LMFDB - Embedded newform 1008.2.t.i.193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(193,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1008.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.t (of order $3$, degree $2$, not 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.3
Root			$1.19343 - 2.06709i$ of defining polynomial
Character	$\chi$	$=$	1008.193
Dual form			1008.2.t.i.961.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.266999 - 1.71135i) q^{3} -2.92087 q^{5} +(-2.35742 - 1.20106i) q^{7} +(-2.85742 + 0.913855i) q^{9} +O(q^{10})$	\(q+(-0.266999 - 1.71135i) q^{3} -2.92087 q^{5} +(-2.35742 - 1.20106i) q^{7} +(-2.85742 + 0.913855i) q^{9} +1.35371 q^{11} +(-0.733001 + 1.26960i) q^{13} +(0.779867 + 4.99862i) q^{15} +(1.65514 - 2.86678i) q^{17} +(1.10329 + 1.91096i) q^{19} +(-1.42601 + 4.35505i) q^{21} -2.62830 q^{23} +3.53146 q^{25} +(2.32685 + 4.64605i) q^{27} +(0.521720 + 0.903646i) q^{29} +(1.63729 + 2.83587i) q^{31} +(-0.361440 - 2.31668i) q^{33} +(6.88572 + 3.50815i) q^{35} +(5.43773 + 9.41842i) q^{37} +(2.36843 + 0.915440i) q^{39} +(-0.904289 + 1.56627i) q^{41} +(2.17129 + 3.76078i) q^{43} +(8.34615 - 2.66925i) q^{45} +(1.98957 - 3.44604i) q^{47} +(4.11489 + 5.66283i) q^{49} +(-5.34798 - 2.06709i) q^{51} +(-3.22743 + 5.59008i) q^{53} -3.95402 q^{55} +(2.97574 - 2.39834i) q^{57} +(-6.10700 - 10.5776i) q^{59} +(-0.279867 + 0.484744i) q^{61} +(7.83376 + 1.27761i) q^{63} +(2.14100 - 3.70832i) q^{65} +(6.40588 + 11.0953i) q^{67} +(0.701751 + 4.49793i) q^{69} -12.9177 q^{71} +(5.22772 - 9.05467i) q^{73} +(-0.942894 - 6.04355i) q^{75} +(-3.19128 - 1.62590i) q^{77} +(0.383838 - 0.664827i) q^{79} +(7.32974 - 5.22254i) q^{81} +(0.983707 + 1.70383i) q^{83} +(-4.83443 + 8.37348i) q^{85} +(1.40715 - 1.13412i) q^{87} +(3.20356 + 5.54872i) q^{89} +(3.25286 - 2.11259i) q^{91} +(4.41601 - 3.55915i) q^{93} +(-3.22257 - 5.58166i) q^{95} +(-4.14143 - 7.17316i) q^{97} +(-3.86814 + 1.23710i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{3} - 8 q^{5} + q^{7} - 4 q^{9}+O(q^{10}) $ 10 * q - 2 * q^3 - 8 * q^5 + q^7 - 4 * q^9	$ 10 q - 2 q^{3} - 8 q^{5} + q^{7} - 4 q^{9} + 8 q^{11} - 8 q^{13} + 19 q^{15} + 12 q^{17} - q^{19} - 2 q^{21} + 6 q^{23} + 2 q^{25} + 7 q^{27} + 7 q^{29} + 3 q^{31} - q^{33} - 5 q^{35} - 20 q^{39} + 5 q^{41} + 7 q^{43} - q^{45} - 27 q^{47} + 25 q^{49} - 24 q^{51} - 21 q^{53} - 4 q^{55} - 4 q^{57} - 30 q^{59} - 14 q^{61} + 35 q^{63} - 11 q^{65} + 2 q^{67} + 15 q^{69} + 6 q^{71} + 15 q^{73} - 31 q^{75} - 31 q^{77} + 4 q^{79} + 8 q^{81} - 9 q^{83} - 6 q^{85} - 32 q^{87} + 28 q^{89} + 4 q^{91} - 12 q^{93} + 14 q^{95} - 12 q^{97} - 35 q^{99}+O(q^{100}) $ 10 * q - 2 * q^3 - 8 * q^5 + q^7 - 4 * q^9 + 8 * q^11 - 8 * q^13 + 19 * q^15 + 12 * q^17 - q^19 - 2 * q^21 + 6 * q^23 + 2 * q^25 + 7 * q^27 + 7 * q^29 + 3 * q^31 - q^33 - 5 * q^35 - 20 * q^39 + 5 * q^41 + 7 * q^43 - q^45 - 27 * q^47 + 25 * q^49 - 24 * q^51 - 21 * q^53 - 4 * q^55 - 4 * q^57 - 30 * q^59 - 14 * q^61 + 35 * q^63 - 11 * q^65 + 2 * q^67 + 15 * q^69 + 6 * q^71 + 15 * q^73 - 31 * q^75 - 31 * q^77 + 4 * q^79 + 8 * q^81 - 9 * q^83 - 6 * q^85 - 32 * q^87 + 28 * q^89 + 4 * q^91 - 12 * q^93 + 14 * q^95 - 12 * q^97 - 35 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	−0.266999	−	1.71135i	−0.154152	−	0.988047i
$3$	−0.266999	−	1.71135i	−0.154152	−	0.988047i
$4$		0			0
$5$	−2.92087			−1.30625			−0.653125	−	0.757250i	$-0.726543\pi$
$5$	−2.92087			−1.30625			−0.653125	+	0.757250i	$0.726543\pi$
$6$		0			0
$7$	−2.35742	−	1.20106i	−0.891022	−	0.453959i
$7$	−2.35742	−	1.20106i	−0.891022	−	0.453959i
$8$		0			0
$9$	−2.85742	+	0.913855i	−0.952475	+	0.304618i
$10$		0			0
$11$	1.35371			0.408160			0.204080	−	0.978954i	$-0.434580\pi$
$11$	1.35371			0.408160			0.204080	+	0.978954i	$0.434580\pi$
$12$		0			0
$13$	−0.733001	+	1.26960i	−0.203298	+	0.352123i	−0.949589	−	0.313497i	$-0.898499\pi$
$13$	−0.733001	+	1.26960i	−0.203298	+	0.352123i	0.746291	+	0.665620i	$0.231833\pi$
$14$		0			0
$15$	0.779867	+	4.99862i	0.201361	+	1.29064i
$16$		0			0
$17$	1.65514	−	2.86678i	0.401430	−	0.695297i	−0.592469	−	0.805593i	$-0.701847\pi$
$17$	1.65514	−	2.86678i	0.401430	−	0.695297i	0.993899	+	0.110297i	$0.0351801\pi$
$18$		0			0
$19$	1.10329	+	1.91096i	0.253113	+	0.438404i	0.964381	−	0.264516i	$-0.0852123\pi$
$19$	1.10329	+	1.91096i	0.253113	+	0.438404i	−0.711268	+	0.702921i	$0.751879\pi$
$20$		0			0
$21$	−1.42601	+	4.35505i	−0.311181	+	0.950351i
$22$		0			0
$23$	−2.62830			−0.548038			−0.274019	−	0.961724i	$-0.588353\pi$
$23$	−2.62830			−0.548038			−0.274019	+	0.961724i	$0.588353\pi$
$24$		0			0
$25$	3.53146			0.706292
$26$		0			0
$27$	2.32685	+	4.64605i	0.447803	+	0.894132i
$28$		0			0
$29$	0.521720	+	0.903646i	0.0968810	+	0.167803i	0.910392	−	0.413747i	$-0.135780\pi$
$29$	0.521720	+	0.903646i	0.0968810	+	0.167803i	−0.813511	+	0.581549i	$0.802447\pi$
$30$		0			0
$31$	1.63729	+	2.83587i	0.294066	+	0.509337i	0.974767	−	0.223224i	$-0.0716581\pi$
$31$	1.63729	+	2.83587i	0.294066	+	0.509337i	−0.680701	+	0.732561i	$0.738325\pi$
$32$		0			0
$33$	−0.361440	−	2.31668i	−0.0629186	−	0.403282i
$34$		0			0
$35$	6.88572	+	3.50815i	1.16390	+	0.592985i
$36$		0			0
$37$	5.43773	+	9.41842i	0.893957	+	1.54838i	0.835090	+	0.550113i	$0.185415\pi$
$37$	5.43773	+	9.41842i	0.893957	+	1.54838i	0.0588664	+	0.998266i	$0.481251\pi$
$38$		0			0
$39$	2.36843	+	0.915440i	0.379252	+	0.146588i
$40$		0			0
$41$	−0.904289	+	1.56627i	−0.141226	+	0.244611i	−0.927959	−	0.372683i	$-0.878438\pi$
$41$	−0.904289	+	1.56627i	−0.141226	+	0.244611i	0.786732	+	0.617294i	$0.211771\pi$
$42$		0			0
$43$	2.17129	+	3.76078i	0.331118	+	0.573514i	0.982731	−	0.185038i	$-0.0592408\pi$
$43$	2.17129	+	3.76078i	0.331118	+	0.573514i	−0.651613	+	0.758551i	$0.725907\pi$
$44$		0			0
$45$	8.34615	−	2.66925i	1.24417	−	0.397908i
$46$		0			0
$47$	1.98957	−	3.44604i	0.290209	−	0.502656i	−0.683650	−	0.729810i	$-0.739609\pi$
$47$	1.98957	−	3.44604i	0.290209	−	0.502656i	0.973859	+	0.227154i	$0.0729419\pi$
$48$		0			0
$49$	4.11489	+	5.66283i	0.587842	+	0.808976i
$50$		0			0
$51$	−5.34798	−	2.06709i	−0.748867	−	0.289450i
$52$		0			0
$53$	−3.22743	+	5.59008i	−0.443322	+	0.767856i	−0.997934	−	0.0642533i	$-0.979533\pi$
$53$	−3.22743	+	5.59008i	−0.443322	+	0.767856i	0.554612	+	0.832109i	$0.312867\pi$
$54$		0			0
$55$	−3.95402			−0.533160
$56$		0			0
$57$	2.97574	−	2.39834i	0.394146	−	0.317668i
$58$		0			0
$59$	−6.10700	−	10.5776i	−0.795064	−	1.37709i	−0.922799	−	0.385283i	$-0.874104\pi$
$59$	−6.10700	−	10.5776i	−0.795064	−	1.37709i	0.127735	−	0.991808i	$-0.459229\pi$
$60$		0			0
$61$	−0.279867	+	0.484744i	−0.0358333	+	0.0620651i	−0.883386	−	0.468646i	$-0.844742\pi$
$61$	−0.279867	+	0.484744i	−0.0358333	+	0.0620651i	0.847553	+	0.530711i	$0.178075\pi$
$62$		0			0
$63$	7.83376	+	1.27761i	0.986960	+	0.160963i
$64$		0			0
$65$	2.14100	−	3.70832i	0.265558	−	0.459960i
$66$		0			0
$67$	6.40588	+	11.0953i	0.782603	+	1.35551i	0.930420	+	0.366494i	$0.119442\pi$
$67$	6.40588	+	11.0953i	0.782603	+	1.35551i	−0.147817	+	0.989015i	$0.547225\pi$
