LMFDB - Embedded newform 630.3.v.b.451.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,3,Mod(271,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("630.271");

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.v (of order $6$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.1
Root			$1.72286 - 0.178197i$ of defining polynomial
Character	$\chi$	$=$	630.451
Dual form			630.3.v.b.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(5.10237 + 4.79227i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(5.10237 + 4.79227i) q^{7} +2.82843 q^{8} +(2.73861 + 1.58114i) q^{10} +(-0.919414 + 1.59247i) q^{11} +5.40765i q^{13} +(2.26139 - 9.63774i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-8.71093 - 5.02926i) q^{17} +(-7.96084 + 4.59619i) q^{19} -4.47214i q^{20} +2.60049 q^{22} +(-0.460644 - 0.797858i) q^{23} +(2.50000 - 4.33013i) q^{25} +(6.62299 - 3.82378i) q^{26} +(-13.4028 + 4.04529i) q^{28} -12.5573 q^{29} +(-36.1874 - 20.8928i) q^{31} +(-2.82843 + 4.89898i) q^{32} +14.2249i q^{34} +(-15.2386 - 3.57557i) q^{35} +(-3.64194 - 6.30803i) q^{37} +(11.2583 + 6.50000i) q^{38} +(-5.47723 + 3.16228i) q^{40} +52.3877i q^{41} -8.12312 q^{43} +(-1.83883 - 3.18494i) q^{44} +(-0.651449 + 1.12834i) q^{46} +(-29.4117 + 16.9809i) q^{47} +(3.06832 + 48.9038i) q^{49} -7.07107 q^{50} +(-9.36632 - 5.40765i) q^{52} +(-52.0396 + 90.1353i) q^{53} -4.11174i q^{55} +(14.4317 + 13.5546i) q^{56} +(8.87938 + 15.3795i) q^{58} +(-12.5918 - 7.26989i) q^{59} +(20.5913 - 11.8884i) q^{61} +59.0937i q^{62} +8.00000 q^{64} +(-6.04593 - 10.4719i) q^{65} +(7.46339 - 12.9270i) q^{67} +(17.4219 - 10.0585i) q^{68} +(6.39617 + 21.1917i) q^{70} +17.9620 q^{71} +(-107.705 - 62.1833i) q^{73} +(-5.15048 + 8.92090i) q^{74} -18.3848i q^{76} +(-12.3227 + 3.71930i) q^{77} +(40.4683 + 70.0931i) q^{79} +(7.74597 + 4.47214i) q^{80} +(64.1616 - 37.0437i) q^{82} +154.716i q^{83} +22.4915 q^{85} +(5.74391 + 9.94875i) q^{86} +(-2.60049 + 4.50419i) q^{88} +(-58.9956 + 34.0611i) q^{89} +(-25.9149 + 27.5918i) q^{91} +1.84258 q^{92} +(41.5944 + 24.0146i) q^{94} +(10.2774 - 17.8010i) q^{95} -88.1736i q^{97} +(57.7251 - 38.3381i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4}+O(q^{10}) $ 8 * q - 8 * q^4	$ 8 q - 8 q^{4} + 4 q^{11} + 40 q^{14} - 16 q^{16} - 84 q^{17} + 108 q^{19} - 48 q^{22} - 12 q^{23} + 20 q^{25} + 96 q^{26} - 72 q^{29} - 132 q^{31} - 100 q^{35} - 96 q^{37} + 168 q^{38} - 112 q^{43} + 8 q^{44} + 8 q^{46} + 24 q^{47} + 156 q^{49} + 48 q^{52} - 32 q^{53} - 16 q^{56} + 104 q^{58} - 132 q^{59} + 96 q^{61} + 64 q^{64} - 20 q^{65} - 120 q^{67} + 168 q^{68} - 8 q^{71} + 24 q^{73} + 16 q^{74} + 216 q^{77} + 12 q^{79} + 24 q^{82} + 120 q^{85} + 40 q^{86} + 48 q^{88} - 492 q^{89} - 308 q^{91} + 48 q^{92} + 480 q^{94} + 40 q^{95}+O(q^{100}) $ 8 * q - 8 * q^4 + 4 * q^11 + 40 * q^14 - 16 * q^16 - 84 * q^17 + 108 * q^19 - 48 * q^22 - 12 * q^23 + 20 * q^25 + 96 * q^26 - 72 * q^29 - 132 * q^31 - 100 * q^35 - 96 * q^37 + 168 * q^38 - 112 * q^43 + 8 * q^44 + 8 * q^46 + 24 * q^47 + 156 * q^49 + 48 * q^52 - 32 * q^53 - 16 * q^56 + 104 * q^58 - 132 * q^59 + 96 * q^61 + 64 * q^64 - 20 * q^65 - 120 * q^67 + 168 * q^68 - 8 * q^71 + 24 * q^73 + 16 * q^74 + 216 * q^77 + 12 * q^79 + 24 * q^82 + 120 * q^85 + 40 * q^86 + 48 * q^88 - 492 * q^89 - 308 * q^91 + 48 * q^92 + 480 * q^94 + 40 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$6$		0			0
$7$	5.10237	+	4.79227i	0.728910	+	0.684610i
$7$	5.10237	+	4.79227i	0.728910	+	0.684610i
$8$	2.82843			0.353553
$9$		0			0
$10$	2.73861	+	1.58114i	0.273861	+	0.158114i
$11$	−0.919414	+	1.59247i	−0.0835831	+	0.144770i	−0.904787	−	0.425865i	$-0.859970\pi$
$11$	−0.919414	+	1.59247i	−0.0835831	+	0.144770i	0.821203	+	0.570635i	$0.193303\pi$
$12$		0			0
$13$			5.40765i			0.415973i	0.978132	+	0.207986i	$0.0666910\pi$
$13$			5.40765i			0.415973i	−0.978132	+	0.207986i	$0.933309\pi$
$14$	2.26139	−	9.63774i	0.161528	−	0.688410i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−8.71093	−	5.02926i	−0.512408	−	0.295839i	0.221415	−	0.975180i	$-0.428932\pi$
$17$	−8.71093	−	5.02926i	−0.512408	−	0.295839i	−0.733823	+	0.679341i	$0.762266\pi$
$18$		0			0
$19$	−7.96084	+	4.59619i	−0.418992	+	0.241905i	−0.694646	−	0.719352i	$-0.744439\pi$
$19$	−7.96084	+	4.59619i	−0.418992	+	0.241905i	0.275654	+	0.961257i	$0.411106\pi$
$20$		−	4.47214i		−	0.223607i
$21$		0			0
$22$	2.60049			0.118204
$23$	−0.460644	−	0.797858i	−0.0200280	−	0.0346895i	0.855838	−	0.517244i	$-0.173042\pi$
$23$	−0.460644	−	0.797858i	−0.0200280	−	0.0346895i	−0.875866	+	0.482555i	$0.839709\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	6.62299	−	3.82378i	0.254730	−	0.147069i
$27$		0			0
$28$	−13.4028	+	4.04529i	−0.478672	+	0.144475i
$29$	−12.5573			−0.433012			−0.216506	−	0.976281i	$-0.569466\pi$
$29$	−12.5573			−0.433012			−0.216506	+	0.976281i	$0.569466\pi$
$30$		0			0
$31$	−36.1874	−	20.8928i	−1.16733	−	0.673961i	−0.214284	−	0.976771i	$-0.568742\pi$
$31$	−36.1874	−	20.8928i	−1.16733	−	0.673961i	−0.953051	+	0.302811i	$0.902075\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$		0			0
$34$			14.2249i			0.418379i
$35$	−15.2386	−	3.57557i	−0.435389	−	0.102159i
$36$		0			0
$37$	−3.64194	−	6.30803i	−0.0984308	−	0.170487i	0.812604	−	0.582816i	$-0.198049\pi$
$37$	−3.64194	−	6.30803i	−0.0984308	−	0.170487i	−0.911035	+	0.412328i	$0.864716\pi$
$38$	11.2583	+	6.50000i	0.296272	+	0.171053i
$39$		0			0
$40$	−5.47723	+	3.16228i	−0.136931	+	0.0790569i
$41$			52.3877i			1.27775i	0.769311	+	0.638875i	$0.220600\pi$
$41$			52.3877i			1.27775i	−0.769311	+	0.638875i	$0.779400\pi$
$42$		0			0
$43$	−8.12312			−0.188910			−0.0944549	−	0.995529i	$-0.530111\pi$
$43$	−8.12312			−0.188910			−0.0944549	+	0.995529i	$0.530111\pi$
$44$	−1.83883	−	3.18494i	−0.0417915	−	0.0723850i
$45$		0			0
$46$	−0.651449	+	1.12834i	−0.0141619	+	0.0245292i
$47$	−29.4117	+	16.9809i	−0.625781	+	0.361295i	−0.779116	−	0.626879i	$-0.784332\pi$
$47$	−29.4117	+	16.9809i	−0.625781	+	0.361295i	0.153335	+	0.988174i	$0.450999\pi$
$48$		0			0
$49$	3.06832	+	48.9038i	0.0626188	+	0.998038i
$50$	−7.07107			−0.141421
$51$		0			0
$52$	−9.36632	−	5.40765i	−0.180122	−	0.103993i
$53$	−52.0396	+	90.1353i	−0.981880	+	1.70067i	−0.326825	+	0.945085i	$0.605979\pi$
$53$	−52.0396	+	90.1353i	−0.981880	+	1.70067i	−0.655055	+	0.755582i	$0.727354\pi$
$54$		0			0
$55$		−	4.11174i		−	0.0747590i
$56$	14.4317	+	13.5546i	0.257709	+	0.242046i
$57$		0			0
$58$	8.87938	+	15.3795i	0.153093	+	0.265164i
$59$	−12.5918	−	7.26989i	−0.213421	−	0.123218i	0.389479	−	0.921035i	$-0.372655\pi$
$59$	−12.5918	−	7.26989i	−0.213421	−	0.123218i	−0.602900	+	0.797817i	$0.705988\pi$
$60$		0			0
$61$	20.5913	−	11.8884i	0.337562	−	0.194892i	−0.321631	−	0.946865i	$-0.604231\pi$
$61$	20.5913	−	11.8884i	0.337562	−	0.194892i	0.659194	+	0.751973i	$0.270898\pi$
$62$			59.0937i			0.953125i
$63$		0			0
$64$	8.00000			0.125000
$65$	−6.04593	−	10.4719i	−0.0930144	−	0.161106i
$66$		0			0
$67$	7.46339	−	12.9270i	0.111394	−	0.192940i	−0.804939	−	0.593358i	$-0.797802\pi$
$67$	7.46339	−	12.9270i	0.111394	−	0.192940i	0.916332	+	0.400418i	$0.131135\pi$
$68$	17.4219	−	10.0585i	0.256204	−	0.147919i
$69$		0			0
$70$	6.39617	+	21.1917i	0.0913738	+	0.302739i
$71$	17.9620			0.252987			0.126493	−	0.991967i	$-0.459628\pi$
$71$	17.9620			0.252987			0.126493	+	0.991967i	$0.459628\pi$
