LMFDB - Embedded newform 300.9.k.e.193.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,9,Mod(157,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 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("300.157");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	300.k (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:	$122.213583018$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 30946474 x^{14} - 8341419336 x^{13} + 380689791299777 x^{12} + \cdots + 57\!\cdots\!00 $ x^16 - 4x^15 - 30946474x^14 - 8341419336x^13 + 380689791299777x^12 + 172233390406399084x^11 - 2382137738311270416524x^10 - 1303628014982980229183568x^9 + 8170157809851151257627202984x^8 + 4722131342312473670415721362432x^7 - 15187994345395678935434992322703872x^6 - 8501142216286271666986373720765290240x^5 + 13719409820001055356751562088159234867776x^4 + 6705290345628598892954879974291445910470400x^3 - 4432537206418276871411586926292645523148742400x^2 - 1274737393430152937401280967045971687758547840000*x + 575975308456587940916620472287127145276670888000000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{20}\cdot 5^{18} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			193.8
Root			$3225.69 - 1.00000i$ of defining polynomial
Character	$\chi$	$=$	300.193
Dual form			300.9.k.e.157.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(33.0681 + 33.0681i) q^{3} +(2961.69 - 2961.69i) q^{7} +2187.00i q^{9} +O(q^{10})$	$q+(33.0681 + 33.0681i) q^{3} +(2961.69 - 2961.69i) q^{7} +2187.00i q^{9} +27026.3 q^{11} +(16380.2 + 16380.2i) q^{13} +(52180.6 - 52180.6i) q^{17} -99387.1i q^{19} +195875. q^{21} +(252536. + 252536. i) q^{23} +(-72320.0 + 72320.0i) q^{27} -183830. i q^{29} +387900. q^{31} +(893709. + 893709. i) q^{33} +(-1.68644e6 + 1.68644e6i) q^{37} +1.08333e6i q^{39} +1.14656e6 q^{41} +(-2.09395e6 - 2.09395e6i) q^{43} +(-27393.8 + 27393.8i) q^{47} -1.17784e7i q^{49} +3.45103e6 q^{51} +(-3.82760e6 - 3.82760e6i) q^{53} +(3.28655e6 - 3.28655e6i) q^{57} -1.30463e7i q^{59} +1.59215e7 q^{61} +(6.47722e6 + 6.47722e6i) q^{63} +(-1.20011e7 + 1.20011e7i) q^{67} +1.67018e7i q^{69} -3.95623e7 q^{71} +(-2.66564e7 - 2.66564e7i) q^{73} +(8.00436e7 - 8.00436e7i) q^{77} +7.09293e7i q^{79} -4.78297e6 q^{81} +(1.06344e7 + 1.06344e7i) q^{83} +(6.07892e6 - 6.07892e6i) q^{87} -4.35480e7i q^{89} +9.70263e7 q^{91} +(1.28271e7 + 1.28271e7i) q^{93} +(-5.13454e6 + 5.13454e6i) q^{97} +5.91065e7i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4220 q^{7}+O(q^{10}) $ 16 * q - 4220 * q^7	$ 16 q - 4220 q^{7} + 23616 q^{11} + 18900 q^{13} + 44940 q^{17} + 163944 q^{21} - 196440 q^{23} + 3742624 q^{31} + 134460 q^{33} + 2141100 q^{37} + 16347000 q^{41} - 12080280 q^{43} + 14942400 q^{47} + 7693704 q^{51} - 23760300 q^{53} + 27530280 q^{57} + 85401912 q^{61} - 9229140 q^{63} + 99451240 q^{67} + 73302480 q^{71} - 124097320 q^{73} + 185945400 q^{77} - 76527504 q^{81} + 22058160 q^{83} + 110300940 q^{87} + 170997360 q^{91} - 9969480 q^{93} - 185269800 q^{97}+O(q^{100}) $ 16 * q - 4220 * q^7 + 23616 * q^11 + 18900 * q^13 + 44940 * q^17 + 163944 * q^21 - 196440 * q^23 + 3742624 * q^31 + 134460 * q^33 + 2141100 * q^37 + 16347000 * q^41 - 12080280 * q^43 + 14942400 * q^47 + 7693704 * q^51 - 23760300 * q^53 + 27530280 * q^57 + 85401912 * q^61 - 9229140 * q^63 + 99451240 * q^67 + 73302480 * q^71 - 124097320 * q^73 + 185945400 * q^77 - 76527504 * q^81 + 22058160 * q^83 + 110300940 * q^87 + 170997360 * q^91 - 9969480 * q^93 - 185269800 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2961.69	−	2961.69i	1.23352	−	1.23352i	0.270923	−	0.962601i	$-0.412671\pi$
$7$	2961.69	−	2961.69i	1.23352	−	1.23352i	0.962601	−	0.270923i	$-0.0873287\pi$
$8$		0			0
$9$			2187.00i			0.333333i
$10$		0			0
$11$	27026.3			1.84593			0.922967	−	0.384880i	$-0.125757\pi$
$11$	27026.3			1.84593			0.922967	+	0.384880i	$0.125757\pi$
$12$		0			0
$13$	16380.2	+	16380.2i	0.573517	+	0.573517i	0.933109	−	0.359593i	$-0.117084\pi$
$13$	16380.2	+	16380.2i	0.573517	+	0.573517i	−0.359593	+	0.933109i	$0.617084\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	52180.6	−	52180.6i	0.624760	−	0.624760i	−0.321985	−	0.946745i	$-0.604350\pi$
$17$	52180.6	−	52180.6i	0.624760	−	0.624760i	0.946745	+	0.321985i	$0.104350\pi$
$18$		0			0
$19$		−	99387.1i		−	0.762633i	−0.924444	−	0.381317i	$-0.875471\pi$
$19$		−	99387.1i		−	0.762633i	0.924444	−	0.381317i	$-0.124529\pi$
$20$		0			0
$21$	195875.			1.00717
$22$		0			0
$23$	252536.	+	252536.i	0.902427	+	0.902427i	0.995646	−	0.0932190i	$-0.0297157\pi$
$23$	252536.	+	252536.i	0.902427	+	0.902427i	−0.0932190	+	0.995646i	$0.529716\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−72320.0	+	72320.0i	−0.136083	+	0.136083i
$28$		0			0
$29$		−	183830.i		−	0.259911i	−0.991520	−	0.129956i	$-0.958517\pi$
$29$		−	183830.i		−	0.259911i	0.991520	−	0.129956i	$-0.0414835\pi$
$30$		0			0
$31$	387900.			0.420022			0.210011	−	0.977699i	$-0.432650\pi$
$31$	387900.			0.420022			0.210011	+	0.977699i	$0.432650\pi$
$32$		0			0
$33$	893709.	+	893709.i	0.753599	+	0.753599i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.68644e6	+	1.68644e6i	−0.899836	+	0.899836i	−0.995421	−	0.0955853i	$-0.969528\pi$
$37$	−1.68644e6	+	1.68644e6i	−0.899836	+	0.899836i	0.0955853	+	0.995421i	$0.469528\pi$
$38$		0			0
$39$			1.08333e6i			0.468275i
$40$		0			0
$41$	1.14656e6			0.405752			0.202876	−	0.979204i	$-0.434971\pi$
$41$	1.14656e6			0.405752			0.202876	+	0.979204i	$0.434971\pi$
$42$		0			0
$43$	−2.09395e6	−	2.09395e6i	−0.612482	−	0.612482i	0.331110	−	0.943592i	$-0.392577\pi$
$43$	−2.09395e6	−	2.09395e6i	−0.612482	−	0.612482i	−0.943592	+	0.331110i	$0.892577\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−27393.8	+	27393.8i	−0.00561385	+	0.00561385i	−0.709908	−	0.704294i	$-0.751264\pi$
$47$	−27393.8	+	27393.8i	−0.00561385	+	0.00561385i	0.704294	+	0.709908i	$0.251264\pi$
$48$		0			0
$49$		−	1.17784e7i		−	2.04316i
$50$		0			0
$51$	3.45103e6			0.510115
$52$		0			0
$53$	−3.82760e6	−	3.82760e6i	−0.485091	−	0.485091i	0.421662	−	0.906753i	$-0.361447\pi$
$53$	−3.82760e6	−	3.82760e6i	−0.485091	−	0.485091i	−0.906753	+	0.421662i	$0.861447\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.28655e6	−	3.28655e6i	0.311344	−	0.311344i
$58$		0			0
$59$		−	1.30463e7i		−	1.07666i	−0.842733	−	0.538332i	$-0.819055\pi$