$68$		0			0
$69$	0.701751	+	4.49793i	0.0844809	+	0.541487i
$70$		0			0
$71$	−12.9177			−1.53305			−0.766525	−	0.642214i	$-0.778016\pi$
$71$	−12.9177			−1.53305			−0.766525	+	0.642214i	$0.778016\pi$
$72$		0			0
$73$	5.22772	−	9.05467i	0.611858	−	1.05977i	−0.379069	−	0.925368i	$-0.623756\pi$
$73$	5.22772	−	9.05467i	0.611858	−	1.05977i	0.990927	−	0.134401i	$-0.0429109\pi$
$74$		0			0
$75$	−0.942894	−	6.04355i	−0.108876	−	0.697849i
$76$		0			0
$77$	−3.19128	−	1.62590i	−0.363680	−	0.185288i
$78$		0			0
$79$	0.383838	−	0.664827i	0.0431852	−	0.0747989i	−0.843625	−	0.536933i	$-0.819583\pi$
$79$	0.383838	−	0.664827i	0.0431852	−	0.0747989i	0.886810	+	0.462134i	$0.152916\pi$
$80$		0			0
$81$	7.32974	−	5.22254i	0.814415	−	0.580282i
$82$		0			0
$83$	0.983707	+	1.70383i	0.107976	+	0.187020i	0.914950	−	0.403567i	$-0.132230\pi$
$83$	0.983707	+	1.70383i	0.107976	+	0.187020i	−0.806974	+	0.590587i	$0.798896\pi$
$84$		0			0
$85$	−4.83443	+	8.37348i	−0.524368	+	0.908232i
$86$		0			0
$87$	1.40715	−	1.13412i	0.150863	−	0.121590i
$88$		0			0
$89$	3.20356	+	5.54872i	0.339576	+	0.588163i	0.984353	−	0.176208i	$-0.0563830\pi$
$89$	3.20356	+	5.54872i	0.339576	+	0.588163i	−0.644777	+	0.764371i	$0.723050\pi$
$90$		0			0
$91$	3.25286	−	2.11259i	0.340992	−	0.221460i
$92$		0			0
$93$	4.41601	−	3.55915i	0.457919	−	0.369066i
$94$		0			0
$95$	−3.22257	−	5.58166i	−0.330629	−	0.572666i
$96$		0			0
$97$	−4.14143	−	7.17316i	−0.420498	−	0.728324i	0.575490	−	0.817809i	$-0.304811\pi$
$97$	−4.14143	−	7.17316i	−0.420498	−	0.728324i	−0.995988	+	0.0894847i	$0.971478\pi$
$98$		0			0
$99$	−3.86814	+	1.23710i	−0.388762	+	0.124333i
$100$		0			0
$101$	−16.2266			−1.61461			−0.807305	−	0.590134i	$-0.799075\pi$
$101$	−16.2266			−1.61461			−0.807305	+	0.590134i	$0.799075\pi$
$102$		0			0
$103$	2.22683			0.219416			0.109708	−	0.993964i	$-0.465008\pi$
$103$	2.22683			0.219416			0.109708	+	0.993964i	$0.465008\pi$
$104$		0			0
$105$	4.16518	−	12.7205i	0.406480	−	1.24140i
$106$		0			0
$107$	8.75403	+	15.1624i	0.846284	+	1.46581i	0.884501	+	0.466537i	$0.154499\pi$
$107$	8.75403	+	15.1624i	0.846284	+	1.46581i	−0.0382175	+	0.999269i	$0.512168\pi$
$108$		0			0
$109$	−7.79917	+	13.5086i	−0.747025	+	1.29388i	0.202218	+	0.979341i	$0.435185\pi$
$109$	−7.79917	+	13.5086i	−0.747025	+	1.29388i	−0.949243	+	0.314544i	$0.898148\pi$
$110$		0			0
$111$	14.6663	−	11.8205i	1.39207	−	1.12196i
$112$		0			0
$113$	−0.844555	+	1.46281i	−0.0794491	+	0.137610i	−0.903012	−	0.429615i	$-0.858649\pi$
$113$	−0.844555	+	1.46281i	−0.0794491	+	0.137610i	0.823563	+	0.567224i	$0.191983\pi$
$114$		0			0
$115$	7.67690			0.715875
$116$		0			0
$117$	0.934270	−	4.29763i	0.0863733	−	0.397316i
$118$		0			0
$119$	−7.34505	+	4.77029i	−0.673319	+	0.437292i
$120$		0			0
$121$	−9.16746			−0.833405
$122$		0			0
$123$	2.92188	+	1.12936i	0.263457	+	0.101831i
$124$		0			0
$125$	4.28942			0.383657
$126$		0			0
$127$	3.96918			0.352208			0.176104	−	0.984372i	$-0.443650\pi$
$127$	3.96918			0.352208			0.176104	+	0.984372i	$0.443650\pi$
$128$		0			0
$129$	5.85627	−	4.71995i	0.515616	−	0.415569i
$130$		0			0
$131$	−5.32863			−0.465565			−0.232782	−	0.972529i	$-0.574783\pi$
$131$	−5.32863			−0.465565			−0.232782	+	0.972529i	$0.574783\pi$
$132$		0			0
$133$	−0.305745	−	5.83007i	−0.0265115	−	0.505531i
$134$		0			0
$135$	−6.79642	−	13.5705i	−0.584943	−	1.16796i
$136$		0			0
$137$	−7.49543			−0.640378			−0.320189	−	0.947354i	$-0.603746\pi$
$137$	−7.49543			−0.640378			−0.320189	+	0.947354i	$0.603746\pi$
$138$		0			0
$139$	−7.03285	+	12.1812i	−0.596518	+	1.03320i	0.396812	+	0.917900i	$0.370116\pi$
$139$	−7.03285	+	12.1812i	−0.596518	+	1.03320i	−0.993331	+	0.115300i	$0.963217\pi$
$140$		0			0
$141$	−6.42858	−	2.48476i	−0.541384	−	0.209255i
$142$		0			0
$143$	−0.992275	+	1.71867i	−0.0829782	+	0.143722i
$144$		0			0
$145$	−1.52388	−	2.63943i	−0.126551	−	0.219193i
$146$		0			0
$147$	8.59241	−	8.55398i	0.708690	−	0.705520i
$148$		0			0
$149$	2.17971			0.178569			0.0892846	−	0.996006i	$-0.471542\pi$
$149$	2.17971			0.178569			0.0892846	+	0.996006i	$0.471542\pi$
$150$		0			0
$151$	−14.0277			−1.14156			−0.570781	−	0.821102i	$-0.693359\pi$
$151$	−14.0277			−1.14156			−0.570781	+	0.821102i	$0.693359\pi$
$152$		0			0
$153$	−2.10961	+	9.70416i	−0.170552	+	0.784535i
$154$		0			0
$155$	−4.78231	−	8.28320i	−0.384124	−	0.665322i
$156$		0			0
$157$	−1.48312	−	2.56883i	−0.118365	−	0.205015i	0.800755	−	0.598993i	$-0.204432\pi$
$157$	−1.48312	−	2.56883i	−0.118365	−	0.205015i	−0.919120	+	0.393978i	$0.871099\pi$
$158$		0			0
$159$	10.4283	+	4.03072i	0.827017	+	0.319657i
$160$		0			0
$161$	6.19601	+	3.15675i	0.488314	+	0.248787i
$162$		0			0
$163$	0.194278	+	0.336499i	0.0152170	+	0.0263566i	0.873534	−	0.486764i	$-0.161823\pi$
$163$	0.194278	+	0.336499i	0.0152170	+	0.0263566i	−0.858317	+	0.513120i	$0.828489\pi$
$164$		0			0
$165$	1.05572	+	6.76670i	0.0821875	+	0.526787i
$166$		0			0
$167$	−3.64889	+	6.32006i	−0.282360	+	0.489061i	−0.971965	−	0.235124i	$-0.924450\pi$
$167$	−3.64889	+	6.32006i	−0.282360	+	0.489061i	0.689606	+	0.724185i	$0.257784\pi$
$168$		0			0
$169$	5.42542	+	9.39710i	0.417340	+	0.722854i
$170$		0			0
$171$	−4.89892	−	4.45217i	−0.374630	−	0.340466i
$172$		0			0
$173$	2.02754	−	3.51181i	0.154151	−	0.266998i	−0.778598	−	0.627522i	$-0.784069\pi$
$173$	2.02754	−	3.51181i	0.154151	−	0.266998i	0.932750	+	0.360525i	$0.117402\pi$
$174$		0			0
$175$	−8.32514	−	4.24151i	−0.629322	−	0.320628i
$176$		0			0
$177$	−16.4715	+	13.2754i	−1.23807	+	0.997842i
$178$		0			0
$179$	−5.29243	+	9.16675i	−0.395575	+	0.685155i	−0.993174	−	0.116639i	$-0.962788\pi$
$179$	−5.29243	+	9.16675i	−0.395575	+	0.685155i	0.597600	+	0.801795i	$0.296121\pi$
$180$		0			0
$181$	−19.6312			−1.45917			−0.729586	−	0.683889i	$-0.760287\pi$
$181$	−19.6312			−1.45917			−0.729586	+	0.683889i	$0.760287\pi$
$182$		0			0
$183$	0.904289	+	0.349524i	0.0668470	+	0.0258375i
$184$		0			0
$185$	−15.8829	−	27.5099i	−1.16773	−	2.02257i
$186$		0			0
$187$	2.24058	−	3.88081i	0.163848	−	0.283793i
$188$		0			0
$189$	0.0948259	−	13.7474i	0.00689757	−	0.999976i
$190$		0			0
$191$	4.14357	−	7.17688i	0.299818	−	0.519301i	−0.676276	−	0.736648i	$-0.736407\pi$
$191$	4.14357	−	7.17688i	0.299818	−	0.519301i	0.976094	+	0.217348i	$0.0697406\pi$
$192$		0			0
$193$	9.39242	+	16.2682i	0.676082	+	1.17101i	0.976152	+	0.217090i	$0.0696566\pi$
$193$	9.39242	+	16.2682i	0.676082	+	1.17101i	−0.300070	+	0.953917i	$0.597010\pi$
$194$		0			0
$195$	−6.91787	−	2.67388i	−0.495399	−	0.191480i
$196$		0			0
$197$	5.99634			0.427222			0.213611	−	0.976919i	$-0.431478\pi$
$197$	5.99634			0.427222			0.213611	+	0.976919i	$0.431478\pi$
$198$		0			0
$199$	−7.20434	+	12.4783i	−0.510702	+	0.884562i	0.489221	+	0.872160i	$0.337281\pi$
$199$	−7.20434	+	12.4783i	−0.510702	+	0.884562i	−0.999923	+	0.0124022i	$0.996052\pi$
$200$		0			0
$201$	17.2776	−	13.9251i	1.21867	−	0.982203i
$202$		0			0
$203$	−0.144579	−	2.75690i	−0.0101475	−	0.193496i
$204$		0			0
$205$	2.64131	−	4.57488i	0.184477	−	0.319523i
$206$		0			0
$207$	7.51015	−	2.40188i	0.521992	−	0.166942i
