.265991	−	0.963975i	$-0.414301\pi$
$397$	−13.9072	−	13.9072i	−0.697984	−	0.697984i	−0.963975	+	0.265991i	$0.914301\pi$
$398$	9.06598	−	9.06598i	0.454437	−	0.454437i
$399$	35.8333	+	20.9946i	1.79391	+	1.05105i
$400$		0			0
$401$	15.0696	+	15.0696i	0.752542	+	0.752542i	0.974953	−	0.222411i	$-0.0713928\pi$
$401$	15.0696	+	15.0696i	0.752542	+	0.752542i	−0.222411	+	0.974953i	$0.571393\pi$
$402$	−10.3059	+	17.5900i	−0.514011	+	0.877307i
$403$	1.50043	+	8.93927i	0.0747418	+	0.445297i
$404$		−	9.63999i		−	0.479607i
$405$		0			0
$406$	47.9147			2.37797
$407$		−	14.4934i		−	0.718411i
$408$	4.80609	−	1.25495i	0.237937	−	0.0621292i
$409$	11.5380	+	11.5380i	0.570517	+	0.570517i	0.932273	−	0.361756i	$-0.117823\pi$
$409$	11.5380	+	11.5380i	0.570517	+	0.570517i	−0.361756	+	0.932273i	$0.617823\pi$
$410$		0			0
$411$	1.21047	+	4.63575i	0.0597081	+	0.228665i
$412$			1.08395i			0.0534026i
$413$			27.5647i			1.35637i
$414$	19.1112	+	5.38335i	0.939263	+	0.264577i
$415$		0			0
$416$	−4.42764	−	26.3790i	−0.217083	−	1.29334i
$417$	12.5952	−	21.4972i	0.616787	−	1.05272i
$418$	−17.5793	+	17.5793i	−0.859830	+	0.859830i
$419$		−	15.8168i		−	0.772702i	−0.922352	−	0.386351i	$-0.873735\pi$
$419$		−	15.8168i		−	0.772702i	0.922352	−	0.386351i	$-0.126265\pi$
$420$		0			0
$421$	−4.66657	−	4.66657i	−0.227435	−	0.227435i	0.584186	−	0.811620i	$-0.301414\pi$
$421$	−4.66657	−	4.66657i	−0.227435	−	0.227435i	−0.811620	+	0.584186i	$0.801414\pi$
$422$	34.3836	+	34.3836i	1.67377	+	1.67377i
$423$	26.7174	+	7.52591i	1.29904	+	0.365922i
$424$	−0.658398	+	0.658398i	−0.0319746	+	0.0319746i
$425$		0			0
$426$	−16.1020	+	27.4827i	−0.780146	+	1.33154i
$427$	13.6280	+	13.6280i	0.659506	+	0.659506i
$428$		−	0.378774i		−	0.0183087i
$429$	−13.6245	−	5.18575i	−0.657798	−	0.250370i
$430$		0			0
$431$	18.0478	−	18.0478i	0.869333	−	0.869333i	−0.123066	−	0.992398i	$-0.539273\pi$
$431$	18.0478	−	18.0478i	0.869333	−	0.869333i	0.992398	+	0.123066i	$0.0392727\pi$
$432$	23.7504	+	0.455073i	1.14269	+	0.0218947i
$433$	−16.9581			−0.814953			−0.407477	−	0.913216i	$-0.633591\pi$
$433$	−16.9581			−0.814953			−0.407477	+	0.913216i	$0.633591\pi$
$434$	14.6264	−	14.6264i	0.702092	−	0.702092i
$435$		0			0
$436$	−16.2798	+	16.2798i	−0.779660	+	0.779660i
$437$	−13.6380	+	13.6380i	−0.652393	+	0.652393i
$438$	29.4997	+	17.2838i	1.40955	+	0.825851i
$439$			1.91889i			0.0915836i	0.998951	+	0.0457918i	$0.0145811\pi$
$439$			1.91889i			0.0915836i	−0.998951	+	0.0457918i	$0.985419\pi$
$440$		0			0
$441$	30.1603	−	16.9032i	1.43621	−	0.804913i
$442$	29.5170	−	4.95434i	1.40398	−	0.235654i
$443$	−14.7100			−0.698891			−0.349446	−	0.936957i	$-0.613630\pi$
$443$	−14.7100			−0.698891			−0.349446	+	0.936957i	$0.613630\pi$
$444$	4.49518	+	17.2152i	0.213332	+	0.817000i
$445$		0			0
$446$	14.0040			0.663109
$447$	2.69507	+	10.3214i	0.127473	+	0.488183i
$448$	−15.3348	+	15.3348i	−0.724502	+	0.724502i
$449$	17.4536	+	17.4536i	0.823684	+	0.823684i	0.986634	−	0.162950i	$-0.0521009\pi$
$449$	17.4536	+	17.4536i	0.823684	+	0.823684i	−0.162950	+	0.986634i	$0.552101\pi$
$450$		0			0
$451$	19.5153			0.918940
$452$		−	10.8916i		−	0.512300i
$453$	2.67031	+	10.2265i	0.125462	+	0.480485i
$454$		−	54.1039i		−	2.53922i
$455$		0			0
$456$	−3.22158	+	5.49855i	−0.150864	+	0.257493i
$457$	−11.4157	+	11.4157i	−0.534003	+	0.534003i	−0.921761	−	0.387758i	$-0.873250\pi$
$457$	−11.4157	+	11.4157i	−0.534003	+	0.534003i	0.387758	+	0.921761i	$0.373250\pi$
$458$	30.4675			1.42365
$459$	−0.432245	+	22.5590i	−0.0201755	+	1.05296i
$460$		0			0
$461$	21.3346	−	21.3346i	0.993652	−	0.993652i	−0.00632789	−	0.999980i	$-0.502014\pi$
$461$	21.3346	−	21.3346i	0.993652	−	0.993652i	0.999980	+	0.00632789i	$0.00201424\pi$
$462$	8.40484	+	32.1881i	0.391029	+	1.49753i
$463$	16.3113	+	16.3113i	0.758050	+	0.758050i	0.975967	−	0.217917i	$-0.0699263\pi$
$463$	16.3113	+	16.3113i	0.758050	+	0.758050i	−0.217917	+	0.975967i	$0.569926\pi$
$464$			26.6224i			1.23591i
$465$		0			0
$466$	13.5356	−	13.5356i	0.627026	−	0.627026i
$467$		−	36.2978i		−	1.67966i	−0.542850	−	0.839830i	$-0.682655\pi$
$467$		−	36.2978i		−	1.67966i	0.542850	−	0.839830i	$-0.317345\pi$
$468$	17.7916	+	1.93394i	0.822416	+	0.0893963i
$469$	−26.5000			−1.22366
$470$		0			0
$471$	26.0166	+	15.2430i	1.19878	+	0.702361i
$472$	−4.22975			−0.194690
$473$	−14.1919	−	14.1919i	−0.652543	−	0.652543i
$474$	8.57612	−	2.23936i	0.393914	−	0.102857i
$475$		0			0
$476$	−21.8650	−	21.8650i	−1.00218	−	1.00218i
$477$	−2.06779	−	3.68956i	−0.0946778	−	0.168933i
$478$	−34.2557			−1.56682
$479$	18.5322	+	18.5322i	0.846756	+	0.846756i	0.989727	−	0.142971i	$-0.0456655\pi$
