LMFDB - Embedded newform 300.9.k.e.157.8

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			157.8
Root			$3225.69 + 1.00000i$ of defining polynomial
Character	$\chi$	$=$	300.157
Dual form			300.9.k.e.193.8

$q$-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 $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		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	0.962601	+	0.270923i	$0.0873287\pi$
$7$	2961.69	+	2961.69i	1.23352	+	1.23352i	0.270923	+	0.962601i	$0.412671\pi$
$8$		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	−0.359593	−	0.933109i	$-0.617084\pi$
$13$	16380.2	−	16380.2i	0.573517	−	0.573517i	0.933109	+	0.359593i	$0.117084\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	52180.6	+	52180.6i	0.624760	+	0.624760i	0.946745	−	0.321985i	$-0.104350\pi$
$17$	52180.6	+	52180.6i	0.624760	+	0.624760i	−0.321985	+	0.946745i	$0.604350\pi$
$18$		0			0
$19$			99387.1i			0.762633i	0.924444	+	0.381317i	$0.124529\pi$
$19$			99387.1i			0.762633i	−0.924444	+	0.381317i	$0.875471\pi$
$20$		0			0
$21$	195875.			1.00717
$22$		0			0
$23$	252536.	−	252536.i	0.902427	−	0.902427i	−0.0932190	−	0.995646i	$-0.529716\pi$
$23$	252536.	−	252536.i	0.902427	−	0.902427i	0.995646	+	0.0932190i	$0.0297157\pi$
$24$		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	$0.0414835\pi$
$29$			183830.i			0.259911i	−0.991520	+	0.129956i	$0.958517\pi$
$30$		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	0.0955853	−	0.995421i	$-0.469528\pi$
$37$	−1.68644e6	−	1.68644e6i	−0.899836	−	0.899836i	−0.995421	+	0.0955853i	$0.969528\pi$
$38$		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	−0.943592	−	0.331110i	$-0.892577\pi$
$43$	−2.09395e6	+	2.09395e6i	−0.612482	+	0.612482i	0.331110	+	0.943592i	$0.392577\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−27393.8	−	27393.8i	−0.00561385	−	0.00561385i	0.704294	−	0.709908i	$-0.251264\pi$
$47$	−27393.8	−	27393.8i	−0.00561385	−	0.00561385i	−0.709908	+	0.704294i	$0.751264\pi$
$48$		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	−0.906753	−	0.421662i	$-0.861447\pi$
$53$	−3.82760e6	+	3.82760e6i	−0.485091	+	0.485091i	0.421662	+	0.906753i	$0.361447\pi$
$54$		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	$0.180945\pi$
$59$			1.30463e7i			1.07666i	−0.842733	+	0.538332i	$0.819055\pi$
$60$		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	0.343572	−	0.939126i	$-0.388363\pi$
$67$	−1.20011e7	−	1.20011e7i	−0.595555	−	0.595555i	−0.939126	+	0.343572i	$0.888363\pi$
$68$		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	−0.998225	−	0.0595621i	$-0.981030\pi$
$73$	−2.66564e7	+	2.66564e7i	−0.938663	+	0.938663i	0.0595621	+	0.998225i	$0.481030\pi$
$74$		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	$-0.635685\pi$
$79$		−	7.09293e7i		−	1.82103i	0.413475	−	0.910515i	$-0.364315\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$		0			0
$83$	1.06344e7	−	1.06344e7i	0.224079	−	0.224079i	−0.586135	−	0.810214i	$-0.699351\pi$
$83$	1.06344e7	−	1.06344e7i	0.224079	−	0.224079i	0.810214	+	0.586135i	$0.199351\pi$
$84$		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	$0.112813\pi$
$89$			4.35480e7i			0.694078i	−0.937851	+	0.347039i	$0.887187\pi$
$90$		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	0.677513	−	0.735511i	$-0.263058\pi$
$97$	−5.13454e6	−	5.13454e6i	−0.0579982	−	0.0579982i	−0.735511	+	0.677513i	$0.763058\pi$
