LMFDB - Embedded newform 325.2.o.b.74.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(74,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("325.74");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.592240896.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 7x^{6} + 40x^{4} - 63x^{2} + 81 $ x^8 - 7x^6 + 40x^4 - 63*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			74.4
Root			$1.99426 + 1.15139i$ of defining polynomial
Character	$\chi$	$=$	325.74
Dual form			325.2.o.b.224.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.99426 + 1.15139i) q^{2} +(0.866025 + 0.500000i) q^{3} +(1.65139 + 2.86029i) q^{4} +(1.15139 + 1.99426i) q^{6} +(-0.866025 + 0.500000i) q^{7} +3.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} +(-0.802776 + 1.39045i) q^{11} +3.30278i q^{12} +3.60555i q^{13} -2.30278 q^{14} +(-0.151388 + 0.262211i) q^{16} +(6.58660 - 3.80278i) q^{17} -4.60555i q^{18} +(-2.80278 - 4.85455i) q^{19} -1.00000 q^{21} +(-3.20189 + 1.84861i) q^{22} +(-2.59808 - 1.50000i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(-4.15139 + 7.19041i) q^{26} -5.00000i q^{27} +(-2.86029 - 1.65139i) q^{28} +(-3.10555 + 5.37897i) q^{29} -4.00000 q^{31} +(4.59234 - 2.65139i) q^{32} +(-1.39045 + 0.802776i) q^{33} +17.5139 q^{34} +(3.30278 - 5.72058i) q^{36} +(-3.12250 - 1.80278i) q^{37} -12.9083i q^{38} +(-1.80278 + 3.12250i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(-1.99426 - 1.15139i) q^{42} +(8.84307 - 5.10555i) q^{43} -5.30278 q^{44} +(-3.45416 - 5.98279i) q^{46} +9.21110i q^{47} +(-0.262211 + 0.151388i) q^{48} +(-3.00000 + 5.19615i) q^{49} +7.60555 q^{51} +(-10.3129 + 5.95416i) q^{52} +3.21110i q^{53} +(5.75694 - 9.97131i) q^{54} +(-1.50000 - 2.59808i) q^{56} -5.60555i q^{57} +(-12.3866 + 7.15139i) q^{58} +(-5.40833 - 9.36750i) q^{59} +(0.500000 + 0.866025i) q^{61} +(-7.97705 - 4.60555i) q^{62} +(1.73205 + 1.00000i) q^{63} +12.8167 q^{64} -3.69722 q^{66} +(6.06218 + 3.50000i) q^{67} +(21.7541 + 12.5597i) q^{68} +(-1.50000 - 2.59808i) q^{69} +(-2.40833 - 4.17134i) q^{71} +(5.19615 - 3.00000i) q^{72} +0.788897i q^{73} +(-4.15139 - 7.19041i) q^{74} +(9.25694 - 16.0335i) q^{76} -1.60555i q^{77} +(-7.19041 + 4.15139i) q^{78} -5.21110 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-5.98279 + 3.45416i) q^{82} +9.21110i q^{83} +(-1.65139 - 2.86029i) q^{84} +23.5139 q^{86} +(-5.37897 + 3.10555i) q^{87} +(-4.17134 - 2.40833i) q^{88} +(-3.10555 + 5.37897i) q^{89} +(-1.80278 - 3.12250i) q^{91} -9.90833i q^{92} +(-3.46410 - 2.00000i) q^{93} +(-10.6056 + 18.3694i) q^{94} +5.30278 q^{96} +(-7.26981 + 4.19722i) q^{97} +(-11.9656 + 6.90833i) q^{98} +3.21110 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{4} + 2 q^{6} - 8 q^{9} + 8 q^{11} - 4 q^{14} + 6 q^{16} - 8 q^{19} - 8 q^{21} - 12 q^{24} - 26 q^{26} + 4 q^{29} - 32 q^{31} + 68 q^{34} + 12 q^{36} - 12 q^{41} - 28 q^{44} - 6 q^{46} - 24 q^{49}+ \cdots - 32 q^{99}+O(q^{100}) $ 8 * q + 6 * q^4 + 2 * q^6 - 8 * q^9 + 8 * q^11 - 4 * q^14 + 6 * q^16 - 8 * q^19 - 8 * q^21 - 12 * q^24 - 26 * q^26 + 4 * q^29 - 32 * q^31 + 68 * q^34 + 12 * q^36 - 12 * q^41 - 28 * q^44 - 6 * q^46 - 24 * q^49 + 32 * q^51 + 10 * q^54 - 12 * q^56 + 4 * q^61 + 16 * q^64 - 44 * q^66 - 12 * q^69 + 24 * q^71 - 26 * q^74 + 38 * q^76 + 16 * q^79 - 4 * q^81 - 6 * q^84 + 116 * q^86 + 4 * q^89 - 56 * q^94 + 28 * q^96 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.99426	+	1.15139i	1.41016	+	0.814154i	0.995403	−	0.0957796i	$-0.0305344\pi$
$2$	1.99426	+	1.15139i	1.41016	+	0.814154i	0.414754	+	0.909934i	$0.363868\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i	0.728714	−	0.684819i	$-0.240119\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i	−0.228714	+	0.973494i	$0.573452\pi$
$4$	1.65139	+	2.86029i	0.825694	+	1.43014i
$5$		0			0
$5$		0			0
$6$	1.15139	+	1.99426i	0.470052	+	0.814154i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i	−0.654654	−	0.755929i	$-0.727186\pi$
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i	0.327327	+	0.944911i	$0.393852\pi$
$8$			3.00000i			1.06066i
$9$	−1.00000	−	1.73205i	−0.333333	−	0.577350i
$10$		0			0
$11$	−0.802776	+	1.39045i	−0.242046	+	0.419236i	−0.961297	−	0.275514i	$-0.911152\pi$
$11$	−0.802776	+	1.39045i	−0.242046	+	0.419236i	0.719251	+	0.694750i	$0.244485\pi$
$12$			3.30278i			0.953429i
$13$			3.60555i			1.00000i
$13$			3.60555i			1.00000i
$14$	−2.30278			−0.615443
$15$		0			0
$16$	−0.151388	+	0.262211i	−0.0378470	+	0.0655528i
$17$	6.58660	−	3.80278i	1.59749	−	0.922309i	0.605516	−	0.795834i	$-0.292967\pi$
$17$	6.58660	−	3.80278i	1.59749	−	0.922309i	0.991970	−	0.126475i	$-0.0403664\pi$
$18$		−	4.60555i		−	1.08554i
$19$	−2.80278	−	4.85455i	−0.643001	−	1.11371i	−0.984759	−	0.173922i	$-0.944356\pi$
$19$	−2.80278	−	4.85455i	−0.643001	−	1.11371i	0.341759	−	0.939788i	$-0.388977\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$	−3.20189	+	1.84861i	−0.682645	+	0.394125i
$23$	−2.59808	−	1.50000i	−0.541736	−	0.312772i	0.204046	−	0.978961i	$-0.434591\pi$
$23$	−2.59808	−	1.50000i	−0.541736	−	0.312772i	−0.745782	+	0.666190i	$0.767924\pi$
$24$	−1.50000	+	2.59808i	−0.306186	+	0.530330i
$25$		0			0
$26$	−4.15139	+	7.19041i	−0.814154	+	1.41016i
$27$		−	5.00000i		−	0.962250i
$28$	−2.86029	−	1.65139i	−0.540544	−	0.312083i
$29$	−3.10555	+	5.37897i	−0.576686	+	0.998850i	0.419170	+	0.907908i	$0.362321\pi$
$29$	−3.10555	+	5.37897i	−0.576686	+	0.998850i	−0.995856	+	0.0909423i	$0.971012\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	4.59234	−	2.65139i	0.811818	−	0.468704i
$33$	−1.39045	+	0.802776i	−0.242046	+	0.139745i
$34$	17.5139			3.00361
$35$		0			0
$36$	3.30278	−	5.72058i	0.550463	−	0.953429i
$37$	−3.12250	−	1.80278i	−0.513336	−	0.296374i	0.220868	−	0.975304i	$-0.429111\pi$
$37$	−3.12250	−	1.80278i	−0.513336	−	0.296374i	−0.734204	+	0.678929i	$0.762444\pi$
$38$		−	12.9083i		−	2.09401i
$39$	−1.80278	+	3.12250i	−0.288675	+	0.500000i
$40$		0			0
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$	−1.99426	−	1.15139i	−0.307721	−	0.177663i
$43$	8.84307	−	5.10555i	1.34856	−	0.778589i	0.360511	−	0.932755i	$-0.382602\pi$
$43$	8.84307	−	5.10555i	1.34856	−	0.778589i	0.988045	+	0.154166i	$0.0492689\pi$
$44$	−5.30278			−0.799424
$45$		0			0
$46$	−3.45416	−	5.98279i	−0.509289	−	0.882114i
$47$			9.21110i			1.34358i	0.740743	+	0.671789i	$0.234474\pi$
$47$			9.21110i			1.34358i	−0.740743	+	0.671789i	$0.765526\pi$
$48$	−0.262211	+	0.151388i	−0.0378470	+	0.0218509i
$49$	−3.00000	+	5.19615i	−0.428571	+	0.742307i
$50$		0			0
$51$	7.60555			1.06499
$52$	−10.3129	+	5.95416i	−1.43014	+	0.825694i
$53$			3.21110i			0.441079i	0.975378	+	0.220539i	$0.0707818\pi$
$53$			3.21110i			0.441079i	−0.975378	+	0.220539i	$0.929218\pi$
$54$	5.75694	−	9.97131i	0.783420	−	1.35692i
$55$		0			0
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$		−	5.60555i		−	0.742473i
$58$	−12.3866	+	7.15139i	−1.62644	+	0.939023i
$59$	−5.40833	−	9.36750i	−0.704104	−	1.21954i	−0.967014	−	0.254724i	$-0.918015\pi$
$59$	−5.40833	−	9.36750i	−0.704104	−	1.21954i	0.262910	−	0.964820i	$-0.415318\pi$
$60$		0			0
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	−7.97705	−	4.60555i	−1.01309	−	0.584906i
$63$	1.73205	+	1.00000i	0.218218	+	0.125988i
$64$	12.8167			1.60208
$65$		0			0
$66$	−3.69722			−0.455097
$67$	6.06218	+	3.50000i	0.740613	+	0.427593i	0.822292	−	0.569066i	$-0.192695\pi$
$67$	6.06218	+	3.50000i	0.740613	+	0.427593i	−0.0816792	+	0.996659i	$0.526028\pi$
$68$	21.7541	+	12.5597i	2.63807	+	1.52309i
$69$	−1.50000	−	2.59808i	−0.180579	−	0.312772i
$70$		0			0
$71$	−2.40833	−	4.17134i	−0.285816	−	0.495048i	0.686991	−	0.726666i	$-0.258931\pi$
$71$	−2.40833	−	4.17134i	−0.285816	−	0.495048i	−0.972807	+	0.231619i	$0.925598\pi$
$72$	5.19615	−	3.00000i	0.612372	−	0.353553i
