LMFDB - Embedded newform 450.4.f.b.107.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,4,Mod(107,450)]

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([2, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("450.107");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	450.f (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:	$26.5508595026$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.2
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	450.107
Dual form			450.4.f.b.143.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41421 - 1.41421i) q^{2} -4.00000i q^{4} +(4.00000 + 4.00000i) q^{7} +(-5.65685 - 5.65685i) q^{8} +O(q^{10})$	\(q+(1.41421 - 1.41421i) q^{2} -4.00000i q^{4} +(4.00000 + 4.00000i) q^{7} +(-5.65685 - 5.65685i) q^{8} +45.2548i q^{11} +(21.0000 - 21.0000i) q^{13} +11.3137 q^{14} -16.0000 q^{16} +(79.1960 - 79.1960i) q^{17} +28.0000i q^{19} +(64.0000 + 64.0000i) q^{22} +(65.0538 + 65.0538i) q^{23} -59.3970i q^{26} +(16.0000 - 16.0000i) q^{28} +111.723 q^{29} +304.000 q^{31} +(-22.6274 + 22.6274i) q^{32} -224.000i q^{34} +(-231.000 - 231.000i) q^{37} +(39.5980 + 39.5980i) q^{38} -179.605i q^{41} +(-180.000 + 180.000i) q^{43} +181.019 q^{44} +184.000 q^{46} +(127.279 - 127.279i) q^{47} -311.000i q^{49} +(-84.0000 - 84.0000i) q^{52} +(359.210 + 359.210i) q^{53} -45.2548i q^{56} +(158.000 - 158.000i) q^{58} +752.362 q^{59} -180.000 q^{61} +(429.921 - 429.921i) q^{62} +64.0000i q^{64} +(-128.000 - 128.000i) q^{67} +(-316.784 - 316.784i) q^{68} +1023.89i q^{71} +(683.000 - 683.000i) q^{73} -653.367 q^{74} +112.000 q^{76} +(-181.019 + 181.019i) q^{77} -1392.00i q^{79} +(-254.000 - 254.000i) q^{82} +(-186.676 - 186.676i) q^{83} +509.117i q^{86} +(256.000 - 256.000i) q^{88} +448.306 q^{89} +168.000 q^{91} +(260.215 - 260.215i) q^{92} -360.000i q^{94} +(-141.000 - 141.000i) q^{97} +(-439.820 - 439.820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 16 q^{7}+O(q^{10}) $ 4 * q + 16 * q^7	$ 4 q + 16 q^{7} + 84 q^{13} - 64 q^{16} + 256 q^{22} + 64 q^{28} + 1216 q^{31} - 924 q^{37} - 720 q^{43} + 736 q^{46} - 336 q^{52} + 632 q^{58} - 720 q^{61} - 512 q^{67} + 2732 q^{73} + 448 q^{76} - 1016 q^{82} + 1024 q^{88} + 672 q^{91} - 564 q^{97}+O(q^{100}) $ 4 * q + 16 * q^7 + 84 * q^13 - 64 * q^16 + 256 * q^22 + 64 * q^28 + 1216 * q^31 - 924 * q^37 - 720 * q^43 + 736 * q^46 - 336 * q^52 + 632 * q^58 - 720 * q^61 - 512 * q^67 + 2732 * q^73 + 448 * q^76 - 1016 * q^82 + 1024 * q^88 + 672 * q^91 - 564 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.41421	−	1.41421i	0.500000	−	0.500000i
$2$	1.41421	−	1.41421i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	4.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	4.00000	+	4.00000i	0.215980	+	0.215980i	0.806802	−	0.590822i	$-0.201197\pi$
$7$	4.00000	+	4.00000i	0.215980	+	0.215980i	−0.590822	+	0.806802i	$0.701197\pi$
$8$	−5.65685	−	5.65685i	−0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$			45.2548i			1.24044i	0.784428	+	0.620220i	$0.212957\pi$
$11$			45.2548i			1.24044i	−0.784428	+	0.620220i	$0.787043\pi$
$12$		0			0
$13$	21.0000	−	21.0000i	0.448027	−	0.448027i	−0.446671	−	0.894698i	$-0.647391\pi$
$13$	21.0000	−	21.0000i	0.448027	−	0.448027i	0.894698	+	0.446671i	$0.147391\pi$
$14$	11.3137			0.215980
$15$		0			0
$16$	−16.0000			−0.250000
$17$	79.1960	−	79.1960i	1.12987	−	1.12987i	0.139676	−	0.990197i	$-0.455394\pi$
$17$	79.1960	−	79.1960i	1.12987	−	1.12987i	0.990197	−	0.139676i	$-0.0446060\pi$
$18$		0			0
$19$			28.0000i			0.338086i	0.985609	+	0.169043i	$0.0540677\pi$
$19$			28.0000i			0.338086i	−0.985609	+	0.169043i	$0.945932\pi$
$20$		0			0
$21$		0			0
$22$	64.0000	+	64.0000i	0.620220	+	0.620220i
$23$	65.0538	+	65.0538i	0.589768	+	0.589768i	0.937568	−	0.347801i	$-0.113071\pi$
$23$	65.0538	+	65.0538i	0.589768	+	0.589768i	−0.347801	+	0.937568i	$0.613071\pi$
$24$		0			0
$25$		0			0
$26$		−	59.3970i		−	0.448027i
$27$		0			0
$28$	16.0000	−	16.0000i	0.107990	−	0.107990i
$29$	111.723			0.715394			0.357697	−	0.933838i	$-0.383562\pi$
$29$	111.723			0.715394			0.357697	+	0.933838i	$0.383562\pi$
$30$		0			0
$31$	304.000			1.76129			0.880645	−	0.473776i	$-0.157109\pi$
$31$	304.000			1.76129			0.880645	+	0.473776i	$0.157109\pi$
$32$	−22.6274	+	22.6274i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	224.000i		−	1.12987i
$35$		0			0
$36$		0			0
$37$	−231.000	−	231.000i	−1.02638	−	1.02638i	−0.999642	−	0.0267405i	$-0.991487\pi$
$37$	−231.000	−	231.000i	−1.02638	−	1.02638i	−0.0267405	−	0.999642i	$-0.508513\pi$
$38$	39.5980	+	39.5980i	0.169043	+	0.169043i
$39$		0			0
$40$		0			0
$41$		−	179.605i		−	0.684137i	−0.939675	−	0.342068i	$-0.888873\pi$
$41$		−	179.605i		−	0.684137i	0.939675	−	0.342068i	$-0.111127\pi$
$42$		0			0
$43$	−180.000	+	180.000i	−0.638366	+	0.638366i	−0.950152	−	0.311786i	$-0.899073\pi$
$43$	−180.000	+	180.000i	−0.638366	+	0.638366i	0.311786	+	0.950152i	$0.399073\pi$
$44$	181.019			0.620220
$45$		0			0
$46$	184.000			0.589768
$47$	127.279	−	127.279i	0.395012	−	0.395012i	−0.481457	−	0.876470i	$-0.659892\pi$
$47$	127.279	−	127.279i	0.395012	−	0.395012i	0.876470	+	0.481457i	$0.159892\pi$
$48$		0			0
$49$		−	311.000i		−	0.906706i
$50$		0			0
$51$		0			0
$52$	−84.0000	−	84.0000i	−0.224014	−	0.224014i
$53$	359.210	+	359.210i	0.930968	+	0.930968i	0.997767	−	0.0667982i	$-0.0212784\pi$
$53$	359.210	+	359.210i	0.930968	+	0.930968i	−0.0667982	+	0.997767i	$0.521278\pi$
$54$		0			0
$55$		0			0
$56$		−	45.2548i		−	0.107990i
$57$		0			0
$58$	158.000	−	158.000i	0.357697	−	0.357697i
$59$	752.362			1.66015			0.830077	−	0.557648i	$-0.188296\pi$
$59$	752.362			1.66015			0.830077	+	0.557648i	$0.188296\pi$
$60$		0			0
$61$	−180.000			−0.377814			−0.188907	−	0.981995i	$-0.560494\pi$
$61$	−180.000			−0.377814			−0.188907	+	0.981995i	$0.560494\pi$
$62$	429.921	−	429.921i	0.880645	−	0.880645i
$63$		0			0
$64$			64.0000i			0.125000i
$65$		0			0
$66$		0			0
$67$	−128.000	−	128.000i	−0.233398	−	0.233398i	0.580711	−	0.814110i	$-0.302775\pi$
$67$	−128.000	−	128.000i	−0.233398	−	0.233398i	−0.814110	+	0.580711i	$0.802775\pi$
$68$	−316.784	−	316.784i	−0.564937	−	0.564937i
$69$		0			0
$70$		0			0
$71$			1023.89i			1.71146i	0.517425	+	0.855729i	$0.326891\pi$
$71$			1023.89i			1.71146i	−0.517425	+	0.855729i	$0.673109\pi$
$72$		0			0