$98$		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	0.562838	−	0.826567i	$-0.309709\pi$
$103$	1.56379e8	−	1.56379e8i	1.38941	−	1.38941i	0.826567	−	0.562838i	$-0.190291\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.44083e6	+	1.44083e6i	0.0109920	+	0.0109920i	0.712581	−	0.701589i	$-0.247526\pi$
$107$	1.44083e6	+	1.44083e6i	0.0109920	+	0.0109920i	−0.701589	+	0.712581i	$0.747526\pi$
$108$		0			0
$109$			1.13282e8i			0.802517i	0.915965	+	0.401259i	$0.131427\pi$
$109$			1.13282e8i			0.802517i	−0.915965	+	0.401259i	$0.868573\pi$
$110$		0			0
$111$	−1.11535e8			−0.734713
$112$		0			0
$113$	−3.01287e7	+	3.01287e7i	−0.184785	+	0.184785i	−0.793437	−	0.608652i	$-0.791710\pi$
$113$	−3.01287e7	+	3.01287e7i	−0.184785	+	0.184785i	0.608652	+	0.793437i	$0.291710\pi$
$114$		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	−0.911760	−	0.410724i	$-0.865276\pi$
$127$	−3.44037e8	−	3.44037e8i	−1.32248	−	1.32248i	−0.410724	−	0.911760i	$-0.634724\pi$
$128$		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	0.316340	−	0.948646i	$-0.397546\pi$
$137$	−2.22746e8	−	2.22746e8i	−0.632305	−	0.632305i	−0.948646	+	0.316340i	$0.897546\pi$
$138$		0			0
$139$			4.51017e8i			1.20819i	0.796914	+	0.604093i	$0.206465\pi$
$139$			4.51017e8i			1.20819i	−0.796914	+	0.604093i	$0.793535\pi$
$140$		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	$-0.768472\pi$
$149$		−	6.55443e8i		−	1.32981i	0.746928	−	0.664905i	$-0.231528\pi$
$150$		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	0.847060	−	0.531497i	$-0.178370\pi$
$157$	1.91728e8	+	1.91728e8i	0.315563	+	0.315563i	−0.531497	+	0.847060i	$0.678370\pi$
$158$		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	−0.0716600	−	0.997429i	$-0.522830\pi$
$163$	6.53511e8	−	6.53511e8i	0.925769	−	0.925769i	0.997429	+	0.0716600i	$0.0228297\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.62387e8	+	8.62387e8i	1.10876	+	1.10876i	0.993314	+	0.115442i	$0.0368285\pi$
$167$	8.62387e8	+	8.62387e8i	1.10876	+	1.10876i	0.115442	+	0.993314i	$0.463171\pi$
$168$		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	−0.0676670	−	0.997708i	$-0.521556\pi$
$173$	8.33080e8	−	8.33080e8i	0.930041	−	0.930041i	0.997708	+	0.0676670i	$0.0215556\pi$
$174$		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	$-0.887138\pi$
$179$		−	7.12857e8i		−	0.694369i	0.937797	−	0.347184i	$-0.112862\pi$
$180$		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	−0.941393	−	0.337313i	$-0.890482\pi$
$193$	−8.38154e8	+	8.38154e8i	−0.604080	+	0.604080i	0.337313	+	0.941393i	$0.390482\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−4.22403e8	−	4.22403e8i	−0.280454	−	0.280454i	0.552836	−	0.833290i	$-0.313546\pi$
$197$	−4.22403e8	−	4.22403e8i	−0.280454	−	0.280454i	−0.833290	+	0.552836i	$0.813546\pi$
$198$		0			0
$199$			1.23810e9i			0.789487i	0.918791	+	0.394743i	$0.129167\pi$
$199$			1.23810e9i			0.789487i	−0.918791	+	0.394743i	$0.870833\pi$
$200$		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	0.0302537	−	0.999542i	$-0.490368\pi$
$223$	2.54666e9	−	2.54666e9i	1.02980	−	1.02980i	0.999542	−	0.0302537i	$-0.00963153\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.96729e8	−	6.96729e8i	−0.262398	−	0.262398i	0.563630	−	0.826028i	$-0.309405\pi$
$227$	−6.96729e8	−	6.96729e8i	−0.262398	−	0.262398i	−0.826028	+	0.563630i	$0.809405\pi$
$228$		0			0
$229$			2.35663e9i			0.856939i	0.903556	+	0.428470i	$0.140947\pi$
$229$			2.35663e9i			0.856939i	−0.903556	+	0.428470i	$0.859053\pi$
