LMFDB - Embedded newform 300.9.k.e.193.5

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			193.5
Root			$-2315.27 - 1.00000i$ of defining polynomial
Character	$\chi$	$=$	300.193
Dual form			300.9.k.e.157.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(33.0681 + 33.0681i) q^{3} +(-2579.27 + 2579.27i) q^{7} +2187.00i q^{9} +O(q^{10})$	$q+(33.0681 + 33.0681i) q^{3} +(-2579.27 + 2579.27i) q^{7} +2187.00i q^{9} +10309.2 q^{11} +(-48.7988 - 48.7988i) q^{13} +(18893.4 - 18893.4i) q^{17} -213030. i q^{19} -170583. q^{21} +(-90598.0 - 90598.0i) q^{23} +(-72320.0 + 72320.0i) q^{27} -593211. i q^{29} -1.46556e6 q^{31} +(340906. + 340906. i) q^{33} +(126131. - 126131. i) q^{37} -3227.37i q^{39} -439139. q^{41} +(967737. + 967737. i) q^{43} +(2.57742e6 - 2.57742e6i) q^{47} -7.54045e6i q^{49} +1.24954e6 q^{51} +(7.87036e6 + 7.87036e6i) q^{53} +(7.04449e6 - 7.04449e6i) q^{57} +1.92434e7i q^{59} +4.73632e6 q^{61} +(-5.64086e6 - 5.64086e6i) q^{63} +(1.13761e7 - 1.13761e7i) q^{67} -5.99181e6i q^{69} +4.70662e7 q^{71} +(-1.10243e7 - 1.10243e7i) q^{73} +(-2.65902e7 + 2.65902e7i) q^{77} -5.16643e7i q^{79} -4.78297e6 q^{81} +(-6.05238e7 - 6.05238e7i) q^{83} +(1.96164e7 - 1.96164e7i) q^{87} +5.57234e7i q^{89} +251730. q^{91} +(-4.84633e7 - 4.84633e7i) q^{93} +(-5.81874e7 + 5.81874e7i) q^{97} +2.25462e7i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−2579.27	+	2579.27i	−1.07425	+	1.07425i	−0.0772346	+	0.997013i	$0.524609\pi$
$7$	−2579.27	+	2579.27i	−1.07425	+	1.07425i	−0.997013	+	0.0772346i	$0.975391\pi$
$8$		0			0
$9$			2187.00i			0.333333i
$10$		0			0
$11$	10309.2			0.704132			0.352066	−	0.935975i	$-0.385479\pi$
$11$	10309.2			0.704132			0.352066	+	0.935975i	$0.385479\pi$
$12$		0			0
$13$	−48.7988	−	48.7988i	−0.00170858	−	0.00170858i	0.706252	−	0.707961i	$-0.250385\pi$
$13$	−48.7988	−	48.7988i	−0.00170858	−	0.00170858i	−0.707961	+	0.706252i	$0.750385\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	18893.4	−	18893.4i	0.226211	−	0.226211i	−0.584897	−	0.811108i	$-0.698865\pi$
$17$	18893.4	−	18893.4i	0.226211	−	0.226211i	0.811108	+	0.584897i	$0.198865\pi$
$18$		0			0
$19$		−	213030.i		−	1.63465i	−0.576174	−	0.817327i	$-0.695455\pi$
$19$		−	213030.i		−	1.63465i	0.576174	−	0.817327i	$-0.304545\pi$
$20$		0			0
$21$	−170583.			−0.877119
$22$		0			0
$23$	−90598.0	−	90598.0i	−0.323748	−	0.323748i	0.526455	−	0.850203i	$-0.323521\pi$
$23$	−90598.0	−	90598.0i	−0.323748	−	0.323748i	−0.850203	+	0.526455i	$0.823521\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−72320.0	+	72320.0i	−0.136083	+	0.136083i
$28$		0			0
$29$		−	593211.i		−	0.838720i	−0.907820	−	0.419360i	$-0.862254\pi$
$29$		−	593211.i		−	0.838720i	0.907820	−	0.419360i	$-0.137746\pi$
$30$		0			0
$31$	−1.46556e6			−1.58693			−0.793464	−	0.608618i	$-0.791724\pi$
$31$	−1.46556e6			−1.58693			−0.793464	+	0.608618i	$0.791724\pi$
$32$		0			0
$33$	340906.	+	340906.i	0.287461	+	0.287461i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	126131.	−	126131.i	0.0672998	−	0.0672998i	−0.672656	−	0.739956i	$-0.734846\pi$
$37$	126131.	−	126131.i	0.0672998	−	0.0672998i	0.739956	+	0.672656i	$0.234846\pi$
$38$		0			0
$39$		−	3227.37i		−	0.00139505i
$40$		0			0
$41$	−439139.			−0.155406			−0.0777028	−	0.996977i	$-0.524759\pi$
$41$	−439139.			−0.155406			−0.0777028	+	0.996977i	$0.524759\pi$
$42$		0			0
$43$	967737.	+	967737.i	0.283063	+	0.283063i	0.834329	−	0.551266i	$-0.185855\pi$
$43$	967737.	+	967737.i	0.283063	+	0.283063i	−0.551266	+	0.834329i	$0.685855\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.57742e6	−	2.57742e6i	0.528195	−	0.528195i	−0.391839	−	0.920034i	$-0.628161\pi$
$47$	2.57742e6	−	2.57742e6i	0.528195	−	0.528195i	0.920034	+	0.391839i	$0.128161\pi$
$48$		0			0
$49$		−	7.54045e6i		−	1.30802i
$50$		0			0
$51$	1.24954e6			0.184701
$52$		0			0
$53$	7.87036e6	+	7.87036e6i	0.997450	+	0.997450i	0.999997	−	0.00254680i	$-0.000810672\pi$
$53$	7.87036e6	+	7.87036e6i	0.997450	+	0.997450i	−0.00254680	+	0.999997i	$0.500811\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	7.04449e6	−	7.04449e6i	0.667345	−	0.667345i
$58$		0			0
$59$			1.92434e7i			1.58809i	0.607862	+	0.794043i	$0.292028\pi$
$59$			1.92434e7i			1.58809i	−0.607862	+	0.794043i	$0.707972\pi$
$60$		0			0
$61$	4.73632e6			0.342075			0.171037	−	0.985265i	$-0.445288\pi$
$61$	4.73632e6			0.342075			0.171037	+	0.985265i	$0.445288\pi$
$62$		0			0
$63$	−5.64086e6	−	5.64086e6i	−0.358083	−	0.358083i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.13761e7	−	1.13761e7i	0.564541	−	0.564541i	−0.366053	−	0.930594i	$-0.619291\pi$
$67$	1.13761e7	−	1.13761e7i	0.564541	−	0.564541i	0.930594	+	0.366053i	$0.119291\pi$
$68$		0			0
$69$		−	5.99181e6i		−	0.264339i
$70$		0			0
$71$	4.70662e7			1.85215			0.926074	−	0.377343i	$-0.123162\pi$
$71$	4.70662e7			1.85215			0.926074	+	0.377343i	$0.123162\pi$
$72$		0			0
$73$	−1.10243e7	−	1.10243e7i	−0.388203	−	0.388203i	0.485843	−	0.874046i	$-0.338513\pi$
$73$	−1.10243e7	−	1.10243e7i	−0.388203	−	0.388203i	−0.874046	+	0.485843i	$0.838513\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.65902e7	+	2.65902e7i	−0.756412	+	0.756412i
$78$		0			0
$79$		−	5.16643e7i		−	1.32642i	−0.748431	−	0.663212i	$-0.769193\pi$
$79$		−	5.16643e7i		−	1.32642i	0.748431	−	0.663212i	$-0.230807\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$		0			0
$83$	−6.05238e7	−	6.05238e7i	−1.27530	−	1.27530i	−0.943266	−	0.332038i	$-0.892264\pi$
$83$	−6.05238e7	−	6.05238e7i	−1.27530	−	1.27530i	−0.332038	−	0.943266i	$-0.607736\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.96164e7	−	1.96164e7i	0.342406	−	0.342406i
$88$		0			0
$89$			5.57234e7i			0.888133i	0.895994	+	0.444066i	$0.146465\pi$
$89$			5.57234e7i			0.888133i	−0.895994	+	0.444066i	$0.853535\pi$
$90$		0			0
$91$	251730.			0.00367088
$92$		0			0
$93$	−4.84633e7	−	4.84633e7i	−0.647860	−	0.647860i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−5.81874e7	+	5.81874e7i	−0.657267	+	0.657267i	−0.954733	−	0.297465i	$-0.903859\pi$
