LMFDB - Embedded newform 630.3.o.f.253.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,3,Mod(127,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("630.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	630.o (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:	$17.1662566547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + \cdots + 2560000 $ x^16 - 8x^15 + 32x^14 + 152x^13 + 1954x^12 - 12664x^11 + 50336x^10 + 231896x^9 + 1093889x^8 - 4595248x^7 + 18837632x^6 + 86081152x^5 + 178889856x^4 + 70149120x^3 + 10035200x^2 - 7168000*x + 2560000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{14}\cdot 5 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.6
Root			$3.76660 - 3.76660i$ of defining polynomial
Character	$\chi$	$=$	630.253
Dual form			630.3.o.f.127.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(4.16484 - 2.76660i) q^{5} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(4.16484 - 2.76660i) q^{5} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(1.39824 - 6.93144i) q^{10} -17.6826 q^{11} +(-12.3956 - 12.3956i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(-18.7246 + 18.7246i) q^{17} -25.5476i q^{19} +(-5.53321 - 8.32968i) q^{20} +(-17.6826 + 17.6826i) q^{22} +(5.90052 + 5.90052i) q^{23} +(9.69181 - 23.0449i) q^{25} -24.7912 q^{26} +(3.74166 + 3.74166i) q^{28} -15.3647i q^{29} +11.3491 q^{31} +(-4.00000 + 4.00000i) q^{32} +37.4492i q^{34} +(-2.61586 + 12.9675i) q^{35} +(25.5981 - 25.5981i) q^{37} +(-25.5476 - 25.5476i) q^{38} +(-13.8629 - 2.79648i) q^{40} -58.8283 q^{41} +(0.282745 + 0.282745i) q^{43} +35.3653i q^{44} +11.8010 q^{46} +(48.6505 - 48.6505i) q^{47} -7.00000i q^{49} +(-13.3531 - 32.7367i) q^{50} +(-24.7912 + 24.7912i) q^{52} +(-3.93909 - 3.93909i) q^{53} +(-73.6454 + 48.9209i) q^{55} +7.48331 q^{56} +(-15.3647 - 15.3647i) q^{58} +86.2636i q^{59} +29.2079 q^{61} +(11.3491 - 11.3491i) q^{62} +8.00000i q^{64} +(-85.9194 - 17.3320i) q^{65} +(-65.7277 + 65.7277i) q^{67} +(37.4492 + 37.4492i) q^{68} +(10.3517 + 15.5834i) q^{70} -1.19194 q^{71} +(-87.0749 - 87.0749i) q^{73} -51.1963i q^{74} -51.0953 q^{76} +(33.0812 - 33.0812i) q^{77} -55.0959i q^{79} +(-16.6594 + 11.0664i) q^{80} +(-58.8283 + 58.8283i) q^{82} +(91.8012 + 91.8012i) q^{83} +(-26.1814 + 129.788i) q^{85} +0.565490 q^{86} +(35.3653 + 35.3653i) q^{88} -103.966i q^{89} +46.3801 q^{91} +(11.8010 - 11.8010i) q^{92} -97.3010i q^{94} +(-70.6802 - 106.402i) q^{95} +(87.4734 - 87.4734i) q^{97} +(-7.00000 - 7.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{5} - 32 q^{8}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^5 - 32 * q^8	$ 16 q + 16 q^{2} + 16 q^{5} - 32 q^{8} + 24 q^{10} - 8 q^{11} - 32 q^{13} - 64 q^{16} - 56 q^{17} + 16 q^{20} - 8 q^{22} - 24 q^{23} + 40 q^{25} - 64 q^{26} - 112 q^{31} - 64 q^{32} - 28 q^{35} - 152 q^{37} - 16 q^{40} - 48 q^{46} - 80 q^{47} + 72 q^{50} - 64 q^{52} - 48 q^{53} - 24 q^{55} + 96 q^{58} + 96 q^{61} - 112 q^{62} - 16 q^{65} - 80 q^{67} + 112 q^{68} - 536 q^{71} + 168 q^{77} - 64 q^{80} + 256 q^{83} + 40 q^{85} + 16 q^{88} - 48 q^{92} - 360 q^{95} + 688 q^{97} - 112 q^{98}+O(q^{100}) $ 16 * q + 16 * q^2 + 16 * q^5 - 32 * q^8 + 24 * q^10 - 8 * q^11 - 32 * q^13 - 64 * q^16 - 56 * q^17 + 16 * q^20 - 8 * q^22 - 24 * q^23 + 40 * q^25 - 64 * q^26 - 112 * q^31 - 64 * q^32 - 28 * q^35 - 152 * q^37 - 16 * q^40 - 48 * q^46 - 80 * q^47 + 72 * q^50 - 64 * q^52 - 48 * q^53 - 24 * q^55 + 96 * q^58 + 96 * q^61 - 112 * q^62 - 16 * q^65 - 80 * q^67 + 112 * q^68 - 536 * q^71 + 168 * q^77 - 64 * q^80 + 256 * q^83 + 40 * q^85 + 16 * q^88 - 48 * q^92 - 360 * q^95 + 688 * q^97 - 112 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	2.00000i		−	0.500000i
$5$	4.16484	−	2.76660i	0.832968	−	0.553321i
$5$	4.16484	−	2.76660i	0.832968	−	0.553321i
$6$		0			0
$7$	−1.87083	+	1.87083i	−0.267261	+	0.267261i
$7$	−1.87083	+	1.87083i	−0.267261	+	0.267261i
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$		0			0
$10$	1.39824	−	6.93144i	0.139824	−	0.693144i
$11$	−17.6826			−1.60751			−0.803757	−	0.594958i	$-0.797169\pi$
$11$	−17.6826			−1.60751			−0.803757	+	0.594958i	$0.797169\pi$
$12$		0			0
$13$	−12.3956	−	12.3956i	−0.953508	−	0.953508i	0.0454585	−	0.998966i	$-0.485525\pi$
$13$	−12.3956	−	12.3956i	−0.953508	−	0.953508i	−0.998966	+	0.0454585i	$0.985525\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	−18.7246	+	18.7246i	−1.10145	+	1.10145i	−0.107210	+	0.994236i	$0.534192\pi$
$17$	−18.7246	+	18.7246i	−1.10145	+	1.10145i	−0.994236	+	0.107210i	$0.965808\pi$
$18$		0			0
$19$		−	25.5476i		−	1.34461i	−0.740273	−	0.672306i	$-0.765304\pi$
$19$		−	25.5476i		−	1.34461i	0.740273	−	0.672306i	$-0.234696\pi$
$20$	−5.53321	−	8.32968i	−0.276660	−	0.416484i
$21$		0			0
$22$	−17.6826	+	17.6826i	−0.803757	+	0.803757i
$23$	5.90052	+	5.90052i	0.256545	+	0.256545i	0.823647	−	0.567103i	$-0.191936\pi$
$23$	5.90052	+	5.90052i	0.256545	+	0.256545i	−0.567103	+	0.823647i	$0.691936\pi$
$24$		0			0
$25$	9.69181	−	23.0449i	0.387673	−	0.921797i
$26$	−24.7912			−0.953508
$27$		0			0
$28$	3.74166	+	3.74166i	0.133631	+	0.133631i
$29$		−	15.3647i		−	0.529816i	−0.964274	−	0.264908i	$-0.914658\pi$
$29$		−	15.3647i		−	0.529816i	0.964274	−	0.264908i	$-0.0853416\pi$
$30$		0			0
$31$	11.3491			0.366102			0.183051	−	0.983103i	$-0.441403\pi$
$31$	11.3491			0.366102			0.183051	+	0.983103i	$0.441403\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$		0			0
$34$			37.4492i			1.10145i
$35$	−2.61586	+	12.9675i	−0.0747390	+	0.370501i
$36$		0			0
$37$	25.5981	−	25.5981i	0.691842	−	0.691842i	−0.270795	−	0.962637i	$-0.587287\pi$
$37$	25.5981	−	25.5981i	0.691842	−	0.691842i	0.962637	+	0.270795i	$0.0872866\pi$
$38$	−25.5476	−	25.5476i	−0.672306	−	0.672306i
$39$		0			0
$40$	−13.8629	−	2.79648i	−0.346572	−	0.0699119i
$41$	−58.8283			−1.43484			−0.717418	−	0.696643i	$-0.754676\pi$
$41$	−58.8283			−1.43484			−0.717418	+	0.696643i	$0.754676\pi$
$42$		0			0
$43$	0.282745	+	0.282745i	0.00657546	+	0.00657546i	0.710387	−	0.703811i	$-0.248520\pi$
$43$	0.282745	+	0.282745i	0.00657546	+	0.00657546i	−0.703811	+	0.710387i	$0.748520\pi$
$44$			35.3653i			0.803757i
$45$		0			0
$46$	11.8010			0.256545
$47$	48.6505	−	48.6505i	1.03512	−	1.03512i	0.0357569	−	0.999361i	$-0.488616\pi$
$47$	48.6505	−	48.6505i	1.03512	−	1.03512i	0.999361	−	0.0357569i	$-0.0113842\pi$
$48$		0			0
$49$		−	7.00000i		−	0.142857i
$50$	−13.3531	−	32.7367i	−0.267062	−	0.654735i
$51$		0			0
$52$	−24.7912	+	24.7912i	−0.476754	+	0.476754i
$53$	−3.93909	−	3.93909i	−0.0743224	−	0.0743224i	0.668968	−	0.743291i	$-0.266736\pi$
$53$	−3.93909	−	3.93909i	−0.0743224	−	0.0743224i	−0.743291	+	0.668968i	$0.766736\pi$
$54$		0			0
$55$	−73.6454	+	48.9209i	−1.33901	+	0.889470i
$56$	7.48331			0.133631
$57$		0			0
$58$	−15.3647	−	15.3647i	−0.264908	−	0.264908i
$59$			86.2636i			1.46210i	0.682326	+	0.731048i	$0.260968\pi$
$59$			86.2636i			1.46210i	−0.682326	+	0.731048i	$0.739032\pi$
$60$		0			0
$61$	29.2079			0.478818			0.239409	−	0.970919i	$-0.423046\pi$
$61$	29.2079			0.478818			0.239409	+	0.970919i	$0.423046\pi$
$62$	11.3491	−	11.3491i	0.183051	−	0.183051i
