LMFDB - Embedded newform 75.9.f.d.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(7,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("75.7");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$30.5533957546$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 192 x^{9} + 27713 x^{8} - 24384 x^{7} + 18432 x^{6} - 2072064 x^{5} + 128589064 x^{4} + \cdots + 846810000 $ x^12 - 192x^9 + 27713x^8 - 24384x^7 + 18432x^6 - 2072064x^5 + 128589064x^4 - 223046400x^3 + 184320000x^2 + 558720000*x + 846810000
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{18}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.1
Root			$-6.36871 - 6.36871i$ of defining polynomial
Character	$\chi$	$=$	75.7
Dual form			75.9.f.d.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-20.7460 - 20.7460i) q^{2} +(-33.0681 + 33.0681i) q^{3} +604.790i q^{4} +1372.06 q^{6} +(500.835 + 500.835i) q^{7} +(7236.00 - 7236.00i) q^{8} -2187.00i q^{9} +O(q^{10})$	\(q+(-20.7460 - 20.7460i) q^{2} +(-33.0681 + 33.0681i) q^{3} +604.790i q^{4} +1372.06 q^{6} +(500.835 + 500.835i) q^{7} +(7236.00 - 7236.00i) q^{8} -2187.00i q^{9} -21711.3 q^{11} +(-19999.3 - 19999.3i) q^{12} +(40229.3 - 40229.3i) q^{13} -20780.6i q^{14} -145409. q^{16} +(-68790.7 - 68790.7i) q^{17} +(-45371.4 + 45371.4i) q^{18} +199066. i q^{19} -33123.3 q^{21} +(450423. + 450423. i) q^{22} +(-124885. + 124885. i) q^{23} +478561. i q^{24} -1.66919e6 q^{26} +(72320.0 + 72320.0i) q^{27} +(-302900. + 302900. i) q^{28} -662313. i q^{29} +247715. q^{31} +(1.16424e6 + 1.16424e6i) q^{32} +(717953. - 717953. i) q^{33} +2.85426e6i q^{34} +1.32268e6 q^{36} +(-1.18893e6 - 1.18893e6i) q^{37} +(4.12981e6 - 4.12981e6i) q^{38} +2.66061e6i q^{39} +1.13938e6 q^{41} +(687176. + 687176. i) q^{42} +(-469792. + 469792. i) q^{43} -1.31308e7i q^{44} +5.18173e6 q^{46} +(2.35160e6 + 2.35160e6i) q^{47} +(4.80841e6 - 4.80841e6i) q^{48} -5.26313e6i q^{49} +4.54956e6 q^{51} +(2.43303e7 + 2.43303e7i) q^{52} +(-1.85494e6 + 1.85494e6i) q^{53} -3.00070e6i q^{54} +7.24808e6 q^{56} +(-6.58272e6 - 6.58272e6i) q^{57} +(-1.37403e7 + 1.37403e7i) q^{58} +1.56294e7i q^{59} +9.55958e6 q^{61} +(-5.13909e6 - 5.13909e6i) q^{62} +(1.09533e6 - 1.09533e6i) q^{63} -1.10818e7i q^{64} -2.97893e7 q^{66} +(1.27488e7 + 1.27488e7i) q^{67} +(4.16040e7 - 4.16040e7i) q^{68} -8.25943e6i q^{69} +2.72447e7 q^{71} +(-1.58251e7 - 1.58251e7i) q^{72} +(-2.23361e7 + 2.23361e7i) q^{73} +4.93308e7i q^{74} -1.20393e8 q^{76} +(-1.08738e7 - 1.08738e7i) q^{77} +(5.51970e7 - 5.51970e7i) q^{78} +5.20522e7i q^{79} -4.78297e6 q^{81} +(-2.36375e7 - 2.36375e7i) q^{82} +(1.12407e7 - 1.12407e7i) q^{83} -2.00327e7i q^{84} +1.94926e7 q^{86} +(2.19015e7 + 2.19015e7i) q^{87} +(-1.57103e8 + 1.57103e8i) q^{88} +9.28002e7i q^{89} +4.02965e7 q^{91} +(-7.55294e7 - 7.55294e7i) q^{92} +(-8.19147e6 + 8.19147e6i) q^{93} -9.75723e7i q^{94} -7.69984e7 q^{96} +(3.35484e7 + 3.35484e7i) q^{97} +(-1.09189e8 + 1.09189e8i) q^{98} +4.74827e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2268 q^{6}+O(q^{10}) $ 12 * q + 2268 * q^6	$ 12 q + 2268 q^{6} - 88920 q^{11} - 485796 q^{16} + 79704 q^{21} - 4055976 q^{26} + 5658696 q^{31} + 5065092 q^{36} + 1798056 q^{41} - 10882464 q^{46} + 4329936 q^{51} + 7268040 q^{56} + 33649848 q^{61} - 141361848 q^{66} + 335506464 q^{71} - 395386536 q^{76} - 57395628 q^{81} + 489958560 q^{86} - 216875664 q^{91} - 710311356 q^{96}+O(q^{100}) $ 12 * q + 2268 * q^6 - 88920 * q^11 - 485796 * q^16 + 79704 * q^21 - 4055976 * q^26 + 5658696 * q^31 + 5065092 * q^36 + 1798056 * q^41 - 10882464 * q^46 + 4329936 * q^51 + 7268040 * q^56 + 33649848 * q^61 - 141361848 * q^66 + 335506464 * q^71 - 395386536 * q^76 - 57395628 * q^81 + 489958560 * q^86 - 216875664 * q^91 - 710311356 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−20.7460	−	20.7460i	−1.29662	−	1.29662i	−0.930610	−	0.366014i	$-0.880722\pi$
$2$	−20.7460	−	20.7460i	−1.29662	−	1.29662i	−0.366014	−	0.930610i	$-0.619278\pi$
$3$	−33.0681	+	33.0681i	−0.408248	+	0.408248i
$3$	−33.0681	+	33.0681i	−0.408248	+	0.408248i
$4$			604.790i			2.36246i
$5$		0			0
$5$		0			0
$6$	1372.06			1.05869
$7$	500.835	+	500.835i	0.208594	+	0.208594i	0.803670	−	0.595075i	$-0.202878\pi$
$7$	500.835	+	500.835i	0.208594	+	0.208594i	−0.595075	+	0.803670i	$0.702878\pi$
$8$	7236.00	−	7236.00i	1.76660	−	1.76660i
$9$		−	2187.00i		−	0.333333i
$10$		0			0
$11$	−21711.3			−1.48291			−0.741457	−	0.671000i	$-0.765865\pi$
$11$	−21711.3			−1.48291			−0.741457	+	0.671000i	$0.765865\pi$
$12$	−19999.3	−	19999.3i	−0.964471	−	0.964471i
$13$	40229.3	−	40229.3i	1.40854	−	1.40854i	0.640983	−	0.767555i	$-0.278527\pi$
$13$	40229.3	−	40229.3i	1.40854	−	1.40854i	0.767555	−	0.640983i	$-0.221473\pi$
$14$		−	20780.6i		−	0.540937i
$15$		0			0
$16$	−145409.			−2.21877
$17$	−68790.7	−	68790.7i	−0.823634	−	0.823634i	0.162993	−	0.986627i	$-0.447885\pi$
$17$	−68790.7	−	68790.7i	−0.823634	−	0.823634i	−0.986627	+	0.162993i	$0.947885\pi$
$18$	−45371.4	+	45371.4i	−0.432208	+	0.432208i
$19$			199066.i			1.52750i	0.645511	+	0.763751i	$0.276645\pi$
$19$			199066.i			1.52750i	−0.645511	+	0.763751i	$0.723355\pi$
$20$		0			0
$21$	−33123.3			−0.170317
$22$	450423.	+	450423.i	1.92278	+	1.92278i
$23$	−124885.	+	124885.i	−0.446272	+	0.446272i	−0.894113	−	0.447841i	$-0.852193\pi$
$23$	−124885.	+	124885.i	−0.446272	+	0.446272i	0.447841	+	0.894113i	$0.352193\pi$
$24$			478561.i			1.44242i
$25$		0			0
$26$	−1.66919e6			−3.65269
$27$	72320.0	+	72320.0i	0.136083	+	0.136083i
$28$	−302900.	+	302900.i	−0.492797	+	0.492797i
$29$		−	662313.i		−	0.936422i	−0.883617	−	0.468211i	$-0.844899\pi$
$29$		−	662313.i		−	0.936422i	0.883617	−	0.468211i	$-0.155101\pi$
$30$		0			0
$31$	247715.			0.268229			0.134115	−	0.990966i	$-0.457181\pi$
$31$	247715.			0.268229			0.134115	+	0.990966i	$0.457181\pi$
$32$	1.16424e6	+	1.16424e6i	1.11030	+	1.11030i
$33$	717953.	−	717953.i	0.605397	−	0.605397i
$34$			2.85426e6i			2.13589i
$35$		0			0
$36$	1.32268e6			0.787488
$37$	−1.18893e6	−	1.18893e6i	−0.634378	−	0.634378i	0.314785	−	0.949163i	$-0.398067\pi$
$37$	−1.18893e6	−	1.18893e6i	−0.634378	−	0.634378i	−0.949163	+	0.314785i	$0.898067\pi$
$38$	4.12981e6	−	4.12981e6i	1.98059	−	1.98059i
$39$			2.66061e6i			1.15007i
$40$		0			0
$41$	1.13938e6			0.403211			0.201605	−	0.979467i	$-0.435384\pi$
$41$	1.13938e6			0.403211			0.201605	+	0.979467i	$0.435384\pi$
$42$	687176.	+	687176.i	0.220836	+	0.220836i
$43$	−469792.	+	469792.i	−0.137414	+	0.137414i	−0.772468	−	0.635054i	$-0.780978\pi$
$43$	−469792.	+	469792.i	−0.137414	+	0.137414i	0.635054	+	0.772468i	$0.280978\pi$
$44$		−	1.31308e7i		−	3.50333i
$45$		0			0
$46$	5.18173e6			1.15729
$47$	2.35160e6	+	2.35160e6i	0.481916	+	0.481916i	0.905743	−	0.423827i	$-0.139314\pi$
$47$	2.35160e6	+	2.35160e6i	0.481916	+	0.481916i	−0.423827	+	0.905743i	$0.639314\pi$
$48$	4.80841e6	−	4.80841e6i	0.905808	−	0.905808i
$49$		−	5.26313e6i		−	0.912977i
$50$		0			0
$51$	4.54956e6			0.672494
$52$	2.43303e7	+	2.43303e7i	3.32762	+	3.32762i
$53$	−1.85494e6	+	1.85494e6i	−0.235086	+	0.235086i	−0.814812	−	0.579726i	$-0.803160\pi$
$53$	−1.85494e6	+	1.85494e6i	−0.235086	+	0.235086i	0.579726	+	0.814812i	$0.303160\pi$
$54$		−	3.00070e6i		−	0.352896i
$55$		0			0
$56$	7.24808e6			0.737006
$57$	−6.58272e6	−	6.58272e6i	−0.623600	−	0.623600i
$58$	−1.37403e7	+	1.37403e7i	−1.21419	+	1.21419i
$59$			1.56294e7i			1.28984i	0.764251	+	0.644919i	$0.223109\pi$
$59$			1.56294e7i			1.28984i	−0.764251	+	0.644919i	$0.776891\pi$
$60$		0			0
$61$	9.55958e6			0.690430			0.345215	−	0.938524i	$-0.387806\pi$
$61$	9.55958e6			0.690430			0.345215	+	0.938524i	$0.387806\pi$
$62$	−5.13909e6	−	5.13909e6i	−0.347792	−	0.347792i
$63$	1.09533e6	−	1.09533e6i	0.0695315	−	0.0695315i
$64$		−	1.10818e7i		−	0.660526i
$65$		0			0
$66$	−2.97893e7			−1.56994
