LMFDB - Embedded newform 300.9.k.e.157.7

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			157.7
Root			$391.920 + 1.00000i$ of defining polynomial
Character	$\chi$	$=$	300.157
Dual form			300.9.k.e.193.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(33.0681 - 33.0681i) q^{3} +(127.920 + 127.920i) q^{7} -2187.00i q^{9} +O(q^{10})$	$q+(33.0681 - 33.0681i) q^{3} +(127.920 + 127.920i) q^{7} -2187.00i q^{9} -3463.97 q^{11} +(9012.59 - 9012.59i) q^{13} +(50722.9 + 50722.9i) q^{17} +23813.1i q^{19} +8460.12 q^{21} +(-302895. + 302895. i) q^{23} +(-72320.0 - 72320.0i) q^{27} -1.01200e6i q^{29} +519677. q^{31} +(-114547. + 114547. i) q^{33} +(1.86920e6 + 1.86920e6i) q^{37} -596059. i q^{39} +1.25013e6 q^{41} +(-2.86962e6 + 2.86962e6i) q^{43} +(888373. + 888373. i) q^{47} -5.73207e6i q^{49} +3.35462e6 q^{51} +(-3.11474e6 + 3.11474e6i) q^{53} +(787453. + 787453. i) q^{57} +9.36105e6i q^{59} +1.53301e6 q^{61} +(279760. - 279760. i) q^{63} +(9.05117e6 + 9.05117e6i) q^{67} +2.00323e7i q^{69} +7.00697e6 q^{71} +(1.60689e7 - 1.60689e7i) q^{73} +(-443111. - 443111. i) q^{77} +1.60292e7i q^{79} -4.78297e6 q^{81} +(2.76208e7 - 2.76208e7i) q^{83} +(-3.34649e7 - 3.34649e7i) q^{87} +8.39844e7i q^{89} +2.30578e6 q^{91} +(1.71848e7 - 1.71848e7i) q^{93} +(8.71059e7 + 8.71059e7i) q^{97} +7.57571e6i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	127.920	+	127.920i	0.0532777	+	0.0532777i	0.733244	−	0.679966i	$-0.238005\pi$
$7$	127.920	+	127.920i	0.0532777	+	0.0532777i	−0.679966	+	0.733244i	$0.738005\pi$
$8$		0			0
$9$		−	2187.00i		−	0.333333i
$10$		0			0
$11$	−3463.97			−0.236594			−0.118297	−	0.992978i	$-0.537744\pi$
$11$	−3463.97			−0.236594			−0.118297	+	0.992978i	$0.537744\pi$
$12$		0			0
$13$	9012.59	−	9012.59i	0.315556	−	0.315556i	−0.531501	−	0.847057i	$-0.678372\pi$
$13$	9012.59	−	9012.59i	0.315556	−	0.315556i	0.847057	+	0.531501i	$0.178372\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	50722.9	+	50722.9i	0.607307	+	0.607307i	0.942241	−	0.334935i	$-0.108714\pi$
$17$	50722.9	+	50722.9i	0.607307	+	0.607307i	−0.334935	+	0.942241i	$0.608714\pi$
$18$		0			0
$19$			23813.1i			0.182726i	0.995818	+	0.0913631i	$0.0291224\pi$
$19$			23813.1i			0.182726i	−0.995818	+	0.0913631i	$0.970878\pi$
$20$		0			0
$21$	8460.12			0.0435010
$22$		0			0
$23$	−302895.	+	302895.i	−1.08238	+	1.08238i	−0.0860967	+	0.996287i	$0.527439\pi$
$23$	−302895.	+	302895.i	−1.08238	+	1.08238i	−0.996287	+	0.0860967i	$0.972561\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−72320.0	−	72320.0i	−0.136083	−	0.136083i
$28$		0			0
$29$		−	1.01200e6i		−	1.43083i	−0.698700	−	0.715415i	$-0.746238\pi$
$29$		−	1.01200e6i		−	1.43083i	0.698700	−	0.715415i	$-0.253762\pi$
$30$		0			0
$31$	519677.			0.562713			0.281357	−	0.959603i	$-0.409216\pi$
$31$	519677.			0.562713			0.281357	+	0.959603i	$0.409216\pi$
$32$		0			0
$33$	−114547.	+	114547.i	−0.0965892	+	0.0965892i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.86920e6	+	1.86920e6i	0.997356	+	0.997356i	0.999997	−	0.00264096i	$-0.000840646\pi$
$37$	1.86920e6	+	1.86920e6i	0.997356	+	0.997356i	−0.00264096	+	0.999997i	$0.500841\pi$
$38$		0			0
$39$		−	596059.i		−	0.257650i
$40$		0			0
$41$	1.25013e6			0.442406			0.221203	−	0.975228i	$-0.429002\pi$
$41$	1.25013e6			0.442406			0.221203	+	0.975228i	$0.429002\pi$
$42$		0			0
$43$	−2.86962e6	+	2.86962e6i	−0.839365	+	0.839365i	−0.988775	−	0.149410i	$-0.952263\pi$
$43$	−2.86962e6	+	2.86962e6i	−0.839365	+	0.839365i	0.149410	+	0.988775i	$0.452263\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	888373.	+	888373.i	0.182056	+	0.182056i	0.792251	−	0.610195i	$-0.208909\pi$
$47$	888373.	+	888373.i	0.182056	+	0.182056i	−0.610195	+	0.792251i	$0.708909\pi$
$48$		0			0
$49$		−	5.73207e6i		−	0.994323i
$50$		0			0
$51$	3.35462e6			0.495864
$52$		0			0
$53$	−3.11474e6	+	3.11474e6i	−0.394747	+	0.394747i	−0.876375	−	0.481629i	$-0.840045\pi$
$53$	−3.11474e6	+	3.11474e6i	−0.394747	+	0.394747i	0.481629	+	0.876375i	$0.340045\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	787453.	+	787453.i	0.0745977	+	0.0745977i
$58$		0			0
$59$			9.36105e6i			0.772532i	0.922387	+	0.386266i	$0.126235\pi$
$59$			9.36105e6i			0.772532i	−0.922387	+	0.386266i	$0.873765\pi$
$60$		0			0
$61$	1.53301e6			0.110720			0.0553598	−	0.998466i	$-0.482369\pi$
$61$	1.53301e6			0.110720			0.0553598	+	0.998466i	$0.482369\pi$
$62$		0			0
$63$	279760.	−	279760.i	0.0177592	−	0.0177592i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	9.05117e6	+	9.05117e6i	0.449164	+	0.449164i	0.895077	−	0.445912i	$-0.147121\pi$
$67$	9.05117e6	+	9.05117e6i	0.449164	+	0.449164i	−0.445912	+	0.895077i	$0.647121\pi$
$68$		0			0
$69$			2.00323e7i			0.883762i
$70$		0			0
$71$	7.00697e6			0.275738			0.137869	−	0.990450i	$-0.455975\pi$
$71$	7.00697e6			0.275738			0.137869	+	0.990450i	$0.455975\pi$
$72$		0			0
$73$	1.60689e7	−	1.60689e7i	0.565841	−	0.565841i	−0.365120	−	0.930961i	$-0.618972\pi$
$73$	1.60689e7	−	1.60689e7i	0.565841	−	0.565841i	0.930961	+	0.365120i	$0.118972\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−443111.	−	443111.i	−0.0126052	−	0.0126052i
$78$		0			0
$79$			1.60292e7i			0.411533i	0.978601	+	0.205766i	$0.0659687\pi$
$79$			1.60292e7i			0.411533i	−0.978601	+	0.205766i	$0.934031\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$		0			0
$83$	2.76208e7	−	2.76208e7i	0.582002	−	0.582002i	−0.353451	−	0.935453i	$-0.614992\pi$
$83$	2.76208e7	−	2.76208e7i	0.582002	−	0.582002i	0.935453	+	0.353451i	$0.114992\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−3.34649e7	−	3.34649e7i	−0.584134	−	0.584134i
$88$		0			0
$89$			8.39844e7i			1.33856i	0.743009	+	0.669281i	$0.233398\pi$
$89$			8.39844e7i			1.33856i	−0.743009	+	0.669281i	$0.766602\pi$
$90$		0			0
$91$	2.30578e6			0.0336242
$92$		0			0
$93$	1.71848e7	−	1.71848e7i	0.229727	−	0.229727i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	8.71059e7	+	8.71059e7i	0.983922	+	0.983922i	0.999873	−	0.0159506i	$-0.00507746\pi$