$63$		0			0
$64$			8.00000i			0.125000i
$65$	−85.9194	−	17.3320i	−1.32184	−	0.266646i
$66$		0			0
$67$	−65.7277	+	65.7277i	−0.981010	+	0.981010i	−0.999823	−	0.0188133i	$-0.994011\pi$
$67$	−65.7277	+	65.7277i	−0.981010	+	0.981010i	0.0188133	+	0.999823i	$0.494011\pi$
$68$	37.4492	+	37.4492i	0.550723	+	0.550723i
$69$		0			0
$70$	10.3517	+	15.5834i	0.147881	+	0.222620i
$71$	−1.19194			−0.0167879			−0.00839397	−	0.999965i	$-0.502672\pi$
$71$	−1.19194			−0.0167879			−0.00839397	+	0.999965i	$0.502672\pi$
$72$		0			0
$73$	−87.0749	−	87.0749i	−1.19281	−	1.19281i	−0.976276	−	0.216531i	$-0.930526\pi$
$73$	−87.0749	−	87.0749i	−1.19281	−	1.19281i	−0.216531	−	0.976276i	$-0.569474\pi$
$74$		−	51.1963i		−	0.691842i
$75$		0			0
$76$	−51.0953			−0.672306
$77$	33.0812	−	33.0812i	0.429626	−	0.429626i
$78$		0			0
$79$		−	55.0959i		−	0.697417i	−0.937231	−	0.348708i	$-0.886620\pi$
$79$		−	55.0959i		−	0.697417i	0.937231	−	0.348708i	$-0.113380\pi$
$80$	−16.6594	+	11.0664i	−0.208242	+	0.138330i
$81$		0			0
$82$	−58.8283	+	58.8283i	−0.717418	+	0.717418i
$83$	91.8012	+	91.8012i	1.10604	+	1.10604i	0.993666	+	0.112372i	$0.0358448\pi$
$83$	91.8012	+	91.8012i	1.10604	+	1.10604i	0.112372	+	0.993666i	$0.464155\pi$
$84$		0			0
$85$	−26.1814	+	129.788i	−0.308017	+	1.52692i
$86$	0.565490			0.00657546
$87$		0			0
$88$	35.3653	+	35.3653i	0.401878	+	0.401878i
$89$		−	103.966i		−	1.16815i	−0.811699	−	0.584076i	$-0.801457\pi$
$89$		−	103.966i		−	1.16815i	0.811699	−	0.584076i	$-0.198543\pi$
$90$		0			0
$91$	46.3801			0.509671
$92$	11.8010	−	11.8010i	0.128272	−	0.128272i
$93$		0			0
$94$		−	97.3010i		−	1.03512i
$95$	−70.6802	−	106.402i	−0.744002	−	1.12002i
$96$		0			0
$97$	87.4734	−	87.4734i	0.901788	−	0.901788i	−0.0938032	−	0.995591i	$-0.529902\pi$
$97$	87.4734	−	87.4734i	0.901788	−	0.901788i	0.995591	+	0.0938032i	$0.0299024\pi$
$98$	−7.00000	−	7.00000i	−0.0714286	−	0.0714286i
$99$		0			0
$100$	−46.0899	−	19.3836i	−0.460899	−	0.193836i
$101$	−5.82092			−0.0576329			−0.0288164	−	0.999585i	$-0.509174\pi$
$101$	−5.82092			−0.0576329			−0.0288164	+	0.999585i	$0.509174\pi$
$102$		0			0
$103$	60.7804	+	60.7804i	0.590101	+	0.590101i	0.937659	−	0.347558i	$-0.112989\pi$
$103$	60.7804	+	60.7804i	0.590101	+	0.590101i	−0.347558	+	0.937659i	$0.612989\pi$
$104$			49.5824i			0.476754i
$105$		0			0
$106$	−7.87818			−0.0743224
$107$	−80.6808	+	80.6808i	−0.754026	+	0.754026i	−0.975228	−	0.221202i	$-0.929002\pi$
$107$	−80.6808	+	80.6808i	−0.754026	+	0.754026i	0.221202	+	0.975228i	$0.429002\pi$
$108$		0			0
$109$		−	64.4450i		−	0.591238i	−0.955306	−	0.295619i	$-0.904474\pi$
$109$		−	64.4450i		−	0.591238i	0.955306	−	0.295619i	$-0.0955259\pi$
$110$	−24.7246	+	122.566i	−0.224769	+	1.11424i
$111$		0			0
$112$	7.48331	−	7.48331i	0.0668153	−	0.0668153i
$113$	−80.8773	−	80.8773i	−0.715729	−	0.715729i	0.251999	−	0.967728i	$-0.418912\pi$
$113$	−80.8773	−	80.8773i	−0.715729	−	0.715729i	−0.967728	+	0.251999i	$0.918912\pi$
$114$		0			0
$115$	40.8992	+	8.25034i	0.355645	+	0.0717421i
$116$	−30.7293			−0.264908
$117$		0			0
$118$	86.2636	+	86.2636i	0.731048	+	0.731048i
$119$		−	70.0610i		−	0.588748i
$120$		0			0
$121$	191.676			1.58410
$122$	29.2079	−	29.2079i	0.239409	−	0.239409i
$123$		0			0
$124$		−	22.6983i		−	0.183051i
$125$	−23.3913	−	122.792i	−0.187130	−	0.982335i
$126$		0			0
$127$	55.3737	−	55.3737i	0.436014	−	0.436014i	−0.454654	−	0.890668i	$-0.650237\pi$
$127$	55.3737	−	55.3737i	0.436014	−	0.436014i	0.890668	+	0.454654i	$0.150237\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		0			0
$130$	−103.251	+	68.5874i	−0.794242	+	0.527596i
$131$	69.2950			0.528969			0.264485	−	0.964390i	$-0.414798\pi$
$131$	69.2950			0.528969			0.264485	+	0.964390i	$0.414798\pi$
$132$		0			0
$133$	47.7953	+	47.7953i	0.359363	+	0.359363i
$134$			131.455i			0.981010i
$135$		0			0
$136$	74.8984			0.550723
$137$	29.0370	−	29.0370i	0.211949	−	0.211949i	−0.593146	−	0.805095i	$-0.702114\pi$
$137$	29.0370	−	29.0370i	0.211949	−	0.211949i	0.805095	+	0.593146i	$0.202114\pi$
$138$		0			0
$139$			80.1068i			0.576308i	0.957584	+	0.288154i	$0.0930415\pi$
$139$			80.1068i			0.576308i	−0.957584	+	0.288154i	$0.906958\pi$
$140$	25.9351	+	5.23173i	0.185251	+	0.0373695i
$141$		0			0
$142$	−1.19194	+	1.19194i	−0.00839397	+	0.00839397i
$143$	219.187	+	219.187i	1.53278	+	1.53278i
$144$		0			0
$145$	−42.5079	−	63.9914i	−0.293158	−	0.441320i
$146$	−174.150			−1.19281
$147$		0			0
$148$	−51.1963	−	51.1963i	−0.345921	−	0.345921i
$149$			216.650i			1.45403i	0.686624	+	0.727013i	$0.259092\pi$
$149$			216.650i			1.45403i	−0.686624	+	0.727013i	$0.740908\pi$
$150$		0			0
$151$	−170.036			−1.12607			−0.563033	−	0.826434i	$-0.690366\pi$
$151$	−170.036			−1.12607			−0.563033	+	0.826434i	$0.690366\pi$
$152$	−51.0953	+	51.0953i	−0.336153	+	0.336153i
$153$		0			0
$154$		−	66.1624i		−	0.429626i
$155$	47.2674	−	31.3986i	0.304951	−	0.202572i
$156$		0			0
$157$	164.649	−	164.649i	1.04872	−	1.04872i	0.0499682	−	0.998751i	$-0.484088\pi$
$157$	164.649	−	164.649i	1.04872	−	1.04872i	0.998751	−	0.0499682i	$-0.0159120\pi$
$158$	−55.0959	−	55.0959i	−0.348708	−	0.348708i
$159$		0			0
$160$	−5.59295	+	27.7258i	−0.0349560	+	0.173286i
$161$	−22.0777			−0.137129
$162$		0			0
$163$	104.632	+	104.632i	0.641912	+	0.641912i	0.951025	−	0.309113i	$-0.100032\pi$
$163$	104.632	+	104.632i	0.641912	+	0.641912i	−0.309113	+	0.951025i	$0.600032\pi$
$164$			117.657i			0.717418i
$165$		0			0
$166$	183.602			1.10604
$167$	215.324	−	215.324i	1.28937	−	1.28937i	0.354196	−	0.935171i	$-0.384754\pi$
$167$	215.324	−	215.324i	1.28937	−	1.28937i	0.935171	−	0.354196i	$-0.115246\pi$
$168$		0			0
$169$			138.302i			0.818354i
$170$	103.607	+	155.970i	0.609453	+	0.917470i
$171$		0			0
$172$	0.565490	−	0.565490i	0.00328773	−	0.00328773i
$173$	50.4009	+	50.4009i	0.291334	+	0.291334i	0.837607	−	0.546273i	$-0.183954\pi$
$173$	50.4009	+	50.4009i	0.291334	+	0.291334i	−0.546273	+	0.837607i	$0.683954\pi$
$174$		0			0
$175$	24.9814	+	61.2448i	0.142751	+	0.349970i
$176$	70.7306			0.401878
$177$		0			0
$178$	−103.966	−	103.966i	−0.584076	−	0.584076i
$179$		−	21.2898i		−	0.118937i	−0.998230	−	0.0594687i	$-0.981059\pi$
$179$		−	21.2898i		−	0.118937i	0.998230	−	0.0594687i	$-0.0189406\pi$
$180$		0			0
$181$	−22.7581			−0.125736			−0.0628678	−	0.998022i	$-0.520025\pi$
$181$	−22.7581			−0.125736			−0.0628678	+	0.998022i	$0.520025\pi$
$182$	46.3801	−	46.3801i	0.254836	−	0.254836i
$183$		0			0
$184$		−	23.6021i		−	0.128272i
$185$	35.7923	−	177.432i	0.193472	−	0.959093i
$186$		0			0
$187$	331.100	−	331.100i	1.77059	−	1.77059i
$188$	−97.3010	−	97.3010i	−0.517559	−	0.517559i
$189$		0			0
$190$	−177.082	−	35.7217i	−0.932011	−	0.188009i
$191$	113.711			0.595344			0.297672	−	0.954668i	$-0.403790\pi$
$191$	113.711			0.595344			0.297672	+	0.954668i	$0.403790\pi$
$192$		0			0
$193$	109.936	+	109.936i	0.569616	+	0.569616i	0.932021	−	0.362405i	$-0.118044\pi$
$193$	109.936	+	109.936i	0.569616	+	0.569616i	−0.362405	+	0.932021i	$0.618044\pi$
$194$		−	174.947i		−	0.901788i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	−82.2107	+	82.2107i	−0.417313	+	0.417313i	−0.884277	−	0.466963i	$-0.845348\pi$
