LMFDB - Embedded newform 300.9.k.e.193.7

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			193.7
Root			$391.920 - 1.00000i$ of defining polynomial
Character	$\chi$	$=$	300.193
Dual form			300.9.k.e.157.7

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

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

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
$7$	127.920	−	127.920i	0.0532777	−	0.0532777i	−0.679966	−	0.733244i	$-0.738005\pi$
$7$	127.920	−	127.920i	0.0532777	−	0.0532777i	0.733244	+	0.679966i	$0.238005\pi$
$8$		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	0.847057	−	0.531501i	$-0.178372\pi$
$13$	9012.59	+	9012.59i	0.315556	+	0.315556i	−0.531501	+	0.847057i	$0.678372\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	50722.9	−	50722.9i	0.607307	−	0.607307i	−0.334935	−	0.942241i	$-0.608714\pi$
$17$	50722.9	−	50722.9i	0.607307	−	0.607307i	0.942241	+	0.334935i	$0.108714\pi$
$18$		0			0
$19$		−	23813.1i		−	0.182726i	−0.995818	−	0.0913631i	$-0.970878\pi$
$19$		−	23813.1i		−	0.182726i	0.995818	−	0.0913631i	$-0.0291224\pi$
$20$		0			0
$21$	8460.12			0.0435010
$22$		0			0
$23$	−302895.	−	302895.i	−1.08238	−	1.08238i	−0.996287	−	0.0860967i	$-0.972561\pi$
$23$	−302895.	−	302895.i	−1.08238	−	1.08238i	−0.0860967	−	0.996287i	$-0.527439\pi$
$24$		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	$0.253762\pi$
$29$			1.01200e6i			1.43083i	−0.698700	+	0.715415i	$0.746238\pi$
$30$		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	−0.00264096	−	0.999997i	$-0.500841\pi$
$37$	1.86920e6	−	1.86920e6i	0.997356	−	0.997356i	0.999997	+	0.00264096i	$0.000840646\pi$
$38$		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	0.149410	−	0.988775i	$-0.452263\pi$
$43$	−2.86962e6	−	2.86962e6i	−0.839365	−	0.839365i	−0.988775	+	0.149410i	$0.952263\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	888373.	−	888373.i	0.182056	−	0.182056i	−0.610195	−	0.792251i	$-0.708909\pi$
$47$	888373.	−	888373.i	0.182056	−	0.182056i	0.792251	+	0.610195i	$0.208909\pi$
$48$		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	0.481629	−	0.876375i	$-0.340045\pi$
$53$	−3.11474e6	−	3.11474e6i	−0.394747	−	0.394747i	−0.876375	+	0.481629i	$0.840045\pi$
$54$		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	$-0.873765\pi$
$59$		−	9.36105e6i		−	0.772532i	0.922387	−	0.386266i	$-0.126235\pi$
$60$		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	−0.445912	−	0.895077i	$-0.647121\pi$
$67$	9.05117e6	−	9.05117e6i	0.449164	−	0.449164i	0.895077	+	0.445912i	$0.147121\pi$
$68$		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	0.930961	−	0.365120i	$-0.118972\pi$
$73$	1.60689e7	+	1.60689e7i	0.565841	+	0.565841i	−0.365120	+	0.930961i	$0.618972\pi$
$74$		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	$-0.934031\pi$
$79$		−	1.60292e7i		−	0.411533i	0.978601	−	0.205766i	$-0.0659687\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$		0			0
$83$	2.76208e7	+	2.76208e7i	0.582002	+	0.582002i	0.935453	−	0.353451i	$-0.114992\pi$
$83$	2.76208e7	+	2.76208e7i	0.582002	+	0.582002i	−0.353451	+	0.935453i	$0.614992\pi$
$84$		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	$-0.766602\pi$
$89$		−	8.39844e7i		−	1.33856i	0.743009	−	0.669281i	$-0.233398\pi$
$90$		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	−0.0159506	−	0.999873i	$-0.505077\pi$
$97$	8.71059e7	−	8.71059e7i	0.983922	−	0.983922i	0.999873	+	0.0159506i	$0.00507746\pi$
