LMFDB - Embedded newform 450.3.g.h.343.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,3,Mod(307,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("450.307");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	450.g (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:	$12.2616118962$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			343.1
Root			$-1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	450.343
Dual form			450.3.g.h.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-7.22474 + 7.22474i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-7.22474 + 7.22474i) q^{7} +(-2.00000 - 2.00000i) q^{8} +8.69694 q^{11} +(15.6742 + 15.6742i) q^{13} +14.4495i q^{14} -4.00000 q^{16} +(13.3485 - 13.3485i) q^{17} +4.30306i q^{19} +(8.69694 - 8.69694i) q^{22} +(28.0454 + 28.0454i) q^{23} +31.3485 q^{26} +(14.4495 + 14.4495i) q^{28} -20.6969i q^{29} +39.0908 q^{31} +(-4.00000 + 4.00000i) q^{32} -26.6969i q^{34} +(-12.4949 + 12.4949i) q^{37} +(4.30306 + 4.30306i) q^{38} -62.6969 q^{41} +(11.8763 + 11.8763i) q^{43} -17.3939i q^{44} +56.0908 q^{46} +(-58.0454 + 58.0454i) q^{47} -55.3939i q^{49} +(31.3485 - 31.3485i) q^{52} +(0.606123 + 0.606123i) q^{53} +28.8990 q^{56} +(-20.6969 - 20.6969i) q^{58} -30.0000i q^{59} +69.7878 q^{61} +(39.0908 - 39.0908i) q^{62} +8.00000i q^{64} +(5.02270 - 5.02270i) q^{67} +(-26.6969 - 26.6969i) q^{68} +38.6969 q^{71} +(46.2929 + 46.2929i) q^{73} +24.9898i q^{74} +8.60612 q^{76} +(-62.8332 + 62.8332i) q^{77} +31.3939i q^{79} +(-62.6969 + 62.6969i) q^{82} +(39.4393 + 39.4393i) q^{83} +23.7526 q^{86} +(-17.3939 - 17.3939i) q^{88} -41.3939i q^{89} -226.485 q^{91} +(56.0908 - 56.0908i) q^{92} +116.091i q^{94} +(-54.1237 + 54.1237i) q^{97} +(-55.3939 - 55.3939i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 24 q^{7} - 8 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 24 * q^7 - 8 * q^8	$ 4 q + 4 q^{2} - 24 q^{7} - 8 q^{8} - 24 q^{11} + 48 q^{13} - 16 q^{16} + 24 q^{17} - 24 q^{22} + 24 q^{23} + 96 q^{26} + 48 q^{28} - 20 q^{31} - 16 q^{32} + 48 q^{37} + 76 q^{38} - 192 q^{41} + 72 q^{43} + 48 q^{46} - 144 q^{47} + 96 q^{52} + 120 q^{53} + 96 q^{56} - 24 q^{58} + 44 q^{61} - 20 q^{62} - 24 q^{67} - 48 q^{68} + 96 q^{71} + 48 q^{73} + 152 q^{76} + 72 q^{77} - 192 q^{82} - 48 q^{83} + 144 q^{86} + 48 q^{88} - 612 q^{91} + 48 q^{92} - 192 q^{97} - 104 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 24 * q^7 - 8 * q^8 - 24 * q^11 + 48 * q^13 - 16 * q^16 + 24 * q^17 - 24 * q^22 + 24 * q^23 + 96 * q^26 + 48 * q^28 - 20 * q^31 - 16 * q^32 + 48 * q^37 + 76 * q^38 - 192 * q^41 + 72 * q^43 + 48 * q^46 - 144 * q^47 + 96 * q^52 + 120 * q^53 + 96 * q^56 - 24 * q^58 + 44 * q^61 - 20 * q^62 - 24 * q^67 - 48 * q^68 + 96 * q^71 + 48 * q^73 + 152 * q^76 + 72 * q^77 - 192 * q^82 - 48 * q^83 + 144 * q^86 + 48 * q^88 - 612 * q^91 + 48 * q^92 - 192 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	2.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−7.22474	+	7.22474i	−1.03211	+	1.03211i	−0.0326392	+	0.999467i	$0.510391\pi$
$7$	−7.22474	+	7.22474i	−1.03211	+	1.03211i	−0.999467	+	0.0326392i	$0.989609\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$	8.69694			0.790631			0.395315	−	0.918545i	$-0.370635\pi$
$11$	8.69694			0.790631			0.395315	+	0.918545i	$0.370635\pi$
$12$		0			0
$13$	15.6742	+	15.6742i	1.20571	+	1.20571i	0.972403	+	0.233307i	$0.0749548\pi$
$13$	15.6742	+	15.6742i	1.20571	+	1.20571i	0.233307	+	0.972403i	$0.425045\pi$
$14$			14.4495i			1.03211i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	13.3485	−	13.3485i	0.785204	−	0.785204i	−0.195500	−	0.980704i	$-0.562633\pi$
$17$	13.3485	−	13.3485i	0.785204	−	0.785204i	0.980704	+	0.195500i	$0.0626329\pi$
$18$		0			0
$19$			4.30306i			0.226477i	0.993568	+	0.113238i	$0.0361224\pi$
$19$			4.30306i			0.226477i	−0.993568	+	0.113238i	$0.963878\pi$
$20$		0			0
$21$		0			0
$22$	8.69694	−	8.69694i	0.395315	−	0.395315i
$23$	28.0454	+	28.0454i	1.21937	+	1.21937i	0.967854	+	0.251511i	$0.0809275\pi$
$23$	28.0454	+	28.0454i	1.21937	+	1.21937i	0.251511	+	0.967854i	$0.419072\pi$
$24$		0			0
$25$		0			0
$26$	31.3485			1.20571
$27$		0			0
$28$	14.4495	+	14.4495i	0.516053	+	0.516053i
$29$		−	20.6969i		−	0.713688i	−0.934164	−	0.356844i	$-0.883853\pi$
$29$		−	20.6969i		−	0.713688i	0.934164	−	0.356844i	$-0.116147\pi$
$30$		0			0
$31$	39.0908			1.26099			0.630497	−	0.776192i	$-0.282851\pi$
$31$	39.0908			1.26099			0.630497	+	0.776192i	$0.282851\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	26.6969i		−	0.785204i
$35$		0			0
$36$		0			0
$37$	−12.4949	+	12.4949i	−0.337700	+	0.337700i	−0.855501	−	0.517801i	$-0.826751\pi$
$37$	−12.4949	+	12.4949i	−0.337700	+	0.337700i	0.517801	+	0.855501i	$0.326751\pi$
$38$	4.30306	+	4.30306i	0.113238	+	0.113238i
$39$		0			0
$40$		0			0
$41$	−62.6969			−1.52919			−0.764597	−	0.644509i	$-0.777062\pi$
$41$	−62.6969			−1.52919			−0.764597	+	0.644509i	$0.777062\pi$
$42$		0			0
$43$	11.8763	+	11.8763i	0.276192	+	0.276192i	0.831587	−	0.555395i	$-0.187433\pi$
$43$	11.8763	+	11.8763i	0.276192	+	0.276192i	−0.555395	+	0.831587i	$0.687433\pi$
$44$		−	17.3939i		−	0.395315i
$45$		0			0
$46$	56.0908			1.21937
$47$	−58.0454	+	58.0454i	−1.23501	+	1.23501i	−0.272993	+	0.962016i	$0.588013\pi$
$47$	−58.0454	+	58.0454i	−1.23501	+	1.23501i	−0.962016	+	0.272993i	$0.911987\pi$
$48$		0			0
$49$		−	55.3939i		−	1.13049i
$50$		0			0
$51$		0			0
$52$	31.3485	−	31.3485i	0.602855	−	0.602855i
$53$	0.606123	+	0.606123i	0.0114363	+	0.0114363i	0.712802	−	0.701366i	$-0.247426\pi$
$53$	0.606123	+	0.606123i	0.0114363	+	0.0114363i	−0.701366	+	0.712802i	$0.747426\pi$
$54$		0			0
$55$		0			0
$56$	28.8990			0.516053
$57$		0			0
$58$	−20.6969	−	20.6969i	−0.356844	−	0.356844i
$59$		−	30.0000i		−	0.508475i	−0.967142	−	0.254237i	$-0.918176\pi$
$59$		−	30.0000i		−	0.508475i	0.967142	−	0.254237i	$-0.0818244\pi$
$60$		0			0
$61$	69.7878			1.14406			0.572031	−	0.820232i	$-0.306156\pi$
$61$	69.7878			1.14406			0.572031	+	0.820232i	$0.306156\pi$
$62$	39.0908	−	39.0908i	0.630497	−	0.630497i
$63$		0			0
$64$			8.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	5.02270	−	5.02270i	0.0749657	−	0.0749657i	−0.668630	−	0.743595i	$-0.733119\pi$
$67$	5.02270	−	5.02270i	0.0749657	−	0.0749657i	0.743595	+	0.668630i	$0.233119\pi$
$68$	−26.6969	−	26.6969i	−0.392602	−	0.392602i
$69$		0			0
$70$		0			0
