LMFDB - Embedded newform 2250.2.f.d.557.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2250,2,Mod(557,2250)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2250.557"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2250, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2250 = 2 \cdot 3^{2} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2250.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.9663404548$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{40})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} + x^{8} - x^{4} + 1 $ x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			557.8
Root			$-0.156434 + 0.987688i$ of defining polynomial
Character	$\chi$	$=$	2250.557
Dual form			2250.2.f.d.1943.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(3.43564 + 3.43564i) q^{7} +(-0.707107 - 0.707107i) q^{8} +2.12883i q^{11} +(-1.12334 + 1.12334i) q^{13} +4.85873 q^{14} -1.00000 q^{16} +(2.28825 - 2.28825i) q^{17} +6.25325i q^{19} +(1.50531 + 1.50531i) q^{22} +(-0.984708 - 0.984708i) q^{23} +1.58865i q^{26} +(3.43564 - 3.43564i) q^{28} +2.31255 q^{29} -8.49338 q^{31} +(-0.707107 + 0.707107i) q^{32} -3.23607i q^{34} +(2.05368 + 2.05368i) q^{37} +(4.42172 + 4.42172i) q^{38} +2.02102i q^{41} +(-6.24669 + 6.24669i) q^{43} +2.12883 q^{44} -1.39259 q^{46} +(-8.57335 + 8.57335i) q^{47} +16.6073i q^{49} +(1.12334 + 1.12334i) q^{52} +(0.103165 + 0.103165i) q^{53} -4.85873i q^{56} +(1.63522 - 1.63522i) q^{58} +14.0510 q^{59} +12.9786 q^{61} +(-6.00573 + 6.00573i) q^{62} +1.00000i q^{64} +(-2.83692 - 2.83692i) q^{67} +(-2.28825 - 2.28825i) q^{68} -10.0363i q^{71} +(7.70820 - 7.70820i) q^{73} +2.90434 q^{74} +6.25325 q^{76} +(-7.31391 + 7.31391i) q^{77} +0.0212431i q^{79} +(1.42908 + 1.42908i) q^{82} +(-7.41994 - 7.41994i) q^{83} +8.83415i q^{86} +(1.50531 - 1.50531i) q^{88} +12.0677 q^{89} -7.71883 q^{91} +(-0.984708 + 0.984708i) q^{92} +12.1245i q^{94} +(-1.48276 - 1.48276i) q^{97} +(11.7431 + 11.7431i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{7} + 12 q^{13} - 16 q^{16} + 12 q^{22} + 12 q^{28} - 16 q^{31} - 28 q^{37} - 40 q^{43} - 16 q^{46} - 12 q^{52} - 24 q^{58} - 24 q^{67} + 16 q^{73} + 32 q^{76} - 12 q^{82} + 12 q^{88} + 8 q^{91}+ \cdots + 72 q^{97}+O(q^{100}) $ 16 * q + 12 * q^7 + 12 * q^13 - 16 * q^16 + 12 * q^22 + 12 * q^28 - 16 * q^31 - 28 * q^37 - 40 * q^43 - 16 * q^46 - 12 * q^52 - 24 * q^58 - 24 * q^67 + 16 * q^73 + 32 * q^76 - 12 * q^82 + 12 * q^88 + 8 * q^91 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2250\mathbb{Z}\right)^\times$.

$n$	$127$	$1001$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	3.43564	+	3.43564i	1.29855	+	1.29855i	0.929349	+	0.369202i	$0.120369\pi$
$7$	3.43564	+	3.43564i	1.29855	+	1.29855i	0.369202	+	0.929349i	$0.379631\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$			2.12883i			0.641867i	0.947102	+	0.320933i	$0.103997\pi$
$11$			2.12883i			0.641867i	−0.947102	+	0.320933i	$0.896003\pi$
$12$		0			0
$13$	−1.12334	+	1.12334i	−0.311560	+	0.311560i	−0.845514	−	0.533954i	$-0.820706\pi$
$13$	−1.12334	+	1.12334i	−0.311560	+	0.311560i	0.533954	+	0.845514i	$0.320706\pi$
$14$	4.85873			1.29855
$15$		0			0
$16$	−1.00000			−0.250000
$17$	2.28825	−	2.28825i	0.554981	−	0.554981i	−0.372893	−	0.927874i	$-0.621634\pi$
$17$	2.28825	−	2.28825i	0.554981	−	0.554981i	0.927874	+	0.372893i	$0.121634\pi$
$18$		0			0
$19$			6.25325i			1.43459i	0.696767	+	0.717297i	$0.254621\pi$
$19$			6.25325i			1.43459i	−0.696767	+	0.717297i	$0.745379\pi$
$20$		0			0
$21$		0			0
$22$	1.50531	+	1.50531i	0.320933	+	0.320933i
$23$	−0.984708	−	0.984708i	−0.205326	−	0.205326i	0.596951	−	0.802277i	$-0.296378\pi$
$23$	−0.984708	−	0.984708i	−0.205326	−	0.205326i	−0.802277	+	0.596951i	$0.796378\pi$
$24$		0			0
$25$		0			0
$26$			1.58865i			0.311560i
$27$		0			0
$28$	3.43564	−	3.43564i	0.649276	−	0.649276i
$29$	2.31255			0.429430			0.214715	−	0.976677i	$-0.431118\pi$
$29$	2.31255			0.429430			0.214715	+	0.976677i	$0.431118\pi$
$30$		0			0
$31$	−8.49338			−1.52546			−0.762728	−	0.646719i	$-0.776140\pi$
$31$	−8.49338			−1.52546			−0.762728	+	0.646719i	$0.776140\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	3.23607i		−	0.554981i
$35$		0			0
$36$		0			0
$37$	2.05368	+	2.05368i	0.337623	+	0.337623i	0.855472	−	0.517849i	$-0.173267\pi$
$37$	2.05368	+	2.05368i	0.337623	+	0.337623i	−0.517849	+	0.855472i	$0.673267\pi$
$38$	4.42172	+	4.42172i	0.717297	+	0.717297i
$39$		0			0
$40$		0			0
$41$			2.02102i			0.315631i	0.987469	+	0.157815i	$0.0504451\pi$
$41$			2.02102i			0.315631i	−0.987469	+	0.157815i	$0.949555\pi$
$42$		0			0
$43$	−6.24669	+	6.24669i	−0.952611	+	0.952611i	−0.998927	−	0.0463156i	$-0.985252\pi$
$43$	−6.24669	+	6.24669i	−0.952611	+	0.952611i	0.0463156	+	0.998927i	$0.485252\pi$
$44$	2.12883			0.320933
$45$		0			0
$46$	−1.39259			−0.205326
$47$	−8.57335	+	8.57335i	−1.25055	+	1.25055i	−0.295078	+	0.955473i	$0.595346\pi$
$47$	−8.57335	+	8.57335i	−1.25055	+	1.25055i	−0.955473	+	0.295078i	$0.904654\pi$
$48$		0			0
$49$			16.6073i			2.37247i
$50$		0			0
$51$		0			0
$52$	1.12334	+	1.12334i	0.155780	+	0.155780i
$53$	0.103165	+	0.103165i	0.0141709	+	0.0141709i	0.714157	−	0.699986i	$-0.246810\pi$
$53$	0.103165	+	0.103165i	0.0141709	+	0.0141709i	−0.699986	+	0.714157i	$0.746810\pi$
$54$		0			0
$55$		0			0
$56$		−	4.85873i		−	0.649276i
$57$		0			0
$58$	1.63522	−	1.63522i	0.214715	−	0.214715i
$59$	14.0510			1.82929			0.914645	−	0.404258i	$-0.132470\pi$
$59$	14.0510			1.82929			0.914645	+	0.404258i	$0.132470\pi$
$60$		0			0
$61$	12.9786			1.66175			0.830873	−	0.556463i	$-0.187842\pi$
$61$	12.9786			1.66175			0.830873	+	0.556463i	$0.187842\pi$
$62$	−6.00573	+	6.00573i	−0.762728	+	0.762728i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	−2.83692	−	2.83692i	−0.346584	−	0.346584i	0.512251	−	0.858836i	$-0.328812\pi$
$67$	−2.83692	−	2.83692i	−0.346584	−	0.346584i	−0.858836	+	0.512251i	$0.828812\pi$
$68$	−2.28825	−	2.28825i	−0.277491	−	0.277491i
$69$		0			0
$70$		0			0
$71$		−	10.0363i		−	1.19109i	−0.803322	−	0.595545i	$-0.796936\pi$
$71$		−	10.0363i		−	1.19109i	0.803322	−	0.595545i	$-0.203064\pi$
$72$		0			0
$73$	7.70820	−	7.70820i	0.902177	−	0.902177i	−0.0934472	−	0.995624i	$-0.529789\pi$