$73$			0.788897i			0.0923335i	0.998934	+	0.0461667i	$0.0147006\pi$
$73$			0.788897i			0.0923335i	−0.998934	+	0.0461667i	$0.985299\pi$
$74$	−4.15139	−	7.19041i	−0.482589	−	0.835869i
$75$		0			0
$76$	9.25694	−	16.0335i	1.06184	−	1.83917i
$77$		−	1.60555i		−	0.182970i
$78$	−7.19041	+	4.15139i	−0.814154	+	0.470052i
$79$	−5.21110			−0.586295			−0.293147	−	0.956067i	$-0.594703\pi$
$79$	−5.21110			−0.586295			−0.293147	+	0.956067i	$0.594703\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−5.98279	+	3.45416i	−0.660688	+	0.381449i
$83$			9.21110i			1.01105i	0.862812	+	0.505525i	$0.168701\pi$
$83$			9.21110i			1.01105i	−0.862812	+	0.505525i	$0.831299\pi$
$84$	−1.65139	−	2.86029i	−0.180181	−	0.312083i
$85$		0			0
$86$	23.5139			2.53557
$87$	−5.37897	+	3.10555i	−0.576686	+	0.332950i
$88$	−4.17134	−	2.40833i	−0.444667	−	0.256729i
$89$	−3.10555	+	5.37897i	−0.329188	+	0.570170i	−0.982351	−	0.187047i	$-0.940108\pi$
$89$	−3.10555	+	5.37897i	−0.329188	+	0.570170i	0.653163	+	0.757217i	$0.273442\pi$
$90$		0			0
$91$	−1.80278	−	3.12250i	−0.188982	−	0.327327i
$92$		−	9.90833i		−	1.03301i
$93$	−3.46410	−	2.00000i	−0.359211	−	0.207390i
$94$	−10.6056	+	18.3694i	−1.09388	+	1.89465i
$95$		0			0
$96$	5.30278			0.541212
$97$	−7.26981	+	4.19722i	−0.738137	+	0.426164i	−0.821392	−	0.570365i	$-0.806802\pi$
$97$	−7.26981	+	4.19722i	−0.738137	+	0.426164i	0.0832546	+	0.996528i	$0.473469\pi$
$98$	−11.9656	+	6.90833i	−1.20871	+	0.697846i
$99$	3.21110			0.322728
$100$		0			0
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$	15.1675	+	8.75694i	1.50180	+	0.867066i
$103$			4.00000i			0.394132i	0.980390	+	0.197066i	$0.0631413\pi$
$103$			4.00000i			0.394132i	−0.980390	+	0.197066i	$0.936859\pi$
$104$	−10.8167			−1.06066
$105$		0			0
$106$	−3.69722	+	6.40378i	−0.359106	+	0.621990i
$107$	−5.37897	−	3.10555i	−0.520005	−	0.300225i	0.216932	−	0.976187i	$-0.430395\pi$
$107$	−5.37897	−	3.10555i	−0.520005	−	0.300225i	−0.736937	+	0.675962i	$0.763728\pi$
$108$	14.3014	−	8.25694i	1.37616	−	0.794524i
$109$	19.2111			1.84009			0.920045	−	0.391813i	$-0.128152\pi$
$109$	19.2111			1.84009			0.920045	+	0.391813i	$0.128152\pi$
$110$		0			0
$111$	−1.80278	−	3.12250i	−0.171112	−	0.296374i
$112$		−	0.302776i		−	0.0286096i
$113$	1.39045	−	0.802776i	0.130802	−	0.0755188i	−0.433171	−	0.901312i	$-0.642605\pi$
$113$	1.39045	−	0.802776i	0.130802	−	0.0755188i	0.563973	+	0.825793i	$0.309272\pi$
$114$	6.45416	−	11.1789i	0.604488	−	1.04700i
$115$		0			0
$116$	−20.5139			−1.90467
$117$	6.24500	−	3.60555i	0.577350	−	0.333333i
$118$		−	24.9083i		−	2.29300i
$119$	−3.80278	+	6.58660i	−0.348600	+	0.603793i
$120$		0			0
$121$	4.21110	+	7.29384i	0.382828	+	0.663077i
$122$			2.30278i			0.208484i
$123$	−2.59808	+	1.50000i	−0.234261	+	0.135250i
$124$	−6.60555	−	11.4412i	−0.593196	−	1.02745i
$125$		0			0
$126$	2.30278	+	3.98852i	0.205148	+	0.355326i
$127$	3.64692	+	2.10555i	0.323612	+	0.186837i	0.653001	−	0.757357i	$-0.273510\pi$
$127$	3.64692	+	2.10555i	0.323612	+	0.186837i	−0.329389	+	0.944194i	$0.606843\pi$
$128$	16.3751	+	9.45416i	1.44737	+	0.835638i
$129$	10.2111			0.899037
$130$		0			0
$131$	−21.2111			−1.85322			−0.926611	−	0.376021i	$-0.877292\pi$
$131$	−21.2111			−1.85322			−0.926611	+	0.376021i	$0.877292\pi$
$132$	−4.59234	−	2.65139i	−0.399712	−	0.230774i
$133$	4.85455	+	2.80278i	0.420943	+	0.243031i
$134$	8.05971	+	13.9598i	0.696253	+	1.20595i
$135$		0			0
$136$	11.4083	+	19.7598i	0.978256	+	1.69439i
$137$	−1.39045	+	0.802776i	−0.118794	+	0.0685858i	−0.558220	−	0.829693i	$-0.688515\pi$
$137$	−1.39045	+	0.802776i	−0.118794	+	0.0685858i	0.439426	+	0.898279i	$0.355182\pi$
$138$		−	6.90833i		−	0.588076i
$139$	3.19722	+	5.53776i	0.271185	+	0.469706i	0.969166	−	0.246410i	$-0.0792511\pi$
$139$	3.19722	+	5.53776i	0.271185	+	0.469706i	−0.697981	+	0.716117i	$0.745918\pi$
$140$		0			0
$141$	−4.60555	+	7.97705i	−0.387857	+	0.671789i
$142$		−	11.0917i		−	0.930793i
$143$	−5.01333	−	2.89445i	−0.419236	−	0.242046i
$144$	0.605551			0.0504626
$145$		0			0
$146$	−0.908327	+	1.57327i	−0.0751737	+	0.130205i
$147$	−5.19615	+	3.00000i	−0.428571	+	0.247436i
$148$		−	11.9083i		−	0.978858i
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	0.920904	−	0.389789i	$-0.127452\pi$
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	−0.798019	+	0.602632i	$0.794119\pi$
$150$		0			0
$151$	−1.21110			−0.0985581			−0.0492791	−	0.998785i	$-0.515692\pi$
$151$	−1.21110			−0.0985581			−0.0492791	+	0.998785i	$0.515692\pi$
$152$	14.5636	−	8.40833i	1.18127	−	0.682005i
$153$	−13.1732	−	7.60555i	−1.06499	−	0.614872i
$154$	1.84861	−	3.20189i	0.148965	−	0.258016i
$155$		0			0
$156$	−11.9083			−0.953429
$157$			11.2111i			0.894743i	0.894348	+	0.447372i	$0.147640\pi$
$157$			11.2111i			0.894743i	−0.894348	+	0.447372i	$0.852360\pi$
$158$	−10.3923	−	6.00000i	−0.826767	−	0.477334i
$159$	−1.60555	+	2.78090i	−0.127328	+	0.220539i
$160$		0			0
$161$	3.00000			0.236433
$162$	−1.99426	+	1.15139i	−0.156684	+	0.0904616i
$163$	3.28128	−	1.89445i	0.257010	−	0.148385i	−0.365960	−	0.930631i	$-0.619259\pi$
$163$	3.28128	−	1.89445i	0.257010	−	0.148385i	0.622970	+	0.782246i	$0.285926\pi$
$164$	−9.90833			−0.773710
$165$		0			0
$166$	−10.6056	+	18.3694i	−0.823150	+	1.42574i
$167$	−7.79423	−	4.50000i	−0.603136	−	0.348220i	0.167139	−	0.985933i	$-0.446547\pi$
$167$	−7.79423	−	4.50000i	−0.603136	−	0.348220i	−0.770274	+	0.637713i	$0.779881\pi$
$168$		−	3.00000i		−	0.231455i
$169$	−13.0000			−1.00000
$170$		0			0
$171$	−5.60555	+	9.70910i	−0.428667	+	0.742473i
$172$	29.2067	+	16.8625i	2.22699	+	1.28575i
$173$	−4.17134	+	2.40833i	−0.317141	+	0.183102i	−0.650118	−	0.759834i	$-0.725280\pi$
$173$	−4.17134	+	2.40833i	−0.317141	+	0.183102i	0.332976	+	0.942935i	$0.391947\pi$
$174$	−14.3028			−1.08429
$175$		0			0
$176$	−0.243061	−	0.420994i	−0.0183214	−	0.0317336i
$177$		−	10.8167i		−	0.813029i
$178$	−12.3866	+	7.15139i	−0.928412	+	0.536019i
$179$	11.4083	−	19.7598i	0.852698	−	1.47692i	−0.0260655	−	0.999660i	$-0.508298\pi$
$179$	11.4083	−	19.7598i	0.852698	−	1.47692i	0.878764	−	0.477257i	$-0.158369\pi$
$180$		0			0
$181$	17.6333			1.31067			0.655337	−	0.755337i	$-0.272527\pi$
$181$	17.6333			1.31067			0.655337	+	0.755337i	$0.272527\pi$
$182$		−	8.30278i		−	0.615443i
$183$			1.00000i			0.0739221i
$184$	4.50000	−	7.79423i	0.331744	−	0.574598i
$185$		0			0
$186$	−4.60555	−	7.97705i	−0.337695	−	0.584906i
$187$			12.2111i			0.892964i
$188$	−26.3464	+	15.2111i	−1.92151	+	1.10938i
$189$	2.50000	+	4.33013i	0.181848	+	0.314970i
$190$		0			0
$191$	−8.40833	−	14.5636i	−0.608405	−	1.05379i	−0.991503	−	0.130081i	$-0.958476\pi$
$191$	−8.40833	−	14.5636i	−0.608405	−	1.05379i	0.383098	−	0.923708i	$-0.374857\pi$
$192$	11.0995	+	6.40833i	0.801041	+	0.462481i
$193$	13.5148	+	7.80278i	0.972817	+	0.561656i	0.900094	−	0.435696i	$-0.143498\pi$
$193$	13.5148	+	7.80278i	0.972817	+	0.561656i	0.0727230	+	0.997352i	$0.476831\pi$
$194$	−19.3305			−1.38785
$195$		0			0
$196$	−19.8167			−1.41548
$197$	−1.02481	−	0.591673i	−0.0730145	−	0.0421550i	0.463048	−	0.886333i	$-0.346756\pi$
$197$	−1.02481	−	0.591673i	−0.0730145	−	0.0421550i	−0.536063	+	0.844178i	$0.680089\pi$
$198$	6.40378	+	3.69722i	0.455097	+	0.262750i
$199$	6.40833	+	11.0995i	0.454274	+	0.786826i	0.998646	−	0.0520179i	$-0.0165653\pi$
$199$	6.40833	+	11.0995i	0.454274	+	0.786826i	−0.544372	+	0.838844i	$0.683232\pi$
$200$		0			0
$201$	3.50000	+	6.06218i	0.246871	+	0.427593i
$202$	17.9484	−	10.3625i	1.26284	−	0.729102i
$203$		−	6.21110i		−	0.435934i
$204$	12.5597	+	21.7541i	0.879356	+	1.52309i
$205$		0			0
$206$	−4.60555	+	7.97705i	−0.320884	+	0.555787i
$207$			6.00000i			0.417029i
$208$	−0.945417	−	0.545837i	−0.0655528	−	0.0378470i
$209$	9.00000			0.622543
$210$		0			0
$211$	11.8028	−	20.4430i	0.812537	−	1.40735i	−0.0985467	−	0.995132i	$-0.531419\pi$