$71$	38.6969			0.545027			0.272514	−	0.962152i	$-0.412145\pi$
$71$	38.6969			0.545027			0.272514	+	0.962152i	$0.412145\pi$
$72$		0			0
$73$	46.2929	+	46.2929i	0.634149	+	0.634149i	0.949106	−	0.314957i	$-0.101990\pi$
$73$	46.2929	+	46.2929i	0.634149	+	0.634149i	−0.314957	+	0.949106i	$0.601990\pi$
$74$			24.9898i			0.337700i
$75$		0			0
$76$	8.60612			0.113238
$77$	−62.8332	+	62.8332i	−0.816015	+	0.816015i
$78$		0			0
$79$			31.3939i			0.397391i	0.980061	+	0.198695i	$0.0636705\pi$
$79$			31.3939i			0.397391i	−0.980061	+	0.198695i	$0.936330\pi$
$80$		0			0
$81$		0			0
$82$	−62.6969	+	62.6969i	−0.764597	+	0.764597i
$83$	39.4393	+	39.4393i	0.475172	+	0.475172i	0.903584	−	0.428412i	$-0.140927\pi$
$83$	39.4393	+	39.4393i	0.475172	+	0.475172i	−0.428412	+	0.903584i	$0.640927\pi$
$84$		0			0
$85$		0			0
$86$	23.7526			0.276192
$87$		0			0
$88$	−17.3939	−	17.3939i	−0.197658	−	0.197658i
$89$		−	41.3939i		−	0.465100i	−0.972584	−	0.232550i	$-0.925293\pi$
$89$		−	41.3939i		−	0.465100i	0.972584	−	0.232550i	$-0.0747069\pi$
$90$		0			0
$91$	−226.485			−2.48884
$92$	56.0908	−	56.0908i	0.609683	−	0.609683i
$93$		0			0
$94$			116.091i			1.23501i
$95$		0			0
$96$		0			0
$97$	−54.1237	+	54.1237i	−0.557977	+	0.557977i	−0.928731	−	0.370754i	$-0.879099\pi$
$97$	−54.1237	+	54.1237i	−0.557977	+	0.557977i	0.370754	+	0.928731i	$0.379099\pi$
$98$	−55.3939	−	55.3939i	−0.565244	−	0.565244i
$99$		0			0
$100$		0			0
$101$	42.8786			0.424540			0.212270	−	0.977211i	$-0.431914\pi$
$101$	42.8786			0.424540			0.212270	+	0.977211i	$0.431914\pi$
$102$		0			0
$103$	−60.9898	−	60.9898i	−0.592134	−	0.592134i	0.346073	−	0.938207i	$-0.387515\pi$
$103$	−60.9898	−	60.9898i	−0.592134	−	0.592134i	−0.938207	+	0.346073i	$0.887515\pi$
$104$		−	62.6969i		−	0.602855i
$105$		0			0
$106$	1.21225			0.0114363
$107$	45.9092	−	45.9092i	0.429058	−	0.429058i	−0.459250	−	0.888307i	$-0.651882\pi$
$107$	45.9092	−	45.9092i	0.429058	−	0.429058i	0.888307	+	0.459250i	$0.151882\pi$
$108$		0			0
$109$		−	145.000i		−	1.33028i	−0.746721	−	0.665138i	$-0.768373\pi$
$109$		−	145.000i		−	1.33028i	0.746721	−	0.665138i	$-0.231627\pi$
$110$		0			0
$111$		0			0
$112$	28.8990	−	28.8990i	0.258027	−	0.258027i
$113$	−130.788	−	130.788i	−1.15741	−	1.15741i	−0.985030	−	0.172384i	$-0.944853\pi$
$113$	−130.788	−	130.788i	−1.15741	−	1.15741i	−0.172384	−	0.985030i	$-0.555147\pi$
$114$		0			0
$115$		0			0
$116$	−41.3939			−0.356844
$117$		0			0
$118$	−30.0000	−	30.0000i	−0.254237	−	0.254237i
$119$			192.879i			1.62083i
$120$		0			0
$121$	−45.3633			−0.374903
$122$	69.7878	−	69.7878i	0.572031	−	0.572031i
$123$		0			0
$124$		−	78.1816i		−	0.630497i
$125$		0			0
$126$		0			0
$127$	21.3031	−	21.3031i	0.167741	−	0.167741i	−0.618245	−	0.785986i	$-0.712156\pi$
$127$	21.3031	−	21.3031i	0.167741	−	0.167741i	0.785986	+	0.618245i	$0.212156\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		0			0
$130$		0			0
$131$	−108.272			−0.826507			−0.413254	−	0.910616i	$-0.635608\pi$
$131$	−108.272			−0.826507			−0.413254	+	0.910616i	$0.635608\pi$
$132$		0			0
$133$	−31.0885	−	31.0885i	−0.233748	−	0.233748i
$134$		−	10.0454i		−	0.0749657i
$135$		0			0
$136$	−53.3939			−0.392602
$137$	−76.6515	+	76.6515i	−0.559500	+	0.559500i	−0.929165	−	0.369665i	$-0.879472\pi$
$137$	−76.6515	+	76.6515i	−0.559500	+	0.559500i	0.369665	+	0.929165i	$0.379472\pi$
$138$		0			0
$139$			152.788i			1.09919i	0.835430	+	0.549596i	$0.185218\pi$
$139$			152.788i			1.09919i	−0.835430	+	0.549596i	$0.814782\pi$
$140$		0			0
$141$		0			0
$142$	38.6969	−	38.6969i	0.272514	−	0.272514i
$143$	136.318	+	136.318i	0.953272	+	0.953272i
$144$		0			0
$145$		0			0
$146$	92.5857			0.634149
$147$		0			0
$148$	24.9898	+	24.9898i	0.168850	+	0.168850i
$149$			112.788i			0.756965i	0.925608	+	0.378482i	$0.123554\pi$
$149$			112.788i			0.756965i	−0.925608	+	0.378482i	$0.876446\pi$
$150$		0			0
$151$	−167.879			−1.11178			−0.555889	−	0.831256i	$-0.687622\pi$
$151$	−167.879			−1.11178			−0.555889	+	0.831256i	$0.687622\pi$
$152$	8.60612	−	8.60612i	0.0566192	−	0.0566192i
$153$		0			0
$154$			125.666i			0.816015i
$155$		0			0
$156$		0			0
$157$	114.866	−	114.866i	0.731631	−	0.731631i	−0.239312	−	0.970943i	$-0.576922\pi$
$157$	114.866	−	114.866i	0.731631	−	0.731631i	0.970943	+	0.239312i	$0.0769218\pi$
$158$	31.3939	+	31.3939i	0.198695	+	0.198695i
$159$		0			0
$160$		0			0
$161$	−405.242			−2.51703
$162$		0			0
$163$	−10.1441	−	10.1441i	−0.0622340	−	0.0622340i	0.675305	−	0.737539i	$-0.264012\pi$
$163$	−10.1441	−	10.1441i	−0.0622340	−	0.0622340i	−0.737539	+	0.675305i	$0.764012\pi$
$164$			125.394i			0.764597i
$165$		0			0
$166$	78.8786			0.475172
$167$	155.666	−	155.666i	0.932134	−	0.932134i	−0.0657054	−	0.997839i	$-0.520930\pi$
$167$	155.666	−	155.666i	0.932134	−	0.932134i	0.997839	+	0.0657054i	$0.0209298\pi$
$168$		0			0
$169$			322.363i			1.90747i
$170$		0			0
$171$		0			0
$172$	23.7526	−	23.7526i	0.138096	−	0.138096i
$173$	−86.8332	−	86.8332i	−0.501926	−	0.501926i	0.410110	−	0.912036i	$-0.365490\pi$
$173$	−86.8332	−	86.8332i	−0.501926	−	0.501926i	−0.912036	+	0.410110i	$0.865490\pi$
$174$		0			0
$175$		0			0
$176$	−34.7878			−0.197658
$177$		0			0
$178$	−41.3939	−	41.3939i	−0.232550	−	0.232550i
$179$		−	241.151i		−	1.34721i	−0.739090	−	0.673606i	$-0.764744\pi$
$179$		−	241.151i		−	1.34721i	0.739090	−	0.673606i	$-0.235256\pi$
$180$		0			0
$181$	41.1816			0.227523			0.113761	−	0.993508i	$-0.463710\pi$
$181$	41.1816			0.227523			0.113761	+	0.993508i	$0.463710\pi$
$182$	−226.485	+	226.485i	−1.24442	+	1.24442i
$183$		0			0
$184$		−	112.182i		−	0.609683i
$185$		0			0
$186$		0			0
$187$	116.091	−	116.091i	0.620806	−	0.620806i
$188$	116.091	+	116.091i	0.617504	+	0.617504i
$189$		0			0
$190$		0			0
$191$	110.091			0.576392			0.288196	−	0.957571i	$-0.406945\pi$
$191$	110.091			0.576392			0.288196	+	0.957571i	$0.406945\pi$
$192$		0			0
$193$	−266.487	−	266.487i	−1.38076	−	1.38076i	−0.843268	−	0.537494i	$-0.819371\pi$
$193$	−266.487	−	266.487i	−1.38076	−	1.38076i	−0.537494	−	0.843268i	$-0.680629\pi$
$194$			108.247i			0.557977i
$195$		0			0
$196$	−110.788			−0.565244
$197$	−39.4393	+	39.4393i	−0.200199	+	0.200199i	−0.800085	−	0.599886i	$-0.795213\pi$
$197$	−39.4393	+	39.4393i	−0.200199	+	0.200199i	0.599886	+	0.800085i	$0.295213\pi$
$198$		0			0
$199$			92.9092i			0.466880i	0.972371	+	0.233440i	$0.0749983\pi$
$199$			92.9092i			0.466880i	−0.972371	+	0.233440i	$0.925002\pi$