$73$	7.70820	−	7.70820i	0.902177	−	0.902177i	0.995624	+	0.0934472i	$0.0297886\pi$
$74$	2.90434			0.337623
$75$		0			0
$76$	6.25325			0.717297
$77$	−7.31391	+	7.31391i	−0.833497	+	0.833497i
$78$		0			0
$79$			0.0212431i			0.00239004i	0.999999	+	0.00119502i	$0.000380387\pi$
$79$			0.0212431i			0.00239004i	−0.999999	+	0.00119502i	$0.999620\pi$
$80$		0			0
$81$		0			0
$82$	1.42908	+	1.42908i	0.157815	+	0.157815i
$83$	−7.41994	−	7.41994i	−0.814444	−	0.814444i	0.170852	−	0.985297i	$-0.445348\pi$
$83$	−7.41994	−	7.41994i	−0.814444	−	0.814444i	−0.985297	+	0.170852i	$0.945348\pi$
$84$		0			0
$85$		0			0
$86$			8.83415i			0.952611i
$87$		0			0
$88$	1.50531	−	1.50531i	0.160467	−	0.160467i
$89$	12.0677			1.27917			0.639584	−	0.768721i	$-0.279107\pi$
$89$	12.0677			1.27917			0.639584	+	0.768721i	$0.279107\pi$
$90$		0			0
$91$	−7.71883			−0.809153
$92$	−0.984708	+	0.984708i	−0.102663	+	0.102663i
$93$		0			0
$94$			12.1245i			1.25055i
$95$		0			0
$96$		0			0
$97$	−1.48276	−	1.48276i	−0.150551	−	0.150551i	0.627813	−	0.778364i	$-0.283950\pi$
$97$	−1.48276	−	1.48276i	−0.150551	−	0.150551i	−0.778364	+	0.627813i	$0.783950\pi$
$98$	11.7431	+	11.7431i	1.18624	+	1.18624i
$99$		0			0
$100$		0			0
$101$			14.2754i			1.42045i	0.703972	+	0.710227i	$0.251408\pi$
$101$			14.2754i			1.42045i	−0.703972	+	0.710227i	$0.748592\pi$
$102$		0			0
$103$	−7.85936	+	7.85936i	−0.774405	+	0.774405i	−0.978873	−	0.204468i	$-0.934454\pi$
$103$	−7.85936	+	7.85936i	−0.774405	+	0.774405i	0.204468	+	0.978873i	$0.434454\pi$
$104$	1.58865			0.155780
$105$		0			0
$106$	0.145898			0.0141709
$107$	−3.16228	+	3.16228i	−0.305709	+	0.305709i	−0.843242	−	0.537533i	$-0.819356\pi$
$107$	−3.16228	+	3.16228i	−0.305709	+	0.305709i	0.537533	+	0.843242i	$0.319356\pi$
$108$		0			0
$109$		−	9.23607i		−	0.884655i	−0.896854	−	0.442327i	$-0.854153\pi$
$109$		−	9.23607i		−	0.884655i	0.896854	−	0.442327i	$-0.145847\pi$
$110$		0			0
$111$		0			0
$112$	−3.43564	−	3.43564i	−0.324638	−	0.324638i
$113$	−4.60080	−	4.60080i	−0.432806	−	0.432806i	0.456776	−	0.889582i	$-0.349004\pi$
$113$	−4.60080	−	4.60080i	−0.432806	−	0.432806i	−0.889582	+	0.456776i	$0.849004\pi$
$114$		0			0
$115$		0			0
$116$		−	2.31255i		−	0.214715i
$117$		0			0
$118$	9.93559	−	9.93559i	0.914645	−	0.914645i
$119$	15.7232			1.44134
$120$		0			0
$121$	6.46808			0.588007
$122$	9.17729	−	9.17729i	0.830873	−	0.830873i
$123$		0			0
$124$			8.49338i			0.762728i
$125$		0			0
$126$		0			0
$127$	7.33280	+	7.33280i	0.650681	+	0.650681i	0.953157	−	0.302476i	$-0.0978132\pi$
$127$	7.33280	+	7.33280i	0.650681	+	0.650681i	−0.302476	+	0.953157i	$0.597813\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$		0			0
$131$		−	17.8463i		−	1.55924i	−0.626254	−	0.779619i	$-0.715413\pi$
$131$		−	17.8463i		−	1.55924i	0.626254	−	0.779619i	$-0.284587\pi$
$132$		0			0
$133$	−21.4840	+	21.4840i	−1.86290	+	1.86290i
$134$	−4.01200			−0.346584
$135$		0			0
$136$	−3.23607			−0.277491
$137$	14.8399	−	14.8399i	1.26786	−	1.26786i	0.320663	−	0.947193i	$-0.396094\pi$
$137$	14.8399	−	14.8399i	1.26786	−	1.26786i	0.947193	−	0.320663i	$-0.103906\pi$
$138$		0			0
$139$			1.94420i			0.164905i	0.996595	+	0.0824525i	$0.0262753\pi$
$139$			1.94420i			0.164905i	−0.996595	+	0.0824525i	$0.973725\pi$
$140$		0			0
$141$		0			0
$142$	−7.09673	−	7.09673i	−0.595545	−	0.595545i
$143$	−2.39141	−	2.39141i	−0.199980	−	0.199980i
$144$		0			0
$145$		0			0
$146$		−	10.9010i		−	0.902177i
$147$		0			0
$148$	2.05368	−	2.05368i	0.168811	−	0.168811i
$149$	19.2193			1.57451			0.787254	−	0.616629i	$-0.211502\pi$
$149$	19.2193			1.57451			0.787254	+	0.616629i	$0.211502\pi$
$150$		0			0
$151$	−3.96563			−0.322718			−0.161359	−	0.986896i	$-0.551588\pi$
$151$	−3.96563			−0.322718			−0.161359	+	0.986896i	$0.551588\pi$
$152$	4.42172	−	4.42172i	0.358649	−	0.358649i
$153$		0			0
$154$			10.3434i			0.833497i
$155$		0			0
$156$		0			0
$157$	4.68696	+	4.68696i	0.374060	+	0.374060i	0.868954	−	0.494893i	$-0.164793\pi$
$157$	4.68696	+	4.68696i	0.374060	+	0.374060i	−0.494893	+	0.868954i	$0.664793\pi$
$158$	0.0150212	+	0.0150212i	0.00119502	+	0.00119502i
$159$		0			0
$160$		0			0
$161$		−	6.76621i		−	0.533252i
$162$		0			0
$163$	11.2361	−	11.2361i	0.880077	−	0.880077i	−0.113465	−	0.993542i	$-0.536195\pi$
$163$	11.2361	−	11.2361i	0.880077	−	0.880077i	0.993542	+	0.113465i	$0.0361950\pi$
$164$	2.02102			0.157815
$165$		0			0
$166$	−10.4934			−0.814444
$167$	13.0252	−	13.0252i	1.00792	−	1.00792i	0.00795464	−	0.999968i	$-0.497468\pi$
$167$	13.0252	−	13.0252i	1.00792	−	1.00792i	0.999968	−	0.00795464i	$-0.00253207\pi$
$168$		0			0
$169$			10.4762i			0.805861i
$170$		0			0
$171$		0			0
$172$	6.24669	+	6.24669i	0.476306	+	0.476306i
$173$	−7.55669	−	7.55669i	−0.574525	−	0.574525i	0.358865	−	0.933390i	$-0.383164\pi$
$173$	−7.55669	−	7.55669i	−0.574525	−	0.574525i	−0.933390	+	0.358865i	$0.883164\pi$
$174$		0			0
$175$		0			0
$176$		−	2.12883i		−	0.160467i
$177$		0			0
$178$	8.53312	−	8.53312i	0.639584	−	0.639584i
$179$	−0.449248			−0.0335784			−0.0167892	−	0.999859i	$-0.505344\pi$
$179$	−0.449248			−0.0335784			−0.0167892	+	0.999859i	$0.505344\pi$
$180$		0			0
$181$	6.94427			0.516164			0.258082	−	0.966123i	$-0.416910\pi$
$181$	6.94427			0.516164			0.258082	+	0.966123i	$0.416910\pi$
$182$	−5.45803	+	5.45803i	−0.404576	+	0.404576i
$183$		0			0
$184$			1.39259i			0.102663i
$185$		0			0
$186$		0			0
$187$	4.87129	+	4.87129i	0.356224	+	0.356224i
$188$	8.57335	+	8.57335i	0.625276	+	0.625276i
$189$		0			0
$190$		0			0
$191$			6.99226i			0.505942i	0.967474	+	0.252971i	$0.0814077\pi$
$191$			6.99226i			0.505942i	−0.967474	+	0.252971i	$0.918592\pi$
$192$		0			0
$193$	−16.5926	+	16.5926i	−1.19436	+	1.19436i	−0.218534	+	0.975829i	$0.570127\pi$
$193$	−16.5926	+	16.5926i	−1.19436	+	1.19436i	−0.975829	+	0.218534i	$0.929873\pi$
$194$	−2.09694			−0.150551
$195$		0			0
$196$	16.6073			1.18624
$197$	12.6977	−	12.6977i	0.904675	−	0.904675i	−0.0911611	−	0.995836i	$-0.529058\pi$
$197$	12.6977	−	12.6977i	0.904675	−	0.904675i	0.995836	+	0.0911611i	$0.0290578\pi$
$198$		0			0
$199$		−	0.785175i		−	0.0556596i	−0.999613	−	0.0278298i	$-0.991140\pi$
$199$		−	0.785175i		−	0.0556596i	0.999613	−	0.0278298i	$-0.00885964\pi$
$200$		0			0
$201$		0			0
$202$	10.0942	+	10.0942i	0.710227	+	0.710227i