$73$	683.000	−	683.000i	1.09506	−	1.09506i	0.100076	−	0.994980i	$-0.468091\pi$
$73$	683.000	−	683.000i	1.09506	−	1.09506i	0.994980	−	0.100076i	$-0.0319087\pi$
$74$	−653.367			−1.02638
$75$		0			0
$76$	112.000			0.169043
$77$	−181.019	+	181.019i	−0.267910	+	0.267910i
$78$		0			0
$79$		−	1392.00i		−	1.98243i	−0.132248	−	0.991217i	$-0.542219\pi$
$79$		−	1392.00i		−	1.98243i	0.132248	−	0.991217i	$-0.457781\pi$
$80$		0			0
$81$		0			0
$82$	−254.000	−	254.000i	−0.342068	−	0.342068i
$83$	−186.676	−	186.676i	−0.246872	−	0.246872i	0.572814	−	0.819686i	$-0.305852\pi$
$83$	−186.676	−	186.676i	−0.246872	−	0.246872i	−0.819686	+	0.572814i	$0.805852\pi$
$84$		0			0
$85$		0			0
$86$			509.117i			0.638366i
$87$		0			0
$88$	256.000	−	256.000i	0.310110	−	0.310110i
$89$	448.306			0.533936			0.266968	−	0.963705i	$-0.413978\pi$
$89$	448.306			0.533936			0.266968	+	0.963705i	$0.413978\pi$
$90$		0			0
$91$	168.000			0.193530
$92$	260.215	−	260.215i	0.294884	−	0.294884i
$93$		0			0
$94$		−	360.000i		−	0.395012i
$95$		0			0
$96$		0			0
$97$	−141.000	−	141.000i	−0.147592	−	0.147592i	0.629450	−	0.777041i	$-0.283280\pi$
$97$	−141.000	−	141.000i	−0.147592	−	0.147592i	−0.777041	+	0.629450i	$0.783280\pi$
$98$	−439.820	−	439.820i	−0.453353	−	0.453353i
$99$		0			0
$100$		0			0
$101$			722.663i			0.711957i	0.934494	+	0.355979i	$0.115852\pi$
$101$			722.663i			0.711957i	−0.934494	+	0.355979i	$0.884148\pi$
$102$		0			0
$103$	−856.000	+	856.000i	−0.818876	+	0.818876i	−0.985945	−	0.167070i	$-0.946570\pi$
$103$	−856.000	+	856.000i	−0.818876	+	0.818876i	0.167070	+	0.985945i	$0.446570\pi$
$104$	−237.588			−0.224014
$105$		0			0
$106$	1016.00			0.930968
$107$	−650.538	+	650.538i	−0.587756	+	0.587756i	−0.937023	−	0.349267i	$-0.886431\pi$
$107$	−650.538	+	650.538i	−0.587756	+	0.587756i	0.349267	+	0.937023i	$0.386431\pi$
$108$		0			0
$109$			1412.00i			1.24078i	0.784293	+	0.620390i	$0.213026\pi$
$109$			1412.00i			1.24078i	−0.784293	+	0.620390i	$0.786974\pi$
$110$		0			0
$111$		0			0
$112$	−64.0000	−	64.0000i	−0.0539949	−	0.0539949i
$113$	923.481	+	923.481i	0.768795	+	0.768795i	0.977894	−	0.209099i	$-0.0670532\pi$
$113$	923.481	+	923.481i	0.768795	+	0.768795i	−0.209099	+	0.977894i	$0.567053\pi$
$114$		0			0
$115$		0			0
$116$		−	446.891i		−	0.357697i
$117$		0			0
$118$	1064.00	−	1064.00i	0.830077	−	0.830077i
$119$	633.568			0.488059
$120$		0			0
$121$	−717.000			−0.538693
$122$	−254.558	+	254.558i	−0.188907	+	0.188907i
$123$		0			0
$124$		−	1216.00i		−	0.880645i
$125$		0			0
$126$		0			0
$127$	−1472.00	−	1472.00i	−1.02850	−	1.02850i	−0.999582	−	0.0289132i	$-0.990795\pi$
$127$	−1472.00	−	1472.00i	−1.02850	−	1.02850i	−0.0289132	−	0.999582i	$-0.509205\pi$
$128$	90.5097	+	90.5097i	0.0625000	+	0.0625000i
$129$		0			0
$130$		0			0
$131$		−	1074.80i		−	0.716839i	−0.933561	−	0.358420i	$-0.883316\pi$
$131$		−	1074.80i		−	0.716839i	0.933561	−	0.358420i	$-0.116684\pi$
$132$		0			0
$133$	−112.000	+	112.000i	−0.0730198	+	0.0730198i
$134$	−362.039			−0.233398
$135$		0			0
$136$	−896.000			−0.564937
$137$	−1200.67	+	1200.67i	−0.748759	+	0.748759i	−0.974246	−	0.225487i	$-0.927603\pi$
$137$	−1200.67	+	1200.67i	−0.748759	+	0.748759i	0.225487	+	0.974246i	$0.427603\pi$
$138$		0			0
$139$			884.000i			0.539424i	0.962941	+	0.269712i	$0.0869285\pi$
$139$			884.000i			0.539424i	−0.962941	+	0.269712i	$0.913072\pi$
$140$		0			0
$141$		0			0
$142$	1448.00	+	1448.00i	0.855729	+	0.855729i
$143$	950.352	+	950.352i	0.555751	+	0.555751i
$144$		0			0
$145$		0			0
$146$		−	1931.82i		−	1.09506i
$147$		0			0
$148$	−924.000	+	924.000i	−0.513191	+	0.513191i
$149$	−1124.30			−0.618163			−0.309081	−	0.951036i	$-0.600022\pi$
$149$	−1124.30			−0.618163			−0.309081	+	0.951036i	$0.600022\pi$
$150$		0			0
$151$	952.000			0.513064			0.256532	−	0.966536i	$-0.417420\pi$
$151$	952.000			0.513064			0.256532	+	0.966536i	$0.417420\pi$
$152$	158.392	−	158.392i	0.0845216	−	0.0845216i
$153$		0			0
$154$			512.000i			0.267910i
$155$		0			0
$156$		0			0
$157$	−153.000	−	153.000i	−0.0777753	−	0.0777753i	0.667149	−	0.744924i	$-0.267514\pi$
$157$	−153.000	−	153.000i	−0.0777753	−	0.0777753i	−0.744924	+	0.667149i	$0.767514\pi$
$158$	−1968.59	−	1968.59i	−0.991217	−	0.991217i
$159$		0			0
$160$		0			0
$161$			520.431i			0.254756i
$162$		0			0
$163$	−1388.00	+	1388.00i	−0.666973	+	0.666973i	−0.957014	−	0.290041i	$-0.906331\pi$
$163$	−1388.00	+	1388.00i	−0.666973	+	0.666973i	0.290041	+	0.957014i	$0.406331\pi$
$164$	−718.420			−0.342068
$165$		0			0
$166$	−528.000			−0.246872
$167$	1745.14	−	1745.14i	0.808640	−	0.808640i	−0.175788	−	0.984428i	$-0.556247\pi$
$167$	1745.14	−	1745.14i	0.808640	−	0.808640i	0.984428	+	0.175788i	$0.0562472\pi$
$168$		0			0
$169$			1315.00i			0.598543i
$170$		0			0
$171$		0			0
$172$	720.000	+	720.000i	0.319183	+	0.319183i
$173$	−948.937	−	948.937i	−0.417031	−	0.417031i	0.467148	−	0.884179i	$-0.345281\pi$
$173$	−948.937	−	948.937i	−0.417031	−	0.417031i	−0.884179	+	0.467148i	$0.845281\pi$
$174$		0			0
$175$		0			0
$176$		−	724.077i		−	0.310110i
$177$		0			0
$178$	634.000	−	634.000i	0.266968	−	0.266968i
$179$	181.019			0.0755867			0.0377934	−	0.999286i	$-0.487967\pi$
$179$	181.019			0.0755867			0.0377934	+	0.999286i	$0.487967\pi$
$180$		0			0
$181$	−2692.00			−1.10550			−0.552748	−	0.833348i	$-0.686421\pi$
$181$	−2692.00			−1.10550			−0.552748	+	0.833348i	$0.686421\pi$
$182$	237.588	−	237.588i	0.0967648	−	0.0967648i
$183$		0			0
$184$		−	736.000i		−	0.294884i
$185$		0			0
$186$		0			0
$187$	3584.00	+	3584.00i	1.40154	+	1.40154i
$188$	−509.117	−	509.117i	−0.197506	−	0.197506i
$189$		0			0
$190$		0			0
$191$			871.156i			0.330024i	0.986292	+	0.165012i	$0.0527663\pi$
$191$			871.156i			0.330024i	−0.986292	+	0.165012i	$0.947234\pi$
$192$		0			0
$193$	−1053.00	+	1053.00i	−0.392728	+	0.392728i	−0.875659	−	0.482930i	$-0.839572\pi$
$193$	−1053.00	+	1053.00i	−0.392728	+	0.392728i	0.482930	+	0.875659i	$0.339572\pi$
$194$	−398.808			−0.147592
$195$		0			0
$196$	−1244.00			−0.453353
$197$	−470.933	+	470.933i	−0.170318	+	0.170318i	−0.787119	−	0.616801i	$-0.788428\pi$
$197$	−470.933	+	470.933i	−0.170318	+	0.170318i	0.616801	+	0.787119i	$0.288428\pi$
$198$		0			0
$199$			5400.00i			1.92360i	0.273758	+	0.961799i	$0.411733\pi$
$199$			5400.00i			1.92360i	−0.273758	+	0.961799i	$0.588267\pi$
$200$		0			0
$201$		0			0
$202$	1022.00	+	1022.00i	0.355979	+	0.355979i