$230$		0			0
$231$	5.29378e9			1.85916
$232$		0			0
$233$	−2.04141e8	+	2.04141e8i	−0.0692639	+	0.0692639i	−0.740890	−	0.671626i	$-0.765596\pi$
$233$	−2.04141e8	+	2.04141e8i	−0.0692639	+	0.0692639i	0.671626	+	0.740890i	$0.265596\pi$
$234$		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	$0.393968\pi$
$239$			6.16691e9i			1.89006i	−0.326982	+	0.945031i	$0.606032\pi$
$240$		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	0.563027	−	0.826439i	$-0.309637\pi$
$257$	−1.14913e9	−	1.14913e9i	−0.263412	−	0.263412i	−0.826439	+	0.563027i	$0.809637\pi$
$258$		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	−0.830134	−	0.557564i	$-0.811736\pi$
$263$	−1.30407e9	+	1.30407e9i	−0.272570	+	0.272570i	0.557564	+	0.830134i	$0.311736\pi$
$264$		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	$0.141490\pi$
$269$			4.50318e9i			0.860022i	−0.902824	+	0.430011i	$0.858510\pi$
$270$		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	0.857580	−	0.514350i	$-0.171967\pi$
$277$	2.02071e9	+	2.02071e9i	0.343230	+	0.343230i	−0.514350	+	0.857580i	$0.671967\pi$
$278$		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	−0.683963	−	0.729517i	$-0.739745\pi$
$283$	2.92195e8	−	2.92195e8i	0.0455541	−	0.0455541i	0.729517	+	0.683963i	$0.239745\pi$
$284$		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	−0.931450	−	0.363870i	$-0.881455\pi$
$293$	−4.18309e9	+	4.18309e9i	−0.567580	+	0.567580i	0.363870	+	0.931450i	$0.381455\pi$
$294$		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	0.576864	−	0.816840i	$-0.304276\pi$
$307$	−2.13168e9	−	2.13168e9i	−0.239976	−	0.239976i	−0.816840	+	0.576864i	$0.804276\pi$
$308$		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	−0.934086	−	0.357047i	$-0.883784\pi$
$313$	−5.53838e9	+	5.53838e9i	−0.577040	+	0.577040i	0.357047	+	0.934086i	$0.383784\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.11969e9	+	2.11969e9i	0.209911	+	0.209911i	0.804230	−	0.594318i	$-0.202578\pi$
$317$	2.11969e9	+	2.11969e9i	0.209911	+	0.209911i	−0.594318	+	0.804230i	$0.702578\pi$
$318$		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	0.0509278	−	0.998702i	$-0.483782\pi$
$337$	−1.22243e10	−	1.22243e10i	−0.947775	−	0.947775i	−0.998702	+	0.0509278i	$0.983782\pi$
$338$		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	−0.987503	−	0.157602i	$-0.949624\pi$
$347$	−1.66021e10	−	1.66021e10i	−1.14510	−	1.14510i	−0.157602	−	0.987503i	$-0.550376\pi$
$348$		0			0
$349$			1.19894e10i			0.808157i	0.914724	+	0.404079i	$0.132408\pi$
$349$			1.19894e10i			0.808157i	−0.914724	+	0.404079i	$0.867592\pi$
$350$		0			0
$351$	−2.36923e9			−0.156092
$352$		0			0
$353$	1.20155e10	−	1.20155e10i	0.773826	−	0.773826i	−0.204947	−	0.978773i	$-0.565702\pi$
$353$	1.20155e10	−	1.20155e10i	0.773826	−	0.773826i	0.978773	+	0.204947i	$0.0657022\pi$
$354$		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	$0.0213353\pi$
$359$			2.22500e9i			0.133953i	−0.997755	+	0.0669765i	$0.978665\pi$
$360$		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	0.648592	−	0.761136i	$-0.275358\pi$
$367$	−2.04168e9	−	2.04168e9i	−0.112545	−	0.112545i	−0.761136	+	0.648592i	$0.775358\pi$
$368$		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	−0.690393	−	0.723435i	$-0.742562\pi$
$373$	6.39591e8	−	6.39591e8i	0.0330420	−	0.0330420i	0.723435	+	0.690393i	$0.242562\pi$
$374$		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	$-0.837978\pi$
