LMFDB - Embedded newform 75.9.f.d.43.1

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			43.1
Root			$-6.36871 + 6.36871i$ of defining polynomial
Character	$\chi$	$=$	75.43
Dual form			75.9.f.d.7.1

$q$-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 $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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	−0.366014	+	0.930610i	$0.619278\pi$
$2$	−20.7460	+	20.7460i	−1.29662	+	1.29662i	−0.930610	+	0.366014i	$0.880722\pi$
$3$	−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	−0.595075	−	0.803670i	$-0.702878\pi$
$7$	500.835	−	500.835i	0.208594	−	0.208594i	0.803670	+	0.595075i	$0.202878\pi$
$8$	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	0.767555	+	0.640983i	$0.221473\pi$
$13$	40229.3	+	40229.3i	1.40854	+	1.40854i	0.640983	+	0.767555i	$0.278527\pi$
$14$			20780.6i			0.540937i
$15$		0			0
$16$	−145409.			−2.21877
$17$	−68790.7	+	68790.7i	−0.823634	+	0.823634i	−0.986627	−	0.162993i	$-0.947885\pi$
$17$	−68790.7	+	68790.7i	−0.823634	+	0.823634i	0.162993	+	0.986627i	$0.447885\pi$
$18$	−45371.4	−	45371.4i	−0.432208	−	0.432208i
$19$		−	199066.i		−	1.52750i	−0.645511	−	0.763751i	$-0.723355\pi$
$19$		−	199066.i		−	1.52750i	0.645511	−	0.763751i	$-0.276645\pi$
$20$		0			0
$21$	−33123.3			−0.170317
$22$	450423.	−	450423.i	1.92278	−	1.92278i
$23$	−124885.	−	124885.i	−0.446272	−	0.446272i	0.447841	−	0.894113i	$-0.352193\pi$
$23$	−124885.	−	124885.i	−0.446272	−	0.446272i	−0.894113	+	0.447841i	$0.852193\pi$
$24$		−	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	$0.155101\pi$
$29$			662313.i			0.936422i	−0.883617	+	0.468211i	$0.844899\pi$
$30$		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	−0.949163	−	0.314785i	$-0.898067\pi$
$37$	−1.18893e6	+	1.18893e6i	−0.634378	+	0.634378i	0.314785	+	0.949163i	$0.398067\pi$
$38$	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	0.635054	−	0.772468i	$-0.280978\pi$
$43$	−469792.	−	469792.i	−0.137414	−	0.137414i	−0.772468	+	0.635054i	$0.780978\pi$
$44$			1.31308e7i			3.50333i
$45$		0			0
$46$	5.18173e6			1.15729
$47$	2.35160e6	−	2.35160e6i	0.481916	−	0.481916i	−0.423827	−	0.905743i	$-0.639314\pi$
$47$	2.35160e6	−	2.35160e6i	0.481916	−	0.481916i	0.905743	+	0.423827i	$0.139314\pi$
$48$	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	0.579726	−	0.814812i	$-0.303160\pi$
$53$	−1.85494e6	−	1.85494e6i	−0.235086	−	0.235086i	−0.814812	+	0.579726i	$0.803160\pi$
$54$			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	$-0.776891\pi$
$59$		−	1.56294e7i		−	1.28984i	0.764251	−	0.644919i	$-0.223109\pi$
$60$		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	−0.316074	−	0.948735i	$-0.602365\pi$
$67$	1.27488e7	−	1.27488e7i	0.632661	−	0.632661i	0.948735	+	0.316074i	$0.102365\pi$
$68$	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	0.194393	−	0.980924i	$-0.437726\pi$
$73$	−2.23361e7	−	2.23361e7i	−0.786531	−	0.786531i	−0.980924	+	0.194393i	$0.937726\pi$
$74$		−	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	$-0.767069\pi$
$79$		−	5.20522e7i		−	1.33638i	0.743990	−	0.668191i	$-0.232931\pi$
$80$		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	0.815546	−	0.578693i	$-0.196437\pi$
$83$	1.12407e7	+	1.12407e7i	0.236853	+	0.236853i	−0.578693	+	0.815546i	$0.696437\pi$
$84$			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	$-0.735045\pi$
$89$		−	9.28002e7i		−	1.47907i	0.673118	−	0.739535i	$-0.264955\pi$
