LMFDB - Embedded newform 975.2.n.q.824.16

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			824.16
Character	$\chi$	$=$	975.824
Dual form			975.2.n.q.749.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35176 - 1.35176i) q^{2} +(0.875587 - 1.49444i) q^{3} -1.65452i q^{4} +(-0.836541 - 3.20371i) q^{6} +(3.04341 - 3.04341i) q^{7} +(0.467005 + 0.467005i) q^{8} +(-1.46670 - 2.61702i) q^{9} +O(q^{10})$	\(q+(1.35176 - 1.35176i) q^{2} +(0.875587 - 1.49444i) q^{3} -1.65452i q^{4} +(-0.836541 - 3.20371i) 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} +(-5.52021 - 1.55497i) q^{18} +(-3.93929 + 3.93929i) q^{19} +(-1.88342 - 7.21296i) q^{21} +4.46254i q^{22} -3.46204i q^{23} +(1.10681 - 0.289007i) 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} +(1.02150 + 3.91206i) q^{33} +(5.86973 + 5.86973i) q^{34} +(-4.32992 + 2.42668i) q^{36} +(-4.39024 + 4.39024i) q^{37} +10.6500i q^{38} +(-0.555794 - 6.22022i) 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} +(-7.15723 + 6.88811i) q^{54} +2.84257 q^{56} +(2.43784 + 9.33623i) q^{57} +(7.87188 + 7.87188i) q^{58} +(-4.52860 + 4.52860i) q^{59} +4.47788 q^{61} -4.80594i q^{62} +(-12.4284 - 3.50091i) 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} +(0.537208 - 1.90712i) q^{72} +(7.30145 - 7.30145i) q^{73} +11.8691i q^{74} +(6.51765 + 6.51765i) q^{76} +10.0471i q^{77} +(-9.15955 - 7.65695i) q^{78} +2.67693 q^{79} +(-4.69761 + 7.67675i) q^{81} -15.9817 q^{82} +(-4.42241 + 4.42241i) q^{83} +(-11.9340 + 3.11616i) 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} +(-1.10011 - 4.21310i) q^{93} +17.6876 q^{94} +(-3.24632 - 12.4325i) q^{96} +(-1.21361 - 1.21361i) q^{97} +(-15.5786 - 15.5786i) q^{98} +(6.74074 + 1.89877i) 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 $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

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	$-0.513763\pi$
$2$	1.35176	−	1.35176i	0.955840	−	0.955840i	0.999065	+	0.0432252i	$0.0137633\pi$
$3$	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
$6$	−0.836541	−	3.20371i	−0.341516	−	1.30791i
$7$	3.04341	−	3.04341i	1.15030	−	1.15030i	0.163808	−	0.986492i	$-0.447622\pi$
$7$	3.04341	−	3.04341i	1.15030	−	1.15030i	0.986492	−	0.163808i	$-0.0523778\pi$
$8$	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	$-0.864470\pi$
$11$	−1.65064	+	1.65064i	−0.497686	+	0.497686i	0.413031	+	0.910717i	$0.364470\pi$
$12$	−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	$0.823475\pi$
$18$	−5.52021	−	1.55497i	−1.30113	−	0.366509i
$19$	−3.93929	+	3.93929i	−0.903736	+	0.903736i	−0.995757	−	0.0920208i	$-0.970667\pi$
$19$	−3.93929	+	3.93929i	−0.903736	+	0.903736i	0.0920208	+	0.995757i	$0.470667\pi$
$20$		0			0
$21$	−1.88342	−	7.21296i	−0.410996	−	1.57400i
$22$			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	$-0.117545\pi$
$24$	1.10681	−	0.289007i	0.225927	−	0.0589933i
$25$		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	−0.529212	−	0.848489i	$-0.677513\pi$
$31$	1.77766	−	1.77766i	0.319277	−	0.319277i	0.848489	+	0.529212i	$0.177513\pi$
$32$	5.24571	−	5.24571i	0.927319	−	0.927319i
$33$	1.02150	+	3.91206i	0.177821	+	0.681002i
$34$	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	−0.968962	−	0.247211i	$-0.920486\pi$
$37$	−4.39024	+	4.39024i	−0.721750	+	0.721750i	0.247211	+	0.968962i	$0.420486\pi$
$38$			10.6500i			1.72765i
$39$	−0.555794	−	6.22022i	−0.0889983	−	0.996032i
$40$		0			0
$41$	−5.91144	−	5.91144i	−0.923212	−	0.923212i	0.0740434	−	0.997255i	$-0.476410\pi$
$41$	−5.91144	−	5.91144i	−0.923212	−	0.923212i	−0.997255	+	0.0740434i	$0.976410\pi$
$42$	−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	$-0.0142305\pi$
$47$	6.54241	+	6.54241i	0.954309	+	0.954309i	−0.0446917	+	0.999001i	$0.514231\pi$
$48$	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	$-0.530870\pi$
$53$	−1.40983			−0.193655			−0.0968277	+	0.995301i	$0.530870\pi$
$54$	−7.15723	+	6.88811i	−0.973976	+	0.937354i
$55$		0			0
$56$	2.84257			0.379855
$57$	2.43784	+	9.33623i	0.322900	+	1.23661i
$58$	7.87188	+	7.87188i	1.03363	+	1.03363i
$59$	−4.52860	+	4.52860i	−0.589573	+	0.589573i	−0.937516	−	0.347943i	$-0.886880\pi$
$59$	−4.52860	+	4.52860i	−0.589573	+	0.589573i	0.347943	+	0.937516i	$0.386880\pi$
$60$		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
$63$	−12.4284	−	3.50091i	−1.56583	−	0.441074i
$64$		−	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	0.389247	−	0.921133i	$-0.372735\pi$
$67$	−4.35368	−	4.35368i	−0.531886	−	0.531886i	−0.921133	+	0.389247i	$0.872735\pi$
$68$	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	$-0.0566215\pi$
$71$	6.80223	+	6.80223i	0.807276	+	0.807276i	−0.176945	+	0.984221i	$0.556622\pi$
$72$	0.537208	−	1.90712i	0.0633106	−	0.224756i
$73$	7.30145	−	7.30145i	0.854571	−	0.854571i	−0.136121	−	0.990692i	$-0.543464\pi$
$73$	7.30145	−	7.30145i	0.854571	−	0.854571i	0.990692	+	0.136121i	$0.0434637\pi$
$74$			11.8691i			1.37976i
$75$		0			0