$479$	18.5322	+	18.5322i	0.846756	+	0.846756i	−0.142971	+	0.989727i	$0.545666\pi$
$480$		0			0
$481$	−3.70557	−	22.0771i	−0.168960	−	1.00663i
$482$	16.9076			0.770119
$483$	6.52047	+	24.9715i	0.296691	+	1.13624i
$484$	9.18389			0.417449
$485$		0			0
$486$	−8.62787	+	28.5238i	−0.391368	+	1.29387i
$487$	−5.87880	+	5.87880i	−0.266394	+	0.266394i	−0.827645	−	0.561252i	$-0.810320\pi$
$487$	−5.87880	+	5.87880i	−0.266394	+	0.266394i	0.561252	+	0.827645i	$0.310320\pi$
$488$	−2.09119	+	2.09119i	−0.0946638	+	0.0946638i
$489$	4.86929	−	1.27145i	0.220197	−	0.0574970i
$490$		0			0
$491$	10.1861			0.459693			0.229847	−	0.973227i	$-0.426178\pi$
$491$	10.1861			0.459693			0.229847	+	0.973227i	$0.426178\pi$
$492$	−23.1803	+	6.05275i	−1.04505	+	0.272879i
$493$	−25.2869			−1.13887
$494$	−22.2831	+	31.2722i	−1.00256	+	1.40700i
$495$		0			0
$496$	8.12675	+	8.12675i	0.364902	+	0.364902i
$497$	−41.4039			−1.85722
$498$	17.8676	+	10.4686i	0.800669	+	0.469109i
$499$	14.5185	+	14.5185i	0.649937	+	0.649937i	0.952978	−	0.303041i	$-0.0980019\pi$
$499$	14.5185	+	14.5185i	0.649937	+	0.649937i	−0.303041	+	0.952978i	$0.598002\pi$
$500$		0			0
$501$	−8.44782	−	32.3527i	−0.377421	−	1.44541i
$502$	−19.2544	−	19.2544i	−0.859368	−	0.859368i
$503$	17.4820			0.779483			0.389742	−	0.920924i	$-0.372564\pi$
$503$	17.4820			0.779483			0.389742	+	0.920924i	$0.372564\pi$
$504$	4.16919	+	7.43907i	0.185710	+	0.331363i
$505$		0			0
$506$	−15.4495			−0.686813
$507$	−22.0794	−	4.41577i	−0.980582	−	0.196111i
$508$			13.5881i			0.602876i
$509$	−7.35152	+	7.35152i	−0.325850	+	0.325850i	−0.851006	−	0.525156i	$-0.824007\pi$
$509$	−7.35152	+	7.35152i	−0.325850	+	0.325850i	0.525156	+	0.851006i	$0.324007\pi$
$510$		0			0
$511$			44.4426i			1.96603i
$512$	−19.7114	−	19.7114i	−0.871128	−	0.871128i
$513$	−20.0733	−	20.8576i	−0.886257	−	0.920883i
$514$	−33.7502	+	33.7502i	−1.48866	+	1.48866i
$515$		0			0
$516$	21.2588	+	12.4554i	0.935865	+	0.548320i
$517$	−21.5983			−0.949893
$518$	−36.1225	+	36.1225i	−1.58713	+	1.58713i
$519$	10.8160	+	6.33706i	0.474770	+	0.278166i
$520$		0			0
$521$			8.94874i			0.392052i	0.980599	+	0.196026i	$0.0628036\pi$
$521$			8.94874i			0.392052i	−0.980599	+	0.196026i	$0.937196\pi$
$522$	−32.1465	−	9.05524i	−1.40702	−	0.396337i
$523$		−	29.1992i		−	1.27679i	−0.769708	−	0.638396i	$-0.779598\pi$
$523$		−	29.1992i		−	1.27679i	0.769708	−	0.638396i	$-0.220402\pi$
$524$	−12.1914			−0.532583
$525$		0			0
$526$	6.36534	+	6.36534i	0.277542	+	0.277542i
$527$	−7.71909	+	7.71909i	−0.336249	+	0.336249i
$528$	−17.8844	+	4.66990i	−0.778317	+	0.203231i
$529$	11.0143			0.478883
$530$		0			0
$531$	5.20937	−	18.4935i	0.226067	−	0.802550i
$532$	39.6717			1.71999
$533$	29.7267	−	4.98955i	1.28761	−	0.216121i
$534$	8.16834	+	4.78581i	0.353479	+	0.207102i
$535$		0			0
$536$		−	4.06638i		−	0.175641i
$537$	8.92033	−	15.2251i	0.384941	−	0.657011i
$538$	−24.8191	+	24.8191i	−1.07003	+	1.07003i
$539$	−19.0231	+	19.0231i	−0.819382	+	0.819382i
$540$		0			0
$541$	7.91853	−	7.91853i	0.340444	−	0.340444i	−0.516090	−	0.856534i	$-0.672613\pi$
$541$	7.91853	−	7.91853i	0.340444	−	0.340444i	0.856534	+	0.516090i	$0.172613\pi$
$542$	−21.0622			−0.904701
$543$	−31.1080	−	18.2261i	−1.33497	−	0.782157i
$544$	22.7783	−	22.7783i	0.976613	−	0.976613i
$545$		0			0
$546$	21.0323	+	46.8817i	0.900101	+	2.00635i
$547$			39.7240i			1.69848i	0.528010	+	0.849238i	$0.322938\pi$
$547$			39.7240i			1.69848i	−0.528010	+	0.849238i	$0.677062\pi$
$548$	3.23623	+	3.23623i	0.138245	+	0.138245i
$549$	−6.56769	−	11.7187i	−0.280302	−	0.500143i
$550$		0			0
$551$	22.9402	−	22.9402i	0.977284	−	0.977284i
$552$	−3.83183	+	1.00055i	−0.163093	+	0.0425863i
$553$	8.14700	+	8.14700i	0.346446	+	0.346446i
$554$	−7.97840	−	7.97840i	−0.338970	−	0.338970i
$555$		0			0
$556$		−	23.8000i		−	1.00934i
$557$	31.1861	−	31.1861i	1.32140	−	1.32140i	0.408752	−	0.912645i	$-0.365964\pi$
$557$	31.1861	−	31.1861i	1.32140	−	1.32140i	0.912645	−	0.408752i	$-0.134036\pi$
$558$	−12.5773	+	7.04885i	−0.532438	+	0.298402i
$559$	−25.2463	−	17.9893i	−1.06780	−	0.760866i
$560$		0			0
$561$	−4.43565	−	16.9872i	−0.187273	−	0.717202i
$562$		−	10.0490i		−	0.423891i
$563$		−	28.5302i		−	1.20240i	−0.799097	−	0.601202i	$-0.794689\pi$
$563$		−	28.5302i		−	1.20240i	0.799097	−	0.601202i	$-0.205311\pi$
$564$	25.6545	−	6.69880i	1.08025	−	0.282071i
$565$		0			0
$566$	3.33318	+	3.33318i	0.140104	+	0.140104i
$567$	−37.6602	+	9.06674i	−1.58158	+	0.380767i
$568$		−	6.35334i		−	0.266580i
$569$	−7.59495			−0.318397			−0.159198	−	0.987247i	$-0.550891\pi$