$98$		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	0.415414	−	0.909633i	$-0.363637\pi$
$103$	−5.56248e7	−	5.56248e7i	−0.494219	−	0.494219i	−0.909633	+	0.415414i	$0.863637\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.98597e7	+	6.98597e7i	−0.532957	+	0.532957i	−0.921451	−	0.388494i	$-0.872995\pi$
$107$	−6.98597e7	+	6.98597e7i	−0.532957	+	0.532957i	0.388494	+	0.921451i	$0.372995\pi$
$108$		0			0
$109$			2.26191e8i			1.60240i	0.598400	+	0.801198i	$0.295803\pi$
$109$			2.26191e8i			1.60240i	−0.598400	+	0.801198i	$0.704197\pi$
$110$		0			0
$111$	1.23622e8			0.814337
$112$		0			0
$113$	6.04513e7	+	6.04513e7i	0.370759	+	0.370759i	0.867754	−	0.496994i	$-0.165563\pi$
$113$	6.04513e7	+	6.04513e7i	0.370759	+	0.370759i	−0.496994	+	0.867754i	$0.665563\pi$
$114$		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	−0.241953	−	0.970288i	$-0.577788\pi$
$127$	1.89473e8	−	1.89473e8i	0.728335	−	0.728335i	0.970288	+	0.241953i	$0.0777879\pi$
$128$		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	−0.621430	−	0.783470i	$-0.713448\pi$
$137$	5.70826e7	−	5.70826e7i	0.162040	−	0.162040i	0.783470	+	0.621430i	$0.213448\pi$
$138$		0			0
$139$			1.35342e8i			0.362556i	0.983432	+	0.181278i	$0.0580233\pi$
$139$			1.35342e8i			0.362556i	−0.983432	+	0.181278i	$0.941977\pi$
$140$		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	$-0.954792\pi$
$149$		−	1.39533e8i		−	0.283095i	0.989931	−	0.141548i	$-0.0452079\pi$
$150$		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	−0.395317	−	0.918545i	$-0.629365\pi$
$157$	3.17899e8	−	3.17899e8i	0.523228	−	0.523228i	0.918545	+	0.395317i	$0.129365\pi$
$158$		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	0.976131	+	0.217182i	$0.0696865\pi$
$163$	8.42374e8	+	8.42374e8i	1.19331	+	1.19331i	0.217182	+	0.976131i	$0.430313\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.32928e8	+	3.32928e8i	−0.428040	+	0.428040i	−0.887960	−	0.459920i	$-0.847878\pi$
$167$	−3.32928e8	+	3.32928e8i	−0.428040	+	0.428040i	0.459920	+	0.887960i	$0.347878\pi$
$168$		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	0.991528	+	0.129896i	$0.0414643\pi$
$173$	1.00451e9	+	1.00451e9i	1.12142	+	1.12142i	0.129896	+	0.991528i	$0.458536\pi$
$174$		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	$-0.620618\pi$
$179$		−	1.90759e9i		−	1.85812i	0.369928	−	0.929060i	$-0.379382\pi$
$180$		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	0.780370	−	0.625318i	$-0.215031\pi$
$193$	2.15132e8	+	2.15132e8i	0.155052	+	0.155052i	−0.625318	+	0.780370i	$0.715031\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	1.19932e9	−	1.19932e9i	0.796291	−	0.796291i	−0.186218	−	0.982508i	$-0.559623\pi$
$197$	1.19932e9	−	1.19932e9i	0.796291	−	0.796291i	0.982508	+	0.186218i	$0.0596230\pi$
$198$		0			0
$199$		−	1.74661e9i		−	1.11374i	−0.830601	−	0.556868i	$-0.812003\pi$
$199$		−	1.74661e9i		−	1.11374i	0.830601	−	0.556868i	$-0.187997\pi$
$200$		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	0.799191	−	0.601078i	$-0.205262\pi$
$223$	4.89928e8	+	4.89928e8i	0.198113	+	0.198113i	−0.601078	+	0.799191i	$0.705262\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.56578e9	−	2.56578e9i	0.966310	−	0.966310i	−0.0331407	−	0.999451i	$-0.510551\pi$
$227$	2.56578e9	−	2.56578e9i	0.966310	−	0.966310i	0.999451	+	0.0331407i	$0.0105509\pi$
$228$		0			0
$229$		−	3.15797e9i		−	1.14833i	−0.818740	−	0.574165i	$-0.805327\pi$