$97$	8.71059e7	+	8.71059e7i	0.983922	+	0.983922i	−0.0159506	+	0.999873i	$0.505077\pi$
$98$		0			0
$99$			7.57571e6i			0.0788647i
$100$		0			0
$101$	8.96815e7			0.861821			0.430911	−	0.902395i	$-0.358192\pi$
$101$	8.96815e7			0.861821			0.430911	+	0.902395i	$0.358192\pi$
$102$		0			0
$103$	−5.56248e7	+	5.56248e7i	−0.494219	+	0.494219i	−0.909633	−	0.415414i	$-0.863637\pi$
$103$	−5.56248e7	+	5.56248e7i	−0.494219	+	0.494219i	0.415414	+	0.909633i	$0.363637\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.98597e7	−	6.98597e7i	−0.532957	−	0.532957i	0.388494	−	0.921451i	$-0.372995\pi$
$107$	−6.98597e7	−	6.98597e7i	−0.532957	−	0.532957i	−0.921451	+	0.388494i	$0.872995\pi$
$108$		0			0
$109$		−	2.26191e8i		−	1.60240i	−0.598400	−	0.801198i	$-0.704197\pi$
$109$		−	2.26191e8i		−	1.60240i	0.598400	−	0.801198i	$-0.295803\pi$
$110$		0			0
$111$	1.23622e8			0.814337
$112$		0			0
$113$	6.04513e7	−	6.04513e7i	0.370759	−	0.370759i	−0.496994	−	0.867754i	$-0.665563\pi$
$113$	6.04513e7	−	6.04513e7i	0.370759	−	0.370759i	0.867754	+	0.496994i	$0.165563\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.97105e7	−	1.97105e7i	−0.105185	−	0.105185i
$118$		0			0
$119$			1.29769e7i			0.0647118i
$120$		0			0
$121$	−2.02360e8			−0.944023
$122$		0			0
$123$	4.13396e7	−	4.13396e7i	0.180612	−	0.180612i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	1.89473e8	+	1.89473e8i	0.728335	+	0.728335i	0.970288	−	0.241953i	$-0.0777879\pi$
$127$	1.89473e8	+	1.89473e8i	0.728335	+	0.728335i	−0.241953	+	0.970288i	$0.577788\pi$
$128$		0			0
$129$			1.89786e8i			0.685339i
$130$		0			0
$131$	2.68824e8			0.912817			0.456408	−	0.889770i	$-0.349136\pi$
$131$	2.68824e8			0.912817			0.456408	+	0.889770i	$0.349136\pi$
$132$		0			0
$133$	−3.04616e6	+	3.04616e6i	−0.00973523	+	0.00973523i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.70826e7	+	5.70826e7i	0.162040	+	0.162040i	0.783470	−	0.621430i	$-0.213448\pi$
$137$	5.70826e7	+	5.70826e7i	0.162040	+	0.162040i	−0.621430	+	0.783470i	$0.713448\pi$
$138$		0			0
$139$		−	1.35342e8i		−	0.362556i	−0.983432	−	0.181278i	$-0.941977\pi$
$139$		−	1.35342e8i		−	0.362556i	0.983432	−	0.181278i	$-0.0580233\pi$
$140$		0			0
$141$	5.87537e7			0.148648
$142$		0			0
$143$	−3.12194e7	+	3.12194e7i	−0.0746587	+	0.0746587i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.89549e8	−	1.89549e8i	−0.405931	−	0.405931i
$148$		0			0
$149$			1.39533e8i			0.283095i	0.989931	+	0.141548i	$0.0452079\pi$
$149$			1.39533e8i			0.283095i	−0.989931	+	0.141548i	$0.954792\pi$
$150$		0			0
$151$	9.47085e8			1.82172			0.910859	−	0.412718i	$-0.135420\pi$
$151$	9.47085e8			1.82172			0.910859	+	0.412718i	$0.135420\pi$
$152$		0			0
$153$	1.10931e8	−	1.10931e8i	0.202436	−	0.202436i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	3.17899e8	+	3.17899e8i	0.523228	+	0.523228i	0.918545	−	0.395317i	$-0.129365\pi$
$157$	3.17899e8	+	3.17899e8i	0.523228	+	0.523228i	−0.395317	+	0.918545i	$0.629365\pi$
$158$		0			0
$159$			2.05997e8i			0.322309i
$160$		0			0
$161$	−7.74925e7			−0.115334
$162$		0			0
$163$	8.42374e8	−	8.42374e8i	1.19331	−	1.19331i	0.217182	−	0.976131i	$-0.430313\pi$
$163$	8.42374e8	−	8.42374e8i	1.19331	−	1.19331i	0.976131	−	0.217182i	$-0.0696865\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.32928e8	−	3.32928e8i	−0.428040	−	0.428040i	0.459920	−	0.887960i	$-0.347878\pi$
$167$	−3.32928e8	−	3.32928e8i	−0.428040	−	0.428040i	−0.887960	+	0.459920i	$0.847878\pi$
$168$		0			0
$169$			6.53277e8i			0.800849i
$170$		0			0
$171$	5.20792e7			0.0609087
$172$		0			0
$173$	1.00451e9	−	1.00451e9i	1.12142	−	1.12142i	0.129896	−	0.991528i	$-0.458536\pi$
$173$	1.00451e9	−	1.00451e9i	1.12142	−	1.12142i	0.991528	−	0.129896i	$-0.0414643\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3.09552e8	+	3.09552e8i	0.315385	+	0.315385i
$178$		0			0
$179$			1.90759e9i			1.85812i	0.369928	+	0.929060i	$0.379382\pi$
$179$			1.90759e9i			1.85812i	−0.369928	+	0.929060i	$0.620618\pi$
$180$		0			0
$181$	−1.39875e7			−0.0130324			−0.00651620	−	0.999979i	$-0.502074\pi$
$181$	−1.39875e7			−0.0130324			−0.00651620	+	0.999979i	$0.502074\pi$
$182$		0			0
$183$	5.06936e7	−	5.06936e7i	0.0452011	−	0.0452011i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.75703e8	−	1.75703e8i	−0.143685	−	0.143685i
$188$		0			0
$189$		−	1.85023e7i		−	0.0145003i
$190$		0			0
$191$	2.38769e9			1.79409			0.897046	−	0.441936i	$-0.145708\pi$
$191$	2.38769e9			1.79409			0.897046	+	0.441936i	$0.145708\pi$
$192$		0			0
$193$	2.15132e8	−	2.15132e8i	0.155052	−	0.155052i	−0.625318	−	0.780370i	$-0.715031\pi$
$193$	2.15132e8	−	2.15132e8i	0.155052	−	0.155052i	0.780370	+	0.625318i	$0.215031\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	1.19932e9	+	1.19932e9i	0.796291	+	0.796291i	0.982508	−	0.186218i	$-0.0596230\pi$
$197$	1.19932e9	+	1.19932e9i	0.796291	+	0.796291i	−0.186218	+	0.982508i	$0.559623\pi$
$198$		0			0
$199$			1.74661e9i			1.11374i	0.830601	+	0.556868i	$0.187997\pi$
$199$			1.74661e9i			1.11374i	−0.830601	+	0.556868i	$0.812003\pi$
$200$		0			0
$201$	5.98610e8			0.366741
$202$		0			0
$203$	1.29455e8	−	1.29455e8i	0.0762313	−	0.0762313i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	6.62432e8	+	6.62432e8i	0.360794	+	0.360794i
$208$		0			0
$209$		−	8.24879e7i		−	0.0432320i
$210$		0			0
$211$	2.33976e9			1.18043			0.590217	−	0.807244i	$-0.299042\pi$
$211$	2.33976e9			1.18043			0.590217	+	0.807244i	$0.299042\pi$
$212$		0			0
$213$	2.31707e8	−	2.31707e8i	0.112570	−	0.112570i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	6.64770e7	+	6.64770e7i	0.0299800	+	0.0299800i
$218$		0			0
$219$		−	1.06274e9i		−	0.462007i
$220$		0			0
$221$	9.14289e8			0.383279
$222$		0			0
$223$	4.89928e8	−	4.89928e8i	0.198113	−	0.198113i	−0.601078	−	0.799191i	$-0.705262\pi$
$223$	4.89928e8	−	4.89928e8i	0.198113	−	0.198113i	0.799191	+	0.601078i	$0.205262\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.56578e9	+	2.56578e9i	0.966310	+	0.966310i	0.999451	−	0.0331407i	$-0.0105509\pi$