$203$	7.94510	+	7.94510i	0.557637	+	0.557637i
$204$		0			0
$205$		0			0
$206$			11.1148i			0.774405i
$207$		0			0
$208$	1.12334	−	1.12334i	0.0778899	−	0.0778899i
$209$	−13.3121			−0.920819
$210$		0			0
$211$	−7.43758			−0.512024			−0.256012	−	0.966674i	$-0.582409\pi$
$211$	−7.43758			−0.512024			−0.256012	+	0.966674i	$0.582409\pi$
$212$	0.103165	−	0.103165i	0.00708543	−	0.00708543i
$213$		0			0
$214$			4.47214i			0.305709i
$215$		0			0
$216$		0			0
$217$	−29.1802	−	29.1802i	−1.98088	−	1.98088i
$218$	−6.53089	−	6.53089i	−0.442327	−	0.442327i
$219$		0			0
$220$		0			0
$221$			5.14098i			0.345820i
$222$		0			0
$223$	−1.93764	+	1.93764i	−0.129754	+	0.129754i	−0.769001	−	0.639247i	$-0.779246\pi$
$223$	−1.93764	+	1.93764i	−0.129754	+	0.129754i	0.639247	+	0.769001i	$0.279246\pi$
$224$	−4.85873			−0.324638
$225$		0			0
$226$	−6.50651			−0.432806
$227$	−6.86474	+	6.86474i	−0.455629	+	0.455629i	−0.897217	−	0.441589i	$-0.854415\pi$
$227$	−6.86474	+	6.86474i	−0.455629	+	0.455629i	0.441589	+	0.897217i	$0.354415\pi$
$228$		0			0
$229$		−	9.98687i		−	0.659951i	−0.943989	−	0.329976i	$-0.892960\pi$
$229$		−	9.98687i		−	0.659951i	0.943989	−	0.329976i	$-0.107040\pi$
$230$		0			0
$231$		0			0
$232$	−1.63522	−	1.63522i	−0.107357	−	0.107357i
$233$	−1.05032	−	1.05032i	−0.0688088	−	0.0688088i	0.671865	−	0.740674i	$-0.265494\pi$
$233$	−1.05032	−	1.05032i	−0.0688088	−	0.0688088i	−0.740674	+	0.671865i	$0.765494\pi$
$234$		0			0
$235$		0			0
$236$		−	14.0510i		−	0.914645i
$237$		0			0
$238$	11.1180	−	11.1180i	0.720671	−	0.720671i
$239$	−17.2556			−1.11617			−0.558087	−	0.829782i	$-0.688465\pi$
$239$	−17.2556			−1.11617			−0.558087	+	0.829782i	$0.688465\pi$
$240$		0			0
$241$	14.1909			0.914116			0.457058	−	0.889437i	$-0.348903\pi$
$241$	14.1909			0.914116			0.457058	+	0.889437i	$0.348903\pi$
$242$	4.57362	−	4.57362i	0.294004	−	0.294004i
$243$		0			0
$244$		−	12.9786i		−	0.830873i
$245$		0			0
$246$		0			0
$247$	−7.02456	−	7.02456i	−0.446962	−	0.446962i
$248$	6.00573	+	6.00573i	0.381364	+	0.381364i
$249$		0			0
$250$		0			0
$251$			17.1074i			1.07981i	0.841727	+	0.539904i	$0.181539\pi$
$251$			17.1074i			1.07981i	−0.841727	+	0.539904i	$0.818461\pi$
$252$		0			0
$253$	2.09628	−	2.09628i	0.131792	−	0.131792i
$254$	10.3701			0.650681
$255$		0			0
$256$	1.00000			0.0625000
$257$	−6.64338	+	6.64338i	−0.414403	+	0.414403i	−0.883269	−	0.468866i	$-0.844663\pi$
$257$	−6.64338	+	6.64338i	−0.414403	+	0.414403i	0.468866	+	0.883269i	$0.344663\pi$
$258$		0			0
$259$			14.1114i			0.876841i
$260$		0			0
$261$		0			0
$262$	−12.6192	−	12.6192i	−0.779619	−	0.779619i
$263$	−7.41699	−	7.41699i	−0.457351	−	0.457351i	0.440434	−	0.897785i	$-0.354825\pi$
$263$	−7.41699	−	7.41699i	−0.457351	−	0.457351i	−0.897785	+	0.440434i	$0.854825\pi$
$264$		0			0
$265$		0			0
$266$			30.3829i			1.86290i
$267$		0			0
$268$	−2.83692	+	2.83692i	−0.173292	+	0.173292i
$269$	27.6746			1.68735			0.843674	−	0.536856i	$-0.180388\pi$
$269$	27.6746			1.68735			0.843674	+	0.536856i	$0.180388\pi$
$270$		0			0
$271$	−3.24920			−0.197375			−0.0986873	−	0.995118i	$-0.531464\pi$
$271$	−3.24920			−0.197375			−0.0986873	+	0.995118i	$0.531464\pi$
$272$	−2.28825	+	2.28825i	−0.138745	+	0.138745i
$273$		0			0
$274$		−	20.9868i		−	1.26786i
$275$		0			0
$276$		0			0
$277$	−13.8076	−	13.8076i	−0.829619	−	0.829619i	0.157845	−	0.987464i	$-0.449545\pi$
$277$	−13.8076	−	13.8076i	−0.829619	−	0.829619i	−0.987464	+	0.157845i	$0.949545\pi$
$278$	1.37476	+	1.37476i	0.0824525	+	0.0824525i
$279$		0			0
$280$		0			0
$281$			21.4606i			1.28023i	0.768279	+	0.640115i	$0.221113\pi$
$281$			21.4606i			1.28023i	−0.768279	+	0.640115i	$0.778887\pi$
$282$		0			0
$283$	−4.65658	+	4.65658i	−0.276805	+	0.276805i	−0.831832	−	0.555027i	$-0.812708\pi$
$283$	−4.65658	+	4.65658i	−0.276805	+	0.276805i	0.555027	+	0.831832i	$0.312708\pi$
$284$	−10.0363			−0.595545
$285$		0			0
$286$	−3.38197			−0.199980
$287$	−6.94352	+	6.94352i	−0.409863	+	0.409863i
$288$		0			0
$289$			6.52786i			0.383992i
$290$		0			0
$291$		0			0
$292$	−7.70820	−	7.70820i	−0.451089	−	0.451089i
$293$	−12.7598	−	12.7598i	−0.745435	−	0.745435i	0.228183	−	0.973618i	$-0.426721\pi$
$293$	−12.7598	−	12.7598i	−0.745435	−	0.745435i	−0.973618	+	0.228183i	$0.926721\pi$
$294$		0			0
$295$		0			0
$296$		−	2.90434i		−	0.168811i
$297$		0			0
$298$	13.5901	−	13.5901i	0.787254	−	0.787254i
$299$	2.21233			0.127943
$300$		0			0
$301$	−42.9228			−2.47403
$302$	−2.80412	+	2.80412i	−0.161359	+	0.161359i
$303$		0			0
$304$		−	6.25325i		−	0.358649i
$305$		0			0
$306$		0			0
$307$	12.4270	+	12.4270i	0.709248	+	0.709248i	0.966377	−	0.257129i	$-0.0827765\pi$
$307$	12.4270	+	12.4270i	0.709248	+	0.709248i	−0.257129	+	0.966377i	$0.582777\pi$
$308$	7.31391	+	7.31391i	0.416748	+	0.416748i
$309$		0			0
$310$		0			0
$311$		−	24.6305i		−	1.39667i	−0.715772	−	0.698334i	$-0.753925\pi$
$311$		−	24.6305i		−	1.39667i	0.715772	−	0.698334i	$-0.246075\pi$
$312$		0			0
$313$	8.97625	−	8.97625i	0.507368	−	0.507368i	−0.406350	−	0.913718i	$-0.633199\pi$
$313$	8.97625	−	8.97625i	0.507368	−	0.507368i	0.913718	+	0.406350i	$0.133199\pi$
$314$	6.62836			0.374060
$315$		0			0
$316$	0.0212431			0.00119502
$317$	6.24392	−	6.24392i	0.350694	−	0.350694i	−0.509674	−	0.860368i	$-0.670234\pi$
$317$	6.24392	−	6.24392i	0.350694	−	0.350694i	0.860368	+	0.509674i	$0.170234\pi$
$318$		0			0
$319$			4.92303i			0.275637i
$320$		0			0
$321$		0			0
$322$	−4.78444	−	4.78444i	−0.266626	−	0.266626i
$323$	14.3090	+	14.3090i	0.796173	+	0.796173i
$324$		0			0
$325$		0			0
$326$		−	15.8902i		−	0.880077i
$327$		0			0
$328$	1.42908	−	1.42908i	0.0789077	−	0.0789077i
$329$	−58.9099			−3.24781
$330$		0			0
$331$	34.7506			1.91006			0.955032	−	0.296502i	$-0.0958201\pi$
$331$	34.7506			1.91006			0.955032	+	0.296502i	$0.0958201\pi$
$332$	−7.41994	+	7.41994i	−0.407222	+	0.407222i
$333$		0			0
$334$		−	18.4205i		−	1.00792i
$335$		0			0
$336$		0			0
$337$	−23.6245	−	23.6245i	−1.28691	−	1.28691i	−0.936655	−	0.350252i	$-0.886096\pi$
$337$	−23.6245	−	23.6245i	−1.28691	−	1.28691i	−0.350252	−	0.936655i	$-0.613904\pi$
$338$	7.40779	+	7.40779i	0.402931	+	0.402931i
$339$		0			0
$340$		0			0
$341$		−	18.0810i		−	0.979139i
$342$		0			0
$343$	−33.0073	+	33.0073i	−1.78222	+	1.78222i
$344$	8.83415			0.476306
$345$		0			0