$569$	−7.59495			−0.318397			−0.159198	+	0.987247i	$0.550891\pi$
$570$		0			0
$571$			38.7934i			1.62345i	0.584039	+	0.811726i	$0.301472\pi$
$571$			38.7934i			1.62345i	−0.584039	+	0.811726i	$0.698528\pi$
$572$	−13.7334	+	2.30511i	−0.574222	+	0.0963816i
$573$	30.8714	+	18.0874i	1.28967	+	0.755614i
$574$	−48.6389	−	48.6389i	−2.03015	−	2.03015i
$575$		0			0
$576$	13.1864	−	7.39023i	0.549432	−	0.307926i
$577$	31.8022	−	31.8022i	1.32394	−	1.32394i	0.413387	−	0.910555i	$-0.364346\pi$
$577$	31.8022	−	31.8022i	1.32394	−	1.32394i	0.910555	−	0.413387i	$-0.135654\pi$
$578$	2.50805	+	2.50805i	0.104321	+	0.104321i
$579$	−6.31890	+	1.64997i	−0.262604	+	0.0685703i
$580$		0			0
$581$			26.9184i			1.11676i
$582$	−2.87283	+	4.90331i	−0.119083	+	0.203249i
$583$	2.32712	+	2.32712i	0.0963796	+	0.0963796i
$584$	−6.81963			−0.282198
$585$		0			0
$586$	6.66570			0.275357
$587$	30.0859	+	30.0859i	1.24178	+	1.24178i	0.959263	+	0.282514i	$0.0911683\pi$
$587$	30.0859	+	30.0859i	1.24178	+	1.24178i	0.282514	+	0.959263i	$0.408832\pi$
$588$	16.6955	−	28.4957i	0.688512	−	1.17514i
$589$		−	14.0054i		−	0.577084i
$590$		0			0
$591$	39.8915	−	10.4163i	1.64092	−	0.428470i
$592$	−20.0704	−	20.0704i	−0.824889	−	0.824889i
$593$	15.4861	−	15.4861i	0.635939	−	0.635939i	−0.313612	−	0.949551i	$-0.601539\pi$
$593$	15.4861	−	15.4861i	0.635939	−	0.635939i	0.949551	+	0.313612i	$0.101539\pi$
$594$	0.444217	−	23.1838i	0.0182264	−	0.951243i
$595$		0			0
$596$	7.20536	+	7.20536i	0.295143	+	0.295143i
$597$	−10.0229	−	5.87238i	−0.410209	−	0.240340i
$598$	−23.5334	+	3.95002i	−0.962354	+	0.161528i
$599$		−	4.96005i		−	0.202662i	−0.994853	−	0.101331i	$-0.967690\pi$
$599$		−	4.96005i		−	0.202662i	0.994853	−	0.101331i	$-0.0323101\pi$
$600$		0			0
$601$	3.48773			0.142267			0.0711336	−	0.997467i	$-0.477338\pi$
$601$	3.48773			0.142267			0.0711336	+	0.997467i	$0.477338\pi$
$602$			70.7421i			2.88323i
$603$	17.7792	+	5.00815i	0.724025	+	0.203948i
$604$	7.13917	+	7.13917i	0.290489	+	0.290489i
$605$		0			0
$606$	−18.6663	+	4.87406i	−0.758265	+	0.197995i
$607$		−	14.2336i		−	0.577725i	−0.957371	−	0.288862i	$-0.906723\pi$
$607$		−	14.2336i		−	0.577725i	0.957371	−	0.288862i	$-0.0932770\pi$
$608$			41.3288i			1.67610i
$609$	−10.9679	−	42.0041i	−0.444444	−	1.70209i
$610$		0			0
$611$	−32.8997	+	5.52212i	−1.33098	+	0.223401i
$612$	10.5373	+	18.8017i	0.425946	+	0.760015i
$613$	14.0265	−	14.0265i	0.566525	−	0.566525i	−0.364628	−	0.931153i	$-0.618804\pi$
$613$	14.0265	−	14.0265i	0.566525	−	0.566525i	0.931153	+	0.364628i	$0.118804\pi$
$614$		−	19.8242i		−	0.800039i
$615$		0			0
$616$	−4.69206	−	4.69206i	−0.189049	−	0.189049i
$617$	10.8617	+	10.8617i	0.437277	+	0.437277i	0.891095	−	0.453817i	$-0.149938\pi$
$617$	10.8617	+	10.8617i	0.437277	+	0.437277i	−0.453817	+	0.891095i	$0.649938\pi$
$618$	2.09890	−	0.548057i	0.0844301	−	0.0220461i
$619$	8.83108	−	8.83108i	0.354951	−	0.354951i	−0.506997	−	0.861948i	$-0.669244\pi$
$619$	8.83108	−	8.83108i	0.354951	−	0.354951i	0.861948	+	0.506997i	$0.169244\pi$
$620$		0			0
$621$	0.344623	−	17.9860i	0.0138292	−	0.721752i
$622$	5.62278	+	5.62278i	0.225453	+	0.225453i
$623$			12.3060i			0.493028i
$624$	−26.0484	+	11.6860i	−1.04277	+	0.467814i
$625$		0			0
$626$	−20.7196	+	20.7196i	−0.828121	+	0.828121i
$627$	19.4347	+	11.3868i	0.776149	+	0.454743i
$628$	28.8034			1.14938
$629$	19.0636	−	19.0636i	0.760117	−	0.760117i
$630$		0			0
$631$	7.70247	−	7.70247i	0.306630	−	0.306630i	−0.536971	−	0.843601i	$-0.680431\pi$
$631$	7.70247	−	7.70247i	0.306630	−	0.306630i	0.843601	+	0.536971i	$0.180431\pi$
$632$	−1.25014	+	1.25014i	−0.0497279	+	0.0497279i
$633$	22.2716	−	38.0128i	0.885216	−	1.51087i
$634$		−	17.3424i		−	0.688753i
$635$		0			0
$636$	−3.48592	−	2.04239i	−0.138226	−	0.0809861i
$637$	−24.1132	+	33.8406i	−0.955400	+	1.34081i
$638$	25.9873			1.02885
$639$	27.7784	+	7.82478i	1.09890	+	0.309544i
$640$		0			0
$641$	−45.3950			−1.79299			−0.896497	−	0.443050i	$-0.853897\pi$
$641$	−45.3950			−1.79299			−0.896497	+	0.443050i	$0.853897\pi$
$642$	−0.733434	+	0.191512i	−0.0289463	+	0.00755836i
$643$	−27.0118	+	27.0118i	−1.06524	+	1.06524i	−0.0675241	+	0.997718i	$0.521510\pi$
$643$	−27.0118	+	27.0118i	−1.06524	+	1.06524i	−0.997718	+	0.0675241i	$0.978490\pi$
$644$	17.4327	+	17.4327i	0.686944	+	0.686944i
$645$		0			0
$646$	−46.2452			−1.81949
$647$		−	45.8906i		−	1.80414i	−0.431585	−	0.902072i	$-0.642046\pi$
$647$		−	45.8906i		−	1.80414i	0.431585	−	0.902072i	$-0.357954\pi$
$648$	−1.39127	−	5.77888i	−0.0546543	−	0.227016i
$649$			14.9502i			0.586845i
$650$		0			0