$67$	1.27488e7	+	1.27488e7i	0.632661	+	0.632661i	0.948735	−	0.316074i	$-0.102365\pi$
$67$	1.27488e7	+	1.27488e7i	0.632661	+	0.632661i	−0.316074	+	0.948735i	$0.602365\pi$
$68$	4.16040e7	−	4.16040e7i	1.94580	−	1.94580i
$69$		−	8.25943e6i		−	0.364380i
$70$		0			0
$71$	2.72447e7			1.07213			0.536066	−	0.844176i	$-0.319910\pi$
$71$	2.72447e7			1.07213			0.536066	+	0.844176i	$0.319910\pi$
$72$	−1.58251e7	−	1.58251e7i	−0.588867	−	0.588867i
$73$	−2.23361e7	+	2.23361e7i	−0.786531	+	0.786531i	−0.980924	−	0.194393i	$-0.937726\pi$
$73$	−2.23361e7	+	2.23361e7i	−0.786531	+	0.786531i	0.194393	+	0.980924i	$0.437726\pi$
$74$			4.93308e7i			1.64510i
$75$		0			0
$76$	−1.20393e8			−3.60867
$77$	−1.08738e7	−	1.08738e7i	−0.309328	−	0.309328i
$78$	5.51970e7	−	5.51970e7i	1.49120	−	1.49120i
$79$			5.20522e7i			1.33638i	0.743990	+	0.668191i	$0.232931\pi$
$79$			5.20522e7i			1.33638i	−0.743990	+	0.668191i	$0.767069\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$	−2.36375e7	−	2.36375e7i	−0.522812	−	0.522812i
$83$	1.12407e7	−	1.12407e7i	0.236853	−	0.236853i	−0.578693	−	0.815546i	$-0.696437\pi$
$83$	1.12407e7	−	1.12407e7i	0.236853	−	0.236853i	0.815546	+	0.578693i	$0.196437\pi$
$84$		−	2.00327e7i		−	0.402367i
$85$		0			0
$86$	1.94926e7			0.356349
$87$	2.19015e7	+	2.19015e7i	0.382293	+	0.382293i
$88$	−1.57103e8	+	1.57103e8i	−2.61972	+	2.61972i
$89$			9.28002e7i			1.47907i	0.673118	+	0.739535i	$0.264955\pi$
$89$			9.28002e7i			1.47907i	−0.673118	+	0.739535i	$0.735045\pi$
$90$		0			0
$91$	4.02965e7			0.587626
$92$	−7.55294e7	−	7.55294e7i	−1.05430	−	1.05430i
$93$	−8.19147e6	+	8.19147e6i	−0.109504	+	0.109504i
$94$		−	9.75723e7i		−	1.24973i
$95$		0			0
$96$	−7.69984e7			−0.906560
$97$	3.35484e7	+	3.35484e7i	0.378953	+	0.378953i	0.870724	−	0.491771i	$-0.163650\pi$
$97$	3.35484e7	+	3.35484e7i	0.378953	+	0.378953i	−0.491771	+	0.870724i	$0.663650\pi$
$98$	−1.09189e8	+	1.09189e8i	−1.18379	+	1.18379i
$99$			4.74827e7i			0.494305i
$100$		0			0
$101$	7.09778e7			0.682083			0.341041	−	0.940048i	$-0.389220\pi$
$101$	7.09778e7			0.682083			0.341041	+	0.940048i	$0.389220\pi$
$102$	−9.43850e7	−	9.43850e7i	−0.871972	−	0.871972i
$103$	491761.	−	491761.i	0.00436923	−	0.00436923i	−0.704919	−	0.709288i	$-0.749017\pi$
$103$	491761.	−	491761.i	0.00436923	−	0.00436923i	0.709288	+	0.704919i	$0.249017\pi$
$104$		−	5.82198e8i		−	4.97665i
$105$		0			0
$106$	7.69650e7			0.609635
$107$	−3.64024e6	−	3.64024e6i	−0.0277712	−	0.0277712i	0.693085	−	0.720856i	$-0.256251\pi$
$107$	−3.64024e6	−	3.64024e6i	−0.0277712	−	0.0277712i	−0.720856	+	0.693085i	$0.756251\pi$
$108$	−4.37384e7	+	4.37384e7i	−0.321490	+	0.321490i
$109$			1.66078e8i			1.17654i	0.808665	+	0.588269i	$0.200191\pi$
$109$			1.66078e8i			1.17654i	−0.808665	+	0.588269i	$0.799809\pi$
$110$		0			0
$111$	7.86311e7			0.517967
$112$	−7.28260e7	−	7.28260e7i	−0.462823	−	0.462823i
$113$	7.40473e7	−	7.40473e7i	0.454146	−	0.454146i	−0.442582	−	0.896728i	$-0.645937\pi$
$113$	7.40473e7	−	7.40473e7i	0.454146	−	0.454146i	0.896728	+	0.442582i	$0.145937\pi$
$114$			2.73130e8i			1.61715i
$115$		0			0
$116$	4.00561e8			2.21226
$117$	−8.79814e7	−	8.79814e7i	−0.469513	−	0.469513i
$118$	3.24248e8	−	3.24248e8i	1.67243	−	1.67243i
$119$		−	6.89056e7i		−	0.343611i
$120$		0			0
$121$	2.57024e8			1.19903
$122$	−1.98323e8	−	1.98323e8i	−0.895227	−	0.895227i
$123$	−3.76770e7	+	3.76770e7i	−0.164610	+	0.164610i
$124$			1.49816e8i			0.633681i
$125$		0			0
$126$	−4.54472e7			−0.180312
$127$	−6.36179e6	−	6.36179e6i	−0.0244548	−	0.0244548i	0.694774	−	0.719228i	$-0.255505\pi$
$127$	−6.36179e6	−	6.36179e6i	−0.0244548	−	0.0244548i	−0.719228	+	0.694774i	$0.755505\pi$
$128$	6.81428e7	−	6.81428e7i	0.253852	−	0.253852i
$129$		−	3.10703e7i		−	0.112198i
$130$		0			0
$131$	−3.15386e8			−1.07092			−0.535460	−	0.844561i	$-0.679862\pi$
$131$	−3.15386e8			−1.07092			−0.535460	+	0.844561i	$0.679862\pi$
$132$	4.34211e8	+	4.34211e8i	1.43023	+	1.43023i
$133$	−9.96991e7	+	9.96991e7i	−0.318628	+	0.318628i
$134$		−	5.28973e8i		−	1.64065i
$135$		0			0
$136$	−9.95539e8			−2.91007
$137$	3.55329e8	+	3.55329e8i	1.00867	+	1.00867i	0.999962	+	0.00870703i	$0.00277157\pi$
$137$	3.55329e8	+	3.55329e8i	1.00867	+	1.00867i	0.00870703	+	0.999962i	$0.497228\pi$
$138$	−1.71350e8	+	1.71350e8i	−0.472463	+	0.472463i
$139$			3.81144e8i			1.02101i	0.859874	+	0.510506i	$0.170542\pi$
$139$			3.81144e8i			1.02101i	−0.859874	+	0.510506i	$0.829458\pi$
$140$		0			0
$141$	−1.55526e8			−0.393483
$142$	−5.65217e8	−	5.65217e8i	−1.39015	−	1.39015i
$143$	−8.73431e8	+	8.73431e8i	−2.08874	+	2.08874i
$144$			3.18010e8i			0.739589i
$145$		0			0
$146$	9.26768e8			2.03967
$147$	1.74042e8	+	1.74042e8i	0.372721	+	0.372721i
$148$	7.19051e8	−	7.19051e8i	1.49869	−	1.49869i
$149$			6.31733e8i			1.28171i	0.767663	+	0.640853i	$0.221419\pi$
$149$			6.31733e8i			1.28171i	−0.767663	+	0.640853i	$0.778581\pi$
$150$		0			0
$151$	−4.19468e8			−0.806846			−0.403423	−	0.915014i	$-0.632180\pi$
$151$	−4.19468e8			−0.806846			−0.403423	+	0.915014i	$0.632180\pi$
$152$	1.44044e9	+	1.44044e9i	2.69849	+	2.69849i
$153$	−1.50445e8	+	1.50445e8i	−0.274545	+	0.274545i
$154$			4.51175e8i			0.802163i
$155$		0			0
$156$	−1.60911e9			−2.71699
$157$	4.25096e8	+	4.25096e8i	0.699662	+	0.699662i	0.964338	−	0.264676i	$-0.0852649\pi$
$157$	4.25096e8	+	4.25096e8i	0.699662	+	0.699662i	−0.264676	+	0.964338i	$0.585265\pi$
$158$	1.07987e9	−	1.07987e9i	1.73278	−	1.73278i
$159$		−	1.22679e8i		−	0.191947i
$160$		0			0
$161$	−1.25094e8			−0.186180
$162$	9.92273e7	+	9.92273e7i	0.144069	+	0.144069i
$163$	5.80994e8	−	5.80994e8i	0.823040	−	0.823040i	−0.163503	−	0.986543i	$-0.552279\pi$
$163$	5.80994e8	−	5.80994e8i	0.823040	−	0.823040i	0.986543	+	0.163503i	$0.0522793\pi$
$164$			6.89084e8i			0.952570i
$165$		0			0
$166$	−4.66396e8			−0.614218
$167$	−8.48074e8	−	8.48074e8i	−1.09035	−	1.09035i	−0.995490	−	0.0948643i	$-0.969758\pi$
$167$	−8.48074e8	−	8.48074e8i	−1.09035	−	1.09035i	−0.0948643	−	0.995490i	$-0.530242\pi$
$168$	−2.39680e8	+	2.39680e8i	−0.300881	+	0.300881i
$169$		−	2.42106e9i		−	2.96796i
$170$		0			0
$171$	4.35357e8			0.509167
$172$	−2.84126e8	−	2.84126e8i	−0.324636	−	0.324636i
$173$	−2.64479e8	+	2.64479e8i	−0.295261	+	0.295261i	−0.839155	−	0.543893i	$-0.816950\pi$
$173$	−2.64479e8	+	2.64479e8i	−0.295261	+	0.295261i	0.543893	+	0.839155i	$0.316950\pi$
$174$		−	9.08734e8i		−	0.991379i
$175$		0			0
$176$	3.15703e9			3.29024
$177$	−5.16836e8	−	5.16836e8i	−0.526574	−	0.526574i
$178$	1.92523e9	−	1.92523e9i	1.91780	−	1.91780i
$179$		−	2.98017e8i		−	0.290288i	−0.989411	−	0.145144i	$-0.953635\pi$
$179$		−	2.98017e8i		−	0.290288i	0.989411	−	0.145144i	$-0.0463646\pi$
$180$		0			0
$181$	−7.53568e8			−0.702115			−0.351057	−	0.936354i	$-0.614178\pi$
$181$	−7.53568e8			−0.702115			−0.351057	+	0.936354i	$0.614178\pi$
$182$	−8.35989e8	−	8.35989e8i	−0.761930	−	0.761930i
$183$	−3.16117e8	+	3.16117e8i	−0.281867	+	0.281867i
$184$			1.80734e9i			1.57677i
$185$		0			0
$186$	3.39880e8			0.283971
$187$	1.49354e9	+	1.49354e9i	1.22138	+	1.22138i
$188$	−1.42222e9	+	1.42222e9i	−1.13851	+	1.13851i
$189$			7.24408e7i			0.0567722i
$190$		0			0
$191$	1.57942e9			1.18677			0.593383	−	0.804921i	$-0.297792\pi$
$191$	1.57942e9			1.18677			0.593383	+	0.804921i	$0.297792\pi$
$192$	3.66454e8	+	3.66454e8i	0.269659	+	0.269659i
$193$	−1.21554e9	+	1.21554e9i	−0.876070	+	0.876070i	−0.993125	−	0.117055i	$-0.962655\pi$
$193$	−1.21554e9	+	1.21554e9i	−0.876070	+	0.876070i	0.117055	+	0.993125i	$0.462655\pi$
$194$		−	1.39199e9i		−	0.982718i
$195$		0			0
$196$	3.18309e9			2.15687
$197$	1.02022e9	+	1.02022e9i	0.677378	+	0.677378i	0.959406	−	0.282028i	$-0.0910072\pi$
$197$	1.02022e9	+	1.02022e9i	0.677378	+	0.677378i	−0.282028	+	0.959406i	$0.591007\pi$
$198$	9.85075e8	−	9.85075e8i	0.640927	−	0.640927i
$199$			4.40178e8i			0.280683i	0.990103	+	0.140342i	$0.0448201\pi$