$211$	11.8028	−	20.4430i	0.812537	−	1.40735i	0.911083	−	0.412222i	$-0.135247\pi$
$212$	−9.18468	+	5.30278i	−0.630806	+	0.364196i
$213$		−	4.81665i		−	0.330032i
$214$	−7.15139	−	12.3866i	−0.488859	−	0.846728i
$215$		0			0
$216$	15.0000			1.02062
$217$	3.46410	−	2.00000i	0.235159	−	0.135769i
$218$	38.3120	+	22.1194i	2.59481	+	1.49812i
$219$	−0.394449	+	0.683205i	−0.0266544	+	0.0461667i
$220$		0			0
$221$	13.7111	+	23.7483i	0.922309	+	1.59749i
$222$		−	8.30278i		−	0.557246i
$223$	−3.64692	−	2.10555i	−0.244216	−	0.140998i	0.372897	−	0.927873i	$-0.378364\pi$
$223$	−3.64692	−	2.10555i	−0.244216	−	0.140998i	−0.617113	+	0.786875i	$0.711698\pi$
$224$	−2.65139	+	4.59234i	−0.177153	+	0.306839i
$225$		0			0
$226$	3.69722			0.245936
$227$	−23.7483	+	13.7111i	−1.57623	+	0.910038i	−0.580853	+	0.814008i	$0.697281\pi$
$227$	−23.7483	+	13.7111i	−1.57623	+	0.910038i	−0.995378	+	0.0960296i	$0.969386\pi$
$228$	16.0335	−	9.25694i	1.06184	−	0.613056i
$229$	−14.0000			−0.925146			−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000			−0.925146			−0.462573	+	0.886581i	$0.653074\pi$
$230$		0			0
$231$	0.802776	−	1.39045i	0.0528188	−	0.0914848i
$232$	−16.1369	−	9.31665i	−1.05944	−	0.611668i
$233$		−	15.2111i		−	0.996512i	−0.867030	−	0.498256i	$-0.833974\pi$
$233$		−	15.2111i		−	0.996512i	0.867030	−	0.498256i	$-0.166026\pi$
$234$	16.6056			1.08554
$235$		0			0
$236$	17.8625	−	30.9387i	1.16275	−	2.01394i
$237$	−4.51295	−	2.60555i	−0.293147	−	0.169249i
$238$	−15.1675	+	8.75694i	−0.983161	+	0.567628i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	−0.894449	−	1.54923i	−0.0576165	−	0.0997947i	0.835778	−	0.549067i	$-0.185017\pi$
$241$	−0.894449	−	1.54923i	−0.0576165	−	0.0997947i	−0.893395	+	0.449272i	$0.851683\pi$
$242$			19.3944i			1.24672i
$243$	−13.8564	+	8.00000i	−0.888889	+	0.513200i
$244$	−1.65139	+	2.86029i	−0.105719	+	0.183111i
$245$		0			0
$246$	−6.90833			−0.440459
$247$	17.5033	−	10.1056i	1.11371	−	0.643001i
$248$		−	12.0000i		−	0.762001i
$249$	−4.60555	+	7.97705i	−0.291865	+	0.505525i
$250$		0			0
$251$	3.59167	+	6.22096i	0.226704	+	0.392664i	0.956829	−	0.290650i	$-0.0938715\pi$
$251$	3.59167	+	6.22096i	0.226704	+	0.392664i	−0.730125	+	0.683314i	$0.760538\pi$
$252$			6.60555i			0.416111i
$253$	4.17134	−	2.40833i	0.262250	−	0.151410i
$254$	4.84861	+	8.39804i	0.304229	+	0.526940i
$255$		0			0
$256$	8.95416	+	15.5091i	0.559635	+	0.969317i
$257$	14.1980	+	8.19722i	0.885647	+	0.511329i	0.872516	−	0.488585i	$-0.162487\pi$
$257$	14.1980	+	8.19722i	0.885647	+	0.511329i	0.0131312	+	0.999914i	$0.495820\pi$
$258$	20.3636	+	11.7569i	1.26778	+	0.731955i
$259$	3.60555			0.224038
$260$		0			0
$261$	12.4222			0.768915
$262$	−42.3005	−	24.4222i	−2.61333	−	1.50881i
$263$	10.2095	+	5.89445i	0.629544	+	0.363467i	0.780575	−	0.625062i	$-0.214926\pi$
$263$	10.2095	+	5.89445i	0.629544	+	0.363467i	−0.151032	+	0.988529i	$0.548260\pi$
$264$	−2.40833	−	4.17134i	−0.148222	−	0.256729i
$265$		0			0
$266$	6.45416	+	11.1789i	0.395730	+	0.685425i
$267$	−5.37897	+	3.10555i	−0.329188	+	0.190057i
$268$			23.1194i			1.41224i
$269$	−4.50000	−	7.79423i	−0.274370	−	0.475223i	0.695606	−	0.718423i	$-0.255136\pi$
$269$	−4.50000	−	7.79423i	−0.274370	−	0.475223i	−0.969976	+	0.243201i	$0.921803\pi$
$270$		0			0
$271$	10.4083	−	18.0278i	0.632261	−	1.09511i	−0.354828	−	0.934932i	$-0.615460\pi$
$271$	10.4083	−	18.0278i	0.632261	−	1.09511i	0.987088	−	0.160176i	$-0.0512062\pi$
$272$			2.30278i			0.139626i
$273$		−	3.60555i		−	0.218218i
$274$	−3.69722			−0.223357
$275$		0			0
$276$	4.95416	−	8.58086i	0.298206	−	0.516507i
$277$	23.9071	−	13.8028i	1.43644	−	0.829328i	0.438839	−	0.898566i	$-0.355390\pi$
$277$	23.9071	−	13.8028i	1.43644	−	0.829328i	0.997600	+	0.0692374i	$0.0220566\pi$
$278$			14.7250i			0.883146i
$279$	4.00000	+	6.92820i	0.239474	+	0.414781i
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$	−18.3694	+	10.6056i	−1.09388	+	0.631551i
$283$	4.33013	+	2.50000i	0.257399	+	0.148610i	0.623148	−	0.782104i	$-0.285854\pi$
$283$	4.33013	+	2.50000i	0.257399	+	0.148610i	−0.365748	+	0.930714i	$0.619187\pi$
$284$	7.95416	−	13.7770i	0.471993	−	0.817515i
$285$		0			0
$286$	−6.66527	−	11.5446i	−0.394125	−	0.682645i
$287$		−	3.00000i		−	0.177084i
$288$	−9.18468	−	5.30278i	−0.541212	−	0.312469i
$289$	20.4222	−	35.3723i	1.20131	−	2.08072i
$290$		0			0
$291$	−8.39445			−0.492091
$292$	−2.25647	+	1.30278i	−0.132050	+	0.0762392i
$293$	−9.00186	+	5.19722i	−0.525894	+	0.303625i	−0.739343	−	0.673329i	$-0.764864\pi$
$293$	−9.00186	+	5.19722i	−0.525894	+	0.303625i	0.213449	+	0.976954i	$0.431530\pi$
$294$	−13.8167			−0.805804
$295$		0			0
$296$	5.40833	−	9.36750i	0.314353	−	0.544475i
$297$	6.95224	+	4.01388i	0.403410	+	0.232909i
$298$			6.90833i			0.400189i
$299$	5.40833	−	9.36750i	0.312772	−	0.541736i
$300$		0			0
$301$	−5.10555	+	8.84307i	−0.294279	+	0.509706i
$302$	−2.41526	−	1.39445i	−0.138982	−	0.0802415i
$303$	7.79423	−	4.50000i	0.447767	−	0.258518i
$304$	1.69722			0.0973425
$305$		0			0
$306$	−17.5139	−	30.3349i	−1.00120	−	1.73413i
$307$		−	16.0000i		−	0.913168i	−0.889680	−	0.456584i	$-0.849073\pi$
$307$		−	16.0000i		−	0.913168i	0.889680	−	0.456584i	$-0.150927\pi$
$308$	4.59234	−	2.65139i	0.261673	−	0.151077i
$309$	−2.00000	+	3.46410i	−0.113776	+	0.197066i
$310$		0			0
$311$	−9.21110			−0.522314			−0.261157	−	0.965296i	$-0.584104\pi$
$311$	−9.21110			−0.522314			−0.261157	+	0.965296i	$0.584104\pi$
$312$	−9.36750	−	5.40833i	−0.530330	−	0.306186i
$313$		−	14.0000i		−	0.791327i	−0.918396	−	0.395663i	$-0.870515\pi$
$313$		−	14.0000i		−	0.791327i	0.918396	−	0.395663i	$-0.129485\pi$
$314$	−12.9083	+	22.3579i	−0.728459	+	1.26173i
$315$		0			0
$316$	−8.60555	−	14.9053i	−0.484100	−	0.838486i
$317$			6.00000i			0.336994i	0.985702	+	0.168497i	$0.0538913\pi$
$317$			6.00000i			0.336994i	−0.985702	+	0.168497i	$0.946109\pi$
$318$	−6.40378	+	3.69722i	−0.359106	+	0.207330i
$319$	−4.98612	−	8.63622i	−0.279169	−	0.483535i
$320$		0			0
$321$	−3.10555	−	5.37897i	−0.173335	−	0.300225i
$322$	5.98279	+	3.45416i	0.333408	+	0.192493i
$323$	−36.9215	−	21.3167i	−2.05437	−	1.18609i
$324$	−3.30278			−0.183488
$325$		0			0
$326$	8.72498			0.483232
$327$	16.6373	+	9.60555i	0.920045	+	0.531188i
$328$	−7.79423	−	4.50000i	−0.430364	−	0.248471i
$329$	−4.60555	−	7.97705i	−0.253912	−	0.439789i
$330$		0			0
$331$	−5.01388	−	8.68429i	−0.275588	−	0.477332i	0.694696	−	0.719304i	$-0.255539\pi$
$331$	−5.01388	−	8.68429i	−0.275588	−	0.477332i	−0.970283	+	0.241972i	$0.922206\pi$
$332$	−26.3464	+	15.2111i	−1.44595	+	0.834818i
$333$			7.21110i			0.395166i
$334$	−10.3625	−	17.9484i	−0.567010	−	0.982091i
$335$		0			0
$336$	0.151388	−	0.262211i	0.00825888	−	0.0143048i
$337$		−	25.6333i		−	1.39634i	−0.715934	−	0.698168i	$-0.753999\pi$
$337$		−	25.6333i		−	1.39634i	0.715934	−	0.698168i	$-0.246001\pi$
$338$	−25.9254	−	14.9680i	−1.41016	−	0.814154i
$339$	1.60555			0.0872016
$340$		0			0
$341$	3.21110	−	5.56179i	0.173891	−	0.301188i
$342$	−22.3579	+	12.9083i	−1.20898	+	0.698002i
$343$		−	13.0000i		−	0.701934i
$344$	15.3167	+	26.5292i	0.825819	+	1.43036i
$345$		0			0
$346$	−11.0917			−0.596292
$347$	5.01333	−	2.89445i	0.269130	−	0.155382i	−0.359362	−	0.933198i	$-0.617006\pi$
$347$	5.01333	−	2.89445i	0.269130	−	0.155382i	0.628492	+	0.777816i	$0.283672\pi$
$348$	−17.7655	−	10.2569i	−0.952333	−	0.549830i
$349$	−1.89445	+	3.28128i	−0.101408	+	0.175643i	−0.912265	−	0.409601i	$-0.865668\pi$
$349$	−1.89445	+	3.28128i	−0.101408	+	0.175643i	0.810857	+	0.585244i	$0.199001\pi$
$350$		0			0
$351$	18.0278			0.962250
$352$			8.51388i			0.453791i
$353$	14.5636	+	8.40833i	0.775145	+	0.447530i	0.834707	−	0.550695i	$-0.185637\pi$
$353$	14.5636	+	8.40833i	0.775145	+	0.447530i	−0.0595620	+	0.998225i	$0.518970\pi$