$90$		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	−0.491771	−	0.870724i	$-0.663650\pi$
$97$	3.35484e7	−	3.35484e7i	0.378953	−	0.378953i	0.870724	+	0.491771i	$0.163650\pi$
$98$	−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	0.709288	−	0.704919i	$-0.249017\pi$
$103$	491761.	+	491761.i	0.00436923	+	0.00436923i	−0.704919	+	0.709288i	$0.749017\pi$
$104$			5.82198e8i			4.97665i
$105$		0			0
$106$	7.69650e7			0.609635
$107$	−3.64024e6	+	3.64024e6i	−0.0277712	+	0.0277712i	−0.720856	−	0.693085i	$-0.756251\pi$
$107$	−3.64024e6	+	3.64024e6i	−0.0277712	+	0.0277712i	0.693085	+	0.720856i	$0.256251\pi$
$108$	−4.37384e7	−	4.37384e7i	−0.321490	−	0.321490i
$109$		−	1.66078e8i		−	1.17654i	−0.808665	−	0.588269i	$-0.799809\pi$
$109$		−	1.66078e8i		−	1.17654i	0.808665	−	0.588269i	$-0.200191\pi$
$110$		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	0.896728	−	0.442582i	$-0.145937\pi$
$113$	7.40473e7	+	7.40473e7i	0.454146	+	0.454146i	−0.442582	+	0.896728i	$0.645937\pi$
$114$		−	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	−0.719228	−	0.694774i	$-0.755505\pi$
$127$	−6.36179e6	+	6.36179e6i	−0.0244548	+	0.0244548i	0.694774	+	0.719228i	$0.255505\pi$
$128$	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	0.00870703	−	0.999962i	$-0.497228\pi$
$137$	3.55329e8	−	3.55329e8i	1.00867	−	1.00867i	0.999962	−	0.00870703i	$-0.00277157\pi$
$138$	−1.71350e8	−	1.71350e8i	−0.472463	−	0.472463i
$139$		−	3.81144e8i		−	1.02101i	−0.859874	−	0.510506i	$-0.829458\pi$
$139$		−	3.81144e8i		−	1.02101i	0.859874	−	0.510506i	$-0.170542\pi$
$140$		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	$-0.778581\pi$
$149$		−	6.31733e8i		−	1.28171i	0.767663	−	0.640853i	$-0.221419\pi$
$150$		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	−0.264676	−	0.964338i	$-0.585265\pi$
$157$	4.25096e8	−	4.25096e8i	0.699662	−	0.699662i	0.964338	+	0.264676i	$0.0852649\pi$
$158$	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	0.986543	−	0.163503i	$-0.0522793\pi$
$163$	5.80994e8	+	5.80994e8i	0.823040	+	0.823040i	−0.163503	+	0.986543i	$0.552279\pi$
$164$		−	6.89084e8i		−	0.952570i
$165$		0			0
$166$	−4.66396e8			−0.614218
$167$	−8.48074e8	+	8.48074e8i	−1.09035	+	1.09035i	−0.0948643	+	0.995490i	$0.530242\pi$
$167$	−8.48074e8	+	8.48074e8i	−1.09035	+	1.09035i	−0.995490	+	0.0948643i	$0.969758\pi$
$168$	−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	0.543893	−	0.839155i	$-0.316950\pi$
$173$	−2.64479e8	−	2.64479e8i	−0.295261	−	0.295261i	−0.839155	+	0.543893i	$0.816950\pi$
$174$			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	$0.0463646\pi$
$179$			2.98017e8i			0.290288i	−0.989411	+	0.145144i	$0.953635\pi$
$180$		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	0.117055	−	0.993125i	$-0.462655\pi$
$193$	−1.21554e9	−	1.21554e9i	−0.876070	−	0.876070i	−0.993125	+	0.117055i	$0.962655\pi$
$194$			1.39199e9i			0.982718i
$195$		0			0
$196$	3.18309e9			2.15687
$197$	1.02022e9	−	1.02022e9i	0.677378	−	0.677378i	−0.282028	−	0.959406i	$-0.591007\pi$
$197$	1.02022e9	−	1.02022e9i	0.677378	−	0.677378i	0.959406	+	0.282028i	$0.0910072\pi$
$198$	9.85075e8	+	9.85075e8i	0.640927	+	0.640927i
$199$		−	4.40178e8i		−	0.280683i	−0.990103	−	0.140342i	$-0.955180\pi$
$199$		−	4.40178e8i		−	0.280683i	0.990103	−	0.140342i	$-0.0448201\pi$
$200$		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	0.525441	−	0.850830i	$-0.323900\pi$
$223$	−8.04678e8	−	8.04678e8i	−0.325389	−	0.325389i	−0.850830	+	0.525441i	$0.823900\pi$