$97$	−5.81874e7	+	5.81874e7i	−0.657267	+	0.657267i	0.297465	+	0.954733i	$0.403859\pi$
$98$		0			0
$99$			2.25462e7i			0.234711i
$100$		0			0
$101$	9.38712e7			0.902083			0.451042	−	0.892503i	$-0.351053\pi$
$101$	9.38712e7			0.902083			0.451042	+	0.892503i	$0.351053\pi$
$102$		0			0
$103$	1.43726e8	+	1.43726e8i	1.27699	+	1.27699i	0.942343	+	0.334647i	$0.108617\pi$
$103$	1.43726e8	+	1.43726e8i	1.27699	+	1.27699i	0.334647	+	0.942343i	$0.391383\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.17737e7	−	9.17737e7i	0.700137	−	0.700137i	−0.264302	−	0.964440i	$-0.585142\pi$
$107$	9.17737e7	−	9.17737e7i	0.700137	−	0.700137i	0.964440	+	0.264302i	$0.0851417\pi$
$108$		0			0
$109$		−	2.51242e8i		−	1.77986i	−0.456093	−	0.889932i	$-0.650751\pi$
$109$		−	2.51242e8i		−	1.77986i	0.456093	−	0.889932i	$-0.349249\pi$
$110$		0			0
$111$	8.34181e6			0.0549501
$112$		0			0
$113$	1.70938e8	+	1.70938e8i	1.04839	+	1.04839i	0.998768	+	0.0496246i	$0.0158025\pi$
$113$	1.70938e8	+	1.70938e8i	1.04839	+	1.04839i	0.0496246	+	0.998768i	$0.484198\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	106723.	−	106723.i	0.000569527	−	0.000569527i
$118$		0			0
$119$			9.74622e7i			0.486013i
$120$		0			0
$121$	−1.08079e8			−0.504198
$122$		0			0
$123$	−1.45215e7	−	1.45215e7i	−0.0634441	−	0.0634441i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	1.64682e8	−	1.64682e8i	0.633039	−	0.633039i	−0.315790	−	0.948829i	$-0.602269\pi$
$127$	1.64682e8	−	1.64682e8i	0.633039	−	0.633039i	0.948829	+	0.315790i	$0.102269\pi$
$128$		0			0
$129$			6.40025e7i			0.231120i
$130$		0			0
$131$	−8.18958e7			−0.278084			−0.139042	−	0.990286i	$-0.544402\pi$
$131$	−8.18958e7			−0.278084			−0.139042	+	0.990286i	$0.544402\pi$
$132$		0			0
$133$	5.49461e8	+	5.49461e8i	1.75602	+	1.75602i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.42723e8	+	1.42723e8i	−0.405145	+	0.405145i	−0.880042	−	0.474897i	$-0.842485\pi$
$137$	−1.42723e8	+	1.42723e8i	−0.405145	+	0.405145i	0.474897	+	0.880042i	$0.342485\pi$
$138$		0			0
$139$		−	1.74157e8i		−	0.466533i	−0.972413	−	0.233267i	$-0.925059\pi$
$139$		−	1.74157e8i		−	0.466533i	0.972413	−	0.233267i	$-0.0749415\pi$
$140$		0			0
$141$	1.70461e8			0.431269
$142$		0			0
$143$	−503076.	−	503076.i	−0.00120307	−	0.00120307i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	2.49348e8	−	2.49348e8i	0.533995	−	0.533995i
$148$		0			0
$149$		−	4.53189e8i		−	0.919462i	−0.888058	−	0.459731i	$-0.847946\pi$
$149$		−	4.53189e8i		−	0.919462i	0.888058	−	0.459731i	$-0.152054\pi$
$150$		0			0
$151$	4.28978e8			0.825139			0.412570	−	0.910926i	$-0.364631\pi$
$151$	4.28978e8			0.825139			0.412570	+	0.910926i	$0.364631\pi$
$152$		0			0
$153$	4.13198e7	+	4.13198e7i	0.0754037	+	0.0754037i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−5.67435e8	+	5.67435e8i	−0.933936	+	0.933936i	−0.997949	−	0.0640129i	$-0.979610\pi$
$157$	−5.67435e8	+	5.67435e8i	−0.933936	+	0.933936i	0.0640129	+	0.997949i	$0.479610\pi$
$158$		0			0
$159$			5.20516e8i			0.814414i
$160$		0			0
$161$	4.67353e8			0.695571
$162$		0			0
$163$	−7.60153e7	−	7.60153e7i	−0.107684	−	0.107684i	0.651212	−	0.758896i	$-0.274261\pi$
$163$	−7.60153e7	−	7.60153e7i	−0.107684	−	0.107684i	−0.758896	+	0.651212i	$0.774261\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.92681e8	−	8.92681e8i	1.14771	−	1.14771i	0.160703	−	0.987003i	$-0.448624\pi$
$167$	8.92681e8	−	8.92681e8i	1.14771	−	1.14771i	0.987003	−	0.160703i	$-0.0513760\pi$
$168$		0			0
$169$		−	8.15726e8i		−	0.999994i
$170$		0			0
$171$	4.65896e8			0.544885
$172$		0			0
$173$	−5.45456e8	−	5.45456e8i	−0.608941	−	0.608941i	0.333729	−	0.942669i	$-0.391693\pi$
$173$	−5.45456e8	−	5.45456e8i	−0.608941	−	0.608941i	−0.942669	+	0.333729i	$0.891693\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−6.36343e8	+	6.36343e8i	−0.648333	+	0.648333i
$178$		0			0
$179$		−	1.22870e9i		−	1.19683i	−0.801185	−	0.598417i	$-0.795796\pi$
$179$		−	1.22870e9i		−	1.19683i	0.801185	−	0.598417i	$-0.204204\pi$
$180$		0			0
$181$	2.03171e9			1.89299			0.946495	−	0.322719i	$-0.104597\pi$
$181$	2.03171e9			1.89299			0.946495	+	0.322719i	$0.104597\pi$
$182$		0			0
$183$	1.56621e8	+	1.56621e8i	0.139652	+	0.139652i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.94776e8	−	1.94776e8i	0.159282	−	0.159282i
$188$		0			0
$189$		−	3.73065e8i		−	0.292373i
$190$		0			0
$191$	1.77977e9			1.33731			0.668653	−	0.743575i	$-0.266871\pi$
$191$	1.77977e9			1.33731			0.668653	+	0.743575i	$0.266871\pi$
$192$		0			0
$193$	−6.93264e8	−	6.93264e8i	−0.499654	−	0.499654i	0.411676	−	0.911330i	$-0.364943\pi$
$193$	−6.93264e8	−	6.93264e8i	−0.499654	−	0.499654i	−0.911330	+	0.411676i	$0.864943\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.74883e8	−	5.74883e8i	0.381694	−	0.381694i	−0.490018	−	0.871712i	$-0.663010\pi$
$197$	5.74883e8	−	5.74883e8i	0.381694	−	0.381694i	0.871712	+	0.490018i	$0.163010\pi$
$198$		0			0
$199$			1.94096e9i			1.23767i	0.785522	+	0.618833i	$0.212394\pi$
$199$			1.94096e9i			1.23767i	−0.785522	+	0.618833i	$0.787606\pi$
$200$		0			0
$201$	7.52374e8			0.460946
$202$		0			0
$203$	1.53005e9	+	1.53005e9i	0.900993	+	0.900993i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.98138e8	−	1.98138e8i	0.107916	−	0.107916i
$208$		0			0
$209$		−	2.19617e9i		−	1.15101i
$210$		0			0
$211$	8.23779e8			0.415605			0.207803	−	0.978171i	$-0.433369\pi$
$211$	8.23779e8			0.415605			0.207803	+	0.978171i	$0.433369\pi$
$212$		0			0
$213$	1.55639e9	+	1.55639e9i	0.756136	+	0.756136i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	3.78007e9	−	3.78007e9i	1.70475	−	1.70475i
$218$		0			0
$219$		−	7.29105e8i		−	0.316967i
$220$		0			0
$221$	−1.84395e6			−0.000772999
$222$		0			0
$223$	2.50172e9	+	2.50172e9i	1.01163	+	1.01163i	0.999932	+	0.0116935i	$0.00372223\pi$
$223$	2.50172e9	+	2.50172e9i	1.01163	+	1.01163i	0.0116935	+	0.999932i	$0.496278\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.16643e7	−	2.16643e7i	0.00815908	−	0.00815908i	−0.703015	−	0.711175i	$-0.748164\pi$