$354$	12.4542	−	21.5712i	0.661931	−	1.14650i
$355$		0			0
$356$	−20.5139			−1.08723
$357$	−6.58660	+	3.80278i	−0.348600	+	0.201264i
$358$	45.5024	−	26.2708i	2.40488	−	1.38846i
$359$	−18.4222			−0.972287			−0.486143	−	0.873879i	$-0.661597\pi$
$359$	−18.4222			−0.972287			−0.486143	+	0.873879i	$0.661597\pi$
$360$		0			0
$361$	−6.21110	+	10.7579i	−0.326900	+	0.566208i
$362$	35.1654	+	20.3028i	1.84825	+	1.06709i
$363$			8.42221i			0.442051i
$364$	5.95416	−	10.3129i	0.312083	−	0.540544i
$365$		0			0
$366$	−1.15139	+	1.99426i	−0.0601840	+	0.104242i
$367$	−9.89192	−	5.71110i	−0.516354	−	0.298117i	0.219088	−	0.975705i	$-0.429692\pi$
$367$	−9.89192	−	5.71110i	−0.516354	−	0.298117i	−0.735442	+	0.677588i	$0.763025\pi$
$368$	0.786634	−	0.454163i	0.0410061	−	0.0236749i
$369$	6.00000			0.312348
$370$		0			0
$371$	−1.60555	−	2.78090i	−0.0833561	−	0.144377i
$372$		−	13.2111i		−	0.684964i
$373$	17.6621	−	10.1972i	0.914509	−	0.527992i	0.0326301	−	0.999467i	$-0.489612\pi$
$373$	17.6621	−	10.1972i	0.914509	−	0.527992i	0.881879	+	0.471475i	$0.156278\pi$
$374$	−14.0597	+	24.3521i	−0.727011	+	1.25922i
$375$		0			0
$376$	−27.6333			−1.42508
$377$	−19.3942	−	11.1972i	−0.998850	−	0.576686i
$378$			11.5139i			0.592210i
$379$	4.80278	−	8.31865i	0.246702	−	0.427300i	−0.715907	−	0.698196i	$-0.753986\pi$
$379$	4.80278	−	8.31865i	0.246702	−	0.427300i	0.962609	+	0.270895i	$0.0873198\pi$
$380$		0			0
$381$	2.10555	+	3.64692i	0.107871	+	0.186837i
$382$		−	38.7250i		−	1.98134i
$383$	21.3331	−	12.3167i	1.09007	−	0.629352i	0.156474	−	0.987682i	$-0.449987\pi$
$383$	21.3331	−	12.3167i	1.09007	−	0.629352i	0.933595	+	0.358330i	$0.116654\pi$
$384$	9.45416	+	16.3751i	0.482456	+	0.835638i
$385$		0			0
$386$	17.9680	+	31.1216i	0.914549	+	1.58405i
$387$	−17.6861	−	10.2111i	−0.899037	−	0.519060i
$388$	−24.0105	−	13.8625i	−1.21895	−	0.703761i
$389$	15.2111			0.771234			0.385617	−	0.922659i	$-0.373989\pi$
$389$	15.2111			0.771234			0.385617	+	0.922659i	$0.373989\pi$
$390$		0			0
$391$	−22.8167			−1.15389
$392$	−15.5885	−	9.00000i	−0.787336	−	0.454569i
$393$	−18.3694	−	10.6056i	−0.926611	−	0.534979i
$394$	−1.36249	−	2.35990i	−0.0686413	−	0.118890i
$395$		0			0
$396$	5.30278	+	9.18468i	0.266475	+	0.461547i
$397$	19.0766	−	11.0139i	0.957427	−	0.552771i	0.0620468	−	0.998073i	$-0.480237\pi$
$397$	19.0766	−	11.0139i	0.957427	−	0.552771i	0.895380	+	0.445303i	$0.146904\pi$
$398$			29.5139i			1.47940i
$399$	2.80278	+	4.85455i	0.140314	+	0.243031i
$400$		0			0
$401$	−6.10555	+	10.5751i	−0.304897	+	0.528097i	−0.977238	−	0.212144i	$-0.931955\pi$
$401$	−6.10555	+	10.5751i	−0.304897	+	0.528097i	0.672342	+	0.740241i	$0.265289\pi$
$402$			16.1194i			0.803964i
$403$		−	14.4222i		−	0.718421i
$404$	29.7250			1.47887
$405$		0			0
$406$	7.15139	−	12.3866i	0.354917	−	0.614735i
$407$	5.01333	−	2.89445i	0.248502	−	0.143472i
$408$			22.8167i			1.12959i
$409$	4.10555	+	7.11102i	0.203006	+	0.351617i	0.949496	−	0.313780i	$-0.101595\pi$
$409$	4.10555	+	7.11102i	0.203006	+	0.351617i	−0.746489	+	0.665397i	$0.768262\pi$
$410$		0			0
$411$	−1.60555			−0.0791960
$412$	−11.4412	+	6.60555i	−0.563665	+	0.325432i
$413$	9.36750	+	5.40833i	0.460944	+	0.266126i
$414$	−6.90833	+	11.9656i	−0.339526	+	0.588076i
$415$		0			0
$416$	9.55971	+	16.5579i	0.468704	+	0.811818i
$417$			6.39445i			0.313138i
$418$	17.9484	+	10.3625i	0.877883	+	0.506846i
$419$	8.61943	−	14.9293i	0.421087	−	0.729344i	−0.574959	−	0.818182i	$-0.694982\pi$
$419$	8.61943	−	14.9293i	0.421087	−	0.729344i	0.996046	+	0.0888384i	$0.0283155\pi$
$420$		0			0
$421$	32.4222			1.58016			0.790081	−	0.613003i	$-0.210039\pi$
$421$	32.4222			1.58016			0.790081	+	0.613003i	$0.210039\pi$
$422$	47.0757	−	27.1791i	2.29161	−	1.32306i
$423$	15.9541	−	9.21110i	0.775715	−	0.447859i
$424$	−9.63331			−0.467835
$425$		0			0
$426$	5.54584	−	9.60567i	0.268697	−	0.465396i
$427$	−0.866025	−	0.500000i	−0.0419099	−	0.0241967i
$428$		−	20.5139i		−	0.991576i
$429$	−2.89445	−	5.01333i	−0.139745	−	0.242046i
$430$		0			0
$431$	−14.6194	+	25.3216i	−0.704193	+	1.21970i	0.262789	+	0.964853i	$0.415358\pi$
$431$	−14.6194	+	25.3216i	−0.704193	+	1.21970i	−0.966982	+	0.254845i	$0.917976\pi$
$432$	1.31106	+	0.756939i	0.0630783	+	0.0364182i
$433$	−3.12250	+	1.80278i	−0.150058	+	0.0866359i	−0.573149	−	0.819451i	$-0.694278\pi$
$433$	−3.12250	+	1.80278i	−0.150058	+	0.0866359i	0.423091	+	0.906087i	$0.360945\pi$
$434$	9.21110			0.442147
$435$		0			0
$436$	31.7250	+	54.9493i	1.51935	+	2.63159i
$437$			16.8167i			0.804450i
$438$	−1.57327	+	0.908327i	−0.0751737	+	0.0434015i
$439$	−13.6194	+	23.5895i	−0.650020	+	1.12587i	0.333098	+	0.942892i	$0.391906\pi$
$439$	−13.6194	+	23.5895i	−0.650020	+	1.12587i	−0.983118	+	0.182975i	$0.941427\pi$
$440$		0			0
$441$	12.0000			0.571429
$442$			63.1472i			3.00361i
$443$		−	6.42221i		−	0.305128i	−0.988294	−	0.152564i	$-0.951247\pi$
$443$		−	6.42221i		−	0.305128i	0.988294	−	0.152564i	$-0.0487530\pi$
$444$	5.95416	−	10.3129i	0.282572	−	0.489429i
$445$		0			0
$446$	−4.84861	−	8.39804i	−0.229588	−	0.397659i
$447$			3.00000i			0.141895i
$448$	−11.0995	+	6.40833i	−0.524404	+	0.302765i
$449$	15.3167	+	26.5292i	0.722838	+	1.25199i	0.959858	+	0.280487i	$0.0904959\pi$
$449$	15.3167	+	26.5292i	0.722838	+	1.25199i	−0.237020	+	0.971505i	$0.576171\pi$
$450$		0			0
$451$	−2.40833	−	4.17134i	−0.113404	−	0.196421i
$452$	4.59234	+	2.65139i	0.216005	+	0.124711i
$453$	−1.04885	−	0.605551i	−0.0492791	−	0.0284513i
$454$	−63.1472			−2.96364
$455$		0			0
$456$	16.8167			0.787512
$457$	23.2239	+	13.4083i	1.08637	+	0.627215i	0.932607	−	0.360893i	$-0.117528\pi$
$457$	23.2239	+	13.4083i	1.08637	+	0.627215i	0.153761	+	0.988108i	$0.450861\pi$
$458$	−27.9197	−	16.1194i	−1.30460	−	0.753211i
$459$	−19.0139	−	32.9330i	−0.887492	−	1.53718i
$460$		0			0
$461$	−18.1056	−	31.3597i	−0.843260	−	1.46057i	−0.887124	−	0.461531i	$-0.847300\pi$
$461$	−18.1056	−	31.3597i	−0.843260	−	1.46057i	0.0438645	−	0.999037i	$-0.486033\pi$
$462$	3.20189	−	1.84861i	0.148965	−	0.0860052i
$463$			34.4222i			1.59974i	0.600176	+	0.799868i	$0.295097\pi$
$463$			34.4222i			1.59974i	−0.600176	+	0.799868i	$0.704903\pi$
$464$	−0.940285	−	1.62862i	−0.0436516	−	0.0756069i
$465$		0			0
$466$	17.5139	−	30.3349i	0.811315	−	1.40524i
$467$			2.78890i			0.129055i	0.997916	+	0.0645274i	$0.0205540\pi$
$467$			2.78890i			0.129055i	−0.997916	+	0.0645274i	$0.979446\pi$
$468$	20.6258	+	11.9083i	0.953429	+	0.550463i
$469$	−7.00000			−0.323230
$470$		0			0
$471$	−5.60555	+	9.70910i	−0.258290	+	0.447372i
$472$	28.1025	−	16.2250i	1.29352	−	0.746815i
$473$			16.3944i			0.753818i
$474$	−6.00000	−	10.3923i	−0.275589	−	0.477334i
$475$		0			0
$476$	−25.1194			−1.15135
$477$	5.56179	−	3.21110i	0.254657	−	0.147026i
$478$		0			0
$479$	−14.4083	+	24.9560i	−0.658333	+	1.14027i	0.322714	+	0.946497i	$0.395405\pi$
$479$	−14.4083	+	24.9560i	−0.658333	+	1.14027i	−0.981047	+	0.193770i	$0.937928\pi$
$480$		0			0
$481$	6.50000	−	11.2583i	0.296374	−	0.513336i
$482$		−	4.11943i		−	0.187635i
$483$	2.59808	+	1.50000i	0.118217	+	0.0682524i
$484$	−13.9083	+	24.0899i	−0.632197	+	1.09500i
$485$		0			0
$486$	−36.8444			−1.67130
$487$	−0.866025	+	0.500000i	−0.0392434	+	0.0226572i	−0.519493	−	0.854475i	$-0.673879\pi$
$487$	−0.866025	+	0.500000i	−0.0392434	+	0.0226572i	0.480250	+	0.877132i	$0.340546\pi$
$488$	−2.59808	+	1.50000i	−0.117609	+	0.0679018i
$489$	3.78890			0.171340
$490$		0			0
$491$	8.40833	−	14.5636i	0.379462	−	0.657248i	−0.611522	−	0.791228i	$-0.709442\pi$
$491$	8.40833	−	14.5636i	0.379462	−	0.657248i	0.990984	+	0.133979i	$0.0427756\pi$
$492$	−8.58086	−	4.95416i	−0.386855	−	0.223351i
$493$			47.2389i			2.12753i
$494$	46.5416			2.09401
$495$		0			0
$496$	0.605551	−	1.04885i	0.0271901	−	0.0470946i
$497$	4.17134	+	2.40833i	0.187110	+	0.108028i
$498$	−18.3694	+	10.6056i	−0.823150	+	0.475246i