$72$		0			0
$73$	−107.705	−	62.1833i	−1.47541	−	0.851826i	−0.475791	−	0.879558i	$-0.657838\pi$
$73$	−107.705	−	62.1833i	−1.47541	−	0.851826i	−0.999615	+	0.0277318i	$0.991172\pi$
$74$	−5.15048	+	8.92090i	−0.0696011	+	0.120553i
$75$		0			0
$76$		−	18.3848i		−	0.241905i
$77$	−12.3227	+	3.71930i	−0.160036	+	0.0483026i
$78$		0			0
$79$	40.4683	+	70.0931i	0.512257	+	0.887254i	0.999899	+	0.0142110i	$0.00452366\pi$
$79$	40.4683	+	70.0931i	0.512257	+	0.887254i	−0.487642	+	0.873043i	$0.662143\pi$
$80$	7.74597	+	4.47214i	0.0968246	+	0.0559017i
$81$		0			0
$82$	64.1616	−	37.0437i	0.782459	−	0.451753i
$83$			154.716i			1.86405i	0.362395	+	0.932025i	$0.381959\pi$
$83$			154.716i			1.86405i	−0.362395	+	0.932025i	$0.618041\pi$
$84$		0			0
$85$	22.4915			0.264606
$86$	5.74391	+	9.94875i	0.0667897	+	0.115683i
$87$		0			0
$88$	−2.60049	+	4.50419i	−0.0295511	+	0.0511840i
$89$	−58.9956	+	34.0611i	−0.662872	+	0.382709i	−0.793371	−	0.608739i	$-0.791676\pi$
$89$	−58.9956	+	34.0611i	−0.662872	+	0.382709i	0.130498	+	0.991449i	$0.458342\pi$
$90$		0			0
$91$	−25.9149	+	27.5918i	−0.284779	+	0.303207i
$92$	1.84258			0.0200280
$93$		0			0
$94$	41.5944	+	24.0146i	0.442494	+	0.255474i
$95$	10.2774	−	17.8010i	0.108183	−	0.187379i
$96$		0			0
$97$		−	88.1736i		−	0.909006i	−0.890745	−	0.454503i	$-0.849817\pi$
$97$		−	88.1736i		−	0.909006i	0.890745	−	0.454503i	$-0.150183\pi$
$98$	57.7251	−	38.3381i	0.589032	−	0.391206i
$99$		0			0
$100$	5.00000	+	8.66025i	0.0500000	+	0.0866025i
$101$	96.4537	+	55.6876i	0.954987	+	0.551362i	0.894627	−	0.446814i	$-0.147442\pi$
$101$	96.4537	+	55.6876i	0.954987	+	0.551362i	0.0603607	+	0.998177i	$0.480775\pi$
$102$		0			0
$103$	−40.6847	+	23.4893i	−0.394997	+	0.228051i	−0.684323	−	0.729179i	$-0.739902\pi$
$103$	−40.6847	+	23.4893i	−0.394997	+	0.228051i	0.289326	+	0.957231i	$0.406569\pi$
$104$			15.2951i			0.147069i
$105$		0			0
$106$	147.190			1.38859
$107$	−92.8409	−	160.805i	−0.867672	−	1.50285i	−0.864370	−	0.502857i	$-0.832282\pi$
$107$	−92.8409	−	160.805i	−0.867672	−	1.50285i	−0.00330196	−	0.999995i	$-0.501051\pi$
$108$		0			0
$109$	−43.1448	+	74.7290i	−0.395824	+	0.685587i	−0.993206	−	0.116369i	$-0.962874\pi$
$109$	−43.1448	+	74.7290i	−0.395824	+	0.685587i	0.597382	+	0.801957i	$0.296208\pi$
$110$	−5.03584	+	2.90744i	−0.0457803	+	0.0264313i
$111$		0			0
$112$	6.39617	−	27.2597i	0.0571087	−	0.243390i
$113$	85.8206			0.759474			0.379737	−	0.925094i	$-0.376014\pi$
$113$	85.8206			0.759474			0.379737	+	0.925094i	$0.376014\pi$
$114$		0			0
$115$	1.78407	+	1.03003i	0.0155136	+	0.00895679i
$116$	12.5573	−	21.7500i	0.108253	−	0.187500i
$117$		0			0
$118$			20.5624i			0.174257i
$119$	−20.3448	−	67.4062i	−0.170965	−	0.566439i
$120$		0			0
$121$	58.8094	+	101.861i	0.486028	+	0.841825i
$122$	−29.1205	−	16.8127i	−0.238693	−	0.137809i
$123$		0			0
$124$	72.3747	−	41.7856i	0.583667	−	0.336980i
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	−131.740			−1.03733			−0.518663	−	0.854979i	$-0.673570\pi$
$127$	−131.740			−1.03733			−0.518663	+	0.854979i	$0.673570\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−8.55024	+	14.8095i	−0.0657711	+	0.113919i
$131$	102.856	−	59.3839i	0.785160	−	0.453312i	−0.0530960	−	0.998589i	$-0.516909\pi$
$131$	102.856	−	59.3839i	0.785160	−	0.453312i	0.838256	+	0.545277i	$0.183576\pi$
$132$		0			0
$133$	−62.6453	−	14.6990i	−0.471017	−	0.110519i
$134$	−21.1096			−0.157535
$135$		0			0
$136$	−24.6382	−	14.2249i	−0.181163	−	0.104595i
$137$	40.5765	−	70.2805i	0.296179	−	0.512997i	−0.679080	−	0.734065i	$-0.737621\pi$
$137$	40.5765	−	70.2805i	0.296179	−	0.512997i	0.975258	+	0.221068i	$0.0709543\pi$
$138$		0			0
$139$			248.311i			1.78641i	0.449646	+	0.893207i	$0.351550\pi$
$139$			248.311i			1.78641i	−0.449646	+	0.893207i	$0.648450\pi$
$140$	21.4317	−	22.8185i	0.153083	−	0.162989i
$141$		0			0
$142$	−12.7011	−	21.9989i	−0.0894442	−	0.154922i
$143$	−8.61152	−	4.97186i	−0.0602204	−	0.0347683i
$144$		0			0
$145$	24.3172	−	14.0395i	0.167705	−	0.0968244i
$146$			175.881i			1.20466i
$147$		0			0
$148$	14.5678			0.0984308
$149$	−75.0048	−	129.912i	−0.503388	−	0.871894i	−0.999992	−	0.00391672i	$-0.998753\pi$
$149$	−75.0048	−	129.912i	−0.503388	−	0.871894i	0.496604	−	0.867977i	$-0.334580\pi$
$150$		0			0
$151$	−91.5149	+	158.509i	−0.606059	+	1.04973i	0.385824	+	0.922572i	$0.373917\pi$
$151$	−91.5149	+	158.509i	−0.606059	+	1.04973i	−0.991883	+	0.127153i	$0.959416\pi$
$152$	−22.5167	+	13.0000i	−0.148136	+	0.0855263i
$153$		0			0
$154$	13.2687	+	12.4623i	0.0861603	+	0.0809238i
$155$	93.4354			0.602809
$156$		0			0
$157$	−255.724	−	147.643i	−1.62882	−	0.940398i	−0.984446	−	0.175685i	$-0.943786\pi$
$157$	−255.724	−	147.643i	−1.62882	−	0.940398i	−0.644371	−	0.764713i	$-0.722881\pi$
$158$	57.2308	−	99.1266i	0.362220	−	0.627384i
$159$		0			0
$160$		−	12.6491i		−	0.0790569i
$161$	1.47318	−	6.27850i	0.00915017	−	0.0389969i
$162$		0			0
$163$	59.1631	+	102.473i	0.362964	+	0.628671i	0.988447	−	0.151566i	$-0.0484316\pi$
$163$	59.1631	+	102.473i	0.362964	+	0.628671i	−0.625484	+	0.780237i	$0.715098\pi$
$164$	−90.7382	−	52.3877i	−0.553282	−	0.319437i
$165$		0			0
$166$	189.488	−	109.401i	1.14149	−	0.659041i
$167$		−	205.186i		−	1.22866i	−0.789050	−	0.614329i	$-0.789427\pi$
$167$		−	205.186i		−	1.22866i	0.789050	−	0.614329i	$-0.210573\pi$
$168$		0			0
$169$	139.757			0.826967
$170$	−15.9039	−	27.5464i	−0.0935524	−	0.162038i
$171$		0			0
$172$	8.12312	−	14.0697i	0.0472274	−	0.0818003i
$173$	−97.4572	+	56.2670i	−0.563337	+	0.325242i	−0.754484	−	0.656319i	$-0.772113\pi$
$173$	−97.4572	+	56.2670i	−0.563337	+	0.325242i	0.191147	+	0.981561i	$0.438779\pi$
$174$		0			0
$175$	33.5071	−	10.1132i	0.191469	−	0.0577899i
$176$	7.35531			0.0417915
$177$		0			0
$178$	83.4324	+	48.1697i	0.468721	+	0.270616i
$179$	−22.2349	+	38.5120i	−0.124217	+	0.215151i	−0.921427	−	0.388552i	$-0.872975\pi$
$179$	−22.2349	+	38.5120i	−0.124217	+	0.215151i	0.797209	+	0.603703i	$0.206309\pi$
$180$		0			0
$181$		−	9.24555i		−	0.0510804i	−0.999674	−	0.0255402i	$-0.991869\pi$
$181$		−	9.24555i		−	0.0510804i	0.999674	−	0.0255402i	$-0.00813058\pi$
$182$	52.1175	+	12.2288i	0.286360	+	0.0671911i
$183$		0			0
$184$	−1.30290	−	2.25668i	−0.00708096	−	0.0122646i
$185$	14.1052	+	8.14363i	0.0762442	+	0.0440196i
$186$		0			0
$187$	16.0179	−	9.24793i	0.0856572	−	0.0494542i
$188$		−	67.9234i		−	0.361295i
$189$		0			0
$190$	−29.0689			−0.152994
$191$	−68.4044	−	118.480i	−0.358138	−	0.620314i	0.629511	−	0.776991i	$-0.283255\pi$
$191$	−68.4044	−	118.480i	−0.358138	−	0.620314i	−0.987650	+	0.156677i	$0.949922\pi$
$192$		0			0
$193$	182.937	−	316.856i	0.947860	−	1.64174i	0.197939	−	0.980214i	$-0.436575\pi$
$193$	182.937	−	316.856i	0.947860	−	1.64174i	0.749921	−	0.661527i	$-0.230091\pi$
$194$	−107.990	+	62.3481i	−0.556650	+	0.321382i
$195$		0			0
$196$	−87.7723	−	43.5893i	−0.447818	−	0.222395i
$197$	194.925			0.989468			0.494734	−	0.869045i	$-0.335266\pi$
$197$	194.925			0.989468			0.494734	+	0.869045i	$0.335266\pi$
$198$		0			0
$199$	−210.301	−	121.418i	−1.05679	−	0.610138i	−0.132248	−	0.991217i	$-0.542219\pi$
$199$	−210.301	−	121.418i	−1.05679	−	0.610138i	−0.924543	+	0.381078i	$0.875553\pi$
$200$	7.07107	−	12.2474i	0.0353553	−	0.0612372i
$201$		0			0
$202$		−	157.508i		−	0.779744i
$203$	−64.0722	−	60.1782i	−0.315627	−	0.296444i
$204$		0			0
$205$	−58.5713	−	101.448i	−0.285714	−	0.494870i