$200$		0			0
$201$		0			0
$202$	42.8786	−	42.8786i	0.212270	−	0.212270i
$203$	149.530	+	149.530i	0.736601	+	0.736601i
$204$		0			0
$205$		0			0
$206$	−121.980			−0.592134
$207$		0			0
$208$	−62.6969	−	62.6969i	−0.301428	−	0.301428i
$209$			37.4235i			0.179060i
$210$		0			0
$211$	293.272			1.38992			0.694958	−	0.719050i	$-0.255423\pi$
$211$	293.272			1.38992			0.694958	+	0.719050i	$0.255423\pi$
$212$	1.21225	−	1.21225i	0.00571814	−	0.00571814i
$213$		0			0
$214$		−	91.8184i		−	0.429058i
$215$		0			0
$216$		0			0
$217$	−282.421	+	282.421i	−1.30148	+	1.30148i
$218$	−145.000	−	145.000i	−0.665138	−	0.665138i
$219$		0			0
$220$		0			0
$221$	418.454			1.89346
$222$		0			0
$223$	74.8207	+	74.8207i	0.335519	+	0.335519i	0.854678	−	0.519159i	$-0.173755\pi$
$223$	74.8207	+	74.8207i	0.335519	+	0.335519i	−0.519159	+	0.854678i	$0.673755\pi$
$224$		−	57.7980i		−	0.258027i
$225$		0			0
$226$	−261.576			−1.15741
$227$	−47.1214	+	47.1214i	−0.207583	+	0.207583i	−0.803240	−	0.595656i	$-0.796892\pi$
$227$	−47.1214	+	47.1214i	−0.207583	+	0.207583i	0.595656	+	0.803240i	$0.296892\pi$
$228$		0			0
$229$		−	275.000i		−	1.20087i	−0.799672	−	0.600437i	$-0.794993\pi$
$229$		−	275.000i		−	1.20087i	0.799672	−	0.600437i	$-0.205007\pi$
$230$		0			0
$231$		0			0
$232$	−41.3939	+	41.3939i	−0.178422	+	0.178422i
$233$	−187.757	−	187.757i	−0.805825	−	0.805825i	0.178174	−	0.983999i	$-0.442981\pi$
$233$	−187.757	−	187.757i	−0.805825	−	0.805825i	−0.983999	+	0.178174i	$0.942981\pi$
$234$		0			0
$235$		0			0
$236$	−60.0000			−0.254237
$237$		0			0
$238$	192.879	+	192.879i	0.810414	+	0.810414i
$239$		−	17.6663i		−	0.0739177i	−0.999317	−	0.0369588i	$-0.988233\pi$
$239$		−	17.6663i		−	0.0739177i	0.999317	−	0.0369588i	$-0.0117670\pi$
$240$		0			0
$241$	167.000			0.692946			0.346473	−	0.938060i	$-0.387379\pi$
$241$	167.000			0.692946			0.346473	+	0.938060i	$0.387379\pi$
$242$	−45.3633	+	45.3633i	−0.187451	+	0.187451i
$243$		0			0
$244$		−	139.576i		−	0.572031i
$245$		0			0
$246$		0			0
$247$	−67.4472	+	67.4472i	−0.273066	+	0.273066i
$248$	−78.1816	−	78.1816i	−0.315249	−	0.315249i
$249$		0			0
$250$		0			0
$251$	−26.4245			−0.105277			−0.0526384	−	0.998614i	$-0.516763\pi$
$251$	−26.4245			−0.105277			−0.0526384	+	0.998614i	$0.516763\pi$
$252$		0			0
$253$	243.909	+	243.909i	0.964068	+	0.964068i
$254$		−	42.6061i		−	0.167741i
$255$		0			0
$256$	16.0000			0.0625000
$257$	241.485	−	241.485i	0.939629	−	0.939629i	−0.0586495	−	0.998279i	$-0.518679\pi$
$257$	241.485	−	241.485i	0.939629	−	0.939629i	0.998279	+	0.0586495i	$0.0186794\pi$
$258$		0			0
$259$		−	180.545i		−	0.697085i
$260$		0			0
$261$		0			0
$262$	−108.272	+	108.272i	−0.413254	+	0.413254i
$263$	−142.182	−	142.182i	−0.540615	−	0.540615i	0.383095	−	0.923709i	$-0.374858\pi$
$263$	−142.182	−	142.182i	−0.540615	−	0.540615i	−0.923709	+	0.383095i	$0.874858\pi$
$264$		0			0
$265$		0			0
$266$	−62.1770			−0.233748
$267$		0			0
$268$	−10.0454	−	10.0454i	−0.0374829	−	0.0374829i
$269$		−	521.605i		−	1.93905i	−0.244988	−	0.969526i	$-0.578784\pi$
$269$		−	521.605i		−	1.93905i	0.244988	−	0.969526i	$-0.421216\pi$
$270$		0			0
$271$	39.2122			0.144695			0.0723473	−	0.997379i	$-0.476951\pi$
$271$	39.2122			0.144695			0.0723473	+	0.997379i	$0.476951\pi$
$272$	−53.3939	+	53.3939i	−0.196301	+	0.196301i
$273$		0			0
$274$			153.303i			0.559500i
$275$		0			0
$276$		0			0
$277$	69.5880	−	69.5880i	0.251220	−	0.251220i	−0.570251	−	0.821471i	$-0.693154\pi$
$277$	69.5880	−	69.5880i	0.251220	−	0.251220i	0.821471	+	0.570251i	$0.193154\pi$
$278$	152.788	+	152.788i	0.549596	+	0.549596i
$279$		0			0
$280$		0			0
$281$	519.848			1.84999			0.924996	−	0.379976i	$-0.124068\pi$
$281$	519.848			1.84999			0.924996	+	0.379976i	$0.124068\pi$
$282$		0			0
$283$	153.427	+	153.427i	0.542144	+	0.542144i	0.924157	−	0.382013i	$-0.124769\pi$
$283$	153.427	+	153.427i	0.542144	+	0.542144i	−0.382013	+	0.924157i	$0.624769\pi$
$284$		−	77.3939i		−	0.272514i
$285$		0			0
$286$	272.636			0.953272
$287$	452.969	−	452.969i	1.57829	−	1.57829i
$288$		0			0
$289$		−	67.3633i		−	0.233091i
$290$		0			0
$291$		0			0
$292$	92.5857	−	92.5857i	0.317074	−	0.317074i
$293$	−19.6209	−	19.6209i	−0.0669656	−	0.0669656i	0.672831	−	0.739796i	$-0.265078\pi$
$293$	−19.6209	−	19.6209i	−0.0669656	−	0.0669656i	−0.739796	+	0.672831i	$0.765078\pi$
$294$		0			0
$295$		0			0
$296$	49.9796			0.168850
$297$		0			0
$298$	112.788	+	112.788i	0.378482	+	0.378482i
$299$			879.181i			2.94040i
$300$		0			0
$301$	−171.606			−0.570120
$302$	−167.879	+	167.879i	−0.555889	+	0.555889i
$303$		0			0
$304$		−	17.2122i		−	0.0566192i
$305$		0			0
$306$		0			0
$307$	10.9115	−	10.9115i	0.0355423	−	0.0355423i	−0.689112	−	0.724655i	$-0.741999\pi$
$307$	10.9115	−	10.9115i	0.0355423	−	0.0355423i	0.724655	+	0.689112i	$0.241999\pi$
$308$	125.666	+	125.666i	0.408008	+	0.408008i
$309$		0			0
$310$		0			0
$311$	−64.7878			−0.208321			−0.104160	−	0.994561i	$-0.533216\pi$
$311$	−64.7878			−0.208321			−0.104160	+	0.994561i	$0.533216\pi$
$312$		0			0
$313$	25.4472	+	25.4472i	0.0813009	+	0.0813009i	0.746588	−	0.665287i	$-0.231691\pi$
$313$	25.4472	+	25.4472i	0.0813009	+	0.0813009i	−0.665287	+	0.746588i	$0.731691\pi$
$314$		−	229.732i		−	0.731631i
$315$		0			0
$316$	62.7878			0.198695
$317$	−431.060	+	431.060i	−1.35981	+	1.35981i	−0.485668	+	0.874143i	$0.661424\pi$
$317$	−431.060	+	431.060i	−1.35981	+	1.35981i	−0.874143	+	0.485668i	$0.838576\pi$
$318$		0			0
$319$		−	180.000i		−	0.564263i
$320$		0			0
$321$		0			0
$322$	−405.242	+	405.242i	−1.25852	+	1.25852i
$323$	57.4393	+	57.4393i	0.177831	+	0.177831i
$324$		0			0
$325$		0			0
$326$	−20.2883			−0.0622340
$327$		0			0
$328$	125.394	+	125.394i	0.382298	+	0.382298i
$329$		−	838.727i		−	2.54932i
$330$		0			0
$331$	295.939			0.894075			0.447037	−	0.894515i	$-0.352479\pi$
$331$	295.939			0.894075			0.447037	+	0.894515i	$0.352479\pi$
$332$	78.8786	−	78.8786i	0.237586	−	0.237586i
$333$		0			0
$334$		−	311.333i		−	0.932134i
$335$		0			0
$336$		0			0
$337$	141.538	−	141.538i	0.419994	−	0.419994i	−0.465208	−	0.885202i	$-0.654020\pi$
$337$	141.538	−	141.538i	0.419994	−	0.419994i	0.885202	+	0.465208i	$0.154020\pi$
$338$	322.363	+	322.363i	0.953737	+	0.953737i
$339$		0			0
$340$		0			0
$341$	339.970			0.996981
$342$		0			0
$343$	46.1941	+	46.1941i	0.134677	+	0.134677i
$344$		−	47.5051i		−	0.138096i
$345$		0			0
$346$	−173.666			−0.501926