$197$	−82.2107	+	82.2107i	−0.417313	+	0.417313i	0.466963	+	0.884277i	$0.345348\pi$
$198$		0			0
$199$		−	232.689i		−	1.16929i	−0.811289	−	0.584646i	$-0.801234\pi$
$199$		−	232.689i		−	1.16929i	0.811289	−	0.584646i	$-0.198766\pi$
$200$	−65.4735	+	26.7062i	−0.327367	+	0.133531i
$201$		0			0
$202$	−5.82092	+	5.82092i	−0.0288164	+	0.0288164i
$203$	28.7447	+	28.7447i	0.141599	+	0.141599i
$204$		0			0
$205$	−245.011	+	162.755i	−1.19517	+	0.793925i
$206$	121.561			0.590101
$207$		0			0
$208$	49.5824	+	49.5824i	0.238377	+	0.238377i
$209$			451.750i			2.16148i
$210$		0			0
$211$	−341.021			−1.61621			−0.808107	−	0.589035i	$-0.799508\pi$
$211$	−341.021			−1.61621			−0.808107	+	0.589035i	$0.799508\pi$
$212$	−7.87818	+	7.87818i	−0.0371612	+	0.0371612i
$213$		0			0
$214$			161.362i			0.754026i
$215$	1.95983	+	0.395345i	0.00911549	+	0.00183881i
$216$		0			0
$217$	−21.2323	+	21.2323i	−0.0978447	+	0.0978447i
$218$	−64.4450	−	64.4450i	−0.295619	−	0.295619i
$219$		0			0
$220$	97.8417	+	147.291i	0.444735	+	0.669504i
$221$	464.205			2.10048
$222$		0			0
$223$	118.521	+	118.521i	0.531482	+	0.531482i	0.921013	−	0.389531i	$-0.127363\pi$
$223$	118.521	+	118.521i	0.531482	+	0.531482i	−0.389531	+	0.921013i	$0.627363\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	−161.755			−0.715729
$227$	1.59958	−	1.59958i	0.00704662	−	0.00704662i	−0.703575	−	0.710621i	$-0.748414\pi$
$227$	1.59958	−	1.59958i	0.00704662	−	0.00704662i	0.710621	+	0.703575i	$0.248414\pi$
$228$		0			0
$229$		−	59.2261i		−	0.258629i	−0.991604	−	0.129315i	$-0.958722\pi$
$229$		−	59.2261i		−	0.258629i	0.991604	−	0.129315i	$-0.0412777\pi$
$230$	49.1495	−	32.6488i	0.213693	−	0.141951i
$231$		0			0
$232$	−30.7293	+	30.7293i	−0.132454	+	0.132454i
$233$	−266.052	−	266.052i	−1.14185	−	1.14185i	−0.988111	−	0.153743i	$-0.950867\pi$
$233$	−266.052	−	266.052i	−1.14185	−	1.14185i	−0.153743	−	0.988111i	$-0.549133\pi$
$234$		0			0
$235$	68.0250	−	337.218i	0.289468	−	1.43497i
$236$	172.527			0.731048
$237$		0			0
$238$	−70.0610	−	70.0610i	−0.294374	−	0.294374i
$239$		−	420.919i		−	1.76117i	−0.473890	−	0.880584i	$-0.657151\pi$
$239$		−	420.919i		−	1.76117i	0.473890	−	0.880584i	$-0.342849\pi$
$240$		0			0
$241$	−347.574			−1.44222			−0.721108	−	0.692823i	$-0.756367\pi$
$241$	−347.574			−1.44222			−0.721108	+	0.692823i	$0.756367\pi$
$242$	191.676	−	191.676i	0.792049	−	0.792049i
$243$		0			0
$244$		−	58.4157i		−	0.239409i
$245$	−19.3662	−	29.1539i	−0.0790458	−	0.118995i
$246$		0			0
$247$	−316.678	+	316.678i	−1.28210	+	1.28210i
$248$	−22.6983	−	22.6983i	−0.0915254	−	0.0915254i
$249$		0			0
$250$	−146.183	−	99.4006i	−0.584733	−	0.397602i
$251$	−175.106			−0.697632			−0.348816	−	0.937191i	$-0.613416\pi$
$251$	−175.106			−0.697632			−0.348816	+	0.937191i	$0.613416\pi$
$252$		0			0
$253$	−104.337	−	104.337i	−0.412399	−	0.412399i
$254$		−	110.747i		−	0.436014i
$255$		0			0
$256$	16.0000			0.0625000
$257$	227.773	−	227.773i	0.886275	−	0.886275i	−0.107888	−	0.994163i	$-0.534409\pi$
$257$	227.773	−	227.773i	0.886275	−	0.886275i	0.994163	+	0.107888i	$0.0344089\pi$
$258$		0			0
$259$			95.7795i			0.369805i
$260$	−34.6640	+	171.839i	−0.133323	+	0.660919i
$261$		0			0
$262$	69.2950	−	69.2950i	0.264485	−	0.264485i
$263$	37.9825	+	37.9825i	0.144420	+	0.144420i	0.775620	−	0.631200i	$-0.217437\pi$
$263$	37.9825	+	37.9825i	0.144420	+	0.144420i	−0.631200	+	0.775620i	$0.717437\pi$
$264$		0			0
$265$	−27.3036	−	5.50778i	−0.103032	−	0.0207841i
$266$	95.5905			0.359363
$267$		0			0
$268$	131.455	+	131.455i	0.490505	+	0.490505i
$269$		−	236.114i		−	0.877748i	−0.898549	−	0.438874i	$-0.855377\pi$
$269$		−	236.114i		−	0.877748i	0.898549	−	0.438874i	$-0.144623\pi$
$270$		0			0
$271$	167.587			0.618404			0.309202	−	0.950996i	$-0.399938\pi$
$271$	167.587			0.618404			0.309202	+	0.950996i	$0.399938\pi$
$272$	74.8984	−	74.8984i	0.275362	−	0.275362i
$273$		0			0
$274$		−	58.0741i		−	0.211949i
$275$	−171.377	+	407.495i	−0.623189	+	1.48180i
$276$		0			0
$277$	354.986	−	354.986i	1.28154	−	1.28154i	0.341743	−	0.939793i	$-0.388983\pi$
$277$	354.986	−	354.986i	1.28154	−	1.28154i	0.939793	−	0.341743i	$-0.111017\pi$
$278$	80.1068	+	80.1068i	0.288154	+	0.288154i
$279$		0			0
$280$	31.1668	−	20.7034i	0.111310	−	0.0739406i
$281$	−396.987			−1.41277			−0.706383	−	0.707829i	$-0.749674\pi$
$281$	−396.987			−1.41277			−0.706383	+	0.707829i	$0.749674\pi$
$282$		0			0
$283$	204.927	+	204.927i	0.724124	+	0.724124i	0.969442	−	0.245319i	$-0.0788926\pi$
$283$	204.927	+	204.927i	0.724124	+	0.724124i	−0.245319	+	0.969442i	$0.578893\pi$
$284$			2.38389i			0.00839397i
$285$		0			0
$286$	438.374			1.53278
$287$	110.058	−	110.058i	0.383476	−	0.383476i
$288$		0			0
$289$		−	412.221i		−	1.42637i
$290$	−106.499	−	21.4835i	−0.367239	−	0.0740809i
$291$		0			0
$292$	−174.150	+	174.150i	−0.596404	+	0.596404i
$293$	320.724	+	320.724i	1.09462	+	1.09462i	0.995028	+	0.0995946i	$0.0317546\pi$
$293$	320.724	+	320.724i	1.09462	+	1.09462i	0.0995946	+	0.995028i	$0.468245\pi$
$294$		0			0
$295$	238.657	+	359.274i	0.809008	+	1.21788i
$296$	−102.393			−0.345921
$297$		0			0
$298$	216.650	+	216.650i	0.727013	+	0.727013i
$299$		−	146.281i		−	0.489234i
$300$		0			0
$301$	−1.05793			−0.00351473
$302$	−170.036	+	170.036i	−0.563033	+	0.563033i
$303$		0			0
$304$			102.191i			0.336153i
$305$	121.646	−	80.8066i	0.398840	−	0.264940i
$306$		0			0
$307$	33.1738	−	33.1738i	0.108058	−	0.108058i	−0.651011	−	0.759069i	$-0.725655\pi$
$307$	33.1738	−	33.1738i	0.108058	−	0.108058i	0.759069	+	0.651011i	$0.225655\pi$
$308$	−66.1624	−	66.1624i	−0.214813	−	0.214813i
$309$		0			0
$310$	15.8688	−	78.6660i	0.0511897	−	0.253761i
$311$	31.4965			0.101275			0.0506375	−	0.998717i	$-0.483875\pi$
$311$	31.4965			0.101275			0.0506375	+	0.998717i	$0.483875\pi$
$312$		0			0
$313$	117.156	+	117.156i	0.374299	+	0.374299i	0.869040	−	0.494741i	$-0.164737\pi$
$313$	117.156	+	117.156i	0.374299	+	0.374299i	−0.494741	+	0.869040i	$0.664737\pi$
$314$		−	329.298i		−	1.04872i
$315$		0			0
$316$	−110.192			−0.348708
$317$	−256.649	+	256.649i	−0.809619	+	0.809619i	−0.984576	−	0.174957i	$-0.944021\pi$
$317$	−256.649	+	256.649i	−0.809619	+	0.809619i	0.174957	+	0.984576i	$0.444021\pi$
$318$		0			0
$319$			271.688i			0.851686i
$320$	22.1328	+	33.3187i	0.0691651	+	0.104121i
$321$		0			0
$322$	−22.0777	+	22.0777i	−0.0685644	+	0.0685644i
$323$	478.369	+	478.369i	1.48102	+	1.48102i
$324$		0			0
$325$	−405.792	+	165.520i	−1.24859	+	0.509292i
$326$	209.263			0.641912
$327$		0			0
$328$	117.657	+	117.657i	0.358709	+	0.358709i
$329$			182.034i			0.553294i
$330$		0			0
$331$	−536.093			−1.61962			−0.809809	−	0.586694i	$-0.800429\pi$
$331$	−536.093			−1.61962			−0.809809	+	0.586694i	$0.800429\pi$
$332$	183.602	−	183.602i	0.553019	−	0.553019i
$333$		0			0
$334$		−	430.649i		−	1.28937i
$335$	−91.9029	+	455.588i	−0.274337	+	1.35996i
$336$		0			0
$337$	147.571	−	147.571i	0.437896	−	0.437896i	−0.453407	−	0.891304i	$-0.649792\pi$
$337$	147.571	−	147.571i	0.437896	−	0.437896i	0.891304	+	0.453407i	$0.149792\pi$