$59$		−	1.30463e7i		−	1.07666i	0.842733	−	0.538332i	$-0.180945\pi$
$60$		0			0
$61$	1.59215e7			1.14991			0.574956	−	0.818185i	$-0.305019\pi$
$61$	1.59215e7			1.14991			0.574956	+	0.818185i	$0.305019\pi$
$62$		0			0
$63$	6.47722e6	+	6.47722e6i	0.411175	+	0.411175i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.20011e7	+	1.20011e7i	−0.595555	+	0.595555i	−0.939126	−	0.343572i	$-0.888363\pi$
$67$	−1.20011e7	+	1.20011e7i	−0.595555	+	0.595555i	0.343572	+	0.939126i	$0.388363\pi$
$68$		0			0
$69$			1.67018e7i			0.736828i
$70$		0			0
$71$	−3.95623e7			−1.55685			−0.778427	−	0.627735i	$-0.783982\pi$
$71$	−3.95623e7			−1.55685			−0.778427	+	0.627735i	$0.783982\pi$
$72$		0			0
$73$	−2.66564e7	−	2.66564e7i	−0.938663	−	0.938663i	0.0595621	−	0.998225i	$-0.481030\pi$
$73$	−2.66564e7	−	2.66564e7i	−0.938663	−	0.938663i	−0.998225	+	0.0595621i	$0.981030\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	8.00436e7	−	8.00436e7i	2.27700	−	2.27700i
$78$		0			0
$79$			7.09293e7i			1.82103i	0.413475	+	0.910515i	$0.364315\pi$
$79$			7.09293e7i			1.82103i	−0.413475	+	0.910515i	$0.635685\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$		0			0
$83$	1.06344e7	+	1.06344e7i	0.224079	+	0.224079i	0.810214	−	0.586135i	$-0.199351\pi$
$83$	1.06344e7	+	1.06344e7i	0.224079	+	0.224079i	−0.586135	+	0.810214i	$0.699351\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	6.07892e6	−	6.07892e6i	0.106108	−	0.106108i
$88$		0			0
$89$		−	4.35480e7i		−	0.694078i	−0.937851	−	0.347039i	$-0.887187\pi$
$89$		−	4.35480e7i		−	0.694078i	0.937851	−	0.347039i	$-0.112813\pi$
$90$		0			0
$91$	9.70263e7			1.41489
$92$		0			0
$93$	1.28271e7	+	1.28271e7i	0.171473	+	0.171473i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−5.13454e6	+	5.13454e6i	−0.0579982	+	0.0579982i	−0.735511	−	0.677513i	$-0.763058\pi$
$97$	−5.13454e6	+	5.13454e6i	−0.0579982	+	0.0579982i	0.677513	+	0.735511i	$0.263058\pi$
$98$		0			0
$99$			5.91065e7i			0.615311i
$100$		0			0
$101$	5.77741e7			0.555197			0.277599	−	0.960697i	$-0.410461\pi$
$101$	5.77741e7			0.555197			0.277599	+	0.960697i	$0.410461\pi$
$102$		0			0
$103$	1.56379e8	+	1.56379e8i	1.38941	+	1.38941i	0.826567	+	0.562838i	$0.190291\pi$
$103$	1.56379e8	+	1.56379e8i	1.38941	+	1.38941i	0.562838	+	0.826567i	$0.309709\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.44083e6	−	1.44083e6i	0.0109920	−	0.0109920i	−0.701589	−	0.712581i	$-0.747526\pi$
$107$	1.44083e6	−	1.44083e6i	0.0109920	−	0.0109920i	0.712581	+	0.701589i	$0.247526\pi$
$108$		0			0
$109$		−	1.13282e8i		−	0.802517i	−0.915965	−	0.401259i	$-0.868573\pi$
$109$		−	1.13282e8i		−	0.802517i	0.915965	−	0.401259i	$-0.131427\pi$
$110$		0			0
$111$	−1.11535e8			−0.734713
$112$		0			0
$113$	−3.01287e7	−	3.01287e7i	−0.184785	−	0.184785i	0.608652	−	0.793437i	$-0.291710\pi$
$113$	−3.01287e7	−	3.01287e7i	−0.184785	−	0.184785i	−0.793437	+	0.608652i	$0.791710\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−3.58235e7	+	3.58235e7i	−0.191172	+	0.191172i
$118$		0			0
$119$		−	3.09086e8i		−	1.54131i
$120$		0			0
$121$	5.16062e8			2.40747
$122$		0			0
$123$	3.79145e7	+	3.79145e7i	0.165648	+	0.165648i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−3.44037e8	+	3.44037e8i	−1.32248	+	1.32248i	−0.410724	+	0.911760i	$0.634724\pi$
$127$	−3.44037e8	+	3.44037e8i	−1.32248	+	1.32248i	−0.911760	+	0.410724i	$0.865276\pi$
$128$		0			0
$129$		−	1.38486e8i		−	0.500089i
$130$		0			0
$131$	−4.08215e8			−1.38613			−0.693065	−	0.720875i	$-0.743740\pi$
$131$	−4.08215e8			−1.38613			−0.693065	+	0.720875i	$0.743740\pi$
$132$		0			0
$133$	−2.94354e8	−	2.94354e8i	−0.940726	−	0.940726i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.22746e8	+	2.22746e8i	−0.632305	+	0.632305i	−0.948646	−	0.316340i	$-0.897546\pi$
$137$	−2.22746e8	+	2.22746e8i	−0.632305	+	0.632305i	0.316340	+	0.948646i	$0.397546\pi$
$138$		0			0
$139$		−	4.51017e8i		−	1.20819i	−0.796914	−	0.604093i	$-0.793535\pi$
$139$		−	4.51017e8i		−	1.20819i	0.796914	−	0.604093i	$-0.206465\pi$
$140$		0			0
$141$	−1.81172e6			−0.00458369
$142$		0			0
$143$	4.42697e8	+	4.42697e8i	1.05867	+	1.05867i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	3.89490e8	−	3.89490e8i	0.834117	−	0.834117i
$148$		0			0
$149$			6.55443e8i			1.32981i	0.746928	+	0.664905i	$0.231528\pi$
$149$			6.55443e8i			1.32981i	−0.746928	+	0.664905i	$0.768472\pi$
$150$		0			0
$151$	1.80398e8			0.346996			0.173498	−	0.984834i	$-0.444493\pi$
$151$	1.80398e8			0.346996			0.173498	+	0.984834i	$0.444493\pi$
$152$		0			0
$153$	1.14119e8	+	1.14119e8i	0.208253	+	0.208253i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	1.91728e8	−	1.91728e8i	0.315563	−	0.315563i	−0.531497	−	0.847060i	$-0.678370\pi$
$157$	1.91728e8	−	1.91728e8i	0.315563	−	0.315563i	0.847060	+	0.531497i	$0.178370\pi$
$158$		0			0
$159$		−	2.53143e8i		−	0.396075i
$160$		0			0
$161$	1.49587e9			2.22633
$162$		0			0
$163$	6.53511e8	+	6.53511e8i	0.925769	+	0.925769i	0.997429	−	0.0716600i	$-0.0228297\pi$
$163$	6.53511e8	+	6.53511e8i	0.925769	+	0.925769i	−0.0716600	+	0.997429i	$0.522830\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.62387e8	−	8.62387e8i	1.10876	−	1.10876i	0.115442	−	0.993314i	$-0.463171\pi$
$167$	8.62387e8	−	8.62387e8i	1.10876	−	1.10876i	0.993314	−	0.115442i	$-0.0368285\pi$
$168$		0			0
$169$		−	2.79108e8i		−	0.342157i
$170$		0			0
$171$	2.17360e8			0.254211
$172$		0			0
$173$	8.33080e8	+	8.33080e8i	0.930041	+	0.930041i	0.997708	−	0.0676670i	$-0.0215556\pi$
$173$	8.33080e8	+	8.33080e8i	0.930041	+	0.930041i	−0.0676670	+	0.997708i	$0.521556\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.31418e8	−	4.31418e8i	0.439546	−	0.439546i
$178$		0			0
$179$			7.12857e8i			0.694369i	0.937797	+	0.347184i	$0.112862\pi$
$179$			7.12857e8i			0.694369i	−0.937797	+	0.347184i	$0.887138\pi$
$180$		0			0
$181$	4.11232e8			0.383153			0.191577	−	0.981478i	$-0.438640\pi$
$181$	4.11232e8			0.383153			0.191577	+	0.981478i	$0.438640\pi$
$182$		0			0
$183$	5.26494e8	+	5.26494e8i	0.469449	+	0.469449i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.41025e9	−	1.41025e9i	1.15327	−	1.15327i
$188$		0			0
$189$			4.28379e8i			0.335723i
$190$		0			0
$191$	1.80426e9			1.35571			0.677854	−	0.735197i	$-0.262910\pi$
$191$	1.80426e9			1.35571			0.677854	+	0.735197i	$0.262910\pi$
$192$		0			0
$193$	−8.38154e8	−	8.38154e8i	−0.604080	−	0.604080i	0.337313	−	0.941393i	$-0.390482\pi$