$227$	2.56578e9	+	2.56578e9i	0.966310	+	0.966310i	−0.0331407	+	0.999451i	$0.510551\pi$
$228$		0			0
$229$			3.15797e9i			1.14833i	0.818740	+	0.574165i	$0.194673\pi$
$229$			3.15797e9i			1.14833i	−0.818740	+	0.574165i	$0.805327\pi$
$230$		0			0
$231$	−2.93057e7			−0.0102921
$232$		0			0
$233$	−1.91681e9	+	1.91681e9i	−0.650362	+	0.650362i	−0.953080	−	0.302719i	$-0.902106\pi$
$233$	−1.91681e9	+	1.91681e9i	−0.650362	+	0.650362i	0.302719	+	0.953080i	$0.402106\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	5.30057e8	+	5.30057e8i	0.168008	+	0.168008i
$238$		0			0
$239$		−	4.05026e9i		−	1.24134i	−0.784072	−	0.620670i	$-0.786861\pi$
$239$		−	4.05026e9i		−	1.24134i	0.784072	−	0.620670i	$-0.213139\pi$
$240$		0			0
$241$	6.65308e9			1.97222			0.986108	−	0.166106i	$-0.0531194\pi$
$241$	6.65308e9			1.97222			0.986108	+	0.166106i	$0.0531194\pi$
$242$		0			0
$243$	−1.58164e8	+	1.58164e8i	−0.0453609	+	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.14617e8	+	2.14617e8i	0.0576603	+	0.0576603i
$248$		0			0
$249$		−	1.82674e9i		−	0.475203i
$250$		0			0
$251$	−1.04975e9			−0.264478			−0.132239	−	0.991218i	$-0.542217\pi$
$251$	−1.04975e9			−0.264478			−0.132239	+	0.991218i	$0.542217\pi$
$252$		0			0
$253$	1.04922e9	−	1.04922e9i	0.256086	−	0.256086i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.67168e9	−	1.67168e9i	−0.383195	−	0.383195i	0.489057	−	0.872252i	$-0.337341\pi$
$257$	−1.67168e9	−	1.67168e9i	−0.383195	−	0.383195i	−0.872252	+	0.489057i	$0.837341\pi$
$258$		0			0
$259$			4.78216e8i			0.106274i
$260$		0			0
$261$	−2.21324e9			−0.476943
$262$		0			0
$263$	1.10121e9	−	1.10121e9i	0.230170	−	0.230170i	−0.582594	−	0.812764i	$-0.697962\pi$
$263$	1.10121e9	−	1.10121e9i	0.230170	−	0.230170i	0.812764	+	0.582594i	$0.197962\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	2.77721e9	+	2.77721e9i	0.546466	+	0.546466i
$268$		0			0
$269$			5.29542e9i			1.01133i	0.862731	+	0.505663i	$0.168752\pi$
$269$			5.29542e9i			1.01133i	−0.862731	+	0.505663i	$0.831248\pi$
$270$		0			0
$271$	−2.10891e9			−0.391004			−0.195502	−	0.980703i	$-0.562634\pi$
$271$	−2.10891e9			−0.391004			−0.195502	+	0.980703i	$0.562634\pi$
$272$		0			0
$273$	7.62477e7	−	7.62477e7i	0.0137270	−	0.0137270i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−5.90559e9	−	5.90559e9i	−1.00310	−	1.00310i	−0.999995	−	0.00310542i	$-0.999012\pi$
$277$	−5.90559e9	−	5.90559e9i	−1.00310	−	1.00310i	−0.00310542	−	0.999995i	$-0.500988\pi$
$278$		0			0
$279$		−	1.13653e9i		−	0.187571i
$280$		0			0
$281$	−3.54117e8			−0.0567965			−0.0283983	−	0.999597i	$-0.509041\pi$
$281$	−3.54117e8			−0.0567965			−0.0283983	+	0.999597i	$0.509041\pi$
$282$		0			0
$283$	5.58276e9	−	5.58276e9i	0.870369	−	0.870369i	−0.122143	−	0.992512i	$-0.538977\pi$
$283$	5.58276e9	−	5.58276e9i	0.870369	−	0.870369i	0.992512	+	0.122143i	$0.0389768\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.59917e8	+	1.59917e8i	0.0235704	+	0.0235704i
$288$		0			0
$289$		−	1.83014e9i		−	0.262357i
$290$		0			0
$291$	5.76086e9			0.803369
$292$		0			0
$293$	−1.40478e8	+	1.40478e8i	−0.0190606	+	0.0190606i	−0.716573	−	0.697512i	$-0.754290\pi$
$293$	−1.40478e8	+	1.40478e8i	−0.0190606	+	0.0190606i	0.697512	+	0.716573i	$0.254290\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	2.50515e8	+	2.50515e8i	0.0321964	+	0.0321964i
$298$		0			0
$299$			5.45974e9i			0.683105i
$300$		0			0
$301$	−7.34163e8			−0.0894389
$302$		0			0
$303$	2.96560e9	−	2.96560e9i	0.351837	−	0.351837i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	2.35713e9	+	2.35713e9i	0.265356	+	0.265356i	0.827226	−	0.561870i	$-0.189918\pi$
$307$	2.35713e9	+	2.35713e9i	0.265356	+	0.265356i	−0.561870	+	0.827226i	$0.689918\pi$
$308$		0			0
$309$			3.67881e9i			0.403528i
$310$		0			0
$311$	−9.39367e9			−1.00414			−0.502069	−	0.864827i	$-0.667428\pi$
$311$	−9.39367e9			−1.00414			−0.502069	+	0.864827i	$0.667428\pi$
$312$		0			0
$313$	−2.25552e9	+	2.25552e9i	−0.235001	+	0.235001i	−0.814776	−	0.579775i	$-0.803140\pi$
$313$	−2.25552e9	+	2.25552e9i	−0.235001	+	0.235001i	0.579775	+	0.814776i	$0.303140\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.91742e9	−	7.91742e9i	−0.784055	−	0.784055i	0.196457	−	0.980512i	$-0.437056\pi$
$317$	−7.91742e9	−	7.91742e9i	−0.784055	−	0.784055i	−0.980512	+	0.196457i	$0.937056\pi$
$318$		0			0
$319$			3.50554e9i			0.338526i
$320$		0			0
$321$	−4.62026e9			−0.435157
$322$		0			0
$323$	−1.20787e9	+	1.20787e9i	−0.110971	+	0.110971i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−7.47971e9	−	7.47971e9i	−0.654175	−	0.654175i
$328$		0			0
$329$			2.27281e8i			0.0193990i
$330$		0			0
$331$	−2.07388e10			−1.72771			−0.863857	−	0.503737i	$-0.831958\pi$
$331$	−2.07388e10			−1.72771			−0.863857	+	0.503737i	$0.831958\pi$
$332$		0			0
$333$	4.08795e9	−	4.08795e9i	0.332452	−	0.332452i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	2.81269e9	+	2.81269e9i	0.218074	+	0.218074i	0.807686	−	0.589613i	$-0.200720\pi$
$337$	2.81269e9	+	2.81269e9i	0.218074	+	0.218074i	−0.589613	+	0.807686i	$0.700720\pi$
$338$		0			0
$339$		−	3.99802e9i		−	0.302724i
$340$		0			0
$341$	−1.80015e9			−0.133135
$342$		0			0
$343$	1.47068e9	−	1.47068e9i	0.106253	−	0.106253i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.83052e9	−	6.83052e9i	−0.471125	−	0.471125i	0.431154	−	0.902278i	$-0.358107\pi$
$347$	−6.83052e9	−	6.83052e9i	−0.471125	−	0.471125i	−0.902278	+	0.431154i	$0.858107\pi$
$348$		0			0
$349$		−	2.13388e10i		−	1.43836i	−0.694823	−	0.719181i	$-0.744517\pi$
$349$		−	2.13388e10i		−	1.43836i	0.694823	−	0.719181i	$-0.255483\pi$
$350$		0			0
$351$	−1.30358e9			−0.0858834
$352$		0			0
$353$	−1.30810e10	+	1.30810e10i	−0.842443	+	0.842443i	−0.989176	−	0.146733i	$-0.953124\pi$
$353$	−1.30810e10	+	1.30810e10i	−0.842443	+	0.842443i	0.146733	+	0.989176i	$0.453124\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	4.29122e8	+	4.29122e8i	0.0264185	+	0.0264185i