$229$		−	3.15797e9i		−	1.14833i	0.818740	−	0.574165i	$-0.194673\pi$
$230$		0			0
$231$	−2.93057e7			−0.0102921
$232$		0			0
$233$	−1.91681e9	−	1.91681e9i	−0.650362	−	0.650362i	0.302719	−	0.953080i	$-0.402106\pi$
$233$	−1.91681e9	−	1.91681e9i	−0.650362	−	0.650362i	−0.953080	+	0.302719i	$0.902106\pi$
$234$		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	$0.213139\pi$
$239$			4.05026e9i			1.24134i	−0.784072	+	0.620670i	$0.786861\pi$
$240$		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	−0.872252	−	0.489057i	$-0.837341\pi$
$257$	−1.67168e9	+	1.67168e9i	−0.383195	+	0.383195i	0.489057	+	0.872252i	$0.337341\pi$
$258$		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	0.812764	−	0.582594i	$-0.197962\pi$
$263$	1.10121e9	+	1.10121e9i	0.230170	+	0.230170i	−0.582594	+	0.812764i	$0.697962\pi$
$264$		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	$-0.831248\pi$
$269$		−	5.29542e9i		−	1.01133i	0.862731	−	0.505663i	$-0.168752\pi$
$270$		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	−0.00310542	+	0.999995i	$0.500988\pi$
$277$	−5.90559e9	+	5.90559e9i	−1.00310	+	1.00310i	−0.999995	+	0.00310542i	$0.999012\pi$
$278$		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	0.992512	−	0.122143i	$-0.0389768\pi$
$283$	5.58276e9	+	5.58276e9i	0.870369	+	0.870369i	−0.122143	+	0.992512i	$0.538977\pi$
$284$		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	0.697512	−	0.716573i	$-0.254290\pi$
$293$	−1.40478e8	−	1.40478e8i	−0.0190606	−	0.0190606i	−0.716573	+	0.697512i	$0.754290\pi$
$294$		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	−0.561870	−	0.827226i	$-0.689918\pi$
$307$	2.35713e9	−	2.35713e9i	0.265356	−	0.265356i	0.827226	+	0.561870i	$0.189918\pi$
$308$		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	0.579775	−	0.814776i	$-0.303140\pi$
$313$	−2.25552e9	−	2.25552e9i	−0.235001	−	0.235001i	−0.814776	+	0.579775i	$0.803140\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.91742e9	+	7.91742e9i	−0.784055	+	0.784055i	−0.980512	−	0.196457i	$-0.937056\pi$
$317$	−7.91742e9	+	7.91742e9i	−0.784055	+	0.784055i	0.196457	+	0.980512i	$0.437056\pi$
$318$		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	−0.589613	−	0.807686i	$-0.700720\pi$
$337$	2.81269e9	−	2.81269e9i	0.218074	−	0.218074i	0.807686	+	0.589613i	$0.200720\pi$
$338$		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	−0.902278	−	0.431154i	$-0.858107\pi$
$347$	−6.83052e9	+	6.83052e9i	−0.471125	+	0.471125i	0.431154	+	0.902278i	$0.358107\pi$
$348$		0			0
$349$			2.13388e10i			1.43836i	0.694823	+	0.719181i	$0.255483\pi$
$349$			2.13388e10i			1.43836i	−0.694823	+	0.719181i	$0.744517\pi$
$350$		0			0
$351$	−1.30358e9			−0.0858834
$352$		0			0
$353$	−1.30810e10	−	1.30810e10i	−0.842443	−	0.842443i	0.146733	−	0.989176i	$-0.453124\pi$
$353$	−1.30810e10	−	1.30810e10i	−0.842443	−	0.842443i	−0.989176	+	0.146733i	$0.953124\pi$
$354$		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	$0.0985907\pi$
$359$			1.01258e10i			0.609607i	−0.952415	+	0.304803i	$0.901409\pi$
$360$		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	0.579347	−	0.815081i	$-0.303308\pi$
$367$	2.52965e10	−	2.52965e10i	1.39443	−	1.39443i	0.815081	−	0.579347i	$-0.196692\pi$
$368$		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	−0.960189	−	0.279352i	$-0.909880\pi$
$373$	−2.39936e10	−	2.39936e10i	−1.23954	−	1.23954i	−0.279352	−	0.960189i	$-0.590120\pi$