$76$	6.51765	+	6.51765i	0.747626	+	0.747626i
$77$			10.0471i			1.14498i
$78$	−9.15955	−	7.65695i	−1.03712	−	0.866979i
$79$	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	$-0.861526\pi$
$83$	−4.42241	+	4.42241i	−0.485423	+	0.485423i	0.421436	+	0.906858i	$0.361526\pi$
$84$	−11.9340	+	3.11616i	−1.30211	+	0.340001i
$85$		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	$-0.798422\pi$
$89$	−2.02174	+	2.02174i	−0.214304	+	0.214304i	0.591789	+	0.806093i	$0.298422\pi$
$90$		0			0
$91$	2.56879	−	15.3043i	0.269282	−	1.60433i
$92$	−5.72801			−0.597187
$93$	−1.10011	−	4.21310i	−0.114076	−	0.436878i
$94$	17.6876			1.82433
$95$		0			0
$96$	−3.24632	−	12.4325i	−0.331326	−	1.26888i
$97$	−1.21361	−	1.21361i	−0.123224	−	0.123224i	0.642806	−	0.766029i	$-0.277770\pi$
$97$	−1.21361	−	1.21361i	−0.123224	−	0.123224i	−0.766029	+	0.642806i	$0.777770\pi$
$98$	−15.5786	−	15.5786i	−1.57368	−	1.57368i
$99$	6.74074	+	1.89877i	0.677470	+	0.190834i
$100$		0			0
$101$	5.82645			0.579754			0.289877	−	0.957064i	$-0.406386\pi$
$101$	5.82645			0.579754			0.289877	+	0.957064i	$0.406386\pi$
$102$	13.9114	−	3.63249i	1.37743	−	0.359671i
$103$	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	$-0.496478\pi$
$107$	0.228933			0.0221318			0.0110659	+	0.999939i	$0.496478\pi$
$108$	−0.164697	+	8.59557i	−0.0158480	+	0.827109i
$109$	9.83957	−	9.83957i	0.942459	−	0.942459i	−0.0559728	−	0.998432i	$-0.517826\pi$
$109$	9.83957	−	9.83957i	0.942459	−	0.942459i	0.998432	+	0.0559728i	$0.0178260\pi$
$110$		0			0
$111$	2.71691	+	10.4050i	0.257877	+	0.987596i
$112$	13.9133	−	13.9133i	1.31468	−	1.31468i
$113$	6.58296			0.619273			0.309636	−	0.950855i	$-0.399793\pi$
$113$	6.58296			0.619273			0.309636	+	0.950855i	$0.399793\pi$
$114$	15.9157	+	9.32498i	1.49065	+	0.873365i
$115$		0			0
$116$	9.63498			0.894585
$117$	−9.78238	−	4.61574i	−0.904381	−	0.426725i
$118$			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
$123$	−14.0103	+	3.65831i	−1.26326	+	0.329858i
$124$	−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	$0.895680\pi$
$132$	6.47258	−	1.69010i	0.563366	−	0.147104i
$133$			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	$-0.287701\pi$
$137$	−1.95599	−	1.95599i	−0.167112	−	0.167112i	−0.785709	+	0.618597i	$0.787701\pi$
$138$	−11.0914	+	2.89613i	−0.944159	+	0.246535i
$139$	−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
$141$	15.5057	−	4.04879i	1.30581	−	0.340969i
$142$	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	$-0.331179\pi$
$149$	−4.35495	−	4.35495i	−0.356772	−	0.356772i	−0.862622	+	0.505850i	$0.831179\pi$
$150$		0			0
$151$	4.31495	+	4.31495i	0.351145	+	0.351145i	0.860536	−	0.509390i	$-0.170129\pi$
$151$	4.31495	+	4.31495i	0.351145	+	0.351145i	−0.509390	+	0.860536i	$0.670129\pi$
$152$	−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
$156$	−10.2915	+	0.919573i	−0.823978	+	0.0736248i
$157$			17.4089i			1.38938i	0.719308	+	0.694691i	$0.244459\pi$
$157$			17.4089i			1.38938i	−0.719308	+	0.694691i	$0.755541\pi$
$158$	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
$162$	4.02709	+	16.7272i	0.316398	+	1.31421i
$163$	−2.05453	+	2.05453i	−0.160923	+	0.160923i	−0.782976	−	0.622052i	$-0.786299\pi$
$163$	−2.05453	+	2.05453i	−0.160923	+	0.160923i	0.622052	+	0.782976i	$0.286299\pi$
$164$	−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	0.998316	+	0.0580142i	$0.0184769\pi$
$167$	13.6508	+	13.6508i	1.05633	+	1.05633i	0.0580142	+	0.998316i	$0.481523\pi$
$168$	2.48892	−	4.24805i	0.192024	−	0.327744i
$169$	4.24445	−	12.2876i	0.326496	−	0.945199i
$170$		0			0
$171$	16.0870	+	4.53148i	1.23020	+	0.346531i
$172$			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	$-0.0887205\pi$
$174$	18.6566	−	4.87153i	1.41435	−	0.369310i
$175$		0			0
$176$	−7.54606	+	7.54606i	−0.568806	+	0.568806i
$177$	2.80253	+	10.7329i	0.210651	+	0.806734i
$178$			5.46583i			0.409681i
$179$	10.1878			0.761474			0.380737	−	0.924683i	$-0.375670\pi$
$179$	10.1878			0.761474			0.380737	+	0.924683i	$0.375670\pi$
$180$		0			0
$181$		−	20.8159i		−	1.54723i	−0.633655	−	0.773616i	$-0.718446\pi$
$181$		−	20.8159i		−	1.54723i	0.633655	−	0.773616i	$-0.281554\pi$
$182$	−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
$189$	−16.1141	+	15.5082i	−1.17213	+	1.12805i
$190$		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	−0.604608	−	0.796523i	$-0.706670\pi$
$193$	2.66617	−	2.66617i	0.191915	−	0.191915i	0.796523	+	0.604608i	$0.206670\pi$
$194$	−3.28104			−0.235565
$195$		0			0
$196$	−19.0678			−1.36199
$197$	16.8317	−	16.8317i	1.19921	−	1.19921i	0.224804	−	0.974404i	$-0.427826\pi$
$197$	16.8317	−	16.8317i	1.19921	−	1.19921i	0.974404	−	0.224804i	$-0.0721741\pi$
$198$	11.6786	−	6.54519i	0.829960	−	0.465146i
$199$		−	6.70679i		−	0.475432i	−0.971335	−	0.237716i	$-0.923601\pi$
$199$		−	6.70679i		−	0.475432i	0.971335	−	0.237716i	$-0.0763987\pi$
$200$		0			0
$201$	−10.3183	+	2.69428i	−0.727799	+	0.190040i
$202$	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