$227$	2.16643e7	−	2.16643e7i	0.00815908	−	0.00815908i	0.711175	+	0.703015i	$0.248164\pi$
$228$		0			0
$229$		−	1.33042e9i		−	0.483780i	−0.970304	−	0.241890i	$-0.922233\pi$
$229$		−	1.33042e9i		−	0.483780i	0.970304	−	0.241890i	$-0.0777673\pi$
$230$		0			0
$231$	−1.75857e9			−0.617608
$232$		0			0
$233$	1.13455e9	+	1.13455e9i	0.384947	+	0.384947i	0.872881	−	0.487934i	$-0.162249\pi$
$233$	1.13455e9	+	1.13455e9i	0.384947	+	0.384947i	−0.487934	+	0.872881i	$0.662249\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.70844e9	−	1.70844e9i	0.541511	−	0.541511i
$238$		0			0
$239$		−	1.07577e9i		−	0.329707i	−0.986318	−	0.164854i	$-0.947285\pi$
$239$		−	1.07577e9i		−	0.329707i	0.986318	−	0.164854i	$-0.0527152\pi$
$240$		0			0
$241$	3.05031e9			0.904225			0.452112	−	0.891961i	$-0.350671\pi$
$241$	3.05031e9			0.904225			0.452112	+	0.891961i	$0.350671\pi$
$242$		0			0
$243$	−1.58164e8	−	1.58164e8i	−0.0453609	−	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.03956e7	+	1.03956e7i	−0.00279294	+	0.00279294i
$248$		0			0
$249$		−	4.00281e9i		−	1.04128i
$250$		0			0
$251$	1.47076e9			0.370550			0.185275	−	0.982687i	$-0.440682\pi$
$251$	1.47076e9			0.370550			0.185275	+	0.982687i	$0.440682\pi$
$252$		0			0
$253$	−9.33992e8	−	9.33992e8i	−0.227961	−	0.227961i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.08195e9	+	5.08195e9i	−1.16493	+	1.16493i	−0.181543	+	0.983383i	$0.558109\pi$
$257$	−5.08195e9	+	5.08195e9i	−1.16493	+	1.16493i	−0.983383	+	0.181543i	$0.941891\pi$
$258$		0			0
$259$			6.50650e8i			0.144593i
$260$		0			0
$261$	1.29735e9			0.279573
$262$		0			0
$263$	5.20674e9	+	5.20674e9i	1.08829	+	1.08829i	0.995705	+	0.0925807i	$0.0295116\pi$
$263$	5.20674e9	+	5.20674e9i	1.08829	+	1.08829i	0.0925807	+	0.995705i	$0.470488\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.84267e9	+	1.84267e9i	−0.362579	+	0.362579i
$268$		0			0
$269$			2.70245e8i			0.0516118i	0.999667	+	0.0258059i	$0.00821518\pi$
$269$			2.70245e8i			0.0516118i	−0.999667	+	0.0258059i	$0.991785\pi$
$270$		0			0
$271$	−2.82556e7			−0.00523875			−0.00261937	−	0.999997i	$-0.500834\pi$
$271$	−2.82556e7			−0.00523875			−0.00261937	+	0.999997i	$0.500834\pi$
$272$		0			0
$273$	8.32424e6	+	8.32424e6i	0.00149863	+	0.00149863i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	3.18639e9	−	3.18639e9i	0.541227	−	0.541227i	−0.382661	−	0.923889i	$-0.624992\pi$
$277$	3.18639e9	−	3.18639e9i	0.541227	−	0.541227i	0.923889	+	0.382661i	$0.124992\pi$
$278$		0			0
$279$		−	3.20518e9i		−	0.528976i
$280$		0			0
$281$	−3.04929e9			−0.489073			−0.244536	−	0.969640i	$-0.578636\pi$
$281$	−3.04929e9			−0.489073			−0.244536	+	0.969640i	$0.578636\pi$
$282$		0			0
$283$	−6.96309e9	−	6.96309e9i	−1.08557	−	1.08557i	−0.995979	−	0.0895865i	$-0.971445\pi$
$283$	−6.96309e9	−	6.96309e9i	−1.08557	−	1.08557i	−0.0895865	−	0.995979i	$-0.528555\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.13266e9	−	1.13266e9i	0.166944	−	0.166944i
$288$		0			0
$289$			6.26184e9i			0.897657i
$290$		0			0
$291$	−3.84829e9			−0.536656
$292$		0			0
$293$	−9.98544e9	−	9.98544e9i	−1.35487	−	1.35487i	−0.880124	−	0.474744i	$-0.842541\pi$
$293$	−9.98544e9	−	9.98544e9i	−1.35487	−	1.35487i	−0.474744	−	0.880124i	$-0.657459\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−7.45561e8	+	7.45561e8i	−0.0958202	+	0.0958202i
$298$		0			0
$299$			8.84214e6i			0.00110630i
$300$		0			0
$301$	−4.99211e9			−0.608160
$302$		0			0
$303$	3.10414e9	+	3.10414e9i	0.368274	+	0.368274i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−9.06632e9	+	9.06632e9i	−1.02065	+	1.02065i	−0.0208694	+	0.999782i	$0.506643\pi$
$307$	−9.06632e9	+	9.06632e9i	−1.02065	+	1.02065i	−0.999782	+	0.0208694i	$0.993357\pi$
$308$		0			0
$309$			9.50552e9i			1.04266i
$310$		0			0
$311$	1.16231e10			1.24245			0.621226	−	0.783632i	$-0.286635\pi$
$311$	1.16231e10			1.24245			0.621226	+	0.783632i	$0.286635\pi$
$312$		0			0
$313$	7.65781e9	+	7.65781e9i	0.797861	+	0.797861i	0.982758	−	0.184897i	$-0.0591952\pi$
$313$	7.65781e9	+	7.65781e9i	0.797861	+	0.797861i	−0.184897	+	0.982758i	$0.559195\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.24298e9	+	5.24298e9i	−0.519208	+	0.519208i	−0.917332	−	0.398124i	$-0.869662\pi$
$317$	−5.24298e9	+	5.24298e9i	−0.519208	+	0.519208i	0.398124	+	0.917332i	$0.369662\pi$
$318$		0			0
$319$		−	6.11553e9i		−	0.590570i
$320$		0			0
$321$	6.06957e9			0.571660
$322$		0			0
$323$	−4.02485e9	−	4.02485e9i	−0.369777	−	0.369777i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	8.30811e9	−	8.30811e9i	0.726627	−	0.726627i
$328$		0			0
$329$			1.32957e10i			1.13482i
$330$		0			0
$331$	6.84919e9			0.570594			0.285297	−	0.958439i	$-0.407908\pi$
$331$	6.84919e9			0.570594			0.285297	+	0.958439i	$0.407908\pi$
$332$		0			0
$333$	2.75848e8	+	2.75848e8i	0.0224333	+	0.0224333i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.05508e9	−	1.05508e9i	0.0818022	−	0.0818022i	−0.665022	−	0.746824i	$-0.731578\pi$
$337$	1.05508e9	−	1.05508e9i	0.0818022	−	0.0818022i	0.746824	+	0.665022i	$0.231578\pi$
$338$		0			0
$339$			1.13052e10i			0.856009i
$340$		0			0
$341$	−1.51088e10			−1.11741
$342$		0			0
$343$	4.57987e9	+	4.57987e9i	0.330885	+	0.330885i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.46983e9	−	1.46983e9i	0.101379	−	0.101379i	−0.654598	−	0.755977i	$-0.727162\pi$
$347$	1.46983e9	−	1.46983e9i	0.101379	−	0.101379i	0.755977	+	0.654598i	$0.227162\pi$
$348$		0			0
$349$			6.94816e9i			0.468348i	0.972195	+	0.234174i	$0.0752385\pi$
$349$			6.94816e9i			0.468348i	−0.972195	+	0.234174i	$0.924762\pi$
$350$		0			0
$351$	7.05825e6			0.000465017
$352$		0			0
$353$	−5.28921e9	−	5.28921e9i	−0.340637	−	0.340637i	0.515970	−	0.856607i	$-0.327432\pi$
$353$	−5.28921e9	−	5.28921e9i	−0.340637	−	0.340637i	−0.856607	+	0.515970i	$0.827432\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−3.22289e9	+	3.22289e9i	−0.198414	+	0.198414i