$199$			4.40178e8i			0.280683i	−0.990103	+	0.140342i	$0.955180\pi$
$200$		0			0
$201$	−8.43159e8			−0.516565
$202$	−1.47250e9	−	1.47250e9i	−0.884404	−	0.884404i
$203$	3.31710e8	−	3.31710e8i	0.195332	−	0.195332i
$204$			2.75153e9i			1.58874i
$205$		0			0
$206$	−2.04041e7			−0.0113305
$207$	2.73124e8	+	2.73124e8i	0.148757	+	0.148757i
$208$	−5.84970e9	+	5.84970e9i	−3.12522	+	3.12522i
$209$		−	4.32198e9i		−	2.26515i
$210$		0			0
$211$	−5.74722e8			−0.289953			−0.144977	−	0.989435i	$-0.546311\pi$
$211$	−5.74722e8			−0.289953			−0.144977	+	0.989435i	$0.546311\pi$
$212$	−1.12185e9	−	1.12185e9i	−0.555381	−	0.555381i
$213$	−9.00930e8	+	9.00930e8i	−0.437696	+	0.437696i
$214$			1.51041e8i			0.0720176i
$215$		0			0
$216$	1.04661e9			0.480808
$217$	1.24064e8	+	1.24064e8i	0.0559511	+	0.0559511i
$218$	3.44545e9	−	3.44545e9i	1.52553	−	1.52553i
$219$		−	1.47723e9i		−	0.642200i
$220$		0			0
$221$	−5.53480e9			−2.32024
$222$	−1.63128e9	−	1.63128e9i	−0.671608	−	0.671608i
$223$	−8.04678e8	+	8.04678e8i	−0.325389	+	0.325389i	−0.850830	−	0.525441i	$-0.823900\pi$
$223$	−8.04678e8	+	8.04678e8i	−0.325389	+	0.325389i	0.525441	+	0.850830i	$0.323900\pi$
$224$			1.16618e9i			0.463207i
$225$		0			0
$226$	−3.07237e9			−1.17771
$227$	−1.06210e9	−	1.06210e9i	−0.400003	−	0.400003i	0.478231	−	0.878234i	$-0.341278\pi$
$227$	−1.06210e9	−	1.06210e9i	−0.400003	−	0.400003i	−0.878234	+	0.478231i	$0.841278\pi$
$228$	3.98117e9	−	3.98117e9i	1.47323	−	1.47323i
$229$			2.28229e8i			0.0829907i	0.999139	+	0.0414954i	$0.0132122\pi$
$229$			2.28229e8i			0.0829907i	−0.999139	+	0.0414954i	$0.986788\pi$
$230$		0			0
$231$	7.19152e8			0.252565
$232$	−4.79250e9	−	4.79250e9i	−1.65428	−	1.65428i
$233$	−1.44765e9	+	1.44765e9i	−0.491179	+	0.491179i	−0.908678	−	0.417498i	$-0.862907\pi$
$233$	−1.44765e9	+	1.44765e9i	−0.491179	+	0.491179i	0.417498	+	0.908678i	$0.362907\pi$
$234$			3.65052e9i			1.21756i
$235$		0			0
$236$	−9.45253e9			−3.04719
$237$	−1.72127e9	−	1.72127e9i	−0.545575	−	0.545575i
$238$	−1.42951e9	+	1.42951e9i	−0.445534	+	0.445534i
$239$			1.50449e9i			0.461104i	0.973060	+	0.230552i	$0.0740532\pi$
$239$			1.50449e9i			0.461104i	−0.973060	+	0.230552i	$0.925947\pi$
$240$		0			0
$241$	4.44300e9			1.31707			0.658535	−	0.752550i	$-0.271177\pi$
$241$	4.44300e9			1.31707			0.658535	+	0.752550i	$0.271177\pi$
$242$	−5.33220e9	−	5.33220e9i	−1.55469	−	1.55469i
$243$	1.58164e8	−	1.58164e8i	0.0453609	−	0.0453609i
$244$			5.78154e9i			1.63112i
$245$		0			0
$246$	1.56329e9			0.426874
$247$	8.00826e9	+	8.00826e9i	2.15155	+	2.15155i
$248$	1.79247e9	−	1.79247e9i	0.473854	−	0.473854i
$249$			7.43414e8i			0.193390i
$250$		0			0
$251$	2.75069e9			0.693022			0.346511	−	0.938046i	$-0.387366\pi$
$251$	2.75069e9			0.693022			0.346511	+	0.938046i	$0.387366\pi$
$252$	6.62443e8	+	6.62443e8i	0.164266	+	0.164266i
$253$	2.71143e9	−	2.71143e9i	0.661783	−	0.661783i
$254$			2.63963e8i			0.0634174i
$255$		0			0
$256$	−5.66431e9			−1.31883
$257$	−1.92294e9	−	1.92294e9i	−0.440792	−	0.440792i	0.451486	−	0.892278i	$-0.350894\pi$
$257$	−1.92294e9	−	1.92294e9i	−0.440792	−	0.440792i	−0.892278	+	0.451486i	$0.850894\pi$
$258$	−6.44583e8	+	6.44583e8i	−0.145479	+	0.145479i
$259$		−	1.19091e9i		−	0.264655i
$260$		0			0
$261$	−1.44848e9			−0.312141
$262$	6.54298e9	+	6.54298e9i	1.38858	+	1.38858i
$263$	−4.93629e9	+	4.93629e9i	−1.03176	+	1.03176i	−0.0322790	+	0.999479i	$0.510277\pi$
$263$	−4.93629e9	+	4.93629e9i	−1.03176	+	1.03176i	−0.999479	+	0.0322790i	$0.989723\pi$
$264$		−	1.03902e10i		−	2.13899i
$265$		0			0
$266$	4.13671e9			0.826282
$267$	−3.06873e9	−	3.06873e9i	−0.603828	−	0.603828i
$268$	−7.71037e9	+	7.71037e9i	−1.49464	+	1.49464i
$269$			5.73937e9i			1.09611i	0.836442	+	0.548056i	$0.184632\pi$
$269$			5.73937e9i			1.09611i	−0.836442	+	0.548056i	$0.815368\pi$
$270$		0			0
$271$	−6.57633e9			−1.21929			−0.609644	−	0.792675i	$-0.708688\pi$
$271$	−6.57633e9			−1.21929			−0.609644	+	0.792675i	$0.708688\pi$
$272$	1.00028e10	+	1.00028e10i	1.82745	+	1.82745i
$273$	−1.33253e9	+	1.33253e9i	−0.239897	+	0.239897i
$274$		−	1.47433e10i		−	2.61573i
$275$		0			0
$276$	4.99523e9			0.860833
$277$	3.68220e9	+	3.68220e9i	0.625443	+	0.625443i	0.946918	−	0.321475i	$-0.104179\pi$
$277$	3.68220e9	+	3.68220e9i	0.625443	+	0.625443i	−0.321475	+	0.946918i	$0.604179\pi$
$278$	7.90721e9	−	7.90721e9i	1.32387	−	1.32387i
$279$		−	5.41753e8i		−	0.0894097i
$280$		0			0
$281$	8.85910e9			1.42090			0.710451	−	0.703747i	$-0.248491\pi$
$281$	8.85910e9			1.42090			0.710451	+	0.703747i	$0.248491\pi$
$282$	3.22653e9	+	3.22653e9i	0.510199	+	0.510199i
$283$	1.41065e9	−	1.41065e9i	0.219925	−	0.219925i	−0.588542	−	0.808467i	$-0.700298\pi$
$283$	1.41065e9	−	1.41065e9i	0.219925	−	0.219925i	0.808467	+	0.588542i	$0.200298\pi$
$284$			1.64773e10i			2.53287i
$285$		0			0
$286$	3.62404e10			5.41662
$287$	5.70640e8	+	5.70640e8i	0.0841075	+	0.0841075i
$288$	2.54619e9	−	2.54619e9i	0.370102	−	0.370102i
$289$			2.48858e9i			0.356746i
$290$		0			0
$291$	−2.21877e9			−0.309414
$292$	−1.35087e10	−	1.35087e10i	−1.85815	−	1.85815i
$293$	−4.16341e9	+	4.16341e9i	−0.564910	+	0.564910i	−0.930698	−	0.365788i	$-0.880799\pi$
$293$	−4.16341e9	+	4.16341e9i	−0.564910	+	0.564910i	0.365788	+	0.930698i	$0.380799\pi$
$294$		−	7.22133e9i		−	0.966558i
$295$		0			0
$296$	−1.72061e10			−2.24138
$297$	−1.57016e9	−	1.57016e9i	−0.201799	−	0.201799i
$298$	1.31059e10	−	1.31059e10i	1.66189	−	1.66189i
$299$			1.00481e10i			1.25718i
$300$		0			0
$301$	−4.70577e8			−0.0573277
$302$	8.70226e9	+	8.70226e9i	1.04618	+	1.04618i
$303$	−2.34710e9	+	2.34710e9i	−0.278459	+	0.278459i
$304$		−	2.89460e10i		−	3.38917i
$305$		0			0
$306$	6.24227e9			0.711962
$307$	−6.29064e9	−	6.29064e9i	−0.708176	−	0.708176i	0.257975	−	0.966152i	$-0.416945\pi$
$307$	−6.29064e9	−	6.29064e9i	−0.708176	−	0.708176i	−0.966152	+	0.257975i	$0.916945\pi$
$308$	6.57637e9	−	6.57637e9i	0.730775	−	0.730775i
$309$			3.25232e7i			0.00356746i
$310$		0			0
$311$	7.87965e9			0.842298			0.421149	−	0.906992i	$-0.361627\pi$
$311$	7.87965e9			0.842298			0.421149	+	0.906992i	$0.361627\pi$
$312$	1.92522e10	+	1.92522e10i	2.03171	+	2.03171i
$313$	9.42141e9	−	9.42141e9i	0.981609	−	0.981609i	−0.0182249	−	0.999834i	$-0.505801\pi$
$313$	9.42141e9	−	9.42141e9i	0.981609	−	0.981609i	0.999834	+	0.0182249i	$0.00580148\pi$
$314$		−	1.76380e10i		−	1.81440i
$315$		0			0
$316$	−3.14806e10			−3.15715
$317$	−4.55980e9	−	4.55980e9i	−0.451553	−	0.451553i	0.444317	−	0.895870i	$-0.353446\pi$
$317$	−4.55980e9	−	4.55980e9i	−0.451553	−	0.451553i	−0.895870	+	0.444317i	$0.853446\pi$
$318$	−2.54509e9	+	2.54509e9i	−0.248882	+	0.248882i
$319$			1.43797e10i			1.38863i
$320$		0			0
$321$	2.40752e8			0.0226751
$322$	2.59519e9	+	2.59519e9i	0.241405	+	0.241405i
$323$	1.36939e10	−	1.36939e10i	1.25810	−	1.25810i
$324$		−	2.89269e9i		−	0.262496i
$325$		0			0
$326$	−2.41066e10			−2.13435
$327$	−5.49189e9	−	5.49189e9i	−0.480320	−	0.480320i
$328$	8.24453e9	−	8.24453e9i	0.712312	−	0.712312i
$329$			2.35552e9i			0.201050i
$330$		0			0
$331$	1.28391e10			1.06961			0.534803	−	0.844977i	$-0.320386\pi$
$331$	1.28391e10			1.06961			0.534803	+	0.844977i	$0.320386\pi$
$332$	6.79824e9	+	6.79824e9i	0.559557	+	0.559557i
$333$	−2.60018e9	+	2.60018e9i	−0.211459	+	0.211459i
$334$			3.51882e10i			2.82756i
$335$		0			0
$336$	4.81644e9			0.377893
$337$	1.18340e10	+	1.18340e10i	0.917512	+	0.917512i	0.996848	−	0.0793356i	$-0.0252799\pi$
$337$	1.18340e10	+	1.18340e10i	0.917512	+	0.917512i	−0.0793356	+	0.996848i	$0.525280\pi$
$338$	−5.02271e10	+	5.02271e10i	−3.84832	+	3.84832i
$339$			4.89721e9i			0.370809i
$340$		0			0
$341$	−5.37823e9			−0.397761
$342$	−9.03189e9	−	9.03189e9i	−0.660198	−	0.660198i
$343$	5.52318e9	−	5.52318e9i	0.399036	−	0.399036i
$344$			6.79883e9i			0.485513i
$345$		0			0