$651$	−16.1702	−	9.47410i	−0.633762	−	0.371319i
$652$	3.39926	−	3.39926i	0.133125	−	0.133125i
$653$	−39.0950			−1.52991			−0.764953	−	0.644086i	$-0.777238\pi$
$653$	−39.0950			−1.52991			−0.764953	+	0.644086i	$0.777238\pi$
$654$	39.7543	+	23.2919i	1.55452	+	0.910786i
$655$		0			0
$656$	27.0247	−	27.0247i	1.05514	−	1.05514i
$657$	8.39906	−	29.8171i	0.327678	−	1.16328i
$658$	53.8305	+	53.8305i	2.09853	+	2.09853i
$659$			19.2439i			0.749637i	0.927098	+	0.374818i	$0.122295\pi$
$659$			19.2439i			0.749637i	−0.927098	+	0.374818i	$0.877705\pi$
$660$		0			0
$661$	−26.9974	+	26.9974i	−1.05008	+	1.05008i	−0.0513985	+	0.998678i	$0.516368\pi$
$661$	−26.9974	+	26.9974i	−1.05008	+	1.05008i	−0.998678	+	0.0513985i	$0.983632\pi$
$662$			31.8047i			1.23612i
$663$	−11.0998	−	24.7418i	−0.431080	−	0.960891i
$664$	−4.13057			−0.160297
$665$		0			0
$666$	31.0617	−	17.4084i	1.20362	−	0.674560i
$667$	20.1609			0.780633
$668$	−22.5855	−	22.5855i	−0.873860	−	0.873860i
$669$	−3.20560	−	12.2765i	−0.123936	−	0.474637i
$670$		0			0
$671$	7.39137	+	7.39137i	0.285341	+	0.285341i
$672$	47.7169	+	27.9572i	1.84072	+	1.07847i
$673$	34.1891			1.31789			0.658946	−	0.752190i	$-0.271002\pi$
$673$	34.1891			1.31789			0.658946	+	0.752190i	$0.271002\pi$
$674$	−14.6631	−	14.6631i	−0.564800	−	0.564800i
$675$		0			0
$676$	−20.3301	+	7.02253i	−0.781926	+	0.270097i
$677$	−14.1540			−0.543984			−0.271992	−	0.962300i	$-0.587682\pi$
$677$	−14.1540			−0.543984			−0.271992	+	0.962300i	$0.587682\pi$
$678$	−21.0899	+	5.50691i	−0.809953	+	0.211492i
$679$	−7.38705			−0.283489
$680$		0			0
$681$	−47.4298	+	12.3847i	−1.81751	+	0.474582i
$682$	7.93288	−	7.93288i	0.303766	−	0.303766i
$683$	−21.9481	+	21.9481i	−0.839819	+	0.839819i	−0.988835	−	0.149016i	$-0.952390\pi$
$683$	−21.9481	+	21.9481i	−0.839819	+	0.839819i	0.149016	+	0.988835i	$0.452390\pi$
$684$	−26.6162	−	7.49742i	−1.01770	−	0.286671i
$685$		0			0
$686$	37.2286			1.42140
$687$	−6.97419	−	26.7091i	−0.266082	−	1.01902i
$688$	−39.3057			−1.49852
$689$	4.13978	+	2.94981i	0.157713	+	0.112379i
$690$		0			0
$691$	−19.1129	−	19.1129i	−0.727090	−	0.727090i	0.242949	−	0.970039i	$-0.421885\pi$
$691$	−19.1129	−	19.1129i	−0.727090	−	0.727090i	−0.970039	+	0.242949i	$0.921885\pi$
$692$	11.9746			0.455206
$693$	26.2936	−	14.7361i	0.998811	−	0.559778i
$694$	−11.7666	−	11.7666i	−0.446654	−	0.446654i
$695$		0			0
$696$	6.44544	−	1.68301i	0.244314	−	0.0637943i
$697$	25.6691	+	25.6691i	0.972287	+	0.972287i
$698$	−64.0690			−2.42505
$699$	−14.9643	−	8.76753i	−0.566002	−	0.331618i
$700$		0			0
$701$	−24.2762			−0.916900			−0.458450	−	0.888720i	$-0.651595\pi$
$701$	−24.2762			−0.916900			−0.458450	+	0.888720i	$0.651595\pi$
$702$	−5.25083	−	35.4283i	−0.198180	−	1.33716i
$703$			34.5889i			1.30454i
$704$	−8.31707	+	8.31707i	−0.313461	+	0.313461i
$705$		0			0
$706$		−	27.3335i		−	1.02871i
$707$	−17.7323	−	17.7323i	−0.666891	−	0.666891i
$708$	−4.63685	−	17.7578i	−0.174263	−	0.667379i
$709$	−11.9543	+	11.9543i	−0.448954	+	0.448954i	−0.895007	−	0.446053i	$-0.852829\pi$
$709$	−11.9543	+	11.9543i	−0.448954	+	0.448954i	0.446053	+	0.895007i	$0.352829\pi$
$710$		0			0
$711$	−3.92624	−	7.00559i	−0.147246	−	0.262730i
$712$	−1.88833			−0.0707680
$713$	6.15432	−	6.15432i	0.230481	−	0.230481i
$714$	−31.2829	+	53.3933i	−1.17073	+	1.99819i
$715$		0			0
$716$		−	16.8560i		−	0.629937i
$717$	7.84132	+	30.0300i	0.292839	+	1.12149i
$718$		−	38.3423i		−	1.43092i
$719$	41.3666			1.54271			0.771357	−	0.636403i	$-0.219578\pi$
$719$	41.3666			1.54271			0.771357	+	0.636403i	$0.219578\pi$
$720$		0			0
$721$	1.99388	+	1.99388i	0.0742559	+	0.0742559i
$722$	16.2699	−	16.2699i	0.605504	−	0.605504i
$723$	−3.87024	−	14.8219i	−0.143936	−	0.551232i
$724$	−34.4403			−1.27996
$725$		0			0
$726$	−4.64345	−	17.7831i	−0.172335	−	0.659993i
$727$	22.9941			0.852803			0.426401	−	0.904534i	$-0.359781\pi$
$727$	22.9941			0.852803			0.426401	+	0.904534i	$0.359781\pi$
$728$	−8.34682	−	5.94755i	−0.309354	−	0.220431i
$729$	26.9802	+	1.03430i	0.999266	+	0.0383073i
$730$		0			0
$731$		−	37.3341i		−	1.38085i
$732$	−11.0719	−	6.48701i	−0.409230	−	0.239767i
$733$	27.5771	−	27.5771i	1.01858	−	1.01858i	0.0187592	−	0.999824i	$-0.494028\pi$
$733$	27.5771	−	27.5771i	1.01858	−	1.01858i	0.999824	−	0.0187592i	$-0.00597159\pi$
$734$	−5.40257	+	5.40257i	−0.199413	+	0.199413i
$735$		0			0
$736$	−18.1608	+	18.1608i	−0.669417	+	0.669417i
$737$	−14.3727			−0.529425
$738$	23.4403	+	41.8245i	0.862850	+	1.53958i
$739$	−7.93961	+	7.93961i	−0.292063	+	0.292063i	−0.837895	−	0.545832i	$-0.816214\pi$
$739$	−7.93961	+	7.93961i	−0.292063	+	0.292063i	0.545832	+	0.837895i	$0.316214\pi$