$193$	−8.38154e8	−	8.38154e8i	−0.604080	−	0.604080i	−0.941393	+	0.337313i	$0.890482\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−4.22403e8	+	4.22403e8i	−0.280454	+	0.280454i	−0.833290	−	0.552836i	$-0.813546\pi$
$197$	−4.22403e8	+	4.22403e8i	−0.280454	+	0.280454i	0.552836	+	0.833290i	$0.313546\pi$
$198$		0			0
$199$		−	1.23810e9i		−	0.789487i	−0.918791	−	0.394743i	$-0.870833\pi$
$199$		−	1.23810e9i		−	0.789487i	0.918791	−	0.394743i	$-0.129167\pi$
$200$		0			0
$201$	−7.93707e8			−0.486269
$202$		0			0
$203$	−5.44448e8	−	5.44448e8i	−0.320607	−	0.320607i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−5.52296e8	+	5.52296e8i	−0.300809	+	0.300809i
$208$		0			0
$209$		−	2.68607e9i		−	1.40777i
$210$		0			0
$211$	−1.56234e8			−0.0788216			−0.0394108	−	0.999223i	$-0.512548\pi$
$211$	−1.56234e8			−0.0788216			−0.0394108	+	0.999223i	$0.512548\pi$
$212$		0			0
$213$	−1.30825e9	−	1.30825e9i	−0.635583	−	0.635583i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	1.14884e9	−	1.14884e9i	0.518108	−	0.518108i
$218$		0			0
$219$		−	1.76295e9i		−	0.766415i
$220$		0			0
$221$	1.70946e9			0.716621
$222$		0			0
$223$	2.54666e9	+	2.54666e9i	1.02980	+	1.02980i	0.999542	+	0.0302537i	$0.00963153\pi$
$223$	2.54666e9	+	2.54666e9i	1.02980	+	1.02980i	0.0302537	+	0.999542i	$0.490368\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.96729e8	+	6.96729e8i	−0.262398	+	0.262398i	−0.826028	−	0.563630i	$-0.809405\pi$
$227$	−6.96729e8	+	6.96729e8i	−0.262398	+	0.262398i	0.563630	+	0.826028i	$0.309405\pi$
$228$		0			0
$229$		−	2.35663e9i		−	0.856939i	−0.903556	−	0.428470i	$-0.859053\pi$
$229$		−	2.35663e9i		−	0.856939i	0.903556	−	0.428470i	$-0.140947\pi$
$230$		0			0
$231$	5.29378e9			1.85916
$232$		0			0
$233$	−2.04141e8	−	2.04141e8i	−0.0692639	−	0.0692639i	0.671626	−	0.740890i	$-0.265596\pi$
$233$	−2.04141e8	−	2.04141e8i	−0.0692639	−	0.0692639i	−0.740890	+	0.671626i	$0.765596\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−2.34550e9	+	2.34550e9i	−0.743433	+	0.743433i
$238$		0			0
$239$		−	6.16691e9i		−	1.89006i	−0.326982	−	0.945031i	$-0.606032\pi$
$239$		−	6.16691e9i		−	1.89006i	0.326982	−	0.945031i	$-0.393968\pi$
$240$		0			0
$241$	1.46581e9			0.434519			0.217260	−	0.976114i	$-0.430288\pi$
$241$	1.46581e9			0.434519			0.217260	+	0.976114i	$0.430288\pi$
$242$		0			0
$243$	−1.58164e8	−	1.58164e8i	−0.0453609	−	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.62798e9	−	1.62798e9i	0.437383	−	0.437383i
$248$		0			0
$249$			7.03319e8i			0.182960i
$250$		0			0
$251$	2.13630e9			0.538229			0.269115	−	0.963108i	$-0.413269\pi$
$251$	2.13630e9			0.538229			0.269115	+	0.963108i	$0.413269\pi$
$252$		0			0
$253$	6.82511e9	+	6.82511e9i	1.66582	+	1.66582i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.14913e9	+	1.14913e9i	−0.263412	+	0.263412i	−0.826439	−	0.563027i	$-0.809637\pi$
$257$	−1.14913e9	+	1.14913e9i	−0.263412	+	0.263412i	0.563027	+	0.826439i	$0.309637\pi$
$258$		0			0
$259$			9.98941e9i			2.21994i
$260$		0			0
$261$	4.02037e8			0.0866371
$262$		0			0
$263$	−1.30407e9	−	1.30407e9i	−0.272570	−	0.272570i	0.557564	−	0.830134i	$-0.311736\pi$
$263$	−1.30407e9	−	1.30407e9i	−0.272570	−	0.272570i	−0.830134	+	0.557564i	$0.811736\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.44005e9	−	1.44005e9i	0.283356	−	0.283356i
$268$		0			0
$269$		−	4.50318e9i		−	0.860022i	−0.902824	−	0.430011i	$-0.858510\pi$
$269$		−	4.50318e9i		−	0.860022i	0.902824	−	0.430011i	$-0.141490\pi$
$270$		0			0
$271$	4.95239e9			0.918201			0.459100	−	0.888384i	$-0.348172\pi$
$271$	4.95239e9			0.918201			0.459100	+	0.888384i	$0.348172\pi$
$272$		0			0
$273$	3.20848e9	+	3.20848e9i	0.577628	+	0.577628i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	2.02071e9	−	2.02071e9i	0.343230	−	0.343230i	−0.514350	−	0.857580i	$-0.671967\pi$
$277$	2.02071e9	−	2.02071e9i	0.343230	−	0.343230i	0.857580	+	0.514350i	$0.171967\pi$
$278$		0			0
$279$			8.48336e8i			0.140007i
$280$		0			0
$281$	−5.28047e9			−0.846930			−0.423465	−	0.905912i	$-0.639186\pi$
$281$	−5.28047e9			−0.846930			−0.423465	+	0.905912i	$0.639186\pi$
$282$		0			0
$283$	2.92195e8	+	2.92195e8i	0.0455541	+	0.0455541i	0.729517	−	0.683963i	$-0.239745\pi$
$283$	2.92195e8	+	2.92195e8i	0.0455541	+	0.0455541i	−0.683963	+	0.729517i	$0.739745\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.39575e9	−	3.39575e9i	0.500505	−	0.500505i
$288$		0			0
$289$			1.53013e9i			0.219349i
$290$		0			0
$291$	−3.39579e8			−0.0473553
$292$		0			0
$293$	−4.18309e9	−	4.18309e9i	−0.567580	−	0.567580i	0.363870	−	0.931450i	$-0.381455\pi$
$293$	−4.18309e9	−	4.18309e9i	−0.567580	−	0.567580i	−0.931450	+	0.363870i	$0.881455\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.95454e9	+	1.95454e9i	−0.251200	+	0.251200i
$298$		0			0
$299$			8.27319e9i			1.03511i
$300$		0			0
$301$	−1.24033e10			−1.51102
$302$		0			0
$303$	1.91048e9	+	1.91048e9i	0.226658	+	0.226658i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−2.13168e9	+	2.13168e9i	−0.239976	+	0.239976i	−0.816840	−	0.576864i	$-0.804276\pi$
$307$	−2.13168e9	+	2.13168e9i	−0.239976	+	0.239976i	0.576864	+	0.816840i	$0.304276\pi$
$308$		0			0
$309$			1.03423e10i			1.13444i
$310$		0			0
$311$	−1.45943e10			−1.56006			−0.780028	−	0.625744i	$-0.784795\pi$
$311$	−1.45943e10			−1.56006			−0.780028	+	0.625744i	$0.784795\pi$
$312$		0			0
$313$	−5.53838e9	−	5.53838e9i	−0.577040	−	0.577040i	0.357047	−	0.934086i	$-0.383784\pi$
$313$	−5.53838e9	−	5.53838e9i	−0.577040	−	0.577040i	−0.934086	+	0.357047i	$0.883784\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.11969e9	−	2.11969e9i	0.209911	−	0.209911i	−0.594318	−	0.804230i	$-0.702578\pi$
$317$	2.11969e9	−	2.11969e9i	0.209911	−	0.209911i	0.804230	+	0.594318i	$0.202578\pi$
$318$		0			0
$319$		−	4.96825e9i		−	0.479779i
$320$		0			0
$321$	9.52912e7			0.00897496
$322$		0			0
$323$	−5.18608e9	−	5.18608e9i	−0.476463	−	0.476463i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	3.74602e9	−	3.74602e9i	0.327626	−	0.327626i
$328$		0			0
$329$			1.62264e8i			0.0138496i
$330$		0			0
$331$	−2.67392e9			−0.222759			−0.111380	−	0.993778i	$-0.535527\pi$
$331$	−2.67392e9			−0.222759			−0.111380	+	0.993778i	$0.535527\pi$
$332$		0			0
$333$	−3.68824e9	−	3.68824e9i	−0.299945	−	0.299945i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.22243e10	+	1.22243e10i	−0.947775	+	0.947775i	−0.998702	−	0.0509278i	$-0.983782\pi$