$347$	−362.227	+	362.227i	−1.04388	+	1.04388i	−0.0448900	+	0.998992i	$0.514294\pi$
$347$	−362.227	+	362.227i	−1.04388	+	1.04388i	−0.998992	+	0.0448900i	$0.985706\pi$
$348$		0			0
$349$		−	403.939i		−	1.15742i	−0.815534	−	0.578709i	$-0.803557\pi$
$349$		−	403.939i		−	1.15742i	0.815534	−	0.578709i	$-0.196443\pi$
$350$		0			0
$351$		0			0
$352$	−34.7878	+	34.7878i	−0.0988288	+	0.0988288i
$353$	18.7423	+	18.7423i	0.0530945	+	0.0530945i	0.733156	−	0.680061i	$-0.238047\pi$
$353$	18.7423	+	18.7423i	0.0530945	+	0.0530945i	−0.680061	+	0.733156i	$0.738047\pi$
$354$		0			0
$355$		0			0
$356$	−82.7878			−0.232550
$357$		0			0
$358$	−241.151	−	241.151i	−0.673606	−	0.673606i
$359$			383.728i			1.06888i	0.845207	+	0.534439i	$0.179477\pi$
$359$			383.728i			1.06888i	−0.845207	+	0.534439i	$0.820523\pi$
$360$		0			0
$361$	342.484			0.948708
$362$	41.1816	−	41.1816i	0.113761	−	0.113761i
$363$		0			0
$364$			452.969i			1.24442i
$365$		0			0
$366$		0			0
$367$	387.341	−	387.341i	1.05542	−	1.05542i	0.0570527	−	0.998371i	$-0.481830\pi$
$367$	387.341	−	387.341i	1.05542	−	1.05542i	0.998371	−	0.0570527i	$-0.0181703\pi$
$368$	−112.182	−	112.182i	−0.304841	−	0.304841i
$369$		0			0
$370$		0			0
$371$	−8.75817			−0.0236069
$372$		0			0
$373$	−419.815	−	419.815i	−1.12551	−	1.12551i	−0.990899	−	0.134611i	$-0.957022\pi$
$373$	−419.815	−	419.815i	−1.12551	−	1.12551i	−0.134611	−	0.990899i	$-0.542978\pi$
$374$		−	232.182i		−	0.620806i
$375$		0			0
$376$	232.182			0.617504
$377$	324.409	−	324.409i	0.860500	−	0.860500i
$378$		0			0
$379$			472.181i			1.24586i	0.782278	+	0.622930i	$0.214058\pi$
$379$			472.181i			1.24586i	−0.782278	+	0.622930i	$0.785942\pi$
$380$		0			0
$381$		0			0
$382$	110.091	−	110.091i	0.288196	−	0.288196i
$383$	67.8184	+	67.8184i	0.177071	+	0.177071i	0.790078	−	0.613006i	$-0.210040\pi$
$383$	67.8184	+	67.8184i	0.177071	+	0.177071i	−0.613006	+	0.790078i	$0.710040\pi$
$384$		0			0
$385$		0			0
$386$	−532.974			−1.38076
$387$		0			0
$388$	108.247	+	108.247i	0.278988	+	0.278988i
$389$			603.242i			1.55075i	0.631501	+	0.775375i	$0.282439\pi$
$389$			603.242i			1.55075i	−0.631501	+	0.775375i	$0.717561\pi$
$390$		0			0
$391$	748.727			1.91490
$392$	−110.788	+	110.788i	−0.282622	+	0.282622i
$393$		0			0
$394$			78.8786i			0.200199i
$395$		0			0
$396$		0			0
$397$	188.648	−	188.648i	0.475184	−	0.475184i	−0.428403	−	0.903588i	$-0.640924\pi$
$397$	188.648	−	188.648i	0.475184	−	0.475184i	0.903588	+	0.428403i	$0.140924\pi$
$398$	92.9092	+	92.9092i	0.233440	+	0.233440i
$399$		0			0
$400$		0			0
$401$	−302.697			−0.754855			−0.377428	−	0.926039i	$-0.623191\pi$
$401$	−302.697			−0.754855			−0.377428	+	0.926039i	$0.623191\pi$
$402$		0			0
$403$	612.719	+	612.719i	1.52039	+	1.52039i
$404$		−	85.7571i		−	0.212270i
$405$		0			0
$406$	299.060			0.736601
$407$	−108.667	+	108.667i	−0.266996	+	0.266996i
$408$		0			0
$409$			20.8184i			0.0509007i	0.999676	+	0.0254503i	$0.00810197\pi$
$409$			20.8184i			0.0509007i	−0.999676	+	0.0254503i	$0.991898\pi$
$410$		0			0
$411$		0			0
$412$	−121.980	+	121.980i	−0.296067	+	0.296067i
$413$	216.742	+	216.742i	0.524800	+	0.524800i
$414$		0			0
$415$		0			0
$416$	−125.394			−0.301428
$417$		0			0
$418$	37.4235	+	37.4235i	0.0895298	+	0.0895298i
$419$			466.515i			1.11340i	0.830713	+	0.556701i	$0.187933\pi$
$419$			466.515i			1.11340i	−0.830713	+	0.556701i	$0.812067\pi$
$420$		0			0
$421$	−636.120			−1.51097			−0.755487	−	0.655163i	$-0.772600\pi$
$421$	−636.120			−1.51097			−0.755487	+	0.655163i	$0.772600\pi$
$422$	293.272	−	293.272i	0.694958	−	0.694958i
$423$		0			0
$424$		−	2.42449i		−	0.00571814i
$425$		0			0
$426$		0			0
$427$	−504.199	+	504.199i	−1.18079	+	1.18079i
$428$	−91.8184	−	91.8184i	−0.214529	−	0.214529i
$429$		0			0
$430$		0			0
$431$	−165.242			−0.383392			−0.191696	−	0.981454i	$-0.561399\pi$
$431$	−165.242			−0.383392			−0.191696	+	0.981454i	$0.561399\pi$
$432$		0			0
$433$	−282.619	−	282.619i	−0.652699	−	0.652699i	0.300943	−	0.953642i	$-0.402699\pi$
$433$	−282.619	−	282.619i	−0.652699	−	0.652699i	−0.953642	+	0.300943i	$0.902699\pi$
$434$			564.842i			1.30148i
$435$		0			0
$436$	−290.000			−0.665138
$437$	−120.681	+	120.681i	−0.276158	+	0.276158i
$438$		0			0
$439$			272.909i			0.621661i	0.950465	+	0.310831i	$0.100607\pi$
$439$			272.909i			0.621661i	−0.950465	+	0.310831i	$0.899393\pi$
$440$		0			0
$441$		0			0
$442$	418.454	−	418.454i	0.946729	−	0.946729i
$443$	176.636	+	176.636i	0.398726	+	0.398726i	0.877784	−	0.479057i	$-0.159021\pi$
$443$	176.636	+	176.636i	0.398726	+	0.398726i	−0.479057	+	0.877784i	$0.659021\pi$
$444$		0			0
$445$		0			0
$446$	149.641			0.335519
$447$		0			0
$448$	−57.7980	−	57.7980i	−0.129013	−	0.129013i
$449$		−	751.151i		−	1.67294i	−0.548011	−	0.836471i	$-0.684615\pi$
$449$		−	751.151i		−	1.67294i	0.548011	−	0.836471i	$-0.315385\pi$
$450$		0			0
$451$	−545.271			−1.20903
$452$	−261.576	+	261.576i	−0.578707	+	0.578707i
$453$		0			0
$454$			94.2429i			0.207583i
$455$		0			0
$456$		0			0
$457$	26.4245	−	26.4245i	0.0578216	−	0.0578216i	−0.677605	−	0.735426i	$-0.736982\pi$
$457$	26.4245	−	26.4245i	0.0578216	−	0.0578216i	0.735426	+	0.677605i	$0.236982\pi$
$458$	−275.000	−	275.000i	−0.600437	−	0.600437i
$459$		0			0
$460$		0			0
$461$	38.6969			0.0839413			0.0419706	−	0.999119i	$-0.486636\pi$
$461$	38.6969			0.0839413			0.0419706	+	0.999119i	$0.486636\pi$
$462$		0			0
$463$	203.505	+	203.505i	0.439536	+	0.439536i	0.891856	−	0.452320i	$-0.149403\pi$
$463$	203.505	+	203.505i	0.439536	+	0.439536i	−0.452320	+	0.891856i	$0.649403\pi$
$464$			82.7878i			0.178422i
$465$		0			0
$466$	−375.514			−0.805825
$467$	557.530	−	557.530i	1.19385	−	1.19385i	0.217879	−	0.975976i	$-0.430086\pi$
$467$	557.530	−	557.530i	1.19385	−	1.19385i	0.975976	−	0.217879i	$-0.0699137\pi$
$468$		0			0
$469$			72.5755i			0.154745i
$470$		0			0
$471$		0			0
$472$	−60.0000	+	60.0000i	−0.127119	+	0.127119i
$473$	103.287	+	103.287i	0.218366	+	0.218366i
$474$		0			0
$475$		0			0
$476$	385.757			0.810414
$477$		0			0
$478$	−17.6663	−	17.6663i	−0.0369588	−	0.0369588i
$479$		−	265.818i		−	0.554944i	−0.960734	−	0.277472i	$-0.910503\pi$
$479$		−	265.818i		−	0.554944i	0.960734	−	0.277472i	$-0.0894966\pi$
$480$		0			0
$481$	−391.696			−0.814337
$482$	167.000	−	167.000i	0.346473	−	0.346473i
$483$		0			0
$484$			90.7265i			0.187451i
$485$		0			0
$486$		0			0
$487$	304.083	−	304.083i	0.624400	−	0.624400i	−0.322253	−	0.946653i	$-0.604440\pi$