$740$		0			0
$741$	32.5153	+	12.3759i	1.19448	+	0.454641i
$742$		−	11.6000i		−	0.425849i
$743$	−23.9349	−	23.9349i	−0.878087	−	0.878087i	0.115249	−	0.993337i	$-0.463233\pi$
$743$	−23.9349	−	23.9349i	−0.878087	−	0.878087i	−0.993337	+	0.115249i	$0.963233\pi$
$744$	1.45378	−	2.48129i	0.0532982	−	0.0909686i
$745$		0			0
$746$	−17.9654	+	17.9654i	−0.657761	+	0.657761i
$747$	5.08722	−	18.0599i	0.186132	−	0.660776i
$748$	−11.8588	−	11.8588i	−0.433602	−	0.433602i
$749$	−0.696736	−	0.696736i	−0.0254582	−	0.0254582i
$750$		0			0
$751$			42.7833i			1.56119i	0.625039	+	0.780593i	$0.285083\pi$
$751$			42.7833i			1.56119i	−0.625039	+	0.780593i	$0.714917\pi$
$752$	−29.9093	+	29.9093i	−1.09068	+	1.09068i
$753$	−12.4718	+	21.2867i	−0.454498	+	0.775731i
$754$	39.5851	−	6.64426i	1.44161	−	0.241970i
$755$		0			0
$756$	−26.6611	+	25.6586i	−0.969653	+	0.933194i
$757$			42.2733i			1.53645i	0.640180	+	0.768225i	$0.278860\pi$
$757$			42.2733i			1.53645i	−0.640180	+	0.768225i	$0.721140\pi$
$758$			9.64784i			0.350425i
$759$	3.53647	+	13.5437i	0.128366	+	0.491605i
$760$		0			0
$761$	18.2564	+	18.2564i	0.661795	+	0.661795i	0.955803	−	0.294008i	$-0.0949893\pi$
$761$	18.2564	+	18.2564i	0.661795	+	0.661795i	−0.294008	+	0.955803i	$0.594989\pi$
$762$	26.3112	−	6.87028i	0.953154	−	0.248884i
$763$			59.8916i			2.16822i
$764$	34.1783			1.23653
$765$		0			0
$766$		−	59.9185i		−	2.16494i
$767$	3.82236	+	22.7728i	0.138017	+	0.822280i
$768$	−17.5355	+	29.9294i	−0.632759	+	1.07998i
$769$	−30.7881	−	30.7881i	−1.11025	−	1.11025i	−0.993116	−	0.117131i	$-0.962630\pi$
$769$	−30.7881	−	30.7881i	−1.11025	−	1.11025i	−0.117131	−	0.993116i	$-0.537370\pi$
$770$		0			0
$771$	37.3125	+	21.8613i	1.34378	+	0.787314i
$772$	−4.41124	+	4.41124i	−0.158764	+	0.158764i
$773$	−3.19753	−	3.19753i	−0.115007	−	0.115007i	0.647261	−	0.762268i	$-0.275914\pi$
$773$	−3.19753	−	3.19753i	−0.115007	−	0.115007i	−0.762268	+	0.647261i	$0.775914\pi$
$774$	13.3693	−	47.4617i	0.480550	−	1.70598i
$775$		0			0
$776$		−	1.13353i		−	0.0406913i
$777$	39.9352	+	23.3979i	1.43267	+	0.839396i
$778$	−28.3091	−	28.3091i	−1.01493	−	1.01493i
$779$	−46.5738			−1.66868
$780$		0			0
$781$	−22.4560			−0.803540
$782$	−20.3212	−	20.3212i	−0.726685	−	0.726685i
$783$	−0.579683	+	30.2538i	−0.0207162	+	1.08118i
$784$			52.6862i			1.88165i
$785$		0			0
$786$	6.16407	+	23.6066i	0.219865	+	0.842021i
$787$	−25.0983	−	25.0983i	−0.894657	−	0.894657i	0.100301	−	0.994957i	$-0.468020\pi$
$787$	−25.0983	−	25.0983i	−0.894657	−	0.894657i	−0.994957	+	0.100301i	$0.968020\pi$
$788$	27.8484	−	27.8484i	0.992058	−	0.992058i
$789$	4.12307	−	7.03719i	0.146785	−	0.250531i
$790$		0			0
$791$	−20.0346	−	20.0346i	−0.712350	−	0.712350i
$792$	2.26122	+	4.03470i	0.0803491	+	0.143367i
$793$	13.1487	+	9.36913i	0.466924	+	0.332708i
$794$			37.5986i			1.33432i
$795$		0			0
$796$	−11.0965			−0.393306
$797$		−	39.5305i		−	1.40024i	−0.714025	−	0.700120i	$-0.753130\pi$
$797$		−	39.5305i		−	1.40024i	0.714025	−	0.700120i	$-0.246870\pi$
$798$	−20.0584	−	76.8178i	−0.710059	−	2.71932i
$799$	−28.4090	−	28.4090i	−1.00504	−	1.00504i
$800$		0			0
$801$	2.32566	−	8.25622i	0.0821733	−	0.291719i
$802$		−	40.7411i		−	1.43862i
$803$			24.1041i			0.850616i
$804$	17.0719	−	4.45775i	0.602079	−	0.157213i
$805$		0			0
$806$	10.0555	−	14.1120i	0.354191	−	0.497074i
$807$	27.4387	+	16.0762i	0.965887	+	0.565910i
$808$	2.72098	−	2.72098i	0.0957238	−	0.0957238i
$809$		−	37.4805i		−	1.31774i	−0.752255	−	0.658872i	$-0.771034\pi$
$809$		−	37.4805i		−	1.31774i	0.752255	−	0.658872i	$-0.228966\pi$
$810$		0			0
$811$	−5.40079	−	5.40079i	−0.189647	−	0.189647i	0.605896	−	0.795544i	$-0.292815\pi$
$811$	−5.40079	−	5.40079i	−0.189647	−	0.189647i	−0.795544	+	0.605896i	$0.792815\pi$
$812$	−29.3232	−	29.3232i	−1.02904	−	1.02904i
$813$	4.82127	+	18.4641i	0.169089	+	0.647563i
$814$	−19.5916	+	19.5916i	−0.686686	+	0.686686i
$815$		0			0
$816$	−29.6664	−	17.3814i	−1.03853	−	0.608472i
$817$	33.8693	+	33.8693i	1.18494	+	1.18494i
$818$		−	31.1933i		−	1.09065i
$819$	36.2841	−	29.1693i	1.26787	−	1.01926i
$820$		0			0
$821$	−26.9025	+	26.9025i	−0.938905	+	0.938905i	−0.998238	−	0.0593332i	$-0.981103\pi$
$821$	−26.9025	+	26.9025i	−0.938905	+	0.938905i	0.0593332	+	0.998238i	$0.481103\pi$
$822$	4.63017	−	7.90270i	0.161496	−	0.275638i
$823$	−22.4341			−0.782003			−0.391002	−	0.920390i	$-0.627871\pi$
$823$	−22.4341			−0.782003			−0.391002	+	0.920390i	$0.627871\pi$
$824$	−0.305956	+	0.305956i	−0.0106585	+	0.0106585i
$825$		0			0
$826$	37.2610	−	37.2610i	1.29648	−	1.29648i