$203$	446.891	+	446.891i	0.154511	+	0.154511i
$204$		0			0
$205$		0			0
$206$			2421.13i			0.818876i
$207$		0			0
$208$	−336.000	+	336.000i	−0.112007	+	0.112007i
$209$	−1267.14			−0.419376
$210$		0			0
$211$	−1924.00			−0.627742			−0.313871	−	0.949466i	$-0.601626\pi$
$211$	−1924.00			−0.627742			−0.313871	+	0.949466i	$0.601626\pi$
$212$	1436.84	−	1436.84i	0.465484	−	0.465484i
$213$		0			0
$214$			1840.00i			0.587756i
$215$		0			0
$216$		0			0
$217$	1216.00	+	1216.00i	0.380403	+	0.380403i
$218$	1996.87	+	1996.87i	0.620390	+	0.620390i
$219$		0			0
$220$		0			0
$221$		−	3326.23i		−	1.01243i
$222$		0			0
$223$	588.000	−	588.000i	0.176571	−	0.176571i	−0.613288	−	0.789859i	$-0.710154\pi$
$223$	588.000	−	588.000i	0.176571	−	0.176571i	0.789859	+	0.613288i	$0.210154\pi$
$224$	−181.019			−0.0539949
$225$		0			0
$226$	2612.00			0.768795
$227$	−1029.55	+	1029.55i	−0.301028	+	0.301028i	−0.841416	−	0.540388i	$-0.818278\pi$
$227$	−1029.55	+	1029.55i	−0.301028	+	0.301028i	0.540388	+	0.841416i	$0.318278\pi$
$228$		0			0
$229$			1506.00i			0.434582i	0.976107	+	0.217291i	$0.0697221\pi$
$229$			1506.00i			0.434582i	−0.976107	+	0.217291i	$0.930278\pi$
$230$		0			0
$231$		0			0
$232$	−632.000	−	632.000i	−0.178848	−	0.178848i
$233$	695.793	+	695.793i	0.195635	+	0.195635i	0.798126	−	0.602491i	$-0.205825\pi$
$233$	695.793	+	695.793i	0.195635	+	0.195635i	−0.602491	+	0.798126i	$0.705825\pi$
$234$		0			0
$235$		0			0
$236$		−	3009.45i		−	0.830077i
$237$		0			0
$238$	896.000	−	896.000i	0.244030	−	0.244030i
$239$	−695.793			−0.188314			−0.0941571	−	0.995557i	$-0.530016\pi$
$239$	−695.793			−0.188314			−0.0941571	+	0.995557i	$0.530016\pi$
$240$		0			0
$241$	622.000			0.166251			0.0831256	−	0.996539i	$-0.473510\pi$
$241$	622.000			0.166251			0.0831256	+	0.996539i	$0.473510\pi$
$242$	−1013.99	+	1013.99i	−0.269346	+	0.269346i
$243$		0			0
$244$			720.000i			0.188907i
$245$		0			0
$246$		0			0
$247$	588.000	+	588.000i	0.151472	+	0.151472i
$248$	−1719.68	−	1719.68i	−0.440323	−	0.440323i
$249$		0			0
$250$		0			0
$251$		−	5209.96i		−	1.31016i	−0.755560	−	0.655080i	$-0.772635\pi$
$251$		−	5209.96i		−	1.31016i	0.755560	−	0.655080i	$-0.227365\pi$
$252$		0			0
$253$	−2944.00	+	2944.00i	−0.731572	+	0.731572i
$254$	−4163.44			−1.02850
$255$		0			0
$256$	256.000			0.0625000
$257$	−3816.96	+	3816.96i	−0.926442	+	0.926442i	−0.997474	−	0.0710321i	$-0.977371\pi$
$257$	−3816.96	+	3816.96i	−0.926442	+	0.926442i	0.0710321	+	0.997474i	$0.477371\pi$
$258$		0			0
$259$		−	1848.00i		−	0.443356i
$260$		0			0
$261$		0			0
$262$	−1520.00	−	1520.00i	−0.358420	−	0.358420i
$263$	902.268	+	902.268i	0.211545	+	0.211545i	0.804923	−	0.593379i	$-0.202206\pi$
$263$	902.268	+	902.268i	0.211545	+	0.211545i	−0.593379	+	0.804923i	$0.702206\pi$
$264$		0			0
$265$		0			0
$266$			316.784i			0.0730198i
$267$		0			0
$268$	−512.000	+	512.000i	−0.116699	+	0.116699i
$269$	−1059.25			−0.240087			−0.120043	−	0.992769i	$-0.538303\pi$
$269$	−1059.25			−0.240087			−0.120043	+	0.992769i	$0.538303\pi$
$270$		0			0
$271$	1440.00			0.322781			0.161391	−	0.986891i	$-0.448402\pi$
$271$	1440.00			0.322781			0.161391	+	0.986891i	$0.448402\pi$
$272$	−1267.14	+	1267.14i	−0.282468	+	0.282468i
$273$		0			0
$274$			3396.00i			0.748759i
$275$		0			0
$276$		0			0
$277$	−2547.00	−	2547.00i	−0.552471	−	0.552471i	0.374682	−	0.927153i	$-0.377752\pi$
$277$	−2547.00	−	2547.00i	−0.552471	−	0.552471i	−0.927153	+	0.374682i	$0.877752\pi$
$278$	1250.16	+	1250.16i	0.269712	+	0.269712i
$279$		0			0
$280$		0			0
$281$			6351.23i			1.34834i	0.738577	+	0.674169i	$0.235498\pi$
$281$			6351.23i			1.34834i	−0.738577	+	0.674169i	$0.764502\pi$
$282$		0			0
$283$	−176.000	+	176.000i	−0.0369686	+	0.0369686i	−0.725349	−	0.688381i	$-0.758322\pi$
$283$	−176.000	+	176.000i	−0.0369686	+	0.0369686i	0.688381	+	0.725349i	$0.258322\pi$
$284$	4095.56			0.855729
$285$		0			0
$286$	2688.00			0.555751
$287$	718.420	−	718.420i	0.147760	−	0.147760i
$288$		0			0
$289$		−	7631.00i		−	1.55323i
$290$		0			0
$291$		0			0
$292$	−2732.00	−	2732.00i	−0.547528	−	0.547528i
$293$	−4925.71	−	4925.71i	−0.982126	−	0.982126i	0.0177174	−	0.999843i	$-0.494360\pi$
$293$	−4925.71	−	4925.71i	−0.982126	−	0.982126i	−0.999843	+	0.0177174i	$0.994360\pi$
$294$		0			0
$295$		0			0
$296$			2613.47i			0.513191i
$297$		0			0
$298$	−1590.00	+	1590.00i	−0.309081	+	0.309081i
$299$	2732.26			0.528464
$300$		0			0
$301$	−1440.00			−0.275748
$302$	1346.33	−	1346.33i	0.256532	−	0.256532i
$303$		0			0
$304$		−	448.000i		−	0.0845216i
$305$		0			0
$306$		0			0
$307$	5220.00	+	5220.00i	0.970427	+	0.970427i	0.999575	−	0.0291480i	$-0.00927940\pi$
$307$	5220.00	+	5220.00i	0.970427	+	0.970427i	−0.0291480	+	0.999575i	$0.509279\pi$
$308$	724.077	+	724.077i	0.133955	+	0.133955i
$309$		0			0
$310$		0			0
$311$		−	6171.63i		−	1.12528i	−0.826703	−	0.562638i	$-0.809786\pi$
$311$		−	6171.63i		−	1.12528i	0.826703	−	0.562638i	$-0.190214\pi$
$312$		0			0
$313$	7257.00	−	7257.00i	1.31051	−	1.31051i	0.389473	−	0.921038i	$-0.372657\pi$
$313$	7257.00	−	7257.00i	1.31051	−	1.31051i	0.921038	−	0.389473i	$-0.127343\pi$
$314$	−432.749			−0.0777753
$315$		0			0
$316$	−5568.00			−0.991217
$317$	398.808	−	398.808i	0.0706603	−	0.0706603i	−0.670893	−	0.741554i	$-0.734089\pi$
$317$	398.808	−	398.808i	0.0706603	−	0.0706603i	0.741554	+	0.670893i	$0.234089\pi$
$318$		0			0
$319$			5056.00i			0.887403i
$320$		0			0
$321$		0			0
$322$	736.000	+	736.000i	0.127378	+	0.127378i
$323$	2217.49	+	2217.49i	0.381995	+	0.381995i
$324$		0			0
$325$		0			0
$326$			3925.86i			0.666973i
$327$		0			0
$328$	−1016.00	+	1016.00i	−0.171034	+	0.171034i
$329$	1018.23			0.170629
$330$		0			0
$331$	−4244.00			−0.704747			−0.352374	−	0.935859i	$-0.614625\pi$
$331$	−4244.00			−0.704747			−0.352374	+	0.935859i	$0.614625\pi$
$332$	−746.705	+	746.705i	−0.123436	+	0.123436i
$333$		0			0
$334$		−	4936.00i		−	0.808640i
$335$		0			0
$336$		0			0
$337$	−6207.00	−	6207.00i	−1.00331	−	1.00331i	−0.999994	−	0.00331956i	$-0.998943\pi$
$337$	−6207.00	−	6207.00i	−1.00331	−	1.00331i	−0.00331956	−	0.999994i	$-0.501057\pi$
$338$	1859.69	+	1859.69i	0.299272	+	0.299272i
$339$		0			0
$340$		0			0
$341$			13757.5i			2.18478i
$342$		0			0
$343$	2616.00	−	2616.00i	0.411810	−	0.411810i
$344$	2036.47			0.319183
$345$		0			0
$346$	−2684.00			−0.417031