$346$	−10.6868			−0.574525
$347$	−15.9631	+	15.9631i	−0.856945	+	0.856945i	−0.990977	−	0.134032i	$-0.957207\pi$
$347$	−15.9631	+	15.9631i	−0.856945	+	0.856945i	0.134032	+	0.990977i	$0.457207\pi$
$348$		0			0
$349$		−	28.7343i		−	1.53811i	−0.639180	−	0.769057i	$-0.720726\pi$
$349$		−	28.7343i		−	1.53811i	0.639180	−	0.769057i	$-0.279274\pi$
$350$		0			0
$351$		0			0
$352$	−1.50531	−	1.50531i	−0.0802333	−	0.0802333i
$353$	−14.6521	−	14.6521i	−0.779853	−	0.779853i	0.199952	−	0.979806i	$-0.435921\pi$
$353$	−14.6521	−	14.6521i	−0.779853	−	0.779853i	−0.979806	+	0.199952i	$0.935921\pi$
$354$		0			0
$355$		0			0
$356$		−	12.0677i		−	0.639584i
$357$		0			0
$358$	−0.317666	+	0.317666i	−0.0167892	+	0.0167892i
$359$	−32.7724			−1.72966			−0.864831	−	0.502063i	$-0.832574\pi$
$359$	−32.7724			−1.72966			−0.864831	+	0.502063i	$0.832574\pi$
$360$		0			0
$361$	−20.1032			−1.05806
$362$	4.91034	−	4.91034i	0.258082	−	0.258082i
$363$		0			0
$364$			7.71883i			0.404576i
$365$		0			0
$366$		0			0
$367$	7.20808	+	7.20808i	0.376259	+	0.376259i	0.869750	−	0.493492i	$-0.164280\pi$
$367$	7.20808	+	7.20808i	0.376259	+	0.376259i	−0.493492	+	0.869750i	$0.664280\pi$
$368$	0.984708	+	0.984708i	0.0513315	+	0.0513315i
$369$		0			0
$370$		0			0
$371$			0.708880i			0.0368032i
$372$		0			0
$373$	9.89465	−	9.89465i	0.512326	−	0.512326i	−0.402913	−	0.915238i	$-0.632002\pi$
$373$	9.89465	−	9.89465i	0.512326	−	0.512326i	0.915238	+	0.402913i	$0.132002\pi$
$374$	6.88904			0.356224
$375$		0			0
$376$	12.1245			0.625276
$377$	−2.59779	+	2.59779i	−0.133793	+	0.133793i
$378$		0			0
$379$		−	18.1670i		−	0.933178i	−0.884474	−	0.466589i	$-0.845483\pi$
$379$		−	18.1670i		−	0.933178i	0.884474	−	0.466589i	$-0.154517\pi$
$380$		0			0
$381$		0			0
$382$	4.94427	+	4.94427i	0.252971	+	0.252971i
$383$	−24.3417	−	24.3417i	−1.24380	−	1.24380i	−0.958411	−	0.285391i	$-0.907877\pi$
$383$	−24.3417	−	24.3417i	−1.24380	−	1.24380i	−0.285391	−	0.958411i	$-0.592123\pi$
$384$		0			0
$385$		0			0
$386$			23.4655i			1.19436i
$387$		0			0
$388$	−1.48276	+	1.48276i	−0.0752756	+	0.0752756i
$389$	−19.3711			−0.982156			−0.491078	−	0.871116i	$-0.663397\pi$
$389$	−19.3711			−0.982156			−0.491078	+	0.871116i	$0.663397\pi$
$390$		0			0
$391$	−4.50651			−0.227904
$392$	11.7431	−	11.7431i	0.593118	−	0.593118i
$393$		0			0
$394$		−	17.9573i		−	0.904675i
$395$		0			0
$396$		0			0
$397$	−2.74470	−	2.74470i	−0.137752	−	0.137752i	0.634868	−	0.772620i	$-0.281054\pi$
$397$	−2.74470	−	2.74470i	−0.137752	−	0.137752i	−0.772620	+	0.634868i	$0.781054\pi$
$398$	−0.555203	−	0.555203i	−0.0278298	−	0.0278298i
$399$		0			0
$400$		0			0
$401$		−	2.95514i		−	0.147573i	−0.997274	−	0.0737863i	$-0.976492\pi$
$401$		−	2.95514i		−	0.147573i	0.997274	−	0.0737863i	$-0.0235083\pi$
$402$		0			0
$403$	9.54099	−	9.54099i	0.475271	−	0.475271i
$404$	14.2754			0.710227
$405$		0			0
$406$	11.2361			0.557637
$407$	−4.37193	+	4.37193i	−0.216709	+	0.216709i
$408$		0			0
$409$			25.2968i			1.25084i	0.780286	+	0.625422i	$0.215073\pi$
$409$			25.2968i			1.25084i	−0.780286	+	0.625422i	$0.784927\pi$
$410$		0			0
$411$		0			0
$412$	7.85936	+	7.85936i	0.387203	+	0.387203i
$413$	48.2744	+	48.2744i	2.37543	+	2.37543i
$414$		0			0
$415$		0			0
$416$		−	1.58865i		−	0.0778899i
$417$		0			0
$418$	−9.41309	+	9.41309i	−0.460409	+	0.460409i
$419$	−12.6095			−0.616016			−0.308008	−	0.951384i	$-0.599662\pi$
$419$	−12.6095			−0.616016			−0.308008	+	0.951384i	$0.599662\pi$
$420$		0			0
$421$	13.4933			0.657622			0.328811	−	0.944396i	$-0.393352\pi$
$421$	13.4933			0.657622			0.328811	+	0.944396i	$0.393352\pi$
$422$	−5.25916	+	5.25916i	−0.256012	+	0.256012i
$423$		0			0
$424$		−	0.145898i		−	0.00708543i
$425$		0			0
$426$		0			0
$427$	44.5900	+	44.5900i	2.15786	+	2.15786i
$428$	3.16228	+	3.16228i	0.152854	+	0.152854i
$429$		0			0
$430$		0			0
$431$			26.4910i			1.27603i	0.770026	+	0.638013i	$0.220243\pi$
$431$			26.4910i			1.27603i	−0.770026	+	0.638013i	$0.779757\pi$
$432$		0			0
$433$	−11.3885	+	11.3885i	−0.547298	+	0.547298i	−0.925658	−	0.378360i	$-0.876488\pi$
$433$	−11.3885	+	11.3885i	−0.547298	+	0.547298i	0.378360	+	0.925658i	$0.376488\pi$
$434$	−41.2671			−1.98088
$435$		0			0
$436$	−9.23607			−0.442327
$437$	6.15763	−	6.15763i	0.294559	−	0.294559i
$438$		0			0
$439$		−	17.0049i		−	0.811600i	−0.913962	−	0.405800i	$-0.866993\pi$
$439$		−	17.0049i		−	0.811600i	0.913962	−	0.405800i	$-0.133007\pi$
$440$		0			0
$441$		0			0
$442$	3.63522	+	3.63522i	0.172910	+	0.172910i
$443$	−15.6839	−	15.6839i	−0.745163	−	0.745163i	0.228403	−	0.973567i	$-0.426649\pi$
$443$	−15.6839	−	15.6839i	−0.745163	−	0.745163i	−0.973567	+	0.228403i	$0.926649\pi$
$444$		0			0
$445$		0			0
$446$			2.74023i			0.129754i
$447$		0			0
$448$	−3.43564	+	3.43564i	−0.162319	+	0.162319i
$449$	−17.3222			−0.817484			−0.408742	−	0.912650i	$-0.634032\pi$
$449$	−17.3222			−0.817484			−0.408742	+	0.912650i	$0.634032\pi$
$450$		0			0
$451$	−4.30242			−0.202593
$452$	−4.60080	+	4.60080i	−0.216403	+	0.216403i
$453$		0			0
$454$			9.70820i			0.455629i
$455$		0			0
$456$		0			0
$457$	15.1246	+	15.1246i	0.707499	+	0.707499i	0.966009	−	0.258509i	$-0.0832313\pi$
$457$	15.1246	+	15.1246i	0.707499	+	0.707499i	−0.258509	+	0.966009i	$0.583231\pi$
$458$	−7.06178	−	7.06178i	−0.329976	−	0.329976i
$459$		0			0
$460$		0			0
$461$		−	18.2142i		−	0.848321i	−0.905587	−	0.424161i	$-0.860569\pi$
$461$		−	18.2142i		−	0.848321i	0.905587	−	0.424161i	$-0.139431\pi$
$462$		0			0
$463$	19.3116	−	19.3116i	0.897484	−	0.897484i	−0.0977288	−	0.995213i	$-0.531158\pi$
$463$	19.3116	−	19.3116i	0.897484	−	0.897484i	0.995213	+	0.0977288i	$0.0311578\pi$
$464$	−2.31255			−0.107357
$465$		0			0
$466$	−1.48538			−0.0688088
$467$	22.8767	−	22.8767i	1.05861	−	1.05861i	0.0604362	−	0.998172i	$-0.480751\pi$
$467$	22.8767	−	22.8767i	1.05861	−	1.05861i	0.998172	−	0.0604362i	$-0.0192492\pi$
$468$		0			0
$469$		−	19.4933i		−	0.900115i
$470$		0			0
$471$		0			0
$472$	−9.93559	−	9.93559i	−0.457322	−	0.457322i
$473$	−13.2981	−	13.2981i	−0.611449	−	0.611449i
$474$		0			0
$475$		0			0
$476$		−	15.7232i		−	0.720671i
$477$		0			0
$478$	−12.2016	+	12.2016i	−0.558087	+	0.558087i
$479$	−4.72832			−0.216042			−0.108021	−	0.994149i	$-0.534451\pi$
$479$	−4.72832			−0.216042			−0.108021	+	0.994149i	$0.534451\pi$