$206$	57.5368	+	33.2189i	0.279305	+	0.161257i
$207$		0			0
$208$	18.7326	−	10.8153i	0.0900608	−	0.0519966i
$209$		−	16.9032i		−	0.0808766i
$210$		0			0
$211$	185.930			0.881184			0.440592	−	0.897707i	$-0.354769\pi$
$211$	185.930			0.881184			0.440592	+	0.897707i	$0.354769\pi$
$212$	−104.079	−	180.271i	−0.490940	−	0.850333i
$213$		0			0
$214$	−131.297	+	227.413i	−0.613537	+	1.06268i
$215$	15.7304	−	9.08192i	0.0731644	−	0.0422415i
$216$		0			0
$217$	−84.5174	−	280.022i	−0.389481	−	1.29043i
$218$	122.032			0.559780
$219$		0			0
$220$	7.12175	+	4.11174i	0.0323716	+	0.0186897i
$221$	27.1965	−	47.1056i	0.123061	−	0.213148i
$222$		0			0
$223$			53.6348i			0.240515i	0.992743	+	0.120257i	$0.0383720\pi$
$223$			53.6348i			0.240515i	−0.992743	+	0.120257i	$0.961628\pi$
$224$	−37.9089	+	11.4418i	−0.169236	+	0.0510795i
$225$		0			0
$226$	−60.6843	−	105.108i	−0.268515	−	0.465081i
$227$	−146.392	−	84.5195i	−0.644899	−	0.372333i	0.141600	−	0.989924i	$-0.454775\pi$
$227$	−146.392	−	84.5195i	−0.644899	−	0.372333i	−0.786499	+	0.617591i	$0.788109\pi$
$228$		0			0
$229$	247.698	−	143.009i	1.08165	−	0.624492i	0.150310	−	0.988639i	$-0.451973\pi$
$229$	247.698	−	143.009i	1.08165	−	0.624492i	0.931342	+	0.364147i	$0.118639\pi$
$230$		−	2.91337i		−	0.0126668i
$231$		0			0
$232$	−35.5175			−0.153093
$233$	−90.9194	−	157.477i	−0.390212	−	0.675867i	0.602265	−	0.798296i	$-0.294265\pi$
$233$	−90.9194	−	157.477i	−0.390212	−	0.675867i	−0.992477	+	0.122429i	$0.960932\pi$
$234$		0			0
$235$	37.9703	−	65.7666i	0.161576	−	0.279858i
$236$	25.1836	−	14.5398i	0.106710	−	0.0616092i
$237$		0			0
$238$	−68.1695	+	72.5806i	−0.286426	+	0.304961i
$239$	382.489			1.60037			0.800185	−	0.599753i	$-0.204734\pi$
$239$	382.489			1.60037			0.800185	+	0.599753i	$0.204734\pi$
$240$		0			0
$241$	−180.324	−	104.110i	−0.748230	−	0.431991i	0.0768238	−	0.997045i	$-0.475522\pi$
$241$	−180.324	−	104.110i	−0.748230	−	0.431991i	−0.825054	+	0.565054i	$0.808855\pi$
$242$	83.1690	−	144.053i	0.343674	−	0.595260i
$243$		0			0
$244$			47.5536i			0.194892i
$245$	−60.6179	−	91.2714i	−0.247420	−	0.372536i
$246$		0			0
$247$	−24.8546	−	43.0494i	−0.100626	−	0.174289i
$248$	−102.353	−	59.0937i	−0.412715	−	0.238281i
$249$		0			0
$250$	13.6931	−	7.90569i	0.0547723	−	0.0316228i
$251$		−	43.4959i		−	0.173291i	−0.996239	−	0.0866453i	$-0.972385\pi$
$251$		−	43.4959i		−	0.173291i	0.996239	−	0.0866453i	$-0.0276147\pi$
$252$		0			0
$253$	1.69409			0.00669600
$254$	93.1545	+	161.348i	0.366750	+	0.635229i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−3.68915	+	2.12993i	−0.0143547	+	0.00828766i	−0.507160	−	0.861852i	$-0.669305\pi$
$257$	−3.68915	+	2.12993i	−0.0143547	+	0.00828766i	0.492806	+	0.870139i	$0.335971\pi$
$258$		0			0
$259$	11.6472	−	49.6390i	0.0449700	−	0.191656i
$260$	24.1837			0.0930144
$261$		0			0
$262$	−145.460	−	83.9815i	−0.555192	−	0.320540i
$263$	−209.187	+	362.323i	−0.795388	+	1.37765i	0.127204	+	0.991877i	$0.459400\pi$
$263$	−209.187	+	362.323i	−0.795388	+	1.37765i	−0.922592	+	0.385776i	$0.873934\pi$
$264$		0			0
$265$		−	232.728i		−	0.878220i
$266$	26.2944	+	87.1183i	0.0988511	+	0.327512i
$267$		0			0
$268$	14.9268	+	25.8539i	0.0556969	+	0.0964699i
$269$	319.086	+	184.224i	1.18619	+	0.684848i	0.957439	−	0.288636i	$-0.0932018\pi$
$269$	319.086	+	184.224i	1.18619	+	0.684848i	0.228753	+	0.973484i	$0.426535\pi$
$270$		0			0
$271$	−191.411	+	110.511i	−0.706312	+	0.407790i	−0.809694	−	0.586852i	$-0.800367\pi$
$271$	−191.411	+	110.511i	−0.706312	+	0.407790i	0.103382	+	0.994642i	$0.467034\pi$
$272$			40.2341i			0.147919i
$273$		0			0
$274$	−114.768			−0.418860
$275$	4.59707	+	7.96235i	0.0167166	+	0.0289540i
$276$		0			0
$277$	198.427	−	343.686i	0.716343	−	1.24074i	−0.246096	−	0.969245i	$-0.579148\pi$
$277$	198.427	−	343.686i	0.716343	−	1.24074i	0.962439	−	0.271497i	$-0.0875187\pi$
$278$	304.118	−	175.583i	1.09395	−	0.631593i
$279$		0			0
$280$	−43.1013	−	10.1132i	−0.153933	−	0.0361187i
$281$	114.244			0.406562			0.203281	−	0.979120i	$-0.434839\pi$
$281$	114.244			0.406562			0.203281	+	0.979120i	$0.434839\pi$
$282$		0			0
$283$	391.819	+	226.217i	1.38452	+	0.799353i	0.992691	−	0.120685i	$-0.0385092\pi$
$283$	391.819	+	226.217i	1.38452	+	0.799353i	0.391829	+	0.920038i	$0.371843\pi$
$284$	−17.9620	+	31.1112i	−0.0632466	+	0.109546i
$285$		0			0
$286$			14.0626i			0.0491698i
$287$	−251.056	+	267.302i	−0.874760	+	0.931364i
$288$		0			0
$289$	−93.9131	−	162.662i	−0.324959	−	0.562845i
$290$	−34.3897	−	19.8549i	−0.118585	−	0.0684652i
$291$		0			0
$292$	215.409	−	124.367i	0.737703	−	0.425913i
$293$			119.134i			0.406600i	0.979116	+	0.203300i	$0.0651667\pi$
$293$			119.134i			0.406600i	−0.979116	+	0.203300i	$0.934833\pi$
$294$		0			0
$295$	32.5119			0.110210
$296$	−10.3010	−	17.8418i	−0.0348006	−	0.0602763i
$297$		0			0
$298$	−106.073	+	183.724i	−0.355949	+	0.616522i
$299$	4.31454	−	2.49100i	0.0144299	−	0.00833110i
$300$		0			0
$301$	−41.4471	−	38.9282i	−0.137698	−	0.129329i
$302$	258.843			0.857097
$303$		0			0
$304$	31.8434	+	18.3848i	0.104748	+	0.0604762i
$305$	−26.5833	+	46.0435i	−0.0871582	+	0.150962i
$306$		0			0
$307$			272.643i			0.888087i	0.896005	+	0.444043i	$0.146456\pi$
$307$			272.643i			0.888087i	−0.896005	+	0.444043i	$0.853544\pi$
$308$	5.88072	−	25.0629i	0.0190933	−	0.0813731i
$309$		0			0
$310$	−66.0688	−	114.435i	−0.213125	−	0.369144i
$311$	−65.4476	−	37.7862i	−0.210443	−	0.121499i	0.391074	−	0.920359i	$-0.372103\pi$
$311$	−65.4476	−	37.7862i	−0.210443	−	0.121499i	−0.601517	+	0.798860i	$0.705437\pi$
$312$		0			0
$313$	−55.1057	+	31.8153i	−0.176057	+	0.101646i	−0.585439	−	0.810717i	$-0.699078\pi$
$313$	−55.1057	+	31.8153i	−0.176057	+	0.101646i	0.409382	+	0.912363i	$0.365744\pi$
$314$			417.596i			1.32992i
$315$		0			0
$316$	−161.873			−0.512257
$317$	7.72605	+	13.3819i	0.0243724	+	0.0422142i	0.877954	−	0.478744i	$-0.158908\pi$
$317$	7.72605	+	13.3819i	0.0243724	+	0.0422142i	−0.853582	+	0.520959i	$0.825575\pi$
$318$		0			0
$319$	11.5454	−	19.9972i	0.0361924	−	0.0626872i
$320$	−15.4919	+	8.94427i	−0.0484123	+	0.0279508i
$321$		0			0
$322$	−8.73125	+	2.63530i	−0.0271157	+	0.00818416i
$323$	92.4617			0.286259
$324$		0			0
$325$	23.4158	+	13.5191i	0.0720486	+	0.0415973i
$326$	83.6692	−	144.919i	0.256654	−	0.444538i
$327$		0			0
$328$			148.175i			0.451753i
$329$	−231.446	−	54.3062i	−0.703484	−	0.165064i
$330$		0			0
$331$	186.540	+	323.096i	0.563564	+	0.976121i	0.997182	+	0.0750241i	$0.0239034\pi$
$331$	186.540	+	323.096i	0.563564	+	0.976121i	−0.433618	+	0.901097i	$0.642763\pi$
$332$	−267.976	−	154.716i	−0.807157	−	0.466012i
$333$		0			0
$334$	−251.301	+	145.088i	−0.752397	+	0.434397i
$335$			33.3773i			0.0996337i
$336$		0			0
$337$	642.919			1.90777			0.953885	−	0.300171i	$-0.0970437\pi$
$337$	642.919			1.90777			0.953885	+	0.300171i	$0.0970437\pi$
$338$	−98.8234	−	171.167i	−0.292377	−	0.506412i
$339$		0			0
$340$	−22.4915	+	38.9565i	−0.0661515	+	0.114578i
$341$	66.5423	−	38.4182i	0.195139	−	0.112663i
$342$		0			0
$343$	−218.705	+	264.230i	−0.637623	+	0.770349i
$344$	−22.9757			−0.0667897
$345$		0			0
$346$	137.825	+	79.5735i	0.398339	+	0.229981i
$347$	72.0043	−	124.715i	0.207505	−	0.359409i	−0.743423	−	0.668822i	$-0.766799\pi$
$347$	72.0043	−	124.715i	0.207505	−	0.359409i	0.950928	+	0.309412i	$0.100132\pi$
$348$		0			0