$358$		0			0
$359$		−	1.01258e10i		−	0.609607i	−0.952415	−	0.304803i	$-0.901409\pi$
$359$		−	1.01258e10i		−	0.609607i	0.952415	−	0.304803i	$-0.0985907\pi$
$360$		0			0
$361$	1.64165e10			0.966611
$362$		0			0
$363$	−6.69166e9	+	6.69166e9i	−0.385396	+	0.385396i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	2.52965e10	+	2.52965e10i	1.39443	+	1.39443i	0.815081	+	0.579347i	$0.196692\pi$
$367$	2.52965e10	+	2.52965e10i	1.39443	+	1.39443i	0.579347	+	0.815081i	$0.303308\pi$
$368$		0			0
$369$		−	2.73405e9i		−	0.147469i
$370$		0			0
$371$	−7.96874e8			−0.0420624
$372$		0			0
$373$	−2.39936e10	+	2.39936e10i	−1.23954	+	1.23954i	−0.279352	+	0.960189i	$0.590120\pi$
$373$	−2.39936e10	+	2.39936e10i	−1.23954	+	1.23954i	−0.960189	+	0.279352i	$0.909880\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−9.12073e9	−	9.12073e9i	−0.451507	−	0.451507i
$378$		0			0
$379$		−	3.64391e10i		−	1.76608i	−0.469296	−	0.883041i	$-0.655492\pi$
$379$		−	3.64391e10i		−	1.76608i	0.469296	−	0.883041i	$-0.344508\pi$
$380$		0			0
$381$	1.25310e10			0.594683
$382$		0			0
$383$	−2.77395e10	+	2.77395e10i	−1.28915	+	1.28915i	−0.353848	+	0.935303i	$0.615127\pi$
$383$	−2.77395e10	+	2.77395e10i	−1.28915	+	1.28915i	−0.935303	+	0.353848i	$0.884873\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.27587e9	+	6.27587e9i	0.279788	+	0.279788i
$388$		0			0
$389$			1.98907e10i			0.868662i	0.900753	+	0.434331i	$0.143015\pi$
$389$			1.98907e10i			0.868662i	−0.900753	+	0.434331i	$0.856985\pi$
$390$		0			0
$391$	−3.07274e10			−1.31468
$392$		0			0
$393$	8.88952e9	−	8.88952e9i	0.372656	−	0.372656i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−4.88872e9	−	4.88872e9i	−0.196804	−	0.196804i	0.601825	−	0.798628i	$-0.294441\pi$
$397$	−4.88872e9	−	4.88872e9i	−0.196804	−	0.196804i	−0.798628	+	0.601825i	$0.794441\pi$
$398$		0			0
$399$			2.01461e8i			0.00794878i
$400$		0			0
$401$	−3.26360e10			−1.26217			−0.631087	−	0.775712i	$-0.717391\pi$
$401$	−3.26360e10			−1.26217			−0.631087	+	0.775712i	$0.717391\pi$
$402$		0			0
$403$	4.68364e9	−	4.68364e9i	0.177567	−	0.177567i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.47488e9	−	6.47488e9i	−0.235968	−	0.235968i
$408$		0			0
$409$		−	4.58566e10i		−	1.63874i	−0.573268	−	0.819368i	$-0.694325\pi$
$409$		−	4.58566e10i		−	1.63874i	0.573268	−	0.819368i	$-0.305675\pi$
$410$		0			0
$411$	3.77523e9			0.132305
$412$		0			0
$413$	−1.19746e9	+	1.19746e9i	−0.0411587	+	0.0411587i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−4.47552e9	−	4.47552e9i	−0.148013	−	0.148013i
$418$		0			0
$419$			2.72753e10i			0.884939i	0.896783	+	0.442470i	$0.145898\pi$
$419$			2.72753e10i			0.884939i	−0.896783	+	0.442470i	$0.854102\pi$
$420$		0			0
$421$	−1.87855e10			−0.597991			−0.298996	−	0.954254i	$-0.596652\pi$
$421$	−1.87855e10			−0.597991			−0.298996	+	0.954254i	$0.596652\pi$
$422$		0			0
$423$	1.94287e9	−	1.94287e9i	0.0606852	−	0.0606852i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.96102e8	+	1.96102e8i	0.00589888	+	0.00589888i
$428$		0			0
$429$			2.06473e9i			0.0609586i
$430$		0			0
$431$	−1.07093e9			−0.0310351			−0.0155176	−	0.999880i	$-0.504940\pi$
$431$	−1.07093e9			−0.0310351			−0.0155176	+	0.999880i	$0.504940\pi$
$432$		0			0
$433$	−1.12604e10	+	1.12604e10i	−0.320333	+	0.320333i	−0.848895	−	0.528562i	$-0.822731\pi$
$433$	−1.12604e10	+	1.12604e10i	−0.320333	+	0.320333i	0.528562	+	0.848895i	$0.322731\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7.21286e9	−	7.21286e9i	−0.197780	−	0.197780i
$438$		0			0
$439$			4.24967e10i			1.14419i	0.820188	+	0.572094i	$0.193869\pi$
$439$			4.24967e10i			1.14419i	−0.820188	+	0.572094i	$0.806131\pi$
$440$		0			0
$441$	−1.25360e10			−0.331441
$442$		0			0
$443$	−4.08519e10	+	4.08519e10i	−1.06071	+	1.06071i	−0.0626775	+	0.998034i	$0.519964\pi$
$443$	−4.08519e10	+	4.08519e10i	−1.06071	+	1.06071i	−0.998034	+	0.0626775i	$0.980036\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	4.61410e9	+	4.61410e9i	0.115573	+	0.115573i
$448$		0			0
$449$		−	3.33706e10i		−	0.821068i	−0.911845	−	0.410534i	$-0.865342\pi$
$449$		−	3.33706e10i		−	0.821068i	0.911845	−	0.410534i	$-0.134658\pi$
$450$		0			0
$451$	−4.33044e9			−0.104671
$452$		0			0
$453$	3.13183e10	−	3.13183e10i	0.743713	−	0.743713i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	2.80783e9	+	2.80783e9i	0.0643734	+	0.0643734i	0.738561	−	0.674187i	$-0.235506\pi$
$457$	2.80783e9	+	2.80783e9i	0.0643734	+	0.0643734i	−0.674187	+	0.738561i	$0.735506\pi$
$458$		0			0
$459$		−	7.33655e9i		−	0.165288i
$460$		0			0
$461$	−5.69032e10			−1.25989			−0.629945	−	0.776639i	$-0.716923\pi$
$461$	−5.69032e10			−1.25989			−0.629945	+	0.776639i	$0.716923\pi$
$462$		0			0
$463$	3.64449e10	−	3.64449e10i	0.793071	−	0.793071i	−0.188921	−	0.981992i	$-0.560499\pi$
$463$	3.64449e10	−	3.64449e10i	0.793071	−	0.793071i	0.981992	+	0.188921i	$0.0604990\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.73598e10	−	5.73598e10i	−1.20598	−	1.20598i	−0.972318	−	0.233663i	$-0.924929\pi$
$467$	−5.73598e10	−	5.73598e10i	−1.20598	−	1.20598i	−0.233663	−	0.972318i	$-0.575071\pi$
$468$		0			0
$469$			2.31564e9i			0.0478609i
$470$		0			0
$471$	2.10246e10			0.427214
$472$		0			0
$473$	9.94030e9	−	9.94030e9i	0.198589	−	0.198589i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	6.81194e9	+	6.81194e9i	0.131582	+	0.131582i
$478$		0			0
$479$			4.26100e10i			0.809412i	0.914447	+	0.404706i	$0.132626\pi$
$479$			4.26100e10i			0.809412i	−0.914447	+	0.404706i	$0.867374\pi$
$480$		0			0
$481$	3.36928e10			0.629443
$482$		0			0
$483$	−2.56253e9	+	2.56253e9i	−0.0470848	+	0.0470848i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−3.61492e10	−	3.61492e10i	−0.642661	−	0.642661i	0.308547	−	0.951209i	$-0.400157\pi$
$487$	−3.61492e10	−	3.61492e10i	−0.642661	−	0.642661i	−0.951209	+	0.308547i	$0.900157\pi$
$488$		0			0
$489$		−	5.57114e10i		−	0.974336i
$490$		0			0