$379$		−	2.01090e10i		−	0.974619i	0.873229	−	0.487309i	$-0.162022\pi$
$380$		0			0
$381$	−2.27533e10			−1.07980
$382$		0			0
$383$	−1.80407e10	+	1.80407e10i	−0.838412	+	0.838412i	−0.988650	−	0.150238i	$-0.951996\pi$
$383$	−1.80407e10	+	1.80407e10i	−0.838412	+	0.838412i	0.150238	+	0.988650i	$0.451996\pi$
$384$		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	$-0.897396\pi$
$389$		−	1.45076e10i		−	0.633572i	0.948497	−	0.316786i	$-0.102604\pi$
$390$		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	0.469880	−	0.882731i	$-0.344297\pi$
$397$	−1.02555e10	−	1.02555e10i	−0.412851	−	0.412851i	−0.882731	+	0.469880i	$0.844297\pi$
$398$		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	$-0.926045\pi$
$409$		−	1.28862e10i		−	0.460501i	0.973131	−	0.230250i	$-0.0739546\pi$
$410$		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	$-0.889680\pi$
$419$		−	2.09392e10i		−	0.679367i	0.940540	−	0.339684i	$-0.110320\pi$
$420$		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	0.0663689	−	0.997795i	$-0.478859\pi$
$433$	3.74076e10	−	3.74076e10i	1.06416	−	1.06416i	0.997795	−	0.0663689i	$-0.0211414\pi$
$434$		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	$-0.954140\pi$
$439$		−	1.06651e10i		−	0.287149i	0.989640	−	0.143574i	$-0.0458596\pi$
$440$		0			0
$441$	2.57594e10			0.681054
$442$		0			0
$443$	−1.89340e10	+	1.89340e10i	−0.491617	+	0.491617i	−0.908815	−	0.417198i	$-0.863012\pi$
$443$	−1.89340e10	+	1.89340e10i	−0.491617	+	0.491617i	0.417198	+	0.908815i	$0.363012\pi$
$444$		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	$0.252760\pi$
$449$			5.79740e10i			1.42642i	−0.700950	+	0.713210i	$0.747240\pi$
$450$		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	−0.987123	−	0.159965i	$-0.948862\pi$
$457$	−5.00335e10	−	5.00335e10i	−1.14709	−	1.14709i	−0.159965	−	0.987123i	$-0.551138\pi$
$458$		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	−0.000373953		1.00000i	$0.500119\pi$
$463$	−4.59712e10	+	4.59712e10i	−1.00037	+	1.00037i	−1.00000		0.000373953i	$0.999881\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.62076e10	+	2.62076e10i	0.551009	+	0.551009i	0.926732	−	0.375723i	$-0.122606\pi$
$467$	2.62076e10	+	2.62076e10i	0.551009	+	0.551009i	−0.375723	+	0.926732i	$0.622606\pi$
$468$		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	$0.171867\pi$
$479$			5.41257e10i			1.02816i	−0.857742	+	0.514081i	$0.828133\pi$
$480$		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	0.998448	−	0.0556955i	$-0.0177376\pi$
$487$	5.30290e10	+	5.30290e10i	0.942752	+	0.942752i	−0.0556955	+	0.998448i	$0.517738\pi$
$488$		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	$0.0177294\pi$
$499$			6.90320e9i			0.111339i	−0.998449	+	0.0556696i	$0.982271\pi$
$500$		0			0
$501$	5.70350e10			0.905296
$502$		0			0
$503$	−2.01629e10	+	2.01629e10i	−0.314978	+	0.314978i	−0.846834	−	0.531856i	$-0.821495\pi$
$503$	−2.01629e10	+	2.01629e10i	−0.314978	+	0.314978i	0.531856	+	0.846834i	$0.321495\pi$
$504$		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	$-0.793670\pi$
$509$		−	8.10518e10i		−	1.20751i	0.797169	−	0.603756i	$-0.206330\pi$
$510$		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	−0.00923057	−	0.999957i	$-0.502938\pi$
$523$	7.41243e10	−	7.41243e10i	0.990727	−	0.990727i	0.999957	+	0.00923057i	$0.00293822\pi$
$524$		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	0.748046	−	0.663647i	$-0.230992\pi$