$374$		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	$0.344508\pi$
$379$			3.64391e10i			1.76608i	−0.469296	+	0.883041i	$0.655492\pi$
$380$		0			0
$381$	1.25310e10			0.594683
$382$		0			0
$383$	−2.77395e10	−	2.77395e10i	−1.28915	−	1.28915i	−0.935303	−	0.353848i	$-0.884873\pi$
$383$	−2.77395e10	−	2.77395e10i	−1.28915	−	1.28915i	−0.353848	−	0.935303i	$-0.615127\pi$
$384$		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	$-0.856985\pi$
$389$		−	1.98907e10i		−	0.868662i	0.900753	−	0.434331i	$-0.143015\pi$
$390$		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	−0.798628	−	0.601825i	$-0.794441\pi$
$397$	−4.88872e9	+	4.88872e9i	−0.196804	+	0.196804i	0.601825	+	0.798628i	$0.294441\pi$
$398$		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	$0.305675\pi$
$409$			4.58566e10i			1.63874i	−0.573268	+	0.819368i	$0.694325\pi$
$410$		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	$-0.854102\pi$
$419$		−	2.72753e10i		−	0.884939i	0.896783	−	0.442470i	$-0.145898\pi$
$420$		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	0.528562	−	0.848895i	$-0.322731\pi$
$433$	−1.12604e10	−	1.12604e10i	−0.320333	−	0.320333i	−0.848895	+	0.528562i	$0.822731\pi$
$434$		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	$-0.806131\pi$
$439$		−	4.24967e10i		−	1.14419i	0.820188	−	0.572094i	$-0.193869\pi$
$440$		0			0
$441$	−1.25360e10			−0.331441
$442$		0			0
$443$	−4.08519e10	−	4.08519e10i	−1.06071	−	1.06071i	−0.998034	−	0.0626775i	$-0.980036\pi$
$443$	−4.08519e10	−	4.08519e10i	−1.06071	−	1.06071i	−0.0626775	−	0.998034i	$-0.519964\pi$
$444$		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	$0.134658\pi$
$449$			3.33706e10i			0.821068i	−0.911845	+	0.410534i	$0.865342\pi$
$450$		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	−0.674187	−	0.738561i	$-0.735506\pi$
$457$	2.80783e9	−	2.80783e9i	0.0643734	−	0.0643734i	0.738561	+	0.674187i	$0.235506\pi$
$458$		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	0.981992	−	0.188921i	$-0.0604990\pi$
$463$	3.64449e10	+	3.64449e10i	0.793071	+	0.793071i	−0.188921	+	0.981992i	$0.560499\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.73598e10	+	5.73598e10i	−1.20598	+	1.20598i	−0.233663	+	0.972318i	$0.575071\pi$
$467$	−5.73598e10	+	5.73598e10i	−1.20598	+	1.20598i	−0.972318	+	0.233663i	$0.924929\pi$
$468$		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	$-0.867374\pi$
$479$		−	4.26100e10i		−	0.809412i	0.914447	−	0.404706i	$-0.132626\pi$
$480$		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	−0.951209	−	0.308547i	$-0.900157\pi$
$487$	−3.61492e10	+	3.61492e10i	−0.642661	+	0.642661i	0.308547	+	0.951209i	$0.400157\pi$
$488$		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	$-0.863615\pi$
$499$		−	5.15202e10i		−	0.830951i	0.909604	−	0.415476i	$-0.136385\pi$
$500$		0			0
$501$	−2.20186e10			−0.349493
$502$		0			0
$503$	−7.49249e10	−	7.49249e10i	−1.17045	−	1.17045i	−0.982102	−	0.188352i	$-0.939685\pi$
$503$	−7.49249e10	−	7.49249e10i	−1.17045	−	1.17045i	−0.188352	−	0.982102i	$-0.560315\pi$
$504$		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	$-0.886747\pi$
$509$		−	4.67625e10i		−	0.696670i	0.937370	−	0.348335i	$-0.113253\pi$
$510$		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	0.815512	−	0.578741i	$-0.196456\pi$
$523$	1.77148e10	+	1.77148e10i	0.236771	+	0.236771i	−0.578741	+	0.815512i	$0.696456\pi$
$524$		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	−0.782275	−	0.622933i	$-0.785941\pi$