$349$			566.507i			1.62323i	0.584194	+	0.811614i	$0.301411\pi$
$349$			566.507i			1.62323i	−0.584194	+	0.811614i	$0.698589\pi$
$350$	−36.0792	−	33.8865i	−0.103083	−	0.0968184i
$351$		0			0
$352$	−5.20099	−	9.00838i	−0.0147755	−	0.0255920i
$353$	−441.814	−	255.082i	−1.25160	−	0.722611i	−0.280172	−	0.959950i	$-0.590391\pi$
$353$	−441.814	−	255.082i	−1.25160	−	0.722611i	−0.971427	+	0.237339i	$0.923725\pi$
$354$		0			0
$355$	−34.7833	+	20.0822i	−0.0979813	+	0.0565695i
$356$		−	136.245i		−	0.382709i
$357$		0			0
$358$	62.8898			0.175670
$359$	333.931	+	578.386i	0.930171	+	1.61110i	0.783026	+	0.621989i	$0.213675\pi$
$359$	333.931	+	578.386i	0.930171	+	1.61110i	0.147145	+	0.989115i	$0.452992\pi$
$360$		0			0
$361$	−138.250	+	239.456i	−0.382964	+	0.663313i
$362$	−11.3234	+	6.53759i	−0.0312802	+	0.0180596i
$363$		0			0
$364$	−21.8755	−	72.4777i	−0.0600976	−	0.199115i
$365$	278.092			0.761897
$366$		0			0
$367$	−30.2216	−	17.4485i	−0.0823478	−	0.0475435i	0.458261	−	0.888818i	$-0.348473\pi$
$367$	−30.2216	−	17.4485i	−0.0823478	−	0.0475435i	−0.540608	+	0.841274i	$0.681806\pi$
$368$	−1.84258	+	3.19143i	−0.00500700	+	0.00867237i
$369$		0			0
$370$		−	23.0337i		−	0.0622531i
$371$	−697.478	+	210.516i	−1.87999	+	0.567427i
$372$		0			0
$373$	204.012	+	353.360i	0.546950	+	0.947345i	0.998481	+	0.0550895i	$0.0175444\pi$
$373$	204.012	+	353.360i	0.546950	+	0.947345i	−0.451532	+	0.892255i	$0.649122\pi$
$374$	−22.6527	−	13.0786i	−0.0605688	−	0.0349694i
$375$		0			0
$376$	−83.1888	+	48.0291i	−0.221247	+	0.127737i
$377$		−	67.9057i		−	0.180121i
$378$		0			0
$379$	−10.4706			−0.0276268			−0.0138134	−	0.999905i	$-0.504397\pi$
$379$	−10.4706			−0.0276268			−0.0138134	+	0.999905i	$0.504397\pi$
$380$	20.5548	+	35.6020i	0.0540916	+	0.0936893i
$381$		0			0
$382$	−96.7385	+	167.556i	−0.253242	+	0.438628i
$383$	199.672	−	115.281i	0.521337	−	0.300994i	−0.216145	−	0.976361i	$-0.569348\pi$
$383$	199.672	−	115.281i	0.521337	−	0.300994i	0.737481	+	0.675367i	$0.236015\pi$
$384$		0			0
$385$	19.7046	−	20.9796i	0.0511807	−	0.0544925i
$386$	−517.424			−1.34048
$387$		0			0
$388$	152.721	+	88.1736i	0.393611	+	0.227251i
$389$	338.107	−	585.619i	0.869170	−	1.50545i	0.00632331	−	0.999980i	$-0.497987\pi$
$389$	338.107	−	585.619i	0.869170	−	1.50545i	0.862846	−	0.505466i	$-0.168679\pi$
$390$		0			0
$391$			9.26678i			0.0237002i
$392$	8.67853	+	138.321i	0.0221391	+	0.352860i
$393$		0			0
$394$	−137.833	−	238.734i	−0.349830	−	0.605923i
$395$	−156.733	−	90.4898i	−0.396792	−	0.229088i
$396$		0			0
$397$	−141.641	+	81.7764i	−0.356778	+	0.205986i	−0.667666	−	0.744461i	$-0.732707\pi$
$397$	−141.641	+	81.7764i	−0.356778	+	0.205986i	0.310889	+	0.950446i	$0.399373\pi$
$398$			343.421i			0.862866i
$399$		0			0
$400$	−20.0000			−0.0500000
$401$	−149.624	−	259.156i	−0.373127	−	0.646274i	0.616918	−	0.787027i	$-0.288381\pi$
$401$	−149.624	−	259.156i	−0.373127	−	0.646274i	−0.990045	+	0.140753i	$0.955048\pi$
$402$		0			0
$403$	112.981	−	195.689i	0.280349	−	0.485579i
$404$	−192.907	+	111.375i	−0.477494	+	0.275681i
$405$		0			0
$406$	−28.3970	+	121.024i	−0.0699434	+	0.298090i
$407$	13.3938			0.0329086
$408$		0			0
$409$	403.264	+	232.825i	0.985976	+	0.569253i	0.904069	−	0.427387i	$-0.140566\pi$
$409$	403.264	+	232.825i	0.985976	+	0.569253i	0.0819067	+	0.996640i	$0.473899\pi$
$410$	−82.8323	+	143.470i	−0.202030	+	0.349926i
$411$		0			0
$412$		−	93.9572i		−	0.228051i
$413$	−29.4088	−	97.4370i	−0.0712078	−	0.235925i
$414$		0			0
$415$	−172.978	−	299.606i	−0.416814	−	0.721943i
$416$	−26.4920	−	15.2951i	−0.0636826	−	0.0367672i
$417$		0			0
$418$	−20.7021	+	11.9524i	−0.0495266	+	0.0285942i
$419$			575.882i			1.37442i	0.726458	+	0.687211i	$0.241165\pi$
$419$			575.882i			1.37442i	−0.726458	+	0.687211i	$0.758835\pi$
$420$		0			0
$421$	571.149			1.35665			0.678324	−	0.734763i	$-0.262706\pi$
$421$	571.149			1.35665			0.678324	+	0.734763i	$0.262706\pi$
$422$	−131.472	−	227.717i	−0.311546	−	0.539613i
$423$		0			0
$424$	−147.190	+	254.941i	−0.347147	+	0.601276i
$425$	−43.5546	+	25.1463i	−0.102482	+	0.0591677i
$426$		0			0
$427$	162.037	+	38.0201i	0.379477	+	0.0890400i
$428$	371.363			0.867672
$429$		0			0
$430$	−22.2461	−	12.8438i	−0.0517351	−	0.0298693i
$431$	−13.5697	+	23.5034i	−0.0314842	+	0.0545322i	−0.881338	−	0.472486i	$-0.843357\pi$
$431$	−13.5697	+	23.5034i	−0.0314842	+	0.0545322i	0.849854	+	0.527018i	$0.176690\pi$
$432$		0			0
$433$			363.408i			0.839279i	0.907691	+	0.419640i	$0.137844\pi$
$433$			363.408i			0.839279i	−0.907691	+	0.419640i	$0.862156\pi$
$434$	−283.193	+	301.518i	−0.652518	+	0.694742i
$435$		0			0
$436$	−86.2897	−	149.458i	−0.197912	−	0.342794i
$437$	7.33422	+	4.23441i	0.0167831	+	0.00968974i
$438$		0			0
$439$	−403.057	+	232.705i	−0.918124	+	0.530079i	−0.883036	−	0.469305i	$-0.844505\pi$
$439$	−403.057	+	232.705i	−0.918124	+	0.530079i	−0.0350882	+	0.999384i	$0.511171\pi$
$440$		−	11.6298i		−	0.0264313i
$441$		0			0
$442$	−76.9232			−0.174034
$443$	243.968	+	422.565i	0.550718	+	0.953871i	0.998223	+	0.0595896i	$0.0189792\pi$
$443$	243.968	+	422.565i	0.550718	+	0.953871i	−0.447505	+	0.894281i	$0.647687\pi$
$444$		0			0
$445$	76.1630	−	131.918i	0.171153	−	0.296445i
$446$	65.6889	−	37.9255i	0.147285	−	0.0850348i
$447$		0			0
$448$	40.8189	+	38.3381i	0.0911137	+	0.0855762i
$449$	285.837			0.636609			0.318304	−	0.947989i	$-0.396887\pi$
$449$	285.837			0.636609			0.318304	+	0.947989i	$0.396887\pi$
$450$		0			0
$451$	−83.4260	−	48.1660i	−0.184980	−	0.106798i
$452$	−85.8206	+	148.646i	−0.189869	+	0.328862i
$453$		0			0
$454$			239.057i			0.526558i
$455$	19.3354	−	82.4050i	0.0424954	−	0.181110i
$456$		0			0
$457$	−211.624	−	366.543i	−0.463071	−	0.802063i	0.536041	−	0.844192i	$-0.319919\pi$
$457$	−211.624	−	366.543i	−0.463071	−	0.802063i	−0.999112	+	0.0421292i	$0.986586\pi$
$458$	−350.298	−	202.245i	−0.764843	−	0.441583i
$459$		0			0
$460$	−3.56813	+	2.06006i	−0.00775681	+	0.00447839i
$461$			471.748i			1.02331i	0.859190	+	0.511657i	$0.170968\pi$
$461$			471.748i			1.02331i	−0.859190	+	0.511657i	$0.829032\pi$
$462$		0			0
$463$	−194.019			−0.419046			−0.209523	−	0.977804i	$-0.567191\pi$
$463$	−194.019			−0.419046			−0.209523	+	0.977804i	$0.567191\pi$
$464$	25.1147	+	43.4999i	0.0541265	+	0.0937498i
$465$		0			0
$466$	−128.579	+	222.706i	−0.275921	+	0.477910i
$467$	9.80955	−	5.66354i	0.0210055	−	0.0121275i	−0.489461	−	0.872025i	$-0.662806\pi$
$467$	9.80955	−	5.66354i	0.0210055	−	0.0121275i	0.510466	+	0.859898i	$0.329473\pi$
$468$		0			0
$469$	100.030	−	30.1916i	0.213285	−	0.0643744i
$470$	−107.396			−0.228503
$471$		0			0
$472$	−35.6150	−	20.5624i	−0.0754556	−	0.0435643i
$473$	7.46851	−	12.9358i	0.0157897	−	0.0273485i
$474$		0			0
$475$			45.9619i			0.0967619i
$476$	137.096	+	32.1680i	0.288016	+	0.0675798i
$477$		0			0
$478$	−270.460	−	468.451i	−0.565816	−	0.980023i
$479$	547.932	+	316.349i	1.14391	+	0.660435i	0.947395	−	0.320066i	$-0.103705\pi$
$479$	547.932	+	316.349i	1.14391	+	0.660435i	0.196512	+	0.980501i	$0.437038\pi$
$480$		0			0
$481$	34.1116	−	19.6943i	0.0709181	−	0.0409446i
$482$			294.467i			0.610927i
$483$		0			0
$484$	−235.237			−0.486028
$485$	98.5811	+	170.747i	0.203260	+	0.352056i
$486$		0			0
$487$	31.5102	−	54.5773i	0.0647027	−	0.112068i	−0.831859	−	0.554986i	$-0.812723\pi$
$487$	31.5102	−	54.5773i	0.0647027	−	0.112068i	0.896562	+	0.442918i	$0.146057\pi$