$213$	16.1214	−	4.20957i	1.10462	−	0.288435i
$214$	0.309463	−	0.309463i	0.0211544	−	0.0211544i
$215$		0			0
$216$	−2.37970	−	2.47267i	−0.161918	−	0.168244i
$217$		−	10.8203i		−	0.734529i
$218$		−	26.6015i		−	1.80168i
$219$	−4.51852	−	17.3046i	−0.305333	−	1.16934i
$220$		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	0.512071	−	0.858943i	$-0.328878\pi$
$223$	−5.17991	−	5.17991i	−0.346872	−	0.346872i	−0.858943	+	0.512071i	$0.828878\pi$
$224$		−	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	−0.421383	+	0.906883i	$0.638455\pi$
$227$	−20.0123	+	20.0123i	−1.32827	+	1.32827i	−0.906883	+	0.421383i	$0.861545\pi$
$228$	15.4470	−	4.03346i	1.02300	−	0.267122i
$229$	−11.2696	−	11.2696i	−0.744713	−	0.744713i	0.228768	−	0.973481i	$-0.426530\pi$
$229$	−11.2696	−	11.2696i	−0.744713	−	0.744713i	−0.973481	+	0.228768i	$0.926530\pi$
$230$		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	$0.893626\pi$
$234$	−19.4628	+	6.98407i	−1.27233	+	0.456563i
$235$		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	$-0.446770\pi$
$239$	−12.6708	−	12.6708i	−0.819603	−	0.819603i	−0.986050	+	0.166448i	$0.946770\pi$
$240$		0			0
$241$	−6.25390	−	6.25390i	−0.402849	−	0.402849i	0.476387	−	0.879236i	$-0.341946\pi$
$241$	−6.25390	−	6.25390i	−0.402849	−	0.402849i	−0.879236	+	0.476387i	$0.841946\pi$
$242$	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
$249$	2.73682	+	10.4812i	0.173439	+	0.664221i
$250$		0			0
$251$	−14.2440			−0.899071			−0.449535	−	0.893263i	$-0.648410\pi$
$251$	−14.2440			−0.899071			−0.449535	+	0.893263i	$0.648410\pi$
$252$	−5.79234	+	20.5631i	−0.364883	+	1.29535i
$253$	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	$-0.284129\pi$
$258$	7.19241	+	27.5449i	0.447780	+	1.71487i
$259$			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	$-0.453623\pi$
$263$	4.70892			0.290364			0.145182	+	0.989405i	$0.453623\pi$
$264$	−1.34990	+	2.30400i	−0.0830808	+	0.141801i
$265$		0			0
$266$	32.4122	+	32.4122i	1.98732	+	1.98732i
$267$	1.25116	+	4.79158i	0.0765697	+	0.293240i
$268$	−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	0.902964	−	0.429715i	$-0.141386\pi$
$271$	7.79066	+	7.79066i	0.473249	+	0.473249i	−0.429715	+	0.902964i	$0.641386\pi$
$272$			19.8512i			1.20365i
$273$	−20.6222	−	17.2392i	−1.24811	−	1.04336i
$274$	−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
$279$	−7.25945	−	2.04489i	−0.434612	−	0.122424i
$280$		0			0
$281$	−3.71699	+	3.71699i	−0.221737	+	0.221737i	−0.809230	−	0.587492i	$-0.800115\pi$
$281$	−3.71699	+	3.71699i	−0.221737	+	0.221737i	0.587492	+	0.809230i	$0.300115\pi$
$282$	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
$288$	−21.4220	−	6.03428i	−1.26230	−	0.355573i
$289$	−1.85540			−0.109141
$290$		0			0
$291$	−2.87630	+	0.751048i	−0.168612	+	0.0440272i
$292$	−12.0804	−	12.0804i	−0.706953	−	0.706953i
$293$	2.46556	+	2.46556i	0.144039	+	0.144039i	0.775449	−	0.631410i	$-0.217523\pi$
$293$	2.46556	+	2.46556i	0.144039	+	0.144039i	−0.631410	+	0.775449i	$0.717523\pi$
$294$	−36.9217	+	9.64086i	−2.15332	+	0.562266i
$295$		0			0
$296$	−4.10052			−0.238338
$297$	8.73971	−	8.41109i	0.507129	−	0.488061i
$298$	−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
$306$	6.75211	−	23.9703i	0.385992	−	1.37029i
$307$	7.33272	−	7.33272i	0.418500	−	0.418500i	−0.466186	−	0.884687i	$-0.654372\pi$
$307$	7.33272	−	7.33272i	0.418500	−	0.418500i	0.884687	+	0.466186i	$0.154372\pi$
$308$	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	$-0.462373\pi$
$311$	4.15959			0.235869			0.117934	+	0.993021i	$0.462373\pi$
$312$	2.64531	−	3.16443i	0.149761	−	0.179151i
$313$			15.3278i			0.866380i	0.901303	+	0.433190i	$0.142612\pi$
$313$			15.3278i			0.866380i	−0.901303	+	0.433190i	$0.857388\pi$
$314$	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	$-0.831997\pi$
$317$	−6.41472	+	6.41472i	−0.360287	+	0.360287i	0.503632	+	0.863918i	$0.331997\pi$
$318$	1.17938	+	4.51669i	0.0661365	+	0.253284i
$319$	−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
$327$	−6.08924	−	23.3200i	−0.336736	−	1.28960i
$328$		−	5.52134i		−	0.304865i
$329$	39.8225			2.19548
$330$		0			0
$331$	−11.7642	+	11.7642i	−0.646616	+	0.646616i	−0.952174	−	0.305557i	$-0.901157\pi$
$331$	−11.7642	+	11.7642i	−0.646616	+	0.646616i	0.305557	+	0.952174i	$0.401157\pi$
$332$	7.31697	+	7.31697i	0.401571	+	0.401571i
$333$	17.9285	+	5.05021i	0.982475	+	0.276750i
$334$	36.9052			2.01937
$335$		0			0
$336$	−8.61024	−	32.9748i	−0.469727	−	1.79892i
$337$	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	$-0.575065\pi$
$347$	−8.70464			−0.467289			−0.233645	+	0.972322i	$0.575065\pi$
$348$	8.43626	−	14.3989i	0.452231	−	0.771861i
$349$	23.6983	+	23.6983i	1.26854	+	1.26854i	0.946842	+	0.321700i	$0.104254\pi$
$349$	23.6983	+	23.6983i	1.26854	+	1.26854i	0.321700	+	0.946842i	$0.395746\pi$
$350$		0			0
$351$	−15.4633	+	10.5777i	−0.825368	+	0.564595i
$352$			17.3175i			0.923028i
$353$	−10.1103	+	10.1103i	−0.538119	+	0.538119i	−0.922976	−	0.384857i	$-0.874251\pi$