$499$	−2.42221			−0.108433			−0.0542164	−	0.998529i	$-0.517266\pi$
$499$	−2.42221			−0.108433			−0.0542164	+	0.998529i	$0.517266\pi$
$500$		0			0
$501$	−4.50000	−	7.79423i	−0.201045	−	0.348220i
$502$			16.5416i			0.738289i
$503$	−2.59808	+	1.50000i	−0.115842	+	0.0668817i	−0.556802	−	0.830645i	$-0.687972\pi$
$503$	−2.59808	+	1.50000i	−0.115842	+	0.0668817i	0.440959	+	0.897527i	$0.354638\pi$
$504$	−3.00000	+	5.19615i	−0.133631	+	0.231455i
$505$		0			0
$506$	11.0917			0.493085
$507$	−11.2583	−	6.50000i	−0.500000	−	0.288675i
$508$			13.9083i			0.617082i
$509$	1.50000	−	2.59808i	0.0664863	−	0.115158i	−0.830866	−	0.556473i	$-0.812154\pi$
$509$	1.50000	−	2.59808i	0.0664863	−	0.115158i	0.897352	+	0.441315i	$0.145488\pi$
$510$		0			0
$511$	−0.394449	−	0.683205i	−0.0174494	−	0.0302232i
$512$			3.42221i			0.151242i
$513$	−24.2727	+	14.0139i	−1.07167	+	0.618728i
$514$	18.8764	+	32.6948i	0.832601	+	1.44211i
$515$		0			0
$516$	16.8625	+	29.2067i	0.742330	+	1.28575i
$517$	−12.8076	−	7.39445i	−0.563276	−	0.325207i
$518$	7.19041	+	4.15139i	0.315929	+	0.182402i
$519$	−4.81665			−0.211428
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$	24.7731	+	14.3028i	1.08429	+	0.626015i
$523$	−1.23167	−	0.711103i	−0.0538570	−	0.0310943i	0.472830	−	0.881154i	$-0.343233\pi$
$523$	−1.23167	−	0.711103i	−0.0538570	−	0.0310943i	−0.526687	+	0.850059i	$0.676566\pi$
$524$	−35.0278	−	60.6699i	−1.53019	−	2.65037i
$525$		0			0
$526$	13.5736	+	23.5102i	0.591837	+	1.02509i
$527$	−26.3464	+	15.2111i	−1.14767	+	0.662606i
$528$		−	0.486122i		−	0.0211557i
$529$	−7.00000	−	12.1244i	−0.304348	−	0.527146i
$530$		0			0
$531$	−10.8167	+	18.7350i	−0.469403	+	0.813029i
$532$			18.5139i			0.802678i
$533$	−9.36750	−	5.40833i	−0.405751	−	0.234261i
$534$	−14.3028			−0.618942
$535$		0			0
$536$	−10.5000	+	18.1865i	−0.453531	+	0.785539i
$537$	19.7598	−	11.4083i	0.852698	−	0.492306i
$538$		−	20.7250i		−	0.893517i
$539$	−4.81665	−	8.34269i	−0.207468	−	0.359345i
$540$		0			0
$541$	−25.6333			−1.10206			−0.551031	−	0.834485i	$-0.685765\pi$
$541$	−25.6333			−1.10206			−0.551031	+	0.834485i	$0.685765\pi$
$542$	41.5139	−	23.9680i	1.78317	−	1.02952i
$543$	15.2709	+	8.81665i	0.655337	+	0.378359i
$544$	20.1653	−	34.9273i	0.864579	−	1.49749i
$545$		0			0
$546$	4.15139	−	7.19041i	0.177663	−	0.307721i
$547$			32.8444i			1.40433i	0.712016	+	0.702163i	$0.247782\pi$
$547$			32.8444i			1.40433i	−0.712016	+	0.702163i	$0.752218\pi$
$548$	−4.59234	−	2.65139i	−0.196175	−	0.113262i
$549$	1.00000	−	1.73205i	0.0426790	−	0.0739221i
$550$		0			0
$551$	34.8167			1.48324
$552$	7.79423	−	4.50000i	0.331744	−	0.191533i
$553$	4.51295	−	2.60555i	0.191910	−	0.110799i
$554$	63.5694			2.70080
$555$		0			0
$556$	−10.5597	+	18.2900i	−0.447832	+	0.775667i
$557$	1.39045	+	0.802776i	0.0589152	+	0.0340147i	0.529168	−	0.848517i	$-0.322504\pi$
$557$	1.39045	+	0.802776i	0.0589152	+	0.0340147i	−0.470253	+	0.882532i	$0.655837\pi$
$558$			18.4222i			0.779874i
$559$	18.4083	+	31.8842i	0.778589	+	1.34856i
$560$		0			0
$561$	−6.10555	+	10.5751i	−0.257777	+	0.446482i
$562$	−11.9656	−	6.90833i	−0.504737	−	0.291410i
$563$	−8.15987	+	4.71110i	−0.343897	+	0.198549i	−0.661994	−	0.749509i	$-0.730290\pi$
$563$	−8.15987	+	4.71110i	−0.343897	+	0.198549i	0.318097	+	0.948058i	$0.396956\pi$
$564$	−30.4222			−1.28101
$565$		0			0
$566$	5.75694	+	9.97131i	0.241982	+	0.419125i
$567$		−	1.00000i		−	0.0419961i
$568$	12.5140	−	7.22498i	0.525077	−	0.303153i
$569$	−13.7111	+	23.7483i	−0.574799	+	0.995582i	0.421264	+	0.906938i	$0.361587\pi$
$569$	−13.7111	+	23.7483i	−0.574799	+	0.995582i	−0.996063	+	0.0886436i	$0.971747\pi$
$570$		0			0
$571$	20.8444			0.872311			0.436156	−	0.899871i	$-0.356340\pi$
$571$	20.8444			0.872311			0.436156	+	0.899871i	$0.356340\pi$
$572$		−	19.1194i		−	0.799424i
$573$		−	16.8167i		−	0.702526i
$574$	3.45416	−	5.98279i	0.144174	−	0.249717i
$575$		0			0
$576$	−12.8167	−	22.1991i	−0.534027	−	0.924962i
$577$		−	13.6333i		−	0.567562i	−0.958889	−	0.283781i	$-0.908411\pi$
$577$		−	13.6333i		−	0.567562i	0.958889	−	0.283781i	$-0.0915889\pi$
$578$	81.4545	−	47.0278i	3.38806	−	1.95610i
$579$	7.80278	+	13.5148i	0.324272	+	0.561656i
$580$		0			0
$581$	−4.60555	−	7.97705i	−0.191070	−	0.330944i
$582$	−16.7407	−	9.66527i	−0.693926	−	0.400638i
$583$	−4.46487	−	2.57779i	−0.184916	−	0.106761i
$584$	−2.36669			−0.0979344
$585$		0			0
$586$	−23.9361			−0.988790
$587$	28.9445	+	16.7111i	1.19467	+	0.689741i	0.959361	−	0.282181i	$-0.0910577\pi$
$587$	28.9445	+	16.7111i	1.19467	+	0.689741i	0.235305	+	0.971922i	$0.424391\pi$
$588$	−17.1617	−	9.90833i	−0.707738	−	0.408613i
$589$	11.2111	+	19.4182i	0.461945	+	0.800113i
$590$		0			0
$591$	−0.591673	−	1.02481i	−0.0243382	−	0.0421550i
$592$	0.945417	−	0.545837i	0.0388564	−	0.0224337i
$593$		−	20.7889i		−	0.853698i	−0.904323	−	0.426849i	$-0.859624\pi$
$593$		−	20.7889i		−	0.853698i	0.904323	−	0.426849i	$-0.140376\pi$
$594$	9.24306	+	16.0095i	0.379247	+	0.656876i
$595$		0			0
$596$	−4.95416	+	8.58086i	−0.202930	+	0.351486i
$597$			12.8167i			0.524551i
$598$	21.5712	−	12.4542i	0.882114	−	0.509289i
$599$	21.2111			0.866662			0.433331	−	0.901235i	$-0.357338\pi$
$599$	21.2111			0.866662			0.433331	+	0.901235i	$0.357338\pi$
$600$		0			0
$601$	−6.89445	+	11.9415i	−0.281230	+	0.487105i	−0.971688	−	0.236267i	$-0.924076\pi$
$601$	−6.89445	+	11.9415i	−0.281230	+	0.487105i	0.690458	+	0.723373i	$0.257409\pi$
$602$	−20.3636	+	11.7569i	−0.829959	+	0.479177i
$603$		−	14.0000i		−	0.570124i
$604$	−2.00000	−	3.46410i	−0.0813788	−	0.140952i
$605$		0			0
$606$	20.7250			0.841895
$607$	−29.6277	+	17.1056i	−1.20255	+	0.694293i	−0.961122	−	0.276126i	$-0.910949\pi$
$607$	−29.6277	+	17.1056i	−1.20255	+	0.694293i	−0.241429	+	0.970418i	$0.577616\pi$
$608$	−25.7426	−	14.8625i	−1.04400	−	0.602754i
$609$	3.10555	−	5.37897i	0.125843	−	0.217967i
$610$		0			0
$611$	−33.2111			−1.34358
$612$		−	50.2389i		−	2.03079i
$613$	−4.85455	−	2.80278i	−0.196073	−	0.113203i	0.398749	−	0.917060i	$-0.369444\pi$
$613$	−4.85455	−	2.80278i	−0.196073	−	0.113203i	−0.594823	+	0.803857i	$0.702778\pi$
$614$	18.4222	−	31.9082i	0.743460	−	1.28771i
$615$		0			0
$616$	4.81665			0.194069
$617$	−33.2986	+	19.2250i	−1.34055	+	0.773969i	−0.986888	−	0.161404i	$-0.948398\pi$
$617$	−33.2986	+	19.2250i	−1.34055	+	0.773969i	−0.353664	+	0.935372i	$0.615065\pi$
$618$	−7.97705	+	4.60555i	−0.320884	+	0.185262i
$619$	−14.4222			−0.579677			−0.289839	−	0.957076i	$-0.593602\pi$
$619$	−14.4222			−0.579677			−0.289839	+	0.957076i	$0.593602\pi$
$620$		0			0
$621$	−7.50000	+	12.9904i	−0.300965	+	0.521286i
$622$	−18.3694	−	10.6056i	−0.736544	−	0.425244i
$623$		−	6.21110i		−	0.248843i
$624$	−0.545837	−	0.945417i	−0.0218509	−	0.0378470i
$625$		0			0
$626$	16.1194	−	27.9197i	0.644262	−	1.11589i
$627$	7.79423	+	4.50000i	0.311272	+	0.179713i
$628$	−32.0670	+	18.5139i	−1.27961	+	0.738784i
$629$	−27.4222			−1.09339
$630$		0			0
$631$	18.0139	+	31.2010i	0.717121	+	1.24209i	0.962136	+	0.272571i	$0.0878739\pi$
$631$	18.0139	+	31.2010i	0.717121	+	1.24209i	−0.245015	+	0.969519i	$0.578793\pi$
$632$		−	15.6333i		−	0.621860i
$633$	20.4430	−	11.8028i	0.812537	−	0.469118i
$634$	−6.90833	+	11.9656i	−0.274365	+	0.475214i
$635$		0			0
$636$	−10.6056			−0.420537
$637$	−18.7350	−	10.8167i	−0.742307	−	0.428571i
$638$		−	22.9638i		−	0.909147i
$639$	−4.81665	+	8.34269i	−0.190544	+	0.330032i
$640$		0			0
$641$	−4.71110	−	8.15987i	−0.186077	−	0.322295i	0.757862	−	0.652415i	$-0.226244\pi$
$641$	−4.71110	−	8.15987i	−0.186077	−	0.322295i	−0.943939	+	0.330120i	$0.892911\pi$
$642$		−	14.3028i		−	0.564486i
$643$	−2.28051	+	1.31665i	−0.0899346	+	0.0519238i	−0.544293	−	0.838895i	$-0.683202\pi$
$643$	−2.28051	+	1.31665i	−0.0899346	+	0.0519238i	0.454358	+	0.890819i	$0.349869\pi$