$488$	58.2410	−	33.6254i	0.119346	−	0.0689046i
$489$		0			0
$490$	−68.9208	+	138.780i	−0.140655	+	0.283225i
$491$	−261.092			−0.531756			−0.265878	−	0.964007i	$-0.585662\pi$
$491$	−261.092			−0.531756			−0.265878	+	0.964007i	$0.585662\pi$
$492$		0			0
$493$	109.386	+	63.1541i	0.221879	+	0.128102i
$494$	−35.1497	+	60.8811i	−0.0711532	+	0.123241i
$495$		0			0
$496$			167.142i			0.336980i
$497$	91.6490	+	86.0789i	0.184404	+	0.173197i
$498$		0			0
$499$	−219.481	−	380.153i	−0.439843	−	0.761830i	0.557834	−	0.829952i	$-0.311632\pi$
$499$	−219.481	−	380.153i	−0.439843	−	0.761830i	−0.997677	+	0.0681226i	$0.978299\pi$
$500$	−19.3649	−	11.1803i	−0.0387298	−	0.0223607i
$501$		0			0
$502$	−53.2714	+	30.7563i	−0.106118	+	0.0612675i
$503$			702.372i			1.39637i	0.715919	+	0.698183i	$0.246008\pi$
$503$			702.372i			1.39637i	−0.715919	+	0.698183i	$0.753992\pi$
$504$		0			0
$505$	−249.042			−0.493153
$506$	−1.19790	−	2.07483i	−0.00236739	−	0.00410045i
$507$		0			0
$508$	131.740	−	228.181i	0.259331	−	0.449175i
$509$	103.188	−	59.5758i	0.202727	−	0.117045i	−0.395200	−	0.918595i	$-0.629325\pi$
$509$	103.188	−	59.5758i	0.202727	−	0.117045i	0.597927	+	0.801551i	$0.295991\pi$
$510$		0			0
$511$	−251.550	−	833.432i	−0.492270	−	1.63098i
$512$	22.6274			0.0441942
$513$		0			0
$514$	5.21724	+	3.01217i	0.0101503	+	0.00586026i
$515$	52.5237	−	90.9736i	0.101988	−	0.176648i
$516$		0			0
$517$		−	62.4497i		−	0.120792i
$518$	−69.0310	+	20.8352i	−0.133264	+	0.0402224i
$519$		0			0
$520$	−17.1005	−	29.6189i	−0.0328855	−	0.0569594i
$521$	391.422	+	225.988i	0.751291	+	0.433758i	0.826160	−	0.563435i	$-0.190521\pi$
$521$	391.422	+	225.988i	0.751291	+	0.433758i	−0.0748694	+	0.997193i	$0.523854\pi$
$522$		0			0
$523$	−775.007	+	447.451i	−1.48185	+	0.855546i	−0.999788	−	0.0205911i	$-0.993445\pi$
$523$	−775.007	+	447.451i	−1.48185	+	0.855546i	−0.482062	+	0.876137i	$0.660112\pi$
$524$			237.536i			0.453312i
$525$		0			0
$526$	591.670			1.12485
$527$	210.150	+	363.991i	0.398767	+	0.690685i
$528$		0			0
$529$	264.076	−	457.392i	0.499198	−	0.864636i
$530$	−285.033	+	164.564i	−0.537798	+	0.310498i
$531$		0			0
$532$	88.1048	−	93.8059i	0.165610	−	0.176327i
$533$	−283.294			−0.531509
$534$		0			0
$535$	359.571	+	207.598i	0.672096	+	0.388035i
$536$	21.1096	−	36.5630i	0.0393837	−	0.0682145i
$537$		0			0
$538$		−	521.065i		−	0.968522i
$539$	−80.6990	−	40.0766i	−0.149720	−	0.0743537i
$540$		0			0
$541$	158.262	+	274.119i	0.292537	+	0.506689i	0.974409	−	0.224783i	$-0.0721672\pi$
$541$	158.262	+	274.119i	0.292537	+	0.506689i	−0.681872	+	0.731472i	$0.738834\pi$
$542$	270.695	+	156.286i	0.499438	+	0.288351i
$543$		0			0
$544$	49.2765	−	28.4498i	0.0905817	−	0.0522974i
$545$		−	192.950i		−	0.354036i
$546$		0			0
$547$	796.193			1.45556			0.727782	−	0.685809i	$-0.240551\pi$
$547$	796.193			1.45556			0.727782	+	0.685809i	$0.240551\pi$
$548$	81.1530	+	140.561i	0.148089	+	0.256498i
$549$		0			0
$550$	6.50124	−	11.2605i	0.0118204	−	0.0204736i
$551$	99.9670	−	57.7160i	0.181428	−	0.104748i
$552$		0			0
$553$	−129.421	+	551.576i	−0.234034	+	0.997424i
$554$	−561.236			−1.01306
$555$		0			0
$556$	−430.088	−	248.311i	−0.773540	−	0.446603i
$557$	155.976	−	270.159i	0.280029	−	0.485025i	−0.691363	−	0.722508i	$-0.742989\pi$
$557$	155.976	−	270.159i	0.280029	−	0.485025i	0.971392	+	0.237484i	$0.0763226\pi$
$558$		0			0
$559$		−	43.9270i		−	0.0785813i
$560$	18.0911	+	59.9392i	0.0323055	+	0.107034i
$561$		0			0
$562$	−80.7827	−	139.920i	−0.143741	−	0.248968i
$563$	−534.350	−	308.507i	−0.949112	−	0.547970i	−0.0563071	−	0.998413i	$-0.517933\pi$
$563$	−534.350	−	308.507i	−0.949112	−	0.547970i	−0.892805	+	0.450443i	$0.851266\pi$
$564$		0			0
$565$	−166.191	+	95.9504i	−0.294143	+	0.169824i
$566$		−	639.838i		−	1.13046i
$567$		0			0
$568$	50.8043			0.0894442
$569$	−391.495	−	678.089i	−0.688041	−	1.19172i	−0.972471	−	0.233025i	$-0.925138\pi$
$569$	−391.495	−	678.089i	−0.688041	−	1.19172i	0.284430	−	0.958697i	$-0.408196\pi$
$570$		0			0
$571$	−1.06600	+	1.84636i	−0.00186689	+	0.00323355i	−0.866957	−	0.498382i	$-0.833928\pi$
$571$	−1.06600	+	1.84636i	−0.00186689	+	0.00323355i	0.865090	+	0.501616i	$0.167261\pi$
$572$	17.2230	−	9.94373i	0.0301102	−	0.0173841i
$573$		0			0
$574$	504.900	+	118.469i	0.879616	+	0.206392i
$575$	−4.60644			−0.00801120
$576$		0			0
$577$	−828.056	−	478.079i	−1.43511	−	0.828559i	−0.437602	−	0.899169i	$-0.644172\pi$
$577$	−828.056	−	478.079i	−1.43511	−	0.828559i	−0.997504	+	0.0706096i	$0.977506\pi$
$578$	−132.813	+	230.039i	−0.229781	+	0.397992i
$579$		0			0
$580$			56.1581i			0.0968244i
$581$	−741.441	+	789.419i	−1.27615	+	1.35872i
$582$		0			0
$583$	−95.6919	−	165.743i	−0.164137	−	0.284294i
$584$	−304.635	−	175.881i	−0.521635	−	0.301166i
$585$		0			0
$586$	145.909	−	84.2403i	0.248991	−	0.143755i
$587$		−	628.961i		−	1.07148i	−0.844382	−	0.535742i	$-0.820032\pi$
$587$		−	628.961i		−	1.07148i	0.844382	−	0.535742i	$-0.179968\pi$
$588$		0			0
$589$	384.109			0.652138
$590$	−22.9894	−	39.8188i	−0.0389651	−	0.0674895i
$591$		0			0
$592$	−14.5678	+	25.2321i	−0.0246077	+	0.0426218i
$593$	417.691	−	241.154i	0.704370	−	0.406668i	−0.104603	−	0.994514i	$-0.533357\pi$
$593$	417.691	−	241.154i	0.704370	−	0.406668i	0.808973	+	0.587846i	$0.200024\pi$
$594$		0			0
$595$	114.760	+	107.785i	0.192874	+	0.181152i
$596$	300.019			0.503388
$597$		0			0
$598$	−6.10168	−	3.52280i	−0.0102035	−	0.00589098i
$599$	181.233	−	313.904i	0.302559	−	0.524047i	−0.674156	−	0.738589i	$-0.735492\pi$
$599$	181.233	−	313.904i	0.302559	−	0.524047i	0.976715	+	0.214542i	$0.0688258\pi$
$600$		0			0
$601$		−	545.450i		−	0.907570i	−0.891111	−	0.453785i	$-0.850073\pi$
$601$		−	545.450i		−	0.907570i	0.891111	−	0.453785i	$-0.149927\pi$
$602$	−18.3695	+	78.2886i	−0.0305142	+	0.130047i
$603$		0			0
$604$	−183.030	−	317.017i	−0.303030	−	0.524863i
$605$	−227.768	−	131.502i	−0.376475	−	0.217358i
$606$		0			0
$607$	−554.426	+	320.098i	−0.913388	+	0.527345i	−0.881520	−	0.472147i	$-0.843479\pi$
$607$	−554.426	+	320.098i	−0.913388	+	0.527345i	−0.0318683	+	0.999492i	$0.510146\pi$
$608$		−	52.0000i		−	0.0855263i
$609$		0			0
$610$	75.1888			0.123260
$611$	−91.8265	−	159.048i	−0.150289	−	0.260308i
$612$		0			0
$613$	198.272	−	343.417i	0.323445	−	0.560223i	−0.657751	−	0.753235i	$-0.728492\pi$
$613$	198.272	−	343.417i	0.323445	−	0.560223i	0.981196	+	0.193012i	$0.0618256\pi$
$614$	333.918	−	192.787i	0.543840	−	0.313986i
$615$		0			0
$616$	−34.8540	+	10.5198i	−0.0565811	+	0.0170775i
$617$	421.502			0.683148			0.341574	−	0.939855i	$-0.389040\pi$
$617$	421.502			0.683148			0.341574	+	0.939855i	$0.389040\pi$
$618$		0			0
$619$	629.261	+	363.304i	1.01658	+	0.586921i	0.913111	−	0.407712i	$-0.133673\pi$
$619$	629.261	+	363.304i	1.01658	+	0.586921i	0.103467	+	0.994633i	$0.467006\pi$
$620$	−93.4354	+	161.835i	−0.150702	+	0.261024i
$621$		0			0
$622$			106.876i			0.171826i
$623$	−464.248	−	108.930i	−0.745181	−	0.174848i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	77.9313	+	44.9936i	0.124491	+	0.0718748i
$627$		0			0
$628$	511.449	−	295.285i	0.814409	−	0.470199i
$629$			73.2650i			0.116479i
$630$		0			0
$631$	−537.550			−0.851901			−0.425950	−	0.904746i	$-0.640060\pi$
$631$	−537.550			−0.851901			−0.425950	+	0.904746i	$0.640060\pi$
$632$	114.462	+	198.253i	0.181110	+	0.313692i
$633$		0			0
$634$	10.9263	−	18.9249i	0.0172339	−	0.0298500i