$208$		0			0
$209$	1.49354	+	2.58690i	0.103311	+	0.178939i
$210$		0			0
$211$	6.92418	−	11.9930i	0.476680	−	0.825634i	−0.522963	−	0.852356i	$-0.675173\pi$
$211$	6.92418	−	11.9930i	0.476680	−	0.825634i	0.999643	+	0.0267212i	$0.00850663\pi$
$212$		0			0
$213$	3.44901	+	22.1067i	0.236322	+	1.51473i
$214$		0			0
$215$	−6.34204	−	10.9847i	−0.432523	−	0.749153i
$216$		0			0
$217$	−0.453726	−	8.65184i	−0.0308010	−	0.587325i
$218$		0			0
$219$	−16.8915	−	6.52886i	−1.14142	−	0.441179i
$220$		0			0
$221$	2.42644	+	4.20271i	0.163220	+	0.282705i
$222$		0			0
$223$	−2.33756	−	4.04878i	−0.156535	−	0.271126i	0.777082	−	0.629399i	$-0.216699\pi$
$223$	−2.33756	−	4.04878i	−0.156535	−	0.271126i	−0.933617	+	0.358273i	$0.883366\pi$
$224$		0			0
$225$	−10.0909	+	3.22724i	−0.672725	+	0.215149i
$226$		0			0
$227$	−19.7126			−1.30837			−0.654187	−	0.756333i	$-0.726989\pi$
$227$	−19.7126			−1.30837			−0.654187	+	0.756333i	$0.726989\pi$
$228$		0			0
$229$	28.0728			1.85510			0.927552	−	0.373694i	$-0.121909\pi$
$229$	28.0728			1.85510			0.927552	+	0.373694i	$0.121909\pi$
$230$		0			0
$231$	−1.93041	+	5.89550i	−0.127012	+	0.387896i
$232$		0			0
$233$	−6.90113	−	11.9531i	−0.452108	−	0.783074i	0.546409	−	0.837518i	$-0.315994\pi$
$233$	−6.90113	−	11.9531i	−0.452108	−	0.783074i	−0.998517	+	0.0544448i	$0.982661\pi$
$234$		0			0
$235$	−5.81127	+	10.0654i	−0.379085	+	0.656595i
$236$		0			0
$237$	−1.24024	−	0.479373i	−0.0805619	−	0.0311386i
$238$		0			0
$239$	−5.53069	+	9.57944i	−0.357751	+	0.619642i	−0.987585	−	0.157087i	$-0.949790\pi$
$239$	−5.53069	+	9.57944i	−0.357751	+	0.619642i	0.629834	+	0.776730i	$0.283123\pi$
$240$		0			0
$241$	−23.1697			−1.49249			−0.746247	−	0.665669i	$-0.768146\pi$
$241$	−23.1697			−1.49249			−0.746247	+	0.665669i	$0.768146\pi$
$242$		0			0
$243$	−10.8946	−	11.1493i	−0.698890	−	0.715229i
$244$		0			0
$245$	−12.0190	−	16.5404i	−0.767869	−	1.05673i
$246$		0			0
$247$	−3.23486			−0.205829
$248$		0			0
$249$	2.65320	−	2.13839i	0.168140	−	0.135515i
$250$		0			0
$251$	7.78402			0.491323			0.245662	−	0.969356i	$-0.420995\pi$
$251$	7.78402			0.491323			0.245662	+	0.969356i	$0.420995\pi$
$252$		0			0
$253$	−3.55796			−0.223687
$254$		0			0
$255$	15.6207	+	6.03769i	0.978208	+	0.378095i
$256$		0			0
$257$	10.3760			0.647235			0.323618	−	0.946188i	$-0.395101\pi$
$257$	10.3760			0.647235			0.323618	+	0.946188i	$0.395101\pi$
$258$		0			0
$259$	−1.50690	−	28.7343i	−0.0936345	−	1.78546i
$260$		0			0
$261$	−2.31658	−	2.10532i	−0.143393	−	0.130316i
$262$		0			0
$263$	19.1331			1.17980			0.589898	−	0.807478i	$-0.299168\pi$
$263$	19.1331			1.17980			0.589898	+	0.807478i	$0.299168\pi$
$264$		0			0
$265$	9.42689	−	16.3279i	0.579090	−	1.00301i
$266$		0			0
$267$	8.64045	−	6.96390i	0.528787	−	0.426184i
$268$		0			0
$269$	−4.41840	+	7.65290i	−0.269395	+	0.466605i	−0.968706	−	0.248212i	$-0.920157\pi$
$269$	−4.41840	+	7.65290i	−0.269395	+	0.466605i	0.699311	+	0.714818i	$0.253490\pi$
$270$		0			0
$271$	9.16955	+	15.8821i	0.557010	+	0.964770i	0.997744	+	0.0671321i	$0.0213849\pi$
$271$	9.16955	+	15.8821i	0.557010	+	0.964770i	−0.440734	+	0.897638i	$0.645282\pi$
$272$		0			0
$273$	−4.48389	−	5.00272i	−0.271377	−	0.302778i
$274$		0			0
$275$	4.78059			0.288280
$276$		0			0
$277$	5.10482			0.306719			0.153360	−	0.988170i	$-0.450991\pi$
$277$	5.10482			0.306719			0.153360	+	0.988170i	$0.450991\pi$
$278$		0			0
$279$	−7.27001	−	6.60704i	−0.435244	−	0.395553i
$280$		0			0
$281$	−0.853180	−	1.47775i	−0.0508964	−	0.0881552i	0.839455	−	0.543430i	$-0.182875\pi$
$281$	−0.853180	−	1.47775i	−0.0508964	−	0.0881552i	−0.890351	+	0.455274i	$0.849541\pi$
$282$		0			0
$283$	−6.24415	−	10.8152i	−0.371176	−	0.642896i	0.618571	−	0.785729i	$-0.287712\pi$
$283$	−6.24415	−	10.8152i	−0.371176	−	0.642896i	−0.989747	+	0.142833i	$0.954379\pi$
$284$		0			0
$285$	−8.69174	+	7.00524i	−0.514854	+	0.414954i
$286$		0			0
$287$	4.01299	−	2.60626i	0.236879	−	0.153843i
$288$		0			0
$289$	3.02104	+	5.23260i	0.177708	+	0.307800i
$290$		0			0
$291$	−11.1700	+	9.00264i	−0.654798	+	0.527744i
$292$		0			0
$293$	−2.60202	+	4.50684i	−0.152012	+	0.263292i	−0.931967	−	0.362543i	$-0.881909\pi$
$293$	−2.60202	+	4.50684i	−0.152012	+	0.263292i	0.779955	+	0.625835i	$0.215242\pi$
$294$		0			0
$295$	17.8377	+	30.8959i	1.03855	+	1.79883i
$296$		0			0
$297$	3.14989	+	6.28942i	0.182775	+	0.364949i
$298$		0			0
$299$	1.92654	−	3.33687i	0.111415	−	0.192976i
$300$		0			0
$301$	−0.601708	−	11.4736i	−0.0346819	−	0.661328i
$302$		0			0
$303$	4.33249	+	27.7694i	0.248895	+	1.59531i
$304$		0			0
$305$	0.817453	−	1.41587i	0.0468072	−	0.0810725i
$306$		0			0
$307$	−5.00136			−0.285442			−0.142721	−	0.989763i	$-0.545585\pi$
$307$	−5.00136			−0.285442			−0.142721	+	0.989763i	$0.545585\pi$
$308$		0			0
$309$	−0.594560	−	3.81088i	−0.0338234	−	0.216793i
$310$		0			0
$311$	−16.1984	−	28.0565i	−0.918528	−	1.59094i	−0.801652	−	0.597791i	$-0.796045\pi$
$311$	−16.1984	−	28.0565i	−0.918528	−	1.59094i	−0.116876	−	0.993146i	$-0.537288\pi$
$312$		0			0
$313$	−0.759535	+	1.31555i	−0.0429315	+	0.0743595i	−0.886693	−	0.462359i	$-0.847003\pi$
$313$	−0.759535	+	1.31555i	−0.0429315	+	0.0743595i	0.843761	+	0.536719i	$0.180336\pi$
$314$		0			0
$315$	−22.8813	−	3.73171i	−1.28922	−	0.210258i
$316$		0			0
$317$	10.7544	−	18.6272i	0.604029	−	1.04621i	−0.388175	−	0.921586i	$-0.626894\pi$
$317$	10.7544	−	18.6272i	0.604029	−	1.04621i	0.992204	−	0.124623i	$-0.0397723\pi$
$318$		0			0
$319$	0.706261	+	1.22328i	0.0395430	+	0.0684905i
$320$		0			0
$321$	23.6109	−	19.0295i	1.31783	−	1.06213i
$322$		0			0
$323$	7.30441			0.406428
$324$		0			0
$325$	−2.58856	+	4.48352i	−0.143588	+	0.248701i
$326$		0			0
$327$	25.2002	+	9.74032i	1.39357	+	0.538641i
$328$		0			0
$329$	−8.82917	+	5.73417i	−0.486768	+	0.316135i
$330$		0			0
$331$	9.73902	−	16.8685i	0.535305	−	0.927175i	−0.463844	−	0.885917i	$-0.653530\pi$
$331$	9.73902	−	16.8685i	0.535305	−	0.927175i	0.999149	−	0.0412580i	$-0.0131366\pi$
$332$		0			0
$333$	−24.1450	−	21.9431i	−1.32314	−	1.20248i
$334$		0			0
$335$	−18.7107	−	32.4079i	−1.02228	−	1.77063i
$336$		0			0
$337$	4.84742	−	8.39598i	0.264056	−	0.457358i	−0.703260	−	0.710933i	$-0.748273\pi$
$337$	4.84742	−	8.39598i	0.264056	−	0.457358i	0.967316	+	0.253575i	$0.0816063\pi$
$338$		0			0
$339$	2.72888	+	1.05476i	0.148212	+	0.0572867i
$340$		0			0
$341$	2.21642	+	3.83896i	0.120026	+	0.207891i
$342$		0			0
$343$	−2.89912	−	18.2919i	−0.156538	−	0.987672i
$344$		0			0
$345$	−2.04972	−	13.1378i	−0.110353	−	0.707318i
$346$		0			0
$347$	1.01302	+	1.75460i	0.0543817	+	0.0941919i	0.891935	−	0.452164i	$-0.149348\pi$
$347$	1.01302	+	1.75460i	0.0543817	+	0.0941919i	−0.837553	+	0.546356i	$0.816015\pi$
$348$		0			0
$349$	8.14577	+	14.1089i	0.436033	+	0.755231i	0.997379	−	0.0723497i	$-0.0230498\pi$
$349$	8.14577	+	14.1089i	0.436033	+	0.755231i	−0.561346	+	0.827581i	$0.689716\pi$
$350$		0			0
$351$	−7.60419	−	0.451400i	−0.405882	−	0.0240939i
$352$		0			0
$353$	17.0614			0.908089			0.454045	−	0.890979i	$-0.349981\pi$
$353$	17.0614			0.908089			0.454045	+	0.890979i	$0.349981\pi$