$347$	5747.36	−	5747.36i	0.889149	−	0.889149i	−0.105292	−	0.994441i	$-0.533578\pi$
$347$	5747.36	−	5747.36i	0.889149	−	0.889149i	0.994441	+	0.105292i	$0.0335779\pi$
$348$		0			0
$349$		−	8996.00i		−	1.37978i	−0.723912	−	0.689892i	$-0.757658\pi$
$349$		−	8996.00i		−	1.37978i	0.723912	−	0.689892i	$-0.242342\pi$
$350$		0			0
$351$		0			0
$352$	−1024.00	−	1024.00i	−0.155055	−	0.155055i
$353$	−7450.08	−	7450.08i	−1.12331	−	1.12331i	−0.991241	−	0.132067i	$-0.957839\pi$
$353$	−7450.08	−	7450.08i	−1.12331	−	1.12331i	−0.132067	−	0.991241i	$-0.542161\pi$
$354$		0			0
$355$		0			0
$356$		−	1793.22i		−	0.266968i
$357$		0			0
$358$	256.000	−	256.000i	0.0377934	−	0.0377934i
$359$	−10221.9			−1.50277			−0.751383	−	0.659866i	$-0.770613\pi$
$359$	−10221.9			−1.50277			−0.751383	+	0.659866i	$0.770613\pi$
$360$		0			0
$361$	6075.00			0.885698
$362$	−3807.06	+	3807.06i	−0.552748	+	0.552748i
$363$		0			0
$364$		−	672.000i		−	0.0967648i
$365$		0			0
$366$		0			0
$367$	−5624.00	−	5624.00i	−0.799919	−	0.799919i	0.183163	−	0.983083i	$-0.441366\pi$
$367$	−5624.00	−	5624.00i	−0.799919	−	0.799919i	−0.983083	+	0.183163i	$0.941366\pi$
$368$	−1040.86	−	1040.86i	−0.147442	−	0.147442i
$369$		0			0
$370$		0			0
$371$			2873.68i			0.402141i
$372$		0			0
$373$	875.000	−	875.000i	0.121463	−	0.121463i	−0.643762	−	0.765226i	$-0.722627\pi$
$373$	875.000	−	875.000i	0.121463	−	0.121463i	0.765226	+	0.643762i	$0.222627\pi$
$374$	10137.1			1.40154
$375$		0			0
$376$	−1440.00			−0.197506
$377$	2346.18	−	2346.18i	0.320516	−	0.320516i
$378$		0			0
$379$		−	9740.00i		−	1.32008i	−0.751231	−	0.660040i	$-0.770539\pi$
$379$		−	9740.00i		−	1.32008i	0.751231	−	0.660040i	$-0.229461\pi$
$380$		0			0
$381$		0			0
$382$	1232.00	+	1232.00i	0.165012	+	0.165012i
$383$	−2027.98	−	2027.98i	−0.270561	−	0.270561i	0.558765	−	0.829326i	$-0.311275\pi$
$383$	−2027.98	−	2027.98i	−0.270561	−	0.270561i	−0.829326	+	0.558765i	$0.811275\pi$
$384$		0			0
$385$		0			0
$386$			2978.33i			0.392728i
$387$		0			0
$388$	−564.000	+	564.000i	−0.0737958	+	0.0737958i
$389$	2651.65			0.345614			0.172807	−	0.984956i	$-0.444716\pi$
$389$	2651.65			0.345614			0.172807	+	0.984956i	$0.444716\pi$
$390$		0			0
$391$	10304.0			1.33273
$392$	−1759.28	+	1759.28i	−0.226676	+	0.226676i
$393$		0			0
$394$			1332.00i			0.170318i
$395$		0			0
$396$		0			0
$397$	−2581.00	−	2581.00i	−0.326289	−	0.326289i	0.524885	−	0.851173i	$-0.324108\pi$
$397$	−2581.00	−	2581.00i	−0.326289	−	0.326289i	−0.851173	+	0.524885i	$0.824108\pi$
$398$	7636.75	+	7636.75i	0.961799	+	0.961799i
$399$		0			0
$400$		0			0
$401$		−	6885.81i		−	0.857508i	−0.903421	−	0.428754i	$-0.858953\pi$
$401$		−	6885.81i		−	0.857508i	0.903421	−	0.428754i	$-0.141047\pi$
$402$		0			0
$403$	6384.00	−	6384.00i	0.789106	−	0.789106i
$404$	2890.65			0.355979
$405$		0			0
$406$	1264.00			0.154511
$407$	10453.9	−	10453.9i	1.27317	−	1.27317i
$408$		0			0
$409$		−	2424.00i		−	0.293054i	−0.989207	−	0.146527i	$-0.953190\pi$
$409$		−	2424.00i		−	0.293054i	0.989207	−	0.146527i	$-0.0468095\pi$
$410$		0			0
$411$		0			0
$412$	3424.00	+	3424.00i	0.409438	+	0.409438i
$413$	3009.45	+	3009.45i	0.358560	+	0.358560i
$414$		0			0
$415$		0			0
$416$			950.352i			0.112007i
$417$		0			0
$418$	−1792.00	+	1792.00i	−0.209688	+	0.209688i
$419$	13898.9			1.62054			0.810269	−	0.586058i	$-0.199321\pi$
$419$	13898.9			1.62054			0.810269	+	0.586058i	$0.199321\pi$
$420$		0			0
$421$	9470.00			1.09629			0.548147	−	0.836382i	$-0.315334\pi$
$421$	9470.00			1.09629			0.548147	+	0.836382i	$0.315334\pi$
$422$	−2720.95	+	2720.95i	−0.313871	+	0.313871i
$423$		0			0
$424$		−	4064.00i		−	0.465484i
$425$		0			0
$426$		0			0
$427$	−720.000	−	720.000i	−0.0816001	−	0.0816001i
$428$	2602.15	+	2602.15i	0.293878	+	0.293878i
$429$		0			0
$430$		0			0
$431$		−	1566.95i		−	0.175121i	−0.996159	−	0.0875606i	$-0.972093\pi$
$431$		−	1566.95i		−	0.175121i	0.996159	−	0.0875606i	$-0.0279072\pi$
$432$		0			0
$433$	−6611.00	+	6611.00i	−0.733728	+	0.733728i	−0.971356	−	0.237628i	$-0.923630\pi$
$433$	−6611.00	+	6611.00i	−0.733728	+	0.733728i	0.237628	+	0.971356i	$0.423630\pi$
$434$	3439.37			0.380403
$435$		0			0
$436$	5648.00			0.620390
$437$	−1821.51	+	1821.51i	−0.199392	+	0.199392i
$438$		0			0
$439$			5672.00i			0.616651i	0.951281	+	0.308326i	$0.0997686\pi$
$439$			5672.00i			0.616651i	−0.951281	+	0.308326i	$0.900231\pi$
$440$		0			0
$441$		0			0
$442$	−4704.00	−	4704.00i	−0.506214	−	0.506214i
$443$	11336.3	+	11336.3i	1.21581	+	1.21581i	0.969084	+	0.246730i	$0.0793559\pi$
$443$	11336.3	+	11336.3i	1.21581	+	1.21581i	0.246730	+	0.969084i	$0.420644\pi$
$444$		0			0
$445$		0			0
$446$		−	1663.12i		−	0.176571i
$447$		0			0
$448$	−256.000	+	256.000i	−0.0269975	+	0.0269975i
$449$	−9519.07			−1.00052			−0.500259	−	0.865876i	$-0.666762\pi$
$449$	−9519.07			−1.00052			−0.500259	+	0.865876i	$0.666762\pi$
$450$		0			0
$451$	8128.00			0.848631
$452$	3693.93	−	3693.93i	0.384397	−	0.384397i
$453$		0			0
$454$			2912.00i			0.301028i
$455$		0			0
$456$		0			0
$457$	1815.00	+	1815.00i	0.185781	+	0.185781i	0.793870	−	0.608088i	$-0.208063\pi$
$457$	1815.00	+	1815.00i	0.185781	+	0.185781i	−0.608088	+	0.793870i	$0.708063\pi$
$458$	2129.81	+	2129.81i	0.217291	+	0.217291i
$459$		0			0
$460$		0			0
$461$		−	3539.78i		−	0.357622i	−0.983883	−	0.178811i	$-0.942775\pi$
$461$		−	3539.78i		−	0.357622i	0.983883	−	0.178811i	$-0.0572251\pi$
$462$		0			0
$463$	3112.00	−	3112.00i	0.312369	−	0.312369i	−0.533458	−	0.845827i	$-0.679108\pi$
$463$	3112.00	−	3112.00i	0.312369	−	0.312369i	0.845827	+	0.533458i	$0.179108\pi$
$464$	−1787.57			−0.178848
$465$		0			0
$466$	1968.00			0.195635
$467$	−4536.80	+	4536.80i	−0.449546	+	0.449546i	−0.895203	−	0.445658i	$-0.852970\pi$
$467$	−4536.80	+	4536.80i	−0.449546	+	0.449546i	0.445658	+	0.895203i	$0.352970\pi$
$468$		0			0
$469$		−	1024.00i		−	0.100819i
$470$		0			0
$471$		0			0
$472$	−4256.00	−	4256.00i	−0.415039	−	0.415039i
$473$	−8145.87	−	8145.87i	−0.791855	−	0.791855i
$474$		0			0
$475$		0			0
$476$		−	2534.27i		−	0.244030i
$477$		0			0
$478$	−984.000	+	984.000i	−0.0941571	+	0.0941571i
$479$	−3626.04			−0.345883			−0.172942	−	0.984932i	$-0.555327\pi$
$479$	−3626.04			−0.345883			−0.172942	+	0.984932i	$0.555327\pi$
$480$		0			0
$481$	−9702.00			−0.919695
$482$	879.641	−	879.641i	0.0831256	−	0.0831256i
$483$		0			0
$484$			2868.00i			0.269346i