$224$		−	1.16618e9i		−	0.463207i
$225$		0			0
$226$	−3.07237e9			−1.17771
$227$	−1.06210e9	+	1.06210e9i	−0.400003	+	0.400003i	−0.878234	−	0.478231i	$-0.841278\pi$
$227$	−1.06210e9	+	1.06210e9i	−0.400003	+	0.400003i	0.478231	+	0.878234i	$0.341278\pi$
$228$	3.98117e9	+	3.98117e9i	1.47323	+	1.47323i
$229$		−	2.28229e8i		−	0.0829907i	−0.999139	−	0.0414954i	$-0.986788\pi$
$229$		−	2.28229e8i		−	0.0829907i	0.999139	−	0.0414954i	$-0.0132122\pi$
$230$		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	0.417498	−	0.908678i	$-0.362907\pi$
$233$	−1.44765e9	−	1.44765e9i	−0.491179	−	0.491179i	−0.908678	+	0.417498i	$0.862907\pi$
$234$		−	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	$-0.925947\pi$
$239$		−	1.50449e9i		−	0.461104i	0.973060	−	0.230552i	$-0.0740532\pi$
$240$		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	−0.892278	−	0.451486i	$-0.850894\pi$
$257$	−1.92294e9	+	1.92294e9i	−0.440792	+	0.440792i	0.451486	+	0.892278i	$0.350894\pi$
$258$	−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	−0.999479	−	0.0322790i	$-0.989723\pi$
$263$	−4.93629e9	−	4.93629e9i	−1.03176	−	1.03176i	−0.0322790	−	0.999479i	$-0.510277\pi$
$264$			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	$-0.815368\pi$
$269$		−	5.73937e9i		−	1.09611i	0.836442	−	0.548056i	$-0.184632\pi$
$270$		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	−0.321475	−	0.946918i	$-0.604179\pi$
$277$	3.68220e9	−	3.68220e9i	0.625443	−	0.625443i	0.946918	+	0.321475i	$0.104179\pi$
$278$	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	0.808467	−	0.588542i	$-0.200298\pi$
$283$	1.41065e9	+	1.41065e9i	0.219925	+	0.219925i	−0.588542	+	0.808467i	$0.700298\pi$
$284$		−	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	0.365788	−	0.930698i	$-0.380799\pi$
$293$	−4.16341e9	−	4.16341e9i	−0.564910	−	0.564910i	−0.930698	+	0.365788i	$0.880799\pi$
$294$			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	−0.966152	−	0.257975i	$-0.916945\pi$
$307$	−6.29064e9	+	6.29064e9i	−0.708176	+	0.708176i	0.257975	+	0.966152i	$0.416945\pi$
$308$	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	0.999834	−	0.0182249i	$-0.00580148\pi$
$313$	9.42141e9	+	9.42141e9i	0.981609	+	0.981609i	−0.0182249	+	0.999834i	$0.505801\pi$
$314$			1.76380e10i			1.81440i
$315$		0			0
$316$	−3.14806e10			−3.15715
$317$	−4.55980e9	+	4.55980e9i	−0.451553	+	0.451553i	−0.895870	−	0.444317i	$-0.853446\pi$
$317$	−4.55980e9	+	4.55980e9i	−0.451553	+	0.451553i	0.444317	+	0.895870i	$0.353446\pi$
$318$	−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	−0.0793356	−	0.996848i	$-0.525280\pi$
$337$	1.18340e10	−	1.18340e10i	0.917512	−	0.917512i	0.996848	+	0.0793356i	$0.0252799\pi$
$338$	−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	−0.889353	−	0.457221i	$-0.848845\pi$
$347$	−6.26520e9	+	6.26520e9i	−0.432133	+	0.432133i	0.457221	+	0.889353i	$0.348845\pi$
$348$	−1.32458e10	−	1.32458e10i	−0.903152	−	0.903152i
$349$			1.26165e10i			0.850425i	0.905094	+	0.425212i	$0.139801\pi$
$349$			1.26165e10i			0.850425i	−0.905094	+	0.425212i	$0.860199\pi$
$350$		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	0.466422	−	0.884562i	$-0.345543\pi$
$353$	−6.49263e9	−	6.49263e9i	−0.418140	−	0.418140i	−0.884562	+	0.466422i	$0.845543\pi$
$354$		−	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	$-0.883036\pi$
$359$		−	1.19342e10i		−	0.718482i	0.933245	−	0.359241i	$-0.116964\pi$