$346$	1.09737e10			0.765686
$347$	−6.26520e9	−	6.26520e9i	−0.432133	−	0.432133i	0.457221	−	0.889353i	$-0.348845\pi$
$347$	−6.26520e9	−	6.26520e9i	−0.432133	−	0.432133i	−0.889353	+	0.457221i	$0.848845\pi$
$348$	−1.32458e10	+	1.32458e10i	−0.903152	+	0.903152i
$349$		−	1.26165e10i		−	0.850425i	−0.905094	−	0.425212i	$-0.860199\pi$
$349$		−	1.26165e10i		−	0.850425i	0.905094	−	0.425212i	$-0.139801\pi$
$350$		0			0
$351$	5.81876e9			0.383355
$352$	−2.52772e10	−	2.52772e10i	−1.64649	−	1.64649i
$353$	−6.49263e9	+	6.49263e9i	−0.418140	+	0.418140i	−0.884562	−	0.466422i	$-0.845543\pi$
$353$	−6.49263e9	+	6.49263e9i	−0.418140	+	0.418140i	0.466422	+	0.884562i	$0.345543\pi$
$354$			2.14445e10i			1.36554i
$355$		0			0
$356$	−5.61247e10			−3.49425
$357$	2.27858e9	+	2.27858e9i	0.140279	+	0.140279i
$358$	−6.18266e9	+	6.18266e9i	−0.376394	+	0.376394i
$359$			1.19342e10i			0.718482i	0.933245	+	0.359241i	$0.116964\pi$
$359$			1.19342e10i			0.718482i	−0.933245	+	0.359241i	$0.883036\pi$
$360$		0			0
$361$	−2.26436e10			−1.33326
$362$	1.56335e10	+	1.56335e10i	0.910378	+	0.910378i
$363$	−8.49928e9	+	8.49928e9i	−0.489504	+	0.489504i
$364$			2.43709e10i			1.38825i
$365$		0			0
$366$	1.31163e10			0.730950
$367$	1.26044e10	+	1.26044e10i	0.694795	+	0.694795i	0.963283	−	0.268488i	$-0.0865240\pi$
$367$	1.26044e10	+	1.26044e10i	0.694795	+	0.694795i	−0.268488	+	0.963283i	$0.586524\pi$
$368$	1.81595e10	−	1.81595e10i	0.990174	−	0.990174i
$369$		−	2.49182e9i		−	0.134404i
$370$		0			0
$371$	−1.85804e9			−0.0980751
$372$	−4.95412e9	−	4.95412e9i	−0.258699	−	0.258699i
$373$	1.81149e10	−	1.81149e10i	0.935839	−	0.935839i	−0.0622229	−	0.998062i	$-0.519819\pi$
$373$	1.81149e10	−	1.81149e10i	0.935839	−	0.935839i	0.998062	+	0.0622229i	$0.0198190\pi$
$374$		−	6.19698e10i		−	3.16734i
$375$		0			0
$376$	3.40323e10			1.70271
$377$	−2.66444e10	−	2.66444e10i	−1.31899	−	1.31899i
$378$	1.50285e9	−	1.50285e9i	0.0736122	−	0.0736122i
$379$		−	7.78531e9i		−	0.377328i	−0.982042	−	0.188664i	$-0.939584\pi$
$379$		−	7.78531e9i		−	0.377328i	0.982042	−	0.188664i	$-0.0604157\pi$
$380$		0			0
$381$	4.20745e8			0.0199673
$382$	−3.27666e10	−	3.27666e10i	−1.53879	−	1.53879i
$383$	3.93489e9	−	3.93489e9i	0.182868	−	0.182868i	−0.609736	−	0.792604i	$-0.708725\pi$
$383$	3.93489e9	−	3.93489e9i	0.182868	−	0.182868i	0.792604	+	0.609736i	$0.208725\pi$
$384$			4.50671e9i			0.207269i
$385$		0			0
$386$	5.04350e10			2.27187
$387$	1.02744e9	+	1.02744e9i	0.0458048	+	0.0458048i
$388$	−2.02898e10	+	2.02898e10i	−0.895262	+	0.895262i
$389$			1.59077e7i			0.000694717i	1.00000		0.000347358i	$0.000110568\pi$
$389$			1.59077e7i			0.000694717i	−1.00000		0.000347358i	$0.999889\pi$
$390$		0			0
$391$	1.71819e10			0.735130
$392$	−3.80840e10	−	3.80840e10i	−1.61287	−	1.61287i
$393$	1.04292e10	−	1.04292e10i	0.437201	−	0.437201i
$394$		−	4.23311e10i		−	1.75661i
$395$		0			0
$396$	−2.87171e10			−1.16778
$397$	−6.16715e9	−	6.16715e9i	−0.248269	−	0.248269i	0.571991	−	0.820260i	$-0.306171\pi$
$397$	−6.16715e9	−	6.16715e9i	−0.248269	−	0.248269i	−0.820260	+	0.571991i	$0.806171\pi$
$398$	9.13192e9	−	9.13192e9i	0.363940	−	0.363940i
$399$		−	6.59372e9i		−	0.260159i
$400$		0			0
$401$	3.64360e10			1.40914			0.704568	−	0.709637i	$-0.251141\pi$
$401$	3.64360e10			1.40914			0.704568	+	0.709637i	$0.251141\pi$
$402$	1.74922e10	+	1.74922e10i	0.669791	+	0.669791i
$403$	9.96540e9	−	9.96540e9i	0.377811	−	0.377811i
$404$			4.29267e10i			1.61140i
$405$		0			0
$406$	−1.37633e10			−0.506545
$407$	2.58132e10	+	2.58132e10i	0.940727	+	0.940727i
$408$	3.29206e10	−	3.29206e10i	1.18803	−	1.18803i
$409$		−	8.50081e9i		−	0.303786i	−0.988397	−	0.151893i	$-0.951463\pi$
$409$		−	8.50081e9i		−	0.303786i	0.988397	−	0.151893i	$-0.0485368\pi$
$410$		0			0
$411$	−2.35001e10			−0.823575
$412$	2.97412e8	+	2.97412e8i	0.0103221	+	0.0103221i
$413$	−7.82777e9	+	7.82777e9i	−0.269053	+	0.269053i
$414$		−	1.13324e10i		−	0.385764i
$415$		0			0
$416$	9.36729e10			3.12781
$417$	−1.26037e10	−	1.26037e10i	−0.416826	−	0.416826i
$418$	−8.96637e10	+	8.96637e10i	−2.93705	+	2.93705i
$419$		−	2.64081e10i		−	0.856803i	−0.903589	−	0.428401i	$-0.859077\pi$
$419$		−	2.64081e10i		−	0.856803i	0.903589	−	0.428401i	$-0.140923\pi$
$420$		0			0
$421$	5.99126e9			0.190717			0.0953586	−	0.995443i	$-0.469600\pi$
$421$	5.99126e9			0.190717			0.0953586	+	0.995443i	$0.469600\pi$
$422$	1.19232e10	+	1.19232e10i	0.375960	+	0.375960i
$423$	5.14294e9	−	5.14294e9i	0.160639	−	0.160639i
$424$			2.68447e10i			0.830605i
$425$		0			0
$426$	3.73813e10			1.13505
$427$	4.78778e9	+	4.78778e9i	0.144020	+	0.144020i
$428$	2.20158e9	−	2.20158e9i	0.0656085	−	0.0656085i
$429$		−	5.77654e10i		−	1.70545i
$430$		0			0
$431$	−3.57513e10			−1.03605			−0.518027	−	0.855364i	$-0.673333\pi$
$431$	−3.57513e10			−1.03605			−0.518027	+	0.855364i	$0.673333\pi$
$432$	−1.05160e10	−	1.05160e10i	−0.301936	−	0.301936i
$433$	−3.08847e10	+	3.08847e10i	−0.878600	+	0.878600i	−0.993390	−	0.114790i	$-0.963381\pi$
$433$	−3.08847e10	+	3.08847e10i	−0.878600	+	0.878600i	0.114790	+	0.993390i	$0.463381\pi$
$434$		−	5.14767e9i		−	0.145095i
$435$		0			0
$436$	−1.00442e11			−2.77953
$437$	−2.48603e10	−	2.48603e10i	−0.681681	−	0.681681i
$438$	−3.06465e10	+	3.06465e10i	−0.832691	+	0.832691i
$439$		−	5.22871e10i		−	1.40778i	−0.710307	−	0.703892i	$-0.751444\pi$
$439$		−	5.22871e10i		−	1.40778i	0.710307	−	0.703892i	$-0.248556\pi$
$440$		0			0
$441$	−1.15105e10			−0.304326
$442$	1.14825e11	+	1.14825e11i	3.00848	+	3.00848i
$443$	4.02212e10	−	4.02212e10i	1.04434	−	1.04434i	0.0453655	−	0.998970i	$-0.485555\pi$
$443$	4.02212e10	−	4.02212e10i	1.04434	−	1.04434i	0.998970	−	0.0453655i	$-0.0144452\pi$
$444$			4.75553e10i			1.22368i
$445$		0			0
$446$	3.33876e10			0.843813
$447$	−2.08902e10	−	2.08902e10i	−0.523254	−	0.523254i
$448$	5.55015e9	−	5.55015e9i	0.137782	−	0.137782i
$449$			3.92922e10i			0.966766i	0.875409	+	0.483383i	$0.160592\pi$
$449$			3.92922e10i			0.966766i	−0.875409	+	0.483383i	$0.839408\pi$
$450$		0			0
$451$	−2.47374e10			−0.597927
$452$	4.47831e10	+	4.47831e10i	1.07290	+	1.07290i
$453$	1.38710e10	−	1.38710e10i	0.329394	−	0.329394i
$454$			4.40687e10i			1.03731i
$455$		0			0
$456$	−9.52651e10			−2.20331
$457$	−2.88222e10	−	2.88222e10i	−0.660789	−	0.660789i	0.294777	−	0.955566i	$-0.404755\pi$
$457$	−2.88222e10	−	2.88222e10i	−0.660789	−	0.660789i	−0.955566	+	0.294777i	$0.904755\pi$
$458$	4.73484e9	−	4.73484e9i	0.107608	−	0.107608i
$459$		−	9.94989e9i		−	0.224165i
$460$		0			0
$461$	1.10771e10			0.245258			0.122629	−	0.992453i	$-0.460868\pi$
$461$	1.10771e10			0.245258			0.122629	+	0.992453i	$0.460868\pi$
$462$	−1.49195e10	−	1.49195e10i	−0.327481	−	0.327481i
$463$	5.95450e10	−	5.95450e10i	1.29575	−	1.29575i	0.364578	−	0.931173i	$-0.381213\pi$
$463$	5.95450e10	−	5.95450e10i	1.29575	−	1.29575i	0.931173	−	0.364578i	$-0.118787\pi$
$464$			9.63064e10i			2.07770i
$465$		0			0
$466$	6.00658e10			1.27375
$467$	1.38247e10	+	1.38247e10i	0.290661	+	0.290661i	0.837342	−	0.546680i	$-0.184109\pi$
$467$	1.38247e10	+	1.38247e10i	0.290661	+	0.290661i	−0.546680	+	0.837342i	$0.684109\pi$
$468$	5.32103e10	−	5.32103e10i	1.10921	−	1.10921i
$469$			1.27701e10i			0.263939i
$470$		0			0
$471$	−2.81142e10			−0.571272
$472$	1.13095e11	+	1.13095e11i	2.27863	+	2.27863i
$473$	1.01998e10	−	1.01998e10i	0.203774	−	0.203774i
$474$			7.14187e10i			1.41481i
$475$		0			0
$476$	4.16735e10			0.811768
$477$	4.05675e9	+	4.05675e9i	0.0783619	+	0.0783619i
$478$	3.12122e10	−	3.12122e10i	0.597878	−	0.597878i
$479$			1.20326e10i			0.228568i	0.993448	+	0.114284i	$0.0364574\pi$
$479$			1.20326e10i			0.228568i	−0.993448	+	0.114284i	$0.963543\pi$
$480$		0			0
$481$	−9.56592e10			−1.78709
$482$	−9.21744e10	−	9.21744e10i	−1.70774	−	1.70774i
$483$	4.13662e9	−	4.13662e9i	0.0760075	−	0.0760075i
$484$			1.55445e11i			2.83267i