$338$	138.302	+	138.302i	0.409177	+	0.409177i
$339$		0			0
$340$	259.577	+	52.3629i	0.763462	+	0.154008i
$341$	−200.683			−0.588513
$342$		0			0
$343$	13.0958	+	13.0958i	0.0381802	+	0.0381802i
$344$		−	1.13098i		−	0.00328773i
$345$		0			0
$346$	100.802			0.291334
$347$	−53.7981	+	53.7981i	−0.155038	+	0.155038i	−0.780364	−	0.625326i	$-0.784966\pi$
$347$	−53.7981	+	53.7981i	−0.155038	+	0.155038i	0.625326	+	0.780364i	$0.284966\pi$
$348$		0			0
$349$		−	71.8031i		−	0.205740i	−0.994695	−	0.102870i	$-0.967197\pi$
$349$		−	71.8031i		−	0.205740i	0.994695	−	0.102870i	$-0.0328025\pi$
$350$	86.2262	+	36.2634i	0.246361	+	0.103610i
$351$		0			0
$352$	70.7306	−	70.7306i	0.200939	−	0.200939i
$353$	−114.588	−	114.588i	−0.324612	−	0.324612i	0.525921	−	0.850533i	$-0.323721\pi$
$353$	−114.588	−	114.588i	−0.324612	−	0.324612i	−0.850533	+	0.525921i	$0.823721\pi$
$354$		0			0
$355$	−4.96426	+	3.29764i	−0.0139838	+	0.00928912i
$356$	−207.931			−0.584076
$357$		0			0
$358$	−21.2898	−	21.2898i	−0.0594687	−	0.0594687i
$359$			60.5664i			0.168709i	0.996436	+	0.0843543i	$0.0268828\pi$
$359$			60.5664i			0.168709i	−0.996436	+	0.0843543i	$0.973117\pi$
$360$		0			0
$361$	−291.682			−0.807983
$362$	−22.7581	+	22.7581i	−0.0628678	+	0.0628678i
$363$		0			0
$364$		−	92.7602i		−	0.254836i
$365$	−603.555	−	121.751i	−1.65358	−	0.333566i
$366$		0			0
$367$	−18.4536	+	18.4536i	−0.0502824	+	0.0502824i	−0.731801	−	0.681519i	$-0.761320\pi$
$367$	−18.4536	+	18.4536i	−0.0502824	+	0.0502824i	0.681519	+	0.731801i	$0.261320\pi$
$368$	−23.6021	−	23.6021i	−0.0641361	−	0.0641361i
$369$		0			0
$370$	−141.640	−	213.224i	−0.382810	−	0.576282i
$371$	14.7387			0.0397270
$372$		0			0
$373$	269.454	+	269.454i	0.722397	+	0.722397i	0.969093	−	0.246696i	$-0.0793448\pi$
$373$	269.454	+	269.454i	0.722397	+	0.722397i	−0.246696	+	0.969093i	$0.579345\pi$
$374$		−	662.201i		−	1.77059i
$375$		0			0
$376$	−194.602			−0.517559
$377$	−190.454	+	190.454i	−0.505184	+	0.505184i
$378$		0			0
$379$		−	10.4860i		−	0.0276676i	−0.999904	−	0.0138338i	$-0.995596\pi$
$379$		−	10.4860i		−	0.0276676i	0.999904	−	0.0138338i	$-0.00440357\pi$
$380$	−212.804	+	141.360i	−0.560010	+	0.372001i
$381$		0			0
$382$	113.711	−	113.711i	0.297672	−	0.297672i
$383$	−93.8346	−	93.8346i	−0.244999	−	0.244999i	0.573916	−	0.818915i	$-0.305424\pi$
$383$	−93.8346	−	93.8346i	−0.244999	−	0.244999i	−0.818915	+	0.573916i	$0.805424\pi$
$384$		0			0
$385$	46.2554	−	229.301i	0.120144	−	0.595586i
$386$	219.872			0.569616
$387$		0			0
$388$	−174.947	−	174.947i	−0.450894	−	0.450894i
$389$		−	130.485i		−	0.335437i	−0.985835	−	0.167718i	$-0.946360\pi$
$389$		−	130.485i		−	0.335437i	0.985835	−	0.167718i	$-0.0536399\pi$
$390$		0			0
$391$	−220.970			−0.565140
$392$	−14.0000	+	14.0000i	−0.0357143	+	0.0357143i
$393$		0			0
$394$			164.421i			0.417313i
$395$	−152.429	−	229.466i	−0.385895	−	0.580926i
$396$		0			0
$397$	44.8845	−	44.8845i	0.113059	−	0.113059i	−0.648314	−	0.761373i	$-0.724526\pi$
$397$	44.8845	−	44.8845i	0.113059	−	0.113059i	0.761373	+	0.648314i	$0.224526\pi$
$398$	−232.689	−	232.689i	−0.584646	−	0.584646i
$399$		0			0
$400$	−38.7673	+	92.1797i	−0.0969181	+	0.230449i
$401$	−329.486			−0.821660			−0.410830	−	0.911712i	$-0.634761\pi$
$401$	−329.486			−0.821660			−0.410830	+	0.911712i	$0.634761\pi$
$402$		0			0
$403$	−140.679	−	140.679i	−0.349081	−	0.349081i
$404$			11.6418i			0.0288164i
$405$		0			0
$406$	57.4893			0.141599
$407$	−452.643	+	452.643i	−1.11214	+	1.11214i
$408$		0			0
$409$			388.439i			0.949730i	0.880059	+	0.474865i	$0.157503\pi$
$409$			388.439i			0.949730i	−0.880059	+	0.474865i	$0.842497\pi$
$410$	−82.2560	+	407.765i	−0.200624	+	0.994549i
$411$		0			0
$412$	121.561	−	121.561i	0.295051	−	0.295051i
$413$	−161.384	−	161.384i	−0.390761	−	0.390761i
$414$		0			0
$415$	636.315	+	128.360i	1.53329	+	0.309301i
$416$	99.1648			0.238377
$417$		0			0
$418$	451.750	+	451.750i	1.08074	+	1.08074i
$419$			268.553i			0.640937i	0.947259	+	0.320469i	$0.103840\pi$
$419$			268.553i			0.640937i	−0.947259	+	0.320469i	$0.896160\pi$
$420$		0			0
$421$	−680.092			−1.61542			−0.807710	−	0.589580i	$-0.799293\pi$
$421$	−680.092			−1.61542			−0.807710	+	0.589580i	$0.799293\pi$
$422$	−341.021	+	341.021i	−0.808107	+	0.808107i
$423$		0			0
$424$			15.7564i			0.0371612i
$425$	250.032	+	612.982i	0.588310	+	1.44231i
$426$		0			0
$427$	−54.6429	+	54.6429i	−0.127969	+	0.127969i
$428$	161.362	+	161.362i	0.377013	+	0.377013i
$429$		0			0
$430$	2.35518	−	1.56449i	0.00547715	−	0.00363834i
$431$	−451.123			−1.04669			−0.523344	−	0.852121i	$-0.675316\pi$
$431$	−451.123			−1.04669			−0.523344	+	0.852121i	$0.675316\pi$
$432$		0			0
$433$	−223.798	−	223.798i	−0.516855	−	0.516855i	0.399763	−	0.916618i	$-0.369092\pi$
$433$	−223.798	−	223.798i	−0.516855	−	0.516855i	−0.916618	+	0.399763i	$0.869092\pi$
$434$			42.4646i			0.0978447i
$435$		0			0
$436$	−128.890			−0.295619
$437$	150.744	−	150.744i	0.344953	−	0.344953i
$438$		0			0
$439$			599.647i			1.36594i	0.730447	+	0.682969i	$0.239312\pi$
$439$			599.647i			1.36594i	−0.730447	+	0.682969i	$0.760688\pi$
$440$	245.133	+	49.4491i	0.557119	+	0.112384i
$441$		0			0
$442$	464.205	−	464.205i	1.05024	−	1.05024i
$443$	−212.227	−	212.227i	−0.479068	−	0.479068i	0.425765	−	0.904834i	$-0.360005\pi$
$443$	−212.227	−	212.227i	−0.479068	−	0.479068i	−0.904834	+	0.425765i	$0.860005\pi$
$444$		0			0
$445$	−287.631	−	433.000i	−0.646362	−	0.973033i
$446$	237.041			0.531482
$447$		0			0
$448$	−14.9666	−	14.9666i	−0.0334077	−	0.0334077i
$449$		−	69.3409i		−	0.154434i	−0.997014	−	0.0772170i	$-0.975397\pi$
$449$		−	69.3409i		−	0.154434i	0.997014	−	0.0772170i	$-0.0246034\pi$
$450$		0			0
$451$	1040.24			2.30652
$452$	−161.755	+	161.755i	−0.357864	+	0.357864i
$453$		0			0
$454$		−	3.19917i		−	0.00704662i
$455$	193.166	−	128.315i	0.424540	−	0.282012i
$456$		0			0
$457$	−399.145	+	399.145i	−0.873404	+	0.873404i	−0.992842	−	0.119438i	$-0.961891\pi$
$457$	−399.145	+	399.145i	−0.873404	+	0.873404i	0.119438	+	0.992842i	$0.461891\pi$
$458$	−59.2261	−	59.2261i	−0.129315	−	0.129315i
$459$		0			0
$460$	16.5007	−	81.7983i	0.0358710	−	0.177822i
$461$	−357.157			−0.774743			−0.387372	−	0.921924i	$-0.626617\pi$
$461$	−357.157			−0.774743			−0.387372	+	0.921924i	$0.626617\pi$
$462$		0			0
$463$	139.822	+	139.822i	0.301991	+	0.301991i	0.841793	−	0.539801i	$-0.181501\pi$
$463$	139.822	+	139.822i	0.301991	+	0.301991i	−0.539801	+	0.841793i	$0.681501\pi$
$464$			61.4587i			0.132454i
$465$		0			0
$466$	−532.104			−1.14185
$467$	429.131	−	429.131i	0.918909	−	0.918909i	−0.0780407	−	0.996950i	$-0.524866\pi$
$467$	429.131	−	429.131i	0.918909	−	0.918909i	0.996950	+	0.0780407i	$0.0248664\pi$
$468$		0			0
$469$		−	245.930i		−	0.524372i
$470$	−269.193	−	405.243i	−0.572752	−	0.862220i
$471$		0			0
$472$	172.527	−	172.527i	0.365524	−	0.365524i
$473$	−4.99968	−	4.99968i	−0.0105701	−	0.0105701i
$474$		0			0
$475$	−588.743	−	247.603i	−1.23946	−	0.521269i
$476$	−140.122			−0.294374
$477$		0			0
$478$	−420.919	−	420.919i	−0.880584	−	0.880584i
$479$		−	524.078i		−	1.09411i	−0.837097	−	0.547054i	$-0.815749\pi$