$635$	255.114	−	147.290i	0.401754	−	0.231953i
$636$		0			0
$637$	−264.455	+	16.5924i	−0.415157	+	0.0260477i
$638$	−32.6553			−0.0511838
$639$		0			0
$640$	21.9089	+	12.6491i	0.0342327	+	0.0197642i
$641$	488.924	−	846.841i	0.762752	−	1.32112i	−0.178675	−	0.983908i	$-0.557181\pi$
$641$	488.924	−	846.841i	0.762752	−	1.32112i	0.941427	−	0.337217i	$-0.109486\pi$
$642$		0			0
$643$		−	276.520i		−	0.430047i	−0.976609	−	0.215023i	$-0.931017\pi$
$643$		−	276.520i		−	0.430047i	0.976609	−	0.215023i	$-0.0689828\pi$
$644$	9.40150	+	8.83011i	0.0145986	+	0.0137114i
$645$		0			0
$646$	−65.3803	−	113.242i	−0.101208	−	0.175297i
$647$	210.206	+	121.362i	0.324893	+	0.187577i	0.653571	−	0.756865i	$-0.273270\pi$
$647$	210.206	+	121.362i	0.324893	+	0.187577i	−0.328679	+	0.944442i	$0.606603\pi$
$648$		0			0
$649$	23.1542	−	13.3681i	0.0356767	−	0.0205980i
$650$		−	38.2378i		−	0.0588275i
$651$		0			0
$652$	−236.652			−0.362964
$653$	−26.6109	−	46.0914i	−0.0407518	−	0.0705841i	0.844930	−	0.534877i	$-0.179642\pi$
$653$	−26.6109	−	46.0914i	−0.0407518	−	0.0705841i	−0.885682	+	0.464293i	$0.846309\pi$
$654$		0			0
$655$	−132.786	+	229.993i	−0.202727	+	0.351134i
$656$	181.476	−	104.775i	0.276641	−	0.159719i
$657$		0			0
$658$	97.1459	+	321.863i	0.147638	+	0.489153i
$659$	−640.732			−0.972279			−0.486139	−	0.873881i	$-0.661595\pi$
$659$	−640.732			−0.972279			−0.486139	+	0.873881i	$0.661595\pi$
$660$		0			0
$661$	10.4335	+	6.02380i	0.0157845	+	0.00911317i	0.507871	−	0.861433i	$-0.330432\pi$
$661$	10.4335	+	6.02380i	0.0157845	+	0.00911317i	−0.492087	+	0.870546i	$0.663766\pi$
$662$	263.807	−	456.927i	0.398500	−	0.690222i
$663$		0			0
$664$			437.603i			0.659041i
$665$	137.746	−	41.5751i	0.207137	−	0.0625189i
$666$		0			0
$667$	5.78446	+	10.0190i	0.00867236	+	0.0150210i
$668$	355.393	+	205.186i	0.532025	+	0.307165i
$669$		0			0
$670$	40.8787	−	23.6013i	0.0610129	−	0.0352258i
$671$			43.7214i			0.0651586i
$672$		0			0
$673$	−952.008			−1.41457			−0.707286	−	0.706927i	$-0.750081\pi$
$673$	−952.008			−1.41457			−0.707286	+	0.706927i	$0.750081\pi$
$674$	−454.612	−	787.412i	−0.674499	−	1.16827i
$675$		0			0
$676$	−139.757	+	242.067i	−0.206742	+	0.358087i
$677$	−18.2965	+	10.5635i	−0.0270259	+	0.0156034i	−0.513452	−	0.858118i	$-0.671634\pi$
$677$	−18.2965	+	10.5635i	−0.0270259	+	0.0156034i	0.486426	+	0.873722i	$0.338300\pi$
$678$		0			0
$679$	422.551	−	449.894i	0.622314	−	0.662583i
$680$	63.6156			0.0935524
$681$		0			0
$682$	−94.1050	−	54.3316i	−0.137984	−	0.0796651i
$683$	−196.448	+	340.259i	−0.287626	+	0.498182i	−0.973243	−	0.229780i	$-0.926199\pi$
$683$	−196.448	+	340.259i	−0.287626	+	0.498182i	0.685617	+	0.727963i	$0.259533\pi$
$684$		0			0
$685$			181.464i			0.264910i
$686$	478.261	+	81.0188i	0.697174	+	0.118103i
$687$		0			0
$688$	16.2462	+	28.1393i	0.0236137	+	0.0409002i
$689$	−487.420	−	281.412i	−0.707431	−	0.408436i
$690$		0			0
$691$	230.954	−	133.342i	0.334232	−	0.192969i	−0.323486	−	0.946233i	$-0.604855\pi$
$691$	230.954	−	133.342i	0.334232	−	0.192969i	0.657718	+	0.753264i	$0.271522\pi$
$692$		−	225.068i		−	0.325242i
$693$		0			0
$694$	−203.659			−0.293457
$695$	−277.621	−	480.853i	−0.399454	−	0.691875i
$696$		0			0
$697$	263.471	−	456.346i	0.378008	−	0.654729i
$698$	693.826	−	400.581i	0.994020	−	0.573898i
$699$		0			0
$700$	−15.9904	+	68.1491i	−0.0228435	+	0.0973559i
$701$	−207.973			−0.296680			−0.148340	−	0.988936i	$-0.547393\pi$
$701$	−207.973			−0.296680			−0.148340	+	0.988936i	$0.547393\pi$
$702$		0			0
$703$	57.9858	+	33.4781i	0.0824834	+	0.0476218i
$704$	−7.35531	+	12.7398i	−0.0104479	+	0.0180963i
$705$		0			0
$706$			721.480i			1.02193i
$707$	225.273	+	746.371i	0.318632	+	1.05569i
$708$		0			0
$709$	447.714	+	775.463i	0.631472	+	1.09374i	0.987251	+	0.159172i	$0.0508823\pi$
$709$	447.714	+	775.463i	0.631472	+	1.09374i	−0.355779	+	0.934570i	$0.615784\pi$
$710$	49.1911	+	28.4005i	0.0692832	+	0.0400007i
$711$		0			0
$712$	−166.865	+	96.3395i	−0.234361	+	0.135308i
$713$			38.4965i			0.0539923i
$714$		0			0
$715$	22.2349			0.0310977
$716$	−44.4698	−	77.0240i	−0.0621087	−	0.107575i
$717$		0			0
$718$	472.250	−	817.962i	0.657730	−	1.13922i
$719$	327.729	−	189.215i	0.455813	−	0.263163i	−0.254469	−	0.967081i	$-0.581901\pi$
$719$	327.729	−	189.215i	0.455813	−	0.263163i	0.710282	+	0.703917i	$0.248567\pi$
$720$		0			0
$721$	−320.155	−	75.1207i	−0.444043	−	0.104190i
$722$	391.030			0.541593
$723$		0			0
$724$	16.0138	+	9.24555i	0.0221185	+	0.0127701i
$725$	−31.3934	+	54.3749i	−0.0433012	+	0.0749998i
$726$		0			0
$727$			456.052i			0.627307i	0.949538	+	0.313653i	$0.101553\pi$
$727$			456.052i			0.627307i	−0.949538	+	0.313653i	$0.898447\pi$
$728$	−73.2984	+	78.0414i	−0.100685	+	0.107200i
$729$		0			0
$730$	−196.641	−	340.592i	−0.269371	−	0.466565i
$731$	70.7599	+	40.8533i	0.0967988	+	0.0558868i
$732$		0			0
$733$	658.892	−	380.412i	0.898898	−	0.518979i	0.0220553	−	0.999757i	$-0.492979\pi$
$733$	658.892	−	380.412i	0.898898	−	0.518979i	0.876842	+	0.480778i	$0.159646\pi$
$734$			49.3517i			0.0672367i
$735$		0			0
$736$	5.21159			0.00708096
$737$	13.7239	+	23.7705i	0.0186213	+	0.0322530i
$738$		0			0
$739$	14.0833	−	24.3930i	0.0190573	−	0.0330081i	−0.856340	−	0.516413i	$-0.827267\pi$
$739$	14.0833	−	24.3930i	0.0190573	−	0.0330081i	0.875397	+	0.483405i	$0.160600\pi$
$740$	−28.2104	+	16.2873i	−0.0381221	+	0.0220098i
$741$		0			0
$742$	751.019	+	705.376i	1.01216	+	0.950641i
$743$	1077.90			1.45073			0.725367	−	0.688362i	$-0.241670\pi$
$743$	1077.90			1.45073			0.725367	+	0.688362i	$0.241670\pi$
$744$		0			0
$745$	290.492	+	167.716i	0.389923	+	0.225122i
$746$	288.517	−	499.726i	0.386752	−	0.669874i
$747$		0			0
$748$			36.9917i			0.0494542i
$749$	296.913	−	1265.41i	0.396412	−	1.68946i
$750$		0			0
$751$	−90.0583	−	155.986i	−0.119918	−	0.207704i	0.799817	−	0.600244i	$-0.204930\pi$
$751$	−90.0583	−	155.986i	−0.119918	−	0.207704i	−0.919735	+	0.392540i	$0.871596\pi$
$752$	117.647	+	67.9234i	0.156445	+	0.0903237i
$753$		0			0
$754$	−83.1671	+	48.0166i	−0.110301	+	0.0636824i
$755$		−	409.267i		−	0.542076i
$756$		0			0
$757$	219.675			0.290192			0.145096	−	0.989418i	$-0.453651\pi$
$757$	219.675			0.290192			0.145096	+	0.989418i	$0.453651\pi$
$758$	7.40380	+	12.8238i	0.00976755	+	0.0169179i
$759$		0			0
$760$	29.0689	−	50.3488i	0.0382485	−	0.0662484i
$761$	−1113.97	+	643.150i	−1.46382	+	0.845138i	−0.999185	−	0.0403636i	$-0.987148\pi$
$761$	−1113.97	+	643.150i	−1.46382	+	0.845138i	−0.464637	+	0.885501i	$0.653815\pi$
$762$		0			0
$763$	−578.262	+	174.533i	−0.757880	+	0.228746i
$764$	273.618			0.358138
$765$		0			0
$766$	−282.379	−	163.031i	−0.368641	−	0.212835i
$767$	39.3130	−	68.0921i	0.0512555	−	0.0887772i
$768$		0			0
$769$		−	365.543i		−	0.475348i	−0.971345	−	0.237674i	$-0.923615\pi$
$769$		−	365.543i		−	0.475348i	0.971345	−	0.237674i	$-0.0763850\pi$
$770$	−39.6279	−	9.29824i	−0.0514648	−	0.0120756i
$771$		0			0
$772$	365.874	+	633.712i	0.473930	+	0.820871i
$773$	−267.183	−	154.258i	−0.345645	−	0.199558i	0.317121	−	0.948385i	$-0.397284\pi$
$773$	−267.183	−	154.258i	−0.345645	−	0.199558i	−0.662765	+	0.748827i	$0.730617\pi$
$774$		0			0
$775$	−180.937	+	104.464i	−0.233467	+	0.134792i
$776$		−	249.393i		−	0.321382i
$777$		0			0
$778$	−956.311			−1.22919
$779$	−240.784	−	417.050i	−0.309094	−	0.535366i
$780$		0			0
$781$	−16.5145	+	28.6040i	−0.0211454	+	0.0366249i