$480$		0			0
$481$	−4.61398			−0.210379
$482$	10.0345	−	10.0345i	0.457058	−	0.457058i
$483$		0			0
$484$		−	6.46808i		−	0.294004i
$485$		0			0
$486$		0			0
$487$	5.41348	+	5.41348i	0.245308	+	0.245308i	0.819042	−	0.573734i	$-0.194506\pi$
$487$	5.41348	+	5.41348i	0.245308	+	0.245308i	−0.573734	+	0.819042i	$0.694506\pi$
$488$	−9.17729	−	9.17729i	−0.415436	−	0.415436i
$489$		0			0
$490$		0			0
$491$			29.3408i			1.32413i	0.749445	+	0.662066i	$0.230320\pi$
$491$			29.3408i			1.32413i	−0.749445	+	0.662066i	$0.769680\pi$
$492$		0			0
$493$	5.29168	−	5.29168i	0.238325	−	0.238325i
$494$	−9.93423			−0.446962
$495$		0			0
$496$	8.49338			0.381364
$497$	34.4811	−	34.4811i	1.54669	−	1.54669i
$498$		0			0
$499$		−	16.1007i		−	0.720765i	−0.932805	−	0.360383i	$-0.882646\pi$
$499$		−	16.1007i		−	0.720765i	0.932805	−	0.360383i	$-0.117354\pi$
$500$		0			0
$501$		0			0
$502$	12.0967	+	12.0967i	0.539904	+	0.539904i
$503$	−2.99540	−	2.99540i	−0.133558	−	0.133558i	0.637167	−	0.770726i	$-0.280106\pi$
$503$	−2.99540	−	2.99540i	−0.133558	−	0.133558i	−0.770726	+	0.637167i	$0.780106\pi$
$504$		0			0
$505$		0			0
$506$		−	2.96458i		−	0.131792i
$507$		0			0
$508$	7.33280	−	7.33280i	0.325340	−	0.325340i
$509$	14.0598			0.623189			0.311594	−	0.950215i	$-0.399137\pi$
$509$	14.0598			0.623189			0.311594	+	0.950215i	$0.399137\pi$
$510$		0			0
$511$	52.9653			2.34305
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			9.39516i			0.414403i
$515$		0			0
$516$		0			0
$517$	−18.2512	−	18.2512i	−0.802687	−	0.802687i
$518$	9.97828	+	9.97828i	0.438420	+	0.438420i
$519$		0			0
$520$		0			0
$521$		−	15.4363i		−	0.676275i	−0.941097	−	0.338137i	$-0.890203\pi$
$521$		−	15.4363i		−	0.676275i	0.941097	−	0.338137i	$-0.109797\pi$
$522$		0			0
$523$	−13.2442	+	13.2442i	−0.579128	+	0.579128i	−0.934663	−	0.355535i	$-0.884299\pi$
$523$	−13.2442	+	13.2442i	−0.579128	+	0.579128i	0.355535	+	0.934663i	$0.384299\pi$
$524$	−17.8463			−0.779619
$525$		0			0
$526$	−10.4892			−0.457351
$527$	−19.4349	+	19.4349i	−0.846599	+	0.846599i
$528$		0			0
$529$		−	21.0607i		−	0.915683i
$530$		0			0
$531$		0			0
$532$	21.4840	+	21.4840i	0.931448	+	0.931448i
$533$	−2.27031	−	2.27031i	−0.0983379	−	0.0983379i
$534$		0			0
$535$		0			0
$536$			4.01200i			0.173292i
$537$		0			0
$538$	19.5689	−	19.5689i	0.843674	−	0.843674i
$539$	−35.3541			−1.52281
$540$		0			0
$541$	−2.51964			−0.108328			−0.0541638	−	0.998532i	$-0.517249\pi$
$541$	−2.51964			−0.108328			−0.0541638	+	0.998532i	$0.517249\pi$
$542$	−2.29753	+	2.29753i	−0.0986873	+	0.0986873i
$543$		0			0
$544$			3.23607i			0.138745i
$545$		0			0
$546$		0			0
$547$	−9.30094	−	9.30094i	−0.397679	−	0.397679i	0.479734	−	0.877414i	$-0.340733\pi$
$547$	−9.30094	−	9.30094i	−0.397679	−	0.397679i	−0.877414	+	0.479734i	$0.840733\pi$
$548$	−14.8399	−	14.8399i	−0.633928	−	0.633928i
$549$		0			0
$550$		0			0
$551$			14.4610i			0.616058i
$552$		0			0
$553$	−0.0729839	+	0.0729839i	−0.00310359	+	0.00310359i
$554$	−19.5269			−0.829619
$555$		0			0
$556$	1.94420			0.0824525
$557$	−3.74765	+	3.74765i	−0.158793	+	0.158793i	−0.782032	−	0.623239i	$-0.785817\pi$
$557$	−3.74765	+	3.74765i	−0.158793	+	0.158793i	0.623239	+	0.782032i	$0.285817\pi$
$558$		0			0
$559$		−	14.0344i		−	0.593591i
$560$		0			0
$561$		0			0
$562$	15.1749	+	15.1749i	0.640115	+	0.640115i
$563$	14.2975	+	14.2975i	0.602568	+	0.602568i	0.940993	−	0.338425i	$-0.109894\pi$
$563$	14.2975	+	14.2975i	0.602568	+	0.602568i	−0.338425	+	0.940993i	$0.609894\pi$
$564$		0			0
$565$		0			0
$566$			6.58539i			0.276805i
$567$		0			0
$568$	−7.09673	+	7.09673i	−0.297772	+	0.297772i
$569$	−19.1723			−0.803745			−0.401872	−	0.915696i	$-0.631640\pi$
$569$	−19.1723			−0.803745			−0.401872	+	0.915696i	$0.631640\pi$
$570$		0			0
$571$	5.24024			0.219297			0.109649	−	0.993970i	$-0.465027\pi$
$571$	5.24024			0.219297			0.109649	+	0.993970i	$0.465027\pi$
$572$	−2.39141	+	2.39141i	−0.0999899	+	0.0999899i
$573$		0			0
$574$			9.81962i			0.409863i
$575$		0			0
$576$		0			0
$577$	25.1778	+	25.1778i	1.04817	+	1.04817i	0.998780	+	0.0493872i	$0.0157268\pi$
$577$	25.1778	+	25.1778i	1.04817	+	1.04817i	0.0493872	+	0.998780i	$0.484273\pi$
$578$	4.61590	+	4.61590i	0.191996	+	0.191996i
$579$		0			0
$580$		0			0
$581$		−	50.9845i		−	2.11520i
$582$		0			0
$583$	−0.219622	+	0.219622i	−0.00909581	+	0.00909581i
$584$	−10.9010			−0.451089
$585$		0			0
$586$	−18.0451			−0.745435
$587$	−9.96886	+	9.96886i	−0.411459	+	0.411459i	−0.882247	−	0.470788i	$-0.843970\pi$
$587$	−9.96886	+	9.96886i	−0.411459	+	0.411459i	0.470788	+	0.882247i	$0.343970\pi$
$588$		0			0
$589$		−	53.1113i		−	2.18841i
$590$		0			0
$591$		0			0
$592$	−2.05368	−	2.05368i	−0.0844056	−	0.0844056i
$593$	−1.73304	−	1.73304i	−0.0711675	−	0.0711675i	0.670627	−	0.741795i	$-0.266025\pi$
$593$	−1.73304	−	1.73304i	−0.0711675	−	0.0711675i	−0.741795	+	0.670627i	$0.766025\pi$
$594$		0			0
$595$		0			0
$596$		−	19.2193i		−	0.787254i
$597$		0			0
$598$	1.56436	−	1.56436i	0.0639713	−	0.0639713i
$599$	30.3812			1.24134			0.620671	−	0.784071i	$-0.286860\pi$
$599$	30.3812			1.24134			0.620671	+	0.784071i	$0.286860\pi$
$600$		0			0
$601$	5.96283			0.243229			0.121614	−	0.992577i	$-0.461193\pi$
$601$	5.96283			0.243229			0.121614	+	0.992577i	$0.461193\pi$
$602$	−30.3510	+	30.3510i	−1.23701	+	1.23701i
$603$		0			0
$604$			3.96563i			0.161359i
$605$		0			0
$606$		0			0
$607$	24.1052	+	24.1052i	0.978400	+	0.978400i	0.999772	−	0.0213720i	$-0.00680343\pi$
$607$	24.1052	+	24.1052i	0.978400	+	0.978400i	−0.0213720	+	0.999772i	$0.506803\pi$
$608$	−4.42172	−	4.42172i	−0.179324	−	0.179324i
$609$		0			0
$610$		0			0
$611$		−	19.2616i		−	0.779243i
$612$		0			0
$613$	3.71763	−	3.71763i	0.150154	−	0.150154i	−0.628033	−	0.778187i	$-0.716140\pi$
$613$	3.71763	−	3.71763i	0.150154	−	0.150154i	0.778187	+	0.628033i	$0.216140\pi$
$614$	17.5745			0.709248
$615$		0			0
$616$	10.3434			0.416748
$617$	−24.8030	+	24.8030i	−0.998531	+	0.998531i	−0.999999	−	0.00146755i	$-0.999533\pi$
$617$	−24.8030	+	24.8030i	−0.998531	+	0.998531i	0.00146755	+	0.999999i	$0.499533\pi$
$618$		0			0
$619$		−	16.3739i		−	0.658121i	−0.944309	−	0.329060i	$-0.893268\pi$
$619$		−	16.3739i		−	0.658121i	0.944309	−	0.329060i	$-0.106732\pi$
$620$		0			0
$621$		0			0