$485$		0			0
$486$		0			0
$487$	9504.00	+	9504.00i	0.884327	+	0.884327i	0.993971	−	0.109644i	$-0.0349710\pi$
$487$	9504.00	+	9504.00i	0.884327	+	0.884327i	−0.109644	+	0.993971i	$0.534971\pi$
$488$	1018.23	+	1018.23i	0.0944534	+	0.0944534i
$489$		0			0
$490$		0			0
$491$		−	16252.1i		−	1.49379i	−0.664944	−	0.746893i	$-0.731545\pi$
$491$		−	16252.1i		−	1.49379i	0.664944	−	0.746893i	$-0.268455\pi$
$492$		0			0
$493$	8848.00	−	8848.00i	0.808304	−	0.808304i
$494$	1663.12			0.151472
$495$		0			0
$496$	−4864.00			−0.440323
$497$	−4095.56	+	4095.56i	−0.369640	+	0.369640i
$498$		0			0
$499$		−	12652.0i		−	1.13503i	−0.823362	−	0.567516i	$-0.807904\pi$
$499$		−	12652.0i		−	1.13503i	0.823362	−	0.567516i	$-0.192096\pi$
$500$		0			0
$501$		0			0
$502$	−7368.00	−	7368.00i	−0.655080	−	0.655080i
$503$	500.632	+	500.632i	0.0443779	+	0.0443779i	0.728947	−	0.684570i	$-0.240010\pi$
$503$	500.632	+	500.632i	0.0443779	+	0.0443779i	−0.684570	+	0.728947i	$0.740010\pi$
$504$		0			0
$505$		0			0
$506$			8326.89i			0.731572i
$507$		0			0
$508$	−5888.00	+	5888.00i	−0.514248	+	0.514248i
$509$	8113.34			0.706518			0.353259	−	0.935526i	$-0.385073\pi$
$509$	8113.34			0.706518			0.353259	+	0.935526i	$0.385073\pi$
$510$		0			0
$511$	5464.00			0.473020
$512$	362.039	−	362.039i	0.0312500	−	0.0312500i
$513$		0			0
$514$			10796.0i			0.926442i
$515$		0			0
$516$		0			0
$517$	5760.00	+	5760.00i	0.489989	+	0.489989i
$518$	−2613.47	−	2613.47i	−0.221678	−	0.221678i
$519$		0			0
$520$		0			0
$521$			13012.2i			1.09419i	0.837070	+	0.547096i	$0.184267\pi$
$521$			13012.2i			1.09419i	−0.837070	+	0.547096i	$0.815733\pi$
$522$		0			0
$523$	−10632.0	+	10632.0i	−0.888920	+	0.888920i	−0.994419	−	0.105500i	$-0.966356\pi$
$523$	−10632.0	+	10632.0i	−0.888920	+	0.888920i	0.105500	+	0.994419i	$0.466356\pi$
$524$	−4299.21			−0.358420
$525$		0			0
$526$	2552.00			0.211545
$527$	24075.6	−	24075.6i	1.99003	−	1.99003i
$528$		0			0
$529$		−	3703.00i		−	0.304348i
$530$		0			0
$531$		0			0
$532$	448.000	+	448.000i	0.0365099	+	0.0365099i
$533$	−3771.71	−	3771.71i	−0.306512	−	0.306512i
$534$		0			0
$535$		0			0
$536$			1448.15i			0.116699i
$537$		0			0
$538$	−1498.00	+	1498.00i	−0.120043	+	0.120043i
$539$	14074.3			1.12471
$540$		0			0
$541$	−14588.0			−1.15931			−0.579655	−	0.814862i	$-0.696813\pi$
$541$	−14588.0			−1.15931			−0.579655	+	0.814862i	$0.696813\pi$
$542$	2036.47	−	2036.47i	0.161391	−	0.161391i
$543$		0			0
$544$			3584.00i			0.282468i
$545$		0			0
$546$		0			0
$547$	10284.0	+	10284.0i	0.803861	+	0.803861i	0.983697	−	0.179835i	$-0.0575565\pi$
$547$	10284.0	+	10284.0i	0.803861	+	0.803861i	−0.179835	+	0.983697i	$0.557557\pi$
$548$	4802.67	+	4802.67i	0.374379	+	0.374379i
$549$		0			0
$550$		0			0
$551$			3128.24i			0.241865i
$552$		0			0
$553$	5568.00	−	5568.00i	0.428165	−	0.428165i
$554$	−7204.00			−0.552471
$555$		0			0
$556$	3536.00			0.269712
$557$	−11090.3	+	11090.3i	−0.843644	+	0.843644i	−0.989331	−	0.145687i	$-0.953461\pi$
$557$	−11090.3	+	11090.3i	−0.843644	+	0.843644i	0.145687	+	0.989331i	$0.453461\pi$
$558$		0			0
$559$			7560.00i			0.572011i
$560$		0			0
$561$		0			0
$562$	8982.00	+	8982.00i	0.674169	+	0.674169i
$563$	−10063.5	−	10063.5i	−0.753335	−	0.753335i	0.221765	−	0.975100i	$-0.428818\pi$
$563$	−10063.5	−	10063.5i	−0.753335	−	0.753335i	−0.975100	+	0.221765i	$0.928818\pi$
$564$		0			0
$565$		0			0
$566$			497.803i			0.0369686i
$567$		0			0
$568$	5792.00	−	5792.00i	0.427864	−	0.427864i
$569$	−14562.2			−1.07290			−0.536448	−	0.843934i	$-0.680234\pi$
$569$	−14562.2			−1.07290			−0.536448	+	0.843934i	$0.680234\pi$
$570$		0			0
$571$	−16492.0			−1.20870			−0.604351	−	0.796718i	$-0.706567\pi$
$571$	−16492.0			−1.20870			−0.604351	+	0.796718i	$0.706567\pi$
$572$	3801.41	−	3801.41i	0.277875	−	0.277875i
$573$		0			0
$574$		−	2032.00i		−	0.147760i
$575$		0			0
$576$		0			0
$577$	−5863.00	−	5863.00i	−0.423015	−	0.423015i	0.463225	−	0.886241i	$-0.346692\pi$
$577$	−5863.00	−	5863.00i	−0.423015	−	0.423015i	−0.886241	+	0.463225i	$0.846692\pi$
$578$	−10791.9	−	10791.9i	−0.776613	−	0.776613i
$579$		0			0
$580$		0			0
$581$		−	1493.41i		−	0.106639i
$582$		0			0
$583$	−16256.0	+	16256.0i	−1.15481	+	1.15481i
$584$	−7727.26			−0.547528
$585$		0			0
$586$	−13932.0			−0.982126
$587$	−9469.57	+	9469.57i	−0.665845	+	0.665845i	−0.956752	−	0.290906i	$-0.906043\pi$
$587$	−9469.57	+	9469.57i	−0.665845	+	0.665845i	0.290906	+	0.956752i	$0.406043\pi$
$588$		0			0
$589$			8512.00i			0.595468i
$590$		0			0
$591$		0			0
$592$	3696.00	+	3696.00i	0.256596	+	0.256596i
$593$	−253.144	−	253.144i	−0.0175302	−	0.0175302i	0.698287	−	0.715818i	$-0.253946\pi$
$593$	−253.144	−	253.144i	−0.0175302	−	0.0175302i	−0.715818	+	0.698287i	$0.753946\pi$
$594$		0			0
$595$		0			0
$596$			4497.20i			0.309081i
$597$		0			0
$598$	3864.00	−	3864.00i	0.264232	−	0.264232i
$599$	−3150.87			−0.214926			−0.107463	−	0.994209i	$-0.534273\pi$
$599$	−3150.87			−0.214926			−0.107463	+	0.994209i	$0.534273\pi$
$600$		0			0
$601$	−20032.0			−1.35960			−0.679802	−	0.733395i	$-0.737934\pi$
$601$	−20032.0			−1.35960			−0.679802	+	0.733395i	$0.737934\pi$
$602$	−2036.47	+	2036.47i	−0.137874	+	0.137874i
$603$		0			0
$604$		−	3808.00i		−	0.256532i
$605$		0			0
$606$		0			0
$607$	−1812.00	−	1812.00i	−0.121164	−	0.121164i	0.643925	−	0.765089i	$-0.277305\pi$
$607$	−1812.00	−	1812.00i	−0.121164	−	0.121164i	−0.765089	+	0.643925i	$0.777305\pi$
$608$	−633.568	−	633.568i	−0.0422608	−	0.0422608i
$609$		0			0
$610$		0			0
$611$		−	5345.73i		−	0.353952i
$612$		0			0
$613$	17841.0	−	17841.0i	1.17552	−	1.17552i	0.194641	−	0.980874i	$-0.437646\pi$
$613$	17841.0	−	17841.0i	1.17552	−	1.17552i	0.980874	−	0.194641i	$-0.0623543\pi$
$614$	14764.4			0.970427
$615$		0			0
$616$	2048.00			0.133955
$617$	−9113.19	+	9113.19i	−0.594624	+	0.594624i	−0.938877	−	0.344253i	$-0.888132\pi$
$617$	−9113.19	+	9113.19i	−0.594624	+	0.594624i	0.344253	+	0.938877i	$0.388132\pi$
$618$		0			0
$619$			14532.0i			0.943603i	0.881705	+	0.471802i	$0.156396\pi$
$619$			14532.0i			0.943603i	−0.881705	+	0.471802i	$0.843604\pi$
$620$		0			0
$621$		0			0
$622$	−8728.00	−	8728.00i	−0.562638	−	0.562638i
$623$	1793.22	+	1793.22i	0.115319	+	0.115319i
$624$		0			0
$625$		0			0
$626$		−	20525.9i		−	1.31051i
$627$		0			0
$628$	−612.000	+	612.000i	−0.0388877	+	0.0388877i