$337$	−1.22243e10	+	1.22243e10i	−0.947775	+	0.947775i	0.0509278	+	0.998702i	$0.483782\pi$
$338$		0			0
$339$		−	1.99260e9i		−	0.150876i
$340$		0			0
$341$	1.04835e10			0.775333
$342$		0			0
$343$	−1.78105e10	−	1.78105e10i	−1.28676	−	1.28676i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.66021e10	+	1.66021e10i	−1.14510	+	1.14510i	−0.157602	+	0.987503i	$0.550376\pi$
$347$	−1.66021e10	+	1.66021e10i	−1.14510	+	1.14510i	−0.987503	+	0.157602i	$0.949624\pi$
$348$		0			0
$349$		−	1.19894e10i		−	0.808157i	−0.914724	−	0.404079i	$-0.867592\pi$
$349$		−	1.19894e10i		−	0.808157i	0.914724	−	0.404079i	$-0.132408\pi$
$350$		0			0
$351$	−2.36923e9			−0.156092
$352$		0			0
$353$	1.20155e10	+	1.20155e10i	0.773826	+	0.773826i	0.978773	−	0.204947i	$-0.0657022\pi$
$353$	1.20155e10	+	1.20155e10i	0.773826	+	0.773826i	−0.204947	+	0.978773i	$0.565702\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	1.02209e10	−	1.02209e10i	0.629238	−	0.629238i
$358$		0			0
$359$		−	2.22500e9i		−	0.133953i	−0.997755	−	0.0669765i	$-0.978665\pi$
$359$		−	2.22500e9i		−	0.133953i	0.997755	−	0.0669765i	$-0.0213353\pi$
$360$		0			0
$361$	7.10576e9			0.418390
$362$		0			0
$363$	1.70652e10	+	1.70652e10i	0.982845	+	0.982845i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−2.04168e9	+	2.04168e9i	−0.112545	+	0.112545i	−0.761136	−	0.648592i	$-0.775358\pi$
$367$	−2.04168e9	+	2.04168e9i	−0.112545	+	0.112545i	0.648592	+	0.761136i	$0.275358\pi$
$368$		0			0
$369$			2.50752e9i			0.135251i
$370$		0			0
$371$	−2.26723e10			−1.19674
$372$		0			0
$373$	6.39591e8	+	6.39591e8i	0.0330420	+	0.0330420i	0.723435	−	0.690393i	$-0.242562\pi$
$373$	6.39591e8	+	6.39591e8i	0.0330420	+	0.0330420i	−0.690393	+	0.723435i	$0.742562\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.01118e9	−	3.01118e9i	0.149063	−	0.149063i
$378$		0			0
$379$			2.01090e10i			0.974619i	0.873229	+	0.487309i	$0.162022\pi$
$379$			2.01090e10i			0.974619i	−0.873229	+	0.487309i	$0.837978\pi$
$380$		0			0
$381$	−2.27533e10			−1.07980
$382$		0			0
$383$	−1.80407e10	−	1.80407e10i	−0.838412	−	0.838412i	0.150238	−	0.988650i	$-0.451996\pi$
$383$	−1.80407e10	−	1.80407e10i	−0.838412	−	0.838412i	−0.988650	+	0.150238i	$0.951996\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	4.57947e9	−	4.57947e9i	0.204161	−	0.204161i
$388$		0			0
$389$			1.45076e10i			0.633572i	0.948497	+	0.316786i	$0.102604\pi$
$389$			1.45076e10i			0.633572i	−0.948497	+	0.316786i	$0.897396\pi$
$390$		0			0
$391$	2.63550e10			1.12760
$392$		0			0
$393$	−1.34989e10	−	1.34989e10i	−0.565886	−	0.565886i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−1.02555e10	+	1.02555e10i	−0.412851	+	0.412851i	−0.882731	−	0.469880i	$-0.844297\pi$
$397$	−1.02555e10	+	1.02555e10i	−0.412851	+	0.412851i	0.469880	+	0.882731i	$0.344297\pi$
$398$		0			0
$399$		−	1.94675e10i		−	0.768100i
$400$		0			0
$401$	5.64668e9			0.218381			0.109191	−	0.994021i	$-0.465174\pi$
$401$	5.64668e9			0.218381			0.109191	+	0.994021i	$0.465174\pi$
$402$		0			0
$403$	6.35388e9	+	6.35388e9i	0.240890	+	0.240890i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.55782e10	+	4.55782e10i	−1.66104	+	1.66104i
$408$		0			0
$409$			1.28862e10i			0.460501i	0.973131	+	0.230250i	$0.0739546\pi$
$409$			1.28862e10i			0.460501i	−0.973131	+	0.230250i	$0.926045\pi$
$410$		0			0
$411$	−1.47316e10			−0.516275
$412$		0			0
$413$	−3.86392e10	−	3.86392e10i	−1.32809	−	1.32809i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.49143e10	−	1.49143e10i	0.493240	−	0.493240i
$418$		0			0
$419$			2.09392e10i			0.679367i	0.940540	+	0.339684i	$0.110320\pi$
$419$			2.09392e10i			0.679367i	−0.940540	+	0.339684i	$0.889680\pi$
$420$		0			0
$421$	−2.79607e10			−0.890060			−0.445030	−	0.895516i	$-0.646807\pi$
$421$	−2.79607e10			−0.890060			−0.445030	+	0.895516i	$0.646807\pi$
$422$		0			0
$423$	−5.99103e7	−	5.99103e7i	−0.00187128	−	0.00187128i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	4.71545e10	−	4.71545e10i	1.41844	−	1.41844i
$428$		0			0
$429$			2.92783e10i			0.864404i
$430$		0			0
$431$	−6.40357e10			−1.85572			−0.927862	−	0.372924i	$-0.878355\pi$
$431$	−6.40357e10			−1.85572			−0.927862	+	0.372924i	$0.878355\pi$
$432$		0			0
$433$	3.74076e10	+	3.74076e10i	1.06416	+	1.06416i	0.997795	+	0.0663689i	$0.0211414\pi$
$433$	3.74076e10	+	3.74076e10i	1.06416	+	1.06416i	0.0663689	+	0.997795i	$0.478859\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.50988e10	−	2.50988e10i	0.688221	−	0.688221i
$438$		0			0
$439$			1.06651e10i			0.287149i	0.989640	+	0.143574i	$0.0458596\pi$
$439$			1.06651e10i			0.287149i	−0.989640	+	0.143574i	$0.954140\pi$
$440$		0			0
$441$	2.57594e10			0.681054
$442$		0			0
$443$	−1.89340e10	−	1.89340e10i	−0.491617	−	0.491617i	0.417198	−	0.908815i	$-0.363012\pi$
$443$	−1.89340e10	−	1.89340e10i	−0.491617	−	0.491617i	−0.908815	+	0.417198i	$0.863012\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−2.16742e10	+	2.16742e10i	−0.542893	+	0.542893i
$448$		0			0
$449$		−	5.79740e10i		−	1.42642i	−0.700950	−	0.713210i	$-0.747240\pi$
$449$		−	5.79740e10i		−	1.42642i	0.700950	−	0.713210i	$-0.252760\pi$
$450$		0			0
$451$	3.09873e10			0.748992
$452$		0			0
$453$	5.96543e9	+	5.96543e9i	0.141660	+	0.141660i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−5.00335e10	+	5.00335e10i	−1.14709	+	1.14709i	−0.159965	+	0.987123i	$0.551138\pi$
$457$	−5.00335e10	+	5.00335e10i	−1.14709	+	1.14709i	−0.987123	+	0.159965i	$0.948862\pi$
$458$		0			0
$459$			7.54740e9i			0.170038i
$460$		0			0
$461$	−5.72025e10			−1.26652			−0.633259	−	0.773940i	$-0.718283\pi$
$461$	−5.72025e10			−1.26652			−0.633259	+	0.773940i	$0.718283\pi$
$462$		0			0
$463$	−4.59712e10	−	4.59712e10i	−1.00037	−	1.00037i	−1.00000		0.000373953i	$-0.999881\pi$
$463$	−4.59712e10	−	4.59712e10i	−1.00037	−	1.00037i	−0.000373953	−	1.00000i	$-0.500119\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.62076e10	−	2.62076e10i	0.551009	−	0.551009i	−0.375723	−	0.926732i	$-0.622606\pi$
$467$	2.62076e10	−	2.62076e10i	0.551009	−	0.551009i	0.926732	+	0.375723i	$0.122606\pi$
$468$		0			0
$469$			7.10871e10i			1.46926i
$470$		0			0
$471$	1.26802e10			0.257656
$472$		0			0
$473$	−5.65918e10	−	5.65918e10i	−1.13060	−	1.13060i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	8.37096e9	−	8.37096e9i	0.161697	−	0.161697i