$358$		0			0
$359$		−	1.87432e10i		−	1.12841i	−0.825636	−	0.564203i	$-0.809184\pi$
$359$		−	1.87432e10i		−	1.12841i	0.825636	−	0.564203i	$-0.190816\pi$
$360$		0			0
$361$	−2.83981e10			−1.67209
$362$		0			0
$363$	−3.57398e9	−	3.57398e9i	−0.205838	−	0.205838i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	2.75314e9	−	2.75314e9i	0.151762	−	0.151762i	−0.627142	−	0.778905i	$-0.715776\pi$
$367$	2.75314e9	−	2.75314e9i	0.151762	−	0.151762i	0.778905	+	0.627142i	$0.215776\pi$
$368$		0			0
$369$		−	9.60397e8i		−	0.0518019i
$370$		0			0
$371$	−4.05995e10			−2.14302
$372$		0			0
$373$	9.00236e9	+	9.00236e9i	0.465073	+	0.465073i	0.900314	−	0.435241i	$-0.143337\pi$
$373$	9.00236e9	+	9.00236e9i	0.465073	+	0.465073i	−0.435241	+	0.900314i	$0.643337\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.89480e7	+	2.89480e7i	−0.00143302	+	0.00143302i
$378$		0			0
$379$		−	1.37734e10i		−	0.667550i	−0.942653	−	0.333775i	$-0.891677\pi$
$379$		−	1.37734e10i		−	0.667550i	0.942653	−	0.333775i	$-0.108323\pi$
$380$		0			0
$381$	1.08914e10			0.516875
$382$		0			0
$383$	−2.06681e10	−	2.06681e10i	−0.960516	−	0.960516i	0.0387336	−	0.999250i	$-0.487668\pi$
$383$	−2.06681e10	−	2.06681e10i	−0.960516	−	0.960516i	−0.999250	+	0.0387336i	$0.987668\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.11644e9	+	2.11644e9i	−0.0943544	+	0.0943544i
$388$		0			0
$389$		−	2.05886e9i		−	0.0899142i	−0.998989	−	0.0449571i	$-0.985685\pi$
$389$		−	2.05886e9i		−	0.0899142i	0.998989	−	0.0449571i	$-0.0143151\pi$
$390$		0			0
$391$	−3.42340e9			−0.146471
$392$		0			0
$393$	−2.70814e9	−	2.70814e9i	−0.113527	−	0.113527i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−1.37467e10	+	1.37467e10i	−0.553397	+	0.553397i	−0.927420	−	0.374023i	$-0.877978\pi$
$397$	−1.37467e10	+	1.37467e10i	−0.553397	+	0.553397i	0.374023	+	0.927420i	$0.377978\pi$
$398$		0			0
$399$			3.63393e10i			1.43379i
$400$		0			0
$401$	−3.72299e10			−1.43984			−0.719920	−	0.694057i	$-0.755822\pi$
$401$	−3.72299e10			−1.43984			−0.719920	+	0.694057i	$0.755822\pi$
$402$		0			0
$403$	7.15175e7	+	7.15175e7i	0.00271139	+	0.00271139i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.30031e9	−	1.30031e9i	0.0473880	−	0.0473880i
$408$		0			0
$409$			1.18452e10i			0.423301i	0.977345	+	0.211650i	$0.0678838\pi$
$409$			1.18452e10i			0.423301i	−0.977345	+	0.211650i	$0.932116\pi$
$410$		0			0
$411$	−9.43913e9			−0.330799
$412$		0			0
$413$	−4.96339e10	−	4.96339e10i	−1.70600	−	1.70600i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	5.75905e9	−	5.75905e9i	0.190461	−	0.190461i
$418$		0			0
$419$		−	4.13222e10i		−	1.34069i	−0.742051	−	0.670343i	$-0.766147\pi$
$419$		−	4.13222e10i		−	1.34069i	0.742051	−	0.670343i	$-0.233853\pi$
$420$		0			0
$421$	−3.00000e8			−0.00954977			−0.00477489	−	0.999989i	$-0.501520\pi$
$421$	−3.00000e8			−0.00954977			−0.00477489	+	0.999989i	$0.501520\pi$
$422$		0			0
$423$	5.63682e9	+	5.63682e9i	0.176065	+	0.176065i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.22162e10	+	1.22162e10i	−0.367473	+	0.367473i
$428$		0			0
$429$		−	3.32715e7i		−	0.000982299i
$430$		0			0
$431$	3.42508e9			0.0992571			0.0496286	−	0.998768i	$-0.484196\pi$
$431$	3.42508e9			0.0992571			0.0496286	+	0.998768i	$0.484196\pi$
$432$		0			0
$433$	2.08642e10	+	2.08642e10i	0.593541	+	0.593541i	0.938586	−	0.345045i	$-0.112137\pi$
$433$	2.08642e10	+	2.08642e10i	0.593541	+	0.593541i	−0.345045	+	0.938586i	$0.612137\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.93001e10	+	1.93001e10i	−0.529216	+	0.529216i
$438$		0			0
$439$			3.52597e10i			0.949338i	0.880164	+	0.474669i	$0.157432\pi$
$439$			3.52597e10i			0.949338i	−0.880164	+	0.474669i	$0.842568\pi$
$440$		0			0
$441$	1.64910e10			0.436005
$442$		0			0
$443$	−3.37468e10	−	3.37468e10i	−0.876230	−	0.876230i	0.116913	−	0.993142i	$-0.462700\pi$
$443$	−3.37468e10	−	3.37468e10i	−0.876230	−	0.876230i	−0.993142	+	0.116913i	$0.962700\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	1.49861e10	−	1.49861e10i	0.375369	−	0.375369i
$448$		0			0
$449$			2.78907e10i			0.686237i	0.939292	+	0.343118i	$0.111483\pi$
$449$			2.78907e10i			0.686237i	−0.939292	+	0.343118i	$0.888517\pi$
$450$		0			0
$451$	−4.52717e9			−0.109426
$452$		0			0
$453$	1.41855e10	+	1.41855e10i	0.336862	+	0.336862i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.30621e10	−	3.30621e10i	0.757993	−	0.757993i	−0.217964	−	0.975957i	$-0.569941\pi$
$457$	3.30621e10	−	3.30621e10i	0.757993	−	0.757993i	0.975957	+	0.217964i	$0.0699414\pi$
$458$		0			0
$459$			2.73274e9i			0.0615669i
$460$		0			0
$461$	7.25764e10			1.60691			0.803456	−	0.595365i	$-0.202992\pi$
$461$	7.25764e10			1.60691			0.803456	+	0.595365i	$0.202992\pi$
$462$		0			0
$463$	−1.93417e10	−	1.93417e10i	−0.420892	−	0.420892i	0.464619	−	0.885511i	$-0.346191\pi$
$463$	−1.93417e10	−	1.93417e10i	−0.420892	−	0.420892i	−0.885511	+	0.464619i	$0.846191\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.53723e9	+	5.53723e9i	−0.116419	+	0.116419i	−0.762916	−	0.646497i	$-0.776233\pi$
$467$	−5.53723e9	+	5.53723e9i	−0.116419	+	0.116419i	0.646497	+	0.762916i	$0.276233\pi$
$468$		0			0
$469$			5.86842e10i			1.21291i
$470$		0			0
$471$	−3.75280e10			−0.762556
$472$		0			0
$473$	9.97659e9	+	9.97659e9i	0.199314	+	0.199314i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.72125e10	+	1.72125e10i	−0.332483	+	0.332483i
$478$		0			0
$479$			5.03380e10i			0.956211i	0.878302	+	0.478106i	$0.158676\pi$
$479$			5.03380e10i			0.956211i	−0.878302	+	0.478106i	$0.841324\pi$
$480$		0			0
$481$	−1.23100e7			−0.000229974
$482$		0			0
$483$	1.54545e10	+	1.54545e10i	0.283966	+	0.283966i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	1.12304e10	−	1.12304e10i	0.199655	−	0.199655i	−0.600197	−	0.799852i	$-0.704911\pi$
$487$	1.12304e10	−	1.12304e10i	0.199655	−	0.199655i	0.799852	+	0.600197i	$0.204911\pi$
$488$		0			0
$489$		−	5.02736e9i		−	0.0879235i
$490$		0			0