$622$	−17.4164	−	17.4164i	−0.698334	−	0.698334i
$623$	41.4602	+	41.4602i	1.66107	+	1.66107i
$624$		0			0
$625$		0			0
$626$		−	12.6943i		−	0.507368i
$627$		0			0
$628$	4.68696	−	4.68696i	0.187030	−	0.187030i
$629$	9.39864			0.374748
$630$		0			0
$631$	−38.0129			−1.51327			−0.756635	−	0.653838i	$-0.773158\pi$
$631$	−38.0129			−1.51327			−0.756635	+	0.653838i	$0.773158\pi$
$632$	0.0150212	−	0.0150212i	0.000597510	−	0.000597510i
$633$		0			0
$634$		−	8.83024i		−	0.350694i
$635$		0			0
$636$		0			0
$637$	−18.6557	−	18.6557i	−0.739167	−	0.739167i
$638$	3.48111	+	3.48111i	0.137818	+	0.137818i
$639$		0			0
$640$		0			0
$641$		−	40.6360i		−	1.60502i	−0.596636	−	0.802512i	$-0.703496\pi$
$641$		−	40.6360i		−	1.60502i	0.596636	−	0.802512i	$-0.296504\pi$
$642$		0			0
$643$	18.5753	−	18.5753i	0.732536	−	0.732536i	−0.238585	−	0.971122i	$-0.576684\pi$
$643$	18.5753	−	18.5753i	0.732536	−	0.732536i	0.971122	+	0.238585i	$0.0766836\pi$
$644$	−6.76621			−0.266626
$645$		0			0
$646$	20.2360			0.796173
$647$	−14.2846	+	14.2846i	−0.561587	+	0.561587i	−0.929758	−	0.368171i	$-0.879984\pi$
$647$	−14.2846	+	14.2846i	−0.561587	+	0.561587i	0.368171	+	0.929758i	$0.379984\pi$
$648$		0			0
$649$			29.9123i			1.17416i
$650$		0			0
$651$		0			0
$652$	−11.2361	−	11.2361i	−0.440038	−	0.440038i
$653$	4.87848	+	4.87848i	0.190910	+	0.190910i	0.796089	−	0.605179i	$-0.206899\pi$
$653$	4.87848	+	4.87848i	0.190910	+	0.190910i	−0.605179	+	0.796089i	$0.706899\pi$
$654$		0			0
$655$		0			0
$656$		−	2.02102i		−	0.0789077i
$657$		0			0
$658$	−41.6556	+	41.6556i	−1.62390	+	1.62390i
$659$	26.5080			1.03260			0.516302	−	0.856407i	$-0.327308\pi$
$659$	26.5080			1.03260			0.516302	+	0.856407i	$0.327308\pi$
$660$		0			0
$661$	−23.3048			−0.906452			−0.453226	−	0.891396i	$-0.649727\pi$
$661$	−23.3048			−0.906452			−0.453226	+	0.891396i	$0.649727\pi$
$662$	24.5724	−	24.5724i	0.955032	−	0.955032i
$663$		0			0
$664$			10.4934i			0.407222i
$665$		0			0
$666$		0			0
$667$	−2.27719	−	2.27719i	−0.0881730	−	0.0881730i
$668$	−13.0252	−	13.0252i	−0.503961	−	0.503961i
$669$		0			0
$670$		0			0
$671$			27.6293i			1.06662i
$672$		0			0
$673$	23.4933	−	23.4933i	0.905599	−	0.905599i	−0.0903144	−	0.995913i	$-0.528787\pi$
$673$	23.4933	−	23.4933i	0.905599	−	0.905599i	0.995913	+	0.0903144i	$0.0287872\pi$
$674$	−33.4101			−1.28691
$675$		0			0
$676$	10.4762			0.402931
$677$	−16.0392	+	16.0392i	−0.616438	+	0.616438i	−0.944616	−	0.328178i	$-0.893565\pi$
$677$	−16.0392	+	16.0392i	−0.616438	+	0.616438i	0.328178	+	0.944616i	$0.393565\pi$
$678$		0			0
$679$		−	10.1885i		−	0.390997i
$680$		0			0
$681$		0			0
$682$	−12.7852	−	12.7852i	−0.489570	−	0.489570i
$683$	−2.46099	−	2.46099i	−0.0941671	−	0.0941671i	0.658454	−	0.752621i	$-0.271211\pi$
$683$	−2.46099	−	2.46099i	−0.0941671	−	0.0941671i	−0.752621	+	0.658454i	$0.771211\pi$
$684$		0			0
$685$		0			0
$686$			46.6793i			1.78222i
$687$		0			0
$688$	6.24669	−	6.24669i	0.238153	−	0.238153i
$689$	−0.231781			−0.00883015
$690$		0			0
$691$	21.8326			0.830550			0.415275	−	0.909696i	$-0.363685\pi$
$691$	21.8326			0.830550			0.415275	+	0.909696i	$0.363685\pi$
$692$	−7.55669	+	7.55669i	−0.287262	+	0.287262i
$693$		0			0
$694$			22.5753i			0.856945i
$695$		0			0
$696$		0			0
$697$	4.62460	+	4.62460i	0.175169	+	0.175169i
$698$	−20.3183	−	20.3183i	−0.769057	−	0.769057i
$699$		0			0
$700$		0			0
$701$			47.5185i			1.79475i	0.441271	+	0.897374i	$0.354528\pi$
$701$			47.5185i			1.79475i	−0.441271	+	0.897374i	$0.645472\pi$
$702$		0			0
$703$	−12.8422	+	12.8422i	−0.484352	+	0.484352i
$704$	−2.12883			−0.0802333
$705$		0			0
$706$	−20.7212			−0.779853
$707$	−49.0452	+	49.0452i	−1.84453	+	1.84453i
$708$		0			0
$709$		−	28.0179i		−	1.05224i	−0.850412	−	0.526118i	$-0.823647\pi$
$709$		−	28.0179i		−	1.05224i	0.850412	−	0.526118i	$-0.176353\pi$
$710$		0			0
$711$		0			0
$712$	−8.53312	−	8.53312i	−0.319792	−	0.319792i
$713$	8.36350	+	8.36350i	0.313216	+	0.313216i
$714$		0			0
$715$		0			0
$716$			0.449248i			0.0167892i
$717$		0			0
$718$	−23.1736	+	23.1736i	−0.864831	+	0.864831i
$719$	−37.9079			−1.41373			−0.706863	−	0.707350i	$-0.749890\pi$
$719$	−37.9079			−1.41373			−0.706863	+	0.707350i	$0.749890\pi$
$720$		0			0
$721$	−54.0039			−2.01121
$722$	−14.2151	+	14.2151i	−0.529031	+	0.529031i
$723$		0			0
$724$		−	6.94427i		−	0.258082i
$725$		0			0
$726$		0			0
$727$	29.5257	+	29.5257i	1.09505	+	1.09505i	0.994981	+	0.100067i	$0.0319057\pi$
$727$	29.5257	+	29.5257i	1.09505	+	1.09505i	0.100067	+	0.994981i	$0.468094\pi$
$728$	5.45803	+	5.45803i	0.202288	+	0.202288i
$729$		0			0
$730$		0			0
$731$			28.5879i			1.05736i
$732$		0			0
$733$	5.56350	−	5.56350i	0.205493	−	0.205493i	−0.596856	−	0.802349i	$-0.703584\pi$
$733$	5.56350	−	5.56350i	0.205493	−	0.205493i	0.802349	+	0.596856i	$0.203584\pi$
$734$	10.1938			0.376259
$735$		0			0
$736$	1.39259			0.0513315
$737$	6.03931	−	6.03931i	0.222461	−	0.222461i
$738$		0			0
$739$		−	14.2270i		−	0.523349i	−0.965156	−	0.261674i	$-0.915725\pi$
$739$		−	14.2270i		−	0.523349i	0.965156	−	0.261674i	$-0.0842746\pi$
$740$		0			0
$741$		0			0
$742$	0.501254	+	0.501254i	0.0184016	+	0.0184016i
$743$	−28.6574	−	28.6574i	−1.05134	−	1.05134i	−0.998609	−	0.0527299i	$-0.983208\pi$
$743$	−28.6574	−	28.6574i	−1.05134	−	1.05134i	−0.0527299	−	0.998609i	$-0.516792\pi$
$744$		0			0
$745$		0			0
$746$		−	13.9931i		−	0.512326i
$747$		0			0
$748$	4.87129	−	4.87129i	0.178112	−	0.178112i
$749$	−21.7289			−0.793957
$750$		0			0
$751$	22.2016			0.810147			0.405074	−	0.914284i	$-0.367246\pi$
$751$	22.2016			0.810147			0.405074	+	0.914284i	$0.367246\pi$
$752$	8.57335	−	8.57335i	0.312638	−	0.312638i
$753$		0			0
$754$			3.67383i			0.133793i
$755$		0			0
$756$		0			0
$757$	−27.6535	−	27.6535i	−1.00508	−	1.00508i	−0.999987	−	0.00509620i	$-0.998378\pi$
$757$	−27.6535	−	27.6535i	−1.00508	−	1.00508i	−0.00509620	−	0.999987i	$-0.501622\pi$
$758$	−12.8460	−	12.8460i	−0.466589	−	0.466589i
$759$		0			0
$760$		0			0
$761$			26.6816i			0.967207i	0.875287	+	0.483603i	$0.160672\pi$
$761$			26.6816i			0.967207i	−0.875287	+	0.483603i	$0.839328\pi$
$762$		0			0
$763$	31.7318	−	31.7318i	1.14877	−	1.14877i
$764$	6.99226			0.252971
$765$		0			0
$766$	−34.4243			−1.24380
$767$	−15.7842	+	15.7842i	−0.569933	+	0.569933i