$547$	7.55594e9	+	7.55594e9i	0.0843994	+	0.0843994i	−0.663647	+	0.748046i	$0.730992\pi$
$548$		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	0.733907	−	0.679250i	$-0.237695\pi$
$557$	5.26098e9	+	5.26098e9i	0.0546570	+	0.0546570i	−0.679250	+	0.733907i	$0.737695\pi$
$558$		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	−0.803074	−	0.595880i	$-0.796803\pi$
$563$	−2.08166e10	+	2.08166e10i	−0.207194	+	0.207194i	0.595880	+	0.803074i	$0.296803\pi$
$564$		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	$-0.979072\pi$
$569$		−	1.37736e10i		−	0.131401i	0.997839	−	0.0657006i	$-0.0209282\pi$
$570$		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	0.890538	−	0.454910i	$-0.150328\pi$
$577$	4.82858e10	+	4.82858e10i	0.435628	+	0.435628i	−0.454910	+	0.890538i	$0.650328\pi$
$578$		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	0.533206	−	0.845985i	$-0.320987\pi$
$587$	−3.71355e10	−	3.71355e10i	−0.312779	−	0.312779i	−0.845985	+	0.533206i	$0.820987\pi$
$588$		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	−0.977942	−	0.208875i	$-0.933020\pi$
$593$	−9.51005e10	+	9.51005e10i	−0.769067	+	0.769067i	0.208875	+	0.977942i	$0.433020\pi$
$594$		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	$0.400250\pi$
$599$			2.44937e11i			1.90260i	−0.308269	+	0.951299i	$0.599750\pi$
$600$		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	0.945027	−	0.326992i	$-0.106035\pi$
$607$	8.39011e10	+	8.39011e10i	0.618035	+	0.618035i	−0.326992	+	0.945027i	$0.606035\pi$
$608$		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	−0.350260	−	0.936652i	$-0.613907\pi$
$613$	8.27999e10	−	8.27999e10i	0.586392	−	0.586392i	0.936652	+	0.350260i	$0.113907\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−9.63193e10	−	9.63193e10i	−0.664619	−	0.664619i	0.291846	−	0.956465i	$-0.405730\pi$
$617$	−9.63193e10	−	9.63193e10i	−0.664619	−	0.664619i	−0.956465	+	0.291846i	$0.905730\pi$
$618$		0			0
$619$		−	2.72015e11i		−	1.85281i	−0.376529	−	0.926405i	$-0.622882\pi$
$619$		−	2.72015e11i		−	1.85281i	0.376529	−	0.926405i	$-0.377118\pi$
$620$		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	−0.484248	−	0.874931i	$-0.660907\pi$
$643$	6.67833e10	−	6.67833e10i	0.390682	−	0.390682i	0.874931	+	0.484248i	$0.160907\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.85945e10	−	2.85945e10i	−0.163180	−	0.163180i	0.620794	−	0.783974i	$-0.286810\pi$
$647$	−2.85945e10	−	2.85945e10i	−0.163180	−	0.163180i	−0.783974	+	0.620794i	$0.786810\pi$
$648$		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	−0.887794	−	0.460242i	$-0.847763\pi$
$653$	−7.77395e10	+	7.77395e10i	−0.427552	+	0.427552i	0.460242	+	0.887794i	$0.347763\pi$
$654$		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	$-0.883445\pi$
$659$		−	1.35053e11i		−	0.716082i	0.933706	−	0.358041i	$-0.116555\pi$
$660$		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	−0.645112	−	0.764088i	$-0.723189\pi$
$673$	2.44074e10	−	2.44074e10i	0.118977	−	0.118977i	0.764088	+	0.645112i	$0.223189\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.40416e8	+	3.40416e8i	0.00162052	+	0.00162052i	0.707917	−	0.706296i	$-0.249635\pi$
$677$	3.40416e8	+	3.40416e8i	0.00162052	+	0.00162052i	−0.706296	+	0.707917i	$0.749635\pi$
$678$		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	−0.114140	−	0.993465i	$-0.536411\pi$
$683$	1.91352e11	−	1.91352e11i	0.879325	−	0.879325i	0.993465	+	0.114140i	$0.0364111\pi$