$479$		−	524.078i		−	1.09411i	0.837097	−	0.547054i	$-0.184251\pi$
$480$		0			0
$481$	−634.609			−1.31935
$482$	−347.574	+	347.574i	−0.721108	+	0.721108i
$483$		0			0
$484$		−	383.352i		−	0.792049i
$485$	122.309	−	606.317i	0.252183	−	1.25014i
$486$		0			0
$487$	234.249	−	234.249i	0.481005	−	0.481005i	−0.424447	−	0.905453i	$-0.639532\pi$
$487$	234.249	−	234.249i	0.481005	−	0.481005i	0.905453	+	0.424447i	$0.139532\pi$
$488$	−58.4157	−	58.4157i	−0.119704	−	0.119704i
$489$		0			0
$490$	−48.5201	−	9.78767i	−0.0990206	−	0.0199748i
$491$	−171.731			−0.349758			−0.174879	−	0.984590i	$-0.555954\pi$
$491$	−171.731			−0.349758			−0.174879	+	0.984590i	$0.555954\pi$
$492$		0			0
$493$	287.697	+	287.697i	0.583564	+	0.583564i
$494$			633.357i			1.28210i
$495$		0			0
$496$	−45.3966			−0.0915254
$497$	2.22992	−	2.22992i	0.00448677	−	0.00448677i
$498$		0			0
$499$			507.901i			1.01784i	0.860814	+	0.508919i	$0.169955\pi$
$499$			507.901i			1.01784i	−0.860814	+	0.508919i	$0.830045\pi$
$500$	−245.584	+	46.7826i	−0.491168	+	0.0935652i
$501$		0			0
$502$	−175.106	+	175.106i	−0.348816	+	0.348816i
$503$	−409.302	−	409.302i	−0.813722	−	0.813722i	0.171468	−	0.985190i	$-0.445149\pi$
$503$	−409.302	−	409.302i	−0.813722	−	0.813722i	−0.985190	+	0.171468i	$0.945149\pi$
$504$		0			0
$505$	−24.2432	+	16.1042i	−0.0480064	+	0.0318895i
$506$	−208.674			−0.412399
$507$		0			0
$508$	−110.747	−	110.747i	−0.218007	−	0.218007i
$509$		−	762.148i		−	1.49734i	−0.662941	−	0.748671i	$-0.730692\pi$
$509$		−	762.148i		−	1.49734i	0.662941	−	0.748671i	$-0.269308\pi$
$510$		0			0
$511$	325.805			0.637582
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	455.545i		−	0.886275i
$515$	421.296	+	84.9855i	0.818051	+	0.165020i
$516$		0			0
$517$	−860.270	+	860.270i	−1.66396	+	1.66396i
$518$	95.7795	+	95.7795i	0.184903	+	0.184903i
$519$		0			0
$520$	137.175	+	206.503i	0.263798	+	0.397121i
$521$	870.243			1.67033			0.835166	−	0.549999i	$-0.185372\pi$
$521$	870.243			1.67033			0.835166	+	0.549999i	$0.185372\pi$
$522$		0			0
$523$	94.5185	+	94.5185i	0.180724	+	0.180724i	0.791671	−	0.610947i	$-0.209211\pi$
$523$	94.5185	+	94.5185i	0.180724	+	0.180724i	−0.610947	+	0.791671i	$0.709211\pi$
$524$		−	138.590i		−	0.264485i
$525$		0			0
$526$	75.9650			0.144420
$527$	−212.508	+	212.508i	−0.403241	+	0.403241i
$528$		0			0
$529$		−	459.368i		−	0.868370i
$530$	−32.8114	+	21.7958i	−0.0619082	+	0.0411241i
$531$		0			0
$532$	95.5905	−	95.5905i	0.179681	−	0.179681i
$533$	729.212	+	729.212i	1.36813	+	1.36813i
$534$		0			0
$535$	−112.811	+	559.234i	−0.210862	+	1.04530i
$536$	262.911			0.490505
$537$		0			0
$538$	−236.114	−	236.114i	−0.438874	−	0.438874i
$539$			123.779i			0.229645i
$540$		0			0
$541$	−211.503			−0.390948			−0.195474	−	0.980709i	$-0.562624\pi$
$541$	−211.503			−0.390948			−0.195474	+	0.980709i	$0.562624\pi$
$542$	167.587	−	167.587i	0.309202	−	0.309202i
$543$		0			0
$544$		−	149.797i		−	0.275362i
$545$	−178.294	−	268.403i	−0.327144	−	0.492483i
$546$		0			0
$547$	76.5236	−	76.5236i	0.139897	−	0.139897i	−0.633690	−	0.773587i	$-0.718461\pi$
$547$	76.5236	−	76.5236i	0.139897	−	0.139897i	0.773587	+	0.633690i	$0.218461\pi$
$548$	−58.0741	−	58.0741i	−0.105975	−	0.105975i
$549$		0			0
$550$	236.118	+	578.872i	0.429306	+	1.05249i
$551$	−392.531			−0.712397
$552$		0			0
$553$	103.075	+	103.075i	0.186392	+	0.186392i
$554$		−	709.971i		−	1.28154i
$555$		0			0
$556$	160.214			0.288154
$557$	−251.466	+	251.466i	−0.451465	+	0.451465i	−0.895841	−	0.444376i	$-0.853426\pi$
$557$	−251.466	+	251.466i	−0.451465	+	0.451465i	0.444376	+	0.895841i	$0.353426\pi$
$558$		0			0
$559$		−	7.00959i		−	0.0125395i
$560$	10.4635	−	51.8702i	0.0186847	−	0.0926253i
$561$		0			0
$562$	−396.987	+	396.987i	−0.706383	+	0.706383i
$563$	89.8908	+	89.8908i	0.159664	+	0.159664i	0.782418	−	0.622754i	$-0.213986\pi$
$563$	89.8908	+	89.8908i	0.159664	+	0.159664i	−0.622754	+	0.782418i	$0.713986\pi$
$564$		0			0
$565$	−560.597	−	113.086i	−0.992207	−	0.200152i
$566$	409.854			0.724124
$567$		0			0
$568$	2.38389	+	2.38389i	0.00419699	+	0.00419699i
$569$			404.950i			0.711687i	0.934545	+	0.355844i	$0.115806\pi$
$569$			404.950i			0.711687i	−0.934545	+	0.355844i	$0.884194\pi$
$570$		0			0
$571$	186.774			0.327099			0.163550	−	0.986535i	$-0.447706\pi$
$571$	186.774			0.327099			0.163550	+	0.986535i	$0.447706\pi$
$572$	438.374	−	438.374i	0.766388	−	0.766388i
$573$		0			0
$574$		−	220.115i		−	0.383476i
$575$	193.164	−	78.7904i	0.335937	−	0.137027i
$576$		0			0
$577$	−428.779	+	428.779i	−0.743117	+	0.743117i	−0.973177	−	0.230059i	$-0.926108\pi$
$577$	−428.779	+	428.779i	−0.743117	+	0.743117i	0.230059	+	0.973177i	$0.426108\pi$
$578$	−412.221	−	412.221i	−0.713184	−	0.713184i
$579$		0			0
$580$	−127.983	+	85.0159i	−0.220660	+	0.146579i
$581$	−343.489			−0.591202
$582$		0			0
$583$	69.6535	+	69.6535i	0.119474	+	0.119474i
$584$			348.300i			0.596404i
$585$		0			0
$586$	641.449			1.09462
$587$	278.861	−	278.861i	0.475061	−	0.475061i	−0.428487	−	0.903548i	$-0.640953\pi$
$587$	278.861	−	278.861i	0.475061	−	0.475061i	0.903548	+	0.428487i	$0.140953\pi$
$588$		0			0
$589$		−	289.944i		−	0.492265i
$590$	597.932	+	120.617i	1.01344	+	0.204436i
$591$		0			0
$592$	−102.393	+	102.393i	−0.172960	+	0.172960i
$593$	−439.594	−	439.594i	−0.741306	−	0.741306i	0.231523	−	0.972829i	$-0.425629\pi$
$593$	−439.594	−	439.594i	−0.741306	−	0.741306i	−0.972829	+	0.231523i	$0.925629\pi$
$594$		0			0
$595$	−193.831	−	291.793i	−0.325766	−	0.490408i
$596$	433.300			0.727013
$597$		0			0
$598$	−146.281	−	146.281i	−0.244617	−	0.244617i
$599$		−	782.181i		−	1.30581i	−0.757439	−	0.652906i	$-0.773550\pi$
$599$		−	782.181i		−	1.30581i	0.757439	−	0.652906i	$-0.226450\pi$
$600$		0			0
$601$	589.687			0.981177			0.490589	−	0.871391i	$-0.336782\pi$
$601$	589.687			0.981177			0.490589	+	0.871391i	$0.336782\pi$
$602$	−1.05793	+	1.05793i	−0.00175737	+	0.00175737i
$603$		0			0
$604$			340.072i			0.563033i
$605$	798.300	−	530.291i	1.31950	−	0.876514i
$606$		0			0
$607$	−167.200	+	167.200i	−0.275453	+	0.275453i	−0.831291	−	0.555838i	$-0.812398\pi$
$607$	−167.200	+	167.200i	−0.275453	+	0.275453i	0.555838	+	0.831291i	$0.312398\pi$
$608$	102.191	+	102.191i	0.168077	+	0.168077i
$609$		0			0
$610$	40.8396	−	202.453i	0.0669501	−	0.331890i
$611$	−1206.10			−1.97398
$612$		0			0
$613$	−334.599	−	334.599i	−0.545838	−	0.545838i	0.379396	−	0.925234i	$-0.376132\pi$
$613$	−334.599	−	334.599i	−0.545838	−	0.545838i	−0.925234	+	0.379396i	$0.876132\pi$
$614$		−	66.3477i		−	0.108058i
$615$		0			0
$616$	−132.325			−0.214813
$617$	79.8866	−	79.8866i	0.129476	−	0.129476i	−0.639399	−	0.768875i	$-0.720817\pi$
$617$	79.8866	−	79.8866i	0.129476	−	0.129476i	0.768875	+	0.639399i	$0.220817\pi$
$618$		0			0
$619$		−	415.380i		−	0.671050i	−0.942031	−	0.335525i	$-0.891086\pi$
$619$		−	415.380i		−	0.671050i	0.942031	−	0.335525i	$-0.108914\pi$
$620$	−62.7972	−	94.5348i	−0.101286	−	0.152475i
$621$		0			0
$622$	31.4965	−	31.4965i	0.0506375	−	0.0506375i
$623$	194.502	+	194.502i	0.312202	+	0.312202i
$624$		0			0
$625$	−437.138	−	446.694i	−0.699420	−	0.714711i