$353$	−10.1103	+	10.1103i	−0.538119	+	0.538119i	0.384857	+	0.922976i	$0.374251\pi$
$354$	18.2967	+	10.7200i	0.972457	+	0.569759i
$355$		0			0
$356$	3.34501	+	3.34501i	0.177285	+	0.177285i
$357$	31.3207	−	8.17834i	1.65767	−	0.432843i
$358$	13.7715	−	13.7715i	0.727847	−	0.727847i
$359$	−14.1823	+	14.1823i	−0.748515	+	0.748515i	−0.974200	−	0.225686i	$-0.927538\pi$
$359$	−14.1823	+	14.1823i	−0.748515	+	0.748515i	0.225686	+	0.974200i	$0.427538\pi$
$360$		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
$366$	−3.74593	−	14.3458i	−0.195803	−	0.749869i
$367$			3.99669i			0.208625i	0.994545	+	0.104313i	$0.0332643\pi$
$367$			3.99669i			0.208625i	−0.994545	+	0.104313i	$0.966736\pi$
$368$		−	15.8270i		−	0.825042i
$369$	−6.80009	+	24.1406i	−0.353998	+	1.25671i
$370$		0			0
$371$	−4.29069	+	4.29069i	−0.222762	+	0.222762i
$372$	−6.97066	+	1.82015i	−0.361412	+	0.0943705i
$373$			13.2904i			0.688150i	0.938942	+	0.344075i	$0.111807\pi$
$373$			13.2904i			0.688150i	−0.938942	+	0.344075i	$0.888193\pi$
$374$	−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	−0.792795	−	0.609488i	$-0.791375\pi$
$379$	−3.56862	+	3.56862i	−0.183308	+	0.183308i	0.609488	+	0.792795i	$0.291375\pi$
$380$		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	−0.142718	+	0.989763i	$0.545584\pi$
$383$	−22.1631	+	22.1631i	−1.13248	+	1.13248i	−0.989763	+	0.142718i	$0.954416\pi$
$384$	8.72240	−	2.27756i	0.445113	−	0.116226i
$385$		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	$-0.678150\pi$
$389$	−20.9424			−1.06182			−0.530910	+	0.847428i	$0.678150\pi$
$390$		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
$396$	3.14156	−	11.1527i	0.157869	−	0.560445i
$397$	−13.9072	+	13.9072i	−0.697984	+	0.697984i	−0.963975	−	0.265991i	$-0.914301\pi$
$397$	−13.9072	+	13.9072i	−0.697984	+	0.697984i	0.265991	+	0.963975i	$0.414301\pi$
$398$	−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	$-0.928607\pi$
$401$	−15.0696	+	15.0696i	−0.752542	+	0.752542i	0.222411	+	0.974953i	$0.428607\pi$
$402$	−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
$408$	1.25495	+	4.80609i	0.0621292	+	0.237937i
$409$	11.5380	−	11.5380i	0.570517	−	0.570517i	−0.361756	−	0.932273i	$-0.617823\pi$
$409$	11.5380	−	11.5380i	0.570517	−	0.570517i	0.932273	+	0.361756i	$0.117823\pi$
$410$		0			0
$411$	−4.63575	+	1.21047i	−0.228665	+	0.0597081i
$412$		−	1.08395i		−	0.0534026i
$413$			27.5647i			1.35637i
$414$	−5.38335	+	19.1112i	−0.264577	+	0.939263i
$415$		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	−0.811620	−	0.584186i	$-0.801414\pi$
$421$	−4.66657	+	4.66657i	−0.227435	+	0.227435i	0.584186	+	0.811620i	$0.301414\pi$
$422$	−34.3836	+	34.3836i	−1.67377	+	1.67377i
$423$	7.52591	−	26.7174i	0.365922	−	1.29904i
$424$	−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
$429$	11.1847	+	9.34992i	0.540005	+	0.451418i
$430$		0			0
$431$	−18.0478	−	18.0478i	−0.869333	−	0.869333i	0.123066	−	0.992398i	$-0.460727\pi$
$431$	−18.0478	−	18.0478i	−0.869333	−	0.869333i	−0.992398	+	0.123066i	$0.960727\pi$
$432$	−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	$-0.985419\pi$
$439$		−	1.91889i		−	0.0915836i	0.998951	−	0.0457918i	$-0.0145811\pi$
$440$		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	$-0.386370\pi$
$443$	14.7100			0.698891			0.349446	+	0.936957i	$0.386370\pi$
$444$	17.2152	−	4.49518i	0.817000	−	0.213332i
$445$		0			0
$446$	−14.0040			−0.663109
$447$	−10.3214	+	2.69507i	−0.488183	+	0.127473i
$448$	−15.3348	−	15.3348i	−0.724502	−	0.724502i
$449$	−17.4536	+	17.4536i	−0.823684	+	0.823684i	−0.986634	−	0.162950i	$-0.947899\pi$
$449$	−17.4536	+	17.4536i	−0.823684	+	0.823684i	0.162950	+	0.986634i	$0.447899\pi$
$450$		0			0
$451$	19.5153			0.918940
$452$		−	10.8916i		−	0.512300i
$453$	10.2265	−	2.67031i	0.480485	−	0.125462i
$454$			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	0.387758	−	0.921761i	$-0.373250\pi$
$457$	−11.4157	−	11.4157i	−0.534003	−	0.534003i	−0.921761	+	0.387758i	$0.873250\pi$
$458$	−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	$-0.497986\pi$
$461$	−21.3346	−	21.3346i	−0.993652	−	0.993652i	−0.999980	+	0.00632789i	$0.997986\pi$
$462$	32.1881	−	8.40484i	1.49753	−	0.391029i
$463$	16.3113	−	16.3113i	0.758050	−	0.758050i	−0.217917	−	0.975967i	$-0.569926\pi$
$463$	16.3113	−	16.3113i	0.758050	−	0.758050i	0.975967	+	0.217917i	$0.0699263\pi$
$464$			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	$-0.317345\pi$
$468$	−7.63684	+	16.1852i	−0.353013	+	0.748159i
$469$	−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
$474$	−2.23936	−	8.57612i	−0.102857	−	0.393914i
$475$		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	$-0.954334\pi$
$479$	−18.5322	+	18.5322i	−0.846756	+	0.846756i	0.142971	+	0.989727i	$0.454334\pi$
$480$		0			0
$481$	−3.70557	+	22.0771i	−0.168960	+	1.00663i
$482$	−16.9076			−0.770119
$483$	−24.9715	+	6.52047i	−1.13624	+	0.296691i
$484$	9.18389			0.417449
$485$		0			0