$629$	−36588.5			−2.31936
$630$		0			0
$631$	17440.0			1.10028			0.550139	−	0.835073i	$-0.314575\pi$
$631$	17440.0			1.10028			0.550139	+	0.835073i	$0.314575\pi$
$632$	−7874.34	+	7874.34i	−0.495608	+	0.495608i
$633$		0			0
$634$		−	1128.00i		−	0.0706603i
$635$		0			0
$636$		0			0
$637$	−6531.00	−	6531.00i	−0.406229	−	0.406229i
$638$	7150.26	+	7150.26i	0.443702	+	0.443702i
$639$		0			0
$640$		0			0
$641$		−	9315.42i		−	0.574005i	−0.957930	−	0.287002i	$-0.907341\pi$
$641$		−	9315.42i		−	0.574005i	0.957930	−	0.287002i	$-0.0926588\pi$
$642$		0			0
$643$	−20604.0	+	20604.0i	−1.26367	+	1.26367i	−0.314375	+	0.949299i	$0.601795\pi$
$643$	−20604.0	+	20604.0i	−1.26367	+	1.26367i	−0.949299	+	0.314375i	$0.898205\pi$
$644$	2081.72			0.127378
$645$		0			0
$646$	6272.00			0.381995
$647$	−9353.61	+	9353.61i	−0.568359	+	0.568359i	−0.931669	−	0.363309i	$-0.881647\pi$
$647$	−9353.61	+	9353.61i	−0.568359	+	0.568359i	0.363309	+	0.931669i	$0.381647\pi$
$648$		0			0
$649$			34048.0i			2.05932i
$650$		0			0
$651$		0			0
$652$	5552.00	+	5552.00i	0.333486	+	0.333486i
$653$	4760.24	+	4760.24i	0.285272	+	0.285272i	0.835207	−	0.549935i	$-0.185348\pi$
$653$	4760.24	+	4760.24i	0.285272	+	0.285272i	−0.549935	+	0.835207i	$0.685348\pi$
$654$		0			0
$655$		0			0
$656$			2873.68i			0.171034i
$657$		0			0
$658$	1440.00	−	1440.00i	0.0853147	−	0.0853147i
$659$	−12631.8			−0.746682			−0.373341	−	0.927694i	$-0.621788\pi$
$659$	−12631.8			−0.746682			−0.373341	+	0.927694i	$0.621788\pi$
$660$		0			0
$661$	5492.00			0.323168			0.161584	−	0.986859i	$-0.448340\pi$
$661$	5492.00			0.323168			0.161584	+	0.986859i	$0.448340\pi$
$662$	−6001.92	+	6001.92i	−0.352374	+	0.352374i
$663$		0			0
$664$			2112.00i			0.123436i
$665$		0			0
$666$		0			0
$667$	7268.00	+	7268.00i	0.421916	+	0.421916i
$668$	−6980.56	−	6980.56i	−0.404320	−	0.404320i
$669$		0			0
$670$		0			0
$671$		−	8145.87i		−	0.468655i
$672$		0			0
$673$	−7285.00	+	7285.00i	−0.417260	+	0.417260i	−0.884258	−	0.466998i	$-0.845335\pi$
$673$	−7285.00	+	7285.00i	−0.417260	+	0.417260i	0.466998	+	0.884258i	$0.345335\pi$
$674$	−17556.0			−1.00331
$675$		0			0
$676$	5260.00			0.299272
$677$	−19445.4	+	19445.4i	−1.10391	+	1.10391i	−0.109979	+	0.993934i	$0.535078\pi$
$677$	−19445.4	+	19445.4i	−1.10391	+	1.10391i	−0.993934	+	0.109979i	$0.964922\pi$
$678$		0			0
$679$		−	1128.00i		−	0.0637536i
$680$		0			0
$681$		0			0
$682$	19456.0	+	19456.0i	1.09239	+	1.09239i
$683$	831.558	+	831.558i	0.0465866	+	0.0465866i	0.730016	−	0.683430i	$-0.239512\pi$
$683$	831.558	+	831.558i	0.0465866	+	0.0465866i	−0.683430	+	0.730016i	$0.739512\pi$
$684$		0			0
$685$		0			0
$686$		−	7399.17i		−	0.411810i
$687$		0			0
$688$	2880.00	−	2880.00i	0.159592	−	0.159592i
$689$	15086.8			0.834198
$690$		0			0
$691$	2340.00			0.128825			0.0644123	−	0.997923i	$-0.479483\pi$
$691$	2340.00			0.128825			0.0644123	+	0.997923i	$0.479483\pi$
$692$	−3795.75	+	3795.75i	−0.208516	+	0.208516i
$693$		0			0
$694$		−	16256.0i		−	0.889149i
$695$		0			0
$696$		0			0
$697$	−14224.0	−	14224.0i	−0.772988	−	0.772988i
$698$	−12722.3	−	12722.3i	−0.689892	−	0.689892i
$699$		0			0
$700$		0			0
$701$			18929.2i			1.01990i	0.860205	+	0.509949i	$0.170336\pi$
$701$			18929.2i			1.01990i	−0.860205	+	0.509949i	$0.829664\pi$
$702$		0			0
$703$	6468.00	−	6468.00i	0.347006	−	0.347006i
$704$	−2896.31			−0.155055
$705$		0			0
$706$	−21072.0			−1.12331
$707$	−2890.65	+	2890.65i	−0.153768	+	0.153768i
$708$		0			0
$709$		−	9794.00i		−	0.518789i	−0.965771	−	0.259394i	$-0.916477\pi$
$709$		−	9794.00i		−	0.518789i	0.965771	−	0.259394i	$-0.0835230\pi$
$710$		0			0
$711$		0			0
$712$	−2536.00	−	2536.00i	−0.133484	−	0.133484i
$713$	19776.4	+	19776.4i	1.03875	+	1.03875i
$714$		0			0
$715$		0			0
$716$		−	724.077i		−	0.0377934i
$717$		0			0
$718$	−14456.0	+	14456.0i	−0.751383	+	0.751383i
$719$	24867.5			1.28985			0.644925	−	0.764246i	$-0.276889\pi$
$719$	24867.5			1.28985			0.644925	+	0.764246i	$0.276889\pi$
$720$		0			0
$721$	−6848.00			−0.353721
$722$	8591.35	−	8591.35i	0.442849	−	0.442849i
$723$		0			0
$724$			10768.0i			0.552748i
$725$		0			0
$726$		0			0
$727$	−7752.00	−	7752.00i	−0.395469	−	0.395469i	0.481163	−	0.876631i	$-0.340215\pi$
$727$	−7752.00	−	7752.00i	−0.395469	−	0.395469i	−0.876631	+	0.481163i	$0.840215\pi$
$728$	−950.352	−	950.352i	−0.0483824	−	0.0483824i
$729$		0			0
$730$		0			0
$731$			28510.5i			1.44255i
$732$		0			0
$733$	1817.00	−	1817.00i	0.0915586	−	0.0915586i	−0.659844	−	0.751403i	$-0.729378\pi$
$733$	1817.00	−	1817.00i	0.0915586	−	0.0915586i	0.751403	+	0.659844i	$0.229378\pi$
$734$	−15907.1			−0.799919
$735$		0			0
$736$	−2944.00			−0.147442
$737$	5792.62	−	5792.62i	0.289517	−	0.289517i
$738$		0			0
$739$			33092.0i			1.64724i	0.567143	+	0.823619i	$0.308048\pi$
$739$			33092.0i			1.64724i	−0.567143	+	0.823619i	$0.691952\pi$
$740$		0			0
$741$		0			0
$742$	4064.00	+	4064.00i	0.201070	+	0.201070i
$743$	−15796.8	−	15796.8i	−0.779983	−	0.779983i	0.199845	−	0.979828i	$-0.435956\pi$
$743$	−15796.8	−	15796.8i	−0.779983	−	0.779983i	−0.979828	+	0.199845i	$0.935956\pi$
$744$		0			0
$745$		0			0
$746$		−	2474.87i		−	0.121463i
$747$		0			0
$748$	14336.0	−	14336.0i	0.700770	−	0.700770i
$749$	−5204.31			−0.253887
$750$		0			0
$751$	16728.0			0.812801			0.406400	−	0.913695i	$-0.366784\pi$
$751$	16728.0			0.812801			0.406400	+	0.913695i	$0.366784\pi$
$752$	−2036.47	+	2036.47i	−0.0987531	+	0.0987531i
$753$		0			0
$754$		−	6636.00i		−	0.320516i
$755$		0			0
$756$		0			0
$757$	5115.00	+	5115.00i	0.245585	+	0.245585i	0.819156	−	0.573571i	$-0.194442\pi$
$757$	5115.00	+	5115.00i	0.245585	+	0.245585i	−0.573571	+	0.819156i	$0.694442\pi$
$758$	−13774.4	−	13774.4i	−0.660040	−	0.660040i
$759$		0			0
$760$		0			0
$761$		−	11583.8i		−	0.551791i	−0.961188	−	0.275896i	$-0.911026\pi$
$761$		−	11583.8i		−	0.551791i	0.961188	−	0.275896i	$-0.0889744\pi$
$762$		0			0
$763$	−5648.00	+	5648.00i	−0.267983	+	0.267983i
$764$	3484.62			0.165012
$765$		0			0
$766$	−5736.00			−0.270561
$767$	15799.6	−	15799.6i	0.743794	−	0.743794i
$768$		0			0
$769$		−	1960.00i		−	0.0919108i	−0.998943	−	0.0459554i	$-0.985367\pi$
$769$		−	1960.00i		−	0.0919108i	0.998943	−	0.0459554i	$-0.0146332\pi$
$770$		0			0
$771$		0			0
$772$	4212.00	+	4212.00i	0.196364	+	0.196364i
$773$	−1332.19	−	1332.19i	−0.0619864	−	0.0619864i	0.675434	−	0.737420i	$-0.263956\pi$