$684$		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	$-0.946374\pi$
$709$		−	8.47385e10i		−	0.335348i	0.985843	−	0.167674i	$-0.0536256\pi$
$710$		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	$0.171681\pi$
$719$			2.74507e11i			1.02716i	−0.858041	+	0.513581i	$0.828319\pi$
$720$		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	−0.922696	−	0.385529i	$-0.874019\pi$
$727$	−3.65443e11	−	3.65443e11i	−1.30822	−	1.30822i	−0.385529	−	0.922696i	$-0.625981\pi$
$728$		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	−0.961891	−	0.273433i	$-0.911841\pi$
$733$	−1.98744e11	+	1.98744e11i	−0.688458	+	0.688458i	0.273433	+	0.961891i	$0.411841\pi$
$734$		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	$0.266460\pi$
$739$			4.43024e11i			1.48542i	−0.669612	+	0.742711i	$0.733540\pi$
$740$		0			0
$741$	1.07669e11			0.357122
$742$		0			0
$743$	−1.79132e11	+	1.79132e11i	−0.587784	+	0.587784i	−0.937031	−	0.349247i	$-0.886437\pi$
$743$	−1.79132e11	+	1.79132e11i	−0.587784	+	0.587784i	0.349247	+	0.937031i	$0.386437\pi$
$744$		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	−0.999181	−	0.0404554i	$-0.987119\pi$
$757$	−3.41401e11	−	3.41401e11i	−1.03964	−	1.03964i	−0.0404554	−	0.999181i	$-0.512881\pi$
$758$		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	$-0.760879\pi$
$769$		−	4.77373e11i		−	1.36506i	0.730856	−	0.682531i	$-0.239121\pi$
$770$		0			0
$771$	−7.59988e10			−0.215075
$772$		0			0
$773$	2.34718e11	−	2.34718e11i	0.657398	−	0.657398i	−0.297366	−	0.954764i	$-0.596108\pi$
$773$	2.34718e11	−	2.34718e11i	0.657398	−	0.657398i	0.954764	+	0.297366i	$0.0961080\pi$
$774$		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	−0.996379	−	0.0850250i	$-0.972903\pi$
$787$	−4.14846e11	−	4.14846e11i	−1.08140	−	1.08140i	−0.0850250	−	0.996379i	$-0.527097\pi$
$788$		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	0.579651	−	0.814865i	$-0.303189\pi$
$797$	−9.49065e10	−	9.49065e10i	−0.235214	−	0.235214i	−0.814865	+	0.579651i	$0.803189\pi$
$798$		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	$0.295976\pi$
$809$			6.86657e11i			1.60305i	−0.597964	+	0.801523i	$0.704024\pi$
$810$		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	−0.512994	−	0.858392i	$-0.671464\pi$
$823$	1.58460e11	−	1.58460e11i	0.345398	−	0.345398i	0.858392	+	0.512994i	$0.171464\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−2.32197e11	−	2.32197e11i	−0.496404	−	0.496404i	0.413913	−	0.910317i	$-0.364162\pi$
$827$	−2.32197e11	−	2.32197e11i	−0.496404	−	0.496404i	−0.910317	+	0.413913i	$0.864162\pi$
$828$		0			0
$829$		−	6.01651e11i		−	1.27387i	−0.770916	−	0.636937i	$-0.780201\pi$
$829$		−	6.01651e11i		−	1.27387i	0.770916	−	0.636937i	$-0.219799\pi$
$830$		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	$0.118256\pi$
$839$			3.59762e11i			0.726052i	−0.931779	+	0.363026i	$0.881744\pi$
$840$		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	−0.889582	−	0.456775i	$-0.849005\pi$
$853$	−2.29135e11	+	2.29135e11i	−0.432808	+	0.432808i	0.456775	+	0.889582i	$0.349005\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.79655e11	+	1.79655e11i	0.333054	+	0.333054i	0.853745	−	0.520691i	$-0.174326\pi$
$857$	1.79655e11	+	1.79655e11i	0.333054	+	0.333054i	−0.520691	+	0.853745i	$0.674326\pi$
$858$		0			0
$859$			2.80475e11i			0.515135i	0.966260	+	0.257568i	$0.0829210\pi$
$859$			2.80475e11i			0.515135i	−0.966260	+	0.257568i	$0.917079\pi$