$644$	4.95416	+	8.58086i	0.195221	+	0.338133i
$645$		0			0
$646$	−49.0875	−	85.0220i	−1.93132	−	3.34515i
$647$	−34.1406	−	19.7111i	−1.34221	−	0.774923i	−0.355076	−	0.934838i	$-0.615545\pi$
$647$	−34.1406	−	19.7111i	−1.34221	−	0.774923i	−0.987131	+	0.159914i	$0.948878\pi$
$648$	−2.59808	−	1.50000i	−0.102062	−	0.0589256i
$649$	17.3667			0.681702
$650$		0			0
$651$	4.00000			0.156772
$652$	10.8373	+	6.25694i	0.424423	+	0.245041i
$653$	−6.22096	−	3.59167i	−0.243445	−	0.140553i	0.373314	−	0.927705i	$-0.378221\pi$
$653$	−6.22096	−	3.59167i	−0.243445	−	0.140553i	−0.616759	+	0.787152i	$0.711555\pi$
$654$	22.1194	+	38.3120i	0.864938	+	1.49812i
$655$		0			0
$656$	−0.454163	−	0.786634i	−0.0177321	−	0.0307129i
$657$	1.36641	−	0.788897i	0.0533087	−	0.0307778i
$658$		−	21.2111i		−	0.826895i
$659$	−17.4083	−	30.1521i	−0.678132	−	1.17456i	−0.975543	−	0.219810i	$-0.929456\pi$
$659$	−17.4083	−	30.1521i	−0.678132	−	1.17456i	0.297411	−	0.954750i	$-0.403877\pi$
$660$		0			0
$661$	2.31665	−	4.01256i	0.0901074	−	0.156071i	−0.817449	−	0.576001i	$-0.804612\pi$
$661$	2.31665	−	4.01256i	0.0901074	−	0.156071i	0.907556	+	0.419931i	$0.137946\pi$
$662$		−	23.0917i		−	0.897483i
$663$			27.4222i			1.06499i
$664$	−27.6333			−1.07238
$665$		0			0
$666$	−8.30278	+	14.3808i	−0.321726	+	0.557246i
$667$	16.1369	−	9.31665i	0.624824	−	0.360742i
$668$		−	29.7250i		−	1.15009i
$669$	−2.10555	−	3.64692i	−0.0814053	−	0.140998i
$670$		0			0
$671$	−1.60555			−0.0619816
$672$	−4.59234	+	2.65139i	−0.177153	+	0.102280i
$673$	−15.2469	−	8.80278i	−0.587723	−	0.339322i	0.176474	−	0.984305i	$-0.443531\pi$
$673$	−15.2469	−	8.80278i	−0.587723	−	0.339322i	−0.764197	+	0.644983i	$0.776864\pi$
$674$	29.5139	−	51.1195i	1.13683	−	1.96905i
$675$		0			0
$676$	−21.4680	−	37.1837i	−0.825694	−	1.43014i
$677$		−	9.63331i		−	0.370238i	−0.982716	−	0.185119i	$-0.940733\pi$
$677$		−	9.63331i		−	0.370238i	0.982716	−	0.185119i	$-0.0592671\pi$
$678$	3.20189	+	1.84861i	0.122968	+	0.0709955i
$679$	4.19722	−	7.26981i	0.161075	−	0.278990i
$680$		0			0
$681$	−27.4222			−1.05082
$682$	12.8076	−	7.39445i	0.490427	−	0.283148i
$683$	−31.3597	+	18.1056i	−1.19995	+	0.692790i	−0.960543	−	0.278130i	$-0.910285\pi$
$683$	−31.3597	+	18.1056i	−1.19995	+	0.692790i	−0.239404	+	0.970920i	$0.576952\pi$
$684$	−37.0278			−1.41579
$685$		0			0
$686$	14.9680	−	25.9254i	0.571482	−	0.989837i
$687$	−12.1244	−	7.00000i	−0.462573	−	0.267067i
$688$			3.09167i			0.117869i
$689$	−11.5778			−0.441079
$690$		0			0
$691$	15.0139	−	26.0048i	0.571155	−	0.989269i	−0.425293	−	0.905056i	$-0.639829\pi$
$691$	15.0139	−	26.0048i	0.571155	−	0.989269i	0.996448	−	0.0842134i	$-0.0268378\pi$
$692$	−13.7770	−	7.95416i	−0.523724	−	0.302372i
$693$	−2.78090	+	1.60555i	−0.105638	+	0.0609898i
$694$	13.3305			0.506020
$695$		0			0
$696$	−9.31665	−	16.1369i	−0.353147	−	0.611668i
$697$			22.8167i			0.864242i
$698$	−7.55605	+	4.36249i	−0.286001	+	0.165123i
$699$	7.60555	−	13.1732i	0.287668	−	0.498256i
$700$		0			0
$701$	−36.4222			−1.37565			−0.687824	−	0.725878i	$-0.741434\pi$
$701$	−36.4222			−1.37565			−0.687824	+	0.725878i	$0.741434\pi$
$702$	35.9521	+	20.7569i	1.35692	+	0.783420i
$703$			20.2111i			0.762276i
$704$	−10.2889	+	17.8209i	−0.387777	+	0.671650i
$705$		0			0
$706$	19.3625	+	33.5368i	0.728717	+	1.26217i
$707$			9.00000i			0.338480i
$708$	30.9387	−	17.8625i	1.16275	−	0.671313i
$709$	−6.92221	−	11.9896i	−0.259969	−	0.450279i	0.706264	−	0.707948i	$-0.250379\pi$
$709$	−6.92221	−	11.9896i	−0.259969	−	0.450279i	−0.966233	+	0.257669i	$0.917046\pi$
$710$		0			0
$711$	5.21110	+	9.02589i	0.195432	+	0.338497i
$712$	−16.1369	−	9.31665i	−0.604757	−	0.349156i
$713$	10.3923	+	6.00000i	0.389195	+	0.224702i
$714$	−17.5139			−0.655440
$715$		0			0
$716$	75.3583			2.81627
$717$		0			0
$718$	−36.7387	−	21.2111i	−1.37108	−	0.791591i
$719$	−12.8028	−	22.1751i	−0.477463	−	0.826990i	0.522203	−	0.852821i	$-0.325110\pi$
$719$	−12.8028	−	22.1751i	−0.477463	−	0.826990i	−0.999666	+	0.0258309i	$0.991777\pi$
$720$		0			0
$721$	−2.00000	−	3.46410i	−0.0744839	−	0.129010i
$722$	−24.7731	+	14.3028i	−0.921961	+	0.532294i
$723$		−	1.78890i		−	0.0665298i
$724$	29.1194	+	50.4363i	1.08222	+	1.87445i
$725$		0			0
$726$	−9.69722	+	16.7961i	−0.359898	+	0.623361i
$727$			13.5778i			0.503573i	0.967783	+	0.251786i	$0.0810180\pi$
$727$			13.5778i			0.503573i	−0.967783	+	0.251786i	$0.918982\pi$
$728$	9.36750	−	5.40833i	0.347183	−	0.200446i
$729$	−13.0000			−0.481481
$730$		0			0
$731$	38.8305	−	67.2565i	1.43620	−	2.48757i
$732$	−2.86029	+	1.65139i	−0.105719	+	0.0610371i
$733$			46.8444i			1.73024i	0.501567	+	0.865119i	$0.332757\pi$
$733$			46.8444i			1.73024i	−0.501567	+	0.865119i	$0.667243\pi$
$734$	−13.1514	−	22.7789i	−0.485427	−	0.840784i
$735$		0			0
$736$	−15.9083			−0.586389
$737$	−9.73314	+	5.61943i	−0.358525	+	0.206994i
$738$	11.9656	+	6.90833i	0.440459	+	0.254299i
$739$	−17.8028	+	30.8353i	−0.654886	+	1.13430i	0.327037	+	0.945012i	$0.393950\pi$
$739$	−17.8028	+	30.8353i	−0.654886	+	1.13430i	−0.981922	+	0.189284i	$0.939383\pi$
$740$		0			0
$741$	20.2111			0.742473
$742$		−	7.39445i		−	0.271459i
$743$	31.7254	+	18.3167i	1.16389	+	0.671973i	0.952233	−	0.305371i	$-0.0987805\pi$
$743$	31.7254	+	18.3167i	1.16389	+	0.671973i	0.211658	+	0.977344i	$0.432114\pi$
$744$	6.00000	−	10.3923i	0.219971	−	0.381000i
$745$		0			0
$746$	46.9638			1.71947
$747$	15.9541	−	9.21110i	0.583730	−	0.337017i
$748$	−34.9273	+	20.1653i	−1.27707	+	0.737315i
$749$	6.21110			0.226949
$750$		0			0
$751$	−23.2250	+	40.2268i	−0.847492	+	1.46790i	0.0359481	+	0.999354i	$0.488555\pi$
$751$	−23.2250	+	40.2268i	−0.847492	+	1.46790i	−0.883440	+	0.468545i	$0.844778\pi$
$752$	−2.41526	−	1.39445i	−0.0880753	−	0.0508503i
$753$			7.18335i			0.261776i
$754$	−25.7847	−	44.6604i	−0.939023	−	1.62644i
$755$		0			0
$756$	−8.25694	+	14.3014i	−0.300302	+	0.520138i
$757$	−0.707243	−	0.408327i	−0.0257052	−	0.0148409i	0.487092	−	0.873350i	$-0.338058\pi$
$757$	−0.707243	−	0.408327i	−0.0257052	−	0.0148409i	−0.512798	+	0.858510i	$0.671391\pi$
$758$	19.1560	−	11.0597i	0.695777	−	0.401707i
$759$	4.81665			0.174833
$760$		0			0
$761$	−9.31665	−	16.1369i	−0.337728	−	0.584963i	0.646277	−	0.763103i	$-0.276325\pi$
$761$	−9.31665	−	16.1369i	−0.337728	−	0.584963i	−0.984005	+	0.178140i	$0.942992\pi$
$762$			9.69722i			0.351293i
$763$	−16.6373	+	9.60555i	−0.602311	+	0.347744i
$764$	27.7708	−	48.1005i	1.00471	−	1.74021i
$765$		0			0
$766$	56.7250			2.04956
$767$	33.7750	−	19.5000i	1.21954	−	0.704104i
$768$			17.9083i			0.646211i
$769$	5.50000	−	9.52628i	0.198335	−	0.343526i	−0.749654	−	0.661830i	$-0.769780\pi$
$769$	5.50000	−	9.52628i	0.198335	−	0.343526i	0.947989	+	0.318304i	$0.103113\pi$
$770$		0			0
$771$	8.19722	+	14.1980i	0.295216	+	0.511329i
$772$			51.5416i			1.85502i
$773$	−19.3942	+	11.1972i	−0.697560	+	0.402736i	−0.806438	−	0.591319i	$-0.798607\pi$
$773$	−19.3942	+	11.1972i	−0.697560	+	0.402736i	0.108878	+	0.994055i	$0.465274\pi$
$774$	−23.5139	−	40.7272i	−0.845189	−	1.46391i
$775$		0			0
$776$	−12.5917	−	21.8094i	−0.452015	−	0.782912i
$777$	3.12250	+	1.80278i	0.112019	+	0.0646742i
$778$	30.3349	+	17.5139i	1.08756	+	0.627903i
$779$	16.8167			0.602519
$780$		0			0
$781$	7.73338			0.276722
$782$	−45.5024	−	26.2708i	−1.62716	−	0.939443i
$783$	26.8949	+	15.5278i	0.961144	+	0.554917i
$784$	−0.908327	−	1.57327i	−0.0324402	−	0.0561882i
$785$		0			0
$786$	−24.4222	−	42.3005i	−0.871111	−	1.50881i
$787$	12.6728	−	7.31665i	0.451737	−	0.260811i	−0.256826	−	0.966458i	$-0.582677\pi$
$787$	12.6728	−	7.31665i	0.451737	−	0.260811i	0.708564	+	0.705647i	$0.249344\pi$
$788$		−	3.90833i		−	0.139228i
$789$	5.89445	+	10.2095i	0.209848	+	0.363467i
$790$		0			0
$791$	−0.802776	+	1.39045i	−0.0285434	+	0.0494386i
$792$			9.63331i			0.342305i
$793$	−3.12250	+	1.80278i	−0.110883	+	0.0640184i