$773$	−1332.19	−	1332.19i	−0.0619864	−	0.0619864i	−0.737420	+	0.675434i	$0.763956\pi$
$774$		0			0
$775$		0			0
$776$			1595.23i			0.0737958i
$777$		0			0
$778$	3750.00	−	3750.00i	0.172807	−	0.172807i
$779$	5028.94			0.231297
$780$		0			0
$781$	−46336.0			−2.12296
$782$	14572.1	−	14572.1i	0.666363	−	0.666363i
$783$		0			0
$784$			4976.00i			0.226676i
$785$		0			0
$786$		0			0
$787$	22400.0	+	22400.0i	1.01458	+	1.01458i	0.999892	+	0.0146870i	$0.00467518\pi$
$787$	22400.0	+	22400.0i	1.01458	+	1.01458i	0.0146870	+	0.999892i	$0.495325\pi$
$788$	1883.73	+	1883.73i	0.0851589	+	0.0851589i
$789$		0			0
$790$		0			0
$791$			7387.85i			0.332088i
$792$		0			0
$793$	−3780.00	+	3780.00i	−0.169271	+	0.169271i
$794$	−7300.17			−0.326289
$795$		0			0
$796$	21600.0			0.961799
$797$	12876.4	−	12876.4i	0.572279	−	0.572279i	−0.360486	−	0.932765i	$-0.617389\pi$
$797$	12876.4	−	12876.4i	0.572279	−	0.572279i	0.932765	+	0.360486i	$0.117389\pi$
$798$		0			0
$799$		−	20160.0i		−	0.892628i
$800$		0			0
$801$		0			0
$802$	−9738.00	−	9738.00i	−0.428754	−	0.428754i
$803$	30909.1	+	30909.1i	1.35835	+	1.35835i
$804$		0			0
$805$		0			0
$806$		−	18056.7i		−	0.789106i
$807$		0			0
$808$	4088.00	−	4088.00i	0.177989	−	0.177989i
$809$	−2954.29			−0.128390			−0.0641949	−	0.997937i	$-0.520448\pi$
$809$	−2954.29			−0.128390			−0.0641949	+	0.997937i	$0.520448\pi$
$810$		0			0
$811$	3620.00			0.156739			0.0783695	−	0.996924i	$-0.475029\pi$
$811$	3620.00			0.156739			0.0783695	+	0.996924i	$0.475029\pi$
$812$	1787.57	−	1787.57i	0.0772553	−	0.0772553i
$813$		0			0
$814$		−	29568.0i		−	1.27317i
$815$		0			0
$816$		0			0
$817$	−5040.00	−	5040.00i	−0.215823	−	0.215823i
$818$	−3428.05	−	3428.05i	−0.146527	−	0.146527i
$819$		0			0
$820$		0			0
$821$		−	1953.03i		−	0.0830221i	−0.999138	−	0.0415111i	$-0.986783\pi$
$821$		−	1953.03i		−	0.0830221i	0.999138	−	0.0415111i	$-0.0132172\pi$
$822$		0			0
$823$	14284.0	−	14284.0i	0.604993	−	0.604993i	−0.336641	−	0.941633i	$-0.609291\pi$
$823$	14284.0	−	14284.0i	0.604993	−	0.604993i	0.941633	+	0.336641i	$0.109291\pi$
$824$	9684.53			0.409438
$825$		0			0
$826$	8512.00			0.358560
$827$	4768.73	−	4768.73i	0.200514	−	0.200514i	−0.599706	−	0.800220i	$-0.704716\pi$
$827$	4768.73	−	4768.73i	0.200514	−	0.200514i	0.800220	+	0.599706i	$0.204716\pi$
$828$		0			0
$829$		−	4516.00i		−	0.189200i	−0.995515	−	0.0946002i	$-0.969843\pi$
$829$		−	4516.00i		−	0.189200i	0.995515	−	0.0946002i	$-0.0301573\pi$
$830$		0			0
$831$		0			0
$832$	1344.00	+	1344.00i	0.0560034	+	0.0560034i
$833$	−24629.9	−	24629.9i	−1.02446	−	1.02446i
$834$		0			0
$835$		0			0
$836$			5068.54i			0.209688i
$837$		0			0
$838$	19656.0	−	19656.0i	0.810269	−	0.810269i
$839$	−4825.30			−0.198555			−0.0992776	−	0.995060i	$-0.531653\pi$
$839$	−4825.30			−0.198555			−0.0992776	+	0.995060i	$0.531653\pi$
$840$		0			0
$841$	−11907.0			−0.488212
$842$	13392.6	−	13392.6i	0.548147	−	0.548147i
$843$		0			0
$844$			7696.00i			0.313871i
$845$		0			0
$846$		0			0
$847$	−2868.00	−	2868.00i	−0.116347	−	0.116347i
$848$	−5747.36	−	5747.36i	−0.232742	−	0.232742i
$849$		0			0
$850$		0			0
$851$		−	30054.9i		−	1.21066i
$852$		0			0
$853$	−23353.0	+	23353.0i	−0.937387	+	0.937387i	−0.998152	−	0.0607647i	$-0.980646\pi$
$853$	−23353.0	+	23353.0i	−0.937387	+	0.937387i	0.0607647	+	0.998152i	$0.480646\pi$
$854$	−2036.47			−0.0816001
$855$		0			0
$856$	7360.00			0.293878
$857$	−17038.4	+	17038.4i	−0.679139	+	0.679139i	−0.959805	−	0.280666i	$-0.909445\pi$
$857$	−17038.4	+	17038.4i	−0.679139	+	0.679139i	0.280666	+	0.959805i	$0.409445\pi$
$858$		0			0
$859$		−	9364.00i		−	0.371939i	−0.982556	−	0.185969i	$-0.940457\pi$
$859$		−	9364.00i		−	0.371939i	0.982556	−	0.185969i	$-0.0595426\pi$
$860$		0			0
$861$		0			0
$862$	−2216.00	−	2216.00i	−0.0875606	−	0.0875606i
$863$	23297.8	+	23297.8i	0.918963	+	0.918963i	0.996954	−	0.0779914i	$-0.0248507\pi$
$863$	23297.8	+	23297.8i	0.918963	+	0.918963i	−0.0779914	+	0.996954i	$0.524851\pi$
$864$		0			0
$865$		0			0
$866$			18698.7i			0.733728i
$867$		0			0
$868$	4864.00	−	4864.00i	0.190202	−	0.190202i
$869$	62994.7			2.45909
$870$		0			0
$871$	−5376.00			−0.209138
$872$	7987.48	−	7987.48i	0.310195	−	0.310195i
$873$		0			0
$874$			5152.00i			0.199392i
$875$		0			0
$876$		0			0
$877$	−10335.0	−	10335.0i	−0.397934	−	0.397934i	0.479570	−	0.877504i	$-0.340793\pi$
$877$	−10335.0	−	10335.0i	−0.397934	−	0.397934i	−0.877504	+	0.479570i	$0.840793\pi$
$878$	8021.42	+	8021.42i	0.308326	+	0.308326i
$879$		0			0
$880$		0			0
$881$			50095.7i			1.91574i	0.287203	+	0.957870i	$0.407275\pi$
$881$			50095.7i			1.91574i	−0.287203	+	0.957870i	$0.592725\pi$
$882$		0			0
$883$	−25612.0	+	25612.0i	−0.976118	+	0.976118i	−0.999721	−	0.0236031i	$-0.992486\pi$
$883$	−25612.0	+	25612.0i	−0.976118	+	0.976118i	0.0236031	+	0.999721i	$0.492486\pi$
$884$	−13304.9			−0.506214
$885$		0			0
$886$	32064.0			1.21581
$887$	−11786.1	+	11786.1i	−0.446152	+	0.446152i	−0.894073	−	0.447921i	$-0.852165\pi$
$887$	−11786.1	+	11786.1i	−0.446152	+	0.446152i	0.447921	+	0.894073i	$0.352165\pi$
$888$		0			0
$889$		−	11776.0i		−	0.444268i
$890$		0			0
$891$		0			0
$892$	−2352.00	−	2352.00i	−0.0882856	−	0.0882856i
$893$	3563.82	+	3563.82i	0.133548	+	0.133548i
$894$		0			0
$895$		0			0
$896$			724.077i			0.0269975i
$897$		0			0
$898$	−13462.0	+	13462.0i	−0.500259	+	0.500259i
$899$	33963.8			1.26002
$900$		0			0
$901$	56896.0			2.10375
$902$	11494.7	−	11494.7i	0.424315	−	0.424315i
$903$		0			0
$904$		−	10448.0i		−	0.384397i
$905$		0			0
$906$		0			0
$907$	−29152.0	−	29152.0i	−1.06723	−	1.06723i	−0.997571	−	0.0696576i	$-0.977809\pi$
$907$	−29152.0	−	29152.0i	−1.06723	−	1.06723i	−0.0696576	−	0.997571i	$-0.522191\pi$
$908$	4118.19	+	4118.19i	0.150514	+	0.150514i
$909$		0			0
$910$		0			0
$911$		−	43201.4i		−	1.57116i	−0.618761	−	0.785580i	$-0.712365\pi$
$911$		−	43201.4i		−	1.57116i	0.618761	−	0.785580i	$-0.287635\pi$
$912$		0			0
$913$	8448.00	−	8448.00i	0.306230	−	0.306230i
$914$	5133.60			0.185781
$915$		0			0
$916$	6024.00			0.217291
$917$	4299.21	−	4299.21i	0.154823	−	0.154823i
$918$		0			0
$919$		−	19240.0i		−	0.690608i	−0.938491	−	0.345304i	$-0.887776\pi$
$919$		−	19240.0i		−	0.690608i	0.938491	−	0.345304i	$-0.112224\pi$
$920$		0			0
$921$		0			0
$922$	−5006.00	−	5006.00i	−0.178811	−	0.178811i
$923$	21501.7	+	21501.7i	0.766779	+	0.766779i