$491$	−5.62859e10			−0.968443			−0.484221	−	0.874946i	$-0.660897\pi$
$491$	−5.62859e10			−0.968443			−0.484221	+	0.874946i	$0.660897\pi$
$492$		0			0
$493$	5.13315e10	−	5.13315e10i	0.868953	−	0.868953i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	8.96330e8	+	8.96330e8i	0.0146907	+	0.0146907i
$498$		0			0
$499$			5.15202e10i			0.830951i	0.909604	+	0.415476i	$0.136385\pi$
$499$			5.15202e10i			0.830951i	−0.909604	+	0.415476i	$0.863615\pi$
$500$		0			0
$501$	−2.20186e10			−0.349493
$502$		0			0
$503$	−7.49249e10	+	7.49249e10i	−1.17045	+	1.17045i	−0.188352	+	0.982102i	$0.560315\pi$
$503$	−7.49249e10	+	7.49249e10i	−1.17045	+	1.17045i	−0.982102	+	0.188352i	$0.939685\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	2.16026e10	+	2.16026e10i	0.326945	+	0.326945i
$508$		0			0
$509$			4.67625e10i			0.696670i	0.937370	+	0.348335i	$0.113253\pi$
$509$			4.67625e10i			0.696670i	−0.937370	+	0.348335i	$0.886747\pi$
$510$		0			0
$511$	4.11105e9			0.0602934
$512$		0			0
$513$	1.72216e9	−	1.72216e9i	0.0248659	−	0.0248659i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−3.07730e9	−	3.07730e9i	−0.0430733	−	0.0430733i
$518$		0			0
$519$		−	6.64345e10i		−	0.915638i
$520$		0			0
$521$	2.19198e10			0.297500			0.148750	−	0.988875i	$-0.452475\pi$
$521$	2.19198e10			0.297500			0.148750	+	0.988875i	$0.452475\pi$
$522$		0			0
$523$	1.77148e10	−	1.77148e10i	0.236771	−	0.236771i	−0.578741	−	0.815512i	$-0.696456\pi$
$523$	1.77148e10	−	1.77148e10i	0.236771	−	0.236771i	0.815512	+	0.578741i	$0.196456\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.63595e10	+	2.63595e10i	0.341740	+	0.341740i
$528$		0			0
$529$		−	1.05180e11i		−	1.34311i
$530$		0			0
$531$	2.04726e10			0.257511
$532$		0			0
$533$	1.12670e10	−	1.12670e10i	0.139604	−	0.139604i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	6.30805e10	+	6.30805e10i	0.758575	+	0.758575i
$538$		0			0
$539$			1.98558e10i			0.235251i
$540$		0			0
$541$	9.00066e10			1.05072			0.525358	−	0.850881i	$-0.323931\pi$
$541$	9.00066e10			1.05072			0.525358	+	0.850881i	$0.323931\pi$
$542$		0			0
$543$	−4.62539e8	+	4.62539e8i	−0.00532045	+	0.00532045i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.42652e10	−	1.42652e10i	−0.159342	−	0.159342i	0.622933	−	0.782275i	$-0.285941\pi$
$547$	−1.42652e10	−	1.42652e10i	−0.159342	−	0.159342i	−0.782275	+	0.622933i	$0.785941\pi$
$548$		0			0
$549$		−	3.35268e9i		−	0.0369065i
$550$		0			0
$551$	2.40988e10			0.261450
$552$		0			0
$553$	−2.05046e9	+	2.05046e9i	−0.0219255	+	0.0219255i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.55308e10	−	2.55308e10i	−0.265242	−	0.265242i	0.561937	−	0.827180i	$-0.310056\pi$
$557$	−2.55308e10	−	2.55308e10i	−0.265242	−	0.265242i	−0.827180	+	0.561937i	$0.810056\pi$
$558$		0			0
$559$			5.17255e10i			0.529734i
$560$		0			0
$561$	−1.16203e10			−0.117319
$562$		0			0
$563$	−5.47346e10	+	5.47346e10i	−0.544789	+	0.544789i	−0.924929	−	0.380140i	$-0.875876\pi$
$563$	−5.47346e10	+	5.47346e10i	−0.544789	+	0.544789i	0.380140	+	0.924929i	$0.375876\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−6.11836e8	−	6.11836e8i	−0.00591974	−	0.00591974i
$568$		0			0
$569$		−	7.93145e10i		−	0.756665i	−0.925670	−	0.378332i	$-0.876498\pi$
$569$		−	7.93145e10i		−	0.756665i	0.925670	−	0.378332i	$-0.123502\pi$
$570$		0			0
$571$	4.08149e10			0.383950			0.191975	−	0.981400i	$-0.438511\pi$
$571$	4.08149e10			0.383950			0.191975	+	0.981400i	$0.438511\pi$
$572$		0			0
$573$	7.89565e10	−	7.89565e10i	0.732435	−	0.732435i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	1.60007e10	+	1.60007e10i	0.144356	+	0.144356i	0.775591	−	0.631235i	$-0.217452\pi$
$577$	1.60007e10	+	1.60007e10i	0.144356	+	0.144356i	−0.631235	+	0.775591i	$0.717452\pi$
$578$		0			0
$579$		−	1.42280e10i		−	0.126599i
$580$		0			0
$581$	7.06650e9			0.0620154
$582$		0			0
$583$	1.07894e10	−	1.07894e10i	0.0933948	−	0.0933948i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	5.25606e10	+	5.25606e10i	0.442698	+	0.442698i	0.892918	−	0.450220i	$-0.148654\pi$
$587$	5.25606e10	+	5.25606e10i	0.442698	+	0.442698i	−0.450220	+	0.892918i	$0.648654\pi$
$588$		0			0
$589$			1.23751e10i			0.102822i
$590$		0			0
$591$	7.93188e10			0.650169
$592$		0			0
$593$	−1.31642e11	+	1.31642e11i	−1.06457	+	1.06457i	−0.0668042	+	0.997766i	$0.521280\pi$
$593$	−1.31642e11	+	1.31642e11i	−1.06457	+	1.06457i	−0.997766	+	0.0668042i	$0.978720\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	5.77569e10	+	5.77569e10i	0.454681	+	0.454681i
$598$		0			0
$599$			2.33478e11i			1.81358i	0.421578	+	0.906792i	$0.361477\pi$
$599$			2.33478e11i			1.81358i	−0.421578	+	0.906792i	$0.638523\pi$
$600$		0			0
$601$	2.47691e11			1.89851			0.949255	−	0.314509i	$-0.101840\pi$
$601$	2.47691e11			1.89851			0.949255	+	0.314509i	$0.101840\pi$
$602$		0			0
$603$	1.97949e10	−	1.97949e10i	0.149721	−	0.149721i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	1.08355e11	+	1.08355e11i	0.798166	+	0.798166i	0.982806	−	0.184641i	$-0.0591121\pi$
$607$	1.08355e11	+	1.08355e11i	0.798166	+	0.798166i	−0.184641	+	0.982806i	$0.559112\pi$
$608$		0			0
$609$		−	8.56164e9i		−	0.0622426i
$610$		0			0
$611$	1.60131e10			0.114897
$612$		0			0
$613$	1.89396e11	−	1.89396e11i	1.34131	−	1.34131i	0.446548	−	0.894760i	$-0.352653\pi$
$613$	1.89396e11	−	1.89396e11i	1.34131	−	1.34131i	0.894760	−	0.446548i	$-0.147347\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−4.27533e10	−	4.27533e10i	−0.295004	−	0.295004i	0.544049	−	0.839053i	$-0.316891\pi$
$617$	−4.27533e10	−	4.27533e10i	−0.295004	−	0.295004i	−0.839053	+	0.544049i	$0.816891\pi$
$618$		0			0
$619$			1.40452e11i			0.956678i	0.878175	+	0.478339i	$0.158761\pi$
$619$			1.40452e11i			0.956678i	−0.878175	+	0.478339i	$0.841239\pi$
$620$		0			0
$621$	4.38107e10			0.294587
$622$		0			0
$623$	−1.07433e10	+	1.07433e10i	−0.0713155	+	0.0713155i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−2.72772e9	−	2.72772e9i	−0.0176494	−	0.0176494i