$360$		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	−0.268488	−	0.963283i	$-0.586524\pi$
$367$	1.26044e10	−	1.26044e10i	0.694795	−	0.694795i	0.963283	+	0.268488i	$0.0865240\pi$
$368$	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	0.998062	−	0.0622229i	$-0.0198190\pi$
$373$	1.81149e10	+	1.81149e10i	0.935839	+	0.935839i	−0.0622229	+	0.998062i	$0.519819\pi$
$374$			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	$0.0604157\pi$
$379$			7.78531e9i			0.377328i	−0.982042	+	0.188664i	$0.939584\pi$
$380$		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	0.792604	−	0.609736i	$-0.208725\pi$
$383$	3.93489e9	+	3.93489e9i	0.182868	+	0.182868i	−0.609736	+	0.792604i	$0.708725\pi$
$384$		−	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	$-0.999889\pi$
$389$		−	1.59077e7i		−	0.000694717i	1.00000		0.000347358i	$-0.000110568\pi$
$390$		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	−0.820260	−	0.571991i	$-0.806171\pi$
$397$	−6.16715e9	+	6.16715e9i	−0.248269	+	0.248269i	0.571991	+	0.820260i	$0.306171\pi$
$398$	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	$0.0485368\pi$
$409$			8.50081e9i			0.303786i	−0.988397	+	0.151893i	$0.951463\pi$
$410$		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	$0.140923\pi$
$419$			2.64081e10i			0.856803i	−0.903589	+	0.428401i	$0.859077\pi$
$420$		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	0.114790	−	0.993390i	$-0.463381\pi$
$433$	−3.08847e10	−	3.08847e10i	−0.878600	−	0.878600i	−0.993390	+	0.114790i	$0.963381\pi$
$434$			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	$0.248556\pi$
$439$			5.22871e10i			1.40778i	−0.710307	+	0.703892i	$0.751444\pi$
$440$		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	0.998970	+	0.0453655i	$0.0144452\pi$
$443$	4.02212e10	+	4.02212e10i	1.04434	+	1.04434i	0.0453655	+	0.998970i	$0.485555\pi$
$444$		−	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	$-0.839408\pi$
$449$		−	3.92922e10i		−	0.966766i	0.875409	−	0.483383i	$-0.160592\pi$
$450$		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	−0.955566	−	0.294777i	$-0.904755\pi$
$457$	−2.88222e10	+	2.88222e10i	−0.660789	+	0.660789i	0.294777	+	0.955566i	$0.404755\pi$
$458$	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	0.931173	+	0.364578i	$0.118787\pi$
$463$	5.95450e10	+	5.95450e10i	1.29575	+	1.29575i	0.364578	+	0.931173i	$0.381213\pi$
$464$		−	9.63064e10i		−	2.07770i
$465$		0			0
$466$	6.00658e10			1.27375
$467$	1.38247e10	−	1.38247e10i	0.290661	−	0.290661i	−0.546680	−	0.837342i	$-0.684109\pi$
$467$	1.38247e10	−	1.38247e10i	0.290661	−	0.290661i	0.837342	+	0.546680i	$0.184109\pi$
$468$	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	$-0.963543\pi$
$479$		−	1.20326e10i		−	0.228568i	0.993448	−	0.114284i	$-0.0364574\pi$
$480$		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	−0.848315	−	0.529491i	$-0.822383\pi$
$487$	−1.79336e10	+	1.79336e10i	−0.318824	+	0.318824i	0.529491	+	0.848315i	$0.322383\pi$
$488$	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	$0.354668\pi$
$499$			1.11301e11i			1.79514i	−0.440877	+	0.897568i	$0.645332\pi$
$500$		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	0.326898	−	0.945060i	$-0.393997\pi$
$503$	−3.95707e10	−	3.95707e10i	−0.618161	−	0.618161i	−0.945060	+	0.326898i	$0.893997\pi$
$504$			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	$-0.909165\pi$
$509$		−	3.77916e10i		−	0.563021i	0.959558	−	0.281510i	$-0.0908354\pi$