$924$		0			0
$925$		0			0
$926$		−	8802.07i		−	0.312369i
$927$		0			0
$928$	−2528.00	+	2528.00i	−0.0894242	+	0.0894242i
$929$	21740.7			0.767803			0.383902	−	0.923374i	$-0.374580\pi$
$929$	21740.7			0.767803			0.383902	+	0.923374i	$0.374580\pi$
$930$		0			0
$931$	8708.00			0.306545
$932$	2783.17	−	2783.17i	0.0978174	−	0.0978174i
$933$		0			0
$934$			12832.0i			0.449546i
$935$		0			0
$936$		0			0
$937$	32483.0	+	32483.0i	1.13252	+	1.13252i	0.989757	+	0.142766i	$0.0455996\pi$
$937$	32483.0	+	32483.0i	1.13252	+	1.13252i	0.142766	+	0.989757i	$0.454400\pi$
$938$	−1448.15	−	1448.15i	−0.0504093	−	0.0504093i
$939$		0			0
$940$		0			0
$941$		−	6461.54i		−	0.223847i	−0.993717	−	0.111924i	$-0.964299\pi$
$941$		−	6461.54i		−	0.223847i	0.993717	−	0.111924i	$-0.0357012\pi$
$942$		0			0
$943$	11684.0	−	11684.0i	0.403482	−	0.403482i
$944$	−12037.8			−0.415039
$945$		0			0
$946$	−23040.0			−0.791855
$947$	23917.2	−	23917.2i	0.820701	−	0.820701i	−0.165507	−	0.986209i	$-0.552926\pi$
$947$	23917.2	−	23917.2i	0.820701	−	0.820701i	0.986209	+	0.165507i	$0.0529262\pi$
$948$		0			0
$949$		−	28686.0i		−	0.981230i
$950$		0			0
$951$		0			0
$952$	−3584.00	−	3584.00i	−0.122015	−	0.122015i
$953$	27208.1	+	27208.1i	0.924822	+	0.924822i	0.997365	−	0.0725433i	$-0.0231115\pi$
$953$	27208.1	+	27208.1i	0.924822	+	0.924822i	−0.0725433	+	0.997365i	$0.523112\pi$
$954$		0			0
$955$		0			0
$956$			2783.17i			0.0941571i
$957$		0			0
$958$	−5128.00	+	5128.00i	−0.172942	+	0.172942i
$959$	−9605.34			−0.323433
$960$		0			0
$961$	62625.0			2.10214
$962$	−13720.7	+	13720.7i	−0.459847	+	0.459847i
$963$		0			0
$964$		−	2488.00i		−	0.0831256i
$965$		0			0
$966$		0			0
$967$	5180.00	+	5180.00i	0.172262	+	0.172262i	0.787973	−	0.615710i	$-0.211131\pi$
$967$	5180.00	+	5180.00i	0.172262	+	0.172262i	−0.615710	+	0.787973i	$0.711131\pi$
$968$	4055.96	+	4055.96i	0.134673	+	0.134673i
$969$		0			0
$970$		0			0
$971$			5945.35i			0.196494i	0.995162	+	0.0982469i	$0.0313235\pi$
$971$			5945.35i			0.196494i	−0.995162	+	0.0982469i	$0.968677\pi$
$972$		0			0
$973$	−3536.00	+	3536.00i	−0.116505	+	0.116505i
$974$	26881.4			0.884327
$975$		0			0
$976$	2880.00			0.0944534
$977$	−746.705	+	746.705i	−0.0244516	+	0.0244516i	−0.719227	−	0.694775i	$-0.755504\pi$
$977$	−746.705	+	746.705i	−0.0244516	+	0.0244516i	0.694775	+	0.719227i	$0.255504\pi$
$978$		0			0
$979$			20288.0i			0.662316i
$980$		0			0
$981$		0			0
$982$	−22984.0	−	22984.0i	−0.746893	−	0.746893i
$983$	−14931.3	−	14931.3i	−0.484469	−	0.484469i	0.422086	−	0.906556i	$-0.361298\pi$
$983$	−14931.3	−	14931.3i	−0.484469	−	0.484469i	−0.906556	+	0.422086i	$0.861298\pi$
$984$		0			0
$985$		0			0
$986$		−	25025.9i		−	0.808304i
$987$		0			0
$988$	2352.00	−	2352.00i	0.0757359	−	0.0757359i
$989$	−23419.4			−0.752976
$990$		0			0
$991$	−30272.0			−0.970355			−0.485177	−	0.874416i	$-0.661245\pi$
$991$	−30272.0			−0.970355			−0.485177	+	0.874416i	$0.661245\pi$
$992$	−6878.73	+	6878.73i	−0.220161	+	0.220161i
$993$		0			0
$994$			11584.0i			0.369640i
$995$		0			0
$996$		0			0
$997$	−43579.0	−	43579.0i	−1.38431	−	1.38431i	−0.836790	−	0.547523i	$-0.815571\pi$
$997$	−43579.0	−	43579.0i	−1.38431	−	1.38431i	−0.547523	−	0.836790i	$-0.684429\pi$
$998$	−17892.6	−	17892.6i	−0.567516	−	0.567516i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.4.f.b.107.2		4
3.2	odd	2	inner	450.4.f.b.107.1		4
5.2	odd	4		90.4.f.a.53.2	yes	4
5.3	odd	4	inner	450.4.f.b.143.1		4
5.4	even	2		90.4.f.a.17.1	✓	4
15.2	even	4		90.4.f.a.53.1	yes	4
15.8	even	4	inner	450.4.f.b.143.2		4
15.14	odd	2		90.4.f.a.17.2	yes	4
20.7	even	4		720.4.w.b.593.1		4
20.19	odd	2		720.4.w.b.17.2		4
60.47	odd	4		720.4.w.b.593.2		4
60.59	even	2		720.4.w.b.17.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.4.f.a.17.1	✓	4	5.4	even	2
90.4.f.a.17.2	yes	4	15.14	odd	2
90.4.f.a.53.1	yes	4	15.2	even	4
90.4.f.a.53.2	yes	4	5.2	odd	4
450.4.f.b.107.1		4	3.2	odd	2	inner
450.4.f.b.107.2		4	1.1	even	1	trivial
450.4.f.b.143.1		4	5.3	odd	4	inner
450.4.f.b.143.2		4	15.8	even	4	inner
720.4.w.b.17.1		4	60.59	even	2
720.4.w.b.17.2		4	20.19	odd	2
720.4.w.b.593.1		4	20.7	even	4
720.4.w.b.593.2		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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	450.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41421 - 1.41421i) q^{2} -4.00000i q^{4} +(4.00000 + 4.00000i) q^{7} +(-5.65685 - 5.65685i) q^{8} +O(q^{10})\)	\(q+(1.41421 - 1.41421i) q^{2} -4.00000i q^{4} +(4.00000 + 4.00000i) q^{7} +(-5.65685 - 5.65685i) q^{8} +45.2548i q^{11} +(21.0000 - 21.0000i) q^{13} +11.3137 q^{14} -16.0000 q^{16} +(79.1960 - 79.1960i) q^{17} +28.0000i q^{19} +(64.0000 + 64.0000i) q^{22} +(65.0538 + 65.0538i) q^{23} -59.3970i q^{26} +(16.0000 - 16.0000i) q^{28} +111.723 q^{29} +304.000 q^{31} +(-22.6274 + 22.6274i) q^{32} -224.000i q^{34} +(-231.000 - 231.000i) q^{37} +(39.5980 + 39.5980i) q^{38} -179.605i q^{41} +(-180.000 + 180.000i) q^{43} +181.019 q^{44} +184.000 q^{46} +(127.279 - 127.279i) q^{47} -311.000i q^{49} +(-84.0000 - 84.0000i) q^{52} +(359.210 + 359.210i) q^{53} -45.2548i q^{56} +(158.000 - 158.000i) q^{58} +752.362 q^{59} -180.000 q^{61} +(429.921 - 429.921i) q^{62} +64.0000i q^{64} +(-128.000 - 128.000i) q^{67} +(-316.784 - 316.784i) q^{68} +1023.89i q^{71} +(683.000 - 683.000i) q^{73} -653.367 q^{74} +112.000 q^{76} +(-181.019 + 181.019i) q^{77} -1392.00i q^{79} +(-254.000 - 254.000i) q^{82} +(-186.676 - 186.676i) q^{83} +509.117i q^{86} +(256.000 - 256.000i) q^{88} +448.306 q^{89} +168.000 q^{91} +(260.215 - 260.215i) q^{92} -360.000i q^{94} +(-141.000 - 141.000i) q^{97} +(-439.820 - 439.820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 16 q^{7}+O(q^{10}) \) 4 * q + 16 * q^7	\( 4 q + 16 q^{7} + 84 q^{13} - 64 q^{16} + 256 q^{22} + 64 q^{28} + 1216 q^{31} - 924 q^{37} - 720 q^{43} + 736 q^{46} - 336 q^{52} + 632 q^{58} - 720 q^{61} - 512 q^{67} + 2732 q^{73} + 448 q^{76} - 1016 q^{82} + 1024 q^{88} + 672 q^{91} - 564 q^{97}+O(q^{100}) \) 4 * q + 16 * q^7 + 84 * q^13 - 64 * q^16 + 256 * q^22 + 64 * q^28 + 1216 * q^31 - 924 * q^37 - 720 * q^43 + 736 * q^46 - 336 * q^52 + 632 * q^58 - 720 * q^61 - 512 * q^67 + 2732 * q^73 + 448 * q^76 - 1016 * q^82 + 1024 * q^88 + 672 * q^91 - 564 * q^97

Introduction

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