$782$	11.3494	−	6.55261i	0.0145134	−	0.00837929i
$783$		0			0
$784$	163.271	−	108.437i	0.208254	−	0.138312i
$785$	660.277			0.841118
$786$		0			0
$787$	1232.85	+	711.787i	1.56652	+	0.904431i	0.996570	+	0.0827517i	$0.0263708\pi$
$787$	1232.85	+	711.787i	1.56652	+	0.904431i	0.569950	+	0.821679i	$0.306963\pi$
$788$	−194.925	+	337.620i	−0.247367	+	0.428452i
$789$		0			0
$790$			255.944i			0.323980i
$791$	437.888	+	411.275i	0.553588	+	0.519944i
$792$		0			0
$793$	64.2882	+	111.350i	0.0810696	+	0.140417i
$794$	200.310	+	115.649i	0.252280	+	0.145654i
$795$		0			0
$796$	420.603	−	242.835i	0.528395	−	0.305069i
$797$			475.713i			0.596880i	0.954428	+	0.298440i	$0.0964663\pi$
$797$			475.713i			0.596880i	−0.954428	+	0.298440i	$0.903534\pi$
$798$		0			0
$799$	341.604			0.427540
$800$	14.1421	+	24.4949i	0.0176777	+	0.0306186i
$801$		0			0
$802$	−211.600	+	366.502i	−0.263840	+	0.456985i
$803$	198.050	−	114.344i	0.246638	−	0.142397i
$804$		0			0
$805$	4.16678	+	13.8053i	0.00517612	+	0.0171495i
$806$	−319.558			−0.396474
$807$		0			0
$808$	272.812	+	157.508i	0.337639	+	0.194936i
$809$	363.710	−	629.965i	0.449580	−	0.778696i	−0.548779	−	0.835968i	$-0.684907\pi$
$809$	363.710	−	629.965i	0.449580	−	0.778696i	0.998359	+	0.0572722i	$0.0182403\pi$
$810$		0			0
$811$		−	673.804i		−	0.830831i	−0.909632	−	0.415415i	$-0.863636\pi$
$811$		−	673.804i		−	0.830831i	0.909632	−	0.415415i	$-0.136364\pi$
$812$	168.304	−	50.7981i	0.207271	−	0.0625593i
$813$		0			0
$814$	−9.47085	−	16.4040i	−0.0116349	−	0.0201523i
$815$	−229.138	−	132.293i	−0.281150	−	0.162322i
$816$		0			0
$817$	64.6668	−	37.3354i	0.0791516	−	0.0456982i
$818$		−	658.527i		−	0.805046i
$819$		0			0
$820$	234.285			0.285714
$821$	−445.465	−	771.568i	−0.542588	−	0.939790i	−0.998754	−	0.0498958i	$-0.984111\pi$
$821$	−445.465	−	771.568i	−0.542588	−	0.939790i	0.456166	−	0.889895i	$-0.349222\pi$
$822$		0			0
$823$	495.873	−	858.877i	0.602519	−	1.04359i	−0.389919	−	0.920849i	$-0.627497\pi$
$823$	495.873	−	858.877i	0.602519	−	1.04359i	0.992438	−	0.122744i	$-0.0391696\pi$
$824$	−115.074	+	66.4378i	−0.139652	+	0.0806283i
$825$		0			0
$826$	−98.5403	+	104.917i	−0.119298	+	0.127018i
$827$	−1264.47			−1.52899			−0.764493	−	0.644632i	$-0.777011\pi$
$827$	−1264.47			−1.52899			−0.764493	+	0.644632i	$0.777011\pi$
$828$		0			0
$829$	−78.3145	−	45.2149i	−0.0944686	−	0.0545415i	0.452021	−	0.892007i	$-0.350703\pi$
$829$	−78.3145	−	45.2149i	−0.0944686	−	0.0545415i	−0.546490	+	0.837466i	$0.684036\pi$
$830$	−244.628	+	423.708i	−0.294732	+	0.510491i
$831$		0			0
$832$			43.2612i			0.0519966i
$833$	219.222	−	441.429i	0.263172	−	0.529927i
$834$		0			0
$835$	229.405	+	397.341i	0.274736	+	0.475858i
$836$	29.2772	+	16.9032i	0.0350206	+	0.0202191i
$837$		0			0
$838$	705.309	−	407.210i	0.841658	−	0.485931i
$839$		−	148.508i		−	0.177006i	−0.996076	−	0.0885032i	$-0.971792\pi$
$839$		−	148.508i		−	0.177006i	0.996076	−	0.0885032i	$-0.0282083\pi$
$840$		0			0
$841$	−683.313			−0.812501
$842$	−403.863	−	699.512i	−0.479648	−	0.830774i
$843$		0			0
$844$	−185.930	+	322.040i	−0.220296	+	0.381564i
$845$	−270.639	+	156.253i	−0.320283	+	0.184915i
$846$		0			0
$847$	−188.077	+	801.562i	−0.222051	+	0.946354i
$848$	416.317			0.490940
$849$		0			0
$850$	61.5956	+	35.5622i	0.0724654	+	0.0418379i
$851$	−3.35527	+	5.81151i	−0.00394274	+	0.00682903i
$852$		0			0
$853$		−	642.996i		−	0.753805i	−0.926253	−	0.376902i	$-0.876989\pi$
$853$		−	642.996i		−	0.753805i	0.926253	−	0.376902i	$-0.123011\pi$
$854$	−68.0124	−	225.338i	−0.0796398	−	0.263862i
$855$		0			0
$856$	−262.594	−	454.826i	−0.306768	−	0.531338i
$857$	109.679	+	63.3232i	0.127980	+	0.0738894i	0.562623	−	0.826713i	$-0.309792\pi$
$857$	109.679	+	63.3232i	0.127980	+	0.0738894i	−0.434643	+	0.900603i	$0.643125\pi$
$858$		0			0
$859$	−435.756	+	251.584i	−0.507283	+	0.292880i	−0.731716	−	0.681610i	$-0.761280\pi$
$859$	−435.756	+	251.584i	−0.507283	+	0.292880i	0.224433	+	0.974489i	$0.427947\pi$
$860$			36.3277i			0.0422415i
$861$		0			0
$862$	38.3809			0.0445254
$863$	633.889	+	1097.93i	0.734518	+	1.27222i	0.954935	+	0.296816i	$0.0959250\pi$
$863$	633.889	+	1097.93i	0.734518	+	1.27222i	−0.220417	+	0.975406i	$0.570742\pi$
$864$		0			0
$865$	125.817	−	217.921i	0.145453	−	0.251932i
$866$	445.082	−	256.968i	0.513951	−	0.296730i
$867$		0			0
$868$	569.530	+	133.634i	0.656141	+	0.153956i
$869$	−148.828			−0.171264
$870$		0			0
$871$	69.9045	+	40.3594i	0.0802577	+	0.0463368i
$872$	−122.032	+	211.366i	−0.139945	+	0.242392i
$873$		0			0
$874$		−	11.9767i		−	0.0137034i
$875$	−53.5792	+	57.0462i	−0.0612334	+	0.0651957i
$876$		0			0
$877$	164.850	+	285.529i	0.187971	+	0.325575i	0.944574	−	0.328300i	$-0.106476\pi$
$877$	164.850	+	285.529i	0.187971	+	0.325575i	−0.756603	+	0.653875i	$0.773142\pi$
$878$	570.008	+	329.094i	0.649212	+	0.374823i
$879$		0			0
$880$	−14.2435	+	8.22348i	−0.0161858	+	0.00934487i
$881$			583.618i			0.662449i	0.943552	+	0.331224i	$0.107462\pi$
$881$			583.618i			0.662449i	−0.943552	+	0.331224i	$0.892538\pi$
$882$		0			0
$883$	−1172.36			−1.32770			−0.663849	−	0.747867i	$-0.731078\pi$
$883$	−1172.36			−1.32770			−0.663849	+	0.747867i	$0.731078\pi$
$884$	54.3929	+	94.2113i	0.0615304	+	0.106574i
$885$		0			0
$886$	345.023	−	597.597i	0.389416	−	0.674489i
$887$	−1274.64	+	735.915i	−1.43703	+	0.829667i	−0.997642	−	0.0686323i	$-0.978136\pi$
$887$	−1274.64	+	735.915i	−1.43703	+	0.829667i	−0.439384	+	0.898299i	$0.644803\pi$
$888$		0			0
$889$	−672.188	−	631.335i	−0.756117	−	0.710163i
$890$	−215.422			−0.242047
$891$		0			0
$892$	−92.8982	−	53.6348i	−0.104146	−	0.0601287i
$893$	156.095	−	270.364i	0.174798	−	0.302759i
$894$		0			0
$895$		−	99.4375i		−	0.111103i
$896$	18.0911	−	77.1020i	0.0201910	−	0.0860513i
$897$		0			0
$898$	−202.118	−	350.078i	−0.225075	−	0.389842i
$899$	454.417	+	262.358i	0.505470	+	0.291833i
$900$		0			0
$901$	906.627	−	523.442i	1.00625	−	0.580956i
$902$			136.234i			0.151035i
$903$		0			0
$904$	242.737			0.268515
$905$	10.3368	+	17.9039i	0.0114219	+	0.0197833i
$906$		0			0
$907$	−498.599	+	863.598i	−0.549723	+	0.952148i	0.448570	+	0.893748i	$0.351933\pi$
$907$	−498.599	+	863.598i	−0.549723	+	0.952148i	−0.998293	+	0.0584006i	$0.981400\pi$
$908$	292.784	−	169.039i	0.322449	−	0.186166i
$909$		0			0
$910$	−114.597	+	34.5882i	−0.125931	+	0.0380090i
$911$	758.955			0.833101			0.416550	−	0.909113i	$-0.363239\pi$
$911$	758.955			0.833101			0.416550	+	0.909113i	$0.363239\pi$
$912$		0			0
$913$	−246.381	−	142.248i	−0.269859	−	0.155803i
$914$	−299.281	+	518.370i	−0.327441	+	0.567144i
$915$		0			0
$916$			572.035i			0.624492i
$917$	809.393	+	189.915i	0.882653	+	0.207104i
$918$		0			0
$919$	−703.781	−	1218.99i	−0.765812	−	1.32643i	−0.939816	−	0.341681i	$-0.889004\pi$
$919$	−703.781	−	1218.99i	−0.765812	−	1.32643i	0.174004	−	0.984745i	$-0.444329\pi$
$920$	5.04610	+	2.91337i	0.00548489	+	0.00316670i
$921$		0			0
$922$	577.771	−	333.576i	0.626649	−	0.361796i
$923$			97.1324i			0.105236i
$924$		0			0
$925$	−36.4194			−0.0393723
$926$	137.192	+	237.623i	0.148155	+	0.256613i
$927$		0			0
$928$	35.5175	−	61.5182i	0.0382732	−	0.0662911i
$929$	−314.575	+	181.620i	−0.338617	+	0.195500i	−0.659660	−	0.751564i	$-0.729300\pi$
$929$	−314.575	+	181.620i	−0.338617	+	0.195500i	0.321044	+	0.947064i	$0.395966\pi$
$930$		0			0
$931$	−249.198	−	375.213i	−0.267667	−	0.403021i