$486$	28.5238	+	8.62787i	1.29387	+	0.391368i
$487$	−5.87880	−	5.87880i	−0.266394	−	0.266394i	0.561252	−	0.827645i	$-0.310320\pi$
$487$	−5.87880	−	5.87880i	−0.266394	−	0.266394i	−0.827645	+	0.561252i	$0.810320\pi$
$488$	2.09119	+	2.09119i	0.0946638	+	0.0946638i
$489$	1.27145	+	4.86929i	0.0574970	+	0.220197i
$490$		0			0
$491$	−10.1861			−0.459693			−0.229847	−	0.973227i	$-0.573822\pi$
$491$	−10.1861			−0.459693			−0.229847	+	0.973227i	$0.573822\pi$
$492$	6.05275	+	23.1803i	0.272879	+	1.04505i
$493$	−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	−0.303041	−	0.952978i	$-0.598002\pi$
$499$	14.5185	−	14.5185i	0.649937	−	0.649937i	0.952978	+	0.303041i	$0.0980019\pi$
$500$		0			0
$501$	32.3527	−	8.44782i	1.44541	−	0.377421i
$502$	−19.2544	+	19.2544i	−0.859368	+	0.859368i
$503$	−17.4820			−0.779483			−0.389742	−	0.920924i	$-0.627436\pi$
$503$	−17.4820			−0.779483			−0.389742	+	0.920924i	$0.627436\pi$
$504$	−4.16919	−	7.43907i	−0.185710	−	0.331363i
$505$		0			0
$506$	15.4495			0.686813
$507$	−14.6467	−	17.1019i	−0.650481	−	0.759523i
$508$		−	13.5881i		−	0.602876i
$509$	7.35152	+	7.35152i	0.325850	+	0.325850i	0.851006	−	0.525156i	$-0.175993\pi$
$509$	7.35152	+	7.35152i	0.325850	+	0.325850i	−0.525156	+	0.851006i	$0.675993\pi$
$510$		0			0
$511$		−	44.4426i		−	1.96603i
$512$	19.7114	−	19.7114i	0.871128	−	0.871128i
$513$	20.8576	−	20.0733i	0.920883	−	0.886257i
$514$	−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	$0.937196\pi$
$522$	9.05524	−	32.1465i	0.396337	−	1.40702i
$523$			29.1992i			1.27679i	0.769708	+	0.638396i	$0.220402\pi$
$523$			29.1992i			1.27679i	−0.769708	+	0.638396i	$0.779598\pi$
$524$	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
$528$	4.66990	+	17.8844i	0.203231	+	0.778317i
$529$	11.0143			0.478883
$530$		0			0
$531$	18.4935	+	5.20937i	0.802550	+	0.226067i
$532$	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	0.856534	−	0.516090i	$-0.172613\pi$
$541$	7.91853	+	7.91853i	0.340444	+	0.340444i	−0.516090	+	0.856534i	$0.672613\pi$
$542$	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
$546$	−51.1795	+	4.57303i	−2.19028	+	0.195708i
$547$		−	39.7240i		−	1.69848i	−0.528010	−	0.849238i	$-0.677062\pi$
$547$		−	39.7240i		−	1.69848i	0.528010	−	0.849238i	$-0.322938\pi$
$548$	−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
$552$	−1.00055	−	3.83183i	−0.0425863	−	0.163093i
$553$	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	−0.912645	−	0.408752i	$-0.865964\pi$
$557$	−31.1861	−	31.1861i	−1.32140	−	1.32140i	−0.408752	−	0.912645i	$-0.634036\pi$
$558$	−12.5773	+	7.04885i	−0.532438	+	0.298402i
$559$	−25.2463	+	17.9893i	−1.06780	+	0.760866i
$560$		0			0
$561$	−16.9872	+	4.43565i	−0.717202	+	0.187273i
$562$			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	$-0.205311\pi$
$564$	−6.69880	−	25.6545i	−0.282071	−	1.08025i
$565$		0			0
$566$	−3.33318	+	3.33318i	−0.140104	+	0.140104i
$567$	9.06674	+	37.6602i	0.380767	+	1.58158i
$568$			6.35334i			0.266580i
$569$	7.59495			0.318397			0.159198	−	0.987247i	$-0.449109\pi$
$569$	7.59495			0.318397			0.159198	+	0.987247i	$0.449109\pi$
$570$		0			0
$571$		−	38.7934i		−	1.62345i	−0.584039	−	0.811726i	$-0.698528\pi$
$571$		−	38.7934i		−	1.62345i	0.584039	−	0.811726i	$-0.301472\pi$
$572$	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	0.910555	+	0.413387i	$0.135654\pi$
$577$	31.8022	+	31.8022i	1.32394	+	1.32394i	0.413387	+	0.910555i	$0.364346\pi$
$578$	−2.50805	+	2.50805i	−0.104321	+	0.104321i
$579$	−1.64997	−	6.31890i	−0.0685703	−	0.262604i
$580$		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	−0.282514	+	0.959263i	$0.591168\pi$
$587$	−30.0859	+	30.0859i	−1.24178	+	1.24178i	−0.959263	+	0.282514i	$0.908832\pi$
$588$	−16.6955	+	28.4957i	−0.688512	+	1.17514i
$589$			14.0054i			0.577084i
$590$		0			0
$591$	−10.4163	−	39.8915i	−0.428470	−	1.64092i
$592$	−20.0704	+	20.0704i	−0.824889	+	0.824889i
$593$	−15.4861	−	15.4861i	−0.635939	−	0.635939i	0.313612	−	0.949551i	$-0.398461\pi$
$593$	−15.4861	−	15.4861i	−0.635939	−	0.635939i	−0.949551	+	0.313612i	$0.898461\pi$
$594$	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
$603$	−5.00815	+	17.7792i	−0.203948	+	0.724025i
$604$	7.13917	−	7.13917i	0.290489	−	0.290489i
$605$		0			0
$606$	−4.87406	−	18.6663i	−0.197995	−	0.758265i
$607$			14.2336i			0.577725i	0.957371	+	0.288862i	$0.0932770\pi$
$607$			14.2336i			0.577725i	−0.957371	+	0.288862i	$0.906723\pi$
$608$			41.3288i			1.67610i
$609$	42.0041	−	10.9679i	1.70209	−	0.444444i
$610$		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	0.931153	−	0.364628i	$-0.118804\pi$
$613$	14.0265	+	14.0265i	0.566525	+	0.566525i	−0.364628	+	0.931153i	$0.618804\pi$
$614$		−	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	$-0.850062\pi$
$617$	−10.8617	+	10.8617i	−0.437277	+	0.437277i	0.453817	+	0.891095i	$0.350062\pi$
$618$	−0.548057	−	2.09890i	−0.0220461	−	0.0844301i
$619$	8.83108	+	8.83108i	0.354951	+	0.354951i	0.861948	−	0.506997i	$-0.169244\pi$