$491$	−8.61893e10			−1.48295			−0.741476	−	0.670979i	$-0.765874\pi$
$491$	−8.61893e10			−1.48295			−0.741476	+	0.670979i	$0.765874\pi$
$492$		0			0
$493$	−1.12078e10	−	1.12078e10i	−0.189728	−	0.189728i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.21396e11	+	1.21396e11i	−1.98966	+	1.98966i
$498$		0			0
$499$			1.74251e10i			0.281042i	0.990078	+	0.140521i	$0.0448778\pi$
$499$			1.74251e10i			0.281042i	−0.990078	+	0.140521i	$0.955122\pi$
$500$		0			0
$501$	5.90386e10			0.937098
$502$		0			0
$503$	2.31698e10	+	2.31698e10i	0.361951	+	0.361951i	0.864531	−	0.502580i	$-0.167616\pi$
$503$	2.31698e10	+	2.31698e10i	0.361951	+	0.361951i	−0.502580	+	0.864531i	$0.667616\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	2.69745e10	−	2.69745e10i	0.408246	−	0.408246i
$508$		0			0
$509$		−	6.10575e10i		−	0.909636i	−0.890584	−	0.454818i	$-0.849704\pi$
$509$		−	6.10575e10i		−	0.909636i	0.890584	−	0.454818i	$-0.150296\pi$
$510$		0			0
$511$	5.68692e10			0.834053
$512$		0			0
$513$	1.54063e10	+	1.54063e10i	0.222448	+	0.222448i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	2.65711e10	−	2.65711e10i	0.371919	−	0.371919i
$518$		0			0
$519$		−	3.60744e10i		−	0.497198i
$520$		0			0
$521$	−5.83376e10			−0.791767			−0.395884	−	0.918301i	$-0.629562\pi$
$521$	−5.83376e10			−0.791767			−0.395884	+	0.918301i	$0.629562\pi$
$522$		0			0
$523$	−8.28028e10	−	8.28028e10i	−1.10672	−	1.10672i	−0.993579	−	0.113142i	$-0.963909\pi$
$523$	−8.28028e10	−	8.28028e10i	−1.10672	−	1.10672i	−0.113142	−	0.993579i	$-0.536091\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.76894e10	+	2.76894e10i	−0.358981	+	0.358981i
$528$		0			0
$529$		−	6.18950e10i		−	0.790374i
$530$		0			0
$531$	−4.20853e10			−0.529362
$532$		0			0
$533$	2.14294e7	+	2.14294e7i	0.000265523	+	0.000265523i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	4.06308e10	−	4.06308e10i	0.488606	−	0.488606i
$538$		0			0
$539$		−	7.77360e10i		−	0.921016i
$540$		0			0
$541$	−3.96928e10			−0.463364			−0.231682	−	0.972792i	$-0.574423\pi$
$541$	−3.96928e10			−0.463364			−0.231682	+	0.972792i	$0.574423\pi$
$542$		0			0
$543$	6.71849e10	+	6.71849e10i	0.772810	+	0.772810i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	6.26056e9	−	6.26056e9i	0.0699300	−	0.0699300i	−0.671277	−	0.741207i	$-0.734254\pi$
$547$	6.26056e9	−	6.26056e9i	0.0699300	−	0.0699300i	0.741207	+	0.671277i	$0.234254\pi$
$548$		0			0
$549$			1.03583e10i			0.114025i
$550$		0			0
$551$	−1.26372e11			−1.37102
$552$		0			0
$553$	1.33256e11	+	1.33256e11i	1.42491	+	1.42491i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.36303e10	−	2.36303e10i	0.245498	−	0.245498i	−0.573622	−	0.819120i	$-0.694462\pi$
$557$	2.36303e10	−	2.36303e10i	0.245498	−	0.245498i	0.819120	+	0.573622i	$0.194462\pi$
$558$		0			0
$559$		−	9.44487e7i		−	0.000967272i
$560$		0			0
$561$	1.28817e10			0.130054
$562$		0			0
$563$	−5.15382e10	−	5.15382e10i	−0.512974	−	0.512974i	0.402462	−	0.915437i	$-0.368154\pi$
$563$	−5.15382e10	−	5.15382e10i	−0.512974	−	0.512974i	−0.915437	+	0.402462i	$0.868154\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.23366e10	−	1.23366e10i	0.119361	−	0.119361i
$568$		0			0
$569$		−	1.94847e11i		−	1.85885i	−0.369011	−	0.929425i	$-0.620304\pi$
$569$		−	1.94847e11i		−	1.85885i	0.369011	−	0.929425i	$-0.379696\pi$
$570$		0			0
$571$	−1.26462e9			−0.0118964			−0.00594820	−	0.999982i	$-0.501893\pi$
$571$	−1.26462e9			−0.0118964			−0.00594820	+	0.999982i	$0.501893\pi$
$572$		0			0
$573$	5.88537e10	+	5.88537e10i	0.545953	+	0.545953i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	7.68003e10	−	7.68003e10i	0.692883	−	0.692883i	−0.269982	−	0.962865i	$-0.587018\pi$
$577$	7.68003e10	−	7.68003e10i	0.692883	−	0.692883i	0.962865	+	0.269982i	$0.0870179\pi$
$578$		0			0
$579$		−	4.58498e10i		−	0.407966i
$580$		0			0
$581$	3.12214e11			2.73998
$582$		0			0
$583$	8.11371e10	+	8.11371e10i	0.702336	+	0.702336i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.84800e10	−	2.84800e10i	0.239876	−	0.239876i	−0.576923	−	0.816799i	$-0.695747\pi$
$587$	2.84800e10	−	2.84800e10i	0.239876	−	0.239876i	0.816799	+	0.576923i	$0.195747\pi$
$588$		0			0
$589$			3.12208e11i			2.59408i
$590$		0			0
$591$	3.80206e10			0.311651
$592$		0			0
$593$	2.17428e10	+	2.17428e10i	0.175831	+	0.175831i	0.789536	−	0.613704i	$-0.210321\pi$
$593$	2.17428e10	+	2.17428e10i	0.175831	+	0.175831i	−0.613704	+	0.789536i	$0.710321\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−6.41838e10	+	6.41838e10i	−0.505275	+	0.505275i
$598$		0			0
$599$		−	1.41045e11i		−	1.09560i	−0.836611	−	0.547798i	$-0.815466\pi$
$599$		−	1.41045e11i		−	1.09560i	0.836611	−	0.547798i	$-0.184534\pi$
$600$		0			0
$601$	2.26757e11			1.73805			0.869025	−	0.494768i	$-0.164747\pi$
$601$	2.26757e11			1.73805			0.869025	+	0.494768i	$0.164747\pi$
$602$		0			0
$603$	2.48796e10	+	2.48796e10i	0.188180	+	0.188180i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	9.47842e10	−	9.47842e10i	0.698202	−	0.698202i	−0.265821	−	0.964022i	$-0.585643\pi$
$607$	9.47842e10	−	9.47842e10i	0.698202	−	0.698202i	0.964022	+	0.265821i	$0.0856429\pi$
$608$		0			0
$609$			1.01192e11i			0.735658i
$610$		0			0
$611$	−2.51550e8			−0.00180493
$612$		0			0
$613$	−3.06989e9	−	3.06989e9i	−0.0217411	−	0.0217411i	0.696153	−	0.717894i	$-0.254894\pi$
$613$	−3.06989e9	−	3.06989e9i	−0.0217411	−	0.0217411i	−0.717894	+	0.696153i	$0.754894\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.06077e10	+	5.06077e10i	−0.349201	+	0.349201i	−0.859812	−	0.510611i	$-0.829419\pi$
$617$	−5.06077e10	+	5.06077e10i	−0.349201	+	0.349201i	0.510611	+	0.859812i	$0.329419\pi$
$618$		0			0
$619$		−	2.51410e11i		−	1.71246i	−0.516597	−	0.856228i	$-0.672802\pi$
$619$		−	2.51410e11i		−	1.71246i	0.516597	−	0.856228i	$-0.327198\pi$
$620$		0			0
$621$	1.31041e10			0.0881131
$622$		0			0
$623$	−1.43726e11	−	1.43726e11i	−0.954074	−	0.954074i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	7.26231e10	−	7.26231e10i	0.469899	−	0.469899i