$478$		0			0
$479$		−	5.41257e10i		−	1.02816i	−0.857742	−	0.514081i	$-0.828133\pi$
$479$		−	5.41257e10i		−	1.02816i	0.857742	−	0.514081i	$-0.171867\pi$
$480$		0			0
$481$	−5.52484e10			−1.03214
$482$		0			0
$483$	4.94655e10	+	4.94655e10i	0.908895	+	0.908895i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	5.30290e10	−	5.30290e10i	0.942752	−	0.942752i	−0.0556955	−	0.998448i	$-0.517738\pi$
$487$	5.30290e10	−	5.30290e10i	0.942752	−	0.942752i	0.998448	+	0.0556955i	$0.0177376\pi$
$488$		0			0
$489$			4.32208e10i			0.755887i
$490$		0			0
$491$	−3.45673e10			−0.594758			−0.297379	−	0.954760i	$-0.596112\pi$
$491$	−3.45673e10			−0.594758			−0.297379	+	0.954760i	$0.596112\pi$
$492$		0			0
$493$	−9.59237e9	−	9.59237e9i	−0.162382	−	0.162382i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.17171e11	+	1.17171e11i	−1.92042	+	1.92042i
$498$		0			0
$499$		−	6.90320e9i		−	0.111339i	−0.998449	−	0.0556696i	$-0.982271\pi$
$499$		−	6.90320e9i		−	0.111339i	0.998449	−	0.0556696i	$-0.0177294\pi$
$500$		0			0
$501$	5.70350e10			0.905296
$502$		0			0
$503$	−2.01629e10	−	2.01629e10i	−0.314978	−	0.314978i	0.531856	−	0.846834i	$-0.321495\pi$
$503$	−2.01629e10	−	2.01629e10i	−0.314978	−	0.314978i	−0.846834	+	0.531856i	$0.821495\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	9.22957e9	−	9.22957e9i	0.139685	−	0.139685i
$508$		0			0
$509$			8.10518e10i			1.20751i	0.797169	+	0.603756i	$0.206330\pi$
$509$			8.10518e10i			1.20751i	−0.797169	+	0.603756i	$0.793670\pi$
$510$		0			0
$511$	−1.57896e11			−2.31572
$512$		0			0
$513$	7.18767e9	+	7.18767e9i	0.103781	+	0.103781i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−7.40354e8	+	7.40354e8i	−0.0103628	+	0.0103628i
$518$		0			0
$519$			5.50967e10i			0.759375i
$520$		0			0
$521$	1.21291e11			1.64618			0.823092	−	0.567908i	$-0.192247\pi$
$521$	1.21291e11			1.64618			0.823092	+	0.567908i	$0.192247\pi$
$522$		0			0
$523$	7.41243e10	+	7.41243e10i	0.990727	+	0.990727i	0.999957	−	0.00923057i	$-0.00293822\pi$
$523$	7.41243e10	+	7.41243e10i	0.990727	+	0.990727i	−0.00923057	+	0.999957i	$0.502938\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.02408e10	−	2.02408e10i	0.262413	−	0.262413i
$528$		0			0
$529$			4.92378e10i			0.628748i
$530$		0			0
$531$	2.85323e10			0.358888
$532$		0			0
$533$	1.87809e10	+	1.87809e10i	0.232706	+	0.232706i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−2.35728e10	+	2.35728e10i	−0.283475	+	0.283475i
$538$		0			0
$539$		−	3.18327e11i		−	3.77154i
$540$		0			0
$541$	1.40365e11			1.63859			0.819294	−	0.573374i	$-0.194366\pi$
$541$	1.40365e11			1.63859			0.819294	+	0.573374i	$0.194366\pi$
$542$		0			0
$543$	1.35987e10	+	1.35987e10i	0.156422	+	0.156422i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	7.55594e9	−	7.55594e9i	0.0843994	−	0.0843994i	−0.663647	−	0.748046i	$-0.730992\pi$
$547$	7.55594e9	−	7.55594e9i	0.0843994	−	0.0843994i	0.748046	+	0.663647i	$0.230992\pi$
$548$		0			0
$549$			3.48203e10i			0.383304i
$550$		0			0
$551$	−1.82704e10			−0.198217
$552$		0			0
$553$	2.10071e11	+	2.10071e11i	2.24628	+	2.24628i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	5.26098e9	−	5.26098e9i	0.0546570	−	0.0546570i	−0.679250	−	0.733907i	$-0.737695\pi$
$557$	5.26098e9	−	5.26098e9i	0.0546570	−	0.0546570i	0.733907	+	0.679250i	$0.237695\pi$
$558$		0			0
$559$		−	6.85988e10i		−	0.702537i
$560$		0			0
$561$	9.32685e10			0.941637
$562$		0			0
$563$	−2.08166e10	−	2.08166e10i	−0.207194	−	0.207194i	0.595880	−	0.803074i	$-0.296803\pi$
$563$	−2.08166e10	−	2.08166e10i	−0.207194	−	0.207194i	−0.803074	+	0.595880i	$0.796803\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.41657e10	+	1.41657e10i	−0.137058	+	0.137058i
$568$		0			0
$569$			1.37736e10i			0.131401i	0.997839	+	0.0657006i	$0.0209282\pi$
$569$			1.37736e10i			0.131401i	−0.997839	+	0.0657006i	$0.979072\pi$
$570$		0			0
$571$	1.32798e11			1.24925			0.624624	−	0.780926i	$-0.285252\pi$
$571$	1.32798e11			1.24925			0.624624	+	0.780926i	$0.285252\pi$
$572$		0			0
$573$	5.96635e10	+	5.96635e10i	0.553465	+	0.553465i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	4.82858e10	−	4.82858e10i	0.435628	−	0.435628i	−0.454910	−	0.890538i	$-0.650328\pi$
$577$	4.82858e10	−	4.82858e10i	0.435628	−	0.435628i	0.890538	+	0.454910i	$0.150328\pi$
$578$		0			0
$579$		−	5.54323e10i		−	0.493229i
$580$		0			0
$581$	6.29916e10			0.552813
$582$		0			0
$583$	−1.03446e11	−	1.03446e11i	−0.895445	−	0.895445i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−3.71355e10	+	3.71355e10i	−0.312779	+	0.312779i	−0.845985	−	0.533206i	$-0.820987\pi$
$587$	−3.71355e10	+	3.71355e10i	−0.312779	+	0.312779i	0.533206	+	0.845985i	$0.320987\pi$
$588$		0			0
$589$		−	3.85522e10i		−	0.320323i
$590$		0			0
$591$	−2.79361e10			−0.228990
$592$		0			0
$593$	−9.51005e10	−	9.51005e10i	−0.769067	−	0.769067i	0.208875	−	0.977942i	$-0.433020\pi$
$593$	−9.51005e10	−	9.51005e10i	−0.769067	−	0.769067i	−0.977942	+	0.208875i	$0.933020\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	4.09418e10	−	4.09418e10i	0.322307	−	0.322307i
$598$		0			0
$599$		−	2.44937e11i		−	1.90260i	−0.308269	−	0.951299i	$-0.599750\pi$
$599$		−	2.44937e11i		−	1.90260i	0.308269	−	0.951299i	$-0.400250\pi$
$600$		0			0
$601$	9.38656e10			0.719463			0.359732	−	0.933056i	$-0.382868\pi$
$601$	9.38656e10			0.719463			0.359732	+	0.933056i	$0.382868\pi$
$602$		0			0
$603$	−2.62464e10	−	2.62464e10i	−0.198518	−	0.198518i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	8.39011e10	−	8.39011e10i	0.618035	−	0.618035i	−0.326992	−	0.945027i	$-0.606035\pi$
$607$	8.39011e10	−	8.39011e10i	0.618035	−	0.618035i	0.945027	+	0.326992i	$0.106035\pi$
$608$		0			0
$609$		−	3.60078e10i		−	0.261774i
$610$		0			0
$611$	−8.97433e8			−0.00643928
$612$		0			0
$613$	8.27999e10	+	8.27999e10i	0.586392	+	0.586392i	0.936652	−	0.350260i	$-0.113907\pi$
$613$	8.27999e10	+	8.27999e10i	0.586392	+	0.586392i	−0.350260	+	0.936652i	$0.613907\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−9.63193e10	+	9.63193e10i	−0.664619	+	0.664619i	−0.956465	−	0.291846i	$-0.905730\pi$
$617$	−9.63193e10	+	9.63193e10i	−0.664619	+	0.664619i	0.291846	+	0.956465i	$0.405730\pi$
$618$		0			0
$619$			2.72015e11i			1.85281i	0.376529	+	0.926405i	$0.377118\pi$
$619$			2.72015e11i			1.85281i	−0.376529	+	0.926405i	$0.622882\pi$
$620$		0			0
$621$	−3.65268e10			−0.245609