$827$	19.5590	−	19.5590i	0.680134	−	0.680134i	−0.279896	−	0.960030i	$-0.590300\pi$
$827$	19.5590	−	19.5590i	0.680134	−	0.680134i	0.960030	+	0.279896i	$0.0903000\pi$
$828$	−8.40125	−	14.9903i	−0.291964	−	0.520950i
$829$		−	3.42144i		−	0.118832i	−0.998233	−	0.0594158i	$-0.981076\pi$
$829$		−	3.42144i		−	0.118832i	0.998233	−	0.0594158i	$-0.0189238\pi$
$830$		0			0
$831$	−5.16791	+	8.82051i	−0.179273	+	0.305980i
$832$	−10.5425	+	14.7954i	−0.365496	+	0.512940i
$833$	−50.0433			−1.73390
$834$	−46.0848	+	12.0335i	−1.59579	+	0.416686i
$835$		0			0
$836$	21.5166			0.744166
$837$	9.05833	+	9.41224i	0.313102	+	0.325335i
$838$	−21.3806	+	21.3806i	−0.738579	+	0.738579i
$839$	−26.6448	−	26.6448i	−0.919880	−	0.919880i	0.0771405	−	0.997020i	$-0.475421\pi$
$839$	−26.6448	−	26.6448i	−0.919880	−	0.919880i	−0.997020	+	0.0771405i	$0.975421\pi$
$840$		0			0
$841$	−4.91224			−0.169388
$842$			12.6162i			0.434782i
$843$	−8.80937	+	2.30027i	−0.303411	+	0.0792255i
$844$		−	42.0847i		−	1.44861i
$845$		0			0
$846$	−25.9423	−	46.2888i	−0.891914	−	1.59144i
$847$	16.8933	−	16.8933i	0.580460	−	0.580460i
$848$	6.44519			0.221329
$849$	2.15902	−	3.68499i	0.0740975	−	0.126469i
$850$		0			0
$851$	−15.1992	+	15.1992i	−0.521020	+	0.521020i
$852$	26.6733	−	6.96483i	0.913812	−	0.238611i
$853$	−1.95181	−	1.95181i	−0.0668287	−	0.0668287i	0.672902	−	0.739731i	$-0.265047\pi$
$853$	−1.95181	−	1.95181i	−0.0668287	−	0.0668287i	−0.739731	+	0.672902i	$0.765047\pi$
$854$		−	36.8437i		−	1.26077i
$855$		0			0
$856$	0.106913	−	0.106913i	0.00365420	−	0.00365420i
$857$			25.9594i			0.886756i	0.896335	+	0.443378i	$0.146220\pi$
$857$			25.9594i			0.886756i	−0.896335	+	0.443378i	$0.853780\pi$
$858$	11.4072	+	25.4270i	0.389436	+	0.868064i
$859$	7.56942			0.258265			0.129133	−	0.991627i	$-0.458781\pi$
$859$	7.56942			0.258265			0.129133	+	0.991627i	$0.458781\pi$
$860$		0			0
$861$	−31.5052	+	53.7727i	−1.07370	+	1.83257i
$862$	−48.7927			−1.66189
$863$	22.0019	+	22.0019i	0.748953	+	0.748953i	0.974283	−	0.225330i	$-0.0723459\pi$
$863$	22.0019	+	22.0019i	0.748953	+	0.748953i	−0.225330	+	0.974283i	$0.572346\pi$
$864$	−26.7303	−	27.7747i	−0.909384	−	0.944914i
$865$		0			0
$866$	22.9233	+	22.9233i	0.778965	+	0.778965i
$867$	1.62456	−	2.77278i	0.0551730	−	0.0941684i
$868$	−17.9024			−0.607647
$869$	4.41865	+	4.41865i	0.149892	+	0.149892i
$870$		0			0
$871$	−21.8932	+	3.67472i	−0.741824	+	0.124513i
$872$	−9.19025			−0.311221
$873$	4.95606	+	1.39605i	0.167737	+	0.0472492i
$874$	36.8706			1.24717
$875$		0			0
$876$	−7.47599	−	28.6309i	−0.252590	−	0.967348i
$877$	19.8856	−	19.8856i	0.671491	−	0.671491i	−0.286569	−	0.958060i	$-0.592515\pi$
$877$	19.8856	−	19.8856i	0.671491	−	0.671491i	0.958060	+	0.286569i	$0.0925148\pi$
$878$	2.59388	−	2.59388i	0.0875393	−	0.0875393i
$879$	−1.52582	−	5.84344i	−0.0514645	−	0.197094i
$880$		0			0
$881$	36.1817			1.21899			0.609497	−	0.792788i	$-0.291371\pi$
$881$	36.1817			1.21899			0.609497	+	0.792788i	$0.291371\pi$
$882$	−63.6186	−	17.9205i	−2.14215	−	0.603414i
$883$	29.6055			0.996305			0.498153	−	0.867089i	$-0.334012\pi$
$883$	29.6055			0.996305			0.498153	+	0.867089i	$0.334012\pi$
$884$	−21.0960	−	15.0320i	−0.709535	−	0.505581i
$885$		0			0
$886$	19.8844	+	19.8844i	0.668028	+	0.668028i
$887$	−35.4670			−1.19087			−0.595433	−	0.803405i	$-0.703020\pi$
$887$	−35.4670			−1.19087			−0.595433	+	0.803405i	$0.703020\pi$
$888$	−3.59036	+	6.12798i	−0.120485	+	0.205642i
$889$	24.9947	+	24.9947i	0.838294	+	0.838294i
$890$		0			0
$891$	−20.4256	+	4.91748i	−0.684283	+	0.164742i
$892$	−8.57027	−	8.57027i	−0.286954	−	0.286954i
$893$	51.5450			1.72489
$894$	10.3089	−	17.5951i	0.344782	−	0.588468i
$895$		0			0
$896$	−22.4013			−0.748375
$897$	8.84970	+	19.7262i	0.295483	+	0.658640i
$898$		−	47.1861i		−	1.57462i
$899$	−10.3521	+	10.3521i	−0.345260	+	0.345260i
$900$		0			0
$901$			6.12188i			0.203950i
$902$	−26.3800	−	26.3800i	−0.878360	−	0.878360i
$903$	62.0156	−	16.1933i	2.06375	−	0.538878i
$904$	3.07427	−	3.07427i	0.102249	−	0.102249i
$905$		0			0
$906$	10.2142	−	17.4335i	0.339345	−	0.579188i
$907$	27.3235			0.907261			0.453630	−	0.891190i	$-0.350129\pi$
$907$	27.3235			0.907261			0.453630	+	0.891190i	$0.350129\pi$
$908$	−33.1109	+	33.1109i	−1.09882	+	1.09882i
$909$	8.54563	+	15.2480i	0.283441	+	0.505743i
$910$		0			0
$911$			33.2417i			1.10135i	0.834721	+	0.550674i	$0.185629\pi$
$911$			33.2417i			1.10135i	−0.834721	+	0.550674i	$0.814371\pi$
$912$	42.6815	−	11.1448i	1.41333	−	0.369042i
$913$			14.5996i			0.483176i
$914$	30.8626			1.02084
$915$		0			0
$916$	−18.6457	−	18.6457i	−0.616072	−	0.616072i