$768$		0			0
$769$			27.4534i			0.989993i	0.868895	+	0.494997i	$0.164831\pi$
$769$			27.4534i			0.989993i	−0.868895	+	0.494997i	$0.835169\pi$
$770$		0			0
$771$		0			0
$772$	16.5926	+	16.5926i	0.597181	+	0.597181i
$773$	6.79730	+	6.79730i	0.244482	+	0.244482i	0.818701	−	0.574219i	$-0.194694\pi$
$773$	6.79730	+	6.79730i	0.244482	+	0.244482i	−0.574219	+	0.818701i	$0.694694\pi$
$774$		0			0
$775$		0			0
$776$			2.09694i			0.0752756i
$777$		0			0
$778$	−13.6975	+	13.6975i	−0.491078	+	0.491078i
$779$	−12.6380			−0.452802
$780$		0			0
$781$	21.3656			0.764521
$782$	−3.18658	+	3.18658i	−0.113952	+	0.113952i
$783$		0			0
$784$		−	16.6073i		−	0.593118i
$785$		0			0
$786$		0			0
$787$	−16.3247	−	16.3247i	−0.581912	−	0.581912i	0.353516	−	0.935428i	$-0.384986\pi$
$787$	−16.3247	−	16.3247i	−0.581912	−	0.581912i	−0.935428	+	0.353516i	$0.884986\pi$
$788$	−12.6977	−	12.6977i	−0.452338	−	0.452338i
$789$		0			0
$790$		0			0
$791$		−	31.6134i		−	1.12404i
$792$		0			0
$793$	−14.5795	+	14.5795i	−0.517733	+	0.517733i
$794$	−3.88159			−0.137752
$795$		0			0
$796$	−0.785175			−0.0278298
$797$	35.8897	−	35.8897i	1.27128	−	1.27128i	0.325859	−	0.945418i	$-0.394346\pi$
$797$	35.8897	−	35.8897i	1.27128	−	1.27128i	0.945418	−	0.325859i	$-0.105654\pi$
$798$		0			0
$799$			39.2358i			1.38806i
$800$		0			0
$801$		0			0
$802$	−2.08960	−	2.08960i	−0.0737863	−	0.0737863i
$803$	16.4095	+	16.4095i	0.579077	+	0.579077i
$804$		0			0
$805$		0			0
$806$		−	13.4930i		−	0.475271i
$807$		0			0
$808$	10.0942	−	10.0942i	0.355114	−	0.355114i
$809$	37.7971			1.32888			0.664438	−	0.747344i	$-0.268671\pi$
$809$	37.7971			1.32888			0.664438	+	0.747344i	$0.268671\pi$
$810$		0			0
$811$	45.5409			1.59916			0.799580	−	0.600560i	$-0.205056\pi$
$811$	45.5409			1.59916			0.799580	+	0.600560i	$0.205056\pi$
$812$	7.94510	−	7.94510i	0.278818	−	0.278818i
$813$		0			0
$814$			6.18285i			0.216709i
$815$		0			0
$816$		0			0
$817$	−39.0621	−	39.0621i	−1.36661	−	1.36661i
$818$	17.8875	+	17.8875i	0.625422	+	0.625422i
$819$		0			0
$820$		0			0
$821$			18.3060i			0.638883i	0.947606	+	0.319441i	$0.103495\pi$
$821$			18.3060i			0.638883i	−0.947606	+	0.319441i	$0.896505\pi$
$822$		0			0
$823$	−12.1305	+	12.1305i	−0.422844	+	0.422844i	−0.886182	−	0.463338i	$-0.846652\pi$
$823$	−12.1305	+	12.1305i	−0.422844	+	0.422844i	0.463338	+	0.886182i	$0.346652\pi$
$824$	11.1148			0.387203
$825$		0			0
$826$	68.2703			2.37543
$827$	22.5033	−	22.5033i	0.782516	−	0.782516i	−0.197739	−	0.980255i	$-0.563360\pi$
$827$	22.5033	−	22.5033i	0.782516	−	0.782516i	0.980255	+	0.197739i	$0.0633598\pi$
$828$		0			0
$829$			17.8326i			0.619351i	0.950842	+	0.309675i	$0.100220\pi$
$829$			17.8326i			0.619351i	−0.950842	+	0.309675i	$0.899780\pi$
$830$		0			0
$831$		0			0
$832$	−1.12334	−	1.12334i	−0.0389450	−	0.0389450i
$833$	38.0016	+	38.0016i	1.31668	+	1.31668i
$834$		0			0
$835$		0			0
$836$			13.3121i			0.460409i
$837$		0			0
$838$	−8.91628	+	8.91628i	−0.308008	+	0.308008i
$839$	9.16784			0.316509			0.158255	−	0.987398i	$-0.449413\pi$
$839$	9.16784			0.316509			0.158255	+	0.987398i	$0.449413\pi$
$840$		0			0
$841$	−23.6521			−0.815590
$842$	9.54118	−	9.54118i	0.328811	−	0.328811i
$843$		0			0
$844$			7.43758i			0.256012i
$845$		0			0
$846$		0			0
$847$	22.2220	+	22.2220i	0.763558	+	0.763558i
$848$	−0.103165	−	0.103165i	−0.00354272	−	0.00354272i
$849$		0			0
$850$		0			0
$851$		−	4.04455i		−	0.138645i
$852$		0			0
$853$	15.4650	−	15.4650i	0.529512	−	0.529512i	−0.390915	−	0.920427i	$-0.627841\pi$
$853$	15.4650	−	15.4650i	0.529512	−	0.529512i	0.920427	+	0.390915i	$0.127841\pi$
$854$	63.0598			2.15786
$855$		0			0
$856$	4.47214			0.152854
$857$	24.2328	−	24.2328i	0.827776	−	0.827776i	−0.159433	−	0.987209i	$-0.550967\pi$
$857$	24.2328	−	24.2328i	0.827776	−	0.827776i	0.987209	+	0.159433i	$0.0509665\pi$
$858$		0			0
$859$			10.1592i			0.346626i	0.984867	+	0.173313i	$0.0554473\pi$
$859$			10.1592i			0.346626i	−0.984867	+	0.173313i	$0.944553\pi$
$860$		0			0
$861$		0			0
$862$	18.7320	+	18.7320i	0.638013	+	0.638013i
$863$	−3.66582	−	3.66582i	−0.124786	−	0.124786i	0.641956	−	0.766742i	$-0.278123\pi$
$863$	−3.66582	−	3.66582i	−0.124786	−	0.124786i	−0.766742	+	0.641956i	$0.778123\pi$
$864$		0			0
$865$		0			0
$866$			16.1058i			0.547298i
$867$		0			0
$868$	−29.1802	+	29.1802i	−0.990441	+	0.990441i
$869$	−0.0452231			−0.00153409
$870$		0			0
$871$	6.37367			0.215964
$872$	−6.53089	+	6.53089i	−0.221164	+	0.221164i
$873$		0			0
$874$		−	8.70820i		−	0.294559i
$875$		0			0
$876$		0			0
$877$	−21.9109	−	21.9109i	−0.739879	−	0.739879i	0.232675	−	0.972554i	$-0.425252\pi$
$877$	−21.9109	−	21.9109i	−0.739879	−	0.739879i	−0.972554	+	0.232675i	$0.925252\pi$
$878$	−12.0243	−	12.0243i	−0.405800	−	0.405800i
$879$		0			0
$880$		0			0
$881$		−	10.7799i		−	0.363184i	−0.983374	−	0.181592i	$-0.941875\pi$
$881$		−	10.7799i		−	0.363184i	0.983374	−	0.181592i	$-0.0581251\pi$
$882$		0			0
$883$	27.9998	−	27.9998i	0.942267	−	0.942267i	−0.0561547	−	0.998422i	$-0.517884\pi$
$883$	27.9998	−	27.9998i	0.942267	−	0.942267i	0.998422	+	0.0561547i	$0.0178840\pi$
$884$	5.14098			0.172910
$885$		0			0
$886$	−22.1803			−0.745163
$887$	−16.6186	+	16.6186i	−0.557997	+	0.557997i	−0.928737	−	0.370739i	$-0.879104\pi$
$887$	−16.6186	+	16.6186i	−0.557997	+	0.557997i	0.370739	+	0.928737i	$0.379104\pi$
$888$		0			0
$889$			50.3858i			1.68989i
$890$		0			0
$891$		0			0
$892$	1.93764	+	1.93764i	0.0648769	+	0.0648769i
$893$	−53.6113	−	53.6113i	−1.79403	−	1.79403i
$894$		0			0
$895$		0			0
$896$			4.85873i			0.162319i
$897$		0			0
$898$	−12.2486	+	12.2486i	−0.408742	+	0.408742i
$899$	−19.6414			−0.655076
$900$		0			0
$901$	0.472136			0.0157291
$902$	−3.04227	+	3.04227i	−0.101296	+	0.101296i
$903$		0			0
$904$			6.50651i			0.216403i
$905$		0			0
$906$		0			0
$907$	27.2122	+	27.2122i	0.903566	+	0.903566i	0.995743	−	0.0921763i	$-0.0293823\pi$
$907$	27.2122	+	27.2122i	0.903566	+	0.903566i	−0.0921763	+	0.995743i	$0.529382\pi$
$908$	6.86474	+	6.86474i	0.227814	+	0.227814i
$909$		0			0
$910$		0			0
$911$		−	9.95765i		−	0.329912i	−0.986301	−	0.164956i	$-0.947252\pi$
$911$		−	9.95765i		−	0.329912i	0.986301	−	0.164956i	$-0.0527481\pi$
$912$		0			0
$913$	15.7958	−	15.7958i	0.522765	−	0.522765i
$914$	21.3894			0.707499