$622$		0			0
$623$	−1.28976e11	−	1.28976e11i	−0.856162	−	0.856162i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	8.88232e10	−	8.88232e10i	0.574720	−	0.574720i
$628$		0			0
$629$			1.75999e11i			1.12436i
$630$		0			0
$631$	−4.03625e10			−0.254601			−0.127301	−	0.991864i	$-0.540631\pi$
$631$	−4.03625e10			−0.254601			−0.127301	+	0.991864i	$0.540631\pi$
$632$		0			0
$633$	−5.16636e9	−	5.16636e9i	−0.0321788	−	0.0321788i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	1.92933e11	−	1.92933e11i	1.17179	−	1.17179i
$638$		0			0
$639$		−	8.65227e10i		−	0.518951i
$640$		0			0
$641$	−1.84524e11			−1.09300			−0.546501	−	0.837458i	$-0.684041\pi$
$641$	−1.84524e11			−1.09300			−0.546501	+	0.837458i	$0.684041\pi$
$642$		0			0
$643$	6.67833e10	+	6.67833e10i	0.390682	+	0.390682i	0.874931	−	0.484248i	$-0.160907\pi$
$643$	6.67833e10	+	6.67833e10i	0.390682	+	0.390682i	−0.484248	+	0.874931i	$0.660907\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.85945e10	+	2.85945e10i	−0.163180	+	0.163180i	−0.783974	−	0.620794i	$-0.786810\pi$
$647$	−2.85945e10	+	2.85945e10i	−0.163180	+	0.163180i	0.620794	+	0.783974i	$0.286810\pi$
$648$		0			0
$649$		−	3.52594e11i		−	1.98745i
$650$		0			0
$651$	7.59798e10			0.423033
$652$		0			0
$653$	−7.77395e10	−	7.77395e10i	−0.427552	−	0.427552i	0.460242	−	0.887794i	$-0.347763\pi$
$653$	−7.77395e10	−	7.77395e10i	−0.427552	−	0.427552i	−0.887794	+	0.460242i	$0.847763\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	5.82975e10	−	5.82975e10i	0.312888	−	0.312888i
$658$		0			0
$659$			1.35053e11i			0.716082i	0.933706	+	0.358041i	$0.116555\pi$
$659$			1.35053e11i			0.716082i	−0.933706	+	0.358041i	$0.883445\pi$
$660$		0			0
$661$	1.64914e11			0.863875			0.431938	−	0.901903i	$-0.357830\pi$
$661$	1.64914e11			0.863875			0.431938	+	0.901903i	$0.357830\pi$
$662$		0			0
$663$	5.65286e10	+	5.65286e10i	0.292559	+	0.292559i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4.64238e10	−	4.64238e10i	0.234551	−	0.234551i
$668$		0			0
$669$			1.68426e11i			0.840825i
$670$		0			0
$671$	4.30299e11			2.12266
$672$		0			0
$673$	2.44074e10	+	2.44074e10i	0.118977	+	0.118977i	0.764088	−	0.645112i	$-0.223189\pi$
$673$	2.44074e10	+	2.44074e10i	0.118977	+	0.118977i	−0.645112	+	0.764088i	$0.723189\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.40416e8	−	3.40416e8i	0.00162052	−	0.00162052i	−0.706296	−	0.707917i	$-0.749635\pi$
$677$	3.40416e8	−	3.40416e8i	0.00162052	−	0.00162052i	0.707917	+	0.706296i	$0.249635\pi$
$678$		0			0
$679$			3.04138e10i			0.143084i
$680$		0			0
$681$	−4.60790e10			−0.214247
$682$		0			0
$683$	1.91352e11	+	1.91352e11i	0.879325	+	0.879325i	0.993465	−	0.114140i	$-0.0364111\pi$
$683$	1.91352e11	+	1.91352e11i	0.879325	+	0.879325i	−0.114140	+	0.993465i	$0.536411\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	7.79294e10	−	7.79294e10i	0.349844	−	0.349844i
$688$		0			0
$689$		−	1.25394e11i		−	0.556416i
$690$		0			0
$691$	−4.98044e9			−0.0218452			−0.0109226	−	0.999940i	$-0.503477\pi$
$691$	−4.98044e9			−0.0218452			−0.0109226	+	0.999940i	$0.503477\pi$
$692$		0			0
$693$	1.75055e11	+	1.75055e11i	0.759001	+	0.759001i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	5.98281e10	−	5.98281e10i	0.253498	−	0.253498i
$698$		0			0
$699$		−	1.35011e10i		−	0.0565538i
$700$		0			0
$701$	−1.27034e11			−0.526074			−0.263037	−	0.964786i	$-0.584724\pi$
$701$	−1.27034e11			−0.526074			−0.263037	+	0.964786i	$0.584724\pi$
$702$		0			0
$703$	1.67610e11	+	1.67610e11i	0.686245	+	0.686245i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.71109e11	−	1.71109e11i	0.684849	−	0.684849i
$708$		0			0
$709$			8.47385e10i			0.335348i	0.985843	+	0.167674i	$0.0536256\pi$
$709$			8.47385e10i			0.335348i	−0.985843	+	0.167674i	$0.946374\pi$
$710$		0			0
$711$	−1.55122e11			−0.607010
$712$		0			0
$713$	9.79586e10	+	9.79586e10i	0.379039	+	0.379039i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	2.03928e11	−	2.03928e11i	0.771614	−	0.771614i
$718$		0			0
$719$		−	2.74507e11i		−	1.02716i	−0.858041	−	0.513581i	$-0.828319\pi$
$719$		−	2.74507e11i		−	1.02716i	0.858041	−	0.513581i	$-0.171681\pi$
$720$		0			0
$721$	9.26291e11			3.42773
$722$		0			0
$723$	4.84715e10	+	4.84715e10i	0.177392	+	0.177392i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−3.65443e11	+	3.65443e11i	−1.30822	+	1.30822i	−0.385529	+	0.922696i	$0.625981\pi$
$727$	−3.65443e11	+	3.65443e11i	−1.30822	+	1.30822i	−0.922696	+	0.385529i	$0.874019\pi$
$728$		0			0
$729$		−	1.04604e10i		−	0.0370370i
$730$		0			0
$731$	−2.18527e11			−0.765308
$732$		0			0
$733$	−1.98744e11	−	1.98744e11i	−0.688458	−	0.688458i	0.273433	−	0.961891i	$-0.411841\pi$
$733$	−1.98744e11	−	1.98744e11i	−0.688458	−	0.688458i	−0.961891	+	0.273433i	$0.911841\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.24345e11	+	3.24345e11i	−1.09935	+	1.09935i
$738$		0			0
$739$		−	4.43024e11i		−	1.48542i	−0.669612	−	0.742711i	$-0.733540\pi$
$739$		−	4.43024e11i		−	1.48542i	0.669612	−	0.742711i	$-0.266460\pi$
$740$		0			0
$741$	1.07669e11			0.357122
$742$		0			0
$743$	−1.79132e11	−	1.79132e11i	−0.587784	−	0.587784i	0.349247	−	0.937031i	$-0.386437\pi$
$743$	−1.79132e11	−	1.79132e11i	−0.587784	−	0.587784i	−0.937031	+	0.349247i	$0.886437\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−2.32574e10	+	2.32574e10i	−0.0746929	+	0.0746929i
$748$		0			0
$749$		−	8.53460e9i		−	0.0271179i
$750$		0			0
$751$	−1.11196e10			−0.0349565			−0.0174782	−	0.999847i	$-0.505564\pi$
$751$	−1.11196e10			−0.0349565			−0.0174782	+	0.999847i	$0.505564\pi$
$752$		0			0
$753$	7.06434e10	+	7.06434e10i	0.219731	+	0.219731i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−3.41401e11	+	3.41401e11i	−1.03964	+	1.03964i	−0.0404554	+	0.999181i	$0.512881\pi$
$757$	−3.41401e11	+	3.41401e11i	−1.03964	+	1.03964i	−0.999181	+	0.0404554i	$0.987119\pi$
$758$		0			0
$759$			4.51387e11i			1.36014i
$760$		0			0
$761$	−4.14614e11			−1.23625			−0.618123	−	0.786081i	$-0.712107\pi$
$761$	−4.14614e11			−1.23625			−0.618123	+	0.786081i	$0.712107\pi$
$762$		0			0
$763$	−3.35506e11	−	3.35506e11i	−0.989924	−	0.989924i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.13702e11	−	2.13702e11i	0.617485	−	0.617485i
$768$		0			0
$769$			4.77373e11i			1.36506i	0.730856	+	0.682531i	$0.239121\pi$
$769$			4.77373e11i			1.36506i	−0.730856	+	0.682531i	$0.760879\pi$