$932$	363.677			0.390212
$933$		0			0
$934$	−13.8728	−	8.00946i	−0.0148531	−	0.00857544i
$935$	−20.6790	+	35.8171i	−0.0221166	+	0.0383071i
$936$		0			0
$937$		−	401.784i		−	0.428798i	−0.976746	−	0.214399i	$-0.931221\pi$
$937$		−	401.784i		−	0.428798i	0.976746	−	0.214399i	$-0.0687793\pi$
$938$	−107.709	−	101.163i	−0.114829	−	0.107850i
$939$		0			0
$940$	75.9407	+	131.533i	0.0807880	+	0.139929i
$941$	731.276	+	422.202i	0.777126	+	0.448674i	0.835411	−	0.549626i	$-0.185230\pi$
$941$	731.276	+	422.202i	0.777126	+	0.448674i	−0.0582845	+	0.998300i	$0.518563\pi$
$942$		0			0
$943$	41.7980	−	24.1321i	0.0443245	−	0.0255908i
$944$			58.1591i			0.0616092i
$945$		0			0
$946$	−21.1241			−0.0223299
$947$	144.083	+	249.560i	0.152147	+	0.263527i	0.932017	−	0.362415i	$-0.118048\pi$
$947$	144.083	+	249.560i	0.152147	+	0.263527i	−0.779869	+	0.625942i	$0.784715\pi$
$948$		0			0
$949$	336.266	−	582.429i	0.354337	−	0.613729i
$950$	56.2916	−	32.5000i	0.0592543	−	0.0342105i
$951$		0			0
$952$	−57.5438	−	190.654i	−0.0604452	−	0.200266i
$953$	−293.080			−0.307534			−0.153767	−	0.988107i	$-0.549141\pi$
$953$	−293.080			−0.307534			−0.153767	+	0.988107i	$0.549141\pi$
$954$		0			0
$955$	264.929	+	152.957i	0.277413	+	0.160164i
$956$	−382.489	+	662.490i	−0.400093	+	0.692981i
$957$		0			0
$958$		−	894.769i		−	0.933997i
$959$	543.839	−	164.144i	0.567090	−	0.171161i
$960$		0			0
$961$	392.517	+	679.859i	0.408446	+	0.707450i
$962$	−48.2411	−	27.8520i	−0.0501466	−	0.0289522i
$963$		0			0
$964$	360.647	−	208.220i	0.374115	−	0.215995i
$965$			818.119i			0.847792i
$966$		0			0
$967$	68.4003			0.0707345			0.0353673	−	0.999374i	$-0.488740\pi$
$967$	68.4003			0.0707345			0.0353673	+	0.999374i	$0.488740\pi$
$968$	166.338	+	288.106i	0.171837	+	0.297630i
$969$		0			0
$970$	139.415	−	241.473i	0.143726	−	0.248942i
$971$	−253.215	+	146.194i	−0.260777	+	0.150560i	−0.624689	−	0.780874i	$-0.714774\pi$
$971$	−253.215	+	146.194i	−0.260777	+	0.150560i	0.363912	+	0.931433i	$0.381441\pi$
$972$		0			0
$973$	−1189.98	+	1266.98i	−1.22300	+	1.30213i
$974$	−89.1243			−0.0915034
$975$		0			0
$976$	−82.3652	−	47.5536i	−0.0843906	−	0.0487229i
$977$	−538.697	+	933.051i	−0.551379	+	0.955016i	0.446796	+	0.894636i	$0.352565\pi$
$977$	−538.697	+	933.051i	−0.551379	+	0.955016i	−0.998175	+	0.0603807i	$0.980769\pi$
$978$		0			0
$979$		−	125.265i		−	0.127952i
$980$	218.705	−	13.7220i	0.223168	−	0.0140020i
$981$		0			0
$982$	184.620	+	319.771i	0.188004	+	0.325632i
$983$	−1354.95	−	782.282i	−1.37839	−	0.795811i	−0.386420	−	0.922323i	$-0.626289\pi$
$983$	−1354.95	−	782.282i	−1.37839	−	0.795811i	−0.991965	+	0.126511i	$0.959622\pi$
$984$		0			0
$985$	−377.471	+	217.933i	−0.383219	+	0.221252i
$986$		−	178.627i		−	0.181163i
$987$		0			0
$988$	99.4184			0.100626
$989$	3.74186	+	6.48110i	0.00378348	+	0.00655318i
$990$		0			0
$991$	−726.967	+	1259.14i	−0.733570	+	1.27058i	0.221779	+	0.975097i	$0.428814\pi$
$991$	−726.967	+	1259.14i	−0.733570	+	1.27058i	−0.955348	+	0.295483i	$0.904520\pi$
$992$	204.707	−	118.187i	0.206358	−	0.119141i
$993$		0			0
$994$	40.6191	−	173.114i	0.0408643	−	0.174159i
$995$	542.996			0.545724
$996$		0			0
$997$	−701.023	−	404.736i	−0.703133	−	0.405954i	0.105380	−	0.994432i	$-0.466394\pi$
$997$	−701.023	−	404.736i	−0.703133	−	0.405954i	−0.808513	+	0.588478i	$0.799727\pi$
$998$	−310.394	+	537.618i	−0.311016	+	0.538695i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.v.b.451.1		8
3.2	odd	2		210.3.o.a.31.4	✓	8
7.5	odd	6	inner	630.3.v.b.271.1		8
15.2	even	4		1050.3.q.c.199.3		16
15.8	even	4		1050.3.q.c.199.6		16
15.14	odd	2		1050.3.p.b.451.1		8
21.5	even	6		210.3.o.a.61.4	yes	8
21.11	odd	6		1470.3.f.a.391.2		8
21.17	even	6		1470.3.f.a.391.3		8
105.47	odd	12		1050.3.q.c.649.6		16
105.68	odd	12		1050.3.q.c.649.3		16
105.89	even	6		1050.3.p.b.901.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.a.31.4	✓	8	3.2	odd	2
210.3.o.a.61.4	yes	8	21.5	even	6
630.3.v.b.271.1		8	7.5	odd	6	inner
630.3.v.b.451.1		8	1.1	even	1	trivial
1050.3.p.b.451.1		8	15.14	odd	2
1050.3.p.b.901.1		8	105.89	even	6
1050.3.q.c.199.3		16	15.2	even	4
1050.3.q.c.199.6		16	15.8	even	4
1050.3.q.c.649.3		16	105.68	odd	12
1050.3.q.c.649.6		16	105.47	odd	12
1470.3.f.a.391.2		8	21.11	odd	6
1470.3.f.a.391.3		8	21.17	even	6

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.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(5.10237 + 4.79227i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(5.10237 + 4.79227i) q^{7} +2.82843 q^{8} +(2.73861 + 1.58114i) q^{10} +(-0.919414 + 1.59247i) q^{11} +5.40765i q^{13} +(2.26139 - 9.63774i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-8.71093 - 5.02926i) q^{17} +(-7.96084 + 4.59619i) q^{19} -4.47214i q^{20} +2.60049 q^{22} +(-0.460644 - 0.797858i) q^{23} +(2.50000 - 4.33013i) q^{25} +(6.62299 - 3.82378i) q^{26} +(-13.4028 + 4.04529i) q^{28} -12.5573 q^{29} +(-36.1874 - 20.8928i) q^{31} +(-2.82843 + 4.89898i) q^{32} +14.2249i q^{34} +(-15.2386 - 3.57557i) q^{35} +(-3.64194 - 6.30803i) q^{37} +(11.2583 + 6.50000i) q^{38} +(-5.47723 + 3.16228i) q^{40} +52.3877i q^{41} -8.12312 q^{43} +(-1.83883 - 3.18494i) q^{44} +(-0.651449 + 1.12834i) q^{46} +(-29.4117 + 16.9809i) q^{47} +(3.06832 + 48.9038i) q^{49} -7.07107 q^{50} +(-9.36632 - 5.40765i) q^{52} +(-52.0396 + 90.1353i) q^{53} -4.11174i q^{55} +(14.4317 + 13.5546i) q^{56} +(8.87938 + 15.3795i) q^{58} +(-12.5918 - 7.26989i) q^{59} +(20.5913 - 11.8884i) q^{61} +59.0937i q^{62} +8.00000 q^{64} +(-6.04593 - 10.4719i) q^{65} +(7.46339 - 12.9270i) q^{67} +(17.4219 - 10.0585i) q^{68} +(6.39617 + 21.1917i) q^{70} +17.9620 q^{71} +(-107.705 - 62.1833i) q^{73} +(-5.15048 + 8.92090i) q^{74} -18.3848i q^{76} +(-12.3227 + 3.71930i) q^{77} +(40.4683 + 70.0931i) q^{79} +(7.74597 + 4.47214i) q^{80} +(64.1616 - 37.0437i) q^{82} +154.716i q^{83} +22.4915 q^{85} +(5.74391 + 9.94875i) q^{86} +(-2.60049 + 4.50419i) q^{88} +(-58.9956 + 34.0611i) q^{89} +(-25.9149 + 27.5918i) q^{91} +1.84258 q^{92} +(41.5944 + 24.0146i) q^{94} +(10.2774 - 17.8010i) q^{95} -88.1736i q^{97} +(57.7251 - 38.3381i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4}+O(q^{10}) \) 8 * q - 8 * q^4	\( 8 q - 8 q^{4} + 4 q^{11} + 40 q^{14} - 16 q^{16} - 84 q^{17} + 108 q^{19} - 48 q^{22} - 12 q^{23} + 20 q^{25} + 96 q^{26} - 72 q^{29} - 132 q^{31} - 100 q^{35} - 96 q^{37} + 168 q^{38} - 112 q^{43} + 8 q^{44} + 8 q^{46} + 24 q^{47} + 156 q^{49} + 48 q^{52} - 32 q^{53} - 16 q^{56} + 104 q^{58} - 132 q^{59} + 96 q^{61} + 64 q^{64} - 20 q^{65} - 120 q^{67} + 168 q^{68} - 8 q^{71} + 24 q^{73} + 16 q^{74} + 216 q^{77} + 12 q^{79} + 24 q^{82} + 120 q^{85} + 40 q^{86} + 48 q^{88} - 492 q^{89} - 308 q^{91} + 48 q^{92} + 480 q^{94} + 40 q^{95}+O(q^{100}) \) 8 * q - 8 * q^4 + 4 * q^11 + 40 * q^14 - 16 * q^16 - 84 * q^17 + 108 * q^19 - 48 * q^22 - 12 * q^23 + 20 * q^25 + 96 * q^26 - 72 * q^29 - 132 * q^31 - 100 * q^35 - 96 * q^37 + 168 * q^38 - 112 * q^43 + 8 * q^44 + 8 * q^46 + 24 * q^47 + 156 * q^49 + 48 * q^52 - 32 * q^53 - 16 * q^56 + 104 * q^58 - 132 * q^59 + 96 * q^61 + 64 * q^64 - 20 * q^65 - 120 * q^67 + 168 * q^68 - 8 * q^71 + 24 * q^73 + 16 * q^74 + 216 * q^77 + 12 * q^79 + 24 * q^82 + 120 * q^85 + 40 * q^86 + 48 * q^88 - 492 * q^89 - 308 * q^91 + 48 * q^92 + 480 * q^94 + 40 * q^95

Introduction

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