$354$		0			0
$355$	37.7309			2.00255
$356$		0			0
$357$	10.1247	+	11.2963i	0.535859	+	0.597862i
$358$		0			0
$359$	−1.48363	−	2.56972i	−0.0783030	−	0.135625i	0.824215	−	0.566277i	$-0.191617\pi$
$359$	−1.48363	−	2.56972i	−0.0783030	−	0.135625i	−0.902518	+	0.430652i	$0.858283\pi$
$360$		0			0
$361$	7.06549	−	12.2378i	0.371868	−	0.644094i
$362$		0			0
$363$	2.44770	+	15.6887i	0.128471	+	0.823444i
$364$		0			0
$365$	−15.2695	+	26.4475i	−0.799240	+	1.38432i
$366$		0			0
$367$	10.1575			0.530216			0.265108	−	0.964219i	$-0.414592\pi$
$367$	10.1575			0.530216			0.265108	+	0.964219i	$0.414592\pi$
$368$		0			0
$369$	1.15259	−	5.30190i	0.0600014	−	0.276006i
$370$		0			0
$371$	14.3225	−	9.30182i	0.743585	−	0.482927i
$372$		0			0
$373$	−25.4846			−1.31954			−0.659771	−	0.751467i	$-0.729347\pi$
$373$	−25.4846			−1.31954			−0.659771	+	0.751467i	$0.729347\pi$
$374$		0			0
$375$	−1.14527	−	7.34068i	−0.0591414	−	0.379071i
$376$		0			0
$377$	−1.52969			−0.0787829
$378$		0			0
$379$	−9.85497			−0.506216			−0.253108	−	0.967438i	$-0.581453\pi$
$379$	−9.85497			−0.506216			−0.253108	+	0.967438i	$0.581453\pi$
$380$		0			0
$381$	−1.05977	−	6.79266i	−0.0542935	−	0.347998i
$382$		0			0
$383$	27.3127			1.39561			0.697806	−	0.716286i	$-0.254160\pi$
$383$	27.3127			1.39561			0.697806	+	0.716286i	$0.254160\pi$
$384$		0			0
$385$	9.32130	+	4.74903i	0.475057	+	0.242033i
$386$		0			0
$387$	−9.64109	−	8.76190i	−0.490084	−	0.445392i
$388$		0			0
$389$	4.18446			0.212161			0.106080	−	0.994358i	$-0.466170\pi$
$389$	4.18446			0.212161			0.106080	+	0.994358i	$0.466170\pi$
$390$		0			0
$391$	−4.35019	+	7.53475i	−0.219999	+	0.381049i
$392$		0			0
$393$	1.42274	+	9.11914i	0.0717676	+	0.460000i
$394$		0			0
$395$	−1.12114	+	1.94187i	−0.0564107	+	0.0977062i
$396$		0			0
$397$	15.3354	+	26.5618i	0.769664	+	1.33310i	0.937745	+	0.347323i	$0.112909\pi$
$397$	15.3354	+	26.5618i	0.769664	+	1.33310i	−0.168082	+	0.985773i	$0.553757\pi$
$398$		0			0
$399$	−9.89564	+	2.07986i	−0.495402	+	0.104123i
$400$		0			0
$401$	−6.84803			−0.341974			−0.170987	−	0.985273i	$-0.554696\pi$
$401$	−6.84803			−0.341974			−0.170987	+	0.985273i	$0.554696\pi$
$402$		0			0
$403$	−4.80055			−0.239132
$404$		0			0
$405$	−21.4092	+	15.2543i	−1.06383	+	0.757994i
$406$		0			0
$407$	7.36113	+	12.7499i	0.364878	+	0.631987i
$408$		0			0
$409$	9.13490	+	15.8221i	0.451692	+	0.782353i	0.998491	−	0.0549104i	$-0.0174873\pi$
$409$	9.13490	+	15.8221i	0.451692	+	0.782353i	−0.546799	+	0.837264i	$0.684154\pi$
$410$		0			0
$411$	2.00127	+	12.8273i	0.0987154	+	0.632724i
$412$		0			0
$413$	1.69237	+	32.2709i	0.0832763	+	1.58795i
$414$		0			0
$415$	−2.87328	−	4.97666i	−0.141044	−	0.244295i
$416$		0			0
$417$	22.7241	+	8.78327i	1.11280	+	0.430119i
$418$		0			0
$419$	−11.2310	+	19.4526i	−0.548669	+	0.950322i	0.449698	+	0.893181i	$0.351532\pi$
$419$	−11.2310	+	19.4526i	−0.548669	+	0.950322i	−0.998366	+	0.0571410i	$0.981802\pi$
$420$		0			0
$421$	10.4177	+	18.0440i	0.507728	+	0.879411i	0.999960	+	0.00894684i	$0.00284791\pi$
$421$	10.4177	+	18.0440i	0.507728	+	0.879411i	−0.492232	+	0.870464i	$0.663819\pi$
$422$		0			0
$423$	−2.53587	+	11.6650i	−0.123298	+	0.567170i
$424$		0			0
$425$	5.84505	−	10.1239i	0.283526	−	0.491082i
$426$		0			0
$427$	1.24197	−	0.806608i	0.0601033	−	0.0390345i
$428$		0			0
$429$	3.20618	+	1.23925i	0.154796	+	0.0598313i
$430$		0			0
$431$	10.1213	−	17.5307i	0.487527	−	0.844422i	−0.512370	−	0.858765i	$-0.671232\pi$
$431$	10.1213	−	17.5307i	0.487527	−	0.844422i	0.999897	+	0.0143427i	$0.00456557\pi$
$432$		0			0
$433$	−21.6764			−1.04170			−0.520851	−	0.853648i	$-0.674385\pi$
$433$	−21.6764			−1.04170			−0.520851	+	0.853648i	$0.674385\pi$
$434$		0			0
$435$	−4.11011	+	3.31260i	−0.197065	+	0.158827i
$436$		0			0
$437$	−2.89978	−	5.02257i	−0.138715	−	0.240262i
$438$		0			0
$439$	−17.7390	+	30.7249i	−0.846639	+	1.46642i	0.0375520	+	0.999295i	$0.488044\pi$
$439$	−17.7390	+	30.7249i	−0.846639	+	1.46642i	−0.884191	+	0.467126i	$0.845289\pi$
$440$		0			0
$441$	−16.9330	−	12.4207i	−0.806333	−	0.591462i
$442$		0			0
$443$	−9.60313	+	16.6331i	−0.456258	+	0.790263i	−0.998760	−	0.0497923i	$-0.984144\pi$
$443$	−9.60313	+	16.6331i	−0.456258	+	0.790263i	0.542501	+	0.840055i	$0.317477\pi$
$444$		0			0
$445$	−9.35716	−	16.2071i	−0.443572	−	0.768289i
$446$		0			0
$447$	−0.581980	−	3.73025i	−0.0275267	−	0.176435i
$448$		0			0
$449$	−29.6082			−1.39730			−0.698648	−	0.715465i	$-0.746215\pi$
$449$	−29.6082			−1.39730			−0.698648	+	0.715465i	$0.746215\pi$
$450$		0			0
$451$	−1.22415	+	2.12029i	−0.0576429	+	0.0998405i
$452$		0			0
$453$	3.74539	+	24.0064i	0.175974	+	1.12792i
$454$		0			0
$455$	−9.50117	+	6.17060i	−0.445422	+	0.289282i
$456$		0			0
$457$	4.78098	−	8.28090i	0.223645	−	0.387364i	−0.732267	−	0.681017i	$-0.761538\pi$
$457$	4.78098	−	8.28090i	0.223645	−	0.387364i	0.955912	+	0.293653i	$0.0948711\pi$
$458$		0			0
$459$	17.1705	+	1.01927i	0.801449	+	0.0475756i
$460$		0			0
$461$	10.9187	+	18.9118i	0.508536	+	0.880809i	0.999951	+	0.00988416i	$0.00314628\pi$
$461$	10.9187	+	18.9118i	0.508536	+	0.880809i	−0.491416	+	0.870925i	$0.663520\pi$
$462$		0			0
$463$	−13.0744	+	22.6456i	−0.607621	+	1.05243i	0.384010	+	0.923329i	$0.374543\pi$
$463$	−13.0744	+	22.6456i	−0.607621	+	1.05243i	−0.991631	+	0.129102i	$0.958791\pi$
$464$		0			0
$465$	−12.8986	+	10.3958i	−0.598157	+	0.482093i
$466$		0			0
$467$	17.4764	+	30.2699i	0.808709	+	1.40073i	0.913758	+	0.406258i	$0.133167\pi$
$467$	17.4764	+	30.2699i	0.808709	+	1.40073i	−0.105049	+	0.994467i	$0.533500\pi$
$468$		0			0
$469$	−1.77520	−	33.8502i	−0.0819711	−	1.56306i
$470$		0			0
$471$	−4.00017	+	3.22400i	−0.184318	+	0.148554i
$472$		0			0
$473$	2.93930	+	5.09102i	0.135149	+	0.234086i
$474$		0			0
$475$	3.89623	+	6.74848i	0.178771	+	0.309641i
$476$		0			0
$477$	4.11362	−	18.9226i	0.188350	−	0.866407i
$478$		0			0
$479$	29.8109			1.36209			0.681047	−	0.732240i	$-0.261525\pi$
$479$	29.8109			1.36209			0.681047	+	0.732240i	$0.261525\pi$
$480$		0			0
$481$	−15.9434			−0.726959
$482$		0			0
$483$	3.74797	−	11.4464i	0.170539	−	0.520828i
$484$		0			0
$485$	12.0965	+	20.9518i	0.549276	+	0.951374i
$486$		0			0
$487$	11.2253	−	19.4428i	0.508667	−	0.881037i	−0.491283	−	0.871000i	$-0.663472\pi$
$487$	11.2253	−	19.4428i	0.508667	−	0.881037i	0.999950	−	0.0100365i	$-0.00319477\pi$
$488$		0			0
$489$	0.523994	−	0.422321i	0.0236958	−	0.0190980i
$490$		0			0
$491$	−17.5222	+	30.3494i	−0.790767	+	1.36965i	0.134726	+	0.990883i	$0.456984\pi$
$491$	−17.5222	+	30.3494i	−0.790767	+	1.36965i	−0.925493	+	0.378765i	$0.876349\pi$
$492$		0			0
$493$	3.45407			0.155564
$494$		0			0
$495$	11.2983	−	3.61340i	0.507821	−	0.162410i
$496$		0			0
$497$	30.4525	+	15.5150i	1.36598	+	0.695943i
$498$		0			0
$499$	8.93520			0.399994			0.199997	−	0.979796i	$-0.435907\pi$
$499$	8.93520			0.399994			0.199997	+	0.979796i	$0.435907\pi$
$500$		0			0
$501$	11.7901	+	4.55707i	0.526742	+	0.203595i
$502$		0			0
$503$	12.6403			0.563603			0.281802	−	0.959473i	$-0.409068\pi$
$503$	12.6403			0.563603			0.281802	+	0.959473i	$0.409068\pi$