$619$	8.83108	+	8.83108i	0.354951	+	0.354951i	−0.506997	+	0.861948i	$0.669244\pi$
$620$		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
$624$	−2.54087	−	28.4364i	−0.101716	−	1.13837i
$625$		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	0.843601	−	0.536971i	$-0.180431\pi$
$631$	7.70247	+	7.70247i	0.306630	+	0.306630i	−0.536971	+	0.843601i	$0.680431\pi$
$632$	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
$639$	7.82478	−	27.7784i	0.309544	−	1.09890i
$640$		0			0
$641$	45.3950			1.79299			0.896497	−	0.443050i	$-0.146103\pi$
$641$	45.3950			1.79299			0.896497	+	0.443050i	$0.146103\pi$
$642$	−0.191512	−	0.733434i	−0.00755836	−	0.0289463i
$643$	−27.0118	−	27.0118i	−1.06524	−	1.06524i	−0.997718	−	0.0675241i	$-0.978490\pi$
$643$	−27.0118	−	27.0118i	−1.06524	−	1.06524i	−0.0675241	−	0.997718i	$-0.521510\pi$
$644$	−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	$-0.357954\pi$
$648$	−5.77888	+	1.39127i	−0.227016	+	0.0546543i
$649$		−	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	$-0.222762\pi$
$653$	39.0950			1.52991			0.764953	+	0.644086i	$0.222762\pi$
$654$	−39.7543	−	23.2919i	−1.55452	−	0.910786i
$655$		0			0
$656$	−27.0247	−	27.0247i	−1.05514	−	1.05514i
$657$	−29.8171	−	8.39906i	−1.16328	−	0.327678i
$658$	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	−0.998678	−	0.0513985i	$-0.983632\pi$
$661$	−26.9974	−	26.9974i	−1.05008	−	1.05008i	−0.0513985	−	0.998678i	$-0.516368\pi$
$662$			31.8047i			1.23612i
$663$	27.0099	−	2.41341i	1.04898	−	0.0937292i
$664$	−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
$669$	−12.2765	+	3.20560i	−0.474637	+	0.123936i
$670$		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	$-0.412318\pi$
$677$	14.1540			0.543984			0.271992	+	0.962300i	$0.412318\pi$
$678$	−5.50691	−	21.0899i	−0.211492	−	0.809953i
$679$	−7.38705			−0.283489
$680$		0			0
$681$	12.3847	+	47.4298i	0.474582	+	1.81751i
$682$	7.93288	+	7.93288i	0.303766	+	0.303766i
$683$	21.9481	+	21.9481i	0.839819	+	0.839819i	0.988835	−	0.149016i	$-0.0476105\pi$
$683$	21.9481	+	21.9481i	0.839819	+	0.839819i	−0.149016	+	0.988835i	$0.547610\pi$
$684$	7.49742	−	26.6162i	0.286671	−	1.01770i
$685$		0			0
$686$	−37.2286			−1.42140
$687$	−26.7091	+	6.97419i	−1.01902	+	0.266082i
$688$	−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	−0.970039	−	0.242949i	$-0.921885\pi$
$691$	−19.1129	+	19.1129i	−0.727090	+	0.727090i	0.242949	+	0.970039i	$0.421885\pi$
$692$	−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
$696$	1.68301	+	6.44544i	0.0637943	+	0.244314i
$697$	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	$-0.348405\pi$
$701$	24.2762			0.916900			0.458450	+	0.888720i	$0.348405\pi$
$702$	−6.60414	+	35.2012i	−0.249257	+	1.32858i
$703$		−	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
$708$	17.7578	−	4.63685i	0.667379	−	0.174263i
$709$	−11.9543	−	11.9543i	−0.448954	−	0.448954i	0.446053	−	0.895007i	$-0.352829\pi$
$709$	−11.9543	−	11.9543i	−0.448954	−	0.448954i	−0.895007	+	0.446053i	$0.852829\pi$
$710$		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
$717$	−30.0300	+	7.84132i	−1.12149	+	0.292839i
$718$			38.3423i			1.43092i
$719$	−41.3666			−1.54271			−0.771357	−	0.636403i	$-0.780422\pi$
$719$	−41.3666			−1.54271			−0.771357	+	0.636403i	$0.780422\pi$
$720$		0			0
$721$	1.99388	−	1.99388i	0.0742559	−	0.0742559i
$722$	−16.2699	−	16.2699i	−0.605504	−	0.605504i
$723$	−14.8219	+	3.87024i	−0.551232	+	0.143936i
$724$	−34.4403			−1.27996
$725$		0			0
$726$	17.7831	−	4.64345i	0.659993	−	0.172335i
$727$	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	0.999824	+	0.0187592i	$0.00597159\pi$
$733$	27.5771	+	27.5771i	1.01858	+	1.01858i	0.0187592	+	0.999824i	$0.494028\pi$
$734$	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	0.545832	−	0.837895i	$-0.316214\pi$
$739$	−7.93961	−	7.93961i	−0.292063	−	0.292063i	−0.837895	+	0.545832i	$0.816214\pi$
$740$		0			0
$741$	26.6927	+	22.3138i	0.980581	+	0.819719i
$742$			11.6000i			0.425849i
$743$	23.9349	−	23.9349i	0.878087	−	0.878087i	−0.115249	−	0.993337i	$-0.536767\pi$
$743$	23.9349	−	23.9349i	0.878087	−	0.878087i	0.993337	+	0.115249i	$0.0367667\pi$
$744$	1.45378	−	2.48129i	0.0532982	−	0.0909686i
$745$		0			0
$746$	17.9654	+	17.9654i	0.657761	+	0.657761i
$747$	18.0599	+	5.08722i	0.660776	+	0.186132i
$748$	−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	$-0.714917\pi$
$751$		−	42.7833i		−	1.56119i	0.625039	−	0.780593i	$-0.285083\pi$
$752$	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
$756$	25.6586	+	26.6611i	0.933194	+	0.969653i
$757$		−	42.2733i		−	1.53645i	−0.640180	−	0.768225i	$-0.721140\pi$
$757$		−	42.2733i		−	1.53645i	0.640180	−	0.768225i	$-0.278860\pi$
$758$			9.64784i			0.350425i
$759$	13.5437	−	3.53647i	0.491605	−	0.128366i
$760$		0			0
$761$	−18.2564	+	18.2564i	−0.661795	+	0.661795i	−0.955803	−	0.294008i	$-0.905011\pi$
$761$	−18.2564	+	18.2564i	−0.661795	+	0.661795i	0.294008	+	0.955803i	$0.405011\pi$