$547$	−1.42652e10	+	1.42652e10i	−0.159342	+	0.159342i	0.622933	+	0.782275i	$0.285941\pi$
$548$		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	−0.827180	−	0.561937i	$-0.810056\pi$
$557$	−2.55308e10	+	2.55308e10i	−0.265242	+	0.265242i	0.561937	+	0.827180i	$0.310056\pi$
$558$		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	0.380140	−	0.924929i	$-0.375876\pi$
$563$	−5.47346e10	−	5.47346e10i	−0.544789	−	0.544789i	−0.924929	+	0.380140i	$0.875876\pi$
$564$		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	$0.123502\pi$
$569$			7.93145e10i			0.756665i	−0.925670	+	0.378332i	$0.876498\pi$
$570$		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	−0.631235	−	0.775591i	$-0.717452\pi$
$577$	1.60007e10	−	1.60007e10i	0.144356	−	0.144356i	0.775591	+	0.631235i	$0.217452\pi$
$578$		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	−0.450220	−	0.892918i	$-0.648654\pi$
$587$	5.25606e10	−	5.25606e10i	0.442698	−	0.442698i	0.892918	+	0.450220i	$0.148654\pi$
$588$		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	−0.997766	−	0.0668042i	$-0.978720\pi$
$593$	−1.31642e11	−	1.31642e11i	−1.06457	−	1.06457i	−0.0668042	−	0.997766i	$-0.521280\pi$
$594$		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	$-0.638523\pi$
$599$		−	2.33478e11i		−	1.81358i	0.421578	−	0.906792i	$-0.361477\pi$
$600$		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	−0.184641	−	0.982806i	$-0.559112\pi$
$607$	1.08355e11	−	1.08355e11i	0.798166	−	0.798166i	0.982806	+	0.184641i	$0.0591121\pi$
$608$		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	0.894760	+	0.446548i	$0.147347\pi$
$613$	1.89396e11	+	1.89396e11i	1.34131	+	1.34131i	0.446548	+	0.894760i	$0.352653\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−4.27533e10	+	4.27533e10i	−0.295004	+	0.295004i	−0.839053	−	0.544049i	$-0.816891\pi$
$617$	−4.27533e10	+	4.27533e10i	−0.295004	+	0.295004i	0.544049	+	0.839053i	$0.316891\pi$
$618$		0			0
$619$		−	1.40452e11i		−	0.956678i	−0.878175	−	0.478339i	$-0.841239\pi$
$619$		−	1.40452e11i		−	0.956678i	0.878175	−	0.478339i	$-0.158761\pi$
$620$		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	0.996781	−	0.0801749i	$-0.0255479\pi$
$643$	1.56685e11	+	1.56685e11i	0.916606	+	0.916606i	−0.0801749	+	0.996781i	$0.525548\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4.42476e10	+	4.42476e10i	−0.252507	+	0.252507i	−0.821998	−	0.569491i	$-0.807140\pi$
$647$	−4.42476e10	+	4.42476e10i	−0.252507	+	0.252507i	0.569491	+	0.821998i	$0.307140\pi$
$648$		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	0.994667	+	0.103136i	$0.0328877\pi$
$653$	1.99608e11	+	1.99608e11i	1.09780	+	1.09780i	0.103136	+	0.994667i	$0.467112\pi$
$654$		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	$-0.754823\pi$
$659$		−	2.62649e11i		−	1.39263i	0.717739	−	0.696313i	$-0.245177\pi$
$660$		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	0.369011	−	0.929425i	$-0.379696\pi$
$673$	−1.14966e11	−	1.14966e11i	−0.560413	−	0.560413i	−0.929425	+	0.369011i	$0.879696\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−2.37680e11	+	2.37680e11i	−1.13146	+	1.13146i	−0.141523	+	0.989935i	$0.545200\pi$
$677$	−2.37680e11	+	2.37680e11i	−1.13146	+	1.13146i	−0.989935	+	0.141523i	$0.954800\pi$
$678$		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	0.308753	−	0.951142i	$-0.400088\pi$