$487$	304.083	−	304.083i	0.624400	−	0.624400i	0.946653	+	0.322253i	$0.104440\pi$
$488$	−139.576	−	139.576i	−0.286015	−	0.286015i
$489$		0			0
$490$		0			0
$491$	−169.212			−0.344628			−0.172314	−	0.985042i	$-0.555124\pi$
$491$	−169.212			−0.344628			−0.172314	+	0.985042i	$0.555124\pi$
$492$		0			0
$493$	−276.272	−	276.272i	−0.560390	−	0.560390i
$494$			134.894i			0.273066i
$495$		0			0
$496$	−156.363			−0.315249
$497$	−279.576	+	279.576i	−0.562526	+	0.562526i
$498$		0			0
$499$		−	699.636i		−	1.40208i	−0.713124	−	0.701038i	$-0.752720\pi$
$499$		−	699.636i		−	1.40208i	0.713124	−	0.701038i	$-0.247280\pi$
$500$		0			0
$501$		0			0
$502$	−26.4245	+	26.4245i	−0.0526384	+	0.0526384i
$503$	−279.848	−	279.848i	−0.556358	−	0.556358i	0.371911	−	0.928268i	$-0.378703\pi$
$503$	−279.848	−	279.848i	−0.556358	−	0.556358i	−0.928268	+	0.371911i	$0.878703\pi$
$504$		0			0
$505$		0			0
$506$	487.818			0.964068
$507$		0			0
$508$	−42.6061	−	42.6061i	−0.0838703	−	0.0838703i
$509$			193.696i			0.380542i	0.981732	+	0.190271i	$0.0609367\pi$
$509$			193.696i			0.380542i	−0.981732	+	0.190271i	$0.939063\pi$
$510$		0			0
$511$	−668.908			−1.30902
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	482.969i		−	0.939629i
$515$		0			0
$516$		0			0
$517$	−504.817	+	504.817i	−0.976436	+	0.976436i
$518$	−180.545	−	180.545i	−0.348542	−	0.348542i
$519$		0			0
$520$		0			0
$521$	−167.121			−0.320771			−0.160385	−	0.987054i	$-0.551274\pi$
$521$	−167.121			−0.320771			−0.160385	+	0.987054i	$0.551274\pi$
$522$		0			0
$523$	−675.860	−	675.860i	−1.29228	−	1.29228i	−0.933376	−	0.358900i	$-0.883152\pi$
$523$	−675.860	−	675.860i	−1.29228	−	1.29228i	−0.358900	−	0.933376i	$-0.616848\pi$
$524$			216.545i			0.413254i
$525$		0			0
$526$	−284.363			−0.540615
$527$	521.803	−	521.803i	0.990138	−	0.990138i
$528$		0			0
$529$			1044.09i			1.97370i
$530$		0			0
$531$		0			0
$532$	−62.1770	+	62.1770i	−0.116874	+	0.116874i
$533$	−982.727	−	982.727i	−1.84376	−	1.84376i
$534$		0			0
$535$		0			0
$536$	−20.0908			−0.0374829
$537$		0			0
$538$	−521.605	−	521.605i	−0.969526	−	0.969526i
$539$		−	481.757i		−	0.893798i
$540$		0			0
$541$	−131.120			−0.242367			−0.121183	−	0.992630i	$-0.538669\pi$
$541$	−131.120			−0.242367			−0.121183	+	0.992630i	$0.538669\pi$
$542$	39.2122	−	39.2122i	0.0723473	−	0.0723473i
$543$		0			0
$544$			106.788i			0.196301i
$545$		0			0
$546$		0			0
$547$	−423.959	+	423.959i	−0.775062	+	0.775062i	−0.978987	−	0.203924i	$-0.934630\pi$
$547$	−423.959	+	423.959i	−0.775062	+	0.775062i	0.203924	+	0.978987i	$0.434630\pi$
$548$	153.303	+	153.303i	0.279750	+	0.279750i
$549$		0			0
$550$		0			0
$551$	89.0602			0.161634
$552$		0			0
$553$	−226.813	−	226.813i	−0.410150	−	0.410150i
$554$		−	139.176i		−	0.251220i
$555$		0			0
$556$	305.576			0.549596
$557$	−341.741	+	341.741i	−0.613539	+	0.613539i	−0.943866	−	0.330327i	$-0.892841\pi$
$557$	−341.741	+	341.741i	−0.613539	+	0.613539i	0.330327	+	0.943866i	$0.392841\pi$
$558$		0			0
$559$			372.303i			0.666016i
$560$		0			0
$561$		0			0
$562$	519.848	−	519.848i	0.924996	−	0.924996i
$563$	13.6209	+	13.6209i	0.0241935	+	0.0241935i	0.719100	−	0.694907i	$-0.244554\pi$
$563$	13.6209	+	13.6209i	0.0241935	+	0.0241935i	−0.694907	+	0.719100i	$0.744554\pi$
$564$		0			0
$565$		0			0
$566$	306.854			0.542144
$567$		0			0
$568$	−77.3939	−	77.3939i	−0.136257	−	0.136257i
$569$			22.9990i			0.0404200i	0.999796	+	0.0202100i	$0.00643348\pi$
$569$			22.9990i			0.0404200i	−0.999796	+	0.0202100i	$0.993567\pi$
$570$		0			0
$571$	−660.666			−1.15703			−0.578517	−	0.815670i	$-0.696368\pi$
$571$	−660.666			−1.15703			−0.578517	+	0.815670i	$0.696368\pi$
$572$	272.636	−	272.636i	0.476636	−	0.476636i
$573$		0			0
$574$		−	905.939i		−	1.57829i
$575$		0			0
$576$		0			0
$577$	−421.547	+	421.547i	−0.730584	+	0.730584i	−0.970736	−	0.240151i	$-0.922803\pi$
$577$	−421.547	+	421.547i	−0.730584	+	0.730584i	0.240151	+	0.970736i	$0.422803\pi$
$578$	−67.3633	−	67.3633i	−0.116545	−	0.116545i
$579$		0			0
$580$		0			0
$581$	−569.878			−0.980856
$582$		0			0
$583$	5.27142	+	5.27142i	0.00904188	+	0.00904188i
$584$		−	185.171i		−	0.317074i
$585$		0			0
$586$	−39.2418			−0.0669656
$587$	−441.514	+	441.514i	−0.752154	+	0.752154i	−0.974881	−	0.222727i	$-0.928504\pi$
$587$	−441.514	+	441.514i	−0.752154	+	0.752154i	0.222727	+	0.974881i	$0.428504\pi$
$588$		0			0
$589$			168.210i			0.285586i
$590$		0			0
$591$		0			0
$592$	49.9796	−	49.9796i	0.0844250	−	0.0844250i
$593$	171.303	+	171.303i	0.288875	+	0.288875i	0.836635	−	0.547760i	$-0.184519\pi$
$593$	171.303	+	171.303i	0.288875	+	0.288875i	−0.547760	+	0.836635i	$0.684519\pi$
$594$		0			0
$595$		0			0
$596$	225.576			0.378482
$597$		0			0
$598$	879.181	+	879.181i	1.47020	+	1.47020i
$599$			64.1816i			0.107148i	0.998564	+	0.0535740i	$0.0170613\pi$
$599$			64.1816i			0.107148i	−0.998564	+	0.0535740i	$0.982939\pi$
$600$		0			0
$601$	469.545			0.781273			0.390636	−	0.920545i	$-0.372255\pi$
$601$	469.545			0.781273			0.390636	+	0.920545i	$0.372255\pi$
$602$	−171.606	+	171.606i	−0.285060	+	0.285060i
$603$		0			0
$604$			335.757i			0.555889i
$605$		0			0
$606$		0			0
$607$	121.930	−	121.930i	0.200872	−	0.200872i	−0.599501	−	0.800374i	$-0.704634\pi$
$607$	121.930	−	121.930i	0.200872	−	0.200872i	0.800374	+	0.599501i	$0.204634\pi$
$608$	−17.2122	−	17.2122i	−0.0283096	−	0.0283096i
$609$		0			0
$610$		0			0
$611$	−1819.63			−2.97813
$612$		0			0
$613$	542.252	+	542.252i	0.884587	+	0.884587i	0.993997	−	0.109409i	$-0.0348960\pi$
$613$	542.252	+	542.252i	0.884587	+	0.884587i	−0.109409	+	0.993997i	$0.534896\pi$
$614$		−	21.8230i		−	0.0355423i
$615$		0			0
$616$	251.333			0.408008
$617$	−117.364	+	117.364i	−0.190218	+	0.190218i	−0.795790	−	0.605572i	$-0.792944\pi$
$617$	−117.364	+	117.364i	−0.190218	+	0.190218i	0.605572	+	0.795790i	$0.292944\pi$
$618$		0			0
$619$			295.697i			0.477701i	0.971056	+	0.238851i	$0.0767706\pi$
$619$			295.697i			0.477701i	−0.971056	+	0.238851i	$0.923229\pi$
$620$		0			0
$621$		0			0
$622$	−64.7878	+	64.7878i	−0.104160	+	0.104160i
$623$	299.060	+	299.060i	0.480032	+	0.480032i
$624$		0			0
$625$		0			0
$626$	50.8944			0.0813009
$627$		0			0
$628$	−229.732	−	229.732i	−0.365816	−	0.365816i
$629$			333.576i			0.530327i
$630$		0			0
$631$	897.454			1.42227			0.711136	−	0.703054i	$-0.248181\pi$
$631$	897.454			1.42227			0.711136	+	0.703054i	$0.248181\pi$