$485$		0			0
$486$	−6.56252e9			−0.117632
$487$	−1.79336e10	−	1.79336e10i	−0.318824	−	0.318824i	0.529491	−	0.848315i	$-0.322383\pi$
$487$	−1.79336e10	−	1.79336e10i	−0.318824	−	0.318824i	−0.848315	+	0.529491i	$0.822383\pi$
$488$	6.91731e10	−	6.91731e10i	1.21971	−	1.21971i
$489$			3.84247e10i			0.672009i
$490$		0			0
$491$	−1.53544e10			−0.264184			−0.132092	−	0.991237i	$-0.542169\pi$
$491$	−1.53544e10			−0.264184			−0.132092	+	0.991237i	$0.542169\pi$
$492$	−2.27867e10	−	2.27867e10i	−0.388885	−	0.388885i
$493$	−4.55610e10	+	4.55610e10i	−0.771269	+	0.771269i
$494$		−	3.32278e11i		−	5.57949i
$495$		0			0
$496$	−3.60201e10			−0.595138
$497$	1.36451e10	+	1.36451e10i	0.223641	+	0.223641i
$498$	1.54228e10	−	1.54228e10i	0.250754	−	0.250754i
$499$		−	1.11301e11i		−	1.79514i	−0.440877	−	0.897568i	$-0.645332\pi$
$499$		−	1.11301e11i		−	1.79514i	0.440877	−	0.897568i	$-0.354668\pi$
$500$		0			0
$501$	5.60884e10			0.890271
$502$	−5.70658e10	−	5.70658e10i	−0.898588	−	0.898588i
$503$	−3.95707e10	+	3.95707e10i	−0.618161	+	0.618161i	−0.945060	−	0.326898i	$-0.893997\pi$
$503$	−3.95707e10	+	3.95707e10i	−0.618161	+	0.618161i	0.326898	+	0.945060i	$0.393997\pi$
$504$		−	1.58516e10i		−	0.245669i
$505$		0			0
$506$	−1.12502e11			−1.71617
$507$	8.00597e10	+	8.00597e10i	1.21166	+	1.21166i
$508$	3.84755e9	−	3.84755e9i	0.0577736	−	0.0577736i
$509$			3.77916e10i			0.563021i	0.959558	+	0.281510i	$0.0908354\pi$
$509$			3.77916e10i			0.563021i	−0.959558	+	0.281510i	$0.909165\pi$
$510$		0			0
$511$	−2.23734e10			−0.328132
$512$	1.00067e11	+	1.00067e11i	1.45617	+	1.45617i
$513$	−1.43964e10	+	1.43964e10i	−0.207867	+	0.207867i
$514$			7.97867e10i			1.14308i
$515$		0			0
$516$	1.87910e10			0.265064
$517$	−5.10563e10	−	5.10563e10i	−0.714640	−	0.714640i
$518$	−2.47066e10	+	2.47066e10i	−0.343158	+	0.343158i
$519$		−	1.74916e10i		−	0.241080i
$520$		0			0
$521$	−1.76695e9			−0.0239813			−0.0119906	−	0.999928i	$-0.503817\pi$
$521$	−1.76695e9			−0.0239813			−0.0119906	+	0.999928i	$0.503817\pi$
$522$	3.00501e10	+	3.00501e10i	0.404729	+	0.404729i
$523$	−9.19094e10	+	9.19094e10i	−1.22844	+	1.22844i	−0.263883	+	0.964555i	$0.585003\pi$
$523$	−9.19094e10	+	9.19094e10i	−1.22844	+	1.22844i	−0.964555	+	0.263883i	$0.914997\pi$
$524$		−	1.90742e11i		−	2.53001i
$525$		0			0
$526$	2.04816e11			2.67560
$527$	−1.70405e10	−	1.70405e10i	−0.220923	−	0.220923i
$528$	−1.04397e11	+	1.04397e11i	−1.34324	+	1.34324i
$529$			4.71184e10i			0.601683i
$530$		0			0
$531$	3.41816e10			0.429946
$532$	−6.02970e10	−	6.02970e10i	−0.752748	−	0.752748i
$533$	4.58363e10	−	4.58363e10i	0.567938	−	0.567938i
$534$			1.27327e11i			1.56587i
$535$		0			0
$536$	1.84501e11			2.23532
$537$	9.85487e9	+	9.85487e9i	0.118510	+	0.118510i
$538$	1.19069e11	−	1.19069e11i	1.42124	−	1.42124i
$539$			1.14270e11i			1.35387i
$540$		0			0
$541$	1.32264e11			1.54402			0.772012	−	0.635608i	$-0.219251\pi$
$541$	1.32264e11			1.54402			0.772012	+	0.635608i	$0.219251\pi$
$542$	1.36432e11	+	1.36432e11i	1.58096	+	1.58096i
$543$	2.49191e10	−	2.49191e10i	0.286637	−	0.286637i
$544$		−	1.60178e11i		−	1.82897i
$545$		0			0
$546$	5.52892e10			0.622113
$547$	4.16822e10	+	4.16822e10i	0.465587	+	0.465587i	0.900482	−	0.434894i	$-0.143214\pi$
$547$	4.16822e10	+	4.16822e10i	0.465587	+	0.465587i	−0.434894	+	0.900482i	$0.643214\pi$
$548$	−2.14900e11	+	2.14900e11i	−2.38294	+	2.38294i
$549$		−	2.09068e10i		−	0.230143i
$550$		0			0
$551$	1.31844e11			1.43039
$552$	−5.97652e10	−	5.97652e10i	−0.643713	−	0.643713i
$553$	−2.60695e10	+	2.60695e10i	−0.278762	+	0.278762i
$554$		−	1.52781e11i		−	1.62193i
$555$		0			0
$556$	−2.30513e11			−2.41210
$557$	8.23689e10	+	8.23689e10i	0.855742	+	0.855742i	0.990833	−	0.135091i	$-0.0431328\pi$
$557$	8.23689e10	+	8.23689e10i	0.855742	+	0.855742i	−0.135091	+	0.990833i	$0.543133\pi$
$558$	−1.12392e10	+	1.12392e10i	−0.115931	+	0.115931i
$559$			3.77988e10i			0.387107i
$560$		0			0
$561$	−9.87771e10			−0.997251
$562$	−1.83791e11	−	1.83791e11i	−1.84237	−	1.84237i
$563$	4.45418e9	−	4.45418e9i	0.0443338	−	0.0443338i	−0.684592	−	0.728926i	$-0.740020\pi$
$563$	4.45418e9	−	4.45418e9i	0.0443338	−	0.0443338i	0.728926	+	0.684592i	$0.240020\pi$
$564$		−	9.40604e10i		−	0.929588i
$565$		0			0
$566$	−5.85308e10			−0.570320
$567$	−2.39548e9	−	2.39548e9i	−0.0231772	−	0.0231772i
$568$	1.97142e11	−	1.97142e11i	1.89403	−	1.89403i
$569$			3.47830e10i			0.331832i	0.986140	+	0.165916i	$0.0530581\pi$
$569$			3.47830e10i			0.331832i	−0.986140	+	0.165916i	$0.946942\pi$
$570$		0			0
$571$	1.80714e10			0.169999			0.0849997	−	0.996381i	$-0.472911\pi$
$571$	1.80714e10			0.169999			0.0849997	+	0.996381i	$0.472911\pi$
$572$	−5.28243e11	−	5.28243e11i	−4.93457	−	4.93457i
$573$	−5.22285e10	+	5.22285e10i	−0.484495	+	0.484495i
$574$		−	2.36770e10i		−	0.218111i
$575$		0			0
$576$	−2.42359e10			−0.220175
$577$	−1.05281e11	−	1.05281e11i	−0.949829	−	0.949829i	0.0489712	−	0.998800i	$-0.484406\pi$
$577$	−1.05281e11	−	1.05281e11i	−0.949829	−	0.949829i	−0.998800	+	0.0489712i	$0.984406\pi$
$578$	5.16279e10	−	5.16279e10i	0.462565	−	0.462565i
$579$		−	8.03910e10i		−	0.715309i
$580$		0			0
$581$	1.12594e10			0.0988125
$582$	4.60305e10	+	4.60305e10i	0.401193	+	0.401193i
$583$	4.02732e10	−	4.02732e10i	0.348612	−	0.348612i
$584$			3.23248e11i			2.77897i
$585$		0			0
$586$	1.72748e11			1.46495
$587$	8.18323e10	+	8.18323e10i	0.689243	+	0.689243i	0.962065	−	0.272822i	$-0.0879569\pi$
$587$	8.18323e10	+	8.18323e10i	0.689243	+	0.689243i	−0.272822	+	0.962065i	$0.587957\pi$
$588$	−1.05259e11	+	1.05259e11i	−0.880540	+	0.880540i
$589$			4.93116e10i			0.409720i
$590$		0			0
$591$	−6.74738e10			−0.553077
$592$	1.72881e11	+	1.72881e11i	1.40754	+	1.40754i
$593$	−3.31785e10	+	3.31785e10i	−0.268311	+	0.268311i	−0.828419	−	0.560108i	$-0.810759\pi$
$593$	−3.31785e10	+	3.31785e10i	−0.268311	+	0.268311i	0.560108	+	0.828419i	$0.310759\pi$
$594$			6.51491e10i			0.523315i
$595$		0			0
$596$	−3.82066e11			−3.02798
$597$	−1.45559e10	−	1.45559e10i	−0.114588	−	0.114588i
$598$	2.08457e11	−	2.08457e11i	1.63009	−	1.63009i
$599$			2.43022e11i			1.88772i	0.330342	+	0.943861i	$0.392836\pi$
$599$			2.43022e11i			1.88772i	−0.330342	+	0.943861i	$0.607164\pi$
$600$		0			0
$601$	−7.30867e10			−0.560197			−0.280098	−	0.959971i	$-0.590367\pi$
$601$	−7.30867e10			−0.560197			−0.280098	+	0.959971i	$0.590367\pi$
$602$	9.76258e9	+	9.76258e9i	0.0743325	+	0.0743325i
$603$	2.78817e10	−	2.78817e10i	0.210887	−	0.210887i
$604$		−	2.53690e11i		−	1.90614i
$605$		0			0
$606$	9.73858e10			0.722113
$607$	8.85735e9	+	8.85735e9i	0.0652453	+	0.0652453i	0.738976	−	0.673731i	$-0.235309\pi$
$607$	8.85735e9	+	8.85735e9i	0.0652453	+	0.0652453i	−0.673731	+	0.738976i	$0.735309\pi$
$608$	−2.31760e11	+	2.31760e11i	−1.69599	+	1.69599i
$609$			2.19380e10i			0.159488i
$610$		0			0
$611$	1.89206e11			1.35759
$612$	−9.09879e10	−	9.09879e10i	−0.648602	−	0.648602i
$613$	−3.84955e10	+	3.84955e10i	−0.272627	+	0.272627i	−0.830157	−	0.557530i	$-0.811749\pi$
$613$	−3.84955e10	+	3.84955e10i	−0.272627	+	0.272627i	0.557530	+	0.830157i	$0.311749\pi$
$614$			2.61011e11i			1.83648i
$615$		0			0
$616$	−1.57366e11			−1.09292
$617$	4.36592e10	+	4.36592e10i	0.301255	+	0.301255i	0.841505	−	0.540249i	$-0.181670\pi$
$617$	4.36592e10	+	4.36592e10i	0.301255	+	0.301255i	−0.540249	+	0.841505i	$0.681670\pi$
$618$	6.74725e8	−	6.74725e8i	0.00462565	−	0.00462565i
$619$			1.33280e11i			0.907824i	0.891046	+	0.453912i	$0.149972\pi$
$619$			1.33280e11i			0.907824i	−0.891046	+	0.453912i	$0.850028\pi$
$620$		0			0
$621$	−1.80634e10			−0.121460
$622$	−1.63471e11	−	1.63471e11i	−1.09214	−	1.09214i
$623$	−4.64776e10	+	4.64776e10i	−0.308526	+	0.308526i
$624$		−	3.86877e11i		−	2.55173i
$625$		0			0
$626$	−3.90913e11			−2.54555
$627$	1.42920e11	+	1.42920e11i	0.924745	+	0.924745i