$628$		0			0
$629$			1.89623e11i			1.21140i
$630$		0			0
$631$	−8.55613e10			−0.539710			−0.269855	−	0.962901i	$-0.586976\pi$
$631$	−8.55613e10			−0.539710			−0.269855	+	0.962901i	$0.586976\pi$
$632$		0			0
$633$	7.73715e10	−	7.73715e10i	0.481910	−	0.481910i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−5.16609e10	−	5.16609e10i	−0.313765	−	0.313765i
$638$		0			0
$639$		−	1.53242e10i		−	0.0919128i
$640$		0			0
$641$	4.28258e10			0.253672			0.126836	−	0.991924i	$-0.459518\pi$
$641$	4.28258e10			0.253672			0.126836	+	0.991924i	$0.459518\pi$
$642$		0			0
$643$	1.56685e11	−	1.56685e11i	0.916606	−	0.916606i	−0.0801749	−	0.996781i	$-0.525548\pi$
$643$	1.56685e11	−	1.56685e11i	0.916606	−	0.916606i	0.996781	+	0.0801749i	$0.0255479\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4.42476e10	−	4.42476e10i	−0.252507	−	0.252507i	0.569491	−	0.821998i	$-0.307140\pi$
$647$	−4.42476e10	−	4.42476e10i	−0.252507	−	0.252507i	−0.821998	+	0.569491i	$0.807140\pi$
$648$		0			0
$649$		−	3.24265e10i		−	0.182777i
$650$		0			0
$651$	4.39654e9			0.0244786
$652$		0			0
$653$	1.99608e11	−	1.99608e11i	1.09780	−	1.09780i	0.103136	−	0.994667i	$-0.467112\pi$
$653$	1.99608e11	−	1.99608e11i	1.09780	−	1.09780i	0.994667	−	0.103136i	$-0.0328877\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−3.51427e10	−	3.51427e10i	−0.188614	−	0.188614i
$658$		0			0
$659$			2.62649e11i			1.39263i	0.717739	+	0.696313i	$0.245177\pi$
$659$			2.62649e11i			1.39263i	−0.717739	+	0.696313i	$0.754823\pi$
$660$		0			0
$661$	1.89284e11			0.991537			0.495768	−	0.868455i	$-0.334887\pi$
$661$	1.89284e11			0.991537			0.495768	+	0.868455i	$0.334887\pi$
$662$		0			0
$663$	3.02338e10	−	3.02338e10i	0.156473	−	0.156473i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.06530e11	+	3.06530e11i	1.54871	+	1.54871i
$668$		0			0
$669$		−	3.24020e10i		−	0.161759i
$670$		0			0
$671$	−5.31029e9			−0.0261956
$672$		0			0
$673$	−1.14966e11	+	1.14966e11i	−0.560413	+	0.560413i	−0.929425	−	0.369011i	$-0.879696\pi$
$673$	−1.14966e11	+	1.14966e11i	−0.560413	+	0.560413i	0.369011	+	0.929425i	$0.379696\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−2.37680e11	−	2.37680e11i	−1.13146	−	1.13146i	−0.989935	−	0.141523i	$-0.954800\pi$
$677$	−2.37680e11	−	2.37680e11i	−1.13146	−	1.13146i	−0.141523	−	0.989935i	$-0.545200\pi$
$678$		0			0
$679$			2.22851e10i			0.104842i
$680$		0			0
$681$	1.69691e11			0.788989
$682$		0			0
$683$	−1.39792e11	+	1.39792e11i	−0.642389	+	0.642389i	−0.951142	−	0.308753i	$-0.900088\pi$
$683$	−1.39792e11	+	1.39792e11i	−0.642389	+	0.642389i	0.308753	+	0.951142i	$0.400088\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	1.04428e11	+	1.04428e11i	0.468803	+	0.468803i
$688$		0			0
$689$			5.61438e10i			0.249129i
$690$		0			0
$691$	−1.49945e11			−0.657686			−0.328843	−	0.944385i	$-0.606659\pi$
$691$	−1.49945e11			−0.657686			−0.328843	+	0.944385i	$0.606659\pi$
$692$		0			0
$693$	−9.69083e8	+	9.69083e8i	−0.00420173	+	0.00420173i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	6.34104e10	+	6.34104e10i	0.268676	+	0.268676i
$698$		0			0
$699$			1.26770e11i			0.531018i
$700$		0			0
$701$	2.39536e11			0.991972			0.495986	−	0.868331i	$-0.334807\pi$
$701$	2.39536e11			0.991972			0.495986	+	0.868331i	$0.334807\pi$
$702$		0			0
$703$	−4.45115e10	+	4.45115e10i	−0.182243	+	0.182243i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.14720e10	+	1.14720e10i	0.0459158	+	0.0459158i
$708$		0			0
$709$		−	2.84237e11i		−	1.12485i	−0.826848	−	0.562426i	$-0.809868\pi$
$709$		−	2.84237e11i		−	1.12485i	0.826848	−	0.562426i	$-0.190132\pi$
$710$		0			0
$711$	3.50559e10			0.137178
$712$		0			0
$713$	−1.57408e11	+	1.57408e11i	−0.609071	+	0.609071i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−1.33934e11	−	1.33934e11i	−0.506775	−	0.506775i
$718$		0			0
$719$			1.14567e11i			0.428689i	0.976758	+	0.214345i	$0.0687615\pi$
$719$			1.14567e11i			0.428689i	−0.976758	+	0.214345i	$0.931238\pi$
$720$		0			0
$721$	−1.42310e10			−0.0526617
$722$		0			0
$723$	2.20005e11	−	2.20005e11i	0.805154	−	0.805154i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	1.94416e11	+	1.94416e11i	0.695975	+	0.695975i	0.963540	−	0.267565i	$-0.0862188\pi$
$727$	1.94416e11	+	1.94416e11i	0.695975	+	0.695975i	−0.267565	+	0.963540i	$0.586219\pi$
$728$		0			0
$729$			1.04604e10i			0.0370370i
$730$		0			0
$731$	−2.91111e11			−1.01950
$732$		0			0
$733$	6.81171e10	−	6.81171e10i	0.235961	−	0.235961i	−0.579214	−	0.815175i	$-0.696641\pi$
$733$	6.81171e10	−	6.81171e10i	0.235961	−	0.235961i	0.815175	+	0.579214i	$0.196641\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.13530e10	−	3.13530e10i	−0.106270	−	0.106270i
$738$		0			0
$739$		−	4.02239e11i		−	1.34867i	−0.738425	−	0.674336i	$-0.764430\pi$
$739$		−	4.02239e11i		−	1.34867i	0.738425	−	0.674336i	$-0.235570\pi$
$740$		0			0
$741$	1.41940e10			0.0470795
$742$		0			0
$743$	1.59507e10	−	1.59507e10i	0.0523388	−	0.0523388i	−0.680453	−	0.732792i	$-0.738217\pi$
$743$	1.59507e10	−	1.59507e10i	0.0523388	−	0.0523388i	0.732792	+	0.680453i	$0.238217\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−6.04068e10	−	6.04068e10i	−0.194001	−	0.194001i
$748$		0			0
$749$		−	1.78729e10i		−	0.0567894i
$750$		0			0
$751$	−7.28968e10			−0.229165			−0.114583	−	0.993414i	$-0.536553\pi$
$751$	−7.28968e10			−0.229165			−0.114583	+	0.993414i	$0.536553\pi$
$752$		0			0
$753$	−3.47131e10	+	3.47131e10i	−0.107973	+	0.107973i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−8.62031e10	−	8.62031e10i	−0.262506	−	0.262506i	0.563565	−	0.826071i	$-0.309429\pi$
$757$	−8.62031e10	−	8.62031e10i	−0.262506	−	0.262506i	−0.826071	+	0.563565i	$0.809429\pi$
$758$		0			0
$759$		−	6.93916e10i		−	0.209093i
$760$		0			0
$761$	1.42463e10			0.0424779			0.0212389	−	0.999774i	$-0.493239\pi$
$761$	1.42463e10			0.0424779			0.0212389	+	0.999774i	$0.493239\pi$
$762$		0			0