$770$		0			0
$771$	−7.59988e10			−0.215075
$772$		0			0
$773$	2.34718e11	+	2.34718e11i	0.657398	+	0.657398i	0.954764	−	0.297366i	$-0.0961080\pi$
$773$	2.34718e11	+	2.34718e11i	0.657398	+	0.657398i	−0.297366	+	0.954764i	$0.596108\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−3.30331e11	+	3.30331e11i	−0.906286	+	0.906286i
$778$		0			0
$779$		−	1.13953e11i		−	0.309440i
$780$		0			0
$781$	−1.06922e12			−2.87385
$782$		0			0
$783$	1.32946e10	+	1.32946e10i	0.0353694	+	0.0353694i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−4.14846e11	+	4.14846e11i	−1.08140	+	1.08140i	−0.0850250	+	0.996379i	$0.527097\pi$
$787$	−4.14846e11	+	4.14846e11i	−1.08140	+	1.08140i	−0.996379	+	0.0850250i	$0.972903\pi$
$788$		0			0
$789$		−	8.62464e10i		−	0.222553i
$790$		0			0
$791$	−1.78464e11			−0.455873
$792$		0			0
$793$	2.60797e11	+	2.60797e11i	0.659494	+	0.659494i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−9.49065e10	+	9.49065e10i	−0.235214	+	0.235214i	−0.814865	−	0.579651i	$-0.803189\pi$
$797$	−9.49065e10	+	9.49065e10i	−0.235214	+	0.235214i	0.579651	+	0.814865i	$0.303189\pi$
$798$		0			0
$799$			2.85885e9i			0.00701462i
$800$		0			0
$801$	9.52395e10			0.231359
$802$		0			0
$803$	−7.20423e11	−	7.20423e11i	−1.73271	−	1.73271i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.48912e11	−	1.48912e11i	0.351103	−	0.351103i
$808$		0			0
$809$		−	6.86657e11i		−	1.60305i	−0.597964	−	0.801523i	$-0.704024\pi$
$809$		−	6.86657e11i		−	1.60305i	0.597964	−	0.801523i	$-0.295976\pi$
$810$		0			0
$811$	−2.19281e11			−0.506894			−0.253447	−	0.967349i	$-0.581564\pi$
$811$	−2.19281e11			−0.506894			−0.253447	+	0.967349i	$0.581564\pi$
$812$		0			0
$813$	1.63766e11	+	1.63766e11i	0.374854	+	0.374854i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−2.08112e11	+	2.08112e11i	−0.467099	+	0.467099i
$818$		0			0
$819$			2.12196e11i			0.471631i
$820$		0			0
$821$	3.06482e11			0.674579			0.337289	−	0.941401i	$-0.390490\pi$
$821$	3.06482e11			0.674579			0.337289	+	0.941401i	$0.390490\pi$
$822$		0			0
$823$	1.58460e11	+	1.58460e11i	0.345398	+	0.345398i	0.858392	−	0.512994i	$-0.171464\pi$
$823$	1.58460e11	+	1.58460e11i	0.345398	+	0.345398i	−0.512994	+	0.858392i	$0.671464\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−2.32197e11	+	2.32197e11i	−0.496404	+	0.496404i	−0.910317	−	0.413913i	$-0.864162\pi$
$827$	−2.32197e11	+	2.32197e11i	−0.496404	+	0.496404i	0.413913	+	0.910317i	$0.364162\pi$
$828$		0			0
$829$			6.01651e11i			1.27387i	0.770916	+	0.636937i	$0.219799\pi$
$829$			6.01651e11i			1.27387i	−0.770916	+	0.636937i	$0.780201\pi$
$830$		0			0
$831$	1.33642e11			0.280246
$832$		0			0
$833$	−6.14605e11	−	6.14605e11i	−1.27649	−	1.27649i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−2.80529e10	+	2.80529e10i	−0.0571578	+	0.0571578i
$838$		0			0
$839$		−	3.59762e11i		−	0.726052i	−0.931779	−	0.363026i	$-0.881744\pi$
$839$		−	3.59762e11i		−	0.726052i	0.931779	−	0.363026i	$-0.118256\pi$
$840$		0			0
$841$	4.66453e11			0.932446
$842$		0			0
$843$	−1.74615e11	−	1.74615e11i	−0.345758	−	0.345758i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	1.52842e12	−	1.52842e12i	2.96967	−	2.96967i
$848$		0			0
$849$			1.93247e10i			0.0371948i
$850$		0			0
$851$	−8.51772e11			−1.62407
$852$		0			0
$853$	−2.29135e11	−	2.29135e11i	−0.432808	−	0.432808i	0.456775	−	0.889582i	$-0.349005\pi$
$853$	−2.29135e11	−	2.29135e11i	−0.432808	−	0.432808i	−0.889582	+	0.456775i	$0.849005\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.79655e11	−	1.79655e11i	0.333054	−	0.333054i	−0.520691	−	0.853745i	$-0.674326\pi$
$857$	1.79655e11	−	1.79655e11i	0.333054	−	0.333054i	0.853745	+	0.520691i	$0.174326\pi$
$858$		0			0
$859$		−	2.80475e11i		−	0.515135i	−0.966260	−	0.257568i	$-0.917079\pi$
$859$		−	2.80475e11i		−	0.515135i	0.966260	−	0.257568i	$-0.0829210\pi$
$860$		0			0
$861$	2.24582e11			0.408661
$862$		0			0
$863$	3.95652e11	+	3.95652e11i	0.713296	+	0.713296i	0.967223	−	0.253927i	$-0.0817223\pi$
$863$	3.95652e11	+	3.95652e11i	0.713296	+	0.713296i	−0.253927	+	0.967223i	$0.581722\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−5.05984e10	+	5.05984e10i	−0.0895489	+	0.0895489i
$868$		0			0
$869$			1.91696e12i			3.36150i
$870$		0			0
$871$	−3.93161e11			−0.683122
$872$		0			0
$873$	−1.12292e10	−	1.12292e10i	−0.0193327	−	0.0193327i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.37678e11	−	1.37678e11i	0.232737	−	0.232737i	−0.581097	−	0.813834i	$-0.697376\pi$
$877$	1.37678e11	−	1.37678e11i	0.232737	−	0.232737i	0.813834	+	0.581097i	$0.197376\pi$
$878$		0			0
$879$		−	2.76654e11i		−	0.463427i
$880$		0			0
$881$	−8.53069e11			−1.41606			−0.708028	−	0.706185i	$-0.750415\pi$
$881$	−8.53069e11			−1.41606			−0.708028	+	0.706185i	$0.750415\pi$
$882$		0			0
$883$	2.21213e11	+	2.21213e11i	0.363888	+	0.363888i	0.865242	−	0.501354i	$-0.167165\pi$
$883$	2.21213e11	+	2.21213e11i	0.363888	+	0.363888i	−0.501354	+	0.865242i	$0.667165\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	5.15132e11	−	5.15132e11i	0.832194	−	0.832194i	−0.155623	−	0.987817i	$-0.549738\pi$
$887$	5.15132e11	−	5.15132e11i	0.832194	−	0.832194i	0.987817	+	0.155623i	$0.0497385\pi$
$888$		0			0
$889$			2.03786e12i			3.26263i
$890$		0			0
$891$	−1.29266e11			−0.205104
$892$		0			0
$893$	2.72259e9	+	2.72259e9i	0.00428131	+	0.00428131i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−2.73579e11	+	2.73579e11i	−0.422583	+	0.422583i
$898$		0			0
$899$		−	7.13077e10i		−	0.109169i
$900$		0			0
$901$	−3.99453e11			−0.606131
$902$		0			0
$903$	−4.10153e11	−	4.10153e11i	−0.616872	−	0.616872i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1.80758e11	−	1.80758e11i	0.267097	−	0.267097i	−0.560833	−	0.827929i	$-0.689519\pi$
$907$	1.80758e11	−	1.80758e11i	0.267097	−	0.267097i	0.827929	+	0.560833i	$0.189519\pi$
$908$		0			0
$909$			1.26352e11i			0.185066i
$910$		0			0
$911$	6.86680e11			0.996967			0.498483	−	0.866899i	$-0.333891\pi$
$911$	6.86680e11			0.996967			0.498483	+	0.866899i	$0.333891\pi$
$912$		0			0
$913$	2.87409e11	+	2.87409e11i	0.413634	+	0.413634i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.20901e12	+	1.20901e12i	−1.70983	+	1.70983i
$918$		0			0
$919$		−	5.74926e11i		−	0.806028i	−0.915194	−	0.403014i	$-0.867963\pi$
$919$		−	5.74926e11i		−	0.806028i	0.915194	−	0.403014i	$-0.132037\pi$
$920$		0			0