$917$	−22.4254	+	22.4254i	−0.740553	+	0.740553i
$918$	31.0787	−	29.9101i	1.02575	−	0.987181i
$919$	1.10008			0.0362882			0.0181441	−	0.999835i	$-0.494224\pi$
$919$	1.10008			0.0362882			0.0181441	+	0.999835i	$0.494224\pi$
$920$		0			0
$921$	−17.3787	+	4.53787i	−0.572649	+	0.149528i
$922$	−57.6786			−1.89955
$923$	−34.2062	+	5.74141i	−1.12591	+	0.188981i
$924$	14.5551	−	24.8424i	0.478826	−	0.817254i
$925$		0			0
$926$		−	44.0980i		−	1.44915i
$927$	−0.960900	−	1.71453i	−0.0315601	−	0.0563126i
$928$	30.5480	−	30.5480i	1.00279	−	1.00279i
$929$	−13.5362	+	13.5362i	−0.444110	+	0.444110i	−0.893391	−	0.449281i	$-0.851680\pi$
$929$	−13.5362	+	13.5362i	−0.444110	+	0.444110i	0.449281	+	0.893391i	$0.351680\pi$
$930$		0			0
$931$	45.3991	−	45.3991i	1.48789	−	1.48789i
$932$	−16.5673			−0.542678
$933$	3.64209	−	6.21626i	0.119237	−	0.203511i
$934$	−49.0659	+	49.0659i	−1.60549	+	1.60549i
$935$		0			0
$936$	4.47597	+	5.56772i	0.146302	+	0.181987i
$937$		−	5.70697i		−	0.186439i	−0.995646	−	0.0932194i	$-0.970284\pi$
$937$		−	5.70697i		−	0.186439i	0.995646	−	0.0932194i	$-0.0297158\pi$
$938$	35.8217	+	35.8217i	1.16962	+	1.16962i
$939$	22.9065	+	13.4208i	0.747526	+	0.437973i
$940$		0			0
$941$	−4.18292	+	4.18292i	−0.136359	+	0.136359i	−0.771992	−	0.635632i	$-0.780739\pi$
$941$	−4.18292	+	4.18292i	−0.136359	+	0.136359i	0.635632	+	0.771992i	$0.280739\pi$
$942$	−14.5633	−	55.7731i	−0.474497	−	1.81719i
$943$	−20.4656	−	20.4656i	−0.666452	−	0.666452i
$944$	20.7029	+	20.7029i	0.673823	+	0.673823i
$945$		0			0
$946$			38.3681i			1.24745i
$947$	−27.3594	+	27.3594i	−0.889060	+	0.889060i	−0.994433	−	0.105372i	$-0.966397\pi$
$947$	−27.3594	+	27.3594i	−0.889060	+	0.889060i	0.105372	+	0.994433i	$0.466397\pi$
$948$	−6.61893	−	3.87801i	−0.214973	−	0.125952i
$949$	6.16279	+	36.7167i	0.200053	+	1.19187i
$950$		0			0
$951$	−15.2031	+	3.96976i	−0.492993	+	0.128728i
$952$		−	12.3432i		−	0.400047i
$953$		−	58.2895i		−	1.88818i	−0.329686	−	0.944091i	$-0.606943\pi$
$953$		−	58.2895i		−	1.88818i	0.329686	−	0.944091i	$-0.393057\pi$
$954$	−2.19224	+	7.78257i	−0.0709765	+	0.251970i
$955$		0			0
$956$	20.9640	+	20.9640i	0.678025	+	0.678025i
$957$	−5.94863	−	22.7816i	−0.192292	−	0.736423i
$958$		−	50.1021i		−	1.61873i
$959$	11.9058			0.384457
$960$		0			0
$961$		−	24.6799i		−	0.796125i
$962$	−24.8339	+	34.8520i	−0.800677	+	1.12367i
$963$	0.335775	+	0.599122i	0.0108202	+	0.0193064i
$964$	−10.3472	−	10.3472i	−0.333261	−	0.333261i
$965$		0			0
$966$	24.9414	−	42.5697i	0.802477	−	1.36966i
$967$	−18.1367	+	18.1367i	−0.583238	+	0.583238i	−0.935792	−	0.352553i	$-0.885313\pi$
$967$	−18.1367	+	18.1367i	−0.583238	+	0.583238i	0.352553	+	0.935792i	$0.385313\pi$
$968$	2.59224	+	2.59224i	0.0833178	+	0.0833178i
$969$	10.5858	+	40.5405i	0.340064	+	1.30235i
$970$		0			0
$971$		−	30.0923i		−	0.965708i	−0.875701	−	0.482854i	$-0.839600\pi$
$971$		−	30.0923i		−	0.965708i	0.875701	−	0.482854i	$-0.160400\pi$
$972$	22.7364	−	12.1761i	0.729269	−	0.390547i
$973$	−43.7789	−	43.7789i	−1.40349	−	1.40349i
$974$	15.8935			0.509260
$975$		0			0
$976$	20.4711			0.655264
$977$	20.4292	+	20.4292i	0.653589	+	0.653589i	0.953855	−	0.300266i	$-0.0970755\pi$
$977$	20.4292	+	20.4292i	0.653589	+	0.653589i	−0.300266	+	0.953855i	$0.597076\pi$
$978$	−8.30082	−	4.86342i	−0.265431	−	0.155515i
$979$			6.67433i			0.213313i
$980$		0			0
$981$	11.3187	−	40.1820i	0.361379	−	1.28291i
$982$	−13.7692	−	13.7692i	−0.439393	−	0.439393i
$983$	16.7861	−	16.7861i	0.535394	−	0.535394i	−0.386778	−	0.922173i	$-0.626412\pi$
$983$	16.7861	−	16.7861i	0.535394	−	0.535394i	0.922173	+	0.386778i	$0.126412\pi$
$984$	−8.25131	−	4.83441i	−0.263042	−	0.154115i
$985$		0			0
$986$	34.1819	+	34.1819i	1.08857	+	1.08857i
$987$	34.8680	−	59.5123i	1.10986	−	1.89430i
$988$	32.7751	−	5.50122i	1.04272	−	0.175017i
$989$			29.7659i			0.946501i
$990$		0			0
$991$	2.34181			0.0743900			0.0371950	−	0.999308i	$-0.488158\pi$
$991$	2.34181			0.0743900			0.0371950	+	0.999308i	$0.488158\pi$
$992$		−	18.6502i		−	0.592143i
$993$	27.8813	−	7.28027i	0.884788	−	0.231032i
$994$	55.9682	+	55.9682i	1.77520	+	1.77520i
$995$		0			0
$996$	−4.52812	−	17.3414i	−0.143479	−	0.549484i
$997$		−	39.0215i		−	1.23582i	−0.786248	−	0.617911i	$-0.787979\pi$
$997$		−	39.0215i		−	1.23582i	0.786248	−	0.617911i	$-0.212021\pi$
$998$		−	39.2511i		−	1.24247i
$999$	−22.3711	−	23.2452i	−0.707791	−	0.735444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.n.q.749.5		40
3.2	odd	2	inner	975.2.n.q.749.16		40
5.2	odd	4		975.2.o.p.476.16		40
5.3	odd	4		195.2.o.a.86.5	✓	40
5.4	even	2		975.2.n.r.749.16		40