$632$	62.7878	−	62.7878i	0.0993477	−	0.0993477i
$633$		0			0
$634$			862.120i			1.35981i
$635$		0			0
$636$		0			0
$637$	868.257	−	868.257i	1.36304	−	1.36304i
$638$	−180.000	−	180.000i	−0.282132	−	0.282132i
$639$		0			0
$640$		0			0
$641$	226.120			0.352762			0.176381	−	0.984322i	$-0.443561\pi$
$641$	226.120			0.352762			0.176381	+	0.984322i	$0.443561\pi$
$642$		0			0
$643$	−472.454	−	472.454i	−0.734765	−	0.734765i	0.236794	−	0.971560i	$-0.423903\pi$
$643$	−472.454	−	472.454i	−0.734765	−	0.734765i	−0.971560	+	0.236794i	$0.923903\pi$
$644$			810.484i			1.25852i
$645$		0			0
$646$	114.879			0.177831
$647$	−583.151	+	583.151i	−0.901315	+	0.901315i	−0.995550	−	0.0942347i	$-0.969960\pi$
$647$	−583.151	+	583.151i	−0.901315	+	0.901315i	0.0942347	+	0.995550i	$0.469960\pi$
$648$		0			0
$649$		−	260.908i		−	0.402016i
$650$		0			0
$651$		0			0
$652$	−20.2883	+	20.2883i	−0.0311170	+	0.0311170i
$653$	36.1975	+	36.1975i	0.0554325	+	0.0554325i	0.734280	−	0.678847i	$-0.237520\pi$
$653$	36.1975	+	36.1975i	0.0554325	+	0.0554325i	−0.678847	+	0.734280i	$0.737520\pi$
$654$		0			0
$655$		0			0
$656$	250.788			0.382298
$657$		0			0
$658$	−838.727	−	838.727i	−1.27466	−	1.27466i
$659$		−	615.787i		−	0.934426i	−0.884145	−	0.467213i	$-0.845258\pi$
$659$		−	615.787i		−	0.934426i	0.884145	−	0.467213i	$-0.154742\pi$
$660$		0			0
$661$	−426.849			−0.645762			−0.322881	−	0.946439i	$-0.604651\pi$
$661$	−426.849			−0.645762			−0.322881	+	0.946439i	$0.604651\pi$
$662$	295.939	−	295.939i	0.447037	−	0.447037i
$663$		0			0
$664$		−	157.757i		−	0.237586i
$665$		0			0
$666$		0			0
$667$	580.454	−	580.454i	0.870246	−	0.870246i
$668$	−311.333	−	311.333i	−0.466067	−	0.466067i
$669$		0			0
$670$		0			0
$671$	606.940			0.904530
$672$		0			0
$673$	350.474	+	350.474i	0.520764	+	0.520764i	0.917802	−	0.397038i	$-0.129962\pi$
$673$	350.474	+	350.474i	0.520764	+	0.520764i	−0.397038	+	0.917802i	$0.629962\pi$
$674$		−	283.076i		−	0.419994i
$675$		0			0
$676$	644.727			0.953737
$677$	−208.985	+	208.985i	−0.308693	+	0.308693i	−0.844402	−	0.535709i	$-0.820044\pi$
$677$	−208.985	+	208.985i	−0.308693	+	0.308693i	0.535709	+	0.844402i	$0.320044\pi$
$678$		0			0
$679$		−	782.060i		−	1.15178i
$680$		0			0
$681$		0			0
$682$	339.970	−	339.970i	0.498490	−	0.498490i
$683$	701.271	+	701.271i	1.02675	+	1.02675i	0.999632	+	0.0271195i	$0.00863347\pi$
$683$	701.271	+	701.271i	1.02675	+	1.02675i	0.0271195	+	0.999632i	$0.491367\pi$
$684$		0			0
$685$		0			0
$686$	92.3883			0.134677
$687$		0			0
$688$	−47.5051	−	47.5051i	−0.0690481	−	0.0690481i
$689$			19.0010i			0.0275777i
$690$		0			0
$691$	−132.910			−0.192345			−0.0961724	−	0.995365i	$-0.530660\pi$
$691$	−132.910			−0.192345			−0.0961724	+	0.995365i	$0.530660\pi$
$692$	−173.666	+	173.666i	−0.250963	+	0.250963i
$693$		0			0
$694$			724.454i			1.04388i
$695$		0			0
$696$		0			0
$697$	−836.908	+	836.908i	−1.20073	+	1.20073i
$698$	−403.939	−	403.939i	−0.578709	−	0.578709i
$699$		0			0
$700$		0			0
$701$	−158.758			−0.226474			−0.113237	−	0.993568i	$-0.536122\pi$
$701$	−158.758			−0.226474			−0.113237	+	0.993568i	$0.536122\pi$
$702$		0			0
$703$	−53.7663	−	53.7663i	−0.0764812	−	0.0764812i
$704$			69.5755i			0.0988288i
$705$		0			0
$706$	37.4847			0.0530945
$707$	−309.787	+	309.787i	−0.438171	+	0.438171i
$708$		0			0
$709$		−	674.514i		−	0.951360i	−0.879618	−	0.475680i	$-0.842202\pi$
$709$		−	674.514i		−	0.951360i	0.879618	−	0.475680i	$-0.157798\pi$
$710$		0			0
$711$		0			0
$712$	−82.7878	+	82.7878i	−0.116275	+	0.116275i
$713$	1096.32	+	1096.32i	1.53761	+	1.53761i
$714$		0			0
$715$		0			0
$716$	−482.302			−0.673606
$717$		0			0
$718$	383.728	+	383.728i	0.534439	+	0.534439i
$719$		−	103.485i		−	0.143929i	−0.997407	−	0.0719643i	$-0.977073\pi$
$719$		−	103.485i		−	0.143929i	0.997407	−	0.0719643i	$-0.0229268\pi$
$720$		0			0
$721$	881.271			1.22229
$722$	342.484	−	342.484i	0.474354	−	0.474354i
$723$		0			0
$724$		−	82.3633i		−	0.113761i
$725$		0			0
$726$		0			0
$727$	−658.392	+	658.392i	−0.905628	+	0.905628i	−0.995916	−	0.0902877i	$-0.971221\pi$
$727$	−658.392	+	658.392i	−0.905628	+	0.905628i	0.0902877	+	0.995916i	$0.471221\pi$
$728$	452.969	+	452.969i	0.622211	+	0.622211i
$729$		0			0
$730$		0			0
$731$	317.060			0.433735
$732$		0			0
$733$	−165.970	−	165.970i	−0.226426	−	0.226426i	0.584772	−	0.811198i	$-0.301184\pi$
$733$	−165.970	−	165.970i	−0.226426	−	0.226426i	−0.811198	+	0.584772i	$0.801184\pi$
$734$		−	774.681i		−	1.05542i
$735$		0			0
$736$	−224.363			−0.304841
$737$	43.6821	−	43.6821i	0.0592702	−	0.0592702i
$738$		0			0
$739$		−	122.545i		−	0.165825i	−0.996557	−	0.0829126i	$-0.973578\pi$
$739$		−	122.545i		−	0.165825i	0.996557	−	0.0829126i	$-0.0264222\pi$
$740$		0			0
$741$		0			0
$742$	−8.75817	+	8.75817i	−0.0118035	+	0.0118035i
$743$	−541.485	−	541.485i	−0.728782	−	0.728782i	0.241595	−	0.970377i	$-0.422329\pi$
$743$	−541.485	−	541.485i	−0.728782	−	0.728782i	−0.970377	+	0.241595i	$0.922329\pi$
$744$		0			0
$745$		0			0
$746$	−839.630			−1.12551
$747$		0			0
$748$	−232.182	−	232.182i	−0.310403	−	0.310403i
$749$			663.364i			0.885667i
$750$		0			0
$751$	−495.212			−0.659404			−0.329702	−	0.944085i	$-0.606948\pi$
$751$	−495.212			−0.659404			−0.329702	+	0.944085i	$0.606948\pi$
$752$	232.182	−	232.182i	0.308752	−	0.308752i
$753$		0			0
$754$		−	648.817i		−	0.860500i
$755$		0			0
$756$		0			0
$757$	565.547	−	565.547i	0.747090	−	0.747090i	−0.226842	−	0.973932i	$-0.572840\pi$
$757$	565.547	−	565.547i	0.747090	−	0.747090i	0.973932	+	0.226842i	$0.0728400\pi$
$758$	472.181	+	472.181i	0.622930	+	0.622930i
$759$		0			0
$760$		0			0
$761$	737.271			0.968819			0.484410	−	0.874841i	$-0.339034\pi$
$761$	737.271			0.968819			0.484410	+	0.874841i	$0.339034\pi$
$762$		0			0
$763$	1047.59	+	1047.59i	1.37299	+	1.37299i
$764$		−	220.182i		−	0.288196i
$765$		0			0
$766$	135.637			0.177071
$767$	470.227	−	470.227i	0.613073	−	0.613073i
$768$		0			0
$769$		−	1014.27i		−	1.31895i	−0.751727	−	0.659474i	$-0.770779\pi$
$769$		−	1014.27i		−	1.31895i	0.751727	−	0.659474i	$-0.229221\pi$
$770$		0			0
$771$		0			0
$772$	−532.974	+	532.974i	−0.690381	+	0.690381i
$773$	−6.39491	−	6.39491i	−0.00827284	−	0.00827284i	0.702958	−	0.711231i	$-0.251862\pi$
$773$	−6.39491	−	6.39491i	−0.00827284	−	0.00827284i	−0.711231	+	0.702958i	$0.751862\pi$
$774$		0			0
$775$		0			0
$776$	216.495			0.278988
$777$		0			0
$778$	603.242	+	603.242i	0.775375	+	0.775375i