$510$		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	−0.964555	−	0.263883i	$-0.914997\pi$
$523$	−9.19094e10	−	9.19094e10i	−1.22844	−	1.22844i	−0.263883	−	0.964555i	$-0.585003\pi$
$524$			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	−0.434894	−	0.900482i	$-0.643214\pi$
$547$	4.16822e10	−	4.16822e10i	0.465587	−	0.465587i	0.900482	+	0.434894i	$0.143214\pi$
$548$	−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	−0.135091	−	0.990833i	$-0.543133\pi$
$557$	8.23689e10	−	8.23689e10i	0.855742	−	0.855742i	0.990833	+	0.135091i	$0.0431328\pi$
$558$	−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	0.728926	−	0.684592i	$-0.240020\pi$
$563$	4.45418e9	+	4.45418e9i	0.0443338	+	0.0443338i	−0.684592	+	0.728926i	$0.740020\pi$
$564$			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	$-0.946942\pi$
$569$		−	3.47830e10i		−	0.331832i	0.986140	−	0.165916i	$-0.0530581\pi$
$570$		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	−0.998800	−	0.0489712i	$-0.984406\pi$
$577$	−1.05281e11	+	1.05281e11i	−0.949829	+	0.949829i	0.0489712	+	0.998800i	$0.484406\pi$
$578$	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	−0.272822	−	0.962065i	$-0.587957\pi$
$587$	8.18323e10	−	8.18323e10i	0.689243	−	0.689243i	0.962065	+	0.272822i	$0.0879569\pi$
$588$	−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	0.560108	−	0.828419i	$-0.310759\pi$
$593$	−3.31785e10	−	3.31785e10i	−0.268311	−	0.268311i	−0.828419	+	0.560108i	$0.810759\pi$
$594$		−	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	$-0.607164\pi$
$599$		−	2.43022e11i		−	1.88772i	0.330342	−	0.943861i	$-0.392836\pi$
$600$		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	−0.673731	−	0.738976i	$-0.735309\pi$
$607$	8.85735e9	−	8.85735e9i	0.0652453	−	0.0652453i	0.738976	+	0.673731i	$0.235309\pi$
$608$	−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	0.557530	−	0.830157i	$-0.311749\pi$
$613$	−3.84955e10	−	3.84955e10i	−0.272627	−	0.272627i	−0.830157	+	0.557530i	$0.811749\pi$
$614$		−	2.61011e11i		−	1.83648i
$615$		0			0
$616$	−1.57366e11			−1.09292
$617$	4.36592e10	−	4.36592e10i	0.301255	−	0.301255i	−0.540249	−	0.841505i	$-0.681670\pi$
$617$	4.36592e10	−	4.36592e10i	0.301255	−	0.301255i	0.841505	+	0.540249i	$0.181670\pi$
$618$	6.74725e8	+	6.74725e8i	0.00462565	+	0.00462565i
$619$		−	1.33280e11i		−	0.907824i	−0.891046	−	0.453912i	$-0.850028\pi$
$619$		−	1.33280e11i		−	0.907824i	0.891046	−	0.453912i	$-0.149972\pi$
$620$		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	0.0552024	−	0.998475i	$-0.482420\pi$
$643$	−1.61243e11	−	1.61243e11i	−0.943273	−	0.943273i	−0.998475	+	0.0552024i	$0.982420\pi$
$644$			7.56555e10i			0.439843i
$645$		0			0
$646$	−5.68185e11			−3.26257
$647$	1.56973e11	−	1.56973e11i	0.895793	−	0.895793i	−0.0992682	−	0.995061i	$-0.531650\pi$
$647$	1.56973e11	−	1.56973e11i	0.895793	−	0.895793i	0.995061	+	0.0992682i	$0.0316502\pi$
$648$	−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	−0.962977	−	0.269582i	$-0.913114\pi$
$653$	−2.24110e11	−	2.24110e11i	−1.23256	−	1.23256i	−0.269582	−	0.962977i	$-0.586886\pi$
$654$		−	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	$0.120727\pi$
$659$			1.39657e11i			0.740495i	−0.928933	+	0.370248i	$0.879273\pi$
$660$		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	−0.989361	−	0.145482i	$-0.953527\pi$
$673$	−2.32807e11	−	2.32807e11i	−1.13484	−	1.13484i	−0.145482	−	0.989361i	$-0.546473\pi$
$674$			4.91016e11i			2.37934i