13.5	odd	4		975.2.n.r.824.5		40
15.2	even	4		975.2.o.p.476.5		40
15.8	even	4		195.2.o.a.86.16	yes	40
15.14	odd	2		975.2.n.r.749.5		40
39.5	even	4		975.2.n.r.824.16		40
65.18	even	4		195.2.o.a.161.16	yes	40
65.44	odd	4	inner	975.2.n.q.824.16		40
65.57	even	4		975.2.o.p.551.5		40
195.44	even	4	inner	975.2.n.q.824.5		40
195.83	odd	4		195.2.o.a.161.5	yes	40
195.122	odd	4		975.2.o.p.551.16		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.o.a.86.5	✓	40	5.3	odd	4
195.2.o.a.86.16	yes	40	15.8	even	4
195.2.o.a.161.5	yes	40	195.83	odd	4
195.2.o.a.161.16	yes	40	65.18	even	4
975.2.n.q.749.5		40	1.1	even	1	trivial
975.2.n.q.749.16		40	3.2	odd	2	inner
975.2.n.q.824.5		40	195.44	even	4	inner
975.2.n.q.824.16		40	65.44	odd	4	inner
975.2.n.r.749.5		40	15.14	odd	2
975.2.n.r.749.16		40	5.4	even	2
975.2.n.r.824.5		40	13.5	odd	4
975.2.n.r.824.16		40	39.5	even	4
975.2.o.p.476.5		40	15.2	even	4
975.2.o.p.476.16		40	5.2	odd	4
975.2.o.p.551.5		40	65.57	even	4
975.2.o.p.551.16		40	195.122	odd	4

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.n (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.35176 - 1.35176i) q^{2} +(-0.875587 + 1.49444i) q^{3} +1.65452i q^{4} +(3.20371 - 0.836541i) q^{6} +(3.04341 + 3.04341i) q^{7} +(-0.467005 + 0.467005i) q^{8} +(-1.46670 - 2.61702i) q^{9} +O(q^{10})\)	\(q+(-1.35176 - 1.35176i) q^{2} +(-0.875587 + 1.49444i) q^{3} +1.65452i q^{4} +(3.20371 - 0.836541i) q^{6} +(3.04341 + 3.04341i) q^{7} +(-0.467005 + 0.467005i) q^{8} +(-1.46670 - 2.61702i) q^{9} +(1.65064 + 1.65064i) q^{11} +(-2.47258 - 1.44868i) q^{12} +(2.93636 + 2.09231i) q^{13} -8.22793i q^{14} +4.57160 q^{16} +4.34228i q^{17} +(-1.55497 + 5.52021i) q^{18} +(-3.93929 - 3.93929i) q^{19} +(-7.21296 + 1.88342i) q^{21} -4.46254i q^{22} -3.46204i q^{23} +(-0.289007 - 1.10681i) q^{24} +(-1.14095 - 6.79757i) q^{26} +(5.19520 + 0.0995434i) q^{27} +(-5.03538 + 5.03538i) q^{28} +5.82342i q^{29} +(1.77766 + 1.77766i) q^{31} +(-5.24571 - 5.24571i) q^{32} +(-3.91206 + 1.02150i) q^{33} +(5.86973 - 5.86973i) q^{34} +(4.32992 - 2.42668i) q^{36} +(-4.39024 - 4.39024i) q^{37} +10.6500i q^{38} +(-5.69787 + 2.55621i) q^{39} +(5.91144 - 5.91144i) q^{41} +(12.2961 + 7.20427i) q^{42} -8.59781 q^{43} +(-2.73102 + 2.73102i) q^{44} +(-4.67985 + 4.67985i) q^{46} +(-6.54241 + 6.54241i) q^{47} +(-4.00283 + 6.83198i) q^{48} +11.5247i q^{49} +(-6.48927 - 3.80204i) q^{51} +(-3.46178 + 4.85827i) q^{52} +1.40983 q^{53} +(-6.88811 - 7.15723i) q^{54} -2.84257 q^{56} +(9.33623 - 2.43784i) q^{57} +(7.87188 - 7.87188i) q^{58} +(4.52860 + 4.52860i) q^{59} +4.47788 q^{61} -4.80594i q^{62} +(3.50091 - 12.4284i) q^{63} +5.03870i q^{64} +(6.66900 + 3.90734i) q^{66} +(-4.35368 + 4.35368i) q^{67} -7.18440 q^{68} +(5.17380 + 3.03131i) q^{69} +(-6.80223 + 6.80223i) q^{71} +(1.90712 + 0.537208i) q^{72} +(7.30145 + 7.30145i) q^{73} +11.8691i q^{74} +(6.51765 - 6.51765i) q^{76} +10.0471i q^{77} +(11.1576 + 4.24678i) q^{78} +2.67693 q^{79} +(-4.69761 + 7.67675i) q^{81} -15.9817 q^{82} +(4.42241 + 4.42241i) q^{83} +(-3.11616 - 11.9340i) q^{84} +(11.6222 + 11.6222i) q^{86} +(-8.70275 - 5.09891i) q^{87} -1.54171 q^{88} +(2.02174 + 2.02174i) q^{89} +(2.56879 + 15.3043i) q^{91} +5.72801 q^{92} +(-4.21310 + 1.10011i) q^{93} +17.6876 q^{94} +(12.4325 - 3.24632i) q^{96} +(-1.21361 + 1.21361i) q^{97} +(15.5786 - 15.5786i) q^{98} +(1.89877 - 6.74074i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{6} - 16 q^{7}+O(q^{10}) \) 40 * q + 12 * q^6 - 16 * q^7	\( 40 q + 12 q^{6} - 16 q^{7} - 24 q^{12} + 24 q^{13} - 64 q^{16} + 4 q^{18} + 16 q^{19} - 12 q^{21} - 8 q^{24} + 32 q^{28} + 32 q^{31} + 4 q^{33} + 16 q^{34} + 32 q^{37} + 8 q^{39} - 32 q^{43} - 40 q^{46} - 8 q^{52} + 32 q^{54} + 36 q^{57} + 24 q^{58} + 8 q^{61} - 8 q^{63} - 48 q^{66} + 32 q^{67} + 132 q^{72} + 64 q^{73} + 16 q^{76} - 108 q^{78} - 40 q^{79} + 72 q^{81} - 128 q^{82} - 124 q^{84} - 80 q^{88} + 8 q^{91} - 108 q^{93} + 32 q^{94} - 76 q^{96} - 24 q^{97} + 20 q^{99}+O(q^{100}) \) 40 * q + 12 * q^6 - 16 * q^7 - 24 * q^12 + 24 * q^13 - 64 * q^16 + 4 * q^18 + 16 * q^19 - 12 * q^21 - 8 * q^24 + 32 * q^28 + 32 * q^31 + 4 * q^33 + 16 * q^34 + 32 * q^37 + 8 * q^39 - 32 * q^43 - 40 * q^46 - 8 * q^52 + 32 * q^54 + 36 * q^57 + 24 * q^58 + 8 * q^61 - 8 * q^63 - 48 * q^66 + 32 * q^67 + 132 * q^72 + 64 * q^73 + 16 * q^76 - 108 * q^78 - 40 * q^79 + 72 * q^81 - 128 * q^82 - 124 * q^84 - 80 * q^88 + 8 * q^91 - 108 * q^93 + 32 * q^94 - 76 * q^96 - 24 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

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