$794$	50.7250			1.80016
$795$		0			0
$796$	−21.1653	+	36.6593i	−0.750183	+	1.29936i
$797$	−12.5140	+	7.22498i	−0.443270	+	0.255922i	−0.704984	−	0.709224i	$-0.749046\pi$
$797$	−12.5140	+	7.22498i	−0.443270	+	0.255922i	0.261714	+	0.965146i	$0.415712\pi$
$798$			12.9083i			0.456950i
$799$	35.0278	+	60.6699i	1.23919	+	2.14635i
$800$		0			0
$801$	12.4222			0.438917
$802$	−24.3521	+	14.0597i	−0.859904	+	0.496466i
$803$	−1.09692	−	0.633308i	−0.0387095	−	0.0223489i
$804$	−11.5597	+	20.0220i	−0.407680	+	0.706122i
$805$		0			0
$806$	16.6056	−	28.7617i	0.584906	−	1.01309i
$807$		−	9.00000i		−	0.316815i
$808$	23.3827	+	13.5000i	0.822600	+	0.474928i
$809$	−27.5278	+	47.6795i	−0.967824	+	1.67632i	−0.265997	+	0.963974i	$0.585701\pi$
$809$	−27.5278	+	47.6795i	−0.967824	+	1.67632i	−0.701827	+	0.712347i	$0.747632\pi$
$810$		0			0
$811$	−46.4222			−1.63010			−0.815052	−	0.579388i	$-0.803292\pi$
$811$	−46.4222			−1.63010			−0.815052	+	0.579388i	$0.803292\pi$
$812$	17.7655	−	10.2569i	0.623448	−	0.359948i
$813$	18.0278	−	10.4083i	0.632261	−	0.365036i
$814$	13.3305			0.467235
$815$		0			0
$816$	−1.15139	+	1.99426i	−0.0403066	+	0.0698131i
$817$	−49.5703	−	28.6194i	−1.73425	−	1.00127i
$818$			18.9083i			0.661114i
$819$	−3.60555	+	6.24500i	−0.125988	+	0.218218i
$820$		0			0
$821$	−10.7111	+	18.5522i	−0.373820	+	0.647475i	−0.990150	−	0.140013i	$-0.955286\pi$
$821$	−10.7111	+	18.5522i	−0.373820	+	0.647475i	0.616330	+	0.787488i	$0.288619\pi$
$822$	−3.20189	−	1.84861i	−0.111679	−	0.0644778i
$823$	14.4049	−	8.31665i	0.502122	−	0.289900i	−0.227467	−	0.973786i	$-0.573045\pi$
$823$	14.4049	−	8.31665i	0.502122	−	0.289900i	0.729589	+	0.683885i	$0.239711\pi$
$824$	−12.0000			−0.418040
$825$		0			0
$826$	12.4542	+	21.5712i	0.433336	+	0.750560i
$827$		−	42.4222i		−	1.47516i	−0.675257	−	0.737582i	$-0.735967\pi$
$827$		−	42.4222i		−	1.47516i	0.675257	−	0.737582i	$-0.264033\pi$
$828$	−17.1617	+	9.90833i	−0.596411	+	0.344338i
$829$	14.7111	−	25.4804i	0.510938	−	0.884970i	−0.488982	−	0.872294i	$-0.662632\pi$
$829$	14.7111	−	25.4804i	0.510938	−	0.884970i	0.999920	−	0.0126762i	$-0.00403506\pi$
$830$		0			0
$831$	27.6056			0.957626
$832$			46.2111i			1.60208i
$833$			45.6333i			1.58110i
$834$	−7.36249	+	12.7522i	−0.254942	+	0.441573i
$835$		0			0
$836$	14.8625	+	25.7426i	0.514030	+	0.890326i
$837$			20.0000i			0.691301i
$838$	34.3788	−	19.8486i	1.18760	−	0.685659i
$839$	−10.0139	−	17.3445i	−0.345717	−	0.598800i	0.639766	−	0.768569i	$-0.279031\pi$
$839$	−10.0139	−	17.3445i	−0.345717	−	0.598800i	−0.985484	+	0.169769i	$0.945698\pi$
$840$		0			0
$841$	−4.78890	−	8.29461i	−0.165134	−	0.286021i
$842$	64.6584	+	37.3305i	2.22827	+	1.28650i
$843$	−5.19615	−	3.00000i	−0.178965	−	0.103325i
$844$	77.9638			2.68363
$845$		0			0
$846$	42.4222			1.45851
$847$	−7.29384	−	4.21110i	−0.250619	−	0.144695i
$848$	−0.841988	−	0.486122i	−0.0289140	−	0.0166935i
$849$	2.50000	+	4.33013i	0.0857998	+	0.148610i
$850$		0			0
$851$	5.40833	+	9.36750i	0.185395	+	0.321114i
$852$	13.7770	−	7.95416i	0.471993	−	0.272505i
$853$		−	47.2111i		−	1.61648i	−0.588855	−	0.808239i	$-0.700421\pi$
$853$		−	47.2111i		−	1.61648i	0.588855	−	0.808239i	$-0.299579\pi$
$854$	−1.15139	−	1.99426i	−0.0393997	−	0.0682422i
$855$		0			0
$856$	9.31665	−	16.1369i	0.318437	−	0.551548i
$857$			6.00000i			0.204956i	0.994735	+	0.102478i	$0.0326771\pi$
$857$			6.00000i			0.204956i	−0.994735	+	0.102478i	$0.967323\pi$
$858$		−	13.3305i		−	0.455097i
$859$	−10.7889			−0.368112			−0.184056	−	0.982916i	$-0.558923\pi$
$859$	−10.7889			−0.368112			−0.184056	+	0.982916i	$0.558923\pi$
$860$		0			0
$861$	1.50000	−	2.59808i	0.0511199	−	0.0885422i
$862$	−58.3100	+	33.6653i	−1.98604	+	1.14664i
$863$		−	36.0000i		−	1.22545i	−0.790295	−	0.612727i	$-0.790072\pi$
$863$		−	36.0000i		−	1.22545i	0.790295	−	0.612727i	$-0.209928\pi$
$864$	−13.2569	−	22.9617i	−0.451010	−	0.781173i
$865$		0			0
$866$	−8.30278			−0.282140
$867$	35.3723	−	20.4222i	1.20131	−	0.693574i
$868$	11.4412	+	6.60555i	0.388338	+	0.224207i
$869$	4.18335	−	7.24577i	0.141910	−	0.245796i
$870$		0			0
$871$	−12.6194	+	21.8575i	−0.427593	+	0.740613i
$872$			57.6333i			1.95171i
$873$	14.5396	+	8.39445i	0.492091	+	0.284109i
$874$	−19.3625	+	33.5368i	−0.654946	+	1.13440i
$875$		0			0
$876$	−2.60555			−0.0880334
$877$	−1.70801	+	0.986122i	−0.0576755	+	0.0332990i	−0.528560	−	0.848896i	$-0.677268\pi$
$877$	−1.70801	+	0.986122i	−0.0576755	+	0.0332990i	0.470885	+	0.882195i	$0.343935\pi$
$878$	−54.3214	+	31.3625i	−1.83326	+	1.05843i
$879$	−10.3944			−0.350596
$880$		0			0
$881$	10.9222	−	18.9178i	0.367978	−	0.637357i	−0.621271	−	0.783596i	$-0.713383\pi$
$881$	10.9222	−	18.9178i	0.367978	−	0.637357i	0.989249	+	0.146238i	$0.0467167\pi$
$882$	23.9311	+	13.8167i	0.805804	+	0.465231i
$883$		−	11.6333i		−	0.391492i	−0.980655	−	0.195746i	$-0.937287\pi$
$883$		−	11.6333i		−	0.391492i	0.980655	−	0.195746i	$-0.0627128\pi$
$884$	−45.2847	+	78.4354i	−1.52309	+	2.63807i
$885$		0			0
$886$	7.39445	−	12.8076i	0.248421	−	0.430278i
$887$	32.0910	+	18.5278i	1.07751	+	0.622101i	0.930224	−	0.366993i	$-0.119613\pi$
$887$	32.0910	+	18.5278i	1.07751	+	0.622101i	0.147287	+	0.989094i	$0.452946\pi$
$888$	9.36750	−	5.40833i	0.314353	−	0.181492i
$889$	−4.21110			−0.141236
$890$		0			0
$891$	−0.802776	−	1.39045i	−0.0268940	−	0.0465818i
$892$		−	13.9083i		−	0.465685i
$893$	44.7158	−	25.8167i	1.49636	−	0.863921i
$894$	−3.45416	+	5.98279i	−0.115525	+	0.200094i
$895$		0			0
$896$	−18.9083			−0.631683
$897$	9.36750	−	5.40833i	0.312772	−	0.180579i
$898$			70.5416i			2.35400i
$899$	12.4222	−	21.5159i	0.414304	−	0.717595i
$900$		0			0
$901$	12.2111	+	21.1503i	0.406811	+	0.704617i
$902$		−	11.0917i		−	0.369312i
$903$	−8.84307	+	5.10555i	−0.294279	+	0.169902i
$904$	2.40833	+	4.17134i	0.0800998	+	0.138737i
$905$		0			0
$906$	−1.39445	−	2.41526i	−0.0463275	−	0.0802415i
$907$	33.1399	+	19.1333i	1.10039	+	0.635311i	0.936324	−	0.351138i	$-0.114205\pi$
$907$	33.1399	+	19.1333i	1.10039	+	0.635311i	0.164067	+	0.986449i	$0.447539\pi$
$908$	−78.4354	−	45.2847i	−2.60297	−	1.50283i
$909$	−18.0000			−0.597022
$910$		0			0
$911$	−36.0000			−1.19273			−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000			−1.19273			−0.596367	+	0.802712i	$0.703390\pi$
$912$	1.46984	+	0.848612i	0.0486712	+	0.0281004i
$913$	−12.8076	−	7.39445i	−0.423868	−	0.244721i
$914$	30.8764	+	53.4794i	1.02130	+	1.76894i
$915$		0			0
$916$	−23.1194	−	40.0440i	−0.763887	−	1.32309i
$917$	18.3694	−	10.6056i	0.606610	−	0.350226i
$918$		−	87.5694i		−	2.89022i
$919$	−19.4083	−	33.6162i	−0.640222	−	1.10890i	−0.985383	−	0.170353i	$-0.945509\pi$
$919$	−19.4083	−	33.6162i	−0.640222	−	1.10890i	0.345161	−	0.938543i	$-0.387824\pi$
$920$		0			0
$921$	8.00000	−	13.8564i	0.263609	−	0.456584i
$922$		−	83.3860i		−	2.74617i
$923$	15.0400	−	8.68335i	0.495048	−	0.285816i
$924$	5.30278			0.174449
$925$		0			0
$926$	−39.6333	+	68.6469i	−1.30243	+	2.25588i
$927$	6.92820	−	4.00000i	0.227552	−	0.131377i
$928$			32.9361i			1.08118i
$929$	−7.71110	−	13.3560i	−0.252993	−	0.438197i	0.711355	−	0.702832i	$-0.248082\pi$
$929$	−7.71110	−	13.3560i	−0.252993	−	0.438197i	−0.964348	+	0.264636i	$0.914748\pi$
$930$		0			0
$931$	33.6333			1.10229
$932$	43.5081	−	25.1194i	1.42516	−	0.822814i
$933$	−7.97705	−	4.60555i	−0.261157	−	0.150779i
$934$	−3.21110	+	5.56179i	−0.105070	+	0.181987i
$935$		0			0
$936$	10.8167	+	18.7350i	0.353553	+	0.612372i
$937$			54.4777i			1.77971i	0.456244	+	0.889855i	$0.349194\pi$
$937$			54.4777i			1.77971i	−0.456244	+	0.889855i	$0.650806\pi$
$938$	−13.9598	−	8.05971i	−0.455805	−	0.263159i
$939$	7.00000	−	12.1244i	0.228436	−	0.395663i
$940$		0			0
$941$	−9.63331			−0.314037			−0.157018	−	0.987596i	$-0.550188\pi$
$941$	−9.63331			−0.314037			−0.157018	+	0.987596i	$0.550188\pi$