$921$	−1.40981e11			−0.195940
$922$		0			0
$923$	−6.48039e11	−	6.48039e11i	−0.892882	−	0.892882i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−3.42000e11	+	3.42000e11i	−0.463135	+	0.463135i
$928$		0			0
$929$		−	4.82390e11i		−	0.647642i	−0.946118	−	0.323821i	$-0.895032\pi$
$929$		−	4.82390e11i		−	0.647642i	0.946118	−	0.323821i	$-0.104968\pi$
$930$		0			0
$931$	−1.17062e12			−1.55818
$932$		0			0
$933$	−4.82604e11	−	4.82604e11i	−0.636890	−	0.636890i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−2.50550e11	+	2.50550e11i	−0.325040	+	0.325040i	−0.850697	−	0.525657i	$-0.823820\pi$
$937$	−2.50550e11	+	2.50550e11i	−0.325040	+	0.325040i	0.525657	+	0.850697i	$0.323820\pi$
$938$		0			0
$939$		−	3.66288e11i		−	0.471151i
$940$		0			0
$941$	8.26476e11			1.05408			0.527038	−	0.849842i	$-0.323303\pi$
$941$	8.26476e11			1.05408			0.527038	+	0.849842i	$0.323303\pi$
$942$		0			0
$943$	2.89547e11	+	2.89547e11i	0.366162	+	0.366162i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.48302e10	+	7.48302e10i	−0.0930416	+	0.0930416i	−0.752096	−	0.659054i	$-0.770957\pi$
$947$	−7.48302e10	+	7.48302e10i	−0.0930416	+	0.0930416i	0.659054	+	0.752096i	$0.270957\pi$
$948$		0			0
$949$		−	8.73274e11i		−	1.07668i
$950$		0			0
$951$	1.40188e11			0.171392
$952$		0			0
$953$	2.50338e11	+	2.50338e11i	0.303498	+	0.303498i	0.842381	−	0.538883i	$-0.181153\pi$
$953$	2.50338e11	+	2.50338e11i	0.303498	+	0.303498i	−0.538883	+	0.842381i	$0.681153\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	1.64291e11	−	1.64291e11i	0.195869	−	0.195869i
$958$		0			0
$959$			1.31941e12i			1.55993i
$960$		0			0
$961$	−7.02425e11			−0.823581
$962$		0			0
$963$	3.15110e9	+	3.15110e9i	0.00366401	+	0.00366401i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−5.78373e10	+	5.78373e10i	−0.0661458	+	0.0661458i	−0.739406	−	0.673260i	$-0.764893\pi$
$967$	−5.78373e10	+	5.78373e10i	−0.0661458	+	0.0661458i	0.673260	+	0.739406i	$0.264893\pi$
$968$		0			0
$969$		−	3.42988e11i		−	0.389030i
$970$		0			0
$971$	−6.95826e11			−0.782751			−0.391376	−	0.920231i	$-0.628001\pi$
$971$	−6.95826e11			−0.782751			−0.391376	+	0.920231i	$0.628001\pi$
$972$		0			0
$973$	−1.33577e12	−	1.33577e12i	−1.49033	−	1.49033i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.05513e11	−	1.05513e11i	0.115805	−	0.115805i	−0.646829	−	0.762635i	$-0.723905\pi$
$977$	1.05513e11	−	1.05513e11i	0.115805	−	0.115805i	0.762635	+	0.646829i	$0.223905\pi$
$978$		0			0
$979$		−	1.17694e12i		−	1.28122i
$980$		0			0
$981$	2.47747e11			0.267506
$982$		0			0
$983$	3.45988e11	+	3.45988e11i	0.370550	+	0.370550i	0.867677	−	0.497128i	$-0.165612\pi$
$983$	3.45988e11	+	3.45988e11i	0.370550	+	0.370550i	−0.497128	+	0.867677i	$0.665612\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−5.36576e9	+	5.36576e9i	−0.00565409	+	0.00565409i
$988$		0			0
$989$		−	1.05760e12i		−	1.10544i
$990$		0			0
$991$	9.71387e10			0.100716			0.0503579	−	0.998731i	$-0.483964\pi$
$991$	9.71387e10			0.100716			0.0503579	+	0.998731i	$0.483964\pi$
$992$		0			0
$993$	−8.84214e10	−	8.84214e10i	−0.0909411	−	0.0909411i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−6.42365e11	+	6.42365e11i	−0.650132	+	0.650132i	−0.953025	−	0.302893i	$-0.902048\pi$
$997$	−6.42365e11	+	6.42365e11i	−0.650132	+	0.650132i	0.302893	+	0.953025i	$0.402048\pi$
$998$		0			0
$999$		−	2.43926e11i		−	0.244904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.9.k.e.193.8		16
5.2	odd	4	inner	300.9.k.e.157.8		16
5.3	odd	4		60.9.k.a.37.1	yes	16
5.4	even	2		60.9.k.a.13.1	✓	16
15.8	even	4		180.9.l.c.37.7		16
15.14	odd	2		180.9.l.c.73.7		16
20.3	even	4		240.9.bg.c.97.5		16
20.19	odd	2		240.9.bg.c.193.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.9.k.a.13.1	✓	16	5.4	even	2
60.9.k.a.37.1	yes	16	5.3	odd	4
180.9.l.c.37.7		16	15.8	even	4
180.9.l.c.73.7		16	15.14	odd	2
240.9.bg.c.97.5		16	20.3	even	4
240.9.bg.c.193.5		16	20.19	odd	2
300.9.k.e.157.8		16	5.2	odd	4	inner
300.9.k.e.193.8		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	300.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(33.0681 + 33.0681i) q^{3} +(2961.69 - 2961.69i) q^{7} +2187.00i q^{9} +O(q^{10})\)	\(q+(33.0681 + 33.0681i) q^{3} +(2961.69 - 2961.69i) q^{7} +2187.00i q^{9} +27026.3 q^{11} +(16380.2 + 16380.2i) q^{13} +(52180.6 - 52180.6i) q^{17} -99387.1i q^{19} +195875. q^{21} +(252536. + 252536. i) q^{23} +(-72320.0 + 72320.0i) q^{27} -183830. i q^{29} +387900. q^{31} +(893709. + 893709. i) q^{33} +(-1.68644e6 + 1.68644e6i) q^{37} +1.08333e6i q^{39} +1.14656e6 q^{41} +(-2.09395e6 - 2.09395e6i) q^{43} +(-27393.8 + 27393.8i) q^{47} -1.17784e7i q^{49} +3.45103e6 q^{51} +(-3.82760e6 - 3.82760e6i) q^{53} +(3.28655e6 - 3.28655e6i) q^{57} -1.30463e7i q^{59} +1.59215e7 q^{61} +(6.47722e6 + 6.47722e6i) q^{63} +(-1.20011e7 + 1.20011e7i) q^{67} +1.67018e7i q^{69} -3.95623e7 q^{71} +(-2.66564e7 - 2.66564e7i) q^{73} +(8.00436e7 - 8.00436e7i) q^{77} +7.09293e7i q^{79} -4.78297e6 q^{81} +(1.06344e7 + 1.06344e7i) q^{83} +(6.07892e6 - 6.07892e6i) q^{87} -4.35480e7i q^{89} +9.70263e7 q^{91} +(1.28271e7 + 1.28271e7i) q^{93} +(-5.13454e6 + 5.13454e6i) q^{97} +5.91065e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4220 q^{7}+O(q^{10}) \) 16 * q - 4220 * q^7	\( 16 q - 4220 q^{7} + 23616 q^{11} + 18900 q^{13} + 44940 q^{17} + 163944 q^{21} - 196440 q^{23} + 3742624 q^{31} + 134460 q^{33} + 2141100 q^{37} + 16347000 q^{41} - 12080280 q^{43} + 14942400 q^{47} + 7693704 q^{51} - 23760300 q^{53} + 27530280 q^{57} + 85401912 q^{61} - 9229140 q^{63} + 99451240 q^{67} + 73302480 q^{71} - 124097320 q^{73} + 185945400 q^{77} - 76527504 q^{81} + 22058160 q^{83} + 110300940 q^{87} + 170997360 q^{91} - 9969480 q^{93} - 185269800 q^{97}+O(q^{100}) \) 16 * q - 4220 * q^7 + 23616 * q^11 + 18900 * q^13 + 44940 * q^17 + 163944 * q^21 - 196440 * q^23 + 3742624 * q^31 + 134460 * q^33 + 2141100 * q^37 + 16347000 * q^41 - 12080280 * q^43 + 14942400 * q^47 + 7693704 * q^51 - 23760300 * q^53 + 27530280 * q^57 + 85401912 * q^61 - 9229140 * q^63 + 99451240 * q^67 + 73302480 * q^71 - 124097320 * q^73 + 185945400 * q^77 - 76527504 * q^81 + 22058160 * q^83 + 110300940 * q^87 + 170997360 * q^91 - 9969480 * q^93 - 185269800 * q^97

Introduction

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Database

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