$628$	−2.57094e11	+	2.57094e11i	−1.65293	+	1.65293i
$629$			1.63574e11i			1.04499i
$630$		0			0
$631$	−6.53879e10			−0.412458			−0.206229	−	0.978504i	$-0.566119\pi$
$631$	−6.53879e10			−0.412458			−0.206229	+	0.978504i	$0.566119\pi$
$632$	3.76649e11	+	3.76649e11i	2.36085	+	2.36085i
$633$	1.90050e10	−	1.90050e10i	0.118373	−	0.118373i
$634$			1.89195e11i			1.17099i
$635$		0			0
$636$	7.41949e10			0.453467
$637$	−2.11732e11	−	2.11732e11i	−1.28596	−	1.28596i
$638$	2.98321e11	−	2.98321e11i	1.80053	−	1.80053i
$639$		−	5.95841e10i		−	0.357377i
$640$		0			0
$641$	2.99872e11			1.77625			0.888125	−	0.459602i	$-0.152008\pi$
$641$	2.99872e11			1.77625			0.888125	+	0.459602i	$0.152008\pi$
$642$	−4.99463e9	−	4.99463e9i	−0.0294011	−	0.0294011i
$643$	−1.61243e11	+	1.61243e11i	−0.943273	+	0.943273i	−0.998475	−	0.0552024i	$-0.982420\pi$
$643$	−1.61243e11	+	1.61243e11i	−0.943273	+	0.943273i	0.0552024	+	0.998475i	$0.482420\pi$
$644$		−	7.56555e10i		−	0.439843i
$645$		0			0
$646$	−5.68185e11			−3.26257
$647$	1.56973e11	+	1.56973e11i	0.895793	+	0.895793i	0.995061	−	0.0992682i	$-0.0316502\pi$
$647$	1.56973e11	+	1.56973e11i	0.895793	+	0.895793i	−0.0992682	+	0.995061i	$0.531650\pi$
$648$	−3.46095e10	+	3.46095e10i	−0.196289	+	0.196289i
$649$		−	3.39336e11i		−	1.91272i
$650$		0			0
$651$	−8.20515e9			−0.0456839
$652$	3.51379e11	+	3.51379e11i	1.94440	+	1.94440i
$653$	−2.24110e11	+	2.24110e11i	−1.23256	+	1.23256i	−0.269582	+	0.962977i	$0.586886\pi$
$653$	−2.24110e11	+	2.24110e11i	−1.23256	+	1.23256i	−0.962977	+	0.269582i	$0.913114\pi$
$654$			2.27869e11i			1.24559i
$655$		0			0
$656$	−1.65676e11			−0.894631
$657$	4.88490e10	+	4.88490e10i	0.262177	+	0.262177i
$658$	4.88676e10	−	4.88676e10i	0.260686	−	0.260686i
$659$		−	1.39657e11i		−	0.740495i	−0.928933	−	0.370248i	$-0.879273\pi$
$659$		−	1.39657e11i		−	0.740495i	0.928933	−	0.370248i	$-0.120727\pi$
$660$		0			0
$661$	2.16936e11			1.13639			0.568194	−	0.822895i	$-0.307642\pi$
$661$	2.16936e11			1.13639			0.568194	+	0.822895i	$0.307642\pi$
$662$	−2.66360e11	−	2.66360e11i	−1.38688	−	1.38688i
$663$	1.83025e11	−	1.83025e11i	0.947234	−	0.947234i
$664$		−	1.62675e11i		−	0.836850i
$665$		0			0
$666$	1.07887e11			0.548366
$667$	8.27131e10	+	8.27131e10i	0.417899	+	0.417899i
$668$	5.12907e11	−	5.12907e11i	2.57592	−	2.57592i
$669$		−	5.32183e10i		−	0.265679i
$670$		0			0
$671$	−2.07551e11			−1.02385
$672$	−3.85635e10	−	3.85635e10i	−0.189103	−	0.189103i
$673$	−2.32807e11	+	2.32807e11i	−1.13484	+	1.13484i	−0.145482	+	0.989361i	$0.546473\pi$
$673$	−2.32807e11	+	2.32807e11i	−1.13484	+	1.13484i	−0.989361	+	0.145482i	$0.953527\pi$
$674$		−	4.91016e11i		−	2.37934i
$675$		0			0
$676$	1.46423e12			7.01169
$677$	−1.47111e11	−	1.47111e11i	−0.700310	−	0.700310i	0.264167	−	0.964477i	$-0.414903\pi$
$677$	−1.47111e11	−	1.47111e11i	−0.700310	−	0.700310i	−0.964477	+	0.264167i	$0.914903\pi$
$678$	1.01597e11	−	1.01597e11i	0.480799	−	0.480799i
$679$			3.36045e10i			0.158095i
$680$		0			0
$681$	7.02435e10			0.326601
$682$	1.11577e11	+	1.11577e11i	0.515746	+	0.515746i
$683$	2.70763e11	−	2.70763e11i	1.24425	−	1.24425i	0.286027	−	0.958221i	$-0.407665\pi$
$683$	2.70763e11	−	2.70763e11i	1.24425	−	1.24425i	0.958221	−	0.286027i	$-0.0923348\pi$
$684$			2.63299e11i			1.20289i
$685$		0			0
$686$	−2.29167e11			−1.03480
$687$	−7.54711e9	−	7.54711e9i	−0.0338808	−	0.0338808i
$688$	6.83121e10	−	6.83121e10i	0.304891	−	0.304891i
$689$			1.49246e11i			0.662254i
$690$		0			0
$691$	−1.55828e11			−0.683492			−0.341746	−	0.939792i	$-0.611018\pi$
$691$	−1.55828e11			−0.683492			−0.341746	+	0.939792i	$0.611018\pi$
$692$	−1.59954e11	−	1.59954e11i	−0.697544	−	0.697544i
$693$	−2.37810e10	+	2.37810e10i	−0.103109	+	0.103109i
$694$			2.59955e11i			1.12063i
$695$		0			0
$696$	3.16958e11			1.35072
$697$	−7.83786e10	−	7.83786e10i	−0.332098	−	0.332098i
$698$	−2.61741e11	+	2.61741e11i	−1.10268	+	1.10268i
$699$		−	9.57422e10i		−	0.401046i
$700$		0			0
$701$	−2.09533e11			−0.867722			−0.433861	−	0.900980i	$-0.642849\pi$
$701$	−2.09533e11			−0.867722			−0.433861	+	0.900980i	$0.642849\pi$
$702$	−1.20716e11	−	1.20716e11i	−0.497068	−	0.497068i
$703$	2.36674e11	−	2.36674e11i	0.969013	−	0.969013i
$704$			2.40600e11i			0.979503i
$705$		0			0
$706$	2.69392e11			1.08434
$707$	3.55482e10	+	3.55482e10i	0.142279	+	0.142279i
$708$	3.12577e11	−	3.12577e11i	1.24401	−	1.24401i
$709$			2.13237e11i			0.843875i	0.906625	+	0.421937i	$0.138650\pi$
$709$			2.13237e11i			0.843875i	−0.906625	+	0.421937i	$0.861350\pi$
$710$		0			0
$711$	1.13838e11			0.445460
$712$	6.71502e11	+	6.71502e11i	2.61293	+	2.61293i
$713$	−3.09360e10	+	3.09360e10i	−0.119703	+	0.119703i
$714$		−	9.45427e10i		−	0.363777i
$715$		0			0
$716$	1.80238e11			0.685795
$717$	−4.97508e10	−	4.97508e10i	−0.188245	−	0.188245i
$718$	2.47587e11	−	2.47587e11i	0.931601	−	0.931601i
$719$		−	3.49495e11i		−	1.30775i	−0.756602	−	0.653876i	$-0.773142\pi$
$719$		−	3.49495e11i		−	1.30775i	0.756602	−	0.653876i	$-0.226858\pi$
$720$		0			0
$721$	4.92582e8			0.00182279
$722$	4.69763e11	+	4.69763e11i	1.72874	+	1.72874i
$723$	−1.46922e11	+	1.46922e11i	−0.537691	+	0.537691i
$724$		−	4.55751e11i		−	1.65872i
$725$		0			0
$726$	3.52652e11			1.26940
$727$	2.45105e11	+	2.45105e11i	0.877433	+	0.877433i	0.993268	−	0.115835i	$-0.0369545\pi$
$727$	2.45105e11	+	2.45105e11i	0.877433	+	0.877433i	−0.115835	+	0.993268i	$0.536955\pi$
$728$	2.91585e11	−	2.91585e11i	1.03810	−	1.03810i
$729$			1.04604e10i			0.0370370i
$730$		0			0
$731$	6.46347e10			0.226358
$732$	−1.91185e11	−	1.91185e11i	−0.665900	−	0.665900i
$733$	−3.63926e11	+	3.63926e11i	−1.26066	+	1.26066i	−0.309884	+	0.950774i	$0.600290\pi$
$733$	−3.63926e11	+	3.63926e11i	−1.26066	+	1.26066i	−0.950774	+	0.309884i	$0.899710\pi$
$734$		−	5.22979e11i		−	1.80177i
$735$		0			0
$736$	−2.90792e11			−0.990996
$737$	−2.76794e11	−	2.76794e11i	−0.938182	−	0.938182i
$738$	−5.16952e10	+	5.16952e10i	−0.174271	+	0.174271i
$739$		−	2.83756e11i		−	0.951409i	−0.879605	−	0.475705i	$-0.842193\pi$
$739$		−	2.83756e11i		−	0.951409i	0.879605	−	0.475705i	$-0.157807\pi$
$740$		0			0
$741$	−5.29636e11			−1.75673
$742$	3.85468e10	+	3.85468e10i	0.127166	+	0.127166i
$743$	−1.40362e11	+	1.40362e11i	−0.460570	+	0.460570i	−0.898842	−	0.438273i	$-0.855590\pi$
$743$	−1.40362e11	+	1.40362e11i	−0.460570	+	0.460570i	0.438273	+	0.898842i	$0.355590\pi$
$744$			1.18547e11i			0.386900i
$745$		0			0
$746$	−7.51624e11			−2.42686
$747$	−2.45833e10	−	2.45833e10i	−0.0789510	−	0.0789510i
$748$	−9.03278e11	+	9.03278e11i	−2.88546	+	2.88546i
$749$		−	3.64632e9i		−	0.0115858i
$750$		0			0
$751$	−4.12133e11			−1.29562			−0.647810	−	0.761802i	$-0.724315\pi$
$751$	−4.12133e11			−1.29562			−0.647810	+	0.761802i	$0.724315\pi$
$752$	−3.41944e11	−	3.41944e11i	−1.06926	−	1.06926i
$753$	−9.09602e10	+	9.09602e10i	−0.282925	+	0.282925i
$754$			1.10553e12i			3.42046i
$755$		0			0
$756$	−4.38115e10			−0.134122
$757$	3.47254e10	+	3.47254e10i	0.105746	+	0.105746i	0.758000	−	0.652254i	$-0.226177\pi$
$757$	3.47254e10	+	3.47254e10i	0.105746	+	0.105746i	−0.652254	+	0.758000i	$0.726177\pi$
$758$	−1.61514e11	+	1.61514e11i	−0.489252	+	0.489252i
$759$			1.79323e11i			0.540343i
$760$		0			0
$761$	1.97925e11			0.590148			0.295074	−	0.955474i	$-0.404656\pi$
$761$	1.97925e11			0.590148			0.295074	+	0.955474i	$0.404656\pi$
$762$	−8.72876e9	−	8.72876e9i	−0.0258900	−	0.0258900i
$763$	−8.31777e10	+	8.31777e10i	−0.245419	+	0.245419i
$764$			9.55220e11i			2.80369i
$765$		0			0
$766$	−1.63266e11			−0.474222
$767$	6.28760e11	+	6.28760e11i	1.81679	+	1.81679i
$768$	1.87308e11	−	1.87308e11i	0.538408	−	0.538408i
$769$		−	6.78277e11i		−	1.93955i	−0.243993	−	0.969777i	$-0.578457\pi$
$769$		−	6.78277e11i		−	1.93955i	0.243993	−	0.969777i	$-0.421543\pi$
$770$		0			0
$771$	1.27176e11			0.359906
$772$	−7.35145e11	−	7.35145e11i	−2.06968	−	2.06968i