$626$	234.311			0.374299
$627$		0			0
$628$	−329.298	−	329.298i	−0.524360	−	0.524360i
$629$			958.630i			1.52405i
$630$		0			0
$631$	−452.429			−0.717002			−0.358501	−	0.933529i	$-0.616712\pi$
$631$	−452.429			−0.717002			−0.358501	+	0.933529i	$0.616712\pi$
$632$	−110.192	+	110.192i	−0.174354	+	0.174354i
$633$		0			0
$634$			513.298i			0.809619i
$635$	77.4257	−	383.820i	0.121930	−	0.604441i
$636$		0			0
$637$	−86.7692	+	86.7692i	−0.136215	+	0.136215i
$638$	271.688	+	271.688i	0.425843	+	0.425843i
$639$		0			0
$640$	55.4516	+	11.1859i	0.0866431	+	0.0174780i
$641$	333.271			0.519924			0.259962	−	0.965619i	$-0.416290\pi$
$641$	333.271			0.519924			0.259962	+	0.965619i	$0.416290\pi$
$642$		0			0
$643$	614.442	+	614.442i	0.955587	+	0.955587i	0.999055	−	0.0434678i	$-0.0138406\pi$
$643$	614.442	+	614.442i	0.955587	+	0.955587i	−0.0434678	+	0.999055i	$0.513841\pi$
$644$			44.1555i			0.0685644i
$645$		0			0
$646$	956.738			1.48102
$647$	−800.292	+	800.292i	−1.23693	+	1.23693i	−0.275678	+	0.961250i	$0.588902\pi$
$647$	−800.292	+	800.292i	−1.23693	+	1.23693i	−0.961250	+	0.275678i	$0.911098\pi$
$648$		0			0
$649$		−	1525.37i		−	2.35034i
$650$	−240.272	+	571.311i	−0.369649	+	0.878941i
$651$		0			0
$652$	209.263	−	209.263i	0.320956	−	0.320956i
$653$	327.250	+	327.250i	0.501148	+	0.501148i	0.911795	−	0.410647i	$-0.134697\pi$
$653$	327.250	+	327.250i	0.501148	+	0.501148i	−0.410647	+	0.911795i	$0.634697\pi$
$654$		0			0
$655$	288.603	−	191.712i	0.440615	−	0.292690i
$656$	235.313			0.358709
$657$		0			0
$658$	182.034	+	182.034i	0.276647	+	0.276647i
$659$			1113.68i			1.68995i	0.534802	+	0.844977i	$0.320386\pi$
$659$			1113.68i			1.68995i	−0.534802	+	0.844977i	$0.679614\pi$
$660$		0			0
$661$	−58.5883			−0.0886359			−0.0443179	−	0.999017i	$-0.514111\pi$
$661$	−58.5883			−0.0886359			−0.0443179	+	0.999017i	$0.514111\pi$
$662$	−536.093	+	536.093i	−0.809809	+	0.809809i
$663$		0			0
$664$		−	367.205i		−	0.553019i
$665$	331.290	+	66.8292i	0.498181	+	0.100495i
$666$		0			0
$667$	90.6596	−	90.6596i	0.135921	−	0.135921i
$668$	−430.649	−	430.649i	−0.644684	−	0.644684i
$669$		0			0
$670$	363.685	+	547.491i	0.542813	+	0.817150i
$671$	−516.472			−0.769706
$672$		0			0
$673$	544.810	+	544.810i	0.809524	+	0.809524i	0.984562	−	0.175038i	$-0.0560048\pi$
$673$	544.810	+	544.810i	0.809524	+	0.809524i	−0.175038	+	0.984562i	$0.556005\pi$
$674$		−	295.142i		−	0.437896i
$675$		0			0
$676$	276.604			0.409177
$677$	654.528	−	654.528i	0.966807	−	0.966807i	−0.0326593	−	0.999467i	$-0.510398\pi$
$677$	654.528	−	654.528i	0.966807	−	0.966807i	0.999467	+	0.0326593i	$0.0103976\pi$
$678$		0			0
$679$			327.295i			0.482026i
$680$	311.940	−	207.214i	0.458735	−	0.304727i
$681$		0			0
$682$	−200.683	+	200.683i	−0.294257	+	0.294257i
$683$	378.585	+	378.585i	0.554298	+	0.554298i	0.927678	−	0.373381i	$-0.121801\pi$
$683$	378.585	+	378.585i	0.554298	+	0.554298i	−0.373381	+	0.927678i	$0.621801\pi$
$684$		0			0
$685$	40.6007	−	201.269i	0.0592711	−	0.293823i
$686$	26.1916			0.0381802
$687$		0			0
$688$	−1.13098	−	1.13098i	−0.00164387	−	0.00164387i
$689$			97.6547i			0.141734i
$690$		0			0
$691$	612.032			0.885719			0.442859	−	0.896591i	$-0.353964\pi$
$691$	612.032			0.885719			0.442859	+	0.896591i	$0.353964\pi$
$692$	100.802	−	100.802i	0.145667	−	0.145667i
$693$		0			0
$694$			107.596i			0.155038i
$695$	221.624	+	333.632i	0.318883	+	0.480046i
$696$		0			0
$697$	1101.54	−	1101.54i	1.58040	−	1.58040i
$698$	−71.8031	−	71.8031i	−0.102870	−	0.102870i
$699$		0			0
$700$	122.490	−	49.9628i	0.174985	−	0.0713754i
$701$	−351.130			−0.500899			−0.250450	−	0.968130i	$-0.580578\pi$
$701$	−351.130			−0.500899			−0.250450	+	0.968130i	$0.580578\pi$
$702$		0			0
$703$	−653.972	−	653.972i	−0.930259	−	0.930259i
$704$		−	141.461i		−	0.200939i
$705$		0			0
$706$	−229.176			−0.324612
$707$	10.8899	−	10.8899i	0.0154030	−	0.0154030i
$708$		0			0
$709$		−	652.326i		−	0.920065i	−0.887902	−	0.460033i	$-0.847838\pi$
$709$		−	652.326i		−	0.920065i	0.887902	−	0.460033i	$-0.152162\pi$
$710$	−1.66662	+	8.26189i	−0.00234735	+	0.0116365i
$711$		0			0
$712$	−207.931	+	207.931i	−0.292038	+	0.292038i
$713$	66.9659	+	66.9659i	0.0939213	+	0.0939213i
$714$		0			0
$715$	1519.28	+	306.476i	2.12487	+	0.428637i
$716$	−42.5796			−0.0594687
$717$		0			0
$718$	60.5664	+	60.5664i	0.0843543	+	0.0843543i
$719$			823.559i			1.14542i	0.819757	+	0.572711i	$0.194108\pi$
$719$			823.559i			1.14542i	−0.819757	+	0.572711i	$0.805892\pi$
$720$		0			0
$721$	−227.419			−0.315422
$722$	−291.682	+	291.682i	−0.403991	+	0.403991i
$723$		0			0
$724$			45.5163i			0.0628678i
$725$	−354.078	−	148.911i	−0.488383	−	0.205395i
$726$		0			0
$727$	−724.914	+	724.914i	−0.997131	+	0.997131i	−0.999996	−	0.00286477i	$-0.999088\pi$
$727$	−724.914	+	724.914i	−0.997131	+	0.997131i	0.00286477	+	0.999996i	$0.499088\pi$
$728$	−92.7602	−	92.7602i	−0.127418	−	0.127418i
$729$		0			0
$730$	−725.306	+	481.804i	−0.993571	+	0.660005i
$731$	−10.5886			−0.0144850
$732$		0			0
$733$	49.2582	+	49.2582i	0.0672008	+	0.0672008i	0.739908	−	0.672708i	$-0.234869\pi$
$733$	49.2582	+	49.2582i	0.0672008	+	0.0672008i	−0.672708	+	0.739908i	$0.734869\pi$
$734$			36.9073i			0.0502824i
$735$		0			0
$736$	−47.2042			−0.0641361
$737$	1162.24	−	1162.24i	1.57699	−	1.57699i
$738$		0			0
$739$		−	417.024i		−	0.564309i	−0.959369	−	0.282154i	$-0.908951\pi$
$739$		−	417.024i		−	0.564309i	0.959369	−	0.282154i	$-0.0910490\pi$
$740$	−354.864	−	71.5846i	−0.479546	−	0.0967360i
$741$		0			0
$742$	14.7387	−	14.7387i	0.0198635	−	0.0198635i
$743$	736.124	+	736.124i	0.990746	+	0.990746i	0.999958	−	0.00921142i	$-0.00293213\pi$
$743$	736.124	+	736.124i	0.990746	+	0.990746i	−0.00921142	+	0.999958i	$0.502932\pi$
$744$		0			0
$745$	599.384	+	902.313i	0.804543	+	1.21116i
$746$	538.908			0.722397
$747$		0			0
$748$	−662.201	−	662.201i	−0.885295	−	0.885295i
$749$		−	301.880i		−	0.403044i
$750$		0			0
$751$	1083.70			1.44301			0.721506	−	0.692409i	$-0.243450\pi$
$751$	1083.70			1.44301			0.721506	+	0.692409i	$0.243450\pi$
$752$	−194.602	+	194.602i	−0.258779	+	0.258779i
$753$		0			0
$754$			380.909i			0.505184i
$755$	−708.173	+	470.422i	−0.937978	+	0.623076i
$756$		0			0
$757$	1002.25	−	1002.25i	1.32397	−	1.32397i	0.413439	−	0.910532i	$-0.364328\pi$
$757$	1002.25	−	1002.25i	1.32397	−	1.32397i	0.910532	−	0.413439i	$-0.135672\pi$
$758$	−10.4860	−	10.4860i	−0.0138338	−	0.0138338i
$759$		0			0
$760$	−71.4434	+	354.164i	−0.0940044	+	0.466005i
$761$	−1104.17			−1.45095			−0.725474	−	0.688250i	$-0.758379\pi$
$761$	−1104.17			−1.45095			−0.725474	+	0.688250i	$0.758379\pi$
$762$		0			0
$763$	120.566	+	120.566i	0.158015	+	0.158015i
$764$		−	227.421i		−	0.297672i
$765$		0			0
$766$	−187.669			−0.244999
$767$	1069.29	−	1069.29i	1.39412	−	1.39412i
$768$		0			0
$769$			198.908i			0.258658i	0.991602	+	0.129329i	$0.0412823\pi$
$769$			198.908i			0.258658i	−0.991602	+	0.129329i	$0.958718\pi$
$770$	−183.045	−	275.556i	−0.237721	−	0.357865i
$771$		0			0
$772$	219.872	−	219.872i	0.284808	−	0.284808i
$773$	−326.316	−	326.316i	−0.422142	−	0.422142i	0.463798	−	0.885941i	$-0.346486\pi$