$504$		0			0
$505$	47.3958			2.10909
$506$		0			0
$507$	14.6331	−	11.7938i	0.649880	−	0.523781i
$508$		0			0
$509$	−28.1110			−1.24600			−0.623000	−	0.782222i	$-0.714086\pi$
$509$	−28.1110			−1.24600			−0.623000	+	0.782222i	$0.714086\pi$
$510$		0			0
$511$	−23.1992	+	15.0669i	−1.02627	+	0.666519i
$512$		0			0
$513$	−6.31121	+	9.57247i	−0.278647	+	0.422635i
$514$		0			0
$515$	−6.50427			−0.286613
$516$		0			0
$517$	2.69331	−	4.66495i	0.118452	−	0.205164i
$518$		0			0
$519$	−6.55127	−	2.53218i	−0.287569	−	0.111150i
$520$		0			0
$521$	4.23768	−	7.33988i	0.185656	−	0.321566i	−0.758141	−	0.652090i	$-0.773892\pi$
$521$	4.23768	−	7.33988i	0.185656	−	0.321566i	0.943797	+	0.330524i	$0.107226\pi$
$522$		0			0
$523$	−16.7236	−	28.9662i	−0.731273	−	1.26660i	−0.956339	−	0.292259i	$-0.905593\pi$
$523$	−16.7236	−	28.9662i	−0.731273	−	1.26660i	0.225066	−	0.974344i	$-0.427740\pi$
$524$		0			0
$525$	−5.03589	+	15.3797i	−0.219784	+	0.671225i
$526$		0			0
$527$	10.8398			0.472187
$528$		0			0
$529$	−16.0921			−0.699655
$530$		0			0
$531$	27.1167	+	24.6439i	1.17677	+	1.06945i
$532$		0			0
$533$	−1.32569	−	2.29616i	−0.0574220	−	0.0994579i
$534$		0			0
$535$	−25.5693	−	44.2874i	−1.10546	−	1.91471i
$536$		0			0
$537$	17.1006	+	6.60968i	0.737944	+	0.285229i
$538$		0			0
$539$	5.57039	+	7.66586i	0.239934	+	0.330192i
$540$		0			0
$541$	−9.12929	−	15.8124i	−0.392499	−	0.679828i	0.600280	−	0.799790i	$-0.295056\pi$
$541$	−9.12929	−	15.8124i	−0.392499	−	0.679828i	−0.992778	+	0.119962i	$0.961723\pi$
$542$		0			0
$543$	5.24149	+	33.5957i	0.224934	+	1.44173i
$544$		0			0
$545$	22.7803	−	39.4567i	0.975802	−	1.69014i
$546$		0			0
$547$	2.88599	+	4.99869i	0.123396	+	0.213728i	0.921105	−	0.389315i	$-0.127288\pi$
$547$	2.88599	+	4.99869i	0.123396	+	0.213728i	−0.797709	+	0.603043i	$0.793955\pi$
$548$		0			0
$549$	0.356713	−	1.64088i	0.0152241	−	0.0700309i
$550$		0			0
$551$	−1.15122	+	1.99397i	−0.0490437	+	0.0849461i
$552$		0			0
$553$	−1.70337	+	1.10627i	−0.0724346	+	0.0470432i
$554$		0			0
$555$	−42.8384	+	34.5262i	−1.81839	+	1.46556i
$556$		0			0
$557$	16.6911	−	28.9098i	0.707223	−	1.22495i	−0.258661	−	0.965968i	$-0.583281\pi$
$557$	16.6911	−	28.9098i	0.707223	−	1.22495i	0.965883	−	0.258977i	$-0.0833855\pi$
$558$		0			0
$559$	−6.36623			−0.269263
$560$		0			0
$561$	−7.23964	−	2.79825i	−0.305658	−	0.118142i
$562$		0			0
$563$	1.09566	+	1.89773i	0.0461764	+	0.0799799i	0.888190	−	0.459477i	$-0.151963\pi$
$563$	1.09566	+	1.89773i	0.0461764	+	0.0799799i	−0.842013	+	0.539457i	$0.818630\pi$
$564$		0			0
$565$	2.46683	−	4.27268i	0.103780	−	0.179753i
$566$		0			0
$567$	−23.5519	+	3.50826i	−0.989087	+	0.147333i
$568$		0			0
$569$	−9.49302	+	16.4424i	−0.397968	+	0.689301i	−0.993475	−	0.114049i	$-0.963618\pi$
$569$	−9.49302	+	16.4424i	−0.397968	+	0.689301i	0.595507	+	0.803350i	$0.296951\pi$
$570$		0			0
$571$	−10.8690	−	18.8257i	−0.454854	−	0.787831i	0.543825	−	0.839198i	$-0.316975\pi$
$571$	−10.8690	−	18.8257i	−0.454854	−	0.787831i	−0.998680	+	0.0513674i	$0.983642\pi$
$572$		0			0
$573$	−13.3885	−	5.17488i	−0.559311	−	0.216184i
$574$		0			0
$575$	−9.28172			−0.387074
$576$		0			0
$577$	−15.4516	+	26.7629i	−0.643258	+	1.11416i	0.341443	+	0.939903i	$0.389084\pi$
$577$	−15.4516	+	26.7629i	−0.643258	+	1.11416i	−0.984701	+	0.174253i	$0.944249\pi$
$578$		0			0
$579$	25.3327	−	20.4173i	1.05279	−	0.848513i
$580$		0			0
$581$	−0.272605	−	5.19815i	−0.0113096	−	0.215655i
$582$		0			0
$583$	−4.36902	+	7.56737i	−0.180946	+	0.313408i
$584$		0			0
$585$	−2.72888	+	12.5528i	−0.112825	+	0.518994i
$586$		0			0
$587$	9.18332	+	15.9060i	0.379036	+	0.656510i	0.990922	−	0.134436i	$-0.0429222\pi$
$587$	9.18332	+	15.9060i	0.379036	+	0.656510i	−0.611886	+	0.790946i	$0.709589\pi$
$588$		0			0
$589$	−3.61282	+	6.25759i	−0.148864	+	0.257840i
$590$		0			0
$591$	−1.60101	−	10.2618i	−0.0658569	−	0.422115i
$592$		0			0
$593$	13.8775	+	24.0365i	0.569880	+	0.987061i	0.996577	+	0.0826662i	$0.0263435\pi$
$593$	13.8775	+	24.0365i	0.569880	+	0.987061i	−0.426698	+	0.904394i	$0.640323\pi$
$594$		0			0
$595$	21.4539	−	13.9334i	0.879524	−	0.571213i
$596$		0			0
$597$	23.2782	+	8.99745i	0.952715	+	0.368241i
$598$		0			0
$599$	0.201412	+	0.348855i	0.00822945	+	0.0142538i	0.870111	−	0.492856i	$-0.164047\pi$
$599$	0.201412	+	0.348855i	0.00822945	+	0.0142538i	−0.861881	+	0.507110i	$0.830714\pi$
$600$		0			0
$601$	12.3733	+	21.4312i	0.504717	+	0.874196i	0.999985	+	0.00545577i	$0.00173663\pi$
$601$	12.3733	+	21.4312i	0.504717	+	0.874196i	−0.495268	+	0.868740i	$0.664930\pi$
$602$		0			0
$603$	−28.4438	−	25.8500i	−1.15832	−	1.05269i
$604$		0			0
$605$	26.7769			1.08864
$606$		0			0
$607$	−24.0697			−0.976957			−0.488479	−	0.872576i	$-0.662448\pi$
$607$	−24.0697			−0.976957			−0.488479	+	0.872576i	$0.662448\pi$
$608$		0			0
$609$	−4.67941	+	0.983513i	−0.189619	+	0.0398539i
$610$		0			0
$611$	2.91672	+	5.05190i	0.117998	+	0.204378i
$612$		0			0
$613$	10.1907	−	17.6509i	0.411600	−	0.712912i	−0.583465	−	0.812138i	$-0.698303\pi$
$613$	10.1907	−	17.6509i	0.411600	−	0.712912i	0.995065	+	0.0992261i	$0.0316367\pi$
$614$		0			0
$615$	−8.53443	−	3.29871i	−0.344142	−	0.133017i
$616$		0			0
$617$	−20.9315	+	36.2544i	−0.842669	+	1.45955i	0.0449604	+	0.998989i	$0.485684\pi$
$617$	−20.9315	+	36.2544i	−0.842669	+	1.45955i	−0.887630	+	0.460558i	$0.847650\pi$
$618$		0			0
$619$	−14.8219			−0.595743			−0.297871	−	0.954606i	$-0.596277\pi$
$619$	−14.8219			−0.595743			−0.297871	+	0.954606i	$0.596277\pi$
$620$		0			0
$621$	−6.11565	−	12.2112i	−0.245413	−	0.490018i
$622$		0			0
$623$	−0.887770	−	16.9284i	−0.0355678	−	0.678221i
$624$		0			0
$625$	−30.1861			−1.20744
$626$		0			0
$627$	4.02830	−	3.24667i	0.160875	−	0.129660i
$628$		0			0
$629$	36.0007			1.43544
$630$		0			0
$631$	21.0294			0.837169			0.418585	−	0.908178i	$-0.362526\pi$
$631$	21.0294			0.837169			0.418585	+	0.908178i	$0.362526\pi$
$632$		0			0
$633$	−22.3730	−	8.64756i	−0.889247	−	0.343710i
$634$		0			0
$635$	−11.5935			−0.460072
$636$		0			0
$637$	−10.2057	+	1.07339i	−0.404366	+	0.0425291i
$638$		0			0
$639$	36.9114	−	11.8049i	1.46019	−	0.466995i
$640$		0			0
$641$	11.9318			0.471279			0.235640	−	0.971840i	$-0.424281\pi$
$641$	11.9318			0.471279			0.235640	+	0.971840i	$0.424281\pi$
$642$		0			0
$643$	19.9678	−	34.5852i	0.787452	−	1.36391i	−0.140072	−	0.990141i	$-0.544733\pi$
$643$	19.9678	−	34.5852i	0.787452	−	1.36391i	0.927524	−	0.373765i	$-0.121933\pi$
$644$		0			0
$645$	−17.1054	+	13.7863i	−0.673524	+	0.542837i
$646$		0			0
$647$	−0.494477	+	0.856459i	−0.0194399	+	0.0336709i	−0.875582	−	0.483070i	$-0.839522\pi$
$647$	−0.494477	+	0.856459i	−0.0194399	+	0.0336709i	0.856142	+	0.516741i	$0.172855\pi$
$648$		0			0
$649$	−8.26714	−	14.3191i	−0.324514	−	0.562074i
$650$		0			0
$651$	−14.6852	+	3.08651i	−0.575557	+	0.120970i
$652$		0			0
$653$	22.7147			0.888894			0.444447	−	0.895805i	$-0.353400\pi$
$653$	22.7147			0.888894			0.444447	+	0.895805i	$0.353400\pi$
$654$		0			0
$655$	15.5642			0.608144
$656$		0			0
$657$	−6.66315	+	30.6504i	−0.259954	+	1.19579i
$658$		0			0