$675$		0			0
$676$	1.46423e12			7.01169
$677$	−1.47111e11	+	1.47111e11i	−0.700310	+	0.700310i	−0.964477	−	0.264167i	$-0.914903\pi$
$677$	−1.47111e11	+	1.47111e11i	−0.700310	+	0.700310i	0.264167	+	0.964477i	$0.414903\pi$
$678$	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	0.958221	+	0.286027i	$0.0923348\pi$
$683$	2.70763e11	+	2.70763e11i	1.24425	+	1.24425i	0.286027	+	0.958221i	$0.407665\pi$
$684$		−	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	$-0.861350\pi$
$709$		−	2.13237e11i		−	0.843875i	0.906625	−	0.421937i	$-0.138650\pi$
$710$		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	$0.226858\pi$
$719$			3.49495e11i			1.30775i	−0.756602	+	0.653876i	$0.773142\pi$
$720$		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	−0.115835	−	0.993268i	$-0.536955\pi$
$727$	2.45105e11	−	2.45105e11i	0.877433	−	0.877433i	0.993268	+	0.115835i	$0.0369545\pi$
$728$	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	−0.950774	−	0.309884i	$-0.899710\pi$
$733$	−3.63926e11	−	3.63926e11i	−1.26066	−	1.26066i	−0.309884	−	0.950774i	$-0.600290\pi$
$734$			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	$0.157807\pi$
$739$			2.83756e11i			0.951409i	−0.879605	+	0.475705i	$0.842193\pi$
$740$		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	0.438273	−	0.898842i	$-0.355590\pi$
$743$	−1.40362e11	−	1.40362e11i	−0.460570	−	0.460570i	−0.898842	+	0.438273i	$0.855590\pi$
$744$		−	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	−0.652254	−	0.758000i	$-0.726177\pi$
$757$	3.47254e10	−	3.47254e10i	0.105746	−	0.105746i	0.758000	+	0.652254i	$0.226177\pi$
$758$	−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	$0.421543\pi$
$769$			6.78277e11i			1.93955i	−0.243993	+	0.969777i	$0.578457\pi$
$770$		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	0.969366	−	0.245622i	$-0.0789923\pi$
$773$	2.58406e11	+	2.58406e11i	0.723743	+	0.723743i	−0.245622	+	0.969366i	$0.578992\pi$
$774$			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	−0.810900	−	0.585185i	$-0.801022\pi$
$787$	−8.65883e10	+	8.65883e10i	−0.225715	+	0.225715i	0.585185	+	0.810900i	$0.301022\pi$
$788$	−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	−0.228528	+	0.973537i	$0.573391\pi$
$797$	−4.85022e11	+	4.85022e11i	−1.20207	+	1.20207i	−0.973537	+	0.228528i	$0.926609\pi$
$798$	−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	$-0.962662\pi$
$809$		−	1.00259e11i		−	0.234061i	0.993128	−	0.117031i	$-0.0373376\pi$
$810$		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	0.999758	+	0.0220206i	$0.00700993\pi$
$823$	4.68766e11	+	4.68766e11i	1.02178	+	1.02178i	0.0220206	+	0.999758i	$0.492990\pi$
$824$			7.11676e9i			0.0154374i
$825$		0			0
$826$	3.24789e11			0.697721
$827$	−1.34620e11	+	1.34620e11i	−0.287799	+	0.287799i	−0.836209	−	0.548410i	$-0.815233\pi$
$827$	−1.34620e11	+	1.34620e11i	−0.287799	+	0.287799i	0.548410	+	0.836209i	$0.315233\pi$
$828$	−1.65183e11	−	1.65183e11i	−0.351434	−	0.351434i
$829$			7.07602e9i			0.0149820i	0.999972	+	0.00749102i	$0.00238449\pi$
$829$			7.07602e9i			0.0149820i	−0.999972	+	0.00749102i	$0.997616\pi$
$830$		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	$-0.674354\pi$
$839$		−	8.46023e11i		−	1.70740i	0.520768	−	0.853698i	$-0.325646\pi$
$840$		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	0.983844	−	0.179030i	$-0.0572959\pi$
$853$	4.26080e11	+	4.26080e11i	0.804814	+	0.804814i	−0.179030	+	0.983844i	$0.557296\pi$