$683$	−1.39792e11	−	1.39792e11i	−0.642389	−	0.642389i	−0.951142	+	0.308753i	$0.900088\pi$
$684$		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	$0.190132\pi$
$709$			2.84237e11i			1.12485i	−0.826848	+	0.562426i	$0.809868\pi$
$710$		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	$-0.931238\pi$
$719$		−	1.14567e11i		−	0.428689i	0.976758	−	0.214345i	$-0.0687615\pi$
$720$		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	−0.267565	−	0.963540i	$-0.586219\pi$
$727$	1.94416e11	−	1.94416e11i	0.695975	−	0.695975i	0.963540	+	0.267565i	$0.0862188\pi$
$728$		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	0.815175	−	0.579214i	$-0.196641\pi$
$733$	6.81171e10	+	6.81171e10i	0.235961	+	0.235961i	−0.579214	+	0.815175i	$0.696641\pi$
$734$		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	$0.235570\pi$
$739$			4.02239e11i			1.34867i	−0.738425	+	0.674336i	$0.764430\pi$
$740$		0			0
$741$	1.41940e10			0.0470795
$742$		0			0
$743$	1.59507e10	+	1.59507e10i	0.0523388	+	0.0523388i	0.732792	−	0.680453i	$-0.238217\pi$
$743$	1.59507e10	+	1.59507e10i	0.0523388	+	0.0523388i	−0.680453	+	0.732792i	$0.738217\pi$
$744$		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	−0.826071	−	0.563565i	$-0.809429\pi$
$757$	−8.62031e10	+	8.62031e10i	−0.262506	+	0.262506i	0.563565	+	0.826071i	$0.309429\pi$
$758$		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	$0.327597\pi$
$769$			5.99311e11i			1.71375i	−0.515526	+	0.856874i	$0.672403\pi$
$770$		0			0
$771$	−1.10559e11			−0.312878
$772$		0			0
$773$	−3.81418e11	−	3.81418e11i	−1.06827	−	1.06827i	−0.997492	−	0.0707824i	$-0.977450\pi$
$773$	−3.81418e11	−	3.81418e11i	−1.06827	−	1.06827i	−0.0707824	−	0.997492i	$-0.522550\pi$
$774$		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	−0.893943	−	0.448181i	$-0.852072\pi$
$787$	−1.71002e11	+	1.71002e11i	−0.445762	+	0.445762i	0.448181	+	0.893943i	$0.352072\pi$
$788$		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	−0.981389	−	0.192028i	$-0.938493\pi$
$797$	−3.18500e11	+	3.18500e11i	−0.789361	+	0.789361i	0.192028	+	0.981389i	$0.438493\pi$
$798$		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	$0.149085\pi$
$809$			3.86733e11i			0.902853i	−0.892308	+	0.451426i	$0.850915\pi$
$810$		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	0.459978	−	0.887930i	$-0.347857\pi$
$823$	−1.96333e11	−	1.96333e11i	−0.427952	−	0.427952i	−0.887930	+	0.459978i	$0.847857\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.28469e11	+	1.28469e11i	−0.274648	+	0.274648i	−0.830968	−	0.556320i	$-0.812213\pi$
$827$	−1.28469e11	+	1.28469e11i	−0.274648	+	0.274648i	0.556320	+	0.830968i	$0.312213\pi$
$828$		0			0
$829$		−	6.44595e11i		−	1.36480i	−0.730980	−	0.682399i	$-0.760937\pi$
$829$		−	6.44595e11i		−	1.36480i	0.730980	−	0.682399i	$-0.239063\pi$
$830$		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	$-0.877461\pi$
$839$		−	3.72154e11i		−	0.751060i	0.926810	−	0.375530i	$-0.122539\pi$
$840$		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	0.965113	−	0.261832i	$-0.0843267\pi$
$853$	3.72328e11	+	3.72328e11i	0.703281	+	0.703281i	−0.261832	+	0.965113i	$0.584327\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−2.41615e11	+	2.41615e11i	−0.447920	+	0.447920i	−0.894662	−	0.446743i	$-0.852584\pi$
$857$	−2.41615e11	+	2.41615e11i	−0.447920	+	0.447920i	0.446743	+	0.894662i	$0.352584\pi$
$858$		0			0
$859$		−	3.66923e11i		−	0.673910i	−0.941521	−	0.336955i	$-0.890603\pi$