$659$	19.1943	+	33.2454i	0.747702	+	1.29506i	0.948922	+	0.315512i	$0.102176\pi$
$659$	19.1943	+	33.2454i	0.747702	+	1.29506i	−0.201220	+	0.979546i	$0.564491\pi$
$660$		0			0
$661$	−16.9629	−	29.3806i	−0.659780	−	1.14277i	−0.980672	−	0.195657i	$-0.937316\pi$
$661$	−16.9629	−	29.3806i	−0.659780	−	1.14277i	0.320892	−	0.947116i	$-0.396017\pi$
$662$		0			0
$663$	6.54444	−	5.27459i	0.254165	−	0.204848i
$664$		0			0
$665$	0.893040	+	17.0288i	0.0346306	+	0.660350i
$666$		0			0
$667$	−1.37124	−	2.37505i	−0.0530944	−	0.0919623i
$668$		0			0
$669$	−6.30475	+	5.08140i	−0.243756	+	0.196458i
$670$		0			0
$671$	−0.378860	+	0.656205i	−0.0146257	+	0.0253325i
$672$		0			0
$673$	−16.1030	−	27.8912i	−0.620725	−	1.07513i	−0.989351	−	0.145549i	$-0.953505\pi$
$673$	−16.1030	−	27.8912i	−0.620725	−	1.07513i	0.368626	−	0.929578i	$-0.379828\pi$
$674$		0			0
$675$	8.21718	+	16.4073i	0.316279	+	0.631518i
$676$		0			0
$677$	18.9842	−	32.8816i	0.729622	−	1.26374i	−0.227421	−	0.973797i	$-0.573029\pi$
$677$	18.9842	−	32.8816i	0.729622	−	1.26374i	0.957043	−	0.289946i	$-0.0936375\pi$
$678$		0			0
$679$	1.14767	+	21.8843i	0.0440436	+	0.839842i
$680$		0			0
$681$	5.26324	+	33.7352i	0.201688	+	1.29273i
$682$		0			0
$683$	−7.59357	+	13.1525i	−0.290560	+	0.503265i	−0.973942	−	0.226796i	$-0.927175\pi$
$683$	−7.59357	+	13.1525i	−0.290560	+	0.503265i	0.683382	+	0.730061i	$0.260508\pi$
$684$		0			0
$685$	21.8932			0.836495
$686$		0			0
$687$	−7.49540	−	48.0424i	−0.285967	−	1.83293i
$688$		0			0
$689$	−4.73142	−	8.19507i	−0.180253	−	0.312207i
$690$		0			0
$691$	1.34574	−	2.33089i	0.0511943	−	0.0886711i	−0.839293	−	0.543680i	$-0.817031\pi$
$691$	1.34574	−	2.33089i	0.0511943	−	0.0886711i	0.890487	+	0.455009i	$0.150364\pi$
$692$		0			0
$693$	10.6047	+	1.72951i	0.402838	+	0.0656988i
$694$		0			0
$695$	20.5420	−	35.5798i	0.779203	−	1.34962i
$696$		0			0
$697$	2.99344	+	5.18480i	0.113385	+	0.196388i
$698$		0			0
$699$	−18.6133	+	15.0017i	−0.704021	+	0.567416i
$700$		0			0
$701$	−11.8515			−0.447625			−0.223813	−	0.974632i	$-0.571850\pi$
$701$	−11.8515			−0.447625			−0.223813	+	0.974632i	$0.571850\pi$
$702$		0			0
$703$	−11.9988	+	20.7826i	−0.452544	+	0.783829i
$704$		0			0
$705$	18.7770	+	7.25765i	0.707184	+	0.273339i
$706$		0			0
$707$	38.2530	+	19.4892i	1.43865	+	0.732967i
$708$		0			0
$709$	20.5167	−	35.5359i	0.770520	−	1.33458i	−0.166759	−	0.985998i	$-0.553330\pi$
$709$	20.5167	−	35.5359i	0.770520	−	1.33458i	0.937278	−	0.348582i	$-0.113337\pi$
$710$		0			0
$711$	−0.489233	+	2.25047i	−0.0183477	+	0.0843991i
$712$		0			0
$713$	−4.30328	−	7.45351i	−0.161159	−	0.279136i
$714$		0			0
$715$	2.89830	−	5.02001i	0.108390	−	0.187738i
$716$		0			0
$717$	17.8704	+	6.90724i	0.667384	+	0.257956i
$718$		0			0
$719$	−10.4555	−	18.1094i	−0.389923	−	0.675366i	0.602516	−	0.798107i	$-0.294165\pi$
$719$	−10.4555	−	18.1094i	−0.389923	−	0.675366i	−0.992439	+	0.122741i	$0.960832\pi$
$720$		0			0
$721$	−5.24958	−	2.67457i	−0.195505	−	0.0996060i
$722$		0			0
$723$	6.18629	+	39.6515i	0.230071	+	1.47466i
$724$		0			0
$725$	1.84243	+	3.19119i	0.0684263	+	0.118518i
$726$		0			0
$727$	−1.32165	−	2.28917i	−0.0490173	−	0.0849005i	0.840476	−	0.541849i	$-0.182276\pi$
$727$	−1.32165	−	2.28917i	−0.0490173	−	0.0849005i	−0.889493	+	0.456949i	$0.848942\pi$
$728$		0			0
$729$	−16.1715	+	21.6213i	−0.598945	+	0.800790i
$730$		0			0
$731$	14.3751			0.531683
$732$		0			0
$733$	14.1489			0.522602			0.261301	−	0.965257i	$-0.415848\pi$
$733$	14.1489			0.522602			0.261301	+	0.965257i	$0.415848\pi$
$734$		0			0
$735$	−25.0973	+	24.9850i	−0.925727	+	0.921587i
$736$		0			0
$737$	8.67174	+	15.0199i	0.319428	+	0.553265i
$738$		0			0
$739$	7.85905	−	13.6123i	0.289100	−	0.500736i	−0.684495	−	0.729017i	$-0.739977\pi$
$739$	7.85905	−	13.6123i	0.289100	−	0.500736i	0.973595	+	0.228282i	$0.0733107\pi$
$740$		0			0
$741$	0.863704	+	5.53598i	0.0317289	+	0.203369i
$742$		0			0
$743$	−10.5496	+	18.2724i	−0.387026	+	0.670348i	−0.992048	−	0.125861i	$-0.959831\pi$
$743$	−10.5496	+	18.2724i	−0.387026	+	0.670348i	0.605022	+	0.796208i	$0.293164\pi$
$744$		0			0
$745$	−6.36665			−0.233256
$746$		0			0
$747$	−4.36792	−	3.96960i	−0.159814	−	0.145240i
$748$		0			0
$749$	−2.42592	−	46.2584i	−0.0886412	−	1.69025i
$750$		0			0
$751$	−13.0370			−0.475725			−0.237863	−	0.971299i	$-0.576447\pi$
$751$	−13.0370			−0.475725			−0.237863	+	0.971299i	$0.576447\pi$
$752$		0			0
$753$	−2.07832	−	13.3212i	−0.0757383	−	0.485451i
$754$		0			0
$755$	40.9732			1.49117
$756$		0			0
$757$	−12.6856			−0.461065			−0.230532	−	0.973065i	$-0.574047\pi$
$757$	−12.6856			−0.461065			−0.230532	+	0.973065i	$0.574047\pi$
$758$		0			0
$759$	0.949971	+	6.08891i	0.0344818	+	0.221014i
$760$		0			0
$761$	−6.04077			−0.218978			−0.109489	−	0.993988i	$-0.534921\pi$
$761$	−6.04077			−0.218978			−0.109489	+	0.993988i	$0.534921\pi$
$762$		0			0
$763$	34.6106	−	22.4781i	1.25299	−	0.813761i
$764$		0			0
$765$	6.16188	−	28.3446i	0.222783	−	1.02480i
$766$		0			0
$767$	17.9058			0.646540
$768$		0			0
$769$	0.108129	−	0.187285i	0.00389924	−	0.00675368i	−0.864069	−	0.503373i	$-0.832092\pi$
$769$	0.108129	−	0.187285i	0.00389924	−	0.00675368i	0.867968	+	0.496619i	$0.165425\pi$
$770$		0			0
$771$	−2.77037	−	17.7569i	−0.0997724	−	0.639499i
$772$		0			0
$773$	18.8132	−	32.5854i	0.676663	−	1.17202i	−0.299316	−	0.954154i	$-0.596759\pi$
$773$	18.8132	−	32.5854i	0.676663	−	1.17202i	0.975980	−	0.217861i	$-0.0699081\pi$
$774$		0			0
$775$	5.78202	+	10.0148i	0.207696	+	0.359741i
$776$		0			0
$777$	−48.7720	+	10.2508i	−1.74968	+	0.367747i
$778$		0			0
$779$	−3.99078			−0.142985
$780$		0			0
$781$	−17.4869			−0.625730
$782$		0			0
$783$	−2.98442	+	4.52659i	−0.106654	+	0.161767i
$784$		0			0
$785$	4.33198	+	7.50321i	0.154615	+	0.267801i
$786$		0			0
$787$	15.4067	+	26.6853i	0.549191	+	0.951226i	0.998330	+	0.0577648i	$0.0183973\pi$
$787$	15.4067	+	26.6853i	0.549191	+	0.951226i	−0.449139	+	0.893462i	$0.648269\pi$
$788$		0			0
$789$	−5.10850	−	32.7433i	−0.181867	−	1.16569i
$790$		0			0
$791$	3.74791	−	2.43410i	0.133260	−	0.0865468i
$792$		0			0
$793$	−0.410286	−	0.710636i	−0.0145697	−	0.0252354i
$794$		0			0
$795$	−30.4596	−	11.7732i	−1.08029	−	0.417552i
$796$		0			0
$797$	−17.9792	+	31.1408i	−0.636855	+	1.10306i	0.349264	+	0.937024i	$0.386431\pi$
$797$	−17.9792	+	31.1408i	−0.636855	+	1.10306i	−0.986119	+	0.166040i	$0.946902\pi$
$798$		0			0
$799$	−6.58602	−	11.4073i	−0.232997	−	0.403562i
$800$		0			0
$801$	−14.2246	−	12.9275i	−0.502603	−	0.456770i
$802$		0			0
$803$	7.07684	−	12.2574i	0.249736	−	0.432556i
$804$		0			0
$805$	−18.0977	−	9.22045i	−0.637860	−	0.324978i
$806$		0			0
$807$	14.2765	+	5.51811i	0.502556	+	0.194247i
$808$		0			0
$809$	−19.4818	+	33.7435i	−0.684943	+	1.18636i	0.288511	+	0.957477i	$0.406840\pi$
$809$	−19.4818	+	33.7435i	−0.684943	+	1.18636i	−0.973455	+	0.228880i	$0.926494\pi$
$810$		0			0
$811$	28.2811			0.993082			0.496541	−	0.868013i	$-0.334603\pi$
$811$	28.2811			0.993082			0.496541	+	0.868013i	$0.334603\pi$
$812$		0			0
$813$	24.7316	−	19.9328i	0.867374	−	0.699073i
$814$		0			0