$915$		0			0
$916$	−9.98687			−0.329976
$917$	61.3135	−	61.3135i	2.02475	−	2.02475i
$918$		0			0
$919$			1.88840i			0.0622927i	0.999515	+	0.0311464i	$0.00991580\pi$
$919$			1.88840i			0.0622927i	−0.999515	+	0.0311464i	$0.990084\pi$
$920$		0			0
$921$		0			0
$922$	−12.8794	−	12.8794i	−0.424161	−	0.424161i
$923$	11.2742	+	11.2742i	0.371096	+	0.371096i
$924$		0			0
$925$		0			0
$926$		−	27.3107i		−	0.897484i
$927$		0			0
$928$	−1.63522	+	1.63522i	−0.0536787	+	0.0536787i
$929$	−14.3747			−0.471619			−0.235810	−	0.971799i	$-0.575774\pi$
$929$	−14.3747			−0.471619			−0.235810	+	0.971799i	$0.575774\pi$
$930$		0			0
$931$	−103.850			−3.40354
$932$	−1.05032	+	1.05032i	−0.0344044	+	0.0344044i
$933$		0			0
$934$		−	32.3526i		−	1.05861i
$935$		0			0
$936$		0			0
$937$	9.58772	+	9.58772i	0.313217	+	0.313217i	0.846155	−	0.532937i	$-0.178912\pi$
$937$	9.58772	+	9.58772i	0.313217	+	0.313217i	−0.532937	+	0.846155i	$0.678912\pi$
$938$	−13.7838	−	13.7838i	−0.450058	−	0.450058i
$939$		0			0
$940$		0			0
$941$			11.1036i			0.361966i	0.983486	+	0.180983i	$0.0579279\pi$
$941$			11.1036i			0.361966i	−0.983486	+	0.180983i	$0.942072\pi$
$942$		0			0
$943$	1.99012	−	1.99012i	0.0648072	−	0.0648072i
$944$	−14.0510			−0.457322
$945$		0			0
$946$	−18.8064			−0.611449
$947$	4.24619	−	4.24619i	0.137983	−	0.137983i	−0.634742	−	0.772724i	$-0.718894\pi$
$947$	4.24619	−	4.24619i	0.137983	−	0.137983i	0.772724	+	0.634742i	$0.218894\pi$
$948$		0			0
$949$			17.3179i			0.562164i
$950$		0			0
$951$		0			0
$952$	−11.1180	−	11.1180i	−0.360336	−	0.360336i
$953$	−4.32510	−	4.32510i	−0.140104	−	0.140104i	0.633576	−	0.773680i	$-0.281586\pi$
$953$	−4.32510	−	4.32510i	−0.140104	−	0.140104i	−0.773680	+	0.633576i	$0.781586\pi$
$954$		0			0
$955$		0			0
$956$			17.2556i			0.558087i
$957$		0			0
$958$	−3.34342	+	3.34342i	−0.108021	+	0.108021i
$959$	101.969			3.29275
$960$		0			0
$961$	41.1375			1.32702
$962$	−3.26257	+	3.26257i	−0.105190	+	0.105190i
$963$		0			0
$964$		−	14.1909i		−	0.457058i
$965$		0			0
$966$		0			0
$967$	16.8487	+	16.8487i	0.541819	+	0.541819i	0.924062	−	0.382243i	$-0.124848\pi$
$967$	16.8487	+	16.8487i	0.541819	+	0.541819i	−0.382243	+	0.924062i	$0.624848\pi$
$968$	−4.57362	−	4.57362i	−0.147002	−	0.147002i
$969$		0			0
$970$		0			0
$971$		−	12.4479i		−	0.399473i	−0.979850	−	0.199736i	$-0.935991\pi$
$971$		−	12.4479i		−	0.399473i	0.979850	−	0.199736i	$-0.0640086\pi$
$972$		0			0
$973$	−6.67959	+	6.67959i	−0.214138	+	0.214138i
$974$	7.65581			0.245308
$975$		0			0
$976$	−12.9786			−0.415436
$977$	13.5625	−	13.5625i	0.433902	−	0.433902i	−0.456052	−	0.889953i	$-0.650737\pi$
$977$	13.5625	−	13.5625i	0.433902	−	0.433902i	0.889953	+	0.456052i	$0.150737\pi$
$978$		0			0
$979$			25.6900i			0.821056i
$980$		0			0
$981$		0			0
$982$	20.7471	+	20.7471i	0.662066	+	0.662066i
$983$	−4.50699	−	4.50699i	−0.143751	−	0.143751i	0.631569	−	0.775320i	$-0.282411\pi$
$983$	−4.50699	−	4.50699i	−0.143751	−	0.143751i	−0.775320	+	0.631569i	$0.782411\pi$
$984$		0			0
$985$		0			0
$986$		−	7.48357i		−	0.238325i
$987$		0			0
$988$	−7.02456	+	7.02456i	−0.223481	+	0.223481i
$989$	12.3023			0.391191
$990$		0			0
$991$	18.7558			0.595798			0.297899	−	0.954597i	$-0.403714\pi$
$991$	18.7558			0.595798			0.297899	+	0.954597i	$0.403714\pi$
$992$	6.00573	−	6.00573i	0.190682	−	0.190682i
$993$		0			0
$994$		−	48.7637i		−	1.54669i
$995$		0			0
$996$		0			0
$997$	−6.46596	−	6.46596i	−0.204779	−	0.204779i	0.597265	−	0.802044i	$-0.296254\pi$
$997$	−6.46596	−	6.46596i	−0.204779	−	0.204779i	−0.802044	+	0.597265i	$0.796254\pi$
$998$	−11.3849	−	11.3849i	−0.360383	−	0.360383i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2250.2.f.d.557.8	yes	16
3.2	odd	2	inner	2250.2.f.d.557.4	yes	16
5.2	odd	4		2250.2.f.a.1943.5	yes	16
5.3	odd	4	inner	2250.2.f.d.1943.4	yes	16
5.4	even	2		2250.2.f.a.557.1	✓	16
15.2	even	4		2250.2.f.a.1943.1	yes	16
15.8	even	4	inner	2250.2.f.d.1943.8	yes	16
15.14	odd	2		2250.2.f.a.557.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2250.2.f.a.557.1	✓	16	5.4	even	2
2250.2.f.a.557.5	yes	16	15.14	odd	2
2250.2.f.a.1943.1	yes	16	15.2	even	4
2250.2.f.a.1943.5	yes	16	5.2	odd	4
2250.2.f.d.557.4	yes	16	3.2	odd	2	inner
2250.2.f.d.557.8	yes	16	1.1	even	1	trivial
2250.2.f.d.1943.4	yes	16	5.3	odd	4	inner
2250.2.f.d.1943.8	yes	16	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2250 = 2 \cdot 3^{2} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2250.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(3.43564 + 3.43564i) q^{7} +(-0.707107 - 0.707107i) q^{8} +2.12883i q^{11} +(-1.12334 + 1.12334i) q^{13} +4.85873 q^{14} -1.00000 q^{16} +(2.28825 - 2.28825i) q^{17} +6.25325i q^{19} +(1.50531 + 1.50531i) q^{22} +(-0.984708 - 0.984708i) q^{23} +1.58865i q^{26} +(3.43564 - 3.43564i) q^{28} +2.31255 q^{29} -8.49338 q^{31} +(-0.707107 + 0.707107i) q^{32} -3.23607i q^{34} +(2.05368 + 2.05368i) q^{37} +(4.42172 + 4.42172i) q^{38} +2.02102i q^{41} +(-6.24669 + 6.24669i) q^{43} +2.12883 q^{44} -1.39259 q^{46} +(-8.57335 + 8.57335i) q^{47} +16.6073i q^{49} +(1.12334 + 1.12334i) q^{52} +(0.103165 + 0.103165i) q^{53} -4.85873i q^{56} +(1.63522 - 1.63522i) q^{58} +14.0510 q^{59} +12.9786 q^{61} +(-6.00573 + 6.00573i) q^{62} +1.00000i q^{64} +(-2.83692 - 2.83692i) q^{67} +(-2.28825 - 2.28825i) q^{68} -10.0363i q^{71} +(7.70820 - 7.70820i) q^{73} +2.90434 q^{74} +6.25325 q^{76} +(-7.31391 + 7.31391i) q^{77} +0.0212431i q^{79} +(1.42908 + 1.42908i) q^{82} +(-7.41994 - 7.41994i) q^{83} +8.83415i q^{86} +(1.50531 - 1.50531i) q^{88} +12.0677 q^{89} -7.71883 q^{91} +(-0.984708 + 0.984708i) q^{92} +12.1245i q^{94} +(-1.48276 - 1.48276i) q^{97} +(11.7431 + 11.7431i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{7} + 12 q^{13} - 16 q^{16} + 12 q^{22} + 12 q^{28} - 16 q^{31} - 28 q^{37} - 40 q^{43} - 16 q^{46} - 12 q^{52} - 24 q^{58} - 24 q^{67} + 16 q^{73} + 32 q^{76} - 12 q^{82} + 12 q^{88} + 8 q^{91}+ \cdots + 72 q^{97}+O(q^{100}) \) 16 * q + 12 * q^7 + 12 * q^13 - 16 * q^16 + 12 * q^22 + 12 * q^28 - 16 * q^31 - 28 * q^37 - 40 * q^43 - 16 * q^46 - 12 * q^52 - 24 * q^58 - 24 * q^67 + 16 * q^73 + 32 * q^76 - 12 * q^82 + 12 * q^88 + 8 * q^91 + 72 * q^97

Introduction

L-functions

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