$854$			1.98654e11i			0.373479i
$855$		0			0
$856$	−5.26815e10			−0.0981213
$857$	−3.58066e11	+	3.58066e11i	−0.663804	+	0.663804i	−0.956275	−	0.292470i	$-0.905523\pi$
$857$	−3.58066e11	+	3.58066e11i	−0.663804	+	0.663804i	0.292470	+	0.956275i	$0.405523\pi$
$858$	−1.19840e12	−	1.19840e12i	−2.21133	−	2.21133i
$859$		−	8.56693e11i		−	1.57345i	−0.617305	−	0.786724i	$-0.711776\pi$
$859$		−	8.56693e11i		−	1.57345i	0.617305	−	0.786724i	$-0.288224\pi$
$860$		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	0.169925	−	0.985457i	$-0.445647\pi$
$863$	−4.52360e11	−	4.52360e11i	−0.815532	−	0.815532i	−0.985457	+	0.169925i	$0.945647\pi$
$864$		−	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	−0.707285	−	0.706929i	$-0.750080\pi$
$877$	−2.10744e8	+	2.10744e8i	−0.000356251	+	0.000356251i	0.706929	+	0.707285i	$0.250080\pi$
$878$	−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	0.957367	+	0.288874i	$0.0932808\pi$
$883$	7.57608e11	+	7.57608e11i	1.24624	+	1.24624i	0.288874	+	0.957367i	$0.406719\pi$
$884$			3.34739e12i			5.48148i
$885$		0			0
$886$	−1.66886e12			−2.70822
$887$	1.38716e11	−	1.38716e11i	0.224095	−	0.224095i	−0.586125	−	0.810220i	$-0.699347\pi$
$887$	1.38716e11	−	1.38716e11i	0.224095	−	0.224095i	0.810220	+	0.586125i	$0.199347\pi$
$888$	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	−0.293600	−	0.955928i	$-0.594853\pi$
$907$	4.48232e11	−	4.48232e11i	0.662329	−	0.662329i	0.955928	+	0.293600i	$0.0948533\pi$
$908$	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	$-0.822357\pi$
$919$		−	7.55454e11i		−	1.05912i	0.848272	−	0.529561i	$-0.177643\pi$
$920$		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	$-0.883306\pi$
$929$		−	5.33972e11i		−	0.716895i	0.933550	−	0.358448i	$-0.116694\pi$
$930$		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	−0.566792	−	0.823861i	$-0.691816\pi$
$937$	1.98156e11	−	1.98156e11i	0.257069	−	0.257069i	0.823861	+	0.566792i	$0.191816\pi$
$938$	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	−0.607876	−	0.794032i	$-0.707978\pi$
$947$	1.49719e11	−	1.49719e11i	0.186156	−	0.186156i	0.794032	+	0.607876i	$0.207978\pi$
$948$	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	0.630365	−	0.776299i	$-0.282905\pi$
$953$	−1.20373e11	−	1.20373e11i	−0.145934	−	0.145934i	−0.776299	+	0.630365i	$0.782905\pi$
$954$			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	−0.543928	−	0.839132i	$-0.683063\pi$
$967$	2.58124e11	−	2.58124e11i	0.295204	−	0.295204i	0.839132	+	0.543928i	$0.183063\pi$
$968$	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	−0.0990833	+	0.995079i	$0.531591\pi$
$977$	−9.96919e11	+	9.96919e11i	−1.09416	+	1.09416i	−0.995079	+	0.0990833i	$0.968409\pi$
$978$	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	0.647903	−	0.761723i	$-0.275646\pi$
$983$	−1.06275e11	−	1.06275e11i	−0.113819	−	0.113819i	−0.761723	+	0.647903i	$0.775646\pi$
$984$		−	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	−0.780772	−	0.624817i	$-0.785174\pi$
$997$	−1.54092e11	+	1.54092e11i	−0.155955	+	0.155955i	0.624817	+	0.780772i	$0.285174\pi$
$998$	−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.43.1	yes	12
5.2	odd	4	inner	75.9.f.d.7.1	✓	12
5.3	odd	4	inner	75.9.f.d.7.6	yes	12
5.4	even	2	inner	75.9.f.d.43.6	yes	12

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

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Database

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