$815$	−0.567459	−	0.982867i	−0.0198772	−	0.0344283i
$816$		0			0
$817$	−4.79113	+	8.29849i	−0.167621	+	0.290327i
$818$		0			0
$819$	−7.36420	+	9.00922i	−0.257326	+	0.314808i
$820$		0			0
$821$	−20.7917	+	36.0123i	−0.725635	+	1.25684i	0.233077	+	0.972458i	$0.425121\pi$
$821$	−20.7917	+	36.0123i	−0.725635	+	1.25684i	−0.958712	+	0.284378i	$0.908213\pi$
$822$		0			0
$823$	4.22999	+	7.32656i	0.147448	+	0.255388i	0.930284	−	0.366841i	$-0.119561\pi$
$823$	4.22999	+	7.32656i	0.147448	+	0.255388i	−0.782835	+	0.622229i	$0.786227\pi$
$824$		0			0
$825$	−1.27641	−	8.18125i	−0.0444389	−	0.284834i
$826$		0			0
$827$	−44.2823			−1.53985			−0.769923	−	0.638137i	$-0.779706\pi$
$827$	−44.2823			−1.53985			−0.769923	+	0.638137i	$0.779706\pi$
$828$		0			0
$829$	−8.31637	+	14.4044i	−0.288839	+	0.500284i	−0.973533	−	0.228547i	$-0.926603\pi$
$829$	−8.31637	+	14.4044i	−0.288839	+	0.500284i	0.684694	+	0.728831i	$0.259936\pi$
$830$		0			0
$831$	−1.36298	−	8.73613i	−0.0472813	−	0.303053i
$832$		0			0
$833$	23.0448	−	2.42373i	0.798455	−	0.0839774i
$834$		0			0
$835$	10.6579	−	18.4601i	0.368832	−	0.638836i
$836$		0			0
$837$	−9.36586	+	14.2056i	−0.323731	+	0.491017i
$838$		0			0
$839$	−14.8006	−	25.6354i	−0.510974	−	0.885033i	−0.999919	−	0.0127182i	$-0.995952\pi$
$839$	−14.8006	−	25.6354i	−0.510974	−	0.885033i	0.488945	−	0.872314i	$-0.337382\pi$
$840$		0			0
$841$	13.9556	−	24.1718i	0.481228	−	0.833512i
$842$		0			0
$843$	−2.30115	+	1.85464i	−0.0792557	+	0.0638773i
$844$		0			0
$845$	−15.8469	−	27.4477i	−0.545151	−	0.944228i
$846$		0			0
$847$	21.6116	+	11.0107i	0.742583	+	0.378332i
$848$		0			0
$849$	−16.8414	+	13.5736i	−0.577994	+	0.465843i
$850$		0			0
$851$	−14.2920	−	24.7544i	−0.489922	−	0.848570i
$852$		0			0
$853$	−15.0619	−	26.0880i	−0.515710	−	0.893236i	−0.999834	−	0.0182366i	$-0.994195\pi$
$853$	−15.0619	−	26.0880i	−0.515710	−	0.893236i	0.484124	−	0.875000i	$-0.339139\pi$
$854$		0			0
$855$	14.3091	+	13.0042i	0.489360	+	0.444734i
$856$		0			0
$857$	37.0894			1.26695			0.633475	−	0.773763i	$-0.281628\pi$
$857$	37.0894			1.26695			0.633475	+	0.773763i	$0.281628\pi$
$858$		0			0
$859$	3.78333			0.129085			0.0645427	−	0.997915i	$-0.479441\pi$
$859$	3.78333			0.129085			0.0645427	+	0.997915i	$0.479441\pi$
$860$		0			0
$861$	−5.53169	−	6.17175i	−0.188519	−	0.210333i
$862$		0			0
$863$	−0.213559	−	0.369895i	−0.00726963	−	0.0125914i	0.862368	−	0.506282i	$-0.168981\pi$
$863$	−0.213559	−	0.369895i	−0.00726963	−	0.0125914i	−0.869637	+	0.493691i	$0.835647\pi$
$864$		0			0
$865$	−5.92218	+	10.2575i	−0.201360	+	0.348766i
$866$		0			0
$867$	8.14818	−	6.56715i	0.276727	−	0.223032i
$868$		0			0
$869$	0.519608	−	0.899987i	0.0176265	−	0.0305300i
$870$		0			0
$871$	−18.7821			−0.636407
$872$		0			0
$873$	18.3890	+	16.7121i	0.622374	+	0.565619i
$874$		0			0
$875$	−10.1120	−	5.15186i	−0.341847	−	0.174165i
$876$		0			0
$877$	11.2608			0.380249			0.190124	−	0.981760i	$-0.439111\pi$
$877$	11.2608			0.380249			0.190124	+	0.981760i	$0.439111\pi$
$878$		0			0
$879$	8.40750	+	3.24965i	0.283578	+	0.109608i
$880$		0			0
$881$	−35.4810			−1.19538			−0.597692	−	0.801726i	$-0.703916\pi$
$881$	−35.4810			−1.19538			−0.597692	+	0.801726i	$0.703916\pi$
$882$		0			0
$883$	5.30092			0.178390			0.0891952	−	0.996014i	$-0.471571\pi$
$883$	5.30092			0.178390			0.0891952	+	0.996014i	$0.471571\pi$
$884$		0			0
$885$	48.1109	−	38.7757i	1.61723	−	1.30343i
$886$		0			0
$887$	−57.5664			−1.93289			−0.966446	−	0.256870i	$-0.917309\pi$
$887$	−57.5664			−1.93289			−0.966446	+	0.256870i	$0.917309\pi$
$888$		0			0
$889$	−9.35705	−	4.76724i	−0.313825	−	0.159888i
$890$		0			0
$891$	9.92238	−	7.06983i	0.332412	−	0.236848i
$892$		0			0
$893$	8.78032			0.293822
$894$		0			0
$895$	15.4585	−	26.7749i	0.516720	−	0.894985i
$896$		0			0
$897$	−6.22494	−	2.40605i	−0.207845	−	0.0803356i
$898$		0			0
$899$	−1.70842	+	2.95906i	−0.0569788	+	0.0986903i
$900$		0			0
$901$	10.6837	+	18.5047i	0.355925	+	0.616480i
$902$		0			0
$903$	−19.4747	+	4.09317i	−0.648077	+	0.136212i
$904$		0			0
$905$	57.3400			1.90605
$906$		0			0
$907$	−20.8972			−0.693879			−0.346939	−	0.937888i	$-0.612779\pi$
$907$	−20.8972			−0.693879			−0.346939	+	0.937888i	$0.612779\pi$
$908$		0			0
$909$	46.3664	−	14.8288i	1.53787	−	0.491840i
$910$		0			0
$911$	−11.3819	−	19.7141i	−0.377101	−	0.653157i	0.613539	−	0.789665i	$-0.289746\pi$
$911$	−11.3819	−	19.7141i	−0.377101	−	0.653157i	−0.990639	+	0.136508i	$0.956412\pi$
$912$		0			0
$913$	1.33166	+	2.30650i	0.0440715	+	0.0763340i
$914$		0			0
$915$	−2.64131	−	1.02091i	−0.0873189	−	0.0337503i
$916$		0			0
$917$	12.5618	+	6.40002i	0.414828	+	0.211347i
$918$		0			0
$919$	−18.6515	−	32.3054i	−0.615257	−	1.06566i	−0.990339	−	0.138664i	$-0.955719\pi$
$919$	−18.6515	−	32.3054i	−0.615257	−	1.06566i	0.375083	−	0.926991i	$-0.377614\pi$
$920$		0			0
$921$	1.33535	+	8.55906i	0.0440014	+	0.282031i
$922$		0			0
$923$	9.46870	−	16.4003i	0.311666	−	0.539822i
$924$		0			0
$925$	19.2031	+	33.2607i	0.631394	+	1.09361i
$926$		0			0
$927$	−6.36300	+	2.03500i	−0.208988	+	0.0668381i
$928$		0			0
$929$	−2.83363	+	4.90799i	−0.0929683	+	0.161026i	−0.908759	−	0.417322i	$-0.862969\pi$
$929$	−2.83363	+	4.90799i	−0.0929683	+	0.161026i	0.815791	+	0.578347i	$0.196302\pi$
$930$		0			0
$931$	−6.28151	+	14.1112i	−0.205868	+	0.462475i
$932$		0			0
$933$	−43.6895	+	35.2122i	−1.43033	+	1.15279i
$934$		0			0
$935$	−6.54444	+	11.3353i	−0.214026	+	0.370704i
$936$		0			0
$937$	−7.64754			−0.249834			−0.124917	−	0.992167i	$-0.539866\pi$
$937$	−7.64754			−0.249834			−0.124917	+	0.992167i	$0.539866\pi$
$938$		0			0
$939$	2.45416	+	0.948578i	0.0800886	+	0.0309557i
$940$		0			0
$941$	−10.2276	−	17.7147i	−0.333410	−	0.577483i	0.649768	−	0.760132i	$-0.274866\pi$
$941$	−10.2276	−	17.7147i	−0.333410	−	0.577483i	−0.983178	+	0.182650i	$0.941533\pi$
$942$		0			0
$943$	2.37674	−	4.11663i	0.0773973	−	0.134056i
$944$		0			0
$945$	−0.276974	+	40.1543i	−0.00900996	+	1.30622i
$946$		0			0
$947$	−2.38343	+	4.12823i	−0.0774512	+	0.134149i	−0.902150	−	0.431423i	$-0.858012\pi$
$947$	−2.38343	+	4.12823i	−0.0774512	+	0.134149i	0.824698	+	0.565573i	$0.191345\pi$
$948$		0			0
$949$	7.66385	+	13.2742i	0.248779	+	0.430898i
$950$		0			0
$951$	−34.7491	−	13.4311i	−1.12682	−	0.435534i
$952$		0			0
$953$	−48.9412			−1.58536			−0.792680	−	0.609638i	$-0.791315\pi$
$953$	−48.9412			−1.58536			−0.792680	+	0.609638i	$0.791315\pi$
$954$		0			0
$955$	−12.1028	+	20.9627i	−0.391638	+	0.678337i
$956$		0			0
$957$	1.90489	−	1.53527i	0.0615762	−	0.0496283i
$958$		0			0
$959$	17.6699	+	9.00249i	0.570591	+	0.290706i
$960$		0			0
$961$	10.1386	−	17.5605i	0.327050	−	0.566468i
$962$		0			0
$963$	−38.8702	−	35.3256i	−1.25258	−	1.13835i
$964$		0			0
$965$	−27.4340	−	47.5171i	−0.883132	−	1.52963i
$966$		0			0
$967$	2.95856	−	5.12438i	0.0951409	−	0.164789i	−0.814526	−	0.580126i	$-0.803003\pi$
$967$	2.95856	−	5.12438i	0.0951409	−	0.164789i	0.909667	+	0.415337i	$0.136336\pi$
$968$		0			0
$969$	−1.95027	−	12.5004i	−0.0626516	−	0.401570i
$970$		0			0