$773$	2.58406e11	−	2.58406e11i	0.723743	−	0.723743i	−0.245622	−	0.969366i	$-0.578992\pi$
$773$	2.58406e11	−	2.58406e11i	0.723743	−	0.723743i	0.969366	+	0.245622i	$0.0789923\pi$
$774$		−	4.26303e10i		−	0.118783i
$775$		0			0
$776$	4.85513e11			1.33892
$777$	3.93812e10	+	3.93812e10i	0.108045	+	0.108045i
$778$	3.30020e8	−	3.30020e8i	0.000900786	−	0.000900786i
$779$			2.26811e11i			0.615905i
$780$		0			0
$781$	−5.91518e11			−1.58988
$782$	−3.56455e11	−	3.56455e11i	−0.953186	−	0.953186i
$783$	4.78985e10	−	4.78985e10i	0.127431	−	0.127431i
$784$			7.65307e11i			2.02568i
$785$		0			0
$786$	−4.32728e11			−1.13377
$787$	−8.65883e10	−	8.65883e10i	−0.225715	−	0.225715i	0.585185	−	0.810900i	$-0.301022\pi$
$787$	−8.65883e10	−	8.65883e10i	−0.225715	−	0.225715i	−0.810900	+	0.585185i	$0.801022\pi$
$788$	−6.17022e11	+	6.17022e11i	−1.60028	+	1.60028i
$789$		−	3.26468e11i		−	0.842427i
$790$		0			0
$791$	7.41710e10			0.189465
$792$	3.43585e11	+	3.43585e11i	0.873239	+	0.873239i
$793$	3.84575e11	−	3.84575e11i	0.972497	−	0.972497i
$794$			2.55887e11i			0.643823i
$795$		0			0
$796$	−2.66216e11			−0.663103
$797$	−4.85022e11	−	4.85022e11i	−1.20207	−	1.20207i	−0.973537	−	0.228528i	$-0.926609\pi$
$797$	−4.85022e11	−	4.85022e11i	−1.20207	−	1.20207i	−0.228528	−	0.973537i	$-0.573391\pi$
$798$	−1.36793e11	+	1.36793e11i	−0.337328	+	0.337328i
$799$		−	3.23536e11i		−	0.793845i
$800$		0			0
$801$	2.02954e11			0.493023
$802$	−7.55900e11	−	7.55900e11i	−1.82712	−	1.82712i
$803$	4.84947e11	−	4.84947e11i	1.16636	−	1.16636i
$804$		−	5.09935e11i		−	1.22037i
$805$		0			0
$806$	−4.13484e11			−0.979756
$807$	−1.89790e11	−	1.89790e11i	−0.447486	−	0.447486i
$808$	5.13595e11	−	5.13595e11i	1.20497	−	1.20497i
$809$			1.00259e11i			0.234061i	0.993128	+	0.117031i	$0.0373376\pi$
$809$			1.00259e11i			0.234061i	−0.993128	+	0.117031i	$0.962662\pi$
$810$		0			0
$811$	1.53883e11			0.355720			0.177860	−	0.984056i	$-0.443083\pi$
$811$	1.53883e11			0.355720			0.177860	+	0.984056i	$0.443083\pi$
$812$	2.00615e11	+	2.00615e11i	0.461465	+	0.461465i
$813$	2.17467e11	−	2.17467e11i	0.497772	−	0.497772i
$814$		−	1.07104e12i		−	2.43954i
$815$		0			0
$816$	−6.61548e11			−1.49211
$817$	−9.35195e10	−	9.35195e10i	−0.209901	−	0.209901i
$818$	−1.76358e11	+	1.76358e11i	−0.393895	+	0.393895i
$819$		−	8.81283e10i		−	0.195875i
$820$		0			0
$821$	−5.31945e11			−1.17083			−0.585415	−	0.810734i	$-0.699068\pi$
$821$	−5.31945e11			−1.17083			−0.585415	+	0.810734i	$0.699068\pi$
$822$	4.87533e11	+	4.87533e11i	1.06787	+	1.06787i
$823$	4.68766e11	−	4.68766e11i	1.02178	−	1.02178i	0.0220206	−	0.999758i	$-0.492990\pi$
$823$	4.68766e11	−	4.68766e11i	1.02178	−	1.02178i	0.999758	−	0.0220206i	$-0.00700993\pi$
$824$		−	7.11676e9i		−	0.0154374i
$825$		0			0
$826$	3.24789e11			0.697721
$827$	−1.34620e11	−	1.34620e11i	−0.287799	−	0.287799i	0.548410	−	0.836209i	$-0.315233\pi$
$827$	−1.34620e11	−	1.34620e11i	−0.287799	−	0.287799i	−0.836209	+	0.548410i	$0.815233\pi$
$828$	−1.65183e11	+	1.65183e11i	−0.351434	+	0.351434i
$829$		−	7.07602e9i		−	0.0149820i	−0.999972	−	0.00749102i	$-0.997616\pi$
$829$		−	7.07602e9i		−	0.0149820i	0.999972	−	0.00749102i	$-0.00238449\pi$
$830$		0			0
$831$	−2.43527e11			−0.510672
$832$	−4.45812e11	−	4.45812e11i	−0.930376	−	0.930376i
$833$	−3.62055e11	+	3.62055e11i	−0.751959	+	0.751959i
$834$			5.22953e11i			1.08093i
$835$		0			0
$836$	2.61389e12			5.35134
$837$	1.79147e10	+	1.79147e10i	0.0365013	+	0.0365013i
$838$	−5.47861e11	+	5.47861e11i	−1.11095	+	1.11095i
$839$			8.46023e11i			1.70740i	0.520768	+	0.853698i	$0.325646\pi$
$839$			8.46023e11i			1.70740i	−0.520768	+	0.853698i	$0.674354\pi$
$840$		0			0
$841$	6.15874e10			0.123114
$842$	−1.24294e11	−	1.24294e11i	−0.247288	−	0.247288i
$843$	−2.92954e11	+	2.92954e11i	−0.580081	+	0.580081i
$844$		−	3.47587e11i		−	0.685004i
$845$		0			0
$846$	−2.13391e11			−0.416576
$847$	1.28726e11	+	1.28726e11i	0.250112	+	0.250112i
$848$	2.69725e11	−	2.69725e11i	0.521600	−	0.521600i
$849$			9.32954e10i			0.179568i
$850$		0			0
$851$	2.96958e11			0.566210
$852$	−5.44874e11	−	5.44874e11i	−1.03404	−	1.03404i
$853$	4.26080e11	−	4.26080e11i	0.804814	−	0.804814i	−0.179030	−	0.983844i	$-0.557296\pi$
$853$	4.26080e11	−	4.26080e11i	0.804814	−	0.804814i	0.983844	+	0.179030i	$0.0572959\pi$
$854$		−	1.98654e11i		−	0.373479i
$855$		0			0
$856$	−5.26815e10			−0.0981213
$857$	−3.58066e11	−	3.58066e11i	−0.663804	−	0.663804i	0.292470	−	0.956275i	$-0.405523\pi$
$857$	−3.58066e11	−	3.58066e11i	−0.663804	−	0.663804i	−0.956275	+	0.292470i	$0.905523\pi$
$858$	−1.19840e12	+	1.19840e12i	−2.21133	+	2.21133i
$859$			8.56693e11i			1.57345i	0.617305	+	0.786724i	$0.288224\pi$
$859$			8.56693e11i			1.57345i	−0.617305	+	0.786724i	$0.711776\pi$
$860$		0			0
$861$	−3.77400e10			−0.0686735
$862$	7.41694e11	+	7.41694e11i	1.34337	+	1.34337i
$863$	−4.52360e11	+	4.52360e11i	−0.815532	+	0.815532i	−0.985457	−	0.169925i	$-0.945647\pi$
$863$	−4.52360e11	+	4.52360e11i	−0.815532	+	0.815532i	0.169925	+	0.985457i	$0.445647\pi$
$864$			1.68395e11i			0.302187i
$865$		0			0
$866$	1.28146e12			2.27843
$867$	−8.22925e10	−	8.22925e10i	−0.145641	−	0.145641i
$868$	−7.50330e10	+	7.50330e10i	−0.132182	+	0.132182i
$869$		−	1.13012e12i		−	1.98174i
$870$		0			0
$871$	1.02575e12			1.78225
$872$	1.20174e12	+	1.20174e12i	2.07847	+	2.07847i
$873$	7.33704e10	−	7.33704e10i	0.126318	−	0.126318i
$874$			1.03150e12i			1.76777i
$875$		0			0
$876$	8.93412e11			1.51717
$877$	−2.10744e8	−	2.10744e8i	−0.000356251	−	0.000356251i	0.706929	−	0.707285i	$-0.250080\pi$
$877$	−2.10744e8	−	2.10744e8i	−0.000356251	−	0.000356251i	−0.707285	+	0.706929i	$0.750080\pi$
$878$	−1.08475e12	+	1.08475e12i	−1.82537	+	1.82537i
$879$		−	2.75352e11i		−	0.461247i
$880$		0			0
$881$	1.39094e11			0.230890			0.115445	−	0.993314i	$-0.463171\pi$
$881$	1.39094e11			0.230890			0.115445	+	0.993314i	$0.463171\pi$
$882$	2.38796e11	+	2.38796e11i	0.394596	+	0.394596i
$883$	7.57608e11	−	7.57608e11i	1.24624	−	1.24624i	0.288874	−	0.957367i	$-0.406719\pi$
$883$	7.57608e11	−	7.57608e11i	1.24624	−	1.24624i	0.957367	−	0.288874i	$-0.0932808\pi$
$884$		−	3.34739e12i		−	5.48148i
$885$		0			0
$886$	−1.66886e12			−2.70822
$887$	1.38716e11	+	1.38716e11i	0.224095	+	0.224095i	0.810220	−	0.586125i	$-0.199347\pi$
$887$	1.38716e11	+	1.38716e11i	0.224095	+	0.224095i	−0.586125	+	0.810220i	$0.699347\pi$
$888$	5.68974e11	−	5.68974e11i	0.915041	−	0.915041i
$889$		−	6.37242e9i		−	0.0102023i
$890$		0			0
$891$	1.03845e11			0.164768
$892$	−4.86661e11	−	4.86661e11i	−0.768719	−	0.768719i
$893$	−4.68122e11	+	4.68122e11i	−0.736128	+	0.736128i
$894$			8.66776e11i			1.35693i
$895$		0			0
$896$	6.82566e10			0.105904
$897$	−3.32271e11	−	3.32271e11i	−0.513242	−	0.513242i
$898$	8.15155e11	−	8.15155e11i	1.25353	−	1.25353i
$899$		−	1.64065e11i		−	0.251176i
$900$		0			0
$901$	2.55205e11			0.387249
$902$	5.13201e11	+	5.13201e11i	0.775286	+	0.775286i
$903$	1.55611e10	−	1.55611e10i	0.0234040	−	0.0234040i
$904$		−	1.07161e12i		−	1.60459i
$905$		0			0
$906$	−5.75535e11			−0.854199
$907$	4.48232e11	+	4.48232e11i	0.662329	+	0.662329i	0.955928	−	0.293600i	$-0.0948533\pi$
$907$	4.48232e11	+	4.48232e11i	0.662329	+	0.662329i	−0.293600	+	0.955928i	$0.594853\pi$
$908$	6.42350e11	−	6.42350e11i	0.944993	−	0.944993i
$909$		−	1.55228e11i		−	0.227361i
$910$		0			0
$911$	−8.14598e11			−1.18269			−0.591344	−	0.806420i	$-0.701402\pi$
$911$	−8.14598e11			−1.18269			−0.591344	+	0.806420i	$0.701402\pi$
$912$	9.57188e11	+	9.57188e11i	1.38362	+	1.38362i
$913$	−2.44050e11	+	2.44050e11i	−0.351233	+	0.351233i
$914$			1.19589e12i			1.71359i
$915$		0			0
$916$	−1.38031e11			−0.196062
$917$	−1.57956e11	−	1.57956e11i	−0.223388	−	0.223388i
$918$	−2.06420e11	+	2.06420e11i	−0.290657	+	0.290657i
$919$			7.55454e11i			1.05912i	0.848272	+	0.529561i	$0.177643\pi$