$859$		−	3.66923e11i		−	0.673910i	0.941521	−	0.336955i	$-0.109397\pi$
$860$		0			0
$861$	1.05763e10			0.0192451
$862$		0			0
$863$	−3.19216e11	−	3.19216e11i	−0.575495	−	0.575495i	0.358164	−	0.933659i	$-0.383403\pi$
$863$	−3.19216e11	−	3.19216e11i	−0.575495	−	0.575495i	−0.933659	+	0.358164i	$0.883403\pi$
$864$		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	−0.876829	−	0.480802i	$-0.840345\pi$
$877$	−2.34273e11	+	2.34273e11i	−0.396027	+	0.396027i	0.480802	+	0.876829i	$0.340345\pi$
$878$		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	0.259302	−	0.965796i	$-0.416508\pi$
$883$	−4.29488e11	−	4.29488e11i	−0.706494	−	0.706494i	−0.965796	+	0.259302i	$0.916508\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	5.76111e11	−	5.76111e11i	0.930704	−	0.930704i	−0.0670462	−	0.997750i	$-0.521357\pi$
$887$	5.76111e11	−	5.76111e11i	0.930704	−	0.930704i	0.997750	+	0.0670462i	$0.0213575\pi$
$888$		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	−0.948967	−	0.315374i	$-0.897870\pi$
$907$	−4.28785e11	+	4.28785e11i	−0.633593	+	0.633593i	0.315374	+	0.948967i	$0.397870\pi$
$908$		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	$-0.906835\pi$
$919$		−	4.11602e11i		−	0.577052i	0.957472	−	0.288526i	$-0.0931652\pi$
$920$		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	$0.219777\pi$
$929$			9.48753e11i			1.27377i	−0.770960	+	0.636884i	$0.780223\pi$
$930$		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	−0.973842	−	0.227227i	$-0.927034\pi$
$937$	−5.75513e11	+	5.75513e11i	−0.746615	+	0.746615i	0.227227	+	0.973842i	$0.427034\pi$
$938$		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	−0.505964	−	0.862555i	$-0.668863\pi$
$947$	2.86794e11	−	2.86794e11i	0.356591	−	0.356591i	0.862555	+	0.505964i	$0.168863\pi$
$948$		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	−0.994278	−	0.106819i	$-0.965933\pi$
$953$	−9.08233e11	−	9.08233e11i	−1.10110	−	1.10110i	−0.106819	−	0.994278i	$-0.534067\pi$
$954$		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	−0.875714	−	0.482831i	$-0.839609\pi$
$967$	−3.43533e11	+	3.43533e11i	−0.392883	+	0.392883i	0.482831	+	0.875714i	$0.339609\pi$
$968$		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	−0.360140	−	0.932898i	$-0.617271\pi$
$977$	5.21854e11	−	5.21854e11i	0.572758	−	0.572758i	0.932898	+	0.360140i	$0.117271\pi$
$978$		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	0.848028	−	0.529951i	$-0.177790\pi$
$983$	2.96993e11	+	2.96993e11i	0.318077	+	0.318077i	−0.529951	+	0.848028i	$0.677790\pi$
$984$		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	−0.255734	−	0.966747i	$-0.582317\pi$
$997$	7.02520e11	−	7.02520e11i	0.711014	−	0.711014i	0.966747	+	0.255734i	$0.0823170\pi$
$998$		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.193.7		16
5.2	odd	4	inner	300.9.k.e.157.7		16
5.3	odd	4		60.9.k.a.37.4	yes	16
5.4	even	2		60.9.k.a.13.4	✓	16
15.8	even	4		180.9.l.c.37.2		16
15.14	odd	2		180.9.l.c.73.2		16
20.3	even	4		240.9.bg.c.97.8		16
20.19	odd	2		240.9.bg.c.193.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.9.k.a.13.4	✓	16	5.4	even	2
60.9.k.a.37.4	yes	16	5.3	odd	4
180.9.l.c.37.2		16	15.8	even	4
180.9.l.c.73.2		16	15.14	odd	2
240.9.bg.c.97.8		16	20.3	even	4
240.9.bg.c.193.8		16	20.19	odd	2
300.9.k.e.157.7		16	5.2	odd	4	inner
300.9.k.e.193.7		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)

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