$942$	−22.3579	+	12.9083i	−0.728459	+	0.420576i
$943$	7.79423	−	4.50000i	0.253815	−	0.146540i
$944$	3.27502			0.106593
$945$		0			0
$946$	−18.8764	+	32.6948i	−0.613724	+	1.06300i
$947$	16.1369	+	9.31665i	0.524379	+	0.302751i	0.738725	−	0.674007i	$-0.235428\pi$
$947$	16.1369	+	9.31665i	0.524379	+	0.302751i	−0.214345	+	0.976758i	$0.568762\pi$
$948$		−	17.2111i		−	0.558991i
$949$	−2.84441			−0.0923335
$950$		0			0
$951$	−3.00000	+	5.19615i	−0.0972817	+	0.168497i
$952$	−19.7598	−	11.4083i	−0.640419	−	0.369746i
$953$	12.5140	−	7.22498i	0.405369	−	0.234040i	−0.283429	−	0.958993i	$-0.591472\pi$
$953$	12.5140	−	7.22498i	0.405369	−	0.234040i	0.688798	+	0.724953i	$0.258139\pi$
$954$	14.7889			0.478808
$955$		0			0
$956$		0			0
$957$		−	9.97224i		−	0.322357i
$958$	−57.4680	+	33.1791i	−1.85671	+	1.07197i
$959$	0.802776	−	1.39045i	0.0259230	−	0.0448999i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	25.9254	−	14.9680i	0.835869	−	0.482589i
$963$			12.4222i			0.400300i
$964$	2.95416	−	5.11676i	0.0951472	−	0.164800i
$965$		0			0
$966$	3.45416	+	5.98279i	0.111136	+	0.192493i
$967$		−	44.4777i		−	1.43031i	−0.698967	−	0.715153i	$-0.746357\pi$
$967$		−	44.4777i		−	1.43031i	0.698967	−	0.715153i	$-0.253643\pi$
$968$	−21.8815	+	12.6333i	−0.703299	+	0.406050i
$969$	−21.3167	−	36.9215i	−0.684790	−	1.18609i
$970$		0			0
$971$	22.0139	+	38.1292i	0.706459	+	1.22362i	0.966162	+	0.257934i	$0.0830418\pi$
$971$	22.0139	+	38.1292i	0.706459	+	1.22362i	−0.259703	+	0.965688i	$0.583625\pi$
$972$	−45.7646	−	26.4222i	−1.46790	−	0.847493i
$973$	−5.53776	−	3.19722i	−0.177532	−	0.102498i
$974$	−2.30278			−0.0737857
$975$		0			0
$976$	−0.302776			−0.00969161
$977$	−24.9560	−	14.4083i	−0.798412	−	0.460963i	0.0445038	−	0.999009i	$-0.485829\pi$
$977$	−24.9560	−	14.4083i	−0.798412	−	0.460963i	−0.842915	+	0.538046i	$0.819163\pi$
$978$	7.55605	+	4.36249i	0.241616	+	0.139497i
$979$	−4.98612	−	8.63622i	−0.159357	−	0.276015i
$980$		0			0
$981$	−19.2111	−	33.2746i	−0.613363	−	1.06238i
$982$	33.5368	−	19.3625i	1.07020	−	0.617882i
$983$		−	18.4222i		−	0.587577i	−0.955870	−	0.293789i	$-0.905084\pi$
$983$		−	18.4222i		−	0.587577i	0.955870	−	0.293789i	$-0.0949162\pi$
$984$	−4.50000	−	7.79423i	−0.143455	−	0.248471i
$985$		0			0
$986$	−54.3902	+	94.2067i	−1.73214	+	3.00015i
$987$		−	9.21110i		−	0.293193i
$988$	57.8096	+	33.3764i	1.83917	+	1.06184i
$989$	−30.6333			−0.974083
$990$		0			0
$991$	−20.0139	+	34.6651i	−0.635762	+	1.10117i	0.350591	+	0.936529i	$0.385981\pi$
$991$	−20.0139	+	34.6651i	−0.635762	+	1.10117i	−0.986353	+	0.164643i	$0.947353\pi$
$992$	−18.3694	+	10.6056i	−0.583228	+	0.336727i
$993$		−	10.0278i		−	0.318221i
$994$	5.54584	+	9.60567i	0.175903	+	0.304673i
$995$		0			0
$996$	−30.4222			−0.963964
$997$	−15.9781	+	9.22498i	−0.506033	+	0.292158i	−0.731201	−	0.682162i	$-0.761040\pi$
$997$	−15.9781	+	9.22498i	−0.506033	+	0.292158i	0.225169	+	0.974320i	$0.427707\pi$
$998$	−4.83051	−	2.78890i	−0.152907	−	0.0882810i
$999$	−9.01388	+	15.6125i	−0.285186	+	0.493957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.o.b.74.4		8
5.2	odd	4		325.2.e.a.126.1		4
5.3	odd	4		65.2.e.b.61.2	yes	4
5.4	even	2	inner	325.2.o.b.74.1		8
13.3	even	3	inner	325.2.o.b.224.1		8
15.8	even	4		585.2.j.d.451.1		4
20.3	even	4		1040.2.q.o.321.2		4
65.3	odd	12		65.2.e.b.16.2	✓	4
65.8	even	4		845.2.m.d.316.4		8
65.17	odd	12		4225.2.a.t.1.1		2
65.18	even	4		845.2.m.d.316.1		8
65.22	odd	12		4225.2.a.x.1.2		2
65.23	odd	12		845.2.e.d.146.1		4
65.28	even	12		845.2.m.d.361.4		8
65.29	even	6	inner	325.2.o.b.224.4		8
65.33	even	12		845.2.c.d.506.1		4
65.38	odd	4		845.2.e.d.191.1		4
65.42	odd	12		325.2.e.a.276.1		4
65.43	odd	12		845.2.a.f.1.2		2
65.48	odd	12		845.2.a.c.1.1		2
65.58	even	12		845.2.c.d.506.4		4
65.63	even	12		845.2.m.d.361.1		8
195.68	even	12		585.2.j.d.406.1		4
195.113	even	12		7605.2.a.bg.1.2		2
195.173	even	12		7605.2.a.bb.1.1		2
260.3	even	12		1040.2.q.o.81.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.e.b.16.2	✓	4	65.3	odd	12
65.2.e.b.61.2	yes	4	5.3	odd	4
325.2.e.a.126.1		4	5.2	odd	4
325.2.e.a.276.1		4	65.42	odd	12
325.2.o.b.74.1		8	5.4	even	2	inner
325.2.o.b.74.4		8	1.1	even	1	trivial
325.2.o.b.224.1		8	13.3	even	3	inner
325.2.o.b.224.4		8	65.29	even	6	inner
585.2.j.d.406.1		4	195.68	even	12
585.2.j.d.451.1		4	15.8	even	4
845.2.a.c.1.1		2	65.48	odd	12
845.2.a.f.1.2		2	65.43	odd	12
845.2.c.d.506.1		4	65.33	even	12
845.2.c.d.506.4		4	65.58	even	12
845.2.e.d.146.1		4	65.23	odd	12
845.2.e.d.191.1		4	65.38	odd	4
845.2.m.d.316.1		8	65.18	even	4
845.2.m.d.316.4		8	65.8	even	4
845.2.m.d.361.1		8	65.63	even	12
845.2.m.d.361.4		8	65.28	even	12
1040.2.q.o.81.2		4	260.3	even	12
1040.2.q.o.321.2		4	20.3	even	4
4225.2.a.t.1.1		2	65.17	odd	12
4225.2.a.x.1.2		2	65.22	odd	12
7605.2.a.bb.1.1		2	195.173	even	12
7605.2.a.bg.1.2		2	195.113	even	12

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.99426 + 1.15139i) q^{2} +(0.866025 + 0.500000i) q^{3} +(1.65139 + 2.86029i) q^{4} +(1.15139 + 1.99426i) q^{6} +(-0.866025 + 0.500000i) q^{7} +3.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} +(-0.802776 + 1.39045i) q^{11} +3.30278i q^{12} +3.60555i q^{13} -2.30278 q^{14} +(-0.151388 + 0.262211i) q^{16} +(6.58660 - 3.80278i) q^{17} -4.60555i q^{18} +(-2.80278 - 4.85455i) q^{19} -1.00000 q^{21} +(-3.20189 + 1.84861i) q^{22} +(-2.59808 - 1.50000i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(-4.15139 + 7.19041i) q^{26} -5.00000i q^{27} +(-2.86029 - 1.65139i) q^{28} +(-3.10555 + 5.37897i) q^{29} -4.00000 q^{31} +(4.59234 - 2.65139i) q^{32} +(-1.39045 + 0.802776i) q^{33} +17.5139 q^{34} +(3.30278 - 5.72058i) q^{36} +(-3.12250 - 1.80278i) q^{37} -12.9083i q^{38} +(-1.80278 + 3.12250i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(-1.99426 - 1.15139i) q^{42} +(8.84307 - 5.10555i) q^{43} -5.30278 q^{44} +(-3.45416 - 5.98279i) q^{46} +9.21110i q^{47} +(-0.262211 + 0.151388i) q^{48} +(-3.00000 + 5.19615i) q^{49} +7.60555 q^{51} +(-10.3129 + 5.95416i) q^{52} +3.21110i q^{53} +(5.75694 - 9.97131i) q^{54} +(-1.50000 - 2.59808i) q^{56} -5.60555i q^{57} +(-12.3866 + 7.15139i) q^{58} +(-5.40833 - 9.36750i) q^{59} +(0.500000 + 0.866025i) q^{61} +(-7.97705 - 4.60555i) q^{62} +(1.73205 + 1.00000i) q^{63} +12.8167 q^{64} -3.69722 q^{66} +(6.06218 + 3.50000i) q^{67} +(21.7541 + 12.5597i) q^{68} +(-1.50000 - 2.59808i) q^{69} +(-2.40833 - 4.17134i) q^{71} +(5.19615 - 3.00000i) q^{72} +0.788897i q^{73} +(-4.15139 - 7.19041i) q^{74} +(9.25694 - 16.0335i) q^{76} -1.60555i q^{77} +(-7.19041 + 4.15139i) q^{78} -5.21110 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-5.98279 + 3.45416i) q^{82} +9.21110i q^{83} +(-1.65139 - 2.86029i) q^{84} +23.5139 q^{86} +(-5.37897 + 3.10555i) q^{87} +(-4.17134 - 2.40833i) q^{88} +(-3.10555 + 5.37897i) q^{89} +(-1.80278 - 3.12250i) q^{91} -9.90833i q^{92} +(-3.46410 - 2.00000i) q^{93} +(-10.6056 + 18.3694i) q^{94} +5.30278 q^{96} +(-7.26981 + 4.19722i) q^{97} +(-11.9656 + 6.90833i) q^{98} +3.21110 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{4} + 2 q^{6} - 8 q^{9} + 8 q^{11} - 4 q^{14} + 6 q^{16} - 8 q^{19} - 8 q^{21} - 12 q^{24} - 26 q^{26} + 4 q^{29} - 32 q^{31} + 68 q^{34} + 12 q^{36} - 12 q^{41} - 28 q^{44} - 6 q^{46} - 24 q^{49}+ \cdots - 32 q^{99}+O(q^{100}) \) 8 * q + 6 * q^4 + 2 * q^6 - 8 * q^9 + 8 * q^11 - 4 * q^14 + 6 * q^16 - 8 * q^19 - 8 * q^21 - 12 * q^24 - 26 * q^26 + 4 * q^29 - 32 * q^31 + 68 * q^34 + 12 * q^36 - 12 * q^41 - 28 * q^44 - 6 * q^46 - 24 * q^49 + 32 * q^51 + 10 * q^54 - 12 * q^56 + 4 * q^61 + 16 * q^64 - 44 * q^66 - 12 * q^69 + 24 * q^71 - 26 * q^74 + 38 * q^76 + 16 * q^79 - 4 * q^81 - 6 * q^84 + 116 * q^86 + 4 * q^89 - 56 * q^94 + 28 * q^96 - 32 * q^99

Introduction

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