$919$			7.55454e11i			1.05912i	−0.848272	+	0.529561i	$0.822357\pi$
$920$		0			0
$921$	4.16039e11			0.578224
$922$	−2.29805e11	−	2.29805e11i	−0.318007	−	0.318007i
$923$	1.09603e12	−	1.09603e12i	1.51014	−	1.51014i
$924$			4.34936e11i			0.596675i
$925$		0			0
$926$	−2.47064e12			−3.36020
$927$	−1.07548e9	−	1.07548e9i	−0.00145641	−	0.00145641i
$928$	7.71091e11	−	7.71091e11i	1.03971	−	1.03971i
$929$			5.33972e11i			0.716895i	0.933550	+	0.358448i	$0.116694\pi$
$929$			5.33972e11i			0.716895i	−0.933550	+	0.358448i	$0.883306\pi$
$930$		0			0
$931$	1.04771e12			1.39457
$932$	−8.75526e11	−	8.75526e11i	−1.16039	−	1.16039i
$933$	−2.60565e11	+	2.60565e11i	−0.343867	+	0.343867i
$934$		−	5.73613e11i		−	0.753757i
$935$		0			0
$936$	−1.27327e12			−1.65888
$937$	1.98156e11	+	1.98156e11i	0.257069	+	0.257069i	0.823861	−	0.566792i	$-0.191816\pi$
$937$	1.98156e11	+	1.98156e11i	0.257069	+	0.257069i	−0.566792	+	0.823861i	$0.691816\pi$
$938$	2.64928e11	−	2.64928e11i	0.342229	−	0.342229i
$939$			6.23096e11i			0.801480i
$940$		0			0
$941$	1.19574e12			1.52503			0.762513	−	0.646973i	$-0.223965\pi$
$941$	1.19574e12			1.52503			0.762513	+	0.646973i	$0.223965\pi$
$942$	5.83257e11	+	5.83257e11i	0.740724	+	0.740724i
$943$	−1.42291e11	+	1.42291e11i	−0.179942	+	0.179942i
$944$		−	2.27266e12i		−	2.86185i
$945$		0			0
$946$	−4.23210e11			−0.528435
$947$	1.49719e11	+	1.49719e11i	0.186156	+	0.186156i	0.794032	−	0.607876i	$-0.207978\pi$
$947$	1.49719e11	+	1.49719e11i	0.186156	+	0.186156i	−0.607876	+	0.794032i	$0.707978\pi$
$948$	1.04101e12	−	1.04101e12i	1.28890	−	1.28890i
$949$			1.79713e12i			2.21572i
$950$		0			0
$951$	3.01568e11			0.368691
$952$	−4.98601e11	−	4.98601e11i	−0.607023	−	0.607023i
$953$	−1.20373e11	+	1.20373e11i	−0.145934	+	0.145934i	−0.776299	−	0.630365i	$-0.782905\pi$
$953$	−1.20373e11	+	1.20373e11i	−0.145934	+	0.145934i	0.630365	+	0.776299i	$0.282905\pi$
$954$		−	1.68322e11i		−	0.203212i
$955$		0			0
$956$	−9.09904e11			−1.08934
$957$	−4.75510e11	−	4.75510e11i	−0.566907	−	0.566907i
$958$	2.49627e11	−	2.49627e11i	0.296367	−	0.296367i
$959$			3.55923e11i			0.420805i
$960$		0			0
$961$	−7.91528e11			−0.928053
$962$	1.98454e12	+	1.98454e12i	2.31718	+	2.31718i
$963$	−7.96121e9	+	7.96121e9i	−0.00925708	+	0.00925708i
$964$			2.68709e12i			3.11153i
$965$		0			0
$966$	−1.71636e11			−0.197106
$967$	2.58124e11	+	2.58124e11i	0.295204	+	0.295204i	0.839132	−	0.543928i	$-0.183063\pi$
$967$	2.58124e11	+	2.58124e11i	0.295204	+	0.295204i	−0.543928	+	0.839132i	$0.683063\pi$
$968$	1.85982e12	−	1.85982e12i	2.11821	−	2.11821i
$969$			9.05661e11i			1.02724i
$970$		0			0
$971$	2.08303e11			0.234325			0.117162	−	0.993113i	$-0.462620\pi$
$971$	2.08303e11			0.234325			0.117162	+	0.993113i	$0.462620\pi$
$972$	9.56559e10	+	9.56559e10i	0.107163	+	0.107163i
$973$	−1.90891e11	+	1.90891e11i	−0.212977	+	0.212977i
$974$			7.44100e11i			0.826790i
$975$		0			0
$976$	−1.39005e12			−1.53190
$977$	−9.96919e11	−	9.96919e11i	−1.09416	−	1.09416i	−0.995079	−	0.0990833i	$-0.968409\pi$
$977$	−9.96919e11	−	9.96919e11i	−1.09416	−	1.09416i	−0.0990833	−	0.995079i	$-0.531591\pi$
$978$	7.97158e11	−	7.97158e11i	0.871343	−	0.871343i
$979$		−	2.01482e12i		−	2.19333i
$980$		0			0
$981$	3.63213e11			0.392180
$982$	3.18542e11	+	3.18542e11i	0.342547	+	0.342547i
$983$	−1.06275e11	+	1.06275e11i	−0.113819	+	0.113819i	−0.761723	−	0.647903i	$-0.775646\pi$
$983$	−1.06275e11	+	1.06275e11i	−0.113819	+	0.113819i	0.647903	+	0.761723i	$0.275646\pi$
$984$			5.45262e11i			0.581601i
$985$		0			0
$986$	1.89042e12			2.00009
$987$	−7.78927e10	−	7.78927e10i	−0.0820783	−	0.0820783i
$988$	−4.84332e12	+	4.84332e12i	−5.08295	+	5.08295i
$989$		−	1.17340e11i		−	0.122648i
$990$		0			0
$991$	−1.44390e12			−1.49707			−0.748535	−	0.663095i	$-0.769242\pi$
$991$	−1.44390e12			−1.49707			−0.748535	+	0.663095i	$0.769242\pi$
$992$	2.88400e11	+	2.88400e11i	0.297816	+	0.297816i
$993$	−4.24566e11	+	4.24566e11i	−0.436665	+	0.436665i
$994$		−	5.66161e11i		−	0.579955i
$995$		0			0
$996$	−4.49610e11			−0.456876
$997$	−1.54092e11	−	1.54092e11i	−0.155955	−	0.155955i	0.624817	−	0.780772i	$-0.285174\pi$
$997$	−1.54092e11	−	1.54092e11i	−0.155955	−	0.155955i	−0.780772	+	0.624817i	$0.785174\pi$
$998$	−2.30905e12	+	2.30905e12i	−2.32761	+	2.32761i
$999$		−	1.71966e11i		−	0.172656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.f.d.7.1	✓	12
5.2	odd	4	inner	75.9.f.d.43.6	yes	12
5.3	odd	4	inner	75.9.f.d.43.1	yes	12
5.4	even	2	inner	75.9.f.d.7.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.9.f.d.7.1	✓	12	1.1	even	1	trivial
75.9.f.d.7.6	yes	12	5.4	even	2	inner
75.9.f.d.43.1	yes	12	5.3	odd	4	inner
75.9.f.d.43.6	yes	12	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-20.7460 - 20.7460i) q^{2} +(-33.0681 + 33.0681i) q^{3} +604.790i q^{4} +1372.06 q^{6} +(500.835 + 500.835i) q^{7} +(7236.00 - 7236.00i) q^{8} -2187.00i q^{9} +O(q^{10})\)	\(q+(-20.7460 - 20.7460i) q^{2} +(-33.0681 + 33.0681i) q^{3} +604.790i q^{4} +1372.06 q^{6} +(500.835 + 500.835i) q^{7} +(7236.00 - 7236.00i) q^{8} -2187.00i q^{9} -21711.3 q^{11} +(-19999.3 - 19999.3i) q^{12} +(40229.3 - 40229.3i) q^{13} -20780.6i q^{14} -145409. q^{16} +(-68790.7 - 68790.7i) q^{17} +(-45371.4 + 45371.4i) q^{18} +199066. i q^{19} -33123.3 q^{21} +(450423. + 450423. i) q^{22} +(-124885. + 124885. i) q^{23} +478561. i q^{24} -1.66919e6 q^{26} +(72320.0 + 72320.0i) q^{27} +(-302900. + 302900. i) q^{28} -662313. i q^{29} +247715. q^{31} +(1.16424e6 + 1.16424e6i) q^{32} +(717953. - 717953. i) q^{33} +2.85426e6i q^{34} +1.32268e6 q^{36} +(-1.18893e6 - 1.18893e6i) q^{37} +(4.12981e6 - 4.12981e6i) q^{38} +2.66061e6i q^{39} +1.13938e6 q^{41} +(687176. + 687176. i) q^{42} +(-469792. + 469792. i) q^{43} -1.31308e7i q^{44} +5.18173e6 q^{46} +(2.35160e6 + 2.35160e6i) q^{47} +(4.80841e6 - 4.80841e6i) q^{48} -5.26313e6i q^{49} +4.54956e6 q^{51} +(2.43303e7 + 2.43303e7i) q^{52} +(-1.85494e6 + 1.85494e6i) q^{53} -3.00070e6i q^{54} +7.24808e6 q^{56} +(-6.58272e6 - 6.58272e6i) q^{57} +(-1.37403e7 + 1.37403e7i) q^{58} +1.56294e7i q^{59} +9.55958e6 q^{61} +(-5.13909e6 - 5.13909e6i) q^{62} +(1.09533e6 - 1.09533e6i) q^{63} -1.10818e7i q^{64} -2.97893e7 q^{66} +(1.27488e7 + 1.27488e7i) q^{67} +(4.16040e7 - 4.16040e7i) q^{68} -8.25943e6i q^{69} +2.72447e7 q^{71} +(-1.58251e7 - 1.58251e7i) q^{72} +(-2.23361e7 + 2.23361e7i) q^{73} +4.93308e7i q^{74} -1.20393e8 q^{76} +(-1.08738e7 - 1.08738e7i) q^{77} +(5.51970e7 - 5.51970e7i) q^{78} +5.20522e7i q^{79} -4.78297e6 q^{81} +(-2.36375e7 - 2.36375e7i) q^{82} +(1.12407e7 - 1.12407e7i) q^{83} -2.00327e7i q^{84} +1.94926e7 q^{86} +(2.19015e7 + 2.19015e7i) q^{87} +(-1.57103e8 + 1.57103e8i) q^{88} +9.28002e7i q^{89} +4.02965e7 q^{91} +(-7.55294e7 - 7.55294e7i) q^{92} +(-8.19147e6 + 8.19147e6i) q^{93} -9.75723e7i q^{94} -7.69984e7 q^{96} +(3.35484e7 + 3.35484e7i) q^{97} +(-1.09189e8 + 1.09189e8i) q^{98} +4.74827e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2268 q^{6}+O(q^{10}) \) 12 * q + 2268 * q^6	\( 12 q + 2268 q^{6} - 88920 q^{11} - 485796 q^{16} + 79704 q^{21} - 4055976 q^{26} + 5658696 q^{31} + 5065092 q^{36} + 1798056 q^{41} - 10882464 q^{46} + 4329936 q^{51} + 7268040 q^{56} + 33649848 q^{61} - 141361848 q^{66} + 335506464 q^{71} - 395386536 q^{76} - 57395628 q^{81} + 489958560 q^{86} - 216875664 q^{91} - 710311356 q^{96}+O(q^{100}) \) 12 * q + 2268 * q^6 - 88920 * q^11 - 485796 * q^16 + 79704 * q^21 - 4055976 * q^26 + 5658696 * q^31 + 5065092 * q^36 + 1798056 * q^41 - 10882464 * q^46 + 4329936 * q^51 + 7268040 * q^56 + 33649848 * q^61 - 141361848 * q^66 + 335506464 * q^71 - 395386536 * q^76 - 57395628 * q^81 + 489958560 * q^86 - 216875664 * q^91 - 710311356 * q^96

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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