$628$		0			0
$629$		−	4.76607e9i		−	0.0304479i
$630$		0			0
$631$	1.83905e11			1.16005			0.580023	−	0.814600i	$-0.303044\pi$
$631$	1.83905e11			1.16005			0.580023	+	0.814600i	$0.303044\pi$
$632$		0			0
$633$	2.72408e10	+	2.72408e10i	0.169670	+	0.169670i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−3.67965e8	+	3.67965e8i	−0.00223485	+	0.00223485i
$638$		0			0
$639$			1.02934e11i			0.617383i
$640$		0			0
$641$	−1.07397e11			−0.636149			−0.318075	−	0.948066i	$-0.603036\pi$
$641$	−1.07397e11			−0.636149			−0.318075	+	0.948066i	$0.603036\pi$
$642$		0			0
$643$	1.22407e11	+	1.22407e11i	0.716080	+	0.716080i	0.967800	−	0.251720i	$-0.0809962\pi$
$643$	1.22407e11	+	1.22407e11i	0.716080	+	0.716080i	−0.251720	+	0.967800i	$0.580996\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.65574e11	−	1.65574e11i	0.944876	−	0.944876i	−0.0536820	−	0.998558i	$-0.517096\pi$
$647$	1.65574e11	−	1.65574e11i	0.944876	−	0.944876i	0.998558	+	0.0536820i	$0.0170957\pi$
$648$		0			0
$649$			1.98384e11i			1.11822i
$650$		0			0
$651$	2.50000e11			1.39192
$652$		0			0
$653$	−1.71543e11	−	1.71543e11i	−0.943451	−	0.943451i	0.0550335	−	0.998485i	$-0.482473\pi$
$653$	−1.71543e11	−	1.71543e11i	−0.943451	−	0.943451i	−0.998485	+	0.0550335i	$0.982473\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.41101e10	−	2.41101e10i	0.129401	−	0.129401i
$658$		0			0
$659$		−	2.52202e11i		−	1.33723i	−0.743607	−	0.668617i	$-0.766887\pi$
$659$		−	2.52202e11i		−	1.33723i	0.743607	−	0.668617i	$-0.233113\pi$
$660$		0			0
$661$	2.74355e11			1.43717			0.718583	−	0.695441i	$-0.244791\pi$
$661$	2.74355e11			1.43717			0.718583	+	0.695441i	$0.244791\pi$
$662$		0			0
$663$	−6.09758e7	−	6.09758e7i	−0.000315576	−	0.000315576i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−5.37437e10	+	5.37437e10i	−0.271534	+	0.271534i
$668$		0			0
$669$			1.65454e11i			0.825988i
$670$		0			0
$671$	4.88276e10			0.240866
$672$		0			0
$673$	2.21002e11	+	2.21002e11i	1.07730	+	1.07730i	0.996751	+	0.0805452i	$0.0256661\pi$
$673$	2.21002e11	+	2.21002e11i	1.07730	+	1.07730i	0.0805452	+	0.996751i	$0.474334\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−6.05052e10	+	6.05052e10i	−0.288030	+	0.288030i	−0.836301	−	0.548271i	$-0.815286\pi$
$677$	−6.05052e10	+	6.05052e10i	−0.288030	+	0.288030i	0.548271	+	0.836301i	$0.315286\pi$
$678$		0			0
$679$		−	3.00162e11i		−	1.41214i
$680$		0			0
$681$	1.43279e9			0.00666186
$682$		0			0
$683$	−1.78953e11	−	1.78953e11i	−0.822349	−	0.822349i	0.164096	−	0.986444i	$-0.447529\pi$
$683$	−1.78953e11	−	1.78953e11i	−0.822349	−	0.822349i	−0.986444	+	0.164096i	$0.947529\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	4.39946e10	−	4.39946e10i	0.197502	−	0.197502i
$688$		0			0
$689$		−	7.68127e8i		−	0.00340845i
$690$		0			0
$691$	1.98163e11			0.869182			0.434591	−	0.900628i	$-0.356893\pi$
$691$	1.98163e11			0.869182			0.434591	+	0.900628i	$0.356893\pi$
$692$		0			0
$693$	−5.81527e10	−	5.81527e10i	−0.252137	−	0.252137i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−8.29682e9	+	8.29682e9i	−0.0351545	+	0.0351545i
$698$		0			0
$699$			7.50350e10i			0.314308i
$700$		0			0
$701$	−2.35855e11			−0.976725			−0.488362	−	0.872641i	$-0.662406\pi$
$701$	−2.35855e11			−0.976725			−0.488362	+	0.872641i	$0.662406\pi$
$702$		0			0
$703$	−2.68696e10	−	2.68696e10i	−0.110012	−	0.110012i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.42119e11	+	2.42119e11i	−0.969061	+	0.969061i
$708$		0			0
$709$		−	2.88125e11i		−	1.14024i	−0.821562	−	0.570119i	$-0.806897\pi$
$709$		−	2.88125e11i		−	1.14024i	0.821562	−	0.570119i	$-0.193103\pi$
$710$		0			0
$711$	1.12990e11			0.442141
$712$		0			0
$713$	1.32777e11	+	1.32777e11i	0.513765	+	0.513765i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	3.55737e10	−	3.55737e10i	0.134602	−	0.134602i
$718$		0			0
$719$		−	4.09006e11i		−	1.53043i	−0.643775	−	0.765215i	$-0.722633\pi$
$719$		−	4.09006e11i		−	1.53043i	0.643775	−	0.765215i	$-0.277367\pi$
$720$		0			0
$721$	−7.41418e11			−2.74361
$722$		0			0
$723$	1.00868e11	+	1.00868e11i	0.369148	+	0.369148i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	1.02790e11	−	1.02790e11i	0.367970	−	0.367970i	−0.498767	−	0.866736i	$-0.666214\pi$
$727$	1.02790e11	−	1.02790e11i	0.367970	−	0.367970i	0.866736	+	0.498767i	$0.166214\pi$
$728$		0			0
$729$		−	1.04604e10i		−	0.0370370i
$730$		0			0
$731$	3.65676e10			0.128064
$732$		0			0
$733$	−3.93488e10	−	3.93488e10i	−0.136306	−	0.136306i	0.635662	−	0.771968i	$-0.280727\pi$
$733$	−3.93488e10	−	3.93488e10i	−0.136306	−	0.136306i	−0.771968	+	0.635662i	$0.780727\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.17279e11	−	1.17279e11i	0.397511	−	0.397511i
$738$		0			0
$739$			1.63661e11i			0.548740i	0.961624	+	0.274370i	$0.0884693\pi$
$739$			1.63661e11i			0.548740i	−0.961624	+	0.274370i	$0.911531\pi$
$740$		0			0
$741$	−6.87525e8			−0.00228042
$742$		0			0
$743$	−1.96664e11	−	1.96664e11i	−0.645313	−	0.645313i	0.306543	−	0.951857i	$-0.400828\pi$
$743$	−1.96664e11	−	1.96664e11i	−0.645313	−	0.645313i	−0.951857	+	0.306543i	$0.900828\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.32366e11	−	1.32366e11i	0.425101	−	0.425101i
$748$		0			0
$749$			4.73418e11i			1.50424i
$750$		0			0
$751$	−3.45868e11			−1.08730			−0.543651	−	0.839311i	$-0.682959\pi$
$751$	−3.45868e11			−1.08730			−0.543651	+	0.839311i	$0.682959\pi$
$752$		0			0
$753$	4.86352e10	+	4.86352e10i	0.151276	+	0.151276i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−3.29498e11	+	3.29498e11i	−1.00339	+	1.00339i	−0.00339454	+	0.999994i	$0.501081\pi$
$757$	−3.29498e11	+	3.29498e11i	−1.00339	+	1.00339i	−0.999994	+	0.00339454i	$0.998919\pi$
$758$		0			0
$759$		−	6.17707e10i		−	0.186130i
$760$		0			0
$761$	4.33843e11			1.29358			0.646791	−	0.762667i	$-0.276111\pi$
$761$	4.33843e11			1.29358			0.646791	+	0.762667i	$0.276111\pi$
$762$		0			0