$860$		0			0
$861$	2.24582e11			0.408661
$862$		0			0
$863$	3.95652e11	−	3.95652e11i	0.713296	−	0.713296i	−0.253927	−	0.967223i	$-0.581722\pi$
$863$	3.95652e11	−	3.95652e11i	0.713296	−	0.713296i	0.967223	+	0.253927i	$0.0817223\pi$
$864$		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	0.813834	−	0.581097i	$-0.197376\pi$
$877$	1.37678e11	+	1.37678e11i	0.232737	+	0.232737i	−0.581097	+	0.813834i	$0.697376\pi$
$878$		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	−0.501354	−	0.865242i	$-0.667165\pi$
$883$	2.21213e11	−	2.21213e11i	0.363888	−	0.363888i	0.865242	+	0.501354i	$0.167165\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	5.15132e11	+	5.15132e11i	0.832194	+	0.832194i	0.987817	−	0.155623i	$-0.0497385\pi$
$887$	5.15132e11	+	5.15132e11i	0.832194	+	0.832194i	−0.155623	+	0.987817i	$0.549738\pi$
$888$		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	0.827929	−	0.560833i	$-0.189519\pi$
$907$	1.80758e11	+	1.80758e11i	0.267097	+	0.267097i	−0.560833	+	0.827929i	$0.689519\pi$
$908$		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	$0.132037\pi$
$919$			5.74926e11i			0.806028i	−0.915194	+	0.403014i	$0.867963\pi$
$920$		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	$0.104968\pi$
$929$			4.82390e11i			0.647642i	−0.946118	+	0.323821i	$0.895032\pi$
$930$		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	0.525657	−	0.850697i	$-0.323820\pi$
$937$	−2.50550e11	−	2.50550e11i	−0.325040	−	0.325040i	−0.850697	+	0.525657i	$0.823820\pi$
$938$		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	0.659054	−	0.752096i	$-0.270957\pi$
$947$	−7.48302e10	−	7.48302e10i	−0.0930416	−	0.0930416i	−0.752096	+	0.659054i	$0.770957\pi$
$948$		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	−0.538883	−	0.842381i	$-0.681153\pi$
$953$	2.50338e11	−	2.50338e11i	0.303498	−	0.303498i	0.842381	+	0.538883i	$0.181153\pi$
$954$		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	0.673260	−	0.739406i	$-0.264893\pi$
$967$	−5.78373e10	−	5.78373e10i	−0.0661458	−	0.0661458i	−0.739406	+	0.673260i	$0.764893\pi$
$968$		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	0.762635	−	0.646829i	$-0.223905\pi$
$977$	1.05513e11	+	1.05513e11i	0.115805	+	0.115805i	−0.646829	+	0.762635i	$0.723905\pi$
$978$		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	−0.497128	−	0.867677i	$-0.665612\pi$
$983$	3.45988e11	−	3.45988e11i	0.370550	−	0.370550i	0.867677	+	0.497128i	$0.165612\pi$
$984$		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	0.302893	−	0.953025i	$-0.402048\pi$
$997$	−6.42365e11	−	6.42365e11i	−0.650132	−	0.650132i	−0.953025	+	0.302893i	$0.902048\pi$
$998$		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.157.8		16
5.2	odd	4		60.9.k.a.13.1	✓	16
5.3	odd	4	inner	300.9.k.e.193.8		16
5.4	even	2		60.9.k.a.37.1	yes	16
15.2	even	4		180.9.l.c.73.7		16
15.14	odd	2		180.9.l.c.37.7		16
20.7	even	4		240.9.bg.c.193.5		16
20.19	odd	2		240.9.bg.c.97.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.9.k.a.13.1	✓	16	5.2	odd	4
60.9.k.a.37.1	yes	16	5.4	even	2
180.9.l.c.37.7		16	15.14	odd	2
180.9.l.c.73.7		16	15.2	even	4
240.9.bg.c.97.5		16	20.19	odd	2
240.9.bg.c.193.5		16	20.7	even	4
300.9.k.e.157.8		16	1.1	even	1	trivial
300.9.k.e.193.8		16	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
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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