$762$	−6.87028	−	26.3112i	−0.248884	−	0.953154i
$763$		−	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	−0.117131	+	0.993116i	$0.537370\pi$
$769$	−30.7881	+	30.7881i	−1.11025	+	1.11025i	−0.993116	+	0.117131i	$0.962630\pi$
$770$		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	$-0.724086\pi$
$773$	3.19753	−	3.19753i	0.115007	−	0.115007i	0.762268	+	0.647261i	$0.224086\pi$
$774$	47.4617	+	13.3693i	1.70598	+	0.480550i
$775$		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
$786$	23.6066	−	6.16407i	0.842021	−	0.219865i
$787$	−25.0983	+	25.0983i	−0.894657	+	0.894657i	−0.994957	−	0.100301i	$-0.968020\pi$
$787$	−25.0983	+	25.0983i	−0.894657	+	0.894657i	0.100301	+	0.994957i	$0.468020\pi$
$788$	−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	$-0.246870\pi$
$798$	76.8178	−	20.0584i	2.71932	−	0.710059i
$799$	−28.4090	+	28.4090i	−1.00504	+	1.00504i
$800$		0			0
$801$	8.25622	+	2.32566i	0.291719	+	0.0821733i
$802$			40.7411i			1.43862i
$803$			24.1041i			0.850616i
$804$	4.45775	+	17.0719i	0.157213	+	0.602079i
$805$		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	−0.795544	−	0.605896i	$-0.792815\pi$
$811$	−5.40079	+	5.40079i	−0.189647	+	0.189647i	0.605896	+	0.795544i	$0.292815\pi$
$812$	29.3232	−	29.3232i	1.02904	−	1.02904i
$813$	18.4641	−	4.82127i	0.647563	−	0.169089i
$814$	−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
$819$	−43.8194	+	15.7242i	−1.53117	+	0.549448i
$820$		0			0
$821$	26.9025	+	26.9025i	0.938905	+	0.938905i	0.998238	−	0.0593332i	$-0.0188974\pi$
$821$	26.9025	+	26.9025i	0.938905	+	0.938905i	−0.0593332	+	0.998238i	$0.518897\pi$
$822$	−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	$-0.409700\pi$
$827$	−19.5590	−	19.5590i	−0.680134	−	0.680134i	−0.960030	+	0.279896i	$0.909700\pi$
$828$	8.40125	+	14.9903i	0.291964	+	0.520950i
$829$			3.42144i			0.118832i	0.998233	+	0.0594158i	$0.0189238\pi$
$829$			3.42144i			0.118832i	−0.998233	+	0.0594158i	$0.981076\pi$
$830$		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
$834$	12.0335	+	46.0848i	0.416686	+	1.59579i
$835$		0			0
$836$	−21.5166			−0.744166
$837$	−9.41224	+	9.05833i	−0.325335	+	0.313102i
$838$	−21.3806	−	21.3806i	−0.738579	−	0.738579i
$839$	26.6448	−	26.6448i	0.919880	−	0.919880i	−0.0771405	−	0.997020i	$-0.524579\pi$
$839$	26.6448	−	26.6448i	0.919880	−	0.919880i	0.997020	+	0.0771405i	$0.0245790\pi$
$840$		0			0
$841$	−4.91224			−0.169388
$842$			12.6162i			0.434782i
$843$	2.30027	+	8.80937i	0.0792255	+	0.303411i
$844$			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
$852$	−6.96483	−	26.6733i	−0.238611	−	0.913812i
$853$	−1.95181	+	1.95181i	−0.0668287	+	0.0668287i	−0.739731	−	0.672902i	$-0.765047\pi$
$853$	−1.95181	+	1.95181i	−0.0668287	+	0.0668287i	0.672902	+	0.739731i	$0.265047\pi$
$854$		−	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	$0.853780\pi$
$858$	27.7580	−	2.48025i	0.947642	−	0.0846745i
$859$	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	$-0.927654\pi$
$863$	−22.0019	+	22.0019i	−0.748953	+	0.748953i	0.225330	+	0.974283i	$0.427654\pi$
$864$	−27.7747	+	26.7303i	−0.944914	+	0.909384i
$865$		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
$873$	−1.39605	+	4.95606i	−0.0472492	+	0.167737i
$874$	36.8706			1.24717
$875$		0			0
$876$	−28.6309	+	7.47599i	−0.967348	+	0.252590i
$877$	19.8856	+	19.8856i	0.671491	+	0.671491i	0.958060	−	0.286569i	$-0.0925148\pi$
$877$	19.8856	+	19.8856i	0.671491	+	0.671491i	−0.286569	+	0.958060i	$0.592515\pi$
$878$	−2.59388	−	2.59388i	−0.0875393	−	0.0875393i
$879$	5.84344	−	1.52582i	0.197094	−	0.0514645i
$880$		0			0
$881$	−36.1817			−1.21899			−0.609497	−	0.792788i	$-0.708629\pi$
$881$	−36.1817			−1.21899			−0.609497	+	0.792788i	$0.708629\pi$
$882$	−17.9205	+	63.6186i	−0.603414	+	2.14215i
$883$	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	$-0.296980\pi$
$887$	35.4670			1.19087			0.595433	+	0.803405i	$0.296980\pi$
$888$	−3.59036	+	6.12798i	−0.120485	+	0.205642i
$889$	24.9947	−	24.9947i	0.838294	−	0.838294i
$890$		0			0
$891$	−4.91748	−	20.4256i	−0.164742	−	0.684283i
$892$	−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
$897$	−21.5346	+	1.92418i	−0.719020	+	0.0642465i
$898$			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
$903$	16.1933	+	62.0156i	0.538878	+	2.06375i
$904$	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	$0.814371\pi$
$912$	11.1448	+	42.6815i	0.369042	+	1.41333i
$913$		−	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
$918$	−29.9101	−	31.0787i	−0.987181	−	1.02575i
$919$	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
$921$	−4.53787	−	17.3787i	−0.149528	−	0.572649i
$922$	−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	$-0.148320\pi$
$929$	13.5362	+	13.5362i	0.444110	+	0.444110i	−0.449281	+	0.893391i	$0.648320\pi$
$930$		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
$936$	−2.41285	−	6.72399i	−0.0788663	−	0.219780i
$937$			5.70697i			0.186439i	0.995646	+	0.0932194i	$0.0297158\pi$