$763$	2.89343e10	−	2.89343e10i	0.0853719	−	0.0853719i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.43674e10	+	8.43674e10i	0.243777	+	0.243777i
$768$		0			0
$769$		−	5.99311e11i		−	1.71375i	−0.515526	−	0.856874i	$-0.672403\pi$
$769$		−	5.99311e11i		−	1.71375i	0.515526	−	0.856874i	$-0.327597\pi$
$770$		0			0
$771$	−1.10559e11			−0.312878
$772$		0			0
$773$	−3.81418e11	+	3.81418e11i	−1.06827	+	1.06827i	−0.0707824	+	0.997492i	$0.522550\pi$
$773$	−3.81418e11	+	3.81418e11i	−1.06827	+	1.06827i	−0.997492	+	0.0707824i	$0.977450\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	1.58137e10	+	1.58137e10i	0.0433860	+	0.0433860i
$778$		0			0
$779$			2.97695e10i			0.0808393i
$780$		0			0
$781$	−2.42720e10			−0.0652381
$782$		0			0
$783$	−7.31877e10	+	7.31877e10i	−0.194711	+	0.194711i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−1.71002e11	−	1.71002e11i	−0.445762	−	0.445762i	0.448181	−	0.893943i	$-0.352072\pi$
$787$	−1.71002e11	−	1.71002e11i	−0.445762	−	0.445762i	−0.893943	+	0.448181i	$0.852072\pi$
$788$		0			0
$789$		−	7.28301e10i		−	0.187933i
$790$		0			0
$791$	1.54658e10			0.0395064
$792$		0			0
$793$	1.38164e10	−	1.38164e10i	0.0349382	−	0.0349382i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−3.18500e11	−	3.18500e11i	−0.789361	−	0.789361i	0.192028	−	0.981389i	$-0.438493\pi$
$797$	−3.18500e11	−	3.18500e11i	−0.789361	−	0.789361i	−0.981389	+	0.192028i	$0.938493\pi$
$798$		0			0
$799$			9.01217e10i			0.221127i
$800$		0			0
$801$	1.83674e11			0.446187
$802$		0			0
$803$	−5.56622e10	+	5.56622e10i	−0.133875	+	0.133875i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.75110e11	+	1.75110e11i	0.412872	+	0.412872i
$808$		0			0
$809$		−	3.86733e11i		−	0.902853i	−0.892308	−	0.451426i	$-0.850915\pi$
$809$		−	3.86733e11i		−	0.902853i	0.892308	−	0.451426i	$-0.149085\pi$
$810$		0			0
$811$	7.34617e9			0.0169816			0.00849078	−	0.999964i	$-0.497297\pi$
$811$	7.34617e9			0.0169816			0.00849078	+	0.999964i	$0.497297\pi$
$812$		0			0
$813$	−6.97378e10	+	6.97378e10i	−0.159627	+	0.159627i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−6.83345e10	−	6.83345e10i	−0.153374	−	0.153374i
$818$		0			0
$819$		−	5.04273e9i		−	0.0112081i
$820$		0			0
$821$	−3.67388e11			−0.808635			−0.404317	−	0.914619i	$-0.632491\pi$
$821$	−3.67388e11			−0.808635			−0.404317	+	0.914619i	$0.632491\pi$
$822$		0			0
$823$	−1.96333e11	+	1.96333e11i	−0.427952	+	0.427952i	−0.887930	−	0.459978i	$-0.847857\pi$
$823$	−1.96333e11	+	1.96333e11i	−0.427952	+	0.427952i	0.459978	+	0.887930i	$0.347857\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.28469e11	−	1.28469e11i	−0.274648	−	0.274648i	0.556320	−	0.830968i	$-0.312213\pi$
$827$	−1.28469e11	−	1.28469e11i	−0.274648	−	0.274648i	−0.830968	+	0.556320i	$0.812213\pi$
$828$		0			0
$829$			6.44595e11i			1.36480i	0.730980	+	0.682399i	$0.239063\pi$
$829$			6.44595e11i			1.36480i	−0.730980	+	0.682399i	$0.760937\pi$
$830$		0			0
$831$	−3.90574e11			−0.819028
$832$		0			0
$833$	2.90747e11	−	2.90747e11i	0.603859	−	0.603859i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−3.75830e10	−	3.75830e10i	−0.0765756	−	0.0765756i
$838$		0			0
$839$			3.72154e11i			0.751060i	0.926810	+	0.375530i	$0.122539\pi$
$839$			3.72154e11i			0.751060i	−0.926810	+	0.375530i	$0.877461\pi$
$840$		0			0
$841$	−5.23895e11			−1.04727
$842$		0			0
$843$	−1.17100e10	+	1.17100e10i	−0.0231871	+	0.0231871i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−2.58858e10	−	2.58858e10i	−0.0502954	−	0.0502954i
$848$		0			0
$849$		−	3.69223e11i		−	0.710653i
$850$		0			0
$851$	−1.13235e12			−2.15904
$852$		0			0
$853$	3.72328e11	−	3.72328e11i	0.703281	−	0.703281i	−0.261832	−	0.965113i	$-0.584327\pi$
$853$	3.72328e11	−	3.72328e11i	0.703281	−	0.703281i	0.965113	+	0.261832i	$0.0843267\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−2.41615e11	−	2.41615e11i	−0.447920	−	0.447920i	0.446743	−	0.894662i	$-0.352584\pi$
$857$	−2.41615e11	−	2.41615e11i	−0.447920	−	0.447920i	−0.894662	+	0.446743i	$0.852584\pi$
$858$		0			0
$859$			3.66923e11i			0.673910i	0.941521	+	0.336955i	$0.109397\pi$
$859$			3.66923e11i			0.673910i	−0.941521	+	0.336955i	$0.890603\pi$
$860$		0			0
$861$	1.05763e10			0.0192451
$862$		0			0
$863$	−3.19216e11	+	3.19216e11i	−0.575495	+	0.575495i	−0.933659	−	0.358164i	$-0.883403\pi$
$863$	−3.19216e11	+	3.19216e11i	−0.575495	+	0.575495i	0.358164	+	0.933659i	$0.383403\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−6.05192e10	−	6.05192e10i	−0.107107	−	0.107107i
$868$		0			0
$869$		−	5.55249e10i		−	0.0973663i
$870$		0			0
$871$	1.63149e11			0.283473
$872$		0			0
$873$	1.90501e11	−	1.90501e11i	0.327974	−	0.327974i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−2.34273e11	−	2.34273e11i	−0.396027	−	0.396027i	0.480802	−	0.876829i	$-0.340345\pi$
$877$	−2.34273e11	−	2.34273e11i	−0.396027	−	0.396027i	−0.876829	+	0.480802i	$0.840345\pi$
$878$		0			0
$879$			9.29066e9i			0.0155629i
$880$		0			0
$881$	4.39872e11			0.730167			0.365084	−	0.930975i	$-0.381040\pi$
$881$	4.39872e11			0.730167			0.365084	+	0.930975i	$0.381040\pi$
$882$		0			0
$883$	−4.29488e11	+	4.29488e11i	−0.706494	+	0.706494i	−0.965796	−	0.259302i	$-0.916508\pi$
$883$	−4.29488e11	+	4.29488e11i	−0.706494	+	0.706494i	0.259302	+	0.965796i	$0.416508\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	5.76111e11	+	5.76111e11i	0.930704	+	0.930704i	0.997750	−	0.0670462i	$-0.0213575\pi$
$887$	5.76111e11	+	5.76111e11i	0.930704	+	0.930704i	−0.0670462	+	0.997750i	$0.521357\pi$
$888$		0			0
$889$			4.84745e10i			0.0776080i
$890$		0			0
$891$	1.65681e10			0.0262882
$892$		0			0
$893$	−2.11549e10	+	2.11549e10i	−0.0332663	+	0.0332663i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1.80543e11	+	1.80543e11i	0.278876	+	0.278876i
$898$		0			0
$899$		−	5.25913e11i		−	0.805147i
$900$		0			0
$901$	−3.15977e11			−0.479465
$902$		0			0
$903$	−2.42774e10	+	2.42774e10i	−0.0365133	+	0.0365133i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−4.28785e11	−	4.28785e11i	−0.633593	−	0.633593i	0.315374	−	0.948967i	$-0.397870\pi$