$779$		−	269.789i		−	0.346327i
$780$		0			0
$781$	336.545			0.430915
$782$	748.727	−	748.727i	0.957451	−	0.957451i
$783$		0			0
$784$			221.576i			0.282622i
$785$		0			0
$786$		0			0
$787$	565.806	−	565.806i	0.718940	−	0.718940i	−0.249448	−	0.968388i	$-0.580249\pi$
$787$	565.806	−	565.806i	0.718940	−	0.718940i	0.968388	+	0.249448i	$0.0802492\pi$
$788$	78.8786	+	78.8786i	0.100100	+	0.100100i
$789$		0			0
$790$		0			0
$791$	1889.82			2.38915
$792$		0			0
$793$	1093.87	+	1093.87i	1.37941	+	1.37941i
$794$		−	377.296i		−	0.475184i
$795$		0			0
$796$	185.818			0.233440
$797$	352.182	−	352.182i	0.441884	−	0.441884i	−0.450761	−	0.892645i	$-0.648847\pi$
$797$	352.182	−	352.182i	0.441884	−	0.441884i	0.892645	+	0.450761i	$0.148847\pi$
$798$		0			0
$799$			1549.63i			1.93947i
$800$		0			0
$801$		0			0
$802$	−302.697	+	302.697i	−0.377428	+	0.377428i
$803$	402.606	+	402.606i	0.501377	+	0.501377i
$804$		0			0
$805$		0			0
$806$	1225.44			1.52039
$807$		0			0
$808$	−85.7571	−	85.7571i	−0.106135	−	0.106135i
$809$			563.728i			0.696820i	0.937342	+	0.348410i	$0.113278\pi$
$809$			563.728i			0.696820i	−0.937342	+	0.348410i	$0.886722\pi$
$810$		0			0
$811$	−205.091			−0.252886			−0.126443	−	0.991974i	$-0.540356\pi$
$811$	−205.091			−0.252886			−0.126443	+	0.991974i	$0.540356\pi$
$812$	299.060	−	299.060i	0.368301	−	0.368301i
$813$		0			0
$814$			217.335i			0.266996i
$815$		0			0
$816$		0			0
$817$	−51.1043	+	51.1043i	−0.0625512	+	0.0625512i
$818$	20.8184	+	20.8184i	0.0254503	+	0.0254503i
$819$		0			0
$820$		0			0
$821$	−867.576			−1.05673			−0.528365	−	0.849017i	$-0.677195\pi$
$821$	−867.576			−1.05673			−0.528365	+	0.849017i	$0.677195\pi$
$822$		0			0
$823$	−80.8094	−	80.8094i	−0.0981889	−	0.0981889i	0.656306	−	0.754495i	$-0.272118\pi$
$823$	−80.8094	−	80.8094i	−0.0981889	−	0.0981889i	−0.754495	+	0.656306i	$0.772118\pi$
$824$			243.959i			0.296067i
$825$		0			0
$826$	433.485			0.524800
$827$	−935.939	+	935.939i	−1.13173	+	1.13173i	−0.141838	+	0.989890i	$0.545301\pi$
$827$	−935.939	+	935.939i	−1.13173	+	1.13173i	−0.989890	+	0.141838i	$0.954699\pi$
$828$		0			0
$829$		−	1097.39i		−	1.32375i	−0.749613	−	0.661877i	$-0.769760\pi$
$829$		−	1097.39i		−	1.32375i	0.749613	−	0.661877i	$-0.230240\pi$
$830$		0			0
$831$		0			0
$832$	−125.394	+	125.394i	−0.150714	+	0.150714i
$833$	−739.423	−	739.423i	−0.887663	−	0.887663i
$834$		0			0
$835$		0			0
$836$	74.8469			0.0895298
$837$		0			0
$838$	466.515	+	466.515i	0.556701	+	0.556701i
$839$			1047.18i			1.24813i	0.781373	+	0.624065i	$0.214520\pi$
$839$			1047.18i			1.24813i	−0.781373	+	0.624065i	$0.785480\pi$
$840$		0			0
$841$	412.637			0.490650
$842$	−636.120	+	636.120i	−0.755487	+	0.755487i
$843$		0			0
$844$		−	586.545i		−	0.694958i
$845$		0			0
$846$		0			0
$847$	327.738	−	327.738i	0.386940	−	0.386940i
$848$	−2.42449	−	2.42449i	−0.00285907	−	0.00285907i
$849$		0			0
$850$		0			0
$851$	−700.849			−0.823559
$852$		0			0
$853$	902.612	+	902.612i	1.05816	+	1.05816i	0.998201	+	0.0599610i	$0.0190976\pi$
$853$	902.612	+	902.612i	1.05816	+	1.05816i	0.0599610	+	0.998201i	$0.480902\pi$
$854$			1008.40i			1.18079i
$855$		0			0
$856$	−183.637			−0.214529
$857$	928.454	−	928.454i	1.08338	−	1.08338i	0.0871848	−	0.996192i	$-0.472213\pi$
$857$	928.454	−	928.454i	1.08338	−	1.08338i	0.996192	−	0.0871848i	$-0.0277871\pi$
$858$		0			0
$859$		−	581.151i		−	0.676544i	−0.941048	−	0.338272i	$-0.890158\pi$
$859$		−	581.151i		−	0.676544i	0.941048	−	0.338272i	$-0.109842\pi$
$860$		0			0
$861$		0			0
$862$	−165.242	+	165.242i	−0.191696	+	0.191696i
$863$	−317.271	−	317.271i	−0.367638	−	0.367638i	0.498977	−	0.866615i	$-0.333709\pi$
$863$	−317.271	−	317.271i	−0.367638	−	0.367638i	−0.866615	+	0.498977i	$0.833709\pi$
$864$		0			0
$865$		0			0
$866$	−565.237			−0.652699
$867$		0			0
$868$	564.842	+	564.842i	0.650740	+	0.650740i
$869$			273.031i			0.314189i
$870$		0			0
$871$	157.454			0.180774
$872$	−290.000	+	290.000i	−0.332569	+	0.332569i
$873$		0			0
$874$			241.362i			0.276158i
$875$		0			0
$876$		0			0
$877$	−1109.75	+	1109.75i	−1.26540	+	1.26540i	−0.316958	+	0.948439i	$0.602662\pi$
$877$	−1109.75	+	1109.75i	−1.26540	+	1.26540i	−0.948439	+	0.316958i	$0.897338\pi$
$878$	272.909	+	272.909i	0.310831	+	0.310831i
$879$		0			0
$880$		0			0
$881$	−119.455			−0.135590			−0.0677952	−	0.997699i	$-0.521596\pi$
$881$	−119.455			−0.135590			−0.0677952	+	0.997699i	$0.521596\pi$
$882$		0			0
$883$	−252.619	−	252.619i	−0.286091	−	0.286091i	0.549441	−	0.835532i	$-0.314841\pi$
$883$	−252.619	−	252.619i	−0.286091	−	0.286091i	−0.835532	+	0.549441i	$0.814841\pi$
$884$		−	836.908i		−	0.946729i
$885$		0			0
$886$	353.271			0.398726
$887$	516.347	−	516.347i	0.582128	−	0.582128i	−0.353360	−	0.935488i	$-0.614961\pi$
$887$	516.347	−	516.347i	0.582128	−	0.582128i	0.935488	+	0.353360i	$0.114961\pi$
$888$		0			0
$889$			307.818i			0.346252i
$890$		0			0
$891$		0			0
$892$	149.641	−	149.641i	0.167759	−	0.167759i
$893$	−249.773	−	249.773i	−0.279701	−	0.279701i
$894$		0			0
$895$		0			0
$896$	−115.596			−0.129013
$897$		0			0
$898$	−751.151	−	751.151i	−0.836471	−	0.836471i
$899$		−	809.060i		−	0.899956i
$900$		0			0
$901$	16.1816			0.0179596
$902$	−545.271	+	545.271i	−0.604514	+	0.604514i
$903$		0			0
$904$			523.151i			0.578707i
$905$		0			0
$906$		0			0
$907$	−983.160	+	983.160i	−1.08397	+	1.08397i	−0.0878342	+	0.996135i	$0.527995\pi$
$907$	−983.160	+	983.160i	−1.08397	+	1.08397i	−0.996135	+	0.0878342i	$0.972005\pi$
$908$	94.2429	+	94.2429i	0.103792	+	0.103792i
$909$		0			0
$910$		0			0
$911$	1698.00			1.86389			0.931943	−	0.362605i	$-0.118113\pi$
$911$	1698.00			1.86389			0.931943	+	0.362605i	$0.118113\pi$
$912$		0			0
$913$	343.001	+	343.001i	0.375686	+	0.375686i
$914$		−	52.8490i		−	0.0578216i
$915$		0			0
$916$	−550.000			−0.600437
$917$	782.241	−	782.241i	0.853043	−	0.853043i
$918$		0			0
$919$		−	581.272i		−	0.632505i	−0.948675	−	0.316253i	$-0.897575\pi$
$919$		−	581.272i		−	0.632505i	0.948675	−	0.316253i	$-0.102425\pi$
$920$		0			0
$921$		0			0
$922$	38.6969	−	38.6969i	0.0419706	−	0.0419706i
$923$	606.545	+	606.545i	0.657145	+	0.657145i
$924$		0			0
$925$		0			0
$926$	407.010			0.439536
$927$		0			0
$928$	82.7878	+	82.7878i	0.0892109	+	0.0892109i
$929$		−	1328.57i		−	1.43011i	−0.699067	−	0.715056i	$-0.746401\pi$
$929$		−	1328.57i		−	1.43011i	0.699067	−	0.715056i	$-0.253599\pi$
$930$		0			0
$931$	238.363			0.256029