$763$	6.48022e11	+	6.48022e11i	1.91202	+	1.91202i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	9.39054e8	−	9.39054e8i	0.00271337	−	0.00271337i
$768$		0			0
$769$		−	6.59329e10i		−	0.188537i	−0.995547	−	0.0942685i	$-0.969949\pi$
$769$		−	6.59329e10i		−	0.188537i	0.995547	−	0.0942685i	$-0.0300512\pi$
$770$		0			0
$771$	−3.36101e11			−0.951158
$772$		0			0
$773$	1.92475e11	+	1.92475e11i	0.539084	+	0.539084i	0.923260	−	0.384176i	$-0.125514\pi$
$773$	1.92475e11	+	1.92475e11i	0.539084	+	0.539084i	−0.384176	+	0.923260i	$0.625514\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−2.15158e10	+	2.15158e10i	−0.0590300	+	0.0590300i
$778$		0			0
$779$			9.35497e10i			0.254035i
$780$		0			0
$781$	4.85215e11			1.30416
$782$		0			0
$783$	4.29010e10	+	4.29010e10i	0.114135	+	0.114135i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	3.02596e10	−	3.02596e10i	0.0788794	−	0.0788794i	−0.666566	−	0.745446i	$-0.732237\pi$
$787$	3.02596e10	−	3.02596e10i	0.0788794	−	0.0788794i	0.745446	+	0.666566i	$0.232237\pi$
$788$		0			0
$789$			3.44354e11i			0.888582i
$790$		0			0
$791$	−8.81788e11			−2.25247
$792$		0			0
$793$	−2.31126e8	−	2.31126e8i	−0.000584462	−	0.000584462i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−2.36145e11	+	2.36145e11i	−0.585254	+	0.585254i	−0.936342	−	0.351088i	$-0.885812\pi$
$797$	−2.36145e11	+	2.36145e11i	−0.585254	+	0.585254i	0.351088	+	0.936342i	$0.385812\pi$
$798$		0			0
$799$		−	9.73924e10i		−	0.238967i
$800$		0			0
$801$	−1.21867e11			−0.296044
$802$		0			0
$803$	−1.13652e11	−	1.13652e11i	−0.273346	−	0.273346i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−8.93649e9	+	8.93649e9i	−0.0210704	+	0.0210704i
$808$		0			0
$809$			6.04017e11i			1.41012i	0.709149	+	0.705059i	$0.249079\pi$
$809$			6.04017e11i			1.41012i	−0.709149	+	0.705059i	$0.750921\pi$
$810$		0			0
$811$	−4.58433e11			−1.05972			−0.529862	−	0.848084i	$-0.677756\pi$
$811$	−4.58433e11			−1.05972			−0.529862	+	0.848084i	$0.677756\pi$
$812$		0			0
$813$	−9.34359e8	−	9.34359e8i	−0.00213871	−	0.00213871i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	2.06157e11	−	2.06157e11i	0.462710	−	0.462710i
$818$		0			0
$819$			5.50534e8i			0.00122363i
$820$		0			0
$821$	2.95041e11			0.649396			0.324698	−	0.945818i	$-0.394737\pi$
$821$	2.95041e11			0.649396			0.324698	+	0.945818i	$0.394737\pi$
$822$		0			0
$823$	−5.73242e11	−	5.73242e11i	−1.24951	−	1.24951i	−0.955938	−	0.293570i	$-0.905157\pi$
$823$	−5.73242e11	−	5.73242e11i	−1.24951	−	1.24951i	−0.293570	−	0.955938i	$-0.594843\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−5.18463e10	+	5.18463e10i	−0.110840	+	0.110840i	−0.760352	−	0.649512i	$-0.774973\pi$
$827$	−5.18463e10	+	5.18463e10i	−0.110840	+	0.110840i	0.649512	+	0.760352i	$0.274973\pi$
$828$		0			0
$829$			5.10411e11i			1.08069i	0.841443	+	0.540346i	$0.181706\pi$
$829$			5.10411e11i			1.08069i	−0.841443	+	0.540346i	$0.818294\pi$
$830$		0			0
$831$	2.10736e11			0.441910
$832$		0			0
$833$	−1.42465e11	−	1.42465e11i	−0.295888	−	0.295888i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.05989e11	−	1.05989e11i	0.215953	−	0.215953i
$838$		0			0
$839$		−	6.29232e10i		−	0.126988i	−0.997982	−	0.0634940i	$-0.979776\pi$
$839$		−	6.29232e10i		−	0.126988i	0.997982	−	0.0634940i	$-0.0202244\pi$
$840$		0			0
$841$	1.48347e11			0.296548
$842$		0			0
$843$	−1.00834e11	−	1.00834e11i	−0.199663	−	0.199663i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	2.78766e11	−	2.78766e11i	0.541634	−	0.541634i
$848$		0			0
$849$		−	4.60512e11i		−	0.886361i
$850$		0			0
$851$	−2.28544e10			−0.0435764
$852$		0			0
$853$	−5.02511e11	−	5.02511e11i	−0.949181	−	0.949181i	0.0495884	−	0.998770i	$-0.484209\pi$
$853$	−5.02511e11	−	5.02511e11i	−0.949181	−	0.949181i	−0.998770	+	0.0495884i	$0.984209\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−4.87959e11	+	4.87959e11i	−0.904607	+	0.904607i	−0.995830	−	0.0912234i	$-0.970922\pi$
$857$	−4.87959e11	+	4.87959e11i	−0.904607	+	0.904607i	0.0912234	+	0.995830i	$0.470922\pi$
$858$		0			0
$859$			1.93521e11i			0.355431i	0.984082	+	0.177716i	$0.0568707\pi$
$859$			1.93521e11i			0.355431i	−0.984082	+	0.177716i	$0.943129\pi$
$860$		0			0
$861$	7.49097e10			0.136309
$862$		0			0
$863$	−2.56399e10	−	2.56399e10i	−0.0462246	−	0.0462246i	0.683617	−	0.729841i	$-0.260406\pi$
$863$	−2.56399e10	−	2.56399e10i	−0.0462246	−	0.0462246i	−0.729841	+	0.683617i	$0.760406\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−2.07067e11	+	2.07067e11i	−0.366467	+	0.366467i
$868$		0			0
$869$		−	5.32618e11i		−	0.933978i
$870$		0			0
$871$	−1.11028e9			−0.00192913
$872$		0			0
$873$	−1.27256e11	−	1.27256e11i	−0.219089	−	0.219089i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−5.00887e11	+	5.00887e11i	−0.846722	+	0.846722i	−0.989723	−	0.143000i	$-0.954325\pi$
$877$	−5.00887e11	+	5.00887e11i	−0.846722	+	0.846722i	0.143000	+	0.989723i	$0.454325\pi$
$878$		0			0
$879$		−	6.60400e11i		−	1.10624i
$880$		0			0
$881$	−5.75843e11			−0.955874			−0.477937	−	0.878394i	$-0.658615\pi$
$881$	−5.75843e11			−0.955874			−0.477937	+	0.878394i	$0.658615\pi$
$882$		0			0
$883$	−5.24136e11	−	5.24136e11i	−0.862187	−	0.862187i	0.129405	−	0.991592i	$-0.458693\pi$
$883$	−5.24136e11	−	5.24136e11i	−0.862187	−	0.862187i	−0.991592	+	0.129405i	$0.958693\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−4.79295e11	+	4.79295e11i	−0.774299	+	0.774299i	−0.978855	−	0.204556i	$-0.934425\pi$
$887$	−4.79295e11	+	4.79295e11i	−0.774299	+	0.774299i	0.204556	+	0.978855i	$0.434425\pi$
$888$		0			0
$889$			8.49517e11i			1.36008i
$890$		0			0
$891$	−4.93086e10			−0.0782369
$892$		0			0
$893$	−5.49068e11	−	5.49068e11i	−0.863416	−	0.863416i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−2.92393e8	+	2.92393e8i	−0.000451645	+	0.000451645i
$898$		0			0
$899$			8.69387e11i			1.33099i
$900$		0			0
$901$	2.97395e11			0.451268
$902$		0			0
$903$	−1.65079e11	−	1.65079e11i	−0.248280	−	0.248280i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	6.95192e11	−	6.95192e11i	1.02725	−	1.02725i	0.0276308	−	0.999618i	$-0.491204\pi$