$773$	−326.316	−	326.316i	−0.422142	−	0.422142i	−0.885941	+	0.463798i	$0.846486\pi$
$774$		0			0
$775$	109.994	−	261.540i	0.141927	−	0.337471i
$776$	−349.894			−0.450894
$777$		0			0
$778$	−130.485	−	130.485i	−0.167718	−	0.167718i
$779$			1502.92i			1.92930i
$780$		0			0
$781$	21.0767			0.0269868
$782$	−220.970	+	220.970i	−0.282570	+	0.282570i
$783$		0			0
$784$			28.0000i			0.0357143i
$785$	230.218	−	1141.25i	0.293272	−	1.45383i
$786$		0			0
$787$	337.521	−	337.521i	0.428870	−	0.428870i	−0.459373	−	0.888243i	$-0.651926\pi$
$787$	337.521	−	337.521i	0.428870	−	0.428870i	0.888243	+	0.459373i	$0.151926\pi$
$788$	164.421	+	164.421i	0.208657	+	0.208657i
$789$		0			0
$790$	−381.894	−	77.0372i	−0.483411	−	0.0975155i
$791$	302.615			0.382573
$792$		0			0
$793$	−362.049	−	362.049i	−0.456556	−	0.456556i
$794$		−	89.7690i		−	0.113059i
$795$		0			0
$796$	−465.378			−0.584646
$797$	−111.780	+	111.780i	−0.140250	+	0.140250i	−0.773746	−	0.633496i	$-0.781619\pi$
$797$	−111.780	+	111.780i	−0.140250	+	0.140250i	0.633496	+	0.773746i	$0.281619\pi$
$798$		0			0
$799$			1821.92i			2.28025i
$800$	53.4125	+	130.947i	0.0667656	+	0.163684i
$801$		0			0
$802$	−329.486	+	329.486i	−0.410830	+	0.410830i
$803$	1539.71	+	1539.71i	1.91745	+	1.91745i
$804$		0			0
$805$	−91.9503	+	61.0803i	−0.114224	+	0.0758762i
$806$	−281.359			−0.349081
$807$		0			0
$808$	11.6418	+	11.6418i	0.0144082	+	0.0144082i
$809$			30.4788i			0.0376746i	0.999823	+	0.0188373i	$0.00599646\pi$
$809$			30.4788i			0.0376746i	−0.999823	+	0.0188373i	$0.994004\pi$
$810$		0			0
$811$	71.2377			0.0878393			0.0439197	−	0.999035i	$-0.486015\pi$
$811$	71.2377			0.0878393			0.0439197	+	0.999035i	$0.486015\pi$
$812$	57.4893	−	57.4893i	0.0707996	−	0.0707996i
$813$		0			0
$814$			905.286i			1.11214i
$815$	725.248	+	146.300i	0.889875	+	0.179509i
$816$		0			0
$817$	7.22346	−	7.22346i	0.00884145	−	0.00884145i
$818$	388.439	+	388.439i	0.474865	+	0.474865i
$819$		0			0
$820$	325.509	+	490.021i	0.396962	+	0.597587i
$821$	232.520			0.283216			0.141608	−	0.989923i	$-0.454773\pi$
$821$	232.520			0.283216			0.141608	+	0.989923i	$0.454773\pi$
$822$		0			0
$823$	−157.877	−	157.877i	−0.191832	−	0.191832i	0.604656	−	0.796487i	$-0.293311\pi$
$823$	−157.877	−	157.877i	−0.191832	−	0.191832i	−0.796487	+	0.604656i	$0.793311\pi$
$824$		−	243.122i		−	0.295051i
$825$		0			0
$826$	−322.769			−0.390761
$827$	654.653	−	654.653i	0.791600	−	0.791600i	−0.190154	−	0.981754i	$-0.560899\pi$
$827$	654.653	−	654.653i	0.791600	−	0.791600i	0.981754	+	0.190154i	$0.0608987\pi$
$828$		0			0
$829$			863.280i			1.04135i	0.853755	+	0.520675i	$0.174320\pi$
$829$			863.280i			1.04135i	−0.853755	+	0.520675i	$0.825680\pi$
$830$	764.675	−	507.955i	0.921295	−	0.611994i
$831$		0			0
$832$	99.1648	−	99.1648i	0.119188	−	0.119188i
$833$	131.072	+	131.072i	0.157349	+	0.157349i
$834$		0			0
$835$	301.075	−	1492.51i	0.360569	−	1.78744i
$836$	903.500			1.08074
$837$		0			0
$838$	268.553	+	268.553i	0.320469	+	0.320469i
$839$		−	1114.46i		−	1.32832i	−0.747593	−	0.664158i	$-0.768790\pi$
$839$		−	1114.46i		−	1.32832i	0.747593	−	0.664158i	$-0.231210\pi$
$840$		0			0
$841$	604.927			0.719295
$842$	−680.092	+	680.092i	−0.807710	+	0.807710i
$843$		0			0
$844$			682.043i			0.808107i
$845$	382.626	+	576.005i	0.452812	+	0.681663i
$846$		0			0
$847$	−358.593	+	358.593i	−0.423368	+	0.423368i
$848$	15.7564	+	15.7564i	0.0185806	+	0.0185806i
$849$		0			0
$850$	863.014	+	362.950i	1.01531	+	0.427001i
$851$	302.085			0.354976
$852$		0			0
$853$	981.738	+	981.738i	1.15092	+	1.15092i	0.986368	+	0.164556i	$0.0526190\pi$
$853$	981.738	+	981.738i	1.15092	+	1.15092i	0.164556	+	0.986368i	$0.447381\pi$
$854$			109.286i			0.127969i
$855$		0			0
$856$	322.723			0.377013
$857$	−52.3297	+	52.3297i	−0.0610615	+	0.0610615i	−0.736978	−	0.675917i	$-0.763748\pi$
$857$	−52.3297	+	52.3297i	−0.0610615	+	0.0610615i	0.675917	+	0.736978i	$0.263748\pi$
$858$		0			0
$859$		−	1321.03i		−	1.53787i	−0.639328	−	0.768934i	$-0.720788\pi$
$859$		−	1321.03i		−	1.53787i	0.639328	−	0.768934i	$-0.279212\pi$
$860$	0.790689	−	3.91966i	0.000919406	−	0.00455775i
$861$		0			0
$862$	−451.123	+	451.123i	−0.523344	+	0.523344i
$863$	−610.077	−	610.077i	−0.706926	−	0.706926i	0.258962	−	0.965888i	$-0.416620\pi$
$863$	−610.077	−	610.077i	−0.706926	−	0.706926i	−0.965888	+	0.258962i	$0.916620\pi$
$864$		0			0
$865$	349.351	+	70.4724i	0.403874	+	0.0814710i
$866$	−447.596			−0.516855
$867$		0			0
$868$	42.4646	+	42.4646i	0.0489224	+	0.0489224i
$869$			974.242i			1.12111i
$870$		0			0
$871$	1629.47			1.87080
$872$	−128.890	+	128.890i	−0.147810	+	0.147810i
$873$		0			0
$874$		−	301.489i		−	0.344953i
$875$	273.484	+	185.961i	0.312553	+	0.212527i
$876$		0			0
$877$	−866.286	+	866.286i	−0.987783	+	0.987783i	−0.999926	−	0.0121430i	$-0.996135\pi$
$877$	−866.286	+	866.286i	−0.987783	+	0.987783i	0.0121430	+	0.999926i	$0.496135\pi$
$878$	599.647	+	599.647i	0.682969	+	0.682969i
$879$		0			0
$880$	294.582	−	195.683i	0.334752	−	0.222368i
$881$	1215.34			1.37950			0.689749	−	0.724049i	$-0.257721\pi$
$881$	1215.34			1.37950			0.689749	+	0.724049i	$0.257721\pi$
$882$		0			0
$883$	−590.925	−	590.925i	−0.669224	−	0.669224i	0.288312	−	0.957536i	$-0.406906\pi$
$883$	−590.925	−	590.925i	−0.669224	−	0.669224i	−0.957536	+	0.288312i	$0.906906\pi$
$884$		−	928.410i		−	1.05024i
$885$		0			0
$886$	−424.454			−0.479068
$887$	−40.6073	+	40.6073i	−0.0457805	+	0.0457805i	−0.729626	−	0.683846i	$-0.760306\pi$
$887$	−40.6073	+	40.6073i	−0.0457805	+	0.0457805i	0.683846	+	0.729626i	$0.260306\pi$
$888$		0			0
$889$			207.189i			0.233059i
$890$	−720.631	−	145.369i	−0.809698	−	0.163335i
$891$		0			0
$892$	237.041	−	237.041i	0.265741	−	0.265741i
$893$	−1242.91	−	1242.91i	−1.39183	−	1.39183i
$894$		0			0
$895$	−58.9004	−	88.6686i	−0.0658105	−	0.0990711i
$896$	−29.9333			−0.0334077
$897$		0			0
$898$	−69.3409	−	69.3409i	−0.0772170	−	0.0772170i
$899$		−	174.376i		−	0.193966i
$900$		0			0
$901$	147.516			0.163724
$902$	1040.24	−	1040.24i	1.15326	−	1.15326i
$903$		0			0
$904$			323.509i			0.357864i
$905$	−94.7841	+	62.9628i	−0.104734	+	0.0695721i
$906$		0			0
$907$	−665.210	+	665.210i	−0.733417	+	0.733417i	−0.971295	−	0.237878i	$-0.923548\pi$
$907$	−665.210	+	665.210i	−0.733417	+	0.733417i	0.237878	+	0.971295i	$0.423548\pi$
$908$	−3.19917	−	3.19917i	−0.00352331	−	0.00352331i
$909$		0			0
$910$	64.8504	−	321.481i	0.0712642	−	0.353276i
$911$	1249.68			1.37177			0.685885	−	0.727710i	$-0.259415\pi$
$911$	1249.68			1.37177			0.685885	+	0.727710i	$0.259415\pi$
$912$		0			0
$913$	−1623.29	−	1623.29i	−1.77797	−	1.77797i
$914$			798.291i			0.873404i
$915$		0			0
$916$	−118.452			−0.129315
$917$	−129.639	+	129.639i	−0.141373	+	0.141373i
$918$		0			0
$919$		−	563.531i		−	0.613200i	−0.951838	−	0.306600i	$-0.900809\pi$
$919$		−	563.531i		−	0.613200i	0.951838	−	0.306600i	$-0.0991914\pi$
$920$	−65.2976	−	98.2990i	−0.0709757	−	0.106847i
$921$		0			0
$922$	−357.157	+	357.157i	−0.387372	+	0.387372i
$923$	14.7749	+	14.7749i	0.0160074	+	0.0160074i
$924$		0			0
$925$	−341.815	−	838.000i	−0.369530	−	0.905946i
$926$	279.644			0.301991