$932$	−375.514	+	375.514i	−0.402912	+	0.402912i
$933$		0			0
$934$		−	1115.06i		−	1.19385i
$935$		0			0
$936$		0			0
$937$	626.487	−	626.487i	0.668609	−	0.668609i	−0.288785	−	0.957394i	$-0.593251\pi$
$937$	626.487	−	626.487i	0.668609	−	0.668609i	0.957394	+	0.288785i	$0.0932512\pi$
$938$	72.5755	+	72.5755i	0.0773726	+	0.0773726i
$939$		0			0
$940$		0			0
$941$	−762.422			−0.810226			−0.405113	−	0.914267i	$-0.632768\pi$
$941$	−762.422			−0.810226			−0.405113	+	0.914267i	$0.632768\pi$
$942$		0			0
$943$	−1758.36	−	1758.36i	−1.86465	−	1.86465i
$944$			120.000i			0.127119i
$945$		0			0
$946$	206.574			0.218366
$947$	−614.983	+	614.983i	−0.649401	+	0.649401i	−0.952848	−	0.303447i	$-0.901862\pi$
$947$	−614.983	+	614.983i	−0.649401	+	0.649401i	0.303447	+	0.952848i	$0.401862\pi$
$948$		0			0
$949$			1451.21i			1.52920i
$950$		0			0
$951$		0			0
$952$	385.757	−	385.757i	0.405207	−	0.405207i
$953$	−328.454	−	328.454i	−0.344653	−	0.344653i	0.513460	−	0.858113i	$-0.328363\pi$
$953$	−328.454	−	328.454i	−0.344653	−	0.344653i	−0.858113	+	0.513460i	$0.828363\pi$
$954$		0			0
$955$		0			0
$956$	−35.3326			−0.0369588
$957$		0			0
$958$	−265.818	−	265.818i	−0.277472	−	0.277472i
$959$		−	1107.58i		−	1.15493i
$960$		0			0
$961$	567.092			0.590106
$962$	−391.696	+	391.696i	−0.407168	+	0.407168i
$963$		0			0
$964$		−	334.000i		−	0.346473i
$965$		0			0
$966$		0			0
$967$	−172.009	+	172.009i	−0.177879	+	0.177879i	−0.790431	−	0.612551i	$-0.790143\pi$
$967$	−172.009	+	172.009i	−0.177879	+	0.177879i	0.612551	+	0.790431i	$0.290143\pi$
$968$	90.7265	+	90.7265i	0.0937257	+	0.0937257i
$969$		0			0
$970$		0			0
$971$	1273.82			1.31186			0.655931	−	0.754821i	$-0.272276\pi$
$971$	1273.82			1.31186			0.655931	+	0.754821i	$0.272276\pi$
$972$		0			0
$973$	−1103.85	−	1103.85i	−1.13448	−	1.13448i
$974$		−	608.166i		−	0.624400i
$975$		0			0
$976$	−279.151			−0.286015
$977$	−1013.86	+	1013.86i	−1.03773	+	1.03773i	−0.0384719	+	0.999260i	$0.512249\pi$
$977$	−1013.86	+	1013.86i	−1.03773	+	1.03773i	−0.999260	+	0.0384719i	$0.987751\pi$
$978$		0			0
$979$		−	360.000i		−	0.367722i
$980$		0			0
$981$		0			0
$982$	−169.212	+	169.212i	−0.172314	+	0.172314i
$983$	−856.332	−	856.332i	−0.871141	−	0.871141i	0.121456	−	0.992597i	$-0.461244\pi$
$983$	−856.332	−	856.332i	−0.871141	−	0.871141i	−0.992597	+	0.121456i	$0.961244\pi$
$984$		0			0
$985$		0			0
$986$	−552.545			−0.560390
$987$		0			0
$988$	134.894	+	134.894i	0.136533	+	0.136533i
$989$			666.150i			0.673559i
$990$		0			0
$991$	688.605			0.694859			0.347429	−	0.937706i	$-0.387055\pi$
$991$	688.605			0.694859			0.347429	+	0.937706i	$0.387055\pi$
$992$	−156.363	+	156.363i	−0.157624	+	0.157624i
$993$		0			0
$994$			559.151i			0.562526i
$995$		0			0
$996$		0			0
$997$	1260.82	−	1260.82i	1.26461	−	1.26461i	0.315778	−	0.948833i	$-0.397734\pi$
$997$	1260.82	−	1260.82i	1.26461	−	1.26461i	0.948833	−	0.315778i	$-0.102266\pi$
$998$	−699.636	−	699.636i	−0.701038	−	0.701038i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.3.g.h.343.1		4
3.2	odd	2		150.3.f.a.43.2	yes	4
5.2	odd	4	inner	450.3.g.h.307.1		4
5.3	odd	4		450.3.g.g.307.2		4
5.4	even	2		450.3.g.g.343.2		4
12.11	even	2		1200.3.bg.p.193.1		4
15.2	even	4		150.3.f.a.7.2	✓	4
15.8	even	4		150.3.f.c.7.1	yes	4
15.14	odd	2		150.3.f.c.43.1	yes	4
60.23	odd	4		1200.3.bg.a.1057.2		4
60.47	odd	4		1200.3.bg.p.1057.1		4
60.59	even	2		1200.3.bg.a.193.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.3.f.a.7.2	✓	4	15.2	even	4
150.3.f.a.43.2	yes	4	3.2	odd	2
150.3.f.c.7.1	yes	4	15.8	even	4
150.3.f.c.43.1	yes	4	15.14	odd	2
450.3.g.g.307.2		4	5.3	odd	4
450.3.g.g.343.2		4	5.4	even	2
450.3.g.h.307.1		4	5.2	odd	4	inner
450.3.g.h.343.1		4	1.1	even	1	trivial
1200.3.bg.a.193.2		4	60.59	even	2
1200.3.bg.a.1057.2		4	60.23	odd	4
1200.3.bg.p.193.1		4	12.11	even	2
1200.3.bg.p.1057.1		4	60.47	odd	4

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	450.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-7.22474 + 7.22474i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-7.22474 + 7.22474i) q^{7} +(-2.00000 - 2.00000i) q^{8} +8.69694 q^{11} +(15.6742 + 15.6742i) q^{13} +14.4495i q^{14} -4.00000 q^{16} +(13.3485 - 13.3485i) q^{17} +4.30306i q^{19} +(8.69694 - 8.69694i) q^{22} +(28.0454 + 28.0454i) q^{23} +31.3485 q^{26} +(14.4495 + 14.4495i) q^{28} -20.6969i q^{29} +39.0908 q^{31} +(-4.00000 + 4.00000i) q^{32} -26.6969i q^{34} +(-12.4949 + 12.4949i) q^{37} +(4.30306 + 4.30306i) q^{38} -62.6969 q^{41} +(11.8763 + 11.8763i) q^{43} -17.3939i q^{44} +56.0908 q^{46} +(-58.0454 + 58.0454i) q^{47} -55.3939i q^{49} +(31.3485 - 31.3485i) q^{52} +(0.606123 + 0.606123i) q^{53} +28.8990 q^{56} +(-20.6969 - 20.6969i) q^{58} -30.0000i q^{59} +69.7878 q^{61} +(39.0908 - 39.0908i) q^{62} +8.00000i q^{64} +(5.02270 - 5.02270i) q^{67} +(-26.6969 - 26.6969i) q^{68} +38.6969 q^{71} +(46.2929 + 46.2929i) q^{73} +24.9898i q^{74} +8.60612 q^{76} +(-62.8332 + 62.8332i) q^{77} +31.3939i q^{79} +(-62.6969 + 62.6969i) q^{82} +(39.4393 + 39.4393i) q^{83} +23.7526 q^{86} +(-17.3939 - 17.3939i) q^{88} -41.3939i q^{89} -226.485 q^{91} +(56.0908 - 56.0908i) q^{92} +116.091i q^{94} +(-54.1237 + 54.1237i) q^{97} +(-55.3939 - 55.3939i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 24 q^{7} - 8 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 24 * q^7 - 8 * q^8	\( 4 q + 4 q^{2} - 24 q^{7} - 8 q^{8} - 24 q^{11} + 48 q^{13} - 16 q^{16} + 24 q^{17} - 24 q^{22} + 24 q^{23} + 96 q^{26} + 48 q^{28} - 20 q^{31} - 16 q^{32} + 48 q^{37} + 76 q^{38} - 192 q^{41} + 72 q^{43} + 48 q^{46} - 144 q^{47} + 96 q^{52} + 120 q^{53} + 96 q^{56} - 24 q^{58} + 44 q^{61} - 20 q^{62} - 24 q^{67} - 48 q^{68} + 96 q^{71} + 48 q^{73} + 152 q^{76} + 72 q^{77} - 192 q^{82} - 48 q^{83} + 144 q^{86} + 48 q^{88} - 612 q^{91} + 48 q^{92} - 192 q^{97} - 104 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 24 * q^7 - 8 * q^8 - 24 * q^11 + 48 * q^13 - 16 * q^16 + 24 * q^17 - 24 * q^22 + 24 * q^23 + 96 * q^26 + 48 * q^28 - 20 * q^31 - 16 * q^32 + 48 * q^37 + 76 * q^38 - 192 * q^41 + 72 * q^43 + 48 * q^46 - 144 * q^47 + 96 * q^52 + 120 * q^53 + 96 * q^56 - 24 * q^58 + 44 * q^61 - 20 * q^62 - 24 * q^67 - 48 * q^68 + 96 * q^71 + 48 * q^73 + 152 * q^76 + 72 * q^77 - 192 * q^82 - 48 * q^83 + 144 * q^86 + 48 * q^88 - 612 * q^91 + 48 * q^92 - 192 * q^97 - 104 * q^98

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