$937$			5.70697i			0.186439i	−0.995646	+	0.0932194i	$0.970284\pi$
$938$	−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	$-0.219261\pi$
$941$	4.18292	+	4.18292i	0.136359	+	0.136359i	−0.635632	+	0.771992i	$0.719261\pi$
$942$	55.7731	−	14.5633i	1.81719	−	0.474497i
$943$	−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	$-0.0336035\pi$
$947$	27.3594	+	27.3594i	0.889060	+	0.889060i	−0.105372	+	0.994433i	$0.533603\pi$
$948$	−6.61893	−	3.87801i	−0.214973	−	0.125952i
$949$	6.16279	−	36.7167i	0.200053	−	1.19187i
$950$		0			0
$951$	3.96976	+	15.2031i	0.128728	+	0.492993i
$952$			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	$-0.393057\pi$
$954$	7.78257	+	2.19224i	0.251970	+	0.0709765i
$955$		0			0
$956$	−20.9640	+	20.9640i	−0.678025	+	0.678025i
$957$	−22.7816	+	5.94863i	−0.736423	+	0.192292i
$958$			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	0.352553	−	0.935792i	$-0.385313\pi$
$967$	−18.1367	−	18.1367i	−0.583238	−	0.583238i	−0.935792	+	0.352553i	$0.885313\pi$
$968$	−2.59224	+	2.59224i	−0.0833178	+	0.0833178i
$969$	−40.5405	+	10.5858i	−1.30235	+	0.340064i
$970$		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	$-0.902924\pi$
$977$	−20.4292	+	20.4292i	−0.653589	+	0.653589i	0.300266	+	0.953855i	$0.402924\pi$
$978$	8.30082	+	4.86342i	0.265431	+	0.155515i
$979$		−	6.67433i		−	0.213313i
$980$		0			0
$981$	−40.1820	−	11.3187i	−1.28291	−	0.361379i
$982$	−13.7692	+	13.7692i	−0.439393	+	0.439393i
$983$	−16.7861	−	16.7861i	−0.535394	−	0.535394i	0.386778	−	0.922173i	$-0.373588\pi$
$983$	−16.7861	−	16.7861i	−0.535394	−	0.535394i	−0.922173	+	0.386778i	$0.873588\pi$
$984$	−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
$993$	7.28027	+	27.8813i	0.231032	+	0.884788i
$994$	55.9682	−	55.9682i	1.77520	−	1.77520i
$995$		0			0
$996$	17.3414	−	4.52812i	0.549484	−	0.143479i
$997$			39.0215i			1.23582i	0.786248	+	0.617911i	$0.212021\pi$
$997$			39.0215i			1.23582i	−0.786248	+	0.617911i	$0.787979\pi$
$998$		−	39.2511i		−	1.24247i
$999$	23.2452	−	22.3711i	0.735444	−	0.707791i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.n.q.824.16		40
3.2	odd	2	inner	975.2.n.q.824.5		40
5.2	odd	4		195.2.o.a.161.16	yes	40
5.3	odd	4		975.2.o.p.551.5		40
5.4	even	2		975.2.n.r.824.5		40
13.8	odd	4		975.2.n.r.749.16		40
15.2	even	4		195.2.o.a.161.5	yes	40
15.8	even	4		975.2.o.p.551.16		40
15.14	odd	2		975.2.n.r.824.16		40
39.8	even	4		975.2.n.r.749.5		40
65.8	even	4		975.2.o.p.476.16		40
65.34	odd	4	inner	975.2.n.q.749.5		40
65.47	even	4		195.2.o.a.86.5	✓	40
195.8	odd	4		975.2.o.p.476.5		40
195.47	odd	4		195.2.o.a.86.16	yes	40
195.164	even	4	inner	975.2.n.q.749.16		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.o.a.86.5	✓	40	65.47	even	4
195.2.o.a.86.16	yes	40	195.47	odd	4
195.2.o.a.161.5	yes	40	15.2	even	4
195.2.o.a.161.16	yes	40	5.2	odd	4
975.2.n.q.749.5		40	65.34	odd	4	inner
975.2.n.q.749.16		40	195.164	even	4	inner
975.2.n.q.824.5		40	3.2	odd	2	inner
975.2.n.q.824.16		40	1.1	even	1	trivial
975.2.n.r.749.5		40	39.8	even	4
975.2.n.r.749.16		40	13.8	odd	4
975.2.n.r.824.5		40	5.4	even	2
975.2.n.r.824.16		40	15.14	odd	2
975.2.o.p.476.5		40	195.8	odd	4
975.2.o.p.476.16		40	65.8	even	4
975.2.o.p.551.5		40	5.3	odd	4
975.2.o.p.551.16		40	15.8	even	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)

\(f(q)\)	\(=\)	\(q+(1.35176 - 1.35176i) q^{2} +(0.875587 - 1.49444i) q^{3} -1.65452i q^{4} +(-0.836541 - 3.20371i) q^{6} +(3.04341 - 3.04341i) q^{7} +(0.467005 + 0.467005i) q^{8} +(-1.46670 - 2.61702i) q^{9} +O(q^{10})\)	\(q+(1.35176 - 1.35176i) q^{2} +(0.875587 - 1.49444i) q^{3} -1.65452i q^{4} +(-0.836541 - 3.20371i) 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} +(-5.52021 - 1.55497i) q^{18} +(-3.93929 + 3.93929i) q^{19} +(-1.88342 - 7.21296i) q^{21} +4.46254i q^{22} -3.46204i q^{23} +(1.10681 - 0.289007i) 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} +(1.02150 + 3.91206i) q^{33} +(5.86973 + 5.86973i) q^{34} +(-4.32992 + 2.42668i) q^{36} +(-4.39024 + 4.39024i) q^{37} +10.6500i q^{38} +(-0.555794 - 6.22022i) 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} +(-7.15723 + 6.88811i) q^{54} +2.84257 q^{56} +(2.43784 + 9.33623i) q^{57} +(7.87188 + 7.87188i) q^{58} +(-4.52860 + 4.52860i) q^{59} +4.47788 q^{61} -4.80594i q^{62} +(-12.4284 - 3.50091i) 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} +(0.537208 - 1.90712i) q^{72} +(7.30145 - 7.30145i) q^{73} +11.8691i q^{74} +(6.51765 + 6.51765i) q^{76} +10.0471i q^{77} +(-9.15955 - 7.65695i) q^{78} +2.67693 q^{79} +(-4.69761 + 7.67675i) q^{81} -15.9817 q^{82} +(-4.42241 + 4.42241i) q^{83} +(-11.9340 + 3.11616i) 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} +(-1.10011 - 4.21310i) q^{93} +17.6876 q^{94} +(-3.24632 - 12.4325i) q^{96} +(-1.21361 - 1.21361i) q^{97} +(-15.5786 - 15.5786i) q^{98} +(6.74074 + 1.89877i) 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

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