$907$	−4.28785e11	−	4.28785e11i	−0.633593	−	0.633593i	−0.948967	+	0.315374i	$0.897870\pi$
$908$		0			0
$909$		−	1.96133e11i		−	0.287274i
$910$		0			0
$911$	5.83687e10			0.0847435			0.0423718	−	0.999102i	$-0.486509\pi$
$911$	5.83687e10			0.0847435			0.0423718	+	0.999102i	$0.486509\pi$
$912$		0			0
$913$	−9.56779e10	+	9.56779e10i	−0.137698	+	0.137698i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.43879e10	+	3.43879e10i	0.0486327	+	0.0486327i
$918$		0			0
$919$			4.11602e11i			0.577052i	0.957472	+	0.288526i	$0.0931652\pi$
$919$			4.11602e11i			0.577052i	−0.957472	+	0.288526i	$0.906835\pi$
$920$		0			0
$921$	1.55891e11			0.216663
$922$		0			0
$923$	6.31510e10	−	6.31510e10i	0.0870108	−	0.0870108i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	1.21651e11	+	1.21651e11i	0.164740	+	0.164740i
$928$		0			0
$929$		−	9.48753e11i		−	1.27377i	−0.770960	−	0.636884i	$-0.780223\pi$
$929$		−	9.48753e11i		−	1.27377i	0.770960	−	0.636884i	$-0.219777\pi$
$930$		0			0
$931$	1.36498e11			0.181689
$932$		0			0
$933$	−3.10631e11	+	3.10631e11i	−0.409938	+	0.409938i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−5.75513e11	−	5.75513e11i	−0.746615	−	0.746615i	0.227227	−	0.973842i	$-0.427034\pi$
$937$	−5.75513e11	−	5.75513e11i	−0.746615	−	0.746615i	−0.973842	+	0.227227i	$0.927034\pi$
$938$		0			0
$939$			1.49172e11i			0.191877i
$940$		0			0
$941$	−9.52635e11			−1.21498			−0.607489	−	0.794328i	$-0.707823\pi$
$941$	−9.52635e11			−1.21498			−0.607489	+	0.794328i	$0.707823\pi$
$942$		0			0
$943$	−3.78660e11	+	3.78660e11i	−0.478853	+	0.478853i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.86794e11	+	2.86794e11i	0.356591	+	0.356591i	0.862555	−	0.505964i	$-0.168863\pi$
$947$	2.86794e11	+	2.86794e11i	0.356591	+	0.356591i	−0.505964	+	0.862555i	$0.668863\pi$
$948$		0			0
$949$		−	2.89645e11i		−	0.357109i
$950$		0			0
$951$	−5.23628e11			−0.640178
$952$		0			0
$953$	−9.08233e11	+	9.08233e11i	−1.10110	+	1.10110i	−0.106819	+	0.994278i	$0.534067\pi$
$953$	−9.08233e11	+	9.08233e11i	−1.10110	+	1.10110i	−0.994278	+	0.106819i	$0.965933\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	1.15922e11	+	1.15922e11i	0.138203	+	0.138203i
$958$		0			0
$959$			1.46040e10i			0.0172662i
$960$		0			0
$961$	−5.82826e11			−0.683354
$962$		0			0
$963$	−1.52783e11	+	1.52783e11i	−0.177652	+	0.177652i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−3.43533e11	−	3.43533e11i	−0.392883	−	0.392883i	0.482831	−	0.875714i	$-0.339609\pi$
$967$	−3.43533e11	−	3.43533e11i	−0.392883	−	0.392883i	−0.875714	+	0.482831i	$0.839609\pi$
$968$		0			0
$969$			7.98838e10i			0.0906074i
$970$		0			0
$971$	1.37103e12			1.54231			0.771154	−	0.636648i	$-0.219680\pi$
$971$	1.37103e12			1.54231			0.771154	+	0.636648i	$0.219680\pi$
$972$		0			0
$973$	1.73130e10	−	1.73130e10i	0.0193161	−	0.0193161i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.21854e11	+	5.21854e11i	0.572758	+	0.572758i	0.932898	−	0.360140i	$-0.117271\pi$
$977$	5.21854e11	+	5.21854e11i	0.572758	+	0.572758i	−0.360140	+	0.932898i	$0.617271\pi$
$978$		0			0
$979$		−	2.90920e11i		−	0.316696i
$980$		0			0
$981$	−4.94680e11			−0.534132
$982$		0			0
$983$	2.96993e11	−	2.96993e11i	0.318077	−	0.318077i	−0.529951	−	0.848028i	$-0.677790\pi$
$983$	2.96993e11	−	2.96993e11i	0.318077	−	0.318077i	0.848028	+	0.529951i	$0.177790\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	7.51575e9	+	7.51575e9i	0.00791961	+	0.00791961i
$988$		0			0
$989$		−	1.73839e12i		−	1.81703i
$990$		0			0
$991$	9.22521e11			0.956492			0.478246	−	0.878226i	$-0.341273\pi$
$991$	9.22521e11			0.956492			0.478246	+	0.878226i	$0.341273\pi$
$992$		0			0
$993$	−6.85793e11	+	6.85793e11i	−0.705336	+	0.705336i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	7.02520e11	+	7.02520e11i	0.711014	+	0.711014i	0.966747	−	0.255734i	$-0.0823170\pi$
$997$	7.02520e11	+	7.02520e11i	0.711014	+	0.711014i	−0.255734	+	0.966747i	$0.582317\pi$
$998$		0			0
$999$		−	2.70362e11i		−	0.271446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.9.k.e.157.7		16
5.2	odd	4		60.9.k.a.13.4	✓	16
5.3	odd	4	inner	300.9.k.e.193.7		16
5.4	even	2		60.9.k.a.37.4	yes	16
15.2	even	4		180.9.l.c.73.2		16
15.14	odd	2		180.9.l.c.37.2		16
20.7	even	4		240.9.bg.c.193.8		16
20.19	odd	2		240.9.bg.c.97.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.9.k.a.13.4	✓	16	5.2	odd	4
60.9.k.a.37.4	yes	16	5.4	even	2
180.9.l.c.37.2		16	15.14	odd	2
180.9.l.c.73.2		16	15.2	even	4
240.9.bg.c.97.8		16	20.19	odd	2
240.9.bg.c.193.8		16	20.7	even	4
300.9.k.e.157.7		16	1.1	even	1	trivial
300.9.k.e.193.7		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)

\(f(q)\)	\(=\)	\(q+(33.0681 - 33.0681i) q^{3} +(127.920 + 127.920i) q^{7} -2187.00i q^{9} +O(q^{10})\)	\(q+(33.0681 - 33.0681i) q^{3} +(127.920 + 127.920i) q^{7} -2187.00i q^{9} -3463.97 q^{11} +(9012.59 - 9012.59i) q^{13} +(50722.9 + 50722.9i) q^{17} +23813.1i q^{19} +8460.12 q^{21} +(-302895. + 302895. i) q^{23} +(-72320.0 - 72320.0i) q^{27} -1.01200e6i q^{29} +519677. q^{31} +(-114547. + 114547. i) q^{33} +(1.86920e6 + 1.86920e6i) q^{37} -596059. i q^{39} +1.25013e6 q^{41} +(-2.86962e6 + 2.86962e6i) q^{43} +(888373. + 888373. i) q^{47} -5.73207e6i q^{49} +3.35462e6 q^{51} +(-3.11474e6 + 3.11474e6i) q^{53} +(787453. + 787453. i) q^{57} +9.36105e6i q^{59} +1.53301e6 q^{61} +(279760. - 279760. i) q^{63} +(9.05117e6 + 9.05117e6i) q^{67} +2.00323e7i q^{69} +7.00697e6 q^{71} +(1.60689e7 - 1.60689e7i) q^{73} +(-443111. - 443111. i) q^{77} +1.60292e7i q^{79} -4.78297e6 q^{81} +(2.76208e7 - 2.76208e7i) q^{83} +(-3.34649e7 - 3.34649e7i) q^{87} +8.39844e7i q^{89} +2.30578e6 q^{91} +(1.71848e7 - 1.71848e7i) q^{93} +(8.71059e7 + 8.71059e7i) q^{97} +7.57571e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4220 q^{7}+O(q^{10}) \) 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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