$907$	6.95192e11	−	6.95192e11i	1.02725	−	1.02725i	0.999618	−	0.0276308i	$-0.00879628\pi$
$908$		0			0
$909$			2.05296e11i			0.300694i
$910$		0			0
$911$	4.72700e11			0.686297			0.343148	−	0.939281i	$-0.388507\pi$
$911$	4.72700e11			0.686297			0.343148	+	0.939281i	$0.388507\pi$
$912$		0			0
$913$	−6.23952e11	−	6.23952e11i	−0.897982	−	0.897982i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.11231e11	−	2.11231e11i	0.298731	−	0.298731i
$918$		0			0
$919$			3.44547e11i			0.483043i	0.970395	+	0.241522i	$0.0776465\pi$
$919$			3.44547e11i			0.483043i	−0.970395	+	0.241522i	$0.922354\pi$
$920$		0			0
$921$	−5.99612e11			−0.833359
$922$		0			0
$923$	−2.29677e9	−	2.29677e9i	−0.00316454	−	0.00316454i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−3.14330e11	+	3.14330e11i	−0.425664	+	0.425664i
$928$		0			0
$929$		−	4.69738e11i		−	0.630657i	−0.948983	−	0.315328i	$-0.897885\pi$
$929$		−	4.69738e11i		−	0.630657i	0.948983	−	0.315328i	$-0.102115\pi$
$930$		0			0
$931$	−1.60634e12			−2.13815
$932$		0			0
$933$	3.84353e11	+	3.84353e11i	0.507229	+	0.507229i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−5.60392e11	+	5.60392e11i	−0.726999	+	0.726999i	−0.970021	−	0.243022i	$-0.921861\pi$
$937$	−5.60392e11	+	5.60392e11i	−0.726999	+	0.726999i	0.243022	+	0.970021i	$0.421861\pi$
$938$		0			0
$939$			5.06458e11i			0.651451i
$940$		0			0
$941$	−8.52147e11			−1.08682			−0.543408	−	0.839469i	$-0.682866\pi$
$941$	−8.52147e11			−1.08682			−0.543408	+	0.839469i	$0.682866\pi$
$942$		0			0
$943$	3.97851e10	+	3.97851e10i	0.0503123	+	0.0503123i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.93913e11	−	9.93913e11i	1.23580	−	1.23580i	0.274100	−	0.961701i	$-0.411620\pi$
$947$	9.93913e11	−	9.93913e11i	1.23580	−	1.23580i	0.961701	−	0.274100i	$-0.0883800\pi$
$948$		0			0
$949$			1.07594e9i			0.00132655i
$950$		0			0
$951$	−3.46751e11			−0.423932
$952$		0			0
$953$	5.73477e11	+	5.73477e11i	0.695255	+	0.695255i	0.963383	−	0.268128i	$-0.0864051\pi$
$953$	5.73477e11	+	5.73477e11i	0.695255	+	0.695255i	−0.268128	+	0.963383i	$0.586405\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	2.02229e11	−	2.02229e11i	0.241099	−	0.241099i
$958$		0			0
$959$		−	7.36240e11i		−	0.870452i
$960$		0			0
$961$	1.29498e12			1.51834
$962$		0			0
$963$	2.00709e11	+	2.00709e11i	0.233379	+	0.233379i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	2.08537e11	−	2.08537e11i	0.238494	−	0.238494i	−0.577733	−	0.816226i	$-0.696062\pi$
$967$	2.08537e11	−	2.08537e11i	0.238494	−	0.238494i	0.816226	+	0.577733i	$0.196062\pi$
$968$		0			0
$969$		−	2.66188e11i		−	0.301922i
$970$		0			0
$971$	−9.04461e11			−1.01745			−0.508725	−	0.860929i	$-0.669883\pi$
$971$	−9.04461e11			−1.01745			−0.508725	+	0.860929i	$0.669883\pi$
$972$		0			0
$973$	4.49198e11	+	4.49198e11i	0.501172	+	0.501172i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−3.04366e11	+	3.04366e11i	−0.334055	+	0.334055i	−0.854124	−	0.520069i	$-0.825906\pi$
$977$	−3.04366e11	+	3.04366e11i	−0.334055	+	0.334055i	0.520069	+	0.854124i	$0.325906\pi$
$978$		0			0
$979$			5.74464e11i			0.625363i
$980$		0			0
$981$	5.49467e11			0.593288
$982$		0			0
$983$	1.24706e11	+	1.24706e11i	0.133559	+	0.133559i	0.770726	−	0.637167i	$-0.219894\pi$
$983$	1.24706e11	+	1.24706e11i	0.133559	+	0.133559i	−0.637167	+	0.770726i	$0.719894\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−4.39665e11	+	4.39665e11i	−0.463290	+	0.463290i
$988$		0			0
$989$		−	1.75350e11i		−	0.183282i
$990$		0			0
$991$	−6.79600e11			−0.704626			−0.352313	−	0.935882i	$-0.614605\pi$
$991$	−6.79600e11			−0.704626			−0.352313	+	0.935882i	$0.614605\pi$
$992$		0			0
$993$	2.26490e11	+	2.26490e11i	0.232944	+	0.232944i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−2.57398e11	+	2.57398e11i	−0.260511	+	0.260511i	−0.825261	−	0.564751i	$-0.808972\pi$
$997$	−2.57398e11	+	2.57398e11i	−0.260511	+	0.260511i	0.564751	+	0.825261i	$0.308972\pi$
$998$		0			0
$999$			1.82435e10i			0.0183167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.9.k.e.193.5		16
5.2	odd	4	inner	300.9.k.e.157.5		16
5.3	odd	4		60.9.k.a.37.3	yes	16
5.4	even	2		60.9.k.a.13.3	✓	16
15.8	even	4		180.9.l.c.37.4		16
15.14	odd	2		180.9.l.c.73.4		16
20.3	even	4		240.9.bg.c.97.7		16
20.19	odd	2		240.9.bg.c.193.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.9.k.a.13.3	✓	16	5.4	even	2
60.9.k.a.37.3	yes	16	5.3	odd	4
180.9.l.c.37.4		16	15.8	even	4
180.9.l.c.73.4		16	15.14	odd	2
240.9.bg.c.97.7		16	20.3	even	4
240.9.bg.c.193.7		16	20.19	odd	2
300.9.k.e.157.5		16	5.2	odd	4	inner
300.9.k.e.193.5		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)

\(f(q)\)	\(=\)	\(q+(33.0681 + 33.0681i) q^{3} +(-2579.27 + 2579.27i) q^{7} +2187.00i q^{9} +O(q^{10})\)	\(q+(33.0681 + 33.0681i) q^{3} +(-2579.27 + 2579.27i) q^{7} +2187.00i q^{9} +10309.2 q^{11} +(-48.7988 - 48.7988i) q^{13} +(18893.4 - 18893.4i) q^{17} -213030. i q^{19} -170583. q^{21} +(-90598.0 - 90598.0i) q^{23} +(-72320.0 + 72320.0i) q^{27} -593211. i q^{29} -1.46556e6 q^{31} +(340906. + 340906. i) q^{33} +(126131. - 126131. i) q^{37} -3227.37i q^{39} -439139. q^{41} +(967737. + 967737. i) q^{43} +(2.57742e6 - 2.57742e6i) q^{47} -7.54045e6i q^{49} +1.24954e6 q^{51} +(7.87036e6 + 7.87036e6i) q^{53} +(7.04449e6 - 7.04449e6i) q^{57} +1.92434e7i q^{59} +4.73632e6 q^{61} +(-5.64086e6 - 5.64086e6i) q^{63} +(1.13761e7 - 1.13761e7i) q^{67} -5.99181e6i q^{69} +4.70662e7 q^{71} +(-1.10243e7 - 1.10243e7i) q^{73} +(-2.65902e7 + 2.65902e7i) q^{77} -5.16643e7i q^{79} -4.78297e6 q^{81} +(-6.05238e7 - 6.05238e7i) q^{83} +(1.96164e7 - 1.96164e7i) q^{87} +5.57234e7i q^{89} +251730. q^{91} +(-4.84633e7 - 4.84633e7i) q^{93} +(-5.81874e7 + 5.81874e7i) q^{97} +2.25462e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4220 q^{7}+O(q^{10}) \) 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

L-functions

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