$927$		0			0
$928$	61.4587	+	61.4587i	0.0662270	+	0.0662270i
$929$			599.537i			0.645358i	0.946509	+	0.322679i	$0.104583\pi$
$929$			599.537i			0.645358i	−0.946509	+	0.322679i	$0.895417\pi$
$930$		0			0
$931$	−178.833			−0.192087
$932$	−532.104	+	532.104i	−0.570927	+	0.570927i
$933$		0			0
$934$		−	858.261i		−	0.918909i
$935$	462.957	−	2295.00i	0.495141	−	2.45455i
$936$		0			0
$937$	630.405	−	630.405i	0.672791	−	0.672791i	−0.285568	−	0.958359i	$-0.592182\pi$
$937$	630.405	−	630.405i	0.672791	−	0.672791i	0.958359	+	0.285568i	$0.0921821\pi$
$938$	−245.930	−	245.930i	−0.262186	−	0.262186i
$939$		0			0
$940$	−674.437	−	136.050i	−0.717486	−	0.144734i
$941$	734.091			0.780118			0.390059	−	0.920790i	$-0.372455\pi$
$941$	734.091			0.780118			0.390059	+	0.920790i	$0.372455\pi$
$942$		0			0
$943$	−347.118	−	347.118i	−0.368099	−	0.368099i
$944$		−	345.055i		−	0.365524i
$945$		0			0
$946$	−9.99935			−0.0105701
$947$	1025.55	−	1025.55i	1.08294	−	1.08294i	0.0867100	−	0.996234i	$-0.472365\pi$
$947$	1025.55	−	1025.55i	1.08294	−	1.08294i	0.996234	−	0.0867100i	$-0.0276354\pi$
$948$		0			0
$949$			2158.69i			2.27470i
$950$	−836.346	+	341.141i	−0.880365	+	0.359095i
$951$		0			0
$952$	−140.122	+	140.122i	−0.147187	+	0.147187i
$953$	−1070.88	−	1070.88i	−1.12370	−	1.12370i	−0.991181	−	0.132515i	$-0.957695\pi$
$953$	−1070.88	−	1070.88i	−1.12370	−	1.12370i	−0.132515	−	0.991181i	$-0.542305\pi$
$954$		0			0
$955$	473.587	−	314.592i	0.495902	−	0.329416i
$956$	−841.838			−0.880584
$957$		0			0
$958$	−524.078	−	524.078i	−0.547054	−	0.547054i
$959$			108.647i			0.113292i
$960$		0			0
$961$	−832.197			−0.865970
$962$	−634.609	+	634.609i	−0.659677	+	0.659677i
$963$		0			0
$964$			695.148i			0.721108i
$965$	762.015	+	153.717i	0.789653	+	0.159292i
$966$		0			0
$967$	−497.222	+	497.222i	−0.514191	+	0.514191i	−0.915808	−	0.401617i	$-0.868448\pi$
$967$	−497.222	+	497.222i	−0.514191	+	0.514191i	0.401617	+	0.915808i	$0.368448\pi$
$968$	−383.352	−	383.352i	−0.396025	−	0.396025i
$969$		0			0
$970$	−484.008	−	728.626i	−0.498978	−	0.751161i
$971$	−978.176			−1.00739			−0.503695	−	0.863881i	$-0.668027\pi$
$971$	−978.176			−1.00739			−0.503695	+	0.863881i	$0.668027\pi$
$972$		0			0
$973$	−149.866	−	149.866i	−0.154025	−	0.154025i
$974$		−	468.499i		−	0.481005i
$975$		0			0
$976$	−116.831			−0.119704
$977$	−964.006	+	964.006i	−0.986700	+	0.986700i	−0.999913	−	0.0132130i	$-0.995794\pi$
$977$	−964.006	+	964.006i	−0.986700	+	0.986700i	0.0132130	+	0.999913i	$0.495794\pi$
$978$		0			0
$979$			1838.39i			1.87782i
$980$	−58.3078	+	38.7324i	−0.0594977	+	0.0395229i
$981$		0			0
$982$	−171.731	+	171.731i	−0.174879	+	0.174879i
$983$	−93.2350	−	93.2350i	−0.0948474	−	0.0948474i	0.658091	−	0.752938i	$-0.271364\pi$
$983$	−93.2350	−	93.2350i	−0.0948474	−	0.0948474i	−0.752938	+	0.658091i	$0.771364\pi$
$984$		0			0
$985$	−114.950	+	569.839i	−0.116701	+	0.578517i
$986$	575.394			0.583564
$987$		0			0
$988$	633.357	+	633.357i	0.641049	+	0.641049i
$989$			3.33669i			0.00337380i
$990$		0			0
$991$	684.463			0.690679			0.345340	−	0.938478i	$-0.387764\pi$
$991$	684.463			0.690679			0.345340	+	0.938478i	$0.387764\pi$
$992$	−45.3966	+	45.3966i	−0.0457627	+	0.0457627i
$993$		0			0
$994$		−	4.45985i		−	0.00448677i
$995$	−643.758	−	969.113i	−0.646993	−	0.973982i
$996$		0			0
$997$	426.193	−	426.193i	0.427476	−	0.427476i	−0.460292	−	0.887768i	$-0.652255\pi$
$997$	426.193	−	426.193i	0.427476	−	0.427476i	0.887768	+	0.460292i	$0.152255\pi$
$998$	507.901	+	507.901i	0.508919	+	0.508919i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.o.f.253.6		16
3.2	odd	2		210.3.l.b.43.2	✓	16
5.2	odd	4	inner	630.3.o.f.127.6		16
15.2	even	4		210.3.l.b.127.2	yes	16
15.8	even	4		1050.3.l.h.757.8		16
15.14	odd	2		1050.3.l.h.43.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.b.43.2	✓	16	3.2	odd	2
210.3.l.b.127.2	yes	16	15.2	even	4
630.3.o.f.127.6		16	5.2	odd	4	inner
630.3.o.f.253.6		16	1.1	even	1	trivial
1050.3.l.h.43.8		16	15.14	odd	2
1050.3.l.h.757.8		16	15.8	even	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	630.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(4.16484 - 2.76660i) q^{5} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(4.16484 - 2.76660i) q^{5} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(1.39824 - 6.93144i) q^{10} -17.6826 q^{11} +(-12.3956 - 12.3956i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(-18.7246 + 18.7246i) q^{17} -25.5476i q^{19} +(-5.53321 - 8.32968i) q^{20} +(-17.6826 + 17.6826i) q^{22} +(5.90052 + 5.90052i) q^{23} +(9.69181 - 23.0449i) q^{25} -24.7912 q^{26} +(3.74166 + 3.74166i) q^{28} -15.3647i q^{29} +11.3491 q^{31} +(-4.00000 + 4.00000i) q^{32} +37.4492i q^{34} +(-2.61586 + 12.9675i) q^{35} +(25.5981 - 25.5981i) q^{37} +(-25.5476 - 25.5476i) q^{38} +(-13.8629 - 2.79648i) q^{40} -58.8283 q^{41} +(0.282745 + 0.282745i) q^{43} +35.3653i q^{44} +11.8010 q^{46} +(48.6505 - 48.6505i) q^{47} -7.00000i q^{49} +(-13.3531 - 32.7367i) q^{50} +(-24.7912 + 24.7912i) q^{52} +(-3.93909 - 3.93909i) q^{53} +(-73.6454 + 48.9209i) q^{55} +7.48331 q^{56} +(-15.3647 - 15.3647i) q^{58} +86.2636i q^{59} +29.2079 q^{61} +(11.3491 - 11.3491i) q^{62} +8.00000i q^{64} +(-85.9194 - 17.3320i) q^{65} +(-65.7277 + 65.7277i) q^{67} +(37.4492 + 37.4492i) q^{68} +(10.3517 + 15.5834i) q^{70} -1.19194 q^{71} +(-87.0749 - 87.0749i) q^{73} -51.1963i q^{74} -51.0953 q^{76} +(33.0812 - 33.0812i) q^{77} -55.0959i q^{79} +(-16.6594 + 11.0664i) q^{80} +(-58.8283 + 58.8283i) q^{82} +(91.8012 + 91.8012i) q^{83} +(-26.1814 + 129.788i) q^{85} +0.565490 q^{86} +(35.3653 + 35.3653i) q^{88} -103.966i q^{89} +46.3801 q^{91} +(11.8010 - 11.8010i) q^{92} -97.3010i q^{94} +(-70.6802 - 106.402i) q^{95} +(87.4734 - 87.4734i) q^{97} +(-7.00000 - 7.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{5} - 32 q^{8}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^5 - 32 * q^8	\( 16 q + 16 q^{2} + 16 q^{5} - 32 q^{8} + 24 q^{10} - 8 q^{11} - 32 q^{13} - 64 q^{16} - 56 q^{17} + 16 q^{20} - 8 q^{22} - 24 q^{23} + 40 q^{25} - 64 q^{26} - 112 q^{31} - 64 q^{32} - 28 q^{35} - 152 q^{37} - 16 q^{40} - 48 q^{46} - 80 q^{47} + 72 q^{50} - 64 q^{52} - 48 q^{53} - 24 q^{55} + 96 q^{58} + 96 q^{61} - 112 q^{62} - 16 q^{65} - 80 q^{67} + 112 q^{68} - 536 q^{71} + 168 q^{77} - 64 q^{80} + 256 q^{83} + 40 q^{85} + 16 q^{88} - 48 q^{92} - 360 q^{95} + 688 q^{97} - 112 q^{98}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^5 - 32 * q^8 + 24 * q^10 - 8 * q^11 - 32 * q^13 - 64 * q^16 - 56 * q^17 + 16 * q^20 - 8 * q^22 - 24 * q^23 + 40 * q^25 - 64 * q^26 - 112 * q^31 - 64 * q^32 - 28 * q^35 - 152 * q^37 - 16 * q^40 - 48 * q^46 - 80 * q^47 + 72 * q^50 - 64 * q^52 - 48 * q^53 - 24 * q^55 + 96 * q^58 + 96 * q^61 - 112 * q^62 - 16 * q^65 - 80 * q^67 + 112 * q^68 - 536 * q^71 + 168 * q^77 - 64 * q^80 + 256 * q^83 + 40 * q^85 + 16 * q^88 - 48 * q^92 - 360 * q^95 + 688 * q^97 - 112 * q^98

Introduction

L-functions

Modular forms

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Database

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