$971$	−14.4888	−	25.0953i	−0.464966	−	0.805345i	0.534234	−	0.845337i	$-0.320600\pi$
$971$	−14.4888	−	25.0953i	−0.464966	−	0.805345i	−0.999200	+	0.0399914i	$0.987267\pi$
$972$		0			0
$973$	31.2099	−	20.2695i	1.00054	−	0.649809i
$974$		0			0
$975$	8.36401	+	3.23284i	0.267863	+	0.103534i
$976$		0			0
$977$	−11.4228	−	19.7848i	−0.365447	−	0.632972i	0.623401	−	0.781902i	$-0.285750\pi$
$977$	−11.4228	−	19.7848i	−0.365447	−	0.632972i	−0.988848	+	0.148930i	$0.952417\pi$
$978$		0			0
$979$	4.33670	+	7.51139i	0.138602	+	0.240065i
$980$		0			0
$981$	9.94067	−	45.7270i	0.317381	−	1.45995i
$982$		0			0
$983$	31.2703			0.997367			0.498684	−	0.866784i	$-0.333817\pi$
$983$	31.2703			0.997367			0.498684	+	0.866784i	$0.333817\pi$
$984$		0			0
$985$	−17.5145			−0.558059
$986$		0			0
$987$	12.1705	+	13.5788i	0.387392	+	0.432217i
$988$		0			0
$989$	−5.70679	−	9.88444i	−0.181465	−	0.314307i
$990$		0			0
$991$	−3.50732	+	6.07485i	−0.111414	+	0.192974i	−0.916340	−	0.400400i	$-0.868871\pi$
$991$	−3.50732	+	6.07485i	−0.111414	+	0.192974i	0.804927	+	0.593374i	$0.202204\pi$
$992$		0			0
$993$	−31.4681	−	12.1630i	−0.998611	−	0.385981i
$994$		0			0
$995$	21.0429	−	36.4474i	0.667105	−	1.15546i
$996$		0			0
$997$	−21.2878			−0.674191			−0.337095	−	0.941470i	$-0.609445\pi$
$997$	−21.2878			−0.674191			−0.337095	+	0.941470i	$0.609445\pi$
$998$		0			0
$999$	−31.1056	+	47.1792i	−0.984139	+	1.49268i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.t.i.193.3		10
3.2	odd	2		3024.2.t.i.1873.4		10
4.3	odd	2		63.2.g.b.4.5	✓	10
7.2	even	3		1008.2.q.i.625.4		10
9.2	odd	6		3024.2.q.i.2881.2		10
9.7	even	3		1008.2.q.i.529.4		10
12.11	even	2		189.2.g.b.172.1		10
21.2	odd	6		3024.2.q.i.2305.2		10
28.3	even	6		441.2.f.f.148.5		10
28.11	odd	6		441.2.f.e.148.5		10
28.19	even	6		441.2.h.f.373.1		10
28.23	odd	6		63.2.h.b.58.1	yes	10
28.27	even	2		441.2.g.f.67.5		10
36.7	odd	6		63.2.h.b.25.1	yes	10
36.11	even	6		189.2.h.b.46.5		10
36.23	even	6		567.2.e.e.487.1		10
36.31	odd	6		567.2.e.f.487.5		10
63.2	odd	6		3024.2.t.i.289.4		10
63.16	even	3	inner	1008.2.t.i.961.3		10
84.11	even	6		1323.2.f.e.442.1		10
84.23	even	6		189.2.h.b.37.5		10
84.47	odd	6		1323.2.h.f.226.5		10
84.59	odd	6		1323.2.f.f.442.1		10
84.83	odd	2		1323.2.g.f.361.1		10
252.11	even	6		1323.2.f.e.883.1		10
252.23	even	6		567.2.e.e.163.1		10
252.31	even	6		3969.2.a.ba.1.1		5
252.47	odd	6		1323.2.g.f.667.1		10
252.59	odd	6		3969.2.a.bb.1.5		5
252.67	odd	6		3969.2.a.z.1.1		5
252.79	odd	6		63.2.g.b.16.5	yes	10
252.83	odd	6		1323.2.h.f.802.5		10
252.95	even	6		3969.2.a.bc.1.5		5
252.115	even	6		441.2.f.f.295.5		10
252.151	odd	6		441.2.f.e.295.5		10
252.187	even	6		441.2.g.f.79.5		10
252.191	even	6		189.2.g.b.100.1		10
252.223	even	6		441.2.h.f.214.1		10
252.227	odd	6		1323.2.f.f.883.1		10
252.247	odd	6		567.2.e.f.163.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.5	✓	10	4.3	odd	2
63.2.g.b.16.5	yes	10	252.79	odd	6
63.2.h.b.25.1	yes	10	36.7	odd	6
63.2.h.b.58.1	yes	10	28.23	odd	6
189.2.g.b.100.1		10	252.191	even	6
189.2.g.b.172.1		10	12.11	even	2
189.2.h.b.37.5		10	84.23	even	6
189.2.h.b.46.5		10	36.11	even	6
441.2.f.e.148.5		10	28.11	odd	6
441.2.f.e.295.5		10	252.151	odd	6
441.2.f.f.148.5		10	28.3	even	6
441.2.f.f.295.5		10	252.115	even	6
441.2.g.f.67.5		10	28.27	even	2
441.2.g.f.79.5		10	252.187	even	6
441.2.h.f.214.1		10	252.223	even	6
441.2.h.f.373.1		10	28.19	even	6
567.2.e.e.163.1		10	252.23	even	6
567.2.e.e.487.1		10	36.23	even	6
567.2.e.f.163.5		10	252.247	odd	6
567.2.e.f.487.5		10	36.31	odd	6
1008.2.q.i.529.4		10	9.7	even	3
1008.2.q.i.625.4		10	7.2	even	3
1008.2.t.i.193.3		10	1.1	even	1	trivial
1008.2.t.i.961.3		10	63.16	even	3	inner
1323.2.f.e.442.1		10	84.11	even	6
1323.2.f.e.883.1		10	252.11	even	6
1323.2.f.f.442.1		10	84.59	odd	6
1323.2.f.f.883.1		10	252.227	odd	6
1323.2.g.f.361.1		10	84.83	odd	2
1323.2.g.f.667.1		10	252.47	odd	6
1323.2.h.f.226.5		10	84.47	odd	6
1323.2.h.f.802.5		10	252.83	odd	6
3024.2.q.i.2305.2		10	21.2	odd	6
3024.2.q.i.2881.2		10	9.2	odd	6
3024.2.t.i.289.4		10	63.2	odd	6
3024.2.t.i.1873.4		10	3.2	odd	2
3969.2.a.z.1.1		5	252.67	odd	6
3969.2.a.ba.1.1		5	252.31	even	6
3969.2.a.bb.1.5		5	252.59	odd	6
3969.2.a.bc.1.5		5	252.95	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.266999 - 1.71135i) q^{3} -2.92087 q^{5} +(-2.35742 - 1.20106i) q^{7} +(-2.85742 + 0.913855i) q^{9} +O(q^{10})\)	\(q+(-0.266999 - 1.71135i) q^{3} -2.92087 q^{5} +(-2.35742 - 1.20106i) q^{7} +(-2.85742 + 0.913855i) q^{9} +1.35371 q^{11} +(-0.733001 + 1.26960i) q^{13} +(0.779867 + 4.99862i) q^{15} +(1.65514 - 2.86678i) q^{17} +(1.10329 + 1.91096i) q^{19} +(-1.42601 + 4.35505i) q^{21} -2.62830 q^{23} +3.53146 q^{25} +(2.32685 + 4.64605i) q^{27} +(0.521720 + 0.903646i) q^{29} +(1.63729 + 2.83587i) q^{31} +(-0.361440 - 2.31668i) q^{33} +(6.88572 + 3.50815i) q^{35} +(5.43773 + 9.41842i) q^{37} +(2.36843 + 0.915440i) q^{39} +(-0.904289 + 1.56627i) q^{41} +(2.17129 + 3.76078i) q^{43} +(8.34615 - 2.66925i) q^{45} +(1.98957 - 3.44604i) q^{47} +(4.11489 + 5.66283i) q^{49} +(-5.34798 - 2.06709i) q^{51} +(-3.22743 + 5.59008i) q^{53} -3.95402 q^{55} +(2.97574 - 2.39834i) q^{57} +(-6.10700 - 10.5776i) q^{59} +(-0.279867 + 0.484744i) q^{61} +(7.83376 + 1.27761i) q^{63} +(2.14100 - 3.70832i) q^{65} +(6.40588 + 11.0953i) q^{67} +(0.701751 + 4.49793i) q^{69} -12.9177 q^{71} +(5.22772 - 9.05467i) q^{73} +(-0.942894 - 6.04355i) q^{75} +(-3.19128 - 1.62590i) q^{77} +(0.383838 - 0.664827i) q^{79} +(7.32974 - 5.22254i) q^{81} +(0.983707 + 1.70383i) q^{83} +(-4.83443 + 8.37348i) q^{85} +(1.40715 - 1.13412i) q^{87} +(3.20356 + 5.54872i) q^{89} +(3.25286 - 2.11259i) q^{91} +(4.41601 - 3.55915i) q^{93} +(-3.22257 - 5.58166i) q^{95} +(-4.14143 - 7.17316i) q^{97} +(-3.86814 + 1.23710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{3} - 8 q^{5} + q^{7} - 4 q^{9}+O(q^{10}) \) 10 * q - 2 * q^3 - 8 * q^5 + q^7 - 4 * q^9	\( 10 q - 2 q^{3} - 8 q^{5} + q^{7} - 4 q^{9} + 8 q^{11} - 8 q^{13} + 19 q^{15} + 12 q^{17} - q^{19} - 2 q^{21} + 6 q^{23} + 2 q^{25} + 7 q^{27} + 7 q^{29} + 3 q^{31} - q^{33} - 5 q^{35} - 20 q^{39} + 5 q^{41} + 7 q^{43} - q^{45} - 27 q^{47} + 25 q^{49} - 24 q^{51} - 21 q^{53} - 4 q^{55} - 4 q^{57} - 30 q^{59} - 14 q^{61} + 35 q^{63} - 11 q^{65} + 2 q^{67} + 15 q^{69} + 6 q^{71} + 15 q^{73} - 31 q^{75} - 31 q^{77} + 4 q^{79} + 8 q^{81} - 9 q^{83} - 6 q^{85} - 32 q^{87} + 28 q^{89} + 4 q^{91} - 12 q^{93} + 14 q^{95} - 12 q^{97} - 35 q^{99}+O(q^{100}) \) 10 * q - 2 * q^3 - 8 * q^5 + q^7 - 4 * q^9 + 8 * q^11 - 8 * q^13 + 19 * q^15 + 12 * q^17 - q^19 - 2 * q^21 + 6 * q^23 + 2 * q^25 + 7 * q^27 + 7 * q^29 + 3 * q^31 - q^33 - 5 * q^35 - 20 * q^39 + 5 * q^41 + 7 * q^43 - q^45 - 27 * q^47 + 25 * q^49 - 24 * q^51 - 21 * q^53 - 4 * q^55 - 4 * q^57 - 30 * q^59 - 14 * q^61 + 35 * q^63 - 11 * q^65 + 2 * q^67 + 15 * q^69 + 6 * q^71 + 15 * q^73 - 31 * q^75 - 31 * q^77 + 4 * q^79 + 8 * q^81 - 9 * q^83 - 6 * q^85 - 32 * q^87 + 28 * q^89 + 4 * q^91 - 12 * q^93 + 14 * q^95 - 12 * q^97 - 35 * q^99

Introduction

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